2.0

298 files changed, 137099 insertions, 0 deletions

diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/__init__.py b/.venv/lib/python3.12/site-packages/numpy/_core/__init__.py
new file mode 100644
index 0000000..d0da7e0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/__init__.py
@@ -0,0 +1,186 @@
+"""
+Contains the core of NumPy: ndarray, ufuncs, dtypes, etc.
+
+Please note that this module is private.  All functions and objects
+are available in the main ``numpy`` namespace - use that instead.
+
+"""
+
+import os
+
+from numpy.version import version as __version__
+
+# disables OpenBLAS affinity setting of the main thread that limits
+# python threads or processes to one core
+env_added = []
+for envkey in ['OPENBLAS_MAIN_FREE', 'GOTOBLAS_MAIN_FREE']:
+    if envkey not in os.environ:
+        os.environ[envkey] = '1'
+        env_added.append(envkey)
+
+try:
+    from . import multiarray
+except ImportError as exc:
+    import sys
+    msg = """
+
+IMPORTANT: PLEASE READ THIS FOR ADVICE ON HOW TO SOLVE THIS ISSUE!
+
+Importing the numpy C-extensions failed. This error can happen for
+many reasons, often due to issues with your setup or how NumPy was
+installed.
+
+We have compiled some common reasons and troubleshooting tips at:
+
+    https://numpy.org/devdocs/user/troubleshooting-importerror.html
+
+Please note and check the following:
+
+  * The Python version is: Python%d.%d from "%s"
+  * The NumPy version is: "%s"
+
+and make sure that they are the versions you expect.
+Please carefully study the documentation linked above for further help.
+
+Original error was: %s
+""" % (sys.version_info[0], sys.version_info[1], sys.executable,
+        __version__, exc)
+    raise ImportError(msg) from exc
+finally:
+    for envkey in env_added:
+        del os.environ[envkey]
+del envkey
+del env_added
+del os
+
+from . import umath
+
+# Check that multiarray,umath are pure python modules wrapping
+# _multiarray_umath and not either of the old c-extension modules
+if not (hasattr(multiarray, '_multiarray_umath') and
+        hasattr(umath, '_multiarray_umath')):
+    import sys
+    path = sys.modules['numpy'].__path__
+    msg = ("Something is wrong with the numpy installation. "
+        "While importing we detected an older version of "
+        "numpy in {}. One method of fixing this is to repeatedly uninstall "
+        "numpy until none is found, then reinstall this version.")
+    raise ImportError(msg.format(path))
+
+from . import numerictypes as nt
+from .numerictypes import sctypeDict, sctypes
+
+multiarray.set_typeDict(nt.sctypeDict)
+from . import (
+    _machar,
+    einsumfunc,
+    fromnumeric,
+    function_base,
+    getlimits,
+    numeric,
+    shape_base,
+)
+from .einsumfunc import *
+from .fromnumeric import *
+from .function_base import *
+from .getlimits import *
+
+# Note: module name memmap is overwritten by a class with same name
+from .memmap import *
+from .numeric import *
+from .records import recarray, record
+from .shape_base import *
+
+del nt
+
+# do this after everything else, to minimize the chance of this misleadingly
+# appearing in an import-time traceback
+# add these for module-freeze analysis (like PyInstaller)
+from . import (
+    _add_newdocs,
+    _add_newdocs_scalars,
+    _dtype,
+    _dtype_ctypes,
+    _internal,
+    _methods,
+)
+from .numeric import absolute as abs
+
+acos = numeric.arccos
+acosh = numeric.arccosh
+asin = numeric.arcsin
+asinh = numeric.arcsinh
+atan = numeric.arctan
+atanh = numeric.arctanh
+atan2 = numeric.arctan2
+concat = numeric.concatenate
+bitwise_left_shift = numeric.left_shift
+bitwise_invert = numeric.invert
+bitwise_right_shift = numeric.right_shift
+permute_dims = numeric.transpose
+pow = numeric.power
+
+__all__ = [
+    "abs", "acos", "acosh", "asin", "asinh", "atan", "atanh", "atan2",
+    "bitwise_invert", "bitwise_left_shift", "bitwise_right_shift", "concat",
+    "pow", "permute_dims", "memmap", "sctypeDict", "record", "recarray"
+]
+__all__ += numeric.__all__
+__all__ += function_base.__all__
+__all__ += getlimits.__all__
+__all__ += shape_base.__all__
+__all__ += einsumfunc.__all__
+
+
+def _ufunc_reduce(func):
+    # Report the `__name__`. pickle will try to find the module. Note that
+    # pickle supports for this `__name__` to be a `__qualname__`. It may
+    # make sense to add a `__qualname__` to ufuncs, to allow this more
+    # explicitly (Numba has ufuncs as attributes).
+    # See also: https://github.com/dask/distributed/issues/3450
+    return func.__name__
+
+
+def _DType_reconstruct(scalar_type):
+    # This is a work-around to pickle type(np.dtype(np.float64)), etc.
+    # and it should eventually be replaced with a better solution, e.g. when
+    # DTypes become HeapTypes.
+    return type(dtype(scalar_type))
+
+
+def _DType_reduce(DType):
+    # As types/classes, most DTypes can simply be pickled by their name:
+    if not DType._legacy or DType.__module__ == "numpy.dtypes":
+        return DType.__name__
+
+    # However, user defined legacy dtypes (like rational) do not end up in
+    # `numpy.dtypes` as module and do not have a public class at all.
+    # For these, we pickle them by reconstructing them from the scalar type:
+    scalar_type = DType.type
+    return _DType_reconstruct, (scalar_type,)
+
+
+def __getattr__(name):
+    # Deprecated 2022-11-22, NumPy 1.25.
+    if name == "MachAr":
+        import warnings
+        warnings.warn(
+            "The `np._core.MachAr` is considered private API (NumPy 1.24)",
+            DeprecationWarning, stacklevel=2,
+        )
+        return _machar.MachAr
+    raise AttributeError(f"Module {__name__!r} has no attribute {name!r}")
+
+
+import copyreg
+
+copyreg.pickle(ufunc, _ufunc_reduce)
+copyreg.pickle(type(dtype), _DType_reduce, _DType_reconstruct)
+
+# Unclutter namespace (must keep _*_reconstruct for unpickling)
+del copyreg, _ufunc_reduce, _DType_reduce
+
+from numpy._pytesttester import PytestTester
+
+test = PytestTester(__name__)
+del PytestTester
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/__init__.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/__init__.pyi
new file mode 100644
index 0000000..40d9c41
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/__init__.pyi
@@ -0,0 +1,2 @@
+# NOTE: The `np._core` namespace is deliberately kept empty due to it
+# being private
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/__pycache__/__init__.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/__pycache__/__init__.cpython-312.pyc
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/__pycache__/umath.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/__pycache__/umath.cpython-312.pyc
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs.py b/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs.py
new file mode 100644
index 0000000..8f5de4b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs.py
@@ -0,0 +1,6967 @@
+"""
+This is only meant to add docs to objects defined in C-extension modules.
+The purpose is to allow easier editing of the docstrings without
+requiring a re-compile.
+
+NOTE: Many of the methods of ndarray have corresponding functions.
+      If you update these docstrings, please keep also the ones in
+      _core/fromnumeric.py, matrixlib/defmatrix.py up-to-date.
+
+"""
+
+from numpy._core.function_base import add_newdoc
+from numpy._core.overrides import get_array_function_like_doc  # noqa: F401
+
+###############################################################################
+#
+# flatiter
+#
+# flatiter needs a toplevel description
+#
+###############################################################################
+
+add_newdoc('numpy._core', 'flatiter',
+    """
+    Flat iterator object to iterate over arrays.
+
+    A `flatiter` iterator is returned by ``x.flat`` for any array `x`.
+    It allows iterating over the array as if it were a 1-D array,
+    either in a for-loop or by calling its `next` method.
+
+    Iteration is done in row-major, C-style order (the last
+    index varying the fastest). The iterator can also be indexed using
+    basic slicing or advanced indexing.
+
+    See Also
+    --------
+    ndarray.flat : Return a flat iterator over an array.
+    ndarray.flatten : Returns a flattened copy of an array.
+
+    Notes
+    -----
+    A `flatiter` iterator can not be constructed directly from Python code
+    by calling the `flatiter` constructor.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6).reshape(2, 3)
+    >>> fl = x.flat
+    >>> type(fl)
+    <class 'numpy.flatiter'>
+    >>> for item in fl:
+    ...     print(item)
+    ...
+    0
+    1
+    2
+    3
+    4
+    5
+
+    >>> fl[2:4]
+    array([2, 3])
+
+    """)
+
+# flatiter attributes
+
+add_newdoc('numpy._core', 'flatiter', ('base',
+    """
+    A reference to the array that is iterated over.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(5)
+    >>> fl = x.flat
+    >>> fl.base is x
+    True
+
+    """))
+
+
+add_newdoc('numpy._core', 'flatiter', ('coords',
+    """
+    An N-dimensional tuple of current coordinates.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6).reshape(2, 3)
+    >>> fl = x.flat
+    >>> fl.coords
+    (0, 0)
+    >>> next(fl)
+    0
+    >>> fl.coords
+    (0, 1)
+
+    """))
+
+
+add_newdoc('numpy._core', 'flatiter', ('index',
+    """
+    Current flat index into the array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6).reshape(2, 3)
+    >>> fl = x.flat
+    >>> fl.index
+    0
+    >>> next(fl)
+    0
+    >>> fl.index
+    1
+
+    """))
+
+# flatiter functions
+
+add_newdoc('numpy._core', 'flatiter', ('__array__',
+    """__array__(type=None) Get array from iterator
+
+    """))
+
+
+add_newdoc('numpy._core', 'flatiter', ('copy',
+    """
+    copy()
+
+    Get a copy of the iterator as a 1-D array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6).reshape(2, 3)
+    >>> x
+    array([[0, 1, 2],
+           [3, 4, 5]])
+    >>> fl = x.flat
+    >>> fl.copy()
+    array([0, 1, 2, 3, 4, 5])
+
+    """))
+
+
+###############################################################################
+#
+# nditer
+#
+###############################################################################
+
+add_newdoc('numpy._core', 'nditer',
+    """
+    nditer(op, flags=None, op_flags=None, op_dtypes=None, order='K',
+        casting='safe', op_axes=None, itershape=None, buffersize=0)
+
+    Efficient multi-dimensional iterator object to iterate over arrays.
+    To get started using this object, see the
+    :ref:`introductory guide to array iteration <arrays.nditer>`.
+
+    Parameters
+    ----------
+    op : ndarray or sequence of array_like
+        The array(s) to iterate over.
+
+    flags : sequence of str, optional
+          Flags to control the behavior of the iterator.
+
+          * ``buffered`` enables buffering when required.
+          * ``c_index`` causes a C-order index to be tracked.
+          * ``f_index`` causes a Fortran-order index to be tracked.
+          * ``multi_index`` causes a multi-index, or a tuple of indices
+            with one per iteration dimension, to be tracked.
+          * ``common_dtype`` causes all the operands to be converted to
+            a common data type, with copying or buffering as necessary.
+          * ``copy_if_overlap`` causes the iterator to determine if read
+            operands have overlap with write operands, and make temporary
+            copies as necessary to avoid overlap. False positives (needless
+            copying) are possible in some cases.
+          * ``delay_bufalloc`` delays allocation of the buffers until
+            a reset() call is made. Allows ``allocate`` operands to
+            be initialized before their values are copied into the buffers.
+          * ``external_loop`` causes the ``values`` given to be
+            one-dimensional arrays with multiple values instead of
+            zero-dimensional arrays.
+          * ``grow_inner`` allows the ``value`` array sizes to be made
+            larger than the buffer size when both ``buffered`` and
+            ``external_loop`` is used.
+          * ``ranged`` allows the iterator to be restricted to a sub-range
+            of the iterindex values.
+          * ``refs_ok`` enables iteration of reference types, such as
+            object arrays.
+          * ``reduce_ok`` enables iteration of ``readwrite`` operands
+            which are broadcasted, also known as reduction operands.
+          * ``zerosize_ok`` allows `itersize` to be zero.
+    op_flags : list of list of str, optional
+          This is a list of flags for each operand. At minimum, one of
+          ``readonly``, ``readwrite``, or ``writeonly`` must be specified.
+
+          * ``readonly`` indicates the operand will only be read from.
+          * ``readwrite`` indicates the operand will be read from and written to.
+          * ``writeonly`` indicates the operand will only be written to.
+          * ``no_broadcast`` prevents the operand from being broadcasted.
+          * ``contig`` forces the operand data to be contiguous.
+          * ``aligned`` forces the operand data to be aligned.
+          * ``nbo`` forces the operand data to be in native byte order.
+          * ``copy`` allows a temporary read-only copy if required.
+          * ``updateifcopy`` allows a temporary read-write copy if required.
+          * ``allocate`` causes the array to be allocated if it is None
+            in the ``op`` parameter.
+          * ``no_subtype`` prevents an ``allocate`` operand from using a subtype.
+          * ``arraymask`` indicates that this operand is the mask to use
+            for selecting elements when writing to operands with the
+            'writemasked' flag set. The iterator does not enforce this,
+            but when writing from a buffer back to the array, it only
+            copies those elements indicated by this mask.
+          * ``writemasked`` indicates that only elements where the chosen
+            ``arraymask`` operand is True will be written to.
+          * ``overlap_assume_elementwise`` can be used to mark operands that are
+            accessed only in the iterator order, to allow less conservative
+            copying when ``copy_if_overlap`` is present.
+    op_dtypes : dtype or tuple of dtype(s), optional
+        The required data type(s) of the operands. If copying or buffering
+        is enabled, the data will be converted to/from their original types.
+    order : {'C', 'F', 'A', 'K'}, optional
+        Controls the iteration order. 'C' means C order, 'F' means
+        Fortran order, 'A' means 'F' order if all the arrays are Fortran
+        contiguous, 'C' order otherwise, and 'K' means as close to the
+        order the array elements appear in memory as possible. This also
+        affects the element memory order of ``allocate`` operands, as they
+        are allocated to be compatible with iteration order.
+        Default is 'K'.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur when making a copy
+        or buffering.  Setting this to 'unsafe' is not recommended,
+        as it can adversely affect accumulations.
+
+        * 'no' means the data types should not be cast at all.
+        * 'equiv' means only byte-order changes are allowed.
+        * 'safe' means only casts which can preserve values are allowed.
+        * 'same_kind' means only safe casts or casts within a kind,
+          like float64 to float32, are allowed.
+        * 'unsafe' means any data conversions may be done.
+    op_axes : list of list of ints, optional
+        If provided, is a list of ints or None for each operands.
+        The list of axes for an operand is a mapping from the dimensions
+        of the iterator to the dimensions of the operand. A value of
+        -1 can be placed for entries, causing that dimension to be
+        treated as `newaxis`.
+    itershape : tuple of ints, optional
+        The desired shape of the iterator. This allows ``allocate`` operands
+        with a dimension mapped by op_axes not corresponding to a dimension
+        of a different operand to get a value not equal to 1 for that
+        dimension.
+    buffersize : int, optional
+        When buffering is enabled, controls the size of the temporary
+        buffers. Set to 0 for the default value.
+
+    Attributes
+    ----------
+    dtypes : tuple of dtype(s)
+        The data types of the values provided in `value`. This may be
+        different from the operand data types if buffering is enabled.
+        Valid only before the iterator is closed.
+    finished : bool
+        Whether the iteration over the operands is finished or not.
+    has_delayed_bufalloc : bool
+        If True, the iterator was created with the ``delay_bufalloc`` flag,
+        and no reset() function was called on it yet.
+    has_index : bool
+        If True, the iterator was created with either the ``c_index`` or
+        the ``f_index`` flag, and the property `index` can be used to
+        retrieve it.
+    has_multi_index : bool
+        If True, the iterator was created with the ``multi_index`` flag,
+        and the property `multi_index` can be used to retrieve it.
+    index
+        When the ``c_index`` or ``f_index`` flag was used, this property
+        provides access to the index. Raises a ValueError if accessed
+        and ``has_index`` is False.
+    iterationneedsapi : bool
+        Whether iteration requires access to the Python API, for example
+        if one of the operands is an object array.
+    iterindex : int
+        An index which matches the order of iteration.
+    itersize : int
+        Size of the iterator.
+    itviews
+        Structured view(s) of `operands` in memory, matching the reordered
+        and optimized iterator access pattern. Valid only before the iterator
+        is closed.
+    multi_index
+        When the ``multi_index`` flag was used, this property
+        provides access to the index. Raises a ValueError if accessed
+        accessed and ``has_multi_index`` is False.
+    ndim : int
+        The dimensions of the iterator.
+    nop : int
+        The number of iterator operands.
+    operands : tuple of operand(s)
+        The array(s) to be iterated over. Valid only before the iterator is
+        closed.
+    shape : tuple of ints
+        Shape tuple, the shape of the iterator.
+    value
+        Value of ``operands`` at current iteration. Normally, this is a
+        tuple of array scalars, but if the flag ``external_loop`` is used,
+        it is a tuple of one dimensional arrays.
+
+    Notes
+    -----
+    `nditer` supersedes `flatiter`.  The iterator implementation behind
+    `nditer` is also exposed by the NumPy C API.
+
+    The Python exposure supplies two iteration interfaces, one which follows
+    the Python iterator protocol, and another which mirrors the C-style
+    do-while pattern.  The native Python approach is better in most cases, but
+    if you need the coordinates or index of an iterator, use the C-style pattern.
+
+    Examples
+    --------
+    Here is how we might write an ``iter_add`` function, using the
+    Python iterator protocol:
+
+    >>> import numpy as np
+
+    >>> def iter_add_py(x, y, out=None):
+    ...     addop = np.add
+    ...     it = np.nditer([x, y, out], [],
+    ...                 [['readonly'], ['readonly'], ['writeonly','allocate']])
+    ...     with it:
+    ...         for (a, b, c) in it:
+    ...             addop(a, b, out=c)
+    ...         return it.operands[2]
+
+    Here is the same function, but following the C-style pattern:
+
+    >>> def iter_add(x, y, out=None):
+    ...    addop = np.add
+    ...    it = np.nditer([x, y, out], [],
+    ...                [['readonly'], ['readonly'], ['writeonly','allocate']])
+    ...    with it:
+    ...        while not it.finished:
+    ...            addop(it[0], it[1], out=it[2])
+    ...            it.iternext()
+    ...        return it.operands[2]
+
+    Here is an example outer product function:
+
+    >>> def outer_it(x, y, out=None):
+    ...     mulop = np.multiply
+    ...     it = np.nditer([x, y, out], ['external_loop'],
+    ...             [['readonly'], ['readonly'], ['writeonly', 'allocate']],
+    ...             op_axes=[list(range(x.ndim)) + [-1] * y.ndim,
+    ...                      [-1] * x.ndim + list(range(y.ndim)),
+    ...                      None])
+    ...     with it:
+    ...         for (a, b, c) in it:
+    ...             mulop(a, b, out=c)
+    ...         return it.operands[2]
+
+    >>> a = np.arange(2)+1
+    >>> b = np.arange(3)+1
+    >>> outer_it(a,b)
+    array([[1, 2, 3],
+           [2, 4, 6]])
+
+    Here is an example function which operates like a "lambda" ufunc:
+
+    >>> def luf(lamdaexpr, *args, **kwargs):
+    ...    '''luf(lambdaexpr, op1, ..., opn, out=None, order='K', casting='safe', buffersize=0)'''
+    ...    nargs = len(args)
+    ...    op = (kwargs.get('out',None),) + args
+    ...    it = np.nditer(op, ['buffered','external_loop'],
+    ...            [['writeonly','allocate','no_broadcast']] +
+    ...                            [['readonly','nbo','aligned']]*nargs,
+    ...            order=kwargs.get('order','K'),
+    ...            casting=kwargs.get('casting','safe'),
+    ...            buffersize=kwargs.get('buffersize',0))
+    ...    while not it.finished:
+    ...        it[0] = lamdaexpr(*it[1:])
+    ...        it.iternext()
+    ...    return it.operands[0]
+
+    >>> a = np.arange(5)
+    >>> b = np.ones(5)
+    >>> luf(lambda i,j:i*i + j/2, a, b)
+    array([  0.5,   1.5,   4.5,   9.5,  16.5])
+
+    If operand flags ``"writeonly"`` or ``"readwrite"`` are used the
+    operands may be views into the original data with the
+    `WRITEBACKIFCOPY` flag. In this case `nditer` must be used as a
+    context manager or the `nditer.close` method must be called before
+    using the result. The temporary data will be written back to the
+    original data when the :meth:`~object.__exit__` function is called
+    but not before:
+
+    >>> a = np.arange(6, dtype='i4')[::-2]
+    >>> with np.nditer(a, [],
+    ...        [['writeonly', 'updateifcopy']],
+    ...        casting='unsafe',
+    ...        op_dtypes=[np.dtype('f4')]) as i:
+    ...    x = i.operands[0]
+    ...    x[:] = [-1, -2, -3]
+    ...    # a still unchanged here
+    >>> a, x
+    (array([-1, -2, -3], dtype=int32), array([-1., -2., -3.], dtype=float32))
+
+    It is important to note that once the iterator is exited, dangling
+    references (like `x` in the example) may or may not share data with
+    the original data `a`. If writeback semantics were active, i.e. if
+    `x.base.flags.writebackifcopy` is `True`, then exiting the iterator
+    will sever the connection between `x` and `a`, writing to `x` will
+    no longer write to `a`. If writeback semantics are not active, then
+    `x.data` will still point at some part of `a.data`, and writing to
+    one will affect the other.
+
+    Context management and the `close` method appeared in version 1.15.0.
+
+    """)
+
+# nditer methods
+
+add_newdoc('numpy._core', 'nditer', ('copy',
+    """
+    copy()
+
+    Get a copy of the iterator in its current state.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(10)
+    >>> y = x + 1
+    >>> it = np.nditer([x, y])
+    >>> next(it)
+    (array(0), array(1))
+    >>> it2 = it.copy()
+    >>> next(it2)
+    (array(1), array(2))
+
+    """))
+
+add_newdoc('numpy._core', 'nditer', ('operands',
+    """
+    operands[`Slice`]
+
+    The array(s) to be iterated over. Valid only before the iterator is closed.
+    """))
+
+add_newdoc('numpy._core', 'nditer', ('debug_print',
+    """
+    debug_print()
+
+    Print the current state of the `nditer` instance and debug info to stdout.
+
+    """))
+
+add_newdoc('numpy._core', 'nditer', ('enable_external_loop',
+    """
+    enable_external_loop()
+
+    When the "external_loop" was not used during construction, but
+    is desired, this modifies the iterator to behave as if the flag
+    was specified.
+
+    """))
+
+add_newdoc('numpy._core', 'nditer', ('iternext',
+    """
+    iternext()
+
+    Check whether iterations are left, and perform a single internal iteration
+    without returning the result.  Used in the C-style pattern do-while
+    pattern.  For an example, see `nditer`.
+
+    Returns
+    -------
+    iternext : bool
+        Whether or not there are iterations left.
+
+    """))
+
+add_newdoc('numpy._core', 'nditer', ('remove_axis',
+    """
+    remove_axis(i, /)
+
+    Removes axis `i` from the iterator. Requires that the flag "multi_index"
+    be enabled.
+
+    """))
+
+add_newdoc('numpy._core', 'nditer', ('remove_multi_index',
+    """
+    remove_multi_index()
+
+    When the "multi_index" flag was specified, this removes it, allowing
+    the internal iteration structure to be optimized further.
+
+    """))
+
+add_newdoc('numpy._core', 'nditer', ('reset',
+    """
+    reset()
+
+    Reset the iterator to its initial state.
+
+    """))
+
+add_newdoc('numpy._core', 'nested_iters',
+    """
+    nested_iters(op, axes, flags=None, op_flags=None, op_dtypes=None, \
+    order="K", casting="safe", buffersize=0)
+
+    Create nditers for use in nested loops
+
+    Create a tuple of `nditer` objects which iterate in nested loops over
+    different axes of the op argument. The first iterator is used in the
+    outermost loop, the last in the innermost loop. Advancing one will change
+    the subsequent iterators to point at its new element.
+
+    Parameters
+    ----------
+    op : ndarray or sequence of array_like
+        The array(s) to iterate over.
+
+    axes : list of list of int
+        Each item is used as an "op_axes" argument to an nditer
+
+    flags, op_flags, op_dtypes, order, casting, buffersize (optional)
+        See `nditer` parameters of the same name
+
+    Returns
+    -------
+    iters : tuple of nditer
+        An nditer for each item in `axes`, outermost first
+
+    See Also
+    --------
+    nditer
+
+    Examples
+    --------
+
+    Basic usage. Note how y is the "flattened" version of
+    [a[:, 0, :], a[:, 1, 0], a[:, 2, :]] since we specified
+    the first iter's axes as [1]
+
+    >>> import numpy as np
+    >>> a = np.arange(12).reshape(2, 3, 2)
+    >>> i, j = np.nested_iters(a, [[1], [0, 2]], flags=["multi_index"])
+    >>> for x in i:
+    ...      print(i.multi_index)
+    ...      for y in j:
+    ...          print('', j.multi_index, y)
+    (0,)
+     (0, 0) 0
+     (0, 1) 1
+     (1, 0) 6
+     (1, 1) 7
+    (1,)
+     (0, 0) 2
+     (0, 1) 3
+     (1, 0) 8
+     (1, 1) 9
+    (2,)
+     (0, 0) 4
+     (0, 1) 5
+     (1, 0) 10
+     (1, 1) 11
+
+    """)
+
+add_newdoc('numpy._core', 'nditer', ('close',
+    """
+    close()
+
+    Resolve all writeback semantics in writeable operands.
+
+    See Also
+    --------
+
+    :ref:`nditer-context-manager`
+
+    """))
+
+
+###############################################################################
+#
+# broadcast
+#
+###############################################################################
+
+add_newdoc('numpy._core', 'broadcast',
+    """
+    Produce an object that mimics broadcasting.
+
+    Parameters
+    ----------
+    in1, in2, ... : array_like
+        Input parameters.
+
+    Returns
+    -------
+    b : broadcast object
+        Broadcast the input parameters against one another, and
+        return an object that encapsulates the result.
+        Amongst others, it has ``shape`` and ``nd`` properties, and
+        may be used as an iterator.
+
+    See Also
+    --------
+    broadcast_arrays
+    broadcast_to
+    broadcast_shapes
+
+    Examples
+    --------
+
+    Manually adding two vectors, using broadcasting:
+
+    >>> import numpy as np
+    >>> x = np.array([[1], [2], [3]])
+    >>> y = np.array([4, 5, 6])
+    >>> b = np.broadcast(x, y)
+
+    >>> out = np.empty(b.shape)
+    >>> out.flat = [u+v for (u,v) in b]
+    >>> out
+    array([[5.,  6.,  7.],
+           [6.,  7.,  8.],
+           [7.,  8.,  9.]])
+
+    Compare against built-in broadcasting:
+
+    >>> x + y
+    array([[5, 6, 7],
+           [6, 7, 8],
+           [7, 8, 9]])
+
+    """)
+
+# attributes
+
+add_newdoc('numpy._core', 'broadcast', ('index',
+    """
+    current index in broadcasted result
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> x = np.array([[1], [2], [3]])
+    >>> y = np.array([4, 5, 6])
+    >>> b = np.broadcast(x, y)
+    >>> b.index
+    0
+    >>> next(b), next(b), next(b)
+    ((1, 4), (1, 5), (1, 6))
+    >>> b.index
+    3
+
+    """))
+
+add_newdoc('numpy._core', 'broadcast', ('iters',
+    """
+    tuple of iterators along ``self``'s "components."
+
+    Returns a tuple of `numpy.flatiter` objects, one for each "component"
+    of ``self``.
+
+    See Also
+    --------
+    numpy.flatiter
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3])
+    >>> y = np.array([[4], [5], [6]])
+    >>> b = np.broadcast(x, y)
+    >>> row, col = b.iters
+    >>> next(row), next(col)
+    (1, 4)
+
+    """))
+
+add_newdoc('numpy._core', 'broadcast', ('ndim',
+    """
+    Number of dimensions of broadcasted result. Alias for `nd`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3])
+    >>> y = np.array([[4], [5], [6]])
+    >>> b = np.broadcast(x, y)
+    >>> b.ndim
+    2
+
+    """))
+
+add_newdoc('numpy._core', 'broadcast', ('nd',
+    """
+    Number of dimensions of broadcasted result. For code intended for NumPy
+    1.12.0 and later the more consistent `ndim` is preferred.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3])
+    >>> y = np.array([[4], [5], [6]])
+    >>> b = np.broadcast(x, y)
+    >>> b.nd
+    2
+
+    """))
+
+add_newdoc('numpy._core', 'broadcast', ('numiter',
+    """
+    Number of iterators possessed by the broadcasted result.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3])
+    >>> y = np.array([[4], [5], [6]])
+    >>> b = np.broadcast(x, y)
+    >>> b.numiter
+    2
+
+    """))
+
+add_newdoc('numpy._core', 'broadcast', ('shape',
+    """
+    Shape of broadcasted result.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3])
+    >>> y = np.array([[4], [5], [6]])
+    >>> b = np.broadcast(x, y)
+    >>> b.shape
+    (3, 3)
+
+    """))
+
+add_newdoc('numpy._core', 'broadcast', ('size',
+    """
+    Total size of broadcasted result.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3])
+    >>> y = np.array([[4], [5], [6]])
+    >>> b = np.broadcast(x, y)
+    >>> b.size
+    9
+
+    """))
+
+add_newdoc('numpy._core', 'broadcast', ('reset',
+    """
+    reset()
+
+    Reset the broadcasted result's iterator(s).
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    None
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3])
+    >>> y = np.array([[4], [5], [6]])
+    >>> b = np.broadcast(x, y)
+    >>> b.index
+    0
+    >>> next(b), next(b), next(b)
+    ((1, 4), (2, 4), (3, 4))
+    >>> b.index
+    3
+    >>> b.reset()
+    >>> b.index
+    0
+
+    """))
+
+###############################################################################
+#
+# numpy functions
+#
+###############################################################################
+
+add_newdoc('numpy._core.multiarray', 'array',
+    """
+    array(object, dtype=None, *, copy=True, order='K', subok=False, ndmin=0,
+          like=None)
+
+    Create an array.
+
+    Parameters
+    ----------
+    object : array_like
+        An array, any object exposing the array interface, an object whose
+        ``__array__`` method returns an array, or any (nested) sequence.
+        If object is a scalar, a 0-dimensional array containing object is
+        returned.
+    dtype : data-type, optional
+        The desired data-type for the array. If not given, NumPy will try to use
+        a default ``dtype`` that can represent the values (by applying promotion
+        rules when necessary.)
+    copy : bool, optional
+        If ``True`` (default), then the array data is copied. If ``None``,
+        a copy will only be made if ``__array__`` returns a copy, if obj is
+        a nested sequence, or if a copy is needed to satisfy any of the other
+        requirements (``dtype``, ``order``, etc.). Note that any copy of
+        the data is shallow, i.e., for arrays with object dtype, the new
+        array will point to the same objects. See Examples for `ndarray.copy`.
+        For ``False`` it raises a ``ValueError`` if a copy cannot be avoided.
+        Default: ``True``.
+    order : {'K', 'A', 'C', 'F'}, optional
+        Specify the memory layout of the array. If object is not an array, the
+        newly created array will be in C order (row major) unless 'F' is
+        specified, in which case it will be in Fortran order (column major).
+        If object is an array the following holds.
+
+        ===== ========= ===================================================
+        order  no copy                     copy=True
+        ===== ========= ===================================================
+        'K'   unchanged F & C order preserved, otherwise most similar order
+        'A'   unchanged F order if input is F and not C, otherwise C order
+        'C'   C order   C order
+        'F'   F order   F order
+        ===== ========= ===================================================
+
+        When ``copy=None`` and a copy is made for other reasons, the result is
+        the same as if ``copy=True``, with some exceptions for 'A', see the
+        Notes section. The default order is 'K'.
+    subok : bool, optional
+        If True, then sub-classes will be passed-through, otherwise
+        the returned array will be forced to be a base-class array (default).
+    ndmin : int, optional
+        Specifies the minimum number of dimensions that the resulting
+        array should have.  Ones will be prepended to the shape as
+        needed to meet this requirement.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        An array object satisfying the specified requirements.
+
+    See Also
+    --------
+    empty_like : Return an empty array with shape and type of input.
+    ones_like : Return an array of ones with shape and type of input.
+    zeros_like : Return an array of zeros with shape and type of input.
+    full_like : Return a new array with shape of input filled with value.
+    empty : Return a new uninitialized array.
+    ones : Return a new array setting values to one.
+    zeros : Return a new array setting values to zero.
+    full : Return a new array of given shape filled with value.
+    copy: Return an array copy of the given object.
+
+
+    Notes
+    -----
+    When order is 'A' and ``object`` is an array in neither 'C' nor 'F' order,
+    and a copy is forced by a change in dtype, then the order of the result is
+    not necessarily 'C' as expected. This is likely a bug.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.array([1, 2, 3])
+    array([1, 2, 3])
+
+    Upcasting:
+
+    >>> np.array([1, 2, 3.0])
+    array([ 1.,  2.,  3.])
+
+    More than one dimension:
+
+    >>> np.array([[1, 2], [3, 4]])
+    array([[1, 2],
+           [3, 4]])
+
+    Minimum dimensions 2:
+
+    >>> np.array([1, 2, 3], ndmin=2)
+    array([[1, 2, 3]])
+
+    Type provided:
+
+    >>> np.array([1, 2, 3], dtype=complex)
+    array([ 1.+0.j,  2.+0.j,  3.+0.j])
+
+    Data-type consisting of more than one element:
+
+    >>> x = np.array([(1,2),(3,4)],dtype=[('a','<i4'),('b','<i4')])
+    >>> x['a']
+    array([1, 3], dtype=int32)
+
+    Creating an array from sub-classes:
+
+    >>> np.array(np.asmatrix('1 2; 3 4'))
+    array([[1, 2],
+           [3, 4]])
+
+    >>> np.array(np.asmatrix('1 2; 3 4'), subok=True)
+    matrix([[1, 2],
+            [3, 4]])
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'asarray',
+    """
+    asarray(a, dtype=None, order=None, *, device=None, copy=None, like=None)
+
+    Convert the input to an array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data, in any form that can be converted to an array.  This
+        includes lists, lists of tuples, tuples, tuples of tuples, tuples
+        of lists and ndarrays.
+    dtype : data-type, optional
+        By default, the data-type is inferred from the input data.
+    order : {'C', 'F', 'A', 'K'}, optional
+        Memory layout.  'A' and 'K' depend on the order of input array a.
+        'C' row-major (C-style),
+        'F' column-major (Fortran-style) memory representation.
+        'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise
+        'K' (keep) preserve input order
+        Defaults to 'K'.
+    device : str, optional
+        The device on which to place the created array. Default: ``None``.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+    copy : bool, optional
+        If ``True``, then the object is copied. If ``None`` then the object is
+        copied only if needed, i.e. if ``__array__`` returns a copy, if obj
+        is a nested sequence, or if a copy is needed to satisfy any of
+        the other requirements (``dtype``, ``order``, etc.).
+        For ``False`` it raises a ``ValueError`` if a copy cannot be avoided.
+        Default: ``None``.
+
+        .. versionadded:: 2.0.0
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        Array interpretation of ``a``.  No copy is performed if the input
+        is already an ndarray with matching dtype and order.  If ``a`` is a
+        subclass of ndarray, a base class ndarray is returned.
+
+    See Also
+    --------
+    asanyarray : Similar function which passes through subclasses.
+    ascontiguousarray : Convert input to a contiguous array.
+    asfortranarray : Convert input to an ndarray with column-major
+                     memory order.
+    asarray_chkfinite : Similar function which checks input for NaNs and Infs.
+    fromiter : Create an array from an iterator.
+    fromfunction : Construct an array by executing a function on grid
+                   positions.
+
+    Examples
+    --------
+    Convert a list into an array:
+
+    >>> a = [1, 2]
+    >>> import numpy as np
+    >>> np.asarray(a)
+    array([1, 2])
+
+    Existing arrays are not copied:
+
+    >>> a = np.array([1, 2])
+    >>> np.asarray(a) is a
+    True
+
+    If `dtype` is set, array is copied only if dtype does not match:
+
+    >>> a = np.array([1, 2], dtype=np.float32)
+    >>> np.shares_memory(np.asarray(a, dtype=np.float32), a)
+    True
+    >>> np.shares_memory(np.asarray(a, dtype=np.float64), a)
+    False
+
+    Contrary to `asanyarray`, ndarray subclasses are not passed through:
+
+    >>> issubclass(np.recarray, np.ndarray)
+    True
+    >>> a = np.array([(1., 2), (3., 4)], dtype='f4,i4').view(np.recarray)
+    >>> np.asarray(a) is a
+    False
+    >>> np.asanyarray(a) is a
+    True
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'asanyarray',
+    """
+    asanyarray(a, dtype=None, order=None, *, device=None, copy=None, like=None)
+
+    Convert the input to an ndarray, but pass ndarray subclasses through.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data, in any form that can be converted to an array.  This
+        includes scalars, lists, lists of tuples, tuples, tuples of tuples,
+        tuples of lists, and ndarrays.
+    dtype : data-type, optional
+        By default, the data-type is inferred from the input data.
+    order : {'C', 'F', 'A', 'K'}, optional
+        Memory layout.  'A' and 'K' depend on the order of input array a.
+        'C' row-major (C-style),
+        'F' column-major (Fortran-style) memory representation.
+        'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise
+        'K' (keep) preserve input order
+        Defaults to 'C'.
+    device : str, optional
+        The device on which to place the created array. Default: ``None``.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.1.0
+
+    copy : bool, optional
+        If ``True``, then the object is copied. If ``None`` then the object is
+        copied only if needed, i.e. if ``__array__`` returns a copy, if obj
+        is a nested sequence, or if a copy is needed to satisfy any of
+        the other requirements (``dtype``, ``order``, etc.).
+        For ``False`` it raises a ``ValueError`` if a copy cannot be avoided.
+        Default: ``None``.
+
+        .. versionadded:: 2.1.0
+
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray or an ndarray subclass
+        Array interpretation of `a`.  If `a` is an ndarray or a subclass
+        of ndarray, it is returned as-is and no copy is performed.
+
+    See Also
+    --------
+    asarray : Similar function which always returns ndarrays.
+    ascontiguousarray : Convert input to a contiguous array.
+    asfortranarray : Convert input to an ndarray with column-major
+                     memory order.
+    asarray_chkfinite : Similar function which checks input for NaNs and
+                        Infs.
+    fromiter : Create an array from an iterator.
+    fromfunction : Construct an array by executing a function on grid
+                   positions.
+
+    Examples
+    --------
+    Convert a list into an array:
+
+    >>> a = [1, 2]
+    >>> import numpy as np
+    >>> np.asanyarray(a)
+    array([1, 2])
+
+    Instances of `ndarray` subclasses are passed through as-is:
+
+    >>> a = np.array([(1., 2), (3., 4)], dtype='f4,i4').view(np.recarray)
+    >>> np.asanyarray(a) is a
+    True
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'ascontiguousarray',
+    """
+    ascontiguousarray(a, dtype=None, *, like=None)
+
+    Return a contiguous array (ndim >= 1) in memory (C order).
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    dtype : str or dtype object, optional
+        Data-type of returned array.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        Contiguous array of same shape and content as `a`, with type `dtype`
+        if specified.
+
+    See Also
+    --------
+    asfortranarray : Convert input to an ndarray with column-major
+                     memory order.
+    require : Return an ndarray that satisfies requirements.
+    ndarray.flags : Information about the memory layout of the array.
+
+    Examples
+    --------
+    Starting with a Fortran-contiguous array:
+
+    >>> import numpy as np
+    >>> x = np.ones((2, 3), order='F')
+    >>> x.flags['F_CONTIGUOUS']
+    True
+
+    Calling ``ascontiguousarray`` makes a C-contiguous copy:
+
+    >>> y = np.ascontiguousarray(x)
+    >>> y.flags['C_CONTIGUOUS']
+    True
+    >>> np.may_share_memory(x, y)
+    False
+
+    Now, starting with a C-contiguous array:
+
+    >>> x = np.ones((2, 3), order='C')
+    >>> x.flags['C_CONTIGUOUS']
+    True
+
+    Then, calling ``ascontiguousarray`` returns the same object:
+
+    >>> y = np.ascontiguousarray(x)
+    >>> x is y
+    True
+
+    Note: This function returns an array with at least one-dimension (1-d)
+    so it will not preserve 0-d arrays.
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'asfortranarray',
+    """
+    asfortranarray(a, dtype=None, *, like=None)
+
+    Return an array (ndim >= 1) laid out in Fortran order in memory.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    dtype : str or dtype object, optional
+        By default, the data-type is inferred from the input data.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        The input `a` in Fortran, or column-major, order.
+
+    See Also
+    --------
+    ascontiguousarray : Convert input to a contiguous (C order) array.
+    asanyarray : Convert input to an ndarray with either row or
+        column-major memory order.
+    require : Return an ndarray that satisfies requirements.
+    ndarray.flags : Information about the memory layout of the array.
+
+    Examples
+    --------
+    Starting with a C-contiguous array:
+
+    >>> import numpy as np
+    >>> x = np.ones((2, 3), order='C')
+    >>> x.flags['C_CONTIGUOUS']
+    True
+
+    Calling ``asfortranarray`` makes a Fortran-contiguous copy:
+
+    >>> y = np.asfortranarray(x)
+    >>> y.flags['F_CONTIGUOUS']
+    True
+    >>> np.may_share_memory(x, y)
+    False
+
+    Now, starting with a Fortran-contiguous array:
+
+    >>> x = np.ones((2, 3), order='F')
+    >>> x.flags['F_CONTIGUOUS']
+    True
+
+    Then, calling ``asfortranarray`` returns the same object:
+
+    >>> y = np.asfortranarray(x)
+    >>> x is y
+    True
+
+    Note: This function returns an array with at least one-dimension (1-d)
+    so it will not preserve 0-d arrays.
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'empty',
+    """
+    empty(shape, dtype=float, order='C', *, device=None, like=None)
+
+    Return a new array of given shape and type, without initializing entries.
+
+    Parameters
+    ----------
+    shape : int or tuple of int
+        Shape of the empty array, e.g., ``(2, 3)`` or ``2``.
+    dtype : data-type, optional
+        Desired output data-type for the array, e.g, `numpy.int8`. Default is
+        `numpy.float64`.
+    order : {'C', 'F'}, optional, default: 'C'
+        Whether to store multi-dimensional data in row-major
+        (C-style) or column-major (Fortran-style) order in
+        memory.
+    device : str, optional
+        The device on which to place the created array. Default: ``None``.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        Array of uninitialized (arbitrary) data of the given shape, dtype, and
+        order.  Object arrays will be initialized to None.
+
+    See Also
+    --------
+    empty_like : Return an empty array with shape and type of input.
+    ones : Return a new array setting values to one.
+    zeros : Return a new array setting values to zero.
+    full : Return a new array of given shape filled with value.
+
+    Notes
+    -----
+    Unlike other array creation functions (e.g. `zeros`, `ones`, `full`),
+    `empty` does not initialize the values of the array, and may therefore be
+    marginally faster. However, the values stored in the newly allocated array
+    are arbitrary. For reproducible behavior, be sure to set each element of
+    the array before reading.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.empty([2, 2])
+    array([[ -9.74499359e+001,   6.69583040e-309],
+           [  2.13182611e-314,   3.06959433e-309]])         #uninitialized
+
+    >>> np.empty([2, 2], dtype=int)
+    array([[-1073741821, -1067949133],
+           [  496041986,    19249760]])                     #uninitialized
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'scalar',
+    """
+    scalar(dtype, obj)
+
+    Return a new scalar array of the given type initialized with obj.
+
+    This function is meant mainly for pickle support. `dtype` must be a
+    valid data-type descriptor. If `dtype` corresponds to an object
+    descriptor, then `obj` can be any object, otherwise `obj` must be a
+    string. If `obj` is not given, it will be interpreted as None for object
+    type and as zeros for all other types.
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'zeros',
+    """
+    zeros(shape, dtype=float, order='C', *, like=None)
+
+    Return a new array of given shape and type, filled with zeros.
+
+    Parameters
+    ----------
+    shape : int or tuple of ints
+        Shape of the new array, e.g., ``(2, 3)`` or ``2``.
+    dtype : data-type, optional
+        The desired data-type for the array, e.g., `numpy.int8`.  Default is
+        `numpy.float64`.
+    order : {'C', 'F'}, optional, default: 'C'
+        Whether to store multi-dimensional data in row-major
+        (C-style) or column-major (Fortran-style) order in
+        memory.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        Array of zeros with the given shape, dtype, and order.
+
+    See Also
+    --------
+    zeros_like : Return an array of zeros with shape and type of input.
+    empty : Return a new uninitialized array.
+    ones : Return a new array setting values to one.
+    full : Return a new array of given shape filled with value.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.zeros(5)
+    array([ 0.,  0.,  0.,  0.,  0.])
+
+    >>> np.zeros((5,), dtype=int)
+    array([0, 0, 0, 0, 0])
+
+    >>> np.zeros((2, 1))
+    array([[ 0.],
+           [ 0.]])
+
+    >>> s = (2,2)
+    >>> np.zeros(s)
+    array([[ 0.,  0.],
+           [ 0.,  0.]])
+
+    >>> np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype
+    array([(0, 0), (0, 0)],
+          dtype=[('x', '<i4'), ('y', '<i4')])
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'set_typeDict',
+    """set_typeDict(dict)
+
+    Set the internal dictionary that can look up an array type using a
+    registered code.
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'fromstring',
+    """
+    fromstring(string, dtype=float, count=-1, *, sep, like=None)
+
+    A new 1-D array initialized from text data in a string.
+
+    Parameters
+    ----------
+    string : str
+        A string containing the data.
+    dtype : data-type, optional
+        The data type of the array; default: float.  For binary input data,
+        the data must be in exactly this format. Most builtin numeric types are
+        supported and extension types may be supported.
+    count : int, optional
+        Read this number of `dtype` elements from the data.  If this is
+        negative (the default), the count will be determined from the
+        length of the data.
+    sep : str, optional
+        The string separating numbers in the data; extra whitespace between
+        elements is also ignored.
+
+        .. deprecated:: 1.14
+            Passing ``sep=''``, the default, is deprecated since it will
+            trigger the deprecated binary mode of this function. This mode
+            interprets `string` as binary bytes, rather than ASCII text with
+            decimal numbers, an operation which is better spelt
+            ``frombuffer(string, dtype, count)``. If `string` contains unicode
+            text, the binary mode of `fromstring` will first encode it into
+            bytes using utf-8, which will not produce sane results.
+
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    arr : ndarray
+        The constructed array.
+
+    Raises
+    ------
+    ValueError
+        If the string is not the correct size to satisfy the requested
+        `dtype` and `count`.
+
+    See Also
+    --------
+    frombuffer, fromfile, fromiter
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.fromstring('1 2', dtype=int, sep=' ')
+    array([1, 2])
+    >>> np.fromstring('1, 2', dtype=int, sep=',')
+    array([1, 2])
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'compare_chararrays',
+    """
+    compare_chararrays(a1, a2, cmp, rstrip)
+
+    Performs element-wise comparison of two string arrays using the
+    comparison operator specified by `cmp`.
+
+    Parameters
+    ----------
+    a1, a2 : array_like
+        Arrays to be compared.
+    cmp : {"<", "<=", "==", ">=", ">", "!="}
+        Type of comparison.
+    rstrip : Boolean
+        If True, the spaces at the end of Strings are removed before the comparison.
+
+    Returns
+    -------
+    out : ndarray
+        The output array of type Boolean with the same shape as a and b.
+
+    Raises
+    ------
+    ValueError
+        If `cmp` is not valid.
+    TypeError
+        If at least one of `a` or `b` is a non-string array
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(["a", "b", "cde"])
+    >>> b = np.array(["a", "a", "dec"])
+    >>> np.char.compare_chararrays(a, b, ">", True)
+    array([False,  True, False])
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'fromiter',
+    """
+    fromiter(iter, dtype, count=-1, *, like=None)
+
+    Create a new 1-dimensional array from an iterable object.
+
+    Parameters
+    ----------
+    iter : iterable object
+        An iterable object providing data for the array.
+    dtype : data-type
+        The data-type of the returned array.
+
+        .. versionchanged:: 1.23
+            Object and subarray dtypes are now supported (note that the final
+            result is not 1-D for a subarray dtype).
+
+    count : int, optional
+        The number of items to read from *iterable*.  The default is -1,
+        which means all data is read.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        The output array.
+
+    Notes
+    -----
+    Specify `count` to improve performance.  It allows ``fromiter`` to
+    pre-allocate the output array, instead of resizing it on demand.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> iterable = (x*x for x in range(5))
+    >>> np.fromiter(iterable, float)
+    array([  0.,   1.,   4.,   9.,  16.])
+
+    A carefully constructed subarray dtype will lead to higher dimensional
+    results:
+
+    >>> iterable = ((x+1, x+2) for x in range(5))
+    >>> np.fromiter(iterable, dtype=np.dtype((int, 2)))
+    array([[1, 2],
+           [2, 3],
+           [3, 4],
+           [4, 5],
+           [5, 6]])
+
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'fromfile',
+    """
+    fromfile(file, dtype=float, count=-1, sep='', offset=0, *, like=None)
+
+    Construct an array from data in a text or binary file.
+
+    A highly efficient way of reading binary data with a known data-type,
+    as well as parsing simply formatted text files.  Data written using the
+    `tofile` method can be read using this function.
+
+    Parameters
+    ----------
+    file : file or str or Path
+        Open file object or filename.
+    dtype : data-type
+        Data type of the returned array.
+        For binary files, it is used to determine the size and byte-order
+        of the items in the file.
+        Most builtin numeric types are supported and extension types may be supported.
+    count : int
+        Number of items to read. ``-1`` means all items (i.e., the complete
+        file).
+    sep : str
+        Separator between items if file is a text file.
+        Empty ("") separator means the file should be treated as binary.
+        Spaces (" ") in the separator match zero or more whitespace characters.
+        A separator consisting only of spaces must match at least one
+        whitespace.
+    offset : int
+        The offset (in bytes) from the file's current position. Defaults to 0.
+        Only permitted for binary files.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    See also
+    --------
+    load, save
+    ndarray.tofile
+    loadtxt : More flexible way of loading data from a text file.
+
+    Notes
+    -----
+    Do not rely on the combination of `tofile` and `fromfile` for
+    data storage, as the binary files generated are not platform
+    independent.  In particular, no byte-order or data-type information is
+    saved.  Data can be stored in the platform independent ``.npy`` format
+    using `save` and `load` instead.
+
+    Examples
+    --------
+    Construct an ndarray:
+
+    >>> import numpy as np
+    >>> dt = np.dtype([('time', [('min', np.int64), ('sec', np.int64)]),
+    ...                ('temp', float)])
+    >>> x = np.zeros((1,), dtype=dt)
+    >>> x['time']['min'] = 10; x['temp'] = 98.25
+    >>> x
+    array([((10, 0), 98.25)],
+          dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])
+
+    Save the raw data to disk:
+
+    >>> import tempfile
+    >>> fname = tempfile.mkstemp()[1]
+    >>> x.tofile(fname)
+
+    Read the raw data from disk:
+
+    >>> np.fromfile(fname, dtype=dt)
+    array([((10, 0), 98.25)],
+          dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])
+
+    The recommended way to store and load data:
+
+    >>> np.save(fname, x)
+    >>> np.load(fname + '.npy')
+    array([((10, 0), 98.25)],
+          dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'frombuffer',
+    """
+    frombuffer(buffer, dtype=float, count=-1, offset=0, *, like=None)
+
+    Interpret a buffer as a 1-dimensional array.
+
+    Parameters
+    ----------
+    buffer : buffer_like
+        An object that exposes the buffer interface.
+    dtype : data-type, optional
+        Data-type of the returned array; default: float.
+    count : int, optional
+        Number of items to read. ``-1`` means all data in the buffer.
+    offset : int, optional
+        Start reading the buffer from this offset (in bytes); default: 0.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+
+    See also
+    --------
+    ndarray.tobytes
+        Inverse of this operation, construct Python bytes from the raw data
+        bytes in the array.
+
+    Notes
+    -----
+    If the buffer has data that is not in machine byte-order, this should
+    be specified as part of the data-type, e.g.::
+
+      >>> dt = np.dtype(int)
+      >>> dt = dt.newbyteorder('>')
+      >>> np.frombuffer(buf, dtype=dt) # doctest: +SKIP
+
+    The data of the resulting array will not be byteswapped, but will be
+    interpreted correctly.
+
+    This function creates a view into the original object.  This should be safe
+    in general, but it may make sense to copy the result when the original
+    object is mutable or untrusted.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> s = b'hello world'
+    >>> np.frombuffer(s, dtype='S1', count=5, offset=6)
+    array([b'w', b'o', b'r', b'l', b'd'], dtype='|S1')
+
+    >>> np.frombuffer(b'\\x01\\x02', dtype=np.uint8)
+    array([1, 2], dtype=uint8)
+    >>> np.frombuffer(b'\\x01\\x02\\x03\\x04\\x05', dtype=np.uint8, count=3)
+    array([1, 2, 3], dtype=uint8)
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'from_dlpack',
+    """
+    from_dlpack(x, /, *, device=None, copy=None)
+
+    Create a NumPy array from an object implementing the ``__dlpack__``
+    protocol. Generally, the returned NumPy array is a view of the input
+    object. See [1]_ and [2]_ for more details.
+
+    Parameters
+    ----------
+    x : object
+        A Python object that implements the ``__dlpack__`` and
+        ``__dlpack_device__`` methods.
+    device : device, optional
+        Device on which to place the created array. Default: ``None``.
+        Must be ``"cpu"`` if passed which may allow importing an array
+        that is not already CPU available.
+    copy : bool, optional
+        Boolean indicating whether or not to copy the input. If ``True``,
+        the copy will be made. If ``False``, the function will never copy,
+        and will raise ``BufferError`` in case a copy is deemed necessary.
+        Passing it requests a copy from the exporter who may or may not
+        implement the capability.
+        If ``None``, the function will reuse the existing memory buffer if
+        possible and copy otherwise. Default: ``None``.
+
+
+    Returns
+    -------
+    out : ndarray
+
+    References
+    ----------
+    .. [1] Array API documentation,
+       https://data-apis.org/array-api/latest/design_topics/data_interchange.html#syntax-for-data-interchange-with-dlpack
+
+    .. [2] Python specification for DLPack,
+       https://dmlc.github.io/dlpack/latest/python_spec.html
+
+    Examples
+    --------
+    >>> import torch  # doctest: +SKIP
+    >>> x = torch.arange(10)  # doctest: +SKIP
+    >>> # create a view of the torch tensor "x" in NumPy
+    >>> y = np.from_dlpack(x)  # doctest: +SKIP
+    """)
+
+add_newdoc('numpy._core.multiarray', 'correlate',
+    """cross_correlate(a,v, mode=0)""")
+
+add_newdoc('numpy._core.multiarray', 'arange',
+    """
+    arange([start,] stop[, step,], dtype=None, *, device=None, like=None)
+
+    Return evenly spaced values within a given interval.
+
+    ``arange`` can be called with a varying number of positional arguments:
+
+    * ``arange(stop)``: Values are generated within the half-open interval
+      ``[0, stop)`` (in other words, the interval including `start` but
+      excluding `stop`).
+    * ``arange(start, stop)``: Values are generated within the half-open
+      interval ``[start, stop)``.
+    * ``arange(start, stop, step)`` Values are generated within the half-open
+      interval ``[start, stop)``, with spacing between values given by
+      ``step``.
+
+    For integer arguments the function is roughly equivalent to the Python
+    built-in :py:class:`range`, but returns an ndarray rather than a ``range``
+    instance.
+
+    When using a non-integer step, such as 0.1, it is often better to use
+    `numpy.linspace`.
+
+    See the Warning sections below for more information.
+
+    Parameters
+    ----------
+    start : integer or real, optional
+        Start of interval.  The interval includes this value.  The default
+        start value is 0.
+    stop : integer or real
+        End of interval.  The interval does not include this value, except
+        in some cases where `step` is not an integer and floating point
+        round-off affects the length of `out`.
+    step : integer or real, optional
+        Spacing between values.  For any output `out`, this is the distance
+        between two adjacent values, ``out[i+1] - out[i]``.  The default
+        step size is 1.  If `step` is specified as a position argument,
+        `start` must also be given.
+    dtype : dtype, optional
+        The type of the output array.  If `dtype` is not given, infer the data
+        type from the other input arguments.
+    device : str, optional
+        The device on which to place the created array. Default: ``None``.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    arange : ndarray
+        Array of evenly spaced values.
+
+        For floating point arguments, the length of the result is
+        ``ceil((stop - start)/step)``.  Because of floating point overflow,
+        this rule may result in the last element of `out` being greater
+        than `stop`.
+
+    Warnings
+    --------
+    The length of the output might not be numerically stable.
+
+    Another stability issue is due to the internal implementation of
+    `numpy.arange`.
+    The actual step value used to populate the array is
+    ``dtype(start + step) - dtype(start)`` and not `step`. Precision loss
+    can occur here, due to casting or due to using floating points when
+    `start` is much larger than `step`. This can lead to unexpected
+    behaviour. For example::
+
+      >>> np.arange(0, 5, 0.5, dtype=int)
+      array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
+      >>> np.arange(-3, 3, 0.5, dtype=int)
+      array([-3, -2, -1,  0,  1,  2,  3,  4,  5,  6,  7,  8])
+
+    In such cases, the use of `numpy.linspace` should be preferred.
+
+    The built-in :py:class:`range` generates :std:doc:`Python built-in integers
+    that have arbitrary size <python:c-api/long>`, while `numpy.arange`
+    produces `numpy.int32` or `numpy.int64` numbers. This may result in
+    incorrect results for large integer values::
+
+      >>> power = 40
+      >>> modulo = 10000
+      >>> x1 = [(n ** power) % modulo for n in range(8)]
+      >>> x2 = [(n ** power) % modulo for n in np.arange(8)]
+      >>> print(x1)
+      [0, 1, 7776, 8801, 6176, 625, 6576, 4001]  # correct
+      >>> print(x2)
+      [0, 1, 7776, 7185, 0, 5969, 4816, 3361]  # incorrect
+
+    See Also
+    --------
+    numpy.linspace : Evenly spaced numbers with careful handling of endpoints.
+    numpy.ogrid: Arrays of evenly spaced numbers in N-dimensions.
+    numpy.mgrid: Grid-shaped arrays of evenly spaced numbers in N-dimensions.
+    :ref:`how-to-partition`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.arange(3)
+    array([0, 1, 2])
+    >>> np.arange(3.0)
+    array([ 0.,  1.,  2.])
+    >>> np.arange(3,7)
+    array([3, 4, 5, 6])
+    >>> np.arange(3,7,2)
+    array([3, 5])
+
+    """)
+
+add_newdoc('numpy._core.multiarray', '_get_ndarray_c_version',
+    """_get_ndarray_c_version()
+
+    Return the compile time NPY_VERSION (formerly called NDARRAY_VERSION) number.
+
+    """)
+
+add_newdoc('numpy._core.multiarray', '_reconstruct',
+    """_reconstruct(subtype, shape, dtype)
+
+    Construct an empty array. Used by Pickles.
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'promote_types',
+    """
+    promote_types(type1, type2)
+
+    Returns the data type with the smallest size and smallest scalar
+    kind to which both ``type1`` and ``type2`` may be safely cast.
+    The returned data type is always considered "canonical", this mainly
+    means that the promoted dtype will always be in native byte order.
+
+    This function is symmetric, but rarely associative.
+
+    Parameters
+    ----------
+    type1 : dtype or dtype specifier
+        First data type.
+    type2 : dtype or dtype specifier
+        Second data type.
+
+    Returns
+    -------
+    out : dtype
+        The promoted data type.
+
+    Notes
+    -----
+    Please see `numpy.result_type` for additional information about promotion.
+
+    Starting in NumPy 1.9, promote_types function now returns a valid string
+    length when given an integer or float dtype as one argument and a string
+    dtype as another argument. Previously it always returned the input string
+    dtype, even if it wasn't long enough to store the max integer/float value
+    converted to a string.
+
+    .. versionchanged:: 1.23.0
+
+    NumPy now supports promotion for more structured dtypes.  It will now
+    remove unnecessary padding from a structure dtype and promote included
+    fields individually.
+
+    See Also
+    --------
+    result_type, dtype, can_cast
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.promote_types('f4', 'f8')
+    dtype('float64')
+
+    >>> np.promote_types('i8', 'f4')
+    dtype('float64')
+
+    >>> np.promote_types('>i8', '<c8')
+    dtype('complex128')
+
+    >>> np.promote_types('i4', 'S8')
+    dtype('S11')
+
+    An example of a non-associative case:
+
+    >>> p = np.promote_types
+    >>> p('S', p('i1', 'u1'))
+    dtype('S6')
+    >>> p(p('S', 'i1'), 'u1')
+    dtype('S4')
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'c_einsum',
+    """
+    c_einsum(subscripts, *operands, out=None, dtype=None, order='K',
+           casting='safe')
+
+    *This documentation shadows that of the native python implementation of the `einsum` function,
+    except all references and examples related to the `optimize` argument (v 0.12.0) have been removed.*
+
+    Evaluates the Einstein summation convention on the operands.
+
+    Using the Einstein summation convention, many common multi-dimensional,
+    linear algebraic array operations can be represented in a simple fashion.
+    In *implicit* mode `einsum` computes these values.
+
+    In *explicit* mode, `einsum` provides further flexibility to compute
+    other array operations that might not be considered classical Einstein
+    summation operations, by disabling, or forcing summation over specified
+    subscript labels.
+
+    See the notes and examples for clarification.
+
+    Parameters
+    ----------
+    subscripts : str
+        Specifies the subscripts for summation as comma separated list of
+        subscript labels. An implicit (classical Einstein summation)
+        calculation is performed unless the explicit indicator '->' is
+        included as well as subscript labels of the precise output form.
+    operands : list of array_like
+        These are the arrays for the operation.
+    out : ndarray, optional
+        If provided, the calculation is done into this array.
+    dtype : {data-type, None}, optional
+        If provided, forces the calculation to use the data type specified.
+        Note that you may have to also give a more liberal `casting`
+        parameter to allow the conversions. Default is None.
+    order : {'C', 'F', 'A', 'K'}, optional
+        Controls the memory layout of the output. 'C' means it should
+        be C contiguous. 'F' means it should be Fortran contiguous,
+        'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise.
+        'K' means it should be as close to the layout of the inputs as
+        is possible, including arbitrarily permuted axes.
+        Default is 'K'.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur.  Setting this to
+        'unsafe' is not recommended, as it can adversely affect accumulations.
+
+          * 'no' means the data types should not be cast at all.
+          * 'equiv' means only byte-order changes are allowed.
+          * 'safe' means only casts which can preserve values are allowed.
+          * 'same_kind' means only safe casts or casts within a kind,
+            like float64 to float32, are allowed.
+          * 'unsafe' means any data conversions may be done.
+
+        Default is 'safe'.
+    optimize : {False, True, 'greedy', 'optimal'}, optional
+        Controls if intermediate optimization should occur. No optimization
+        will occur if False and True will default to the 'greedy' algorithm.
+        Also accepts an explicit contraction list from the ``np.einsum_path``
+        function. See ``np.einsum_path`` for more details. Defaults to False.
+
+    Returns
+    -------
+    output : ndarray
+        The calculation based on the Einstein summation convention.
+
+    See Also
+    --------
+    einsum_path, dot, inner, outer, tensordot, linalg.multi_dot
+
+    Notes
+    -----
+    The Einstein summation convention can be used to compute
+    many multi-dimensional, linear algebraic array operations. `einsum`
+    provides a succinct way of representing these.
+
+    A non-exhaustive list of these operations,
+    which can be computed by `einsum`, is shown below along with examples:
+
+    * Trace of an array, :py:func:`numpy.trace`.
+    * Return a diagonal, :py:func:`numpy.diag`.
+    * Array axis summations, :py:func:`numpy.sum`.
+    * Transpositions and permutations, :py:func:`numpy.transpose`.
+    * Matrix multiplication and dot product, :py:func:`numpy.matmul` :py:func:`numpy.dot`.
+    * Vector inner and outer products, :py:func:`numpy.inner` :py:func:`numpy.outer`.
+    * Broadcasting, element-wise and scalar multiplication, :py:func:`numpy.multiply`.
+    * Tensor contractions, :py:func:`numpy.tensordot`.
+    * Chained array operations, in efficient calculation order, :py:func:`numpy.einsum_path`.
+
+    The subscripts string is a comma-separated list of subscript labels,
+    where each label refers to a dimension of the corresponding operand.
+    Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)``
+    is equivalent to :py:func:`np.inner(a,b) <numpy.inner>`. If a label
+    appears only once, it is not summed, so ``np.einsum('i', a)`` produces a
+    view of ``a`` with no changes. A further example ``np.einsum('ij,jk', a, b)``
+    describes traditional matrix multiplication and is equivalent to
+    :py:func:`np.matmul(a,b) <numpy.matmul>`. Repeated subscript labels in one
+    operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent
+    to :py:func:`np.trace(a) <numpy.trace>`.
+
+    In *implicit mode*, the chosen subscripts are important
+    since the axes of the output are reordered alphabetically.  This
+    means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
+    ``np.einsum('ji', a)`` takes its transpose. Additionally,
+    ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while,
+    ``np.einsum('ij,jh', a, b)`` returns the transpose of the
+    multiplication since subscript 'h' precedes subscript 'i'.
+
+    In *explicit mode* the output can be directly controlled by
+    specifying output subscript labels.  This requires the
+    identifier '->' as well as the list of output subscript labels.
+    This feature increases the flexibility of the function since
+    summing can be disabled or forced when required. The call
+    ``np.einsum('i->', a)`` is like :py:func:`np.sum(a) <numpy.sum>`
+    if ``a`` is a 1-D array, and ``np.einsum('ii->i', a)``
+    is like :py:func:`np.diag(a) <numpy.diag>` if ``a`` is a square 2-D array.
+    The difference is that `einsum` does not allow broadcasting by default.
+    Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the
+    order of the output subscript labels and therefore returns matrix
+    multiplication, unlike the example above in implicit mode.
+
+    To enable and control broadcasting, use an ellipsis.  Default
+    NumPy-style broadcasting is done by adding an ellipsis
+    to the left of each term, like ``np.einsum('...ii->...i', a)``.
+    ``np.einsum('...i->...', a)`` is like
+    :py:func:`np.sum(a, axis=-1) <numpy.sum>` for array ``a`` of any shape.
+    To take the trace along the first and last axes,
+    you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
+    product with the left-most indices instead of rightmost, one can do
+    ``np.einsum('ij...,jk...->ik...', a, b)``.
+
+    When there is only one operand, no axes are summed, and no output
+    parameter is provided, a view into the operand is returned instead
+    of a new array.  Thus, taking the diagonal as ``np.einsum('ii->i', a)``
+    produces a view (changed in version 1.10.0).
+
+    `einsum` also provides an alternative way to provide the subscripts
+    and operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``.
+    If the output shape is not provided in this format `einsum` will be
+    calculated in implicit mode, otherwise it will be performed explicitly.
+    The examples below have corresponding `einsum` calls with the two
+    parameter methods.
+
+    Views returned from einsum are now writeable whenever the input array
+    is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now
+    have the same effect as :py:func:`np.swapaxes(a, 0, 2) <numpy.swapaxes>`
+    and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal
+    of a 2D array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.arange(25).reshape(5,5)
+    >>> b = np.arange(5)
+    >>> c = np.arange(6).reshape(2,3)
+
+    Trace of a matrix:
+
+    >>> np.einsum('ii', a)
+    60
+    >>> np.einsum(a, [0,0])
+    60
+    >>> np.trace(a)
+    60
+
+    Extract the diagonal (requires explicit form):
+
+    >>> np.einsum('ii->i', a)
+    array([ 0,  6, 12, 18, 24])
+    >>> np.einsum(a, [0,0], [0])
+    array([ 0,  6, 12, 18, 24])
+    >>> np.diag(a)
+    array([ 0,  6, 12, 18, 24])
+
+    Sum over an axis (requires explicit form):
+
+    >>> np.einsum('ij->i', a)
+    array([ 10,  35,  60,  85, 110])
+    >>> np.einsum(a, [0,1], [0])
+    array([ 10,  35,  60,  85, 110])
+    >>> np.sum(a, axis=1)
+    array([ 10,  35,  60,  85, 110])
+
+    For higher dimensional arrays summing a single axis can be done with ellipsis:
+
+    >>> np.einsum('...j->...', a)
+    array([ 10,  35,  60,  85, 110])
+    >>> np.einsum(a, [Ellipsis,1], [Ellipsis])
+    array([ 10,  35,  60,  85, 110])
+
+    Compute a matrix transpose, or reorder any number of axes:
+
+    >>> np.einsum('ji', c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.einsum('ij->ji', c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.einsum(c, [1,0])
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.transpose(c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+
+    Vector inner products:
+
+    >>> np.einsum('i,i', b, b)
+    30
+    >>> np.einsum(b, [0], b, [0])
+    30
+    >>> np.inner(b,b)
+    30
+
+    Matrix vector multiplication:
+
+    >>> np.einsum('ij,j', a, b)
+    array([ 30,  80, 130, 180, 230])
+    >>> np.einsum(a, [0,1], b, [1])
+    array([ 30,  80, 130, 180, 230])
+    >>> np.dot(a, b)
+    array([ 30,  80, 130, 180, 230])
+    >>> np.einsum('...j,j', a, b)
+    array([ 30,  80, 130, 180, 230])
+
+    Broadcasting and scalar multiplication:
+
+    >>> np.einsum('..., ...', 3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.einsum(',ij', 3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.einsum(3, [Ellipsis], c, [Ellipsis])
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.multiply(3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+
+    Vector outer product:
+
+    >>> np.einsum('i,j', np.arange(2)+1, b)
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+    >>> np.einsum(np.arange(2)+1, [0], b, [1])
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+    >>> np.outer(np.arange(2)+1, b)
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+
+    Tensor contraction:
+
+    >>> a = np.arange(60.).reshape(3,4,5)
+    >>> b = np.arange(24.).reshape(4,3,2)
+    >>> np.einsum('ijk,jil->kl', a, b)
+    array([[ 4400.,  4730.],
+           [ 4532.,  4874.],
+           [ 4664.,  5018.],
+           [ 4796.,  5162.],
+           [ 4928.,  5306.]])
+    >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])
+    array([[ 4400.,  4730.],
+           [ 4532.,  4874.],
+           [ 4664.,  5018.],
+           [ 4796.,  5162.],
+           [ 4928.,  5306.]])
+    >>> np.tensordot(a,b, axes=([1,0],[0,1]))
+    array([[ 4400.,  4730.],
+           [ 4532.,  4874.],
+           [ 4664.,  5018.],
+           [ 4796.,  5162.],
+           [ 4928.,  5306.]])
+
+    Writeable returned arrays (since version 1.10.0):
+
+    >>> a = np.zeros((3, 3))
+    >>> np.einsum('ii->i', a)[:] = 1
+    >>> a
+    array([[ 1.,  0.,  0.],
+           [ 0.,  1.,  0.],
+           [ 0.,  0.,  1.]])
+
+    Example of ellipsis use:
+
+    >>> a = np.arange(6).reshape((3,2))
+    >>> b = np.arange(12).reshape((4,3))
+    >>> np.einsum('ki,jk->ij', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+    >>> np.einsum('ki,...k->i...', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+    >>> np.einsum('k...,jk', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+
+    """)
+
+
+##############################################################################
+#
+# Documentation for ndarray attributes and methods
+#
+##############################################################################
+
+
+##############################################################################
+#
+# ndarray object
+#
+##############################################################################
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray',
+    """
+    ndarray(shape, dtype=float, buffer=None, offset=0,
+            strides=None, order=None)
+
+    An array object represents a multidimensional, homogeneous array
+    of fixed-size items.  An associated data-type object describes the
+    format of each element in the array (its byte-order, how many bytes it
+    occupies in memory, whether it is an integer, a floating point number,
+    or something else, etc.)
+
+    Arrays should be constructed using `array`, `zeros` or `empty` (refer
+    to the See Also section below).  The parameters given here refer to
+    a low-level method (`ndarray(...)`) for instantiating an array.
+
+    For more information, refer to the `numpy` module and examine the
+    methods and attributes of an array.
+
+    Parameters
+    ----------
+    (for the __new__ method; see Notes below)
+
+    shape : tuple of ints
+        Shape of created array.
+    dtype : data-type, optional
+        Any object that can be interpreted as a numpy data type.
+    buffer : object exposing buffer interface, optional
+        Used to fill the array with data.
+    offset : int, optional
+        Offset of array data in buffer.
+    strides : tuple of ints, optional
+        Strides of data in memory.
+    order : {'C', 'F'}, optional
+        Row-major (C-style) or column-major (Fortran-style) order.
+
+    Attributes
+    ----------
+    T : ndarray
+        Transpose of the array.
+    data : buffer
+        The array's elements, in memory.
+    dtype : dtype object
+        Describes the format of the elements in the array.
+    flags : dict
+        Dictionary containing information related to memory use, e.g.,
+        'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
+    flat : numpy.flatiter object
+        Flattened version of the array as an iterator.  The iterator
+        allows assignments, e.g., ``x.flat = 3`` (See `ndarray.flat` for
+        assignment examples; TODO).
+    imag : ndarray
+        Imaginary part of the array.
+    real : ndarray
+        Real part of the array.
+    size : int
+        Number of elements in the array.
+    itemsize : int
+        The memory use of each array element in bytes.
+    nbytes : int
+        The total number of bytes required to store the array data,
+        i.e., ``itemsize * size``.
+    ndim : int
+        The array's number of dimensions.
+    shape : tuple of ints
+        Shape of the array.
+    strides : tuple of ints
+        The step-size required to move from one element to the next in
+        memory. For example, a contiguous ``(3, 4)`` array of type
+        ``int16`` in C-order has strides ``(8, 2)``.  This implies that
+        to move from element to element in memory requires jumps of 2 bytes.
+        To move from row-to-row, one needs to jump 8 bytes at a time
+        (``2 * 4``).
+    ctypes : ctypes object
+        Class containing properties of the array needed for interaction
+        with ctypes.
+    base : ndarray
+        If the array is a view into another array, that array is its `base`
+        (unless that array is also a view).  The `base` array is where the
+        array data is actually stored.
+
+    See Also
+    --------
+    array : Construct an array.
+    zeros : Create an array, each element of which is zero.
+    empty : Create an array, but leave its allocated memory unchanged (i.e.,
+            it contains "garbage").
+    dtype : Create a data-type.
+    numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`
+                           w.r.t. its `dtype.type <numpy.dtype.type>`.
+
+    Notes
+    -----
+    There are two modes of creating an array using ``__new__``:
+
+    1. If `buffer` is None, then only `shape`, `dtype`, and `order`
+       are used.
+    2. If `buffer` is an object exposing the buffer interface, then
+       all keywords are interpreted.
+
+    No ``__init__`` method is needed because the array is fully initialized
+    after the ``__new__`` method.
+
+    Examples
+    --------
+    These examples illustrate the low-level `ndarray` constructor.  Refer
+    to the `See Also` section above for easier ways of constructing an
+    ndarray.
+
+    First mode, `buffer` is None:
+
+    >>> import numpy as np
+    >>> np.ndarray(shape=(2,2), dtype=float, order='F')
+    array([[0.0e+000, 0.0e+000], # random
+           [     nan, 2.5e-323]])
+
+    Second mode:
+
+    >>> np.ndarray((2,), buffer=np.array([1,2,3]),
+    ...            offset=np.int_().itemsize,
+    ...            dtype=int) # offset = 1*itemsize, i.e. skip first element
+    array([2, 3])
+
+    """)
+
+
+##############################################################################
+#
+# ndarray attributes
+#
+##############################################################################
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__array_interface__',
+    """Array protocol: Python side."""))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__array_priority__',
+    """Array priority."""))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__array_struct__',
+    """Array protocol: C-struct side."""))
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__dlpack__',
+    """
+    a.__dlpack__(*, stream=None, max_version=None, dl_device=None, copy=None)
+
+    DLPack Protocol: Part of the Array API.
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__dlpack_device__',
+    """
+    a.__dlpack_device__()
+
+    DLPack Protocol: Part of the Array API.
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('base',
+    """
+    Base object if memory is from some other object.
+
+    Examples
+    --------
+    The base of an array that owns its memory is None:
+
+    >>> import numpy as np
+    >>> x = np.array([1,2,3,4])
+    >>> x.base is None
+    True
+
+    Slicing creates a view, whose memory is shared with x:
+
+    >>> y = x[2:]
+    >>> y.base is x
+    True
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('ctypes',
+    """
+    An object to simplify the interaction of the array with the ctypes
+    module.
+
+    This attribute creates an object that makes it easier to use arrays
+    when calling shared libraries with the ctypes module. The returned
+    object has, among others, data, shape, and strides attributes (see
+    Notes below) which themselves return ctypes objects that can be used
+    as arguments to a shared library.
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    c : Python object
+        Possessing attributes data, shape, strides, etc.
+
+    See Also
+    --------
+    numpy.ctypeslib
+
+    Notes
+    -----
+    Below are the public attributes of this object which were documented
+    in "Guide to NumPy" (we have omitted undocumented public attributes,
+    as well as documented private attributes):
+
+    .. autoattribute:: numpy._core._internal._ctypes.data
+        :noindex:
+
+    .. autoattribute:: numpy._core._internal._ctypes.shape
+        :noindex:
+
+    .. autoattribute:: numpy._core._internal._ctypes.strides
+        :noindex:
+
+    .. automethod:: numpy._core._internal._ctypes.data_as
+        :noindex:
+
+    .. automethod:: numpy._core._internal._ctypes.shape_as
+        :noindex:
+
+    .. automethod:: numpy._core._internal._ctypes.strides_as
+        :noindex:
+
+    If the ctypes module is not available, then the ctypes attribute
+    of array objects still returns something useful, but ctypes objects
+    are not returned and errors may be raised instead. In particular,
+    the object will still have the ``as_parameter`` attribute which will
+    return an integer equal to the data attribute.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import ctypes
+    >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)
+    >>> x
+    array([[0, 1],
+           [2, 3]], dtype=int32)
+    >>> x.ctypes.data
+    31962608 # may vary
+    >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))
+    <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary
+    >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents
+    c_uint(0)
+    >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents
+    c_ulong(4294967296)
+    >>> x.ctypes.shape
+    <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary
+    >>> x.ctypes.strides
+    <numpy._core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('data',
+    """Python buffer object pointing to the start of the array's data."""))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('dtype',
+    """
+    Data-type of the array's elements.
+
+    .. warning::
+
+        Setting ``arr.dtype`` is discouraged and may be deprecated in the
+        future.  Setting will replace the ``dtype`` without modifying the
+        memory (see also `ndarray.view` and `ndarray.astype`).
+
+    Parameters
+    ----------
+    None
+
+    Returns
+    -------
+    d : numpy dtype object
+
+    See Also
+    --------
+    ndarray.astype : Cast the values contained in the array to a new data-type.
+    ndarray.view : Create a view of the same data but a different data-type.
+    numpy.dtype
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(4).reshape((2, 2))
+    >>> x
+    array([[0, 1],
+           [2, 3]])
+    >>> x.dtype
+    dtype('int64')   # may vary (OS, bitness)
+    >>> isinstance(x.dtype, np.dtype)
+    True
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('imag',
+    """
+    The imaginary part of the array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.sqrt([1+0j, 0+1j])
+    >>> x.imag
+    array([ 0.        ,  0.70710678])
+    >>> x.imag.dtype
+    dtype('float64')
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('itemsize',
+    """
+    Length of one array element in bytes.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1,2,3], dtype=np.float64)
+    >>> x.itemsize
+    8
+    >>> x = np.array([1,2,3], dtype=np.complex128)
+    >>> x.itemsize
+    16
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('flags',
+    """
+    Information about the memory layout of the array.
+
+    Attributes
+    ----------
+    C_CONTIGUOUS (C)
+        The data is in a single, C-style contiguous segment.
+    F_CONTIGUOUS (F)
+        The data is in a single, Fortran-style contiguous segment.
+    OWNDATA (O)
+        The array owns the memory it uses or borrows it from another object.
+    WRITEABLE (W)
+        The data area can be written to.  Setting this to False locks
+        the data, making it read-only.  A view (slice, etc.) inherits WRITEABLE
+        from its base array at creation time, but a view of a writeable
+        array may be subsequently locked while the base array remains writeable.
+        (The opposite is not true, in that a view of a locked array may not
+        be made writeable.  However, currently, locking a base object does not
+        lock any views that already reference it, so under that circumstance it
+        is possible to alter the contents of a locked array via a previously
+        created writeable view onto it.)  Attempting to change a non-writeable
+        array raises a RuntimeError exception.
+    ALIGNED (A)
+        The data and all elements are aligned appropriately for the hardware.
+    WRITEBACKIFCOPY (X)
+        This array is a copy of some other array. The C-API function
+        PyArray_ResolveWritebackIfCopy must be called before deallocating
+        to the base array will be updated with the contents of this array.
+    FNC
+        F_CONTIGUOUS and not C_CONTIGUOUS.
+    FORC
+        F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
+    BEHAVED (B)
+        ALIGNED and WRITEABLE.
+    CARRAY (CA)
+        BEHAVED and C_CONTIGUOUS.
+    FARRAY (FA)
+        BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
+
+    Notes
+    -----
+    The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),
+    or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag
+    names are only supported in dictionary access.
+
+    Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be
+    changed by the user, via direct assignment to the attribute or dictionary
+    entry, or by calling `ndarray.setflags`.
+
+    The array flags cannot be set arbitrarily:
+
+    - WRITEBACKIFCOPY can only be set ``False``.
+    - ALIGNED can only be set ``True`` if the data is truly aligned.
+    - WRITEABLE can only be set ``True`` if the array owns its own memory
+      or the ultimate owner of the memory exposes a writeable buffer
+      interface or is a string.
+
+    Arrays can be both C-style and Fortran-style contiguous simultaneously.
+    This is clear for 1-dimensional arrays, but can also be true for higher
+    dimensional arrays.
+
+    Even for contiguous arrays a stride for a given dimension
+    ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``
+    or the array has no elements.
+    It does *not* generally hold that ``self.strides[-1] == self.itemsize``
+    for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for
+    Fortran-style contiguous arrays is true.
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('flat',
+    """
+    A 1-D iterator over the array.
+
+    This is a `numpy.flatiter` instance, which acts similarly to, but is not
+    a subclass of, Python's built-in iterator object.
+
+    See Also
+    --------
+    flatten : Return a copy of the array collapsed into one dimension.
+
+    flatiter
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(1, 7).reshape(2, 3)
+    >>> x
+    array([[1, 2, 3],
+           [4, 5, 6]])
+    >>> x.flat[3]
+    4
+    >>> x.T
+    array([[1, 4],
+           [2, 5],
+           [3, 6]])
+    >>> x.T.flat[3]
+    5
+    >>> type(x.flat)
+    <class 'numpy.flatiter'>
+
+    An assignment example:
+
+    >>> x.flat = 3; x
+    array([[3, 3, 3],
+           [3, 3, 3]])
+    >>> x.flat[[1,4]] = 1; x
+    array([[3, 1, 3],
+           [3, 1, 3]])
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('nbytes',
+    """
+    Total bytes consumed by the elements of the array.
+
+    Notes
+    -----
+    Does not include memory consumed by non-element attributes of the
+    array object.
+
+    See Also
+    --------
+    sys.getsizeof
+        Memory consumed by the object itself without parents in case view.
+        This does include memory consumed by non-element attributes.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.zeros((3,5,2), dtype=np.complex128)
+    >>> x.nbytes
+    480
+    >>> np.prod(x.shape) * x.itemsize
+    480
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('ndim',
+    """
+    Number of array dimensions.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3])
+    >>> x.ndim
+    1
+    >>> y = np.zeros((2, 3, 4))
+    >>> y.ndim
+    3
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('real',
+    """
+    The real part of the array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.sqrt([1+0j, 0+1j])
+    >>> x.real
+    array([ 1.        ,  0.70710678])
+    >>> x.real.dtype
+    dtype('float64')
+
+    See Also
+    --------
+    numpy.real : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('shape',
+    """
+    Tuple of array dimensions.
+
+    The shape property is usually used to get the current shape of an array,
+    but may also be used to reshape the array in-place by assigning a tuple of
+    array dimensions to it.  As with `numpy.reshape`, one of the new shape
+    dimensions can be -1, in which case its value is inferred from the size of
+    the array and the remaining dimensions. Reshaping an array in-place will
+    fail if a copy is required.
+
+    .. warning::
+
+        Setting ``arr.shape`` is discouraged and may be deprecated in the
+        future.  Using `ndarray.reshape` is the preferred approach.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3, 4])
+    >>> x.shape
+    (4,)
+    >>> y = np.zeros((2, 3, 4))
+    >>> y.shape
+    (2, 3, 4)
+    >>> y.shape = (3, 8)
+    >>> y
+    array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
+           [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
+           [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
+    >>> y.shape = (3, 6)
+    Traceback (most recent call last):
+      File "<stdin>", line 1, in <module>
+    ValueError: cannot reshape array of size 24 into shape (3,6)
+    >>> np.zeros((4,2))[::2].shape = (-1,)
+    Traceback (most recent call last):
+      File "<stdin>", line 1, in <module>
+    AttributeError: Incompatible shape for in-place modification. Use
+    `.reshape()` to make a copy with the desired shape.
+
+    See Also
+    --------
+    numpy.shape : Equivalent getter function.
+    numpy.reshape : Function similar to setting ``shape``.
+    ndarray.reshape : Method similar to setting ``shape``.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('size',
+    """
+    Number of elements in the array.
+
+    Equal to ``np.prod(a.shape)``, i.e., the product of the array's
+    dimensions.
+
+    Notes
+    -----
+    `a.size` returns a standard arbitrary precision Python integer. This
+    may not be the case with other methods of obtaining the same value
+    (like the suggested ``np.prod(a.shape)``, which returns an instance
+    of ``np.int_``), and may be relevant if the value is used further in
+    calculations that may overflow a fixed size integer type.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.zeros((3, 5, 2), dtype=np.complex128)
+    >>> x.size
+    30
+    >>> np.prod(x.shape)
+    30
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('strides',
+    """
+    Tuple of bytes to step in each dimension when traversing an array.
+
+    The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`
+    is::
+
+        offset = sum(np.array(i) * a.strides)
+
+    A more detailed explanation of strides can be found in
+    :ref:`arrays.ndarray`.
+
+    .. warning::
+
+        Setting ``arr.strides`` is discouraged and may be deprecated in the
+        future.  `numpy.lib.stride_tricks.as_strided` should be preferred
+        to create a new view of the same data in a safer way.
+
+    Notes
+    -----
+    Imagine an array of 32-bit integers (each 4 bytes)::
+
+      x = np.array([[0, 1, 2, 3, 4],
+                    [5, 6, 7, 8, 9]], dtype=np.int32)
+
+    This array is stored in memory as 40 bytes, one after the other
+    (known as a contiguous block of memory).  The strides of an array tell
+    us how many bytes we have to skip in memory to move to the next position
+    along a certain axis.  For example, we have to skip 4 bytes (1 value) to
+    move to the next column, but 20 bytes (5 values) to get to the same
+    position in the next row.  As such, the strides for the array `x` will be
+    ``(20, 4)``.
+
+    See Also
+    --------
+    numpy.lib.stride_tricks.as_strided
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> y = np.reshape(np.arange(2 * 3 * 4, dtype=np.int32), (2, 3, 4))
+    >>> y
+    array([[[ 0,  1,  2,  3],
+            [ 4,  5,  6,  7],
+            [ 8,  9, 10, 11]],
+           [[12, 13, 14, 15],
+            [16, 17, 18, 19],
+            [20, 21, 22, 23]]], dtype=np.int32)
+    >>> y.strides
+    (48, 16, 4)
+    >>> y[1, 1, 1]
+    np.int32(17)
+    >>> offset = sum(y.strides * np.array((1, 1, 1)))
+    >>> offset // y.itemsize
+    np.int64(17)
+
+    >>> x = np.reshape(np.arange(5*6*7*8, dtype=np.int32), (5, 6, 7, 8))
+    >>> x = x.transpose(2, 3, 1, 0)
+    >>> x.strides
+    (32, 4, 224, 1344)
+    >>> i = np.array([3, 5, 2, 2], dtype=np.int32)
+    >>> offset = sum(i * x.strides)
+    >>> x[3, 5, 2, 2]
+    np.int32(813)
+    >>> offset // x.itemsize
+    np.int64(813)
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('T',
+    """
+    View of the transposed array.
+
+    Same as ``self.transpose()``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> a
+    array([[1, 2],
+           [3, 4]])
+    >>> a.T
+    array([[1, 3],
+           [2, 4]])
+
+    >>> a = np.array([1, 2, 3, 4])
+    >>> a
+    array([1, 2, 3, 4])
+    >>> a.T
+    array([1, 2, 3, 4])
+
+    See Also
+    --------
+    transpose
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('mT',
+    """
+    View of the matrix transposed array.
+
+    The matrix transpose is the transpose of the last two dimensions, even
+    if the array is of higher dimension.
+
+    .. versionadded:: 2.0
+
+    Raises
+    ------
+    ValueError
+        If the array is of dimension less than 2.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> a
+    array([[1, 2],
+           [3, 4]])
+    >>> a.mT
+    array([[1, 3],
+           [2, 4]])
+
+    >>> a = np.arange(8).reshape((2, 2, 2))
+    >>> a
+    array([[[0, 1],
+            [2, 3]],
+    <BLANKLINE>
+           [[4, 5],
+            [6, 7]]])
+    >>> a.mT
+    array([[[0, 2],
+            [1, 3]],
+    <BLANKLINE>
+           [[4, 6],
+            [5, 7]]])
+
+    """))
+##############################################################################
+#
+# ndarray methods
+#
+##############################################################################
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__array__',
+    """
+    a.__array__([dtype], *, copy=None)
+
+    For ``dtype`` parameter it returns a new reference to self if
+    ``dtype`` is not given or it matches array's data type.
+    A new array of provided data type is returned if ``dtype``
+    is different from the current data type of the array.
+    For ``copy`` parameter it returns a new reference to self if
+    ``copy=False`` or ``copy=None`` and copying isn't enforced by ``dtype``
+    parameter. The method returns a new array for ``copy=True``, regardless of
+    ``dtype`` parameter.
+
+    A more detailed explanation of the ``__array__`` interface
+    can be found in :ref:`dunder_array.interface`.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__array_finalize__',
+    """
+    a.__array_finalize__(obj, /)
+
+    Present so subclasses can call super. Does nothing.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__array_wrap__',
+    """
+    a.__array_wrap__(array[, context], /)
+
+    Returns a view of `array` with the same type as self.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__copy__',
+    """
+    a.__copy__()
+
+    Used if :func:`copy.copy` is called on an array. Returns a copy of the array.
+
+    Equivalent to ``a.copy(order='K')``.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__class_getitem__',
+    """
+    a.__class_getitem__(item, /)
+
+    Return a parametrized wrapper around the `~numpy.ndarray` type.
+
+    .. versionadded:: 1.22
+
+    Returns
+    -------
+    alias : types.GenericAlias
+        A parametrized `~numpy.ndarray` type.
+
+    Examples
+    --------
+    >>> from typing import Any
+    >>> import numpy as np
+
+    >>> np.ndarray[Any, np.dtype[np.uint8]]
+    numpy.ndarray[typing.Any, numpy.dtype[numpy.uint8]]
+
+    See Also
+    --------
+    :pep:`585` : Type hinting generics in standard collections.
+    numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`
+                        w.r.t. its `dtype.type <numpy.dtype.type>`.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__deepcopy__',
+    """
+    a.__deepcopy__(memo, /)
+
+    Used if :func:`copy.deepcopy` is called on an array.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__reduce__',
+    """
+    a.__reduce__()
+
+    For pickling.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('__setstate__',
+    """
+    a.__setstate__(state, /)
+
+    For unpickling.
+
+    The `state` argument must be a sequence that contains the following
+    elements:
+
+    Parameters
+    ----------
+    version : int
+        optional pickle version. If omitted defaults to 0.
+    shape : tuple
+    dtype : data-type
+    isFortran : bool
+    rawdata : string or list
+        a binary string with the data (or a list if 'a' is an object array)
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('all',
+    """
+    a.all(axis=None, out=None, keepdims=False, *, where=True)
+
+    Returns True if all elements evaluate to True.
+
+    Refer to `numpy.all` for full documentation.
+
+    See Also
+    --------
+    numpy.all : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('any',
+    """
+    a.any(axis=None, out=None, keepdims=False, *, where=True)
+
+    Returns True if any of the elements of `a` evaluate to True.
+
+    Refer to `numpy.any` for full documentation.
+
+    See Also
+    --------
+    numpy.any : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('argmax',
+    """
+    a.argmax(axis=None, out=None, *, keepdims=False)
+
+    Return indices of the maximum values along the given axis.
+
+    Refer to `numpy.argmax` for full documentation.
+
+    See Also
+    --------
+    numpy.argmax : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('argmin',
+    """
+    a.argmin(axis=None, out=None, *, keepdims=False)
+
+    Return indices of the minimum values along the given axis.
+
+    Refer to `numpy.argmin` for detailed documentation.
+
+    See Also
+    --------
+    numpy.argmin : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('argsort',
+    """
+    a.argsort(axis=-1, kind=None, order=None)
+
+    Returns the indices that would sort this array.
+
+    Refer to `numpy.argsort` for full documentation.
+
+    See Also
+    --------
+    numpy.argsort : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('argpartition',
+    """
+    a.argpartition(kth, axis=-1, kind='introselect', order=None)
+
+    Returns the indices that would partition this array.
+
+    Refer to `numpy.argpartition` for full documentation.
+
+    See Also
+    --------
+    numpy.argpartition : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('astype',
+    """
+    a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)
+
+    Copy of the array, cast to a specified type.
+
+    Parameters
+    ----------
+    dtype : str or dtype
+        Typecode or data-type to which the array is cast.
+    order : {'C', 'F', 'A', 'K'}, optional
+        Controls the memory layout order of the result.
+        'C' means C order, 'F' means Fortran order, 'A'
+        means 'F' order if all the arrays are Fortran contiguous,
+        'C' order otherwise, and 'K' means as close to the
+        order the array elements appear in memory as possible.
+        Default is 'K'.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur. Defaults to 'unsafe'
+        for backwards compatibility.
+
+        * 'no' means the data types should not be cast at all.
+        * 'equiv' means only byte-order changes are allowed.
+        * 'safe' means only casts which can preserve values are allowed.
+        * 'same_kind' means only safe casts or casts within a kind,
+          like float64 to float32, are allowed.
+        * 'unsafe' means any data conversions may be done.
+    subok : bool, optional
+        If True, then sub-classes will be passed-through (default), otherwise
+        the returned array will be forced to be a base-class array.
+    copy : bool, optional
+        By default, astype always returns a newly allocated array. If this
+        is set to false, and the `dtype`, `order`, and `subok`
+        requirements are satisfied, the input array is returned instead
+        of a copy.
+
+    Returns
+    -------
+    arr_t : ndarray
+        Unless `copy` is False and the other conditions for returning the input
+        array are satisfied (see description for `copy` input parameter), `arr_t`
+        is a new array of the same shape as the input array, with dtype, order
+        given by `dtype`, `order`.
+
+    Raises
+    ------
+    ComplexWarning
+        When casting from complex to float or int. To avoid this,
+        one should use ``a.real.astype(t)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 2.5])
+    >>> x
+    array([1. ,  2. ,  2.5])
+
+    >>> x.astype(int)
+    array([1, 2, 2])
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('byteswap',
+    """
+    a.byteswap(inplace=False)
+
+    Swap the bytes of the array elements
+
+    Toggle between low-endian and big-endian data representation by
+    returning a byteswapped array, optionally swapped in-place.
+    Arrays of byte-strings are not swapped. The real and imaginary
+    parts of a complex number are swapped individually.
+
+    Parameters
+    ----------
+    inplace : bool, optional
+        If ``True``, swap bytes in-place, default is ``False``.
+
+    Returns
+    -------
+    out : ndarray
+        The byteswapped array. If `inplace` is ``True``, this is
+        a view to self.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> A = np.array([1, 256, 8755], dtype=np.int16)
+    >>> list(map(hex, A))
+    ['0x1', '0x100', '0x2233']
+    >>> A.byteswap(inplace=True)
+    array([  256,     1, 13090], dtype=int16)
+    >>> list(map(hex, A))
+    ['0x100', '0x1', '0x3322']
+
+    Arrays of byte-strings are not swapped
+
+    >>> A = np.array([b'ceg', b'fac'])
+    >>> A.byteswap()
+    array([b'ceg', b'fac'], dtype='|S3')
+
+    ``A.view(A.dtype.newbyteorder()).byteswap()`` produces an array with
+    the same values but different representation in memory
+
+    >>> A = np.array([1, 2, 3],dtype=np.int64)
+    >>> A.view(np.uint8)
+    array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,
+           0, 0], dtype=uint8)
+    >>> A.view(A.dtype.newbyteorder()).byteswap(inplace=True)
+    array([1, 2, 3], dtype='>i8')
+    >>> A.view(np.uint8)
+    array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,
+           0, 3], dtype=uint8)
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('choose',
+    """
+    a.choose(choices, out=None, mode='raise')
+
+    Use an index array to construct a new array from a set of choices.
+
+    Refer to `numpy.choose` for full documentation.
+
+    See Also
+    --------
+    numpy.choose : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('clip',
+    """
+    a.clip(min=None, max=None, out=None, **kwargs)
+
+    Return an array whose values are limited to ``[min, max]``.
+    One of max or min must be given.
+
+    Refer to `numpy.clip` for full documentation.
+
+    See Also
+    --------
+    numpy.clip : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('compress',
+    """
+    a.compress(condition, axis=None, out=None)
+
+    Return selected slices of this array along given axis.
+
+    Refer to `numpy.compress` for full documentation.
+
+    See Also
+    --------
+    numpy.compress : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('conj',
+    """
+    a.conj()
+
+    Complex-conjugate all elements.
+
+    Refer to `numpy.conjugate` for full documentation.
+
+    See Also
+    --------
+    numpy.conjugate : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('conjugate',
+    """
+    a.conjugate()
+
+    Return the complex conjugate, element-wise.
+
+    Refer to `numpy.conjugate` for full documentation.
+
+    See Also
+    --------
+    numpy.conjugate : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('copy',
+    """
+    a.copy(order='C')
+
+    Return a copy of the array.
+
+    Parameters
+    ----------
+    order : {'C', 'F', 'A', 'K'}, optional
+        Controls the memory layout of the copy. 'C' means C-order,
+        'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
+        'C' otherwise. 'K' means match the layout of `a` as closely
+        as possible. (Note that this function and :func:`numpy.copy` are very
+        similar but have different default values for their order=
+        arguments, and this function always passes sub-classes through.)
+
+    See also
+    --------
+    numpy.copy : Similar function with different default behavior
+    numpy.copyto
+
+    Notes
+    -----
+    This function is the preferred method for creating an array copy.  The
+    function :func:`numpy.copy` is similar, but it defaults to using order 'K',
+    and will not pass sub-classes through by default.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([[1,2,3],[4,5,6]], order='F')
+
+    >>> y = x.copy()
+
+    >>> x.fill(0)
+
+    >>> x
+    array([[0, 0, 0],
+           [0, 0, 0]])
+
+    >>> y
+    array([[1, 2, 3],
+           [4, 5, 6]])
+
+    >>> y.flags['C_CONTIGUOUS']
+    True
+
+    For arrays containing Python objects (e.g. dtype=object),
+    the copy is a shallow one. The new array will contain the
+    same object which may lead to surprises if that object can
+    be modified (is mutable):
+
+    >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
+    >>> b = a.copy()
+    >>> b[2][0] = 10
+    >>> a
+    array([1, 'm', list([10, 3, 4])], dtype=object)
+
+    To ensure all elements within an ``object`` array are copied,
+    use `copy.deepcopy`:
+
+    >>> import copy
+    >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)
+    >>> c = copy.deepcopy(a)
+    >>> c[2][0] = 10
+    >>> c
+    array([1, 'm', list([10, 3, 4])], dtype=object)
+    >>> a
+    array([1, 'm', list([2, 3, 4])], dtype=object)
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('cumprod',
+    """
+    a.cumprod(axis=None, dtype=None, out=None)
+
+    Return the cumulative product of the elements along the given axis.
+
+    Refer to `numpy.cumprod` for full documentation.
+
+    See Also
+    --------
+    numpy.cumprod : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('cumsum',
+    """
+    a.cumsum(axis=None, dtype=None, out=None)
+
+    Return the cumulative sum of the elements along the given axis.
+
+    Refer to `numpy.cumsum` for full documentation.
+
+    See Also
+    --------
+    numpy.cumsum : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('diagonal',
+    """
+    a.diagonal(offset=0, axis1=0, axis2=1)
+
+    Return specified diagonals. In NumPy 1.9 the returned array is a
+    read-only view instead of a copy as in previous NumPy versions.  In
+    a future version the read-only restriction will be removed.
+
+    Refer to :func:`numpy.diagonal` for full documentation.
+
+    See Also
+    --------
+    numpy.diagonal : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('dot'))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('dump',
+    """
+    a.dump(file)
+
+    Dump a pickle of the array to the specified file.
+    The array can be read back with pickle.load or numpy.load.
+
+    Parameters
+    ----------
+    file : str or Path
+        A string naming the dump file.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('dumps',
+    """
+    a.dumps()
+
+    Returns the pickle of the array as a string.
+    pickle.loads will convert the string back to an array.
+
+    Parameters
+    ----------
+    None
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('fill',
+    """
+    a.fill(value)
+
+    Fill the array with a scalar value.
+
+    Parameters
+    ----------
+    value : scalar
+        All elements of `a` will be assigned this value.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([1, 2])
+    >>> a.fill(0)
+    >>> a
+    array([0, 0])
+    >>> a = np.empty(2)
+    >>> a.fill(1)
+    >>> a
+    array([1.,  1.])
+
+    Fill expects a scalar value and always behaves the same as assigning
+    to a single array element.  The following is a rare example where this
+    distinction is important:
+
+    >>> a = np.array([None, None], dtype=object)
+    >>> a[0] = np.array(3)
+    >>> a
+    array([array(3), None], dtype=object)
+    >>> a.fill(np.array(3))
+    >>> a
+    array([array(3), array(3)], dtype=object)
+
+    Where other forms of assignments will unpack the array being assigned:
+
+    >>> a[...] = np.array(3)
+    >>> a
+    array([3, 3], dtype=object)
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('flatten',
+    """
+    a.flatten(order='C')
+
+    Return a copy of the array collapsed into one dimension.
+
+    Parameters
+    ----------
+    order : {'C', 'F', 'A', 'K'}, optional
+        'C' means to flatten in row-major (C-style) order.
+        'F' means to flatten in column-major (Fortran-
+        style) order. 'A' means to flatten in column-major
+        order if `a` is Fortran *contiguous* in memory,
+        row-major order otherwise. 'K' means to flatten
+        `a` in the order the elements occur in memory.
+        The default is 'C'.
+
+    Returns
+    -------
+    y : ndarray
+        A copy of the input array, flattened to one dimension.
+
+    See Also
+    --------
+    ravel : Return a flattened array.
+    flat : A 1-D flat iterator over the array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1,2], [3,4]])
+    >>> a.flatten()
+    array([1, 2, 3, 4])
+    >>> a.flatten('F')
+    array([1, 3, 2, 4])
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('getfield',
+    """
+    a.getfield(dtype, offset=0)
+
+    Returns a field of the given array as a certain type.
+
+    A field is a view of the array data with a given data-type. The values in
+    the view are determined by the given type and the offset into the current
+    array in bytes. The offset needs to be such that the view dtype fits in the
+    array dtype; for example an array of dtype complex128 has 16-byte elements.
+    If taking a view with a 32-bit integer (4 bytes), the offset needs to be
+    between 0 and 12 bytes.
+
+    Parameters
+    ----------
+    dtype : str or dtype
+        The data type of the view. The dtype size of the view can not be larger
+        than that of the array itself.
+    offset : int
+        Number of bytes to skip before beginning the element view.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.diag([1.+1.j]*2)
+    >>> x[1, 1] = 2 + 4.j
+    >>> x
+    array([[1.+1.j,  0.+0.j],
+           [0.+0.j,  2.+4.j]])
+    >>> x.getfield(np.float64)
+    array([[1.,  0.],
+           [0.,  2.]])
+
+    By choosing an offset of 8 bytes we can select the complex part of the
+    array for our view:
+
+    >>> x.getfield(np.float64, offset=8)
+    array([[1.,  0.],
+           [0.,  4.]])
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('item',
+    """
+    a.item(*args)
+
+    Copy an element of an array to a standard Python scalar and return it.
+
+    Parameters
+    ----------
+    \\*args : Arguments (variable number and type)
+
+        * none: in this case, the method only works for arrays
+          with one element (`a.size == 1`), which element is
+          copied into a standard Python scalar object and returned.
+
+        * int_type: this argument is interpreted as a flat index into
+          the array, specifying which element to copy and return.
+
+        * tuple of int_types: functions as does a single int_type argument,
+          except that the argument is interpreted as an nd-index into the
+          array.
+
+    Returns
+    -------
+    z : Standard Python scalar object
+        A copy of the specified element of the array as a suitable
+        Python scalar
+
+    Notes
+    -----
+    When the data type of `a` is longdouble or clongdouble, item() returns
+    a scalar array object because there is no available Python scalar that
+    would not lose information. Void arrays return a buffer object for item(),
+    unless fields are defined, in which case a tuple is returned.
+
+    `item` is very similar to a[args], except, instead of an array scalar,
+    a standard Python scalar is returned. This can be useful for speeding up
+    access to elements of the array and doing arithmetic on elements of the
+    array using Python's optimized math.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.random.seed(123)
+    >>> x = np.random.randint(9, size=(3, 3))
+    >>> x
+    array([[2, 2, 6],
+           [1, 3, 6],
+           [1, 0, 1]])
+    >>> x.item(3)
+    1
+    >>> x.item(7)
+    0
+    >>> x.item((0, 1))
+    2
+    >>> x.item((2, 2))
+    1
+
+    For an array with object dtype, elements are returned as-is.
+
+    >>> a = np.array([np.int64(1)], dtype=object)
+    >>> a.item() #return np.int64
+    np.int64(1)
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('max',
+    """
+    a.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
+
+    Return the maximum along a given axis.
+
+    Refer to `numpy.amax` for full documentation.
+
+    See Also
+    --------
+    numpy.amax : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('mean',
+    """
+    a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)
+
+    Returns the average of the array elements along given axis.
+
+    Refer to `numpy.mean` for full documentation.
+
+    See Also
+    --------
+    numpy.mean : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('min',
+    """
+    a.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)
+
+    Return the minimum along a given axis.
+
+    Refer to `numpy.amin` for full documentation.
+
+    See Also
+    --------
+    numpy.amin : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('nonzero',
+    """
+    a.nonzero()
+
+    Return the indices of the elements that are non-zero.
+
+    Refer to `numpy.nonzero` for full documentation.
+
+    See Also
+    --------
+    numpy.nonzero : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('prod',
+    """
+    a.prod(axis=None, dtype=None, out=None, keepdims=False,
+        initial=1, where=True)
+
+    Return the product of the array elements over the given axis
+
+    Refer to `numpy.prod` for full documentation.
+
+    See Also
+    --------
+    numpy.prod : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('put',
+    """
+    a.put(indices, values, mode='raise')
+
+    Set ``a.flat[n] = values[n]`` for all `n` in indices.
+
+    Refer to `numpy.put` for full documentation.
+
+    See Also
+    --------
+    numpy.put : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('ravel',
+    """
+    a.ravel([order])
+
+    Return a flattened array.
+
+    Refer to `numpy.ravel` for full documentation.
+
+    See Also
+    --------
+    numpy.ravel : equivalent function
+
+    ndarray.flat : a flat iterator on the array.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('repeat',
+    """
+    a.repeat(repeats, axis=None)
+
+    Repeat elements of an array.
+
+    Refer to `numpy.repeat` for full documentation.
+
+    See Also
+    --------
+    numpy.repeat : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('reshape',
+    """
+    a.reshape(shape, /, *, order='C', copy=None)
+
+    Returns an array containing the same data with a new shape.
+
+    Refer to `numpy.reshape` for full documentation.
+
+    See Also
+    --------
+    numpy.reshape : equivalent function
+
+    Notes
+    -----
+    Unlike the free function `numpy.reshape`, this method on `ndarray` allows
+    the elements of the shape parameter to be passed in as separate arguments.
+    For example, ``a.reshape(10, 11)`` is equivalent to
+    ``a.reshape((10, 11))``.
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('resize',
+    """
+    a.resize(new_shape, refcheck=True)
+
+    Change shape and size of array in-place.
+
+    Parameters
+    ----------
+    new_shape : tuple of ints, or `n` ints
+        Shape of resized array.
+    refcheck : bool, optional
+        If False, reference count will not be checked. Default is True.
+
+    Returns
+    -------
+    None
+
+    Raises
+    ------
+    ValueError
+        If `a` does not own its own data or references or views to it exist,
+        and the data memory must be changed.
+        PyPy only: will always raise if the data memory must be changed, since
+        there is no reliable way to determine if references or views to it
+        exist.
+
+    SystemError
+        If the `order` keyword argument is specified. This behaviour is a
+        bug in NumPy.
+
+    See Also
+    --------
+    resize : Return a new array with the specified shape.
+
+    Notes
+    -----
+    This reallocates space for the data area if necessary.
+
+    Only contiguous arrays (data elements consecutive in memory) can be
+    resized.
+
+    The purpose of the reference count check is to make sure you
+    do not use this array as a buffer for another Python object and then
+    reallocate the memory. However, reference counts can increase in
+    other ways so if you are sure that you have not shared the memory
+    for this array with another Python object, then you may safely set
+    `refcheck` to False.
+
+    Examples
+    --------
+    Shrinking an array: array is flattened (in the order that the data are
+    stored in memory), resized, and reshaped:
+
+    >>> import numpy as np
+
+    >>> a = np.array([[0, 1], [2, 3]], order='C')
+    >>> a.resize((2, 1))
+    >>> a
+    array([[0],
+           [1]])
+
+    >>> a = np.array([[0, 1], [2, 3]], order='F')
+    >>> a.resize((2, 1))
+    >>> a
+    array([[0],
+           [2]])
+
+    Enlarging an array: as above, but missing entries are filled with zeros:
+
+    >>> b = np.array([[0, 1], [2, 3]])
+    >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
+    >>> b
+    array([[0, 1, 2],
+           [3, 0, 0]])
+
+    Referencing an array prevents resizing...
+
+    >>> c = a
+    >>> a.resize((1, 1))
+    Traceback (most recent call last):
+    ...
+    ValueError: cannot resize an array that references or is referenced ...
+
+    Unless `refcheck` is False:
+
+    >>> a.resize((1, 1), refcheck=False)
+    >>> a
+    array([[0]])
+    >>> c
+    array([[0]])
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('round',
+    """
+    a.round(decimals=0, out=None)
+
+    Return `a` with each element rounded to the given number of decimals.
+
+    Refer to `numpy.around` for full documentation.
+
+    See Also
+    --------
+    numpy.around : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('searchsorted',
+    """
+    a.searchsorted(v, side='left', sorter=None)
+
+    Find indices where elements of v should be inserted in a to maintain order.
+
+    For full documentation, see `numpy.searchsorted`
+
+    See Also
+    --------
+    numpy.searchsorted : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('setfield',
+    """
+    a.setfield(val, dtype, offset=0)
+
+    Put a value into a specified place in a field defined by a data-type.
+
+    Place `val` into `a`'s field defined by `dtype` and beginning `offset`
+    bytes into the field.
+
+    Parameters
+    ----------
+    val : object
+        Value to be placed in field.
+    dtype : dtype object
+        Data-type of the field in which to place `val`.
+    offset : int, optional
+        The number of bytes into the field at which to place `val`.
+
+    Returns
+    -------
+    None
+
+    See Also
+    --------
+    getfield
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.eye(3)
+    >>> x.getfield(np.float64)
+    array([[1.,  0.,  0.],
+           [0.,  1.,  0.],
+           [0.,  0.,  1.]])
+    >>> x.setfield(3, np.int32)
+    >>> x.getfield(np.int32)
+    array([[3, 3, 3],
+           [3, 3, 3],
+           [3, 3, 3]], dtype=int32)
+    >>> x
+    array([[1.0e+000, 1.5e-323, 1.5e-323],
+           [1.5e-323, 1.0e+000, 1.5e-323],
+           [1.5e-323, 1.5e-323, 1.0e+000]])
+    >>> x.setfield(np.eye(3), np.int32)
+    >>> x
+    array([[1.,  0.,  0.],
+           [0.,  1.,  0.],
+           [0.,  0.,  1.]])
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('setflags',
+    """
+    a.setflags(write=None, align=None, uic=None)
+
+    Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,
+    respectively.
+
+    These Boolean-valued flags affect how numpy interprets the memory
+    area used by `a` (see Notes below). The ALIGNED flag can only
+    be set to True if the data is actually aligned according to the type.
+    The WRITEBACKIFCOPY flag can never be set
+    to True. The flag WRITEABLE can only be set to True if the array owns its
+    own memory, or the ultimate owner of the memory exposes a writeable buffer
+    interface, or is a string. (The exception for string is made so that
+    unpickling can be done without copying memory.)
+
+    Parameters
+    ----------
+    write : bool, optional
+        Describes whether or not `a` can be written to.
+    align : bool, optional
+        Describes whether or not `a` is aligned properly for its type.
+    uic : bool, optional
+        Describes whether or not `a` is a copy of another "base" array.
+
+    Notes
+    -----
+    Array flags provide information about how the memory area used
+    for the array is to be interpreted. There are 7 Boolean flags
+    in use, only three of which can be changed by the user:
+    WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.
+
+    WRITEABLE (W) the data area can be written to;
+
+    ALIGNED (A) the data and strides are aligned appropriately for the hardware
+    (as determined by the compiler);
+
+    WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced
+    by .base). When the C-API function PyArray_ResolveWritebackIfCopy is
+    called, the base array will be updated with the contents of this array.
+
+    All flags can be accessed using the single (upper case) letter as well
+    as the full name.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> y = np.array([[3, 1, 7],
+    ...               [2, 0, 0],
+    ...               [8, 5, 9]])
+    >>> y
+    array([[3, 1, 7],
+           [2, 0, 0],
+           [8, 5, 9]])
+    >>> y.flags
+      C_CONTIGUOUS : True
+      F_CONTIGUOUS : False
+      OWNDATA : True
+      WRITEABLE : True
+      ALIGNED : True
+      WRITEBACKIFCOPY : False
+    >>> y.setflags(write=0, align=0)
+    >>> y.flags
+      C_CONTIGUOUS : True
+      F_CONTIGUOUS : False
+      OWNDATA : True
+      WRITEABLE : False
+      ALIGNED : False
+      WRITEBACKIFCOPY : False
+    >>> y.setflags(uic=1)
+    Traceback (most recent call last):
+      File "<stdin>", line 1, in <module>
+    ValueError: cannot set WRITEBACKIFCOPY flag to True
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('sort',
+    """
+    a.sort(axis=-1, kind=None, order=None)
+
+    Sort an array in-place. Refer to `numpy.sort` for full documentation.
+
+    Parameters
+    ----------
+    axis : int, optional
+        Axis along which to sort. Default is -1, which means sort along the
+        last axis.
+    kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
+        Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
+        and 'mergesort' use timsort under the covers and, in general, the
+        actual implementation will vary with datatype. The 'mergesort' option
+        is retained for backwards compatibility.
+    order : str or list of str, optional
+        When `a` is an array with fields defined, this argument specifies
+        which fields to compare first, second, etc.  A single field can
+        be specified as a string, and not all fields need be specified,
+        but unspecified fields will still be used, in the order in which
+        they come up in the dtype, to break ties.
+
+    See Also
+    --------
+    numpy.sort : Return a sorted copy of an array.
+    numpy.argsort : Indirect sort.
+    numpy.lexsort : Indirect stable sort on multiple keys.
+    numpy.searchsorted : Find elements in sorted array.
+    numpy.partition: Partial sort.
+
+    Notes
+    -----
+    See `numpy.sort` for notes on the different sorting algorithms.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1,4], [3,1]])
+    >>> a.sort(axis=1)
+    >>> a
+    array([[1, 4],
+           [1, 3]])
+    >>> a.sort(axis=0)
+    >>> a
+    array([[1, 3],
+           [1, 4]])
+
+    Use the `order` keyword to specify a field to use when sorting a
+    structured array:
+
+    >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
+    >>> a.sort(order='y')
+    >>> a
+    array([(b'c', 1), (b'a', 2)],
+          dtype=[('x', 'S1'), ('y', '<i8')])
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('partition',
+    """
+    a.partition(kth, axis=-1, kind='introselect', order=None)
+
+    Partially sorts the elements in the array in such a way that the value of
+    the element in k-th position is in the position it would be in a sorted
+    array. In the output array, all elements smaller than the k-th element
+    are located to the left of this element and all equal or greater are
+    located to its right. The ordering of the elements in the two partitions
+    on the either side of the k-th element in the output array is undefined.
+
+    Parameters
+    ----------
+    kth : int or sequence of ints
+        Element index to partition by. The kth element value will be in its
+        final sorted position and all smaller elements will be moved before it
+        and all equal or greater elements behind it.
+        The order of all elements in the partitions is undefined.
+        If provided with a sequence of kth it will partition all elements
+        indexed by kth of them into their sorted position at once.
+
+        .. deprecated:: 1.22.0
+            Passing booleans as index is deprecated.
+    axis : int, optional
+        Axis along which to sort. Default is -1, which means sort along the
+        last axis.
+    kind : {'introselect'}, optional
+        Selection algorithm. Default is 'introselect'.
+    order : str or list of str, optional
+        When `a` is an array with fields defined, this argument specifies
+        which fields to compare first, second, etc. A single field can
+        be specified as a string, and not all fields need to be specified,
+        but unspecified fields will still be used, in the order in which
+        they come up in the dtype, to break ties.
+
+    See Also
+    --------
+    numpy.partition : Return a partitioned copy of an array.
+    argpartition : Indirect partition.
+    sort : Full sort.
+
+    Notes
+    -----
+    See ``np.partition`` for notes on the different algorithms.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([3, 4, 2, 1])
+    >>> a.partition(3)
+    >>> a
+    array([2, 1, 3, 4]) # may vary
+
+    >>> a.partition((1, 3))
+    >>> a
+    array([1, 2, 3, 4])
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('squeeze',
+    """
+    a.squeeze(axis=None)
+
+    Remove axes of length one from `a`.
+
+    Refer to `numpy.squeeze` for full documentation.
+
+    See Also
+    --------
+    numpy.squeeze : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('std',
+    """
+    a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)
+
+    Returns the standard deviation of the array elements along given axis.
+
+    Refer to `numpy.std` for full documentation.
+
+    See Also
+    --------
+    numpy.std : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('sum',
+    """
+    a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)
+
+    Return the sum of the array elements over the given axis.
+
+    Refer to `numpy.sum` for full documentation.
+
+    See Also
+    --------
+    numpy.sum : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('swapaxes',
+    """
+    a.swapaxes(axis1, axis2)
+
+    Return a view of the array with `axis1` and `axis2` interchanged.
+
+    Refer to `numpy.swapaxes` for full documentation.
+
+    See Also
+    --------
+    numpy.swapaxes : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('take',
+    """
+    a.take(indices, axis=None, out=None, mode='raise')
+
+    Return an array formed from the elements of `a` at the given indices.
+
+    Refer to `numpy.take` for full documentation.
+
+    See Also
+    --------
+    numpy.take : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('tofile',
+    """
+    a.tofile(fid, sep="", format="%s")
+
+    Write array to a file as text or binary (default).
+
+    Data is always written in 'C' order, independent of the order of `a`.
+    The data produced by this method can be recovered using the function
+    fromfile().
+
+    Parameters
+    ----------
+    fid : file or str or Path
+        An open file object, or a string containing a filename.
+    sep : str
+        Separator between array items for text output.
+        If "" (empty), a binary file is written, equivalent to
+        ``file.write(a.tobytes())``.
+    format : str
+        Format string for text file output.
+        Each entry in the array is formatted to text by first converting
+        it to the closest Python type, and then using "format" % item.
+
+    Notes
+    -----
+    This is a convenience function for quick storage of array data.
+    Information on endianness and precision is lost, so this method is not a
+    good choice for files intended to archive data or transport data between
+    machines with different endianness. Some of these problems can be overcome
+    by outputting the data as text files, at the expense of speed and file
+    size.
+
+    When fid is a file object, array contents are directly written to the
+    file, bypassing the file object's ``write`` method. As a result, tofile
+    cannot be used with files objects supporting compression (e.g., GzipFile)
+    or file-like objects that do not support ``fileno()`` (e.g., BytesIO).
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('tolist',
+    """
+    a.tolist()
+
+    Return the array as an ``a.ndim``-levels deep nested list of Python scalars.
+
+    Return a copy of the array data as a (nested) Python list.
+    Data items are converted to the nearest compatible builtin Python type, via
+    the `~numpy.ndarray.item` function.
+
+    If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will
+    not be a list at all, but a simple Python scalar.
+
+    Parameters
+    ----------
+    none
+
+    Returns
+    -------
+    y : object, or list of object, or list of list of object, or ...
+        The possibly nested list of array elements.
+
+    Notes
+    -----
+    The array may be recreated via ``a = np.array(a.tolist())``, although this
+    may sometimes lose precision.
+
+    Examples
+    --------
+    For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``,
+    except that ``tolist`` changes numpy scalars to Python scalars:
+
+    >>> import numpy as np
+    >>> a = np.uint32([1, 2])
+    >>> a_list = list(a)
+    >>> a_list
+    [np.uint32(1), np.uint32(2)]
+    >>> type(a_list[0])
+    <class 'numpy.uint32'>
+    >>> a_tolist = a.tolist()
+    >>> a_tolist
+    [1, 2]
+    >>> type(a_tolist[0])
+    <class 'int'>
+
+    Additionally, for a 2D array, ``tolist`` applies recursively:
+
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> list(a)
+    [array([1, 2]), array([3, 4])]
+    >>> a.tolist()
+    [[1, 2], [3, 4]]
+
+    The base case for this recursion is a 0D array:
+
+    >>> a = np.array(1)
+    >>> list(a)
+    Traceback (most recent call last):
+      ...
+    TypeError: iteration over a 0-d array
+    >>> a.tolist()
+    1
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('tobytes', """
+    a.tobytes(order='C')
+
+    Construct Python bytes containing the raw data bytes in the array.
+
+    Constructs Python bytes showing a copy of the raw contents of
+    data memory. The bytes object is produced in C-order by default.
+    This behavior is controlled by the ``order`` parameter.
+
+    Parameters
+    ----------
+    order : {'C', 'F', 'A'}, optional
+        Controls the memory layout of the bytes object. 'C' means C-order,
+        'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is
+        Fortran contiguous, 'C' otherwise. Default is 'C'.
+
+    Returns
+    -------
+    s : bytes
+        Python bytes exhibiting a copy of `a`'s raw data.
+
+    See also
+    --------
+    frombuffer
+        Inverse of this operation, construct a 1-dimensional array from Python
+        bytes.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')
+    >>> x.tobytes()
+    b'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'
+    >>> x.tobytes('C') == x.tobytes()
+    True
+    >>> x.tobytes('F')
+    b'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('trace',
+    """
+    a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)
+
+    Return the sum along diagonals of the array.
+
+    Refer to `numpy.trace` for full documentation.
+
+    See Also
+    --------
+    numpy.trace : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('transpose',
+    """
+    a.transpose(*axes)
+
+    Returns a view of the array with axes transposed.
+
+    Refer to `numpy.transpose` for full documentation.
+
+    Parameters
+    ----------
+    axes : None, tuple of ints, or `n` ints
+
+     * None or no argument: reverses the order of the axes.
+
+     * tuple of ints: `i` in the `j`-th place in the tuple means that the
+       array's `i`-th axis becomes the transposed array's `j`-th axis.
+
+     * `n` ints: same as an n-tuple of the same ints (this form is
+       intended simply as a "convenience" alternative to the tuple form).
+
+    Returns
+    -------
+    p : ndarray
+        View of the array with its axes suitably permuted.
+
+    See Also
+    --------
+    transpose : Equivalent function.
+    ndarray.T : Array property returning the array transposed.
+    ndarray.reshape : Give a new shape to an array without changing its data.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> a
+    array([[1, 2],
+           [3, 4]])
+    >>> a.transpose()
+    array([[1, 3],
+           [2, 4]])
+    >>> a.transpose((1, 0))
+    array([[1, 3],
+           [2, 4]])
+    >>> a.transpose(1, 0)
+    array([[1, 3],
+           [2, 4]])
+
+    >>> a = np.array([1, 2, 3, 4])
+    >>> a
+    array([1, 2, 3, 4])
+    >>> a.transpose()
+    array([1, 2, 3, 4])
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('var',
+    """
+    a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)
+
+    Returns the variance of the array elements, along given axis.
+
+    Refer to `numpy.var` for full documentation.
+
+    See Also
+    --------
+    numpy.var : equivalent function
+
+    """))
+
+
+add_newdoc('numpy._core.multiarray', 'ndarray', ('view',
+    """
+    a.view([dtype][, type])
+
+    New view of array with the same data.
+
+    .. note::
+        Passing None for ``dtype`` is different from omitting the parameter,
+        since the former invokes ``dtype(None)`` which is an alias for
+        ``dtype('float64')``.
+
+    Parameters
+    ----------
+    dtype : data-type or ndarray sub-class, optional
+        Data-type descriptor of the returned view, e.g., float32 or int16.
+        Omitting it results in the view having the same data-type as `a`.
+        This argument can also be specified as an ndarray sub-class, which
+        then specifies the type of the returned object (this is equivalent to
+        setting the ``type`` parameter).
+    type : Python type, optional
+        Type of the returned view, e.g., ndarray or matrix.  Again, omission
+        of the parameter results in type preservation.
+
+    Notes
+    -----
+    ``a.view()`` is used two different ways:
+
+    ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view
+    of the array's memory with a different data-type.  This can cause a
+    reinterpretation of the bytes of memory.
+
+    ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just
+    returns an instance of `ndarray_subclass` that looks at the same array
+    (same shape, dtype, etc.)  This does not cause a reinterpretation of the
+    memory.
+
+    For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of
+    bytes per entry than the previous dtype (for example, converting a regular
+    array to a structured array), then the last axis of ``a`` must be
+    contiguous. This axis will be resized in the result.
+
+    .. versionchanged:: 1.23.0
+       Only the last axis needs to be contiguous. Previously, the entire array
+       had to be C-contiguous.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([(-1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
+
+    Viewing array data using a different type and dtype:
+
+    >>> nonneg = np.dtype([("a", np.uint8), ("b", np.uint8)])
+    >>> y = x.view(dtype=nonneg, type=np.recarray)
+    >>> x["a"]
+    array([-1], dtype=int8)
+    >>> y.a
+    array([255], dtype=uint8)
+
+    Creating a view on a structured array so it can be used in calculations
+
+    >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
+    >>> xv = x.view(dtype=np.int8).reshape(-1,2)
+    >>> xv
+    array([[1, 2],
+           [3, 4]], dtype=int8)
+    >>> xv.mean(0)
+    array([2.,  3.])
+
+    Making changes to the view changes the underlying array
+
+    >>> xv[0,1] = 20
+    >>> x
+    array([(1, 20), (3,  4)], dtype=[('a', 'i1'), ('b', 'i1')])
+
+    Using a view to convert an array to a recarray:
+
+    >>> z = x.view(np.recarray)
+    >>> z.a
+    array([1, 3], dtype=int8)
+
+    Views share data:
+
+    >>> x[0] = (9, 10)
+    >>> z[0]
+    np.record((9, 10), dtype=[('a', 'i1'), ('b', 'i1')])
+
+    Views that change the dtype size (bytes per entry) should normally be
+    avoided on arrays defined by slices, transposes, fortran-ordering, etc.:
+
+    >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)
+    >>> y = x[:, ::2]
+    >>> y
+    array([[1, 3],
+           [4, 6]], dtype=int16)
+    >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
+    Traceback (most recent call last):
+        ...
+    ValueError: To change to a dtype of a different size, the last axis must be contiguous
+    >>> z = y.copy()
+    >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
+    array([[(1, 3)],
+           [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])
+
+    However, views that change dtype are totally fine for arrays with a
+    contiguous last axis, even if the rest of the axes are not C-contiguous:
+
+    >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)
+    >>> x.transpose(1, 0, 2).view(np.int16)
+    array([[[ 256,  770],
+            [3340, 3854]],
+    <BLANKLINE>
+           [[1284, 1798],
+            [4368, 4882]],
+    <BLANKLINE>
+           [[2312, 2826],
+            [5396, 5910]]], dtype=int16)
+
+    """))
+
+
+##############################################################################
+#
+# umath functions
+#
+##############################################################################
+
+add_newdoc('numpy._core.umath', 'frompyfunc',
+    """
+    frompyfunc(func, /, nin, nout, *[, identity])
+
+    Takes an arbitrary Python function and returns a NumPy ufunc.
+
+    Can be used, for example, to add broadcasting to a built-in Python
+    function (see Examples section).
+
+    Parameters
+    ----------
+    func : Python function object
+        An arbitrary Python function.
+    nin : int
+        The number of input arguments.
+    nout : int
+        The number of objects returned by `func`.
+    identity : object, optional
+        The value to use for the `~numpy.ufunc.identity` attribute of the resulting
+        object. If specified, this is equivalent to setting the underlying
+        C ``identity`` field to ``PyUFunc_IdentityValue``.
+        If omitted, the identity is set to ``PyUFunc_None``. Note that this is
+        _not_ equivalent to setting the identity to ``None``, which implies the
+        operation is reorderable.
+
+    Returns
+    -------
+    out : ufunc
+        Returns a NumPy universal function (``ufunc``) object.
+
+    See Also
+    --------
+    vectorize : Evaluates pyfunc over input arrays using broadcasting rules of numpy.
+
+    Notes
+    -----
+    The returned ufunc always returns PyObject arrays.
+
+    Examples
+    --------
+    Use frompyfunc to add broadcasting to the Python function ``oct``:
+
+    >>> import numpy as np
+    >>> oct_array = np.frompyfunc(oct, 1, 1)
+    >>> oct_array(np.array((10, 30, 100)))
+    array(['0o12', '0o36', '0o144'], dtype=object)
+    >>> np.array((oct(10), oct(30), oct(100))) # for comparison
+    array(['0o12', '0o36', '0o144'], dtype='<U5')
+
+    """)
+
+
+##############################################################################
+#
+# compiled_base functions
+#
+##############################################################################
+
+add_newdoc('numpy._core.multiarray', 'add_docstring',
+    """
+    add_docstring(obj, docstring)
+
+    Add a docstring to a built-in obj if possible.
+    If the obj already has a docstring raise a RuntimeError
+    If this routine does not know how to add a docstring to the object
+    raise a TypeError
+    """)
+
+add_newdoc('numpy._core.umath', '_add_newdoc_ufunc',
+    """
+    add_ufunc_docstring(ufunc, new_docstring)
+
+    Replace the docstring for a ufunc with new_docstring.
+    This method will only work if the current docstring for
+    the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.)
+
+    Parameters
+    ----------
+    ufunc : numpy.ufunc
+        A ufunc whose current doc is NULL.
+    new_docstring : string
+        The new docstring for the ufunc.
+
+    Notes
+    -----
+    This method allocates memory for new_docstring on
+    the heap. Technically this creates a memory leak, since this
+    memory will not be reclaimed until the end of the program
+    even if the ufunc itself is removed. However this will only
+    be a problem if the user is repeatedly creating ufuncs with
+    no documentation, adding documentation via add_newdoc_ufunc,
+    and then throwing away the ufunc.
+    """)
+
+add_newdoc('numpy._core.multiarray', 'get_handler_name',
+    """
+    get_handler_name(a: ndarray) -> str,None
+
+    Return the name of the memory handler used by `a`. If not provided, return
+    the name of the memory handler that will be used to allocate data for the
+    next `ndarray` in this context. May return None if `a` does not own its
+    memory, in which case you can traverse ``a.base`` for a memory handler.
+    """)
+
+add_newdoc('numpy._core.multiarray', 'get_handler_version',
+    """
+    get_handler_version(a: ndarray) -> int,None
+
+    Return the version of the memory handler used by `a`. If not provided,
+    return the version of the memory handler that will be used to allocate data
+    for the next `ndarray` in this context. May return None if `a` does not own
+    its memory, in which case you can traverse ``a.base`` for a memory handler.
+    """)
+
+add_newdoc('numpy._core._multiarray_umath', '_array_converter',
+    """
+    _array_converter(*array_likes)
+
+    Helper to convert one or more objects to arrays.  Integrates machinery
+    to deal with the ``result_type`` and ``__array_wrap__``.
+
+    The reason for this is that e.g. ``result_type`` needs to convert to arrays
+    to find the ``dtype``.  But converting to an array before calling
+    ``result_type`` would incorrectly "forget" whether it was a Python int,
+    float, or complex.
+    """)
+
+add_newdoc(
+    'numpy._core._multiarray_umath', '_array_converter', ('scalar_input',
+    """
+    A tuple which indicates for each input whether it was a scalar that
+    was coerced to a 0-D array (and was not already an array or something
+    converted via a protocol like ``__array__()``).
+    """))
+
+add_newdoc('numpy._core._multiarray_umath', '_array_converter', ('as_arrays',
+    """
+    as_arrays(/, subok=True, pyscalars="convert_if_no_array")
+
+    Return the inputs as arrays or scalars.
+
+    Parameters
+    ----------
+    subok : True or False, optional
+        Whether array subclasses are preserved.
+    pyscalars : {"convert", "preserve", "convert_if_no_array"}, optional
+        To allow NEP 50 weak promotion later, it may be desirable to preserve
+        Python scalars.  As default, these are preserved unless all inputs
+        are Python scalars.  "convert" enforces an array return.
+    """))
+
+add_newdoc('numpy._core._multiarray_umath', '_array_converter', ('result_type',
+    """result_type(/, extra_dtype=None, ensure_inexact=False)
+
+    Find the ``result_type`` just as ``np.result_type`` would, but taking
+    into account that the original inputs (before converting to an array) may
+    have been Python scalars with weak promotion.
+
+    Parameters
+    ----------
+    extra_dtype : dtype instance or class
+        An additional DType or dtype instance to promote (e.g. could be used
+        to ensure the result precision is at least float32).
+    ensure_inexact : True or False
+        When ``True``, ensures a floating point (or complex) result replacing
+        the ``arr * 1.`` or ``result_type(..., 0.0)`` pattern.
+    """))
+
+add_newdoc('numpy._core._multiarray_umath', '_array_converter', ('wrap',
+    """
+    wrap(arr, /, to_scalar=None)
+
+    Call ``__array_wrap__`` on ``arr`` if ``arr`` is not the same subclass
+    as the input the ``__array_wrap__`` method was retrieved from.
+
+    Parameters
+    ----------
+    arr : ndarray
+        The object to be wrapped. Normally an ndarray or subclass,
+        although for backward compatibility NumPy scalars are also accepted
+        (these will be converted to a NumPy array before being passed on to
+        the ``__array_wrap__`` method).
+    to_scalar : {True, False, None}, optional
+        When ``True`` will convert a 0-d array to a scalar via ``result[()]``
+        (with a fast-path for non-subclasses).  If ``False`` the result should
+        be an array-like (as ``__array_wrap__`` is free to return a non-array).
+        By default (``None``), a scalar is returned if all inputs were scalar.
+    """))
+
+
+add_newdoc('numpy._core.multiarray', '_get_madvise_hugepage',
+    """
+    _get_madvise_hugepage() -> bool
+
+    Get use of ``madvise (2)`` MADV_HUGEPAGE support when
+    allocating the array data. Returns the currently set value.
+    See `global_state` for more information.
+    """)
+
+add_newdoc('numpy._core.multiarray', '_set_madvise_hugepage',
+    """
+    _set_madvise_hugepage(enabled: bool) -> bool
+
+    Set  or unset use of ``madvise (2)`` MADV_HUGEPAGE support when
+    allocating the array data. Returns the previously set value.
+    See `global_state` for more information.
+    """)
+
+
+##############################################################################
+#
+# Documentation for ufunc attributes and methods
+#
+##############################################################################
+
+
+##############################################################################
+#
+# ufunc object
+#
+##############################################################################
+
+add_newdoc('numpy._core', 'ufunc',
+    """
+    Functions that operate element by element on whole arrays.
+
+    To see the documentation for a specific ufunc, use `info`.  For
+    example, ``np.info(np.sin)``.  Because ufuncs are written in C
+    (for speed) and linked into Python with NumPy's ufunc facility,
+    Python's help() function finds this page whenever help() is called
+    on a ufunc.
+
+    A detailed explanation of ufuncs can be found in the docs for :ref:`ufuncs`.
+
+    **Calling ufuncs:** ``op(*x[, out], where=True, **kwargs)``
+
+    Apply `op` to the arguments `*x` elementwise, broadcasting the arguments.
+
+    The broadcasting rules are:
+
+    * Dimensions of length 1 may be prepended to either array.
+    * Arrays may be repeated along dimensions of length 1.
+
+    Parameters
+    ----------
+    *x : array_like
+        Input arrays.
+    out : ndarray, None, ..., or tuple of ndarray and None, optional
+        Location(s) into which the result(s) are stored.
+        If not provided or None, new array(s) are created by the ufunc.
+        If passed as a keyword argument, can be Ellipses (``out=...``) to
+        ensure an array is returned even if the result is 0-dimensional,
+        or a tuple with length equal to the number of outputs (where None
+        can be used for allocation by the ufunc).
+
+        .. versionadded:: 2.3
+            Support for ``out=...`` was added.
+
+    where : array_like, optional
+        This condition is broadcast over the input. At locations where the
+        condition is True, the `out` array will be set to the ufunc result.
+        Elsewhere, the `out` array will retain its original value.
+        Note that if an uninitialized `out` array is created via the default
+        ``out=None``, locations within it where the condition is False will
+        remain uninitialized.
+    **kwargs
+        For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`.
+
+    Returns
+    -------
+    r : ndarray or tuple of ndarray
+        `r` will have the shape that the arrays in `x` broadcast to; if `out` is
+        provided, it will be returned. If not, `r` will be allocated and
+        may contain uninitialized values. If the function has more than one
+        output, then the result will be a tuple of arrays.
+
+    """)
+
+
+##############################################################################
+#
+# ufunc attributes
+#
+##############################################################################
+
+add_newdoc('numpy._core', 'ufunc', ('identity',
+    """
+    The identity value.
+
+    Data attribute containing the identity element for the ufunc,
+    if it has one. If it does not, the attribute value is None.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.add.identity
+    0
+    >>> np.multiply.identity
+    1
+    >>> print(np.power.identity)
+    None
+    >>> print(np.exp.identity)
+    None
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('nargs',
+    """
+    The number of arguments.
+
+    Data attribute containing the number of arguments the ufunc takes, including
+    optional ones.
+
+    Notes
+    -----
+    Typically this value will be one more than what you might expect
+    because all ufuncs take  the optional "out" argument.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.add.nargs
+    3
+    >>> np.multiply.nargs
+    3
+    >>> np.power.nargs
+    3
+    >>> np.exp.nargs
+    2
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('nin',
+    """
+    The number of inputs.
+
+    Data attribute containing the number of arguments the ufunc treats as input.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.add.nin
+    2
+    >>> np.multiply.nin
+    2
+    >>> np.power.nin
+    2
+    >>> np.exp.nin
+    1
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('nout',
+    """
+    The number of outputs.
+
+    Data attribute containing the number of arguments the ufunc treats as output.
+
+    Notes
+    -----
+    Since all ufuncs can take output arguments, this will always be at least 1.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.add.nout
+    1
+    >>> np.multiply.nout
+    1
+    >>> np.power.nout
+    1
+    >>> np.exp.nout
+    1
+
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('ntypes',
+    """
+    The number of types.
+
+    The number of numerical NumPy types - of which there are 18 total - on which
+    the ufunc can operate.
+
+    See Also
+    --------
+    numpy.ufunc.types
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.add.ntypes
+    22
+    >>> np.multiply.ntypes
+    23
+    >>> np.power.ntypes
+    21
+    >>> np.exp.ntypes
+    10
+    >>> np.remainder.ntypes
+    16
+
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('types',
+    """
+    Returns a list with types grouped input->output.
+
+    Data attribute listing the data-type "Domain-Range" groupings the ufunc can
+    deliver. The data-types are given using the character codes.
+
+    See Also
+    --------
+    numpy.ufunc.ntypes
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.add.types
+    ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', ...
+
+    >>> np.power.types
+    ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', ...
+
+    >>> np.exp.types
+    ['e->e', 'f->f', 'd->d', 'f->f', 'd->d', 'g->g', 'F->F', 'D->D', 'G->G', 'O->O']
+
+    >>> np.remainder.types
+    ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', ...
+
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('signature',
+    """
+    Definition of the core elements a generalized ufunc operates on.
+
+    The signature determines how the dimensions of each input/output array
+    are split into core and loop dimensions:
+
+    1. Each dimension in the signature is matched to a dimension of the
+       corresponding passed-in array, starting from the end of the shape tuple.
+    2. Core dimensions assigned to the same label in the signature must have
+       exactly matching sizes, no broadcasting is performed.
+    3. The core dimensions are removed from all inputs and the remaining
+       dimensions are broadcast together, defining the loop dimensions.
+
+    Notes
+    -----
+    Generalized ufuncs are used internally in many linalg functions, and in
+    the testing suite; the examples below are taken from these.
+    For ufuncs that operate on scalars, the signature is None, which is
+    equivalent to '()' for every argument.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.linalg._umath_linalg.det.signature
+    '(m,m)->()'
+    >>> np.matmul.signature
+    '(n?,k),(k,m?)->(n?,m?)'
+    >>> np.add.signature is None
+    True  # equivalent to '(),()->()'
+    """))
+
+##############################################################################
+#
+# ufunc methods
+#
+##############################################################################
+
+add_newdoc('numpy._core', 'ufunc', ('reduce',
+    """
+    reduce(array, axis=0, dtype=None, out=None, keepdims=False, initial=<no value>, where=True)
+
+    Reduces `array`'s dimension by one, by applying ufunc along one axis.
+
+    Let :math:`array.shape = (N_0, ..., N_i, ..., N_{M-1})`.  Then
+    :math:`ufunc.reduce(array, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` =
+    the result of iterating `j` over :math:`range(N_i)`, cumulatively applying
+    ufunc to each :math:`array[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`.
+    For a one-dimensional array, reduce produces results equivalent to:
+    ::
+
+     r = op.identity # op = ufunc
+     for i in range(len(A)):
+       r = op(r, A[i])
+     return r
+
+    For example, add.reduce() is equivalent to sum().
+
+    Parameters
+    ----------
+    array : array_like
+        The array to act on.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which a reduction is performed.
+        The default (`axis` = 0) is perform a reduction over the first
+        dimension of the input array. `axis` may be negative, in
+        which case it counts from the last to the first axis.
+
+        If this is None, a reduction is performed over all the axes.
+        If this is a tuple of ints, a reduction is performed on multiple
+        axes, instead of a single axis or all the axes as before.
+
+        For operations which are either not commutative or not associative,
+        doing a reduction over multiple axes is not well-defined. The
+        ufuncs do not currently raise an exception in this case, but will
+        likely do so in the future.
+    dtype : data-type code, optional
+        The data type used to perform the operation. Defaults to that of
+        ``out`` if given, and the data type of ``array`` otherwise (though
+        upcast to conserve precision for some cases, such as
+        ``numpy.add.reduce`` for integer or boolean input).
+    out : ndarray, None, ..., or tuple of ndarray and None, optional
+        Location into which the result is stored.
+        If not provided or None, a freshly-allocated array is returned.
+        If passed as a keyword argument, can be Ellipses (``out=...``) to
+        ensure an array is returned even if the result is 0-dimensional
+        (which is useful especially for object dtype), or a 1-element tuple
+        (latter for consistency with ``ufunc.__call__``).
+
+        .. versionadded:: 2.3
+            Support for ``out=...`` was added.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the original `array`.
+    initial : scalar, optional
+        The value with which to start the reduction.
+        If the ufunc has no identity or the dtype is object, this defaults
+        to None - otherwise it defaults to ufunc.identity.
+        If ``None`` is given, the first element of the reduction is used,
+        and an error is thrown if the reduction is empty.
+    where : array_like of bool, optional
+        A boolean array which is broadcasted to match the dimensions
+        of `array`, and selects elements to include in the reduction. Note
+        that for ufuncs like ``minimum`` that do not have an identity
+        defined, one has to pass in also ``initial``.
+
+    Returns
+    -------
+    r : ndarray
+        The reduced array. If `out` was supplied, `r` is a reference to it.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.multiply.reduce([2,3,5])
+    30
+
+    A multi-dimensional array example:
+
+    >>> X = np.arange(8).reshape((2,2,2))
+    >>> X
+    array([[[0, 1],
+            [2, 3]],
+           [[4, 5],
+            [6, 7]]])
+    >>> np.add.reduce(X, 0)
+    array([[ 4,  6],
+           [ 8, 10]])
+    >>> np.add.reduce(X) # confirm: default axis value is 0
+    array([[ 4,  6],
+           [ 8, 10]])
+    >>> np.add.reduce(X, 1)
+    array([[ 2,  4],
+           [10, 12]])
+    >>> np.add.reduce(X, 2)
+    array([[ 1,  5],
+           [ 9, 13]])
+
+    You can use the ``initial`` keyword argument to initialize the reduction
+    with a different value, and ``where`` to select specific elements to include:
+
+    >>> np.add.reduce([10], initial=5)
+    15
+    >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initial=10)
+    array([14., 14.])
+    >>> a = np.array([10., np.nan, 10])
+    >>> np.add.reduce(a, where=~np.isnan(a))
+    20.0
+
+    Allows reductions of empty arrays where they would normally fail, i.e.
+    for ufuncs without an identity.
+
+    >>> np.minimum.reduce([], initial=np.inf)
+    inf
+    >>> np.minimum.reduce([[1., 2.], [3., 4.]], initial=10., where=[True, False])
+    array([ 1., 10.])
+    >>> np.minimum.reduce([])
+    Traceback (most recent call last):
+        ...
+    ValueError: zero-size array to reduction operation minimum which has no identity
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('accumulate',
+    """
+    accumulate(array, axis=0, dtype=None, out=None)
+
+    Accumulate the result of applying the operator to all elements.
+
+    For a one-dimensional array, accumulate produces results equivalent to::
+
+      r = np.empty(len(A))
+      t = op.identity        # op = the ufunc being applied to A's  elements
+      for i in range(len(A)):
+          t = op(t, A[i])
+          r[i] = t
+      return r
+
+    For example, add.accumulate() is equivalent to np.cumsum().
+
+    For a multi-dimensional array, accumulate is applied along only one
+    axis (axis zero by default; see Examples below) so repeated use is
+    necessary if one wants to accumulate over multiple axes.
+
+    Parameters
+    ----------
+    array : array_like
+        The array to act on.
+    axis : int, optional
+        The axis along which to apply the accumulation; default is zero.
+    dtype : data-type code, optional
+        The data-type used to represent the intermediate results. Defaults
+        to the data-type of the output array if such is provided, or the
+        data-type of the input array if no output array is provided.
+    out : ndarray, None, or tuple of ndarray and None, optional
+        Location into which the result is stored.
+        If not provided or None, a freshly-allocated array is returned.
+        For consistency with ``ufunc.__call__``, if passed as a keyword
+        argument, can be Ellipses (``out=...``, which has the same effect
+        as None as an array is always returned), or a 1-element tuple.
+
+    Returns
+    -------
+    r : ndarray
+        The accumulated values. If `out` was supplied, `r` is a reference to
+        `out`.
+
+    Examples
+    --------
+    1-D array examples:
+
+    >>> import numpy as np
+    >>> np.add.accumulate([2, 3, 5])
+    array([ 2,  5, 10])
+    >>> np.multiply.accumulate([2, 3, 5])
+    array([ 2,  6, 30])
+
+    2-D array examples:
+
+    >>> I = np.eye(2)
+    >>> I
+    array([[1.,  0.],
+           [0.,  1.]])
+
+    Accumulate along axis 0 (rows), down columns:
+
+    >>> np.add.accumulate(I, 0)
+    array([[1.,  0.],
+           [1.,  1.]])
+    >>> np.add.accumulate(I) # no axis specified = axis zero
+    array([[1.,  0.],
+           [1.,  1.]])
+
+    Accumulate along axis 1 (columns), through rows:
+
+    >>> np.add.accumulate(I, 1)
+    array([[1.,  1.],
+           [0.,  1.]])
+
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('reduceat',
+    """
+    reduceat(array, indices, axis=0, dtype=None, out=None)
+
+    Performs a (local) reduce with specified slices over a single axis.
+
+    For i in ``range(len(indices))``, `reduceat` computes
+    ``ufunc.reduce(array[indices[i]:indices[i+1]])``, which becomes the i-th
+    generalized "row" parallel to `axis` in the final result (i.e., in a
+    2-D array, for example, if `axis = 0`, it becomes the i-th row, but if
+    `axis = 1`, it becomes the i-th column).  There are three exceptions to this:
+
+    * when ``i = len(indices) - 1`` (so for the last index),
+      ``indices[i+1] = array.shape[axis]``.
+    * if ``indices[i] >= indices[i + 1]``, the i-th generalized "row" is
+      simply ``array[indices[i]]``.
+    * if ``indices[i] >= len(array)`` or ``indices[i] < 0``, an error is raised.
+
+    The shape of the output depends on the size of `indices`, and may be
+    larger than `array` (this happens if ``len(indices) > array.shape[axis]``).
+
+    Parameters
+    ----------
+    array : array_like
+        The array to act on.
+    indices : array_like
+        Paired indices, comma separated (not colon), specifying slices to
+        reduce.
+    axis : int, optional
+        The axis along which to apply the reduceat.
+    dtype : data-type code, optional
+        The data type used to perform the operation. Defaults to that of
+        ``out`` if given, and the data type of ``array`` otherwise (though
+        upcast to conserve precision for some cases, such as
+        ``numpy.add.reduce`` for integer or boolean input).
+    out : ndarray, None, or tuple of ndarray and None, optional
+        Location into which the result is stored.
+        If not provided or None, a freshly-allocated array is returned.
+        For consistency with ``ufunc.__call__``, if passed as a keyword
+        argument, can be Ellipses (``out=...``, which has the same effect
+        as None as an array is always returned), or a 1-element tuple.
+
+    Returns
+    -------
+    r : ndarray
+        The reduced values. If `out` was supplied, `r` is a reference to
+        `out`.
+
+    Notes
+    -----
+    A descriptive example:
+
+    If `array` is 1-D, the function `ufunc.accumulate(array)` is the same as
+    ``ufunc.reduceat(array, indices)[::2]`` where `indices` is
+    ``range(len(array) - 1)`` with a zero placed
+    in every other element:
+    ``indices = zeros(2 * len(array) - 1)``,
+    ``indices[1::2] = range(1, len(array))``.
+
+    Don't be fooled by this attribute's name: `reduceat(array)` is not
+    necessarily smaller than `array`.
+
+    Examples
+    --------
+    To take the running sum of four successive values:
+
+    >>> import numpy as np
+    >>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2]
+    array([ 6, 10, 14, 18])
+
+    A 2-D example:
+
+    >>> x = np.linspace(0, 15, 16).reshape(4,4)
+    >>> x
+    array([[ 0.,   1.,   2.,   3.],
+           [ 4.,   5.,   6.,   7.],
+           [ 8.,   9.,  10.,  11.],
+           [12.,  13.,  14.,  15.]])
+
+    ::
+
+     # reduce such that the result has the following five rows:
+     # [row1 + row2 + row3]
+     # [row4]
+     # [row2]
+     # [row3]
+     # [row1 + row2 + row3 + row4]
+
+    >>> np.add.reduceat(x, [0, 3, 1, 2, 0])
+    array([[12.,  15.,  18.,  21.],
+           [12.,  13.,  14.,  15.],
+           [ 4.,   5.,   6.,   7.],
+           [ 8.,   9.,  10.,  11.],
+           [24.,  28.,  32.,  36.]])
+
+    ::
+
+     # reduce such that result has the following two columns:
+     # [col1 * col2 * col3, col4]
+
+    >>> np.multiply.reduceat(x, [0, 3], 1)
+    array([[   0.,     3.],
+           [ 120.,     7.],
+           [ 720.,    11.],
+           [2184.,    15.]])
+
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('outer',
+    r"""
+    outer(A, B, /, **kwargs)
+
+    Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`.
+
+    Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of
+    ``op.outer(A, B)`` is an array of dimension M + N such that:
+
+    .. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] =
+       op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}])
+
+    For `A` and `B` one-dimensional, this is equivalent to::
+
+      r = empty(len(A),len(B))
+      for i in range(len(A)):
+          for j in range(len(B)):
+              r[i,j] = op(A[i], B[j])  # op = ufunc in question
+
+    Parameters
+    ----------
+    A : array_like
+        First array
+    B : array_like
+        Second array
+    kwargs : any
+        Arguments to pass on to the ufunc. Typically `dtype` or `out`.
+        See `ufunc` for a comprehensive overview of all available arguments.
+
+    Returns
+    -------
+    r : ndarray
+        Output array
+
+    See Also
+    --------
+    numpy.outer : A less powerful version of ``np.multiply.outer``
+                  that `ravel`\ s all inputs to 1D. This exists
+                  primarily for compatibility with old code.
+
+    tensordot : ``np.tensordot(a, b, axes=((), ()))`` and
+                ``np.multiply.outer(a, b)`` behave same for all
+                dimensions of a and b.
+
+    Examples
+    --------
+    >>> np.multiply.outer([1, 2, 3], [4, 5, 6])
+    array([[ 4,  5,  6],
+           [ 8, 10, 12],
+           [12, 15, 18]])
+
+    A multi-dimensional example:
+
+    >>> A = np.array([[1, 2, 3], [4, 5, 6]])
+    >>> A.shape
+    (2, 3)
+    >>> B = np.array([[1, 2, 3, 4]])
+    >>> B.shape
+    (1, 4)
+    >>> C = np.multiply.outer(A, B)
+    >>> C.shape; C
+    (2, 3, 1, 4)
+    array([[[[ 1,  2,  3,  4]],
+            [[ 2,  4,  6,  8]],
+            [[ 3,  6,  9, 12]]],
+           [[[ 4,  8, 12, 16]],
+            [[ 5, 10, 15, 20]],
+            [[ 6, 12, 18, 24]]]])
+
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('at',
+    """
+    at(a, indices, b=None, /)
+
+    Performs unbuffered in place operation on operand 'a' for elements
+    specified by 'indices'. For addition ufunc, this method is equivalent to
+    ``a[indices] += b``, except that results are accumulated for elements that
+    are indexed more than once. For example, ``a[[0,0]] += 1`` will only
+    increment the first element once because of buffering, whereas
+    ``add.at(a, [0,0], 1)`` will increment the first element twice.
+
+    Parameters
+    ----------
+    a : array_like
+        The array to perform in place operation on.
+    indices : array_like or tuple
+        Array like index object or slice object for indexing into first
+        operand. If first operand has multiple dimensions, indices can be a
+        tuple of array like index objects or slice objects.
+    b : array_like
+        Second operand for ufuncs requiring two operands. Operand must be
+        broadcastable over first operand after indexing or slicing.
+
+    Examples
+    --------
+    Set items 0 and 1 to their negative values:
+
+    >>> import numpy as np
+    >>> a = np.array([1, 2, 3, 4])
+    >>> np.negative.at(a, [0, 1])
+    >>> a
+    array([-1, -2,  3,  4])
+
+    Increment items 0 and 1, and increment item 2 twice:
+
+    >>> a = np.array([1, 2, 3, 4])
+    >>> np.add.at(a, [0, 1, 2, 2], 1)
+    >>> a
+    array([2, 3, 5, 4])
+
+    Add items 0 and 1 in first array to second array,
+    and store results in first array:
+
+    >>> a = np.array([1, 2, 3, 4])
+    >>> b = np.array([1, 2])
+    >>> np.add.at(a, [0, 1], b)
+    >>> a
+    array([2, 4, 3, 4])
+
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('resolve_dtypes',
+    """
+    resolve_dtypes(dtypes, *, signature=None, casting=None, reduction=False)
+
+    Find the dtypes NumPy will use for the operation.  Both input and
+    output dtypes are returned and may differ from those provided.
+
+    .. note::
+
+        This function always applies NEP 50 rules since it is not provided
+        any actual values.  The Python types ``int``, ``float``, and
+        ``complex`` thus behave weak and should be passed for "untyped"
+        Python input.
+
+    Parameters
+    ----------
+    dtypes : tuple of dtypes, None, or literal int, float, complex
+        The input dtypes for each operand.  Output operands can be
+        None, indicating that the dtype must be found.
+    signature : tuple of DTypes or None, optional
+        If given, enforces exact DType (classes) of the specific operand.
+        The ufunc ``dtype`` argument is equivalent to passing a tuple with
+        only output dtypes set.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        The casting mode when casting is necessary.  This is identical to
+        the ufunc call casting modes.
+    reduction : boolean
+        If given, the resolution assumes a reduce operation is happening
+        which slightly changes the promotion and type resolution rules.
+        `dtypes` is usually something like ``(None, np.dtype("i2"), None)``
+        for reductions (first input is also the output).
+
+        .. note::
+
+            The default casting mode is "same_kind", however, as of
+            NumPy 1.24, NumPy uses "unsafe" for reductions.
+
+    Returns
+    -------
+    dtypes : tuple of dtypes
+        The dtypes which NumPy would use for the calculation.  Note that
+        dtypes may not match the passed in ones (casting is necessary).
+
+
+    Examples
+    --------
+    This API requires passing dtypes, define them for convenience:
+
+    >>> import numpy as np
+    >>> int32 = np.dtype("int32")
+    >>> float32 = np.dtype("float32")
+
+    The typical ufunc call does not pass an output dtype.  `numpy.add` has two
+    inputs and one output, so leave the output as ``None`` (not provided):
+
+    >>> np.add.resolve_dtypes((int32, float32, None))
+    (dtype('float64'), dtype('float64'), dtype('float64'))
+
+    The loop found uses "float64" for all operands (including the output), the
+    first input would be cast.
+
+    ``resolve_dtypes`` supports "weak" handling for Python scalars by passing
+    ``int``, ``float``, or ``complex``:
+
+    >>> np.add.resolve_dtypes((float32, float, None))
+    (dtype('float32'), dtype('float32'), dtype('float32'))
+
+    Where the Python ``float`` behaves similar to a Python value ``0.0``
+    in a ufunc call.  (See :ref:`NEP 50 <NEP50>` for details.)
+
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('_resolve_dtypes_and_context',
+    """
+    _resolve_dtypes_and_context(dtypes, *, signature=None, casting=None, reduction=False)
+
+    See `numpy.ufunc.resolve_dtypes` for parameter information.  This
+    function is considered *unstable*.  You may use it, but the returned
+    information is NumPy version specific and expected to change.
+    Large API/ABI changes are not expected, but a new NumPy version is
+    expected to require updating code using this functionality.
+
+    This function is designed to be used in conjunction with
+    `numpy.ufunc._get_strided_loop`.  The calls are split to mirror the C API
+    and allow future improvements.
+
+    Returns
+    -------
+    dtypes : tuple of dtypes
+    call_info :
+        PyCapsule with all necessary information to get access to low level
+        C calls.  See `numpy.ufunc._get_strided_loop` for more information.
+
+    """))
+
+add_newdoc('numpy._core', 'ufunc', ('_get_strided_loop',
+    """
+    _get_strided_loop(call_info, /, *, fixed_strides=None)
+
+    This function fills in the ``call_info`` capsule to include all
+    information necessary to call the low-level strided loop from NumPy.
+
+    See notes for more information.
+
+    Parameters
+    ----------
+    call_info : PyCapsule
+        The PyCapsule returned by `numpy.ufunc._resolve_dtypes_and_context`.
+    fixed_strides : tuple of int or None, optional
+        A tuple with fixed byte strides of all input arrays.  NumPy may use
+        this information to find specialized loops, so any call must follow
+        the given stride.  Use ``None`` to indicate that the stride is not
+        known (or not fixed) for all calls.
+
+    Notes
+    -----
+    Together with `numpy.ufunc._resolve_dtypes_and_context` this function
+    gives low-level access to the NumPy ufunc loops.
+    The first function does general preparation and returns the required
+    information. It returns this as a C capsule with the version specific
+    name ``numpy_1.24_ufunc_call_info``.
+    The NumPy 1.24 ufunc call info capsule has the following layout::
+
+        typedef struct {
+            PyArrayMethod_StridedLoop *strided_loop;
+            PyArrayMethod_Context *context;
+            NpyAuxData *auxdata;
+
+            /* Flag information (expected to change) */
+            npy_bool requires_pyapi;  /* GIL is required by loop */
+
+            /* Loop doesn't set FPE flags; if not set check FPE flags */
+            npy_bool no_floatingpoint_errors;
+        } ufunc_call_info;
+
+    Note that the first call only fills in the ``context``.  The call to
+    ``_get_strided_loop`` fills in all other data.  The main thing to note is
+    that the new-style loops return 0 on success, -1 on failure.  They are
+    passed context as new first input and ``auxdata`` as (replaced) last.
+
+    Only the ``strided_loop``signature is considered guaranteed stable
+    for NumPy bug-fix releases.  All other API is tied to the experimental
+    API versioning.
+
+    The reason for the split call is that cast information is required to
+    decide what the fixed-strides will be.
+
+    NumPy ties the lifetime of the ``auxdata`` information to the capsule.
+
+    """))
+
+
+##############################################################################
+#
+# Documentation for dtype attributes and methods
+#
+##############################################################################
+
+##############################################################################
+#
+# dtype object
+#
+##############################################################################
+
+add_newdoc('numpy._core.multiarray', 'dtype',
+    """
+    dtype(dtype, align=False, copy=False, [metadata])
+
+    Create a data type object.
+
+    A numpy array is homogeneous, and contains elements described by a
+    dtype object. A dtype object can be constructed from different
+    combinations of fundamental numeric types.
+
+    Parameters
+    ----------
+    dtype
+        Object to be converted to a data type object.
+    align : bool, optional
+        Add padding to the fields to match what a C compiler would output
+        for a similar C-struct. Can be ``True`` only if `obj` is a dictionary
+        or a comma-separated string. If a struct dtype is being created,
+        this also sets a sticky alignment flag ``isalignedstruct``.
+    copy : bool, optional
+        Make a new copy of the data-type object. If ``False``, the result
+        may just be a reference to a built-in data-type object.
+    metadata : dict, optional
+        An optional dictionary with dtype metadata.
+
+    See also
+    --------
+    result_type
+
+    Examples
+    --------
+    Using array-scalar type:
+
+    >>> import numpy as np
+    >>> np.dtype(np.int16)
+    dtype('int16')
+
+    Structured type, one field name 'f1', containing int16:
+
+    >>> np.dtype([('f1', np.int16)])
+    dtype([('f1', '<i2')])
+
+    Structured type, one field named 'f1', in itself containing a structured
+    type with one field:
+
+    >>> np.dtype([('f1', [('f1', np.int16)])])
+    dtype([('f1', [('f1', '<i2')])])
+
+    Structured type, two fields: the first field contains an unsigned int, the
+    second an int32:
+
+    >>> np.dtype([('f1', np.uint64), ('f2', np.int32)])
+    dtype([('f1', '<u8'), ('f2', '<i4')])
+
+    Using array-protocol type strings:
+
+    >>> np.dtype([('a','f8'),('b','S10')])
+    dtype([('a', '<f8'), ('b', 'S10')])
+
+    Using comma-separated field formats.  The shape is (2,3):
+
+    >>> np.dtype("i4, (2,3)f8")
+    dtype([('f0', '<i4'), ('f1', '<f8', (2, 3))])
+
+    Using tuples.  ``int`` is a fixed type, 3 the field's shape.  ``void``
+    is a flexible type, here of size 10:
+
+    >>> np.dtype([('hello',(np.int64,3)),('world',np.void,10)])
+    dtype([('hello', '<i8', (3,)), ('world', 'V10')])
+
+    Subdivide ``int16`` into 2 ``int8``'s, called x and y.  0 and 1 are
+    the offsets in bytes:
+
+    >>> np.dtype((np.int16, {'x':(np.int8,0), 'y':(np.int8,1)}))
+    dtype((numpy.int16, [('x', 'i1'), ('y', 'i1')]))
+
+    Using dictionaries.  Two fields named 'gender' and 'age':
+
+    >>> np.dtype({'names':['gender','age'], 'formats':['S1',np.uint8]})
+    dtype([('gender', 'S1'), ('age', 'u1')])
+
+    Offsets in bytes, here 0 and 25:
+
+    >>> np.dtype({'surname':('S25',0),'age':(np.uint8,25)})
+    dtype([('surname', 'S25'), ('age', 'u1')])
+
+    """)
+
+##############################################################################
+#
+# dtype attributes
+#
+##############################################################################
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('alignment',
+    """
+    The required alignment (bytes) of this data-type according to the compiler.
+
+    More information is available in the C-API section of the manual.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> x = np.dtype('i4')
+    >>> x.alignment
+    4
+
+    >>> x = np.dtype(float)
+    >>> x.alignment
+    8
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('byteorder',
+    """
+    A character indicating the byte-order of this data-type object.
+
+    One of:
+
+    ===  ==============
+    '='  native
+    '<'  little-endian
+    '>'  big-endian
+    '|'  not applicable
+    ===  ==============
+
+    All built-in data-type objects have byteorder either '=' or '|'.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> dt = np.dtype('i2')
+    >>> dt.byteorder
+    '='
+    >>> # endian is not relevant for 8 bit numbers
+    >>> np.dtype('i1').byteorder
+    '|'
+    >>> # or ASCII strings
+    >>> np.dtype('S2').byteorder
+    '|'
+    >>> # Even if specific code is given, and it is native
+    >>> # '=' is the byteorder
+    >>> import sys
+    >>> sys_is_le = sys.byteorder == 'little'
+    >>> native_code = '<' if sys_is_le else '>'
+    >>> swapped_code = '>' if sys_is_le else '<'
+    >>> dt = np.dtype(native_code + 'i2')
+    >>> dt.byteorder
+    '='
+    >>> # Swapped code shows up as itself
+    >>> dt = np.dtype(swapped_code + 'i2')
+    >>> dt.byteorder == swapped_code
+    True
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('char',
+    """A unique character code for each of the 21 different built-in types.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> x = np.dtype(float)
+    >>> x.char
+    'd'
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('descr',
+    """
+    `__array_interface__` description of the data-type.
+
+    The format is that required by the 'descr' key in the
+    `__array_interface__` attribute.
+
+    Warning: This attribute exists specifically for `__array_interface__`,
+    and passing it directly to `numpy.dtype` will not accurately reconstruct
+    some dtypes (e.g., scalar and subarray dtypes).
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> x = np.dtype(float)
+    >>> x.descr
+    [('', '<f8')]
+
+    >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
+    >>> dt.descr
+    [('name', '<U16'), ('grades', '<f8', (2,))]
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('fields',
+    """
+    Dictionary of named fields defined for this data type, or ``None``.
+
+    The dictionary is indexed by keys that are the names of the fields.
+    Each entry in the dictionary is a tuple fully describing the field::
+
+      (dtype, offset[, title])
+
+    Offset is limited to C int, which is signed and usually 32 bits.
+    If present, the optional title can be any object (if it is a string
+    or unicode then it will also be a key in the fields dictionary,
+    otherwise it's meta-data). Notice also that the first two elements
+    of the tuple can be passed directly as arguments to the
+    ``ndarray.getfield`` and ``ndarray.setfield`` methods.
+
+    See Also
+    --------
+    ndarray.getfield, ndarray.setfield
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
+    >>> print(dt.fields)
+    {'name': (dtype('|S16'), 0), 'grades': (dtype(('float64',(2,))), 16)}
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('flags',
+    """
+    Bit-flags describing how this data type is to be interpreted.
+
+    Bit-masks are in ``numpy._core.multiarray`` as the constants
+    `ITEM_HASOBJECT`, `LIST_PICKLE`, `ITEM_IS_POINTER`, `NEEDS_INIT`,
+    `NEEDS_PYAPI`, `USE_GETITEM`, `USE_SETITEM`. A full explanation
+    of these flags is in C-API documentation; they are largely useful
+    for user-defined data-types.
+
+    The following example demonstrates that operations on this particular
+    dtype requires Python C-API.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> x = np.dtype([('a', np.int32, 8), ('b', np.float64, 6)])
+    >>> x.flags
+    16
+    >>> np._core.multiarray.NEEDS_PYAPI
+    16
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('hasobject',
+    """
+    Boolean indicating whether this dtype contains any reference-counted
+    objects in any fields or sub-dtypes.
+
+    Recall that what is actually in the ndarray memory representing
+    the Python object is the memory address of that object (a pointer).
+    Special handling may be required, and this attribute is useful for
+    distinguishing data types that may contain arbitrary Python objects
+    and data-types that won't.
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('isbuiltin',
+    """
+    Integer indicating how this dtype relates to the built-in dtypes.
+
+    Read-only.
+
+    =  ========================================================================
+    0  if this is a structured array type, with fields
+    1  if this is a dtype compiled into numpy (such as ints, floats etc)
+    2  if the dtype is for a user-defined numpy type
+       A user-defined type uses the numpy C-API machinery to extend
+       numpy to handle a new array type. See
+       :ref:`user.user-defined-data-types` in the NumPy manual.
+    =  ========================================================================
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> dt = np.dtype('i2')
+    >>> dt.isbuiltin
+    1
+    >>> dt = np.dtype('f8')
+    >>> dt.isbuiltin
+    1
+    >>> dt = np.dtype([('field1', 'f8')])
+    >>> dt.isbuiltin
+    0
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('isnative',
+    """
+    Boolean indicating whether the byte order of this dtype is native
+    to the platform.
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('isalignedstruct',
+    """
+    Boolean indicating whether the dtype is a struct which maintains
+    field alignment. This flag is sticky, so when combining multiple
+    structs together, it is preserved and produces new dtypes which
+    are also aligned.
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('itemsize',
+    """
+    The element size of this data-type object.
+
+    For 18 of the 21 types this number is fixed by the data-type.
+    For the flexible data-types, this number can be anything.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> arr = np.array([[1, 2], [3, 4]])
+    >>> arr.dtype
+    dtype('int64')
+    >>> arr.itemsize
+    8
+
+    >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
+    >>> dt.itemsize
+    80
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('kind',
+    """
+    A character code (one of 'biufcmMOSTUV') identifying the general kind of data.
+
+    =  ======================
+    b  boolean
+    i  signed integer
+    u  unsigned integer
+    f  floating-point
+    c  complex floating-point
+    m  timedelta
+    M  datetime
+    O  object
+    S  (byte-)string
+    T  string (StringDType)
+    U  Unicode
+    V  void
+    =  ======================
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> dt = np.dtype('i4')
+    >>> dt.kind
+    'i'
+    >>> dt = np.dtype('f8')
+    >>> dt.kind
+    'f'
+    >>> dt = np.dtype([('field1', 'f8')])
+    >>> dt.kind
+    'V'
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('metadata',
+    """
+    Either ``None`` or a readonly dictionary of metadata (mappingproxy).
+
+    The metadata field can be set using any dictionary at data-type
+    creation. NumPy currently has no uniform approach to propagating
+    metadata; although some array operations preserve it, there is no
+    guarantee that others will.
+
+    .. warning::
+
+        Although used in certain projects, this feature was long undocumented
+        and is not well supported. Some aspects of metadata propagation
+        are expected to change in the future.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> dt = np.dtype(float, metadata={"key": "value"})
+    >>> dt.metadata["key"]
+    'value'
+    >>> arr = np.array([1, 2, 3], dtype=dt)
+    >>> arr.dtype.metadata
+    mappingproxy({'key': 'value'})
+
+    Adding arrays with identical datatypes currently preserves the metadata:
+
+    >>> (arr + arr).dtype.metadata
+    mappingproxy({'key': 'value'})
+
+    If the arrays have different dtype metadata, the first one wins:
+
+    >>> dt2 = np.dtype(float, metadata={"key2": "value2"})
+    >>> arr2 = np.array([3, 2, 1], dtype=dt2)
+    >>> print((arr + arr2).dtype.metadata)
+    {'key': 'value'}
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('name',
+    """
+    A bit-width name for this data-type.
+
+    Un-sized flexible data-type objects do not have this attribute.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> x = np.dtype(float)
+    >>> x.name
+    'float64'
+    >>> x = np.dtype([('a', np.int32, 8), ('b', np.float64, 6)])
+    >>> x.name
+    'void640'
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('names',
+    """
+    Ordered list of field names, or ``None`` if there are no fields.
+
+    The names are ordered according to increasing byte offset. This can be
+    used, for example, to walk through all of the named fields in offset order.
+
+    Examples
+    --------
+    >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
+    >>> dt.names
+    ('name', 'grades')
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('num',
+    """
+    A unique number for each of the 21 different built-in types.
+
+    These are roughly ordered from least-to-most precision.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> dt = np.dtype(str)
+    >>> dt.num
+    19
+
+    >>> dt = np.dtype(float)
+    >>> dt.num
+    12
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('shape',
+    """
+    Shape tuple of the sub-array if this data type describes a sub-array,
+    and ``()`` otherwise.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> dt = np.dtype(('i4', 4))
+    >>> dt.shape
+    (4,)
+
+    >>> dt = np.dtype(('i4', (2, 3)))
+    >>> dt.shape
+    (2, 3)
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('ndim',
+    """
+    Number of dimensions of the sub-array if this data type describes a
+    sub-array, and ``0`` otherwise.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.dtype(float)
+    >>> x.ndim
+    0
+
+    >>> x = np.dtype((float, 8))
+    >>> x.ndim
+    1
+
+    >>> x = np.dtype(('i4', (3, 4)))
+    >>> x.ndim
+    2
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('str',
+    """The array-protocol typestring of this data-type object."""))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('subdtype',
+    """
+    Tuple ``(item_dtype, shape)`` if this `dtype` describes a sub-array, and
+    None otherwise.
+
+    The *shape* is the fixed shape of the sub-array described by this
+    data type, and *item_dtype* the data type of the array.
+
+    If a field whose dtype object has this attribute is retrieved,
+    then the extra dimensions implied by *shape* are tacked on to
+    the end of the retrieved array.
+
+    See Also
+    --------
+    dtype.base
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.dtype('8f')
+    >>> x.subdtype
+    (dtype('float32'), (8,))
+
+    >>> x =  np.dtype('i2')
+    >>> x.subdtype
+    >>>
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('base',
+    """
+    Returns dtype for the base element of the subarrays,
+    regardless of their dimension or shape.
+
+    See Also
+    --------
+    dtype.subdtype
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.dtype('8f')
+    >>> x.base
+    dtype('float32')
+
+    >>> x =  np.dtype('i2')
+    >>> x.base
+    dtype('int16')
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('type',
+    """The type object used to instantiate a scalar of this data-type."""))
+
+##############################################################################
+#
+# dtype methods
+#
+##############################################################################
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('newbyteorder',
+    """
+    newbyteorder(new_order='S', /)
+
+    Return a new dtype with a different byte order.
+
+    Changes are also made in all fields and sub-arrays of the data type.
+
+    Parameters
+    ----------
+    new_order : string, optional
+        Byte order to force; a value from the byte order specifications
+        below.  The default value ('S') results in swapping the current
+        byte order.  `new_order` codes can be any of:
+
+        * 'S' - swap dtype from current to opposite endian
+        * {'<', 'little'} - little endian
+        * {'>', 'big'} - big endian
+        * {'=', 'native'} - native order
+        * {'|', 'I'} - ignore (no change to byte order)
+
+    Returns
+    -------
+    new_dtype : dtype
+        New dtype object with the given change to the byte order.
+
+    Notes
+    -----
+    Changes are also made in all fields and sub-arrays of the data type.
+
+    Examples
+    --------
+    >>> import sys
+    >>> sys_is_le = sys.byteorder == 'little'
+    >>> native_code = '<' if sys_is_le else '>'
+    >>> swapped_code = '>' if sys_is_le else '<'
+    >>> import numpy as np
+    >>> native_dt = np.dtype(native_code+'i2')
+    >>> swapped_dt = np.dtype(swapped_code+'i2')
+    >>> native_dt.newbyteorder('S') == swapped_dt
+    True
+    >>> native_dt.newbyteorder() == swapped_dt
+    True
+    >>> native_dt == swapped_dt.newbyteorder('S')
+    True
+    >>> native_dt == swapped_dt.newbyteorder('=')
+    True
+    >>> native_dt == swapped_dt.newbyteorder('N')
+    True
+    >>> native_dt == native_dt.newbyteorder('|')
+    True
+    >>> np.dtype('<i2') == native_dt.newbyteorder('<')
+    True
+    >>> np.dtype('<i2') == native_dt.newbyteorder('L')
+    True
+    >>> np.dtype('>i2') == native_dt.newbyteorder('>')
+    True
+    >>> np.dtype('>i2') == native_dt.newbyteorder('B')
+    True
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('__class_getitem__',
+    """
+    __class_getitem__(item, /)
+
+    Return a parametrized wrapper around the `~numpy.dtype` type.
+
+    .. versionadded:: 1.22
+
+    Returns
+    -------
+    alias : types.GenericAlias
+        A parametrized `~numpy.dtype` type.
+
+    Examples
+    --------
+    >>> import numpy as np
+
+    >>> np.dtype[np.int64]
+    numpy.dtype[numpy.int64]
+
+    See Also
+    --------
+    :pep:`585` : Type hinting generics in standard collections.
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('__ge__',
+    """
+    __ge__(value, /)
+
+    Return ``self >= value``.
+
+    Equivalent to ``np.can_cast(value, self, casting="safe")``.
+
+    See Also
+    --------
+    can_cast : Returns True if cast between data types can occur according to
+               the casting rule.
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('__le__',
+    """
+    __le__(value, /)
+
+    Return ``self <= value``.
+
+    Equivalent to ``np.can_cast(self, value, casting="safe")``.
+
+    See Also
+    --------
+    can_cast : Returns True if cast between data types can occur according to
+               the casting rule.
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('__gt__',
+    """
+    __ge__(value, /)
+
+    Return ``self > value``.
+
+    Equivalent to
+    ``self != value and np.can_cast(value, self, casting="safe")``.
+
+    See Also
+    --------
+    can_cast : Returns True if cast between data types can occur according to
+               the casting rule.
+
+    """))
+
+add_newdoc('numpy._core.multiarray', 'dtype', ('__lt__',
+    """
+    __lt__(value, /)
+
+    Return ``self < value``.
+
+    Equivalent to
+    ``self != value and np.can_cast(self, value, casting="safe")``.
+
+    See Also
+    --------
+    can_cast : Returns True if cast between data types can occur according to
+               the casting rule.
+
+    """))
+
+##############################################################################
+#
+# Datetime-related Methods
+#
+##############################################################################
+
+add_newdoc('numpy._core.multiarray', 'busdaycalendar',
+    """
+    busdaycalendar(weekmask='1111100', holidays=None)
+
+    A business day calendar object that efficiently stores information
+    defining valid days for the busday family of functions.
+
+    The default valid days are Monday through Friday ("business days").
+    A busdaycalendar object can be specified with any set of weekly
+    valid days, plus an optional "holiday" dates that always will be invalid.
+
+    Once a busdaycalendar object is created, the weekmask and holidays
+    cannot be modified.
+
+    Parameters
+    ----------
+    weekmask : str or array_like of bool, optional
+        A seven-element array indicating which of Monday through Sunday are
+        valid days. May be specified as a length-seven list or array, like
+        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
+        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
+        weekdays, optionally separated by white space. Valid abbreviations
+        are: Mon Tue Wed Thu Fri Sat Sun
+    holidays : array_like of datetime64[D], optional
+        An array of dates to consider as invalid dates, no matter which
+        weekday they fall upon.  Holiday dates may be specified in any
+        order, and NaT (not-a-time) dates are ignored.  This list is
+        saved in a normalized form that is suited for fast calculations
+        of valid days.
+
+    Returns
+    -------
+    out : busdaycalendar
+        A business day calendar object containing the specified
+        weekmask and holidays values.
+
+    See Also
+    --------
+    is_busday : Returns a boolean array indicating valid days.
+    busday_offset : Applies an offset counted in valid days.
+    busday_count : Counts how many valid days are in a half-open date range.
+
+    Attributes
+    ----------
+    weekmask : (copy) seven-element array of bool
+    holidays : (copy) sorted array of datetime64[D]
+
+    Notes
+    -----
+    Once a busdaycalendar object is created, you cannot modify the
+    weekmask or holidays.  The attributes return copies of internal data.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> # Some important days in July
+    ... bdd = np.busdaycalendar(
+    ...             holidays=['2011-07-01', '2011-07-04', '2011-07-17'])
+    >>> # Default is Monday to Friday weekdays
+    ... bdd.weekmask
+    array([ True,  True,  True,  True,  True, False, False])
+    >>> # Any holidays already on the weekend are removed
+    ... bdd.holidays
+    array(['2011-07-01', '2011-07-04'], dtype='datetime64[D]')
+    """)
+
+add_newdoc('numpy._core.multiarray', 'busdaycalendar', ('weekmask',
+    """A copy of the seven-element boolean mask indicating valid days."""))
+
+add_newdoc('numpy._core.multiarray', 'busdaycalendar', ('holidays',
+    """A copy of the holiday array indicating additional invalid days."""))
+
+add_newdoc('numpy._core.multiarray', 'normalize_axis_index',
+    """
+    normalize_axis_index(axis, ndim, msg_prefix=None)
+
+    Normalizes an axis index, `axis`, such that is a valid positive index into
+    the shape of array with `ndim` dimensions. Raises an AxisError with an
+    appropriate message if this is not possible.
+
+    Used internally by all axis-checking logic.
+
+    Parameters
+    ----------
+    axis : int
+        The un-normalized index of the axis. Can be negative
+    ndim : int
+        The number of dimensions of the array that `axis` should be normalized
+        against
+    msg_prefix : str
+        A prefix to put before the message, typically the name of the argument
+
+    Returns
+    -------
+    normalized_axis : int
+        The normalized axis index, such that `0 <= normalized_axis < ndim`
+
+    Raises
+    ------
+    AxisError
+        If the axis index is invalid, when `-ndim <= axis < ndim` is false.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from numpy.lib.array_utils import normalize_axis_index
+    >>> normalize_axis_index(0, ndim=3)
+    0
+    >>> normalize_axis_index(1, ndim=3)
+    1
+    >>> normalize_axis_index(-1, ndim=3)
+    2
+
+    >>> normalize_axis_index(3, ndim=3)
+    Traceback (most recent call last):
+    ...
+    numpy.exceptions.AxisError: axis 3 is out of bounds for array ...
+    >>> normalize_axis_index(-4, ndim=3, msg_prefix='axes_arg')
+    Traceback (most recent call last):
+    ...
+    numpy.exceptions.AxisError: axes_arg: axis -4 is out of bounds ...
+    """)
+
+add_newdoc('numpy._core.multiarray', 'datetime_data',
+    """
+    datetime_data(dtype, /)
+
+    Get information about the step size of a date or time type.
+
+    The returned tuple can be passed as the second argument of `numpy.datetime64` and
+    `numpy.timedelta64`.
+
+    Parameters
+    ----------
+    dtype : dtype
+        The dtype object, which must be a `datetime64` or `timedelta64` type.
+
+    Returns
+    -------
+    unit : str
+        The :ref:`datetime unit <arrays.dtypes.dateunits>` on which this dtype
+        is based.
+    count : int
+        The number of base units in a step.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> dt_25s = np.dtype('timedelta64[25s]')
+    >>> np.datetime_data(dt_25s)
+    ('s', 25)
+    >>> np.array(10, dt_25s).astype('timedelta64[s]')
+    array(250, dtype='timedelta64[s]')
+
+    The result can be used to construct a datetime that uses the same units
+    as a timedelta
+
+    >>> np.datetime64('2010', np.datetime_data(dt_25s))
+    np.datetime64('2010-01-01T00:00:00','25s')
+    """)
+
+
+##############################################################################
+#
+# Documentation for `generic` attributes and methods
+#
+##############################################################################
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+    """
+    Base class for numpy scalar types.
+
+    Class from which most (all?) numpy scalar types are derived.  For
+    consistency, exposes the same API as `ndarray`, despite many
+    consequent attributes being either "get-only," or completely irrelevant.
+    This is the class from which it is strongly suggested users should derive
+    custom scalar types.
+
+    """)
+
+# Attributes
+
+def refer_to_array_attribute(attr, method=True):
+    docstring = """
+    Scalar {} identical to the corresponding array attribute.
+
+    Please see `ndarray.{}`.
+    """
+
+    return attr, docstring.format("method" if method else "attribute", attr)
+
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('T', method=False))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('base', method=False))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('data',
+    """Pointer to start of data."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('dtype',
+    """Get array data-descriptor."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('flags',
+    """The integer value of flags."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('flat',
+    """A 1-D view of the scalar."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('imag',
+    """The imaginary part of the scalar."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('itemsize',
+    """The length of one element in bytes."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('ndim',
+    """The number of array dimensions."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('real',
+    """The real part of the scalar."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('shape',
+    """Tuple of array dimensions."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('size',
+    """The number of elements in the gentype."""))
+
+add_newdoc('numpy._core.numerictypes', 'generic', ('strides',
+    """Tuple of bytes steps in each dimension."""))
+
+# Methods
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('all'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('any'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('argmax'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('argmin'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('argsort'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('astype'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('byteswap'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('choose'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('clip'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('compress'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('conjugate'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('copy'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('cumprod'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('cumsum'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('diagonal'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('dump'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('dumps'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('fill'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('flatten'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('getfield'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('item'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('max'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('mean'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('min'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('nonzero'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('prod'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('put'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('ravel'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('repeat'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('reshape'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('resize'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('round'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('searchsorted'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('setfield'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('setflags'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('sort'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('squeeze'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('std'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('sum'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('swapaxes'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('take'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('tofile'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('tolist'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('tostring'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('trace'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('transpose'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('var'))
+
+add_newdoc('numpy._core.numerictypes', 'generic',
+           refer_to_array_attribute('view'))
+
+add_newdoc('numpy._core.numerictypes', 'number', ('__class_getitem__',
+    """
+    __class_getitem__(item, /)
+
+    Return a parametrized wrapper around the `~numpy.number` type.
+
+    .. versionadded:: 1.22
+
+    Returns
+    -------
+    alias : types.GenericAlias
+        A parametrized `~numpy.number` type.
+
+    Examples
+    --------
+    >>> from typing import Any
+    >>> import numpy as np
+
+    >>> np.signedinteger[Any]
+    numpy.signedinteger[typing.Any]
+
+    See Also
+    --------
+    :pep:`585` : Type hinting generics in standard collections.
+
+    """))
+
+##############################################################################
+#
+# Documentation for scalar type abstract base classes in type hierarchy
+#
+##############################################################################
+
+
+add_newdoc('numpy._core.numerictypes', 'number',
+    """
+    Abstract base class of all numeric scalar types.
+
+    """)
+
+add_newdoc('numpy._core.numerictypes', 'integer',
+    """
+    Abstract base class of all integer scalar types.
+
+    """)
+
+add_newdoc('numpy._core.numerictypes', 'signedinteger',
+    """
+    Abstract base class of all signed integer scalar types.
+
+    """)
+
+add_newdoc('numpy._core.numerictypes', 'unsignedinteger',
+    """
+    Abstract base class of all unsigned integer scalar types.
+
+    """)
+
+add_newdoc('numpy._core.numerictypes', 'inexact',
+    """
+    Abstract base class of all numeric scalar types with a (potentially)
+    inexact representation of the values in its range, such as
+    floating-point numbers.
+
+    """)
+
+add_newdoc('numpy._core.numerictypes', 'floating',
+    """
+    Abstract base class of all floating-point scalar types.
+
+    """)
+
+add_newdoc('numpy._core.numerictypes', 'complexfloating',
+    """
+    Abstract base class of all complex number scalar types that are made up of
+    floating-point numbers.
+
+    """)
+
+add_newdoc('numpy._core.numerictypes', 'flexible',
+    """
+    Abstract base class of all scalar types without predefined length.
+    The actual size of these types depends on the specific `numpy.dtype`
+    instantiation.
+
+    """)
+
+add_newdoc('numpy._core.numerictypes', 'character',
+    """
+    Abstract base class of all character string scalar types.
+
+    """)
+
+add_newdoc('numpy._core.multiarray', 'StringDType',
+    """
+    StringDType(*, na_object=np._NoValue, coerce=True)
+
+    Create a StringDType instance.
+
+    StringDType can be used to store UTF-8 encoded variable-width strings in
+    a NumPy array.
+
+    Parameters
+    ----------
+    na_object : object, optional
+        Object used to represent missing data. If unset, the array will not
+        use a missing data sentinel.
+    coerce : bool, optional
+        Whether or not items in an array-like passed to an array creation
+        function that are neither a str or str subtype should be coerced to
+        str. Defaults to True. If set to False, creating a StringDType
+        array from an array-like containing entries that are not already
+        strings will raise an error.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+
+    >>> from numpy.dtypes import StringDType
+    >>> np.array(["hello", "world"], dtype=StringDType())
+    array(["hello", "world"], dtype=StringDType())
+
+    >>> arr = np.array(["hello", None, "world"],
+    ...                dtype=StringDType(na_object=None))
+    >>> arr
+    array(["hello", None, "world"], dtype=StringDType(na_object=None))
+    >>> arr[1] is None
+    True
+
+    >>> arr = np.array(["hello", np.nan, "world"],
+    ...                dtype=StringDType(na_object=np.nan))
+    >>> np.isnan(arr)
+    array([False, True, False])
+
+    >>> np.array([1.2, object(), "hello world"],
+    ...          dtype=StringDType(coerce=False))
+    Traceback (most recent call last):
+        ...
+    ValueError: StringDType only allows string data when string coercion is disabled.
+
+    >>> np.array(["hello", "world"], dtype=StringDType(coerce=True))
+    array(["hello", "world"], dtype=StringDType(coerce=True))
+    """)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs.pyi
new file mode 100644
index 0000000..b23c3b1
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs.pyi
@@ -0,0 +1,3 @@
+from .overrides import get_array_function_like_doc as get_array_function_like_doc
+
+def refer_to_array_attribute(attr: str, method: bool = True) -> tuple[str, str]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs_scalars.py b/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs_scalars.py
new file mode 100644
index 0000000..96170d8
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs_scalars.py
@@ -0,0 +1,390 @@
+"""
+This file is separate from ``_add_newdocs.py`` so that it can be mocked out by
+our sphinx ``conf.py`` during doc builds, where we want to avoid showing
+platform-dependent information.
+"""
+import os
+import sys
+
+from numpy._core import dtype
+from numpy._core import numerictypes as _numerictypes
+from numpy._core.function_base import add_newdoc
+
+##############################################################################
+#
+# Documentation for concrete scalar classes
+#
+##############################################################################
+
+def numeric_type_aliases(aliases):
+    def type_aliases_gen():
+        for alias, doc in aliases:
+            try:
+                alias_type = getattr(_numerictypes, alias)
+            except AttributeError:
+                # The set of aliases that actually exist varies between platforms
+                pass
+            else:
+                yield (alias_type, alias, doc)
+    return list(type_aliases_gen())
+
+
+possible_aliases = numeric_type_aliases([
+    ('int8', '8-bit signed integer (``-128`` to ``127``)'),
+    ('int16', '16-bit signed integer (``-32_768`` to ``32_767``)'),
+    ('int32', '32-bit signed integer (``-2_147_483_648`` to ``2_147_483_647``)'),
+    ('int64', '64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``)'),
+    ('intp', 'Signed integer large enough to fit pointer, compatible with C ``intptr_t``'),
+    ('uint8', '8-bit unsigned integer (``0`` to ``255``)'),
+    ('uint16', '16-bit unsigned integer (``0`` to ``65_535``)'),
+    ('uint32', '32-bit unsigned integer (``0`` to ``4_294_967_295``)'),
+    ('uint64', '64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``)'),
+    ('uintp', 'Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``'),
+    ('float16', '16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa'),
+    ('float32', '32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa'),
+    ('float64', '64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa'),
+    ('float96', '96-bit extended-precision floating-point number type'),
+    ('float128', '128-bit extended-precision floating-point number type'),
+    ('complex64', 'Complex number type composed of 2 32-bit-precision floating-point numbers'),
+    ('complex128', 'Complex number type composed of 2 64-bit-precision floating-point numbers'),
+    ('complex192', 'Complex number type composed of 2 96-bit extended-precision floating-point numbers'),
+    ('complex256', 'Complex number type composed of 2 128-bit extended-precision floating-point numbers'),
+    ])
+
+
+def _get_platform_and_machine():
+    try:
+        system, _, _, _, machine = os.uname()
+    except AttributeError:
+        system = sys.platform
+        if system == 'win32':
+            machine = os.environ.get('PROCESSOR_ARCHITEW6432', '') \
+                    or os.environ.get('PROCESSOR_ARCHITECTURE', '')
+        else:
+            machine = 'unknown'
+    return system, machine
+
+
+_system, _machine = _get_platform_and_machine()
+_doc_alias_string = f":Alias on this platform ({_system} {_machine}):"
+
+
+def add_newdoc_for_scalar_type(obj, fixed_aliases, doc):
+    # note: `:field: value` is rST syntax which renders as field lists.
+    o = getattr(_numerictypes, obj)
+
+    character_code = dtype(o).char
+    canonical_name_doc = "" if obj == o.__name__ else \
+                        f":Canonical name: `numpy.{obj}`\n    "
+    if fixed_aliases:
+        alias_doc = ''.join(f":Alias: `numpy.{alias}`\n    "
+                            for alias in fixed_aliases)
+    else:
+        alias_doc = ''
+    alias_doc += ''.join(f"{_doc_alias_string} `numpy.{alias}`: {doc}.\n    "
+                         for (alias_type, alias, doc) in possible_aliases if alias_type is o)
+
+    docstring = f"""
+    {doc.strip()}
+
+    :Character code: ``'{character_code}'``
+    {canonical_name_doc}{alias_doc}
+    """
+
+    add_newdoc('numpy._core.numerictypes', obj, docstring)
+
+
+_bool_docstring = (
+    """
+    Boolean type (True or False), stored as a byte.
+
+    .. warning::
+
+       The :class:`bool` type is not a subclass of the :class:`int_` type
+       (the :class:`bool` is not even a number type). This is different
+       than Python's default implementation of :class:`bool` as a
+       sub-class of :class:`int`.
+    """
+)
+
+add_newdoc_for_scalar_type('bool', [], _bool_docstring)
+
+add_newdoc_for_scalar_type('bool_', [], _bool_docstring)
+
+add_newdoc_for_scalar_type('byte', [],
+    """
+    Signed integer type, compatible with C ``char``.
+    """)
+
+add_newdoc_for_scalar_type('short', [],
+    """
+    Signed integer type, compatible with C ``short``.
+    """)
+
+add_newdoc_for_scalar_type('intc', [],
+    """
+    Signed integer type, compatible with C ``int``.
+    """)
+
+# TODO: These docs probably need an if to highlight the default rather than
+#       the C-types (and be correct).
+add_newdoc_for_scalar_type('int_', [],
+    """
+    Default signed integer type, 64bit on 64bit systems and 32bit on 32bit
+    systems.
+    """)
+
+add_newdoc_for_scalar_type('longlong', [],
+    """
+    Signed integer type, compatible with C ``long long``.
+    """)
+
+add_newdoc_for_scalar_type('ubyte', [],
+    """
+    Unsigned integer type, compatible with C ``unsigned char``.
+    """)
+
+add_newdoc_for_scalar_type('ushort', [],
+    """
+    Unsigned integer type, compatible with C ``unsigned short``.
+    """)
+
+add_newdoc_for_scalar_type('uintc', [],
+    """
+    Unsigned integer type, compatible with C ``unsigned int``.
+    """)
+
+add_newdoc_for_scalar_type('uint', [],
+    """
+    Unsigned signed integer type, 64bit on 64bit systems and 32bit on 32bit
+    systems.
+    """)
+
+add_newdoc_for_scalar_type('ulonglong', [],
+    """
+    Signed integer type, compatible with C ``unsigned long long``.
+    """)
+
+add_newdoc_for_scalar_type('half', [],
+    """
+    Half-precision floating-point number type.
+    """)
+
+add_newdoc_for_scalar_type('single', [],
+    """
+    Single-precision floating-point number type, compatible with C ``float``.
+    """)
+
+add_newdoc_for_scalar_type('double', [],
+    """
+    Double-precision floating-point number type, compatible with Python
+    :class:`float` and C ``double``.
+    """)
+
+add_newdoc_for_scalar_type('longdouble', [],
+    """
+    Extended-precision floating-point number type, compatible with C
+    ``long double`` but not necessarily with IEEE 754 quadruple-precision.
+    """)
+
+add_newdoc_for_scalar_type('csingle', [],
+    """
+    Complex number type composed of two single-precision floating-point
+    numbers.
+    """)
+
+add_newdoc_for_scalar_type('cdouble', [],
+    """
+    Complex number type composed of two double-precision floating-point
+    numbers, compatible with Python :class:`complex`.
+    """)
+
+add_newdoc_for_scalar_type('clongdouble', [],
+    """
+    Complex number type composed of two extended-precision floating-point
+    numbers.
+    """)
+
+add_newdoc_for_scalar_type('object_', [],
+    """
+    Any Python object.
+    """)
+
+add_newdoc_for_scalar_type('str_', [],
+    r"""
+    A unicode string.
+
+    This type strips trailing null codepoints.
+
+    >>> s = np.str_("abc\x00")
+    >>> s
+    'abc'
+
+    Unlike the builtin :class:`str`, this supports the
+    :ref:`python:bufferobjects`, exposing its contents as UCS4:
+
+    >>> m = memoryview(np.str_("abc"))
+    >>> m.format
+    '3w'
+    >>> m.tobytes()
+    b'a\x00\x00\x00b\x00\x00\x00c\x00\x00\x00'
+    """)
+
+add_newdoc_for_scalar_type('bytes_', [],
+    r"""
+    A byte string.
+
+    When used in arrays, this type strips trailing null bytes.
+    """)
+
+add_newdoc_for_scalar_type('void', [],
+    r"""
+    np.void(length_or_data, /, dtype=None)
+
+    Create a new structured or unstructured void scalar.
+
+    Parameters
+    ----------
+    length_or_data : int, array-like, bytes-like, object
+       One of multiple meanings (see notes).  The length or
+       bytes data of an unstructured void.  Or alternatively,
+       the data to be stored in the new scalar when `dtype`
+       is provided.
+       This can be an array-like, in which case an array may
+       be returned.
+    dtype : dtype, optional
+       If provided the dtype of the new scalar.  This dtype must
+       be "void" dtype (i.e. a structured or unstructured void,
+       see also :ref:`defining-structured-types`).
+
+       .. versionadded:: 1.24
+
+    Notes
+    -----
+    For historical reasons and because void scalars can represent both
+    arbitrary byte data and structured dtypes, the void constructor
+    has three calling conventions:
+
+    1. ``np.void(5)`` creates a ``dtype="V5"`` scalar filled with five
+       ``\0`` bytes.  The 5 can be a Python or NumPy integer.
+    2. ``np.void(b"bytes-like")`` creates a void scalar from the byte string.
+       The dtype itemsize will match the byte string length, here ``"V10"``.
+    3. When a ``dtype=`` is passed the call is roughly the same as an
+       array creation.  However, a void scalar rather than array is returned.
+
+    Please see the examples which show all three different conventions.
+
+    Examples
+    --------
+    >>> np.void(5)
+    np.void(b'\x00\x00\x00\x00\x00')
+    >>> np.void(b'abcd')
+    np.void(b'\x61\x62\x63\x64')
+    >>> np.void((3.2, b'eggs'), dtype="d,S5")
+    np.void((3.2, b'eggs'), dtype=[('f0', '<f8'), ('f1', 'S5')])
+    >>> np.void(3, dtype=[('x', np.int8), ('y', np.int8)])
+    np.void((3, 3), dtype=[('x', 'i1'), ('y', 'i1')])
+
+    """)
+
+add_newdoc_for_scalar_type('datetime64', [],
+    """
+    If created from a 64-bit integer, it represents an offset from
+    ``1970-01-01T00:00:00``.
+    If created from string, the string can be in ISO 8601 date
+    or datetime format.
+
+    When parsing a string to create a datetime object, if the string contains
+    a trailing timezone (A 'Z' or a timezone offset), the timezone will be
+    dropped and a User Warning is given.
+
+    Datetime64 objects should be considered to be UTC and therefore have an
+    offset of +0000.
+
+    >>> np.datetime64(10, 'Y')
+    np.datetime64('1980')
+    >>> np.datetime64('1980', 'Y')
+    np.datetime64('1980')
+    >>> np.datetime64(10, 'D')
+    np.datetime64('1970-01-11')
+
+    See :ref:`arrays.datetime` for more information.
+    """)
+
+add_newdoc_for_scalar_type('timedelta64', [],
+    """
+    A timedelta stored as a 64-bit integer.
+
+    See :ref:`arrays.datetime` for more information.
+    """)
+
+add_newdoc('numpy._core.numerictypes', "integer", ('is_integer',
+    """
+    integer.is_integer() -> bool
+
+    Return ``True`` if the number is finite with integral value.
+
+    .. versionadded:: 1.22
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.int64(-2).is_integer()
+    True
+    >>> np.uint32(5).is_integer()
+    True
+    """))
+
+# TODO: work out how to put this on the base class, np.floating
+for float_name in ('half', 'single', 'double', 'longdouble'):
+    add_newdoc('numpy._core.numerictypes', float_name, ('as_integer_ratio',
+        f"""
+        {float_name}.as_integer_ratio() -> (int, int)
+
+        Return a pair of integers, whose ratio is exactly equal to the original
+        floating point number, and with a positive denominator.
+        Raise `OverflowError` on infinities and a `ValueError` on NaNs.
+
+        >>> np.{float_name}(10.0).as_integer_ratio()
+        (10, 1)
+        >>> np.{float_name}(0.0).as_integer_ratio()
+        (0, 1)
+        >>> np.{float_name}(-.25).as_integer_ratio()
+        (-1, 4)
+        """))
+
+    add_newdoc('numpy._core.numerictypes', float_name, ('is_integer',
+        f"""
+        {float_name}.is_integer() -> bool
+
+        Return ``True`` if the floating point number is finite with integral
+        value, and ``False`` otherwise.
+
+        .. versionadded:: 1.22
+
+        Examples
+        --------
+        >>> np.{float_name}(-2.0).is_integer()
+        True
+        >>> np.{float_name}(3.2).is_integer()
+        False
+        """))
+
+for int_name in ('int8', 'uint8', 'int16', 'uint16', 'int32', 'uint32',
+        'int64', 'uint64', 'int64', 'uint64', 'int64', 'uint64'):
+    # Add negative examples for signed cases by checking typecode
+    add_newdoc('numpy._core.numerictypes', int_name, ('bit_count',
+        f"""
+        {int_name}.bit_count() -> int
+
+        Computes the number of 1-bits in the absolute value of the input.
+        Analogous to the builtin `int.bit_count` or ``popcount`` in C++.
+
+        Examples
+        --------
+        >>> np.{int_name}(127).bit_count()
+        7""" +
+        (f"""
+        >>> np.{int_name}(-127).bit_count()
+        7
+        """ if dtype(int_name).char.islower() else "")))
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs_scalars.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs_scalars.pyi
new file mode 100644
index 0000000..4a06c9b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_add_newdocs_scalars.pyi
@@ -0,0 +1,16 @@
+from collections.abc import Iterable
+from typing import Final
+
+import numpy as np
+
+possible_aliases: Final[list[tuple[type[np.number], str, str]]] = ...
+_system: Final[str] = ...
+_machine: Final[str] = ...
+_doc_alias_string: Final[str] = ...
+_bool_docstring: Final[str] = ...
+int_name: str = ...
+float_name: str = ...
+
+def numeric_type_aliases(aliases: list[tuple[str, str]]) -> list[tuple[type[np.number], str, str]]: ...
+def add_newdoc_for_scalar_type(obj: str, fixed_aliases: Iterable[str], doc: str) -> None: ...
+def _get_platform_and_machine() -> tuple[str, str]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_asarray.py b/.venv/lib/python3.12/site-packages/numpy/_core/_asarray.py
new file mode 100644
index 0000000..613c5cf
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_asarray.py
@@ -0,0 +1,134 @@
+"""
+Functions in the ``as*array`` family that promote array-likes into arrays.
+
+`require` fits this category despite its name not matching this pattern.
+"""
+from .multiarray import array, asanyarray
+from .overrides import (
+    array_function_dispatch,
+    finalize_array_function_like,
+    set_module,
+)
+
+__all__ = ["require"]
+
+
+POSSIBLE_FLAGS = {
+    'C': 'C', 'C_CONTIGUOUS': 'C', 'CONTIGUOUS': 'C',
+    'F': 'F', 'F_CONTIGUOUS': 'F', 'FORTRAN': 'F',
+    'A': 'A', 'ALIGNED': 'A',
+    'W': 'W', 'WRITEABLE': 'W',
+    'O': 'O', 'OWNDATA': 'O',
+    'E': 'E', 'ENSUREARRAY': 'E'
+}
+
+
+@finalize_array_function_like
+@set_module('numpy')
+def require(a, dtype=None, requirements=None, *, like=None):
+    """
+    Return an ndarray of the provided type that satisfies requirements.
+
+    This function is useful to be sure that an array with the correct flags
+    is returned for passing to compiled code (perhaps through ctypes).
+
+    Parameters
+    ----------
+    a : array_like
+       The object to be converted to a type-and-requirement-satisfying array.
+    dtype : data-type
+       The required data-type. If None preserve the current dtype. If your
+       application requires the data to be in native byteorder, include
+       a byteorder specification as a part of the dtype specification.
+    requirements : str or sequence of str
+       The requirements list can be any of the following
+
+       * 'F_CONTIGUOUS' ('F') - ensure a Fortran-contiguous array
+       * 'C_CONTIGUOUS' ('C') - ensure a C-contiguous array
+       * 'ALIGNED' ('A')      - ensure a data-type aligned array
+       * 'WRITEABLE' ('W')    - ensure a writable array
+       * 'OWNDATA' ('O')      - ensure an array that owns its own data
+       * 'ENSUREARRAY', ('E') - ensure a base array, instead of a subclass
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        Array with specified requirements and type if given.
+
+    See Also
+    --------
+    asarray : Convert input to an ndarray.
+    asanyarray : Convert to an ndarray, but pass through ndarray subclasses.
+    ascontiguousarray : Convert input to a contiguous array.
+    asfortranarray : Convert input to an ndarray with column-major
+                     memory order.
+    ndarray.flags : Information about the memory layout of the array.
+
+    Notes
+    -----
+    The returned array will be guaranteed to have the listed requirements
+    by making a copy if needed.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6).reshape(2,3)
+    >>> x.flags
+      C_CONTIGUOUS : True
+      F_CONTIGUOUS : False
+      OWNDATA : False
+      WRITEABLE : True
+      ALIGNED : True
+      WRITEBACKIFCOPY : False
+
+    >>> y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F'])
+    >>> y.flags
+      C_CONTIGUOUS : False
+      F_CONTIGUOUS : True
+      OWNDATA : True
+      WRITEABLE : True
+      ALIGNED : True
+      WRITEBACKIFCOPY : False
+
+    """
+    if like is not None:
+        return _require_with_like(
+            like,
+            a,
+            dtype=dtype,
+            requirements=requirements,
+        )
+
+    if not requirements:
+        return asanyarray(a, dtype=dtype)
+
+    requirements = {POSSIBLE_FLAGS[x.upper()] for x in requirements}
+
+    if 'E' in requirements:
+        requirements.remove('E')
+        subok = False
+    else:
+        subok = True
+
+    order = 'A'
+    if requirements >= {'C', 'F'}:
+        raise ValueError('Cannot specify both "C" and "F" order')
+    elif 'F' in requirements:
+        order = 'F'
+        requirements.remove('F')
+    elif 'C' in requirements:
+        order = 'C'
+        requirements.remove('C')
+
+    arr = array(a, dtype=dtype, order=order, copy=None, subok=subok)
+
+    for prop in requirements:
+        if not arr.flags[prop]:
+            return arr.copy(order)
+    return arr
+
+
+_require_with_like = array_function_dispatch()(require)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_asarray.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_asarray.pyi
new file mode 100644
index 0000000..a4bee00
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_asarray.pyi
@@ -0,0 +1,41 @@
+from collections.abc import Iterable
+from typing import Any, Literal, TypeAlias, TypeVar, overload
+
+from numpy._typing import DTypeLike, NDArray, _SupportsArrayFunc
+
+_ArrayT = TypeVar("_ArrayT", bound=NDArray[Any])
+
+_Requirements: TypeAlias = Literal[
+    "C", "C_CONTIGUOUS", "CONTIGUOUS",
+    "F", "F_CONTIGUOUS", "FORTRAN",
+    "A", "ALIGNED",
+    "W", "WRITEABLE",
+    "O", "OWNDATA"
+]
+_E: TypeAlias = Literal["E", "ENSUREARRAY"]
+_RequirementsWithE: TypeAlias = _Requirements | _E
+
+@overload
+def require(
+    a: _ArrayT,
+    dtype: None = ...,
+    requirements: _Requirements | Iterable[_Requirements] | None = ...,
+    *,
+    like: _SupportsArrayFunc = ...
+) -> _ArrayT: ...
+@overload
+def require(
+    a: object,
+    dtype: DTypeLike = ...,
+    requirements: _E | Iterable[_RequirementsWithE] = ...,
+    *,
+    like: _SupportsArrayFunc = ...
+) -> NDArray[Any]: ...
+@overload
+def require(
+    a: object,
+    dtype: DTypeLike = ...,
+    requirements: _Requirements | Iterable[_Requirements] | None = ...,
+    *,
+    like: _SupportsArrayFunc = ...
+) -> NDArray[Any]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_dtype.py b/.venv/lib/python3.12/site-packages/numpy/_core/_dtype.py
new file mode 100644
index 0000000..6a8a091
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_dtype.py
@@ -0,0 +1,366 @@
+"""
+A place for code to be called from the implementation of np.dtype
+
+String handling is much easier to do correctly in python.
+"""
+import numpy as np
+
+_kind_to_stem = {
+    'u': 'uint',
+    'i': 'int',
+    'c': 'complex',
+    'f': 'float',
+    'b': 'bool',
+    'V': 'void',
+    'O': 'object',
+    'M': 'datetime',
+    'm': 'timedelta',
+    'S': 'bytes',
+    'U': 'str',
+}
+
+
+def _kind_name(dtype):
+    try:
+        return _kind_to_stem[dtype.kind]
+    except KeyError as e:
+        raise RuntimeError(
+            f"internal dtype error, unknown kind {dtype.kind!r}"
+        ) from None
+
+
+def __str__(dtype):
+    if dtype.fields is not None:
+        return _struct_str(dtype, include_align=True)
+    elif dtype.subdtype:
+        return _subarray_str(dtype)
+    elif issubclass(dtype.type, np.flexible) or not dtype.isnative:
+        return dtype.str
+    else:
+        return dtype.name
+
+
+def __repr__(dtype):
+    arg_str = _construction_repr(dtype, include_align=False)
+    if dtype.isalignedstruct:
+        arg_str = arg_str + ", align=True"
+    return f"dtype({arg_str})"
+
+
+def _unpack_field(dtype, offset, title=None):
+    """
+    Helper function to normalize the items in dtype.fields.
+
+    Call as:
+
+    dtype, offset, title = _unpack_field(*dtype.fields[name])
+    """
+    return dtype, offset, title
+
+
+def _isunsized(dtype):
+    # PyDataType_ISUNSIZED
+    return dtype.itemsize == 0
+
+
+def _construction_repr(dtype, include_align=False, short=False):
+    """
+    Creates a string repr of the dtype, excluding the 'dtype()' part
+    surrounding the object. This object may be a string, a list, or
+    a dict depending on the nature of the dtype. This
+    is the object passed as the first parameter to the dtype
+    constructor, and if no additional constructor parameters are
+    given, will reproduce the exact memory layout.
+
+    Parameters
+    ----------
+    short : bool
+        If true, this creates a shorter repr using 'kind' and 'itemsize',
+        instead of the longer type name.
+
+    include_align : bool
+        If true, this includes the 'align=True' parameter
+        inside the struct dtype construction dict when needed. Use this flag
+        if you want a proper repr string without the 'dtype()' part around it.
+
+        If false, this does not preserve the
+        'align=True' parameter or sticky NPY_ALIGNED_STRUCT flag for
+        struct arrays like the regular repr does, because the 'align'
+        flag is not part of first dtype constructor parameter. This
+        mode is intended for a full 'repr', where the 'align=True' is
+        provided as the second parameter.
+    """
+    if dtype.fields is not None:
+        return _struct_str(dtype, include_align=include_align)
+    elif dtype.subdtype:
+        return _subarray_str(dtype)
+    else:
+        return _scalar_str(dtype, short=short)
+
+
+def _scalar_str(dtype, short):
+    byteorder = _byte_order_str(dtype)
+
+    if dtype.type == np.bool:
+        if short:
+            return "'?'"
+        else:
+            return "'bool'"
+
+    elif dtype.type == np.object_:
+        # The object reference may be different sizes on different
+        # platforms, so it should never include the itemsize here.
+        return "'O'"
+
+    elif dtype.type == np.bytes_:
+        if _isunsized(dtype):
+            return "'S'"
+        else:
+            return "'S%d'" % dtype.itemsize
+
+    elif dtype.type == np.str_:
+        if _isunsized(dtype):
+            return f"'{byteorder}U'"
+        else:
+            return "'%sU%d'" % (byteorder, dtype.itemsize / 4)
+
+    elif dtype.type == str:
+        return "'T'"
+
+    elif not type(dtype)._legacy:
+        return f"'{byteorder}{type(dtype).__name__}{dtype.itemsize * 8}'"
+
+    # unlike the other types, subclasses of void are preserved - but
+    # historically the repr does not actually reveal the subclass
+    elif issubclass(dtype.type, np.void):
+        if _isunsized(dtype):
+            return "'V'"
+        else:
+            return "'V%d'" % dtype.itemsize
+
+    elif dtype.type == np.datetime64:
+        return f"'{byteorder}M8{_datetime_metadata_str(dtype)}'"
+
+    elif dtype.type == np.timedelta64:
+        return f"'{byteorder}m8{_datetime_metadata_str(dtype)}'"
+
+    elif dtype.isbuiltin == 2:
+        return dtype.type.__name__
+
+    elif np.issubdtype(dtype, np.number):
+        # Short repr with endianness, like '<f8'
+        if short or dtype.byteorder not in ('=', '|'):
+            return "'%s%c%d'" % (byteorder, dtype.kind, dtype.itemsize)
+
+        # Longer repr, like 'float64'
+        else:
+            return "'%s%d'" % (_kind_name(dtype), 8 * dtype.itemsize)
+
+    else:
+        raise RuntimeError(
+            "Internal error: NumPy dtype unrecognized type number")
+
+
+def _byte_order_str(dtype):
+    """ Normalize byteorder to '<' or '>' """
+    # hack to obtain the native and swapped byte order characters
+    swapped = np.dtype(int).newbyteorder('S')
+    native = swapped.newbyteorder('S')
+
+    byteorder = dtype.byteorder
+    if byteorder == '=':
+        return native.byteorder
+    if byteorder == 'S':
+        # TODO: this path can never be reached
+        return swapped.byteorder
+    elif byteorder == '|':
+        return ''
+    else:
+        return byteorder
+
+
+def _datetime_metadata_str(dtype):
+    # TODO: this duplicates the C metastr_to_unicode functionality
+    unit, count = np.datetime_data(dtype)
+    if unit == 'generic':
+        return ''
+    elif count == 1:
+        return f'[{unit}]'
+    else:
+        return f'[{count}{unit}]'
+
+
+def _struct_dict_str(dtype, includealignedflag):
+    # unpack the fields dictionary into ls
+    names = dtype.names
+    fld_dtypes = []
+    offsets = []
+    titles = []
+    for name in names:
+        fld_dtype, offset, title = _unpack_field(*dtype.fields[name])
+        fld_dtypes.append(fld_dtype)
+        offsets.append(offset)
+        titles.append(title)
+
+    # Build up a string to make the dictionary
+
+    if np._core.arrayprint._get_legacy_print_mode() <= 121:
+        colon = ":"
+        fieldsep = ","
+    else:
+        colon = ": "
+        fieldsep = ", "
+
+    # First, the names
+    ret = "{'names'%s[" % colon
+    ret += fieldsep.join(repr(name) for name in names)
+
+    # Second, the formats
+    ret += f"], 'formats'{colon}["
+    ret += fieldsep.join(
+        _construction_repr(fld_dtype, short=True) for fld_dtype in fld_dtypes)
+
+    # Third, the offsets
+    ret += f"], 'offsets'{colon}["
+    ret += fieldsep.join("%d" % offset for offset in offsets)
+
+    # Fourth, the titles
+    if any(title is not None for title in titles):
+        ret += f"], 'titles'{colon}["
+        ret += fieldsep.join(repr(title) for title in titles)
+
+    # Fifth, the itemsize
+    ret += "], 'itemsize'%s%d" % (colon, dtype.itemsize)
+
+    if (includealignedflag and dtype.isalignedstruct):
+        # Finally, the aligned flag
+        ret += ", 'aligned'%sTrue}" % colon
+    else:
+        ret += "}"
+
+    return ret
+
+
+def _aligned_offset(offset, alignment):
+    # round up offset:
+    return - (-offset // alignment) * alignment
+
+
+def _is_packed(dtype):
+    """
+    Checks whether the structured data type in 'dtype'
+    has a simple layout, where all the fields are in order,
+    and follow each other with no alignment padding.
+
+    When this returns true, the dtype can be reconstructed
+    from a list of the field names and dtypes with no additional
+    dtype parameters.
+
+    Duplicates the C `is_dtype_struct_simple_unaligned_layout` function.
+    """
+    align = dtype.isalignedstruct
+    max_alignment = 1
+    total_offset = 0
+    for name in dtype.names:
+        fld_dtype, fld_offset, title = _unpack_field(*dtype.fields[name])
+
+        if align:
+            total_offset = _aligned_offset(total_offset, fld_dtype.alignment)
+            max_alignment = max(max_alignment, fld_dtype.alignment)
+
+        if fld_offset != total_offset:
+            return False
+        total_offset += fld_dtype.itemsize
+
+    if align:
+        total_offset = _aligned_offset(total_offset, max_alignment)
+
+    return total_offset == dtype.itemsize
+
+
+def _struct_list_str(dtype):
+    items = []
+    for name in dtype.names:
+        fld_dtype, fld_offset, title = _unpack_field(*dtype.fields[name])
+
+        item = "("
+        if title is not None:
+            item += f"({title!r}, {name!r}), "
+        else:
+            item += f"{name!r}, "
+        # Special case subarray handling here
+        if fld_dtype.subdtype is not None:
+            base, shape = fld_dtype.subdtype
+            item += f"{_construction_repr(base, short=True)}, {shape}"
+        else:
+            item += _construction_repr(fld_dtype, short=True)
+
+        item += ")"
+        items.append(item)
+
+    return "[" + ", ".join(items) + "]"
+
+
+def _struct_str(dtype, include_align):
+    # The list str representation can't include the 'align=' flag,
+    # so if it is requested and the struct has the aligned flag set,
+    # we must use the dict str instead.
+    if not (include_align and dtype.isalignedstruct) and _is_packed(dtype):
+        sub = _struct_list_str(dtype)
+
+    else:
+        sub = _struct_dict_str(dtype, include_align)
+
+    # If the data type isn't the default, void, show it
+    if dtype.type != np.void:
+        return f"({dtype.type.__module__}.{dtype.type.__name__}, {sub})"
+    else:
+        return sub
+
+
+def _subarray_str(dtype):
+    base, shape = dtype.subdtype
+    return f"({_construction_repr(base, short=True)}, {shape})"
+
+
+def _name_includes_bit_suffix(dtype):
+    if dtype.type == np.object_:
+        # pointer size varies by system, best to omit it
+        return False
+    elif dtype.type == np.bool:
+        # implied
+        return False
+    elif dtype.type is None:
+        return True
+    elif np.issubdtype(dtype, np.flexible) and _isunsized(dtype):
+        # unspecified
+        return False
+    else:
+        return True
+
+
+def _name_get(dtype):
+    # provides dtype.name.__get__, documented as returning a "bit name"
+
+    if dtype.isbuiltin == 2:
+        # user dtypes don't promise to do anything special
+        return dtype.type.__name__
+
+    if not type(dtype)._legacy:
+        name = type(dtype).__name__
+
+    elif issubclass(dtype.type, np.void):
+        # historically, void subclasses preserve their name, eg `record64`
+        name = dtype.type.__name__
+    else:
+        name = _kind_name(dtype)
+
+    # append bit counts
+    if _name_includes_bit_suffix(dtype):
+        name += f"{dtype.itemsize * 8}"
+
+    # append metadata to datetimes
+    if dtype.type in (np.datetime64, np.timedelta64):
+        name += _datetime_metadata_str(dtype)
+
+    return name
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_dtype.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_dtype.pyi
new file mode 100644
index 0000000..6cdd77b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_dtype.pyi
@@ -0,0 +1,58 @@
+from typing import Final, TypeAlias, TypedDict, overload, type_check_only
+from typing import Literal as L
+
+from typing_extensions import ReadOnly, TypeVar
+
+import numpy as np
+
+###
+
+_T = TypeVar("_T")
+
+_Name: TypeAlias = L["uint", "int", "complex", "float", "bool", "void", "object", "datetime", "timedelta", "bytes", "str"]
+
+@type_check_only
+class _KindToStemType(TypedDict):
+    u: ReadOnly[L["uint"]]
+    i: ReadOnly[L["int"]]
+    c: ReadOnly[L["complex"]]
+    f: ReadOnly[L["float"]]
+    b: ReadOnly[L["bool"]]
+    V: ReadOnly[L["void"]]
+    O: ReadOnly[L["object"]]
+    M: ReadOnly[L["datetime"]]
+    m: ReadOnly[L["timedelta"]]
+    S: ReadOnly[L["bytes"]]
+    U: ReadOnly[L["str"]]
+
+###
+
+_kind_to_stem: Final[_KindToStemType] = ...
+
+#
+def _kind_name(dtype: np.dtype) -> _Name: ...
+def __str__(dtype: np.dtype) -> str: ...
+def __repr__(dtype: np.dtype) -> str: ...
+
+#
+def _isunsized(dtype: np.dtype) -> bool: ...
+def _is_packed(dtype: np.dtype) -> bool: ...
+def _name_includes_bit_suffix(dtype: np.dtype) -> bool: ...
+
+#
+def _construction_repr(dtype: np.dtype, include_align: bool = False, short: bool = False) -> str: ...
+def _scalar_str(dtype: np.dtype, short: bool) -> str: ...
+def _byte_order_str(dtype: np.dtype) -> str: ...
+def _datetime_metadata_str(dtype: np.dtype) -> str: ...
+def _struct_dict_str(dtype: np.dtype, includealignedflag: bool) -> str: ...
+def _struct_list_str(dtype: np.dtype) -> str: ...
+def _struct_str(dtype: np.dtype, include_align: bool) -> str: ...
+def _subarray_str(dtype: np.dtype) -> str: ...
+def _name_get(dtype: np.dtype) -> str: ...
+
+#
+@overload
+def _unpack_field(dtype: np.dtype, offset: int, title: _T) -> tuple[np.dtype, int, _T]: ...
+@overload
+def _unpack_field(dtype: np.dtype, offset: int, title: None = None) -> tuple[np.dtype, int, None]: ...
+def _aligned_offset(offset: int, alignment: int) -> int: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_dtype_ctypes.py b/.venv/lib/python3.12/site-packages/numpy/_core/_dtype_ctypes.py
new file mode 100644
index 0000000..4de6df6
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_dtype_ctypes.py
@@ -0,0 +1,120 @@
+"""
+Conversion from ctypes to dtype.
+
+In an ideal world, we could achieve this through the PEP3118 buffer protocol,
+something like::
+
+    def dtype_from_ctypes_type(t):
+        # needed to ensure that the shape of `t` is within memoryview.format
+        class DummyStruct(ctypes.Structure):
+            _fields_ = [('a', t)]
+
+        # empty to avoid memory allocation
+        ctype_0 = (DummyStruct * 0)()
+        mv = memoryview(ctype_0)
+
+        # convert the struct, and slice back out the field
+        return _dtype_from_pep3118(mv.format)['a']
+
+Unfortunately, this fails because:
+
+* ctypes cannot handle length-0 arrays with PEP3118 (bpo-32782)
+* PEP3118 cannot represent unions, but both numpy and ctypes can
+* ctypes cannot handle big-endian structs with PEP3118 (bpo-32780)
+"""
+
+# We delay-import ctypes for distributions that do not include it.
+# While this module is not used unless the user passes in ctypes
+# members, it is eagerly imported from numpy/_core/__init__.py.
+import numpy as np
+
+
+def _from_ctypes_array(t):
+    return np.dtype((dtype_from_ctypes_type(t._type_), (t._length_,)))
+
+
+def _from_ctypes_structure(t):
+    for item in t._fields_:
+        if len(item) > 2:
+            raise TypeError(
+                "ctypes bitfields have no dtype equivalent")
+
+    if hasattr(t, "_pack_"):
+        import ctypes
+        formats = []
+        offsets = []
+        names = []
+        current_offset = 0
+        for fname, ftyp in t._fields_:
+            names.append(fname)
+            formats.append(dtype_from_ctypes_type(ftyp))
+            # Each type has a default offset, this is platform dependent
+            # for some types.
+            effective_pack = min(t._pack_, ctypes.alignment(ftyp))
+            current_offset = (
+                (current_offset + effective_pack - 1) // effective_pack
+            ) * effective_pack
+            offsets.append(current_offset)
+            current_offset += ctypes.sizeof(ftyp)
+
+        return np.dtype({
+            "formats": formats,
+            "offsets": offsets,
+            "names": names,
+            "itemsize": ctypes.sizeof(t)})
+    else:
+        fields = []
+        for fname, ftyp in t._fields_:
+            fields.append((fname, dtype_from_ctypes_type(ftyp)))
+
+        # by default, ctypes structs are aligned
+        return np.dtype(fields, align=True)
+
+
+def _from_ctypes_scalar(t):
+    """
+    Return the dtype type with endianness included if it's the case
+    """
+    if getattr(t, '__ctype_be__', None) is t:
+        return np.dtype('>' + t._type_)
+    elif getattr(t, '__ctype_le__', None) is t:
+        return np.dtype('<' + t._type_)
+    else:
+        return np.dtype(t._type_)
+
+
+def _from_ctypes_union(t):
+    import ctypes
+    formats = []
+    offsets = []
+    names = []
+    for fname, ftyp in t._fields_:
+        names.append(fname)
+        formats.append(dtype_from_ctypes_type(ftyp))
+        offsets.append(0)  # Union fields are offset to 0
+
+    return np.dtype({
+        "formats": formats,
+        "offsets": offsets,
+        "names": names,
+        "itemsize": ctypes.sizeof(t)})
+
+
+def dtype_from_ctypes_type(t):
+    """
+    Construct a dtype object from a ctypes type
+    """
+    import _ctypes
+    if issubclass(t, _ctypes.Array):
+        return _from_ctypes_array(t)
+    elif issubclass(t, _ctypes._Pointer):
+        raise TypeError("ctypes pointers have no dtype equivalent")
+    elif issubclass(t, _ctypes.Structure):
+        return _from_ctypes_structure(t)
+    elif issubclass(t, _ctypes.Union):
+        return _from_ctypes_union(t)
+    elif isinstance(getattr(t, '_type_', None), str):
+        return _from_ctypes_scalar(t)
+    else:
+        raise NotImplementedError(
+            f"Unknown ctypes type {t.__name__}")
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_dtype_ctypes.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_dtype_ctypes.pyi
new file mode 100644
index 0000000..69438a2
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_dtype_ctypes.pyi
@@ -0,0 +1,83 @@
+import _ctypes
+import ctypes as ct
+from typing import Any, overload
+
+import numpy as np
+
+#
+@overload
+def dtype_from_ctypes_type(t: type[_ctypes.Array[Any] | _ctypes.Structure]) -> np.dtype[np.void]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_bool]) -> np.dtype[np.bool]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_int8 | ct.c_byte]) -> np.dtype[np.int8]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_uint8 | ct.c_ubyte]) -> np.dtype[np.uint8]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_int16 | ct.c_short]) -> np.dtype[np.int16]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_uint16 | ct.c_ushort]) -> np.dtype[np.uint16]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_int32 | ct.c_int]) -> np.dtype[np.int32]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_uint32 | ct.c_uint]) -> np.dtype[np.uint32]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_ssize_t | ct.c_long]) -> np.dtype[np.int32 | np.int64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_size_t | ct.c_ulong]) -> np.dtype[np.uint32 | np.uint64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_int64 | ct.c_longlong]) -> np.dtype[np.int64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_uint64 | ct.c_ulonglong]) -> np.dtype[np.uint64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_float]) -> np.dtype[np.float32]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_double]) -> np.dtype[np.float64]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_longdouble]) -> np.dtype[np.longdouble]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.c_char]) -> np.dtype[np.bytes_]: ...
+@overload
+def dtype_from_ctypes_type(t: type[ct.py_object[Any]]) -> np.dtype[np.object_]: ...
+
+# NOTE: the complex ctypes on python>=3.14 are not yet supported at runtim, see
+# https://github.com/numpy/numpy/issues/28360
+
+#
+def _from_ctypes_array(t: type[_ctypes.Array[Any]]) -> np.dtype[np.void]: ...
+def _from_ctypes_structure(t: type[_ctypes.Structure]) -> np.dtype[np.void]: ...
+def _from_ctypes_union(t: type[_ctypes.Union]) -> np.dtype[np.void]: ...
+
+# keep in sync with `dtype_from_ctypes_type` (minus the first overload)
+@overload
+def _from_ctypes_scalar(t: type[ct.c_bool]) -> np.dtype[np.bool]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_int8 | ct.c_byte]) -> np.dtype[np.int8]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_uint8 | ct.c_ubyte]) -> np.dtype[np.uint8]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_int16 | ct.c_short]) -> np.dtype[np.int16]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_uint16 | ct.c_ushort]) -> np.dtype[np.uint16]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_int32 | ct.c_int]) -> np.dtype[np.int32]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_uint32 | ct.c_uint]) -> np.dtype[np.uint32]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_ssize_t | ct.c_long]) -> np.dtype[np.int32 | np.int64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_size_t | ct.c_ulong]) -> np.dtype[np.uint32 | np.uint64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_int64 | ct.c_longlong]) -> np.dtype[np.int64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_uint64 | ct.c_ulonglong]) -> np.dtype[np.uint64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_float]) -> np.dtype[np.float32]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_double]) -> np.dtype[np.float64]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_longdouble]) -> np.dtype[np.longdouble]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.c_char]) -> np.dtype[np.bytes_]: ...
+@overload
+def _from_ctypes_scalar(t: type[ct.py_object[Any]]) -> np.dtype[np.object_]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_exceptions.py b/.venv/lib/python3.12/site-packages/numpy/_core/_exceptions.py
new file mode 100644
index 0000000..73b07d2
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_exceptions.py
@@ -0,0 +1,162 @@
+"""
+Various richly-typed exceptions, that also help us deal with string formatting
+in python where it's easier.
+
+By putting the formatting in `__str__`, we also avoid paying the cost for
+users who silence the exceptions.
+"""
+
+def _unpack_tuple(tup):
+    if len(tup) == 1:
+        return tup[0]
+    else:
+        return tup
+
+
+def _display_as_base(cls):
+    """
+    A decorator that makes an exception class look like its base.
+
+    We use this to hide subclasses that are implementation details - the user
+    should catch the base type, which is what the traceback will show them.
+
+    Classes decorated with this decorator are subject to removal without a
+    deprecation warning.
+    """
+    assert issubclass(cls, Exception)
+    cls.__name__ = cls.__base__.__name__
+    return cls
+
+
+class UFuncTypeError(TypeError):
+    """ Base class for all ufunc exceptions """
+    def __init__(self, ufunc):
+        self.ufunc = ufunc
+
+
+@_display_as_base
+class _UFuncNoLoopError(UFuncTypeError):
+    """ Thrown when a ufunc loop cannot be found """
+    def __init__(self, ufunc, dtypes):
+        super().__init__(ufunc)
+        self.dtypes = tuple(dtypes)
+
+    def __str__(self):
+        return (
+            f"ufunc {self.ufunc.__name__!r} did not contain a loop with signature "
+            f"matching types {_unpack_tuple(self.dtypes[:self.ufunc.nin])!r} "
+            f"-> {_unpack_tuple(self.dtypes[self.ufunc.nin:])!r}"
+        )
+
+
+@_display_as_base
+class _UFuncBinaryResolutionError(_UFuncNoLoopError):
+    """ Thrown when a binary resolution fails """
+    def __init__(self, ufunc, dtypes):
+        super().__init__(ufunc, dtypes)
+        assert len(self.dtypes) == 2
+
+    def __str__(self):
+        return (
+            "ufunc {!r} cannot use operands with types {!r} and {!r}"
+        ).format(
+            self.ufunc.__name__, *self.dtypes
+        )
+
+
+@_display_as_base
+class _UFuncCastingError(UFuncTypeError):
+    def __init__(self, ufunc, casting, from_, to):
+        super().__init__(ufunc)
+        self.casting = casting
+        self.from_ = from_
+        self.to = to
+
+
+@_display_as_base
+class _UFuncInputCastingError(_UFuncCastingError):
+    """ Thrown when a ufunc input cannot be casted """
+    def __init__(self, ufunc, casting, from_, to, i):
+        super().__init__(ufunc, casting, from_, to)
+        self.in_i = i
+
+    def __str__(self):
+        # only show the number if more than one input exists
+        i_str = f"{self.in_i} " if self.ufunc.nin != 1 else ""
+        return (
+            f"Cannot cast ufunc {self.ufunc.__name__!r} input {i_str}from "
+            f"{self.from_!r} to {self.to!r} with casting rule {self.casting!r}"
+        )
+
+
+@_display_as_base
+class _UFuncOutputCastingError(_UFuncCastingError):
+    """ Thrown when a ufunc output cannot be casted """
+    def __init__(self, ufunc, casting, from_, to, i):
+        super().__init__(ufunc, casting, from_, to)
+        self.out_i = i
+
+    def __str__(self):
+        # only show the number if more than one output exists
+        i_str = f"{self.out_i} " if self.ufunc.nout != 1 else ""
+        return (
+            f"Cannot cast ufunc {self.ufunc.__name__!r} output {i_str}from "
+            f"{self.from_!r} to {self.to!r} with casting rule {self.casting!r}"
+        )
+
+
+@_display_as_base
+class _ArrayMemoryError(MemoryError):
+    """ Thrown when an array cannot be allocated"""
+    def __init__(self, shape, dtype):
+        self.shape = shape
+        self.dtype = dtype
+
+    @property
+    def _total_size(self):
+        num_bytes = self.dtype.itemsize
+        for dim in self.shape:
+            num_bytes *= dim
+        return num_bytes
+
+    @staticmethod
+    def _size_to_string(num_bytes):
+        """ Convert a number of bytes into a binary size string """
+
+        # https://en.wikipedia.org/wiki/Binary_prefix
+        LOG2_STEP = 10
+        STEP = 1024
+        units = ['bytes', 'KiB', 'MiB', 'GiB', 'TiB', 'PiB', 'EiB']
+
+        unit_i = max(num_bytes.bit_length() - 1, 1) // LOG2_STEP
+        unit_val = 1 << (unit_i * LOG2_STEP)
+        n_units = num_bytes / unit_val
+        del unit_val
+
+        # ensure we pick a unit that is correct after rounding
+        if round(n_units) == STEP:
+            unit_i += 1
+            n_units /= STEP
+
+        # deal with sizes so large that we don't have units for them
+        if unit_i >= len(units):
+            new_unit_i = len(units) - 1
+            n_units *= 1 << ((unit_i - new_unit_i) * LOG2_STEP)
+            unit_i = new_unit_i
+
+        unit_name = units[unit_i]
+        # format with a sensible number of digits
+        if unit_i == 0:
+            # no decimal point on bytes
+            return f'{n_units:.0f} {unit_name}'
+        elif round(n_units) < 1000:
+            # 3 significant figures, if none are dropped to the left of the .
+            return f'{n_units:#.3g} {unit_name}'
+        else:
+            # just give all the digits otherwise
+            return f'{n_units:#.0f} {unit_name}'
+
+    def __str__(self):
+        size_str = self._size_to_string(self._total_size)
+        return (f"Unable to allocate {size_str} for an array with shape "
+                f"{self.shape} and data type {self.dtype}")
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_exceptions.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_exceptions.pyi
new file mode 100644
index 0000000..02637a1
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_exceptions.pyi
@@ -0,0 +1,55 @@
+from collections.abc import Iterable
+from typing import Any, Final, TypeVar, overload
+
+import numpy as np
+from numpy import _CastingKind
+from numpy._utils import set_module as set_module
+
+###
+
+_T = TypeVar("_T")
+_TupleT = TypeVar("_TupleT", bound=tuple[()] | tuple[Any, Any, *tuple[Any, ...]])
+_ExceptionT = TypeVar("_ExceptionT", bound=Exception)
+
+###
+
+class UFuncTypeError(TypeError):
+    ufunc: Final[np.ufunc]
+    def __init__(self, /, ufunc: np.ufunc) -> None: ...
+
+class _UFuncNoLoopError(UFuncTypeError):
+    dtypes: tuple[np.dtype, ...]
+    def __init__(self, /, ufunc: np.ufunc, dtypes: Iterable[np.dtype]) -> None: ...
+
+class _UFuncBinaryResolutionError(_UFuncNoLoopError):
+    dtypes: tuple[np.dtype, np.dtype]
+    def __init__(self, /, ufunc: np.ufunc, dtypes: Iterable[np.dtype]) -> None: ...
+
+class _UFuncCastingError(UFuncTypeError):
+    casting: Final[_CastingKind]
+    from_: Final[np.dtype]
+    to: Final[np.dtype]
+    def __init__(self, /, ufunc: np.ufunc, casting: _CastingKind, from_: np.dtype, to: np.dtype) -> None: ...
+
+class _UFuncInputCastingError(_UFuncCastingError):
+    in_i: Final[int]
+    def __init__(self, /, ufunc: np.ufunc, casting: _CastingKind, from_: np.dtype, to: np.dtype, i: int) -> None: ...
+
+class _UFuncOutputCastingError(_UFuncCastingError):
+    out_i: Final[int]
+    def __init__(self, /, ufunc: np.ufunc, casting: _CastingKind, from_: np.dtype, to: np.dtype, i: int) -> None: ...
+
+class _ArrayMemoryError(MemoryError):
+    shape: tuple[int, ...]
+    dtype: np.dtype
+    def __init__(self, /, shape: tuple[int, ...], dtype: np.dtype) -> None: ...
+    @property
+    def _total_size(self) -> int: ...
+    @staticmethod
+    def _size_to_string(num_bytes: int) -> str: ...
+
+@overload
+def _unpack_tuple(tup: tuple[_T]) -> _T: ...
+@overload
+def _unpack_tuple(tup: _TupleT) -> _TupleT: ...
+def _display_as_base(cls: type[_ExceptionT]) -> type[_ExceptionT]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_internal.py b/.venv/lib/python3.12/site-packages/numpy/_core/_internal.py
new file mode 100644
index 0000000..e00e1b2
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_internal.py
@@ -0,0 +1,958 @@
+"""
+A place for internal code
+
+Some things are more easily handled Python.
+
+"""
+import ast
+import math
+import re
+import sys
+import warnings
+
+from numpy import _NoValue
+from numpy.exceptions import DTypePromotionError
+
+from .multiarray import StringDType, array, dtype, promote_types
+
+try:
+    import ctypes
+except ImportError:
+    ctypes = None
+
+IS_PYPY = sys.implementation.name == 'pypy'
+
+if sys.byteorder == 'little':
+    _nbo = '<'
+else:
+    _nbo = '>'
+
+def _makenames_list(adict, align):
+    allfields = []
+
+    for fname, obj in adict.items():
+        n = len(obj)
+        if not isinstance(obj, tuple) or n not in (2, 3):
+            raise ValueError("entry not a 2- or 3- tuple")
+        if n > 2 and obj[2] == fname:
+            continue
+        num = int(obj[1])
+        if num < 0:
+            raise ValueError("invalid offset.")
+        format = dtype(obj[0], align=align)
+        if n > 2:
+            title = obj[2]
+        else:
+            title = None
+        allfields.append((fname, format, num, title))
+    # sort by offsets
+    allfields.sort(key=lambda x: x[2])
+    names = [x[0] for x in allfields]
+    formats = [x[1] for x in allfields]
+    offsets = [x[2] for x in allfields]
+    titles = [x[3] for x in allfields]
+
+    return names, formats, offsets, titles
+
+# Called in PyArray_DescrConverter function when
+#  a dictionary without "names" and "formats"
+#  fields is used as a data-type descriptor.
+def _usefields(adict, align):
+    try:
+        names = adict[-1]
+    except KeyError:
+        names = None
+    if names is None:
+        names, formats, offsets, titles = _makenames_list(adict, align)
+    else:
+        formats = []
+        offsets = []
+        titles = []
+        for name in names:
+            res = adict[name]
+            formats.append(res[0])
+            offsets.append(res[1])
+            if len(res) > 2:
+                titles.append(res[2])
+            else:
+                titles.append(None)
+
+    return dtype({"names": names,
+                  "formats": formats,
+                  "offsets": offsets,
+                  "titles": titles}, align)
+
+
+# construct an array_protocol descriptor list
+#  from the fields attribute of a descriptor
+# This calls itself recursively but should eventually hit
+#  a descriptor that has no fields and then return
+#  a simple typestring
+
+def _array_descr(descriptor):
+    fields = descriptor.fields
+    if fields is None:
+        subdtype = descriptor.subdtype
+        if subdtype is None:
+            if descriptor.metadata is None:
+                return descriptor.str
+            else:
+                new = descriptor.metadata.copy()
+                if new:
+                    return (descriptor.str, new)
+                else:
+                    return descriptor.str
+        else:
+            return (_array_descr(subdtype[0]), subdtype[1])
+
+    names = descriptor.names
+    ordered_fields = [fields[x] + (x,) for x in names]
+    result = []
+    offset = 0
+    for field in ordered_fields:
+        if field[1] > offset:
+            num = field[1] - offset
+            result.append(('', f'|V{num}'))
+            offset += num
+        elif field[1] < offset:
+            raise ValueError(
+                "dtype.descr is not defined for types with overlapping or "
+                "out-of-order fields")
+        if len(field) > 3:
+            name = (field[2], field[3])
+        else:
+            name = field[2]
+        if field[0].subdtype:
+            tup = (name, _array_descr(field[0].subdtype[0]),
+                   field[0].subdtype[1])
+        else:
+            tup = (name, _array_descr(field[0]))
+        offset += field[0].itemsize
+        result.append(tup)
+
+    if descriptor.itemsize > offset:
+        num = descriptor.itemsize - offset
+        result.append(('', f'|V{num}'))
+
+    return result
+
+
+# format_re was originally from numarray by J. Todd Miller
+
+format_re = re.compile(r'(?P<order1>[<>|=]?)'
+                       r'(?P<repeats> *[(]?[ ,0-9]*[)]? *)'
+                       r'(?P<order2>[<>|=]?)'
+                       r'(?P<dtype>[A-Za-z0-9.?]*(?:\[[a-zA-Z0-9,.]+\])?)')
+sep_re = re.compile(r'\s*,\s*')
+space_re = re.compile(r'\s+$')
+
+# astr is a string (perhaps comma separated)
+
+_convorder = {'=': _nbo}
+
+def _commastring(astr):
+    startindex = 0
+    result = []
+    islist = False
+    while startindex < len(astr):
+        mo = format_re.match(astr, pos=startindex)
+        try:
+            (order1, repeats, order2, dtype) = mo.groups()
+        except (TypeError, AttributeError):
+            raise ValueError(
+                f'format number {len(result) + 1} of "{astr}" is not recognized'
+                ) from None
+        startindex = mo.end()
+        # Separator or ending padding
+        if startindex < len(astr):
+            if space_re.match(astr, pos=startindex):
+                startindex = len(astr)
+            else:
+                mo = sep_re.match(astr, pos=startindex)
+                if not mo:
+                    raise ValueError(
+                        'format number %d of "%s" is not recognized' %
+                        (len(result) + 1, astr))
+                startindex = mo.end()
+                islist = True
+
+        if order2 == '':
+            order = order1
+        elif order1 == '':
+            order = order2
+        else:
+            order1 = _convorder.get(order1, order1)
+            order2 = _convorder.get(order2, order2)
+            if (order1 != order2):
+                raise ValueError(
+                    f'inconsistent byte-order specification {order1} and {order2}')
+            order = order1
+
+        if order in ('|', '=', _nbo):
+            order = ''
+        dtype = order + dtype
+        if repeats == '':
+            newitem = dtype
+        else:
+            if (repeats[0] == "(" and repeats[-1] == ")"
+                    and repeats[1:-1].strip() != ""
+                    and "," not in repeats):
+                warnings.warn(
+                    'Passing in a parenthesized single number for repeats '
+                    'is deprecated; pass either a single number or indicate '
+                    'a tuple with a comma, like "(2,)".', DeprecationWarning,
+                    stacklevel=2)
+            newitem = (dtype, ast.literal_eval(repeats))
+
+        result.append(newitem)
+
+    return result if islist else result[0]
+
+class dummy_ctype:
+
+    def __init__(self, cls):
+        self._cls = cls
+
+    def __mul__(self, other):
+        return self
+
+    def __call__(self, *other):
+        return self._cls(other)
+
+    def __eq__(self, other):
+        return self._cls == other._cls
+
+    def __ne__(self, other):
+        return self._cls != other._cls
+
+def _getintp_ctype():
+    val = _getintp_ctype.cache
+    if val is not None:
+        return val
+    if ctypes is None:
+        import numpy as np
+        val = dummy_ctype(np.intp)
+    else:
+        char = dtype('n').char
+        if char == 'i':
+            val = ctypes.c_int
+        elif char == 'l':
+            val = ctypes.c_long
+        elif char == 'q':
+            val = ctypes.c_longlong
+        else:
+            val = ctypes.c_long
+    _getintp_ctype.cache = val
+    return val
+
+
+_getintp_ctype.cache = None
+
+# Used for .ctypes attribute of ndarray
+
+class _missing_ctypes:
+    def cast(self, num, obj):
+        return num.value
+
+    class c_void_p:
+        def __init__(self, ptr):
+            self.value = ptr
+
+
+class _ctypes:
+    def __init__(self, array, ptr=None):
+        self._arr = array
+
+        if ctypes:
+            self._ctypes = ctypes
+            self._data = self._ctypes.c_void_p(ptr)
+        else:
+            # fake a pointer-like object that holds onto the reference
+            self._ctypes = _missing_ctypes()
+            self._data = self._ctypes.c_void_p(ptr)
+            self._data._objects = array
+
+        if self._arr.ndim == 0:
+            self._zerod = True
+        else:
+            self._zerod = False
+
+    def data_as(self, obj):
+        """
+        Return the data pointer cast to a particular c-types object.
+        For example, calling ``self._as_parameter_`` is equivalent to
+        ``self.data_as(ctypes.c_void_p)``. Perhaps you want to use
+        the data as a pointer to a ctypes array of floating-point data:
+        ``self.data_as(ctypes.POINTER(ctypes.c_double))``.
+
+        The returned pointer will keep a reference to the array.
+        """
+        # _ctypes.cast function causes a circular reference of self._data in
+        # self._data._objects. Attributes of self._data cannot be released
+        # until gc.collect is called. Make a copy of the pointer first then
+        # let it hold the array reference. This is a workaround to circumvent
+        # the CPython bug https://bugs.python.org/issue12836.
+        ptr = self._ctypes.cast(self._data, obj)
+        ptr._arr = self._arr
+        return ptr
+
+    def shape_as(self, obj):
+        """
+        Return the shape tuple as an array of some other c-types
+        type. For example: ``self.shape_as(ctypes.c_short)``.
+        """
+        if self._zerod:
+            return None
+        return (obj * self._arr.ndim)(*self._arr.shape)
+
+    def strides_as(self, obj):
+        """
+        Return the strides tuple as an array of some other
+        c-types type. For example: ``self.strides_as(ctypes.c_longlong)``.
+        """
+        if self._zerod:
+            return None
+        return (obj * self._arr.ndim)(*self._arr.strides)
+
+    @property
+    def data(self):
+        """
+        A pointer to the memory area of the array as a Python integer.
+        This memory area may contain data that is not aligned, or not in
+        correct byte-order. The memory area may not even be writeable.
+        The array flags and data-type of this array should be respected
+        when passing this attribute to arbitrary C-code to avoid trouble
+        that can include Python crashing. User Beware! The value of this
+        attribute is exactly the same as:
+        ``self._array_interface_['data'][0]``.
+
+        Note that unlike ``data_as``, a reference won't be kept to the array:
+        code like ``ctypes.c_void_p((a + b).ctypes.data)`` will result in a
+        pointer to a deallocated array, and should be spelt
+        ``(a + b).ctypes.data_as(ctypes.c_void_p)``
+        """
+        return self._data.value
+
+    @property
+    def shape(self):
+        """
+        (c_intp*self.ndim): A ctypes array of length self.ndim where
+        the basetype is the C-integer corresponding to ``dtype('p')`` on this
+        platform (see `~numpy.ctypeslib.c_intp`). This base-type could be
+        `ctypes.c_int`, `ctypes.c_long`, or `ctypes.c_longlong` depending on
+        the platform. The ctypes array contains the shape of
+        the underlying array.
+        """
+        return self.shape_as(_getintp_ctype())
+
+    @property
+    def strides(self):
+        """
+        (c_intp*self.ndim): A ctypes array of length self.ndim where
+        the basetype is the same as for the shape attribute. This ctypes
+        array contains the strides information from the underlying array.
+        This strides information is important for showing how many bytes
+        must be jumped to get to the next element in the array.
+        """
+        return self.strides_as(_getintp_ctype())
+
+    @property
+    def _as_parameter_(self):
+        """
+        Overrides the ctypes semi-magic method
+
+        Enables `c_func(some_array.ctypes)`
+        """
+        return self.data_as(ctypes.c_void_p)
+
+    # Numpy 1.21.0, 2021-05-18
+
+    def get_data(self):
+        """Deprecated getter for the `_ctypes.data` property.
+
+        .. deprecated:: 1.21
+        """
+        warnings.warn('"get_data" is deprecated. Use "data" instead',
+                      DeprecationWarning, stacklevel=2)
+        return self.data
+
+    def get_shape(self):
+        """Deprecated getter for the `_ctypes.shape` property.
+
+        .. deprecated:: 1.21
+        """
+        warnings.warn('"get_shape" is deprecated. Use "shape" instead',
+                      DeprecationWarning, stacklevel=2)
+        return self.shape
+
+    def get_strides(self):
+        """Deprecated getter for the `_ctypes.strides` property.
+
+        .. deprecated:: 1.21
+        """
+        warnings.warn('"get_strides" is deprecated. Use "strides" instead',
+                      DeprecationWarning, stacklevel=2)
+        return self.strides
+
+    def get_as_parameter(self):
+        """Deprecated getter for the `_ctypes._as_parameter_` property.
+
+        .. deprecated:: 1.21
+        """
+        warnings.warn(
+            '"get_as_parameter" is deprecated. Use "_as_parameter_" instead',
+            DeprecationWarning, stacklevel=2,
+        )
+        return self._as_parameter_
+
+
+def _newnames(datatype, order):
+    """
+    Given a datatype and an order object, return a new names tuple, with the
+    order indicated
+    """
+    oldnames = datatype.names
+    nameslist = list(oldnames)
+    if isinstance(order, str):
+        order = [order]
+    seen = set()
+    if isinstance(order, (list, tuple)):
+        for name in order:
+            try:
+                nameslist.remove(name)
+            except ValueError:
+                if name in seen:
+                    raise ValueError(f"duplicate field name: {name}") from None
+                else:
+                    raise ValueError(f"unknown field name: {name}") from None
+            seen.add(name)
+        return tuple(list(order) + nameslist)
+    raise ValueError(f"unsupported order value: {order}")
+
+def _copy_fields(ary):
+    """Return copy of structured array with padding between fields removed.
+
+    Parameters
+    ----------
+    ary : ndarray
+       Structured array from which to remove padding bytes
+
+    Returns
+    -------
+    ary_copy : ndarray
+       Copy of ary with padding bytes removed
+    """
+    dt = ary.dtype
+    copy_dtype = {'names': dt.names,
+                  'formats': [dt.fields[name][0] for name in dt.names]}
+    return array(ary, dtype=copy_dtype, copy=True)
+
+def _promote_fields(dt1, dt2):
+    """ Perform type promotion for two structured dtypes.
+
+    Parameters
+    ----------
+    dt1 : structured dtype
+        First dtype.
+    dt2 : structured dtype
+        Second dtype.
+
+    Returns
+    -------
+    out : dtype
+        The promoted dtype
+
+    Notes
+    -----
+    If one of the inputs is aligned, the result will be.  The titles of
+    both descriptors must match (point to the same field).
+    """
+    # Both must be structured and have the same names in the same order
+    if (dt1.names is None or dt2.names is None) or dt1.names != dt2.names:
+        raise DTypePromotionError(
+                f"field names `{dt1.names}` and `{dt2.names}` mismatch.")
+
+    # if both are identical, we can (maybe!) just return the same dtype.
+    identical = dt1 is dt2
+    new_fields = []
+    for name in dt1.names:
+        field1 = dt1.fields[name]
+        field2 = dt2.fields[name]
+        new_descr = promote_types(field1[0], field2[0])
+        identical = identical and new_descr is field1[0]
+
+        # Check that the titles match (if given):
+        if field1[2:] != field2[2:]:
+            raise DTypePromotionError(
+                    f"field titles of field '{name}' mismatch")
+        if len(field1) == 2:
+            new_fields.append((name, new_descr))
+        else:
+            new_fields.append(((field1[2], name), new_descr))
+
+    res = dtype(new_fields, align=dt1.isalignedstruct or dt2.isalignedstruct)
+
+    # Might as well preserve identity (and metadata) if the dtype is identical
+    # and the itemsize, offsets are also unmodified.  This could probably be
+    # sped up, but also probably just be removed entirely.
+    if identical and res.itemsize == dt1.itemsize:
+        for name in dt1.names:
+            if dt1.fields[name][1] != res.fields[name][1]:
+                return res  # the dtype changed.
+        return dt1
+
+    return res
+
+
+def _getfield_is_safe(oldtype, newtype, offset):
+    """ Checks safety of getfield for object arrays.
+
+    As in _view_is_safe, we need to check that memory containing objects is not
+    reinterpreted as a non-object datatype and vice versa.
+
+    Parameters
+    ----------
+    oldtype : data-type
+        Data type of the original ndarray.
+    newtype : data-type
+        Data type of the field being accessed by ndarray.getfield
+    offset : int
+        Offset of the field being accessed by ndarray.getfield
+
+    Raises
+    ------
+    TypeError
+        If the field access is invalid
+
+    """
+    if newtype.hasobject or oldtype.hasobject:
+        if offset == 0 and newtype == oldtype:
+            return
+        if oldtype.names is not None:
+            for name in oldtype.names:
+                if (oldtype.fields[name][1] == offset and
+                        oldtype.fields[name][0] == newtype):
+                    return
+        raise TypeError("Cannot get/set field of an object array")
+    return
+
+def _view_is_safe(oldtype, newtype):
+    """ Checks safety of a view involving object arrays, for example when
+    doing::
+
+        np.zeros(10, dtype=oldtype).view(newtype)
+
+    Parameters
+    ----------
+    oldtype : data-type
+        Data type of original ndarray
+    newtype : data-type
+        Data type of the view
+
+    Raises
+    ------
+    TypeError
+        If the new type is incompatible with the old type.
+
+    """
+
+    # if the types are equivalent, there is no problem.
+    # for example: dtype((np.record, 'i4,i4')) == dtype((np.void, 'i4,i4'))
+    if oldtype == newtype:
+        return
+
+    if newtype.hasobject or oldtype.hasobject:
+        raise TypeError("Cannot change data-type for array of references.")
+    return
+
+
+# Given a string containing a PEP 3118 format specifier,
+# construct a NumPy dtype
+
+_pep3118_native_map = {
+    '?': '?',
+    'c': 'S1',
+    'b': 'b',
+    'B': 'B',
+    'h': 'h',
+    'H': 'H',
+    'i': 'i',
+    'I': 'I',
+    'l': 'l',
+    'L': 'L',
+    'q': 'q',
+    'Q': 'Q',
+    'e': 'e',
+    'f': 'f',
+    'd': 'd',
+    'g': 'g',
+    'Zf': 'F',
+    'Zd': 'D',
+    'Zg': 'G',
+    's': 'S',
+    'w': 'U',
+    'O': 'O',
+    'x': 'V',  # padding
+}
+_pep3118_native_typechars = ''.join(_pep3118_native_map.keys())
+
+_pep3118_standard_map = {
+    '?': '?',
+    'c': 'S1',
+    'b': 'b',
+    'B': 'B',
+    'h': 'i2',
+    'H': 'u2',
+    'i': 'i4',
+    'I': 'u4',
+    'l': 'i4',
+    'L': 'u4',
+    'q': 'i8',
+    'Q': 'u8',
+    'e': 'f2',
+    'f': 'f',
+    'd': 'd',
+    'Zf': 'F',
+    'Zd': 'D',
+    's': 'S',
+    'w': 'U',
+    'O': 'O',
+    'x': 'V',  # padding
+}
+_pep3118_standard_typechars = ''.join(_pep3118_standard_map.keys())
+
+_pep3118_unsupported_map = {
+    'u': 'UCS-2 strings',
+    '&': 'pointers',
+    't': 'bitfields',
+    'X': 'function pointers',
+}
+
+class _Stream:
+    def __init__(self, s):
+        self.s = s
+        self.byteorder = '@'
+
+    def advance(self, n):
+        res = self.s[:n]
+        self.s = self.s[n:]
+        return res
+
+    def consume(self, c):
+        if self.s[:len(c)] == c:
+            self.advance(len(c))
+            return True
+        return False
+
+    def consume_until(self, c):
+        if callable(c):
+            i = 0
+            while i < len(self.s) and not c(self.s[i]):
+                i = i + 1
+            return self.advance(i)
+        else:
+            i = self.s.index(c)
+            res = self.advance(i)
+            self.advance(len(c))
+            return res
+
+    @property
+    def next(self):
+        return self.s[0]
+
+    def __bool__(self):
+        return bool(self.s)
+
+
+def _dtype_from_pep3118(spec):
+    stream = _Stream(spec)
+    dtype, align = __dtype_from_pep3118(stream, is_subdtype=False)
+    return dtype
+
+def __dtype_from_pep3118(stream, is_subdtype):
+    field_spec = {
+        'names': [],
+        'formats': [],
+        'offsets': [],
+        'itemsize': 0
+    }
+    offset = 0
+    common_alignment = 1
+    is_padding = False
+
+    # Parse spec
+    while stream:
+        value = None
+
+        # End of structure, bail out to upper level
+        if stream.consume('}'):
+            break
+
+        # Sub-arrays (1)
+        shape = None
+        if stream.consume('('):
+            shape = stream.consume_until(')')
+            shape = tuple(map(int, shape.split(',')))
+
+        # Byte order
+        if stream.next in ('@', '=', '<', '>', '^', '!'):
+            byteorder = stream.advance(1)
+            if byteorder == '!':
+                byteorder = '>'
+            stream.byteorder = byteorder
+
+        # Byte order characters also control native vs. standard type sizes
+        if stream.byteorder in ('@', '^'):
+            type_map = _pep3118_native_map
+            type_map_chars = _pep3118_native_typechars
+        else:
+            type_map = _pep3118_standard_map
+            type_map_chars = _pep3118_standard_typechars
+
+        # Item sizes
+        itemsize_str = stream.consume_until(lambda c: not c.isdigit())
+        if itemsize_str:
+            itemsize = int(itemsize_str)
+        else:
+            itemsize = 1
+
+        # Data types
+        is_padding = False
+
+        if stream.consume('T{'):
+            value, align = __dtype_from_pep3118(
+                stream, is_subdtype=True)
+        elif stream.next in type_map_chars:
+            if stream.next == 'Z':
+                typechar = stream.advance(2)
+            else:
+                typechar = stream.advance(1)
+
+            is_padding = (typechar == 'x')
+            dtypechar = type_map[typechar]
+            if dtypechar in 'USV':
+                dtypechar += '%d' % itemsize
+                itemsize = 1
+            numpy_byteorder = {'@': '=', '^': '='}.get(
+                stream.byteorder, stream.byteorder)
+            value = dtype(numpy_byteorder + dtypechar)
+            align = value.alignment
+        elif stream.next in _pep3118_unsupported_map:
+            desc = _pep3118_unsupported_map[stream.next]
+            raise NotImplementedError(
+                f"Unrepresentable PEP 3118 data type {stream.next!r} ({desc})")
+        else:
+            raise ValueError(
+                f"Unknown PEP 3118 data type specifier {stream.s!r}"
+            )
+
+        #
+        # Native alignment may require padding
+        #
+        # Here we assume that the presence of a '@' character implicitly
+        # implies that the start of the array is *already* aligned.
+        #
+        extra_offset = 0
+        if stream.byteorder == '@':
+            start_padding = (-offset) % align
+            intra_padding = (-value.itemsize) % align
+
+            offset += start_padding
+
+            if intra_padding != 0:
+                if itemsize > 1 or (shape is not None and _prod(shape) > 1):
+                    # Inject internal padding to the end of the sub-item
+                    value = _add_trailing_padding(value, intra_padding)
+                else:
+                    # We can postpone the injection of internal padding,
+                    # as the item appears at most once
+                    extra_offset += intra_padding
+
+            # Update common alignment
+            common_alignment = _lcm(align, common_alignment)
+
+        # Convert itemsize to sub-array
+        if itemsize != 1:
+            value = dtype((value, (itemsize,)))
+
+        # Sub-arrays (2)
+        if shape is not None:
+            value = dtype((value, shape))
+
+        # Field name
+        if stream.consume(':'):
+            name = stream.consume_until(':')
+        else:
+            name = None
+
+        if not (is_padding and name is None):
+            if name is not None and name in field_spec['names']:
+                raise RuntimeError(
+                    f"Duplicate field name '{name}' in PEP3118 format"
+                )
+            field_spec['names'].append(name)
+            field_spec['formats'].append(value)
+            field_spec['offsets'].append(offset)
+
+        offset += value.itemsize
+        offset += extra_offset
+
+        field_spec['itemsize'] = offset
+
+    # extra final padding for aligned types
+    if stream.byteorder == '@':
+        field_spec['itemsize'] += (-offset) % common_alignment
+
+    # Check if this was a simple 1-item type, and unwrap it
+    if (field_spec['names'] == [None]
+            and field_spec['offsets'][0] == 0
+            and field_spec['itemsize'] == field_spec['formats'][0].itemsize
+            and not is_subdtype):
+        ret = field_spec['formats'][0]
+    else:
+        _fix_names(field_spec)
+        ret = dtype(field_spec)
+
+    # Finished
+    return ret, common_alignment
+
+def _fix_names(field_spec):
+    """ Replace names which are None with the next unused f%d name """
+    names = field_spec['names']
+    for i, name in enumerate(names):
+        if name is not None:
+            continue
+
+        j = 0
+        while True:
+            name = f'f{j}'
+            if name not in names:
+                break
+            j = j + 1
+        names[i] = name
+
+def _add_trailing_padding(value, padding):
+    """Inject the specified number of padding bytes at the end of a dtype"""
+    if value.fields is None:
+        field_spec = {
+            'names': ['f0'],
+            'formats': [value],
+            'offsets': [0],
+            'itemsize': value.itemsize
+        }
+    else:
+        fields = value.fields
+        names = value.names
+        field_spec = {
+            'names': names,
+            'formats': [fields[name][0] for name in names],
+            'offsets': [fields[name][1] for name in names],
+            'itemsize': value.itemsize
+        }
+
+    field_spec['itemsize'] += padding
+    return dtype(field_spec)
+
+def _prod(a):
+    p = 1
+    for x in a:
+        p *= x
+    return p
+
+def _gcd(a, b):
+    """Calculate the greatest common divisor of a and b"""
+    if not (math.isfinite(a) and math.isfinite(b)):
+        raise ValueError('Can only find greatest common divisor of '
+                         f'finite arguments, found "{a}" and "{b}"')
+    while b:
+        a, b = b, a % b
+    return a
+
+def _lcm(a, b):
+    return a // _gcd(a, b) * b
+
+def array_ufunc_errmsg_formatter(dummy, ufunc, method, *inputs, **kwargs):
+    """ Format the error message for when __array_ufunc__ gives up. """
+    args_string = ', '.join([f'{arg!r}' for arg in inputs] +
+                            [f'{k}={v!r}'
+                             for k, v in kwargs.items()])
+    args = inputs + kwargs.get('out', ())
+    types_string = ', '.join(repr(type(arg).__name__) for arg in args)
+    return ('operand type(s) all returned NotImplemented from '
+            f'__array_ufunc__({ufunc!r}, {method!r}, {args_string}): {types_string}'
+            )
+
+
+def array_function_errmsg_formatter(public_api, types):
+    """ Format the error message for when __array_ufunc__ gives up. """
+    func_name = f'{public_api.__module__}.{public_api.__name__}'
+    return (f"no implementation found for '{func_name}' on types that implement "
+            f'__array_function__: {list(types)}')
+
+
+def _ufunc_doc_signature_formatter(ufunc):
+    """
+    Builds a signature string which resembles PEP 457
+
+    This is used to construct the first line of the docstring
+    """
+
+    # input arguments are simple
+    if ufunc.nin == 1:
+        in_args = 'x'
+    else:
+        in_args = ', '.join(f'x{i + 1}' for i in range(ufunc.nin))
+
+    # output arguments are both keyword or positional
+    if ufunc.nout == 0:
+        out_args = ', /, out=()'
+    elif ufunc.nout == 1:
+        out_args = ', /, out=None'
+    else:
+        out_args = '[, {positional}], / [, out={default}]'.format(
+            positional=', '.join(
+                f'out{i + 1}' for i in range(ufunc.nout)),
+            default=repr((None,) * ufunc.nout)
+        )
+
+    # keyword only args depend on whether this is a gufunc
+    kwargs = (
+        ", casting='same_kind'"
+        ", order='K'"
+        ", dtype=None"
+        ", subok=True"
+    )
+
+    # NOTE: gufuncs may or may not support the `axis` parameter
+    if ufunc.signature is None:
+        kwargs = f", where=True{kwargs}[, signature]"
+    else:
+        kwargs += "[, signature, axes, axis]"
+
+    # join all the parts together
+    return f'{ufunc.__name__}({in_args}{out_args}, *{kwargs})'
+
+
+def npy_ctypes_check(cls):
+    # determine if a class comes from ctypes, in order to work around
+    # a bug in the buffer protocol for those objects, bpo-10746
+    try:
+        # ctypes class are new-style, so have an __mro__. This probably fails
+        # for ctypes classes with multiple inheritance.
+        if IS_PYPY:
+            # (..., _ctypes.basics._CData, Bufferable, object)
+            ctype_base = cls.__mro__[-3]
+        else:
+            # # (..., _ctypes._CData, object)
+            ctype_base = cls.__mro__[-2]
+        # right now, they're part of the _ctypes module
+        return '_ctypes' in ctype_base.__module__
+    except Exception:
+        return False
+
+# used to handle the _NoValue default argument for na_object
+# in the C implementation of the __reduce__ method for stringdtype
+def _convert_to_stringdtype_kwargs(coerce, na_object=_NoValue):
+    if na_object is _NoValue:
+        return StringDType(coerce=coerce)
+    return StringDType(coerce=coerce, na_object=na_object)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_internal.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_internal.pyi
new file mode 100644
index 0000000..3038297
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_internal.pyi
@@ -0,0 +1,72 @@
+import ctypes as ct
+import re
+from collections.abc import Callable, Iterable
+from typing import Any, Final, Generic, Self, overload
+
+from typing_extensions import TypeVar, deprecated
+
+import numpy as np
+import numpy.typing as npt
+from numpy.ctypeslib import c_intp
+
+_CastT = TypeVar("_CastT", bound=ct._CanCastTo)
+_T_co = TypeVar("_T_co", covariant=True)
+_CT = TypeVar("_CT", bound=ct._CData)
+_PT_co = TypeVar("_PT_co", bound=int | None, default=None, covariant=True)
+
+###
+
+IS_PYPY: Final[bool] = ...
+
+format_re: Final[re.Pattern[str]] = ...
+sep_re: Final[re.Pattern[str]] = ...
+space_re: Final[re.Pattern[str]] = ...
+
+###
+
+# TODO: Let the likes of `shape_as` and `strides_as` return `None`
+# for 0D arrays once we've got shape-support
+
+class _ctypes(Generic[_PT_co]):
+    @overload
+    def __init__(self: _ctypes[None], /, array: npt.NDArray[Any], ptr: None = None) -> None: ...
+    @overload
+    def __init__(self, /, array: npt.NDArray[Any], ptr: _PT_co) -> None: ...
+
+    #
+    @property
+    def data(self) -> _PT_co: ...
+    @property
+    def shape(self) -> ct.Array[c_intp]: ...
+    @property
+    def strides(self) -> ct.Array[c_intp]: ...
+    @property
+    def _as_parameter_(self) -> ct.c_void_p: ...
+
+    #
+    def data_as(self, /, obj: type[_CastT]) -> _CastT: ...
+    def shape_as(self, /, obj: type[_CT]) -> ct.Array[_CT]: ...
+    def strides_as(self, /, obj: type[_CT]) -> ct.Array[_CT]: ...
+
+    #
+    @deprecated('"get_data" is deprecated. Use "data" instead')
+    def get_data(self, /) -> _PT_co: ...
+    @deprecated('"get_shape" is deprecated. Use "shape" instead')
+    def get_shape(self, /) -> ct.Array[c_intp]: ...
+    @deprecated('"get_strides" is deprecated. Use "strides" instead')
+    def get_strides(self, /) -> ct.Array[c_intp]: ...
+    @deprecated('"get_as_parameter" is deprecated. Use "_as_parameter_" instead')
+    def get_as_parameter(self, /) -> ct.c_void_p: ...
+
+class dummy_ctype(Generic[_T_co]):
+    _cls: type[_T_co]
+
+    def __init__(self, /, cls: type[_T_co]) -> None: ...
+    def __eq__(self, other: Self, /) -> bool: ...  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
+    def __ne__(self, other: Self, /) -> bool: ...  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
+    def __mul__(self, other: object, /) -> Self: ...
+    def __call__(self, /, *other: object) -> _T_co: ...
+
+def array_ufunc_errmsg_formatter(dummy: object, ufunc: np.ufunc, method: str, *inputs: object, **kwargs: object) -> str: ...
+def array_function_errmsg_formatter(public_api: Callable[..., object], types: Iterable[str]) -> str: ...
+def npy_ctypes_check(cls: type) -> bool: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_machar.py b/.venv/lib/python3.12/site-packages/numpy/_core/_machar.py
new file mode 100644
index 0000000..b49742a
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_machar.py
@@ -0,0 +1,355 @@
+"""
+Machine arithmetic - determine the parameters of the
+floating-point arithmetic system
+
+Author: Pearu Peterson, September 2003
+
+"""
+__all__ = ['MachAr']
+
+from ._ufunc_config import errstate
+from .fromnumeric import any
+
+# Need to speed this up...especially for longdouble
+
+# Deprecated 2021-10-20, NumPy 1.22
+class MachAr:
+    """
+    Diagnosing machine parameters.
+
+    Attributes
+    ----------
+    ibeta : int
+        Radix in which numbers are represented.
+    it : int
+        Number of base-`ibeta` digits in the floating point mantissa M.
+    machep : int
+        Exponent of the smallest (most negative) power of `ibeta` that,
+        added to 1.0, gives something different from 1.0
+    eps : float
+        Floating-point number ``beta**machep`` (floating point precision)
+    negep : int
+        Exponent of the smallest power of `ibeta` that, subtracted
+        from 1.0, gives something different from 1.0.
+    epsneg : float
+        Floating-point number ``beta**negep``.
+    iexp : int
+        Number of bits in the exponent (including its sign and bias).
+    minexp : int
+        Smallest (most negative) power of `ibeta` consistent with there
+        being no leading zeros in the mantissa.
+    xmin : float
+        Floating-point number ``beta**minexp`` (the smallest [in
+        magnitude] positive floating point number with full precision).
+    maxexp : int
+        Smallest (positive) power of `ibeta` that causes overflow.
+    xmax : float
+        ``(1-epsneg) * beta**maxexp`` (the largest [in magnitude]
+        usable floating value).
+    irnd : int
+        In ``range(6)``, information on what kind of rounding is done
+        in addition, and on how underflow is handled.
+    ngrd : int
+        Number of 'guard digits' used when truncating the product
+        of two mantissas to fit the representation.
+    epsilon : float
+        Same as `eps`.
+    tiny : float
+        An alias for `smallest_normal`, kept for backwards compatibility.
+    huge : float
+        Same as `xmax`.
+    precision : float
+        ``- int(-log10(eps))``
+    resolution : float
+        ``- 10**(-precision)``
+    smallest_normal : float
+        The smallest positive floating point number with 1 as leading bit in
+        the mantissa following IEEE-754. Same as `xmin`.
+    smallest_subnormal : float
+        The smallest positive floating point number with 0 as leading bit in
+        the mantissa following IEEE-754.
+
+    Parameters
+    ----------
+    float_conv : function, optional
+        Function that converts an integer or integer array to a float
+        or float array. Default is `float`.
+    int_conv : function, optional
+        Function that converts a float or float array to an integer or
+        integer array. Default is `int`.
+    float_to_float : function, optional
+        Function that converts a float array to float. Default is `float`.
+        Note that this does not seem to do anything useful in the current
+        implementation.
+    float_to_str : function, optional
+        Function that converts a single float to a string. Default is
+        ``lambda v:'%24.16e' %v``.
+    title : str, optional
+        Title that is printed in the string representation of `MachAr`.
+
+    See Also
+    --------
+    finfo : Machine limits for floating point types.
+    iinfo : Machine limits for integer types.
+
+    References
+    ----------
+    .. [1] Press, Teukolsky, Vetterling and Flannery,
+           "Numerical Recipes in C++," 2nd ed,
+           Cambridge University Press, 2002, p. 31.
+
+    """
+
+    def __init__(self, float_conv=float, int_conv=int,
+                 float_to_float=float,
+                 float_to_str=lambda v: f'{v:24.16e}',
+                 title='Python floating point number'):
+        """
+
+        float_conv - convert integer to float (array)
+        int_conv   - convert float (array) to integer
+        float_to_float - convert float array to float
+        float_to_str - convert array float to str
+        title        - description of used floating point numbers
+
+        """
+        # We ignore all errors here because we are purposely triggering
+        # underflow to detect the properties of the running arch.
+        with errstate(under='ignore'):
+            self._do_init(float_conv, int_conv, float_to_float, float_to_str, title)
+
+    def _do_init(self, float_conv, int_conv, float_to_float, float_to_str, title):
+        max_iterN = 10000
+        msg = "Did not converge after %d tries with %s"
+        one = float_conv(1)
+        two = one + one
+        zero = one - one
+
+        # Do we really need to do this?  Aren't they 2 and 2.0?
+        # Determine ibeta and beta
+        a = one
+        for _ in range(max_iterN):
+            a = a + a
+            temp = a + one
+            temp1 = temp - a
+            if any(temp1 - one != zero):
+                break
+        else:
+            raise RuntimeError(msg % (_, one.dtype))
+        b = one
+        for _ in range(max_iterN):
+            b = b + b
+            temp = a + b
+            itemp = int_conv(temp - a)
+            if any(itemp != 0):
+                break
+        else:
+            raise RuntimeError(msg % (_, one.dtype))
+        ibeta = itemp
+        beta = float_conv(ibeta)
+
+        # Determine it and irnd
+        it = -1
+        b = one
+        for _ in range(max_iterN):
+            it = it + 1
+            b = b * beta
+            temp = b + one
+            temp1 = temp - b
+            if any(temp1 - one != zero):
+                break
+        else:
+            raise RuntimeError(msg % (_, one.dtype))
+
+        betah = beta / two
+        a = one
+        for _ in range(max_iterN):
+            a = a + a
+            temp = a + one
+            temp1 = temp - a
+            if any(temp1 - one != zero):
+                break
+        else:
+            raise RuntimeError(msg % (_, one.dtype))
+        temp = a + betah
+        irnd = 0
+        if any(temp - a != zero):
+            irnd = 1
+        tempa = a + beta
+        temp = tempa + betah
+        if irnd == 0 and any(temp - tempa != zero):
+            irnd = 2
+
+        # Determine negep and epsneg
+        negep = it + 3
+        betain = one / beta
+        a = one
+        for i in range(negep):
+            a = a * betain
+        b = a
+        for _ in range(max_iterN):
+            temp = one - a
+            if any(temp - one != zero):
+                break
+            a = a * beta
+            negep = negep - 1
+            # Prevent infinite loop on PPC with gcc 4.0:
+            if negep < 0:
+                raise RuntimeError("could not determine machine tolerance "
+                                   "for 'negep', locals() -> %s" % (locals()))
+        else:
+            raise RuntimeError(msg % (_, one.dtype))
+        negep = -negep
+        epsneg = a
+
+        # Determine machep and eps
+        machep = - it - 3
+        a = b
+
+        for _ in range(max_iterN):
+            temp = one + a
+            if any(temp - one != zero):
+                break
+            a = a * beta
+            machep = machep + 1
+        else:
+            raise RuntimeError(msg % (_, one.dtype))
+        eps = a
+
+        # Determine ngrd
+        ngrd = 0
+        temp = one + eps
+        if irnd == 0 and any(temp * one - one != zero):
+            ngrd = 1
+
+        # Determine iexp
+        i = 0
+        k = 1
+        z = betain
+        t = one + eps
+        nxres = 0
+        for _ in range(max_iterN):
+            y = z
+            z = y * y
+            a = z * one  # Check here for underflow
+            temp = z * t
+            if any(a + a == zero) or any(abs(z) >= y):
+                break
+            temp1 = temp * betain
+            if any(temp1 * beta == z):
+                break
+            i = i + 1
+            k = k + k
+        else:
+            raise RuntimeError(msg % (_, one.dtype))
+        if ibeta != 10:
+            iexp = i + 1
+            mx = k + k
+        else:
+            iexp = 2
+            iz = ibeta
+            while k >= iz:
+                iz = iz * ibeta
+                iexp = iexp + 1
+            mx = iz + iz - 1
+
+        # Determine minexp and xmin
+        for _ in range(max_iterN):
+            xmin = y
+            y = y * betain
+            a = y * one
+            temp = y * t
+            if any((a + a) != zero) and any(abs(y) < xmin):
+                k = k + 1
+                temp1 = temp * betain
+                if any(temp1 * beta == y) and any(temp != y):
+                    nxres = 3
+                    xmin = y
+                    break
+            else:
+                break
+        else:
+            raise RuntimeError(msg % (_, one.dtype))
+        minexp = -k
+
+        # Determine maxexp, xmax
+        if mx <= k + k - 3 and ibeta != 10:
+            mx = mx + mx
+            iexp = iexp + 1
+        maxexp = mx + minexp
+        irnd = irnd + nxres
+        if irnd >= 2:
+            maxexp = maxexp - 2
+        i = maxexp + minexp
+        if ibeta == 2 and not i:
+            maxexp = maxexp - 1
+        if i > 20:
+            maxexp = maxexp - 1
+        if any(a != y):
+            maxexp = maxexp - 2
+        xmax = one - epsneg
+        if any(xmax * one != xmax):
+            xmax = one - beta * epsneg
+        xmax = xmax / (xmin * beta * beta * beta)
+        i = maxexp + minexp + 3
+        for j in range(i):
+            if ibeta == 2:
+                xmax = xmax + xmax
+            else:
+                xmax = xmax * beta
+
+        smallest_subnormal = abs(xmin / beta ** (it))
+
+        self.ibeta = ibeta
+        self.it = it
+        self.negep = negep
+        self.epsneg = float_to_float(epsneg)
+        self._str_epsneg = float_to_str(epsneg)
+        self.machep = machep
+        self.eps = float_to_float(eps)
+        self._str_eps = float_to_str(eps)
+        self.ngrd = ngrd
+        self.iexp = iexp
+        self.minexp = minexp
+        self.xmin = float_to_float(xmin)
+        self._str_xmin = float_to_str(xmin)
+        self.maxexp = maxexp
+        self.xmax = float_to_float(xmax)
+        self._str_xmax = float_to_str(xmax)
+        self.irnd = irnd
+
+        self.title = title
+        # Commonly used parameters
+        self.epsilon = self.eps
+        self.tiny = self.xmin
+        self.huge = self.xmax
+        self.smallest_normal = self.xmin
+        self._str_smallest_normal = float_to_str(self.xmin)
+        self.smallest_subnormal = float_to_float(smallest_subnormal)
+        self._str_smallest_subnormal = float_to_str(smallest_subnormal)
+
+        import math
+        self.precision = int(-math.log10(float_to_float(self.eps)))
+        ten = two + two + two + two + two
+        resolution = ten ** (-self.precision)
+        self.resolution = float_to_float(resolution)
+        self._str_resolution = float_to_str(resolution)
+
+    def __str__(self):
+        fmt = (
+           'Machine parameters for %(title)s\n'
+           '---------------------------------------------------------------------\n'
+           'ibeta=%(ibeta)s it=%(it)s iexp=%(iexp)s ngrd=%(ngrd)s irnd=%(irnd)s\n'
+           'machep=%(machep)s     eps=%(_str_eps)s (beta**machep == epsilon)\n'
+           'negep =%(negep)s  epsneg=%(_str_epsneg)s (beta**epsneg)\n'
+           'minexp=%(minexp)s   xmin=%(_str_xmin)s (beta**minexp == tiny)\n'
+           'maxexp=%(maxexp)s    xmax=%(_str_xmax)s ((1-epsneg)*beta**maxexp == huge)\n'
+           'smallest_normal=%(smallest_normal)s    '
+           'smallest_subnormal=%(smallest_subnormal)s\n'
+           '---------------------------------------------------------------------\n'
+           )
+        return fmt % self.__dict__
+
+
+if __name__ == '__main__':
+    print(MachAr())
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_machar.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_machar.pyi
new file mode 100644
index 0000000..02637a1
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_machar.pyi
@@ -0,0 +1,55 @@
+from collections.abc import Iterable
+from typing import Any, Final, TypeVar, overload
+
+import numpy as np
+from numpy import _CastingKind
+from numpy._utils import set_module as set_module
+
+###
+
+_T = TypeVar("_T")
+_TupleT = TypeVar("_TupleT", bound=tuple[()] | tuple[Any, Any, *tuple[Any, ...]])
+_ExceptionT = TypeVar("_ExceptionT", bound=Exception)
+
+###
+
+class UFuncTypeError(TypeError):
+    ufunc: Final[np.ufunc]
+    def __init__(self, /, ufunc: np.ufunc) -> None: ...
+
+class _UFuncNoLoopError(UFuncTypeError):
+    dtypes: tuple[np.dtype, ...]
+    def __init__(self, /, ufunc: np.ufunc, dtypes: Iterable[np.dtype]) -> None: ...
+
+class _UFuncBinaryResolutionError(_UFuncNoLoopError):
+    dtypes: tuple[np.dtype, np.dtype]
+    def __init__(self, /, ufunc: np.ufunc, dtypes: Iterable[np.dtype]) -> None: ...
+
+class _UFuncCastingError(UFuncTypeError):
+    casting: Final[_CastingKind]
+    from_: Final[np.dtype]
+    to: Final[np.dtype]
+    def __init__(self, /, ufunc: np.ufunc, casting: _CastingKind, from_: np.dtype, to: np.dtype) -> None: ...
+
+class _UFuncInputCastingError(_UFuncCastingError):
+    in_i: Final[int]
+    def __init__(self, /, ufunc: np.ufunc, casting: _CastingKind, from_: np.dtype, to: np.dtype, i: int) -> None: ...
+
+class _UFuncOutputCastingError(_UFuncCastingError):
+    out_i: Final[int]
+    def __init__(self, /, ufunc: np.ufunc, casting: _CastingKind, from_: np.dtype, to: np.dtype, i: int) -> None: ...
+
+class _ArrayMemoryError(MemoryError):
+    shape: tuple[int, ...]
+    dtype: np.dtype
+    def __init__(self, /, shape: tuple[int, ...], dtype: np.dtype) -> None: ...
+    @property
+    def _total_size(self) -> int: ...
+    @staticmethod
+    def _size_to_string(num_bytes: int) -> str: ...
+
+@overload
+def _unpack_tuple(tup: tuple[_T]) -> _T: ...
+@overload
+def _unpack_tuple(tup: _TupleT) -> _TupleT: ...
+def _display_as_base(cls: type[_ExceptionT]) -> type[_ExceptionT]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_methods.py b/.venv/lib/python3.12/site-packages/numpy/_core/_methods.py
new file mode 100644
index 0000000..21ad790
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_methods.py
@@ -0,0 +1,255 @@
+"""
+Array methods which are called by both the C-code for the method
+and the Python code for the NumPy-namespace function
+
+"""
+import os
+import pickle
+import warnings
+from contextlib import nullcontext
+
+import numpy as np
+from numpy._core import multiarray as mu
+from numpy._core import numerictypes as nt
+from numpy._core import umath as um
+from numpy._core.multiarray import asanyarray
+from numpy._globals import _NoValue
+
+# save those O(100) nanoseconds!
+bool_dt = mu.dtype("bool")
+umr_maximum = um.maximum.reduce
+umr_minimum = um.minimum.reduce
+umr_sum = um.add.reduce
+umr_prod = um.multiply.reduce
+umr_bitwise_count = um.bitwise_count
+umr_any = um.logical_or.reduce
+umr_all = um.logical_and.reduce
+
+# Complex types to -> (2,)float view for fast-path computation in _var()
+_complex_to_float = {
+    nt.dtype(nt.csingle): nt.dtype(nt.single),
+    nt.dtype(nt.cdouble): nt.dtype(nt.double),
+}
+# Special case for windows: ensure double takes precedence
+if nt.dtype(nt.longdouble) != nt.dtype(nt.double):
+    _complex_to_float.update({
+        nt.dtype(nt.clongdouble): nt.dtype(nt.longdouble),
+    })
+
+# avoid keyword arguments to speed up parsing, saves about 15%-20% for very
+# small reductions
+def _amax(a, axis=None, out=None, keepdims=False,
+          initial=_NoValue, where=True):
+    return umr_maximum(a, axis, None, out, keepdims, initial, where)
+
+def _amin(a, axis=None, out=None, keepdims=False,
+          initial=_NoValue, where=True):
+    return umr_minimum(a, axis, None, out, keepdims, initial, where)
+
+def _sum(a, axis=None, dtype=None, out=None, keepdims=False,
+         initial=_NoValue, where=True):
+    return umr_sum(a, axis, dtype, out, keepdims, initial, where)
+
+def _prod(a, axis=None, dtype=None, out=None, keepdims=False,
+          initial=_NoValue, where=True):
+    return umr_prod(a, axis, dtype, out, keepdims, initial, where)
+
+def _any(a, axis=None, dtype=None, out=None, keepdims=False, *, where=True):
+    # By default, return a boolean for any and all
+    if dtype is None:
+        dtype = bool_dt
+    # Parsing keyword arguments is currently fairly slow, so avoid it for now
+    if where is True:
+        return umr_any(a, axis, dtype, out, keepdims)
+    return umr_any(a, axis, dtype, out, keepdims, where=where)
+
+def _all(a, axis=None, dtype=None, out=None, keepdims=False, *, where=True):
+    # By default, return a boolean for any and all
+    if dtype is None:
+        dtype = bool_dt
+    # Parsing keyword arguments is currently fairly slow, so avoid it for now
+    if where is True:
+        return umr_all(a, axis, dtype, out, keepdims)
+    return umr_all(a, axis, dtype, out, keepdims, where=where)
+
+def _count_reduce_items(arr, axis, keepdims=False, where=True):
+    # fast-path for the default case
+    if where is True:
+        # no boolean mask given, calculate items according to axis
+        if axis is None:
+            axis = tuple(range(arr.ndim))
+        elif not isinstance(axis, tuple):
+            axis = (axis,)
+        items = 1
+        for ax in axis:
+            items *= arr.shape[mu.normalize_axis_index(ax, arr.ndim)]
+        items = nt.intp(items)
+    else:
+        # TODO: Optimize case when `where` is broadcast along a non-reduction
+        # axis and full sum is more excessive than needed.
+
+        # guarded to protect circular imports
+        from numpy.lib._stride_tricks_impl import broadcast_to
+        # count True values in (potentially broadcasted) boolean mask
+        items = umr_sum(broadcast_to(where, arr.shape), axis, nt.intp, None,
+                        keepdims)
+    return items
+
+def _clip(a, min=None, max=None, out=None, **kwargs):
+    if a.dtype.kind in "iu":
+        # If min/max is a Python integer, deal with out-of-bound values here.
+        # (This enforces NEP 50 rules as no value based promotion is done.)
+        if type(min) is int and min <= np.iinfo(a.dtype).min:
+            min = None
+        if type(max) is int and max >= np.iinfo(a.dtype).max:
+            max = None
+
+    if min is None and max is None:
+        # return identity
+        return um.positive(a, out=out, **kwargs)
+    elif min is None:
+        return um.minimum(a, max, out=out, **kwargs)
+    elif max is None:
+        return um.maximum(a, min, out=out, **kwargs)
+    else:
+        return um.clip(a, min, max, out=out, **kwargs)
+
+def _mean(a, axis=None, dtype=None, out=None, keepdims=False, *, where=True):
+    arr = asanyarray(a)
+
+    is_float16_result = False
+
+    rcount = _count_reduce_items(arr, axis, keepdims=keepdims, where=where)
+    if rcount == 0 if where is True else umr_any(rcount == 0, axis=None):
+        warnings.warn("Mean of empty slice.", RuntimeWarning, stacklevel=2)
+
+    # Cast bool, unsigned int, and int to float64 by default
+    if dtype is None:
+        if issubclass(arr.dtype.type, (nt.integer, nt.bool)):
+            dtype = mu.dtype('f8')
+        elif issubclass(arr.dtype.type, nt.float16):
+            dtype = mu.dtype('f4')
+            is_float16_result = True
+
+    ret = umr_sum(arr, axis, dtype, out, keepdims, where=where)
+    if isinstance(ret, mu.ndarray):
+        ret = um.true_divide(
+                ret, rcount, out=ret, casting='unsafe', subok=False)
+        if is_float16_result and out is None:
+            ret = arr.dtype.type(ret)
+    elif hasattr(ret, 'dtype'):
+        if is_float16_result:
+            ret = arr.dtype.type(ret / rcount)
+        else:
+            ret = ret.dtype.type(ret / rcount)
+    else:
+        ret = ret / rcount
+
+    return ret
+
+def _var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False, *,
+         where=True, mean=None):
+    arr = asanyarray(a)
+
+    rcount = _count_reduce_items(arr, axis, keepdims=keepdims, where=where)
+    # Make this warning show up on top.
+    if ddof >= rcount if where is True else umr_any(ddof >= rcount, axis=None):
+        warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning,
+                      stacklevel=2)
+
+    # Cast bool, unsigned int, and int to float64 by default
+    if dtype is None and issubclass(arr.dtype.type, (nt.integer, nt.bool)):
+        dtype = mu.dtype('f8')
+
+    if mean is not None:
+        arrmean = mean
+    else:
+        # Compute the mean.
+        # Note that if dtype is not of inexact type then arraymean will
+        # not be either.
+        arrmean = umr_sum(arr, axis, dtype, keepdims=True, where=where)
+        # The shape of rcount has to match arrmean to not change the shape of
+        # out in broadcasting. Otherwise, it cannot be stored back to arrmean.
+        if rcount.ndim == 0:
+            # fast-path for default case when where is True
+            div = rcount
+        else:
+            # matching rcount to arrmean when where is specified as array
+            div = rcount.reshape(arrmean.shape)
+        if isinstance(arrmean, mu.ndarray):
+            arrmean = um.true_divide(arrmean, div, out=arrmean,
+                                     casting='unsafe', subok=False)
+        elif hasattr(arrmean, "dtype"):
+            arrmean = arrmean.dtype.type(arrmean / rcount)
+        else:
+            arrmean = arrmean / rcount
+
+    # Compute sum of squared deviations from mean
+    # Note that x may not be inexact and that we need it to be an array,
+    # not a scalar.
+    x = asanyarray(arr - arrmean)
+
+    if issubclass(arr.dtype.type, (nt.floating, nt.integer)):
+        x = um.multiply(x, x, out=x)
+    # Fast-paths for built-in complex types
+    elif x.dtype in _complex_to_float:
+        xv = x.view(dtype=(_complex_to_float[x.dtype], (2,)))
+        um.multiply(xv, xv, out=xv)
+        x = um.add(xv[..., 0], xv[..., 1], out=x.real).real
+    # Most general case; includes handling object arrays containing imaginary
+    # numbers and complex types with non-native byteorder
+    else:
+        x = um.multiply(x, um.conjugate(x), out=x).real
+
+    ret = umr_sum(x, axis, dtype, out, keepdims=keepdims, where=where)
+
+    # Compute degrees of freedom and make sure it is not negative.
+    rcount = um.maximum(rcount - ddof, 0)
+
+    # divide by degrees of freedom
+    if isinstance(ret, mu.ndarray):
+        ret = um.true_divide(
+                ret, rcount, out=ret, casting='unsafe', subok=False)
+    elif hasattr(ret, 'dtype'):
+        ret = ret.dtype.type(ret / rcount)
+    else:
+        ret = ret / rcount
+
+    return ret
+
+def _std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False, *,
+         where=True, mean=None):
+    ret = _var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
+               keepdims=keepdims, where=where, mean=mean)
+
+    if isinstance(ret, mu.ndarray):
+        ret = um.sqrt(ret, out=ret)
+    elif hasattr(ret, 'dtype'):
+        ret = ret.dtype.type(um.sqrt(ret))
+    else:
+        ret = um.sqrt(ret)
+
+    return ret
+
+def _ptp(a, axis=None, out=None, keepdims=False):
+    return um.subtract(
+        umr_maximum(a, axis, None, out, keepdims),
+        umr_minimum(a, axis, None, None, keepdims),
+        out
+    )
+
+def _dump(self, file, protocol=2):
+    if hasattr(file, 'write'):
+        ctx = nullcontext(file)
+    else:
+        ctx = open(os.fspath(file), "wb")
+    with ctx as f:
+        pickle.dump(self, f, protocol=protocol)
+
+def _dumps(self, protocol=2):
+    return pickle.dumps(self, protocol=protocol)
+
+def _bitwise_count(a, out=None, *, where=True, casting='same_kind',
+          order='K', dtype=None, subok=True):
+    return umr_bitwise_count(a, out, where=where, casting=casting,
+            order=order, dtype=dtype, subok=subok)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_methods.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_methods.pyi
new file mode 100644
index 0000000..3c80683
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_methods.pyi
@@ -0,0 +1,22 @@
+from collections.abc import Callable
+from typing import Any, Concatenate, TypeAlias
+
+import numpy as np
+
+from . import _exceptions as _exceptions
+
+###
+
+_Reduce2: TypeAlias = Callable[Concatenate[object, ...], Any]
+
+###
+
+bool_dt: np.dtype[np.bool] = ...
+umr_maximum: _Reduce2 = ...
+umr_minimum: _Reduce2 = ...
+umr_sum: _Reduce2 = ...
+umr_prod: _Reduce2 = ...
+umr_bitwise_count = np.bitwise_count
+umr_any: _Reduce2 = ...
+umr_all: _Reduce2 = ...
+_complex_to_float: dict[np.dtype[np.complexfloating], np.dtype[np.floating]] = ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_multiarray_tests.cpython-312-x86_64-linux-gnu.so b/.venv/lib/python3.12/site-packages/numpy/_core/_multiarray_tests.cpython-312-x86_64-linux-gnu.so
new file mode 100755
index 0000000..ce78182
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_multiarray_tests.cpython-312-x86_64-linux-gnu.so
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_multiarray_umath.cpython-312-x86_64-linux-gnu.so b/.venv/lib/python3.12/site-packages/numpy/_core/_multiarray_umath.cpython-312-x86_64-linux-gnu.so
new file mode 100755
index 0000000..8b2a78b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_multiarray_umath.cpython-312-x86_64-linux-gnu.so
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_operand_flag_tests.cpython-312-x86_64-linux-gnu.so b/.venv/lib/python3.12/site-packages/numpy/_core/_operand_flag_tests.cpython-312-x86_64-linux-gnu.so
new file mode 100755
index 0000000..bf24fe0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_operand_flag_tests.cpython-312-x86_64-linux-gnu.so
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_rational_tests.cpython-312-x86_64-linux-gnu.so b/.venv/lib/python3.12/site-packages/numpy/_core/_rational_tests.cpython-312-x86_64-linux-gnu.so
new file mode 100755
index 0000000..b9a7717
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_rational_tests.cpython-312-x86_64-linux-gnu.so
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_simd.cpython-312-x86_64-linux-gnu.so b/.venv/lib/python3.12/site-packages/numpy/_core/_simd.cpython-312-x86_64-linux-gnu.so
new file mode 100755
index 0000000..54bbb83
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_simd.cpython-312-x86_64-linux-gnu.so
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_simd.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_simd.pyi
new file mode 100644
index 0000000..70bb707
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_simd.pyi
@@ -0,0 +1,25 @@
+from types import ModuleType
+from typing import TypedDict, type_check_only
+
+# NOTE: these 5 are only defined on systems with an intel processor
+SSE42: ModuleType | None = ...
+FMA3: ModuleType | None = ...
+AVX2: ModuleType | None = ...
+AVX512F: ModuleType | None = ...
+AVX512_SKX: ModuleType | None = ...
+
+baseline: ModuleType | None = ...
+
+@type_check_only
+class SimdTargets(TypedDict):
+    SSE42: ModuleType | None
+    AVX2: ModuleType | None
+    FMA3: ModuleType | None
+    AVX512F: ModuleType | None
+    AVX512_SKX: ModuleType | None
+    baseline: ModuleType | None
+
+targets: SimdTargets = ...
+
+def clear_floatstatus() -> None: ...
+def get_floatstatus() -> int: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_string_helpers.py b/.venv/lib/python3.12/site-packages/numpy/_core/_string_helpers.py
new file mode 100644
index 0000000..87085d4
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_string_helpers.py
@@ -0,0 +1,100 @@
+"""
+String-handling utilities to avoid locale-dependence.
+
+Used primarily to generate type name aliases.
+"""
+# "import string" is costly to import!
+# Construct the translation tables directly
+#   "A" = chr(65), "a" = chr(97)
+_all_chars = tuple(map(chr, range(256)))
+_ascii_upper = _all_chars[65:65 + 26]
+_ascii_lower = _all_chars[97:97 + 26]
+LOWER_TABLE = _all_chars[:65] + _ascii_lower + _all_chars[65 + 26:]
+UPPER_TABLE = _all_chars[:97] + _ascii_upper + _all_chars[97 + 26:]
+
+
+def english_lower(s):
+    """ Apply English case rules to convert ASCII strings to all lower case.
+
+    This is an internal utility function to replace calls to str.lower() such
+    that we can avoid changing behavior with changing locales. In particular,
+    Turkish has distinct dotted and dotless variants of the Latin letter "I" in
+    both lowercase and uppercase. Thus, "I".lower() != "i" in a "tr" locale.
+
+    Parameters
+    ----------
+    s : str
+
+    Returns
+    -------
+    lowered : str
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import english_lower
+    >>> english_lower('ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789_')
+    'abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz0123456789_'
+    >>> english_lower('')
+    ''
+    """
+    lowered = s.translate(LOWER_TABLE)
+    return lowered
+
+
+def english_upper(s):
+    """ Apply English case rules to convert ASCII strings to all upper case.
+
+    This is an internal utility function to replace calls to str.upper() such
+    that we can avoid changing behavior with changing locales. In particular,
+    Turkish has distinct dotted and dotless variants of the Latin letter "I" in
+    both lowercase and uppercase. Thus, "i".upper() != "I" in a "tr" locale.
+
+    Parameters
+    ----------
+    s : str
+
+    Returns
+    -------
+    uppered : str
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import english_upper
+    >>> english_upper('ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789_')
+    'ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789_'
+    >>> english_upper('')
+    ''
+    """
+    uppered = s.translate(UPPER_TABLE)
+    return uppered
+
+
+def english_capitalize(s):
+    """ Apply English case rules to convert the first character of an ASCII
+    string to upper case.
+
+    This is an internal utility function to replace calls to str.capitalize()
+    such that we can avoid changing behavior with changing locales.
+
+    Parameters
+    ----------
+    s : str
+
+    Returns
+    -------
+    capitalized : str
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import english_capitalize
+    >>> english_capitalize('int8')
+    'Int8'
+    >>> english_capitalize('Int8')
+    'Int8'
+    >>> english_capitalize('')
+    ''
+    """
+    if s:
+        return english_upper(s[0]) + s[1:]
+    else:
+        return s
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_string_helpers.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_string_helpers.pyi
new file mode 100644
index 0000000..6a85832
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_string_helpers.pyi
@@ -0,0 +1,12 @@
+from typing import Final
+
+_all_chars: Final[tuple[str, ...]] = ...
+_ascii_upper: Final[tuple[str, ...]] = ...
+_ascii_lower: Final[tuple[str, ...]] = ...
+
+LOWER_TABLE: Final[tuple[str, ...]] = ...
+UPPER_TABLE: Final[tuple[str, ...]] = ...
+
+def english_lower(s: str) -> str: ...
+def english_upper(s: str) -> str: ...
+def english_capitalize(s: str) -> str: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_struct_ufunc_tests.cpython-312-x86_64-linux-gnu.so b/.venv/lib/python3.12/site-packages/numpy/_core/_struct_ufunc_tests.cpython-312-x86_64-linux-gnu.so
new file mode 100755
index 0000000..10747a3
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_struct_ufunc_tests.cpython-312-x86_64-linux-gnu.so
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_type_aliases.py b/.venv/lib/python3.12/site-packages/numpy/_core/_type_aliases.py
new file mode 100644
index 0000000..de6c309
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_type_aliases.py
@@ -0,0 +1,119 @@
+"""
+Due to compatibility, numpy has a very large number of different naming
+conventions for the scalar types (those subclassing from `numpy.generic`).
+This file produces a convoluted set of dictionaries mapping names to types,
+and sometimes other mappings too.
+
+.. data:: allTypes
+    A dictionary of names to types that will be exposed as attributes through
+    ``np._core.numerictypes.*``
+
+.. data:: sctypeDict
+    Similar to `allTypes`, but maps a broader set of aliases to their types.
+
+.. data:: sctypes
+    A dictionary keyed by a "type group" string, providing a list of types
+    under that group.
+
+"""
+
+import numpy._core.multiarray as ma
+from numpy._core.multiarray import dtype, typeinfo
+
+######################################
+# Building `sctypeDict` and `allTypes`
+######################################
+
+sctypeDict = {}
+allTypes = {}
+c_names_dict = {}
+
+_abstract_type_names = {
+    "generic", "integer", "inexact", "floating", "number",
+    "flexible", "character", "complexfloating", "unsignedinteger",
+    "signedinteger"
+}
+
+for _abstract_type_name in _abstract_type_names:
+    allTypes[_abstract_type_name] = getattr(ma, _abstract_type_name)
+
+for k, v in typeinfo.items():
+    if k.startswith("NPY_") and v not in c_names_dict:
+        c_names_dict[k[4:]] = v
+    else:
+        concrete_type = v.type
+        allTypes[k] = concrete_type
+        sctypeDict[k] = concrete_type
+
+_aliases = {
+    "double": "float64",
+    "cdouble": "complex128",
+    "single": "float32",
+    "csingle": "complex64",
+    "half": "float16",
+    "bool_": "bool",
+    # Default integer:
+    "int_": "intp",
+    "uint": "uintp",
+}
+
+for k, v in _aliases.items():
+    sctypeDict[k] = allTypes[v]
+    allTypes[k] = allTypes[v]
+
+# extra aliases are added only to `sctypeDict`
+# to support dtype name access, such as`np.dtype("float")`
+_extra_aliases = {
+    "float": "float64",
+    "complex": "complex128",
+    "object": "object_",
+    "bytes": "bytes_",
+    "a": "bytes_",
+    "int": "int_",
+    "str": "str_",
+    "unicode": "str_",
+}
+
+for k, v in _extra_aliases.items():
+    sctypeDict[k] = allTypes[v]
+
+# include extended precision sized aliases
+for is_complex, full_name in [(False, "longdouble"), (True, "clongdouble")]:
+    longdouble_type: type = allTypes[full_name]
+
+    bits: int = dtype(longdouble_type).itemsize * 8
+    base_name: str = "complex" if is_complex else "float"
+    extended_prec_name: str = f"{base_name}{bits}"
+    if extended_prec_name not in allTypes:
+        sctypeDict[extended_prec_name] = longdouble_type
+        allTypes[extended_prec_name] = longdouble_type
+
+
+####################
+# Building `sctypes`
+####################
+
+sctypes = {"int": set(), "uint": set(), "float": set(),
+           "complex": set(), "others": set()}
+
+for type_info in typeinfo.values():
+    if type_info.kind in ["M", "m"]:  # exclude timedelta and datetime
+        continue
+
+    concrete_type = type_info.type
+
+    # find proper group for each concrete type
+    for type_group, abstract_type in [
+        ("int", ma.signedinteger), ("uint", ma.unsignedinteger),
+        ("float", ma.floating), ("complex", ma.complexfloating),
+        ("others", ma.generic)
+    ]:
+        if issubclass(concrete_type, abstract_type):
+            sctypes[type_group].add(concrete_type)
+            break
+
+# sort sctype groups by bitsize
+for sctype_key in sctypes.keys():
+    sctype_list = list(sctypes[sctype_key])
+    sctype_list.sort(key=lambda x: dtype(x).itemsize)
+    sctypes[sctype_key] = sctype_list
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_type_aliases.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_type_aliases.pyi
new file mode 100644
index 0000000..3c9dac7
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_type_aliases.pyi
@@ -0,0 +1,97 @@
+from collections.abc import Collection
+from typing import Final, TypeAlias, TypedDict, type_check_only
+from typing import Literal as L
+
+import numpy as np
+
+__all__ = (
+    "_abstract_type_names",
+    "_aliases",
+    "_extra_aliases",
+    "allTypes",
+    "c_names_dict",
+    "sctypeDict",
+    "sctypes",
+)
+
+sctypeDict: Final[dict[str, type[np.generic]]]
+allTypes: Final[dict[str, type[np.generic]]]
+
+@type_check_only
+class _CNamesDict(TypedDict):
+    BOOL: np.dtype[np.bool]
+    HALF: np.dtype[np.half]
+    FLOAT: np.dtype[np.single]
+    DOUBLE: np.dtype[np.double]
+    LONGDOUBLE: np.dtype[np.longdouble]
+    CFLOAT: np.dtype[np.csingle]
+    CDOUBLE: np.dtype[np.cdouble]
+    CLONGDOUBLE: np.dtype[np.clongdouble]
+    STRING: np.dtype[np.bytes_]
+    UNICODE: np.dtype[np.str_]
+    VOID: np.dtype[np.void]
+    OBJECT: np.dtype[np.object_]
+    DATETIME: np.dtype[np.datetime64]
+    TIMEDELTA: np.dtype[np.timedelta64]
+    BYTE: np.dtype[np.byte]
+    UBYTE: np.dtype[np.ubyte]
+    SHORT: np.dtype[np.short]
+    USHORT: np.dtype[np.ushort]
+    INT: np.dtype[np.intc]
+    UINT: np.dtype[np.uintc]
+    LONG: np.dtype[np.long]
+    ULONG: np.dtype[np.ulong]
+    LONGLONG: np.dtype[np.longlong]
+    ULONGLONG: np.dtype[np.ulonglong]
+
+c_names_dict: Final[_CNamesDict]
+
+_AbstractTypeName: TypeAlias = L[
+    "generic",
+    "flexible",
+    "character",
+    "number",
+    "integer",
+    "inexact",
+    "unsignedinteger",
+    "signedinteger",
+    "floating",
+    "complexfloating",
+]
+_abstract_type_names: Final[set[_AbstractTypeName]]
+
+@type_check_only
+class _AliasesType(TypedDict):
+    double: L["float64"]
+    cdouble: L["complex128"]
+    single: L["float32"]
+    csingle: L["complex64"]
+    half: L["float16"]
+    bool_: L["bool"]
+    int_: L["intp"]
+    uint: L["intp"]
+
+_aliases: Final[_AliasesType]
+
+@type_check_only
+class _ExtraAliasesType(TypedDict):
+    float: L["float64"]
+    complex: L["complex128"]
+    object: L["object_"]
+    bytes: L["bytes_"]
+    a: L["bytes_"]
+    int: L["int_"]
+    str: L["str_"]
+    unicode: L["str_"]
+
+_extra_aliases: Final[_ExtraAliasesType]
+
+@type_check_only
+class _SCTypes(TypedDict):
+    int: Collection[type[np.signedinteger]]
+    uint: Collection[type[np.unsignedinteger]]
+    float: Collection[type[np.floating]]
+    complex: Collection[type[np.complexfloating]]
+    others: Collection[type[np.flexible | np.bool | np.object_]]
+
+sctypes: Final[_SCTypes]
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_ufunc_config.py b/.venv/lib/python3.12/site-packages/numpy/_core/_ufunc_config.py
new file mode 100644
index 0000000..24abecd
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_ufunc_config.py
@@ -0,0 +1,489 @@
+"""
+Functions for changing global ufunc configuration
+
+This provides helpers which wrap `_get_extobj_dict` and `_make_extobj`, and
+`_extobj_contextvar` from umath.
+"""
+import functools
+
+from numpy._utils import set_module
+
+from .umath import _extobj_contextvar, _get_extobj_dict, _make_extobj
+
+__all__ = [
+    "seterr", "geterr", "setbufsize", "getbufsize", "seterrcall", "geterrcall",
+    "errstate"
+]
+
+
+@set_module('numpy')
+def seterr(all=None, divide=None, over=None, under=None, invalid=None):
+    """
+    Set how floating-point errors are handled.
+
+    Note that operations on integer scalar types (such as `int16`) are
+    handled like floating point, and are affected by these settings.
+
+    Parameters
+    ----------
+    all : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Set treatment for all types of floating-point errors at once:
+
+        - ignore: Take no action when the exception occurs.
+        - warn: Print a :exc:`RuntimeWarning` (via the Python `warnings`
+          module).
+        - raise: Raise a :exc:`FloatingPointError`.
+        - call: Call a function specified using the `seterrcall` function.
+        - print: Print a warning directly to ``stdout``.
+        - log: Record error in a Log object specified by `seterrcall`.
+
+        The default is not to change the current behavior.
+    divide : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Treatment for division by zero.
+    over : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Treatment for floating-point overflow.
+    under : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Treatment for floating-point underflow.
+    invalid : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional
+        Treatment for invalid floating-point operation.
+
+    Returns
+    -------
+    old_settings : dict
+        Dictionary containing the old settings.
+
+    See also
+    --------
+    seterrcall : Set a callback function for the 'call' mode.
+    geterr, geterrcall, errstate
+
+    Notes
+    -----
+    The floating-point exceptions are defined in the IEEE 754 standard [1]_:
+
+    - Division by zero: infinite result obtained from finite numbers.
+    - Overflow: result too large to be expressed.
+    - Underflow: result so close to zero that some precision
+      was lost.
+    - Invalid operation: result is not an expressible number, typically
+      indicates that a NaN was produced.
+
+    .. [1] https://en.wikipedia.org/wiki/IEEE_754
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> orig_settings = np.seterr(all='ignore')  # seterr to known value
+    >>> np.int16(32000) * np.int16(3)
+    np.int16(30464)
+    >>> np.seterr(over='raise')
+    {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'}
+    >>> old_settings = np.seterr(all='warn', over='raise')
+    >>> np.int16(32000) * np.int16(3)
+    Traceback (most recent call last):
+      File "<stdin>", line 1, in <module>
+    FloatingPointError: overflow encountered in scalar multiply
+
+    >>> old_settings = np.seterr(all='print')
+    >>> np.geterr()
+    {'divide': 'print', 'over': 'print', 'under': 'print', 'invalid': 'print'}
+    >>> np.int16(32000) * np.int16(3)
+    np.int16(30464)
+    >>> np.seterr(**orig_settings)  # restore original
+    {'divide': 'print', 'over': 'print', 'under': 'print', 'invalid': 'print'}
+
+    """
+
+    old = _get_extobj_dict()
+    # The errstate doesn't include call and bufsize, so pop them:
+    old.pop("call", None)
+    old.pop("bufsize", None)
+
+    extobj = _make_extobj(
+            all=all, divide=divide, over=over, under=under, invalid=invalid)
+    _extobj_contextvar.set(extobj)
+    return old
+
+
+@set_module('numpy')
+def geterr():
+    """
+    Get the current way of handling floating-point errors.
+
+    Returns
+    -------
+    res : dict
+        A dictionary with keys "divide", "over", "under", and "invalid",
+        whose values are from the strings "ignore", "print", "log", "warn",
+        "raise", and "call". The keys represent possible floating-point
+        exceptions, and the values define how these exceptions are handled.
+
+    See Also
+    --------
+    geterrcall, seterr, seterrcall
+
+    Notes
+    -----
+    For complete documentation of the types of floating-point exceptions and
+    treatment options, see `seterr`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.geterr()
+    {'divide': 'warn', 'over': 'warn', 'under': 'ignore', 'invalid': 'warn'}
+    >>> np.arange(3.) / np.arange(3.)  # doctest: +SKIP
+    array([nan,  1.,  1.])
+    RuntimeWarning: invalid value encountered in divide
+
+    >>> oldsettings = np.seterr(all='warn', invalid='raise')
+    >>> np.geterr()
+    {'divide': 'warn', 'over': 'warn', 'under': 'warn', 'invalid': 'raise'}
+    >>> np.arange(3.) / np.arange(3.)
+    Traceback (most recent call last):
+      ...
+    FloatingPointError: invalid value encountered in divide
+    >>> oldsettings = np.seterr(**oldsettings)  # restore original
+
+    """
+    res = _get_extobj_dict()
+    # The "geterr" doesn't include call and bufsize,:
+    res.pop("call", None)
+    res.pop("bufsize", None)
+    return res
+
+
+@set_module('numpy')
+def setbufsize(size):
+    """
+    Set the size of the buffer used in ufuncs.
+
+    .. versionchanged:: 2.0
+        The scope of setting the buffer is tied to the `numpy.errstate`
+        context.  Exiting a ``with errstate():`` will also restore the bufsize.
+
+    Parameters
+    ----------
+    size : int
+        Size of buffer.
+
+    Returns
+    -------
+    bufsize : int
+        Previous size of ufunc buffer in bytes.
+
+    Examples
+    --------
+    When exiting a `numpy.errstate` context manager the bufsize is restored:
+
+    >>> import numpy as np
+    >>> with np.errstate():
+    ...     np.setbufsize(4096)
+    ...     print(np.getbufsize())
+    ...
+    8192
+    4096
+    >>> np.getbufsize()
+    8192
+
+    """
+    old = _get_extobj_dict()["bufsize"]
+    extobj = _make_extobj(bufsize=size)
+    _extobj_contextvar.set(extobj)
+    return old
+
+
+@set_module('numpy')
+def getbufsize():
+    """
+    Return the size of the buffer used in ufuncs.
+
+    Returns
+    -------
+    getbufsize : int
+        Size of ufunc buffer in bytes.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.getbufsize()
+    8192
+
+    """
+    return _get_extobj_dict()["bufsize"]
+
+
+@set_module('numpy')
+def seterrcall(func):
+    """
+    Set the floating-point error callback function or log object.
+
+    There are two ways to capture floating-point error messages.  The first
+    is to set the error-handler to 'call', using `seterr`.  Then, set
+    the function to call using this function.
+
+    The second is to set the error-handler to 'log', using `seterr`.
+    Floating-point errors then trigger a call to the 'write' method of
+    the provided object.
+
+    Parameters
+    ----------
+    func : callable f(err, flag) or object with write method
+        Function to call upon floating-point errors ('call'-mode) or
+        object whose 'write' method is used to log such message ('log'-mode).
+
+        The call function takes two arguments. The first is a string describing
+        the type of error (such as "divide by zero", "overflow", "underflow",
+        or "invalid value"), and the second is the status flag.  The flag is a
+        byte, whose four least-significant bits indicate the type of error, one
+        of "divide", "over", "under", "invalid"::
+
+          [0 0 0 0 divide over under invalid]
+
+        In other words, ``flags = divide + 2*over + 4*under + 8*invalid``.
+
+        If an object is provided, its write method should take one argument,
+        a string.
+
+    Returns
+    -------
+    h : callable, log instance or None
+        The old error handler.
+
+    See Also
+    --------
+    seterr, geterr, geterrcall
+
+    Examples
+    --------
+    Callback upon error:
+
+    >>> def err_handler(type, flag):
+    ...     print("Floating point error (%s), with flag %s" % (type, flag))
+    ...
+
+    >>> import numpy as np
+
+    >>> orig_handler = np.seterrcall(err_handler)
+    >>> orig_err = np.seterr(all='call')
+
+    >>> np.array([1, 2, 3]) / 0.0
+    Floating point error (divide by zero), with flag 1
+    array([inf, inf, inf])
+
+    >>> np.seterrcall(orig_handler)
+    <function err_handler at 0x...>
+    >>> np.seterr(**orig_err)
+    {'divide': 'call', 'over': 'call', 'under': 'call', 'invalid': 'call'}
+
+    Log error message:
+
+    >>> class Log:
+    ...     def write(self, msg):
+    ...         print("LOG: %s" % msg)
+    ...
+
+    >>> log = Log()
+    >>> saved_handler = np.seterrcall(log)
+    >>> save_err = np.seterr(all='log')
+
+    >>> np.array([1, 2, 3]) / 0.0
+    LOG: Warning: divide by zero encountered in divide
+    array([inf, inf, inf])
+
+    >>> np.seterrcall(orig_handler)
+    <numpy.Log object at 0x...>
+    >>> np.seterr(**orig_err)
+    {'divide': 'log', 'over': 'log', 'under': 'log', 'invalid': 'log'}
+
+    """
+    old = _get_extobj_dict()["call"]
+    extobj = _make_extobj(call=func)
+    _extobj_contextvar.set(extobj)
+    return old
+
+
+@set_module('numpy')
+def geterrcall():
+    """
+    Return the current callback function used on floating-point errors.
+
+    When the error handling for a floating-point error (one of "divide",
+    "over", "under", or "invalid") is set to 'call' or 'log', the function
+    that is called or the log instance that is written to is returned by
+    `geterrcall`. This function or log instance has been set with
+    `seterrcall`.
+
+    Returns
+    -------
+    errobj : callable, log instance or None
+        The current error handler. If no handler was set through `seterrcall`,
+        ``None`` is returned.
+
+    See Also
+    --------
+    seterrcall, seterr, geterr
+
+    Notes
+    -----
+    For complete documentation of the types of floating-point exceptions and
+    treatment options, see `seterr`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.geterrcall()  # we did not yet set a handler, returns None
+
+    >>> orig_settings = np.seterr(all='call')
+    >>> def err_handler(type, flag):
+    ...     print("Floating point error (%s), with flag %s" % (type, flag))
+    >>> old_handler = np.seterrcall(err_handler)
+    >>> np.array([1, 2, 3]) / 0.0
+    Floating point error (divide by zero), with flag 1
+    array([inf, inf, inf])
+
+    >>> cur_handler = np.geterrcall()
+    >>> cur_handler is err_handler
+    True
+    >>> old_settings = np.seterr(**orig_settings)  # restore original
+    >>> old_handler = np.seterrcall(None)  # restore original
+
+    """
+    return _get_extobj_dict()["call"]
+
+
+class _unspecified:
+    pass
+
+
+_Unspecified = _unspecified()
+
+
+@set_module('numpy')
+class errstate:
+    """
+    errstate(**kwargs)
+
+    Context manager for floating-point error handling.
+
+    Using an instance of `errstate` as a context manager allows statements in
+    that context to execute with a known error handling behavior. Upon entering
+    the context the error handling is set with `seterr` and `seterrcall`, and
+    upon exiting it is reset to what it was before.
+
+    ..  versionchanged:: 1.17.0
+        `errstate` is also usable as a function decorator, saving
+        a level of indentation if an entire function is wrapped.
+
+    .. versionchanged:: 2.0
+        `errstate` is now fully thread and asyncio safe, but may not be
+        entered more than once.
+        It is not safe to decorate async functions using ``errstate``.
+
+    Parameters
+    ----------
+    kwargs : {divide, over, under, invalid}
+        Keyword arguments. The valid keywords are the possible floating-point
+        exceptions. Each keyword should have a string value that defines the
+        treatment for the particular error. Possible values are
+        {'ignore', 'warn', 'raise', 'call', 'print', 'log'}.
+
+    See Also
+    --------
+    seterr, geterr, seterrcall, geterrcall
+
+    Notes
+    -----
+    For complete documentation of the types of floating-point exceptions and
+    treatment options, see `seterr`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> olderr = np.seterr(all='ignore')  # Set error handling to known state.
+
+    >>> np.arange(3) / 0.
+    array([nan, inf, inf])
+    >>> with np.errstate(divide='ignore'):
+    ...     np.arange(3) / 0.
+    array([nan, inf, inf])
+
+    >>> np.sqrt(-1)
+    np.float64(nan)
+    >>> with np.errstate(invalid='raise'):
+    ...     np.sqrt(-1)
+    Traceback (most recent call last):
+      File "<stdin>", line 2, in <module>
+    FloatingPointError: invalid value encountered in sqrt
+
+    Outside the context the error handling behavior has not changed:
+
+    >>> np.geterr()
+    {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'}
+    >>> olderr = np.seterr(**olderr)  # restore original state
+
+    """
+    __slots__ = (
+        "_all",
+        "_call",
+        "_divide",
+        "_invalid",
+        "_over",
+        "_token",
+        "_under",
+    )
+
+    def __init__(self, *, call=_Unspecified,
+                 all=None, divide=None, over=None, under=None, invalid=None):
+        self._token = None
+        self._call = call
+        self._all = all
+        self._divide = divide
+        self._over = over
+        self._under = under
+        self._invalid = invalid
+
+    def __enter__(self):
+        # Note that __call__ duplicates much of this logic
+        if self._token is not None:
+            raise TypeError("Cannot enter `np.errstate` twice.")
+        if self._call is _Unspecified:
+            extobj = _make_extobj(
+                    all=self._all, divide=self._divide, over=self._over,
+                    under=self._under, invalid=self._invalid)
+        else:
+            extobj = _make_extobj(
+                    call=self._call,
+                    all=self._all, divide=self._divide, over=self._over,
+                    under=self._under, invalid=self._invalid)
+
+        self._token = _extobj_contextvar.set(extobj)
+
+    def __exit__(self, *exc_info):
+        _extobj_contextvar.reset(self._token)
+
+    def __call__(self, func):
+        # We need to customize `__call__` compared to `ContextDecorator`
+        # because we must store the token per-thread so cannot store it on
+        # the instance (we could create a new instance for this).
+        # This duplicates the code from `__enter__`.
+        @functools.wraps(func)
+        def inner(*args, **kwargs):
+            if self._call is _Unspecified:
+                extobj = _make_extobj(
+                        all=self._all, divide=self._divide, over=self._over,
+                        under=self._under, invalid=self._invalid)
+            else:
+                extobj = _make_extobj(
+                        call=self._call,
+                        all=self._all, divide=self._divide, over=self._over,
+                        under=self._under, invalid=self._invalid)
+
+            _token = _extobj_contextvar.set(extobj)
+            try:
+                # Call the original, decorated, function:
+                return func(*args, **kwargs)
+            finally:
+                _extobj_contextvar.reset(_token)
+
+        return inner
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_ufunc_config.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/_ufunc_config.pyi
new file mode 100644
index 0000000..1a66131
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_ufunc_config.pyi
@@ -0,0 +1,32 @@
+from collections.abc import Callable
+from typing import Any, Literal, TypeAlias, TypedDict, type_check_only
+
+from _typeshed import SupportsWrite
+
+from numpy import errstate as errstate
+
+_ErrKind: TypeAlias = Literal["ignore", "warn", "raise", "call", "print", "log"]
+_ErrFunc: TypeAlias = Callable[[str, int], Any]
+_ErrCall: TypeAlias = _ErrFunc | SupportsWrite[str]
+
+@type_check_only
+class _ErrDict(TypedDict):
+    divide: _ErrKind
+    over: _ErrKind
+    under: _ErrKind
+    invalid: _ErrKind
+
+def seterr(
+    all: _ErrKind | None = ...,
+    divide: _ErrKind | None = ...,
+    over: _ErrKind | None = ...,
+    under: _ErrKind | None = ...,
+    invalid: _ErrKind | None = ...,
+) -> _ErrDict: ...
+def geterr() -> _ErrDict: ...
+def setbufsize(size: int) -> int: ...
+def getbufsize() -> int: ...
+def seterrcall(func: _ErrCall | None) -> _ErrCall | None: ...
+def geterrcall() -> _ErrCall | None: ...
+
+# See `numpy/__init__.pyi` for the `errstate` class and `no_nep5_warnings`
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/_umath_tests.cpython-312-x86_64-linux-gnu.so b/.venv/lib/python3.12/site-packages/numpy/_core/_umath_tests.cpython-312-x86_64-linux-gnu.so
new file mode 100755
index 0000000..51212e8
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/_umath_tests.cpython-312-x86_64-linux-gnu.so
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/arrayprint.py b/.venv/lib/python3.12/site-packages/numpy/_core/arrayprint.py
new file mode 100644
index 0000000..2a68428
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/arrayprint.py
@@ -0,0 +1,1775 @@
+"""Array printing function
+
+$Id: arrayprint.py,v 1.9 2005/09/13 13:58:44 teoliphant Exp $
+
+"""
+__all__ = ["array2string", "array_str", "array_repr",
+           "set_printoptions", "get_printoptions", "printoptions",
+           "format_float_positional", "format_float_scientific"]
+__docformat__ = 'restructuredtext'
+
+#
+# Written by Konrad Hinsen <hinsenk@ere.umontreal.ca>
+# last revision: 1996-3-13
+# modified by Jim Hugunin 1997-3-3 for repr's and str's (and other details)
+# and by Perry Greenfield 2000-4-1 for numarray
+# and by Travis Oliphant  2005-8-22 for numpy
+
+
+# Note: Both scalartypes.c.src and arrayprint.py implement strs for numpy
+# scalars but for different purposes. scalartypes.c.src has str/reprs for when
+# the scalar is printed on its own, while arrayprint.py has strs for when
+# scalars are printed inside an ndarray. Only the latter strs are currently
+# user-customizable.
+
+import functools
+import numbers
+import sys
+
+try:
+    from _thread import get_ident
+except ImportError:
+    from _dummy_thread import get_ident
+
+import contextlib
+import operator
+import warnings
+
+import numpy as np
+
+from . import numerictypes as _nt
+from .fromnumeric import any
+from .multiarray import (
+    array,
+    datetime_as_string,
+    datetime_data,
+    dragon4_positional,
+    dragon4_scientific,
+    ndarray,
+)
+from .numeric import asarray, concatenate, errstate
+from .numerictypes import complex128, flexible, float64, int_
+from .overrides import array_function_dispatch, set_module
+from .printoptions import format_options
+from .umath import absolute, isfinite, isinf, isnat
+
+
+def _make_options_dict(precision=None, threshold=None, edgeitems=None,
+                       linewidth=None, suppress=None, nanstr=None, infstr=None,
+                       sign=None, formatter=None, floatmode=None, legacy=None,
+                       override_repr=None):
+    """
+    Make a dictionary out of the non-None arguments, plus conversion of
+    *legacy* and sanity checks.
+    """
+
+    options = {k: v for k, v in list(locals().items()) if v is not None}
+
+    if suppress is not None:
+        options['suppress'] = bool(suppress)
+
+    modes = ['fixed', 'unique', 'maxprec', 'maxprec_equal']
+    if floatmode not in modes + [None]:
+        raise ValueError("floatmode option must be one of " +
+                         ", ".join(f'"{m}"' for m in modes))
+
+    if sign not in [None, '-', '+', ' ']:
+        raise ValueError("sign option must be one of ' ', '+', or '-'")
+
+    if legacy is False:
+        options['legacy'] = sys.maxsize
+    elif legacy == False:  # noqa: E712
+        warnings.warn(
+            f"Passing `legacy={legacy!r}` is deprecated.",
+            FutureWarning, stacklevel=3
+        )
+        options['legacy'] = sys.maxsize
+    elif legacy == '1.13':
+        options['legacy'] = 113
+    elif legacy == '1.21':
+        options['legacy'] = 121
+    elif legacy == '1.25':
+        options['legacy'] = 125
+    elif legacy == '2.1':
+        options['legacy'] = 201
+    elif legacy == '2.2':
+        options['legacy'] = 202
+    elif legacy is None:
+        pass  # OK, do nothing.
+    else:
+        warnings.warn(
+            "legacy printing option can currently only be '1.13', '1.21', "
+            "'1.25', '2.1', '2.2' or `False`", stacklevel=3)
+
+    if threshold is not None:
+        # forbid the bad threshold arg suggested by stack overflow, gh-12351
+        if not isinstance(threshold, numbers.Number):
+            raise TypeError("threshold must be numeric")
+        if np.isnan(threshold):
+            raise ValueError("threshold must be non-NAN, try "
+                             "sys.maxsize for untruncated representation")
+
+    if precision is not None:
+        # forbid the bad precision arg as suggested by issue #18254
+        try:
+            options['precision'] = operator.index(precision)
+        except TypeError as e:
+            raise TypeError('precision must be an integer') from e
+
+    return options
+
+
+@set_module('numpy')
+def set_printoptions(precision=None, threshold=None, edgeitems=None,
+                     linewidth=None, suppress=None, nanstr=None,
+                     infstr=None, formatter=None, sign=None, floatmode=None,
+                     *, legacy=None, override_repr=None):
+    """
+    Set printing options.
+
+    These options determine the way floating point numbers, arrays and
+    other NumPy objects are displayed.
+
+    Parameters
+    ----------
+    precision : int or None, optional
+        Number of digits of precision for floating point output (default 8).
+        May be None if `floatmode` is not `fixed`, to print as many digits as
+        necessary to uniquely specify the value.
+    threshold : int, optional
+        Total number of array elements which trigger summarization
+        rather than full repr (default 1000).
+        To always use the full repr without summarization, pass `sys.maxsize`.
+    edgeitems : int, optional
+        Number of array items in summary at beginning and end of
+        each dimension (default 3).
+    linewidth : int, optional
+        The number of characters per line for the purpose of inserting
+        line breaks (default 75).
+    suppress : bool, optional
+        If True, always print floating point numbers using fixed point
+        notation, in which case numbers equal to zero in the current precision
+        will print as zero.  If False, then scientific notation is used when
+        absolute value of the smallest number is < 1e-4 or the ratio of the
+        maximum absolute value to the minimum is > 1e3. The default is False.
+    nanstr : str, optional
+        String representation of floating point not-a-number (default nan).
+    infstr : str, optional
+        String representation of floating point infinity (default inf).
+    sign : string, either '-', '+', or ' ', optional
+        Controls printing of the sign of floating-point types. If '+', always
+        print the sign of positive values. If ' ', always prints a space
+        (whitespace character) in the sign position of positive values.  If
+        '-', omit the sign character of positive values. (default '-')
+
+        .. versionchanged:: 2.0
+             The sign parameter can now be an integer type, previously
+             types were floating-point types.
+
+    formatter : dict of callables, optional
+        If not None, the keys should indicate the type(s) that the respective
+        formatting function applies to.  Callables should return a string.
+        Types that are not specified (by their corresponding keys) are handled
+        by the default formatters.  Individual types for which a formatter
+        can be set are:
+
+        - 'bool'
+        - 'int'
+        - 'timedelta' : a `numpy.timedelta64`
+        - 'datetime' : a `numpy.datetime64`
+        - 'float'
+        - 'longfloat' : 128-bit floats
+        - 'complexfloat'
+        - 'longcomplexfloat' : composed of two 128-bit floats
+        - 'numpystr' : types `numpy.bytes_` and `numpy.str_`
+        - 'object' : `np.object_` arrays
+
+        Other keys that can be used to set a group of types at once are:
+
+        - 'all' : sets all types
+        - 'int_kind' : sets 'int'
+        - 'float_kind' : sets 'float' and 'longfloat'
+        - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'
+        - 'str_kind' : sets 'numpystr'
+    floatmode : str, optional
+        Controls the interpretation of the `precision` option for
+        floating-point types. Can take the following values
+        (default maxprec_equal):
+
+        * 'fixed': Always print exactly `precision` fractional digits,
+                even if this would print more or fewer digits than
+                necessary to specify the value uniquely.
+        * 'unique': Print the minimum number of fractional digits necessary
+                to represent each value uniquely. Different elements may
+                have a different number of digits. The value of the
+                `precision` option is ignored.
+        * 'maxprec': Print at most `precision` fractional digits, but if
+                an element can be uniquely represented with fewer digits
+                only print it with that many.
+        * 'maxprec_equal': Print at most `precision` fractional digits,
+                but if every element in the array can be uniquely
+                represented with an equal number of fewer digits, use that
+                many digits for all elements.
+    legacy : string or `False`, optional
+        If set to the string ``'1.13'`` enables 1.13 legacy printing mode. This
+        approximates numpy 1.13 print output by including a space in the sign
+        position of floats and different behavior for 0d arrays. This also
+        enables 1.21 legacy printing mode (described below).
+
+        If set to the string ``'1.21'`` enables 1.21 legacy printing mode. This
+        approximates numpy 1.21 print output of complex structured dtypes
+        by not inserting spaces after commas that separate fields and after
+        colons.
+
+        If set to ``'1.25'`` approximates printing of 1.25 which mainly means
+        that numeric scalars are printed without their type information, e.g.
+        as ``3.0`` rather than ``np.float64(3.0)``.
+
+        If set to ``'2.1'``, shape information is not given when arrays are
+        summarized (i.e., multiple elements replaced with ``...``).
+
+        If set to ``'2.2'``, the transition to use scientific notation for
+        printing ``np.float16`` and ``np.float32`` types may happen later or
+        not at all for larger values.
+
+        If set to `False`, disables legacy mode.
+
+        Unrecognized strings will be ignored with a warning for forward
+        compatibility.
+
+        .. versionchanged:: 1.22.0
+        .. versionchanged:: 2.2
+
+    override_repr: callable, optional
+        If set a passed function will be used for generating arrays' repr.
+        Other options will be ignored.
+
+    See Also
+    --------
+    get_printoptions, printoptions, array2string
+
+    Notes
+    -----
+    `formatter` is always reset with a call to `set_printoptions`.
+
+    Use `printoptions` as a context manager to set the values temporarily.
+
+    Examples
+    --------
+    Floating point precision can be set:
+
+    >>> import numpy as np
+    >>> np.set_printoptions(precision=4)
+    >>> np.array([1.123456789])
+    [1.1235]
+
+    Long arrays can be summarised:
+
+    >>> np.set_printoptions(threshold=5)
+    >>> np.arange(10)
+    array([0, 1, 2, ..., 7, 8, 9], shape=(10,))
+
+    Small results can be suppressed:
+
+    >>> eps = np.finfo(float).eps
+    >>> x = np.arange(4.)
+    >>> x**2 - (x + eps)**2
+    array([-4.9304e-32, -4.4409e-16,  0.0000e+00,  0.0000e+00])
+    >>> np.set_printoptions(suppress=True)
+    >>> x**2 - (x + eps)**2
+    array([-0., -0.,  0.,  0.])
+
+    A custom formatter can be used to display array elements as desired:
+
+    >>> np.set_printoptions(formatter={'all':lambda x: 'int: '+str(-x)})
+    >>> x = np.arange(3)
+    >>> x
+    array([int: 0, int: -1, int: -2])
+    >>> np.set_printoptions()  # formatter gets reset
+    >>> x
+    array([0, 1, 2])
+
+    To put back the default options, you can use:
+
+    >>> np.set_printoptions(edgeitems=3, infstr='inf',
+    ... linewidth=75, nanstr='nan', precision=8,
+    ... suppress=False, threshold=1000, formatter=None)
+
+    Also to temporarily override options, use `printoptions`
+    as a context manager:
+
+    >>> with np.printoptions(precision=2, suppress=True, threshold=5):
+    ...     np.linspace(0, 10, 10)
+    array([ 0.  ,  1.11,  2.22, ...,  7.78,  8.89, 10.  ], shape=(10,))
+
+    """
+    _set_printoptions(precision, threshold, edgeitems, linewidth, suppress,
+                      nanstr, infstr, formatter, sign, floatmode,
+                      legacy=legacy, override_repr=override_repr)
+
+
+def _set_printoptions(precision=None, threshold=None, edgeitems=None,
+                      linewidth=None, suppress=None, nanstr=None,
+                      infstr=None, formatter=None, sign=None, floatmode=None,
+                      *, legacy=None, override_repr=None):
+    new_opt = _make_options_dict(precision, threshold, edgeitems, linewidth,
+                                 suppress, nanstr, infstr, sign, formatter,
+                                 floatmode, legacy)
+    # formatter and override_repr are always reset
+    new_opt['formatter'] = formatter
+    new_opt['override_repr'] = override_repr
+
+    updated_opt = format_options.get() | new_opt
+    updated_opt.update(new_opt)
+
+    if updated_opt['legacy'] == 113:
+        updated_opt['sign'] = '-'
+
+    return format_options.set(updated_opt)
+
+
+@set_module('numpy')
+def get_printoptions():
+    """
+    Return the current print options.
+
+    Returns
+    -------
+    print_opts : dict
+        Dictionary of current print options with keys
+
+        - precision : int
+        - threshold : int
+        - edgeitems : int
+        - linewidth : int
+        - suppress : bool
+        - nanstr : str
+        - infstr : str
+        - sign : str
+        - formatter : dict of callables
+        - floatmode : str
+        - legacy : str or False
+
+        For a full description of these options, see `set_printoptions`.
+
+    See Also
+    --------
+    set_printoptions, printoptions
+
+    Examples
+    --------
+    >>> import numpy as np
+
+    >>> np.get_printoptions()
+    {'edgeitems': 3, 'threshold': 1000, ..., 'override_repr': None}
+
+    >>> np.get_printoptions()['linewidth']
+    75
+    >>> np.set_printoptions(linewidth=100)
+    >>> np.get_printoptions()['linewidth']
+    100
+
+    """
+    opts = format_options.get().copy()
+    opts['legacy'] = {
+        113: '1.13', 121: '1.21', 125: '1.25', 201: '2.1',
+        202: '2.2', sys.maxsize: False,
+    }[opts['legacy']]
+    return opts
+
+
+def _get_legacy_print_mode():
+    """Return the legacy print mode as an int."""
+    return format_options.get()['legacy']
+
+
+@set_module('numpy')
+@contextlib.contextmanager
+def printoptions(*args, **kwargs):
+    """Context manager for setting print options.
+
+    Set print options for the scope of the `with` block, and restore the old
+    options at the end. See `set_printoptions` for the full description of
+    available options.
+
+    Examples
+    --------
+    >>> import numpy as np
+
+    >>> from numpy.testing import assert_equal
+    >>> with np.printoptions(precision=2):
+    ...     np.array([2.0]) / 3
+    array([0.67])
+
+    The `as`-clause of the `with`-statement gives the current print options:
+
+    >>> with np.printoptions(precision=2) as opts:
+    ...      assert_equal(opts, np.get_printoptions())
+
+    See Also
+    --------
+    set_printoptions, get_printoptions
+
+    """
+    token = _set_printoptions(*args, **kwargs)
+
+    try:
+        yield get_printoptions()
+    finally:
+        format_options.reset(token)
+
+
+def _leading_trailing(a, edgeitems, index=()):
+    """
+    Keep only the N-D corners (leading and trailing edges) of an array.
+
+    Should be passed a base-class ndarray, since it makes no guarantees about
+    preserving subclasses.
+    """
+    axis = len(index)
+    if axis == a.ndim:
+        return a[index]
+
+    if a.shape[axis] > 2 * edgeitems:
+        return concatenate((
+            _leading_trailing(a, edgeitems, index + np.index_exp[:edgeitems]),
+            _leading_trailing(a, edgeitems, index + np.index_exp[-edgeitems:])
+        ), axis=axis)
+    else:
+        return _leading_trailing(a, edgeitems, index + np.index_exp[:])
+
+
+def _object_format(o):
+    """ Object arrays containing lists should be printed unambiguously """
+    if type(o) is list:
+        fmt = 'list({!r})'
+    else:
+        fmt = '{!r}'
+    return fmt.format(o)
+
+def repr_format(x):
+    if isinstance(x, (np.str_, np.bytes_)):
+        return repr(x.item())
+    return repr(x)
+
+def str_format(x):
+    if isinstance(x, (np.str_, np.bytes_)):
+        return str(x.item())
+    return str(x)
+
+def _get_formatdict(data, *, precision, floatmode, suppress, sign, legacy,
+                    formatter, **kwargs):
+    # note: extra arguments in kwargs are ignored
+
+    # wrapped in lambdas to avoid taking a code path
+    # with the wrong type of data
+    formatdict = {
+        'bool': lambda: BoolFormat(data),
+        'int': lambda: IntegerFormat(data, sign),
+        'float': lambda: FloatingFormat(
+            data, precision, floatmode, suppress, sign, legacy=legacy),
+        'longfloat': lambda: FloatingFormat(
+            data, precision, floatmode, suppress, sign, legacy=legacy),
+        'complexfloat': lambda: ComplexFloatingFormat(
+            data, precision, floatmode, suppress, sign, legacy=legacy),
+        'longcomplexfloat': lambda: ComplexFloatingFormat(
+            data, precision, floatmode, suppress, sign, legacy=legacy),
+        'datetime': lambda: DatetimeFormat(data, legacy=legacy),
+        'timedelta': lambda: TimedeltaFormat(data),
+        'object': lambda: _object_format,
+        'void': lambda: str_format,
+        'numpystr': lambda: repr_format}
+
+    # we need to wrap values in `formatter` in a lambda, so that the interface
+    # is the same as the above values.
+    def indirect(x):
+        return lambda: x
+
+    if formatter is not None:
+        fkeys = [k for k in formatter.keys() if formatter[k] is not None]
+        if 'all' in fkeys:
+            for key in formatdict.keys():
+                formatdict[key] = indirect(formatter['all'])
+        if 'int_kind' in fkeys:
+            for key in ['int']:
+                formatdict[key] = indirect(formatter['int_kind'])
+        if 'float_kind' in fkeys:
+            for key in ['float', 'longfloat']:
+                formatdict[key] = indirect(formatter['float_kind'])
+        if 'complex_kind' in fkeys:
+            for key in ['complexfloat', 'longcomplexfloat']:
+                formatdict[key] = indirect(formatter['complex_kind'])
+        if 'str_kind' in fkeys:
+            formatdict['numpystr'] = indirect(formatter['str_kind'])
+        for key in formatdict.keys():
+            if key in fkeys:
+                formatdict[key] = indirect(formatter[key])
+
+    return formatdict
+
+def _get_format_function(data, **options):
+    """
+    find the right formatting function for the dtype_
+    """
+    dtype_ = data.dtype
+    dtypeobj = dtype_.type
+    formatdict = _get_formatdict(data, **options)
+    if dtypeobj is None:
+        return formatdict["numpystr"]()
+    elif issubclass(dtypeobj, _nt.bool):
+        return formatdict['bool']()
+    elif issubclass(dtypeobj, _nt.integer):
+        if issubclass(dtypeobj, _nt.timedelta64):
+            return formatdict['timedelta']()
+        else:
+            return formatdict['int']()
+    elif issubclass(dtypeobj, _nt.floating):
+        if issubclass(dtypeobj, _nt.longdouble):
+            return formatdict['longfloat']()
+        else:
+            return formatdict['float']()
+    elif issubclass(dtypeobj, _nt.complexfloating):
+        if issubclass(dtypeobj, _nt.clongdouble):
+            return formatdict['longcomplexfloat']()
+        else:
+            return formatdict['complexfloat']()
+    elif issubclass(dtypeobj, (_nt.str_, _nt.bytes_)):
+        return formatdict['numpystr']()
+    elif issubclass(dtypeobj, _nt.datetime64):
+        return formatdict['datetime']()
+    elif issubclass(dtypeobj, _nt.object_):
+        return formatdict['object']()
+    elif issubclass(dtypeobj, _nt.void):
+        if dtype_.names is not None:
+            return StructuredVoidFormat.from_data(data, **options)
+        else:
+            return formatdict['void']()
+    else:
+        return formatdict['numpystr']()
+
+
+def _recursive_guard(fillvalue='...'):
+    """
+    Like the python 3.2 reprlib.recursive_repr, but forwards *args and **kwargs
+
+    Decorates a function such that if it calls itself with the same first
+    argument, it returns `fillvalue` instead of recursing.
+
+    Largely copied from reprlib.recursive_repr
+    """
+
+    def decorating_function(f):
+        repr_running = set()
+
+        @functools.wraps(f)
+        def wrapper(self, *args, **kwargs):
+            key = id(self), get_ident()
+            if key in repr_running:
+                return fillvalue
+            repr_running.add(key)
+            try:
+                return f(self, *args, **kwargs)
+            finally:
+                repr_running.discard(key)
+
+        return wrapper
+
+    return decorating_function
+
+
+# gracefully handle recursive calls, when object arrays contain themselves
+@_recursive_guard()
+def _array2string(a, options, separator=' ', prefix=""):
+    # The formatter __init__s in _get_format_function cannot deal with
+    # subclasses yet, and we also need to avoid recursion issues in
+    # _formatArray with subclasses which return 0d arrays in place of scalars
+    data = asarray(a)
+    if a.shape == ():
+        a = data
+
+    if a.size > options['threshold']:
+        summary_insert = "..."
+        data = _leading_trailing(data, options['edgeitems'])
+    else:
+        summary_insert = ""
+
+    # find the right formatting function for the array
+    format_function = _get_format_function(data, **options)
+
+    # skip over "["
+    next_line_prefix = " "
+    # skip over array(
+    next_line_prefix += " " * len(prefix)
+
+    lst = _formatArray(a, format_function, options['linewidth'],
+                       next_line_prefix, separator, options['edgeitems'],
+                       summary_insert, options['legacy'])
+    return lst
+
+
+def _array2string_dispatcher(
+        a, max_line_width=None, precision=None,
+        suppress_small=None, separator=None, prefix=None,
+        style=None, formatter=None, threshold=None,
+        edgeitems=None, sign=None, floatmode=None, suffix=None,
+        *, legacy=None):
+    return (a,)
+
+
+@array_function_dispatch(_array2string_dispatcher, module='numpy')
+def array2string(a, max_line_width=None, precision=None,
+                 suppress_small=None, separator=' ', prefix="",
+                 style=np._NoValue, formatter=None, threshold=None,
+                 edgeitems=None, sign=None, floatmode=None, suffix="",
+                 *, legacy=None):
+    """
+    Return a string representation of an array.
+
+    Parameters
+    ----------
+    a : ndarray
+        Input array.
+    max_line_width : int, optional
+        Inserts newlines if text is longer than `max_line_width`.
+        Defaults to ``numpy.get_printoptions()['linewidth']``.
+    precision : int or None, optional
+        Floating point precision.
+        Defaults to ``numpy.get_printoptions()['precision']``.
+    suppress_small : bool, optional
+        Represent numbers "very close" to zero as zero; default is False.
+        Very close is defined by precision: if the precision is 8, e.g.,
+        numbers smaller (in absolute value) than 5e-9 are represented as
+        zero.
+        Defaults to ``numpy.get_printoptions()['suppress']``.
+    separator : str, optional
+        Inserted between elements.
+    prefix : str, optional
+    suffix : str, optional
+        The length of the prefix and suffix strings are used to respectively
+        align and wrap the output. An array is typically printed as::
+
+          prefix + array2string(a) + suffix
+
+        The output is left-padded by the length of the prefix string, and
+        wrapping is forced at the column ``max_line_width - len(suffix)``.
+        It should be noted that the content of prefix and suffix strings are
+        not included in the output.
+    style : _NoValue, optional
+        Has no effect, do not use.
+
+        .. deprecated:: 1.14.0
+    formatter : dict of callables, optional
+        If not None, the keys should indicate the type(s) that the respective
+        formatting function applies to.  Callables should return a string.
+        Types that are not specified (by their corresponding keys) are handled
+        by the default formatters.  Individual types for which a formatter
+        can be set are:
+
+        - 'bool'
+        - 'int'
+        - 'timedelta' : a `numpy.timedelta64`
+        - 'datetime' : a `numpy.datetime64`
+        - 'float'
+        - 'longfloat' : 128-bit floats
+        - 'complexfloat'
+        - 'longcomplexfloat' : composed of two 128-bit floats
+        - 'void' : type `numpy.void`
+        - 'numpystr' : types `numpy.bytes_` and `numpy.str_`
+
+        Other keys that can be used to set a group of types at once are:
+
+        - 'all' : sets all types
+        - 'int_kind' : sets 'int'
+        - 'float_kind' : sets 'float' and 'longfloat'
+        - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'
+        - 'str_kind' : sets 'numpystr'
+    threshold : int, optional
+        Total number of array elements which trigger summarization
+        rather than full repr.
+        Defaults to ``numpy.get_printoptions()['threshold']``.
+    edgeitems : int, optional
+        Number of array items in summary at beginning and end of
+        each dimension.
+        Defaults to ``numpy.get_printoptions()['edgeitems']``.
+    sign : string, either '-', '+', or ' ', optional
+        Controls printing of the sign of floating-point types. If '+', always
+        print the sign of positive values. If ' ', always prints a space
+        (whitespace character) in the sign position of positive values.  If
+        '-', omit the sign character of positive values.
+        Defaults to ``numpy.get_printoptions()['sign']``.
+
+        .. versionchanged:: 2.0
+             The sign parameter can now be an integer type, previously
+             types were floating-point types.
+
+    floatmode : str, optional
+        Controls the interpretation of the `precision` option for
+        floating-point types.
+        Defaults to ``numpy.get_printoptions()['floatmode']``.
+        Can take the following values:
+
+        - 'fixed': Always print exactly `precision` fractional digits,
+          even if this would print more or fewer digits than
+          necessary to specify the value uniquely.
+        - 'unique': Print the minimum number of fractional digits necessary
+          to represent each value uniquely. Different elements may
+          have a different number of digits.  The value of the
+          `precision` option is ignored.
+        - 'maxprec': Print at most `precision` fractional digits, but if
+          an element can be uniquely represented with fewer digits
+          only print it with that many.
+        - 'maxprec_equal': Print at most `precision` fractional digits,
+          but if every element in the array can be uniquely
+          represented with an equal number of fewer digits, use that
+          many digits for all elements.
+    legacy : string or `False`, optional
+        If set to the string ``'1.13'`` enables 1.13 legacy printing mode. This
+        approximates numpy 1.13 print output by including a space in the sign
+        position of floats and different behavior for 0d arrays. If set to
+        `False`, disables legacy mode. Unrecognized strings will be ignored
+        with a warning for forward compatibility.
+
+    Returns
+    -------
+    array_str : str
+        String representation of the array.
+
+    Raises
+    ------
+    TypeError
+        if a callable in `formatter` does not return a string.
+
+    See Also
+    --------
+    array_str, array_repr, set_printoptions, get_printoptions
+
+    Notes
+    -----
+    If a formatter is specified for a certain type, the `precision` keyword is
+    ignored for that type.
+
+    This is a very flexible function; `array_repr` and `array_str` are using
+    `array2string` internally so keywords with the same name should work
+    identically in all three functions.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1e-16,1,2,3])
+    >>> np.array2string(x, precision=2, separator=',',
+    ...                       suppress_small=True)
+    '[0.,1.,2.,3.]'
+
+    >>> x  = np.arange(3.)
+    >>> np.array2string(x, formatter={'float_kind':lambda x: "%.2f" % x})
+    '[0.00 1.00 2.00]'
+
+    >>> x  = np.arange(3)
+    >>> np.array2string(x, formatter={'int':lambda x: hex(x)})
+    '[0x0 0x1 0x2]'
+
+    """
+
+    overrides = _make_options_dict(precision, threshold, edgeitems,
+                                   max_line_width, suppress_small, None, None,
+                                   sign, formatter, floatmode, legacy)
+    options = format_options.get().copy()
+    options.update(overrides)
+
+    if options['legacy'] <= 113:
+        if style is np._NoValue:
+            style = repr
+
+        if a.shape == () and a.dtype.names is None:
+            return style(a.item())
+    elif style is not np._NoValue:
+        # Deprecation 11-9-2017  v1.14
+        warnings.warn("'style' argument is deprecated and no longer functional"
+                      " except in 1.13 'legacy' mode",
+                      DeprecationWarning, stacklevel=2)
+
+    if options['legacy'] > 113:
+        options['linewidth'] -= len(suffix)
+
+    # treat as a null array if any of shape elements == 0
+    if a.size == 0:
+        return "[]"
+
+    return _array2string(a, options, separator, prefix)
+
+
+def _extendLine(s, line, word, line_width, next_line_prefix, legacy):
+    needs_wrap = len(line) + len(word) > line_width
+    if legacy > 113:
+        # don't wrap lines if it won't help
+        if len(line) <= len(next_line_prefix):
+            needs_wrap = False
+
+    if needs_wrap:
+        s += line.rstrip() + "\n"
+        line = next_line_prefix
+    line += word
+    return s, line
+
+
+def _extendLine_pretty(s, line, word, line_width, next_line_prefix, legacy):
+    """
+    Extends line with nicely formatted (possibly multi-line) string ``word``.
+    """
+    words = word.splitlines()
+    if len(words) == 1 or legacy <= 113:
+        return _extendLine(s, line, word, line_width, next_line_prefix, legacy)
+
+    max_word_length = max(len(word) for word in words)
+    if (len(line) + max_word_length > line_width and
+            len(line) > len(next_line_prefix)):
+        s += line.rstrip() + '\n'
+        line = next_line_prefix + words[0]
+        indent = next_line_prefix
+    else:
+        indent = len(line) * ' '
+        line += words[0]
+
+    for word in words[1::]:
+        s += line.rstrip() + '\n'
+        line = indent + word
+
+    suffix_length = max_word_length - len(words[-1])
+    line += suffix_length * ' '
+
+    return s, line
+
+def _formatArray(a, format_function, line_width, next_line_prefix,
+                 separator, edge_items, summary_insert, legacy):
+    """formatArray is designed for two modes of operation:
+
+    1. Full output
+
+    2. Summarized output
+
+    """
+    def recurser(index, hanging_indent, curr_width):
+        """
+        By using this local function, we don't need to recurse with all the
+        arguments. Since this function is not created recursively, the cost is
+        not significant
+        """
+        axis = len(index)
+        axes_left = a.ndim - axis
+
+        if axes_left == 0:
+            return format_function(a[index])
+
+        # when recursing, add a space to align with the [ added, and reduce the
+        # length of the line by 1
+        next_hanging_indent = hanging_indent + ' '
+        if legacy <= 113:
+            next_width = curr_width
+        else:
+            next_width = curr_width - len(']')
+
+        a_len = a.shape[axis]
+        show_summary = summary_insert and 2 * edge_items < a_len
+        if show_summary:
+            leading_items = edge_items
+            trailing_items = edge_items
+        else:
+            leading_items = 0
+            trailing_items = a_len
+
+        # stringify the array with the hanging indent on the first line too
+        s = ''
+
+        # last axis (rows) - wrap elements if they would not fit on one line
+        if axes_left == 1:
+            # the length up until the beginning of the separator / bracket
+            if legacy <= 113:
+                elem_width = curr_width - len(separator.rstrip())
+            else:
+                elem_width = curr_width - max(
+                    len(separator.rstrip()), len(']')
+                )
+
+            line = hanging_indent
+            for i in range(leading_items):
+                word = recurser(index + (i,), next_hanging_indent, next_width)
+                s, line = _extendLine_pretty(
+                    s, line, word, elem_width, hanging_indent, legacy)
+                line += separator
+
+            if show_summary:
+                s, line = _extendLine(
+                    s, line, summary_insert, elem_width, hanging_indent, legacy
+                )
+                if legacy <= 113:
+                    line += ", "
+                else:
+                    line += separator
+
+            for i in range(trailing_items, 1, -1):
+                word = recurser(index + (-i,), next_hanging_indent, next_width)
+                s, line = _extendLine_pretty(
+                    s, line, word, elem_width, hanging_indent, legacy)
+                line += separator
+
+            if legacy <= 113:
+                # width of the separator is not considered on 1.13
+                elem_width = curr_width
+            word = recurser(index + (-1,), next_hanging_indent, next_width)
+            s, line = _extendLine_pretty(
+                s, line, word, elem_width, hanging_indent, legacy)
+
+            s += line
+
+        # other axes - insert newlines between rows
+        else:
+            s = ''
+            line_sep = separator.rstrip() + '\n' * (axes_left - 1)
+
+            for i in range(leading_items):
+                nested = recurser(
+                    index + (i,), next_hanging_indent, next_width
+                )
+                s += hanging_indent + nested + line_sep
+
+            if show_summary:
+                if legacy <= 113:
+                    # trailing space, fixed nbr of newlines,
+                    # and fixed separator
+                    s += hanging_indent + summary_insert + ", \n"
+                else:
+                    s += hanging_indent + summary_insert + line_sep
+
+            for i in range(trailing_items, 1, -1):
+                nested = recurser(index + (-i,), next_hanging_indent,
+                                  next_width)
+                s += hanging_indent + nested + line_sep
+
+            nested = recurser(index + (-1,), next_hanging_indent, next_width)
+            s += hanging_indent + nested
+
+        # remove the hanging indent, and wrap in []
+        s = '[' + s[len(hanging_indent):] + ']'
+        return s
+
+    try:
+        # invoke the recursive part with an initial index and prefix
+        return recurser(index=(),
+                        hanging_indent=next_line_prefix,
+                        curr_width=line_width)
+    finally:
+        # recursive closures have a cyclic reference to themselves, which
+        # requires gc to collect (gh-10620). To avoid this problem, for
+        # performance and PyPy friendliness, we break the cycle:
+        recurser = None
+
+def _none_or_positive_arg(x, name):
+    if x is None:
+        return -1
+    if x < 0:
+        raise ValueError(f"{name} must be >= 0")
+    return x
+
+class FloatingFormat:
+    """ Formatter for subtypes of np.floating """
+    def __init__(self, data, precision, floatmode, suppress_small, sign=False,
+                 *, legacy=None):
+        # for backcompatibility, accept bools
+        if isinstance(sign, bool):
+            sign = '+' if sign else '-'
+
+        self._legacy = legacy
+        if self._legacy <= 113:
+            # when not 0d, legacy does not support '-'
+            if data.shape != () and sign == '-':
+                sign = ' '
+
+        self.floatmode = floatmode
+        if floatmode == 'unique':
+            self.precision = None
+        else:
+            self.precision = precision
+
+        self.precision = _none_or_positive_arg(self.precision, 'precision')
+
+        self.suppress_small = suppress_small
+        self.sign = sign
+        self.exp_format = False
+        self.large_exponent = False
+        self.fillFormat(data)
+
+    def fillFormat(self, data):
+        # only the finite values are used to compute the number of digits
+        finite_vals = data[isfinite(data)]
+
+        # choose exponential mode based on the non-zero finite values:
+        abs_non_zero = absolute(finite_vals[finite_vals != 0])
+        if len(abs_non_zero) != 0:
+            max_val = np.max(abs_non_zero)
+            min_val = np.min(abs_non_zero)
+            if self._legacy <= 202:
+                exp_cutoff_max = 1.e8
+            else:
+                # consider data type while deciding the max cutoff for exp format
+                exp_cutoff_max = 10.**min(8, np.finfo(data.dtype).precision)
+            with errstate(over='ignore'):  # division can overflow
+                if max_val >= exp_cutoff_max or (not self.suppress_small and
+                        (min_val < 0.0001 or max_val / min_val > 1000.)):
+                    self.exp_format = True
+
+        # do a first pass of printing all the numbers, to determine sizes
+        if len(finite_vals) == 0:
+            self.pad_left = 0
+            self.pad_right = 0
+            self.trim = '.'
+            self.exp_size = -1
+            self.unique = True
+            self.min_digits = None
+        elif self.exp_format:
+            trim, unique = '.', True
+            if self.floatmode == 'fixed' or self._legacy <= 113:
+                trim, unique = 'k', False
+            strs = (dragon4_scientific(x, precision=self.precision,
+                               unique=unique, trim=trim, sign=self.sign == '+')
+                    for x in finite_vals)
+            frac_strs, _, exp_strs = zip(*(s.partition('e') for s in strs))
+            int_part, frac_part = zip(*(s.split('.') for s in frac_strs))
+            self.exp_size = max(len(s) for s in exp_strs) - 1
+
+            self.trim = 'k'
+            self.precision = max(len(s) for s in frac_part)
+            self.min_digits = self.precision
+            self.unique = unique
+
+            # for back-compat with np 1.13, use 2 spaces & sign and full prec
+            if self._legacy <= 113:
+                self.pad_left = 3
+            else:
+                # this should be only 1 or 2. Can be calculated from sign.
+                self.pad_left = max(len(s) for s in int_part)
+            # pad_right is only needed for nan length calculation
+            self.pad_right = self.exp_size + 2 + self.precision
+        else:
+            trim, unique = '.', True
+            if self.floatmode == 'fixed':
+                trim, unique = 'k', False
+            strs = (dragon4_positional(x, precision=self.precision,
+                                       fractional=True,
+                                       unique=unique, trim=trim,
+                                       sign=self.sign == '+')
+                    for x in finite_vals)
+            int_part, frac_part = zip(*(s.split('.') for s in strs))
+            if self._legacy <= 113:
+                self.pad_left = 1 + max(len(s.lstrip('-+')) for s in int_part)
+            else:
+                self.pad_left = max(len(s) for s in int_part)
+            self.pad_right = max(len(s) for s in frac_part)
+            self.exp_size = -1
+            self.unique = unique
+
+            if self.floatmode in ['fixed', 'maxprec_equal']:
+                self.precision = self.min_digits = self.pad_right
+                self.trim = 'k'
+            else:
+                self.trim = '.'
+                self.min_digits = 0
+
+        if self._legacy > 113:
+            # account for sign = ' ' by adding one to pad_left
+            if self.sign == ' ' and not any(np.signbit(finite_vals)):
+                self.pad_left += 1
+
+        # if there are non-finite values, may need to increase pad_left
+        if data.size != finite_vals.size:
+            neginf = self.sign != '-' or any(data[isinf(data)] < 0)
+            offset = self.pad_right + 1  # +1 for decimal pt
+            current_options = format_options.get()
+            self.pad_left = max(
+                self.pad_left, len(current_options['nanstr']) - offset,
+                len(current_options['infstr']) + neginf - offset
+            )
+
+    def __call__(self, x):
+        if not np.isfinite(x):
+            with errstate(invalid='ignore'):
+                current_options = format_options.get()
+                if np.isnan(x):
+                    sign = '+' if self.sign == '+' else ''
+                    ret = sign + current_options['nanstr']
+                else:  # isinf
+                    sign = '-' if x < 0 else '+' if self.sign == '+' else ''
+                    ret = sign + current_options['infstr']
+                return ' ' * (
+                    self.pad_left + self.pad_right + 1 - len(ret)
+                ) + ret
+
+        if self.exp_format:
+            return dragon4_scientific(x,
+                                      precision=self.precision,
+                                      min_digits=self.min_digits,
+                                      unique=self.unique,
+                                      trim=self.trim,
+                                      sign=self.sign == '+',
+                                      pad_left=self.pad_left,
+                                      exp_digits=self.exp_size)
+        else:
+            return dragon4_positional(x,
+                                      precision=self.precision,
+                                      min_digits=self.min_digits,
+                                      unique=self.unique,
+                                      fractional=True,
+                                      trim=self.trim,
+                                      sign=self.sign == '+',
+                                      pad_left=self.pad_left,
+                                      pad_right=self.pad_right)
+
+
+@set_module('numpy')
+def format_float_scientific(x, precision=None, unique=True, trim='k',
+                            sign=False, pad_left=None, exp_digits=None,
+                            min_digits=None):
+    """
+    Format a floating-point scalar as a decimal string in scientific notation.
+
+    Provides control over rounding, trimming and padding. Uses and assumes
+    IEEE unbiased rounding. Uses the "Dragon4" algorithm.
+
+    Parameters
+    ----------
+    x : python float or numpy floating scalar
+        Value to format.
+    precision : non-negative integer or None, optional
+        Maximum number of digits to print. May be None if `unique` is
+        `True`, but must be an integer if unique is `False`.
+    unique : boolean, optional
+        If `True`, use a digit-generation strategy which gives the shortest
+        representation which uniquely identifies the floating-point number from
+        other values of the same type, by judicious rounding. If `precision`
+        is given fewer digits than necessary can be printed. If `min_digits`
+        is given more can be printed, in which cases the last digit is rounded
+        with unbiased rounding.
+        If `False`, digits are generated as if printing an infinite-precision
+        value and stopping after `precision` digits, rounding the remaining
+        value with unbiased rounding
+    trim : one of 'k', '.', '0', '-', optional
+        Controls post-processing trimming of trailing digits, as follows:
+
+        * 'k' : keep trailing zeros, keep decimal point (no trimming)
+        * '.' : trim all trailing zeros, leave decimal point
+        * '0' : trim all but the zero before the decimal point. Insert the
+          zero if it is missing.
+        * '-' : trim trailing zeros and any trailing decimal point
+    sign : boolean, optional
+        Whether to show the sign for positive values.
+    pad_left : non-negative integer, optional
+        Pad the left side of the string with whitespace until at least that
+        many characters are to the left of the decimal point.
+    exp_digits : non-negative integer, optional
+        Pad the exponent with zeros until it contains at least this
+        many digits. If omitted, the exponent will be at least 2 digits.
+    min_digits : non-negative integer or None, optional
+        Minimum number of digits to print. This only has an effect for
+        `unique=True`. In that case more digits than necessary to uniquely
+        identify the value may be printed and rounded unbiased.
+
+        .. versionadded:: 1.21.0
+
+    Returns
+    -------
+    rep : string
+        The string representation of the floating point value
+
+    See Also
+    --------
+    format_float_positional
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.format_float_scientific(np.float32(np.pi))
+    '3.1415927e+00'
+    >>> s = np.float32(1.23e24)
+    >>> np.format_float_scientific(s, unique=False, precision=15)
+    '1.230000071797338e+24'
+    >>> np.format_float_scientific(s, exp_digits=4)
+    '1.23e+0024'
+    """
+    precision = _none_or_positive_arg(precision, 'precision')
+    pad_left = _none_or_positive_arg(pad_left, 'pad_left')
+    exp_digits = _none_or_positive_arg(exp_digits, 'exp_digits')
+    min_digits = _none_or_positive_arg(min_digits, 'min_digits')
+    if min_digits > 0 and precision > 0 and min_digits > precision:
+        raise ValueError("min_digits must be less than or equal to precision")
+    return dragon4_scientific(x, precision=precision, unique=unique,
+                              trim=trim, sign=sign, pad_left=pad_left,
+                              exp_digits=exp_digits, min_digits=min_digits)
+
+
+@set_module('numpy')
+def format_float_positional(x, precision=None, unique=True,
+                            fractional=True, trim='k', sign=False,
+                            pad_left=None, pad_right=None, min_digits=None):
+    """
+    Format a floating-point scalar as a decimal string in positional notation.
+
+    Provides control over rounding, trimming and padding. Uses and assumes
+    IEEE unbiased rounding. Uses the "Dragon4" algorithm.
+
+    Parameters
+    ----------
+    x : python float or numpy floating scalar
+        Value to format.
+    precision : non-negative integer or None, optional
+        Maximum number of digits to print. May be None if `unique` is
+        `True`, but must be an integer if unique is `False`.
+    unique : boolean, optional
+        If `True`, use a digit-generation strategy which gives the shortest
+        representation which uniquely identifies the floating-point number from
+        other values of the same type, by judicious rounding. If `precision`
+        is given fewer digits than necessary can be printed, or if `min_digits`
+        is given more can be printed, in which cases the last digit is rounded
+        with unbiased rounding.
+        If `False`, digits are generated as if printing an infinite-precision
+        value and stopping after `precision` digits, rounding the remaining
+        value with unbiased rounding
+    fractional : boolean, optional
+        If `True`, the cutoffs of `precision` and `min_digits` refer to the
+        total number of digits after the decimal point, including leading
+        zeros.
+        If `False`, `precision` and `min_digits` refer to the total number of
+        significant digits, before or after the decimal point, ignoring leading
+        zeros.
+    trim : one of 'k', '.', '0', '-', optional
+        Controls post-processing trimming of trailing digits, as follows:
+
+        * 'k' : keep trailing zeros, keep decimal point (no trimming)
+        * '.' : trim all trailing zeros, leave decimal point
+        * '0' : trim all but the zero before the decimal point. Insert the
+          zero if it is missing.
+        * '-' : trim trailing zeros and any trailing decimal point
+    sign : boolean, optional
+        Whether to show the sign for positive values.
+    pad_left : non-negative integer, optional
+        Pad the left side of the string with whitespace until at least that
+        many characters are to the left of the decimal point.
+    pad_right : non-negative integer, optional
+        Pad the right side of the string with whitespace until at least that
+        many characters are to the right of the decimal point.
+    min_digits : non-negative integer or None, optional
+        Minimum number of digits to print. Only has an effect if `unique=True`
+        in which case additional digits past those necessary to uniquely
+        identify the value may be printed, rounding the last additional digit.
+
+        .. versionadded:: 1.21.0
+
+    Returns
+    -------
+    rep : string
+        The string representation of the floating point value
+
+    See Also
+    --------
+    format_float_scientific
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.format_float_positional(np.float32(np.pi))
+    '3.1415927'
+    >>> np.format_float_positional(np.float16(np.pi))
+    '3.14'
+    >>> np.format_float_positional(np.float16(0.3))
+    '0.3'
+    >>> np.format_float_positional(np.float16(0.3), unique=False, precision=10)
+    '0.3000488281'
+    """
+    precision = _none_or_positive_arg(precision, 'precision')
+    pad_left = _none_or_positive_arg(pad_left, 'pad_left')
+    pad_right = _none_or_positive_arg(pad_right, 'pad_right')
+    min_digits = _none_or_positive_arg(min_digits, 'min_digits')
+    if not fractional and precision == 0:
+        raise ValueError("precision must be greater than 0 if "
+                         "fractional=False")
+    if min_digits > 0 and precision > 0 and min_digits > precision:
+        raise ValueError("min_digits must be less than or equal to precision")
+    return dragon4_positional(x, precision=precision, unique=unique,
+                              fractional=fractional, trim=trim,
+                              sign=sign, pad_left=pad_left,
+                              pad_right=pad_right, min_digits=min_digits)
+
+class IntegerFormat:
+    def __init__(self, data, sign='-'):
+        if data.size > 0:
+            data_max = np.max(data)
+            data_min = np.min(data)
+            data_max_str_len = len(str(data_max))
+            if sign == ' ' and data_min < 0:
+                sign = '-'
+            if data_max >= 0 and sign in "+ ":
+                data_max_str_len += 1
+            max_str_len = max(data_max_str_len,
+                              len(str(data_min)))
+        else:
+            max_str_len = 0
+        self.format = f'{{:{sign}{max_str_len}d}}'
+
+    def __call__(self, x):
+        return self.format.format(x)
+
+class BoolFormat:
+    def __init__(self, data, **kwargs):
+        # add an extra space so " True" and "False" have the same length and
+        # array elements align nicely when printed, except in 0d arrays
+        self.truestr = ' True' if data.shape != () else 'True'
+
+    def __call__(self, x):
+        return self.truestr if x else "False"
+
+
+class ComplexFloatingFormat:
+    """ Formatter for subtypes of np.complexfloating """
+    def __init__(self, x, precision, floatmode, suppress_small,
+                 sign=False, *, legacy=None):
+        # for backcompatibility, accept bools
+        if isinstance(sign, bool):
+            sign = '+' if sign else '-'
+
+        floatmode_real = floatmode_imag = floatmode
+        if legacy <= 113:
+            floatmode_real = 'maxprec_equal'
+            floatmode_imag = 'maxprec'
+
+        self.real_format = FloatingFormat(
+            x.real, precision, floatmode_real, suppress_small,
+            sign=sign, legacy=legacy
+        )
+        self.imag_format = FloatingFormat(
+            x.imag, precision, floatmode_imag, suppress_small,
+            sign='+', legacy=legacy
+        )
+
+    def __call__(self, x):
+        r = self.real_format(x.real)
+        i = self.imag_format(x.imag)
+
+        # add the 'j' before the terminal whitespace in i
+        sp = len(i.rstrip())
+        i = i[:sp] + 'j' + i[sp:]
+
+        return r + i
+
+
+class _TimelikeFormat:
+    def __init__(self, data):
+        non_nat = data[~isnat(data)]
+        if len(non_nat) > 0:
+            # Max str length of non-NaT elements
+            max_str_len = max(len(self._format_non_nat(np.max(non_nat))),
+                              len(self._format_non_nat(np.min(non_nat))))
+        else:
+            max_str_len = 0
+        if len(non_nat) < data.size:
+            # data contains a NaT
+            max_str_len = max(max_str_len, 5)
+        self._format = f'%{max_str_len}s'
+        self._nat = "'NaT'".rjust(max_str_len)
+
+    def _format_non_nat(self, x):
+        # override in subclass
+        raise NotImplementedError
+
+    def __call__(self, x):
+        if isnat(x):
+            return self._nat
+        else:
+            return self._format % self._format_non_nat(x)
+
+
+class DatetimeFormat(_TimelikeFormat):
+    def __init__(self, x, unit=None, timezone=None, casting='same_kind',
+                 legacy=False):
+        # Get the unit from the dtype
+        if unit is None:
+            if x.dtype.kind == 'M':
+                unit = datetime_data(x.dtype)[0]
+            else:
+                unit = 's'
+
+        if timezone is None:
+            timezone = 'naive'
+        self.timezone = timezone
+        self.unit = unit
+        self.casting = casting
+        self.legacy = legacy
+
+        # must be called after the above are configured
+        super().__init__(x)
+
+    def __call__(self, x):
+        if self.legacy <= 113:
+            return self._format_non_nat(x)
+        return super().__call__(x)
+
+    def _format_non_nat(self, x):
+        return "'%s'" % datetime_as_string(x,
+                                    unit=self.unit,
+                                    timezone=self.timezone,
+                                    casting=self.casting)
+
+
+class TimedeltaFormat(_TimelikeFormat):
+    def _format_non_nat(self, x):
+        return str(x.astype('i8'))
+
+
+class SubArrayFormat:
+    def __init__(self, format_function, **options):
+        self.format_function = format_function
+        self.threshold = options['threshold']
+        self.edge_items = options['edgeitems']
+
+    def __call__(self, a):
+        self.summary_insert = "..." if a.size > self.threshold else ""
+        return self.format_array(a)
+
+    def format_array(self, a):
+        if np.ndim(a) == 0:
+            return self.format_function(a)
+
+        if self.summary_insert and a.shape[0] > 2 * self.edge_items:
+            formatted = (
+                [self.format_array(a_) for a_ in a[:self.edge_items]]
+                + [self.summary_insert]
+                + [self.format_array(a_) for a_ in a[-self.edge_items:]]
+            )
+        else:
+            formatted = [self.format_array(a_) for a_ in a]
+
+        return "[" + ", ".join(formatted) + "]"
+
+
+class StructuredVoidFormat:
+    """
+    Formatter for structured np.void objects.
+
+    This does not work on structured alias types like
+    np.dtype(('i4', 'i2,i2')), as alias scalars lose their field information,
+    and the implementation relies upon np.void.__getitem__.
+    """
+    def __init__(self, format_functions):
+        self.format_functions = format_functions
+
+    @classmethod
+    def from_data(cls, data, **options):
+        """
+        This is a second way to initialize StructuredVoidFormat,
+        using the raw data as input. Added to avoid changing
+        the signature of __init__.
+        """
+        format_functions = []
+        for field_name in data.dtype.names:
+            format_function = _get_format_function(data[field_name], **options)
+            if data.dtype[field_name].shape != ():
+                format_function = SubArrayFormat(format_function, **options)
+            format_functions.append(format_function)
+        return cls(format_functions)
+
+    def __call__(self, x):
+        str_fields = [
+            format_function(field)
+            for field, format_function in zip(x, self.format_functions)
+        ]
+        if len(str_fields) == 1:
+            return f"({str_fields[0]},)"
+        else:
+            return f"({', '.join(str_fields)})"
+
+
+def _void_scalar_to_string(x, is_repr=True):
+    """
+    Implements the repr for structured-void scalars. It is called from the
+    scalartypes.c.src code, and is placed here because it uses the elementwise
+    formatters defined above.
+    """
+    options = format_options.get().copy()
+
+    if options["legacy"] <= 125:
+        return StructuredVoidFormat.from_data(array(x), **options)(x)
+
+    if options.get('formatter') is None:
+        options['formatter'] = {}
+    options['formatter'].setdefault('float_kind', str)
+    val_repr = StructuredVoidFormat.from_data(array(x), **options)(x)
+    if not is_repr:
+        return val_repr
+    cls = type(x)
+    cls_fqn = cls.__module__.replace("numpy", "np") + "." + cls.__name__
+    void_dtype = np.dtype((np.void, x.dtype))
+    return f"{cls_fqn}({val_repr}, dtype={void_dtype!s})"
+
+
+_typelessdata = [int_, float64, complex128, _nt.bool]
+
+
+def dtype_is_implied(dtype):
+    """
+    Determine if the given dtype is implied by the representation
+    of its values.
+
+    Parameters
+    ----------
+    dtype : dtype
+        Data type
+
+    Returns
+    -------
+    implied : bool
+        True if the dtype is implied by the representation of its values.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np._core.arrayprint.dtype_is_implied(int)
+    True
+    >>> np.array([1, 2, 3], int)
+    array([1, 2, 3])
+    >>> np._core.arrayprint.dtype_is_implied(np.int8)
+    False
+    >>> np.array([1, 2, 3], np.int8)
+    array([1, 2, 3], dtype=int8)
+    """
+    dtype = np.dtype(dtype)
+    if format_options.get()['legacy'] <= 113 and dtype.type == np.bool:
+        return False
+
+    # not just void types can be structured, and names are not part of the repr
+    if dtype.names is not None:
+        return False
+
+    # should care about endianness *unless size is 1* (e.g., int8, bool)
+    if not dtype.isnative:
+        return False
+
+    return dtype.type in _typelessdata
+
+
+def dtype_short_repr(dtype):
+    """
+    Convert a dtype to a short form which evaluates to the same dtype.
+
+    The intent is roughly that the following holds
+
+    >>> from numpy import *
+    >>> dt = np.int64([1, 2]).dtype
+    >>> assert eval(dtype_short_repr(dt)) == dt
+    """
+    if type(dtype).__repr__ != np.dtype.__repr__:
+        # TODO: Custom repr for user DTypes, logic should likely move.
+        return repr(dtype)
+    if dtype.names is not None:
+        # structured dtypes give a list or tuple repr
+        return str(dtype)
+    elif issubclass(dtype.type, flexible):
+        # handle these separately so they don't give garbage like str256
+        return f"'{str(dtype)}'"
+
+    typename = dtype.name
+    if not dtype.isnative:
+        # deal with cases like dtype('<u2') that are identical to an
+        # established dtype (in this case uint16)
+        # except that they have a different endianness.
+        return f"'{str(dtype)}'"
+    # quote typenames which can't be represented as python variable names
+    if typename and not (typename[0].isalpha() and typename.isalnum()):
+        typename = repr(typename)
+    return typename
+
+
+def _array_repr_implementation(
+        arr, max_line_width=None, precision=None, suppress_small=None,
+        array2string=array2string):
+    """Internal version of array_repr() that allows overriding array2string."""
+    current_options = format_options.get()
+    override_repr = current_options["override_repr"]
+    if override_repr is not None:
+        return override_repr(arr)
+
+    if max_line_width is None:
+        max_line_width = current_options['linewidth']
+
+    if type(arr) is not ndarray:
+        class_name = type(arr).__name__
+    else:
+        class_name = "array"
+
+    prefix = class_name + "("
+    if (current_options['legacy'] <= 113 and
+            arr.shape == () and not arr.dtype.names):
+        lst = repr(arr.item())
+    else:
+        lst = array2string(arr, max_line_width, precision, suppress_small,
+                           ', ', prefix, suffix=")")
+
+    # Add dtype and shape information if these cannot be inferred from
+    # the array string.
+    extras = []
+    if ((arr.size == 0 and arr.shape != (0,))
+            or (current_options['legacy'] > 210
+            and arr.size > current_options['threshold'])):
+        extras.append(f"shape={arr.shape}")
+    if not dtype_is_implied(arr.dtype) or arr.size == 0:
+        extras.append(f"dtype={dtype_short_repr(arr.dtype)}")
+
+    if not extras:
+        return prefix + lst + ")"
+
+    arr_str = prefix + lst + ","
+    extra_str = ", ".join(extras) + ")"
+    # compute whether we should put extras on a new line: Do so if adding the
+    # extras would extend the last line past max_line_width.
+    # Note: This line gives the correct result even when rfind returns -1.
+    last_line_len = len(arr_str) - (arr_str.rfind('\n') + 1)
+    spacer = " "
+    if current_options['legacy'] <= 113:
+        if issubclass(arr.dtype.type, flexible):
+            spacer = '\n' + ' ' * len(prefix)
+    elif last_line_len + len(extra_str) + 1 > max_line_width:
+        spacer = '\n' + ' ' * len(prefix)
+
+    return arr_str + spacer + extra_str
+
+
+def _array_repr_dispatcher(
+        arr, max_line_width=None, precision=None, suppress_small=None):
+    return (arr,)
+
+
+@array_function_dispatch(_array_repr_dispatcher, module='numpy')
+def array_repr(arr, max_line_width=None, precision=None, suppress_small=None):
+    """
+    Return the string representation of an array.
+
+    Parameters
+    ----------
+    arr : ndarray
+        Input array.
+    max_line_width : int, optional
+        Inserts newlines if text is longer than `max_line_width`.
+        Defaults to ``numpy.get_printoptions()['linewidth']``.
+    precision : int, optional
+        Floating point precision.
+        Defaults to ``numpy.get_printoptions()['precision']``.
+    suppress_small : bool, optional
+        Represent numbers "very close" to zero as zero; default is False.
+        Very close is defined by precision: if the precision is 8, e.g.,
+        numbers smaller (in absolute value) than 5e-9 are represented as
+        zero.
+        Defaults to ``numpy.get_printoptions()['suppress']``.
+
+    Returns
+    -------
+    string : str
+      The string representation of an array.
+
+    See Also
+    --------
+    array_str, array2string, set_printoptions
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.array_repr(np.array([1,2]))
+    'array([1, 2])'
+    >>> np.array_repr(np.ma.array([0.]))
+    'MaskedArray([0.])'
+    >>> np.array_repr(np.array([], np.int32))
+    'array([], dtype=int32)'
+
+    >>> x = np.array([1e-6, 4e-7, 2, 3])
+    >>> np.array_repr(x, precision=6, suppress_small=True)
+    'array([0.000001,  0.      ,  2.      ,  3.      ])'
+
+    """
+    return _array_repr_implementation(
+        arr, max_line_width, precision, suppress_small)
+
+
+@_recursive_guard()
+def _guarded_repr_or_str(v):
+    if isinstance(v, bytes):
+        return repr(v)
+    return str(v)
+
+
+def _array_str_implementation(
+        a, max_line_width=None, precision=None, suppress_small=None,
+        array2string=array2string):
+    """Internal version of array_str() that allows overriding array2string."""
+    if (format_options.get()['legacy'] <= 113 and
+            a.shape == () and not a.dtype.names):
+        return str(a.item())
+
+    # the str of 0d arrays is a special case: It should appear like a scalar,
+    # so floats are not truncated by `precision`, and strings are not wrapped
+    # in quotes. So we return the str of the scalar value.
+    if a.shape == ():
+        # obtain a scalar and call str on it, avoiding problems for subclasses
+        # for which indexing with () returns a 0d instead of a scalar by using
+        # ndarray's getindex. Also guard against recursive 0d object arrays.
+        return _guarded_repr_or_str(np.ndarray.__getitem__(a, ()))
+
+    return array2string(a, max_line_width, precision, suppress_small, ' ', "")
+
+
+def _array_str_dispatcher(
+        a, max_line_width=None, precision=None, suppress_small=None):
+    return (a,)
+
+
+@array_function_dispatch(_array_str_dispatcher, module='numpy')
+def array_str(a, max_line_width=None, precision=None, suppress_small=None):
+    """
+    Return a string representation of the data in an array.
+
+    The data in the array is returned as a single string.  This function is
+    similar to `array_repr`, the difference being that `array_repr` also
+    returns information on the kind of array and its data type.
+
+    Parameters
+    ----------
+    a : ndarray
+        Input array.
+    max_line_width : int, optional
+        Inserts newlines if text is longer than `max_line_width`.
+        Defaults to ``numpy.get_printoptions()['linewidth']``.
+    precision : int, optional
+        Floating point precision.
+        Defaults to ``numpy.get_printoptions()['precision']``.
+    suppress_small : bool, optional
+        Represent numbers "very close" to zero as zero; default is False.
+        Very close is defined by precision: if the precision is 8, e.g.,
+        numbers smaller (in absolute value) than 5e-9 are represented as
+        zero.
+        Defaults to ``numpy.get_printoptions()['suppress']``.
+
+    See Also
+    --------
+    array2string, array_repr, set_printoptions
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.array_str(np.arange(3))
+    '[0 1 2]'
+
+    """
+    return _array_str_implementation(
+        a, max_line_width, precision, suppress_small)
+
+
+# needed if __array_function__ is disabled
+_array2string_impl = getattr(array2string, '__wrapped__', array2string)
+_default_array_str = functools.partial(_array_str_implementation,
+                                       array2string=_array2string_impl)
+_default_array_repr = functools.partial(_array_repr_implementation,
+                                        array2string=_array2string_impl)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/arrayprint.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/arrayprint.pyi
new file mode 100644
index 0000000..fec03a6
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/arrayprint.pyi
@@ -0,0 +1,238 @@
+from collections.abc import Callable
+
+# Using a private class is by no means ideal, but it is simply a consequence
+# of a `contextlib.context` returning an instance of aforementioned class
+from contextlib import _GeneratorContextManager
+from typing import (
+    Any,
+    Final,
+    Literal,
+    SupportsIndex,
+    TypeAlias,
+    TypedDict,
+    overload,
+    type_check_only,
+)
+
+from typing_extensions import deprecated
+
+import numpy as np
+from numpy._globals import _NoValueType
+from numpy._typing import NDArray, _CharLike_co, _FloatLike_co
+
+__all__ = [
+    "array2string",
+    "array_repr",
+    "array_str",
+    "format_float_positional",
+    "format_float_scientific",
+    "get_printoptions",
+    "printoptions",
+    "set_printoptions",
+]
+
+###
+
+_FloatMode: TypeAlias = Literal["fixed", "unique", "maxprec", "maxprec_equal"]
+_LegacyNoStyle: TypeAlias = Literal["1.21", "1.25", "2.1", False]
+_Legacy: TypeAlias = Literal["1.13", _LegacyNoStyle]
+_Sign: TypeAlias = Literal["-", "+", " "]
+_Trim: TypeAlias = Literal["k", ".", "0", "-"]
+_ReprFunc: TypeAlias = Callable[[NDArray[Any]], str]
+
+@type_check_only
+class _FormatDict(TypedDict, total=False):
+    bool: Callable[[np.bool], str]
+    int: Callable[[np.integer], str]
+    timedelta: Callable[[np.timedelta64], str]
+    datetime: Callable[[np.datetime64], str]
+    float: Callable[[np.floating], str]
+    longfloat: Callable[[np.longdouble], str]
+    complexfloat: Callable[[np.complexfloating], str]
+    longcomplexfloat: Callable[[np.clongdouble], str]
+    void: Callable[[np.void], str]
+    numpystr: Callable[[_CharLike_co], str]
+    object: Callable[[object], str]
+    all: Callable[[object], str]
+    int_kind: Callable[[np.integer], str]
+    float_kind: Callable[[np.floating], str]
+    complex_kind: Callable[[np.complexfloating], str]
+    str_kind: Callable[[_CharLike_co], str]
+
+@type_check_only
+class _FormatOptions(TypedDict):
+    precision: int
+    threshold: int
+    edgeitems: int
+    linewidth: int
+    suppress: bool
+    nanstr: str
+    infstr: str
+    formatter: _FormatDict | None
+    sign: _Sign
+    floatmode: _FloatMode
+    legacy: _Legacy
+
+###
+
+__docformat__: Final = "restructuredtext"  # undocumented
+
+def set_printoptions(
+    precision: SupportsIndex | None = ...,
+    threshold: int | None = ...,
+    edgeitems: int | None = ...,
+    linewidth: int | None = ...,
+    suppress: bool | None = ...,
+    nanstr: str | None = ...,
+    infstr: str | None = ...,
+    formatter: _FormatDict | None = ...,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    *,
+    legacy: _Legacy | None = None,
+    override_repr: _ReprFunc | None = None,
+) -> None: ...
+def get_printoptions() -> _FormatOptions: ...
+
+# public numpy export
+@overload  # no style
+def array2string(
+    a: NDArray[Any],
+    max_line_width: int | None = None,
+    precision: SupportsIndex | None = None,
+    suppress_small: bool | None = None,
+    separator: str = " ",
+    prefix: str = "",
+    style: _NoValueType = ...,
+    formatter: _FormatDict | None = None,
+    threshold: int | None = None,
+    edgeitems: int | None = None,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    suffix: str = "",
+    *,
+    legacy: _Legacy | None = None,
+) -> str: ...
+@overload  # style=<given> (positional), legacy="1.13"
+def array2string(
+    a: NDArray[Any],
+    max_line_width: int | None,
+    precision: SupportsIndex | None,
+    suppress_small: bool | None,
+    separator: str,
+    prefix: str,
+    style: _ReprFunc,
+    formatter: _FormatDict | None = None,
+    threshold: int | None = None,
+    edgeitems: int | None = None,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    suffix: str = "",
+    *,
+    legacy: Literal["1.13"],
+) -> str: ...
+@overload  # style=<given> (keyword), legacy="1.13"
+def array2string(
+    a: NDArray[Any],
+    max_line_width: int | None = None,
+    precision: SupportsIndex | None = None,
+    suppress_small: bool | None = None,
+    separator: str = " ",
+    prefix: str = "",
+    *,
+    style: _ReprFunc,
+    formatter: _FormatDict | None = None,
+    threshold: int | None = None,
+    edgeitems: int | None = None,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    suffix: str = "",
+    legacy: Literal["1.13"],
+) -> str: ...
+@overload  # style=<given> (positional), legacy!="1.13"
+@deprecated("'style' argument is deprecated and no longer functional except in 1.13 'legacy' mode")
+def array2string(
+    a: NDArray[Any],
+    max_line_width: int | None,
+    precision: SupportsIndex | None,
+    suppress_small: bool | None,
+    separator: str,
+    prefix: str,
+    style: _ReprFunc,
+    formatter: _FormatDict | None = None,
+    threshold: int | None = None,
+    edgeitems: int | None = None,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    suffix: str = "",
+    *,
+    legacy: _LegacyNoStyle | None = None,
+) -> str: ...
+@overload  # style=<given> (keyword), legacy="1.13"
+@deprecated("'style' argument is deprecated and no longer functional except in 1.13 'legacy' mode")
+def array2string(
+    a: NDArray[Any],
+    max_line_width: int | None = None,
+    precision: SupportsIndex | None = None,
+    suppress_small: bool | None = None,
+    separator: str = " ",
+    prefix: str = "",
+    *,
+    style: _ReprFunc,
+    formatter: _FormatDict | None = None,
+    threshold: int | None = None,
+    edgeitems: int | None = None,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    suffix: str = "",
+    legacy: _LegacyNoStyle | None = None,
+) -> str: ...
+
+def format_float_scientific(
+    x: _FloatLike_co,
+    precision: int | None = ...,
+    unique: bool = ...,
+    trim: _Trim = "k",
+    sign: bool = ...,
+    pad_left: int | None = ...,
+    exp_digits: int | None = ...,
+    min_digits: int | None = ...,
+) -> str: ...
+def format_float_positional(
+    x: _FloatLike_co,
+    precision: int | None = ...,
+    unique: bool = ...,
+    fractional: bool = ...,
+    trim: _Trim = "k",
+    sign: bool = ...,
+    pad_left: int | None = ...,
+    pad_right: int | None = ...,
+    min_digits: int | None = ...,
+) -> str: ...
+def array_repr(
+    arr: NDArray[Any],
+    max_line_width: int | None = ...,
+    precision: SupportsIndex | None = ...,
+    suppress_small: bool | None = ...,
+) -> str: ...
+def array_str(
+    a: NDArray[Any],
+    max_line_width: int | None = ...,
+    precision: SupportsIndex | None = ...,
+    suppress_small: bool | None = ...,
+) -> str: ...
+def printoptions(
+    precision: SupportsIndex | None = ...,
+    threshold: int | None = ...,
+    edgeitems: int | None = ...,
+    linewidth: int | None = ...,
+    suppress: bool | None = ...,
+    nanstr: str | None = ...,
+    infstr: str | None = ...,
+    formatter: _FormatDict | None = ...,
+    sign: _Sign | None = None,
+    floatmode: _FloatMode | None = None,
+    *,
+    legacy: _Legacy | None = None,
+    override_repr: _ReprFunc | None = None,
+) -> _GeneratorContextManager[_FormatOptions]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/cversions.py b/.venv/lib/python3.12/site-packages/numpy/_core/cversions.py
new file mode 100644
index 0000000..00159c3
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/cversions.py
@@ -0,0 +1,13 @@
+"""Simple script to compute the api hash of the current API.
+
+The API has is defined by numpy_api_order and ufunc_api_order.
+
+"""
+from os.path import dirname
+
+from code_generators.genapi import fullapi_hash
+from code_generators.numpy_api import full_api
+
+if __name__ == '__main__':
+    curdir = dirname(__file__)
+    print(fullapi_hash(full_api))
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/defchararray.py b/.venv/lib/python3.12/site-packages/numpy/_core/defchararray.py
new file mode 100644
index 0000000..bde8921
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/defchararray.py
@@ -0,0 +1,1427 @@
+"""
+This module contains a set of functions for vectorized string
+operations and methods.
+
+.. note::
+   The `chararray` class exists for backwards compatibility with
+   Numarray, it is not recommended for new development. Starting from numpy
+   1.4, if one needs arrays of strings, it is recommended to use arrays of
+   `dtype` `object_`, `bytes_` or `str_`, and use the free functions
+   in the `numpy.char` module for fast vectorized string operations.
+
+Some methods will only be available if the corresponding string method is
+available in your version of Python.
+
+The preferred alias for `defchararray` is `numpy.char`.
+
+"""
+import functools
+
+import numpy as np
+from numpy._core import overrides
+from numpy._core.multiarray import compare_chararrays
+from numpy._core.strings import (
+    _join as join,
+)
+from numpy._core.strings import (
+    _rsplit as rsplit,
+)
+from numpy._core.strings import (
+    _split as split,
+)
+from numpy._core.strings import (
+    _splitlines as splitlines,
+)
+from numpy._utils import set_module
+from numpy.strings import *
+from numpy.strings import (
+    multiply as strings_multiply,
+)
+from numpy.strings import (
+    partition as strings_partition,
+)
+from numpy.strings import (
+    rpartition as strings_rpartition,
+)
+
+from .numeric import array as narray
+from .numeric import asarray as asnarray
+from .numeric import ndarray
+from .numerictypes import bytes_, character, str_
+
+__all__ = [
+    'equal', 'not_equal', 'greater_equal', 'less_equal',
+    'greater', 'less', 'str_len', 'add', 'multiply', 'mod', 'capitalize',
+    'center', 'count', 'decode', 'encode', 'endswith', 'expandtabs',
+    'find', 'index', 'isalnum', 'isalpha', 'isdigit', 'islower', 'isspace',
+    'istitle', 'isupper', 'join', 'ljust', 'lower', 'lstrip', 'partition',
+    'replace', 'rfind', 'rindex', 'rjust', 'rpartition', 'rsplit',
+    'rstrip', 'split', 'splitlines', 'startswith', 'strip', 'swapcase',
+    'title', 'translate', 'upper', 'zfill', 'isnumeric', 'isdecimal',
+    'array', 'asarray', 'compare_chararrays', 'chararray'
+    ]
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy.char')
+
+
+def _binary_op_dispatcher(x1, x2):
+    return (x1, x2)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def equal(x1, x2):
+    """
+    Return (x1 == x2) element-wise.
+
+    Unlike `numpy.equal`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> y = "aa "
+    >>> x = "aa"
+    >>> np.char.equal(x, y)
+    array(True)
+
+    See Also
+    --------
+    not_equal, greater_equal, less_equal, greater, less
+    """
+    return compare_chararrays(x1, x2, '==', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def not_equal(x1, x2):
+    """
+    Return (x1 != x2) element-wise.
+
+    Unlike `numpy.not_equal`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, greater_equal, less_equal, greater, less
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.not_equal(x1, 'b')
+    array([ True, False,  True])
+
+    """
+    return compare_chararrays(x1, x2, '!=', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def greater_equal(x1, x2):
+    """
+    Return (x1 >= x2) element-wise.
+
+    Unlike `numpy.greater_equal`, this comparison is performed by
+    first stripping whitespace characters from the end of the string.
+    This behavior is provided for backward-compatibility with
+    numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, not_equal, less_equal, greater, less
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.greater_equal(x1, 'b')
+    array([False,  True,  True])
+
+    """
+    return compare_chararrays(x1, x2, '>=', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def less_equal(x1, x2):
+    """
+    Return (x1 <= x2) element-wise.
+
+    Unlike `numpy.less_equal`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, not_equal, greater_equal, greater, less
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.less_equal(x1, 'b')
+    array([ True,  True, False])
+
+    """
+    return compare_chararrays(x1, x2, '<=', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def greater(x1, x2):
+    """
+    Return (x1 > x2) element-wise.
+
+    Unlike `numpy.greater`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, not_equal, greater_equal, less_equal, less
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.greater(x1, 'b')
+    array([False, False,  True])
+
+    """
+    return compare_chararrays(x1, x2, '>', True)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def less(x1, x2):
+    """
+    Return (x1 < x2) element-wise.
+
+    Unlike `numpy.greater`, this comparison is performed by first
+    stripping whitespace characters from the end of the string.  This
+    behavior is provided for backward-compatibility with numarray.
+
+    Parameters
+    ----------
+    x1, x2 : array_like of str or unicode
+        Input arrays of the same shape.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools.
+
+    See Also
+    --------
+    equal, not_equal, greater_equal, less_equal, greater
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x1 = np.array(['a', 'b', 'c'])
+    >>> np.char.less(x1, 'b')
+    array([True, False, False])
+
+    """
+    return compare_chararrays(x1, x2, '<', True)
+
+
+@set_module("numpy.char")
+def multiply(a, i):
+    """
+    Return (a * i), that is string multiple concatenation,
+    element-wise.
+
+    Values in ``i`` of less than 0 are treated as 0 (which yields an
+    empty string).
+
+    Parameters
+    ----------
+    a : array_like, with `np.bytes_` or `np.str_` dtype
+
+    i : array_like, with any integer dtype
+
+    Returns
+    -------
+    out : ndarray
+        Output array of str or unicode, depending on input types
+
+    Notes
+    -----
+    This is a thin wrapper around np.strings.multiply that raises
+    `ValueError` when ``i`` is not an integer. It only
+    exists for backwards-compatibility.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(["a", "b", "c"])
+    >>> np.strings.multiply(a, 3)
+    array(['aaa', 'bbb', 'ccc'], dtype='<U3')
+    >>> i = np.array([1, 2, 3])
+    >>> np.strings.multiply(a, i)
+    array(['a', 'bb', 'ccc'], dtype='<U3')
+    >>> np.strings.multiply(np.array(['a']), i)
+    array(['a', 'aa', 'aaa'], dtype='<U3')
+    >>> a = np.array(['a', 'b', 'c', 'd', 'e', 'f']).reshape((2, 3))
+    >>> np.strings.multiply(a, 3)
+    array([['aaa', 'bbb', 'ccc'],
+           ['ddd', 'eee', 'fff']], dtype='<U3')
+    >>> np.strings.multiply(a, i)
+    array([['a', 'bb', 'ccc'],
+           ['d', 'ee', 'fff']], dtype='<U3')
+
+    """
+    try:
+        return strings_multiply(a, i)
+    except TypeError:
+        raise ValueError("Can only multiply by integers")
+
+
+@set_module("numpy.char")
+def partition(a, sep):
+    """
+    Partition each element in `a` around `sep`.
+
+    Calls :meth:`str.partition` element-wise.
+
+    For each element in `a`, split the element as the first
+    occurrence of `sep`, and return 3 strings containing the part
+    before the separator, the separator itself, and the part after
+    the separator. If the separator is not found, return 3 strings
+    containing the string itself, followed by two empty strings.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array
+    sep : {str, unicode}
+        Separator to split each string element in `a`.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types. The output array will have an extra
+        dimension with 3 elements per input element.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array(["Numpy is nice!"])
+    >>> np.char.partition(x, " ")
+    array([['Numpy', ' ', 'is nice!']], dtype='<U8')
+
+    See Also
+    --------
+    str.partition
+
+    """
+    return np.stack(strings_partition(a, sep), axis=-1)
+
+
+@set_module("numpy.char")
+def rpartition(a, sep):
+    """
+    Partition (split) each element around the right-most separator.
+
+    Calls :meth:`str.rpartition` element-wise.
+
+    For each element in `a`, split the element as the last
+    occurrence of `sep`, and return 3 strings containing the part
+    before the separator, the separator itself, and the part after
+    the separator. If the separator is not found, return 3 strings
+    containing the string itself, followed by two empty strings.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array
+    sep : str or unicode
+        Right-most separator to split each element in array.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types. The output array will have an extra
+        dimension with 3 elements per input element.
+
+    See Also
+    --------
+    str.rpartition
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(['aAaAaA', '  aA  ', 'abBABba'])
+    >>> np.char.rpartition(a, 'A')
+    array([['aAaAa', 'A', ''],
+       ['  a', 'A', '  '],
+       ['abB', 'A', 'Bba']], dtype='<U5')
+
+    """
+    return np.stack(strings_rpartition(a, sep), axis=-1)
+
+
+@set_module("numpy.char")
+class chararray(ndarray):
+    """
+    chararray(shape, itemsize=1, unicode=False, buffer=None, offset=0,
+              strides=None, order=None)
+
+    Provides a convenient view on arrays of string and unicode values.
+
+    .. note::
+       The `chararray` class exists for backwards compatibility with
+       Numarray, it is not recommended for new development. Starting from numpy
+       1.4, if one needs arrays of strings, it is recommended to use arrays of
+       `dtype` `~numpy.object_`, `~numpy.bytes_` or `~numpy.str_`, and use
+       the free functions in the `numpy.char` module for fast vectorized
+       string operations.
+
+    Versus a NumPy array of dtype `~numpy.bytes_` or `~numpy.str_`, this
+    class adds the following functionality:
+
+    1) values automatically have whitespace removed from the end
+       when indexed
+
+    2) comparison operators automatically remove whitespace from the
+       end when comparing values
+
+    3) vectorized string operations are provided as methods
+       (e.g. `.endswith`) and infix operators (e.g. ``"+", "*", "%"``)
+
+    chararrays should be created using `numpy.char.array` or
+    `numpy.char.asarray`, rather than this constructor directly.
+
+    This constructor creates the array, using `buffer` (with `offset`
+    and `strides`) if it is not ``None``. If `buffer` is ``None``, then
+    constructs a new array with `strides` in "C order", unless both
+    ``len(shape) >= 2`` and ``order='F'``, in which case `strides`
+    is in "Fortran order".
+
+    Methods
+    -------
+    astype
+    argsort
+    copy
+    count
+    decode
+    dump
+    dumps
+    encode
+    endswith
+    expandtabs
+    fill
+    find
+    flatten
+    getfield
+    index
+    isalnum
+    isalpha
+    isdecimal
+    isdigit
+    islower
+    isnumeric
+    isspace
+    istitle
+    isupper
+    item
+    join
+    ljust
+    lower
+    lstrip
+    nonzero
+    put
+    ravel
+    repeat
+    replace
+    reshape
+    resize
+    rfind
+    rindex
+    rjust
+    rsplit
+    rstrip
+    searchsorted
+    setfield
+    setflags
+    sort
+    split
+    splitlines
+    squeeze
+    startswith
+    strip
+    swapaxes
+    swapcase
+    take
+    title
+    tofile
+    tolist
+    tostring
+    translate
+    transpose
+    upper
+    view
+    zfill
+
+    Parameters
+    ----------
+    shape : tuple
+        Shape of the array.
+    itemsize : int, optional
+        Length of each array element, in number of characters. Default is 1.
+    unicode : bool, optional
+        Are the array elements of type unicode (True) or string (False).
+        Default is False.
+    buffer : object exposing the buffer interface or str, optional
+        Memory address of the start of the array data.  Default is None,
+        in which case a new array is created.
+    offset : int, optional
+        Fixed stride displacement from the beginning of an axis?
+        Default is 0. Needs to be >=0.
+    strides : array_like of ints, optional
+        Strides for the array (see `~numpy.ndarray.strides` for
+        full description). Default is None.
+    order : {'C', 'F'}, optional
+        The order in which the array data is stored in memory: 'C' ->
+        "row major" order (the default), 'F' -> "column major"
+        (Fortran) order.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> charar = np.char.chararray((3, 3))
+    >>> charar[:] = 'a'
+    >>> charar
+    chararray([[b'a', b'a', b'a'],
+               [b'a', b'a', b'a'],
+               [b'a', b'a', b'a']], dtype='|S1')
+
+    >>> charar = np.char.chararray(charar.shape, itemsize=5)
+    >>> charar[:] = 'abc'
+    >>> charar
+    chararray([[b'abc', b'abc', b'abc'],
+               [b'abc', b'abc', b'abc'],
+               [b'abc', b'abc', b'abc']], dtype='|S5')
+
+    """
+    def __new__(subtype, shape, itemsize=1, unicode=False, buffer=None,
+                offset=0, strides=None, order='C'):
+        if unicode:
+            dtype = str_
+        else:
+            dtype = bytes_
+
+        # force itemsize to be a Python int, since using NumPy integer
+        # types results in itemsize.itemsize being used as the size of
+        # strings in the new array.
+        itemsize = int(itemsize)
+
+        if isinstance(buffer, str):
+            # unicode objects do not have the buffer interface
+            filler = buffer
+            buffer = None
+        else:
+            filler = None
+
+        if buffer is None:
+            self = ndarray.__new__(subtype, shape, (dtype, itemsize),
+                                   order=order)
+        else:
+            self = ndarray.__new__(subtype, shape, (dtype, itemsize),
+                                   buffer=buffer,
+                                   offset=offset, strides=strides,
+                                   order=order)
+        if filler is not None:
+            self[...] = filler
+
+        return self
+
+    def __array_wrap__(self, arr, context=None, return_scalar=False):
+        # When calling a ufunc (and some other functions), we return a
+        # chararray if the ufunc output is a string-like array,
+        # or an ndarray otherwise
+        if arr.dtype.char in "SUbc":
+            return arr.view(type(self))
+        return arr
+
+    def __array_finalize__(self, obj):
+        # The b is a special case because it is used for reconstructing.
+        if self.dtype.char not in 'VSUbc':
+            raise ValueError("Can only create a chararray from string data.")
+
+    def __getitem__(self, obj):
+        val = ndarray.__getitem__(self, obj)
+        if isinstance(val, character):
+            return val.rstrip()
+        return val
+
+    # IMPLEMENTATION NOTE: Most of the methods of this class are
+    # direct delegations to the free functions in this module.
+    # However, those that return an array of strings should instead
+    # return a chararray, so some extra wrapping is required.
+
+    def __eq__(self, other):
+        """
+        Return (self == other) element-wise.
+
+        See Also
+        --------
+        equal
+        """
+        return equal(self, other)
+
+    def __ne__(self, other):
+        """
+        Return (self != other) element-wise.
+
+        See Also
+        --------
+        not_equal
+        """
+        return not_equal(self, other)
+
+    def __ge__(self, other):
+        """
+        Return (self >= other) element-wise.
+
+        See Also
+        --------
+        greater_equal
+        """
+        return greater_equal(self, other)
+
+    def __le__(self, other):
+        """
+        Return (self <= other) element-wise.
+
+        See Also
+        --------
+        less_equal
+        """
+        return less_equal(self, other)
+
+    def __gt__(self, other):
+        """
+        Return (self > other) element-wise.
+
+        See Also
+        --------
+        greater
+        """
+        return greater(self, other)
+
+    def __lt__(self, other):
+        """
+        Return (self < other) element-wise.
+
+        See Also
+        --------
+        less
+        """
+        return less(self, other)
+
+    def __add__(self, other):
+        """
+        Return (self + other), that is string concatenation,
+        element-wise for a pair of array_likes of str or unicode.
+
+        See Also
+        --------
+        add
+        """
+        return add(self, other)
+
+    def __radd__(self, other):
+        """
+        Return (other + self), that is string concatenation,
+        element-wise for a pair of array_likes of `bytes_` or `str_`.
+
+        See Also
+        --------
+        add
+        """
+        return add(other, self)
+
+    def __mul__(self, i):
+        """
+        Return (self * i), that is string multiple concatenation,
+        element-wise.
+
+        See Also
+        --------
+        multiply
+        """
+        return asarray(multiply(self, i))
+
+    def __rmul__(self, i):
+        """
+        Return (self * i), that is string multiple concatenation,
+        element-wise.
+
+        See Also
+        --------
+        multiply
+        """
+        return asarray(multiply(self, i))
+
+    def __mod__(self, i):
+        """
+        Return (self % i), that is pre-Python 2.6 string formatting
+        (interpolation), element-wise for a pair of array_likes of `bytes_`
+        or `str_`.
+
+        See Also
+        --------
+        mod
+        """
+        return asarray(mod(self, i))
+
+    def __rmod__(self, other):
+        return NotImplemented
+
+    def argsort(self, axis=-1, kind=None, order=None):
+        """
+        Return the indices that sort the array lexicographically.
+
+        For full documentation see `numpy.argsort`, for which this method is
+        in fact merely a "thin wrapper."
+
+        Examples
+        --------
+        >>> c = np.array(['a1b c', '1b ca', 'b ca1', 'Ca1b'], 'S5')
+        >>> c = c.view(np.char.chararray); c
+        chararray(['a1b c', '1b ca', 'b ca1', 'Ca1b'],
+              dtype='|S5')
+        >>> c[c.argsort()]
+        chararray(['1b ca', 'Ca1b', 'a1b c', 'b ca1'],
+              dtype='|S5')
+
+        """
+        return self.__array__().argsort(axis, kind, order)
+    argsort.__doc__ = ndarray.argsort.__doc__
+
+    def capitalize(self):
+        """
+        Return a copy of `self` with only the first character of each element
+        capitalized.
+
+        See Also
+        --------
+        char.capitalize
+
+        """
+        return asarray(capitalize(self))
+
+    def center(self, width, fillchar=' '):
+        """
+        Return a copy of `self` with its elements centered in a
+        string of length `width`.
+
+        See Also
+        --------
+        center
+        """
+        return asarray(center(self, width, fillchar))
+
+    def count(self, sub, start=0, end=None):
+        """
+        Returns an array with the number of non-overlapping occurrences of
+        substring `sub` in the range [`start`, `end`].
+
+        See Also
+        --------
+        char.count
+
+        """
+        return count(self, sub, start, end)
+
+    def decode(self, encoding=None, errors=None):
+        """
+        Calls ``bytes.decode`` element-wise.
+
+        See Also
+        --------
+        char.decode
+
+        """
+        return decode(self, encoding, errors)
+
+    def encode(self, encoding=None, errors=None):
+        """
+        Calls :meth:`str.encode` element-wise.
+
+        See Also
+        --------
+        char.encode
+
+        """
+        return encode(self, encoding, errors)
+
+    def endswith(self, suffix, start=0, end=None):
+        """
+        Returns a boolean array which is `True` where the string element
+        in `self` ends with `suffix`, otherwise `False`.
+
+        See Also
+        --------
+        char.endswith
+
+        """
+        return endswith(self, suffix, start, end)
+
+    def expandtabs(self, tabsize=8):
+        """
+        Return a copy of each string element where all tab characters are
+        replaced by one or more spaces.
+
+        See Also
+        --------
+        char.expandtabs
+
+        """
+        return asarray(expandtabs(self, tabsize))
+
+    def find(self, sub, start=0, end=None):
+        """
+        For each element, return the lowest index in the string where
+        substring `sub` is found.
+
+        See Also
+        --------
+        char.find
+
+        """
+        return find(self, sub, start, end)
+
+    def index(self, sub, start=0, end=None):
+        """
+        Like `find`, but raises :exc:`ValueError` when the substring is not
+        found.
+
+        See Also
+        --------
+        char.index
+
+        """
+        return index(self, sub, start, end)
+
+    def isalnum(self):
+        """
+        Returns true for each element if all characters in the string
+        are alphanumeric and there is at least one character, false
+        otherwise.
+
+        See Also
+        --------
+        char.isalnum
+
+        """
+        return isalnum(self)
+
+    def isalpha(self):
+        """
+        Returns true for each element if all characters in the string
+        are alphabetic and there is at least one character, false
+        otherwise.
+
+        See Also
+        --------
+        char.isalpha
+
+        """
+        return isalpha(self)
+
+    def isdigit(self):
+        """
+        Returns true for each element if all characters in the string are
+        digits and there is at least one character, false otherwise.
+
+        See Also
+        --------
+        char.isdigit
+
+        """
+        return isdigit(self)
+
+    def islower(self):
+        """
+        Returns true for each element if all cased characters in the
+        string are lowercase and there is at least one cased character,
+        false otherwise.
+
+        See Also
+        --------
+        char.islower
+
+        """
+        return islower(self)
+
+    def isspace(self):
+        """
+        Returns true for each element if there are only whitespace
+        characters in the string and there is at least one character,
+        false otherwise.
+
+        See Also
+        --------
+        char.isspace
+
+        """
+        return isspace(self)
+
+    def istitle(self):
+        """
+        Returns true for each element if the element is a titlecased
+        string and there is at least one character, false otherwise.
+
+        See Also
+        --------
+        char.istitle
+
+        """
+        return istitle(self)
+
+    def isupper(self):
+        """
+        Returns true for each element if all cased characters in the
+        string are uppercase and there is at least one character, false
+        otherwise.
+
+        See Also
+        --------
+        char.isupper
+
+        """
+        return isupper(self)
+
+    def join(self, seq):
+        """
+        Return a string which is the concatenation of the strings in the
+        sequence `seq`.
+
+        See Also
+        --------
+        char.join
+
+        """
+        return join(self, seq)
+
+    def ljust(self, width, fillchar=' '):
+        """
+        Return an array with the elements of `self` left-justified in a
+        string of length `width`.
+
+        See Also
+        --------
+        char.ljust
+
+        """
+        return asarray(ljust(self, width, fillchar))
+
+    def lower(self):
+        """
+        Return an array with the elements of `self` converted to
+        lowercase.
+
+        See Also
+        --------
+        char.lower
+
+        """
+        return asarray(lower(self))
+
+    def lstrip(self, chars=None):
+        """
+        For each element in `self`, return a copy with the leading characters
+        removed.
+
+        See Also
+        --------
+        char.lstrip
+
+        """
+        return lstrip(self, chars)
+
+    def partition(self, sep):
+        """
+        Partition each element in `self` around `sep`.
+
+        See Also
+        --------
+        partition
+        """
+        return asarray(partition(self, sep))
+
+    def replace(self, old, new, count=None):
+        """
+        For each element in `self`, return a copy of the string with all
+        occurrences of substring `old` replaced by `new`.
+
+        See Also
+        --------
+        char.replace
+
+        """
+        return replace(self, old, new, count if count is not None else -1)
+
+    def rfind(self, sub, start=0, end=None):
+        """
+        For each element in `self`, return the highest index in the string
+        where substring `sub` is found, such that `sub` is contained
+        within [`start`, `end`].
+
+        See Also
+        --------
+        char.rfind
+
+        """
+        return rfind(self, sub, start, end)
+
+    def rindex(self, sub, start=0, end=None):
+        """
+        Like `rfind`, but raises :exc:`ValueError` when the substring `sub` is
+        not found.
+
+        See Also
+        --------
+        char.rindex
+
+        """
+        return rindex(self, sub, start, end)
+
+    def rjust(self, width, fillchar=' '):
+        """
+        Return an array with the elements of `self`
+        right-justified in a string of length `width`.
+
+        See Also
+        --------
+        char.rjust
+
+        """
+        return asarray(rjust(self, width, fillchar))
+
+    def rpartition(self, sep):
+        """
+        Partition each element in `self` around `sep`.
+
+        See Also
+        --------
+        rpartition
+        """
+        return asarray(rpartition(self, sep))
+
+    def rsplit(self, sep=None, maxsplit=None):
+        """
+        For each element in `self`, return a list of the words in
+        the string, using `sep` as the delimiter string.
+
+        See Also
+        --------
+        char.rsplit
+
+        """
+        return rsplit(self, sep, maxsplit)
+
+    def rstrip(self, chars=None):
+        """
+        For each element in `self`, return a copy with the trailing
+        characters removed.
+
+        See Also
+        --------
+        char.rstrip
+
+        """
+        return rstrip(self, chars)
+
+    def split(self, sep=None, maxsplit=None):
+        """
+        For each element in `self`, return a list of the words in the
+        string, using `sep` as the delimiter string.
+
+        See Also
+        --------
+        char.split
+
+        """
+        return split(self, sep, maxsplit)
+
+    def splitlines(self, keepends=None):
+        """
+        For each element in `self`, return a list of the lines in the
+        element, breaking at line boundaries.
+
+        See Also
+        --------
+        char.splitlines
+
+        """
+        return splitlines(self, keepends)
+
+    def startswith(self, prefix, start=0, end=None):
+        """
+        Returns a boolean array which is `True` where the string element
+        in `self` starts with `prefix`, otherwise `False`.
+
+        See Also
+        --------
+        char.startswith
+
+        """
+        return startswith(self, prefix, start, end)
+
+    def strip(self, chars=None):
+        """
+        For each element in `self`, return a copy with the leading and
+        trailing characters removed.
+
+        See Also
+        --------
+        char.strip
+
+        """
+        return strip(self, chars)
+
+    def swapcase(self):
+        """
+        For each element in `self`, return a copy of the string with
+        uppercase characters converted to lowercase and vice versa.
+
+        See Also
+        --------
+        char.swapcase
+
+        """
+        return asarray(swapcase(self))
+
+    def title(self):
+        """
+        For each element in `self`, return a titlecased version of the
+        string: words start with uppercase characters, all remaining cased
+        characters are lowercase.
+
+        See Also
+        --------
+        char.title
+
+        """
+        return asarray(title(self))
+
+    def translate(self, table, deletechars=None):
+        """
+        For each element in `self`, return a copy of the string where
+        all characters occurring in the optional argument
+        `deletechars` are removed, and the remaining characters have
+        been mapped through the given translation table.
+
+        See Also
+        --------
+        char.translate
+
+        """
+        return asarray(translate(self, table, deletechars))
+
+    def upper(self):
+        """
+        Return an array with the elements of `self` converted to
+        uppercase.
+
+        See Also
+        --------
+        char.upper
+
+        """
+        return asarray(upper(self))
+
+    def zfill(self, width):
+        """
+        Return the numeric string left-filled with zeros in a string of
+        length `width`.
+
+        See Also
+        --------
+        char.zfill
+
+        """
+        return asarray(zfill(self, width))
+
+    def isnumeric(self):
+        """
+        For each element in `self`, return True if there are only
+        numeric characters in the element.
+
+        See Also
+        --------
+        char.isnumeric
+
+        """
+        return isnumeric(self)
+
+    def isdecimal(self):
+        """
+        For each element in `self`, return True if there are only
+        decimal characters in the element.
+
+        See Also
+        --------
+        char.isdecimal
+
+        """
+        return isdecimal(self)
+
+
+@set_module("numpy.char")
+def array(obj, itemsize=None, copy=True, unicode=None, order=None):
+    """
+    Create a `~numpy.char.chararray`.
+
+    .. note::
+       This class is provided for numarray backward-compatibility.
+       New code (not concerned with numarray compatibility) should use
+       arrays of type `bytes_` or `str_` and use the free functions
+       in :mod:`numpy.char` for fast vectorized string operations instead.
+
+    Versus a NumPy array of dtype `bytes_` or `str_`, this
+    class adds the following functionality:
+
+    1) values automatically have whitespace removed from the end
+       when indexed
+
+    2) comparison operators automatically remove whitespace from the
+       end when comparing values
+
+    3) vectorized string operations are provided as methods
+       (e.g. `chararray.endswith <numpy.char.chararray.endswith>`)
+       and infix operators (e.g. ``+, *, %``)
+
+    Parameters
+    ----------
+    obj : array of str or unicode-like
+
+    itemsize : int, optional
+        `itemsize` is the number of characters per scalar in the
+        resulting array.  If `itemsize` is None, and `obj` is an
+        object array or a Python list, the `itemsize` will be
+        automatically determined.  If `itemsize` is provided and `obj`
+        is of type str or unicode, then the `obj` string will be
+        chunked into `itemsize` pieces.
+
+    copy : bool, optional
+        If true (default), then the object is copied.  Otherwise, a copy
+        will only be made if ``__array__`` returns a copy, if obj is a
+        nested sequence, or if a copy is needed to satisfy any of the other
+        requirements (`itemsize`, unicode, `order`, etc.).
+
+    unicode : bool, optional
+        When true, the resulting `~numpy.char.chararray` can contain Unicode
+        characters, when false only 8-bit characters.  If unicode is
+        None and `obj` is one of the following:
+
+        - a `~numpy.char.chararray`,
+        - an ndarray of type :class:`str_` or :class:`bytes_`
+        - a Python :class:`str` or :class:`bytes` object,
+
+        then the unicode setting of the output array will be
+        automatically determined.
+
+    order : {'C', 'F', 'A'}, optional
+        Specify the order of the array.  If order is 'C' (default), then the
+        array will be in C-contiguous order (last-index varies the
+        fastest).  If order is 'F', then the returned array
+        will be in Fortran-contiguous order (first-index varies the
+        fastest).  If order is 'A', then the returned array may
+        be in any order (either C-, Fortran-contiguous, or even
+        discontiguous).
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> char_array = np.char.array(['hello', 'world', 'numpy','array'])
+    >>> char_array
+    chararray(['hello', 'world', 'numpy', 'array'], dtype='<U5')
+
+    """
+    if isinstance(obj, (bytes, str)):
+        if unicode is None:
+            if isinstance(obj, str):
+                unicode = True
+            else:
+                unicode = False
+
+        if itemsize is None:
+            itemsize = len(obj)
+        shape = len(obj) // itemsize
+
+        return chararray(shape, itemsize=itemsize, unicode=unicode,
+                         buffer=obj, order=order)
+
+    if isinstance(obj, (list, tuple)):
+        obj = asnarray(obj)
+
+    if isinstance(obj, ndarray) and issubclass(obj.dtype.type, character):
+        # If we just have a vanilla chararray, create a chararray
+        # view around it.
+        if not isinstance(obj, chararray):
+            obj = obj.view(chararray)
+
+        if itemsize is None:
+            itemsize = obj.itemsize
+            # itemsize is in 8-bit chars, so for Unicode, we need
+            # to divide by the size of a single Unicode character,
+            # which for NumPy is always 4
+            if issubclass(obj.dtype.type, str_):
+                itemsize //= 4
+
+        if unicode is None:
+            if issubclass(obj.dtype.type, str_):
+                unicode = True
+            else:
+                unicode = False
+
+        if unicode:
+            dtype = str_
+        else:
+            dtype = bytes_
+
+        if order is not None:
+            obj = asnarray(obj, order=order)
+        if (copy or
+                (itemsize != obj.itemsize) or
+                (not unicode and isinstance(obj, str_)) or
+                (unicode and isinstance(obj, bytes_))):
+            obj = obj.astype((dtype, int(itemsize)))
+        return obj
+
+    if isinstance(obj, ndarray) and issubclass(obj.dtype.type, object):
+        if itemsize is None:
+            # Since no itemsize was specified, convert the input array to
+            # a list so the ndarray constructor will automatically
+            # determine the itemsize for us.
+            obj = obj.tolist()
+            # Fall through to the default case
+
+    if unicode:
+        dtype = str_
+    else:
+        dtype = bytes_
+
+    if itemsize is None:
+        val = narray(obj, dtype=dtype, order=order, subok=True)
+    else:
+        val = narray(obj, dtype=(dtype, itemsize), order=order, subok=True)
+    return val.view(chararray)
+
+
+@set_module("numpy.char")
+def asarray(obj, itemsize=None, unicode=None, order=None):
+    """
+    Convert the input to a `~numpy.char.chararray`, copying the data only if
+    necessary.
+
+    Versus a NumPy array of dtype `bytes_` or `str_`, this
+    class adds the following functionality:
+
+    1) values automatically have whitespace removed from the end
+       when indexed
+
+    2) comparison operators automatically remove whitespace from the
+       end when comparing values
+
+    3) vectorized string operations are provided as methods
+       (e.g. `chararray.endswith <numpy.char.chararray.endswith>`)
+       and infix operators (e.g. ``+``, ``*``, ``%``)
+
+    Parameters
+    ----------
+    obj : array of str or unicode-like
+
+    itemsize : int, optional
+        `itemsize` is the number of characters per scalar in the
+        resulting array.  If `itemsize` is None, and `obj` is an
+        object array or a Python list, the `itemsize` will be
+        automatically determined.  If `itemsize` is provided and `obj`
+        is of type str or unicode, then the `obj` string will be
+        chunked into `itemsize` pieces.
+
+    unicode : bool, optional
+        When true, the resulting `~numpy.char.chararray` can contain Unicode
+        characters, when false only 8-bit characters.  If unicode is
+        None and `obj` is one of the following:
+
+        - a `~numpy.char.chararray`,
+        - an ndarray of type `str_` or `unicode_`
+        - a Python str or unicode object,
+
+        then the unicode setting of the output array will be
+        automatically determined.
+
+    order : {'C', 'F'}, optional
+        Specify the order of the array.  If order is 'C' (default), then the
+        array will be in C-contiguous order (last-index varies the
+        fastest).  If order is 'F', then the returned array
+        will be in Fortran-contiguous order (first-index varies the
+        fastest).
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.char.asarray(['hello', 'world'])
+    chararray(['hello', 'world'], dtype='<U5')
+
+    """
+    return array(obj, itemsize, copy=False,
+                 unicode=unicode, order=order)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/defchararray.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/defchararray.pyi
new file mode 100644
index 0000000..2361fff
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/defchararray.pyi
@@ -0,0 +1,1135 @@
+from typing import Any, Self, SupportsIndex, SupportsInt, TypeAlias, overload
+from typing import Literal as L
+
+from typing_extensions import TypeVar
+
+import numpy as np
+from numpy import (
+    _OrderKACF,
+    _SupportsBuffer,
+    bytes_,
+    dtype,
+    int_,
+    ndarray,
+    object_,
+    str_,
+)
+from numpy._core.multiarray import compare_chararrays
+from numpy._typing import NDArray, _AnyShape, _Shape, _ShapeLike, _SupportsArray
+from numpy._typing import _ArrayLikeAnyString_co as UST_co
+from numpy._typing import _ArrayLikeBool_co as b_co
+from numpy._typing import _ArrayLikeBytes_co as S_co
+from numpy._typing import _ArrayLikeInt_co as i_co
+from numpy._typing import _ArrayLikeStr_co as U_co
+from numpy._typing import _ArrayLikeString_co as T_co
+
+__all__ = [
+    "equal",
+    "not_equal",
+    "greater_equal",
+    "less_equal",
+    "greater",
+    "less",
+    "str_len",
+    "add",
+    "multiply",
+    "mod",
+    "capitalize",
+    "center",
+    "count",
+    "decode",
+    "encode",
+    "endswith",
+    "expandtabs",
+    "find",
+    "index",
+    "isalnum",
+    "isalpha",
+    "isdigit",
+    "islower",
+    "isspace",
+    "istitle",
+    "isupper",
+    "join",
+    "ljust",
+    "lower",
+    "lstrip",
+    "partition",
+    "replace",
+    "rfind",
+    "rindex",
+    "rjust",
+    "rpartition",
+    "rsplit",
+    "rstrip",
+    "split",
+    "splitlines",
+    "startswith",
+    "strip",
+    "swapcase",
+    "title",
+    "translate",
+    "upper",
+    "zfill",
+    "isnumeric",
+    "isdecimal",
+    "array",
+    "asarray",
+    "compare_chararrays",
+    "chararray",
+]
+
+_ShapeT_co = TypeVar("_ShapeT_co", bound=_Shape, default=_AnyShape, covariant=True)
+_CharacterT = TypeVar("_CharacterT", bound=np.character)
+_CharDTypeT_co = TypeVar("_CharDTypeT_co", bound=dtype[np.character], default=dtype, covariant=True)
+
+_CharArray: TypeAlias = chararray[_AnyShape, dtype[_CharacterT]]
+
+_StringDTypeArray: TypeAlias = np.ndarray[_AnyShape, np.dtypes.StringDType]
+_StringDTypeOrUnicodeArray: TypeAlias = _StringDTypeArray | NDArray[np.str_]
+_StringDTypeSupportsArray: TypeAlias = _SupportsArray[np.dtypes.StringDType]
+
+class chararray(ndarray[_ShapeT_co, _CharDTypeT_co]):
+    @overload
+    def __new__(
+        subtype,
+        shape: _ShapeLike,
+        itemsize: SupportsIndex | SupportsInt = ...,
+        unicode: L[False] = ...,
+        buffer: _SupportsBuffer = ...,
+        offset: SupportsIndex = ...,
+        strides: _ShapeLike = ...,
+        order: _OrderKACF = ...,
+    ) -> _CharArray[bytes_]: ...
+    @overload
+    def __new__(
+        subtype,
+        shape: _ShapeLike,
+        itemsize: SupportsIndex | SupportsInt = ...,
+        unicode: L[True] = ...,
+        buffer: _SupportsBuffer = ...,
+        offset: SupportsIndex = ...,
+        strides: _ShapeLike = ...,
+        order: _OrderKACF = ...,
+    ) -> _CharArray[str_]: ...
+
+    def __array_finalize__(self, obj: object) -> None: ...
+    def __mul__(self, other: i_co) -> chararray[_AnyShape, _CharDTypeT_co]: ...
+    def __rmul__(self, other: i_co) -> chararray[_AnyShape, _CharDTypeT_co]: ...
+    def __mod__(self, i: Any) -> chararray[_AnyShape, _CharDTypeT_co]: ...
+
+    @overload
+    def __eq__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __eq__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload
+    def __ne__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __ne__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload
+    def __ge__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __ge__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload
+    def __le__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __le__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload
+    def __gt__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __gt__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload
+    def __lt__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def __lt__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> NDArray[np.bool]: ...
+
+    @overload
+    def __add__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def __add__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def __radd__(
+        self: _CharArray[str_],
+        other: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def __radd__(
+        self: _CharArray[bytes_],
+        other: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def center(
+        self: _CharArray[str_],
+        width: i_co,
+        fillchar: U_co = ...,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def center(
+        self: _CharArray[bytes_],
+        width: i_co,
+        fillchar: S_co = ...,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def count(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+    @overload
+    def count(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+
+    def decode(
+        self: _CharArray[bytes_],
+        encoding: str | None = ...,
+        errors: str | None = ...,
+    ) -> _CharArray[str_]: ...
+
+    def encode(
+        self: _CharArray[str_],
+        encoding: str | None = ...,
+        errors: str | None = ...,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def endswith(
+        self: _CharArray[str_],
+        suffix: U_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def endswith(
+        self: _CharArray[bytes_],
+        suffix: S_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[np.bool]: ...
+
+    def expandtabs(
+        self,
+        tabsize: i_co = ...,
+    ) -> Self: ...
+
+    @overload
+    def find(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+    @overload
+    def find(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+
+    @overload
+    def index(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+    @overload
+    def index(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+
+    @overload
+    def join(
+        self: _CharArray[str_],
+        seq: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def join(
+        self: _CharArray[bytes_],
+        seq: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def ljust(
+        self: _CharArray[str_],
+        width: i_co,
+        fillchar: U_co = ...,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def ljust(
+        self: _CharArray[bytes_],
+        width: i_co,
+        fillchar: S_co = ...,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def lstrip(
+        self: _CharArray[str_],
+        chars: U_co | None = ...,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def lstrip(
+        self: _CharArray[bytes_],
+        chars: S_co | None = ...,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def partition(
+        self: _CharArray[str_],
+        sep: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def partition(
+        self: _CharArray[bytes_],
+        sep: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def replace(
+        self: _CharArray[str_],
+        old: U_co,
+        new: U_co,
+        count: i_co | None = ...,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def replace(
+        self: _CharArray[bytes_],
+        old: S_co,
+        new: S_co,
+        count: i_co | None = ...,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def rfind(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+    @overload
+    def rfind(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+
+    @overload
+    def rindex(
+        self: _CharArray[str_],
+        sub: U_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+    @overload
+    def rindex(
+        self: _CharArray[bytes_],
+        sub: S_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[int_]: ...
+
+    @overload
+    def rjust(
+        self: _CharArray[str_],
+        width: i_co,
+        fillchar: U_co = ...,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def rjust(
+        self: _CharArray[bytes_],
+        width: i_co,
+        fillchar: S_co = ...,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def rpartition(
+        self: _CharArray[str_],
+        sep: U_co,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def rpartition(
+        self: _CharArray[bytes_],
+        sep: S_co,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def rsplit(
+        self: _CharArray[str_],
+        sep: U_co | None = ...,
+        maxsplit: i_co | None = ...,
+    ) -> NDArray[object_]: ...
+    @overload
+    def rsplit(
+        self: _CharArray[bytes_],
+        sep: S_co | None = ...,
+        maxsplit: i_co | None = ...,
+    ) -> NDArray[object_]: ...
+
+    @overload
+    def rstrip(
+        self: _CharArray[str_],
+        chars: U_co | None = ...,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def rstrip(
+        self: _CharArray[bytes_],
+        chars: S_co | None = ...,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def split(
+        self: _CharArray[str_],
+        sep: U_co | None = ...,
+        maxsplit: i_co | None = ...,
+    ) -> NDArray[object_]: ...
+    @overload
+    def split(
+        self: _CharArray[bytes_],
+        sep: S_co | None = ...,
+        maxsplit: i_co | None = ...,
+    ) -> NDArray[object_]: ...
+
+    def splitlines(self, keepends: b_co | None = ...) -> NDArray[object_]: ...
+
+    @overload
+    def startswith(
+        self: _CharArray[str_],
+        prefix: U_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[np.bool]: ...
+    @overload
+    def startswith(
+        self: _CharArray[bytes_],
+        prefix: S_co,
+        start: i_co = ...,
+        end: i_co | None = ...,
+    ) -> NDArray[np.bool]: ...
+
+    @overload
+    def strip(
+        self: _CharArray[str_],
+        chars: U_co | None = ...,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def strip(
+        self: _CharArray[bytes_],
+        chars: S_co | None = ...,
+    ) -> _CharArray[bytes_]: ...
+
+    @overload
+    def translate(
+        self: _CharArray[str_],
+        table: U_co,
+        deletechars: U_co | None = ...,
+    ) -> _CharArray[str_]: ...
+    @overload
+    def translate(
+        self: _CharArray[bytes_],
+        table: S_co,
+        deletechars: S_co | None = ...,
+    ) -> _CharArray[bytes_]: ...
+
+    def zfill(self, width: i_co) -> Self: ...
+    def capitalize(self) -> Self: ...
+    def title(self) -> Self: ...
+    def swapcase(self) -> Self: ...
+    def lower(self) -> Self: ...
+    def upper(self) -> Self: ...
+    def isalnum(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isalpha(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isdigit(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def islower(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isspace(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def istitle(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isupper(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isnumeric(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+    def isdecimal(self) -> ndarray[_ShapeT_co, dtype[np.bool]]: ...
+
+# Comparison
+@overload
+def equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def not_equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def not_equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def not_equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def greater_equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def greater_equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def greater_equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def less_equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def less_equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def less_equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def greater(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def greater(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def greater(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def less(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def less(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def less(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def add(x1: U_co, x2: U_co) -> NDArray[np.str_]: ...
+@overload
+def add(x1: S_co, x2: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def add(x1: _StringDTypeSupportsArray, x2: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def add(x1: T_co, x2: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def multiply(a: U_co, i: i_co) -> NDArray[np.str_]: ...
+@overload
+def multiply(a: S_co, i: i_co) -> NDArray[np.bytes_]: ...
+@overload
+def multiply(a: _StringDTypeSupportsArray, i: i_co) -> _StringDTypeArray: ...
+@overload
+def multiply(a: T_co, i: i_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def mod(a: U_co, value: Any) -> NDArray[np.str_]: ...
+@overload
+def mod(a: S_co, value: Any) -> NDArray[np.bytes_]: ...
+@overload
+def mod(a: _StringDTypeSupportsArray, value: Any) -> _StringDTypeArray: ...
+@overload
+def mod(a: T_co, value: Any) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def capitalize(a: U_co) -> NDArray[str_]: ...
+@overload
+def capitalize(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def capitalize(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def capitalize(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def center(a: U_co, width: i_co, fillchar: U_co = ...) -> NDArray[str_]: ...
+@overload
+def center(a: S_co, width: i_co, fillchar: S_co = ...) -> NDArray[bytes_]: ...
+@overload
+def center(a: _StringDTypeSupportsArray, width: i_co, fillchar: _StringDTypeSupportsArray = ...) -> _StringDTypeArray: ...
+@overload
+def center(a: T_co, width: i_co, fillchar: T_co = ...) -> _StringDTypeOrUnicodeArray: ...
+
+def decode(
+    a: S_co,
+    encoding: str | None = ...,
+    errors: str | None = ...,
+) -> NDArray[str_]: ...
+def encode(
+    a: U_co | T_co,
+    encoding: str | None = ...,
+    errors: str | None = ...,
+) -> NDArray[bytes_]: ...
+
+@overload
+def expandtabs(a: U_co, tabsize: i_co = ...) -> NDArray[str_]: ...
+@overload
+def expandtabs(a: S_co, tabsize: i_co = ...) -> NDArray[bytes_]: ...
+@overload
+def expandtabs(a: _StringDTypeSupportsArray, tabsize: i_co = ...) -> _StringDTypeArray: ...
+@overload
+def expandtabs(a: T_co, tabsize: i_co = ...) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def join(sep: U_co, seq: U_co) -> NDArray[str_]: ...
+@overload
+def join(sep: S_co, seq: S_co) -> NDArray[bytes_]: ...
+@overload
+def join(sep: _StringDTypeSupportsArray, seq: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def join(sep: T_co, seq: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def ljust(a: U_co, width: i_co, fillchar: U_co = ...) -> NDArray[str_]: ...
+@overload
+def ljust(a: S_co, width: i_co, fillchar: S_co = ...) -> NDArray[bytes_]: ...
+@overload
+def ljust(a: _StringDTypeSupportsArray, width: i_co, fillchar: _StringDTypeSupportsArray = ...) -> _StringDTypeArray: ...
+@overload
+def ljust(a: T_co, width: i_co, fillchar: T_co = ...) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def lower(a: U_co) -> NDArray[str_]: ...
+@overload
+def lower(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def lower(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def lower(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def lstrip(a: U_co, chars: U_co | None = ...) -> NDArray[str_]: ...
+@overload
+def lstrip(a: S_co, chars: S_co | None = ...) -> NDArray[bytes_]: ...
+@overload
+def lstrip(a: _StringDTypeSupportsArray, chars: _StringDTypeSupportsArray | None = ...) -> _StringDTypeArray: ...
+@overload
+def lstrip(a: T_co, chars: T_co | None = ...) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def partition(a: U_co, sep: U_co) -> NDArray[str_]: ...
+@overload
+def partition(a: S_co, sep: S_co) -> NDArray[bytes_]: ...
+@overload
+def partition(a: _StringDTypeSupportsArray, sep: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def partition(a: T_co, sep: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def replace(
+    a: U_co,
+    old: U_co,
+    new: U_co,
+    count: i_co | None = ...,
+) -> NDArray[str_]: ...
+@overload
+def replace(
+    a: S_co,
+    old: S_co,
+    new: S_co,
+    count: i_co | None = ...,
+) -> NDArray[bytes_]: ...
+@overload
+def replace(
+    a: _StringDTypeSupportsArray,
+    old: _StringDTypeSupportsArray,
+    new: _StringDTypeSupportsArray,
+    count: i_co = ...,
+) -> _StringDTypeArray: ...
+@overload
+def replace(
+    a: T_co,
+    old: T_co,
+    new: T_co,
+    count: i_co = ...,
+) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def rjust(
+    a: U_co,
+    width: i_co,
+    fillchar: U_co = ...,
+) -> NDArray[str_]: ...
+@overload
+def rjust(
+    a: S_co,
+    width: i_co,
+    fillchar: S_co = ...,
+) -> NDArray[bytes_]: ...
+@overload
+def rjust(
+    a: _StringDTypeSupportsArray,
+    width: i_co,
+    fillchar: _StringDTypeSupportsArray = ...,
+) -> _StringDTypeArray: ...
+@overload
+def rjust(
+    a: T_co,
+    width: i_co,
+    fillchar: T_co = ...,
+) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def rpartition(a: U_co, sep: U_co) -> NDArray[str_]: ...
+@overload
+def rpartition(a: S_co, sep: S_co) -> NDArray[bytes_]: ...
+@overload
+def rpartition(a: _StringDTypeSupportsArray, sep: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def rpartition(a: T_co, sep: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def rsplit(
+    a: U_co,
+    sep: U_co | None = ...,
+    maxsplit: i_co | None = ...,
+) -> NDArray[object_]: ...
+@overload
+def rsplit(
+    a: S_co,
+    sep: S_co | None = ...,
+    maxsplit: i_co | None = ...,
+) -> NDArray[object_]: ...
+@overload
+def rsplit(
+    a: _StringDTypeSupportsArray,
+    sep: _StringDTypeSupportsArray | None = ...,
+    maxsplit: i_co | None = ...,
+) -> NDArray[object_]: ...
+@overload
+def rsplit(
+    a: T_co,
+    sep: T_co | None = ...,
+    maxsplit: i_co | None = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def rstrip(a: U_co, chars: U_co | None = ...) -> NDArray[str_]: ...
+@overload
+def rstrip(a: S_co, chars: S_co | None = ...) -> NDArray[bytes_]: ...
+@overload
+def rstrip(a: _StringDTypeSupportsArray, chars: _StringDTypeSupportsArray | None = ...) -> _StringDTypeArray: ...
+@overload
+def rstrip(a: T_co, chars: T_co | None = ...) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def split(
+    a: U_co,
+    sep: U_co | None = ...,
+    maxsplit: i_co | None = ...,
+) -> NDArray[object_]: ...
+@overload
+def split(
+    a: S_co,
+    sep: S_co | None = ...,
+    maxsplit: i_co | None = ...,
+) -> NDArray[object_]: ...
+@overload
+def split(
+    a: _StringDTypeSupportsArray,
+    sep: _StringDTypeSupportsArray | None = ...,
+    maxsplit: i_co | None = ...,
+) -> NDArray[object_]: ...
+@overload
+def split(
+    a: T_co,
+    sep: T_co | None = ...,
+    maxsplit: i_co | None = ...,
+) -> NDArray[object_]: ...
+
+def splitlines(a: UST_co, keepends: b_co | None = ...) -> NDArray[np.object_]: ...
+
+@overload
+def strip(a: U_co, chars: U_co | None = ...) -> NDArray[str_]: ...
+@overload
+def strip(a: S_co, chars: S_co | None = ...) -> NDArray[bytes_]: ...
+@overload
+def strip(a: _StringDTypeSupportsArray, chars: _StringDTypeSupportsArray | None = ...) -> _StringDTypeArray: ...
+@overload
+def strip(a: T_co, chars: T_co | None = ...) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def swapcase(a: U_co) -> NDArray[str_]: ...
+@overload
+def swapcase(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def swapcase(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def swapcase(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def title(a: U_co) -> NDArray[str_]: ...
+@overload
+def title(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def title(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def title(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def translate(
+    a: U_co,
+    table: str,
+    deletechars: str | None = ...,
+) -> NDArray[str_]: ...
+@overload
+def translate(
+    a: S_co,
+    table: str,
+    deletechars: str | None = ...,
+) -> NDArray[bytes_]: ...
+@overload
+def translate(
+    a: _StringDTypeSupportsArray,
+    table: str,
+    deletechars: str | None = ...,
+) -> _StringDTypeArray: ...
+@overload
+def translate(
+    a: T_co,
+    table: str,
+    deletechars: str | None = ...,
+) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def upper(a: U_co) -> NDArray[str_]: ...
+@overload
+def upper(a: S_co) -> NDArray[bytes_]: ...
+@overload
+def upper(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def upper(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def zfill(a: U_co, width: i_co) -> NDArray[str_]: ...
+@overload
+def zfill(a: S_co, width: i_co) -> NDArray[bytes_]: ...
+@overload
+def zfill(a: _StringDTypeSupportsArray, width: i_co) -> _StringDTypeArray: ...
+@overload
+def zfill(a: T_co, width: i_co) -> _StringDTypeOrUnicodeArray: ...
+
+# String information
+@overload
+def count(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def count(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def count(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+@overload
+def endswith(
+    a: U_co,
+    suffix: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def endswith(
+    a: S_co,
+    suffix: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def endswith(
+    a: T_co,
+    suffix: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+
+@overload
+def find(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def find(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def find(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+@overload
+def index(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def index(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def index(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+def isalpha(a: UST_co) -> NDArray[np.bool]: ...
+def isalnum(a: UST_co) -> NDArray[np.bool]: ...
+def isdecimal(a: U_co | T_co) -> NDArray[np.bool]: ...
+def isdigit(a: UST_co) -> NDArray[np.bool]: ...
+def islower(a: UST_co) -> NDArray[np.bool]: ...
+def isnumeric(a: U_co | T_co) -> NDArray[np.bool]: ...
+def isspace(a: UST_co) -> NDArray[np.bool]: ...
+def istitle(a: UST_co) -> NDArray[np.bool]: ...
+def isupper(a: UST_co) -> NDArray[np.bool]: ...
+
+@overload
+def rfind(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def rfind(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def rfind(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+@overload
+def rindex(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def rindex(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[int_]: ...
+@overload
+def rindex(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+@overload
+def startswith(
+    a: U_co,
+    prefix: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def startswith(
+    a: S_co,
+    prefix: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def startswith(
+    a: T_co,
+    suffix: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+
+def str_len(A: UST_co) -> NDArray[int_]: ...
+
+# Overload 1 and 2: str- or bytes-based array-likes
+# overload 3 and 4: arbitrary object with unicode=False  (-> bytes_)
+# overload 5 and 6: arbitrary object with unicode=True  (-> str_)
+# overload 7: arbitrary object with unicode=None (default)  (-> str_ | bytes_)
+@overload
+def array(
+    obj: U_co,
+    itemsize: int | None = ...,
+    copy: bool = ...,
+    unicode: L[True] | None = ...,
+    order: _OrderKACF = ...,
+) -> _CharArray[str_]: ...
+@overload
+def array(
+    obj: S_co,
+    itemsize: int | None = ...,
+    copy: bool = ...,
+    unicode: L[False] | None = ...,
+    order: _OrderKACF = ...,
+) -> _CharArray[bytes_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None,
+    copy: bool,
+    unicode: L[False],
+    order: _OrderKACF = ...,
+) -> _CharArray[bytes_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None = ...,
+    copy: bool = ...,
+    *,
+    unicode: L[False],
+    order: _OrderKACF = ...,
+) -> _CharArray[bytes_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None,
+    copy: bool,
+    unicode: L[True],
+    order: _OrderKACF = ...,
+) -> _CharArray[str_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None = ...,
+    copy: bool = ...,
+    *,
+    unicode: L[True],
+    order: _OrderKACF = ...,
+) -> _CharArray[str_]: ...
+@overload
+def array(
+    obj: object,
+    itemsize: int | None = ...,
+    copy: bool = ...,
+    unicode: bool | None = ...,
+    order: _OrderKACF = ...,
+) -> _CharArray[str_] | _CharArray[bytes_]: ...
+
+@overload
+def asarray(
+    obj: U_co,
+    itemsize: int | None = ...,
+    unicode: L[True] | None = ...,
+    order: _OrderKACF = ...,
+) -> _CharArray[str_]: ...
+@overload
+def asarray(
+    obj: S_co,
+    itemsize: int | None = ...,
+    unicode: L[False] | None = ...,
+    order: _OrderKACF = ...,
+) -> _CharArray[bytes_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None,
+    unicode: L[False],
+    order: _OrderKACF = ...,
+) -> _CharArray[bytes_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None = ...,
+    *,
+    unicode: L[False],
+    order: _OrderKACF = ...,
+) -> _CharArray[bytes_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None,
+    unicode: L[True],
+    order: _OrderKACF = ...,
+) -> _CharArray[str_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None = ...,
+    *,
+    unicode: L[True],
+    order: _OrderKACF = ...,
+) -> _CharArray[str_]: ...
+@overload
+def asarray(
+    obj: object,
+    itemsize: int | None = ...,
+    unicode: bool | None = ...,
+    order: _OrderKACF = ...,
+) -> _CharArray[str_] | _CharArray[bytes_]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/einsumfunc.py b/.venv/lib/python3.12/site-packages/numpy/_core/einsumfunc.py
new file mode 100644
index 0000000..8e71e6d
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/einsumfunc.py
@@ -0,0 +1,1498 @@
+"""
+Implementation of optimized einsum.
+
+"""
+import itertools
+import operator
+
+from numpy._core.multiarray import c_einsum
+from numpy._core.numeric import asanyarray, tensordot
+from numpy._core.overrides import array_function_dispatch
+
+__all__ = ['einsum', 'einsum_path']
+
+# importing string for string.ascii_letters would be too slow
+# the first import before caching has been measured to take 800 µs (#23777)
+# imports begin with uppercase to mimic ASCII values to avoid sorting issues
+einsum_symbols = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'
+einsum_symbols_set = set(einsum_symbols)
+
+
+def _flop_count(idx_contraction, inner, num_terms, size_dictionary):
+    """
+    Computes the number of FLOPS in the contraction.
+
+    Parameters
+    ----------
+    idx_contraction : iterable
+        The indices involved in the contraction
+    inner : bool
+        Does this contraction require an inner product?
+    num_terms : int
+        The number of terms in a contraction
+    size_dictionary : dict
+        The size of each of the indices in idx_contraction
+
+    Returns
+    -------
+    flop_count : int
+        The total number of FLOPS required for the contraction.
+
+    Examples
+    --------
+
+    >>> _flop_count('abc', False, 1, {'a': 2, 'b':3, 'c':5})
+    30
+
+    >>> _flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5})
+    60
+
+    """
+
+    overall_size = _compute_size_by_dict(idx_contraction, size_dictionary)
+    op_factor = max(1, num_terms - 1)
+    if inner:
+        op_factor += 1
+
+    return overall_size * op_factor
+
+def _compute_size_by_dict(indices, idx_dict):
+    """
+    Computes the product of the elements in indices based on the dictionary
+    idx_dict.
+
+    Parameters
+    ----------
+    indices : iterable
+        Indices to base the product on.
+    idx_dict : dictionary
+        Dictionary of index sizes
+
+    Returns
+    -------
+    ret : int
+        The resulting product.
+
+    Examples
+    --------
+    >>> _compute_size_by_dict('abbc', {'a': 2, 'b':3, 'c':5})
+    90
+
+    """
+    ret = 1
+    for i in indices:
+        ret *= idx_dict[i]
+    return ret
+
+
+def _find_contraction(positions, input_sets, output_set):
+    """
+    Finds the contraction for a given set of input and output sets.
+
+    Parameters
+    ----------
+    positions : iterable
+        Integer positions of terms used in the contraction.
+    input_sets : list
+        List of sets that represent the lhs side of the einsum subscript
+    output_set : set
+        Set that represents the rhs side of the overall einsum subscript
+
+    Returns
+    -------
+    new_result : set
+        The indices of the resulting contraction
+    remaining : list
+        List of sets that have not been contracted, the new set is appended to
+        the end of this list
+    idx_removed : set
+        Indices removed from the entire contraction
+    idx_contraction : set
+        The indices used in the current contraction
+
+    Examples
+    --------
+
+    # A simple dot product test case
+    >>> pos = (0, 1)
+    >>> isets = [set('ab'), set('bc')]
+    >>> oset = set('ac')
+    >>> _find_contraction(pos, isets, oset)
+    ({'a', 'c'}, [{'a', 'c'}], {'b'}, {'a', 'b', 'c'})
+
+    # A more complex case with additional terms in the contraction
+    >>> pos = (0, 2)
+    >>> isets = [set('abd'), set('ac'), set('bdc')]
+    >>> oset = set('ac')
+    >>> _find_contraction(pos, isets, oset)
+    ({'a', 'c'}, [{'a', 'c'}, {'a', 'c'}], {'b', 'd'}, {'a', 'b', 'c', 'd'})
+    """
+
+    idx_contract = set()
+    idx_remain = output_set.copy()
+    remaining = []
+    for ind, value in enumerate(input_sets):
+        if ind in positions:
+            idx_contract |= value
+        else:
+            remaining.append(value)
+            idx_remain |= value
+
+    new_result = idx_remain & idx_contract
+    idx_removed = (idx_contract - new_result)
+    remaining.append(new_result)
+
+    return (new_result, remaining, idx_removed, idx_contract)
+
+
+def _optimal_path(input_sets, output_set, idx_dict, memory_limit):
+    """
+    Computes all possible pair contractions, sieves the results based
+    on ``memory_limit`` and returns the lowest cost path. This algorithm
+    scales factorial with respect to the elements in the list ``input_sets``.
+
+    Parameters
+    ----------
+    input_sets : list
+        List of sets that represent the lhs side of the einsum subscript
+    output_set : set
+        Set that represents the rhs side of the overall einsum subscript
+    idx_dict : dictionary
+        Dictionary of index sizes
+    memory_limit : int
+        The maximum number of elements in a temporary array
+
+    Returns
+    -------
+    path : list
+        The optimal contraction order within the memory limit constraint.
+
+    Examples
+    --------
+    >>> isets = [set('abd'), set('ac'), set('bdc')]
+    >>> oset = set()
+    >>> idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+    >>> _optimal_path(isets, oset, idx_sizes, 5000)
+    [(0, 2), (0, 1)]
+    """
+
+    full_results = [(0, [], input_sets)]
+    for iteration in range(len(input_sets) - 1):
+        iter_results = []
+
+        # Compute all unique pairs
+        for curr in full_results:
+            cost, positions, remaining = curr
+            for con in itertools.combinations(
+                range(len(input_sets) - iteration), 2
+            ):
+
+                # Find the contraction
+                cont = _find_contraction(con, remaining, output_set)
+                new_result, new_input_sets, idx_removed, idx_contract = cont
+
+                # Sieve the results based on memory_limit
+                new_size = _compute_size_by_dict(new_result, idx_dict)
+                if new_size > memory_limit:
+                    continue
+
+                # Build (total_cost, positions, indices_remaining)
+                total_cost = cost + _flop_count(
+                    idx_contract, idx_removed, len(con), idx_dict
+                )
+                new_pos = positions + [con]
+                iter_results.append((total_cost, new_pos, new_input_sets))
+
+        # Update combinatorial list, if we did not find anything return best
+        # path + remaining contractions
+        if iter_results:
+            full_results = iter_results
+        else:
+            path = min(full_results, key=lambda x: x[0])[1]
+            path += [tuple(range(len(input_sets) - iteration))]
+            return path
+
+    # If we have not found anything return single einsum contraction
+    if len(full_results) == 0:
+        return [tuple(range(len(input_sets)))]
+
+    path = min(full_results, key=lambda x: x[0])[1]
+    return path
+
+def _parse_possible_contraction(
+        positions, input_sets, output_set, idx_dict,
+        memory_limit, path_cost, naive_cost
+    ):
+    """Compute the cost (removed size + flops) and resultant indices for
+    performing the contraction specified by ``positions``.
+
+    Parameters
+    ----------
+    positions : tuple of int
+        The locations of the proposed tensors to contract.
+    input_sets : list of sets
+        The indices found on each tensors.
+    output_set : set
+        The output indices of the expression.
+    idx_dict : dict
+        Mapping of each index to its size.
+    memory_limit : int
+        The total allowed size for an intermediary tensor.
+    path_cost : int
+        The contraction cost so far.
+    naive_cost : int
+        The cost of the unoptimized expression.
+
+    Returns
+    -------
+    cost : (int, int)
+        A tuple containing the size of any indices removed, and the flop cost.
+    positions : tuple of int
+        The locations of the proposed tensors to contract.
+    new_input_sets : list of sets
+        The resulting new list of indices if this proposed contraction
+        is performed.
+
+    """
+
+    # Find the contraction
+    contract = _find_contraction(positions, input_sets, output_set)
+    idx_result, new_input_sets, idx_removed, idx_contract = contract
+
+    # Sieve the results based on memory_limit
+    new_size = _compute_size_by_dict(idx_result, idx_dict)
+    if new_size > memory_limit:
+        return None
+
+    # Build sort tuple
+    old_sizes = (
+        _compute_size_by_dict(input_sets[p], idx_dict) for p in positions
+    )
+    removed_size = sum(old_sizes) - new_size
+
+    # NB: removed_size used to be just the size of any removed indices i.e.:
+    #     helpers.compute_size_by_dict(idx_removed, idx_dict)
+    cost = _flop_count(idx_contract, idx_removed, len(positions), idx_dict)
+    sort = (-removed_size, cost)
+
+    # Sieve based on total cost as well
+    if (path_cost + cost) > naive_cost:
+        return None
+
+    # Add contraction to possible choices
+    return [sort, positions, new_input_sets]
+
+
+def _update_other_results(results, best):
+    """Update the positions and provisional input_sets of ``results``
+    based on performing the contraction result ``best``. Remove any
+    involving the tensors contracted.
+
+    Parameters
+    ----------
+    results : list
+        List of contraction results produced by
+        ``_parse_possible_contraction``.
+    best : list
+        The best contraction of ``results`` i.e. the one that
+        will be performed.
+
+    Returns
+    -------
+    mod_results : list
+        The list of modified results, updated with outcome of
+        ``best`` contraction.
+    """
+
+    best_con = best[1]
+    bx, by = best_con
+    mod_results = []
+
+    for cost, (x, y), con_sets in results:
+
+        # Ignore results involving tensors just contracted
+        if x in best_con or y in best_con:
+            continue
+
+        # Update the input_sets
+        del con_sets[by - int(by > x) - int(by > y)]
+        del con_sets[bx - int(bx > x) - int(bx > y)]
+        con_sets.insert(-1, best[2][-1])
+
+        # Update the position indices
+        mod_con = x - int(x > bx) - int(x > by), y - int(y > bx) - int(y > by)
+        mod_results.append((cost, mod_con, con_sets))
+
+    return mod_results
+
+def _greedy_path(input_sets, output_set, idx_dict, memory_limit):
+    """
+    Finds the path by contracting the best pair until the input list is
+    exhausted. The best pair is found by minimizing the tuple
+    ``(-prod(indices_removed), cost)``.  What this amounts to is prioritizing
+    matrix multiplication or inner product operations, then Hadamard like
+    operations, and finally outer operations. Outer products are limited by
+    ``memory_limit``. This algorithm scales cubically with respect to the
+    number of elements in the list ``input_sets``.
+
+    Parameters
+    ----------
+    input_sets : list
+        List of sets that represent the lhs side of the einsum subscript
+    output_set : set
+        Set that represents the rhs side of the overall einsum subscript
+    idx_dict : dictionary
+        Dictionary of index sizes
+    memory_limit : int
+        The maximum number of elements in a temporary array
+
+    Returns
+    -------
+    path : list
+        The greedy contraction order within the memory limit constraint.
+
+    Examples
+    --------
+    >>> isets = [set('abd'), set('ac'), set('bdc')]
+    >>> oset = set()
+    >>> idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+    >>> _greedy_path(isets, oset, idx_sizes, 5000)
+    [(0, 2), (0, 1)]
+    """
+
+    # Handle trivial cases that leaked through
+    if len(input_sets) == 1:
+        return [(0,)]
+    elif len(input_sets) == 2:
+        return [(0, 1)]
+
+    # Build up a naive cost
+    contract = _find_contraction(
+        range(len(input_sets)), input_sets, output_set
+    )
+    idx_result, new_input_sets, idx_removed, idx_contract = contract
+    naive_cost = _flop_count(
+        idx_contract, idx_removed, len(input_sets), idx_dict
+    )
+
+    # Initially iterate over all pairs
+    comb_iter = itertools.combinations(range(len(input_sets)), 2)
+    known_contractions = []
+
+    path_cost = 0
+    path = []
+
+    for iteration in range(len(input_sets) - 1):
+
+        # Iterate over all pairs on the first step, only previously
+        # found pairs on subsequent steps
+        for positions in comb_iter:
+
+            # Always initially ignore outer products
+            if input_sets[positions[0]].isdisjoint(input_sets[positions[1]]):
+                continue
+
+            result = _parse_possible_contraction(
+                positions, input_sets, output_set, idx_dict,
+                memory_limit, path_cost, naive_cost
+            )
+            if result is not None:
+                known_contractions.append(result)
+
+        # If we do not have a inner contraction, rescan pairs
+        # including outer products
+        if len(known_contractions) == 0:
+
+            # Then check the outer products
+            for positions in itertools.combinations(
+                range(len(input_sets)), 2
+            ):
+                result = _parse_possible_contraction(
+                    positions, input_sets, output_set, idx_dict,
+                    memory_limit, path_cost, naive_cost
+                )
+                if result is not None:
+                    known_contractions.append(result)
+
+            # If we still did not find any remaining contractions,
+            # default back to einsum like behavior
+            if len(known_contractions) == 0:
+                path.append(tuple(range(len(input_sets))))
+                break
+
+        # Sort based on first index
+        best = min(known_contractions, key=lambda x: x[0])
+
+        # Now propagate as many unused contractions as possible
+        # to the next iteration
+        known_contractions = _update_other_results(known_contractions, best)
+
+        # Next iteration only compute contractions with the new tensor
+        # All other contractions have been accounted for
+        input_sets = best[2]
+        new_tensor_pos = len(input_sets) - 1
+        comb_iter = ((i, new_tensor_pos) for i in range(new_tensor_pos))
+
+        # Update path and total cost
+        path.append(best[1])
+        path_cost += best[0][1]
+
+    return path
+
+
+def _can_dot(inputs, result, idx_removed):
+    """
+    Checks if we can use BLAS (np.tensordot) call and its beneficial to do so.
+
+    Parameters
+    ----------
+    inputs : list of str
+        Specifies the subscripts for summation.
+    result : str
+        Resulting summation.
+    idx_removed : set
+        Indices that are removed in the summation
+
+
+    Returns
+    -------
+    type : bool
+        Returns true if BLAS should and can be used, else False
+
+    Notes
+    -----
+    If the operations is BLAS level 1 or 2 and is not already aligned
+    we default back to einsum as the memory movement to copy is more
+    costly than the operation itself.
+
+
+    Examples
+    --------
+
+    # Standard GEMM operation
+    >>> _can_dot(['ij', 'jk'], 'ik', set('j'))
+    True
+
+    # Can use the standard BLAS, but requires odd data movement
+    >>> _can_dot(['ijj', 'jk'], 'ik', set('j'))
+    False
+
+    # DDOT where the memory is not aligned
+    >>> _can_dot(['ijk', 'ikj'], '', set('ijk'))
+    False
+
+    """
+
+    # All `dot` calls remove indices
+    if len(idx_removed) == 0:
+        return False
+
+    # BLAS can only handle two operands
+    if len(inputs) != 2:
+        return False
+
+    input_left, input_right = inputs
+
+    for c in set(input_left + input_right):
+        # can't deal with repeated indices on same input or more than 2 total
+        nl, nr = input_left.count(c), input_right.count(c)
+        if (nl > 1) or (nr > 1) or (nl + nr > 2):
+            return False
+
+        # can't do implicit summation or dimension collapse e.g.
+        #     "ab,bc->c" (implicitly sum over 'a')
+        #     "ab,ca->ca" (take diagonal of 'a')
+        if nl + nr - 1 == int(c in result):
+            return False
+
+    # Build a few temporaries
+    set_left = set(input_left)
+    set_right = set(input_right)
+    keep_left = set_left - idx_removed
+    keep_right = set_right - idx_removed
+    rs = len(idx_removed)
+
+    # At this point we are a DOT, GEMV, or GEMM operation
+
+    # Handle inner products
+
+    # DDOT with aligned data
+    if input_left == input_right:
+        return True
+
+    # DDOT without aligned data (better to use einsum)
+    if set_left == set_right:
+        return False
+
+    # Handle the 4 possible (aligned) GEMV or GEMM cases
+
+    # GEMM or GEMV no transpose
+    if input_left[-rs:] == input_right[:rs]:
+        return True
+
+    # GEMM or GEMV transpose both
+    if input_left[:rs] == input_right[-rs:]:
+        return True
+
+    # GEMM or GEMV transpose right
+    if input_left[-rs:] == input_right[-rs:]:
+        return True
+
+    # GEMM or GEMV transpose left
+    if input_left[:rs] == input_right[:rs]:
+        return True
+
+    # Einsum is faster than GEMV if we have to copy data
+    if not keep_left or not keep_right:
+        return False
+
+    # We are a matrix-matrix product, but we need to copy data
+    return True
+
+
+def _parse_einsum_input(operands):
+    """
+    A reproduction of einsum c side einsum parsing in python.
+
+    Returns
+    -------
+    input_strings : str
+        Parsed input strings
+    output_string : str
+        Parsed output string
+    operands : list of array_like
+        The operands to use in the numpy contraction
+
+    Examples
+    --------
+    The operand list is simplified to reduce printing:
+
+    >>> np.random.seed(123)
+    >>> a = np.random.rand(4, 4)
+    >>> b = np.random.rand(4, 4, 4)
+    >>> _parse_einsum_input(('...a,...a->...', a, b))
+    ('za,xza', 'xz', [a, b]) # may vary
+
+    >>> _parse_einsum_input((a, [Ellipsis, 0], b, [Ellipsis, 0]))
+    ('za,xza', 'xz', [a, b]) # may vary
+    """
+
+    if len(operands) == 0:
+        raise ValueError("No input operands")
+
+    if isinstance(operands[0], str):
+        subscripts = operands[0].replace(" ", "")
+        operands = [asanyarray(v) for v in operands[1:]]
+
+        # Ensure all characters are valid
+        for s in subscripts:
+            if s in '.,->':
+                continue
+            if s not in einsum_symbols:
+                raise ValueError(f"Character {s} is not a valid symbol.")
+
+    else:
+        tmp_operands = list(operands)
+        operand_list = []
+        subscript_list = []
+        for p in range(len(operands) // 2):
+            operand_list.append(tmp_operands.pop(0))
+            subscript_list.append(tmp_operands.pop(0))
+
+        output_list = tmp_operands[-1] if len(tmp_operands) else None
+        operands = [asanyarray(v) for v in operand_list]
+        subscripts = ""
+        last = len(subscript_list) - 1
+        for num, sub in enumerate(subscript_list):
+            for s in sub:
+                if s is Ellipsis:
+                    subscripts += "..."
+                else:
+                    try:
+                        s = operator.index(s)
+                    except TypeError as e:
+                        raise TypeError(
+                            "For this input type lists must contain "
+                            "either int or Ellipsis"
+                        ) from e
+                    subscripts += einsum_symbols[s]
+            if num != last:
+                subscripts += ","
+
+        if output_list is not None:
+            subscripts += "->"
+            for s in output_list:
+                if s is Ellipsis:
+                    subscripts += "..."
+                else:
+                    try:
+                        s = operator.index(s)
+                    except TypeError as e:
+                        raise TypeError(
+                            "For this input type lists must contain "
+                            "either int or Ellipsis"
+                        ) from e
+                    subscripts += einsum_symbols[s]
+    # Check for proper "->"
+    if ("-" in subscripts) or (">" in subscripts):
+        invalid = (subscripts.count("-") > 1) or (subscripts.count(">") > 1)
+        if invalid or (subscripts.count("->") != 1):
+            raise ValueError("Subscripts can only contain one '->'.")
+
+    # Parse ellipses
+    if "." in subscripts:
+        used = subscripts.replace(".", "").replace(",", "").replace("->", "")
+        unused = list(einsum_symbols_set - set(used))
+        ellipse_inds = "".join(unused)
+        longest = 0
+
+        if "->" in subscripts:
+            input_tmp, output_sub = subscripts.split("->")
+            split_subscripts = input_tmp.split(",")
+            out_sub = True
+        else:
+            split_subscripts = subscripts.split(',')
+            out_sub = False
+
+        for num, sub in enumerate(split_subscripts):
+            if "." in sub:
+                if (sub.count(".") != 3) or (sub.count("...") != 1):
+                    raise ValueError("Invalid Ellipses.")
+
+                # Take into account numerical values
+                if operands[num].shape == ():
+                    ellipse_count = 0
+                else:
+                    ellipse_count = max(operands[num].ndim, 1)
+                    ellipse_count -= (len(sub) - 3)
+
+                if ellipse_count > longest:
+                    longest = ellipse_count
+
+                if ellipse_count < 0:
+                    raise ValueError("Ellipses lengths do not match.")
+                elif ellipse_count == 0:
+                    split_subscripts[num] = sub.replace('...', '')
+                else:
+                    rep_inds = ellipse_inds[-ellipse_count:]
+                    split_subscripts[num] = sub.replace('...', rep_inds)
+
+        subscripts = ",".join(split_subscripts)
+        if longest == 0:
+            out_ellipse = ""
+        else:
+            out_ellipse = ellipse_inds[-longest:]
+
+        if out_sub:
+            subscripts += "->" + output_sub.replace("...", out_ellipse)
+        else:
+            # Special care for outputless ellipses
+            output_subscript = ""
+            tmp_subscripts = subscripts.replace(",", "")
+            for s in sorted(set(tmp_subscripts)):
+                if s not in (einsum_symbols):
+                    raise ValueError(f"Character {s} is not a valid symbol.")
+                if tmp_subscripts.count(s) == 1:
+                    output_subscript += s
+            normal_inds = ''.join(sorted(set(output_subscript) -
+                                         set(out_ellipse)))
+
+            subscripts += "->" + out_ellipse + normal_inds
+
+    # Build output string if does not exist
+    if "->" in subscripts:
+        input_subscripts, output_subscript = subscripts.split("->")
+    else:
+        input_subscripts = subscripts
+        # Build output subscripts
+        tmp_subscripts = subscripts.replace(",", "")
+        output_subscript = ""
+        for s in sorted(set(tmp_subscripts)):
+            if s not in einsum_symbols:
+                raise ValueError(f"Character {s} is not a valid symbol.")
+            if tmp_subscripts.count(s) == 1:
+                output_subscript += s
+
+    # Make sure output subscripts are in the input
+    for char in output_subscript:
+        if output_subscript.count(char) != 1:
+            raise ValueError("Output character %s appeared more than once in "
+                             "the output." % char)
+        if char not in input_subscripts:
+            raise ValueError(f"Output character {char} did not appear in the input")
+
+    # Make sure number operands is equivalent to the number of terms
+    if len(input_subscripts.split(',')) != len(operands):
+        raise ValueError("Number of einsum subscripts must be equal to the "
+                         "number of operands.")
+
+    return (input_subscripts, output_subscript, operands)
+
+
+def _einsum_path_dispatcher(*operands, optimize=None, einsum_call=None):
+    # NOTE: technically, we should only dispatch on array-like arguments, not
+    # subscripts (given as strings). But separating operands into
+    # arrays/subscripts is a little tricky/slow (given einsum's two supported
+    # signatures), so as a practical shortcut we dispatch on everything.
+    # Strings will be ignored for dispatching since they don't define
+    # __array_function__.
+    return operands
+
+
+@array_function_dispatch(_einsum_path_dispatcher, module='numpy')
+def einsum_path(*operands, optimize='greedy', einsum_call=False):
+    """
+    einsum_path(subscripts, *operands, optimize='greedy')
+
+    Evaluates the lowest cost contraction order for an einsum expression by
+    considering the creation of intermediate arrays.
+
+    Parameters
+    ----------
+    subscripts : str
+        Specifies the subscripts for summation.
+    *operands : list of array_like
+        These are the arrays for the operation.
+    optimize : {bool, list, tuple, 'greedy', 'optimal'}
+        Choose the type of path. If a tuple is provided, the second argument is
+        assumed to be the maximum intermediate size created. If only a single
+        argument is provided the largest input or output array size is used
+        as a maximum intermediate size.
+
+        * if a list is given that starts with ``einsum_path``, uses this as the
+          contraction path
+        * if False no optimization is taken
+        * if True defaults to the 'greedy' algorithm
+        * 'optimal' An algorithm that combinatorially explores all possible
+          ways of contracting the listed tensors and chooses the least costly
+          path. Scales exponentially with the number of terms in the
+          contraction.
+        * 'greedy' An algorithm that chooses the best pair contraction
+          at each step. Effectively, this algorithm searches the largest inner,
+          Hadamard, and then outer products at each step. Scales cubically with
+          the number of terms in the contraction. Equivalent to the 'optimal'
+          path for most contractions.
+
+        Default is 'greedy'.
+
+    Returns
+    -------
+    path : list of tuples
+        A list representation of the einsum path.
+    string_repr : str
+        A printable representation of the einsum path.
+
+    Notes
+    -----
+    The resulting path indicates which terms of the input contraction should be
+    contracted first, the result of this contraction is then appended to the
+    end of the contraction list. This list can then be iterated over until all
+    intermediate contractions are complete.
+
+    See Also
+    --------
+    einsum, linalg.multi_dot
+
+    Examples
+    --------
+
+    We can begin with a chain dot example. In this case, it is optimal to
+    contract the ``b`` and ``c`` tensors first as represented by the first
+    element of the path ``(1, 2)``. The resulting tensor is added to the end
+    of the contraction and the remaining contraction ``(0, 1)`` is then
+    completed.
+
+    >>> np.random.seed(123)
+    >>> a = np.random.rand(2, 2)
+    >>> b = np.random.rand(2, 5)
+    >>> c = np.random.rand(5, 2)
+    >>> path_info = np.einsum_path('ij,jk,kl->il', a, b, c, optimize='greedy')
+    >>> print(path_info[0])
+    ['einsum_path', (1, 2), (0, 1)]
+    >>> print(path_info[1])
+      Complete contraction:  ij,jk,kl->il # may vary
+             Naive scaling:  4
+         Optimized scaling:  3
+          Naive FLOP count:  1.600e+02
+      Optimized FLOP count:  5.600e+01
+       Theoretical speedup:  2.857
+      Largest intermediate:  4.000e+00 elements
+    -------------------------------------------------------------------------
+    scaling                  current                                remaining
+    -------------------------------------------------------------------------
+       3                   kl,jk->jl                                ij,jl->il
+       3                   jl,ij->il                                   il->il
+
+
+    A more complex index transformation example.
+
+    >>> I = np.random.rand(10, 10, 10, 10)
+    >>> C = np.random.rand(10, 10)
+    >>> path_info = np.einsum_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C,
+    ...                            optimize='greedy')
+
+    >>> print(path_info[0])
+    ['einsum_path', (0, 2), (0, 3), (0, 2), (0, 1)]
+    >>> print(path_info[1])
+      Complete contraction:  ea,fb,abcd,gc,hd->efgh # may vary
+             Naive scaling:  8
+         Optimized scaling:  5
+          Naive FLOP count:  8.000e+08
+      Optimized FLOP count:  8.000e+05
+       Theoretical speedup:  1000.000
+      Largest intermediate:  1.000e+04 elements
+    --------------------------------------------------------------------------
+    scaling                  current                                remaining
+    --------------------------------------------------------------------------
+       5               abcd,ea->bcde                      fb,gc,hd,bcde->efgh
+       5               bcde,fb->cdef                         gc,hd,cdef->efgh
+       5               cdef,gc->defg                            hd,defg->efgh
+       5               defg,hd->efgh                               efgh->efgh
+    """
+
+    # Figure out what the path really is
+    path_type = optimize
+    if path_type is True:
+        path_type = 'greedy'
+    if path_type is None:
+        path_type = False
+
+    explicit_einsum_path = False
+    memory_limit = None
+
+    # No optimization or a named path algorithm
+    if (path_type is False) or isinstance(path_type, str):
+        pass
+
+    # Given an explicit path
+    elif len(path_type) and (path_type[0] == 'einsum_path'):
+        explicit_einsum_path = True
+
+    # Path tuple with memory limit
+    elif ((len(path_type) == 2) and isinstance(path_type[0], str) and
+            isinstance(path_type[1], (int, float))):
+        memory_limit = int(path_type[1])
+        path_type = path_type[0]
+
+    else:
+        raise TypeError(f"Did not understand the path: {str(path_type)}")
+
+    # Hidden option, only einsum should call this
+    einsum_call_arg = einsum_call
+
+    # Python side parsing
+    input_subscripts, output_subscript, operands = (
+        _parse_einsum_input(operands)
+    )
+
+    # Build a few useful list and sets
+    input_list = input_subscripts.split(',')
+    input_sets = [set(x) for x in input_list]
+    output_set = set(output_subscript)
+    indices = set(input_subscripts.replace(',', ''))
+
+    # Get length of each unique dimension and ensure all dimensions are correct
+    dimension_dict = {}
+    broadcast_indices = [[] for x in range(len(input_list))]
+    for tnum, term in enumerate(input_list):
+        sh = operands[tnum].shape
+        if len(sh) != len(term):
+            raise ValueError("Einstein sum subscript %s does not contain the "
+                             "correct number of indices for operand %d."
+                             % (input_subscripts[tnum], tnum))
+        for cnum, char in enumerate(term):
+            dim = sh[cnum]
+
+            # Build out broadcast indices
+            if dim == 1:
+                broadcast_indices[tnum].append(char)
+
+            if char in dimension_dict.keys():
+                # For broadcasting cases we always want the largest dim size
+                if dimension_dict[char] == 1:
+                    dimension_dict[char] = dim
+                elif dim not in (1, dimension_dict[char]):
+                    raise ValueError("Size of label '%s' for operand %d (%d) "
+                                     "does not match previous terms (%d)."
+                                     % (char, tnum, dimension_dict[char], dim))
+            else:
+                dimension_dict[char] = dim
+
+    # Convert broadcast inds to sets
+    broadcast_indices = [set(x) for x in broadcast_indices]
+
+    # Compute size of each input array plus the output array
+    size_list = [_compute_size_by_dict(term, dimension_dict)
+                 for term in input_list + [output_subscript]]
+    max_size = max(size_list)
+
+    if memory_limit is None:
+        memory_arg = max_size
+    else:
+        memory_arg = memory_limit
+
+    # Compute naive cost
+    # This isn't quite right, need to look into exactly how einsum does this
+    inner_product = (sum(len(x) for x in input_sets) - len(indices)) > 0
+    naive_cost = _flop_count(
+        indices, inner_product, len(input_list), dimension_dict
+    )
+
+    # Compute the path
+    if explicit_einsum_path:
+        path = path_type[1:]
+    elif (
+        (path_type is False)
+        or (len(input_list) in [1, 2])
+        or (indices == output_set)
+    ):
+        # Nothing to be optimized, leave it to einsum
+        path = [tuple(range(len(input_list)))]
+    elif path_type == "greedy":
+        path = _greedy_path(
+            input_sets, output_set, dimension_dict, memory_arg
+        )
+    elif path_type == "optimal":
+        path = _optimal_path(
+            input_sets, output_set, dimension_dict, memory_arg
+        )
+    else:
+        raise KeyError("Path name %s not found", path_type)
+
+    cost_list, scale_list, size_list, contraction_list = [], [], [], []
+
+    # Build contraction tuple (positions, gemm, einsum_str, remaining)
+    for cnum, contract_inds in enumerate(path):
+        # Make sure we remove inds from right to left
+        contract_inds = tuple(sorted(contract_inds, reverse=True))
+
+        contract = _find_contraction(contract_inds, input_sets, output_set)
+        out_inds, input_sets, idx_removed, idx_contract = contract
+
+        cost = _flop_count(
+            idx_contract, idx_removed, len(contract_inds), dimension_dict
+        )
+        cost_list.append(cost)
+        scale_list.append(len(idx_contract))
+        size_list.append(_compute_size_by_dict(out_inds, dimension_dict))
+
+        bcast = set()
+        tmp_inputs = []
+        for x in contract_inds:
+            tmp_inputs.append(input_list.pop(x))
+            bcast |= broadcast_indices.pop(x)
+
+        new_bcast_inds = bcast - idx_removed
+
+        # If we're broadcasting, nix blas
+        if not len(idx_removed & bcast):
+            do_blas = _can_dot(tmp_inputs, out_inds, idx_removed)
+        else:
+            do_blas = False
+
+        # Last contraction
+        if (cnum - len(path)) == -1:
+            idx_result = output_subscript
+        else:
+            sort_result = [(dimension_dict[ind], ind) for ind in out_inds]
+            idx_result = "".join([x[1] for x in sorted(sort_result)])
+
+        input_list.append(idx_result)
+        broadcast_indices.append(new_bcast_inds)
+        einsum_str = ",".join(tmp_inputs) + "->" + idx_result
+
+        contraction = (
+            contract_inds, idx_removed, einsum_str, input_list[:], do_blas
+        )
+        contraction_list.append(contraction)
+
+    opt_cost = sum(cost_list) + 1
+
+    if len(input_list) != 1:
+        # Explicit "einsum_path" is usually trusted, but we detect this kind of
+        # mistake in order to prevent from returning an intermediate value.
+        raise RuntimeError(
+            f"Invalid einsum_path is specified: {len(input_list) - 1} more "
+            "operands has to be contracted.")
+
+    if einsum_call_arg:
+        return (operands, contraction_list)
+
+    # Return the path along with a nice string representation
+    overall_contraction = input_subscripts + "->" + output_subscript
+    header = ("scaling", "current", "remaining")
+
+    speedup = naive_cost / opt_cost
+    max_i = max(size_list)
+
+    path_print = f"  Complete contraction:  {overall_contraction}\n"
+    path_print += f"         Naive scaling:  {len(indices)}\n"
+    path_print += "     Optimized scaling:  %d\n" % max(scale_list)
+    path_print += f"      Naive FLOP count:  {naive_cost:.3e}\n"
+    path_print += f"  Optimized FLOP count:  {opt_cost:.3e}\n"
+    path_print += f"   Theoretical speedup:  {speedup:3.3f}\n"
+    path_print += f"  Largest intermediate:  {max_i:.3e} elements\n"
+    path_print += "-" * 74 + "\n"
+    path_print += "%6s %24s %40s\n" % header
+    path_print += "-" * 74
+
+    for n, contraction in enumerate(contraction_list):
+        inds, idx_rm, einsum_str, remaining, blas = contraction
+        remaining_str = ",".join(remaining) + "->" + output_subscript
+        path_run = (scale_list[n], einsum_str, remaining_str)
+        path_print += "\n%4d    %24s %40s" % path_run
+
+    path = ['einsum_path'] + path
+    return (path, path_print)
+
+
+def _einsum_dispatcher(*operands, out=None, optimize=None, **kwargs):
+    # Arguably we dispatch on more arguments than we really should; see note in
+    # _einsum_path_dispatcher for why.
+    yield from operands
+    yield out
+
+
+# Rewrite einsum to handle different cases
+@array_function_dispatch(_einsum_dispatcher, module='numpy')
+def einsum(*operands, out=None, optimize=False, **kwargs):
+    """
+    einsum(subscripts, *operands, out=None, dtype=None, order='K',
+           casting='safe', optimize=False)
+
+    Evaluates the Einstein summation convention on the operands.
+
+    Using the Einstein summation convention, many common multi-dimensional,
+    linear algebraic array operations can be represented in a simple fashion.
+    In *implicit* mode `einsum` computes these values.
+
+    In *explicit* mode, `einsum` provides further flexibility to compute
+    other array operations that might not be considered classical Einstein
+    summation operations, by disabling, or forcing summation over specified
+    subscript labels.
+
+    See the notes and examples for clarification.
+
+    Parameters
+    ----------
+    subscripts : str
+        Specifies the subscripts for summation as comma separated list of
+        subscript labels. An implicit (classical Einstein summation)
+        calculation is performed unless the explicit indicator '->' is
+        included as well as subscript labels of the precise output form.
+    operands : list of array_like
+        These are the arrays for the operation.
+    out : ndarray, optional
+        If provided, the calculation is done into this array.
+    dtype : {data-type, None}, optional
+        If provided, forces the calculation to use the data type specified.
+        Note that you may have to also give a more liberal `casting`
+        parameter to allow the conversions. Default is None.
+    order : {'C', 'F', 'A', 'K'}, optional
+        Controls the memory layout of the output. 'C' means it should
+        be C contiguous. 'F' means it should be Fortran contiguous,
+        'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise.
+        'K' means it should be as close to the layout as the inputs as
+        is possible, including arbitrarily permuted axes.
+        Default is 'K'.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur.  Setting this to
+        'unsafe' is not recommended, as it can adversely affect accumulations.
+
+        * 'no' means the data types should not be cast at all.
+        * 'equiv' means only byte-order changes are allowed.
+        * 'safe' means only casts which can preserve values are allowed.
+        * 'same_kind' means only safe casts or casts within a kind,
+          like float64 to float32, are allowed.
+        * 'unsafe' means any data conversions may be done.
+
+        Default is 'safe'.
+    optimize : {False, True, 'greedy', 'optimal'}, optional
+        Controls if intermediate optimization should occur. No optimization
+        will occur if False and True will default to the 'greedy' algorithm.
+        Also accepts an explicit contraction list from the ``np.einsum_path``
+        function. See ``np.einsum_path`` for more details. Defaults to False.
+
+    Returns
+    -------
+    output : ndarray
+        The calculation based on the Einstein summation convention.
+
+    See Also
+    --------
+    einsum_path, dot, inner, outer, tensordot, linalg.multi_dot
+    einsum:
+        Similar verbose interface is provided by the
+        `einops <https://github.com/arogozhnikov/einops>`_ package to cover
+        additional operations: transpose, reshape/flatten, repeat/tile,
+        squeeze/unsqueeze and reductions.
+        The `opt_einsum <https://optimized-einsum.readthedocs.io/en/stable/>`_
+        optimizes contraction order for einsum-like expressions
+        in backend-agnostic manner.
+
+    Notes
+    -----
+    The Einstein summation convention can be used to compute
+    many multi-dimensional, linear algebraic array operations. `einsum`
+    provides a succinct way of representing these.
+
+    A non-exhaustive list of these operations,
+    which can be computed by `einsum`, is shown below along with examples:
+
+    * Trace of an array, :py:func:`numpy.trace`.
+    * Return a diagonal, :py:func:`numpy.diag`.
+    * Array axis summations, :py:func:`numpy.sum`.
+    * Transpositions and permutations, :py:func:`numpy.transpose`.
+    * Matrix multiplication and dot product, :py:func:`numpy.matmul`
+        :py:func:`numpy.dot`.
+    * Vector inner and outer products, :py:func:`numpy.inner`
+        :py:func:`numpy.outer`.
+    * Broadcasting, element-wise and scalar multiplication,
+        :py:func:`numpy.multiply`.
+    * Tensor contractions, :py:func:`numpy.tensordot`.
+    * Chained array operations, in efficient calculation order,
+        :py:func:`numpy.einsum_path`.
+
+    The subscripts string is a comma-separated list of subscript labels,
+    where each label refers to a dimension of the corresponding operand.
+    Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)``
+    is equivalent to :py:func:`np.inner(a,b) <numpy.inner>`. If a label
+    appears only once, it is not summed, so ``np.einsum('i', a)``
+    produces a view of ``a`` with no changes. A further example
+    ``np.einsum('ij,jk', a, b)`` describes traditional matrix multiplication
+    and is equivalent to :py:func:`np.matmul(a,b) <numpy.matmul>`.
+    Repeated subscript labels in one operand take the diagonal.
+    For example, ``np.einsum('ii', a)`` is equivalent to
+    :py:func:`np.trace(a) <numpy.trace>`.
+
+    In *implicit mode*, the chosen subscripts are important
+    since the axes of the output are reordered alphabetically.  This
+    means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
+    ``np.einsum('ji', a)`` takes its transpose. Additionally,
+    ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while,
+    ``np.einsum('ij,jh', a, b)`` returns the transpose of the
+    multiplication since subscript 'h' precedes subscript 'i'.
+
+    In *explicit mode* the output can be directly controlled by
+    specifying output subscript labels.  This requires the
+    identifier '->' as well as the list of output subscript labels.
+    This feature increases the flexibility of the function since
+    summing can be disabled or forced when required. The call
+    ``np.einsum('i->', a)`` is like :py:func:`np.sum(a) <numpy.sum>`
+    if ``a`` is a 1-D array, and ``np.einsum('ii->i', a)``
+    is like :py:func:`np.diag(a) <numpy.diag>` if ``a`` is a square 2-D array.
+    The difference is that `einsum` does not allow broadcasting by default.
+    Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the
+    order of the output subscript labels and therefore returns matrix
+    multiplication, unlike the example above in implicit mode.
+
+    To enable and control broadcasting, use an ellipsis.  Default
+    NumPy-style broadcasting is done by adding an ellipsis
+    to the left of each term, like ``np.einsum('...ii->...i', a)``.
+    ``np.einsum('...i->...', a)`` is like
+    :py:func:`np.sum(a, axis=-1) <numpy.sum>` for array ``a`` of any shape.
+    To take the trace along the first and last axes,
+    you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
+    product with the left-most indices instead of rightmost, one can do
+    ``np.einsum('ij...,jk...->ik...', a, b)``.
+
+    When there is only one operand, no axes are summed, and no output
+    parameter is provided, a view into the operand is returned instead
+    of a new array.  Thus, taking the diagonal as ``np.einsum('ii->i', a)``
+    produces a view (changed in version 1.10.0).
+
+    `einsum` also provides an alternative way to provide the subscripts and
+    operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``.
+    If the output shape is not provided in this format `einsum` will be
+    calculated in implicit mode, otherwise it will be performed explicitly.
+    The examples below have corresponding `einsum` calls with the two
+    parameter methods.
+
+    Views returned from einsum are now writeable whenever the input array
+    is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now
+    have the same effect as :py:func:`np.swapaxes(a, 0, 2) <numpy.swapaxes>`
+    and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal
+    of a 2D array.
+
+    Added the ``optimize`` argument which will optimize the contraction order
+    of an einsum expression. For a contraction with three or more operands
+    this can greatly increase the computational efficiency at the cost of
+    a larger memory footprint during computation.
+
+    Typically a 'greedy' algorithm is applied which empirical tests have shown
+    returns the optimal path in the majority of cases. In some cases 'optimal'
+    will return the superlative path through a more expensive, exhaustive
+    search. For iterative calculations it may be advisable to calculate
+    the optimal path once and reuse that path by supplying it as an argument.
+    An example is given below.
+
+    See :py:func:`numpy.einsum_path` for more details.
+
+    Examples
+    --------
+    >>> a = np.arange(25).reshape(5,5)
+    >>> b = np.arange(5)
+    >>> c = np.arange(6).reshape(2,3)
+
+    Trace of a matrix:
+
+    >>> np.einsum('ii', a)
+    60
+    >>> np.einsum(a, [0,0])
+    60
+    >>> np.trace(a)
+    60
+
+    Extract the diagonal (requires explicit form):
+
+    >>> np.einsum('ii->i', a)
+    array([ 0,  6, 12, 18, 24])
+    >>> np.einsum(a, [0,0], [0])
+    array([ 0,  6, 12, 18, 24])
+    >>> np.diag(a)
+    array([ 0,  6, 12, 18, 24])
+
+    Sum over an axis (requires explicit form):
+
+    >>> np.einsum('ij->i', a)
+    array([ 10,  35,  60,  85, 110])
+    >>> np.einsum(a, [0,1], [0])
+    array([ 10,  35,  60,  85, 110])
+    >>> np.sum(a, axis=1)
+    array([ 10,  35,  60,  85, 110])
+
+    For higher dimensional arrays summing a single axis can be done
+    with ellipsis:
+
+    >>> np.einsum('...j->...', a)
+    array([ 10,  35,  60,  85, 110])
+    >>> np.einsum(a, [Ellipsis,1], [Ellipsis])
+    array([ 10,  35,  60,  85, 110])
+
+    Compute a matrix transpose, or reorder any number of axes:
+
+    >>> np.einsum('ji', c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.einsum('ij->ji', c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.einsum(c, [1,0])
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+    >>> np.transpose(c)
+    array([[0, 3],
+           [1, 4],
+           [2, 5]])
+
+    Vector inner products:
+
+    >>> np.einsum('i,i', b, b)
+    30
+    >>> np.einsum(b, [0], b, [0])
+    30
+    >>> np.inner(b,b)
+    30
+
+    Matrix vector multiplication:
+
+    >>> np.einsum('ij,j', a, b)
+    array([ 30,  80, 130, 180, 230])
+    >>> np.einsum(a, [0,1], b, [1])
+    array([ 30,  80, 130, 180, 230])
+    >>> np.dot(a, b)
+    array([ 30,  80, 130, 180, 230])
+    >>> np.einsum('...j,j', a, b)
+    array([ 30,  80, 130, 180, 230])
+
+    Broadcasting and scalar multiplication:
+
+    >>> np.einsum('..., ...', 3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.einsum(',ij', 3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.einsum(3, [Ellipsis], c, [Ellipsis])
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+    >>> np.multiply(3, c)
+    array([[ 0,  3,  6],
+           [ 9, 12, 15]])
+
+    Vector outer product:
+
+    >>> np.einsum('i,j', np.arange(2)+1, b)
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+    >>> np.einsum(np.arange(2)+1, [0], b, [1])
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+    >>> np.outer(np.arange(2)+1, b)
+    array([[0, 1, 2, 3, 4],
+           [0, 2, 4, 6, 8]])
+
+    Tensor contraction:
+
+    >>> a = np.arange(60.).reshape(3,4,5)
+    >>> b = np.arange(24.).reshape(4,3,2)
+    >>> np.einsum('ijk,jil->kl', a, b)
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+    >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+    >>> np.tensordot(a,b, axes=([1,0],[0,1]))
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+
+    Writeable returned arrays (since version 1.10.0):
+
+    >>> a = np.zeros((3, 3))
+    >>> np.einsum('ii->i', a)[:] = 1
+    >>> a
+    array([[1., 0., 0.],
+           [0., 1., 0.],
+           [0., 0., 1.]])
+
+    Example of ellipsis use:
+
+    >>> a = np.arange(6).reshape((3,2))
+    >>> b = np.arange(12).reshape((4,3))
+    >>> np.einsum('ki,jk->ij', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+    >>> np.einsum('ki,...k->i...', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+    >>> np.einsum('k...,jk', a, b)
+    array([[10, 28, 46, 64],
+           [13, 40, 67, 94]])
+
+    Chained array operations. For more complicated contractions, speed ups
+    might be achieved by repeatedly computing a 'greedy' path or pre-computing
+    the 'optimal' path and repeatedly applying it, using an `einsum_path`
+    insertion (since version 1.12.0). Performance improvements can be
+    particularly significant with larger arrays:
+
+    >>> a = np.ones(64).reshape(2,4,8)
+
+    Basic `einsum`: ~1520ms  (benchmarked on 3.1GHz Intel i5.)
+
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a)
+
+    Sub-optimal `einsum` (due to repeated path calculation time): ~330ms
+
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a,
+    ...         optimize='optimal')
+
+    Greedy `einsum` (faster optimal path approximation): ~160ms
+
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='greedy')
+
+    Optimal `einsum` (best usage pattern in some use cases): ~110ms
+
+    >>> path = np.einsum_path('ijk,ilm,njm,nlk,abc->',a,a,a,a,a,
+    ...     optimize='optimal')[0]
+    >>> for iteration in range(500):
+    ...     _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=path)
+
+    """
+    # Special handling if out is specified
+    specified_out = out is not None
+
+    # If no optimization, run pure einsum
+    if optimize is False:
+        if specified_out:
+            kwargs['out'] = out
+        return c_einsum(*operands, **kwargs)
+
+    # Check the kwargs to avoid a more cryptic error later, without having to
+    # repeat default values here
+    valid_einsum_kwargs = ['dtype', 'order', 'casting']
+    unknown_kwargs = [k for (k, v) in kwargs.items() if
+                      k not in valid_einsum_kwargs]
+    if len(unknown_kwargs):
+        raise TypeError(f"Did not understand the following kwargs: {unknown_kwargs}")
+
+    # Build the contraction list and operand
+    operands, contraction_list = einsum_path(*operands, optimize=optimize,
+                                             einsum_call=True)
+
+    # Handle order kwarg for output array, c_einsum allows mixed case
+    output_order = kwargs.pop('order', 'K')
+    if output_order.upper() == 'A':
+        if all(arr.flags.f_contiguous for arr in operands):
+            output_order = 'F'
+        else:
+            output_order = 'C'
+
+    # Start contraction loop
+    for num, contraction in enumerate(contraction_list):
+        inds, idx_rm, einsum_str, remaining, blas = contraction
+        tmp_operands = [operands.pop(x) for x in inds]
+
+        # Do we need to deal with the output?
+        handle_out = specified_out and ((num + 1) == len(contraction_list))
+
+        # Call tensordot if still possible
+        if blas:
+            # Checks have already been handled
+            input_str, results_index = einsum_str.split('->')
+            input_left, input_right = input_str.split(',')
+
+            tensor_result = input_left + input_right
+            for s in idx_rm:
+                tensor_result = tensor_result.replace(s, "")
+
+            # Find indices to contract over
+            left_pos, right_pos = [], []
+            for s in sorted(idx_rm):
+                left_pos.append(input_left.find(s))
+                right_pos.append(input_right.find(s))
+
+            # Contract!
+            new_view = tensordot(
+                *tmp_operands, axes=(tuple(left_pos), tuple(right_pos))
+            )
+
+            # Build a new view if needed
+            if (tensor_result != results_index) or handle_out:
+                if handle_out:
+                    kwargs["out"] = out
+                new_view = c_einsum(
+                    tensor_result + '->' + results_index, new_view, **kwargs
+                )
+
+        # Call einsum
+        else:
+            # If out was specified
+            if handle_out:
+                kwargs["out"] = out
+
+            # Do the contraction
+            new_view = c_einsum(einsum_str, *tmp_operands, **kwargs)
+
+        # Append new items and dereference what we can
+        operands.append(new_view)
+        del tmp_operands, new_view
+
+    if specified_out:
+        return out
+    else:
+        return asanyarray(operands[0], order=output_order)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/einsumfunc.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/einsumfunc.pyi
new file mode 100644
index 0000000..9653a26
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/einsumfunc.pyi
@@ -0,0 +1,184 @@
+from collections.abc import Sequence
+from typing import Any, Literal, TypeAlias, TypeVar, overload
+
+import numpy as np
+from numpy import _OrderKACF, number
+from numpy._typing import (
+    NDArray,
+    _ArrayLikeBool_co,
+    _ArrayLikeComplex_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeInt_co,
+    _ArrayLikeObject_co,
+    _ArrayLikeUInt_co,
+    _DTypeLikeBool,
+    _DTypeLikeComplex,
+    _DTypeLikeComplex_co,
+    _DTypeLikeFloat,
+    _DTypeLikeInt,
+    _DTypeLikeObject,
+    _DTypeLikeUInt,
+)
+
+__all__ = ["einsum", "einsum_path"]
+
+_ArrayT = TypeVar(
+    "_ArrayT",
+    bound=NDArray[np.bool | number],
+)
+
+_OptimizeKind: TypeAlias = bool | Literal["greedy", "optimal"] | Sequence[Any] | None
+_CastingSafe: TypeAlias = Literal["no", "equiv", "safe", "same_kind"]
+_CastingUnsafe: TypeAlias = Literal["unsafe"]
+
+# TODO: Properly handle the `casting`-based combinatorics
+# TODO: We need to evaluate the content `__subscripts` in order
+# to identify whether or an array or scalar is returned. At a cursory
+# glance this seems like something that can quite easily be done with
+# a mypy plugin.
+# Something like `is_scalar = bool(__subscripts.partition("->")[-1])`
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeBool_co,
+    out: None = ...,
+    dtype: _DTypeLikeBool | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = ...,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeUInt_co,
+    out: None = ...,
+    dtype: _DTypeLikeUInt | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = ...,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeInt_co,
+    out: None = ...,
+    dtype: _DTypeLikeInt | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = ...,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeFloat_co,
+    out: None = ...,
+    dtype: _DTypeLikeFloat | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = ...,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeComplex_co,
+    out: None = ...,
+    dtype: _DTypeLikeComplex | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = ...,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: Any,
+    casting: _CastingUnsafe,
+    dtype: _DTypeLikeComplex_co | None = ...,
+    out: None = ...,
+    order: _OrderKACF = ...,
+    optimize: _OptimizeKind = ...,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeComplex_co,
+    out: _ArrayT,
+    dtype: _DTypeLikeComplex_co | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = ...,
+) -> _ArrayT: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: Any,
+    out: _ArrayT,
+    casting: _CastingUnsafe,
+    dtype: _DTypeLikeComplex_co | None = ...,
+    order: _OrderKACF = ...,
+    optimize: _OptimizeKind = ...,
+) -> _ArrayT: ...
+
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeObject_co,
+    out: None = ...,
+    dtype: _DTypeLikeObject | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = ...,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: Any,
+    casting: _CastingUnsafe,
+    dtype: _DTypeLikeObject | None = ...,
+    out: None = ...,
+    order: _OrderKACF = ...,
+    optimize: _OptimizeKind = ...,
+) -> Any: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeObject_co,
+    out: _ArrayT,
+    dtype: _DTypeLikeObject | None = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingSafe = ...,
+    optimize: _OptimizeKind = ...,
+) -> _ArrayT: ...
+@overload
+def einsum(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: Any,
+    out: _ArrayT,
+    casting: _CastingUnsafe,
+    dtype: _DTypeLikeObject | None = ...,
+    order: _OrderKACF = ...,
+    optimize: _OptimizeKind = ...,
+) -> _ArrayT: ...
+
+# NOTE: `einsum_call` is a hidden kwarg unavailable for public use.
+# It is therefore excluded from the signatures below.
+# NOTE: In practice the list consists of a `str` (first element)
+# and a variable number of integer tuples.
+def einsum_path(
+    subscripts: str | _ArrayLikeInt_co,
+    /,
+    *operands: _ArrayLikeComplex_co | _DTypeLikeObject,
+    optimize: _OptimizeKind = "greedy",
+    einsum_call: Literal[False] = False,
+) -> tuple[list[Any], str]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.py b/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.py
new file mode 100644
index 0000000..e20d774
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.py
@@ -0,0 +1,4269 @@
+"""Module containing non-deprecated functions borrowed from Numeric.
+
+"""
+import functools
+import types
+import warnings
+
+import numpy as np
+from numpy._utils import set_module
+
+from . import _methods, overrides
+from . import multiarray as mu
+from . import numerictypes as nt
+from . import umath as um
+from ._multiarray_umath import _array_converter
+from .multiarray import asanyarray, asarray, concatenate
+
+_dt_ = nt.sctype2char
+
+# functions that are methods
+__all__ = [
+    'all', 'amax', 'amin', 'any', 'argmax',
+    'argmin', 'argpartition', 'argsort', 'around', 'choose', 'clip',
+    'compress', 'cumprod', 'cumsum', 'cumulative_prod', 'cumulative_sum',
+    'diagonal', 'mean', 'max', 'min', 'matrix_transpose',
+    'ndim', 'nonzero', 'partition', 'prod', 'ptp', 'put',
+    'ravel', 'repeat', 'reshape', 'resize', 'round',
+    'searchsorted', 'shape', 'size', 'sort', 'squeeze',
+    'std', 'sum', 'swapaxes', 'take', 'trace', 'transpose', 'var',
+]
+
+_gentype = types.GeneratorType
+# save away Python sum
+_sum_ = sum
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+# functions that are now methods
+def _wrapit(obj, method, *args, **kwds):
+    conv = _array_converter(obj)
+    # As this already tried the method, subok is maybe quite reasonable here
+    # but this follows what was done before. TODO: revisit this.
+    arr, = conv.as_arrays(subok=False)
+    result = getattr(arr, method)(*args, **kwds)
+
+    return conv.wrap(result, to_scalar=False)
+
+
+def _wrapfunc(obj, method, *args, **kwds):
+    bound = getattr(obj, method, None)
+    if bound is None:
+        return _wrapit(obj, method, *args, **kwds)
+
+    try:
+        return bound(*args, **kwds)
+    except TypeError:
+        # A TypeError occurs if the object does have such a method in its
+        # class, but its signature is not identical to that of NumPy's. This
+        # situation has occurred in the case of a downstream library like
+        # 'pandas'.
+        #
+        # Call _wrapit from within the except clause to ensure a potential
+        # exception has a traceback chain.
+        return _wrapit(obj, method, *args, **kwds)
+
+
+def _wrapreduction(obj, ufunc, method, axis, dtype, out, **kwargs):
+    passkwargs = {k: v for k, v in kwargs.items()
+                  if v is not np._NoValue}
+
+    if type(obj) is not mu.ndarray:
+        try:
+            reduction = getattr(obj, method)
+        except AttributeError:
+            pass
+        else:
+            # This branch is needed for reductions like any which don't
+            # support a dtype.
+            if dtype is not None:
+                return reduction(axis=axis, dtype=dtype, out=out, **passkwargs)
+            else:
+                return reduction(axis=axis, out=out, **passkwargs)
+
+    return ufunc.reduce(obj, axis, dtype, out, **passkwargs)
+
+
+def _wrapreduction_any_all(obj, ufunc, method, axis, out, **kwargs):
+    # Same as above function, but dtype is always bool (but never passed on)
+    passkwargs = {k: v for k, v in kwargs.items()
+                  if v is not np._NoValue}
+
+    if type(obj) is not mu.ndarray:
+        try:
+            reduction = getattr(obj, method)
+        except AttributeError:
+            pass
+        else:
+            return reduction(axis=axis, out=out, **passkwargs)
+
+    return ufunc.reduce(obj, axis, bool, out, **passkwargs)
+
+
+def _take_dispatcher(a, indices, axis=None, out=None, mode=None):
+    return (a, out)
+
+
+@array_function_dispatch(_take_dispatcher)
+def take(a, indices, axis=None, out=None, mode='raise'):
+    """
+    Take elements from an array along an axis.
+
+    When axis is not None, this function does the same thing as "fancy"
+    indexing (indexing arrays using arrays); however, it can be easier to use
+    if you need elements along a given axis. A call such as
+    ``np.take(arr, indices, axis=3)`` is equivalent to
+    ``arr[:,:,:,indices,...]``.
+
+    Explained without fancy indexing, this is equivalent to the following use
+    of `ndindex`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of
+    indices::
+
+        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
+        Nj = indices.shape
+        for ii in ndindex(Ni):
+            for jj in ndindex(Nj):
+                for kk in ndindex(Nk):
+                    out[ii + jj + kk] = a[ii + (indices[jj],) + kk]
+
+    Parameters
+    ----------
+    a : array_like (Ni..., M, Nk...)
+        The source array.
+    indices : array_like (Nj...)
+        The indices of the values to extract.
+        Also allow scalars for indices.
+    axis : int, optional
+        The axis over which to select values. By default, the flattened
+        input array is used.
+    out : ndarray, optional (Ni..., Nj..., Nk...)
+        If provided, the result will be placed in this array. It should
+        be of the appropriate shape and dtype. Note that `out` is always
+        buffered if `mode='raise'`; use other modes for better performance.
+    mode : {'raise', 'wrap', 'clip'}, optional
+        Specifies how out-of-bounds indices will behave.
+
+        * 'raise' -- raise an error (default)
+        * 'wrap' -- wrap around
+        * 'clip' -- clip to the range
+
+        'clip' mode means that all indices that are too large are replaced
+        by the index that addresses the last element along that axis. Note
+        that this disables indexing with negative numbers.
+
+    Returns
+    -------
+    out : ndarray (Ni..., Nj..., Nk...)
+        The returned array has the same type as `a`.
+
+    See Also
+    --------
+    compress : Take elements using a boolean mask
+    ndarray.take : equivalent method
+    take_along_axis : Take elements by matching the array and the index arrays
+
+    Notes
+    -----
+    By eliminating the inner loop in the description above, and using `s_` to
+    build simple slice objects, `take` can be expressed  in terms of applying
+    fancy indexing to each 1-d slice::
+
+        Ni, Nk = a.shape[:axis], a.shape[axis+1:]
+        for ii in ndindex(Ni):
+            for kk in ndindex(Nj):
+                out[ii + s_[...,] + kk] = a[ii + s_[:,] + kk][indices]
+
+    For this reason, it is equivalent to (but faster than) the following use
+    of `apply_along_axis`::
+
+        out = np.apply_along_axis(lambda a_1d: a_1d[indices], axis, a)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = [4, 3, 5, 7, 6, 8]
+    >>> indices = [0, 1, 4]
+    >>> np.take(a, indices)
+    array([4, 3, 6])
+
+    In this example if `a` is an ndarray, "fancy" indexing can be used.
+
+    >>> a = np.array(a)
+    >>> a[indices]
+    array([4, 3, 6])
+
+    If `indices` is not one dimensional, the output also has these dimensions.
+
+    >>> np.take(a, [[0, 1], [2, 3]])
+    array([[4, 3],
+           [5, 7]])
+    """
+    return _wrapfunc(a, 'take', indices, axis=axis, out=out, mode=mode)
+
+
+def _reshape_dispatcher(a, /, shape=None, order=None, *, newshape=None,
+                        copy=None):
+    return (a,)
+
+
+@array_function_dispatch(_reshape_dispatcher)
+def reshape(a, /, shape=None, order='C', *, newshape=None, copy=None):
+    """
+    Gives a new shape to an array without changing its data.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to be reshaped.
+    shape : int or tuple of ints
+        The new shape should be compatible with the original shape. If
+        an integer, then the result will be a 1-D array of that length.
+        One shape dimension can be -1. In this case, the value is
+        inferred from the length of the array and remaining dimensions.
+    order : {'C', 'F', 'A'}, optional
+        Read the elements of ``a`` using this index order, and place the
+        elements into the reshaped array using this index order. 'C'
+        means to read / write the elements using C-like index order,
+        with the last axis index changing fastest, back to the first
+        axis index changing slowest. 'F' means to read / write the
+        elements using Fortran-like index order, with the first index
+        changing fastest, and the last index changing slowest. Note that
+        the 'C' and 'F' options take no account of the memory layout of
+        the underlying array, and only refer to the order of indexing.
+        'A' means to read / write the elements in Fortran-like index
+        order if ``a`` is Fortran *contiguous* in memory, C-like order
+        otherwise.
+    newshape : int or tuple of ints
+        .. deprecated:: 2.1
+            Replaced by ``shape`` argument. Retained for backward
+            compatibility.
+    copy : bool, optional
+        If ``True``, then the array data is copied. If ``None``, a copy will
+        only be made if it's required by ``order``. For ``False`` it raises
+        a ``ValueError`` if a copy cannot be avoided. Default: ``None``.
+
+    Returns
+    -------
+    reshaped_array : ndarray
+        This will be a new view object if possible; otherwise, it will
+        be a copy.  Note there is no guarantee of the *memory layout* (C- or
+        Fortran- contiguous) of the returned array.
+
+    See Also
+    --------
+    ndarray.reshape : Equivalent method.
+
+    Notes
+    -----
+    It is not always possible to change the shape of an array without copying
+    the data.
+
+    The ``order`` keyword gives the index ordering both for *fetching*
+    the values from ``a``, and then *placing* the values into the output
+    array. For example, let's say you have an array:
+
+    >>> a = np.arange(6).reshape((3, 2))
+    >>> a
+    array([[0, 1],
+           [2, 3],
+           [4, 5]])
+
+    You can think of reshaping as first raveling the array (using the given
+    index order), then inserting the elements from the raveled array into the
+    new array using the same kind of index ordering as was used for the
+    raveling.
+
+    >>> np.reshape(a, (2, 3)) # C-like index ordering
+    array([[0, 1, 2],
+           [3, 4, 5]])
+    >>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape
+    array([[0, 1, 2],
+           [3, 4, 5]])
+    >>> np.reshape(a, (2, 3), order='F') # Fortran-like index ordering
+    array([[0, 4, 3],
+           [2, 1, 5]])
+    >>> np.reshape(np.ravel(a, order='F'), (2, 3), order='F')
+    array([[0, 4, 3],
+           [2, 1, 5]])
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1,2,3], [4,5,6]])
+    >>> np.reshape(a, 6)
+    array([1, 2, 3, 4, 5, 6])
+    >>> np.reshape(a, 6, order='F')
+    array([1, 4, 2, 5, 3, 6])
+
+    >>> np.reshape(a, (3,-1))       # the unspecified value is inferred to be 2
+    array([[1, 2],
+           [3, 4],
+           [5, 6]])
+    """
+    if newshape is None and shape is None:
+        raise TypeError(
+            "reshape() missing 1 required positional argument: 'shape'")
+    if newshape is not None:
+        if shape is not None:
+            raise TypeError(
+                "You cannot specify 'newshape' and 'shape' arguments "
+                "at the same time.")
+        # Deprecated in NumPy 2.1, 2024-04-18
+        warnings.warn(
+            "`newshape` keyword argument is deprecated, "
+            "use `shape=...` or pass shape positionally instead. "
+            "(deprecated in NumPy 2.1)",
+            DeprecationWarning,
+            stacklevel=2,
+        )
+        shape = newshape
+    if copy is not None:
+        return _wrapfunc(a, 'reshape', shape, order=order, copy=copy)
+    return _wrapfunc(a, 'reshape', shape, order=order)
+
+
+def _choose_dispatcher(a, choices, out=None, mode=None):
+    yield a
+    yield from choices
+    yield out
+
+
+@array_function_dispatch(_choose_dispatcher)
+def choose(a, choices, out=None, mode='raise'):
+    """
+    Construct an array from an index array and a list of arrays to choose from.
+
+    First of all, if confused or uncertain, definitely look at the Examples -
+    in its full generality, this function is less simple than it might
+    seem from the following code description::
+
+        np.choose(a,c) == np.array([c[a[I]][I] for I in np.ndindex(a.shape)])
+
+    But this omits some subtleties.  Here is a fully general summary:
+
+    Given an "index" array (`a`) of integers and a sequence of ``n`` arrays
+    (`choices`), `a` and each choice array are first broadcast, as necessary,
+    to arrays of a common shape; calling these *Ba* and *Bchoices[i], i =
+    0,...,n-1* we have that, necessarily, ``Ba.shape == Bchoices[i].shape``
+    for each ``i``.  Then, a new array with shape ``Ba.shape`` is created as
+    follows:
+
+    * if ``mode='raise'`` (the default), then, first of all, each element of
+      ``a`` (and thus ``Ba``) must be in the range ``[0, n-1]``; now, suppose
+      that ``i`` (in that range) is the value at the ``(j0, j1, ..., jm)``
+      position in ``Ba`` - then the value at the same position in the new array
+      is the value in ``Bchoices[i]`` at that same position;
+
+    * if ``mode='wrap'``, values in `a` (and thus `Ba`) may be any (signed)
+      integer; modular arithmetic is used to map integers outside the range
+      `[0, n-1]` back into that range; and then the new array is constructed
+      as above;
+
+    * if ``mode='clip'``, values in `a` (and thus ``Ba``) may be any (signed)
+      integer; negative integers are mapped to 0; values greater than ``n-1``
+      are mapped to ``n-1``; and then the new array is constructed as above.
+
+    Parameters
+    ----------
+    a : int array
+        This array must contain integers in ``[0, n-1]``, where ``n`` is the
+        number of choices, unless ``mode=wrap`` or ``mode=clip``, in which
+        cases any integers are permissible.
+    choices : sequence of arrays
+        Choice arrays. `a` and all of the choices must be broadcastable to the
+        same shape.  If `choices` is itself an array (not recommended), then
+        its outermost dimension (i.e., the one corresponding to
+        ``choices.shape[0]``) is taken as defining the "sequence".
+    out : array, optional
+        If provided, the result will be inserted into this array. It should
+        be of the appropriate shape and dtype. Note that `out` is always
+        buffered if ``mode='raise'``; use other modes for better performance.
+    mode : {'raise' (default), 'wrap', 'clip'}, optional
+        Specifies how indices outside ``[0, n-1]`` will be treated:
+
+        * 'raise' : an exception is raised
+        * 'wrap' : value becomes value mod ``n``
+        * 'clip' : values < 0 are mapped to 0, values > n-1 are mapped to n-1
+
+    Returns
+    -------
+    merged_array : array
+        The merged result.
+
+    Raises
+    ------
+    ValueError: shape mismatch
+        If `a` and each choice array are not all broadcastable to the same
+        shape.
+
+    See Also
+    --------
+    ndarray.choose : equivalent method
+    numpy.take_along_axis : Preferable if `choices` is an array
+
+    Notes
+    -----
+    To reduce the chance of misinterpretation, even though the following
+    "abuse" is nominally supported, `choices` should neither be, nor be
+    thought of as, a single array, i.e., the outermost sequence-like container
+    should be either a list or a tuple.
+
+    Examples
+    --------
+
+    >>> import numpy as np
+    >>> choices = [[0, 1, 2, 3], [10, 11, 12, 13],
+    ...   [20, 21, 22, 23], [30, 31, 32, 33]]
+    >>> np.choose([2, 3, 1, 0], choices
+    ... # the first element of the result will be the first element of the
+    ... # third (2+1) "array" in choices, namely, 20; the second element
+    ... # will be the second element of the fourth (3+1) choice array, i.e.,
+    ... # 31, etc.
+    ... )
+    array([20, 31, 12,  3])
+    >>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1)
+    array([20, 31, 12,  3])
+    >>> # because there are 4 choice arrays
+    >>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4)
+    array([20,  1, 12,  3])
+    >>> # i.e., 0
+
+    A couple examples illustrating how choose broadcasts:
+
+    >>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]]
+    >>> choices = [-10, 10]
+    >>> np.choose(a, choices)
+    array([[ 10, -10,  10],
+           [-10,  10, -10],
+           [ 10, -10,  10]])
+
+    >>> # With thanks to Anne Archibald
+    >>> a = np.array([0, 1]).reshape((2,1,1))
+    >>> c1 = np.array([1, 2, 3]).reshape((1,3,1))
+    >>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5))
+    >>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2
+    array([[[ 1,  1,  1,  1,  1],
+            [ 2,  2,  2,  2,  2],
+            [ 3,  3,  3,  3,  3]],
+           [[-1, -2, -3, -4, -5],
+            [-1, -2, -3, -4, -5],
+            [-1, -2, -3, -4, -5]]])
+
+    """
+    return _wrapfunc(a, 'choose', choices, out=out, mode=mode)
+
+
+def _repeat_dispatcher(a, repeats, axis=None):
+    return (a,)
+
+
+@array_function_dispatch(_repeat_dispatcher)
+def repeat(a, repeats, axis=None):
+    """
+    Repeat each element of an array after themselves
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    repeats : int or array of ints
+        The number of repetitions for each element.  `repeats` is broadcasted
+        to fit the shape of the given axis.
+    axis : int, optional
+        The axis along which to repeat values.  By default, use the
+        flattened input array, and return a flat output array.
+
+    Returns
+    -------
+    repeated_array : ndarray
+        Output array which has the same shape as `a`, except along
+        the given axis.
+
+    See Also
+    --------
+    tile : Tile an array.
+    unique : Find the unique elements of an array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.repeat(3, 4)
+    array([3, 3, 3, 3])
+    >>> x = np.array([[1,2],[3,4]])
+    >>> np.repeat(x, 2)
+    array([1, 1, 2, 2, 3, 3, 4, 4])
+    >>> np.repeat(x, 3, axis=1)
+    array([[1, 1, 1, 2, 2, 2],
+           [3, 3, 3, 4, 4, 4]])
+    >>> np.repeat(x, [1, 2], axis=0)
+    array([[1, 2],
+           [3, 4],
+           [3, 4]])
+
+    """
+    return _wrapfunc(a, 'repeat', repeats, axis=axis)
+
+
+def _put_dispatcher(a, ind, v, mode=None):
+    return (a, ind, v)
+
+
+@array_function_dispatch(_put_dispatcher)
+def put(a, ind, v, mode='raise'):
+    """
+    Replaces specified elements of an array with given values.
+
+    The indexing works on the flattened target array. `put` is roughly
+    equivalent to:
+
+    ::
+
+        a.flat[ind] = v
+
+    Parameters
+    ----------
+    a : ndarray
+        Target array.
+    ind : array_like
+        Target indices, interpreted as integers.
+    v : array_like
+        Values to place in `a` at target indices. If `v` is shorter than
+        `ind` it will be repeated as necessary.
+    mode : {'raise', 'wrap', 'clip'}, optional
+        Specifies how out-of-bounds indices will behave.
+
+        * 'raise' -- raise an error (default)
+        * 'wrap' -- wrap around
+        * 'clip' -- clip to the range
+
+        'clip' mode means that all indices that are too large are replaced
+        by the index that addresses the last element along that axis. Note
+        that this disables indexing with negative numbers. In 'raise' mode,
+        if an exception occurs the target array may still be modified.
+
+    See Also
+    --------
+    putmask, place
+    put_along_axis : Put elements by matching the array and the index arrays
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.arange(5)
+    >>> np.put(a, [0, 2], [-44, -55])
+    >>> a
+    array([-44,   1, -55,   3,   4])
+
+    >>> a = np.arange(5)
+    >>> np.put(a, 22, -5, mode='clip')
+    >>> a
+    array([ 0,  1,  2,  3, -5])
+
+    """
+    try:
+        put = a.put
+    except AttributeError as e:
+        raise TypeError(f"argument 1 must be numpy.ndarray, not {type(a)}") from e
+
+    return put(ind, v, mode=mode)
+
+
+def _swapaxes_dispatcher(a, axis1, axis2):
+    return (a,)
+
+
+@array_function_dispatch(_swapaxes_dispatcher)
+def swapaxes(a, axis1, axis2):
+    """
+    Interchange two axes of an array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis1 : int
+        First axis.
+    axis2 : int
+        Second axis.
+
+    Returns
+    -------
+    a_swapped : ndarray
+        For NumPy >= 1.10.0, if `a` is an ndarray, then a view of `a` is
+        returned; otherwise a new array is created. For earlier NumPy
+        versions a view of `a` is returned only if the order of the
+        axes is changed, otherwise the input array is returned.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([[1,2,3]])
+    >>> np.swapaxes(x,0,1)
+    array([[1],
+           [2],
+           [3]])
+
+    >>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])
+    >>> x
+    array([[[0, 1],
+            [2, 3]],
+           [[4, 5],
+            [6, 7]]])
+
+    >>> np.swapaxes(x,0,2)
+    array([[[0, 4],
+            [2, 6]],
+           [[1, 5],
+            [3, 7]]])
+
+    """
+    return _wrapfunc(a, 'swapaxes', axis1, axis2)
+
+
+def _transpose_dispatcher(a, axes=None):
+    return (a,)
+
+
+@array_function_dispatch(_transpose_dispatcher)
+def transpose(a, axes=None):
+    """
+    Returns an array with axes transposed.
+
+    For a 1-D array, this returns an unchanged view of the original array, as a
+    transposed vector is simply the same vector.
+    To convert a 1-D array into a 2-D column vector, an additional dimension
+    must be added, e.g., ``np.atleast_2d(a).T`` achieves this, as does
+    ``a[:, np.newaxis]``.
+    For a 2-D array, this is the standard matrix transpose.
+    For an n-D array, if axes are given, their order indicates how the
+    axes are permuted (see Examples). If axes are not provided, then
+    ``transpose(a).shape == a.shape[::-1]``.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axes : tuple or list of ints, optional
+        If specified, it must be a tuple or list which contains a permutation
+        of [0, 1, ..., N-1] where N is the number of axes of `a`. Negative
+        indices can also be used to specify axes. The i-th axis of the returned
+        array will correspond to the axis numbered ``axes[i]`` of the input.
+        If not specified, defaults to ``range(a.ndim)[::-1]``, which reverses
+        the order of the axes.
+
+    Returns
+    -------
+    p : ndarray
+        `a` with its axes permuted. A view is returned whenever possible.
+
+    See Also
+    --------
+    ndarray.transpose : Equivalent method.
+    moveaxis : Move axes of an array to new positions.
+    argsort : Return the indices that would sort an array.
+
+    Notes
+    -----
+    Use ``transpose(a, argsort(axes))`` to invert the transposition of tensors
+    when using the `axes` keyword argument.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> a
+    array([[1, 2],
+           [3, 4]])
+    >>> np.transpose(a)
+    array([[1, 3],
+           [2, 4]])
+
+    >>> a = np.array([1, 2, 3, 4])
+    >>> a
+    array([1, 2, 3, 4])
+    >>> np.transpose(a)
+    array([1, 2, 3, 4])
+
+    >>> a = np.ones((1, 2, 3))
+    >>> np.transpose(a, (1, 0, 2)).shape
+    (2, 1, 3)
+
+    >>> a = np.ones((2, 3, 4, 5))
+    >>> np.transpose(a).shape
+    (5, 4, 3, 2)
+
+    >>> a = np.arange(3*4*5).reshape((3, 4, 5))
+    >>> np.transpose(a, (-1, 0, -2)).shape
+    (5, 3, 4)
+
+    """
+    return _wrapfunc(a, 'transpose', axes)
+
+
+def _matrix_transpose_dispatcher(x):
+    return (x,)
+
+@array_function_dispatch(_matrix_transpose_dispatcher)
+def matrix_transpose(x, /):
+    """
+    Transposes a matrix (or a stack of matrices) ``x``.
+
+    This function is Array API compatible.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array having shape (..., M, N) and whose two innermost
+        dimensions form ``MxN`` matrices.
+
+    Returns
+    -------
+    out : ndarray
+        An array containing the transpose for each matrix and having shape
+        (..., N, M).
+
+    See Also
+    --------
+    transpose : Generic transpose method.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.matrix_transpose([[1, 2], [3, 4]])
+    array([[1, 3],
+           [2, 4]])
+
+    >>> np.matrix_transpose([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
+    array([[[1, 3],
+            [2, 4]],
+           [[5, 7],
+            [6, 8]]])
+
+    """
+    x = asanyarray(x)
+    if x.ndim < 2:
+        raise ValueError(
+            f"Input array must be at least 2-dimensional, but it is {x.ndim}"
+        )
+    return swapaxes(x, -1, -2)
+
+
+def _partition_dispatcher(a, kth, axis=None, kind=None, order=None):
+    return (a,)
+
+
+@array_function_dispatch(_partition_dispatcher)
+def partition(a, kth, axis=-1, kind='introselect', order=None):
+    """
+    Return a partitioned copy of an array.
+
+    Creates a copy of the array and partially sorts it in such a way that
+    the value of the element in k-th position is in the position it would be
+    in a sorted array. In the output array, all elements smaller than the k-th
+    element are located to the left of this element and all equal or greater
+    are located to its right. The ordering of the elements in the two
+    partitions on the either side of the k-th element in the output array is
+    undefined.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to be sorted.
+    kth : int or sequence of ints
+        Element index to partition by. The k-th value of the element
+        will be in its final sorted position and all smaller elements
+        will be moved before it and all equal or greater elements behind
+        it. The order of all elements in the partitions is undefined. If
+        provided with a sequence of k-th it will partition all elements
+        indexed by k-th  of them into their sorted position at once.
+
+        .. deprecated:: 1.22.0
+            Passing booleans as index is deprecated.
+    axis : int or None, optional
+        Axis along which to sort. If None, the array is flattened before
+        sorting. The default is -1, which sorts along the last axis.
+    kind : {'introselect'}, optional
+        Selection algorithm. Default is 'introselect'.
+    order : str or list of str, optional
+        When `a` is an array with fields defined, this argument
+        specifies which fields to compare first, second, etc.  A single
+        field can be specified as a string.  Not all fields need be
+        specified, but unspecified fields will still be used, in the
+        order in which they come up in the dtype, to break ties.
+
+    Returns
+    -------
+    partitioned_array : ndarray
+        Array of the same type and shape as `a`.
+
+    See Also
+    --------
+    ndarray.partition : Method to sort an array in-place.
+    argpartition : Indirect partition.
+    sort : Full sorting
+
+    Notes
+    -----
+    The various selection algorithms are characterized by their average
+    speed, worst case performance, work space size, and whether they are
+    stable. A stable sort keeps items with the same key in the same
+    relative order. The available algorithms have the following
+    properties:
+
+    ================= ======= ============= ============ =======
+       kind            speed   worst case    work space  stable
+    ================= ======= ============= ============ =======
+    'introselect'        1        O(n)           0         no
+    ================= ======= ============= ============ =======
+
+    All the partition algorithms make temporary copies of the data when
+    partitioning along any but the last axis.  Consequently,
+    partitioning along the last axis is faster and uses less space than
+    partitioning along any other axis.
+
+    The sort order for complex numbers is lexicographic. If both the
+    real and imaginary parts are non-nan then the order is determined by
+    the real parts except when they are equal, in which case the order
+    is determined by the imaginary parts.
+
+    The sort order of ``np.nan`` is bigger than ``np.inf``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([7, 1, 7, 7, 1, 5, 7, 2, 3, 2, 6, 2, 3, 0])
+    >>> p = np.partition(a, 4)
+    >>> p
+    array([0, 1, 2, 1, 2, 5, 2, 3, 3, 6, 7, 7, 7, 7]) # may vary
+
+    ``p[4]`` is 2;  all elements in ``p[:4]`` are less than or equal
+    to ``p[4]``, and all elements in ``p[5:]`` are greater than or
+    equal to ``p[4]``.  The partition is::
+
+        [0, 1, 2, 1], [2], [5, 2, 3, 3, 6, 7, 7, 7, 7]
+
+    The next example shows the use of multiple values passed to `kth`.
+
+    >>> p2 = np.partition(a, (4, 8))
+    >>> p2
+    array([0, 1, 2, 1, 2, 3, 3, 2, 5, 6, 7, 7, 7, 7])
+
+    ``p2[4]`` is 2  and ``p2[8]`` is 5.  All elements in ``p2[:4]``
+    are less than or equal to ``p2[4]``, all elements in ``p2[5:8]``
+    are greater than or equal to ``p2[4]`` and less than or equal to
+    ``p2[8]``, and all elements in ``p2[9:]`` are greater than or
+    equal to ``p2[8]``.  The partition is::
+
+        [0, 1, 2, 1], [2], [3, 3, 2], [5], [6, 7, 7, 7, 7]
+    """
+    if axis is None:
+        # flatten returns (1, N) for np.matrix, so always use the last axis
+        a = asanyarray(a).flatten()
+        axis = -1
+    else:
+        a = asanyarray(a).copy(order="K")
+    a.partition(kth, axis=axis, kind=kind, order=order)
+    return a
+
+
+def _argpartition_dispatcher(a, kth, axis=None, kind=None, order=None):
+    return (a,)
+
+
+@array_function_dispatch(_argpartition_dispatcher)
+def argpartition(a, kth, axis=-1, kind='introselect', order=None):
+    """
+    Perform an indirect partition along the given axis using the
+    algorithm specified by the `kind` keyword. It returns an array of
+    indices of the same shape as `a` that index data along the given
+    axis in partitioned order.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to sort.
+    kth : int or sequence of ints
+        Element index to partition by. The k-th element will be in its
+        final sorted position and all smaller elements will be moved
+        before it and all larger elements behind it. The order of all
+        elements in the partitions is undefined. If provided with a
+        sequence of k-th it will partition all of them into their sorted
+        position at once.
+
+        .. deprecated:: 1.22.0
+            Passing booleans as index is deprecated.
+    axis : int or None, optional
+        Axis along which to sort. The default is -1 (the last axis). If
+        None, the flattened array is used.
+    kind : {'introselect'}, optional
+        Selection algorithm. Default is 'introselect'
+    order : str or list of str, optional
+        When `a` is an array with fields defined, this argument
+        specifies which fields to compare first, second, etc. A single
+        field can be specified as a string, and not all fields need be
+        specified, but unspecified fields will still be used, in the
+        order in which they come up in the dtype, to break ties.
+
+    Returns
+    -------
+    index_array : ndarray, int
+        Array of indices that partition `a` along the specified axis.
+        If `a` is one-dimensional, ``a[index_array]`` yields a partitioned `a`.
+        More generally, ``np.take_along_axis(a, index_array, axis=axis)``
+        always yields the partitioned `a`, irrespective of dimensionality.
+
+    See Also
+    --------
+    partition : Describes partition algorithms used.
+    ndarray.partition : Inplace partition.
+    argsort : Full indirect sort.
+    take_along_axis : Apply ``index_array`` from argpartition
+                      to an array as if by calling partition.
+
+    Notes
+    -----
+    The returned indices are not guaranteed to be sorted according to
+    the values. Furthermore, the default selection algorithm ``introselect``
+    is unstable, and hence the returned indices are not guaranteed
+    to be the earliest/latest occurrence of the element.
+
+    `argpartition` works for real/complex inputs with nan values,
+    see `partition` for notes on the enhanced sort order and
+    different selection algorithms.
+
+    Examples
+    --------
+    One dimensional array:
+
+    >>> import numpy as np
+    >>> x = np.array([3, 4, 2, 1])
+    >>> x[np.argpartition(x, 3)]
+    array([2, 1, 3, 4]) # may vary
+    >>> x[np.argpartition(x, (1, 3))]
+    array([1, 2, 3, 4]) # may vary
+
+    >>> x = [3, 4, 2, 1]
+    >>> np.array(x)[np.argpartition(x, 3)]
+    array([2, 1, 3, 4]) # may vary
+
+    Multi-dimensional array:
+
+    >>> x = np.array([[3, 4, 2], [1, 3, 1]])
+    >>> index_array = np.argpartition(x, kth=1, axis=-1)
+    >>> # below is the same as np.partition(x, kth=1)
+    >>> np.take_along_axis(x, index_array, axis=-1)
+    array([[2, 3, 4],
+           [1, 1, 3]])
+
+    """
+    return _wrapfunc(a, 'argpartition', kth, axis=axis, kind=kind, order=order)
+
+
+def _sort_dispatcher(a, axis=None, kind=None, order=None, *, stable=None):
+    return (a,)
+
+
+@array_function_dispatch(_sort_dispatcher)
+def sort(a, axis=-1, kind=None, order=None, *, stable=None):
+    """
+    Return a sorted copy of an array.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to be sorted.
+    axis : int or None, optional
+        Axis along which to sort. If None, the array is flattened before
+        sorting. The default is -1, which sorts along the last axis.
+    kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
+        Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
+        and 'mergesort' use timsort or radix sort under the covers and,
+        in general, the actual implementation will vary with data type.
+        The 'mergesort' option is retained for backwards compatibility.
+    order : str or list of str, optional
+        When `a` is an array with fields defined, this argument specifies
+        which fields to compare first, second, etc.  A single field can
+        be specified as a string, and not all fields need be specified,
+        but unspecified fields will still be used, in the order in which
+        they come up in the dtype, to break ties.
+    stable : bool, optional
+        Sort stability. If ``True``, the returned array will maintain
+        the relative order of ``a`` values which compare as equal.
+        If ``False`` or ``None``, this is not guaranteed. Internally,
+        this option selects ``kind='stable'``. Default: ``None``.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    sorted_array : ndarray
+        Array of the same type and shape as `a`.
+
+    See Also
+    --------
+    ndarray.sort : Method to sort an array in-place.
+    argsort : Indirect sort.
+    lexsort : Indirect stable sort on multiple keys.
+    searchsorted : Find elements in a sorted array.
+    partition : Partial sort.
+
+    Notes
+    -----
+    The various sorting algorithms are characterized by their average speed,
+    worst case performance, work space size, and whether they are stable. A
+    stable sort keeps items with the same key in the same relative
+    order. The four algorithms implemented in NumPy have the following
+    properties:
+
+    =========== ======= ============= ============ ========
+       kind      speed   worst case    work space   stable
+    =========== ======= ============= ============ ========
+    'quicksort'    1     O(n^2)            0          no
+    'heapsort'     3     O(n*log(n))       0          no
+    'mergesort'    2     O(n*log(n))      ~n/2        yes
+    'timsort'      2     O(n*log(n))      ~n/2        yes
+    =========== ======= ============= ============ ========
+
+    .. note:: The datatype determines which of 'mergesort' or 'timsort'
+       is actually used, even if 'mergesort' is specified. User selection
+       at a finer scale is not currently available.
+
+    For performance, ``sort`` makes a temporary copy if needed to make the data
+    `contiguous <https://numpy.org/doc/stable/glossary.html#term-contiguous>`_
+    in memory along the sort axis. For even better performance and reduced
+    memory consumption, ensure that the array is already contiguous along the
+    sort axis.
+
+    The sort order for complex numbers is lexicographic. If both the real
+    and imaginary parts are non-nan then the order is determined by the
+    real parts except when they are equal, in which case the order is
+    determined by the imaginary parts.
+
+    Previous to numpy 1.4.0 sorting real and complex arrays containing nan
+    values led to undefined behaviour. In numpy versions >= 1.4.0 nan
+    values are sorted to the end. The extended sort order is:
+
+      * Real: [R, nan]
+      * Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj]
+
+    where R is a non-nan real value. Complex values with the same nan
+    placements are sorted according to the non-nan part if it exists.
+    Non-nan values are sorted as before.
+
+    quicksort has been changed to:
+    `introsort <https://en.wikipedia.org/wiki/Introsort>`_.
+    When sorting does not make enough progress it switches to
+    `heapsort <https://en.wikipedia.org/wiki/Heapsort>`_.
+    This implementation makes quicksort O(n*log(n)) in the worst case.
+
+    'stable' automatically chooses the best stable sorting algorithm
+    for the data type being sorted.
+    It, along with 'mergesort' is currently mapped to
+    `timsort <https://en.wikipedia.org/wiki/Timsort>`_
+    or `radix sort <https://en.wikipedia.org/wiki/Radix_sort>`_
+    depending on the data type.
+    API forward compatibility currently limits the
+    ability to select the implementation and it is hardwired for the different
+    data types.
+
+    Timsort is added for better performance on already or nearly
+    sorted data. On random data timsort is almost identical to
+    mergesort. It is now used for stable sort while quicksort is still the
+    default sort if none is chosen. For timsort details, refer to
+    `CPython listsort.txt
+    <https://github.com/python/cpython/blob/3.7/Objects/listsort.txt>`_
+    'mergesort' and 'stable' are mapped to radix sort for integer data types.
+    Radix sort is an O(n) sort instead of O(n log n).
+
+    NaT now sorts to the end of arrays for consistency with NaN.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1,4],[3,1]])
+    >>> np.sort(a)                # sort along the last axis
+    array([[1, 4],
+           [1, 3]])
+    >>> np.sort(a, axis=None)     # sort the flattened array
+    array([1, 1, 3, 4])
+    >>> np.sort(a, axis=0)        # sort along the first axis
+    array([[1, 1],
+           [3, 4]])
+
+    Use the `order` keyword to specify a field to use when sorting a
+    structured array:
+
+    >>> dtype = [('name', 'S10'), ('height', float), ('age', int)]
+    >>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38),
+    ...           ('Galahad', 1.7, 38)]
+    >>> a = np.array(values, dtype=dtype)       # create a structured array
+    >>> np.sort(a, order='height')                        # doctest: +SKIP
+    array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),
+           ('Lancelot', 1.8999999999999999, 38)],
+          dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])
+
+    Sort by age, then height if ages are equal:
+
+    >>> np.sort(a, order=['age', 'height'])               # doctest: +SKIP
+    array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38),
+           ('Arthur', 1.8, 41)],
+          dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])
+
+    """
+    if axis is None:
+        # flatten returns (1, N) for np.matrix, so always use the last axis
+        a = asanyarray(a).flatten()
+        axis = -1
+    else:
+        a = asanyarray(a).copy(order="K")
+    a.sort(axis=axis, kind=kind, order=order, stable=stable)
+    return a
+
+
+def _argsort_dispatcher(a, axis=None, kind=None, order=None, *, stable=None):
+    return (a,)
+
+
+@array_function_dispatch(_argsort_dispatcher)
+def argsort(a, axis=-1, kind=None, order=None, *, stable=None):
+    """
+    Returns the indices that would sort an array.
+
+    Perform an indirect sort along the given axis using the algorithm specified
+    by the `kind` keyword. It returns an array of indices of the same shape as
+    `a` that index data along the given axis in sorted order.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to sort.
+    axis : int or None, optional
+        Axis along which to sort.  The default is -1 (the last axis). If None,
+        the flattened array is used.
+    kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
+        Sorting algorithm. The default is 'quicksort'. Note that both 'stable'
+        and 'mergesort' use timsort under the covers and, in general, the
+        actual implementation will vary with data type. The 'mergesort' option
+        is retained for backwards compatibility.
+    order : str or list of str, optional
+        When `a` is an array with fields defined, this argument specifies
+        which fields to compare first, second, etc.  A single field can
+        be specified as a string, and not all fields need be specified,
+        but unspecified fields will still be used, in the order in which
+        they come up in the dtype, to break ties.
+    stable : bool, optional
+        Sort stability. If ``True``, the returned array will maintain
+        the relative order of ``a`` values which compare as equal.
+        If ``False`` or ``None``, this is not guaranteed. Internally,
+        this option selects ``kind='stable'``. Default: ``None``.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    index_array : ndarray, int
+        Array of indices that sort `a` along the specified `axis`.
+        If `a` is one-dimensional, ``a[index_array]`` yields a sorted `a`.
+        More generally, ``np.take_along_axis(a, index_array, axis=axis)``
+        always yields the sorted `a`, irrespective of dimensionality.
+
+    See Also
+    --------
+    sort : Describes sorting algorithms used.
+    lexsort : Indirect stable sort with multiple keys.
+    ndarray.sort : Inplace sort.
+    argpartition : Indirect partial sort.
+    take_along_axis : Apply ``index_array`` from argsort
+                      to an array as if by calling sort.
+
+    Notes
+    -----
+    See `sort` for notes on the different sorting algorithms.
+
+    As of NumPy 1.4.0 `argsort` works with real/complex arrays containing
+    nan values. The enhanced sort order is documented in `sort`.
+
+    Examples
+    --------
+    One dimensional array:
+
+    >>> import numpy as np
+    >>> x = np.array([3, 1, 2])
+    >>> np.argsort(x)
+    array([1, 2, 0])
+
+    Two-dimensional array:
+
+    >>> x = np.array([[0, 3], [2, 2]])
+    >>> x
+    array([[0, 3],
+           [2, 2]])
+
+    >>> ind = np.argsort(x, axis=0)  # sorts along first axis (down)
+    >>> ind
+    array([[0, 1],
+           [1, 0]])
+    >>> np.take_along_axis(x, ind, axis=0)  # same as np.sort(x, axis=0)
+    array([[0, 2],
+           [2, 3]])
+
+    >>> ind = np.argsort(x, axis=1)  # sorts along last axis (across)
+    >>> ind
+    array([[0, 1],
+           [0, 1]])
+    >>> np.take_along_axis(x, ind, axis=1)  # same as np.sort(x, axis=1)
+    array([[0, 3],
+           [2, 2]])
+
+    Indices of the sorted elements of a N-dimensional array:
+
+    >>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape)
+    >>> ind
+    (array([0, 1, 1, 0]), array([0, 0, 1, 1]))
+    >>> x[ind]  # same as np.sort(x, axis=None)
+    array([0, 2, 2, 3])
+
+    Sorting with keys:
+
+    >>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '<i4'), ('y', '<i4')])
+    >>> x
+    array([(1, 0), (0, 1)],
+          dtype=[('x', '<i4'), ('y', '<i4')])
+
+    >>> np.argsort(x, order=('x','y'))
+    array([1, 0])
+
+    >>> np.argsort(x, order=('y','x'))
+    array([0, 1])
+
+    """
+    return _wrapfunc(
+        a, 'argsort', axis=axis, kind=kind, order=order, stable=stable
+    )
+
+def _argmax_dispatcher(a, axis=None, out=None, *, keepdims=np._NoValue):
+    return (a, out)
+
+
+@array_function_dispatch(_argmax_dispatcher)
+def argmax(a, axis=None, out=None, *, keepdims=np._NoValue):
+    """
+    Returns the indices of the maximum values along an axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        By default, the index is into the flattened array, otherwise
+        along the specified axis.
+    out : array, optional
+        If provided, the result will be inserted into this array. It should
+        be of the appropriate shape and dtype.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the array.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    index_array : ndarray of ints
+        Array of indices into the array. It has the same shape as ``a.shape``
+        with the dimension along `axis` removed. If `keepdims` is set to True,
+        then the size of `axis` will be 1 with the resulting array having same
+        shape as ``a.shape``.
+
+    See Also
+    --------
+    ndarray.argmax, argmin
+    amax : The maximum value along a given axis.
+    unravel_index : Convert a flat index into an index tuple.
+    take_along_axis : Apply ``np.expand_dims(index_array, axis)``
+                      from argmax to an array as if by calling max.
+
+    Notes
+    -----
+    In case of multiple occurrences of the maximum values, the indices
+    corresponding to the first occurrence are returned.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.arange(6).reshape(2,3) + 10
+    >>> a
+    array([[10, 11, 12],
+           [13, 14, 15]])
+    >>> np.argmax(a)
+    5
+    >>> np.argmax(a, axis=0)
+    array([1, 1, 1])
+    >>> np.argmax(a, axis=1)
+    array([2, 2])
+
+    Indexes of the maximal elements of a N-dimensional array:
+
+    >>> ind = np.unravel_index(np.argmax(a, axis=None), a.shape)
+    >>> ind
+    (1, 2)
+    >>> a[ind]
+    15
+
+    >>> b = np.arange(6)
+    >>> b[1] = 5
+    >>> b
+    array([0, 5, 2, 3, 4, 5])
+    >>> np.argmax(b)  # Only the first occurrence is returned.
+    1
+
+    >>> x = np.array([[4,2,3], [1,0,3]])
+    >>> index_array = np.argmax(x, axis=-1)
+    >>> # Same as np.amax(x, axis=-1, keepdims=True)
+    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
+    array([[4],
+           [3]])
+    >>> # Same as np.amax(x, axis=-1)
+    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1),
+    ...     axis=-1).squeeze(axis=-1)
+    array([4, 3])
+
+    Setting `keepdims` to `True`,
+
+    >>> x = np.arange(24).reshape((2, 3, 4))
+    >>> res = np.argmax(x, axis=1, keepdims=True)
+    >>> res.shape
+    (2, 1, 4)
+    """
+    kwds = {'keepdims': keepdims} if keepdims is not np._NoValue else {}
+    return _wrapfunc(a, 'argmax', axis=axis, out=out, **kwds)
+
+
+def _argmin_dispatcher(a, axis=None, out=None, *, keepdims=np._NoValue):
+    return (a, out)
+
+
+@array_function_dispatch(_argmin_dispatcher)
+def argmin(a, axis=None, out=None, *, keepdims=np._NoValue):
+    """
+    Returns the indices of the minimum values along an axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        By default, the index is into the flattened array, otherwise
+        along the specified axis.
+    out : array, optional
+        If provided, the result will be inserted into this array. It should
+        be of the appropriate shape and dtype.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the array.
+
+        .. versionadded:: 1.22.0
+
+    Returns
+    -------
+    index_array : ndarray of ints
+        Array of indices into the array. It has the same shape as `a.shape`
+        with the dimension along `axis` removed. If `keepdims` is set to True,
+        then the size of `axis` will be 1 with the resulting array having same
+        shape as `a.shape`.
+
+    See Also
+    --------
+    ndarray.argmin, argmax
+    amin : The minimum value along a given axis.
+    unravel_index : Convert a flat index into an index tuple.
+    take_along_axis : Apply ``np.expand_dims(index_array, axis)``
+                      from argmin to an array as if by calling min.
+
+    Notes
+    -----
+    In case of multiple occurrences of the minimum values, the indices
+    corresponding to the first occurrence are returned.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.arange(6).reshape(2,3) + 10
+    >>> a
+    array([[10, 11, 12],
+           [13, 14, 15]])
+    >>> np.argmin(a)
+    0
+    >>> np.argmin(a, axis=0)
+    array([0, 0, 0])
+    >>> np.argmin(a, axis=1)
+    array([0, 0])
+
+    Indices of the minimum elements of a N-dimensional array:
+
+    >>> ind = np.unravel_index(np.argmin(a, axis=None), a.shape)
+    >>> ind
+    (0, 0)
+    >>> a[ind]
+    10
+
+    >>> b = np.arange(6) + 10
+    >>> b[4] = 10
+    >>> b
+    array([10, 11, 12, 13, 10, 15])
+    >>> np.argmin(b)  # Only the first occurrence is returned.
+    0
+
+    >>> x = np.array([[4,2,3], [1,0,3]])
+    >>> index_array = np.argmin(x, axis=-1)
+    >>> # Same as np.amin(x, axis=-1, keepdims=True)
+    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
+    array([[2],
+           [0]])
+    >>> # Same as np.amax(x, axis=-1)
+    >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1),
+    ...     axis=-1).squeeze(axis=-1)
+    array([2, 0])
+
+    Setting `keepdims` to `True`,
+
+    >>> x = np.arange(24).reshape((2, 3, 4))
+    >>> res = np.argmin(x, axis=1, keepdims=True)
+    >>> res.shape
+    (2, 1, 4)
+    """
+    kwds = {'keepdims': keepdims} if keepdims is not np._NoValue else {}
+    return _wrapfunc(a, 'argmin', axis=axis, out=out, **kwds)
+
+
+def _searchsorted_dispatcher(a, v, side=None, sorter=None):
+    return (a, v, sorter)
+
+
+@array_function_dispatch(_searchsorted_dispatcher)
+def searchsorted(a, v, side='left', sorter=None):
+    """
+    Find indices where elements should be inserted to maintain order.
+
+    Find the indices into a sorted array `a` such that, if the
+    corresponding elements in `v` were inserted before the indices, the
+    order of `a` would be preserved.
+
+    Assuming that `a` is sorted:
+
+    ======  ============================
+    `side`  returned index `i` satisfies
+    ======  ============================
+    left    ``a[i-1] < v <= a[i]``
+    right   ``a[i-1] <= v < a[i]``
+    ======  ============================
+
+    Parameters
+    ----------
+    a : 1-D array_like
+        Input array. If `sorter` is None, then it must be sorted in
+        ascending order, otherwise `sorter` must be an array of indices
+        that sort it.
+    v : array_like
+        Values to insert into `a`.
+    side : {'left', 'right'}, optional
+        If 'left', the index of the first suitable location found is given.
+        If 'right', return the last such index.  If there is no suitable
+        index, return either 0 or N (where N is the length of `a`).
+    sorter : 1-D array_like, optional
+        Optional array of integer indices that sort array a into ascending
+        order. They are typically the result of argsort.
+
+    Returns
+    -------
+    indices : int or array of ints
+        Array of insertion points with the same shape as `v`,
+        or an integer if `v` is a scalar.
+
+    See Also
+    --------
+    sort : Return a sorted copy of an array.
+    histogram : Produce histogram from 1-D data.
+
+    Notes
+    -----
+    Binary search is used to find the required insertion points.
+
+    As of NumPy 1.4.0 `searchsorted` works with real/complex arrays containing
+    `nan` values. The enhanced sort order is documented in `sort`.
+
+    This function uses the same algorithm as the builtin python
+    `bisect.bisect_left` (``side='left'``) and `bisect.bisect_right`
+    (``side='right'``) functions, which is also vectorized
+    in the `v` argument.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.searchsorted([11,12,13,14,15], 13)
+    2
+    >>> np.searchsorted([11,12,13,14,15], 13, side='right')
+    3
+    >>> np.searchsorted([11,12,13,14,15], [-10, 20, 12, 13])
+    array([0, 5, 1, 2])
+
+    When `sorter` is used, the returned indices refer to the sorted
+    array of `a` and not `a` itself:
+
+    >>> a = np.array([40, 10, 20, 30])
+    >>> sorter = np.argsort(a)
+    >>> sorter
+    array([1, 2, 3, 0])  # Indices that would sort the array 'a'
+    >>> result = np.searchsorted(a, 25, sorter=sorter)
+    >>> result
+    2
+    >>> a[sorter[result]]
+    30  # The element at index 2 of the sorted array is 30.
+    """
+    return _wrapfunc(a, 'searchsorted', v, side=side, sorter=sorter)
+
+
+def _resize_dispatcher(a, new_shape):
+    return (a,)
+
+
+@array_function_dispatch(_resize_dispatcher)
+def resize(a, new_shape):
+    """
+    Return a new array with the specified shape.
+
+    If the new array is larger than the original array, then the new
+    array is filled with repeated copies of `a`.  Note that this behavior
+    is different from a.resize(new_shape) which fills with zeros instead
+    of repeated copies of `a`.
+
+    Parameters
+    ----------
+    a : array_like
+        Array to be resized.
+
+    new_shape : int or tuple of int
+        Shape of resized array.
+
+    Returns
+    -------
+    reshaped_array : ndarray
+        The new array is formed from the data in the old array, repeated
+        if necessary to fill out the required number of elements.  The
+        data are repeated iterating over the array in C-order.
+
+    See Also
+    --------
+    numpy.reshape : Reshape an array without changing the total size.
+    numpy.pad : Enlarge and pad an array.
+    numpy.repeat : Repeat elements of an array.
+    ndarray.resize : resize an array in-place.
+
+    Notes
+    -----
+    When the total size of the array does not change `~numpy.reshape` should
+    be used.  In most other cases either indexing (to reduce the size)
+    or padding (to increase the size) may be a more appropriate solution.
+
+    Warning: This functionality does **not** consider axes separately,
+    i.e. it does not apply interpolation/extrapolation.
+    It fills the return array with the required number of elements, iterating
+    over `a` in C-order, disregarding axes (and cycling back from the start if
+    the new shape is larger).  This functionality is therefore not suitable to
+    resize images, or data where each axis represents a separate and distinct
+    entity.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[0,1],[2,3]])
+    >>> np.resize(a,(2,3))
+    array([[0, 1, 2],
+           [3, 0, 1]])
+    >>> np.resize(a,(1,4))
+    array([[0, 1, 2, 3]])
+    >>> np.resize(a,(2,4))
+    array([[0, 1, 2, 3],
+           [0, 1, 2, 3]])
+
+    """
+    if isinstance(new_shape, (int, nt.integer)):
+        new_shape = (new_shape,)
+
+    a = ravel(a)
+
+    new_size = 1
+    for dim_length in new_shape:
+        new_size *= dim_length
+        if dim_length < 0:
+            raise ValueError(
+                'all elements of `new_shape` must be non-negative'
+            )
+
+    if a.size == 0 or new_size == 0:
+        # First case must zero fill. The second would have repeats == 0.
+        return np.zeros_like(a, shape=new_shape)
+
+    # ceiling division without negating new_size
+    repeats = (new_size + a.size - 1) // a.size
+    a = concatenate((a,) * repeats)[:new_size]
+
+    return reshape(a, new_shape)
+
+
+def _squeeze_dispatcher(a, axis=None):
+    return (a,)
+
+
+@array_function_dispatch(_squeeze_dispatcher)
+def squeeze(a, axis=None):
+    """
+    Remove axes of length one from `a`.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : None or int or tuple of ints, optional
+        Selects a subset of the entries of length one in the
+        shape. If an axis is selected with shape entry greater than
+        one, an error is raised.
+
+    Returns
+    -------
+    squeezed : ndarray
+        The input array, but with all or a subset of the
+        dimensions of length 1 removed. This is always `a` itself
+        or a view into `a`. Note that if all axes are squeezed,
+        the result is a 0d array and not a scalar.
+
+    Raises
+    ------
+    ValueError
+        If `axis` is not None, and an axis being squeezed is not of length 1
+
+    See Also
+    --------
+    expand_dims : The inverse operation, adding entries of length one
+    reshape : Insert, remove, and combine dimensions, and resize existing ones
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([[[0], [1], [2]]])
+    >>> x.shape
+    (1, 3, 1)
+    >>> np.squeeze(x).shape
+    (3,)
+    >>> np.squeeze(x, axis=0).shape
+    (3, 1)
+    >>> np.squeeze(x, axis=1).shape
+    Traceback (most recent call last):
+    ...
+    ValueError: cannot select an axis to squeeze out which has size
+    not equal to one
+    >>> np.squeeze(x, axis=2).shape
+    (1, 3)
+    >>> x = np.array([[1234]])
+    >>> x.shape
+    (1, 1)
+    >>> np.squeeze(x)
+    array(1234)  # 0d array
+    >>> np.squeeze(x).shape
+    ()
+    >>> np.squeeze(x)[()]
+    1234
+
+    """
+    try:
+        squeeze = a.squeeze
+    except AttributeError:
+        return _wrapit(a, 'squeeze', axis=axis)
+    if axis is None:
+        return squeeze()
+    else:
+        return squeeze(axis=axis)
+
+
+def _diagonal_dispatcher(a, offset=None, axis1=None, axis2=None):
+    return (a,)
+
+
+@array_function_dispatch(_diagonal_dispatcher)
+def diagonal(a, offset=0, axis1=0, axis2=1):
+    """
+    Return specified diagonals.
+
+    If `a` is 2-D, returns the diagonal of `a` with the given offset,
+    i.e., the collection of elements of the form ``a[i, i+offset]``.  If
+    `a` has more than two dimensions, then the axes specified by `axis1`
+    and `axis2` are used to determine the 2-D sub-array whose diagonal is
+    returned.  The shape of the resulting array can be determined by
+    removing `axis1` and `axis2` and appending an index to the right equal
+    to the size of the resulting diagonals.
+
+    In versions of NumPy prior to 1.7, this function always returned a new,
+    independent array containing a copy of the values in the diagonal.
+
+    In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal,
+    but depending on this fact is deprecated. Writing to the resulting
+    array continues to work as it used to, but a FutureWarning is issued.
+
+    Starting in NumPy 1.9 it returns a read-only view on the original array.
+    Attempting to write to the resulting array will produce an error.
+
+    In some future release, it will return a read/write view and writing to
+    the returned array will alter your original array.  The returned array
+    will have the same type as the input array.
+
+    If you don't write to the array returned by this function, then you can
+    just ignore all of the above.
+
+    If you depend on the current behavior, then we suggest copying the
+    returned array explicitly, i.e., use ``np.diagonal(a).copy()`` instead
+    of just ``np.diagonal(a)``. This will work with both past and future
+    versions of NumPy.
+
+    Parameters
+    ----------
+    a : array_like
+        Array from which the diagonals are taken.
+    offset : int, optional
+        Offset of the diagonal from the main diagonal.  Can be positive or
+        negative.  Defaults to main diagonal (0).
+    axis1 : int, optional
+        Axis to be used as the first axis of the 2-D sub-arrays from which
+        the diagonals should be taken.  Defaults to first axis (0).
+    axis2 : int, optional
+        Axis to be used as the second axis of the 2-D sub-arrays from
+        which the diagonals should be taken. Defaults to second axis (1).
+
+    Returns
+    -------
+    array_of_diagonals : ndarray
+        If `a` is 2-D, then a 1-D array containing the diagonal and of the
+        same type as `a` is returned unless `a` is a `matrix`, in which case
+        a 1-D array rather than a (2-D) `matrix` is returned in order to
+        maintain backward compatibility.
+
+        If ``a.ndim > 2``, then the dimensions specified by `axis1` and `axis2`
+        are removed, and a new axis inserted at the end corresponding to the
+        diagonal.
+
+    Raises
+    ------
+    ValueError
+        If the dimension of `a` is less than 2.
+
+    See Also
+    --------
+    diag : MATLAB work-a-like for 1-D and 2-D arrays.
+    diagflat : Create diagonal arrays.
+    trace : Sum along diagonals.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.arange(4).reshape(2,2)
+    >>> a
+    array([[0, 1],
+           [2, 3]])
+    >>> a.diagonal()
+    array([0, 3])
+    >>> a.diagonal(1)
+    array([1])
+
+    A 3-D example:
+
+    >>> a = np.arange(8).reshape(2,2,2); a
+    array([[[0, 1],
+            [2, 3]],
+           [[4, 5],
+            [6, 7]]])
+    >>> a.diagonal(0,  # Main diagonals of two arrays created by skipping
+    ...            0,  # across the outer(left)-most axis last and
+    ...            1)  # the "middle" (row) axis first.
+    array([[0, 6],
+           [1, 7]])
+
+    The sub-arrays whose main diagonals we just obtained; note that each
+    corresponds to fixing the right-most (column) axis, and that the
+    diagonals are "packed" in rows.
+
+    >>> a[:,:,0]  # main diagonal is [0 6]
+    array([[0, 2],
+           [4, 6]])
+    >>> a[:,:,1]  # main diagonal is [1 7]
+    array([[1, 3],
+           [5, 7]])
+
+    The anti-diagonal can be obtained by reversing the order of elements
+    using either `numpy.flipud` or `numpy.fliplr`.
+
+    >>> a = np.arange(9).reshape(3, 3)
+    >>> a
+    array([[0, 1, 2],
+           [3, 4, 5],
+           [6, 7, 8]])
+    >>> np.fliplr(a).diagonal()  # Horizontal flip
+    array([2, 4, 6])
+    >>> np.flipud(a).diagonal()  # Vertical flip
+    array([6, 4, 2])
+
+    Note that the order in which the diagonal is retrieved varies depending
+    on the flip function.
+    """
+    if isinstance(a, np.matrix):
+        # Make diagonal of matrix 1-D to preserve backward compatibility.
+        return asarray(a).diagonal(offset=offset, axis1=axis1, axis2=axis2)
+    else:
+        return asanyarray(a).diagonal(offset=offset, axis1=axis1, axis2=axis2)
+
+
+def _trace_dispatcher(
+        a, offset=None, axis1=None, axis2=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_trace_dispatcher)
+def trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None):
+    """
+    Return the sum along diagonals of the array.
+
+    If `a` is 2-D, the sum along its diagonal with the given offset
+    is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i.
+
+    If `a` has more than two dimensions, then the axes specified by axis1 and
+    axis2 are used to determine the 2-D sub-arrays whose traces are returned.
+    The shape of the resulting array is the same as that of `a` with `axis1`
+    and `axis2` removed.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array, from which the diagonals are taken.
+    offset : int, optional
+        Offset of the diagonal from the main diagonal. Can be both positive
+        and negative. Defaults to 0.
+    axis1, axis2 : int, optional
+        Axes to be used as the first and second axis of the 2-D sub-arrays
+        from which the diagonals should be taken. Defaults are the first two
+        axes of `a`.
+    dtype : dtype, optional
+        Determines the data-type of the returned array and of the accumulator
+        where the elements are summed. If dtype has the value None and `a` is
+        of integer type of precision less than the default integer
+        precision, then the default integer precision is used. Otherwise,
+        the precision is the same as that of `a`.
+    out : ndarray, optional
+        Array into which the output is placed. Its type is preserved and
+        it must be of the right shape to hold the output.
+
+    Returns
+    -------
+    sum_along_diagonals : ndarray
+        If `a` is 2-D, the sum along the diagonal is returned.  If `a` has
+        larger dimensions, then an array of sums along diagonals is returned.
+
+    See Also
+    --------
+    diag, diagonal, diagflat
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.trace(np.eye(3))
+    3.0
+    >>> a = np.arange(8).reshape((2,2,2))
+    >>> np.trace(a)
+    array([6, 8])
+
+    >>> a = np.arange(24).reshape((2,2,2,3))
+    >>> np.trace(a).shape
+    (2, 3)
+
+    """
+    if isinstance(a, np.matrix):
+        # Get trace of matrix via an array to preserve backward compatibility.
+        return asarray(a).trace(
+            offset=offset, axis1=axis1, axis2=axis2, dtype=dtype, out=out
+        )
+    else:
+        return asanyarray(a).trace(
+            offset=offset, axis1=axis1, axis2=axis2, dtype=dtype, out=out
+        )
+
+
+def _ravel_dispatcher(a, order=None):
+    return (a,)
+
+
+@array_function_dispatch(_ravel_dispatcher)
+def ravel(a, order='C'):
+    """Return a contiguous flattened array.
+
+    A 1-D array, containing the elements of the input, is returned.  A copy is
+    made only if needed.
+
+    As of NumPy 1.10, the returned array will have the same type as the input
+    array. (for example, a masked array will be returned for a masked array
+    input)
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.  The elements in `a` are read in the order specified by
+        `order`, and packed as a 1-D array.
+    order : {'C','F', 'A', 'K'}, optional
+
+        The elements of `a` are read using this index order. 'C' means
+        to index the elements in row-major, C-style order,
+        with the last axis index changing fastest, back to the first
+        axis index changing slowest.  'F' means to index the elements
+        in column-major, Fortran-style order, with the
+        first index changing fastest, and the last index changing
+        slowest. Note that the 'C' and 'F' options take no account of
+        the memory layout of the underlying array, and only refer to
+        the order of axis indexing.  'A' means to read the elements in
+        Fortran-like index order if `a` is Fortran *contiguous* in
+        memory, C-like order otherwise.  'K' means to read the
+        elements in the order they occur in memory, except for
+        reversing the data when strides are negative.  By default, 'C'
+        index order is used.
+
+    Returns
+    -------
+    y : array_like
+        y is a contiguous 1-D array of the same subtype as `a`,
+        with shape ``(a.size,)``.
+        Note that matrices are special cased for backward compatibility,
+        if `a` is a matrix, then y is a 1-D ndarray.
+
+    See Also
+    --------
+    ndarray.flat : 1-D iterator over an array.
+    ndarray.flatten : 1-D array copy of the elements of an array
+                      in row-major order.
+    ndarray.reshape : Change the shape of an array without changing its data.
+
+    Notes
+    -----
+    In row-major, C-style order, in two dimensions, the row index
+    varies the slowest, and the column index the quickest.  This can
+    be generalized to multiple dimensions, where row-major order
+    implies that the index along the first axis varies slowest, and
+    the index along the last quickest.  The opposite holds for
+    column-major, Fortran-style index ordering.
+
+    When a view is desired in as many cases as possible, ``arr.reshape(-1)``
+    may be preferable. However, ``ravel`` supports ``K`` in the optional
+    ``order`` argument while ``reshape`` does not.
+
+    Examples
+    --------
+    It is equivalent to ``reshape(-1, order=order)``.
+
+    >>> import numpy as np
+    >>> x = np.array([[1, 2, 3], [4, 5, 6]])
+    >>> np.ravel(x)
+    array([1, 2, 3, 4, 5, 6])
+
+    >>> x.reshape(-1)
+    array([1, 2, 3, 4, 5, 6])
+
+    >>> np.ravel(x, order='F')
+    array([1, 4, 2, 5, 3, 6])
+
+    When ``order`` is 'A', it will preserve the array's 'C' or 'F' ordering:
+
+    >>> np.ravel(x.T)
+    array([1, 4, 2, 5, 3, 6])
+    >>> np.ravel(x.T, order='A')
+    array([1, 2, 3, 4, 5, 6])
+
+    When ``order`` is 'K', it will preserve orderings that are neither 'C'
+    nor 'F', but won't reverse axes:
+
+    >>> a = np.arange(3)[::-1]; a
+    array([2, 1, 0])
+    >>> a.ravel(order='C')
+    array([2, 1, 0])
+    >>> a.ravel(order='K')
+    array([2, 1, 0])
+
+    >>> a = np.arange(12).reshape(2,3,2).swapaxes(1,2); a
+    array([[[ 0,  2,  4],
+            [ 1,  3,  5]],
+           [[ 6,  8, 10],
+            [ 7,  9, 11]]])
+    >>> a.ravel(order='C')
+    array([ 0,  2,  4,  1,  3,  5,  6,  8, 10,  7,  9, 11])
+    >>> a.ravel(order='K')
+    array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])
+
+    """
+    if isinstance(a, np.matrix):
+        return asarray(a).ravel(order=order)
+    else:
+        return asanyarray(a).ravel(order=order)
+
+
+def _nonzero_dispatcher(a):
+    return (a,)
+
+
+@array_function_dispatch(_nonzero_dispatcher)
+def nonzero(a):
+    """
+    Return the indices of the elements that are non-zero.
+
+    Returns a tuple of arrays, one for each dimension of `a`,
+    containing the indices of the non-zero elements in that
+    dimension. The values in `a` are always tested and returned in
+    row-major, C-style order.
+
+    To group the indices by element, rather than dimension, use `argwhere`,
+    which returns a row for each non-zero element.
+
+    .. note::
+
+       When called on a zero-d array or scalar, ``nonzero(a)`` is treated
+       as ``nonzero(atleast_1d(a))``.
+
+       .. deprecated:: 1.17.0
+
+          Use `atleast_1d` explicitly if this behavior is deliberate.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+
+    Returns
+    -------
+    tuple_of_arrays : tuple
+        Indices of elements that are non-zero.
+
+    See Also
+    --------
+    flatnonzero :
+        Return indices that are non-zero in the flattened version of the input
+        array.
+    ndarray.nonzero :
+        Equivalent ndarray method.
+    count_nonzero :
+        Counts the number of non-zero elements in the input array.
+
+    Notes
+    -----
+    While the nonzero values can be obtained with ``a[nonzero(a)]``, it is
+    recommended to use ``x[x.astype(bool)]`` or ``x[x != 0]`` instead, which
+    will correctly handle 0-d arrays.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]])
+    >>> x
+    array([[3, 0, 0],
+           [0, 4, 0],
+           [5, 6, 0]])
+    >>> np.nonzero(x)
+    (array([0, 1, 2, 2]), array([0, 1, 0, 1]))
+
+    >>> x[np.nonzero(x)]
+    array([3, 4, 5, 6])
+    >>> np.transpose(np.nonzero(x))
+    array([[0, 0],
+           [1, 1],
+           [2, 0],
+           [2, 1]])
+
+    A common use for ``nonzero`` is to find the indices of an array, where
+    a condition is True.  Given an array `a`, the condition `a` > 3 is a
+    boolean array and since False is interpreted as 0, np.nonzero(a > 3)
+    yields the indices of the `a` where the condition is true.
+
+    >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> a > 3
+    array([[False, False, False],
+           [ True,  True,  True],
+           [ True,  True,  True]])
+    >>> np.nonzero(a > 3)
+    (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
+
+    Using this result to index `a` is equivalent to using the mask directly:
+
+    >>> a[np.nonzero(a > 3)]
+    array([4, 5, 6, 7, 8, 9])
+    >>> a[a > 3]  # prefer this spelling
+    array([4, 5, 6, 7, 8, 9])
+
+    ``nonzero`` can also be called as a method of the array.
+
+    >>> (a > 3).nonzero()
+    (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
+
+    """
+    return _wrapfunc(a, 'nonzero')
+
+
+def _shape_dispatcher(a):
+    return (a,)
+
+
+@array_function_dispatch(_shape_dispatcher)
+def shape(a):
+    """
+    Return the shape of an array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+
+    Returns
+    -------
+    shape : tuple of ints
+        The elements of the shape tuple give the lengths of the
+        corresponding array dimensions.
+
+    See Also
+    --------
+    len : ``len(a)`` is equivalent to ``np.shape(a)[0]`` for N-D arrays with
+          ``N>=1``.
+    ndarray.shape : Equivalent array method.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.shape(np.eye(3))
+    (3, 3)
+    >>> np.shape([[1, 3]])
+    (1, 2)
+    >>> np.shape([0])
+    (1,)
+    >>> np.shape(0)
+    ()
+
+    >>> a = np.array([(1, 2), (3, 4), (5, 6)],
+    ...              dtype=[('x', 'i4'), ('y', 'i4')])
+    >>> np.shape(a)
+    (3,)
+    >>> a.shape
+    (3,)
+
+    """
+    try:
+        result = a.shape
+    except AttributeError:
+        result = asarray(a).shape
+    return result
+
+
+def _compress_dispatcher(condition, a, axis=None, out=None):
+    return (condition, a, out)
+
+
+@array_function_dispatch(_compress_dispatcher)
+def compress(condition, a, axis=None, out=None):
+    """
+    Return selected slices of an array along given axis.
+
+    When working along a given axis, a slice along that axis is returned in
+    `output` for each index where `condition` evaluates to True. When
+    working on a 1-D array, `compress` is equivalent to `extract`.
+
+    Parameters
+    ----------
+    condition : 1-D array of bools
+        Array that selects which entries to return. If len(condition)
+        is less than the size of `a` along the given axis, then output is
+        truncated to the length of the condition array.
+    a : array_like
+        Array from which to extract a part.
+    axis : int, optional
+        Axis along which to take slices. If None (default), work on the
+        flattened array.
+    out : ndarray, optional
+        Output array.  Its type is preserved and it must be of the right
+        shape to hold the output.
+
+    Returns
+    -------
+    compressed_array : ndarray
+        A copy of `a` without the slices along axis for which `condition`
+        is false.
+
+    See Also
+    --------
+    take, choose, diag, diagonal, select
+    ndarray.compress : Equivalent method in ndarray
+    extract : Equivalent method when working on 1-D arrays
+    :ref:`ufuncs-output-type`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1, 2], [3, 4], [5, 6]])
+    >>> a
+    array([[1, 2],
+           [3, 4],
+           [5, 6]])
+    >>> np.compress([0, 1], a, axis=0)
+    array([[3, 4]])
+    >>> np.compress([False, True, True], a, axis=0)
+    array([[3, 4],
+           [5, 6]])
+    >>> np.compress([False, True], a, axis=1)
+    array([[2],
+           [4],
+           [6]])
+
+    Working on the flattened array does not return slices along an axis but
+    selects elements.
+
+    >>> np.compress([False, True], a)
+    array([2])
+
+    """
+    return _wrapfunc(a, 'compress', condition, axis=axis, out=out)
+
+
+def _clip_dispatcher(a, a_min=None, a_max=None, out=None, *, min=None,
+                     max=None, **kwargs):
+    return (a, a_min, a_max, out, min, max)
+
+
+@array_function_dispatch(_clip_dispatcher)
+def clip(a, a_min=np._NoValue, a_max=np._NoValue, out=None, *,
+         min=np._NoValue, max=np._NoValue, **kwargs):
+    """
+    Clip (limit) the values in an array.
+
+    Given an interval, values outside the interval are clipped to
+    the interval edges.  For example, if an interval of ``[0, 1]``
+    is specified, values smaller than 0 become 0, and values larger
+    than 1 become 1.
+
+    Equivalent to but faster than ``np.minimum(a_max, np.maximum(a, a_min))``.
+
+    No check is performed to ensure ``a_min < a_max``.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing elements to clip.
+    a_min, a_max : array_like or None
+        Minimum and maximum value. If ``None``, clipping is not performed on
+        the corresponding edge. If both ``a_min`` and ``a_max`` are ``None``,
+        the elements of the returned array stay the same. Both are broadcasted
+        against ``a``.
+    out : ndarray, optional
+        The results will be placed in this array. It may be the input
+        array for in-place clipping.  `out` must be of the right shape
+        to hold the output.  Its type is preserved.
+    min, max : array_like or None
+        Array API compatible alternatives for ``a_min`` and ``a_max``
+        arguments. Either ``a_min`` and ``a_max`` or ``min`` and ``max``
+        can be passed at the same time. Default: ``None``.
+
+        .. versionadded:: 2.1.0
+    **kwargs
+        For other keyword-only arguments, see the
+        :ref:`ufunc docs <ufuncs.kwargs>`.
+
+    Returns
+    -------
+    clipped_array : ndarray
+        An array with the elements of `a`, but where values
+        < `a_min` are replaced with `a_min`, and those > `a_max`
+        with `a_max`.
+
+    See Also
+    --------
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    When `a_min` is greater than `a_max`, `clip` returns an
+    array in which all values are equal to `a_max`,
+    as shown in the second example.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.arange(10)
+    >>> a
+    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+    >>> np.clip(a, 1, 8)
+    array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8])
+    >>> np.clip(a, 8, 1)
+    array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
+    >>> np.clip(a, 3, 6, out=a)
+    array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
+    >>> a
+    array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
+    >>> a = np.arange(10)
+    >>> a
+    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+    >>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8)
+    array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])
+
+    """
+    if a_min is np._NoValue and a_max is np._NoValue:
+        a_min = None if min is np._NoValue else min
+        a_max = None if max is np._NoValue else max
+    elif a_min is np._NoValue:
+        raise TypeError("clip() missing 1 required positional "
+                        "argument: 'a_min'")
+    elif a_max is np._NoValue:
+        raise TypeError("clip() missing 1 required positional "
+                        "argument: 'a_max'")
+    elif min is not np._NoValue or max is not np._NoValue:
+        raise ValueError("Passing `min` or `max` keyword argument when "
+                         "`a_min` and `a_max` are provided is forbidden.")
+
+    return _wrapfunc(a, 'clip', a_min, a_max, out=out, **kwargs)
+
+
+def _sum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                    initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_sum_dispatcher)
+def sum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+        initial=np._NoValue, where=np._NoValue):
+    """
+    Sum of array elements over a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Elements to sum.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which a sum is performed.  The default,
+        axis=None, will sum all of the elements of the input array.  If
+        axis is negative it counts from the last to the first axis. If
+        axis is a tuple of ints, a sum is performed on all of the axes
+        specified in the tuple instead of a single axis or all the axes as
+        before.
+    dtype : dtype, optional
+        The type of the returned array and of the accumulator in which the
+        elements are summed.  The dtype of `a` is used by default unless `a`
+        has an integer dtype of less precision than the default platform
+        integer.  In that case, if `a` is signed then the platform integer
+        is used while if `a` is unsigned then an unsigned integer of the
+        same precision as the platform integer is used.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must have
+        the same shape as the expected output, but the type of the output
+        values will be cast if necessary.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `sum` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+    initial : scalar, optional
+        Starting value for the sum. See `~numpy.ufunc.reduce` for details.
+    where : array_like of bool, optional
+        Elements to include in the sum. See `~numpy.ufunc.reduce` for details.
+
+    Returns
+    -------
+    sum_along_axis : ndarray
+        An array with the same shape as `a`, with the specified
+        axis removed.   If `a` is a 0-d array, or if `axis` is None, a scalar
+        is returned.  If an output array is specified, a reference to
+        `out` is returned.
+
+    See Also
+    --------
+    ndarray.sum : Equivalent method.
+    add: ``numpy.add.reduce`` equivalent function.
+    cumsum : Cumulative sum of array elements.
+    trapezoid : Integration of array values using composite trapezoidal rule.
+
+    mean, average
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.
+
+    The sum of an empty array is the neutral element 0:
+
+    >>> np.sum([])
+    0.0
+
+    For floating point numbers the numerical precision of sum (and
+    ``np.add.reduce``) is in general limited by directly adding each number
+    individually to the result causing rounding errors in every step.
+    However, often numpy will use a  numerically better approach (partial
+    pairwise summation) leading to improved precision in many use-cases.
+    This improved precision is always provided when no ``axis`` is given.
+    When ``axis`` is given, it will depend on which axis is summed.
+    Technically, to provide the best speed possible, the improved precision
+    is only used when the summation is along the fast axis in memory.
+    Note that the exact precision may vary depending on other parameters.
+    In contrast to NumPy, Python's ``math.fsum`` function uses a slower but
+    more precise approach to summation.
+    Especially when summing a large number of lower precision floating point
+    numbers, such as ``float32``, numerical errors can become significant.
+    In such cases it can be advisable to use `dtype="float64"` to use a higher
+    precision for the output.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.sum([0.5, 1.5])
+    2.0
+    >>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32)
+    np.int32(1)
+    >>> np.sum([[0, 1], [0, 5]])
+    6
+    >>> np.sum([[0, 1], [0, 5]], axis=0)
+    array([0, 6])
+    >>> np.sum([[0, 1], [0, 5]], axis=1)
+    array([1, 5])
+    >>> np.sum([[0, 1], [np.nan, 5]], where=[False, True], axis=1)
+    array([1., 5.])
+
+    If the accumulator is too small, overflow occurs:
+
+    >>> np.ones(128, dtype=np.int8).sum(dtype=np.int8)
+    np.int8(-128)
+
+    You can also start the sum with a value other than zero:
+
+    >>> np.sum([10], initial=5)
+    15
+    """
+    if isinstance(a, _gentype):
+        # 2018-02-25, 1.15.0
+        warnings.warn(
+            "Calling np.sum(generator) is deprecated, and in the future will "
+            "give a different result. Use np.sum(np.fromiter(generator)) or "
+            "the python sum builtin instead.",
+            DeprecationWarning, stacklevel=2
+        )
+
+        res = _sum_(a)
+        if out is not None:
+            out[...] = res
+            return out
+        return res
+
+    return _wrapreduction(
+        a, np.add, 'sum', axis, dtype, out,
+        keepdims=keepdims, initial=initial, where=where
+    )
+
+
+def _any_dispatcher(a, axis=None, out=None, keepdims=None, *,
+                    where=np._NoValue):
+    return (a, where, out)
+
+
+@array_function_dispatch(_any_dispatcher)
+def any(a, axis=None, out=None, keepdims=np._NoValue, *, where=np._NoValue):
+    """
+    Test whether any array element along a given axis evaluates to True.
+
+    Returns single boolean if `axis` is ``None``
+
+    Parameters
+    ----------
+    a : array_like
+        Input array or object that can be converted to an array.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which a logical OR reduction is performed.
+        The default (``axis=None``) is to perform a logical OR over all
+        the dimensions of the input array. `axis` may be negative, in
+        which case it counts from the last to the first axis. If this
+        is a tuple of ints, a reduction is performed on multiple
+        axes, instead of a single axis or all the axes as before.
+    out : ndarray, optional
+        Alternate output array in which to place the result.  It must have
+        the same shape as the expected output and its type is preserved
+        (e.g., if it is of type float, then it will remain so, returning
+        1.0 for True and 0.0 for False, regardless of the type of `a`).
+        See :ref:`ufuncs-output-type` for more details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `any` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    where : array_like of bool, optional
+        Elements to include in checking for any `True` values.
+        See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    any : bool or ndarray
+        A new boolean or `ndarray` is returned unless `out` is specified,
+        in which case a reference to `out` is returned.
+
+    See Also
+    --------
+    ndarray.any : equivalent method
+
+    all : Test whether all elements along a given axis evaluate to True.
+
+    Notes
+    -----
+    Not a Number (NaN), positive infinity and negative infinity evaluate
+    to `True` because these are not equal to zero.
+
+    .. versionchanged:: 2.0
+       Before NumPy 2.0, ``any`` did not return booleans for object dtype
+       input arrays.
+       This behavior is still available via ``np.logical_or.reduce``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.any([[True, False], [True, True]])
+    True
+
+    >>> np.any([[True,  False, True ],
+    ...         [False, False, False]], axis=0)
+    array([ True, False, True])
+
+    >>> np.any([-1, 0, 5])
+    True
+
+    >>> np.any([[np.nan], [np.inf]], axis=1, keepdims=True)
+    array([[ True],
+           [ True]])
+
+    >>> np.any([[True, False], [False, False]], where=[[False], [True]])
+    False
+
+    >>> a = np.array([[1, 0, 0],
+    ...               [0, 0, 1],
+    ...               [0, 0, 0]])
+    >>> np.any(a, axis=0)
+    array([ True, False,  True])
+    >>> np.any(a, axis=1)
+    array([ True,  True, False])
+
+    >>> o=np.array(False)
+    >>> z=np.any([-1, 4, 5], out=o)
+    >>> z, o
+    (array(True), array(True))
+    >>> # Check now that z is a reference to o
+    >>> z is o
+    True
+    >>> id(z), id(o) # identity of z and o              # doctest: +SKIP
+    (191614240, 191614240)
+
+    """
+    return _wrapreduction_any_all(a, np.logical_or, 'any', axis, out,
+                                  keepdims=keepdims, where=where)
+
+
+def _all_dispatcher(a, axis=None, out=None, keepdims=None, *,
+                    where=None):
+    return (a, where, out)
+
+
+@array_function_dispatch(_all_dispatcher)
+def all(a, axis=None, out=None, keepdims=np._NoValue, *, where=np._NoValue):
+    """
+    Test whether all array elements along a given axis evaluate to True.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array or object that can be converted to an array.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which a logical AND reduction is performed.
+        The default (``axis=None``) is to perform a logical AND over all
+        the dimensions of the input array. `axis` may be negative, in
+        which case it counts from the last to the first axis. If this
+        is a tuple of ints, a reduction is performed on multiple
+        axes, instead of a single axis or all the axes as before.
+    out : ndarray, optional
+        Alternate output array in which to place the result.
+        It must have the same shape as the expected output and its
+        type is preserved (e.g., if ``dtype(out)`` is float, the result
+        will consist of 0.0's and 1.0's). See :ref:`ufuncs-output-type`
+        for more details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `all` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    where : array_like of bool, optional
+        Elements to include in checking for all `True` values.
+        See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    all : ndarray, bool
+        A new boolean or array is returned unless `out` is specified,
+        in which case a reference to `out` is returned.
+
+    See Also
+    --------
+    ndarray.all : equivalent method
+
+    any : Test whether any element along a given axis evaluates to True.
+
+    Notes
+    -----
+    Not a Number (NaN), positive infinity and negative infinity
+    evaluate to `True` because these are not equal to zero.
+
+    .. versionchanged:: 2.0
+       Before NumPy 2.0, ``all`` did not return booleans for object dtype
+       input arrays.
+       This behavior is still available via ``np.logical_and.reduce``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.all([[True,False],[True,True]])
+    False
+
+    >>> np.all([[True,False],[True,True]], axis=0)
+    array([ True, False])
+
+    >>> np.all([-1, 4, 5])
+    True
+
+    >>> np.all([1.0, np.nan])
+    True
+
+    >>> np.all([[True, True], [False, True]], where=[[True], [False]])
+    True
+
+    >>> o=np.array(False)
+    >>> z=np.all([-1, 4, 5], out=o)
+    >>> id(z), id(o), z
+    (28293632, 28293632, array(True)) # may vary
+
+    """
+    return _wrapreduction_any_all(a, np.logical_and, 'all', axis, out,
+                                  keepdims=keepdims, where=where)
+
+
+def _cumulative_func(x, func, axis, dtype, out, include_initial):
+    x = np.atleast_1d(x)
+    x_ndim = x.ndim
+    if axis is None:
+        if x_ndim >= 2:
+            raise ValueError("For arrays which have more than one dimension "
+                            "``axis`` argument is required.")
+        axis = 0
+
+    if out is not None and include_initial:
+        item = [slice(None)] * x_ndim
+        item[axis] = slice(1, None)
+        func.accumulate(x, axis=axis, dtype=dtype, out=out[tuple(item)])
+        item[axis] = 0
+        out[tuple(item)] = func.identity
+        return out
+
+    res = func.accumulate(x, axis=axis, dtype=dtype, out=out)
+    if include_initial:
+        initial_shape = list(x.shape)
+        initial_shape[axis] = 1
+        res = np.concat(
+            [np.full_like(res, func.identity, shape=initial_shape), res],
+            axis=axis,
+        )
+
+    return res
+
+
+def _cumulative_prod_dispatcher(x, /, *, axis=None, dtype=None, out=None,
+                                include_initial=None):
+    return (x, out)
+
+
+@array_function_dispatch(_cumulative_prod_dispatcher)
+def cumulative_prod(x, /, *, axis=None, dtype=None, out=None,
+                    include_initial=False):
+    """
+    Return the cumulative product of elements along a given axis.
+
+    This function is an Array API compatible alternative to `numpy.cumprod`.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the cumulative product is computed. The default
+        (None) is only allowed for one-dimensional arrays. For arrays
+        with more than one dimension ``axis`` is required.
+    dtype : dtype, optional
+        Type of the returned array, as well as of the accumulator in which
+        the elements are multiplied.  If ``dtype`` is not specified, it
+        defaults to the dtype of ``x``, unless ``x`` has an integer dtype
+        with a precision less than that of the default platform integer.
+        In that case, the default platform integer is used instead.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must
+        have the same shape and buffer length as the expected output
+        but the type of the resulting values will be cast if necessary.
+        See :ref:`ufuncs-output-type` for more details.
+    include_initial : bool, optional
+        Boolean indicating whether to include the initial value (ones) as
+        the first value in the output. With ``include_initial=True``
+        the shape of the output is different than the shape of the input.
+        Default: ``False``.
+
+    Returns
+    -------
+    cumulative_prod_along_axis : ndarray
+        A new array holding the result is returned unless ``out`` is
+        specified, in which case a reference to ``out`` is returned. The
+        result has the same shape as ``x`` if ``include_initial=False``.
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.
+
+    Examples
+    --------
+    >>> a = np.array([1, 2, 3])
+    >>> np.cumulative_prod(a)  # intermediate results 1, 1*2
+    ...                        # total product 1*2*3 = 6
+    array([1, 2, 6])
+    >>> a = np.array([1, 2, 3, 4, 5, 6])
+    >>> np.cumulative_prod(a, dtype=float) # specify type of output
+    array([   1.,    2.,    6.,   24.,  120.,  720.])
+
+    The cumulative product for each column (i.e., over the rows) of ``b``:
+
+    >>> b = np.array([[1, 2, 3], [4, 5, 6]])
+    >>> np.cumulative_prod(b, axis=0)
+    array([[ 1,  2,  3],
+           [ 4, 10, 18]])
+
+    The cumulative product for each row (i.e. over the columns) of ``b``:
+
+    >>> np.cumulative_prod(b, axis=1)
+    array([[  1,   2,   6],
+           [  4,  20, 120]])
+
+    """
+    return _cumulative_func(x, um.multiply, axis, dtype, out, include_initial)
+
+
+def _cumulative_sum_dispatcher(x, /, *, axis=None, dtype=None, out=None,
+                               include_initial=None):
+    return (x, out)
+
+
+@array_function_dispatch(_cumulative_sum_dispatcher)
+def cumulative_sum(x, /, *, axis=None, dtype=None, out=None,
+                   include_initial=False):
+    """
+    Return the cumulative sum of the elements along a given axis.
+
+    This function is an Array API compatible alternative to `numpy.cumsum`.
+
+    Parameters
+    ----------
+    x : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the cumulative sum is computed. The default
+        (None) is only allowed for one-dimensional arrays. For arrays
+        with more than one dimension ``axis`` is required.
+    dtype : dtype, optional
+        Type of the returned array and of the accumulator in which the
+        elements are summed.  If ``dtype`` is not specified, it defaults
+        to the dtype of ``x``, unless ``x`` has an integer dtype with
+        a precision less than that of the default platform integer.
+        In that case, the default platform integer is used.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must
+        have the same shape and buffer length as the expected output
+        but the type will be cast if necessary. See :ref:`ufuncs-output-type`
+        for more details.
+    include_initial : bool, optional
+        Boolean indicating whether to include the initial value (zeros) as
+        the first value in the output. With ``include_initial=True``
+        the shape of the output is different than the shape of the input.
+        Default: ``False``.
+
+    Returns
+    -------
+    cumulative_sum_along_axis : ndarray
+        A new array holding the result is returned unless ``out`` is
+        specified, in which case a reference to ``out`` is returned. The
+        result has the same shape as ``x`` if ``include_initial=False``.
+
+    See Also
+    --------
+    sum : Sum array elements.
+    trapezoid : Integration of array values using composite trapezoidal rule.
+    diff : Calculate the n-th discrete difference along given axis.
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.
+
+    ``cumulative_sum(a)[-1]`` may not be equal to ``sum(a)`` for
+    floating-point values since ``sum`` may use a pairwise summation routine,
+    reducing the roundoff-error. See `sum` for more information.
+
+    Examples
+    --------
+    >>> a = np.array([1, 2, 3, 4, 5, 6])
+    >>> a
+    array([1, 2, 3, 4, 5, 6])
+    >>> np.cumulative_sum(a)
+    array([ 1,  3,  6, 10, 15, 21])
+    >>> np.cumulative_sum(a, dtype=float)  # specifies type of output value(s)
+    array([  1.,   3.,   6.,  10.,  15.,  21.])
+
+    >>> b = np.array([[1, 2, 3], [4, 5, 6]])
+    >>> np.cumulative_sum(b,axis=0)  # sum over rows for each of the 3 columns
+    array([[1, 2, 3],
+           [5, 7, 9]])
+    >>> np.cumulative_sum(b,axis=1)  # sum over columns for each of the 2 rows
+    array([[ 1,  3,  6],
+           [ 4,  9, 15]])
+
+    ``cumulative_sum(c)[-1]`` may not be equal to ``sum(c)``
+
+    >>> c = np.array([1, 2e-9, 3e-9] * 1000000)
+    >>> np.cumulative_sum(c)[-1]
+    1000000.0050045159
+    >>> c.sum()
+    1000000.0050000029
+
+    """
+    return _cumulative_func(x, um.add, axis, dtype, out, include_initial)
+
+
+def _cumsum_dispatcher(a, axis=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_cumsum_dispatcher)
+def cumsum(a, axis=None, dtype=None, out=None):
+    """
+    Return the cumulative sum of the elements along a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the cumulative sum is computed. The default
+        (None) is to compute the cumsum over the flattened array.
+    dtype : dtype, optional
+        Type of the returned array and of the accumulator in which the
+        elements are summed.  If `dtype` is not specified, it defaults
+        to the dtype of `a`, unless `a` has an integer dtype with a
+        precision less than that of the default platform integer.  In
+        that case, the default platform integer is used.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must
+        have the same shape and buffer length as the expected output
+        but the type will be cast if necessary. See :ref:`ufuncs-output-type`
+        for more details.
+
+    Returns
+    -------
+    cumsum_along_axis : ndarray.
+        A new array holding the result is returned unless `out` is
+        specified, in which case a reference to `out` is returned. The
+        result has the same size as `a`, and the same shape as `a` if
+        `axis` is not None or `a` is a 1-d array.
+
+    See Also
+    --------
+    cumulative_sum : Array API compatible alternative for ``cumsum``.
+    sum : Sum array elements.
+    trapezoid : Integration of array values using composite trapezoidal rule.
+    diff : Calculate the n-th discrete difference along given axis.
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.
+
+    ``cumsum(a)[-1]`` may not be equal to ``sum(a)`` for floating-point
+    values since ``sum`` may use a pairwise summation routine, reducing
+    the roundoff-error. See `sum` for more information.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1,2,3], [4,5,6]])
+    >>> a
+    array([[1, 2, 3],
+           [4, 5, 6]])
+    >>> np.cumsum(a)
+    array([ 1,  3,  6, 10, 15, 21])
+    >>> np.cumsum(a, dtype=float)     # specifies type of output value(s)
+    array([  1.,   3.,   6.,  10.,  15.,  21.])
+
+    >>> np.cumsum(a,axis=0)      # sum over rows for each of the 3 columns
+    array([[1, 2, 3],
+           [5, 7, 9]])
+    >>> np.cumsum(a,axis=1)      # sum over columns for each of the 2 rows
+    array([[ 1,  3,  6],
+           [ 4,  9, 15]])
+
+    ``cumsum(b)[-1]`` may not be equal to ``sum(b)``
+
+    >>> b = np.array([1, 2e-9, 3e-9] * 1000000)
+    >>> b.cumsum()[-1]
+    1000000.0050045159
+    >>> b.sum()
+    1000000.0050000029
+
+    """
+    return _wrapfunc(a, 'cumsum', axis=axis, dtype=dtype, out=out)
+
+
+def _ptp_dispatcher(a, axis=None, out=None, keepdims=None):
+    return (a, out)
+
+
+@array_function_dispatch(_ptp_dispatcher)
+def ptp(a, axis=None, out=None, keepdims=np._NoValue):
+    """
+    Range of values (maximum - minimum) along an axis.
+
+    The name of the function comes from the acronym for 'peak to peak'.
+
+    .. warning::
+        `ptp` preserves the data type of the array. This means the
+        return value for an input of signed integers with n bits
+        (e.g. `numpy.int8`, `numpy.int16`, etc) is also a signed integer
+        with n bits.  In that case, peak-to-peak values greater than
+        ``2**(n-1)-1`` will be returned as negative values. An example
+        with a work-around is shown below.
+
+    Parameters
+    ----------
+    a : array_like
+        Input values.
+    axis : None or int or tuple of ints, optional
+        Axis along which to find the peaks.  By default, flatten the
+        array.  `axis` may be negative, in
+        which case it counts from the last to the first axis.
+        If this is a tuple of ints, a reduction is performed on multiple
+        axes, instead of a single axis or all the axes as before.
+    out : array_like
+        Alternative output array in which to place the result. It must
+        have the same shape and buffer length as the expected output,
+        but the type of the output values will be cast if necessary.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `ptp` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    Returns
+    -------
+    ptp : ndarray or scalar
+        The range of a given array - `scalar` if array is one-dimensional
+        or a new array holding the result along the given axis
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([[4, 9, 2, 10],
+    ...               [6, 9, 7, 12]])
+
+    >>> np.ptp(x, axis=1)
+    array([8, 6])
+
+    >>> np.ptp(x, axis=0)
+    array([2, 0, 5, 2])
+
+    >>> np.ptp(x)
+    10
+
+    This example shows that a negative value can be returned when
+    the input is an array of signed integers.
+
+    >>> y = np.array([[1, 127],
+    ...               [0, 127],
+    ...               [-1, 127],
+    ...               [-2, 127]], dtype=np.int8)
+    >>> np.ptp(y, axis=1)
+    array([ 126,  127, -128, -127], dtype=int8)
+
+    A work-around is to use the `view()` method to view the result as
+    unsigned integers with the same bit width:
+
+    >>> np.ptp(y, axis=1).view(np.uint8)
+    array([126, 127, 128, 129], dtype=uint8)
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    return _methods._ptp(a, axis=axis, out=out, **kwargs)
+
+
+def _max_dispatcher(a, axis=None, out=None, keepdims=None, initial=None,
+                    where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_max_dispatcher)
+@set_module('numpy')
+def max(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+         where=np._NoValue):
+    """
+    Return the maximum of an array or maximum along an axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which to operate.  By default, flattened input is
+        used. If this is a tuple of ints, the maximum is selected over
+        multiple axes, instead of a single axis or all the axes as before.
+
+    out : ndarray, optional
+        Alternative output array in which to place the result.  Must
+        be of the same shape and buffer length as the expected output.
+        See :ref:`ufuncs-output-type` for more details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the ``max`` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    initial : scalar, optional
+        The minimum value of an output element. Must be present to allow
+        computation on empty slice. See `~numpy.ufunc.reduce` for details.
+
+    where : array_like of bool, optional
+        Elements to compare for the maximum. See `~numpy.ufunc.reduce`
+        for details.
+
+    Returns
+    -------
+    max : ndarray or scalar
+        Maximum of `a`. If `axis` is None, the result is a scalar value.
+        If `axis` is an int, the result is an array of dimension
+        ``a.ndim - 1``. If `axis` is a tuple, the result is an array of
+        dimension ``a.ndim - len(axis)``.
+
+    See Also
+    --------
+    amin :
+        The minimum value of an array along a given axis, propagating any NaNs.
+    nanmax :
+        The maximum value of an array along a given axis, ignoring any NaNs.
+    maximum :
+        Element-wise maximum of two arrays, propagating any NaNs.
+    fmax :
+        Element-wise maximum of two arrays, ignoring any NaNs.
+    argmax :
+        Return the indices of the maximum values.
+
+    nanmin, minimum, fmin
+
+    Notes
+    -----
+    NaN values are propagated, that is if at least one item is NaN, the
+    corresponding max value will be NaN as well. To ignore NaN values
+    (MATLAB behavior), please use nanmax.
+
+    Don't use `~numpy.max` for element-wise comparison of 2 arrays; when
+    ``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than
+    ``max(a, axis=0)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.arange(4).reshape((2,2))
+    >>> a
+    array([[0, 1],
+           [2, 3]])
+    >>> np.max(a)           # Maximum of the flattened array
+    3
+    >>> np.max(a, axis=0)   # Maxima along the first axis
+    array([2, 3])
+    >>> np.max(a, axis=1)   # Maxima along the second axis
+    array([1, 3])
+    >>> np.max(a, where=[False, True], initial=-1, axis=0)
+    array([-1,  3])
+    >>> b = np.arange(5, dtype=float)
+    >>> b[2] = np.nan
+    >>> np.max(b)
+    np.float64(nan)
+    >>> np.max(b, where=~np.isnan(b), initial=-1)
+    4.0
+    >>> np.nanmax(b)
+    4.0
+
+    You can use an initial value to compute the maximum of an empty slice, or
+    to initialize it to a different value:
+
+    >>> np.max([[-50], [10]], axis=-1, initial=0)
+    array([ 0, 10])
+
+    Notice that the initial value is used as one of the elements for which the
+    maximum is determined, unlike for the default argument Python's max
+    function, which is only used for empty iterables.
+
+    >>> np.max([5], initial=6)
+    6
+    >>> max([5], default=6)
+    5
+    """
+    return _wrapreduction(a, np.maximum, 'max', axis, None, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+@array_function_dispatch(_max_dispatcher)
+def amax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+         where=np._NoValue):
+    """
+    Return the maximum of an array or maximum along an axis.
+
+    `amax` is an alias of `~numpy.max`.
+
+    See Also
+    --------
+    max : alias of this function
+    ndarray.max : equivalent method
+    """
+    return _wrapreduction(a, np.maximum, 'max', axis, None, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+def _min_dispatcher(a, axis=None, out=None, keepdims=None, initial=None,
+                    where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_min_dispatcher)
+def min(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+        where=np._NoValue):
+    """
+    Return the minimum of an array or minimum along an axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which to operate.  By default, flattened input is
+        used.
+
+        If this is a tuple of ints, the minimum is selected over multiple axes,
+        instead of a single axis or all the axes as before.
+    out : ndarray, optional
+        Alternative output array in which to place the result.  Must
+        be of the same shape and buffer length as the expected output.
+        See :ref:`ufuncs-output-type` for more details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the ``min`` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    initial : scalar, optional
+        The maximum value of an output element. Must be present to allow
+        computation on empty slice. See `~numpy.ufunc.reduce` for details.
+
+    where : array_like of bool, optional
+        Elements to compare for the minimum. See `~numpy.ufunc.reduce`
+        for details.
+
+    Returns
+    -------
+    min : ndarray or scalar
+        Minimum of `a`. If `axis` is None, the result is a scalar value.
+        If `axis` is an int, the result is an array of dimension
+        ``a.ndim - 1``.  If `axis` is a tuple, the result is an array of
+        dimension ``a.ndim - len(axis)``.
+
+    See Also
+    --------
+    amax :
+        The maximum value of an array along a given axis, propagating any NaNs.
+    nanmin :
+        The minimum value of an array along a given axis, ignoring any NaNs.
+    minimum :
+        Element-wise minimum of two arrays, propagating any NaNs.
+    fmin :
+        Element-wise minimum of two arrays, ignoring any NaNs.
+    argmin :
+        Return the indices of the minimum values.
+
+    nanmax, maximum, fmax
+
+    Notes
+    -----
+    NaN values are propagated, that is if at least one item is NaN, the
+    corresponding min value will be NaN as well. To ignore NaN values
+    (MATLAB behavior), please use nanmin.
+
+    Don't use `~numpy.min` for element-wise comparison of 2 arrays; when
+    ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than
+    ``min(a, axis=0)``.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.arange(4).reshape((2,2))
+    >>> a
+    array([[0, 1],
+           [2, 3]])
+    >>> np.min(a)           # Minimum of the flattened array
+    0
+    >>> np.min(a, axis=0)   # Minima along the first axis
+    array([0, 1])
+    >>> np.min(a, axis=1)   # Minima along the second axis
+    array([0, 2])
+    >>> np.min(a, where=[False, True], initial=10, axis=0)
+    array([10,  1])
+
+    >>> b = np.arange(5, dtype=float)
+    >>> b[2] = np.nan
+    >>> np.min(b)
+    np.float64(nan)
+    >>> np.min(b, where=~np.isnan(b), initial=10)
+    0.0
+    >>> np.nanmin(b)
+    0.0
+
+    >>> np.min([[-50], [10]], axis=-1, initial=0)
+    array([-50,   0])
+
+    Notice that the initial value is used as one of the elements for which the
+    minimum is determined, unlike for the default argument Python's max
+    function, which is only used for empty iterables.
+
+    Notice that this isn't the same as Python's ``default`` argument.
+
+    >>> np.min([6], initial=5)
+    5
+    >>> min([6], default=5)
+    6
+    """
+    return _wrapreduction(a, np.minimum, 'min', axis, None, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+@array_function_dispatch(_min_dispatcher)
+def amin(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+         where=np._NoValue):
+    """
+    Return the minimum of an array or minimum along an axis.
+
+    `amin` is an alias of `~numpy.min`.
+
+    See Also
+    --------
+    min : alias of this function
+    ndarray.min : equivalent method
+    """
+    return _wrapreduction(a, np.minimum, 'min', axis, None, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+def _prod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                     initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_prod_dispatcher)
+def prod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+         initial=np._NoValue, where=np._NoValue):
+    """
+    Return the product of array elements over a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which a product is performed.  The default,
+        axis=None, will calculate the product of all the elements in the
+        input array. If axis is negative it counts from the last to the
+        first axis.
+
+        If axis is a tuple of ints, a product is performed on all of the
+        axes specified in the tuple instead of a single axis or all the
+        axes as before.
+    dtype : dtype, optional
+        The type of the returned array, as well as of the accumulator in
+        which the elements are multiplied.  The dtype of `a` is used by
+        default unless `a` has an integer dtype of less precision than the
+        default platform integer.  In that case, if `a` is signed then the
+        platform integer is used while if `a` is unsigned then an unsigned
+        integer of the same precision as the platform integer is used.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must have
+        the same shape as the expected output, but the type of the output
+        values will be cast if necessary.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left in the
+        result as dimensions with size one. With this option, the result
+        will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `prod` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+    initial : scalar, optional
+        The starting value for this product. See `~numpy.ufunc.reduce`
+        for details.
+    where : array_like of bool, optional
+        Elements to include in the product. See `~numpy.ufunc.reduce`
+        for details.
+
+    Returns
+    -------
+    product_along_axis : ndarray, see `dtype` parameter above.
+        An array shaped as `a` but with the specified axis removed.
+        Returns a reference to `out` if specified.
+
+    See Also
+    --------
+    ndarray.prod : equivalent method
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.  That means that, on a 32-bit platform:
+
+    >>> x = np.array([536870910, 536870910, 536870910, 536870910])
+    >>> np.prod(x)
+    16 # may vary
+
+    The product of an empty array is the neutral element 1:
+
+    >>> np.prod([])
+    1.0
+
+    Examples
+    --------
+    By default, calculate the product of all elements:
+
+    >>> import numpy as np
+    >>> np.prod([1.,2.])
+    2.0
+
+    Even when the input array is two-dimensional:
+
+    >>> a = np.array([[1., 2.], [3., 4.]])
+    >>> np.prod(a)
+    24.0
+
+    But we can also specify the axis over which to multiply:
+
+    >>> np.prod(a, axis=1)
+    array([  2.,  12.])
+    >>> np.prod(a, axis=0)
+    array([3., 8.])
+
+    Or select specific elements to include:
+
+    >>> np.prod([1., np.nan, 3.], where=[True, False, True])
+    3.0
+
+    If the type of `x` is unsigned, then the output type is
+    the unsigned platform integer:
+
+    >>> x = np.array([1, 2, 3], dtype=np.uint8)
+    >>> np.prod(x).dtype == np.uint
+    True
+
+    If `x` is of a signed integer type, then the output type
+    is the default platform integer:
+
+    >>> x = np.array([1, 2, 3], dtype=np.int8)
+    >>> np.prod(x).dtype == int
+    True
+
+    You can also start the product with a value other than one:
+
+    >>> np.prod([1, 2], initial=5)
+    10
+    """
+    return _wrapreduction(a, np.multiply, 'prod', axis, dtype, out,
+                          keepdims=keepdims, initial=initial, where=where)
+
+
+def _cumprod_dispatcher(a, axis=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_cumprod_dispatcher)
+def cumprod(a, axis=None, dtype=None, out=None):
+    """
+    Return the cumulative product of elements along a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the cumulative product is computed.  By default
+        the input is flattened.
+    dtype : dtype, optional
+        Type of the returned array, as well as of the accumulator in which
+        the elements are multiplied.  If *dtype* is not specified, it
+        defaults to the dtype of `a`, unless `a` has an integer dtype with
+        a precision less than that of the default platform integer.  In
+        that case, the default platform integer is used instead.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must
+        have the same shape and buffer length as the expected output
+        but the type of the resulting values will be cast if necessary.
+
+    Returns
+    -------
+    cumprod : ndarray
+        A new array holding the result is returned unless `out` is
+        specified, in which case a reference to out is returned.
+
+    See Also
+    --------
+    cumulative_prod : Array API compatible alternative for ``cumprod``.
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    Arithmetic is modular when using integer types, and no error is
+    raised on overflow.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([1,2,3])
+    >>> np.cumprod(a) # intermediate results 1, 1*2
+    ...               # total product 1*2*3 = 6
+    array([1, 2, 6])
+    >>> a = np.array([[1, 2, 3], [4, 5, 6]])
+    >>> np.cumprod(a, dtype=float) # specify type of output
+    array([   1.,    2.,    6.,   24.,  120.,  720.])
+
+    The cumulative product for each column (i.e., over the rows) of `a`:
+
+    >>> np.cumprod(a, axis=0)
+    array([[ 1,  2,  3],
+           [ 4, 10, 18]])
+
+    The cumulative product for each row (i.e. over the columns) of `a`:
+
+    >>> np.cumprod(a,axis=1)
+    array([[  1,   2,   6],
+           [  4,  20, 120]])
+
+    """
+    return _wrapfunc(a, 'cumprod', axis=axis, dtype=dtype, out=out)
+
+
+def _ndim_dispatcher(a):
+    return (a,)
+
+
+@array_function_dispatch(_ndim_dispatcher)
+def ndim(a):
+    """
+    Return the number of dimensions of an array.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.  If it is not already an ndarray, a conversion is
+        attempted.
+
+    Returns
+    -------
+    number_of_dimensions : int
+        The number of dimensions in `a`.  Scalars are zero-dimensional.
+
+    See Also
+    --------
+    ndarray.ndim : equivalent method
+    shape : dimensions of array
+    ndarray.shape : dimensions of array
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.ndim([[1,2,3],[4,5,6]])
+    2
+    >>> np.ndim(np.array([[1,2,3],[4,5,6]]))
+    2
+    >>> np.ndim(1)
+    0
+
+    """
+    try:
+        return a.ndim
+    except AttributeError:
+        return asarray(a).ndim
+
+
+def _size_dispatcher(a, axis=None):
+    return (a,)
+
+
+@array_function_dispatch(_size_dispatcher)
+def size(a, axis=None):
+    """
+    Return the number of elements along a given axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    axis : int, optional
+        Axis along which the elements are counted.  By default, give
+        the total number of elements.
+
+    Returns
+    -------
+    element_count : int
+        Number of elements along the specified axis.
+
+    See Also
+    --------
+    shape : dimensions of array
+    ndarray.shape : dimensions of array
+    ndarray.size : number of elements in array
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1,2,3],[4,5,6]])
+    >>> np.size(a)
+    6
+    >>> np.size(a,1)
+    3
+    >>> np.size(a,0)
+    2
+
+    """
+    if axis is None:
+        try:
+            return a.size
+        except AttributeError:
+            return asarray(a).size
+    else:
+        try:
+            return a.shape[axis]
+        except AttributeError:
+            return asarray(a).shape[axis]
+
+
+def _round_dispatcher(a, decimals=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_round_dispatcher)
+def round(a, decimals=0, out=None):
+    """
+    Evenly round to the given number of decimals.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+    decimals : int, optional
+        Number of decimal places to round to (default: 0).  If
+        decimals is negative, it specifies the number of positions to
+        the left of the decimal point.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must have
+        the same shape as the expected output, but the type of the output
+        values will be cast if necessary. See :ref:`ufuncs-output-type`
+        for more details.
+
+    Returns
+    -------
+    rounded_array : ndarray
+        An array of the same type as `a`, containing the rounded values.
+        Unless `out` was specified, a new array is created.  A reference to
+        the result is returned.
+
+        The real and imaginary parts of complex numbers are rounded
+        separately.  The result of rounding a float is a float.
+
+    See Also
+    --------
+    ndarray.round : equivalent method
+    around : an alias for this function
+    ceil, fix, floor, rint, trunc
+
+
+    Notes
+    -----
+    For values exactly halfway between rounded decimal values, NumPy
+    rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0,
+    -0.5 and 0.5 round to 0.0, etc.
+
+    ``np.round`` uses a fast but sometimes inexact algorithm to round
+    floating-point datatypes. For positive `decimals` it is equivalent to
+    ``np.true_divide(np.rint(a * 10**decimals), 10**decimals)``, which has
+    error due to the inexact representation of decimal fractions in the IEEE
+    floating point standard [1]_ and errors introduced when scaling by powers
+    of ten. For instance, note the extra "1" in the following:
+
+        >>> np.round(56294995342131.5, 3)
+        56294995342131.51
+
+    If your goal is to print such values with a fixed number of decimals, it is
+    preferable to use numpy's float printing routines to limit the number of
+    printed decimals:
+
+        >>> np.format_float_positional(56294995342131.5, precision=3)
+        '56294995342131.5'
+
+    The float printing routines use an accurate but much more computationally
+    demanding algorithm to compute the number of digits after the decimal
+    point.
+
+    Alternatively, Python's builtin `round` function uses a more accurate
+    but slower algorithm for 64-bit floating point values:
+
+        >>> round(56294995342131.5, 3)
+        56294995342131.5
+        >>> np.round(16.055, 2), round(16.055, 2)  # equals 16.0549999999999997
+        (16.06, 16.05)
+
+
+    References
+    ----------
+    .. [1] "Lecture Notes on the Status of IEEE 754", William Kahan,
+           https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.round([0.37, 1.64])
+    array([0., 2.])
+    >>> np.round([0.37, 1.64], decimals=1)
+    array([0.4, 1.6])
+    >>> np.round([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
+    array([0., 2., 2., 4., 4.])
+    >>> np.round([1,2,3,11], decimals=1) # ndarray of ints is returned
+    array([ 1,  2,  3, 11])
+    >>> np.round([1,2,3,11], decimals=-1)
+    array([ 0,  0,  0, 10])
+
+    """
+    return _wrapfunc(a, 'round', decimals=decimals, out=out)
+
+
+@array_function_dispatch(_round_dispatcher)
+def around(a, decimals=0, out=None):
+    """
+    Round an array to the given number of decimals.
+
+    `around` is an alias of `~numpy.round`.
+
+    See Also
+    --------
+    ndarray.round : equivalent method
+    round : alias for this function
+    ceil, fix, floor, rint, trunc
+
+    """
+    return _wrapfunc(a, 'round', decimals=decimals, out=out)
+
+
+def _mean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None, *,
+                     where=None):
+    return (a, where, out)
+
+
+@array_function_dispatch(_mean_dispatcher)
+def mean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue, *,
+         where=np._NoValue):
+    """
+    Compute the arithmetic mean along the specified axis.
+
+    Returns the average of the array elements.  The average is taken over
+    the flattened array by default, otherwise over the specified axis.
+    `float64` intermediate and return values are used for integer inputs.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose mean is desired. If `a` is not an
+        array, a conversion is attempted.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which the means are computed. The default is to
+        compute the mean of the flattened array.
+
+        If this is a tuple of ints, a mean is performed over multiple axes,
+        instead of a single axis or all the axes as before.
+    dtype : data-type, optional
+        Type to use in computing the mean.  For integer inputs, the default
+        is `float64`; for floating point inputs, it is the same as the
+        input dtype.
+    out : ndarray, optional
+        Alternate output array in which to place the result.  The default
+        is ``None``; if provided, it must have the same shape as the
+        expected output, but the type will be cast if necessary.
+        See :ref:`ufuncs-output-type` for more details.
+        See :ref:`ufuncs-output-type` for more details.
+
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `mean` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+
+    where : array_like of bool, optional
+        Elements to include in the mean. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    m : ndarray, see dtype parameter above
+        If `out=None`, returns a new array containing the mean values,
+        otherwise a reference to the output array is returned.
+
+    See Also
+    --------
+    average : Weighted average
+    std, var, nanmean, nanstd, nanvar
+
+    Notes
+    -----
+    The arithmetic mean is the sum of the elements along the axis divided
+    by the number of elements.
+
+    Note that for floating-point input, the mean is computed using the
+    same precision the input has.  Depending on the input data, this can
+    cause the results to be inaccurate, especially for `float32` (see
+    example below).  Specifying a higher-precision accumulator using the
+    `dtype` keyword can alleviate this issue.
+
+    By default, `float16` results are computed using `float32` intermediates
+    for extra precision.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> np.mean(a)
+    2.5
+    >>> np.mean(a, axis=0)
+    array([2., 3.])
+    >>> np.mean(a, axis=1)
+    array([1.5, 3.5])
+
+    In single precision, `mean` can be inaccurate:
+
+    >>> a = np.zeros((2, 512*512), dtype=np.float32)
+    >>> a[0, :] = 1.0
+    >>> a[1, :] = 0.1
+    >>> np.mean(a)
+    np.float32(0.54999924)
+
+    Computing the mean in float64 is more accurate:
+
+    >>> np.mean(a, dtype=np.float64)
+    0.55000000074505806 # may vary
+
+    Computing the mean in timedelta64 is available:
+
+    >>> b = np.array([1, 3], dtype="timedelta64[D]")
+    >>> np.mean(b)
+    np.timedelta64(2,'D')
+
+    Specifying a where argument:
+
+    >>> a = np.array([[5, 9, 13], [14, 10, 12], [11, 15, 19]])
+    >>> np.mean(a)
+    12.0
+    >>> np.mean(a, where=[[True], [False], [False]])
+    9.0
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if where is not np._NoValue:
+        kwargs['where'] = where
+    if type(a) is not mu.ndarray:
+        try:
+            mean = a.mean
+        except AttributeError:
+            pass
+        else:
+            return mean(axis=axis, dtype=dtype, out=out, **kwargs)
+
+    return _methods._mean(a, axis=axis, dtype=dtype,
+                          out=out, **kwargs)
+
+
+def _std_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
+                    keepdims=None, *, where=None, mean=None, correction=None):
+    return (a, where, out, mean)
+
+
+@array_function_dispatch(_std_dispatcher)
+def std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue, *,
+        where=np._NoValue, mean=np._NoValue, correction=np._NoValue):
+    r"""
+    Compute the standard deviation along the specified axis.
+
+    Returns the standard deviation, a measure of the spread of a distribution,
+    of the array elements. The standard deviation is computed for the
+    flattened array by default, otherwise over the specified axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Calculate the standard deviation of these values.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which the standard deviation is computed. The
+        default is to compute the standard deviation of the flattened array.
+        If this is a tuple of ints, a standard deviation is performed over
+        multiple axes, instead of a single axis or all the axes as before.
+    dtype : dtype, optional
+        Type to use in computing the standard deviation. For arrays of
+        integer type the default is float64, for arrays of float types it is
+        the same as the array type.
+    out : ndarray, optional
+        Alternative output array in which to place the result. It must have
+        the same shape as the expected output but the type (of the calculated
+        values) will be cast if necessary.
+        See :ref:`ufuncs-output-type` for more details.
+    ddof : {int, float}, optional
+        Means Delta Degrees of Freedom.  The divisor used in calculations
+        is ``N - ddof``, where ``N`` represents the number of elements.
+        By default `ddof` is zero. See Notes for details about use of `ddof`.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `std` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+    where : array_like of bool, optional
+        Elements to include in the standard deviation.
+        See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.20.0
+
+    mean : array_like, optional
+        Provide the mean to prevent its recalculation. The mean should have
+        a shape as if it was calculated with ``keepdims=True``.
+        The axis for the calculation of the mean should be the same as used in
+        the call to this std function.
+
+        .. versionadded:: 2.0.0
+
+    correction : {int, float}, optional
+        Array API compatible name for the ``ddof`` parameter. Only one of them
+        can be provided at the same time.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    standard_deviation : ndarray, see dtype parameter above.
+        If `out` is None, return a new array containing the standard deviation,
+        otherwise return a reference to the output array.
+
+    See Also
+    --------
+    var, mean, nanmean, nanstd, nanvar
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    There are several common variants of the array standard deviation
+    calculation. Assuming the input `a` is a one-dimensional NumPy array
+    and ``mean`` is either provided as an argument or computed as
+    ``a.mean()``, NumPy computes the standard deviation of an array as::
+
+        N = len(a)
+        d2 = abs(a - mean)**2  # abs is for complex `a`
+        var = d2.sum() / (N - ddof)  # note use of `ddof`
+        std = var**0.5
+
+    Different values of the argument `ddof` are useful in different
+    contexts. NumPy's default ``ddof=0`` corresponds with the expression:
+
+    .. math::
+
+        \sqrt{\frac{\sum_i{|a_i - \bar{a}|^2 }}{N}}
+
+    which is sometimes called the "population standard deviation" in the field
+    of statistics because it applies the definition of standard deviation to
+    `a` as if `a` were a complete population of possible observations.
+
+    Many other libraries define the standard deviation of an array
+    differently, e.g.:
+
+    .. math::
+
+        \sqrt{\frac{\sum_i{|a_i - \bar{a}|^2 }}{N - 1}}
+
+    In statistics, the resulting quantity is sometimes called the "sample
+    standard deviation" because if `a` is a random sample from a larger
+    population, this calculation provides the square root of an unbiased
+    estimate of the variance of the population. The use of :math:`N-1` in the
+    denominator is often called "Bessel's correction" because it corrects for
+    bias (toward lower values) in the variance estimate introduced when the
+    sample mean of `a` is used in place of the true mean of the population.
+    The resulting estimate of the standard deviation is still biased, but less
+    than it would have been without the correction. For this quantity, use
+    ``ddof=1``.
+
+    Note that, for complex numbers, `std` takes the absolute
+    value before squaring, so that the result is always real and nonnegative.
+
+    For floating-point input, the standard deviation is computed using the same
+    precision the input has. Depending on the input data, this can cause
+    the results to be inaccurate, especially for float32 (see example below).
+    Specifying a higher-accuracy accumulator using the `dtype` keyword can
+    alleviate this issue.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> np.std(a)
+    1.1180339887498949 # may vary
+    >>> np.std(a, axis=0)
+    array([1.,  1.])
+    >>> np.std(a, axis=1)
+    array([0.5,  0.5])
+
+    In single precision, std() can be inaccurate:
+
+    >>> a = np.zeros((2, 512*512), dtype=np.float32)
+    >>> a[0, :] = 1.0
+    >>> a[1, :] = 0.1
+    >>> np.std(a)
+    np.float32(0.45000005)
+
+    Computing the standard deviation in float64 is more accurate:
+
+    >>> np.std(a, dtype=np.float64)
+    0.44999999925494177 # may vary
+
+    Specifying a where argument:
+
+    >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
+    >>> np.std(a)
+    2.614064523559687 # may vary
+    >>> np.std(a, where=[[True], [True], [False]])
+    2.0
+
+    Using the mean keyword to save computation time:
+
+    >>> import numpy as np
+    >>> from timeit import timeit
+    >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
+    >>> mean = np.mean(a, axis=1, keepdims=True)
+    >>>
+    >>> g = globals()
+    >>> n = 10000
+    >>> t1 = timeit("std = np.std(a, axis=1, mean=mean)", globals=g, number=n)
+    >>> t2 = timeit("std = np.std(a, axis=1)", globals=g, number=n)
+    >>> print(f'Percentage execution time saved {100*(t2-t1)/t2:.0f}%')
+    #doctest: +SKIP
+    Percentage execution time saved 30%
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if where is not np._NoValue:
+        kwargs['where'] = where
+    if mean is not np._NoValue:
+        kwargs['mean'] = mean
+
+    if correction != np._NoValue:
+        if ddof != 0:
+            raise ValueError(
+                "ddof and correction can't be provided simultaneously."
+            )
+        else:
+            ddof = correction
+
+    if type(a) is not mu.ndarray:
+        try:
+            std = a.std
+        except AttributeError:
+            pass
+        else:
+            return std(axis=axis, dtype=dtype, out=out, ddof=ddof, **kwargs)
+
+    return _methods._std(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
+                         **kwargs)
+
+
+def _var_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
+                    keepdims=None, *, where=None, mean=None, correction=None):
+    return (a, where, out, mean)
+
+
+@array_function_dispatch(_var_dispatcher)
+def var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue, *,
+        where=np._NoValue, mean=np._NoValue, correction=np._NoValue):
+    r"""
+    Compute the variance along the specified axis.
+
+    Returns the variance of the array elements, a measure of the spread of a
+    distribution.  The variance is computed for the flattened array by
+    default, otherwise over the specified axis.
+
+    Parameters
+    ----------
+    a : array_like
+        Array containing numbers whose variance is desired.  If `a` is not an
+        array, a conversion is attempted.
+    axis : None or int or tuple of ints, optional
+        Axis or axes along which the variance is computed.  The default is to
+        compute the variance of the flattened array.
+        If this is a tuple of ints, a variance is performed over multiple axes,
+        instead of a single axis or all the axes as before.
+    dtype : data-type, optional
+        Type to use in computing the variance.  For arrays of integer type
+        the default is `float64`; for arrays of float types it is the same as
+        the array type.
+    out : ndarray, optional
+        Alternate output array in which to place the result.  It must have
+        the same shape as the expected output, but the type is cast if
+        necessary.
+    ddof : {int, float}, optional
+        "Delta Degrees of Freedom": the divisor used in the calculation is
+        ``N - ddof``, where ``N`` represents the number of elements. By
+        default `ddof` is zero. See notes for details about use of `ddof`.
+    keepdims : bool, optional
+        If this is set to True, the axes which are reduced are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+        If the default value is passed, then `keepdims` will not be
+        passed through to the `var` method of sub-classes of
+        `ndarray`, however any non-default value will be.  If the
+        sub-class' method does not implement `keepdims` any
+        exceptions will be raised.
+    where : array_like of bool, optional
+        Elements to include in the variance. See `~numpy.ufunc.reduce` for
+        details.
+
+        .. versionadded:: 1.20.0
+
+    mean : array like, optional
+        Provide the mean to prevent its recalculation. The mean should have
+        a shape as if it was calculated with ``keepdims=True``.
+        The axis for the calculation of the mean should be the same as used in
+        the call to this var function.
+
+        .. versionadded:: 2.0.0
+
+    correction : {int, float}, optional
+        Array API compatible name for the ``ddof`` parameter. Only one of them
+        can be provided at the same time.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    variance : ndarray, see dtype parameter above
+        If ``out=None``, returns a new array containing the variance;
+        otherwise, a reference to the output array is returned.
+
+    See Also
+    --------
+    std, mean, nanmean, nanstd, nanvar
+    :ref:`ufuncs-output-type`
+
+    Notes
+    -----
+    There are several common variants of the array variance calculation.
+    Assuming the input `a` is a one-dimensional NumPy array and ``mean`` is
+    either provided as an argument or computed as ``a.mean()``, NumPy
+    computes the variance of an array as::
+
+        N = len(a)
+        d2 = abs(a - mean)**2  # abs is for complex `a`
+        var = d2.sum() / (N - ddof)  # note use of `ddof`
+
+    Different values of the argument `ddof` are useful in different
+    contexts. NumPy's default ``ddof=0`` corresponds with the expression:
+
+    .. math::
+
+        \frac{\sum_i{|a_i - \bar{a}|^2 }}{N}
+
+    which is sometimes called the "population variance" in the field of
+    statistics because it applies the definition of variance to `a` as if `a`
+    were a complete population of possible observations.
+
+    Many other libraries define the variance of an array differently, e.g.:
+
+    .. math::
+
+        \frac{\sum_i{|a_i - \bar{a}|^2}}{N - 1}
+
+    In statistics, the resulting quantity is sometimes called the "sample
+    variance" because if `a` is a random sample from a larger population,
+    this calculation provides an unbiased estimate of the variance of the
+    population.  The use of :math:`N-1` in the denominator is often called
+    "Bessel's correction" because it corrects for bias (toward lower values)
+    in the variance estimate introduced when the sample mean of `a` is used
+    in place of the true mean of the population. For this quantity, use
+    ``ddof=1``.
+
+    Note that for complex numbers, the absolute value is taken before
+    squaring, so that the result is always real and nonnegative.
+
+    For floating-point input, the variance is computed using the same
+    precision the input has.  Depending on the input data, this can cause
+    the results to be inaccurate, especially for `float32` (see example
+    below).  Specifying a higher-accuracy accumulator using the ``dtype``
+    keyword can alleviate this issue.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> np.var(a)
+    1.25
+    >>> np.var(a, axis=0)
+    array([1.,  1.])
+    >>> np.var(a, axis=1)
+    array([0.25,  0.25])
+
+    In single precision, var() can be inaccurate:
+
+    >>> a = np.zeros((2, 512*512), dtype=np.float32)
+    >>> a[0, :] = 1.0
+    >>> a[1, :] = 0.1
+    >>> np.var(a)
+    np.float32(0.20250003)
+
+    Computing the variance in float64 is more accurate:
+
+    >>> np.var(a, dtype=np.float64)
+    0.20249999932944759 # may vary
+    >>> ((1-0.55)**2 + (0.1-0.55)**2)/2
+    0.2025
+
+    Specifying a where argument:
+
+    >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
+    >>> np.var(a)
+    6.833333333333333 # may vary
+    >>> np.var(a, where=[[True], [True], [False]])
+    4.0
+
+    Using the mean keyword to save computation time:
+
+    >>> import numpy as np
+    >>> from timeit import timeit
+    >>>
+    >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
+    >>> mean = np.mean(a, axis=1, keepdims=True)
+    >>>
+    >>> g = globals()
+    >>> n = 10000
+    >>> t1 = timeit("var = np.var(a, axis=1, mean=mean)", globals=g, number=n)
+    >>> t2 = timeit("var = np.var(a, axis=1)", globals=g, number=n)
+    >>> print(f'Percentage execution time saved {100*(t2-t1)/t2:.0f}%')
+    #doctest: +SKIP
+    Percentage execution time saved 32%
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if where is not np._NoValue:
+        kwargs['where'] = where
+    if mean is not np._NoValue:
+        kwargs['mean'] = mean
+
+    if correction != np._NoValue:
+        if ddof != 0:
+            raise ValueError(
+                "ddof and correction can't be provided simultaneously."
+            )
+        else:
+            ddof = correction
+
+    if type(a) is not mu.ndarray:
+        try:
+            var = a.var
+
+        except AttributeError:
+            pass
+        else:
+            return var(axis=axis, dtype=dtype, out=out, ddof=ddof, **kwargs)
+
+    return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
+                         **kwargs)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.pyi
new file mode 100644
index 0000000..f0f8309
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.pyi
@@ -0,0 +1,1750 @@
+# ruff: noqa: ANN401
+from collections.abc import Sequence
+from typing import (
+    Any,
+    Literal,
+    Never,
+    Protocol,
+    SupportsIndex,
+    TypeAlias,
+    TypeVar,
+    overload,
+    type_check_only,
+)
+
+from _typeshed import Incomplete
+from typing_extensions import deprecated
+
+import numpy as np
+from numpy import (
+    _AnyShapeT,
+    _CastingKind,
+    _ModeKind,
+    _OrderACF,
+    _OrderKACF,
+    _PartitionKind,
+    _SortKind,
+    _SortSide,
+    complexfloating,
+    float16,
+    floating,
+    generic,
+    int64,
+    int_,
+    intp,
+    object_,
+    timedelta64,
+    uint64,
+)
+from numpy._globals import _NoValueType
+from numpy._typing import (
+    ArrayLike,
+    DTypeLike,
+    NDArray,
+    _AnyShape,
+    _ArrayLike,
+    _ArrayLikeBool_co,
+    _ArrayLikeComplex_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeInt,
+    _ArrayLikeInt_co,
+    _ArrayLikeObject_co,
+    _ArrayLikeUInt_co,
+    _BoolLike_co,
+    _ComplexLike_co,
+    _DTypeLike,
+    _IntLike_co,
+    _NestedSequence,
+    _NumberLike_co,
+    _ScalarLike_co,
+    _ShapeLike,
+)
+
+__all__ = [
+    "all",
+    "amax",
+    "amin",
+    "any",
+    "argmax",
+    "argmin",
+    "argpartition",
+    "argsort",
+    "around",
+    "choose",
+    "clip",
+    "compress",
+    "cumprod",
+    "cumsum",
+    "cumulative_prod",
+    "cumulative_sum",
+    "diagonal",
+    "mean",
+    "max",
+    "min",
+    "matrix_transpose",
+    "ndim",
+    "nonzero",
+    "partition",
+    "prod",
+    "ptp",
+    "put",
+    "ravel",
+    "repeat",
+    "reshape",
+    "resize",
+    "round",
+    "searchsorted",
+    "shape",
+    "size",
+    "sort",
+    "squeeze",
+    "std",
+    "sum",
+    "swapaxes",
+    "take",
+    "trace",
+    "transpose",
+    "var",
+]
+
+_ScalarT = TypeVar("_ScalarT", bound=generic)
+_NumberOrObjectT = TypeVar("_NumberOrObjectT", bound=np.number | np.object_)
+_ArrayT = TypeVar("_ArrayT", bound=np.ndarray[Any, Any])
+_ShapeT = TypeVar("_ShapeT", bound=tuple[int, ...])
+_ShapeT_co = TypeVar("_ShapeT_co", bound=tuple[int, ...], covariant=True)
+_BoolOrIntArrayT = TypeVar("_BoolOrIntArrayT", bound=NDArray[np.integer | np.bool])
+
+@type_check_only
+class _SupportsShape(Protocol[_ShapeT_co]):
+    # NOTE: it matters that `self` is positional only
+    @property
+    def shape(self, /) -> _ShapeT_co: ...
+
+# a "sequence" that isn't a string, bytes, bytearray, or memoryview
+_T = TypeVar("_T")
+_PyArray: TypeAlias = list[_T] | tuple[_T, ...]
+# `int` also covers `bool`
+_PyScalar: TypeAlias = complex | bytes | str
+
+@overload
+def take(
+    a: _ArrayLike[_ScalarT],
+    indices: _IntLike_co,
+    axis: None = ...,
+    out: None = ...,
+    mode: _ModeKind = ...,
+) -> _ScalarT: ...
+@overload
+def take(
+    a: ArrayLike,
+    indices: _IntLike_co,
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+    mode: _ModeKind = ...,
+) -> Any: ...
+@overload
+def take(
+    a: _ArrayLike[_ScalarT],
+    indices: _ArrayLikeInt_co,
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+    mode: _ModeKind = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def take(
+    a: ArrayLike,
+    indices: _ArrayLikeInt_co,
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+    mode: _ModeKind = ...,
+) -> NDArray[Any]: ...
+@overload
+def take(
+    a: ArrayLike,
+    indices: _ArrayLikeInt_co,
+    axis: SupportsIndex | None,
+    out: _ArrayT,
+    mode: _ModeKind = ...,
+) -> _ArrayT: ...
+@overload
+def take(
+    a: ArrayLike,
+    indices: _ArrayLikeInt_co,
+    axis: SupportsIndex | None = ...,
+    *,
+    out: _ArrayT,
+    mode: _ModeKind = ...,
+) -> _ArrayT: ...
+
+@overload
+def reshape(  # shape: index
+    a: _ArrayLike[_ScalarT],
+    /,
+    shape: SupportsIndex,
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> np.ndarray[tuple[int], np.dtype[_ScalarT]]: ...
+@overload
+def reshape(  # shape: (int, ...) @ _AnyShapeT
+    a: _ArrayLike[_ScalarT],
+    /,
+    shape: _AnyShapeT,
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> np.ndarray[_AnyShapeT, np.dtype[_ScalarT]]: ...
+@overload  # shape: Sequence[index]
+def reshape(
+    a: _ArrayLike[_ScalarT],
+    /,
+    shape: Sequence[SupportsIndex],
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> NDArray[_ScalarT]: ...
+@overload  # shape: index
+def reshape(
+    a: ArrayLike,
+    /,
+    shape: SupportsIndex,
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> np.ndarray[tuple[int], np.dtype]: ...
+@overload
+def reshape(  # shape: (int, ...) @ _AnyShapeT
+    a: ArrayLike,
+    /,
+    shape: _AnyShapeT,
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> np.ndarray[_AnyShapeT, np.dtype]: ...
+@overload  # shape: Sequence[index]
+def reshape(
+    a: ArrayLike,
+    /,
+    shape: Sequence[SupportsIndex],
+    order: _OrderACF = "C",
+    *,
+    copy: bool | None = None,
+) -> NDArray[Any]: ...
+@overload
+@deprecated(
+    "`newshape` keyword argument is deprecated, "
+    "use `shape=...` or pass shape positionally instead. "
+    "(deprecated in NumPy 2.1)",
+)
+def reshape(
+    a: ArrayLike,
+    /,
+    shape: None = None,
+    order: _OrderACF = "C",
+    *,
+    newshape: _ShapeLike,
+    copy: bool | None = None,
+) -> NDArray[Any]: ...
+
+@overload
+def choose(
+    a: _IntLike_co,
+    choices: ArrayLike,
+    out: None = ...,
+    mode: _ModeKind = ...,
+) -> Any: ...
+@overload
+def choose(
+    a: _ArrayLikeInt_co,
+    choices: _ArrayLike[_ScalarT],
+    out: None = ...,
+    mode: _ModeKind = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def choose(
+    a: _ArrayLikeInt_co,
+    choices: ArrayLike,
+    out: None = ...,
+    mode: _ModeKind = ...,
+) -> NDArray[Any]: ...
+@overload
+def choose(
+    a: _ArrayLikeInt_co,
+    choices: ArrayLike,
+    out: _ArrayT,
+    mode: _ModeKind = ...,
+) -> _ArrayT: ...
+
+@overload
+def repeat(
+    a: _ArrayLike[_ScalarT],
+    repeats: _ArrayLikeInt_co,
+    axis: None = None,
+) -> np.ndarray[tuple[int], np.dtype[_ScalarT]]: ...
+@overload
+def repeat(
+    a: _ArrayLike[_ScalarT],
+    repeats: _ArrayLikeInt_co,
+    axis: SupportsIndex,
+) -> NDArray[_ScalarT]: ...
+@overload
+def repeat(
+    a: ArrayLike,
+    repeats: _ArrayLikeInt_co,
+    axis: None = None,
+) -> np.ndarray[tuple[int], np.dtype[Any]]: ...
+@overload
+def repeat(
+    a: ArrayLike,
+    repeats: _ArrayLikeInt_co,
+    axis: SupportsIndex,
+) -> NDArray[Any]: ...
+
+def put(
+    a: NDArray[Any],
+    ind: _ArrayLikeInt_co,
+    v: ArrayLike,
+    mode: _ModeKind = ...,
+) -> None: ...
+
+@overload
+def swapaxes(
+    a: _ArrayLike[_ScalarT],
+    axis1: SupportsIndex,
+    axis2: SupportsIndex,
+) -> NDArray[_ScalarT]: ...
+@overload
+def swapaxes(
+    a: ArrayLike,
+    axis1: SupportsIndex,
+    axis2: SupportsIndex,
+) -> NDArray[Any]: ...
+
+@overload
+def transpose(
+    a: _ArrayLike[_ScalarT],
+    axes: _ShapeLike | None = ...
+) -> NDArray[_ScalarT]: ...
+@overload
+def transpose(
+    a: ArrayLike,
+    axes: _ShapeLike | None = ...
+) -> NDArray[Any]: ...
+
+@overload
+def matrix_transpose(x: _ArrayLike[_ScalarT], /) -> NDArray[_ScalarT]: ...
+@overload
+def matrix_transpose(x: ArrayLike, /) -> NDArray[Any]: ...
+
+#
+@overload
+def partition(
+    a: _ArrayLike[_ScalarT],
+    kth: _ArrayLikeInt,
+    axis: SupportsIndex | None = -1,
+    kind: _PartitionKind = "introselect",
+    order: None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def partition(
+    a: _ArrayLike[np.void],
+    kth: _ArrayLikeInt,
+    axis: SupportsIndex | None = -1,
+    kind: _PartitionKind = "introselect",
+    order: str | Sequence[str] | None = None,
+) -> NDArray[np.void]: ...
+@overload
+def partition(
+    a: ArrayLike,
+    kth: _ArrayLikeInt,
+    axis: SupportsIndex | None = -1,
+    kind: _PartitionKind = "introselect",
+    order: str | Sequence[str] | None = None,
+) -> NDArray[Any]: ...
+
+#
+def argpartition(
+    a: ArrayLike,
+    kth: _ArrayLikeInt,
+    axis: SupportsIndex | None = -1,
+    kind: _PartitionKind = "introselect",
+    order: str | Sequence[str] | None = None,
+) -> NDArray[intp]: ...
+
+#
+@overload
+def sort(
+    a: _ArrayLike[_ScalarT],
+    axis: SupportsIndex | None = ...,
+    kind: _SortKind | None = ...,
+    order: str | Sequence[str] | None = ...,
+    *,
+    stable: bool | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def sort(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    kind: _SortKind | None = ...,
+    order: str | Sequence[str] | None = ...,
+    *,
+    stable: bool | None = ...,
+) -> NDArray[Any]: ...
+
+def argsort(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    kind: _SortKind | None = ...,
+    order: str | Sequence[str] | None = ...,
+    *,
+    stable: bool | None = ...,
+) -> NDArray[intp]: ...
+
+@overload
+def argmax(
+    a: ArrayLike,
+    axis: None = ...,
+    out: None = ...,
+    *,
+    keepdims: Literal[False] = ...,
+) -> intp: ...
+@overload
+def argmax(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+    *,
+    keepdims: bool = ...,
+) -> Any: ...
+@overload
+def argmax(
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    out: _BoolOrIntArrayT,
+    *,
+    keepdims: bool = ...,
+) -> _BoolOrIntArrayT: ...
+@overload
+def argmax(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    *,
+    out: _BoolOrIntArrayT,
+    keepdims: bool = ...,
+) -> _BoolOrIntArrayT: ...
+
+@overload
+def argmin(
+    a: ArrayLike,
+    axis: None = ...,
+    out: None = ...,
+    *,
+    keepdims: Literal[False] = ...,
+) -> intp: ...
+@overload
+def argmin(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+    *,
+    keepdims: bool = ...,
+) -> Any: ...
+@overload
+def argmin(
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    out: _BoolOrIntArrayT,
+    *,
+    keepdims: bool = ...,
+) -> _BoolOrIntArrayT: ...
+@overload
+def argmin(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    *,
+    out: _BoolOrIntArrayT,
+    keepdims: bool = ...,
+) -> _BoolOrIntArrayT: ...
+
+@overload
+def searchsorted(
+    a: ArrayLike,
+    v: _ScalarLike_co,
+    side: _SortSide = ...,
+    sorter: _ArrayLikeInt_co | None = ...,  # 1D int array
+) -> intp: ...
+@overload
+def searchsorted(
+    a: ArrayLike,
+    v: ArrayLike,
+    side: _SortSide = ...,
+    sorter: _ArrayLikeInt_co | None = ...,  # 1D int array
+) -> NDArray[intp]: ...
+
+#
+@overload
+def resize(a: _ArrayLike[_ScalarT], new_shape: SupportsIndex | tuple[SupportsIndex]) -> np.ndarray[tuple[int], np.dtype[_ScalarT]]: ...
+@overload
+def resize(a: _ArrayLike[_ScalarT], new_shape: _AnyShapeT) -> np.ndarray[_AnyShapeT, np.dtype[_ScalarT]]: ...
+@overload
+def resize(a: _ArrayLike[_ScalarT], new_shape: _ShapeLike) -> NDArray[_ScalarT]: ...
+@overload
+def resize(a: ArrayLike, new_shape: SupportsIndex | tuple[SupportsIndex]) -> np.ndarray[tuple[int], np.dtype]: ...
+@overload
+def resize(a: ArrayLike, new_shape: _AnyShapeT) -> np.ndarray[_AnyShapeT, np.dtype]: ...
+@overload
+def resize(a: ArrayLike, new_shape: _ShapeLike) -> NDArray[Any]: ...
+
+@overload
+def squeeze(
+    a: _ScalarT,
+    axis: _ShapeLike | None = ...,
+) -> _ScalarT: ...
+@overload
+def squeeze(
+    a: _ArrayLike[_ScalarT],
+    axis: _ShapeLike | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def squeeze(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def diagonal(
+    a: _ArrayLike[_ScalarT],
+    offset: SupportsIndex = ...,
+    axis1: SupportsIndex = ...,
+    axis2: SupportsIndex = ...,  # >= 2D array
+) -> NDArray[_ScalarT]: ...
+@overload
+def diagonal(
+    a: ArrayLike,
+    offset: SupportsIndex = ...,
+    axis1: SupportsIndex = ...,
+    axis2: SupportsIndex = ...,  # >= 2D array
+) -> NDArray[Any]: ...
+
+@overload
+def trace(
+    a: ArrayLike,  # >= 2D array
+    offset: SupportsIndex = ...,
+    axis1: SupportsIndex = ...,
+    axis2: SupportsIndex = ...,
+    dtype: DTypeLike = ...,
+    out: None = ...,
+) -> Any: ...
+@overload
+def trace(
+    a: ArrayLike,  # >= 2D array
+    offset: SupportsIndex,
+    axis1: SupportsIndex,
+    axis2: SupportsIndex,
+    dtype: DTypeLike,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def trace(
+    a: ArrayLike,  # >= 2D array
+    offset: SupportsIndex = ...,
+    axis1: SupportsIndex = ...,
+    axis2: SupportsIndex = ...,
+    dtype: DTypeLike = ...,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+_Array1D: TypeAlias = np.ndarray[tuple[int], np.dtype[_ScalarT]]
+
+@overload
+def ravel(a: _ArrayLike[_ScalarT], order: _OrderKACF = "C") -> _Array1D[_ScalarT]: ...
+@overload
+def ravel(a: bytes | _NestedSequence[bytes], order: _OrderKACF = "C") -> _Array1D[np.bytes_]: ...
+@overload
+def ravel(a: str | _NestedSequence[str], order: _OrderKACF = "C") -> _Array1D[np.str_]: ...
+@overload
+def ravel(a: bool | _NestedSequence[bool], order: _OrderKACF = "C") -> _Array1D[np.bool]: ...
+@overload
+def ravel(a: int | _NestedSequence[int], order: _OrderKACF = "C") -> _Array1D[np.int_ | np.bool]: ...
+@overload
+def ravel(a: float | _NestedSequence[float], order: _OrderKACF = "C") -> _Array1D[np.float64 | np.int_ | np.bool]: ...
+@overload
+def ravel(
+    a: complex | _NestedSequence[complex],
+    order: _OrderKACF = "C",
+) -> _Array1D[np.complex128 | np.float64 | np.int_ | np.bool]: ...
+@overload
+def ravel(a: ArrayLike, order: _OrderKACF = "C") -> np.ndarray[tuple[int], np.dtype]: ...
+
+def nonzero(a: _ArrayLike[Any]) -> tuple[NDArray[intp], ...]: ...
+
+# this prevents `Any` from being returned with Pyright
+@overload
+def shape(a: _SupportsShape[Never]) -> _AnyShape: ...
+@overload
+def shape(a: _SupportsShape[_ShapeT]) -> _ShapeT: ...
+@overload
+def shape(a: _PyScalar) -> tuple[()]: ...
+# `collections.abc.Sequence` can't be used hesre, since `bytes` and `str` are
+# subtypes of it, which would make the return types incompatible.
+@overload
+def shape(a: _PyArray[_PyScalar]) -> tuple[int]: ...
+@overload
+def shape(a: _PyArray[_PyArray[_PyScalar]]) -> tuple[int, int]: ...
+# this overload will be skipped by typecheckers that don't support PEP 688
+@overload
+def shape(a: memoryview | bytearray) -> tuple[int]: ...
+@overload
+def shape(a: ArrayLike) -> _AnyShape: ...
+
+@overload
+def compress(
+    condition: _ArrayLikeBool_co,  # 1D bool array
+    a: _ArrayLike[_ScalarT],
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def compress(
+    condition: _ArrayLikeBool_co,  # 1D bool array
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+) -> NDArray[Any]: ...
+@overload
+def compress(
+    condition: _ArrayLikeBool_co,  # 1D bool array
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def compress(
+    condition: _ArrayLikeBool_co,  # 1D bool array
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+@overload
+def clip(
+    a: _ScalarT,
+    a_min: ArrayLike | None,
+    a_max: ArrayLike | None,
+    out: None = ...,
+    *,
+    min: ArrayLike | None = ...,
+    max: ArrayLike | None = ...,
+    dtype: None = ...,
+    where: _ArrayLikeBool_co | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    signature: str | tuple[str | None, ...] = ...,
+    casting: _CastingKind = ...,
+) -> _ScalarT: ...
+@overload
+def clip(
+    a: _ScalarLike_co,
+    a_min: ArrayLike | None,
+    a_max: ArrayLike | None,
+    out: None = ...,
+    *,
+    min: ArrayLike | None = ...,
+    max: ArrayLike | None = ...,
+    dtype: None = ...,
+    where: _ArrayLikeBool_co | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    signature: str | tuple[str | None, ...] = ...,
+    casting: _CastingKind = ...,
+) -> Any: ...
+@overload
+def clip(
+    a: _ArrayLike[_ScalarT],
+    a_min: ArrayLike | None,
+    a_max: ArrayLike | None,
+    out: None = ...,
+    *,
+    min: ArrayLike | None = ...,
+    max: ArrayLike | None = ...,
+    dtype: None = ...,
+    where: _ArrayLikeBool_co | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    signature: str | tuple[str | None, ...] = ...,
+    casting: _CastingKind = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def clip(
+    a: ArrayLike,
+    a_min: ArrayLike | None,
+    a_max: ArrayLike | None,
+    out: None = ...,
+    *,
+    min: ArrayLike | None = ...,
+    max: ArrayLike | None = ...,
+    dtype: None = ...,
+    where: _ArrayLikeBool_co | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    signature: str | tuple[str | None, ...] = ...,
+    casting: _CastingKind = ...,
+) -> NDArray[Any]: ...
+@overload
+def clip(
+    a: ArrayLike,
+    a_min: ArrayLike | None,
+    a_max: ArrayLike | None,
+    out: _ArrayT,
+    *,
+    min: ArrayLike | None = ...,
+    max: ArrayLike | None = ...,
+    dtype: DTypeLike = ...,
+    where: _ArrayLikeBool_co | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    signature: str | tuple[str | None, ...] = ...,
+    casting: _CastingKind = ...,
+) -> _ArrayT: ...
+@overload
+def clip(
+    a: ArrayLike,
+    a_min: ArrayLike | None,
+    a_max: ArrayLike | None,
+    out: ArrayLike = ...,
+    *,
+    min: ArrayLike | None = ...,
+    max: ArrayLike | None = ...,
+    dtype: DTypeLike,
+    where: _ArrayLikeBool_co | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    signature: str | tuple[str | None, ...] = ...,
+    casting: _CastingKind = ...,
+) -> Any: ...
+
+@overload
+def sum(
+    a: _ArrayLike[_ScalarT],
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT: ...
+@overload
+def sum(
+    a: _ArrayLike[_ScalarT],
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike = ...,
+    out: None = ...,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> Any: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike,
+    out: _ArrayT,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ArrayT: ...
+@overload
+def sum(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike = ...,
+    *,
+    out: _ArrayT,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ArrayT: ...
+
+# keep in sync with `any`
+@overload
+def all(
+    a: ArrayLike | None,
+    axis: None = None,
+    out: None = None,
+    keepdims: Literal[False, 0] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> np.bool: ...
+@overload
+def all(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None = None,
+    out: None = None,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Incomplete: ...
+@overload
+def all(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None,
+    out: _ArrayT,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def all(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+
+# keep in sync with `all`
+@overload
+def any(
+    a: ArrayLike | None,
+    axis: None = None,
+    out: None = None,
+    keepdims: Literal[False, 0] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> np.bool: ...
+@overload
+def any(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None = None,
+    out: None = None,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Incomplete: ...
+@overload
+def any(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None,
+    out: _ArrayT,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def any(
+    a: ArrayLike | None,
+    axis: int | tuple[int, ...] | None = None,
+    *,
+    out: _ArrayT,
+    keepdims: _BoolLike_co | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+
+#
+@overload
+def cumsum(
+    a: _ArrayLike[_ScalarT],
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+) -> NDArray[Any]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    dtype: DTypeLike = ...,
+    out: None = ...,
+) -> NDArray[Any]: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None,
+    dtype: DTypeLike,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def cumsum(
+    a: ArrayLike,
+    axis: SupportsIndex | None = ...,
+    dtype: DTypeLike = ...,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+@overload
+def cumulative_sum(
+    x: _ArrayLike[_ScalarT],
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumulative_sum(
+    x: ArrayLike,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[Any]: ...
+@overload
+def cumulative_sum(
+    x: ArrayLike,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumulative_sum(
+    x: ArrayLike,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: DTypeLike = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[Any]: ...
+@overload
+def cumulative_sum(
+    x: ArrayLike,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: DTypeLike = ...,
+    out: _ArrayT,
+    include_initial: bool = ...,
+) -> _ArrayT: ...
+
+@overload
+def ptp(
+    a: _ArrayLike[_ScalarT],
+    axis: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+) -> _ScalarT: ...
+@overload
+def ptp(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+    out: None = ...,
+    keepdims: bool = ...,
+) -> Any: ...
+@overload
+def ptp(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    out: _ArrayT,
+    keepdims: bool = ...,
+) -> _ArrayT: ...
+@overload
+def ptp(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+    *,
+    out: _ArrayT,
+    keepdims: bool = ...,
+) -> _ArrayT: ...
+
+@overload
+def amax(
+    a: _ArrayLike[_ScalarT],
+    axis: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT: ...
+@overload
+def amax(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+    out: None = ...,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> Any: ...
+@overload
+def amax(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    out: _ArrayT,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ArrayT: ...
+@overload
+def amax(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+    *,
+    out: _ArrayT,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ArrayT: ...
+
+@overload
+def amin(
+    a: _ArrayLike[_ScalarT],
+    axis: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT: ...
+@overload
+def amin(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+    out: None = ...,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> Any: ...
+@overload
+def amin(
+    a: ArrayLike,
+    axis: _ShapeLike | None,
+    out: _ArrayT,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ArrayT: ...
+@overload
+def amin(
+    a: ArrayLike,
+    axis: _ShapeLike | None = ...,
+    *,
+    out: _ArrayT,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ArrayT: ...
+
+# TODO: `np.prod()``: For object arrays `initial` does not necessarily
+# have to be a numerical scalar.
+# The only requirement is that it is compatible
+# with the `.__mul__()` method(s) of the passed array's elements.
+
+# Note that the same situation holds for all wrappers around
+# `np.ufunc.reduce`, e.g. `np.sum()` (`.__add__()`).
+@overload
+def prod(
+    a: _ArrayLikeBool_co,
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> int_: ...
+@overload
+def prod(
+    a: _ArrayLikeUInt_co,
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> uint64: ...
+@overload
+def prod(
+    a: _ArrayLikeInt_co,
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> int64: ...
+@overload
+def prod(
+    a: _ArrayLikeFloat_co,
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> floating: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co,
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> complexfloating: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> Any: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    keepdims: Literal[False] = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ScalarT: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike | None = ...,
+    out: None = ...,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> Any: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike | None,
+    out: _ArrayT,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ArrayT: ...
+@overload
+def prod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike | None = ...,
+    *,
+    out: _ArrayT,
+    keepdims: bool = ...,
+    initial: _NumberLike_co = ...,
+    where: _ArrayLikeBool_co = ...,
+) -> _ArrayT: ...
+
+@overload
+def cumprod(
+    a: _ArrayLikeBool_co,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+) -> NDArray[int_]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeUInt_co,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+) -> NDArray[uint64]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeInt_co,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+) -> NDArray[int64]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeFloat_co,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+) -> NDArray[floating]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+) -> NDArray[complexfloating]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeObject_co,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+) -> NDArray[object_]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None = ...,
+    dtype: DTypeLike = ...,
+    out: None = ...,
+) -> NDArray[Any]: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None,
+    dtype: DTypeLike,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def cumprod(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: SupportsIndex | None = ...,
+    dtype: DTypeLike = ...,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+@overload
+def cumulative_prod(
+    x: _ArrayLikeBool_co,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[int_]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeUInt_co,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[uint64]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeInt_co,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[int64]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeFloat_co,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[floating]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeComplex_co,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[complexfloating]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeObject_co,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[object_]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: DTypeLike = ...,
+    out: None = ...,
+    include_initial: bool = ...,
+) -> NDArray[Any]: ...
+@overload
+def cumulative_prod(
+    x: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    /,
+    *,
+    axis: SupportsIndex | None = ...,
+    dtype: DTypeLike = ...,
+    out: _ArrayT,
+    include_initial: bool = ...,
+) -> _ArrayT: ...
+
+def ndim(a: ArrayLike) -> int: ...
+
+def size(a: ArrayLike, axis: int | None = ...) -> int: ...
+
+@overload
+def around(
+    a: _BoolLike_co,
+    decimals: SupportsIndex = ...,
+    out: None = ...,
+) -> float16: ...
+@overload
+def around(
+    a: _NumberOrObjectT,
+    decimals: SupportsIndex = ...,
+    out: None = ...,
+) -> _NumberOrObjectT: ...
+@overload
+def around(
+    a: _ComplexLike_co | object_,
+    decimals: SupportsIndex = ...,
+    out: None = ...,
+) -> Any: ...
+@overload
+def around(
+    a: _ArrayLikeBool_co,
+    decimals: SupportsIndex = ...,
+    out: None = ...,
+) -> NDArray[float16]: ...
+@overload
+def around(
+    a: _ArrayLike[_NumberOrObjectT],
+    decimals: SupportsIndex = ...,
+    out: None = ...,
+) -> NDArray[_NumberOrObjectT]: ...
+@overload
+def around(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    decimals: SupportsIndex = ...,
+    out: None = ...,
+) -> NDArray[Any]: ...
+@overload
+def around(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    decimals: SupportsIndex,
+    out: _ArrayT,
+) -> _ArrayT: ...
+@overload
+def around(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    decimals: SupportsIndex = ...,
+    *,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+@overload
+def mean(
+    a: _ArrayLikeFloat_co,
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> floating: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co,
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> complexfloating: ...
+@overload
+def mean(
+    a: _ArrayLike[np.timedelta64],
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> timedelta64: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike | None = ...,
+    *,
+    out: _ArrayT,
+    keepdims: bool | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    keepdims: Literal[False] | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    keepdims: Literal[False] | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None,
+    keepdims: Literal[True, 1],
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    *,
+    keepdims: bool | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    keepdims: bool | _NoValueType = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> _ScalarT | NDArray[_ScalarT]: ...
+@overload
+def mean(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike | None = ...,
+    out: None = ...,
+    keepdims: bool | _NoValueType = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+) -> Incomplete: ...
+
+@overload
+def std(
+    a: _ArrayLikeComplex_co,
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: Literal[False] = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> floating: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: bool = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> Any: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: Literal[False] = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: Literal[False] = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike = ...,
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: bool = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> Any: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike,
+    out: _ArrayT,
+    ddof: float = ...,
+    keepdims: bool = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def std(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike = ...,
+    *,
+    out: _ArrayT,
+    ddof: float = ...,
+    keepdims: bool = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ArrayT: ...
+
+@overload
+def var(
+    a: _ArrayLikeComplex_co,
+    axis: None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: Literal[False] = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> floating: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: None = ...,
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: bool = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> Any: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: Literal[False] = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: Literal[False] = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ScalarT: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike = ...,
+    out: None = ...,
+    ddof: float = ...,
+    keepdims: bool = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> Any: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None,
+    dtype: DTypeLike,
+    out: _ArrayT,
+    ddof: float = ...,
+    keepdims: bool = ...,
+    *,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ArrayT: ...
+@overload
+def var(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: _ShapeLike | None = ...,
+    dtype: DTypeLike = ...,
+    *,
+    out: _ArrayT,
+    ddof: float = ...,
+    keepdims: bool = ...,
+    where: _ArrayLikeBool_co | _NoValueType = ...,
+    mean: _ArrayLikeComplex_co | _ArrayLikeObject_co | _NoValueType = ...,
+    correction: float | _NoValueType = ...,
+) -> _ArrayT: ...
+
+max = amax
+min = amin
+round = around
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/function_base.py b/.venv/lib/python3.12/site-packages/numpy/_core/function_base.py
new file mode 100644
index 0000000..12ab2a7
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/function_base.py
@@ -0,0 +1,545 @@
+import functools
+import operator
+import types
+import warnings
+
+import numpy as np
+from numpy._core import overrides
+from numpy._core._multiarray_umath import _array_converter
+from numpy._core.multiarray import add_docstring
+
+from . import numeric as _nx
+from .numeric import asanyarray, nan, ndim, result_type
+
+__all__ = ['logspace', 'linspace', 'geomspace']
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+def _linspace_dispatcher(start, stop, num=None, endpoint=None, retstep=None,
+                         dtype=None, axis=None, *, device=None):
+    return (start, stop)
+
+
+@array_function_dispatch(_linspace_dispatcher)
+def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None,
+             axis=0, *, device=None):
+    """
+    Return evenly spaced numbers over a specified interval.
+
+    Returns `num` evenly spaced samples, calculated over the
+    interval [`start`, `stop`].
+
+    The endpoint of the interval can optionally be excluded.
+
+    .. versionchanged:: 1.20.0
+        Values are rounded towards ``-inf`` instead of ``0`` when an
+        integer ``dtype`` is specified. The old behavior can
+        still be obtained with ``np.linspace(start, stop, num).astype(int)``
+
+    Parameters
+    ----------
+    start : array_like
+        The starting value of the sequence.
+    stop : array_like
+        The end value of the sequence, unless `endpoint` is set to False.
+        In that case, the sequence consists of all but the last of ``num + 1``
+        evenly spaced samples, so that `stop` is excluded.  Note that the step
+        size changes when `endpoint` is False.
+    num : int, optional
+        Number of samples to generate. Default is 50. Must be non-negative.
+    endpoint : bool, optional
+        If True, `stop` is the last sample. Otherwise, it is not included.
+        Default is True.
+    retstep : bool, optional
+        If True, return (`samples`, `step`), where `step` is the spacing
+        between samples.
+    dtype : dtype, optional
+        The type of the output array.  If `dtype` is not given, the data type
+        is inferred from `start` and `stop`. The inferred dtype will never be
+        an integer; `float` is chosen even if the arguments would produce an
+        array of integers.
+    axis : int, optional
+        The axis in the result to store the samples.  Relevant only if start
+        or stop are array-like.  By default (0), the samples will be along a
+        new axis inserted at the beginning. Use -1 to get an axis at the end.
+    device : str, optional
+        The device on which to place the created array. Default: None.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    samples : ndarray
+        There are `num` equally spaced samples in the closed interval
+        ``[start, stop]`` or the half-open interval ``[start, stop)``
+        (depending on whether `endpoint` is True or False).
+    step : float, optional
+        Only returned if `retstep` is True
+
+        Size of spacing between samples.
+
+
+    See Also
+    --------
+    arange : Similar to `linspace`, but uses a step size (instead of the
+             number of samples).
+    geomspace : Similar to `linspace`, but with numbers spaced evenly on a log
+                scale (a geometric progression).
+    logspace : Similar to `geomspace`, but with the end points specified as
+               logarithms.
+    :ref:`how-to-partition`
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.linspace(2.0, 3.0, num=5)
+    array([2.  , 2.25, 2.5 , 2.75, 3.  ])
+    >>> np.linspace(2.0, 3.0, num=5, endpoint=False)
+    array([2. ,  2.2,  2.4,  2.6,  2.8])
+    >>> np.linspace(2.0, 3.0, num=5, retstep=True)
+    (array([2.  ,  2.25,  2.5 ,  2.75,  3.  ]), 0.25)
+
+    Graphical illustration:
+
+    >>> import matplotlib.pyplot as plt
+    >>> N = 8
+    >>> y = np.zeros(N)
+    >>> x1 = np.linspace(0, 10, N, endpoint=True)
+    >>> x2 = np.linspace(0, 10, N, endpoint=False)
+    >>> plt.plot(x1, y, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.plot(x2, y + 0.5, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.ylim([-0.5, 1])
+    (-0.5, 1)
+    >>> plt.show()
+
+    """
+    num = operator.index(num)
+    if num < 0:
+        raise ValueError(
+            f"Number of samples, {num}, must be non-negative."
+        )
+    div = (num - 1) if endpoint else num
+
+    conv = _array_converter(start, stop)
+    start, stop = conv.as_arrays()
+    dt = conv.result_type(ensure_inexact=True)
+
+    if dtype is None:
+        dtype = dt
+        integer_dtype = False
+    else:
+        integer_dtype = _nx.issubdtype(dtype, _nx.integer)
+
+    # Use `dtype=type(dt)` to enforce a floating point evaluation:
+    delta = np.subtract(stop, start, dtype=type(dt))
+    y = _nx.arange(
+        0, num, dtype=dt, device=device
+    ).reshape((-1,) + (1,) * ndim(delta))
+
+    # In-place multiplication y *= delta/div is faster, but prevents
+    # the multiplicant from overriding what class is produced, and thus
+    # prevents, e.g. use of Quantities, see gh-7142. Hence, we multiply
+    # in place only for standard scalar types.
+    if div > 0:
+        _mult_inplace = _nx.isscalar(delta)
+        step = delta / div
+        any_step_zero = (
+            step == 0 if _mult_inplace else _nx.asanyarray(step == 0).any())
+        if any_step_zero:
+            # Special handling for denormal numbers, gh-5437
+            y /= div
+            if _mult_inplace:
+                y *= delta
+            else:
+                y = y * delta
+        elif _mult_inplace:
+            y *= step
+        else:
+            y = y * step
+    else:
+        # sequences with 0 items or 1 item with endpoint=True (i.e. div <= 0)
+        # have an undefined step
+        step = nan
+        # Multiply with delta to allow possible override of output class.
+        y = y * delta
+
+    y += start
+
+    if endpoint and num > 1:
+        y[-1, ...] = stop
+
+    if axis != 0:
+        y = _nx.moveaxis(y, 0, axis)
+
+    if integer_dtype:
+        _nx.floor(y, out=y)
+
+    y = conv.wrap(y.astype(dtype, copy=False))
+    if retstep:
+        return y, step
+    else:
+        return y
+
+
+def _logspace_dispatcher(start, stop, num=None, endpoint=None, base=None,
+                         dtype=None, axis=None):
+    return (start, stop, base)
+
+
+@array_function_dispatch(_logspace_dispatcher)
+def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None,
+             axis=0):
+    """
+    Return numbers spaced evenly on a log scale.
+
+    In linear space, the sequence starts at ``base ** start``
+    (`base` to the power of `start`) and ends with ``base ** stop``
+    (see `endpoint` below).
+
+    .. versionchanged:: 1.25.0
+        Non-scalar 'base` is now supported
+
+    Parameters
+    ----------
+    start : array_like
+        ``base ** start`` is the starting value of the sequence.
+    stop : array_like
+        ``base ** stop`` is the final value of the sequence, unless `endpoint`
+        is False.  In that case, ``num + 1`` values are spaced over the
+        interval in log-space, of which all but the last (a sequence of
+        length `num`) are returned.
+    num : integer, optional
+        Number of samples to generate.  Default is 50.
+    endpoint : boolean, optional
+        If true, `stop` is the last sample. Otherwise, it is not included.
+        Default is True.
+    base : array_like, optional
+        The base of the log space. The step size between the elements in
+        ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform.
+        Default is 10.0.
+    dtype : dtype
+        The type of the output array.  If `dtype` is not given, the data type
+        is inferred from `start` and `stop`. The inferred type will never be
+        an integer; `float` is chosen even if the arguments would produce an
+        array of integers.
+    axis : int, optional
+        The axis in the result to store the samples.  Relevant only if start,
+        stop, or base are array-like.  By default (0), the samples will be
+        along a new axis inserted at the beginning. Use -1 to get an axis at
+        the end.
+
+    Returns
+    -------
+    samples : ndarray
+        `num` samples, equally spaced on a log scale.
+
+    See Also
+    --------
+    arange : Similar to linspace, with the step size specified instead of the
+             number of samples. Note that, when used with a float endpoint, the
+             endpoint may or may not be included.
+    linspace : Similar to logspace, but with the samples uniformly distributed
+               in linear space, instead of log space.
+    geomspace : Similar to logspace, but with endpoints specified directly.
+    :ref:`how-to-partition`
+
+    Notes
+    -----
+    If base is a scalar, logspace is equivalent to the code
+
+    >>> y = np.linspace(start, stop, num=num, endpoint=endpoint)
+    ... # doctest: +SKIP
+    >>> power(base, y).astype(dtype)
+    ... # doctest: +SKIP
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.logspace(2.0, 3.0, num=4)
+    array([ 100.        ,  215.443469  ,  464.15888336, 1000.        ])
+    >>> np.logspace(2.0, 3.0, num=4, endpoint=False)
+    array([100.        ,  177.827941  ,  316.22776602,  562.34132519])
+    >>> np.logspace(2.0, 3.0, num=4, base=2.0)
+    array([4.        ,  5.0396842 ,  6.34960421,  8.        ])
+    >>> np.logspace(2.0, 3.0, num=4, base=[2.0, 3.0], axis=-1)
+    array([[ 4.        ,  5.0396842 ,  6.34960421,  8.        ],
+           [ 9.        , 12.98024613, 18.72075441, 27.        ]])
+
+    Graphical illustration:
+
+    >>> import matplotlib.pyplot as plt
+    >>> N = 10
+    >>> x1 = np.logspace(0.1, 1, N, endpoint=True)
+    >>> x2 = np.logspace(0.1, 1, N, endpoint=False)
+    >>> y = np.zeros(N)
+    >>> plt.plot(x1, y, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.plot(x2, y + 0.5, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.ylim([-0.5, 1])
+    (-0.5, 1)
+    >>> plt.show()
+
+    """
+    if not isinstance(base, (float, int)) and np.ndim(base):
+        # If base is non-scalar, broadcast it with the others, since it
+        # may influence how axis is interpreted.
+        ndmax = np.broadcast(start, stop, base).ndim
+        start, stop, base = (
+            np.array(a, copy=None, subok=True, ndmin=ndmax)
+            for a in (start, stop, base)
+        )
+        base = np.expand_dims(base, axis=axis)
+    y = linspace(start, stop, num=num, endpoint=endpoint, axis=axis)
+    if dtype is None:
+        return _nx.power(base, y)
+    return _nx.power(base, y).astype(dtype, copy=False)
+
+
+def _geomspace_dispatcher(start, stop, num=None, endpoint=None, dtype=None,
+                          axis=None):
+    return (start, stop)
+
+
+@array_function_dispatch(_geomspace_dispatcher)
+def geomspace(start, stop, num=50, endpoint=True, dtype=None, axis=0):
+    """
+    Return numbers spaced evenly on a log scale (a geometric progression).
+
+    This is similar to `logspace`, but with endpoints specified directly.
+    Each output sample is a constant multiple of the previous.
+
+    Parameters
+    ----------
+    start : array_like
+        The starting value of the sequence.
+    stop : array_like
+        The final value of the sequence, unless `endpoint` is False.
+        In that case, ``num + 1`` values are spaced over the
+        interval in log-space, of which all but the last (a sequence of
+        length `num`) are returned.
+    num : integer, optional
+        Number of samples to generate.  Default is 50.
+    endpoint : boolean, optional
+        If true, `stop` is the last sample. Otherwise, it is not included.
+        Default is True.
+    dtype : dtype
+        The type of the output array.  If `dtype` is not given, the data type
+        is inferred from `start` and `stop`. The inferred dtype will never be
+        an integer; `float` is chosen even if the arguments would produce an
+        array of integers.
+    axis : int, optional
+        The axis in the result to store the samples.  Relevant only if start
+        or stop are array-like.  By default (0), the samples will be along a
+        new axis inserted at the beginning. Use -1 to get an axis at the end.
+
+    Returns
+    -------
+    samples : ndarray
+        `num` samples, equally spaced on a log scale.
+
+    See Also
+    --------
+    logspace : Similar to geomspace, but with endpoints specified using log
+               and base.
+    linspace : Similar to geomspace, but with arithmetic instead of geometric
+               progression.
+    arange : Similar to linspace, with the step size specified instead of the
+             number of samples.
+    :ref:`how-to-partition`
+
+    Notes
+    -----
+    If the inputs or dtype are complex, the output will follow a logarithmic
+    spiral in the complex plane.  (There are an infinite number of spirals
+    passing through two points; the output will follow the shortest such path.)
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.geomspace(1, 1000, num=4)
+    array([    1.,    10.,   100.,  1000.])
+    >>> np.geomspace(1, 1000, num=3, endpoint=False)
+    array([   1.,   10.,  100.])
+    >>> np.geomspace(1, 1000, num=4, endpoint=False)
+    array([   1.        ,    5.62341325,   31.6227766 ,  177.827941  ])
+    >>> np.geomspace(1, 256, num=9)
+    array([   1.,    2.,    4.,    8.,   16.,   32.,   64.,  128.,  256.])
+
+    Note that the above may not produce exact integers:
+
+    >>> np.geomspace(1, 256, num=9, dtype=int)
+    array([  1,   2,   4,   7,  16,  32,  63, 127, 256])
+    >>> np.around(np.geomspace(1, 256, num=9)).astype(int)
+    array([  1,   2,   4,   8,  16,  32,  64, 128, 256])
+
+    Negative, decreasing, and complex inputs are allowed:
+
+    >>> np.geomspace(1000, 1, num=4)
+    array([1000.,  100.,   10.,    1.])
+    >>> np.geomspace(-1000, -1, num=4)
+    array([-1000.,  -100.,   -10.,    -1.])
+    >>> np.geomspace(1j, 1000j, num=4)  # Straight line
+    array([0.   +1.j, 0.  +10.j, 0. +100.j, 0.+1000.j])
+    >>> np.geomspace(-1+0j, 1+0j, num=5)  # Circle
+    array([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j,
+            6.12323400e-17+1.00000000e+00j,  7.07106781e-01+7.07106781e-01j,
+            1.00000000e+00+0.00000000e+00j])
+
+    Graphical illustration of `endpoint` parameter:
+
+    >>> import matplotlib.pyplot as plt
+    >>> N = 10
+    >>> y = np.zeros(N)
+    >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o')
+    [<matplotlib.lines.Line2D object at 0x...>]
+    >>> plt.axis([0.5, 2000, 0, 3])
+    [0.5, 2000, 0, 3]
+    >>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both')
+    >>> plt.show()
+
+    """
+    start = asanyarray(start)
+    stop = asanyarray(stop)
+    if _nx.any(start == 0) or _nx.any(stop == 0):
+        raise ValueError('Geometric sequence cannot include zero')
+
+    dt = result_type(start, stop, float(num), _nx.zeros((), dtype))
+    if dtype is None:
+        dtype = dt
+    else:
+        # complex to dtype('complex128'), for instance
+        dtype = _nx.dtype(dtype)
+
+    # Promote both arguments to the same dtype in case, for instance, one is
+    # complex and another is negative and log would produce NaN otherwise.
+    # Copy since we may change things in-place further down.
+    start = start.astype(dt, copy=True)
+    stop = stop.astype(dt, copy=True)
+
+    # Allow negative real values and ensure a consistent result for complex
+    # (including avoiding negligible real or imaginary parts in output) by
+    # rotating start to positive real, calculating, then undoing rotation.
+    out_sign = _nx.sign(start)
+    start /= out_sign
+    stop = stop / out_sign
+
+    log_start = _nx.log10(start)
+    log_stop = _nx.log10(stop)
+    result = logspace(log_start, log_stop, num=num,
+                      endpoint=endpoint, base=10.0, dtype=dt)
+
+    # Make sure the endpoints match the start and stop arguments. This is
+    # necessary because np.exp(np.log(x)) is not necessarily equal to x.
+    if num > 0:
+        result[0] = start
+        if num > 1 and endpoint:
+            result[-1] = stop
+
+    result *= out_sign
+
+    if axis != 0:
+        result = _nx.moveaxis(result, 0, axis)
+
+    return result.astype(dtype, copy=False)
+
+
+def _needs_add_docstring(obj):
+    """
+    Returns true if the only way to set the docstring of `obj` from python is
+    via add_docstring.
+
+    This function errs on the side of being overly conservative.
+    """
+    Py_TPFLAGS_HEAPTYPE = 1 << 9
+
+    if isinstance(obj, (types.FunctionType, types.MethodType, property)):
+        return False
+
+    if isinstance(obj, type) and obj.__flags__ & Py_TPFLAGS_HEAPTYPE:
+        return False
+
+    return True
+
+
+def _add_docstring(obj, doc, warn_on_python):
+    if warn_on_python and not _needs_add_docstring(obj):
+        warnings.warn(
+            f"add_newdoc was used on a pure-python object {obj}. "
+            "Prefer to attach it directly to the source.",
+            UserWarning,
+            stacklevel=3)
+    try:
+        add_docstring(obj, doc)
+    except Exception:
+        pass
+
+
+def add_newdoc(place, obj, doc, warn_on_python=True):
+    """
+    Add documentation to an existing object, typically one defined in C
+
+    The purpose is to allow easier editing of the docstrings without requiring
+    a re-compile. This exists primarily for internal use within numpy itself.
+
+    Parameters
+    ----------
+    place : str
+        The absolute name of the module to import from
+    obj : str or None
+        The name of the object to add documentation to, typically a class or
+        function name.
+    doc : {str, Tuple[str, str], List[Tuple[str, str]]}
+        If a string, the documentation to apply to `obj`
+
+        If a tuple, then the first element is interpreted as an attribute
+        of `obj` and the second as the docstring to apply -
+        ``(method, docstring)``
+
+        If a list, then each element of the list should be a tuple of length
+        two - ``[(method1, docstring1), (method2, docstring2), ...]``
+    warn_on_python : bool
+        If True, the default, emit `UserWarning` if this is used to attach
+        documentation to a pure-python object.
+
+    Notes
+    -----
+    This routine never raises an error if the docstring can't be written, but
+    will raise an error if the object being documented does not exist.
+
+    This routine cannot modify read-only docstrings, as appear
+    in new-style classes or built-in functions. Because this
+    routine never raises an error the caller must check manually
+    that the docstrings were changed.
+
+    Since this function grabs the ``char *`` from a c-level str object and puts
+    it into the ``tp_doc`` slot of the type of `obj`, it violates a number of
+    C-API best-practices, by:
+
+    - modifying a `PyTypeObject` after calling `PyType_Ready`
+    - calling `Py_INCREF` on the str and losing the reference, so the str
+      will never be released
+
+    If possible it should be avoided.
+    """
+    new = getattr(__import__(place, globals(), {}, [obj]), obj)
+    if isinstance(doc, str):
+        if "${ARRAY_FUNCTION_LIKE}" in doc:
+            doc = overrides.get_array_function_like_doc(new, doc)
+        _add_docstring(new, doc.strip(), warn_on_python)
+    elif isinstance(doc, tuple):
+        attr, docstring = doc
+        _add_docstring(getattr(new, attr), docstring.strip(), warn_on_python)
+    elif isinstance(doc, list):
+        for attr, docstring in doc:
+            _add_docstring(
+                getattr(new, attr), docstring.strip(), warn_on_python
+            )
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/function_base.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/function_base.pyi
new file mode 100644
index 0000000..44d1311
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/function_base.pyi
@@ -0,0 +1,278 @@
+from typing import Literal as L
+from typing import SupportsIndex, TypeAlias, TypeVar, overload
+
+from _typeshed import Incomplete
+
+import numpy as np
+from numpy._typing import (
+    DTypeLike,
+    NDArray,
+    _ArrayLikeComplex_co,
+    _ArrayLikeFloat_co,
+    _DTypeLike,
+)
+from numpy._typing._array_like import _DualArrayLike
+
+__all__ = ["geomspace", "linspace", "logspace"]
+
+_ScalarT = TypeVar("_ScalarT", bound=np.generic)
+
+_ToArrayFloat64: TypeAlias = _DualArrayLike[np.dtype[np.float64 | np.integer | np.bool], float]
+
+@overload
+def linspace(
+    start: _ToArrayFloat64,
+    stop: _ToArrayFloat64,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[np.float64]: ...
+@overload
+def linspace(
+    start: _ArrayLikeFloat_co,
+    stop: _ArrayLikeFloat_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[np.floating]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[np.complexfloating]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex,
+    endpoint: bool,
+    retstep: L[False],
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> NDArray[_ScalarT]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    retstep: L[False] = False,
+    dtype: DTypeLike | None = None,
+    axis: SupportsIndex = 0,
+    *,
+    device: L["cpu"] | None = None,
+) -> NDArray[Incomplete]: ...
+@overload
+def linspace(
+    start: _ToArrayFloat64,
+    stop: _ToArrayFloat64,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[np.float64], np.float64]: ...
+@overload
+def linspace(
+    start: _ArrayLikeFloat_co,
+    stop: _ArrayLikeFloat_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[np.floating], np.floating]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[np.complexfloating], np.complexfloating]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[_ScalarT], _ScalarT]: ...
+@overload
+def linspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    retstep: L[True],
+    dtype: DTypeLike | None = None,
+    axis: SupportsIndex = 0,
+    device: L["cpu"] | None = None,
+) -> tuple[NDArray[Incomplete], Incomplete]: ...
+
+@overload
+def logspace(
+    start: _ToArrayFloat64,
+    stop: _ToArrayFloat64,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ToArrayFloat64 = 10.0,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.float64]: ...
+@overload
+def logspace(
+    start: _ArrayLikeFloat_co,
+    stop: _ArrayLikeFloat_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ArrayLikeFloat_co = 10.0,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.floating]: ...
+@overload
+def logspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ArrayLikeComplex_co = 10.0,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.complexfloating]: ...
+@overload
+def logspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex,
+    endpoint: bool,
+    base: _ArrayLikeComplex_co,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+) -> NDArray[_ScalarT]: ...
+@overload
+def logspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ArrayLikeComplex_co = 10.0,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+) -> NDArray[_ScalarT]: ...
+@overload
+def logspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    base: _ArrayLikeComplex_co = 10.0,
+    dtype: DTypeLike | None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[Incomplete]: ...
+
+@overload
+def geomspace(
+    start: _ToArrayFloat64,
+    stop: _ToArrayFloat64,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.float64]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeFloat_co,
+    stop: _ArrayLikeFloat_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.floating]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    dtype: None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[np.complexfloating]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex,
+    endpoint: bool,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+) -> NDArray[_ScalarT]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    axis: SupportsIndex = 0,
+) -> NDArray[_ScalarT]: ...
+@overload
+def geomspace(
+    start: _ArrayLikeComplex_co,
+    stop: _ArrayLikeComplex_co,
+    num: SupportsIndex = 50,
+    endpoint: bool = True,
+    dtype: DTypeLike | None = None,
+    axis: SupportsIndex = 0,
+) -> NDArray[Incomplete]: ...
+
+def add_newdoc(
+    place: str,
+    obj: str,
+    doc: str | tuple[str, str] | list[tuple[str, str]],
+    warn_on_python: bool = True,
+) -> None: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/getlimits.py b/.venv/lib/python3.12/site-packages/numpy/_core/getlimits.py
new file mode 100644
index 0000000..afa2cce
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/getlimits.py
@@ -0,0 +1,748 @@
+"""Machine limits for Float32 and Float64 and (long double) if available...
+
+"""
+__all__ = ['finfo', 'iinfo']
+
+import types
+import warnings
+
+from numpy._utils import set_module
+
+from . import numeric
+from . import numerictypes as ntypes
+from ._machar import MachAr
+from .numeric import array, inf, nan
+from .umath import exp2, isnan, log10, nextafter
+
+
+def _fr0(a):
+    """fix rank-0 --> rank-1"""
+    if a.ndim == 0:
+        a = a.copy()
+        a.shape = (1,)
+    return a
+
+
+def _fr1(a):
+    """fix rank > 0 --> rank-0"""
+    if a.size == 1:
+        a = a.copy()
+        a.shape = ()
+    return a
+
+
+class MachArLike:
+    """ Object to simulate MachAr instance """
+    def __init__(self, ftype, *, eps, epsneg, huge, tiny,
+                 ibeta, smallest_subnormal=None, **kwargs):
+        self.params = _MACHAR_PARAMS[ftype]
+        self.ftype = ftype
+        self.title = self.params['title']
+        # Parameter types same as for discovered MachAr object.
+        if not smallest_subnormal:
+            self._smallest_subnormal = nextafter(
+                self.ftype(0), self.ftype(1), dtype=self.ftype)
+        else:
+            self._smallest_subnormal = smallest_subnormal
+        self.epsilon = self.eps = self._float_to_float(eps)
+        self.epsneg = self._float_to_float(epsneg)
+        self.xmax = self.huge = self._float_to_float(huge)
+        self.xmin = self._float_to_float(tiny)
+        self.smallest_normal = self.tiny = self._float_to_float(tiny)
+        self.ibeta = self.params['itype'](ibeta)
+        self.__dict__.update(kwargs)
+        self.precision = int(-log10(self.eps))
+        self.resolution = self._float_to_float(
+            self._float_conv(10) ** (-self.precision))
+        self._str_eps = self._float_to_str(self.eps)
+        self._str_epsneg = self._float_to_str(self.epsneg)
+        self._str_xmin = self._float_to_str(self.xmin)
+        self._str_xmax = self._float_to_str(self.xmax)
+        self._str_resolution = self._float_to_str(self.resolution)
+        self._str_smallest_normal = self._float_to_str(self.xmin)
+
+    @property
+    def smallest_subnormal(self):
+        """Return the value for the smallest subnormal.
+
+        Returns
+        -------
+        smallest_subnormal : float
+            value for the smallest subnormal.
+
+        Warns
+        -----
+        UserWarning
+            If the calculated value for the smallest subnormal is zero.
+        """
+        # Check that the calculated value is not zero, in case it raises a
+        # warning.
+        value = self._smallest_subnormal
+        if self.ftype(0) == value:
+            warnings.warn(
+                f'The value of the smallest subnormal for {self.ftype} type is zero.',
+                UserWarning, stacklevel=2)
+
+        return self._float_to_float(value)
+
+    @property
+    def _str_smallest_subnormal(self):
+        """Return the string representation of the smallest subnormal."""
+        return self._float_to_str(self.smallest_subnormal)
+
+    def _float_to_float(self, value):
+        """Converts float to float.
+
+        Parameters
+        ----------
+        value : float
+            value to be converted.
+        """
+        return _fr1(self._float_conv(value))
+
+    def _float_conv(self, value):
+        """Converts float to conv.
+
+        Parameters
+        ----------
+        value : float
+            value to be converted.
+        """
+        return array([value], self.ftype)
+
+    def _float_to_str(self, value):
+        """Converts float to str.
+
+        Parameters
+        ----------
+        value : float
+            value to be converted.
+        """
+        return self.params['fmt'] % array(_fr0(value)[0], self.ftype)
+
+
+_convert_to_float = {
+    ntypes.csingle: ntypes.single,
+    ntypes.complex128: ntypes.float64,
+    ntypes.clongdouble: ntypes.longdouble
+    }
+
+# Parameters for creating MachAr / MachAr-like objects
+_title_fmt = 'numpy {} precision floating point number'
+_MACHAR_PARAMS = {
+    ntypes.double: {
+        'itype': ntypes.int64,
+        'fmt': '%24.16e',
+        'title': _title_fmt.format('double')},
+    ntypes.single: {
+        'itype': ntypes.int32,
+        'fmt': '%15.7e',
+        'title': _title_fmt.format('single')},
+    ntypes.longdouble: {
+        'itype': ntypes.longlong,
+        'fmt': '%s',
+        'title': _title_fmt.format('long double')},
+    ntypes.half: {
+        'itype': ntypes.int16,
+        'fmt': '%12.5e',
+        'title': _title_fmt.format('half')}}
+
+# Key to identify the floating point type.  Key is result of
+#
+#    ftype = np.longdouble        # or float64, float32, etc.
+#    v = (ftype(-1.0) / ftype(10.0))
+#    v.view(v.dtype.newbyteorder('<')).tobytes()
+#
+# Uses division to work around deficiencies in strtold on some platforms.
+# See:
+# https://perl5.git.perl.org/perl.git/blob/3118d7d684b56cbeb702af874f4326683c45f045:/Configure
+
+_KNOWN_TYPES = {}
+def _register_type(machar, bytepat):
+    _KNOWN_TYPES[bytepat] = machar
+
+
+_float_ma = {}
+
+
+def _register_known_types():
+    # Known parameters for float16
+    # See docstring of MachAr class for description of parameters.
+    f16 = ntypes.float16
+    float16_ma = MachArLike(f16,
+                            machep=-10,
+                            negep=-11,
+                            minexp=-14,
+                            maxexp=16,
+                            it=10,
+                            iexp=5,
+                            ibeta=2,
+                            irnd=5,
+                            ngrd=0,
+                            eps=exp2(f16(-10)),
+                            epsneg=exp2(f16(-11)),
+                            huge=f16(65504),
+                            tiny=f16(2 ** -14))
+    _register_type(float16_ma, b'f\xae')
+    _float_ma[16] = float16_ma
+
+    # Known parameters for float32
+    f32 = ntypes.float32
+    float32_ma = MachArLike(f32,
+                            machep=-23,
+                            negep=-24,
+                            minexp=-126,
+                            maxexp=128,
+                            it=23,
+                            iexp=8,
+                            ibeta=2,
+                            irnd=5,
+                            ngrd=0,
+                            eps=exp2(f32(-23)),
+                            epsneg=exp2(f32(-24)),
+                            huge=f32((1 - 2 ** -24) * 2**128),
+                            tiny=exp2(f32(-126)))
+    _register_type(float32_ma, b'\xcd\xcc\xcc\xbd')
+    _float_ma[32] = float32_ma
+
+    # Known parameters for float64
+    f64 = ntypes.float64
+    epsneg_f64 = 2.0 ** -53.0
+    tiny_f64 = 2.0 ** -1022.0
+    float64_ma = MachArLike(f64,
+                            machep=-52,
+                            negep=-53,
+                            minexp=-1022,
+                            maxexp=1024,
+                            it=52,
+                            iexp=11,
+                            ibeta=2,
+                            irnd=5,
+                            ngrd=0,
+                            eps=2.0 ** -52.0,
+                            epsneg=epsneg_f64,
+                            huge=(1.0 - epsneg_f64) / tiny_f64 * f64(4),
+                            tiny=tiny_f64)
+    _register_type(float64_ma, b'\x9a\x99\x99\x99\x99\x99\xb9\xbf')
+    _float_ma[64] = float64_ma
+
+    # Known parameters for IEEE 754 128-bit binary float
+    ld = ntypes.longdouble
+    epsneg_f128 = exp2(ld(-113))
+    tiny_f128 = exp2(ld(-16382))
+    # Ignore runtime error when this is not f128
+    with numeric.errstate(all='ignore'):
+        huge_f128 = (ld(1) - epsneg_f128) / tiny_f128 * ld(4)
+    float128_ma = MachArLike(ld,
+                             machep=-112,
+                             negep=-113,
+                             minexp=-16382,
+                             maxexp=16384,
+                             it=112,
+                             iexp=15,
+                             ibeta=2,
+                             irnd=5,
+                             ngrd=0,
+                             eps=exp2(ld(-112)),
+                             epsneg=epsneg_f128,
+                             huge=huge_f128,
+                             tiny=tiny_f128)
+    # IEEE 754 128-bit binary float
+    _register_type(float128_ma,
+        b'\x9a\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\x99\xfb\xbf')
+    _float_ma[128] = float128_ma
+
+    # Known parameters for float80 (Intel 80-bit extended precision)
+    epsneg_f80 = exp2(ld(-64))
+    tiny_f80 = exp2(ld(-16382))
+    # Ignore runtime error when this is not f80
+    with numeric.errstate(all='ignore'):
+        huge_f80 = (ld(1) - epsneg_f80) / tiny_f80 * ld(4)
+    float80_ma = MachArLike(ld,
+                            machep=-63,
+                            negep=-64,
+                            minexp=-16382,
+                            maxexp=16384,
+                            it=63,
+                            iexp=15,
+                            ibeta=2,
+                            irnd=5,
+                            ngrd=0,
+                            eps=exp2(ld(-63)),
+                            epsneg=epsneg_f80,
+                            huge=huge_f80,
+                            tiny=tiny_f80)
+    # float80, first 10 bytes containing actual storage
+    _register_type(float80_ma, b'\xcd\xcc\xcc\xcc\xcc\xcc\xcc\xcc\xfb\xbf')
+    _float_ma[80] = float80_ma
+
+    # Guessed / known parameters for double double; see:
+    # https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format#Double-double_arithmetic
+    # These numbers have the same exponent range as float64, but extended
+    # number of digits in the significand.
+    huge_dd = nextafter(ld(inf), ld(0), dtype=ld)
+    # As the smallest_normal in double double is so hard to calculate we set
+    # it to NaN.
+    smallest_normal_dd = nan
+    # Leave the same value for the smallest subnormal as double
+    smallest_subnormal_dd = ld(nextafter(0., 1.))
+    float_dd_ma = MachArLike(ld,
+                             machep=-105,
+                             negep=-106,
+                             minexp=-1022,
+                             maxexp=1024,
+                             it=105,
+                             iexp=11,
+                             ibeta=2,
+                             irnd=5,
+                             ngrd=0,
+                             eps=exp2(ld(-105)),
+                             epsneg=exp2(ld(-106)),
+                             huge=huge_dd,
+                             tiny=smallest_normal_dd,
+                             smallest_subnormal=smallest_subnormal_dd)
+    # double double; low, high order (e.g. PPC 64)
+    _register_type(float_dd_ma,
+        b'\x9a\x99\x99\x99\x99\x99Y<\x9a\x99\x99\x99\x99\x99\xb9\xbf')
+    # double double; high, low order (e.g. PPC 64 le)
+    _register_type(float_dd_ma,
+        b'\x9a\x99\x99\x99\x99\x99\xb9\xbf\x9a\x99\x99\x99\x99\x99Y<')
+    _float_ma['dd'] = float_dd_ma
+
+
+def _get_machar(ftype):
+    """ Get MachAr instance or MachAr-like instance
+
+    Get parameters for floating point type, by first trying signatures of
+    various known floating point types, then, if none match, attempting to
+    identify parameters by analysis.
+
+    Parameters
+    ----------
+    ftype : class
+        Numpy floating point type class (e.g. ``np.float64``)
+
+    Returns
+    -------
+    ma_like : instance of :class:`MachAr` or :class:`MachArLike`
+        Object giving floating point parameters for `ftype`.
+
+    Warns
+    -----
+    UserWarning
+        If the binary signature of the float type is not in the dictionary of
+        known float types.
+    """
+    params = _MACHAR_PARAMS.get(ftype)
+    if params is None:
+        raise ValueError(repr(ftype))
+    # Detect known / suspected types
+    # ftype(-1.0) / ftype(10.0) is better than ftype('-0.1') because stold
+    # may be deficient
+    key = (ftype(-1.0) / ftype(10.))
+    key = key.view(key.dtype.newbyteorder("<")).tobytes()
+    ma_like = None
+    if ftype == ntypes.longdouble:
+        # Could be 80 bit == 10 byte extended precision, where last bytes can
+        # be random garbage.
+        # Comparing first 10 bytes to pattern first to avoid branching on the
+        # random garbage.
+        ma_like = _KNOWN_TYPES.get(key[:10])
+    if ma_like is None:
+        # see if the full key is known.
+        ma_like = _KNOWN_TYPES.get(key)
+    if ma_like is None and len(key) == 16:
+        # machine limits could be f80 masquerading as np.float128,
+        # find all keys with length 16 and make new dict, but make the keys
+        # only 10 bytes long, the last bytes can be random garbage
+        _kt = {k[:10]: v for k, v in _KNOWN_TYPES.items() if len(k) == 16}
+        ma_like = _kt.get(key[:10])
+    if ma_like is not None:
+        return ma_like
+    # Fall back to parameter discovery
+    warnings.warn(
+        f'Signature {key} for {ftype} does not match any known type: '
+        'falling back to type probe function.\n'
+        'This warnings indicates broken support for the dtype!',
+        UserWarning, stacklevel=2)
+    return _discovered_machar(ftype)
+
+
+def _discovered_machar(ftype):
+    """ Create MachAr instance with found information on float types
+
+    TODO: MachAr should be retired completely ideally.  We currently only
+          ever use it system with broken longdouble (valgrind, WSL).
+    """
+    params = _MACHAR_PARAMS[ftype]
+    return MachAr(lambda v: array([v], ftype),
+                  lambda v: _fr0(v.astype(params['itype']))[0],
+                  lambda v: array(_fr0(v)[0], ftype),
+                  lambda v: params['fmt'] % array(_fr0(v)[0], ftype),
+                  params['title'])
+
+
+@set_module('numpy')
+class finfo:
+    """
+    finfo(dtype)
+
+    Machine limits for floating point types.
+
+    Attributes
+    ----------
+    bits : int
+        The number of bits occupied by the type.
+    dtype : dtype
+        Returns the dtype for which `finfo` returns information. For complex
+        input, the returned dtype is the associated ``float*`` dtype for its
+        real and complex components.
+    eps : float
+        The difference between 1.0 and the next smallest representable float
+        larger than 1.0. For example, for 64-bit binary floats in the IEEE-754
+        standard, ``eps = 2**-52``, approximately 2.22e-16.
+    epsneg : float
+        The difference between 1.0 and the next smallest representable float
+        less than 1.0. For example, for 64-bit binary floats in the IEEE-754
+        standard, ``epsneg = 2**-53``, approximately 1.11e-16.
+    iexp : int
+        The number of bits in the exponent portion of the floating point
+        representation.
+    machep : int
+        The exponent that yields `eps`.
+    max : floating point number of the appropriate type
+        The largest representable number.
+    maxexp : int
+        The smallest positive power of the base (2) that causes overflow.
+    min : floating point number of the appropriate type
+        The smallest representable number, typically ``-max``.
+    minexp : int
+        The most negative power of the base (2) consistent with there
+        being no leading 0's in the mantissa.
+    negep : int
+        The exponent that yields `epsneg`.
+    nexp : int
+        The number of bits in the exponent including its sign and bias.
+    nmant : int
+        The number of bits in the mantissa.
+    precision : int
+        The approximate number of decimal digits to which this kind of
+        float is precise.
+    resolution : floating point number of the appropriate type
+        The approximate decimal resolution of this type, i.e.,
+        ``10**-precision``.
+    tiny : float
+        An alias for `smallest_normal`, kept for backwards compatibility.
+    smallest_normal : float
+        The smallest positive floating point number with 1 as leading bit in
+        the mantissa following IEEE-754 (see Notes).
+    smallest_subnormal : float
+        The smallest positive floating point number with 0 as leading bit in
+        the mantissa following IEEE-754.
+
+    Parameters
+    ----------
+    dtype : float, dtype, or instance
+        Kind of floating point or complex floating point
+        data-type about which to get information.
+
+    See Also
+    --------
+    iinfo : The equivalent for integer data types.
+    spacing : The distance between a value and the nearest adjacent number
+    nextafter : The next floating point value after x1 towards x2
+
+    Notes
+    -----
+    For developers of NumPy: do not instantiate this at the module level.
+    The initial calculation of these parameters is expensive and negatively
+    impacts import times.  These objects are cached, so calling ``finfo()``
+    repeatedly inside your functions is not a problem.
+
+    Note that ``smallest_normal`` is not actually the smallest positive
+    representable value in a NumPy floating point type. As in the IEEE-754
+    standard [1]_, NumPy floating point types make use of subnormal numbers to
+    fill the gap between 0 and ``smallest_normal``. However, subnormal numbers
+    may have significantly reduced precision [2]_.
+
+    This function can also be used for complex data types as well. If used,
+    the output will be the same as the corresponding real float type
+    (e.g. numpy.finfo(numpy.csingle) is the same as numpy.finfo(numpy.single)).
+    However, the output is true for the real and imaginary components.
+
+    References
+    ----------
+    .. [1] IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2008,
+           pp.1-70, 2008, https://doi.org/10.1109/IEEESTD.2008.4610935
+    .. [2] Wikipedia, "Denormal Numbers",
+           https://en.wikipedia.org/wiki/Denormal_number
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.finfo(np.float64).dtype
+    dtype('float64')
+    >>> np.finfo(np.complex64).dtype
+    dtype('float32')
+
+    """
+
+    _finfo_cache = {}
+
+    __class_getitem__ = classmethod(types.GenericAlias)
+
+    def __new__(cls, dtype):
+        try:
+            obj = cls._finfo_cache.get(dtype)  # most common path
+            if obj is not None:
+                return obj
+        except TypeError:
+            pass
+
+        if dtype is None:
+            # Deprecated in NumPy 1.25, 2023-01-16
+            warnings.warn(
+                "finfo() dtype cannot be None. This behavior will "
+                "raise an error in the future. (Deprecated in NumPy 1.25)",
+                DeprecationWarning,
+                stacklevel=2
+            )
+
+        try:
+            dtype = numeric.dtype(dtype)
+        except TypeError:
+            # In case a float instance was given
+            dtype = numeric.dtype(type(dtype))
+
+        obj = cls._finfo_cache.get(dtype)
+        if obj is not None:
+            return obj
+        dtypes = [dtype]
+        newdtype = ntypes.obj2sctype(dtype)
+        if newdtype is not dtype:
+            dtypes.append(newdtype)
+            dtype = newdtype
+        if not issubclass(dtype, numeric.inexact):
+            raise ValueError(f"data type {dtype!r} not inexact")
+        obj = cls._finfo_cache.get(dtype)
+        if obj is not None:
+            return obj
+        if not issubclass(dtype, numeric.floating):
+            newdtype = _convert_to_float[dtype]
+            if newdtype is not dtype:
+                # dtype changed, for example from complex128 to float64
+                dtypes.append(newdtype)
+                dtype = newdtype
+
+                obj = cls._finfo_cache.get(dtype, None)
+                if obj is not None:
+                    # the original dtype was not in the cache, but the new
+                    # dtype is in the cache. we add the original dtypes to
+                    # the cache and return the result
+                    for dt in dtypes:
+                        cls._finfo_cache[dt] = obj
+                    return obj
+        obj = object.__new__(cls)._init(dtype)
+        for dt in dtypes:
+            cls._finfo_cache[dt] = obj
+        return obj
+
+    def _init(self, dtype):
+        self.dtype = numeric.dtype(dtype)
+        machar = _get_machar(dtype)
+
+        for word in ['precision', 'iexp',
+                     'maxexp', 'minexp', 'negep',
+                     'machep']:
+            setattr(self, word, getattr(machar, word))
+        for word in ['resolution', 'epsneg', 'smallest_subnormal']:
+            setattr(self, word, getattr(machar, word).flat[0])
+        self.bits = self.dtype.itemsize * 8
+        self.max = machar.huge.flat[0]
+        self.min = -self.max
+        self.eps = machar.eps.flat[0]
+        self.nexp = machar.iexp
+        self.nmant = machar.it
+        self._machar = machar
+        self._str_tiny = machar._str_xmin.strip()
+        self._str_max = machar._str_xmax.strip()
+        self._str_epsneg = machar._str_epsneg.strip()
+        self._str_eps = machar._str_eps.strip()
+        self._str_resolution = machar._str_resolution.strip()
+        self._str_smallest_normal = machar._str_smallest_normal.strip()
+        self._str_smallest_subnormal = machar._str_smallest_subnormal.strip()
+        return self
+
+    def __str__(self):
+        fmt = (
+            'Machine parameters for %(dtype)s\n'
+            '---------------------------------------------------------------\n'
+            'precision = %(precision)3s   resolution = %(_str_resolution)s\n'
+            'machep = %(machep)6s   eps =        %(_str_eps)s\n'
+            'negep =  %(negep)6s   epsneg =     %(_str_epsneg)s\n'
+            'minexp = %(minexp)6s   tiny =       %(_str_tiny)s\n'
+            'maxexp = %(maxexp)6s   max =        %(_str_max)s\n'
+            'nexp =   %(nexp)6s   min =        -max\n'
+            'smallest_normal = %(_str_smallest_normal)s   '
+            'smallest_subnormal = %(_str_smallest_subnormal)s\n'
+            '---------------------------------------------------------------\n'
+            )
+        return fmt % self.__dict__
+
+    def __repr__(self):
+        c = self.__class__.__name__
+        d = self.__dict__.copy()
+        d['klass'] = c
+        return (("%(klass)s(resolution=%(resolution)s, min=-%(_str_max)s,"
+                 " max=%(_str_max)s, dtype=%(dtype)s)") % d)
+
+    @property
+    def smallest_normal(self):
+        """Return the value for the smallest normal.
+
+        Returns
+        -------
+        smallest_normal : float
+            Value for the smallest normal.
+
+        Warns
+        -----
+        UserWarning
+            If the calculated value for the smallest normal is requested for
+            double-double.
+        """
+        # This check is necessary because the value for smallest_normal is
+        # platform dependent for longdouble types.
+        if isnan(self._machar.smallest_normal.flat[0]):
+            warnings.warn(
+                'The value of smallest normal is undefined for double double',
+                UserWarning, stacklevel=2)
+        return self._machar.smallest_normal.flat[0]
+
+    @property
+    def tiny(self):
+        """Return the value for tiny, alias of smallest_normal.
+
+        Returns
+        -------
+        tiny : float
+            Value for the smallest normal, alias of smallest_normal.
+
+        Warns
+        -----
+        UserWarning
+            If the calculated value for the smallest normal is requested for
+            double-double.
+        """
+        return self.smallest_normal
+
+
+@set_module('numpy')
+class iinfo:
+    """
+    iinfo(type)
+
+    Machine limits for integer types.
+
+    Attributes
+    ----------
+    bits : int
+        The number of bits occupied by the type.
+    dtype : dtype
+        Returns the dtype for which `iinfo` returns information.
+    min : int
+        The smallest integer expressible by the type.
+    max : int
+        The largest integer expressible by the type.
+
+    Parameters
+    ----------
+    int_type : integer type, dtype, or instance
+        The kind of integer data type to get information about.
+
+    See Also
+    --------
+    finfo : The equivalent for floating point data types.
+
+    Examples
+    --------
+    With types:
+
+    >>> import numpy as np
+    >>> ii16 = np.iinfo(np.int16)
+    >>> ii16.min
+    -32768
+    >>> ii16.max
+    32767
+    >>> ii32 = np.iinfo(np.int32)
+    >>> ii32.min
+    -2147483648
+    >>> ii32.max
+    2147483647
+
+    With instances:
+
+    >>> ii32 = np.iinfo(np.int32(10))
+    >>> ii32.min
+    -2147483648
+    >>> ii32.max
+    2147483647
+
+    """
+
+    _min_vals = {}
+    _max_vals = {}
+
+    __class_getitem__ = classmethod(types.GenericAlias)
+
+    def __init__(self, int_type):
+        try:
+            self.dtype = numeric.dtype(int_type)
+        except TypeError:
+            self.dtype = numeric.dtype(type(int_type))
+        self.kind = self.dtype.kind
+        self.bits = self.dtype.itemsize * 8
+        self.key = "%s%d" % (self.kind, self.bits)
+        if self.kind not in 'iu':
+            raise ValueError(f"Invalid integer data type {self.kind!r}.")
+
+    @property
+    def min(self):
+        """Minimum value of given dtype."""
+        if self.kind == 'u':
+            return 0
+        else:
+            try:
+                val = iinfo._min_vals[self.key]
+            except KeyError:
+                val = int(-(1 << (self.bits - 1)))
+                iinfo._min_vals[self.key] = val
+            return val
+
+    @property
+    def max(self):
+        """Maximum value of given dtype."""
+        try:
+            val = iinfo._max_vals[self.key]
+        except KeyError:
+            if self.kind == 'u':
+                val = int((1 << self.bits) - 1)
+            else:
+                val = int((1 << (self.bits - 1)) - 1)
+            iinfo._max_vals[self.key] = val
+        return val
+
+    def __str__(self):
+        """String representation."""
+        fmt = (
+            'Machine parameters for %(dtype)s\n'
+            '---------------------------------------------------------------\n'
+            'min = %(min)s\n'
+            'max = %(max)s\n'
+            '---------------------------------------------------------------\n'
+            )
+        return fmt % {'dtype': self.dtype, 'min': self.min, 'max': self.max}
+
+    def __repr__(self):
+        return "%s(min=%s, max=%s, dtype=%s)" % (self.__class__.__name__,
+                                    self.min, self.max, self.dtype)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/getlimits.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/getlimits.pyi
new file mode 100644
index 0000000..9d79b17
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/getlimits.pyi
@@ -0,0 +1,3 @@
+from numpy import finfo, iinfo
+
+__all__ = ["finfo", "iinfo"]
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__multiarray_api.c b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__multiarray_api.c
new file mode 100644
index 0000000..8398c62
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__multiarray_api.c
@@ -0,0 +1,376 @@
+
+/* These pointers will be stored in the C-object for use in other
+    extension modules
+*/
+
+void *PyArray_API[] = {
+        (void *) PyArray_GetNDArrayCVersion,
+        NULL,
+        (void *) &PyArray_Type,
+        (void *) &PyArrayDescr_Type,
+        NULL,
+        (void *) &PyArrayIter_Type,
+        (void *) &PyArrayMultiIter_Type,
+        (int *) &NPY_NUMUSERTYPES,
+        (void *) &PyBoolArrType_Type,
+        (void *) &_PyArrayScalar_BoolValues,
+        (void *) &PyGenericArrType_Type,
+        (void *) &PyNumberArrType_Type,
+        (void *) &PyIntegerArrType_Type,
+        (void *) &PySignedIntegerArrType_Type,
+        (void *) &PyUnsignedIntegerArrType_Type,
+        (void *) &PyInexactArrType_Type,
+        (void *) &PyFloatingArrType_Type,
+        (void *) &PyComplexFloatingArrType_Type,
+        (void *) &PyFlexibleArrType_Type,
+        (void *) &PyCharacterArrType_Type,
+        (void *) &PyByteArrType_Type,
+        (void *) &PyShortArrType_Type,
+        (void *) &PyIntArrType_Type,
+        (void *) &PyLongArrType_Type,
+        (void *) &PyLongLongArrType_Type,
+        (void *) &PyUByteArrType_Type,
+        (void *) &PyUShortArrType_Type,
+        (void *) &PyUIntArrType_Type,
+        (void *) &PyULongArrType_Type,
+        (void *) &PyULongLongArrType_Type,
+        (void *) &PyFloatArrType_Type,
+        (void *) &PyDoubleArrType_Type,
+        (void *) &PyLongDoubleArrType_Type,
+        (void *) &PyCFloatArrType_Type,
+        (void *) &PyCDoubleArrType_Type,
+        (void *) &PyCLongDoubleArrType_Type,
+        (void *) &PyObjectArrType_Type,
+        (void *) &PyStringArrType_Type,
+        (void *) &PyUnicodeArrType_Type,
+        (void *) &PyVoidArrType_Type,
+        NULL,
+        NULL,
+        (void *) PyArray_INCREF,
+        (void *) PyArray_XDECREF,
+        (void *) PyArray_SetStringFunction,
+        (void *) PyArray_DescrFromType,
+        (void *) PyArray_TypeObjectFromType,
+        (void *) PyArray_Zero,
+        (void *) PyArray_One,
+        (void *) PyArray_CastToType,
+        (void *) PyArray_CopyInto,
+        (void *) PyArray_CopyAnyInto,
+        (void *) PyArray_CanCastSafely,
+        (void *) PyArray_CanCastTo,
+        (void *) PyArray_ObjectType,
+        (void *) PyArray_DescrFromObject,
+        (void *) PyArray_ConvertToCommonType,
+        (void *) PyArray_DescrFromScalar,
+        (void *) PyArray_DescrFromTypeObject,
+        (void *) PyArray_Size,
+        (void *) PyArray_Scalar,
+        (void *) PyArray_FromScalar,
+        (void *) PyArray_ScalarAsCtype,
+        (void *) PyArray_CastScalarToCtype,
+        (void *) PyArray_CastScalarDirect,
+        (void *) PyArray_Pack,
+        NULL,
+        NULL,
+        NULL,
+        (void *) PyArray_FromAny,
+        (void *) PyArray_EnsureArray,
+        (void *) PyArray_EnsureAnyArray,
+        (void *) PyArray_FromFile,
+        (void *) PyArray_FromString,
+        (void *) PyArray_FromBuffer,
+        (void *) PyArray_FromIter,
+        (void *) PyArray_Return,
+        (void *) PyArray_GetField,
+        (void *) PyArray_SetField,
+        (void *) PyArray_Byteswap,
+        (void *) PyArray_Resize,
+        NULL,
+        NULL,
+        NULL,
+        (void *) PyArray_CopyObject,
+        (void *) PyArray_NewCopy,
+        (void *) PyArray_ToList,
+        (void *) PyArray_ToString,
+        (void *) PyArray_ToFile,
+        (void *) PyArray_Dump,
+        (void *) PyArray_Dumps,
+        (void *) PyArray_ValidType,
+        (void *) PyArray_UpdateFlags,
+        (void *) PyArray_New,
+        (void *) PyArray_NewFromDescr,
+        (void *) PyArray_DescrNew,
+        (void *) PyArray_DescrNewFromType,
+        (void *) PyArray_GetPriority,
+        (void *) PyArray_IterNew,
+        (void *) PyArray_MultiIterNew,
+        (void *) PyArray_PyIntAsInt,
+        (void *) PyArray_PyIntAsIntp,
+        (void *) PyArray_Broadcast,
+        NULL,
+        (void *) PyArray_FillWithScalar,
+        (void *) PyArray_CheckStrides,
+        (void *) PyArray_DescrNewByteorder,
+        (void *) PyArray_IterAllButAxis,
+        (void *) PyArray_CheckFromAny,
+        (void *) PyArray_FromArray,
+        (void *) PyArray_FromInterface,
+        (void *) PyArray_FromStructInterface,
+        (void *) PyArray_FromArrayAttr,
+        (void *) PyArray_ScalarKind,
+        (void *) PyArray_CanCoerceScalar,
+        NULL,
+        (void *) PyArray_CanCastScalar,
+        NULL,
+        (void *) PyArray_RemoveSmallest,
+        (void *) PyArray_ElementStrides,
+        (void *) PyArray_Item_INCREF,
+        (void *) PyArray_Item_XDECREF,
+        NULL,
+        (void *) PyArray_Transpose,
+        (void *) PyArray_TakeFrom,
+        (void *) PyArray_PutTo,
+        (void *) PyArray_PutMask,
+        (void *) PyArray_Repeat,
+        (void *) PyArray_Choose,
+        (void *) PyArray_Sort,
+        (void *) PyArray_ArgSort,
+        (void *) PyArray_SearchSorted,
+        (void *) PyArray_ArgMax,
+        (void *) PyArray_ArgMin,
+        (void *) PyArray_Reshape,
+        (void *) PyArray_Newshape,
+        (void *) PyArray_Squeeze,
+        (void *) PyArray_View,
+        (void *) PyArray_SwapAxes,
+        (void *) PyArray_Max,
+        (void *) PyArray_Min,
+        (void *) PyArray_Ptp,
+        (void *) PyArray_Mean,
+        (void *) PyArray_Trace,
+        (void *) PyArray_Diagonal,
+        (void *) PyArray_Clip,
+        (void *) PyArray_Conjugate,
+        (void *) PyArray_Nonzero,
+        (void *) PyArray_Std,
+        (void *) PyArray_Sum,
+        (void *) PyArray_CumSum,
+        (void *) PyArray_Prod,
+        (void *) PyArray_CumProd,
+        (void *) PyArray_All,
+        (void *) PyArray_Any,
+        (void *) PyArray_Compress,
+        (void *) PyArray_Flatten,
+        (void *) PyArray_Ravel,
+        (void *) PyArray_MultiplyList,
+        (void *) PyArray_MultiplyIntList,
+        (void *) PyArray_GetPtr,
+        (void *) PyArray_CompareLists,
+        (void *) PyArray_AsCArray,
+        NULL,
+        NULL,
+        (void *) PyArray_Free,
+        (void *) PyArray_Converter,
+        (void *) PyArray_IntpFromSequence,
+        (void *) PyArray_Concatenate,
+        (void *) PyArray_InnerProduct,
+        (void *) PyArray_MatrixProduct,
+        NULL,
+        (void *) PyArray_Correlate,
+        NULL,
+        (void *) PyArray_DescrConverter,
+        (void *) PyArray_DescrConverter2,
+        (void *) PyArray_IntpConverter,
+        (void *) PyArray_BufferConverter,
+        (void *) PyArray_AxisConverter,
+        (void *) PyArray_BoolConverter,
+        (void *) PyArray_ByteorderConverter,
+        (void *) PyArray_OrderConverter,
+        (void *) PyArray_EquivTypes,
+        (void *) PyArray_Zeros,
+        (void *) PyArray_Empty,
+        (void *) PyArray_Where,
+        (void *) PyArray_Arange,
+        (void *) PyArray_ArangeObj,
+        (void *) PyArray_SortkindConverter,
+        (void *) PyArray_LexSort,
+        (void *) PyArray_Round,
+        (void *) PyArray_EquivTypenums,
+        (void *) PyArray_RegisterDataType,
+        (void *) PyArray_RegisterCastFunc,
+        (void *) PyArray_RegisterCanCast,
+        (void *) PyArray_InitArrFuncs,
+        (void *) PyArray_IntTupleFromIntp,
+        NULL,
+        (void *) PyArray_ClipmodeConverter,
+        (void *) PyArray_OutputConverter,
+        (void *) PyArray_BroadcastToShape,
+        NULL,
+        NULL,
+        (void *) PyArray_DescrAlignConverter,
+        (void *) PyArray_DescrAlignConverter2,
+        (void *) PyArray_SearchsideConverter,
+        (void *) PyArray_CheckAxis,
+        (void *) PyArray_OverflowMultiplyList,
+        NULL,
+        (void *) PyArray_MultiIterFromObjects,
+        (void *) PyArray_GetEndianness,
+        (void *) PyArray_GetNDArrayCFeatureVersion,
+        (void *) PyArray_Correlate2,
+        (void *) PyArray_NeighborhoodIterNew,
+        (void *) &PyTimeIntegerArrType_Type,
+        (void *) &PyDatetimeArrType_Type,
+        (void *) &PyTimedeltaArrType_Type,
+        (void *) &PyHalfArrType_Type,
+        (void *) &NpyIter_Type,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        (void *) NpyIter_GetTransferFlags,
+        (void *) NpyIter_New,
+        (void *) NpyIter_MultiNew,
+        (void *) NpyIter_AdvancedNew,
+        (void *) NpyIter_Copy,
+        (void *) NpyIter_Deallocate,
+        (void *) NpyIter_HasDelayedBufAlloc,
+        (void *) NpyIter_HasExternalLoop,
+        (void *) NpyIter_EnableExternalLoop,
+        (void *) NpyIter_GetInnerStrideArray,
+        (void *) NpyIter_GetInnerLoopSizePtr,
+        (void *) NpyIter_Reset,
+        (void *) NpyIter_ResetBasePointers,
+        (void *) NpyIter_ResetToIterIndexRange,
+        (void *) NpyIter_GetNDim,
+        (void *) NpyIter_GetNOp,
+        (void *) NpyIter_GetIterNext,
+        (void *) NpyIter_GetIterSize,
+        (void *) NpyIter_GetIterIndexRange,
+        (void *) NpyIter_GetIterIndex,
+        (void *) NpyIter_GotoIterIndex,
+        (void *) NpyIter_HasMultiIndex,
+        (void *) NpyIter_GetShape,
+        (void *) NpyIter_GetGetMultiIndex,
+        (void *) NpyIter_GotoMultiIndex,
+        (void *) NpyIter_RemoveMultiIndex,
+        (void *) NpyIter_HasIndex,
+        (void *) NpyIter_IsBuffered,
+        (void *) NpyIter_IsGrowInner,
+        (void *) NpyIter_GetBufferSize,
+        (void *) NpyIter_GetIndexPtr,
+        (void *) NpyIter_GotoIndex,
+        (void *) NpyIter_GetDataPtrArray,
+        (void *) NpyIter_GetDescrArray,
+        (void *) NpyIter_GetOperandArray,
+        (void *) NpyIter_GetIterView,
+        (void *) NpyIter_GetReadFlags,
+        (void *) NpyIter_GetWriteFlags,
+        (void *) NpyIter_DebugPrint,
+        (void *) NpyIter_IterationNeedsAPI,
+        (void *) NpyIter_GetInnerFixedStrideArray,
+        (void *) NpyIter_RemoveAxis,
+        (void *) NpyIter_GetAxisStrideArray,
+        (void *) NpyIter_RequiresBuffering,
+        (void *) NpyIter_GetInitialDataPtrArray,
+        (void *) NpyIter_CreateCompatibleStrides,
+        (void *) PyArray_CastingConverter,
+        (void *) PyArray_CountNonzero,
+        (void *) PyArray_PromoteTypes,
+        (void *) PyArray_MinScalarType,
+        (void *) PyArray_ResultType,
+        (void *) PyArray_CanCastArrayTo,
+        (void *) PyArray_CanCastTypeTo,
+        (void *) PyArray_EinsteinSum,
+        (void *) PyArray_NewLikeArray,
+        NULL,
+        (void *) PyArray_ConvertClipmodeSequence,
+        (void *) PyArray_MatrixProduct2,
+        (void *) NpyIter_IsFirstVisit,
+        (void *) PyArray_SetBaseObject,
+        (void *) PyArray_CreateSortedStridePerm,
+        (void *) PyArray_RemoveAxesInPlace,
+        (void *) PyArray_DebugPrint,
+        (void *) PyArray_FailUnlessWriteable,
+        (void *) PyArray_SetUpdateIfCopyBase,
+        (void *) PyDataMem_NEW,
+        (void *) PyDataMem_FREE,
+        (void *) PyDataMem_RENEW,
+        NULL,
+        (NPY_CASTING *) &NPY_DEFAULT_ASSIGN_CASTING,
+        NULL,
+        NULL,
+        NULL,
+        (void *) PyArray_Partition,
+        (void *) PyArray_ArgPartition,
+        (void *) PyArray_SelectkindConverter,
+        (void *) PyDataMem_NEW_ZEROED,
+        (void *) PyArray_CheckAnyScalarExact,
+        NULL,
+        (void *) PyArray_ResolveWritebackIfCopy,
+        (void *) PyArray_SetWritebackIfCopyBase,
+        (void *) PyDataMem_SetHandler,
+        (void *) PyDataMem_GetHandler,
+        (PyObject* *) &PyDataMem_DefaultHandler,
+        (void *) NpyDatetime_ConvertDatetime64ToDatetimeStruct,
+        (void *) NpyDatetime_ConvertDatetimeStructToDatetime64,
+        (void *) NpyDatetime_ConvertPyDateTimeToDatetimeStruct,
+        (void *) NpyDatetime_GetDatetimeISO8601StrLen,
+        (void *) NpyDatetime_MakeISO8601Datetime,
+        (void *) NpyDatetime_ParseISO8601Datetime,
+        (void *) NpyString_load,
+        (void *) NpyString_pack,
+        (void *) NpyString_pack_null,
+        (void *) NpyString_acquire_allocator,
+        (void *) NpyString_acquire_allocators,
+        (void *) NpyString_release_allocator,
+        (void *) NpyString_release_allocators,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        NULL,
+        (void *) PyArray_GetDefaultDescr,
+        (void *) PyArrayInitDTypeMeta_FromSpec,
+        (void *) PyArray_CommonDType,
+        (void *) PyArray_PromoteDTypeSequence,
+        (void *) _PyDataType_GetArrFuncs,
+        NULL,
+        NULL,
+        NULL
+};
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__multiarray_api.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__multiarray_api.h
new file mode 100644
index 0000000..34363fb
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__multiarray_api.h
@@ -0,0 +1,1622 @@
+
+#if defined(_MULTIARRAYMODULE) || defined(WITH_CPYCHECKER_STEALS_REFERENCE_TO_ARG_ATTRIBUTE)
+
+typedef struct {
+        PyObject_HEAD
+        npy_bool obval;
+} PyBoolScalarObject;
+
+extern NPY_NO_EXPORT PyTypeObject PyArrayNeighborhoodIter_Type;
+extern NPY_NO_EXPORT PyBoolScalarObject _PyArrayScalar_BoolValues[2];
+
+NPY_NO_EXPORT  unsigned int PyArray_GetNDArrayCVersion \
+       (void);
+extern NPY_NO_EXPORT PyTypeObject PyArray_Type;
+
+extern NPY_NO_EXPORT PyArray_DTypeMeta PyArrayDescr_TypeFull;
+#define PyArrayDescr_Type (*(PyTypeObject *)(&PyArrayDescr_TypeFull))
+
+extern NPY_NO_EXPORT PyTypeObject PyArrayIter_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyArrayMultiIter_Type;
+
+extern NPY_NO_EXPORT int NPY_NUMUSERTYPES;
+
+extern NPY_NO_EXPORT PyTypeObject PyBoolArrType_Type;
+
+extern NPY_NO_EXPORT PyBoolScalarObject _PyArrayScalar_BoolValues[2];
+
+extern NPY_NO_EXPORT PyTypeObject PyGenericArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyNumberArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyIntegerArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PySignedIntegerArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyUnsignedIntegerArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyInexactArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyFloatingArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyComplexFloatingArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyFlexibleArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyCharacterArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyByteArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyShortArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyIntArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyLongArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyLongLongArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyUByteArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyUShortArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyUIntArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyULongArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyULongLongArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyFloatArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyDoubleArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyLongDoubleArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyCFloatArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyCDoubleArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyCLongDoubleArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyObjectArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyStringArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyUnicodeArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyVoidArrType_Type;
+
+NPY_NO_EXPORT  int PyArray_INCREF \
+       (PyArrayObject *);
+NPY_NO_EXPORT  int PyArray_XDECREF \
+       (PyArrayObject *);
+NPY_NO_EXPORT  void PyArray_SetStringFunction \
+       (PyObject *, int);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_DescrFromType \
+       (int);
+NPY_NO_EXPORT  PyObject * PyArray_TypeObjectFromType \
+       (int);
+NPY_NO_EXPORT  char * PyArray_Zero \
+       (PyArrayObject *);
+NPY_NO_EXPORT  char * PyArray_One \
+       (PyArrayObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_CastToType \
+       (PyArrayObject *, PyArray_Descr *, int);
+NPY_NO_EXPORT  int PyArray_CopyInto \
+       (PyArrayObject *, PyArrayObject *);
+NPY_NO_EXPORT  int PyArray_CopyAnyInto \
+       (PyArrayObject *, PyArrayObject *);
+NPY_NO_EXPORT  int PyArray_CanCastSafely \
+       (int, int);
+NPY_NO_EXPORT  npy_bool PyArray_CanCastTo \
+       (PyArray_Descr *, PyArray_Descr *);
+NPY_NO_EXPORT  int PyArray_ObjectType \
+       (PyObject *, int);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_DescrFromObject \
+       (PyObject *, PyArray_Descr *);
+NPY_NO_EXPORT  PyArrayObject ** PyArray_ConvertToCommonType \
+       (PyObject *, int *);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_DescrFromScalar \
+       (PyObject *);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_DescrFromTypeObject \
+       (PyObject *);
+NPY_NO_EXPORT  npy_intp PyArray_Size \
+       (PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Scalar \
+       (void *, PyArray_Descr *, PyObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_FromScalar \
+       (PyObject *, PyArray_Descr *);
+NPY_NO_EXPORT  void PyArray_ScalarAsCtype \
+       (PyObject *, void *);
+NPY_NO_EXPORT  int PyArray_CastScalarToCtype \
+       (PyObject *, void *, PyArray_Descr *);
+NPY_NO_EXPORT  int PyArray_CastScalarDirect \
+       (PyObject *, PyArray_Descr *, void *, int);
+NPY_NO_EXPORT  int PyArray_Pack \
+       (PyArray_Descr *, void *, PyObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_FromAny \
+       (PyObject *, PyArray_Descr *, int, int, int, PyObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(1) PyObject * PyArray_EnsureArray \
+       (PyObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(1) PyObject * PyArray_EnsureAnyArray \
+       (PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_FromFile \
+       (FILE *, PyArray_Descr *, npy_intp, char *);
+NPY_NO_EXPORT  PyObject * PyArray_FromString \
+       (char *, npy_intp, PyArray_Descr *, npy_intp, char *);
+NPY_NO_EXPORT  PyObject * PyArray_FromBuffer \
+       (PyObject *, PyArray_Descr *, npy_intp, npy_intp);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_FromIter \
+       (PyObject *, PyArray_Descr *, npy_intp);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(1) PyObject * PyArray_Return \
+       (PyArrayObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_GetField \
+       (PyArrayObject *, PyArray_Descr *, int);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) int PyArray_SetField \
+       (PyArrayObject *, PyArray_Descr *, int, PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Byteswap \
+       (PyArrayObject *, npy_bool);
+NPY_NO_EXPORT  PyObject * PyArray_Resize \
+       (PyArrayObject *, PyArray_Dims *, int, NPY_ORDER NPY_UNUSED(order));
+NPY_NO_EXPORT  int PyArray_CopyObject \
+       (PyArrayObject *, PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_NewCopy \
+       (PyArrayObject *, NPY_ORDER);
+NPY_NO_EXPORT  PyObject * PyArray_ToList \
+       (PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_ToString \
+       (PyArrayObject *, NPY_ORDER);
+NPY_NO_EXPORT  int PyArray_ToFile \
+       (PyArrayObject *, FILE *, char *, char *);
+NPY_NO_EXPORT  int PyArray_Dump \
+       (PyObject *, PyObject *, int);
+NPY_NO_EXPORT  PyObject * PyArray_Dumps \
+       (PyObject *, int);
+NPY_NO_EXPORT  int PyArray_ValidType \
+       (int);
+NPY_NO_EXPORT  void PyArray_UpdateFlags \
+       (PyArrayObject *, int);
+NPY_NO_EXPORT  PyObject * PyArray_New \
+       (PyTypeObject *, int, npy_intp const *, int, npy_intp const *, void *, int, int, PyObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_NewFromDescr \
+       (PyTypeObject *, PyArray_Descr *, int, npy_intp const *, npy_intp const *, void *, int, PyObject *);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_DescrNew \
+       (PyArray_Descr *);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_DescrNewFromType \
+       (int);
+NPY_NO_EXPORT  double PyArray_GetPriority \
+       (PyObject *, double);
+NPY_NO_EXPORT  PyObject * PyArray_IterNew \
+       (PyObject *);
+NPY_NO_EXPORT  PyObject* PyArray_MultiIterNew \
+       (int, ...);
+NPY_NO_EXPORT  int PyArray_PyIntAsInt \
+       (PyObject *);
+NPY_NO_EXPORT  npy_intp PyArray_PyIntAsIntp \
+       (PyObject *);
+NPY_NO_EXPORT  int PyArray_Broadcast \
+       (PyArrayMultiIterObject *);
+NPY_NO_EXPORT  int PyArray_FillWithScalar \
+       (PyArrayObject *, PyObject *);
+NPY_NO_EXPORT  npy_bool PyArray_CheckStrides \
+       (int, int, npy_intp, npy_intp, npy_intp const *, npy_intp const *);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_DescrNewByteorder \
+       (PyArray_Descr *, char);
+NPY_NO_EXPORT  PyObject * PyArray_IterAllButAxis \
+       (PyObject *, int *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_CheckFromAny \
+       (PyObject *, PyArray_Descr *, int, int, int, PyObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_FromArray \
+       (PyArrayObject *, PyArray_Descr *, int);
+NPY_NO_EXPORT  PyObject * PyArray_FromInterface \
+       (PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_FromStructInterface \
+       (PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_FromArrayAttr \
+       (PyObject *, PyArray_Descr *, PyObject *);
+NPY_NO_EXPORT  NPY_SCALARKIND PyArray_ScalarKind \
+       (int, PyArrayObject **);
+NPY_NO_EXPORT  int PyArray_CanCoerceScalar \
+       (int, int, NPY_SCALARKIND);
+NPY_NO_EXPORT  npy_bool PyArray_CanCastScalar \
+       (PyTypeObject *, PyTypeObject *);
+NPY_NO_EXPORT  int PyArray_RemoveSmallest \
+       (PyArrayMultiIterObject *);
+NPY_NO_EXPORT  int PyArray_ElementStrides \
+       (PyObject *);
+NPY_NO_EXPORT  void PyArray_Item_INCREF \
+       (char *, PyArray_Descr *);
+NPY_NO_EXPORT  void PyArray_Item_XDECREF \
+       (char *, PyArray_Descr *);
+NPY_NO_EXPORT  PyObject * PyArray_Transpose \
+       (PyArrayObject *, PyArray_Dims *);
+NPY_NO_EXPORT  PyObject * PyArray_TakeFrom \
+       (PyArrayObject *, PyObject *, int, PyArrayObject *, NPY_CLIPMODE);
+NPY_NO_EXPORT  PyObject * PyArray_PutTo \
+       (PyArrayObject *, PyObject*, PyObject *, NPY_CLIPMODE);
+NPY_NO_EXPORT  PyObject * PyArray_PutMask \
+       (PyArrayObject *, PyObject*, PyObject*);
+NPY_NO_EXPORT  PyObject * PyArray_Repeat \
+       (PyArrayObject *, PyObject *, int);
+NPY_NO_EXPORT  PyObject * PyArray_Choose \
+       (PyArrayObject *, PyObject *, PyArrayObject *, NPY_CLIPMODE);
+NPY_NO_EXPORT  int PyArray_Sort \
+       (PyArrayObject *, int, NPY_SORTKIND);
+NPY_NO_EXPORT  PyObject * PyArray_ArgSort \
+       (PyArrayObject *, int, NPY_SORTKIND);
+NPY_NO_EXPORT  PyObject * PyArray_SearchSorted \
+       (PyArrayObject *, PyObject *, NPY_SEARCHSIDE, PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_ArgMax \
+       (PyArrayObject *, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_ArgMin \
+       (PyArrayObject *, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Reshape \
+       (PyArrayObject *, PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Newshape \
+       (PyArrayObject *, PyArray_Dims *, NPY_ORDER);
+NPY_NO_EXPORT  PyObject * PyArray_Squeeze \
+       (PyArrayObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_View \
+       (PyArrayObject *, PyArray_Descr *, PyTypeObject *);
+NPY_NO_EXPORT  PyObject * PyArray_SwapAxes \
+       (PyArrayObject *, int, int);
+NPY_NO_EXPORT  PyObject * PyArray_Max \
+       (PyArrayObject *, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Min \
+       (PyArrayObject *, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Ptp \
+       (PyArrayObject *, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Mean \
+       (PyArrayObject *, int, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Trace \
+       (PyArrayObject *, int, int, int, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Diagonal \
+       (PyArrayObject *, int, int, int);
+NPY_NO_EXPORT  PyObject * PyArray_Clip \
+       (PyArrayObject *, PyObject *, PyObject *, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Conjugate \
+       (PyArrayObject *, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Nonzero \
+       (PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Std \
+       (PyArrayObject *, int, int, PyArrayObject *, int);
+NPY_NO_EXPORT  PyObject * PyArray_Sum \
+       (PyArrayObject *, int, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_CumSum \
+       (PyArrayObject *, int, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Prod \
+       (PyArrayObject *, int, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_CumProd \
+       (PyArrayObject *, int, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_All \
+       (PyArrayObject *, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Any \
+       (PyArrayObject *, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Compress \
+       (PyArrayObject *, PyObject *, int, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Flatten \
+       (PyArrayObject *, NPY_ORDER);
+NPY_NO_EXPORT  PyObject * PyArray_Ravel \
+       (PyArrayObject *, NPY_ORDER);
+NPY_NO_EXPORT  npy_intp PyArray_MultiplyList \
+       (npy_intp const *, int);
+NPY_NO_EXPORT  int PyArray_MultiplyIntList \
+       (int const *, int);
+NPY_NO_EXPORT  void * PyArray_GetPtr \
+       (PyArrayObject *, npy_intp const*);
+NPY_NO_EXPORT  int PyArray_CompareLists \
+       (npy_intp const *, npy_intp const *, int);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(5) int PyArray_AsCArray \
+       (PyObject **, void *, npy_intp *, int, PyArray_Descr*);
+NPY_NO_EXPORT  int PyArray_Free \
+       (PyObject *, void *);
+NPY_NO_EXPORT  int PyArray_Converter \
+       (PyObject *, PyObject **);
+NPY_NO_EXPORT  int PyArray_IntpFromSequence \
+       (PyObject *, npy_intp *, int);
+NPY_NO_EXPORT  PyObject * PyArray_Concatenate \
+       (PyObject *, int);
+NPY_NO_EXPORT  PyObject * PyArray_InnerProduct \
+       (PyObject *, PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_MatrixProduct \
+       (PyObject *, PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Correlate \
+       (PyObject *, PyObject *, int);
+NPY_NO_EXPORT  int PyArray_DescrConverter \
+       (PyObject *, PyArray_Descr **);
+NPY_NO_EXPORT  int PyArray_DescrConverter2 \
+       (PyObject *, PyArray_Descr **);
+NPY_NO_EXPORT  int PyArray_IntpConverter \
+       (PyObject *, PyArray_Dims *);
+NPY_NO_EXPORT  int PyArray_BufferConverter \
+       (PyObject *, PyArray_Chunk *);
+NPY_NO_EXPORT  int PyArray_AxisConverter \
+       (PyObject *, int *);
+NPY_NO_EXPORT  int PyArray_BoolConverter \
+       (PyObject *, npy_bool *);
+NPY_NO_EXPORT  int PyArray_ByteorderConverter \
+       (PyObject *, char *);
+NPY_NO_EXPORT  int PyArray_OrderConverter \
+       (PyObject *, NPY_ORDER *);
+NPY_NO_EXPORT  unsigned char PyArray_EquivTypes \
+       (PyArray_Descr *, PyArray_Descr *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(3) PyObject * PyArray_Zeros \
+       (int, npy_intp const *, PyArray_Descr *, int);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(3) PyObject * PyArray_Empty \
+       (int, npy_intp const *, PyArray_Descr *, int);
+NPY_NO_EXPORT  PyObject * PyArray_Where \
+       (PyObject *, PyObject *, PyObject *);
+NPY_NO_EXPORT  PyObject * PyArray_Arange \
+       (double, double, double, int);
+NPY_NO_EXPORT  PyObject * PyArray_ArangeObj \
+       (PyObject *, PyObject *, PyObject *, PyArray_Descr *);
+NPY_NO_EXPORT  int PyArray_SortkindConverter \
+       (PyObject *, NPY_SORTKIND *);
+NPY_NO_EXPORT  PyObject * PyArray_LexSort \
+       (PyObject *, int);
+NPY_NO_EXPORT  PyObject * PyArray_Round \
+       (PyArrayObject *, int, PyArrayObject *);
+NPY_NO_EXPORT  unsigned char PyArray_EquivTypenums \
+       (int, int);
+NPY_NO_EXPORT  int PyArray_RegisterDataType \
+       (PyArray_DescrProto *);
+NPY_NO_EXPORT  int PyArray_RegisterCastFunc \
+       (PyArray_Descr *, int, PyArray_VectorUnaryFunc *);
+NPY_NO_EXPORT  int PyArray_RegisterCanCast \
+       (PyArray_Descr *, int, NPY_SCALARKIND);
+NPY_NO_EXPORT  void PyArray_InitArrFuncs \
+       (PyArray_ArrFuncs *);
+NPY_NO_EXPORT  PyObject * PyArray_IntTupleFromIntp \
+       (int, npy_intp const *);
+NPY_NO_EXPORT  int PyArray_ClipmodeConverter \
+       (PyObject *, NPY_CLIPMODE *);
+NPY_NO_EXPORT  int PyArray_OutputConverter \
+       (PyObject *, PyArrayObject **);
+NPY_NO_EXPORT  PyObject * PyArray_BroadcastToShape \
+       (PyObject *, npy_intp *, int);
+NPY_NO_EXPORT  int PyArray_DescrAlignConverter \
+       (PyObject *, PyArray_Descr **);
+NPY_NO_EXPORT  int PyArray_DescrAlignConverter2 \
+       (PyObject *, PyArray_Descr **);
+NPY_NO_EXPORT  int PyArray_SearchsideConverter \
+       (PyObject *, void *);
+NPY_NO_EXPORT  PyObject * PyArray_CheckAxis \
+       (PyArrayObject *, int *, int);
+NPY_NO_EXPORT  npy_intp PyArray_OverflowMultiplyList \
+       (npy_intp const *, int);
+NPY_NO_EXPORT  PyObject* PyArray_MultiIterFromObjects \
+       (PyObject **, int, int, ...);
+NPY_NO_EXPORT  int PyArray_GetEndianness \
+       (void);
+NPY_NO_EXPORT  unsigned int PyArray_GetNDArrayCFeatureVersion \
+       (void);
+NPY_NO_EXPORT  PyObject * PyArray_Correlate2 \
+       (PyObject *, PyObject *, int);
+NPY_NO_EXPORT  PyObject* PyArray_NeighborhoodIterNew \
+       (PyArrayIterObject *, const npy_intp *, int, PyArrayObject*);
+extern NPY_NO_EXPORT PyTypeObject PyTimeIntegerArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyDatetimeArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyTimedeltaArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyHalfArrType_Type;
+
+extern NPY_NO_EXPORT PyTypeObject NpyIter_Type;
+
+NPY_NO_EXPORT  NPY_ARRAYMETHOD_FLAGS NpyIter_GetTransferFlags \
+       (NpyIter *);
+NPY_NO_EXPORT  NpyIter * NpyIter_New \
+       (PyArrayObject *, npy_uint32, NPY_ORDER, NPY_CASTING, PyArray_Descr*);
+NPY_NO_EXPORT  NpyIter * NpyIter_MultiNew \
+       (int, PyArrayObject **, npy_uint32, NPY_ORDER, NPY_CASTING, npy_uint32 *, PyArray_Descr **);
+NPY_NO_EXPORT  NpyIter * NpyIter_AdvancedNew \
+       (int, PyArrayObject **, npy_uint32, NPY_ORDER, NPY_CASTING, npy_uint32 *, PyArray_Descr **, int, int **, npy_intp *, npy_intp);
+NPY_NO_EXPORT  NpyIter * NpyIter_Copy \
+       (NpyIter *);
+NPY_NO_EXPORT  int NpyIter_Deallocate \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_bool NpyIter_HasDelayedBufAlloc \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_bool NpyIter_HasExternalLoop \
+       (NpyIter *);
+NPY_NO_EXPORT  int NpyIter_EnableExternalLoop \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_intp * NpyIter_GetInnerStrideArray \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_intp * NpyIter_GetInnerLoopSizePtr \
+       (NpyIter *);
+NPY_NO_EXPORT  int NpyIter_Reset \
+       (NpyIter *, char **);
+NPY_NO_EXPORT  int NpyIter_ResetBasePointers \
+       (NpyIter *, char **, char **);
+NPY_NO_EXPORT  int NpyIter_ResetToIterIndexRange \
+       (NpyIter *, npy_intp, npy_intp, char **);
+NPY_NO_EXPORT  int NpyIter_GetNDim \
+       (NpyIter *);
+NPY_NO_EXPORT  int NpyIter_GetNOp \
+       (NpyIter *);
+NPY_NO_EXPORT  NpyIter_IterNextFunc * NpyIter_GetIterNext \
+       (NpyIter *, char **);
+NPY_NO_EXPORT  npy_intp NpyIter_GetIterSize \
+       (NpyIter *);
+NPY_NO_EXPORT  void NpyIter_GetIterIndexRange \
+       (NpyIter *, npy_intp *, npy_intp *);
+NPY_NO_EXPORT  npy_intp NpyIter_GetIterIndex \
+       (NpyIter *);
+NPY_NO_EXPORT  int NpyIter_GotoIterIndex \
+       (NpyIter *, npy_intp);
+NPY_NO_EXPORT  npy_bool NpyIter_HasMultiIndex \
+       (NpyIter *);
+NPY_NO_EXPORT  int NpyIter_GetShape \
+       (NpyIter *, npy_intp *);
+NPY_NO_EXPORT  NpyIter_GetMultiIndexFunc * NpyIter_GetGetMultiIndex \
+       (NpyIter *, char **);
+NPY_NO_EXPORT  int NpyIter_GotoMultiIndex \
+       (NpyIter *, npy_intp const *);
+NPY_NO_EXPORT  int NpyIter_RemoveMultiIndex \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_bool NpyIter_HasIndex \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_bool NpyIter_IsBuffered \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_bool NpyIter_IsGrowInner \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_intp NpyIter_GetBufferSize \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_intp * NpyIter_GetIndexPtr \
+       (NpyIter *);
+NPY_NO_EXPORT  int NpyIter_GotoIndex \
+       (NpyIter *, npy_intp);
+NPY_NO_EXPORT  char ** NpyIter_GetDataPtrArray \
+       (NpyIter *);
+NPY_NO_EXPORT  PyArray_Descr ** NpyIter_GetDescrArray \
+       (NpyIter *);
+NPY_NO_EXPORT  PyArrayObject ** NpyIter_GetOperandArray \
+       (NpyIter *);
+NPY_NO_EXPORT  PyArrayObject * NpyIter_GetIterView \
+       (NpyIter *, npy_intp);
+NPY_NO_EXPORT  void NpyIter_GetReadFlags \
+       (NpyIter *, char *);
+NPY_NO_EXPORT  void NpyIter_GetWriteFlags \
+       (NpyIter *, char *);
+NPY_NO_EXPORT  void NpyIter_DebugPrint \
+       (NpyIter *);
+NPY_NO_EXPORT  npy_bool NpyIter_IterationNeedsAPI \
+       (NpyIter *);
+NPY_NO_EXPORT  void NpyIter_GetInnerFixedStrideArray \
+       (NpyIter *, npy_intp *);
+NPY_NO_EXPORT  int NpyIter_RemoveAxis \
+       (NpyIter *, int);
+NPY_NO_EXPORT  npy_intp * NpyIter_GetAxisStrideArray \
+       (NpyIter *, int);
+NPY_NO_EXPORT  npy_bool NpyIter_RequiresBuffering \
+       (NpyIter *);
+NPY_NO_EXPORT  char ** NpyIter_GetInitialDataPtrArray \
+       (NpyIter *);
+NPY_NO_EXPORT  int NpyIter_CreateCompatibleStrides \
+       (NpyIter *, npy_intp, npy_intp *);
+NPY_NO_EXPORT  int PyArray_CastingConverter \
+       (PyObject *, NPY_CASTING *);
+NPY_NO_EXPORT  npy_intp PyArray_CountNonzero \
+       (PyArrayObject *);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_PromoteTypes \
+       (PyArray_Descr *, PyArray_Descr *);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_MinScalarType \
+       (PyArrayObject *);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_ResultType \
+       (npy_intp, PyArrayObject *arrs[], npy_intp, PyArray_Descr *descrs[]);
+NPY_NO_EXPORT  npy_bool PyArray_CanCastArrayTo \
+       (PyArrayObject *, PyArray_Descr *, NPY_CASTING);
+NPY_NO_EXPORT  npy_bool PyArray_CanCastTypeTo \
+       (PyArray_Descr *, PyArray_Descr *, NPY_CASTING);
+NPY_NO_EXPORT  PyArrayObject * PyArray_EinsteinSum \
+       (char *, npy_intp, PyArrayObject **, PyArray_Descr *, NPY_ORDER, NPY_CASTING, PyArrayObject *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(3) PyObject * PyArray_NewLikeArray \
+       (PyArrayObject *, NPY_ORDER, PyArray_Descr *, int);
+NPY_NO_EXPORT  int PyArray_ConvertClipmodeSequence \
+       (PyObject *, NPY_CLIPMODE *, int);
+NPY_NO_EXPORT  PyObject * PyArray_MatrixProduct2 \
+       (PyObject *, PyObject *, PyArrayObject*);
+NPY_NO_EXPORT  npy_bool NpyIter_IsFirstVisit \
+       (NpyIter *, int);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) int PyArray_SetBaseObject \
+       (PyArrayObject *, PyObject *);
+NPY_NO_EXPORT  void PyArray_CreateSortedStridePerm \
+       (int, npy_intp const *, npy_stride_sort_item *);
+NPY_NO_EXPORT  void PyArray_RemoveAxesInPlace \
+       (PyArrayObject *, const npy_bool *);
+NPY_NO_EXPORT  void PyArray_DebugPrint \
+       (PyArrayObject *);
+NPY_NO_EXPORT  int PyArray_FailUnlessWriteable \
+       (PyArrayObject *, const char *);
+NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) int PyArray_SetUpdateIfCopyBase \
+       (PyArrayObject *, PyArrayObject *);
+NPY_NO_EXPORT  void * PyDataMem_NEW \
+       (size_t);
+NPY_NO_EXPORT  void PyDataMem_FREE \
+       (void *);
+NPY_NO_EXPORT  void * PyDataMem_RENEW \
+       (void *, size_t);
+extern NPY_NO_EXPORT NPY_CASTING NPY_DEFAULT_ASSIGN_CASTING;
+
+NPY_NO_EXPORT  int PyArray_Partition \
+       (PyArrayObject *, PyArrayObject *, int, NPY_SELECTKIND);
+NPY_NO_EXPORT  PyObject * PyArray_ArgPartition \
+       (PyArrayObject *, PyArrayObject *, int, NPY_SELECTKIND);
+NPY_NO_EXPORT  int PyArray_SelectkindConverter \
+       (PyObject *, NPY_SELECTKIND *);
+NPY_NO_EXPORT  void * PyDataMem_NEW_ZEROED \
+       (size_t, size_t);
+NPY_NO_EXPORT  int PyArray_CheckAnyScalarExact \
+       (PyObject *);
+NPY_NO_EXPORT  int PyArray_ResolveWritebackIfCopy \
+       (PyArrayObject *);
+NPY_NO_EXPORT  int PyArray_SetWritebackIfCopyBase \
+       (PyArrayObject *, PyArrayObject *);
+NPY_NO_EXPORT  PyObject * PyDataMem_SetHandler \
+       (PyObject *);
+NPY_NO_EXPORT  PyObject * PyDataMem_GetHandler \
+       (void);
+extern NPY_NO_EXPORT PyObject* PyDataMem_DefaultHandler;
+
+NPY_NO_EXPORT  int NpyDatetime_ConvertDatetime64ToDatetimeStruct \
+       (PyArray_DatetimeMetaData *, npy_datetime, npy_datetimestruct *);
+NPY_NO_EXPORT  int NpyDatetime_ConvertDatetimeStructToDatetime64 \
+       (PyArray_DatetimeMetaData *, const npy_datetimestruct *, npy_datetime *);
+NPY_NO_EXPORT  int NpyDatetime_ConvertPyDateTimeToDatetimeStruct \
+       (PyObject *, npy_datetimestruct *, NPY_DATETIMEUNIT *, int);
+NPY_NO_EXPORT  int NpyDatetime_GetDatetimeISO8601StrLen \
+       (int, NPY_DATETIMEUNIT);
+NPY_NO_EXPORT  int NpyDatetime_MakeISO8601Datetime \
+       (npy_datetimestruct *, char *, npy_intp, int, int, NPY_DATETIMEUNIT, int, NPY_CASTING);
+NPY_NO_EXPORT  int NpyDatetime_ParseISO8601Datetime \
+       (char const *, Py_ssize_t, NPY_DATETIMEUNIT, NPY_CASTING, npy_datetimestruct *, NPY_DATETIMEUNIT *, npy_bool *);
+NPY_NO_EXPORT  int NpyString_load \
+       (npy_string_allocator *, const npy_packed_static_string *, npy_static_string *);
+NPY_NO_EXPORT  int NpyString_pack \
+       (npy_string_allocator *, npy_packed_static_string *, const char *, size_t);
+NPY_NO_EXPORT  int NpyString_pack_null \
+       (npy_string_allocator *, npy_packed_static_string *);
+NPY_NO_EXPORT  npy_string_allocator * NpyString_acquire_allocator \
+       (const PyArray_StringDTypeObject *);
+NPY_NO_EXPORT  void NpyString_acquire_allocators \
+       (size_t, PyArray_Descr *const descrs[], npy_string_allocator *allocators[]);
+NPY_NO_EXPORT  void NpyString_release_allocator \
+       (npy_string_allocator *);
+NPY_NO_EXPORT  void NpyString_release_allocators \
+       (size_t, npy_string_allocator *allocators[]);
+NPY_NO_EXPORT  PyArray_Descr * PyArray_GetDefaultDescr \
+       (PyArray_DTypeMeta *);
+NPY_NO_EXPORT  int PyArrayInitDTypeMeta_FromSpec \
+       (PyArray_DTypeMeta *, PyArrayDTypeMeta_Spec *);
+NPY_NO_EXPORT  PyArray_DTypeMeta * PyArray_CommonDType \
+       (PyArray_DTypeMeta *, PyArray_DTypeMeta *);
+NPY_NO_EXPORT  PyArray_DTypeMeta * PyArray_PromoteDTypeSequence \
+       (npy_intp, PyArray_DTypeMeta **);
+NPY_NO_EXPORT  PyArray_ArrFuncs * _PyDataType_GetArrFuncs \
+       (const PyArray_Descr *);
+
+#else
+
+#if defined(PY_ARRAY_UNIQUE_SYMBOL)
+    #define PyArray_API PY_ARRAY_UNIQUE_SYMBOL
+    #define _NPY_VERSION_CONCAT_HELPER2(x, y) x ## y
+    #define _NPY_VERSION_CONCAT_HELPER(arg) \
+        _NPY_VERSION_CONCAT_HELPER2(arg, PyArray_RUNTIME_VERSION)
+    #define PyArray_RUNTIME_VERSION \
+        _NPY_VERSION_CONCAT_HELPER(PY_ARRAY_UNIQUE_SYMBOL)
+#endif
+
+/* By default do not export API in an .so (was never the case on windows) */
+#ifndef NPY_API_SYMBOL_ATTRIBUTE
+    #define NPY_API_SYMBOL_ATTRIBUTE NPY_VISIBILITY_HIDDEN
+#endif
+
+#if defined(NO_IMPORT) || defined(NO_IMPORT_ARRAY)
+extern NPY_API_SYMBOL_ATTRIBUTE void **PyArray_API;
+extern NPY_API_SYMBOL_ATTRIBUTE int PyArray_RUNTIME_VERSION;
+#else
+#if defined(PY_ARRAY_UNIQUE_SYMBOL)
+NPY_API_SYMBOL_ATTRIBUTE void **PyArray_API;
+NPY_API_SYMBOL_ATTRIBUTE int PyArray_RUNTIME_VERSION;
+#else
+static void **PyArray_API = NULL;
+static int PyArray_RUNTIME_VERSION = 0;
+#endif
+#endif
+
+#define PyArray_GetNDArrayCVersion \
+        (*(unsigned int (*)(void)) \
+    PyArray_API[0])
+#define PyArray_Type (*(PyTypeObject *)PyArray_API[2])
+#define PyArrayDescr_Type (*(PyTypeObject *)PyArray_API[3])
+#define PyArrayIter_Type (*(PyTypeObject *)PyArray_API[5])
+#define PyArrayMultiIter_Type (*(PyTypeObject *)PyArray_API[6])
+#define NPY_NUMUSERTYPES (*(int *)PyArray_API[7])
+#define PyBoolArrType_Type (*(PyTypeObject *)PyArray_API[8])
+#define _PyArrayScalar_BoolValues ((PyBoolScalarObject *)PyArray_API[9])
+#define PyGenericArrType_Type (*(PyTypeObject *)PyArray_API[10])
+#define PyNumberArrType_Type (*(PyTypeObject *)PyArray_API[11])
+#define PyIntegerArrType_Type (*(PyTypeObject *)PyArray_API[12])
+#define PySignedIntegerArrType_Type (*(PyTypeObject *)PyArray_API[13])
+#define PyUnsignedIntegerArrType_Type (*(PyTypeObject *)PyArray_API[14])
+#define PyInexactArrType_Type (*(PyTypeObject *)PyArray_API[15])
+#define PyFloatingArrType_Type (*(PyTypeObject *)PyArray_API[16])
+#define PyComplexFloatingArrType_Type (*(PyTypeObject *)PyArray_API[17])
+#define PyFlexibleArrType_Type (*(PyTypeObject *)PyArray_API[18])
+#define PyCharacterArrType_Type (*(PyTypeObject *)PyArray_API[19])
+#define PyByteArrType_Type (*(PyTypeObject *)PyArray_API[20])
+#define PyShortArrType_Type (*(PyTypeObject *)PyArray_API[21])
+#define PyIntArrType_Type (*(PyTypeObject *)PyArray_API[22])
+#define PyLongArrType_Type (*(PyTypeObject *)PyArray_API[23])
+#define PyLongLongArrType_Type (*(PyTypeObject *)PyArray_API[24])
+#define PyUByteArrType_Type (*(PyTypeObject *)PyArray_API[25])
+#define PyUShortArrType_Type (*(PyTypeObject *)PyArray_API[26])
+#define PyUIntArrType_Type (*(PyTypeObject *)PyArray_API[27])
+#define PyULongArrType_Type (*(PyTypeObject *)PyArray_API[28])
+#define PyULongLongArrType_Type (*(PyTypeObject *)PyArray_API[29])
+#define PyFloatArrType_Type (*(PyTypeObject *)PyArray_API[30])
+#define PyDoubleArrType_Type (*(PyTypeObject *)PyArray_API[31])
+#define PyLongDoubleArrType_Type (*(PyTypeObject *)PyArray_API[32])
+#define PyCFloatArrType_Type (*(PyTypeObject *)PyArray_API[33])
+#define PyCDoubleArrType_Type (*(PyTypeObject *)PyArray_API[34])
+#define PyCLongDoubleArrType_Type (*(PyTypeObject *)PyArray_API[35])
+#define PyObjectArrType_Type (*(PyTypeObject *)PyArray_API[36])
+#define PyStringArrType_Type (*(PyTypeObject *)PyArray_API[37])
+#define PyUnicodeArrType_Type (*(PyTypeObject *)PyArray_API[38])
+#define PyVoidArrType_Type (*(PyTypeObject *)PyArray_API[39])
+#define PyArray_INCREF \
+        (*(int (*)(PyArrayObject *)) \
+    PyArray_API[42])
+#define PyArray_XDECREF \
+        (*(int (*)(PyArrayObject *)) \
+    PyArray_API[43])
+#define PyArray_SetStringFunction \
+        (*(void (*)(PyObject *, int)) \
+    PyArray_API[44])
+#define PyArray_DescrFromType \
+        (*(PyArray_Descr * (*)(int)) \
+    PyArray_API[45])
+#define PyArray_TypeObjectFromType \
+        (*(PyObject * (*)(int)) \
+    PyArray_API[46])
+#define PyArray_Zero \
+        (*(char * (*)(PyArrayObject *)) \
+    PyArray_API[47])
+#define PyArray_One \
+        (*(char * (*)(PyArrayObject *)) \
+    PyArray_API[48])
+#define PyArray_CastToType \
+        (*(PyObject * (*)(PyArrayObject *, PyArray_Descr *, int)) \
+    PyArray_API[49])
+#define PyArray_CopyInto \
+        (*(int (*)(PyArrayObject *, PyArrayObject *)) \
+    PyArray_API[50])
+#define PyArray_CopyAnyInto \
+        (*(int (*)(PyArrayObject *, PyArrayObject *)) \
+    PyArray_API[51])
+#define PyArray_CanCastSafely \
+        (*(int (*)(int, int)) \
+    PyArray_API[52])
+#define PyArray_CanCastTo \
+        (*(npy_bool (*)(PyArray_Descr *, PyArray_Descr *)) \
+    PyArray_API[53])
+#define PyArray_ObjectType \
+        (*(int (*)(PyObject *, int)) \
+    PyArray_API[54])
+#define PyArray_DescrFromObject \
+        (*(PyArray_Descr * (*)(PyObject *, PyArray_Descr *)) \
+    PyArray_API[55])
+#define PyArray_ConvertToCommonType \
+        (*(PyArrayObject ** (*)(PyObject *, int *)) \
+    PyArray_API[56])
+#define PyArray_DescrFromScalar \
+        (*(PyArray_Descr * (*)(PyObject *)) \
+    PyArray_API[57])
+#define PyArray_DescrFromTypeObject \
+        (*(PyArray_Descr * (*)(PyObject *)) \
+    PyArray_API[58])
+#define PyArray_Size \
+        (*(npy_intp (*)(PyObject *)) \
+    PyArray_API[59])
+#define PyArray_Scalar \
+        (*(PyObject * (*)(void *, PyArray_Descr *, PyObject *)) \
+    PyArray_API[60])
+#define PyArray_FromScalar \
+        (*(PyObject * (*)(PyObject *, PyArray_Descr *)) \
+    PyArray_API[61])
+#define PyArray_ScalarAsCtype \
+        (*(void (*)(PyObject *, void *)) \
+    PyArray_API[62])
+#define PyArray_CastScalarToCtype \
+        (*(int (*)(PyObject *, void *, PyArray_Descr *)) \
+    PyArray_API[63])
+#define PyArray_CastScalarDirect \
+        (*(int (*)(PyObject *, PyArray_Descr *, void *, int)) \
+    PyArray_API[64])
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define PyArray_Pack \
+        (*(int (*)(PyArray_Descr *, void *, PyObject *)) \
+    PyArray_API[65])
+#endif
+#define PyArray_FromAny \
+        (*(PyObject * (*)(PyObject *, PyArray_Descr *, int, int, int, PyObject *)) \
+    PyArray_API[69])
+#define PyArray_EnsureArray \
+        (*(PyObject * (*)(PyObject *)) \
+    PyArray_API[70])
+#define PyArray_EnsureAnyArray \
+        (*(PyObject * (*)(PyObject *)) \
+    PyArray_API[71])
+#define PyArray_FromFile \
+        (*(PyObject * (*)(FILE *, PyArray_Descr *, npy_intp, char *)) \
+    PyArray_API[72])
+#define PyArray_FromString \
+        (*(PyObject * (*)(char *, npy_intp, PyArray_Descr *, npy_intp, char *)) \
+    PyArray_API[73])
+#define PyArray_FromBuffer \
+        (*(PyObject * (*)(PyObject *, PyArray_Descr *, npy_intp, npy_intp)) \
+    PyArray_API[74])
+#define PyArray_FromIter \
+        (*(PyObject * (*)(PyObject *, PyArray_Descr *, npy_intp)) \
+    PyArray_API[75])
+#define PyArray_Return \
+        (*(PyObject * (*)(PyArrayObject *)) \
+    PyArray_API[76])
+#define PyArray_GetField \
+        (*(PyObject * (*)(PyArrayObject *, PyArray_Descr *, int)) \
+    PyArray_API[77])
+#define PyArray_SetField \
+        (*(int (*)(PyArrayObject *, PyArray_Descr *, int, PyObject *)) \
+    PyArray_API[78])
+#define PyArray_Byteswap \
+        (*(PyObject * (*)(PyArrayObject *, npy_bool)) \
+    PyArray_API[79])
+#define PyArray_Resize \
+        (*(PyObject * (*)(PyArrayObject *, PyArray_Dims *, int, NPY_ORDER NPY_UNUSED(order))) \
+    PyArray_API[80])
+#define PyArray_CopyObject \
+        (*(int (*)(PyArrayObject *, PyObject *)) \
+    PyArray_API[84])
+#define PyArray_NewCopy \
+        (*(PyObject * (*)(PyArrayObject *, NPY_ORDER)) \
+    PyArray_API[85])
+#define PyArray_ToList \
+        (*(PyObject * (*)(PyArrayObject *)) \
+    PyArray_API[86])
+#define PyArray_ToString \
+        (*(PyObject * (*)(PyArrayObject *, NPY_ORDER)) \
+    PyArray_API[87])
+#define PyArray_ToFile \
+        (*(int (*)(PyArrayObject *, FILE *, char *, char *)) \
+    PyArray_API[88])
+#define PyArray_Dump \
+        (*(int (*)(PyObject *, PyObject *, int)) \
+    PyArray_API[89])
+#define PyArray_Dumps \
+        (*(PyObject * (*)(PyObject *, int)) \
+    PyArray_API[90])
+#define PyArray_ValidType \
+        (*(int (*)(int)) \
+    PyArray_API[91])
+#define PyArray_UpdateFlags \
+        (*(void (*)(PyArrayObject *, int)) \
+    PyArray_API[92])
+#define PyArray_New \
+        (*(PyObject * (*)(PyTypeObject *, int, npy_intp const *, int, npy_intp const *, void *, int, int, PyObject *)) \
+    PyArray_API[93])
+#define PyArray_NewFromDescr \
+        (*(PyObject * (*)(PyTypeObject *, PyArray_Descr *, int, npy_intp const *, npy_intp const *, void *, int, PyObject *)) \
+    PyArray_API[94])
+#define PyArray_DescrNew \
+        (*(PyArray_Descr * (*)(PyArray_Descr *)) \
+    PyArray_API[95])
+#define PyArray_DescrNewFromType \
+        (*(PyArray_Descr * (*)(int)) \
+    PyArray_API[96])
+#define PyArray_GetPriority \
+        (*(double (*)(PyObject *, double)) \
+    PyArray_API[97])
+#define PyArray_IterNew \
+        (*(PyObject * (*)(PyObject *)) \
+    PyArray_API[98])
+#define PyArray_MultiIterNew \
+        (*(PyObject* (*)(int, ...)) \
+    PyArray_API[99])
+#define PyArray_PyIntAsInt \
+        (*(int (*)(PyObject *)) \
+    PyArray_API[100])
+#define PyArray_PyIntAsIntp \
+        (*(npy_intp (*)(PyObject *)) \
+    PyArray_API[101])
+#define PyArray_Broadcast \
+        (*(int (*)(PyArrayMultiIterObject *)) \
+    PyArray_API[102])
+#define PyArray_FillWithScalar \
+        (*(int (*)(PyArrayObject *, PyObject *)) \
+    PyArray_API[104])
+#define PyArray_CheckStrides \
+        (*(npy_bool (*)(int, int, npy_intp, npy_intp, npy_intp const *, npy_intp const *)) \
+    PyArray_API[105])
+#define PyArray_DescrNewByteorder \
+        (*(PyArray_Descr * (*)(PyArray_Descr *, char)) \
+    PyArray_API[106])
+#define PyArray_IterAllButAxis \
+        (*(PyObject * (*)(PyObject *, int *)) \
+    PyArray_API[107])
+#define PyArray_CheckFromAny \
+        (*(PyObject * (*)(PyObject *, PyArray_Descr *, int, int, int, PyObject *)) \
+    PyArray_API[108])
+#define PyArray_FromArray \
+        (*(PyObject * (*)(PyArrayObject *, PyArray_Descr *, int)) \
+    PyArray_API[109])
+#define PyArray_FromInterface \
+        (*(PyObject * (*)(PyObject *)) \
+    PyArray_API[110])
+#define PyArray_FromStructInterface \
+        (*(PyObject * (*)(PyObject *)) \
+    PyArray_API[111])
+#define PyArray_FromArrayAttr \
+        (*(PyObject * (*)(PyObject *, PyArray_Descr *, PyObject *)) \
+    PyArray_API[112])
+#define PyArray_ScalarKind \
+        (*(NPY_SCALARKIND (*)(int, PyArrayObject **)) \
+    PyArray_API[113])
+#define PyArray_CanCoerceScalar \
+        (*(int (*)(int, int, NPY_SCALARKIND)) \
+    PyArray_API[114])
+#define PyArray_CanCastScalar \
+        (*(npy_bool (*)(PyTypeObject *, PyTypeObject *)) \
+    PyArray_API[116])
+#define PyArray_RemoveSmallest \
+        (*(int (*)(PyArrayMultiIterObject *)) \
+    PyArray_API[118])
+#define PyArray_ElementStrides \
+        (*(int (*)(PyObject *)) \
+    PyArray_API[119])
+#define PyArray_Item_INCREF \
+        (*(void (*)(char *, PyArray_Descr *)) \
+    PyArray_API[120])
+#define PyArray_Item_XDECREF \
+        (*(void (*)(char *, PyArray_Descr *)) \
+    PyArray_API[121])
+#define PyArray_Transpose \
+        (*(PyObject * (*)(PyArrayObject *, PyArray_Dims *)) \
+    PyArray_API[123])
+#define PyArray_TakeFrom \
+        (*(PyObject * (*)(PyArrayObject *, PyObject *, int, PyArrayObject *, NPY_CLIPMODE)) \
+    PyArray_API[124])
+#define PyArray_PutTo \
+        (*(PyObject * (*)(PyArrayObject *, PyObject*, PyObject *, NPY_CLIPMODE)) \
+    PyArray_API[125])
+#define PyArray_PutMask \
+        (*(PyObject * (*)(PyArrayObject *, PyObject*, PyObject*)) \
+    PyArray_API[126])
+#define PyArray_Repeat \
+        (*(PyObject * (*)(PyArrayObject *, PyObject *, int)) \
+    PyArray_API[127])
+#define PyArray_Choose \
+        (*(PyObject * (*)(PyArrayObject *, PyObject *, PyArrayObject *, NPY_CLIPMODE)) \
+    PyArray_API[128])
+#define PyArray_Sort \
+        (*(int (*)(PyArrayObject *, int, NPY_SORTKIND)) \
+    PyArray_API[129])
+#define PyArray_ArgSort \
+        (*(PyObject * (*)(PyArrayObject *, int, NPY_SORTKIND)) \
+    PyArray_API[130])
+#define PyArray_SearchSorted \
+        (*(PyObject * (*)(PyArrayObject *, PyObject *, NPY_SEARCHSIDE, PyObject *)) \
+    PyArray_API[131])
+#define PyArray_ArgMax \
+        (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \
+    PyArray_API[132])
+#define PyArray_ArgMin \
+        (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \
+    PyArray_API[133])
+#define PyArray_Reshape \
+        (*(PyObject * (*)(PyArrayObject *, PyObject *)) \
+    PyArray_API[134])
+#define PyArray_Newshape \
+        (*(PyObject * (*)(PyArrayObject *, PyArray_Dims *, NPY_ORDER)) \
+    PyArray_API[135])
+#define PyArray_Squeeze \
+        (*(PyObject * (*)(PyArrayObject *)) \
+    PyArray_API[136])
+#define PyArray_View \
+        (*(PyObject * (*)(PyArrayObject *, PyArray_Descr *, PyTypeObject *)) \
+    PyArray_API[137])
+#define PyArray_SwapAxes \
+        (*(PyObject * (*)(PyArrayObject *, int, int)) \
+    PyArray_API[138])
+#define PyArray_Max \
+        (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \
+    PyArray_API[139])
+#define PyArray_Min \
+        (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \
+    PyArray_API[140])
+#define PyArray_Ptp \
+        (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \
+    PyArray_API[141])
+#define PyArray_Mean \
+        (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \
+    PyArray_API[142])
+#define PyArray_Trace \
+        (*(PyObject * (*)(PyArrayObject *, int, int, int, int, PyArrayObject *)) \
+    PyArray_API[143])
+#define PyArray_Diagonal \
+        (*(PyObject * (*)(PyArrayObject *, int, int, int)) \
+    PyArray_API[144])
+#define PyArray_Clip \
+        (*(PyObject * (*)(PyArrayObject *, PyObject *, PyObject *, PyArrayObject *)) \
+    PyArray_API[145])
+#define PyArray_Conjugate \
+        (*(PyObject * (*)(PyArrayObject *, PyArrayObject *)) \
+    PyArray_API[146])
+#define PyArray_Nonzero \
+        (*(PyObject * (*)(PyArrayObject *)) \
+    PyArray_API[147])
+#define PyArray_Std \
+        (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *, int)) \
+    PyArray_API[148])
+#define PyArray_Sum \
+        (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \
+    PyArray_API[149])
+#define PyArray_CumSum \
+        (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \
+    PyArray_API[150])
+#define PyArray_Prod \
+        (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \
+    PyArray_API[151])
+#define PyArray_CumProd \
+        (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \
+    PyArray_API[152])
+#define PyArray_All \
+        (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \
+    PyArray_API[153])
+#define PyArray_Any \
+        (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \
+    PyArray_API[154])
+#define PyArray_Compress \
+        (*(PyObject * (*)(PyArrayObject *, PyObject *, int, PyArrayObject *)) \
+    PyArray_API[155])
+#define PyArray_Flatten \
+        (*(PyObject * (*)(PyArrayObject *, NPY_ORDER)) \
+    PyArray_API[156])
+#define PyArray_Ravel \
+        (*(PyObject * (*)(PyArrayObject *, NPY_ORDER)) \
+    PyArray_API[157])
+#define PyArray_MultiplyList \
+        (*(npy_intp (*)(npy_intp const *, int)) \
+    PyArray_API[158])
+#define PyArray_MultiplyIntList \
+        (*(int (*)(int const *, int)) \
+    PyArray_API[159])
+#define PyArray_GetPtr \
+        (*(void * (*)(PyArrayObject *, npy_intp const*)) \
+    PyArray_API[160])
+#define PyArray_CompareLists \
+        (*(int (*)(npy_intp const *, npy_intp const *, int)) \
+    PyArray_API[161])
+#define PyArray_AsCArray \
+        (*(int (*)(PyObject **, void *, npy_intp *, int, PyArray_Descr*)) \
+    PyArray_API[162])
+#define PyArray_Free \
+        (*(int (*)(PyObject *, void *)) \
+    PyArray_API[165])
+#define PyArray_Converter \
+        (*(int (*)(PyObject *, PyObject **)) \
+    PyArray_API[166])
+#define PyArray_IntpFromSequence \
+        (*(int (*)(PyObject *, npy_intp *, int)) \
+    PyArray_API[167])
+#define PyArray_Concatenate \
+        (*(PyObject * (*)(PyObject *, int)) \
+    PyArray_API[168])
+#define PyArray_InnerProduct \
+        (*(PyObject * (*)(PyObject *, PyObject *)) \
+    PyArray_API[169])
+#define PyArray_MatrixProduct \
+        (*(PyObject * (*)(PyObject *, PyObject *)) \
+    PyArray_API[170])
+#define PyArray_Correlate \
+        (*(PyObject * (*)(PyObject *, PyObject *, int)) \
+    PyArray_API[172])
+#define PyArray_DescrConverter \
+        (*(int (*)(PyObject *, PyArray_Descr **)) \
+    PyArray_API[174])
+#define PyArray_DescrConverter2 \
+        (*(int (*)(PyObject *, PyArray_Descr **)) \
+    PyArray_API[175])
+#define PyArray_IntpConverter \
+        (*(int (*)(PyObject *, PyArray_Dims *)) \
+    PyArray_API[176])
+#define PyArray_BufferConverter \
+        (*(int (*)(PyObject *, PyArray_Chunk *)) \
+    PyArray_API[177])
+#define PyArray_AxisConverter \
+        (*(int (*)(PyObject *, int *)) \
+    PyArray_API[178])
+#define PyArray_BoolConverter \
+        (*(int (*)(PyObject *, npy_bool *)) \
+    PyArray_API[179])
+#define PyArray_ByteorderConverter \
+        (*(int (*)(PyObject *, char *)) \
+    PyArray_API[180])
+#define PyArray_OrderConverter \
+        (*(int (*)(PyObject *, NPY_ORDER *)) \
+    PyArray_API[181])
+#define PyArray_EquivTypes \
+        (*(unsigned char (*)(PyArray_Descr *, PyArray_Descr *)) \
+    PyArray_API[182])
+#define PyArray_Zeros \
+        (*(PyObject * (*)(int, npy_intp const *, PyArray_Descr *, int)) \
+    PyArray_API[183])
+#define PyArray_Empty \
+        (*(PyObject * (*)(int, npy_intp const *, PyArray_Descr *, int)) \
+    PyArray_API[184])
+#define PyArray_Where \
+        (*(PyObject * (*)(PyObject *, PyObject *, PyObject *)) \
+    PyArray_API[185])
+#define PyArray_Arange \
+        (*(PyObject * (*)(double, double, double, int)) \
+    PyArray_API[186])
+#define PyArray_ArangeObj \
+        (*(PyObject * (*)(PyObject *, PyObject *, PyObject *, PyArray_Descr *)) \
+    PyArray_API[187])
+#define PyArray_SortkindConverter \
+        (*(int (*)(PyObject *, NPY_SORTKIND *)) \
+    PyArray_API[188])
+#define PyArray_LexSort \
+        (*(PyObject * (*)(PyObject *, int)) \
+    PyArray_API[189])
+#define PyArray_Round \
+        (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \
+    PyArray_API[190])
+#define PyArray_EquivTypenums \
+        (*(unsigned char (*)(int, int)) \
+    PyArray_API[191])
+#define PyArray_RegisterDataType \
+        (*(int (*)(PyArray_DescrProto *)) \
+    PyArray_API[192])
+#define PyArray_RegisterCastFunc \
+        (*(int (*)(PyArray_Descr *, int, PyArray_VectorUnaryFunc *)) \
+    PyArray_API[193])
+#define PyArray_RegisterCanCast \
+        (*(int (*)(PyArray_Descr *, int, NPY_SCALARKIND)) \
+    PyArray_API[194])
+#define PyArray_InitArrFuncs \
+        (*(void (*)(PyArray_ArrFuncs *)) \
+    PyArray_API[195])
+#define PyArray_IntTupleFromIntp \
+        (*(PyObject * (*)(int, npy_intp const *)) \
+    PyArray_API[196])
+#define PyArray_ClipmodeConverter \
+        (*(int (*)(PyObject *, NPY_CLIPMODE *)) \
+    PyArray_API[198])
+#define PyArray_OutputConverter \
+        (*(int (*)(PyObject *, PyArrayObject **)) \
+    PyArray_API[199])
+#define PyArray_BroadcastToShape \
+        (*(PyObject * (*)(PyObject *, npy_intp *, int)) \
+    PyArray_API[200])
+#define PyArray_DescrAlignConverter \
+        (*(int (*)(PyObject *, PyArray_Descr **)) \
+    PyArray_API[203])
+#define PyArray_DescrAlignConverter2 \
+        (*(int (*)(PyObject *, PyArray_Descr **)) \
+    PyArray_API[204])
+#define PyArray_SearchsideConverter \
+        (*(int (*)(PyObject *, void *)) \
+    PyArray_API[205])
+#define PyArray_CheckAxis \
+        (*(PyObject * (*)(PyArrayObject *, int *, int)) \
+    PyArray_API[206])
+#define PyArray_OverflowMultiplyList \
+        (*(npy_intp (*)(npy_intp const *, int)) \
+    PyArray_API[207])
+#define PyArray_MultiIterFromObjects \
+        (*(PyObject* (*)(PyObject **, int, int, ...)) \
+    PyArray_API[209])
+#define PyArray_GetEndianness \
+        (*(int (*)(void)) \
+    PyArray_API[210])
+#define PyArray_GetNDArrayCFeatureVersion \
+        (*(unsigned int (*)(void)) \
+    PyArray_API[211])
+#define PyArray_Correlate2 \
+        (*(PyObject * (*)(PyObject *, PyObject *, int)) \
+    PyArray_API[212])
+#define PyArray_NeighborhoodIterNew \
+        (*(PyObject* (*)(PyArrayIterObject *, const npy_intp *, int, PyArrayObject*)) \
+    PyArray_API[213])
+#define PyTimeIntegerArrType_Type (*(PyTypeObject *)PyArray_API[214])
+#define PyDatetimeArrType_Type (*(PyTypeObject *)PyArray_API[215])
+#define PyTimedeltaArrType_Type (*(PyTypeObject *)PyArray_API[216])
+#define PyHalfArrType_Type (*(PyTypeObject *)PyArray_API[217])
+#define NpyIter_Type (*(PyTypeObject *)PyArray_API[218])
+
+#if NPY_FEATURE_VERSION >= NPY_2_3_API_VERSION
+#define NpyIter_GetTransferFlags \
+        (*(NPY_ARRAYMETHOD_FLAGS (*)(NpyIter *)) \
+    PyArray_API[223])
+#endif
+#define NpyIter_New \
+        (*(NpyIter * (*)(PyArrayObject *, npy_uint32, NPY_ORDER, NPY_CASTING, PyArray_Descr*)) \
+    PyArray_API[224])
+#define NpyIter_MultiNew \
+        (*(NpyIter * (*)(int, PyArrayObject **, npy_uint32, NPY_ORDER, NPY_CASTING, npy_uint32 *, PyArray_Descr **)) \
+    PyArray_API[225])
+#define NpyIter_AdvancedNew \
+        (*(NpyIter * (*)(int, PyArrayObject **, npy_uint32, NPY_ORDER, NPY_CASTING, npy_uint32 *, PyArray_Descr **, int, int **, npy_intp *, npy_intp)) \
+    PyArray_API[226])
+#define NpyIter_Copy \
+        (*(NpyIter * (*)(NpyIter *)) \
+    PyArray_API[227])
+#define NpyIter_Deallocate \
+        (*(int (*)(NpyIter *)) \
+    PyArray_API[228])
+#define NpyIter_HasDelayedBufAlloc \
+        (*(npy_bool (*)(NpyIter *)) \
+    PyArray_API[229])
+#define NpyIter_HasExternalLoop \
+        (*(npy_bool (*)(NpyIter *)) \
+    PyArray_API[230])
+#define NpyIter_EnableExternalLoop \
+        (*(int (*)(NpyIter *)) \
+    PyArray_API[231])
+#define NpyIter_GetInnerStrideArray \
+        (*(npy_intp * (*)(NpyIter *)) \
+    PyArray_API[232])
+#define NpyIter_GetInnerLoopSizePtr \
+        (*(npy_intp * (*)(NpyIter *)) \
+    PyArray_API[233])
+#define NpyIter_Reset \
+        (*(int (*)(NpyIter *, char **)) \
+    PyArray_API[234])
+#define NpyIter_ResetBasePointers \
+        (*(int (*)(NpyIter *, char **, char **)) \
+    PyArray_API[235])
+#define NpyIter_ResetToIterIndexRange \
+        (*(int (*)(NpyIter *, npy_intp, npy_intp, char **)) \
+    PyArray_API[236])
+#define NpyIter_GetNDim \
+        (*(int (*)(NpyIter *)) \
+    PyArray_API[237])
+#define NpyIter_GetNOp \
+        (*(int (*)(NpyIter *)) \
+    PyArray_API[238])
+#define NpyIter_GetIterNext \
+        (*(NpyIter_IterNextFunc * (*)(NpyIter *, char **)) \
+    PyArray_API[239])
+#define NpyIter_GetIterSize \
+        (*(npy_intp (*)(NpyIter *)) \
+    PyArray_API[240])
+#define NpyIter_GetIterIndexRange \
+        (*(void (*)(NpyIter *, npy_intp *, npy_intp *)) \
+    PyArray_API[241])
+#define NpyIter_GetIterIndex \
+        (*(npy_intp (*)(NpyIter *)) \
+    PyArray_API[242])
+#define NpyIter_GotoIterIndex \
+        (*(int (*)(NpyIter *, npy_intp)) \
+    PyArray_API[243])
+#define NpyIter_HasMultiIndex \
+        (*(npy_bool (*)(NpyIter *)) \
+    PyArray_API[244])
+#define NpyIter_GetShape \
+        (*(int (*)(NpyIter *, npy_intp *)) \
+    PyArray_API[245])
+#define NpyIter_GetGetMultiIndex \
+        (*(NpyIter_GetMultiIndexFunc * (*)(NpyIter *, char **)) \
+    PyArray_API[246])
+#define NpyIter_GotoMultiIndex \
+        (*(int (*)(NpyIter *, npy_intp const *)) \
+    PyArray_API[247])
+#define NpyIter_RemoveMultiIndex \
+        (*(int (*)(NpyIter *)) \
+    PyArray_API[248])
+#define NpyIter_HasIndex \
+        (*(npy_bool (*)(NpyIter *)) \
+    PyArray_API[249])
+#define NpyIter_IsBuffered \
+        (*(npy_bool (*)(NpyIter *)) \
+    PyArray_API[250])
+#define NpyIter_IsGrowInner \
+        (*(npy_bool (*)(NpyIter *)) \
+    PyArray_API[251])
+#define NpyIter_GetBufferSize \
+        (*(npy_intp (*)(NpyIter *)) \
+    PyArray_API[252])
+#define NpyIter_GetIndexPtr \
+        (*(npy_intp * (*)(NpyIter *)) \
+    PyArray_API[253])
+#define NpyIter_GotoIndex \
+        (*(int (*)(NpyIter *, npy_intp)) \
+    PyArray_API[254])
+#define NpyIter_GetDataPtrArray \
+        (*(char ** (*)(NpyIter *)) \
+    PyArray_API[255])
+#define NpyIter_GetDescrArray \
+        (*(PyArray_Descr ** (*)(NpyIter *)) \
+    PyArray_API[256])
+#define NpyIter_GetOperandArray \
+        (*(PyArrayObject ** (*)(NpyIter *)) \
+    PyArray_API[257])
+#define NpyIter_GetIterView \
+        (*(PyArrayObject * (*)(NpyIter *, npy_intp)) \
+    PyArray_API[258])
+#define NpyIter_GetReadFlags \
+        (*(void (*)(NpyIter *, char *)) \
+    PyArray_API[259])
+#define NpyIter_GetWriteFlags \
+        (*(void (*)(NpyIter *, char *)) \
+    PyArray_API[260])
+#define NpyIter_DebugPrint \
+        (*(void (*)(NpyIter *)) \
+    PyArray_API[261])
+#define NpyIter_IterationNeedsAPI \
+        (*(npy_bool (*)(NpyIter *)) \
+    PyArray_API[262])
+#define NpyIter_GetInnerFixedStrideArray \
+        (*(void (*)(NpyIter *, npy_intp *)) \
+    PyArray_API[263])
+#define NpyIter_RemoveAxis \
+        (*(int (*)(NpyIter *, int)) \
+    PyArray_API[264])
+#define NpyIter_GetAxisStrideArray \
+        (*(npy_intp * (*)(NpyIter *, int)) \
+    PyArray_API[265])
+#define NpyIter_RequiresBuffering \
+        (*(npy_bool (*)(NpyIter *)) \
+    PyArray_API[266])
+#define NpyIter_GetInitialDataPtrArray \
+        (*(char ** (*)(NpyIter *)) \
+    PyArray_API[267])
+#define NpyIter_CreateCompatibleStrides \
+        (*(int (*)(NpyIter *, npy_intp, npy_intp *)) \
+    PyArray_API[268])
+#define PyArray_CastingConverter \
+        (*(int (*)(PyObject *, NPY_CASTING *)) \
+    PyArray_API[269])
+#define PyArray_CountNonzero \
+        (*(npy_intp (*)(PyArrayObject *)) \
+    PyArray_API[270])
+#define PyArray_PromoteTypes \
+        (*(PyArray_Descr * (*)(PyArray_Descr *, PyArray_Descr *)) \
+    PyArray_API[271])
+#define PyArray_MinScalarType \
+        (*(PyArray_Descr * (*)(PyArrayObject *)) \
+    PyArray_API[272])
+#define PyArray_ResultType \
+        (*(PyArray_Descr * (*)(npy_intp, PyArrayObject *arrs[], npy_intp, PyArray_Descr *descrs[])) \
+    PyArray_API[273])
+#define PyArray_CanCastArrayTo \
+        (*(npy_bool (*)(PyArrayObject *, PyArray_Descr *, NPY_CASTING)) \
+    PyArray_API[274])
+#define PyArray_CanCastTypeTo \
+        (*(npy_bool (*)(PyArray_Descr *, PyArray_Descr *, NPY_CASTING)) \
+    PyArray_API[275])
+#define PyArray_EinsteinSum \
+        (*(PyArrayObject * (*)(char *, npy_intp, PyArrayObject **, PyArray_Descr *, NPY_ORDER, NPY_CASTING, PyArrayObject *)) \
+    PyArray_API[276])
+#define PyArray_NewLikeArray \
+        (*(PyObject * (*)(PyArrayObject *, NPY_ORDER, PyArray_Descr *, int)) \
+    PyArray_API[277])
+#define PyArray_ConvertClipmodeSequence \
+        (*(int (*)(PyObject *, NPY_CLIPMODE *, int)) \
+    PyArray_API[279])
+#define PyArray_MatrixProduct2 \
+        (*(PyObject * (*)(PyObject *, PyObject *, PyArrayObject*)) \
+    PyArray_API[280])
+#define NpyIter_IsFirstVisit \
+        (*(npy_bool (*)(NpyIter *, int)) \
+    PyArray_API[281])
+#define PyArray_SetBaseObject \
+        (*(int (*)(PyArrayObject *, PyObject *)) \
+    PyArray_API[282])
+#define PyArray_CreateSortedStridePerm \
+        (*(void (*)(int, npy_intp const *, npy_stride_sort_item *)) \
+    PyArray_API[283])
+#define PyArray_RemoveAxesInPlace \
+        (*(void (*)(PyArrayObject *, const npy_bool *)) \
+    PyArray_API[284])
+#define PyArray_DebugPrint \
+        (*(void (*)(PyArrayObject *)) \
+    PyArray_API[285])
+#define PyArray_FailUnlessWriteable \
+        (*(int (*)(PyArrayObject *, const char *)) \
+    PyArray_API[286])
+#define PyArray_SetUpdateIfCopyBase \
+        (*(int (*)(PyArrayObject *, PyArrayObject *)) \
+    PyArray_API[287])
+#define PyDataMem_NEW \
+        (*(void * (*)(size_t)) \
+    PyArray_API[288])
+#define PyDataMem_FREE \
+        (*(void (*)(void *)) \
+    PyArray_API[289])
+#define PyDataMem_RENEW \
+        (*(void * (*)(void *, size_t)) \
+    PyArray_API[290])
+#define NPY_DEFAULT_ASSIGN_CASTING (*(NPY_CASTING *)PyArray_API[292])
+#define PyArray_Partition \
+        (*(int (*)(PyArrayObject *, PyArrayObject *, int, NPY_SELECTKIND)) \
+    PyArray_API[296])
+#define PyArray_ArgPartition \
+        (*(PyObject * (*)(PyArrayObject *, PyArrayObject *, int, NPY_SELECTKIND)) \
+    PyArray_API[297])
+#define PyArray_SelectkindConverter \
+        (*(int (*)(PyObject *, NPY_SELECTKIND *)) \
+    PyArray_API[298])
+#define PyDataMem_NEW_ZEROED \
+        (*(void * (*)(size_t, size_t)) \
+    PyArray_API[299])
+#define PyArray_CheckAnyScalarExact \
+        (*(int (*)(PyObject *)) \
+    PyArray_API[300])
+#define PyArray_ResolveWritebackIfCopy \
+        (*(int (*)(PyArrayObject *)) \
+    PyArray_API[302])
+#define PyArray_SetWritebackIfCopyBase \
+        (*(int (*)(PyArrayObject *, PyArrayObject *)) \
+    PyArray_API[303])
+
+#if NPY_FEATURE_VERSION >= NPY_1_22_API_VERSION
+#define PyDataMem_SetHandler \
+        (*(PyObject * (*)(PyObject *)) \
+    PyArray_API[304])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_1_22_API_VERSION
+#define PyDataMem_GetHandler \
+        (*(PyObject * (*)(void)) \
+    PyArray_API[305])
+#endif
+#define PyDataMem_DefaultHandler (*(PyObject* *)PyArray_API[306])
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyDatetime_ConvertDatetime64ToDatetimeStruct \
+        (*(int (*)(PyArray_DatetimeMetaData *, npy_datetime, npy_datetimestruct *)) \
+    PyArray_API[307])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyDatetime_ConvertDatetimeStructToDatetime64 \
+        (*(int (*)(PyArray_DatetimeMetaData *, const npy_datetimestruct *, npy_datetime *)) \
+    PyArray_API[308])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyDatetime_ConvertPyDateTimeToDatetimeStruct \
+        (*(int (*)(PyObject *, npy_datetimestruct *, NPY_DATETIMEUNIT *, int)) \
+    PyArray_API[309])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyDatetime_GetDatetimeISO8601StrLen \
+        (*(int (*)(int, NPY_DATETIMEUNIT)) \
+    PyArray_API[310])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyDatetime_MakeISO8601Datetime \
+        (*(int (*)(npy_datetimestruct *, char *, npy_intp, int, int, NPY_DATETIMEUNIT, int, NPY_CASTING)) \
+    PyArray_API[311])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyDatetime_ParseISO8601Datetime \
+        (*(int (*)(char const *, Py_ssize_t, NPY_DATETIMEUNIT, NPY_CASTING, npy_datetimestruct *, NPY_DATETIMEUNIT *, npy_bool *)) \
+    PyArray_API[312])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyString_load \
+        (*(int (*)(npy_string_allocator *, const npy_packed_static_string *, npy_static_string *)) \
+    PyArray_API[313])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyString_pack \
+        (*(int (*)(npy_string_allocator *, npy_packed_static_string *, const char *, size_t)) \
+    PyArray_API[314])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyString_pack_null \
+        (*(int (*)(npy_string_allocator *, npy_packed_static_string *)) \
+    PyArray_API[315])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyString_acquire_allocator \
+        (*(npy_string_allocator * (*)(const PyArray_StringDTypeObject *)) \
+    PyArray_API[316])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyString_acquire_allocators \
+        (*(void (*)(size_t, PyArray_Descr *const descrs[], npy_string_allocator *allocators[])) \
+    PyArray_API[317])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyString_release_allocator \
+        (*(void (*)(npy_string_allocator *)) \
+    PyArray_API[318])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define NpyString_release_allocators \
+        (*(void (*)(size_t, npy_string_allocator *allocators[])) \
+    PyArray_API[319])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define PyArray_GetDefaultDescr \
+        (*(PyArray_Descr * (*)(PyArray_DTypeMeta *)) \
+    PyArray_API[361])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define PyArrayInitDTypeMeta_FromSpec \
+        (*(int (*)(PyArray_DTypeMeta *, PyArrayDTypeMeta_Spec *)) \
+    PyArray_API[362])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define PyArray_CommonDType \
+        (*(PyArray_DTypeMeta * (*)(PyArray_DTypeMeta *, PyArray_DTypeMeta *)) \
+    PyArray_API[363])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define PyArray_PromoteDTypeSequence \
+        (*(PyArray_DTypeMeta * (*)(npy_intp, PyArray_DTypeMeta **)) \
+    PyArray_API[364])
+#endif
+#define _PyDataType_GetArrFuncs \
+        (*(PyArray_ArrFuncs * (*)(const PyArray_Descr *)) \
+    PyArray_API[365])
+
+/*
+ * The DType classes are inconvenient for the Python generation so exposed
+ * manually in the header below  (may be moved).
+ */
+#include "numpy/_public_dtype_api_table.h"
+
+#if !defined(NO_IMPORT_ARRAY) && !defined(NO_IMPORT)
+static int
+_import_array(void)
+{
+  int st;
+  PyObject *numpy = PyImport_ImportModule("numpy._core._multiarray_umath");
+  PyObject *c_api;
+  if (numpy == NULL && PyErr_ExceptionMatches(PyExc_ModuleNotFoundError)) {
+    PyErr_Clear();
+    numpy = PyImport_ImportModule("numpy.core._multiarray_umath");
+  }
+
+  if (numpy == NULL) {
+      return -1;
+  }
+
+  c_api = PyObject_GetAttrString(numpy, "_ARRAY_API");
+  Py_DECREF(numpy);
+  if (c_api == NULL) {
+      return -1;
+  }
+
+  if (!PyCapsule_CheckExact(c_api)) {
+      PyErr_SetString(PyExc_RuntimeError, "_ARRAY_API is not PyCapsule object");
+      Py_DECREF(c_api);
+      return -1;
+  }
+  PyArray_API = (void **)PyCapsule_GetPointer(c_api, NULL);
+  Py_DECREF(c_api);
+  if (PyArray_API == NULL) {
+      PyErr_SetString(PyExc_RuntimeError, "_ARRAY_API is NULL pointer");
+      return -1;
+  }
+
+  /*
+   * On exceedingly few platforms these sizes may not match, in which case
+   * We do not support older NumPy versions at all.
+   */
+  if (sizeof(Py_ssize_t) != sizeof(Py_intptr_t) &&
+        PyArray_RUNTIME_VERSION < NPY_2_0_API_VERSION) {
+    PyErr_Format(PyExc_RuntimeError,
+        "module compiled against NumPy 2.0 but running on NumPy 1.x. "
+        "Unfortunately, this is not supported on niche platforms where "
+        "`sizeof(size_t) != sizeof(inptr_t)`.");
+  }
+  /*
+   * Perform runtime check of C API version.  As of now NumPy 2.0 is ABI
+   * backwards compatible (in the exposed feature subset!) for all practical
+   * purposes.
+   */
+  if (NPY_VERSION < PyArray_GetNDArrayCVersion()) {
+      PyErr_Format(PyExc_RuntimeError, "module compiled against "\
+             "ABI version 0x%x but this version of numpy is 0x%x", \
+             (int) NPY_VERSION, (int) PyArray_GetNDArrayCVersion());
+      return -1;
+  }
+  PyArray_RUNTIME_VERSION = (int)PyArray_GetNDArrayCFeatureVersion();
+  if (NPY_FEATURE_VERSION > PyArray_RUNTIME_VERSION) {
+      PyErr_Format(PyExc_RuntimeError,
+             "module was compiled against NumPy C-API version 0x%x "
+             "(NumPy " NPY_FEATURE_VERSION_STRING ") "
+             "but the running NumPy has C-API version 0x%x. "
+             "Check the section C-API incompatibility at the "
+             "Troubleshooting ImportError section at "
+             "https://numpy.org/devdocs/user/troubleshooting-importerror.html"
+             "#c-api-incompatibility "
+             "for indications on how to solve this problem.",
+             (int)NPY_FEATURE_VERSION, PyArray_RUNTIME_VERSION);
+      return -1;
+  }
+
+  /*
+   * Perform runtime check of endianness and check it matches the one set by
+   * the headers (npy_endian.h) as a safeguard
+   */
+  st = PyArray_GetEndianness();
+  if (st == NPY_CPU_UNKNOWN_ENDIAN) {
+      PyErr_SetString(PyExc_RuntimeError,
+                      "FATAL: module compiled as unknown endian");
+      return -1;
+  }
+#if NPY_BYTE_ORDER == NPY_BIG_ENDIAN
+  if (st != NPY_CPU_BIG) {
+      PyErr_SetString(PyExc_RuntimeError,
+                      "FATAL: module compiled as big endian, but "
+                      "detected different endianness at runtime");
+      return -1;
+  }
+#elif NPY_BYTE_ORDER == NPY_LITTLE_ENDIAN
+  if (st != NPY_CPU_LITTLE) {
+      PyErr_SetString(PyExc_RuntimeError,
+                      "FATAL: module compiled as little endian, but "
+                      "detected different endianness at runtime");
+      return -1;
+  }
+#endif
+
+  return 0;
+}
+
+#define import_array() { \
+  if (_import_array() < 0) { \
+    PyErr_Print(); \
+    PyErr_SetString( \
+        PyExc_ImportError, \
+        "numpy._core.multiarray failed to import" \
+    ); \
+    return NULL; \
+  } \
+}
+
+#define import_array1(ret) { \
+  if (_import_array() < 0) { \
+    PyErr_Print(); \
+    PyErr_SetString( \
+        PyExc_ImportError, \
+        "numpy._core.multiarray failed to import" \
+    ); \
+    return ret; \
+  } \
+}
+
+#define import_array2(msg, ret) { \
+  if (_import_array() < 0) { \
+    PyErr_Print(); \
+    PyErr_SetString(PyExc_ImportError, msg); \
+    return ret; \
+  } \
+}
+
+#endif
+
+#endif
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__ufunc_api.c b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__ufunc_api.c
new file mode 100644
index 0000000..10fcbc4
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__ufunc_api.c
@@ -0,0 +1,54 @@
+
+/* These pointers will be stored in the C-object for use in other
+    extension modules
+*/
+
+void *PyUFunc_API[] = {
+        (void *) &PyUFunc_Type,
+        (void *) PyUFunc_FromFuncAndData,
+        (void *) PyUFunc_RegisterLoopForType,
+        NULL,
+        (void *) PyUFunc_f_f_As_d_d,
+        (void *) PyUFunc_d_d,
+        (void *) PyUFunc_f_f,
+        (void *) PyUFunc_g_g,
+        (void *) PyUFunc_F_F_As_D_D,
+        (void *) PyUFunc_F_F,
+        (void *) PyUFunc_D_D,
+        (void *) PyUFunc_G_G,
+        (void *) PyUFunc_O_O,
+        (void *) PyUFunc_ff_f_As_dd_d,
+        (void *) PyUFunc_ff_f,
+        (void *) PyUFunc_dd_d,
+        (void *) PyUFunc_gg_g,
+        (void *) PyUFunc_FF_F_As_DD_D,
+        (void *) PyUFunc_DD_D,
+        (void *) PyUFunc_FF_F,
+        (void *) PyUFunc_GG_G,
+        (void *) PyUFunc_OO_O,
+        (void *) PyUFunc_O_O_method,
+        (void *) PyUFunc_OO_O_method,
+        (void *) PyUFunc_On_Om,
+        NULL,
+        NULL,
+        (void *) PyUFunc_clearfperr,
+        (void *) PyUFunc_getfperr,
+        NULL,
+        (void *) PyUFunc_ReplaceLoopBySignature,
+        (void *) PyUFunc_FromFuncAndDataAndSignature,
+        NULL,
+        (void *) PyUFunc_e_e,
+        (void *) PyUFunc_e_e_As_f_f,
+        (void *) PyUFunc_e_e_As_d_d,
+        (void *) PyUFunc_ee_e,
+        (void *) PyUFunc_ee_e_As_ff_f,
+        (void *) PyUFunc_ee_e_As_dd_d,
+        (void *) PyUFunc_DefaultTypeResolver,
+        (void *) PyUFunc_ValidateCasting,
+        (void *) PyUFunc_RegisterLoopForDescr,
+        (void *) PyUFunc_FromFuncAndDataAndSignatureAndIdentity,
+        (void *) PyUFunc_AddLoopFromSpec,
+        (void *) PyUFunc_AddPromoter,
+        (void *) PyUFunc_AddWrappingLoop,
+        (void *) PyUFunc_GiveFloatingpointErrors
+};
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__ufunc_api.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__ufunc_api.h
new file mode 100644
index 0000000..b05dce3
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/__ufunc_api.h
@@ -0,0 +1,341 @@
+
+#ifdef _UMATHMODULE
+
+extern NPY_NO_EXPORT PyTypeObject PyUFunc_Type;
+
+extern NPY_NO_EXPORT PyTypeObject PyUFunc_Type;
+
+NPY_NO_EXPORT  PyObject * PyUFunc_FromFuncAndData \
+       (PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, int);
+NPY_NO_EXPORT  int PyUFunc_RegisterLoopForType \
+       (PyUFuncObject *, int, PyUFuncGenericFunction, const int *, void *);
+NPY_NO_EXPORT  void PyUFunc_f_f_As_d_d \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_d_d \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_f_f \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_g_g \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_F_F_As_D_D \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_F_F \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_D_D \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_G_G \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_O_O \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_ff_f_As_dd_d \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_ff_f \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_dd_d \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_gg_g \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_FF_F_As_DD_D \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_DD_D \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_FF_F \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_GG_G \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_OO_O \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_O_O_method \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_OO_O_method \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_On_Om \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_clearfperr \
+       (void);
+NPY_NO_EXPORT  int PyUFunc_getfperr \
+       (void);
+NPY_NO_EXPORT  int PyUFunc_ReplaceLoopBySignature \
+       (PyUFuncObject *, PyUFuncGenericFunction, const int *, PyUFuncGenericFunction *);
+NPY_NO_EXPORT  PyObject * PyUFunc_FromFuncAndDataAndSignature \
+       (PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, int, const char *);
+NPY_NO_EXPORT  void PyUFunc_e_e \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_e_e_As_f_f \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_e_e_As_d_d \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_ee_e \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_ee_e_As_ff_f \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  void PyUFunc_ee_e_As_dd_d \
+       (char **, npy_intp const *, npy_intp const *, void *);
+NPY_NO_EXPORT  int PyUFunc_DefaultTypeResolver \
+       (PyUFuncObject *, NPY_CASTING, PyArrayObject **, PyObject *, PyArray_Descr **);
+NPY_NO_EXPORT  int PyUFunc_ValidateCasting \
+       (PyUFuncObject *, NPY_CASTING, PyArrayObject **, PyArray_Descr *const *);
+NPY_NO_EXPORT  int PyUFunc_RegisterLoopForDescr \
+       (PyUFuncObject *, PyArray_Descr *, PyUFuncGenericFunction, PyArray_Descr **, void *);
+NPY_NO_EXPORT  PyObject * PyUFunc_FromFuncAndDataAndSignatureAndIdentity \
+       (PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, const int, const char *, PyObject *);
+NPY_NO_EXPORT  int PyUFunc_AddLoopFromSpec \
+       (PyObject *, PyArrayMethod_Spec *);
+NPY_NO_EXPORT  int PyUFunc_AddPromoter \
+       (PyObject *, PyObject *, PyObject *);
+NPY_NO_EXPORT  int PyUFunc_AddWrappingLoop \
+       (PyObject *, PyArray_DTypeMeta *new_dtypes[], PyArray_DTypeMeta *wrapped_dtypes[], PyArrayMethod_TranslateGivenDescriptors *, PyArrayMethod_TranslateLoopDescriptors *);
+NPY_NO_EXPORT  int PyUFunc_GiveFloatingpointErrors \
+       (const char *, int);
+
+#else
+
+#if defined(PY_UFUNC_UNIQUE_SYMBOL)
+#define PyUFunc_API PY_UFUNC_UNIQUE_SYMBOL
+#endif
+
+/* By default do not export API in an .so (was never the case on windows) */
+#ifndef NPY_API_SYMBOL_ATTRIBUTE
+    #define NPY_API_SYMBOL_ATTRIBUTE NPY_VISIBILITY_HIDDEN
+#endif
+
+#if defined(NO_IMPORT) || defined(NO_IMPORT_UFUNC)
+extern NPY_API_SYMBOL_ATTRIBUTE void **PyUFunc_API;
+#else
+#if defined(PY_UFUNC_UNIQUE_SYMBOL)
+NPY_API_SYMBOL_ATTRIBUTE void **PyUFunc_API;
+#else
+static void **PyUFunc_API=NULL;
+#endif
+#endif
+
+#define PyUFunc_Type (*(PyTypeObject *)PyUFunc_API[0])
+#define PyUFunc_FromFuncAndData \
+        (*(PyObject * (*)(PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, int)) \
+    PyUFunc_API[1])
+#define PyUFunc_RegisterLoopForType \
+        (*(int (*)(PyUFuncObject *, int, PyUFuncGenericFunction, const int *, void *)) \
+    PyUFunc_API[2])
+#define PyUFunc_f_f_As_d_d \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[4])
+#define PyUFunc_d_d \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[5])
+#define PyUFunc_f_f \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[6])
+#define PyUFunc_g_g \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[7])
+#define PyUFunc_F_F_As_D_D \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[8])
+#define PyUFunc_F_F \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[9])
+#define PyUFunc_D_D \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[10])
+#define PyUFunc_G_G \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[11])
+#define PyUFunc_O_O \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[12])
+#define PyUFunc_ff_f_As_dd_d \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[13])
+#define PyUFunc_ff_f \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[14])
+#define PyUFunc_dd_d \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[15])
+#define PyUFunc_gg_g \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[16])
+#define PyUFunc_FF_F_As_DD_D \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[17])
+#define PyUFunc_DD_D \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[18])
+#define PyUFunc_FF_F \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[19])
+#define PyUFunc_GG_G \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[20])
+#define PyUFunc_OO_O \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[21])
+#define PyUFunc_O_O_method \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[22])
+#define PyUFunc_OO_O_method \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[23])
+#define PyUFunc_On_Om \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[24])
+#define PyUFunc_clearfperr \
+        (*(void (*)(void)) \
+    PyUFunc_API[27])
+#define PyUFunc_getfperr \
+        (*(int (*)(void)) \
+    PyUFunc_API[28])
+#define PyUFunc_ReplaceLoopBySignature \
+        (*(int (*)(PyUFuncObject *, PyUFuncGenericFunction, const int *, PyUFuncGenericFunction *)) \
+    PyUFunc_API[30])
+#define PyUFunc_FromFuncAndDataAndSignature \
+        (*(PyObject * (*)(PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, int, const char *)) \
+    PyUFunc_API[31])
+#define PyUFunc_e_e \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[33])
+#define PyUFunc_e_e_As_f_f \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[34])
+#define PyUFunc_e_e_As_d_d \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[35])
+#define PyUFunc_ee_e \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[36])
+#define PyUFunc_ee_e_As_ff_f \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[37])
+#define PyUFunc_ee_e_As_dd_d \
+        (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \
+    PyUFunc_API[38])
+#define PyUFunc_DefaultTypeResolver \
+        (*(int (*)(PyUFuncObject *, NPY_CASTING, PyArrayObject **, PyObject *, PyArray_Descr **)) \
+    PyUFunc_API[39])
+#define PyUFunc_ValidateCasting \
+        (*(int (*)(PyUFuncObject *, NPY_CASTING, PyArrayObject **, PyArray_Descr *const *)) \
+    PyUFunc_API[40])
+#define PyUFunc_RegisterLoopForDescr \
+        (*(int (*)(PyUFuncObject *, PyArray_Descr *, PyUFuncGenericFunction, PyArray_Descr **, void *)) \
+    PyUFunc_API[41])
+
+#if NPY_FEATURE_VERSION >= NPY_1_16_API_VERSION
+#define PyUFunc_FromFuncAndDataAndSignatureAndIdentity \
+        (*(PyObject * (*)(PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, const int, const char *, PyObject *)) \
+    PyUFunc_API[42])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define PyUFunc_AddLoopFromSpec \
+        (*(int (*)(PyObject *, PyArrayMethod_Spec *)) \
+    PyUFunc_API[43])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define PyUFunc_AddPromoter \
+        (*(int (*)(PyObject *, PyObject *, PyObject *)) \
+    PyUFunc_API[44])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define PyUFunc_AddWrappingLoop \
+        (*(int (*)(PyObject *, PyArray_DTypeMeta *new_dtypes[], PyArray_DTypeMeta *wrapped_dtypes[], PyArrayMethod_TranslateGivenDescriptors *, PyArrayMethod_TranslateLoopDescriptors *)) \
+    PyUFunc_API[45])
+#endif
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+#define PyUFunc_GiveFloatingpointErrors \
+        (*(int (*)(const char *, int)) \
+    PyUFunc_API[46])
+#endif
+
+static inline int
+_import_umath(void)
+{
+  PyObject *c_api;
+  PyObject *numpy = PyImport_ImportModule("numpy._core._multiarray_umath");
+  if (numpy == NULL && PyErr_ExceptionMatches(PyExc_ModuleNotFoundError)) {
+    PyErr_Clear();
+    numpy = PyImport_ImportModule("numpy.core._multiarray_umath");
+  }
+
+  if (numpy == NULL) {
+      PyErr_SetString(PyExc_ImportError,
+                      "_multiarray_umath failed to import");
+      return -1;
+  }
+
+  c_api = PyObject_GetAttrString(numpy, "_UFUNC_API");
+  Py_DECREF(numpy);
+  if (c_api == NULL) {
+      PyErr_SetString(PyExc_AttributeError, "_UFUNC_API not found");
+      return -1;
+  }
+
+  if (!PyCapsule_CheckExact(c_api)) {
+      PyErr_SetString(PyExc_RuntimeError, "_UFUNC_API is not PyCapsule object");
+      Py_DECREF(c_api);
+      return -1;
+  }
+  PyUFunc_API = (void **)PyCapsule_GetPointer(c_api, NULL);
+  Py_DECREF(c_api);
+  if (PyUFunc_API == NULL) {
+      PyErr_SetString(PyExc_RuntimeError, "_UFUNC_API is NULL pointer");
+      return -1;
+  }
+  return 0;
+}
+
+#define import_umath() \
+    do {\
+        UFUNC_NOFPE\
+        if (_import_umath() < 0) {\
+            PyErr_Print();\
+            PyErr_SetString(PyExc_ImportError,\
+                    "numpy._core.umath failed to import");\
+            return NULL;\
+        }\
+    } while(0)
+
+#define import_umath1(ret) \
+    do {\
+        UFUNC_NOFPE\
+        if (_import_umath() < 0) {\
+            PyErr_Print();\
+            PyErr_SetString(PyExc_ImportError,\
+                    "numpy._core.umath failed to import");\
+            return ret;\
+        }\
+    } while(0)
+
+#define import_umath2(ret, msg) \
+    do {\
+        UFUNC_NOFPE\
+        if (_import_umath() < 0) {\
+            PyErr_Print();\
+            PyErr_SetString(PyExc_ImportError, msg);\
+            return ret;\
+        }\
+    } while(0)
+
+#define import_ufunc() \
+    do {\
+        UFUNC_NOFPE\
+        if (_import_umath() < 0) {\
+            PyErr_Print();\
+            PyErr_SetString(PyExc_ImportError,\
+                    "numpy._core.umath failed to import");\
+        }\
+    } while(0)
+
+
+static inline int
+PyUFunc_ImportUFuncAPI()
+{
+    if (NPY_UNLIKELY(PyUFunc_API == NULL)) {
+        import_umath1(-1);
+    }
+    return 0;
+}
+
+#endif
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/_neighborhood_iterator_imp.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/_neighborhood_iterator_imp.h
new file mode 100644
index 0000000..b365cb5
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/_neighborhood_iterator_imp.h
@@ -0,0 +1,90 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY__NEIGHBORHOOD_IMP_H_
+#error You should not include this header directly
+#endif
+/*
+ * Private API (here for inline)
+ */
+static inline int
+_PyArrayNeighborhoodIter_IncrCoord(PyArrayNeighborhoodIterObject* iter);
+
+/*
+ * Update to next item of the iterator
+ *
+ * Note: this simply increment the coordinates vector, last dimension
+ * incremented first , i.e, for dimension 3
+ * ...
+ * -1, -1, -1
+ * -1, -1,  0
+ * -1, -1,  1
+ *  ....
+ * -1,  0, -1
+ * -1,  0,  0
+ *  ....
+ * 0,  -1, -1
+ * 0,  -1,  0
+ *  ....
+ */
+#define _UPDATE_COORD_ITER(c) \
+    wb = iter->coordinates[c] < iter->bounds[c][1]; \
+    if (wb) { \
+        iter->coordinates[c] += 1; \
+        return 0; \
+    } \
+    else { \
+        iter->coordinates[c] = iter->bounds[c][0]; \
+    }
+
+static inline int
+_PyArrayNeighborhoodIter_IncrCoord(PyArrayNeighborhoodIterObject* iter)
+{
+    npy_intp i, wb;
+
+    for (i = iter->nd - 1; i >= 0; --i) {
+        _UPDATE_COORD_ITER(i)
+    }
+
+    return 0;
+}
+
+/*
+ * Version optimized for 2d arrays, manual loop unrolling
+ */
+static inline int
+_PyArrayNeighborhoodIter_IncrCoord2D(PyArrayNeighborhoodIterObject* iter)
+{
+    npy_intp wb;
+
+    _UPDATE_COORD_ITER(1)
+    _UPDATE_COORD_ITER(0)
+
+    return 0;
+}
+#undef _UPDATE_COORD_ITER
+
+/*
+ * Advance to the next neighbour
+ */
+static inline int
+PyArrayNeighborhoodIter_Next(PyArrayNeighborhoodIterObject* iter)
+{
+    _PyArrayNeighborhoodIter_IncrCoord (iter);
+    iter->dataptr = iter->translate((PyArrayIterObject*)iter, iter->coordinates);
+
+    return 0;
+}
+
+/*
+ * Reset functions
+ */
+static inline int
+PyArrayNeighborhoodIter_Reset(PyArrayNeighborhoodIterObject* iter)
+{
+    npy_intp i;
+
+    for (i = 0; i < iter->nd; ++i) {
+        iter->coordinates[i] = iter->bounds[i][0];
+    }
+    iter->dataptr = iter->translate((PyArrayIterObject*)iter, iter->coordinates);
+
+    return 0;
+}
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/_numpyconfig.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/_numpyconfig.h
new file mode 100644
index 0000000..16a4b44
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/_numpyconfig.h
@@ -0,0 +1,33 @@
+#define NPY_HAVE_ENDIAN_H 1
+
+#define NPY_SIZEOF_SHORT 2
+#define NPY_SIZEOF_INT 4
+#define NPY_SIZEOF_LONG 8
+#define NPY_SIZEOF_FLOAT 4
+#define NPY_SIZEOF_COMPLEX_FLOAT 8
+#define NPY_SIZEOF_DOUBLE 8
+#define NPY_SIZEOF_COMPLEX_DOUBLE 16
+#define NPY_SIZEOF_LONGDOUBLE 16
+#define NPY_SIZEOF_COMPLEX_LONGDOUBLE 32
+#define NPY_SIZEOF_PY_INTPTR_T 8
+#define NPY_SIZEOF_INTP 8
+#define NPY_SIZEOF_UINTP 8
+#define NPY_SIZEOF_WCHAR_T 4
+#define NPY_SIZEOF_OFF_T 8
+#define NPY_SIZEOF_PY_LONG_LONG 8
+#define NPY_SIZEOF_LONGLONG 8
+
+/*
+ * Defined to 1 or 0. Note that Pyodide hardcodes NPY_NO_SMP (and other defines
+ * in this header) for better cross-compilation, so don't rename them without a
+ * good reason.
+ */
+#define NPY_NO_SMP 0
+
+#define NPY_VISIBILITY_HIDDEN __attribute__((visibility("hidden")))
+#define NPY_ABI_VERSION 0x02000000
+#define NPY_API_VERSION 0x00000014
+
+#ifndef __STDC_FORMAT_MACROS
+#define __STDC_FORMAT_MACROS 1
+#endif
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/_public_dtype_api_table.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/_public_dtype_api_table.h
new file mode 100644
index 0000000..51f3905
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/_public_dtype_api_table.h
@@ -0,0 +1,86 @@
+/*
+ * Public exposure of the DType Classes.  These are tricky to expose
+ * via the Python API, so they are exposed through this header for now.
+ *
+ * These definitions are only relevant for the public API and we reserve
+ * the slots 320-360 in the API table generation for this (currently).
+ *
+ * TODO: This file should be consolidated with the API table generation
+ *       (although not sure the current generation is worth preserving).
+ */
+#ifndef NUMPY_CORE_INCLUDE_NUMPY__PUBLIC_DTYPE_API_TABLE_H_
+#define NUMPY_CORE_INCLUDE_NUMPY__PUBLIC_DTYPE_API_TABLE_H_
+
+#if !(defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD)
+
+/* All of these require NumPy 2.0 support */
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+
+/*
+ * The type of the DType metaclass
+ */
+#define PyArrayDTypeMeta_Type (*(PyTypeObject *)(PyArray_API + 320)[0])
+/*
+ * NumPy's builtin DTypes:
+ */
+#define PyArray_BoolDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[1])
+/* Integers */
+#define PyArray_ByteDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[2])
+#define PyArray_UByteDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[3])
+#define PyArray_ShortDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[4])
+#define PyArray_UShortDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[5])
+#define PyArray_IntDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[6])
+#define PyArray_UIntDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[7])
+#define PyArray_LongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[8])
+#define PyArray_ULongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[9])
+#define PyArray_LongLongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[10])
+#define PyArray_ULongLongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[11])
+/* Integer aliases */
+#define PyArray_Int8DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[12])
+#define PyArray_UInt8DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[13])
+#define PyArray_Int16DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[14])
+#define PyArray_UInt16DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[15])
+#define PyArray_Int32DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[16])
+#define PyArray_UInt32DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[17])
+#define PyArray_Int64DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[18])
+#define PyArray_UInt64DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[19])
+#define PyArray_IntpDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[20])
+#define PyArray_UIntpDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[21])
+/* Floats */
+#define PyArray_HalfDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[22])
+#define PyArray_FloatDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[23])
+#define PyArray_DoubleDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[24])
+#define PyArray_LongDoubleDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[25])
+/* Complex */
+#define PyArray_CFloatDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[26])
+#define PyArray_CDoubleDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[27])
+#define PyArray_CLongDoubleDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[28])
+/* String/Bytes */
+#define PyArray_BytesDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[29])
+#define PyArray_UnicodeDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[30])
+/* Datetime/Timedelta */
+#define PyArray_DatetimeDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[31])
+#define PyArray_TimedeltaDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[32])
+/* Object/Void */
+#define PyArray_ObjectDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[33])
+#define PyArray_VoidDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[34])
+/* Python types (used as markers for scalars) */
+#define PyArray_PyLongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[35])
+#define PyArray_PyFloatDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[36])
+#define PyArray_PyComplexDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[37])
+/* Default integer type */
+#define PyArray_DefaultIntDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[38])
+/* New non-legacy DTypes follow in the order they were added */
+#define PyArray_StringDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[39])
+
+/* NOTE: offset 40 is free */
+
+/* Need to start with a larger offset again for the abstract classes: */
+#define PyArray_IntAbstractDType (*(PyArray_DTypeMeta *)PyArray_API[366])
+#define PyArray_FloatAbstractDType (*(PyArray_DTypeMeta *)PyArray_API[367])
+#define PyArray_ComplexAbstractDType (*(PyArray_DTypeMeta *)PyArray_API[368])
+
+#endif /* NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION */
+
+#endif  /* NPY_INTERNAL_BUILD */
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY__PUBLIC_DTYPE_API_TABLE_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/arrayobject.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/arrayobject.h
new file mode 100644
index 0000000..97d9359
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/arrayobject.h
@@ -0,0 +1,7 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_ARRAYOBJECT_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_ARRAYOBJECT_H_
+#define Py_ARRAYOBJECT_H
+
+#include "ndarrayobject.h"
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_ARRAYOBJECT_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/arrayscalars.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/arrayscalars.h
new file mode 100644
index 0000000..ff04806
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/arrayscalars.h
@@ -0,0 +1,196 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_ARRAYSCALARS_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_ARRAYSCALARS_H_
+
+#ifndef _MULTIARRAYMODULE
+typedef struct {
+        PyObject_HEAD
+        npy_bool obval;
+} PyBoolScalarObject;
+#endif
+
+
+typedef struct {
+        PyObject_HEAD
+        signed char obval;
+} PyByteScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        short obval;
+} PyShortScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        int obval;
+} PyIntScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        long obval;
+} PyLongScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        npy_longlong obval;
+} PyLongLongScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        unsigned char obval;
+} PyUByteScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        unsigned short obval;
+} PyUShortScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        unsigned int obval;
+} PyUIntScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        unsigned long obval;
+} PyULongScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        npy_ulonglong obval;
+} PyULongLongScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        npy_half obval;
+} PyHalfScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        float obval;
+} PyFloatScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        double obval;
+} PyDoubleScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        npy_longdouble obval;
+} PyLongDoubleScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        npy_cfloat obval;
+} PyCFloatScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        npy_cdouble obval;
+} PyCDoubleScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        npy_clongdouble obval;
+} PyCLongDoubleScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        PyObject * obval;
+} PyObjectScalarObject;
+
+typedef struct {
+        PyObject_HEAD
+        npy_datetime obval;
+        PyArray_DatetimeMetaData obmeta;
+} PyDatetimeScalarObject;
+
+typedef struct {
+        PyObject_HEAD
+        npy_timedelta obval;
+        PyArray_DatetimeMetaData obmeta;
+} PyTimedeltaScalarObject;
+
+
+typedef struct {
+        PyObject_HEAD
+        char obval;
+} PyScalarObject;
+
+#define PyStringScalarObject PyBytesObject
+#ifndef Py_LIMITED_API
+typedef struct {
+        /* note that the PyObject_HEAD macro lives right here */
+        PyUnicodeObject base;
+        Py_UCS4 *obval;
+    #if NPY_FEATURE_VERSION >= NPY_1_20_API_VERSION
+        char *buffer_fmt;
+    #endif
+} PyUnicodeScalarObject;
+#endif
+
+
+typedef struct {
+        PyObject_VAR_HEAD
+        char *obval;
+#if defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD
+        /* Internally use the subclass to allow accessing names/fields */
+        _PyArray_LegacyDescr *descr;
+#else
+        PyArray_Descr *descr;
+#endif
+        int flags;
+        PyObject *base;
+    #if NPY_FEATURE_VERSION >= NPY_1_20_API_VERSION
+        void *_buffer_info;  /* private buffer info, tagged to allow warning */
+    #endif
+} PyVoidScalarObject;
+
+/* Macros
+     Py<Cls><bitsize>ScalarObject
+     Py<Cls><bitsize>ArrType_Type
+   are defined in ndarrayobject.h
+*/
+
+#define PyArrayScalar_False ((PyObject *)(&(_PyArrayScalar_BoolValues[0])))
+#define PyArrayScalar_True ((PyObject *)(&(_PyArrayScalar_BoolValues[1])))
+#define PyArrayScalar_FromLong(i) \
+        ((PyObject *)(&(_PyArrayScalar_BoolValues[((i)!=0)])))
+#define PyArrayScalar_RETURN_BOOL_FROM_LONG(i)                  \
+        return Py_INCREF(PyArrayScalar_FromLong(i)), \
+                PyArrayScalar_FromLong(i)
+#define PyArrayScalar_RETURN_FALSE              \
+        return Py_INCREF(PyArrayScalar_False),  \
+                PyArrayScalar_False
+#define PyArrayScalar_RETURN_TRUE               \
+        return Py_INCREF(PyArrayScalar_True),   \
+                PyArrayScalar_True
+
+#define PyArrayScalar_New(cls) \
+        Py##cls##ArrType_Type.tp_alloc(&Py##cls##ArrType_Type, 0)
+#ifndef Py_LIMITED_API
+/* For the limited API, use PyArray_ScalarAsCtype instead */
+#define PyArrayScalar_VAL(obj, cls)             \
+        ((Py##cls##ScalarObject *)obj)->obval
+#define PyArrayScalar_ASSIGN(obj, cls, val) \
+        PyArrayScalar_VAL(obj, cls) = val
+#endif
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_ARRAYSCALARS_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/dtype_api.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/dtype_api.h
new file mode 100644
index 0000000..b37c9fb
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/dtype_api.h
@@ -0,0 +1,480 @@
+/*
+ * The public DType API
+ */
+
+#ifndef NUMPY_CORE_INCLUDE_NUMPY___DTYPE_API_H_
+#define NUMPY_CORE_INCLUDE_NUMPY___DTYPE_API_H_
+
+struct PyArrayMethodObject_tag;
+
+/*
+ * Largely opaque struct for DType classes (i.e. metaclass instances).
+ * The internal definition is currently in `ndarraytypes.h` (export is a bit
+ * more complex because `PyArray_Descr` is a DTypeMeta internally but not
+ * externally).
+ */
+#if !(defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD)
+
+#ifndef Py_LIMITED_API
+
+    typedef struct PyArray_DTypeMeta_tag {
+        PyHeapTypeObject super;
+
+        /*
+        * Most DTypes will have a singleton default instance, for the
+        * parametric legacy DTypes (bytes, string, void, datetime) this
+        * may be a pointer to the *prototype* instance?
+        */
+        PyArray_Descr *singleton;
+        /* Copy of the legacy DTypes type number, usually invalid. */
+        int type_num;
+
+        /* The type object of the scalar instances (may be NULL?) */
+        PyTypeObject *scalar_type;
+        /*
+        * DType flags to signal legacy, parametric, or
+        * abstract.  But plenty of space for additional information/flags.
+        */
+        npy_uint64 flags;
+
+        /*
+        * Use indirection in order to allow a fixed size for this struct.
+        * A stable ABI size makes creating a static DType less painful
+        * while also ensuring flexibility for all opaque API (with one
+        * indirection due the pointer lookup).
+        */
+        void *dt_slots;
+        /* Allow growing (at the moment also beyond this) */
+        void *reserved[3];
+    } PyArray_DTypeMeta;
+
+#else
+
+typedef PyTypeObject PyArray_DTypeMeta;
+
+#endif /* Py_LIMITED_API */
+
+#endif  /* not internal build */
+
+/*
+ * ******************************************************
+ *         ArrayMethod API (Casting and UFuncs)
+ * ******************************************************
+ */
+
+
+typedef enum {
+    /* Flag for whether the GIL is required */
+    NPY_METH_REQUIRES_PYAPI = 1 << 0,
+    /*
+     * Some functions cannot set floating point error flags, this flag
+     * gives us the option (not requirement) to skip floating point error
+     * setup/check. No function should set error flags and ignore them
+     * since it would interfere with chaining operations (e.g. casting).
+     */
+    NPY_METH_NO_FLOATINGPOINT_ERRORS = 1 << 1,
+    /* Whether the method supports unaligned access (not runtime) */
+    NPY_METH_SUPPORTS_UNALIGNED = 1 << 2,
+    /*
+     * Used for reductions to allow reordering the operation.  At this point
+     * assume that if set, it also applies to normal operations though!
+     */
+    NPY_METH_IS_REORDERABLE = 1 << 3,
+    /*
+     * Private flag for now for *logic* functions.  The logical functions
+     * `logical_or` and `logical_and` can always cast the inputs to booleans
+     * "safely" (because that is how the cast to bool is defined).
+     * @seberg: I am not sure this is the best way to handle this, so its
+     * private for now (also it is very limited anyway).
+     * There is one "exception". NA aware dtypes cannot cast to bool
+     * (hopefully), so the `??->?` loop should error even with this flag.
+     * But a second NA fallback loop will be necessary.
+     */
+    _NPY_METH_FORCE_CAST_INPUTS = 1 << 17,
+
+    /* All flags which can change at runtime */
+    NPY_METH_RUNTIME_FLAGS = (
+            NPY_METH_REQUIRES_PYAPI |
+            NPY_METH_NO_FLOATINGPOINT_ERRORS),
+} NPY_ARRAYMETHOD_FLAGS;
+
+
+typedef struct PyArrayMethod_Context_tag {
+    /* The caller, which is typically the original ufunc.  May be NULL */
+    PyObject *caller;
+    /* The method "self".  Currently an opaque object. */
+    struct PyArrayMethodObject_tag *method;
+
+    /* Operand descriptors, filled in by resolve_descriptors */
+    PyArray_Descr *const *descriptors;
+    /* Structure may grow (this is harmless for DType authors) */
+} PyArrayMethod_Context;
+
+
+/*
+ * The main object for creating a new ArrayMethod. We use the typical `slots`
+ * mechanism used by the Python limited API (see below for the slot defs).
+ */
+typedef struct {
+    const char *name;
+    int nin, nout;
+    NPY_CASTING casting;
+    NPY_ARRAYMETHOD_FLAGS flags;
+    PyArray_DTypeMeta **dtypes;
+    PyType_Slot *slots;
+} PyArrayMethod_Spec;
+
+
+/*
+ * ArrayMethod slots
+ * -----------------
+ *
+ * SLOTS IDs For the ArrayMethod creation, once fully public, IDs are fixed
+ * but can be deprecated and arbitrarily extended.
+ */
+#define _NPY_METH_resolve_descriptors_with_scalars 1
+#define NPY_METH_resolve_descriptors 2
+#define NPY_METH_get_loop 3
+#define NPY_METH_get_reduction_initial 4
+/* specific loops for constructions/default get_loop: */
+#define NPY_METH_strided_loop 5
+#define NPY_METH_contiguous_loop 6
+#define NPY_METH_unaligned_strided_loop 7
+#define NPY_METH_unaligned_contiguous_loop 8
+#define NPY_METH_contiguous_indexed_loop 9
+#define _NPY_METH_static_data 10
+
+
+/*
+ * The resolve descriptors function, must be able to handle NULL values for
+ * all output (but not input) `given_descrs` and fill `loop_descrs`.
+ * Return -1 on error or 0 if the operation is not possible without an error
+ * set.  (This may still be in flux.)
+ * Otherwise must return the "casting safety", for normal functions, this is
+ * almost always "safe" (or even "equivalent"?).
+ *
+ * `resolve_descriptors` is optional if all output DTypes are non-parametric.
+ */
+typedef NPY_CASTING (PyArrayMethod_ResolveDescriptors)(
+        /* "method" is currently opaque (necessary e.g. to wrap Python) */
+        struct PyArrayMethodObject_tag *method,
+        /* DTypes the method was created for */
+        PyArray_DTypeMeta *const *dtypes,
+        /* Input descriptors (instances).  Outputs may be NULL. */
+        PyArray_Descr *const *given_descrs,
+        /* Exact loop descriptors to use, must not hold references on error */
+        PyArray_Descr **loop_descrs,
+        npy_intp *view_offset);
+
+
+/*
+ * Rarely needed, slightly more powerful version of `resolve_descriptors`.
+ * See also `PyArrayMethod_ResolveDescriptors` for details on shared arguments.
+ *
+ * NOTE: This function is private now as it is unclear how and what to pass
+ *       exactly as additional information to allow dealing with the scalars.
+ *       See also gh-24915.
+ */
+typedef NPY_CASTING (PyArrayMethod_ResolveDescriptorsWithScalar)(
+        struct PyArrayMethodObject_tag *method,
+        PyArray_DTypeMeta *const *dtypes,
+        /* Unlike above, these can have any DType and we may allow NULL. */
+        PyArray_Descr *const *given_descrs,
+        /*
+         * Input scalars or NULL.  Only ever passed for python scalars.
+         * WARNING: In some cases, a loop may be explicitly selected and the
+         *     value passed is not available (NULL) or does not have the
+         *     expected type.
+         */
+        PyObject *const *input_scalars,
+        PyArray_Descr **loop_descrs,
+        npy_intp *view_offset);
+
+
+
+typedef int (PyArrayMethod_StridedLoop)(PyArrayMethod_Context *context,
+        char *const *data, const npy_intp *dimensions, const npy_intp *strides,
+        NpyAuxData *transferdata);
+
+
+typedef int (PyArrayMethod_GetLoop)(
+        PyArrayMethod_Context *context,
+        int aligned, int move_references,
+        const npy_intp *strides,
+        PyArrayMethod_StridedLoop **out_loop,
+        NpyAuxData **out_transferdata,
+        NPY_ARRAYMETHOD_FLAGS *flags);
+
+/**
+ * Query an ArrayMethod for the initial value for use in reduction.
+ *
+ * @param context The arraymethod context, mainly to access the descriptors.
+ * @param reduction_is_empty Whether the reduction is empty. When it is, the
+ *     value returned may differ.  In this case it is a "default" value that
+ *     may differ from the "identity" value normally used.  For example:
+ *     - `0.0` is the default for `sum([])`.  But `-0.0` is the correct
+ *       identity otherwise as it preserves the sign for `sum([-0.0])`.
+ *     - We use no identity for object, but return the default of `0` and `1`
+ *       for the empty `sum([], dtype=object)` and `prod([], dtype=object)`.
+ *       This allows `np.sum(np.array(["a", "b"], dtype=object))` to work.
+ *     - `-inf` or `INT_MIN` for `max` is an identity, but at least `INT_MIN`
+ *       not a good *default* when there are no items.
+ * @param initial Pointer to initial data to be filled (if possible)
+ *
+ * @returns -1, 0, or 1 indicating error, no initial value, and initial being
+ *     successfully filled.  Errors must not be given where 0 is correct, NumPy
+ *     may call this even when not strictly necessary.
+ */
+typedef int (PyArrayMethod_GetReductionInitial)(
+        PyArrayMethod_Context *context, npy_bool reduction_is_empty,
+        void *initial);
+
+/*
+ * The following functions are only used by the wrapping array method defined
+ * in umath/wrapping_array_method.c
+ */
+
+
+/*
+ * The function to convert the given descriptors (passed in to
+ * `resolve_descriptors`) and translates them for the wrapped loop.
+ * The new descriptors MUST be viewable with the old ones, `NULL` must be
+ * supported (for outputs) and should normally be forwarded.
+ *
+ * The function must clean up on error.
+ *
+ * NOTE: We currently assume that this translation gives "viewable" results.
+ *       I.e. there is no additional casting related to the wrapping process.
+ *       In principle that could be supported, but not sure it is useful.
+ *       This currently also means that e.g. alignment must apply identically
+ *       to the new dtypes.
+ *
+ * TODO: Due to the fact that `resolve_descriptors` is also used for `can_cast`
+ *       there is no way to "pass out" the result of this function.  This means
+ *       it will be called twice for every ufunc call.
+ *       (I am considering including `auxdata` as an "optional" parameter to
+ *       `resolve_descriptors`, so that it can be filled there if not NULL.)
+ */
+typedef int (PyArrayMethod_TranslateGivenDescriptors)(int nin, int nout,
+        PyArray_DTypeMeta *const wrapped_dtypes[],
+        PyArray_Descr *const given_descrs[], PyArray_Descr *new_descrs[]);
+
+/**
+ * The function to convert the actual loop descriptors (as returned by the
+ * original `resolve_descriptors` function) to the ones the output array
+ * should use.
+ * This function must return "viewable" types, it must not mutate them in any
+ * form that would break the inner-loop logic.  Does not need to support NULL.
+ *
+ * The function must clean up on error.
+ *
+ * @param nin Number of input arguments
+ * @param nout Number of output arguments
+ * @param new_dtypes The DTypes of the output (usually probably not needed)
+ * @param given_descrs Original given_descrs to the resolver, necessary to
+ *        fetch any information related to the new dtypes from the original.
+ * @param original_descrs The `loop_descrs` returned by the wrapped loop.
+ * @param loop_descrs The output descriptors, compatible to `original_descrs`.
+ *
+ * @returns 0 on success, -1 on failure.
+ */
+typedef int (PyArrayMethod_TranslateLoopDescriptors)(int nin, int nout,
+        PyArray_DTypeMeta *const new_dtypes[], PyArray_Descr *const given_descrs[],
+        PyArray_Descr *original_descrs[], PyArray_Descr *loop_descrs[]);
+
+
+
+/*
+ * A traverse loop working on a single array. This is similar to the general
+ * strided-loop function. This is designed for loops that need to visit every
+ * element of a single array.
+ *
+ * Currently this is used for array clearing, via the NPY_DT_get_clear_loop
+ * API hook, and zero-filling, via the NPY_DT_get_fill_zero_loop API hook.
+ * These are most useful for handling arrays storing embedded references to
+ * python objects or heap-allocated data.
+ *
+ * The `void *traverse_context` is passed in because we may need to pass in
+ * Interpreter state or similar in the future, but we don't want to pass in
+ * a full context (with pointers to dtypes, method, caller which all make
+ * no sense for a traverse function).
+ *
+ * We assume for now that this context can be just passed through in the
+ * the future (for structured dtypes).
+ *
+ */
+typedef int (PyArrayMethod_TraverseLoop)(
+        void *traverse_context, const PyArray_Descr *descr, char *data,
+        npy_intp size, npy_intp stride, NpyAuxData *auxdata);
+
+
+/*
+ * Simplified get_loop function specific to dtype traversal
+ *
+ * It should set the flags needed for the traversal loop and set out_loop to the
+ * loop function, which must be a valid PyArrayMethod_TraverseLoop
+ * pointer. Currently this is used for zero-filling and clearing arrays storing
+ * embedded references.
+ *
+ */
+typedef int (PyArrayMethod_GetTraverseLoop)(
+        void *traverse_context, const PyArray_Descr *descr,
+        int aligned, npy_intp fixed_stride,
+        PyArrayMethod_TraverseLoop **out_loop, NpyAuxData **out_auxdata,
+        NPY_ARRAYMETHOD_FLAGS *flags);
+
+
+/*
+ * Type of the C promoter function, which must be wrapped into a
+ * PyCapsule with name "numpy._ufunc_promoter".
+ *
+ * Note that currently the output dtypes are always NULL unless they are
+ * also part of the signature. This is an implementation detail and could
+ * change in the future. However, in general promoters should not have a
+ * need for output dtypes.
+ * (There are potential use-cases, these are currently unsupported.)
+ */
+typedef int (PyArrayMethod_PromoterFunction)(PyObject *ufunc,
+        PyArray_DTypeMeta *const op_dtypes[], PyArray_DTypeMeta *const signature[],
+        PyArray_DTypeMeta *new_op_dtypes[]);
+
+/*
+ * ****************************
+ *          DTYPE API
+ * ****************************
+ */
+
+#define NPY_DT_ABSTRACT 1 << 1
+#define NPY_DT_PARAMETRIC 1 << 2
+#define NPY_DT_NUMERIC 1 << 3
+
+/*
+ * These correspond to slots in the NPY_DType_Slots struct and must
+ * be in the same order as the members of that struct. If new slots
+ * get added or old slots get removed NPY_NUM_DTYPE_SLOTS must also
+ * be updated
+ */
+
+#define NPY_DT_discover_descr_from_pyobject 1
+// this slot is considered private because its API hasn't been decided
+#define _NPY_DT_is_known_scalar_type 2
+#define NPY_DT_default_descr 3
+#define NPY_DT_common_dtype 4
+#define NPY_DT_common_instance 5
+#define NPY_DT_ensure_canonical 6
+#define NPY_DT_setitem 7
+#define NPY_DT_getitem 8
+#define NPY_DT_get_clear_loop 9
+#define NPY_DT_get_fill_zero_loop 10
+#define NPY_DT_finalize_descr 11
+
+// These PyArray_ArrFunc slots will be deprecated and replaced eventually
+// getitem and setitem can be defined as a performance optimization;
+// by default the user dtypes call `legacy_getitem_using_DType` and
+// `legacy_setitem_using_DType`, respectively. This functionality is
+// only supported for basic NumPy DTypes.
+
+
+// used to separate dtype slots from arrfuncs slots
+// intended only for internal use but defined here for clarity
+#define _NPY_DT_ARRFUNCS_OFFSET (1 << 10)
+
+// Cast is disabled
+// #define NPY_DT_PyArray_ArrFuncs_cast 0 + _NPY_DT_ARRFUNCS_OFFSET
+
+#define NPY_DT_PyArray_ArrFuncs_getitem 1 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_setitem 2 + _NPY_DT_ARRFUNCS_OFFSET
+
+// Copyswap is disabled
+// #define NPY_DT_PyArray_ArrFuncs_copyswapn 3 + _NPY_DT_ARRFUNCS_OFFSET
+// #define NPY_DT_PyArray_ArrFuncs_copyswap 4 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_compare 5 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_argmax 6 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_dotfunc 7 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_scanfunc 8 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_fromstr 9 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_nonzero 10 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_fill 11 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_fillwithscalar 12 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_sort 13 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_argsort 14 + _NPY_DT_ARRFUNCS_OFFSET
+
+// Casting related slots are disabled. See
+// https://github.com/numpy/numpy/pull/23173#discussion_r1101098163
+// #define NPY_DT_PyArray_ArrFuncs_castdict 15 + _NPY_DT_ARRFUNCS_OFFSET
+// #define NPY_DT_PyArray_ArrFuncs_scalarkind 16 + _NPY_DT_ARRFUNCS_OFFSET
+// #define NPY_DT_PyArray_ArrFuncs_cancastscalarkindto 17 + _NPY_DT_ARRFUNCS_OFFSET
+// #define NPY_DT_PyArray_ArrFuncs_cancastto 18 + _NPY_DT_ARRFUNCS_OFFSET
+
+// These are deprecated in NumPy 1.19, so are disabled here.
+// #define NPY_DT_PyArray_ArrFuncs_fastclip 19 + _NPY_DT_ARRFUNCS_OFFSET
+// #define NPY_DT_PyArray_ArrFuncs_fastputmask 20 + _NPY_DT_ARRFUNCS_OFFSET
+// #define NPY_DT_PyArray_ArrFuncs_fasttake 21 + _NPY_DT_ARRFUNCS_OFFSET
+#define NPY_DT_PyArray_ArrFuncs_argmin 22 + _NPY_DT_ARRFUNCS_OFFSET
+
+
+// TODO: These slots probably still need some thought, and/or a way to "grow"?
+typedef struct {
+    PyTypeObject *typeobj;    /* type of python scalar or NULL */
+    int flags;                /* flags, including parametric and abstract */
+    /* NULL terminated cast definitions. Use NULL for the newly created DType */
+    PyArrayMethod_Spec **casts;
+    PyType_Slot *slots;
+    /* Baseclass or NULL (will always subclass `np.dtype`) */
+    PyTypeObject *baseclass;
+} PyArrayDTypeMeta_Spec;
+
+
+typedef PyArray_Descr *(PyArrayDTypeMeta_DiscoverDescrFromPyobject)(
+        PyArray_DTypeMeta *cls, PyObject *obj);
+
+/*
+ * Before making this public, we should decide whether it should pass
+ * the type, or allow looking at the object. A possible use-case:
+ * `np.array(np.array([0]), dtype=np.ndarray)`
+ * Could consider arrays that are not `dtype=ndarray` "scalars".
+ */
+typedef int (PyArrayDTypeMeta_IsKnownScalarType)(
+        PyArray_DTypeMeta *cls, PyTypeObject *obj);
+
+typedef PyArray_Descr *(PyArrayDTypeMeta_DefaultDescriptor)(PyArray_DTypeMeta *cls);
+typedef PyArray_DTypeMeta *(PyArrayDTypeMeta_CommonDType)(
+        PyArray_DTypeMeta *dtype1, PyArray_DTypeMeta *dtype2);
+
+
+/*
+ * Convenience utility for getting a reference to the DType metaclass associated
+ * with a dtype instance.
+ */
+#define NPY_DTYPE(descr) ((PyArray_DTypeMeta *)Py_TYPE(descr))
+
+static inline PyArray_DTypeMeta *
+NPY_DT_NewRef(PyArray_DTypeMeta *o) {
+    Py_INCREF((PyObject *)o);
+    return o;
+}
+
+
+typedef PyArray_Descr *(PyArrayDTypeMeta_CommonInstance)(
+        PyArray_Descr *dtype1, PyArray_Descr *dtype2);
+typedef PyArray_Descr *(PyArrayDTypeMeta_EnsureCanonical)(PyArray_Descr *dtype);
+/*
+ * Returns either a new reference to *dtype* or a new descriptor instance
+ * initialized with the same parameters as *dtype*. The caller cannot know
+ * which choice a dtype will make. This function is called just before the
+ * array buffer is created for a newly created array, it is not called for
+ * views and the descriptor returned by this function is attached to the array.
+ */
+typedef PyArray_Descr *(PyArrayDTypeMeta_FinalizeDescriptor)(PyArray_Descr *dtype);
+
+/*
+ * TODO: These two functions are currently only used for experimental DType
+ *       API support.  Their relation should be "reversed": NumPy should
+ *       always use them internally.
+ *       There are open points about "casting safety" though, e.g. setting
+ *       elements is currently always unsafe.
+ */
+typedef int(PyArrayDTypeMeta_SetItem)(PyArray_Descr *, PyObject *, char *);
+typedef PyObject *(PyArrayDTypeMeta_GetItem)(PyArray_Descr *, char *);
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY___DTYPE_API_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/halffloat.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/halffloat.h
new file mode 100644
index 0000000..9504016
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/halffloat.h
@@ -0,0 +1,70 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_HALFFLOAT_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_HALFFLOAT_H_
+
+#include <Python.h>
+#include <numpy/npy_math.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/*
+ * Half-precision routines
+ */
+
+/* Conversions */
+float npy_half_to_float(npy_half h);
+double npy_half_to_double(npy_half h);
+npy_half npy_float_to_half(float f);
+npy_half npy_double_to_half(double d);
+/* Comparisons */
+int npy_half_eq(npy_half h1, npy_half h2);
+int npy_half_ne(npy_half h1, npy_half h2);
+int npy_half_le(npy_half h1, npy_half h2);
+int npy_half_lt(npy_half h1, npy_half h2);
+int npy_half_ge(npy_half h1, npy_half h2);
+int npy_half_gt(npy_half h1, npy_half h2);
+/* faster *_nonan variants for when you know h1 and h2 are not NaN */
+int npy_half_eq_nonan(npy_half h1, npy_half h2);
+int npy_half_lt_nonan(npy_half h1, npy_half h2);
+int npy_half_le_nonan(npy_half h1, npy_half h2);
+/* Miscellaneous functions */
+int npy_half_iszero(npy_half h);
+int npy_half_isnan(npy_half h);
+int npy_half_isinf(npy_half h);
+int npy_half_isfinite(npy_half h);
+int npy_half_signbit(npy_half h);
+npy_half npy_half_copysign(npy_half x, npy_half y);
+npy_half npy_half_spacing(npy_half h);
+npy_half npy_half_nextafter(npy_half x, npy_half y);
+npy_half npy_half_divmod(npy_half x, npy_half y, npy_half *modulus);
+
+/*
+ * Half-precision constants
+ */
+
+#define NPY_HALF_ZERO   (0x0000u)
+#define NPY_HALF_PZERO  (0x0000u)
+#define NPY_HALF_NZERO  (0x8000u)
+#define NPY_HALF_ONE    (0x3c00u)
+#define NPY_HALF_NEGONE (0xbc00u)
+#define NPY_HALF_PINF   (0x7c00u)
+#define NPY_HALF_NINF   (0xfc00u)
+#define NPY_HALF_NAN    (0x7e00u)
+
+#define NPY_MAX_HALF    (0x7bffu)
+
+/*
+ * Bit-level conversions
+ */
+
+npy_uint16 npy_floatbits_to_halfbits(npy_uint32 f);
+npy_uint16 npy_doublebits_to_halfbits(npy_uint64 d);
+npy_uint32 npy_halfbits_to_floatbits(npy_uint16 h);
+npy_uint64 npy_halfbits_to_doublebits(npy_uint16 h);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_HALFFLOAT_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/ndarrayobject.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/ndarrayobject.h
new file mode 100644
index 0000000..f06bafe
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/ndarrayobject.h
@@ -0,0 +1,304 @@
+/*
+ * DON'T INCLUDE THIS DIRECTLY.
+ */
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NDARRAYOBJECT_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NDARRAYOBJECT_H_
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <Python.h>
+#include "ndarraytypes.h"
+#include "dtype_api.h"
+
+/* Includes the "function" C-API -- these are all stored in a
+   list of pointers --- one for each file
+   The two lists are concatenated into one in multiarray.
+
+   They are available as import_array()
+*/
+
+#include "__multiarray_api.h"
+
+/*
+ * Include any definitions which are defined differently for 1.x and 2.x
+ * (Symbols only available on 2.x are not there, but rather guarded.)
+ */
+#include "npy_2_compat.h"
+
+/* C-API that requires previous API to be defined */
+
+#define PyArray_DescrCheck(op) PyObject_TypeCheck(op, &PyArrayDescr_Type)
+
+#define PyArray_Check(op) PyObject_TypeCheck(op, &PyArray_Type)
+#define PyArray_CheckExact(op) (((PyObject*)(op))->ob_type == &PyArray_Type)
+
+#define PyArray_HasArrayInterfaceType(op, type, context, out)                 \
+        ((((out)=PyArray_FromStructInterface(op)) != Py_NotImplemented) ||    \
+         (((out)=PyArray_FromInterface(op)) != Py_NotImplemented) ||          \
+         (((out)=PyArray_FromArrayAttr(op, type, context)) !=                 \
+          Py_NotImplemented))
+
+#define PyArray_HasArrayInterface(op, out)                                    \
+        PyArray_HasArrayInterfaceType(op, NULL, NULL, out)
+
+#define PyArray_IsZeroDim(op) (PyArray_Check(op) && \
+                               (PyArray_NDIM((PyArrayObject *)op) == 0))
+
+#define PyArray_IsScalar(obj, cls)                                            \
+        (PyObject_TypeCheck(obj, &Py##cls##ArrType_Type))
+
+#define PyArray_CheckScalar(m) (PyArray_IsScalar(m, Generic) ||               \
+                                PyArray_IsZeroDim(m))
+#define PyArray_IsPythonNumber(obj)                                           \
+        (PyFloat_Check(obj) || PyComplex_Check(obj) ||                        \
+         PyLong_Check(obj) || PyBool_Check(obj))
+#define PyArray_IsIntegerScalar(obj) (PyLong_Check(obj)                       \
+              || PyArray_IsScalar((obj), Integer))
+#define PyArray_IsPythonScalar(obj)                                           \
+        (PyArray_IsPythonNumber(obj) || PyBytes_Check(obj) ||                 \
+         PyUnicode_Check(obj))
+
+#define PyArray_IsAnyScalar(obj)                                              \
+        (PyArray_IsScalar(obj, Generic) || PyArray_IsPythonScalar(obj))
+
+#define PyArray_CheckAnyScalar(obj) (PyArray_IsPythonScalar(obj) ||           \
+                                     PyArray_CheckScalar(obj))
+
+
+#define PyArray_GETCONTIGUOUS(m) (PyArray_ISCONTIGUOUS(m) ?                   \
+                                  Py_INCREF(m), (m) :                         \
+                                  (PyArrayObject *)(PyArray_Copy(m)))
+
+#define PyArray_SAMESHAPE(a1,a2) ((PyArray_NDIM(a1) == PyArray_NDIM(a2)) &&   \
+                                  PyArray_CompareLists(PyArray_DIMS(a1),      \
+                                                       PyArray_DIMS(a2),      \
+                                                       PyArray_NDIM(a1)))
+
+#define PyArray_SIZE(m) PyArray_MultiplyList(PyArray_DIMS(m), PyArray_NDIM(m))
+#define PyArray_NBYTES(m) (PyArray_ITEMSIZE(m) * PyArray_SIZE(m))
+#define PyArray_FROM_O(m) PyArray_FromAny(m, NULL, 0, 0, 0, NULL)
+
+#define PyArray_FROM_OF(m,flags) PyArray_CheckFromAny(m, NULL, 0, 0, flags,   \
+                                                      NULL)
+
+#define PyArray_FROM_OT(m,type) PyArray_FromAny(m,                            \
+                                PyArray_DescrFromType(type), 0, 0, 0, NULL)
+
+#define PyArray_FROM_OTF(m, type, flags) \
+        PyArray_FromAny(m, PyArray_DescrFromType(type), 0, 0, \
+                        (((flags) & NPY_ARRAY_ENSURECOPY) ? \
+                         ((flags) | NPY_ARRAY_DEFAULT) : (flags)), NULL)
+
+#define PyArray_FROMANY(m, type, min, max, flags) \
+        PyArray_FromAny(m, PyArray_DescrFromType(type), min, max, \
+                        (((flags) & NPY_ARRAY_ENSURECOPY) ? \
+                         (flags) | NPY_ARRAY_DEFAULT : (flags)), NULL)
+
+#define PyArray_ZEROS(m, dims, type, is_f_order) \
+        PyArray_Zeros(m, dims, PyArray_DescrFromType(type), is_f_order)
+
+#define PyArray_EMPTY(m, dims, type, is_f_order) \
+        PyArray_Empty(m, dims, PyArray_DescrFromType(type), is_f_order)
+
+#define PyArray_FILLWBYTE(obj, val) memset(PyArray_DATA(obj), val, \
+                                           PyArray_NBYTES(obj))
+
+#define PyArray_ContiguousFromAny(op, type, min_depth, max_depth) \
+        PyArray_FromAny(op, PyArray_DescrFromType(type), min_depth, \
+                              max_depth, NPY_ARRAY_DEFAULT, NULL)
+
+#define PyArray_EquivArrTypes(a1, a2) \
+        PyArray_EquivTypes(PyArray_DESCR(a1), PyArray_DESCR(a2))
+
+#define PyArray_EquivByteorders(b1, b2) \
+        (((b1) == (b2)) || (PyArray_ISNBO(b1) == PyArray_ISNBO(b2)))
+
+#define PyArray_SimpleNew(nd, dims, typenum) \
+        PyArray_New(&PyArray_Type, nd, dims, typenum, NULL, NULL, 0, 0, NULL)
+
+#define PyArray_SimpleNewFromData(nd, dims, typenum, data) \
+        PyArray_New(&PyArray_Type, nd, dims, typenum, NULL, \
+                    data, 0, NPY_ARRAY_CARRAY, NULL)
+
+#define PyArray_SimpleNewFromDescr(nd, dims, descr) \
+        PyArray_NewFromDescr(&PyArray_Type, descr, nd, dims, \
+                             NULL, NULL, 0, NULL)
+
+#define PyArray_ToScalar(data, arr) \
+        PyArray_Scalar(data, PyArray_DESCR(arr), (PyObject *)arr)
+
+
+/* These might be faster without the dereferencing of obj
+   going on inside -- of course an optimizing compiler should
+   inline the constants inside a for loop making it a moot point
+*/
+
+#define PyArray_GETPTR1(obj, i) ((void *)(PyArray_BYTES(obj) + \
+                                         (i)*PyArray_STRIDES(obj)[0]))
+
+#define PyArray_GETPTR2(obj, i, j) ((void *)(PyArray_BYTES(obj) + \
+                                            (i)*PyArray_STRIDES(obj)[0] + \
+                                            (j)*PyArray_STRIDES(obj)[1]))
+
+#define PyArray_GETPTR3(obj, i, j, k) ((void *)(PyArray_BYTES(obj) + \
+                                            (i)*PyArray_STRIDES(obj)[0] + \
+                                            (j)*PyArray_STRIDES(obj)[1] + \
+                                            (k)*PyArray_STRIDES(obj)[2]))
+
+#define PyArray_GETPTR4(obj, i, j, k, l) ((void *)(PyArray_BYTES(obj) + \
+                                            (i)*PyArray_STRIDES(obj)[0] + \
+                                            (j)*PyArray_STRIDES(obj)[1] + \
+                                            (k)*PyArray_STRIDES(obj)[2] + \
+                                            (l)*PyArray_STRIDES(obj)[3]))
+
+static inline void
+PyArray_DiscardWritebackIfCopy(PyArrayObject *arr)
+{
+    PyArrayObject_fields *fa = (PyArrayObject_fields *)arr;
+    if (fa && fa->base) {
+        if (fa->flags & NPY_ARRAY_WRITEBACKIFCOPY) {
+            PyArray_ENABLEFLAGS((PyArrayObject*)fa->base, NPY_ARRAY_WRITEABLE);
+            Py_DECREF(fa->base);
+            fa->base = NULL;
+            PyArray_CLEARFLAGS(arr, NPY_ARRAY_WRITEBACKIFCOPY);
+        }
+    }
+}
+
+#define PyArray_DESCR_REPLACE(descr) do { \
+                PyArray_Descr *_new_; \
+                _new_ = PyArray_DescrNew(descr); \
+                Py_XDECREF(descr); \
+                descr = _new_; \
+        } while(0)
+
+/* Copy should always return contiguous array */
+#define PyArray_Copy(obj) PyArray_NewCopy(obj, NPY_CORDER)
+
+#define PyArray_FromObject(op, type, min_depth, max_depth) \
+        PyArray_FromAny(op, PyArray_DescrFromType(type), min_depth, \
+                              max_depth, NPY_ARRAY_BEHAVED | \
+                                         NPY_ARRAY_ENSUREARRAY, NULL)
+
+#define PyArray_ContiguousFromObject(op, type, min_depth, max_depth) \
+        PyArray_FromAny(op, PyArray_DescrFromType(type), min_depth, \
+                              max_depth, NPY_ARRAY_DEFAULT | \
+                                         NPY_ARRAY_ENSUREARRAY, NULL)
+
+#define PyArray_CopyFromObject(op, type, min_depth, max_depth) \
+        PyArray_FromAny(op, PyArray_DescrFromType(type), min_depth, \
+                        max_depth, NPY_ARRAY_ENSURECOPY | \
+                                   NPY_ARRAY_DEFAULT | \
+                                   NPY_ARRAY_ENSUREARRAY, NULL)
+
+#define PyArray_Cast(mp, type_num)                                            \
+        PyArray_CastToType(mp, PyArray_DescrFromType(type_num), 0)
+
+#define PyArray_Take(ap, items, axis)                                         \
+        PyArray_TakeFrom(ap, items, axis, NULL, NPY_RAISE)
+
+#define PyArray_Put(ap, items, values)                                        \
+        PyArray_PutTo(ap, items, values, NPY_RAISE)
+
+
+/*
+   Check to see if this key in the dictionary is the "title"
+   entry of the tuple (i.e. a duplicate dictionary entry in the fields
+   dict).
+*/
+
+static inline int
+NPY_TITLE_KEY_check(PyObject *key, PyObject *value)
+{
+    PyObject *title;
+    if (PyTuple_Size(value) != 3) {
+        return 0;
+    }
+    title = PyTuple_GetItem(value, 2);
+    if (key == title) {
+        return 1;
+    }
+#ifdef PYPY_VERSION
+    /*
+     * On PyPy, dictionary keys do not always preserve object identity.
+     * Fall back to comparison by value.
+     */
+    if (PyUnicode_Check(title) && PyUnicode_Check(key)) {
+        return PyUnicode_Compare(title, key) == 0 ? 1 : 0;
+    }
+#endif
+    return 0;
+}
+
+/* Macro, for backward compat with "if NPY_TITLE_KEY(key, value) { ..." */
+#define NPY_TITLE_KEY(key, value) (NPY_TITLE_KEY_check((key), (value)))
+
+#define DEPRECATE(msg) PyErr_WarnEx(PyExc_DeprecationWarning,msg,1)
+#define DEPRECATE_FUTUREWARNING(msg) PyErr_WarnEx(PyExc_FutureWarning,msg,1)
+
+
+/*
+ * These macros and functions unfortunately require runtime version checks
+ * that are only defined in `npy_2_compat.h`.  For that reasons they cannot be
+ * part of `ndarraytypes.h` which tries to be self contained.
+ */
+
+static inline npy_intp
+PyArray_ITEMSIZE(const PyArrayObject *arr)
+{
+    return PyDataType_ELSIZE(((PyArrayObject_fields *)arr)->descr);
+}
+
+#define PyDataType_HASFIELDS(obj) (PyDataType_ISLEGACY((PyArray_Descr*)(obj)) && PyDataType_NAMES((PyArray_Descr*)(obj)) != NULL)
+#define PyDataType_HASSUBARRAY(dtype) (PyDataType_ISLEGACY(dtype) && PyDataType_SUBARRAY(dtype) != NULL)
+#define PyDataType_ISUNSIZED(dtype) ((dtype)->elsize == 0 && \
+                                      !PyDataType_HASFIELDS(dtype))
+
+#define PyDataType_FLAGCHK(dtype, flag) \
+        ((PyDataType_FLAGS(dtype) & (flag)) == (flag))
+
+#define PyDataType_REFCHK(dtype) \
+        PyDataType_FLAGCHK(dtype, NPY_ITEM_REFCOUNT)
+
+#define NPY_BEGIN_THREADS_DESCR(dtype) \
+        do {if (!(PyDataType_FLAGCHK((dtype), NPY_NEEDS_PYAPI))) \
+                NPY_BEGIN_THREADS;} while (0);
+
+#define NPY_END_THREADS_DESCR(dtype) \
+        do {if (!(PyDataType_FLAGCHK((dtype), NPY_NEEDS_PYAPI))) \
+                NPY_END_THREADS; } while (0);
+
+#if !(defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD)
+/* The internal copy of this is now defined in `dtypemeta.h` */
+/*
+ * `PyArray_Scalar` is the same as this function but converts will convert
+ * most NumPy types to Python scalars.
+ */
+static inline PyObject *
+PyArray_GETITEM(const PyArrayObject *arr, const char *itemptr)
+{
+    return PyDataType_GetArrFuncs(((PyArrayObject_fields *)arr)->descr)->getitem(
+                                        (void *)itemptr, (PyArrayObject *)arr);
+}
+
+/*
+ * SETITEM should only be used if it is known that the value is a scalar
+ * and of a type understood by the arrays dtype.
+ * Use `PyArray_Pack` if the value may be of a different dtype.
+ */
+static inline int
+PyArray_SETITEM(PyArrayObject *arr, char *itemptr, PyObject *v)
+{
+    return PyDataType_GetArrFuncs(((PyArrayObject_fields *)arr)->descr)->setitem(v, itemptr, arr);
+}
+#endif  /* not internal */
+
+
+#ifdef __cplusplus
+}
+#endif
+
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NDARRAYOBJECT_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/ndarraytypes.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/ndarraytypes.h
new file mode 100644
index 0000000..baa4240
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/ndarraytypes.h
@@ -0,0 +1,1950 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NDARRAYTYPES_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NDARRAYTYPES_H_
+
+#include "npy_common.h"
+#include "npy_endian.h"
+#include "npy_cpu.h"
+#include "utils.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#define NPY_NO_EXPORT NPY_VISIBILITY_HIDDEN
+
+/* Always allow threading unless it was explicitly disabled at build time */
+#if !NPY_NO_SMP
+        #define NPY_ALLOW_THREADS 1
+#else
+        #define NPY_ALLOW_THREADS 0
+#endif
+
+#ifndef __has_extension
+#define __has_extension(x) 0
+#endif
+
+/*
+ * There are several places in the code where an array of dimensions
+ * is allocated statically.  This is the size of that static
+ * allocation.
+ *
+ * The array creation itself could have arbitrary dimensions but all
+ * the places where static allocation is used would need to be changed
+ * to dynamic (including inside of several structures)
+ *
+ * As of NumPy 2.0, we strongly discourage the downstream use of NPY_MAXDIMS,
+ * but since auditing everything seems a big ask, define it as 64.
+ * A future version could:
+ * - Increase or remove the limit and require recompilation (like 2.0 did)
+ * - Deprecate or remove the macro but keep the limit (at basically any time)
+ */
+#define NPY_MAXDIMS 64
+/* We cannot change this as it would break ABI: */
+#define NPY_MAXDIMS_LEGACY_ITERS 32
+/* NPY_MAXARGS is version dependent and defined in npy_2_compat.h */
+
+/* Used for Converter Functions "O&" code in ParseTuple */
+#define NPY_FAIL 0
+#define NPY_SUCCEED 1
+
+
+enum NPY_TYPES {    NPY_BOOL=0,
+                    NPY_BYTE, NPY_UBYTE,
+                    NPY_SHORT, NPY_USHORT,
+                    NPY_INT, NPY_UINT,
+                    NPY_LONG, NPY_ULONG,
+                    NPY_LONGLONG, NPY_ULONGLONG,
+                    NPY_FLOAT, NPY_DOUBLE, NPY_LONGDOUBLE,
+                    NPY_CFLOAT, NPY_CDOUBLE, NPY_CLONGDOUBLE,
+                    NPY_OBJECT=17,
+                    NPY_STRING, NPY_UNICODE,
+                    NPY_VOID,
+                    /*
+                     * New 1.6 types appended, may be integrated
+                     * into the above in 2.0.
+                     */
+                    NPY_DATETIME, NPY_TIMEDELTA, NPY_HALF,
+
+                    NPY_CHAR, /* Deprecated, will raise if used */
+
+                    /* The number of *legacy* dtypes */
+                    NPY_NTYPES_LEGACY=24,
+
+                    /* assign a high value to avoid changing this in the
+                       future when new dtypes are added */
+                    NPY_NOTYPE=25,
+
+                    NPY_USERDEF=256,  /* leave room for characters */
+
+                    /* The number of types not including the new 1.6 types */
+                    NPY_NTYPES_ABI_COMPATIBLE=21,
+
+                    /*
+                     * New DTypes which do not share the legacy layout
+                     * (added after NumPy 2.0).  VSTRING is the first of these
+                     * we may open up a block for user-defined dtypes in the
+                     * future.
+                     */
+                    NPY_VSTRING=2056,
+};
+
+
+/* basetype array priority */
+#define NPY_PRIORITY 0.0
+
+/* default subtype priority */
+#define NPY_SUBTYPE_PRIORITY 1.0
+
+/* default scalar priority */
+#define NPY_SCALAR_PRIORITY -1000000.0
+
+/* How many floating point types are there (excluding half) */
+#define NPY_NUM_FLOATTYPE 3
+
+/*
+ * These characters correspond to the array type and the struct
+ * module
+ */
+
+enum NPY_TYPECHAR {
+        NPY_BOOLLTR = '?',
+        NPY_BYTELTR = 'b',
+        NPY_UBYTELTR = 'B',
+        NPY_SHORTLTR = 'h',
+        NPY_USHORTLTR = 'H',
+        NPY_INTLTR = 'i',
+        NPY_UINTLTR = 'I',
+        NPY_LONGLTR = 'l',
+        NPY_ULONGLTR = 'L',
+        NPY_LONGLONGLTR = 'q',
+        NPY_ULONGLONGLTR = 'Q',
+        NPY_HALFLTR = 'e',
+        NPY_FLOATLTR = 'f',
+        NPY_DOUBLELTR = 'd',
+        NPY_LONGDOUBLELTR = 'g',
+        NPY_CFLOATLTR = 'F',
+        NPY_CDOUBLELTR = 'D',
+        NPY_CLONGDOUBLELTR = 'G',
+        NPY_OBJECTLTR = 'O',
+        NPY_STRINGLTR = 'S',
+        NPY_DEPRECATED_STRINGLTR2 = 'a',
+        NPY_UNICODELTR = 'U',
+        NPY_VOIDLTR = 'V',
+        NPY_DATETIMELTR = 'M',
+        NPY_TIMEDELTALTR = 'm',
+        NPY_CHARLTR = 'c',
+
+        /*
+         * New non-legacy DTypes
+         */
+        NPY_VSTRINGLTR = 'T',
+
+        /*
+         * Note, we removed `NPY_INTPLTR` due to changing its definition
+         * to 'n', rather than 'p'.  On any typical platform this is the
+         * same integer.  'n' should be used for the `np.intp` with the same
+         * size as `size_t` while 'p' remains pointer sized.
+         *
+         * 'p', 'P', 'n', and 'N' are valid and defined explicitly
+         * in `arraytypes.c.src`.
+         */
+
+        /*
+         * These are for dtype 'kinds', not dtype 'typecodes'
+         * as the above are for.
+         */
+        NPY_GENBOOLLTR ='b',
+        NPY_SIGNEDLTR = 'i',
+        NPY_UNSIGNEDLTR = 'u',
+        NPY_FLOATINGLTR = 'f',
+        NPY_COMPLEXLTR = 'c',
+
+};
+
+/*
+ * Changing this may break Numpy API compatibility
+ * due to changing offsets in PyArray_ArrFuncs, so be
+ * careful. Here we have reused the mergesort slot for
+ * any kind of stable sort, the actual implementation will
+ * depend on the data type.
+ */
+typedef enum {
+        _NPY_SORT_UNDEFINED=-1,
+        NPY_QUICKSORT=0,
+        NPY_HEAPSORT=1,
+        NPY_MERGESORT=2,
+        NPY_STABLESORT=2,
+} NPY_SORTKIND;
+#define NPY_NSORTS (NPY_STABLESORT + 1)
+
+
+typedef enum {
+        NPY_INTROSELECT=0
+} NPY_SELECTKIND;
+#define NPY_NSELECTS (NPY_INTROSELECT + 1)
+
+
+typedef enum {
+        NPY_SEARCHLEFT=0,
+        NPY_SEARCHRIGHT=1
+} NPY_SEARCHSIDE;
+#define NPY_NSEARCHSIDES (NPY_SEARCHRIGHT + 1)
+
+
+typedef enum {
+        NPY_NOSCALAR=-1,
+        NPY_BOOL_SCALAR,
+        NPY_INTPOS_SCALAR,
+        NPY_INTNEG_SCALAR,
+        NPY_FLOAT_SCALAR,
+        NPY_COMPLEX_SCALAR,
+        NPY_OBJECT_SCALAR
+} NPY_SCALARKIND;
+#define NPY_NSCALARKINDS (NPY_OBJECT_SCALAR + 1)
+
+/* For specifying array memory layout or iteration order */
+typedef enum {
+        /* Fortran order if inputs are all Fortran, C otherwise */
+        NPY_ANYORDER=-1,
+        /* C order */
+        NPY_CORDER=0,
+        /* Fortran order */
+        NPY_FORTRANORDER=1,
+        /* An order as close to the inputs as possible */
+        NPY_KEEPORDER=2
+} NPY_ORDER;
+
+/* For specifying allowed casting in operations which support it */
+typedef enum {
+        _NPY_ERROR_OCCURRED_IN_CAST = -1,
+        /* Only allow identical types */
+        NPY_NO_CASTING=0,
+        /* Allow identical and byte swapped types */
+        NPY_EQUIV_CASTING=1,
+        /* Only allow safe casts */
+        NPY_SAFE_CASTING=2,
+        /* Allow safe casts or casts within the same kind */
+        NPY_SAME_KIND_CASTING=3,
+        /* Allow any casts */
+        NPY_UNSAFE_CASTING=4,
+} NPY_CASTING;
+
+typedef enum {
+        NPY_CLIP=0,
+        NPY_WRAP=1,
+        NPY_RAISE=2
+} NPY_CLIPMODE;
+
+typedef enum {
+        NPY_VALID=0,
+        NPY_SAME=1,
+        NPY_FULL=2
+} NPY_CORRELATEMODE;
+
+/* The special not-a-time (NaT) value */
+#define NPY_DATETIME_NAT NPY_MIN_INT64
+
+/*
+ * Upper bound on the length of a DATETIME ISO 8601 string
+ *   YEAR: 21 (64-bit year)
+ *   MONTH: 3
+ *   DAY: 3
+ *   HOURS: 3
+ *   MINUTES: 3
+ *   SECONDS: 3
+ *   ATTOSECONDS: 1 + 3*6
+ *   TIMEZONE: 5
+ *   NULL TERMINATOR: 1
+ */
+#define NPY_DATETIME_MAX_ISO8601_STRLEN (21 + 3*5 + 1 + 3*6 + 6 + 1)
+
+/* The FR in the unit names stands for frequency */
+typedef enum {
+        /* Force signed enum type, must be -1 for code compatibility */
+        NPY_FR_ERROR = -1,      /* error or undetermined */
+
+        /* Start of valid units */
+        NPY_FR_Y = 0,           /* Years */
+        NPY_FR_M = 1,           /* Months */
+        NPY_FR_W = 2,           /* Weeks */
+        /* Gap where 1.6 NPY_FR_B (value 3) was */
+        NPY_FR_D = 4,           /* Days */
+        NPY_FR_h = 5,           /* hours */
+        NPY_FR_m = 6,           /* minutes */
+        NPY_FR_s = 7,           /* seconds */
+        NPY_FR_ms = 8,          /* milliseconds */
+        NPY_FR_us = 9,          /* microseconds */
+        NPY_FR_ns = 10,         /* nanoseconds */
+        NPY_FR_ps = 11,         /* picoseconds */
+        NPY_FR_fs = 12,         /* femtoseconds */
+        NPY_FR_as = 13,         /* attoseconds */
+        NPY_FR_GENERIC = 14     /* unbound units, can convert to anything */
+} NPY_DATETIMEUNIT;
+
+/*
+ * NOTE: With the NPY_FR_B gap for 1.6 ABI compatibility, NPY_DATETIME_NUMUNITS
+ * is technically one more than the actual number of units.
+ */
+#define NPY_DATETIME_NUMUNITS (NPY_FR_GENERIC + 1)
+#define NPY_DATETIME_DEFAULTUNIT NPY_FR_GENERIC
+
+/*
+ * Business day conventions for mapping invalid business
+ * days to valid business days.
+ */
+typedef enum {
+    /* Go forward in time to the following business day. */
+    NPY_BUSDAY_FORWARD,
+    NPY_BUSDAY_FOLLOWING = NPY_BUSDAY_FORWARD,
+    /* Go backward in time to the preceding business day. */
+    NPY_BUSDAY_BACKWARD,
+    NPY_BUSDAY_PRECEDING = NPY_BUSDAY_BACKWARD,
+    /*
+     * Go forward in time to the following business day, unless it
+     * crosses a month boundary, in which case go backward
+     */
+    NPY_BUSDAY_MODIFIEDFOLLOWING,
+    /*
+     * Go backward in time to the preceding business day, unless it
+     * crosses a month boundary, in which case go forward.
+     */
+    NPY_BUSDAY_MODIFIEDPRECEDING,
+    /* Produce a NaT for non-business days. */
+    NPY_BUSDAY_NAT,
+    /* Raise an exception for non-business days. */
+    NPY_BUSDAY_RAISE
+} NPY_BUSDAY_ROLL;
+
+
+/************************************************************
+ * NumPy Auxiliary Data for inner loops, sort functions, etc.
+ ************************************************************/
+
+/*
+ * When creating an auxiliary data struct, this should always appear
+ * as the first member, like this:
+ *
+ * typedef struct {
+ *     NpyAuxData base;
+ *     double constant;
+ * } constant_multiplier_aux_data;
+ */
+typedef struct NpyAuxData_tag NpyAuxData;
+
+/* Function pointers for freeing or cloning auxiliary data */
+typedef void (NpyAuxData_FreeFunc) (NpyAuxData *);
+typedef NpyAuxData *(NpyAuxData_CloneFunc) (NpyAuxData *);
+
+struct NpyAuxData_tag {
+    NpyAuxData_FreeFunc *free;
+    NpyAuxData_CloneFunc *clone;
+    /* To allow for a bit of expansion without breaking the ABI */
+    void *reserved[2];
+};
+
+/* Macros to use for freeing and cloning auxiliary data */
+#define NPY_AUXDATA_FREE(auxdata) \
+    do { \
+        if ((auxdata) != NULL) { \
+            (auxdata)->free(auxdata); \
+        } \
+    } while(0)
+#define NPY_AUXDATA_CLONE(auxdata) \
+    ((auxdata)->clone(auxdata))
+
+#define NPY_ERR(str) fprintf(stderr, #str); fflush(stderr);
+#define NPY_ERR2(str) fprintf(stderr, str); fflush(stderr);
+
+/*
+* Macros to define how array, and dimension/strides data is
+* allocated. These should be made private
+*/
+
+#define NPY_USE_PYMEM 1
+
+
+#if NPY_USE_PYMEM == 1
+/* use the Raw versions which are safe to call with the GIL released */
+#define PyArray_malloc PyMem_RawMalloc
+#define PyArray_free PyMem_RawFree
+#define PyArray_realloc PyMem_RawRealloc
+#else
+#define PyArray_malloc malloc
+#define PyArray_free free
+#define PyArray_realloc realloc
+#endif
+
+/* Dimensions and strides */
+#define PyDimMem_NEW(size)                                         \
+    ((npy_intp *)PyArray_malloc(size*sizeof(npy_intp)))
+
+#define PyDimMem_FREE(ptr) PyArray_free(ptr)
+
+#define PyDimMem_RENEW(ptr,size)                                   \
+        ((npy_intp *)PyArray_realloc(ptr,size*sizeof(npy_intp)))
+
+/* forward declaration */
+struct _PyArray_Descr;
+
+/* These must deal with unaligned and swapped data if necessary */
+typedef PyObject * (PyArray_GetItemFunc) (void *, void *);
+typedef int (PyArray_SetItemFunc)(PyObject *, void *, void *);
+
+typedef void (PyArray_CopySwapNFunc)(void *, npy_intp, void *, npy_intp,
+                                     npy_intp, int, void *);
+
+typedef void (PyArray_CopySwapFunc)(void *, void *, int, void *);
+typedef npy_bool (PyArray_NonzeroFunc)(void *, void *);
+
+
+/*
+ * These assume aligned and notswapped data -- a buffer will be used
+ * before or contiguous data will be obtained
+ */
+
+typedef int (PyArray_CompareFunc)(const void *, const void *, void *);
+typedef int (PyArray_ArgFunc)(void*, npy_intp, npy_intp*, void *);
+
+typedef void (PyArray_DotFunc)(void *, npy_intp, void *, npy_intp, void *,
+                               npy_intp, void *);
+
+typedef void (PyArray_VectorUnaryFunc)(void *, void *, npy_intp, void *,
+                                       void *);
+
+/*
+ * XXX the ignore argument should be removed next time the API version
+ * is bumped. It used to be the separator.
+ */
+typedef int (PyArray_ScanFunc)(FILE *fp, void *dptr,
+                               char *ignore, struct _PyArray_Descr *);
+typedef int (PyArray_FromStrFunc)(char *s, void *dptr, char **endptr,
+                                  struct _PyArray_Descr *);
+
+typedef int (PyArray_FillFunc)(void *, npy_intp, void *);
+
+typedef int (PyArray_SortFunc)(void *, npy_intp, void *);
+typedef int (PyArray_ArgSortFunc)(void *, npy_intp *, npy_intp, void *);
+
+typedef int (PyArray_FillWithScalarFunc)(void *, npy_intp, void *, void *);
+
+typedef int (PyArray_ScalarKindFunc)(void *);
+
+typedef struct {
+        npy_intp *ptr;
+        int len;
+} PyArray_Dims;
+
+typedef struct {
+        /*
+         * Functions to cast to most other standard types
+         * Can have some NULL entries. The types
+         * DATETIME, TIMEDELTA, and HALF go into the castdict
+         * even though they are built-in.
+         */
+        PyArray_VectorUnaryFunc *cast[NPY_NTYPES_ABI_COMPATIBLE];
+
+        /* The next four functions *cannot* be NULL */
+
+        /*
+         * Functions to get and set items with standard Python types
+         * -- not array scalars
+         */
+        PyArray_GetItemFunc *getitem;
+        PyArray_SetItemFunc *setitem;
+
+        /*
+         * Copy and/or swap data.  Memory areas may not overlap
+         * Use memmove first if they might
+         */
+        PyArray_CopySwapNFunc *copyswapn;
+        PyArray_CopySwapFunc *copyswap;
+
+        /*
+         * Function to compare items
+         * Can be NULL
+         */
+        PyArray_CompareFunc *compare;
+
+        /*
+         * Function to select largest
+         * Can be NULL
+         */
+        PyArray_ArgFunc *argmax;
+
+        /*
+         * Function to compute dot product
+         * Can be NULL
+         */
+        PyArray_DotFunc *dotfunc;
+
+        /*
+         * Function to scan an ASCII file and
+         * place a single value plus possible separator
+         * Can be NULL
+         */
+        PyArray_ScanFunc *scanfunc;
+
+        /*
+         * Function to read a single value from a string
+         * and adjust the pointer; Can be NULL
+         */
+        PyArray_FromStrFunc *fromstr;
+
+        /*
+         * Function to determine if data is zero or not
+         * If NULL a default version is
+         * used at Registration time.
+         */
+        PyArray_NonzeroFunc *nonzero;
+
+        /*
+         * Used for arange. Should return 0 on success
+         * and -1 on failure.
+         * Can be NULL.
+         */
+        PyArray_FillFunc *fill;
+
+        /*
+         * Function to fill arrays with scalar values
+         * Can be NULL
+         */
+        PyArray_FillWithScalarFunc *fillwithscalar;
+
+        /*
+         * Sorting functions
+         * Can be NULL
+         */
+        PyArray_SortFunc *sort[NPY_NSORTS];
+        PyArray_ArgSortFunc *argsort[NPY_NSORTS];
+
+        /*
+         * Dictionary of additional casting functions
+         * PyArray_VectorUnaryFuncs
+         * which can be populated to support casting
+         * to other registered types. Can be NULL
+         */
+        PyObject *castdict;
+
+        /*
+         * Functions useful for generalizing
+         * the casting rules.
+         * Can be NULL;
+         */
+        PyArray_ScalarKindFunc *scalarkind;
+        int **cancastscalarkindto;
+        int *cancastto;
+
+        void *_unused1;
+        void *_unused2;
+        void *_unused3;
+
+        /*
+         * Function to select smallest
+         * Can be NULL
+         */
+        PyArray_ArgFunc *argmin;
+
+} PyArray_ArrFuncs;
+
+
+/* The item must be reference counted when it is inserted or extracted. */
+#define NPY_ITEM_REFCOUNT   0x01
+/* Same as needing REFCOUNT */
+#define NPY_ITEM_HASOBJECT  0x01
+/* Convert to list for pickling */
+#define NPY_LIST_PICKLE     0x02
+/* The item is a POINTER  */
+#define NPY_ITEM_IS_POINTER 0x04
+/* memory needs to be initialized for this data-type */
+#define NPY_NEEDS_INIT      0x08
+/* operations need Python C-API so don't give-up thread. */
+#define NPY_NEEDS_PYAPI     0x10
+/* Use f.getitem when extracting elements of this data-type */
+#define NPY_USE_GETITEM     0x20
+/* Use f.setitem when setting creating 0-d array from this data-type.*/
+#define NPY_USE_SETITEM     0x40
+/* A sticky flag specifically for structured arrays */
+#define NPY_ALIGNED_STRUCT  0x80
+
+/*
+ *These are inherited for global data-type if any data-types in the
+ * field have them
+ */
+#define NPY_FROM_FIELDS    (NPY_NEEDS_INIT | NPY_LIST_PICKLE | \
+                            NPY_ITEM_REFCOUNT | NPY_NEEDS_PYAPI)
+
+#define NPY_OBJECT_DTYPE_FLAGS (NPY_LIST_PICKLE | NPY_USE_GETITEM | \
+                                NPY_ITEM_IS_POINTER | NPY_ITEM_REFCOUNT | \
+                                NPY_NEEDS_INIT | NPY_NEEDS_PYAPI)
+
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+/*
+ * Public version of the Descriptor struct as of 2.x
+ */
+typedef struct _PyArray_Descr {
+        PyObject_HEAD
+        /*
+         * the type object representing an
+         * instance of this type -- should not
+         * be two type_numbers with the same type
+         * object.
+         */
+        PyTypeObject *typeobj;
+        /* kind for this type */
+        char kind;
+        /* unique-character representing this type */
+        char type;
+        /*
+         * '>' (big), '<' (little), '|'
+         * (not-applicable), or '=' (native).
+         */
+        char byteorder;
+        /* Former flags flags space (unused) to ensure type_num is stable. */
+        char _former_flags;
+        /* number representing this type */
+        int type_num;
+        /* Space for dtype instance specific flags. */
+        npy_uint64 flags;
+        /* element size (itemsize) for this type */
+        npy_intp elsize;
+        /* alignment needed for this type */
+        npy_intp alignment;
+        /* metadata dict or NULL */
+        PyObject *metadata;
+        /* Cached hash value (-1 if not yet computed). */
+        npy_hash_t hash;
+        /* Unused slot (must be initialized to NULL) for future use */
+        void *reserved_null[2];
+} PyArray_Descr;
+
+#else  /* 1.x and 2.x compatible version (only shared fields): */
+
+typedef struct _PyArray_Descr {
+        PyObject_HEAD
+        PyTypeObject *typeobj;
+        char kind;
+        char type;
+        char byteorder;
+        char _former_flags;
+        int type_num;
+} PyArray_Descr;
+
+/* To access modified fields, define the full 2.0 struct: */
+typedef struct {
+        PyObject_HEAD
+        PyTypeObject *typeobj;
+        char kind;
+        char type;
+        char byteorder;
+        char _former_flags;
+        int type_num;
+        npy_uint64 flags;
+        npy_intp elsize;
+        npy_intp alignment;
+        PyObject *metadata;
+        npy_hash_t hash;
+        void *reserved_null[2];
+} _PyArray_DescrNumPy2;
+
+#endif  /* 1.x and 2.x compatible version */
+
+/*
+ * Semi-private struct with additional field of legacy descriptors (must
+ * check NPY_DT_is_legacy before casting/accessing).  The struct is also not
+ * valid when running on 1.x (i.e. in public API use).
+ */
+typedef struct {
+        PyObject_HEAD
+        PyTypeObject *typeobj;
+        char kind;
+        char type;
+        char byteorder;
+        char _former_flags;
+        int type_num;
+        npy_uint64 flags;
+        npy_intp elsize;
+        npy_intp alignment;
+        PyObject *metadata;
+        npy_hash_t hash;
+        void *reserved_null[2];
+        struct _arr_descr *subarray;
+        PyObject *fields;
+        PyObject *names;
+        NpyAuxData *c_metadata;
+} _PyArray_LegacyDescr;
+
+
+/*
+ * Umodified PyArray_Descr struct identical to NumPy 1.x.  This struct is
+ * used as a prototype for registering a new legacy DType.
+ * It is also used to access the fields in user code running on 1.x.
+ */
+typedef struct {
+        PyObject_HEAD
+        PyTypeObject *typeobj;
+        char kind;
+        char type;
+        char byteorder;
+        char flags;
+        int type_num;
+        int elsize;
+        int alignment;
+        struct _arr_descr *subarray;
+        PyObject *fields;
+        PyObject *names;
+        PyArray_ArrFuncs *f;
+        PyObject *metadata;
+        NpyAuxData *c_metadata;
+        npy_hash_t hash;
+} PyArray_DescrProto;
+
+
+typedef struct _arr_descr {
+        PyArray_Descr *base;
+        PyObject *shape;       /* a tuple */
+} PyArray_ArrayDescr;
+
+/*
+ * Memory handler structure for array data.
+ */
+/* The declaration of free differs from PyMemAllocatorEx */
+typedef struct {
+    void *ctx;
+    void* (*malloc) (void *ctx, size_t size);
+    void* (*calloc) (void *ctx, size_t nelem, size_t elsize);
+    void* (*realloc) (void *ctx, void *ptr, size_t new_size);
+    void (*free) (void *ctx, void *ptr, size_t size);
+    /*
+     * This is the end of the version=1 struct. Only add new fields after
+     * this line
+     */
+} PyDataMemAllocator;
+
+typedef struct {
+    char name[127];  /* multiple of 64 to keep the struct aligned */
+    uint8_t version; /* currently 1 */
+    PyDataMemAllocator allocator;
+} PyDataMem_Handler;
+
+
+/*
+ * The main array object structure.
+ *
+ * It has been recommended to use the inline functions defined below
+ * (PyArray_DATA and friends) to access fields here for a number of
+ * releases. Direct access to the members themselves is deprecated.
+ * To ensure that your code does not use deprecated access,
+ * #define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION
+ * (or NPY_1_8_API_VERSION or higher as required).
+ */
+/* This struct will be moved to a private header in a future release */
+typedef struct tagPyArrayObject_fields {
+    PyObject_HEAD
+    /* Pointer to the raw data buffer */
+    char *data;
+    /* The number of dimensions, also called 'ndim' */
+    int nd;
+    /* The size in each dimension, also called 'shape' */
+    npy_intp *dimensions;
+    /*
+     * Number of bytes to jump to get to the
+     * next element in each dimension
+     */
+    npy_intp *strides;
+    /*
+     * This object is decref'd upon
+     * deletion of array. Except in the
+     * case of WRITEBACKIFCOPY which has
+     * special handling.
+     *
+     * For views it points to the original
+     * array, collapsed so no chains of
+     * views occur.
+     *
+     * For creation from buffer object it
+     * points to an object that should be
+     * decref'd on deletion
+     *
+     * For WRITEBACKIFCOPY flag this is an
+     * array to-be-updated upon calling
+     * PyArray_ResolveWritebackIfCopy
+     */
+    PyObject *base;
+    /* Pointer to type structure */
+    PyArray_Descr *descr;
+    /* Flags describing array -- see below */
+    int flags;
+    /* For weak references */
+    PyObject *weakreflist;
+#if NPY_FEATURE_VERSION >= NPY_1_20_API_VERSION
+    void *_buffer_info;  /* private buffer info, tagged to allow warning */
+#endif
+    /*
+     * For malloc/calloc/realloc/free per object
+     */
+#if NPY_FEATURE_VERSION >= NPY_1_22_API_VERSION
+    PyObject *mem_handler;
+#endif
+} PyArrayObject_fields;
+
+/*
+ * To hide the implementation details, we only expose
+ * the Python struct HEAD.
+ */
+#if !defined(NPY_NO_DEPRECATED_API) || \
+    (NPY_NO_DEPRECATED_API < NPY_1_7_API_VERSION)
+/*
+ * Can't put this in npy_deprecated_api.h like the others.
+ * PyArrayObject field access is deprecated as of NumPy 1.7.
+ */
+typedef PyArrayObject_fields PyArrayObject;
+#else
+typedef struct tagPyArrayObject {
+        PyObject_HEAD
+} PyArrayObject;
+#endif
+
+/*
+ * Removed 2020-Nov-25, NumPy 1.20
+ * #define NPY_SIZEOF_PYARRAYOBJECT (sizeof(PyArrayObject_fields))
+ *
+ * The above macro was removed as it gave a false sense of a stable ABI
+ * with respect to the structures size.  If you require a runtime constant,
+ * you can use `PyArray_Type.tp_basicsize` instead.  Otherwise, please
+ * see the PyArrayObject documentation or ask the NumPy developers for
+ * information on how to correctly replace the macro in a way that is
+ * compatible with multiple NumPy versions.
+ */
+
+/* Mirrors buffer object to ptr */
+
+typedef struct {
+        PyObject_HEAD
+        PyObject *base;
+        void *ptr;
+        npy_intp len;
+        int flags;
+} PyArray_Chunk;
+
+typedef struct {
+    NPY_DATETIMEUNIT base;
+    int num;
+} PyArray_DatetimeMetaData;
+
+typedef struct {
+    NpyAuxData base;
+    PyArray_DatetimeMetaData meta;
+} PyArray_DatetimeDTypeMetaData;
+
+/*
+ * This structure contains an exploded view of a date-time value.
+ * NaT is represented by year == NPY_DATETIME_NAT.
+ */
+typedef struct {
+        npy_int64 year;
+        npy_int32 month, day, hour, min, sec, us, ps, as;
+} npy_datetimestruct;
+
+/* This structure contains an exploded view of a timedelta value */
+typedef struct {
+        npy_int64 day;
+        npy_int32 sec, us, ps, as;
+} npy_timedeltastruct;
+
+typedef int (PyArray_FinalizeFunc)(PyArrayObject *, PyObject *);
+
+/*
+ * Means c-style contiguous (last index varies the fastest). The data
+ * elements right after each other.
+ *
+ * This flag may be requested in constructor functions.
+ * This flag may be tested for in PyArray_FLAGS(arr).
+ */
+#define NPY_ARRAY_C_CONTIGUOUS    0x0001
+
+/*
+ * Set if array is a contiguous Fortran array: the first index varies
+ * the fastest in memory (strides array is reverse of C-contiguous
+ * array)
+ *
+ * This flag may be requested in constructor functions.
+ * This flag may be tested for in PyArray_FLAGS(arr).
+ */
+#define NPY_ARRAY_F_CONTIGUOUS    0x0002
+
+/*
+ * Note: all 0-d arrays are C_CONTIGUOUS and F_CONTIGUOUS. If a
+ * 1-d array is C_CONTIGUOUS it is also F_CONTIGUOUS. Arrays with
+ * more then one dimension can be C_CONTIGUOUS and F_CONTIGUOUS
+ * at the same time if they have either zero or one element.
+ * A higher dimensional array always has the same contiguity flags as
+ * `array.squeeze()`; dimensions with `array.shape[dimension] == 1` are
+ * effectively ignored when checking for contiguity.
+ */
+
+/*
+ * If set, the array owns the data: it will be free'd when the array
+ * is deleted.
+ *
+ * This flag may be tested for in PyArray_FLAGS(arr).
+ */
+#define NPY_ARRAY_OWNDATA         0x0004
+
+/*
+ * An array never has the next four set; they're only used as parameter
+ * flags to the various FromAny functions
+ *
+ * This flag may be requested in constructor functions.
+ */
+
+/* Cause a cast to occur regardless of whether or not it is safe. */
+#define NPY_ARRAY_FORCECAST       0x0010
+
+/*
+ * Always copy the array. Returned arrays are always CONTIGUOUS,
+ * ALIGNED, and WRITEABLE. See also: NPY_ARRAY_ENSURENOCOPY = 0x4000.
+ *
+ * This flag may be requested in constructor functions.
+ */
+#define NPY_ARRAY_ENSURECOPY      0x0020
+
+/*
+ * Make sure the returned array is a base-class ndarray
+ *
+ * This flag may be requested in constructor functions.
+ */
+#define NPY_ARRAY_ENSUREARRAY     0x0040
+
+/*
+ * Make sure that the strides are in units of the element size Needed
+ * for some operations with record-arrays.
+ *
+ * This flag may be requested in constructor functions.
+ */
+#define NPY_ARRAY_ELEMENTSTRIDES  0x0080
+
+/*
+ * Array data is aligned on the appropriate memory address for the type
+ * stored according to how the compiler would align things (e.g., an
+ * array of integers (4 bytes each) starts on a memory address that's
+ * a multiple of 4)
+ *
+ * This flag may be requested in constructor functions.
+ * This flag may be tested for in PyArray_FLAGS(arr).
+ */
+#define NPY_ARRAY_ALIGNED         0x0100
+
+/*
+ * Array data has the native endianness
+ *
+ * This flag may be requested in constructor functions.
+ */
+#define NPY_ARRAY_NOTSWAPPED      0x0200
+
+/*
+ * Array data is writeable
+ *
+ * This flag may be requested in constructor functions.
+ * This flag may be tested for in PyArray_FLAGS(arr).
+ */
+#define NPY_ARRAY_WRITEABLE       0x0400
+
+/*
+ * If this flag is set, then base contains a pointer to an array of
+ * the same size that should be updated with the current contents of
+ * this array when PyArray_ResolveWritebackIfCopy is called.
+ *
+ * This flag may be requested in constructor functions.
+ * This flag may be tested for in PyArray_FLAGS(arr).
+ */
+#define NPY_ARRAY_WRITEBACKIFCOPY 0x2000
+
+/*
+ * No copy may be made while converting from an object/array (result is a view)
+ *
+ * This flag may be requested in constructor functions.
+ */
+#define NPY_ARRAY_ENSURENOCOPY 0x4000
+
+/*
+ * NOTE: there are also internal flags defined in multiarray/arrayobject.h,
+ * which start at bit 31 and work down.
+ */
+
+#define NPY_ARRAY_BEHAVED      (NPY_ARRAY_ALIGNED | \
+                                NPY_ARRAY_WRITEABLE)
+#define NPY_ARRAY_BEHAVED_NS   (NPY_ARRAY_ALIGNED | \
+                                NPY_ARRAY_WRITEABLE | \
+                                NPY_ARRAY_NOTSWAPPED)
+#define NPY_ARRAY_CARRAY       (NPY_ARRAY_C_CONTIGUOUS | \
+                                NPY_ARRAY_BEHAVED)
+#define NPY_ARRAY_CARRAY_RO    (NPY_ARRAY_C_CONTIGUOUS | \
+                                NPY_ARRAY_ALIGNED)
+#define NPY_ARRAY_FARRAY       (NPY_ARRAY_F_CONTIGUOUS | \
+                                NPY_ARRAY_BEHAVED)
+#define NPY_ARRAY_FARRAY_RO    (NPY_ARRAY_F_CONTIGUOUS | \
+                                NPY_ARRAY_ALIGNED)
+#define NPY_ARRAY_DEFAULT      (NPY_ARRAY_CARRAY)
+#define NPY_ARRAY_IN_ARRAY     (NPY_ARRAY_CARRAY_RO)
+#define NPY_ARRAY_OUT_ARRAY    (NPY_ARRAY_CARRAY)
+#define NPY_ARRAY_INOUT_ARRAY  (NPY_ARRAY_CARRAY)
+#define NPY_ARRAY_INOUT_ARRAY2 (NPY_ARRAY_CARRAY | \
+                                NPY_ARRAY_WRITEBACKIFCOPY)
+#define NPY_ARRAY_IN_FARRAY    (NPY_ARRAY_FARRAY_RO)
+#define NPY_ARRAY_OUT_FARRAY   (NPY_ARRAY_FARRAY)
+#define NPY_ARRAY_INOUT_FARRAY (NPY_ARRAY_FARRAY)
+#define NPY_ARRAY_INOUT_FARRAY2 (NPY_ARRAY_FARRAY | \
+                                NPY_ARRAY_WRITEBACKIFCOPY)
+
+#define NPY_ARRAY_UPDATE_ALL   (NPY_ARRAY_C_CONTIGUOUS | \
+                                NPY_ARRAY_F_CONTIGUOUS | \
+                                NPY_ARRAY_ALIGNED)
+
+/* This flag is for the array interface, not PyArrayObject */
+#define NPY_ARR_HAS_DESCR  0x0800
+
+
+
+
+/*
+ * Size of internal buffers used for alignment Make BUFSIZE a multiple
+ * of sizeof(npy_cdouble) -- usually 16 so that ufunc buffers are aligned
+ */
+#define NPY_MIN_BUFSIZE ((int)sizeof(npy_cdouble))
+#define NPY_MAX_BUFSIZE (((int)sizeof(npy_cdouble))*1000000)
+#define NPY_BUFSIZE 8192
+/* buffer stress test size: */
+/*#define NPY_BUFSIZE 17*/
+
+/*
+ * C API: consists of Macros and functions.  The MACROS are defined
+ * here.
+ */
+
+
+#define PyArray_ISCONTIGUOUS(m) PyArray_CHKFLAGS((m), NPY_ARRAY_C_CONTIGUOUS)
+#define PyArray_ISWRITEABLE(m) PyArray_CHKFLAGS((m), NPY_ARRAY_WRITEABLE)
+#define PyArray_ISALIGNED(m) PyArray_CHKFLAGS((m), NPY_ARRAY_ALIGNED)
+
+#define PyArray_IS_C_CONTIGUOUS(m) PyArray_CHKFLAGS((m), NPY_ARRAY_C_CONTIGUOUS)
+#define PyArray_IS_F_CONTIGUOUS(m) PyArray_CHKFLAGS((m), NPY_ARRAY_F_CONTIGUOUS)
+
+/* the variable is used in some places, so always define it */
+#define NPY_BEGIN_THREADS_DEF PyThreadState *_save=NULL;
+#if NPY_ALLOW_THREADS
+#define NPY_BEGIN_ALLOW_THREADS Py_BEGIN_ALLOW_THREADS
+#define NPY_END_ALLOW_THREADS Py_END_ALLOW_THREADS
+#define NPY_BEGIN_THREADS do {_save = PyEval_SaveThread();} while (0);
+#define NPY_END_THREADS   do { if (_save) \
+                { PyEval_RestoreThread(_save); _save = NULL;} } while (0);
+#define NPY_BEGIN_THREADS_THRESHOLDED(loop_size) do { if ((loop_size) > 500) \
+                { _save = PyEval_SaveThread();} } while (0);
+
+
+#define NPY_ALLOW_C_API_DEF  PyGILState_STATE __save__;
+#define NPY_ALLOW_C_API      do {__save__ = PyGILState_Ensure();} while (0);
+#define NPY_DISABLE_C_API    do {PyGILState_Release(__save__);} while (0);
+#else
+#define NPY_BEGIN_ALLOW_THREADS
+#define NPY_END_ALLOW_THREADS
+#define NPY_BEGIN_THREADS
+#define NPY_END_THREADS
+#define NPY_BEGIN_THREADS_THRESHOLDED(loop_size)
+#define NPY_BEGIN_THREADS_DESCR(dtype)
+#define NPY_END_THREADS_DESCR(dtype)
+#define NPY_ALLOW_C_API_DEF
+#define NPY_ALLOW_C_API
+#define NPY_DISABLE_C_API
+#endif
+
+/**********************************
+ * The nditer object, added in 1.6
+ **********************************/
+
+/* The actual structure of the iterator is an internal detail */
+typedef struct NpyIter_InternalOnly NpyIter;
+
+/* Iterator function pointers that may be specialized */
+typedef int (NpyIter_IterNextFunc)(NpyIter *iter);
+typedef void (NpyIter_GetMultiIndexFunc)(NpyIter *iter,
+                                      npy_intp *outcoords);
+
+/*** Global flags that may be passed to the iterator constructors ***/
+
+/* Track an index representing C order */
+#define NPY_ITER_C_INDEX                    0x00000001
+/* Track an index representing Fortran order */
+#define NPY_ITER_F_INDEX                    0x00000002
+/* Track a multi-index */
+#define NPY_ITER_MULTI_INDEX                0x00000004
+/* User code external to the iterator does the 1-dimensional innermost loop */
+#define NPY_ITER_EXTERNAL_LOOP              0x00000008
+/* Convert all the operands to a common data type */
+#define NPY_ITER_COMMON_DTYPE               0x00000010
+/* Operands may hold references, requiring API access during iteration */
+#define NPY_ITER_REFS_OK                    0x00000020
+/* Zero-sized operands should be permitted, iteration checks IterSize for 0 */
+#define NPY_ITER_ZEROSIZE_OK                0x00000040
+/* Permits reductions (size-0 stride with dimension size > 1) */
+#define NPY_ITER_REDUCE_OK                  0x00000080
+/* Enables sub-range iteration */
+#define NPY_ITER_RANGED                     0x00000100
+/* Enables buffering */
+#define NPY_ITER_BUFFERED                   0x00000200
+/* When buffering is enabled, grows the inner loop if possible */
+#define NPY_ITER_GROWINNER                  0x00000400
+/* Delay allocation of buffers until first Reset* call */
+#define NPY_ITER_DELAY_BUFALLOC             0x00000800
+/* When NPY_KEEPORDER is specified, disable reversing negative-stride axes */
+#define NPY_ITER_DONT_NEGATE_STRIDES        0x00001000
+/*
+ * If output operands overlap with other operands (based on heuristics that
+ * has false positives but no false negatives), make temporary copies to
+ * eliminate overlap.
+ */
+#define NPY_ITER_COPY_IF_OVERLAP            0x00002000
+
+/*** Per-operand flags that may be passed to the iterator constructors ***/
+
+/* The operand will be read from and written to */
+#define NPY_ITER_READWRITE                  0x00010000
+/* The operand will only be read from */
+#define NPY_ITER_READONLY                   0x00020000
+/* The operand will only be written to */
+#define NPY_ITER_WRITEONLY                  0x00040000
+/* The operand's data must be in native byte order */
+#define NPY_ITER_NBO                        0x00080000
+/* The operand's data must be aligned */
+#define NPY_ITER_ALIGNED                    0x00100000
+/* The operand's data must be contiguous (within the inner loop) */
+#define NPY_ITER_CONTIG                     0x00200000
+/* The operand may be copied to satisfy requirements */
+#define NPY_ITER_COPY                       0x00400000
+/* The operand may be copied with WRITEBACKIFCOPY to satisfy requirements */
+#define NPY_ITER_UPDATEIFCOPY               0x00800000
+/* Allocate the operand if it is NULL */
+#define NPY_ITER_ALLOCATE                   0x01000000
+/* If an operand is allocated, don't use any subtype */
+#define NPY_ITER_NO_SUBTYPE                 0x02000000
+/* This is a virtual array slot, operand is NULL but temporary data is there */
+#define NPY_ITER_VIRTUAL                    0x04000000
+/* Require that the dimension match the iterator dimensions exactly */
+#define NPY_ITER_NO_BROADCAST               0x08000000
+/* A mask is being used on this array, affects buffer -> array copy */
+#define NPY_ITER_WRITEMASKED                0x10000000
+/* This array is the mask for all WRITEMASKED operands */
+#define NPY_ITER_ARRAYMASK                  0x20000000
+/* Assume iterator order data access for COPY_IF_OVERLAP */
+#define NPY_ITER_OVERLAP_ASSUME_ELEMENTWISE 0x40000000
+
+#define NPY_ITER_GLOBAL_FLAGS               0x0000ffff
+#define NPY_ITER_PER_OP_FLAGS               0xffff0000
+
+
+/*****************************
+ * Basic iterator object
+ *****************************/
+
+/* FWD declaration */
+typedef struct PyArrayIterObject_tag PyArrayIterObject;
+
+/*
+ * type of the function which translates a set of coordinates to a
+ * pointer to the data
+ */
+typedef char* (*npy_iter_get_dataptr_t)(
+        PyArrayIterObject* iter, const npy_intp*);
+
+struct PyArrayIterObject_tag {
+        PyObject_HEAD
+        int               nd_m1;            /* number of dimensions - 1 */
+        npy_intp          index, size;
+        npy_intp          coordinates[NPY_MAXDIMS_LEGACY_ITERS];/* N-dimensional loop */
+        npy_intp          dims_m1[NPY_MAXDIMS_LEGACY_ITERS];    /* ao->dimensions - 1 */
+        npy_intp          strides[NPY_MAXDIMS_LEGACY_ITERS];    /* ao->strides or fake */
+        npy_intp          backstrides[NPY_MAXDIMS_LEGACY_ITERS];/* how far to jump back */
+        npy_intp          factors[NPY_MAXDIMS_LEGACY_ITERS];     /* shape factors */
+        PyArrayObject     *ao;
+        char              *dataptr;        /* pointer to current item*/
+        npy_bool          contiguous;
+
+        npy_intp          bounds[NPY_MAXDIMS_LEGACY_ITERS][2];
+        npy_intp          limits[NPY_MAXDIMS_LEGACY_ITERS][2];
+        npy_intp          limits_sizes[NPY_MAXDIMS_LEGACY_ITERS];
+        npy_iter_get_dataptr_t translate;
+} ;
+
+
+/* Iterator API */
+#define PyArrayIter_Check(op) PyObject_TypeCheck((op), &PyArrayIter_Type)
+
+#define _PyAIT(it) ((PyArrayIterObject *)(it))
+#define PyArray_ITER_RESET(it) do { \
+        _PyAIT(it)->index = 0; \
+        _PyAIT(it)->dataptr = PyArray_BYTES(_PyAIT(it)->ao); \
+        memset(_PyAIT(it)->coordinates, 0, \
+               (_PyAIT(it)->nd_m1+1)*sizeof(npy_intp)); \
+} while (0)
+
+#define _PyArray_ITER_NEXT1(it) do { \
+        (it)->dataptr += _PyAIT(it)->strides[0]; \
+        (it)->coordinates[0]++; \
+} while (0)
+
+#define _PyArray_ITER_NEXT2(it) do { \
+        if ((it)->coordinates[1] < (it)->dims_m1[1]) { \
+                (it)->coordinates[1]++; \
+                (it)->dataptr += (it)->strides[1]; \
+        } \
+        else { \
+                (it)->coordinates[1] = 0; \
+                (it)->coordinates[0]++; \
+                (it)->dataptr += (it)->strides[0] - \
+                        (it)->backstrides[1]; \
+        } \
+} while (0)
+
+#define PyArray_ITER_NEXT(it) do { \
+        _PyAIT(it)->index++; \
+        if (_PyAIT(it)->nd_m1 == 0) { \
+                _PyArray_ITER_NEXT1(_PyAIT(it)); \
+        } \
+        else if (_PyAIT(it)->contiguous) \
+                _PyAIT(it)->dataptr += PyArray_ITEMSIZE(_PyAIT(it)->ao); \
+        else if (_PyAIT(it)->nd_m1 == 1) { \
+                _PyArray_ITER_NEXT2(_PyAIT(it)); \
+        } \
+        else { \
+                int __npy_i; \
+                for (__npy_i=_PyAIT(it)->nd_m1; __npy_i >= 0; __npy_i--) { \
+                        if (_PyAIT(it)->coordinates[__npy_i] < \
+                            _PyAIT(it)->dims_m1[__npy_i]) { \
+                                _PyAIT(it)->coordinates[__npy_i]++; \
+                                _PyAIT(it)->dataptr += \
+                                        _PyAIT(it)->strides[__npy_i]; \
+                                break; \
+                        } \
+                        else { \
+                                _PyAIT(it)->coordinates[__npy_i] = 0; \
+                                _PyAIT(it)->dataptr -= \
+                                        _PyAIT(it)->backstrides[__npy_i]; \
+                        } \
+                } \
+        } \
+} while (0)
+
+#define PyArray_ITER_GOTO(it, destination) do { \
+        int __npy_i; \
+        _PyAIT(it)->index = 0; \
+        _PyAIT(it)->dataptr = PyArray_BYTES(_PyAIT(it)->ao); \
+        for (__npy_i = _PyAIT(it)->nd_m1; __npy_i>=0; __npy_i--) { \
+                if (destination[__npy_i] < 0) { \
+                        destination[__npy_i] += \
+                                _PyAIT(it)->dims_m1[__npy_i]+1; \
+                } \
+                _PyAIT(it)->dataptr += destination[__npy_i] * \
+                        _PyAIT(it)->strides[__npy_i]; \
+                _PyAIT(it)->coordinates[__npy_i] = \
+                        destination[__npy_i]; \
+                _PyAIT(it)->index += destination[__npy_i] * \
+                        ( __npy_i==_PyAIT(it)->nd_m1 ? 1 : \
+                          _PyAIT(it)->dims_m1[__npy_i+1]+1) ; \
+        } \
+} while (0)
+
+#define PyArray_ITER_GOTO1D(it, ind) do { \
+        int __npy_i; \
+        npy_intp __npy_ind = (npy_intp)(ind); \
+        if (__npy_ind < 0) __npy_ind += _PyAIT(it)->size; \
+        _PyAIT(it)->index = __npy_ind; \
+        if (_PyAIT(it)->nd_m1 == 0) { \
+                _PyAIT(it)->dataptr = PyArray_BYTES(_PyAIT(it)->ao) + \
+                        __npy_ind * _PyAIT(it)->strides[0]; \
+        } \
+        else if (_PyAIT(it)->contiguous) \
+                _PyAIT(it)->dataptr = PyArray_BYTES(_PyAIT(it)->ao) + \
+                        __npy_ind * PyArray_ITEMSIZE(_PyAIT(it)->ao); \
+        else { \
+                _PyAIT(it)->dataptr = PyArray_BYTES(_PyAIT(it)->ao); \
+                for (__npy_i = 0; __npy_i<=_PyAIT(it)->nd_m1; \
+                     __npy_i++) { \
+                        _PyAIT(it)->coordinates[__npy_i] = \
+                                (__npy_ind / _PyAIT(it)->factors[__npy_i]); \
+                        _PyAIT(it)->dataptr += \
+                                (__npy_ind / _PyAIT(it)->factors[__npy_i]) \
+                                * _PyAIT(it)->strides[__npy_i]; \
+                        __npy_ind %= _PyAIT(it)->factors[__npy_i]; \
+                } \
+        } \
+} while (0)
+
+#define PyArray_ITER_DATA(it) ((void *)(_PyAIT(it)->dataptr))
+
+#define PyArray_ITER_NOTDONE(it) (_PyAIT(it)->index < _PyAIT(it)->size)
+
+
+/*
+ * Any object passed to PyArray_Broadcast must be binary compatible
+ * with this structure.
+ */
+
+typedef struct {
+        PyObject_HEAD
+        int                  numiter;                 /* number of iters */
+        npy_intp             size;                    /* broadcasted size */
+        npy_intp             index;                   /* current index */
+        int                  nd;                      /* number of dims */
+        npy_intp             dimensions[NPY_MAXDIMS_LEGACY_ITERS]; /* dimensions */
+        /*
+         * Space for the individual iterators, do not specify size publicly
+         * to allow changing it more easily.
+         * One reason is that Cython uses this for checks and only allows
+         * growing structs (as of Cython 3.0.6).  It also allows NPY_MAXARGS
+         * to be runtime dependent.
+         */
+#if (defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD)
+        PyArrayIterObject    *iters[64];
+#elif defined(__cplusplus)
+        /*
+         * C++ doesn't strictly support flexible members and gives compilers
+         * warnings (pedantic only), so we lie.  We can't make it 64 because
+         * then Cython is unhappy (larger struct at runtime is OK smaller not).
+         */
+        PyArrayIterObject    *iters[32];
+#else
+        PyArrayIterObject    *iters[];
+#endif
+} PyArrayMultiIterObject;
+
+#define _PyMIT(m) ((PyArrayMultiIterObject *)(m))
+#define PyArray_MultiIter_RESET(multi) do {                                   \
+        int __npy_mi;                                                         \
+        _PyMIT(multi)->index = 0;                                             \
+        for (__npy_mi=0; __npy_mi < _PyMIT(multi)->numiter;  __npy_mi++) {    \
+                PyArray_ITER_RESET(_PyMIT(multi)->iters[__npy_mi]);           \
+        }                                                                     \
+} while (0)
+
+#define PyArray_MultiIter_NEXT(multi) do {                                    \
+        int __npy_mi;                                                         \
+        _PyMIT(multi)->index++;                                               \
+        for (__npy_mi=0; __npy_mi < _PyMIT(multi)->numiter;   __npy_mi++) {   \
+                PyArray_ITER_NEXT(_PyMIT(multi)->iters[__npy_mi]);            \
+        }                                                                     \
+} while (0)
+
+#define PyArray_MultiIter_GOTO(multi, dest) do {                            \
+        int __npy_mi;                                                       \
+        for (__npy_mi=0; __npy_mi < _PyMIT(multi)->numiter; __npy_mi++) {   \
+                PyArray_ITER_GOTO(_PyMIT(multi)->iters[__npy_mi], dest);    \
+        }                                                                   \
+        _PyMIT(multi)->index = _PyMIT(multi)->iters[0]->index;              \
+} while (0)
+
+#define PyArray_MultiIter_GOTO1D(multi, ind) do {                          \
+        int __npy_mi;                                                      \
+        for (__npy_mi=0; __npy_mi < _PyMIT(multi)->numiter; __npy_mi++) {  \
+                PyArray_ITER_GOTO1D(_PyMIT(multi)->iters[__npy_mi], ind);  \
+        }                                                                  \
+        _PyMIT(multi)->index = _PyMIT(multi)->iters[0]->index;             \
+} while (0)
+
+#define PyArray_MultiIter_DATA(multi, i)                \
+        ((void *)(_PyMIT(multi)->iters[i]->dataptr))
+
+#define PyArray_MultiIter_NEXTi(multi, i)               \
+        PyArray_ITER_NEXT(_PyMIT(multi)->iters[i])
+
+#define PyArray_MultiIter_NOTDONE(multi)                \
+        (_PyMIT(multi)->index < _PyMIT(multi)->size)
+
+
+static NPY_INLINE int
+PyArray_MultiIter_NUMITER(PyArrayMultiIterObject *multi)
+{
+    return multi->numiter;
+}
+
+
+static NPY_INLINE npy_intp
+PyArray_MultiIter_SIZE(PyArrayMultiIterObject *multi)
+{
+    return multi->size;
+}
+
+
+static NPY_INLINE npy_intp
+PyArray_MultiIter_INDEX(PyArrayMultiIterObject *multi)
+{
+    return multi->index;
+}
+
+
+static NPY_INLINE int
+PyArray_MultiIter_NDIM(PyArrayMultiIterObject *multi)
+{
+    return multi->nd;
+}
+
+
+static NPY_INLINE npy_intp *
+PyArray_MultiIter_DIMS(PyArrayMultiIterObject *multi)
+{
+    return multi->dimensions;
+}
+
+
+static NPY_INLINE void **
+PyArray_MultiIter_ITERS(PyArrayMultiIterObject *multi)
+{
+    return (void**)multi->iters;
+}
+
+
+enum {
+    NPY_NEIGHBORHOOD_ITER_ZERO_PADDING,
+    NPY_NEIGHBORHOOD_ITER_ONE_PADDING,
+    NPY_NEIGHBORHOOD_ITER_CONSTANT_PADDING,
+    NPY_NEIGHBORHOOD_ITER_CIRCULAR_PADDING,
+    NPY_NEIGHBORHOOD_ITER_MIRROR_PADDING
+};
+
+typedef struct {
+    PyObject_HEAD
+
+    /*
+     * PyArrayIterObject part: keep this in this exact order
+     */
+    int               nd_m1;            /* number of dimensions - 1 */
+    npy_intp          index, size;
+    npy_intp          coordinates[NPY_MAXDIMS_LEGACY_ITERS];/* N-dimensional loop */
+    npy_intp          dims_m1[NPY_MAXDIMS_LEGACY_ITERS];    /* ao->dimensions - 1 */
+    npy_intp          strides[NPY_MAXDIMS_LEGACY_ITERS];    /* ao->strides or fake */
+    npy_intp          backstrides[NPY_MAXDIMS_LEGACY_ITERS];/* how far to jump back */
+    npy_intp          factors[NPY_MAXDIMS_LEGACY_ITERS];     /* shape factors */
+    PyArrayObject     *ao;
+    char              *dataptr;        /* pointer to current item*/
+    npy_bool          contiguous;
+
+    npy_intp          bounds[NPY_MAXDIMS_LEGACY_ITERS][2];
+    npy_intp          limits[NPY_MAXDIMS_LEGACY_ITERS][2];
+    npy_intp          limits_sizes[NPY_MAXDIMS_LEGACY_ITERS];
+    npy_iter_get_dataptr_t translate;
+
+    /*
+     * New members
+     */
+    npy_intp nd;
+
+    /* Dimensions is the dimension of the array */
+    npy_intp dimensions[NPY_MAXDIMS_LEGACY_ITERS];
+
+    /*
+     * Neighborhood points coordinates are computed relatively to the
+     * point pointed by _internal_iter
+     */
+    PyArrayIterObject* _internal_iter;
+    /*
+     * To keep a reference to the representation of the constant value
+     * for constant padding
+     */
+    char* constant;
+
+    int mode;
+} PyArrayNeighborhoodIterObject;
+
+/*
+ * Neighborhood iterator API
+ */
+
+/* General: those work for any mode */
+static inline int
+PyArrayNeighborhoodIter_Reset(PyArrayNeighborhoodIterObject* iter);
+static inline int
+PyArrayNeighborhoodIter_Next(PyArrayNeighborhoodIterObject* iter);
+#if 0
+static inline int
+PyArrayNeighborhoodIter_Next2D(PyArrayNeighborhoodIterObject* iter);
+#endif
+
+/*
+ * Include inline implementations - functions defined there are not
+ * considered public API
+ */
+#define NUMPY_CORE_INCLUDE_NUMPY__NEIGHBORHOOD_IMP_H_
+#include "_neighborhood_iterator_imp.h"
+#undef NUMPY_CORE_INCLUDE_NUMPY__NEIGHBORHOOD_IMP_H_
+
+
+
+/* The default array type */
+#define NPY_DEFAULT_TYPE NPY_DOUBLE
+/* default integer type defined in npy_2_compat header */
+
+/*
+ * All sorts of useful ways to look into a PyArrayObject. It is recommended
+ * to use PyArrayObject * objects instead of always casting from PyObject *,
+ * for improved type checking.
+ *
+ * In many cases here the macro versions of the accessors are deprecated,
+ * but can't be immediately changed to inline functions because the
+ * preexisting macros accept PyObject * and do automatic casts. Inline
+ * functions accepting PyArrayObject * provides for some compile-time
+ * checking of correctness when working with these objects in C.
+ */
+
+#define PyArray_ISONESEGMENT(m) (PyArray_CHKFLAGS(m, NPY_ARRAY_C_CONTIGUOUS) || \
+                                 PyArray_CHKFLAGS(m, NPY_ARRAY_F_CONTIGUOUS))
+
+#define PyArray_ISFORTRAN(m) (PyArray_CHKFLAGS(m, NPY_ARRAY_F_CONTIGUOUS) && \
+                             (!PyArray_CHKFLAGS(m, NPY_ARRAY_C_CONTIGUOUS)))
+
+#define PyArray_FORTRAN_IF(m) ((PyArray_CHKFLAGS(m, NPY_ARRAY_F_CONTIGUOUS) ? \
+                               NPY_ARRAY_F_CONTIGUOUS : 0))
+
+static inline int
+PyArray_NDIM(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->nd;
+}
+
+static inline void *
+PyArray_DATA(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->data;
+}
+
+static inline char *
+PyArray_BYTES(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->data;
+}
+
+static inline npy_intp *
+PyArray_DIMS(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->dimensions;
+}
+
+static inline npy_intp *
+PyArray_STRIDES(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->strides;
+}
+
+static inline npy_intp
+PyArray_DIM(const PyArrayObject *arr, int idim)
+{
+    return ((PyArrayObject_fields *)arr)->dimensions[idim];
+}
+
+static inline npy_intp
+PyArray_STRIDE(const PyArrayObject *arr, int istride)
+{
+    return ((PyArrayObject_fields *)arr)->strides[istride];
+}
+
+static inline NPY_RETURNS_BORROWED_REF PyObject *
+PyArray_BASE(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->base;
+}
+
+static inline NPY_RETURNS_BORROWED_REF PyArray_Descr *
+PyArray_DESCR(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->descr;
+}
+
+static inline int
+PyArray_FLAGS(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->flags;
+}
+
+
+static inline int
+PyArray_TYPE(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->descr->type_num;
+}
+
+static inline int
+PyArray_CHKFLAGS(const PyArrayObject *arr, int flags)
+{
+    return (PyArray_FLAGS(arr) & flags) == flags;
+}
+
+static inline PyArray_Descr *
+PyArray_DTYPE(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->descr;
+}
+
+static inline npy_intp *
+PyArray_SHAPE(const PyArrayObject *arr)
+{
+    return ((PyArrayObject_fields *)arr)->dimensions;
+}
+
+/*
+ * Enables the specified array flags. Does no checking,
+ * assumes you know what you're doing.
+ */
+static inline void
+PyArray_ENABLEFLAGS(PyArrayObject *arr, int flags)
+{
+    ((PyArrayObject_fields *)arr)->flags |= flags;
+}
+
+/*
+ * Clears the specified array flags. Does no checking,
+ * assumes you know what you're doing.
+ */
+static inline void
+PyArray_CLEARFLAGS(PyArrayObject *arr, int flags)
+{
+    ((PyArrayObject_fields *)arr)->flags &= ~flags;
+}
+
+#if NPY_FEATURE_VERSION >= NPY_1_22_API_VERSION
+    static inline NPY_RETURNS_BORROWED_REF PyObject *
+    PyArray_HANDLER(PyArrayObject *arr)
+    {
+        return ((PyArrayObject_fields *)arr)->mem_handler;
+    }
+#endif
+
+#define PyTypeNum_ISBOOL(type) ((type) == NPY_BOOL)
+
+#define PyTypeNum_ISUNSIGNED(type) (((type) == NPY_UBYTE) ||   \
+                                 ((type) == NPY_USHORT) ||     \
+                                 ((type) == NPY_UINT) ||       \
+                                 ((type) == NPY_ULONG) ||      \
+                                 ((type) == NPY_ULONGLONG))
+
+#define PyTypeNum_ISSIGNED(type) (((type) == NPY_BYTE) ||      \
+                               ((type) == NPY_SHORT) ||        \
+                               ((type) == NPY_INT) ||          \
+                               ((type) == NPY_LONG) ||         \
+                               ((type) == NPY_LONGLONG))
+
+#define PyTypeNum_ISINTEGER(type) (((type) >= NPY_BYTE) &&     \
+                                ((type) <= NPY_ULONGLONG))
+
+#define PyTypeNum_ISFLOAT(type) ((((type) >= NPY_FLOAT) && \
+                              ((type) <= NPY_LONGDOUBLE)) || \
+                              ((type) == NPY_HALF))
+
+#define PyTypeNum_ISNUMBER(type) (((type) <= NPY_CLONGDOUBLE) || \
+                                  ((type) == NPY_HALF))
+
+#define PyTypeNum_ISSTRING(type) (((type) == NPY_STRING) ||    \
+                                  ((type) == NPY_UNICODE))
+
+#define PyTypeNum_ISCOMPLEX(type) (((type) >= NPY_CFLOAT) &&   \
+                                ((type) <= NPY_CLONGDOUBLE))
+
+#define PyTypeNum_ISFLEXIBLE(type) (((type) >=NPY_STRING) &&  \
+                                    ((type) <=NPY_VOID))
+
+#define PyTypeNum_ISDATETIME(type) (((type) >=NPY_DATETIME) &&  \
+                                    ((type) <=NPY_TIMEDELTA))
+
+#define PyTypeNum_ISUSERDEF(type) (((type) >= NPY_USERDEF) && \
+                                   ((type) < NPY_USERDEF+     \
+                                    NPY_NUMUSERTYPES))
+
+#define PyTypeNum_ISEXTENDED(type) (PyTypeNum_ISFLEXIBLE(type) ||  \
+                                    PyTypeNum_ISUSERDEF(type))
+
+#define PyTypeNum_ISOBJECT(type) ((type) == NPY_OBJECT)
+
+
+#define PyDataType_ISLEGACY(dtype) ((dtype)->type_num < NPY_VSTRING && ((dtype)->type_num >= 0))
+#define PyDataType_ISBOOL(obj) PyTypeNum_ISBOOL(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISUNSIGNED(obj) PyTypeNum_ISUNSIGNED(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISSIGNED(obj) PyTypeNum_ISSIGNED(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISINTEGER(obj) PyTypeNum_ISINTEGER(((PyArray_Descr*)(obj))->type_num )
+#define PyDataType_ISFLOAT(obj) PyTypeNum_ISFLOAT(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISNUMBER(obj) PyTypeNum_ISNUMBER(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISSTRING(obj) PyTypeNum_ISSTRING(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISCOMPLEX(obj) PyTypeNum_ISCOMPLEX(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISFLEXIBLE(obj) PyTypeNum_ISFLEXIBLE(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISDATETIME(obj) PyTypeNum_ISDATETIME(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISUSERDEF(obj) PyTypeNum_ISUSERDEF(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISEXTENDED(obj) PyTypeNum_ISEXTENDED(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_ISOBJECT(obj) PyTypeNum_ISOBJECT(((PyArray_Descr*)(obj))->type_num)
+#define PyDataType_MAKEUNSIZED(dtype) ((dtype)->elsize = 0)
+/*
+ * PyDataType_* FLAGS, FLACHK, REFCHK, HASFIELDS, HASSUBARRAY, UNSIZED,
+ * SUBARRAY, NAMES, FIELDS, C_METADATA, and METADATA require version specific
+ * lookup and are defined in npy_2_compat.h.
+ */
+
+
+#define PyArray_ISBOOL(obj) PyTypeNum_ISBOOL(PyArray_TYPE(obj))
+#define PyArray_ISUNSIGNED(obj) PyTypeNum_ISUNSIGNED(PyArray_TYPE(obj))
+#define PyArray_ISSIGNED(obj) PyTypeNum_ISSIGNED(PyArray_TYPE(obj))
+#define PyArray_ISINTEGER(obj) PyTypeNum_ISINTEGER(PyArray_TYPE(obj))
+#define PyArray_ISFLOAT(obj) PyTypeNum_ISFLOAT(PyArray_TYPE(obj))
+#define PyArray_ISNUMBER(obj) PyTypeNum_ISNUMBER(PyArray_TYPE(obj))
+#define PyArray_ISSTRING(obj) PyTypeNum_ISSTRING(PyArray_TYPE(obj))
+#define PyArray_ISCOMPLEX(obj) PyTypeNum_ISCOMPLEX(PyArray_TYPE(obj))
+#define PyArray_ISFLEXIBLE(obj) PyTypeNum_ISFLEXIBLE(PyArray_TYPE(obj))
+#define PyArray_ISDATETIME(obj) PyTypeNum_ISDATETIME(PyArray_TYPE(obj))
+#define PyArray_ISUSERDEF(obj) PyTypeNum_ISUSERDEF(PyArray_TYPE(obj))
+#define PyArray_ISEXTENDED(obj) PyTypeNum_ISEXTENDED(PyArray_TYPE(obj))
+#define PyArray_ISOBJECT(obj) PyTypeNum_ISOBJECT(PyArray_TYPE(obj))
+#define PyArray_HASFIELDS(obj) PyDataType_HASFIELDS(PyArray_DESCR(obj))
+
+    /*
+     * FIXME: This should check for a flag on the data-type that
+     * states whether or not it is variable length.  Because the
+     * ISFLEXIBLE check is hard-coded to the built-in data-types.
+     */
+#define PyArray_ISVARIABLE(obj) PyTypeNum_ISFLEXIBLE(PyArray_TYPE(obj))
+
+#define PyArray_SAFEALIGNEDCOPY(obj) (PyArray_ISALIGNED(obj) && !PyArray_ISVARIABLE(obj))
+
+
+#define NPY_LITTLE '<'
+#define NPY_BIG '>'
+#define NPY_NATIVE '='
+#define NPY_SWAP 's'
+#define NPY_IGNORE '|'
+
+#if NPY_BYTE_ORDER == NPY_BIG_ENDIAN
+#define NPY_NATBYTE NPY_BIG
+#define NPY_OPPBYTE NPY_LITTLE
+#else
+#define NPY_NATBYTE NPY_LITTLE
+#define NPY_OPPBYTE NPY_BIG
+#endif
+
+#define PyArray_ISNBO(arg) ((arg) != NPY_OPPBYTE)
+#define PyArray_IsNativeByteOrder PyArray_ISNBO
+#define PyArray_ISNOTSWAPPED(m) PyArray_ISNBO(PyArray_DESCR(m)->byteorder)
+#define PyArray_ISBYTESWAPPED(m) (!PyArray_ISNOTSWAPPED(m))
+
+#define PyArray_FLAGSWAP(m, flags) (PyArray_CHKFLAGS(m, flags) &&       \
+                                    PyArray_ISNOTSWAPPED(m))
+
+#define PyArray_ISCARRAY(m) PyArray_FLAGSWAP(m, NPY_ARRAY_CARRAY)
+#define PyArray_ISCARRAY_RO(m) PyArray_FLAGSWAP(m, NPY_ARRAY_CARRAY_RO)
+#define PyArray_ISFARRAY(m) PyArray_FLAGSWAP(m, NPY_ARRAY_FARRAY)
+#define PyArray_ISFARRAY_RO(m) PyArray_FLAGSWAP(m, NPY_ARRAY_FARRAY_RO)
+#define PyArray_ISBEHAVED(m) PyArray_FLAGSWAP(m, NPY_ARRAY_BEHAVED)
+#define PyArray_ISBEHAVED_RO(m) PyArray_FLAGSWAP(m, NPY_ARRAY_ALIGNED)
+
+
+#define PyDataType_ISNOTSWAPPED(d) PyArray_ISNBO(((PyArray_Descr *)(d))->byteorder)
+#define PyDataType_ISBYTESWAPPED(d) (!PyDataType_ISNOTSWAPPED(d))
+
+/************************************************************
+ * A struct used by PyArray_CreateSortedStridePerm, new in 1.7.
+ ************************************************************/
+
+typedef struct {
+    npy_intp perm, stride;
+} npy_stride_sort_item;
+
+/************************************************************
+ * This is the form of the struct that's stored in the
+ * PyCapsule returned by an array's __array_struct__ attribute. See
+ * https://docs.scipy.org/doc/numpy/reference/arrays.interface.html for the full
+ * documentation.
+ ************************************************************/
+typedef struct {
+    int two;              /*
+                           * contains the integer 2 as a sanity
+                           * check
+                           */
+
+    int nd;               /* number of dimensions */
+
+    char typekind;        /*
+                           * kind in array --- character code of
+                           * typestr
+                           */
+
+    int itemsize;         /* size of each element */
+
+    int flags;            /*
+                           * how should be data interpreted. Valid
+                           * flags are CONTIGUOUS (1), F_CONTIGUOUS (2),
+                           * ALIGNED (0x100), NOTSWAPPED (0x200), and
+                           * WRITEABLE (0x400).  ARR_HAS_DESCR (0x800)
+                           * states that arrdescr field is present in
+                           * structure
+                           */
+
+    npy_intp *shape;       /*
+                            * A length-nd array of shape
+                            * information
+                            */
+
+    npy_intp *strides;    /* A length-nd array of stride information */
+
+    void *data;           /* A pointer to the first element of the array */
+
+    PyObject *descr;      /*
+                           * A list of fields or NULL (ignored if flags
+                           * does not have ARR_HAS_DESCR flag set)
+                           */
+} PyArrayInterface;
+
+
+/****************************************
+ * NpyString
+ *
+ * Types used by the NpyString API.
+ ****************************************/
+
+/*
+ * A "packed" encoded string. The string data must be accessed by first unpacking the string.
+ */
+typedef struct npy_packed_static_string npy_packed_static_string;
+
+/*
+ * An unpacked read-only view onto the data in a packed string
+ */
+typedef struct npy_unpacked_static_string {
+    size_t size;
+    const char *buf;
+} npy_static_string;
+
+/*
+ * Handles heap allocations for static strings.
+ */
+typedef struct npy_string_allocator npy_string_allocator;
+
+typedef struct {
+    PyArray_Descr base;
+    // The object representing a null value
+    PyObject *na_object;
+    // Flag indicating whether or not to coerce arbitrary objects to strings
+    char coerce;
+    // Flag indicating the na object is NaN-like
+    char has_nan_na;
+    // Flag indicating the na object is a string
+    char has_string_na;
+    // If nonzero, indicates that this instance is owned by an array already
+    char array_owned;
+    // The string data to use when a default string is needed
+    npy_static_string default_string;
+    // The name of the missing data object, if any
+    npy_static_string na_name;
+    // the allocator should only be directly accessed after
+    // acquiring the allocator_lock and the lock should
+    // be released immediately after the allocator is
+    // no longer needed
+    npy_string_allocator *allocator;
+} PyArray_StringDTypeObject;
+
+/*
+ * PyArray_DTypeMeta related definitions.
+ *
+ * As of now, this API is preliminary and will be extended as necessary.
+ */
+#if defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD
+    /*
+     * The Structures defined in this block are currently considered
+     * private API and may change without warning!
+     * Part of this (at least the size) is expected to be public API without
+     * further modifications.
+     */
+    /* TODO: Make this definition public in the API, as soon as its settled */
+    NPY_NO_EXPORT extern PyTypeObject PyArrayDTypeMeta_Type;
+
+    /*
+     * While NumPy DTypes would not need to be heap types the plan is to
+     * make DTypes available in Python at which point they will be heap types.
+     * Since we also wish to add fields to the DType class, this looks like
+     * a typical instance definition, but with PyHeapTypeObject instead of
+     * only the PyObject_HEAD.
+     * This must only be exposed very extremely careful consideration, since
+     * it is a fairly complex construct which may be better to allow
+     * refactoring of.
+     */
+    typedef struct {
+        PyHeapTypeObject super;
+
+        /*
+         * Most DTypes will have a singleton default instance, for the
+         * parametric legacy DTypes (bytes, string, void, datetime) this
+         * may be a pointer to the *prototype* instance?
+         */
+        PyArray_Descr *singleton;
+        /* Copy of the legacy DTypes type number, usually invalid. */
+        int type_num;
+
+        /* The type object of the scalar instances (may be NULL?) */
+        PyTypeObject *scalar_type;
+        /*
+         * DType flags to signal legacy, parametric, or
+         * abstract.  But plenty of space for additional information/flags.
+         */
+        npy_uint64 flags;
+
+        /*
+         * Use indirection in order to allow a fixed size for this struct.
+         * A stable ABI size makes creating a static DType less painful
+         * while also ensuring flexibility for all opaque API (with one
+         * indirection due the pointer lookup).
+         */
+        void *dt_slots;
+        void *reserved[3];
+    } PyArray_DTypeMeta;
+
+#endif  /* NPY_INTERNAL_BUILD */
+
+
+/*
+ * Use the keyword NPY_DEPRECATED_INCLUDES to ensure that the header files
+ * npy_*_*_deprecated_api.h are only included from here and nowhere else.
+ */
+#ifdef NPY_DEPRECATED_INCLUDES
+#error "Do not use the reserved keyword NPY_DEPRECATED_INCLUDES."
+#endif
+#define NPY_DEPRECATED_INCLUDES
+/*
+ * There is no file npy_1_8_deprecated_api.h since there are no additional
+ * deprecated API features in NumPy 1.8.
+ *
+ * Note to maintainers: insert code like the following in future NumPy
+ * versions.
+ *
+ * #if !defined(NPY_NO_DEPRECATED_API) || \
+ *     (NPY_NO_DEPRECATED_API < NPY_1_9_API_VERSION)
+ * #include "npy_1_9_deprecated_api.h"
+ * #endif
+ * Then in the npy_1_9_deprecated_api.h header add something like this
+ * --------------------
+ * #ifndef NPY_DEPRECATED_INCLUDES
+ * #error "Should never include npy_*_*_deprecated_api directly."
+ * #endif
+ * #ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_1_7_DEPRECATED_API_H_
+ * #define NUMPY_CORE_INCLUDE_NUMPY_NPY_1_7_DEPRECATED_API_H_
+ * 
+ * #ifndef NPY_NO_DEPRECATED_API
+ * #if defined(_WIN32)
+ * #define _WARN___STR2__(x) #x
+ * #define _WARN___STR1__(x) _WARN___STR2__(x)
+ * #define _WARN___LOC__ __FILE__ "(" _WARN___STR1__(__LINE__) ") : Warning Msg: "
+ * #pragma message(_WARN___LOC__"Using deprecated NumPy API, disable it with " \
+ *                          "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION")
+ * #else
+ * #warning "Using deprecated NumPy API, disable it with " \
+ *          "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION"
+ * #endif
+ * #endif
+ * --------------------
+ */
+#undef NPY_DEPRECATED_INCLUDES
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NDARRAYTYPES_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_2_compat.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_2_compat.h
new file mode 100644
index 0000000..e39e65a
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_2_compat.h
@@ -0,0 +1,249 @@
+/*
+ * This header file defines relevant features which:
+ * - Require runtime inspection depending on the NumPy version.
+ * - May be needed when compiling with an older version of NumPy to allow
+ *   a smooth transition.
+ *
+ * As such, it is shipped with NumPy 2.0, but designed to be vendored in full
+ * or parts by downstream projects.
+ *
+ * It must be included after any other includes.  `import_array()` must have
+ * been called in the scope or version dependency will misbehave, even when
+ * only `PyUFunc_` API is used.
+ *
+ * If required complicated defs (with inline functions) should be written as:
+ *
+ *     #if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+ *         Simple definition when NumPy 2.0 API is guaranteed.
+ *     #else
+ *         static inline definition of a 1.x compatibility shim
+ *         #if NPY_ABI_VERSION < 0x02000000
+ *            Make 1.x compatibility shim the public API (1.x only branch)
+ *         #else
+ *             Runtime dispatched version (1.x or 2.x)
+ *         #endif
+ *     #endif
+ *
+ * An internal build always passes NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+ */
+
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_2_COMPAT_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NPY_2_COMPAT_H_
+
+/*
+ * New macros for accessing real and complex part of a complex number can be
+ * found in "npy_2_complexcompat.h".
+ */
+
+
+/*
+ * This header is meant to be included by downstream directly for 1.x compat.
+ * In that case we need to ensure that users first included the full headers
+ * and not just `ndarraytypes.h`.
+ */
+
+#ifndef NPY_FEATURE_VERSION
+  #error "The NumPy 2 compat header requires `import_array()` for which "  \
+         "the `ndarraytypes.h` header include is not sufficient.  Please "  \
+         "include it after `numpy/ndarrayobject.h` or similar.\n"  \
+         "To simplify inclusion, you may use `PyArray_ImportNumPy()` " \
+         "which is defined in the compat header and is lightweight (can be)."
+#endif
+
+#if NPY_ABI_VERSION < 0x02000000
+  /*
+   * Define 2.0 feature version as it is needed below to decide whether we
+   * compile for both 1.x and 2.x (defining it guarantees 1.x only).
+   */
+  #define NPY_2_0_API_VERSION 0x00000012
+  /*
+   * If we are compiling with NumPy 1.x, PyArray_RUNTIME_VERSION so we
+   * pretend the `PyArray_RUNTIME_VERSION` is `NPY_FEATURE_VERSION`.
+   * This allows downstream to use `PyArray_RUNTIME_VERSION` if they need to.
+   */
+  #define PyArray_RUNTIME_VERSION NPY_FEATURE_VERSION
+  /* Compiling on NumPy 1.x where these are the same: */
+  #define PyArray_DescrProto PyArray_Descr
+#endif
+
+
+/*
+ * Define a better way to call `_import_array()` to simplify backporting as
+ * we now require imports more often (necessary to make ABI flexible).
+ */
+#ifdef import_array1
+
+static inline int
+PyArray_ImportNumPyAPI(void)
+{
+    if (NPY_UNLIKELY(PyArray_API == NULL)) {
+        import_array1(-1);
+    }
+    return 0;
+}
+
+#endif  /* import_array1 */
+
+
+/*
+ * NPY_DEFAULT_INT
+ *
+ * The default integer has changed, `NPY_DEFAULT_INT` is available at runtime
+ * for use as type number, e.g. `PyArray_DescrFromType(NPY_DEFAULT_INT)`.
+ *
+ * NPY_RAVEL_AXIS
+ *
+ * This was introduced in NumPy 2.0 to allow indicating that an axis should be
+ * raveled in an operation. Before NumPy 2.0, NPY_MAXDIMS was used for this purpose.
+ *
+ * NPY_MAXDIMS
+ *
+ * A constant indicating the maximum number dimensions allowed when creating
+ * an ndarray.
+ *
+ * NPY_NTYPES_LEGACY
+ *
+ * The number of built-in NumPy dtypes.
+ */
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+    #define NPY_DEFAULT_INT NPY_INTP
+    #define NPY_RAVEL_AXIS NPY_MIN_INT
+    #define NPY_MAXARGS 64
+
+#elif NPY_ABI_VERSION < 0x02000000
+    #define NPY_DEFAULT_INT NPY_LONG
+    #define NPY_RAVEL_AXIS 32
+    #define NPY_MAXARGS 32
+
+    /* Aliases of 2.x names to 1.x only equivalent names */
+    #define NPY_NTYPES NPY_NTYPES_LEGACY
+    #define PyArray_DescrProto PyArray_Descr
+    #define _PyArray_LegacyDescr PyArray_Descr
+    /* NumPy 2 definition always works, but add it for 1.x only */
+    #define PyDataType_ISLEGACY(dtype) (1)
+#else
+    #define NPY_DEFAULT_INT  \
+        (PyArray_RUNTIME_VERSION >= NPY_2_0_API_VERSION ? NPY_INTP : NPY_LONG)
+    #define NPY_RAVEL_AXIS  \
+        (PyArray_RUNTIME_VERSION >= NPY_2_0_API_VERSION ? NPY_MIN_INT : 32)
+    #define NPY_MAXARGS  \
+        (PyArray_RUNTIME_VERSION >= NPY_2_0_API_VERSION ? 64 : 32)
+#endif
+
+
+/*
+ * Access inline functions for descriptor fields.  Except for the first
+ * few fields, these needed to be moved (elsize, alignment) for
+ * additional space.  Or they are descriptor specific and are not generally
+ * available anymore (metadata, c_metadata, subarray, names, fields).
+ *
+ * Most of these are defined via the `DESCR_ACCESSOR` macro helper.
+ */
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION || NPY_ABI_VERSION < 0x02000000
+    /* Compiling for 1.x or 2.x only, direct field access is OK: */
+
+    static inline void
+    PyDataType_SET_ELSIZE(PyArray_Descr *dtype, npy_intp size)
+    {
+        dtype->elsize = size;
+    }
+
+    static inline npy_uint64
+    PyDataType_FLAGS(const PyArray_Descr *dtype)
+    {
+    #if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+        return dtype->flags;
+    #else
+        return (unsigned char)dtype->flags;  /* Need unsigned cast on 1.x */
+    #endif
+    }
+
+    #define DESCR_ACCESSOR(FIELD, field, type, legacy_only)    \
+        static inline type                                     \
+        PyDataType_##FIELD(const PyArray_Descr *dtype) {       \
+            if (legacy_only && !PyDataType_ISLEGACY(dtype)) {  \
+                return (type)0;                                \
+            }                                                  \
+            return ((_PyArray_LegacyDescr *)dtype)->field;     \
+        }
+#else  /* compiling for both 1.x and 2.x */
+
+    static inline void
+    PyDataType_SET_ELSIZE(PyArray_Descr *dtype, npy_intp size)
+    {
+        if (PyArray_RUNTIME_VERSION >= NPY_2_0_API_VERSION) {
+            ((_PyArray_DescrNumPy2 *)dtype)->elsize = size;
+        }
+        else {
+            ((PyArray_DescrProto *)dtype)->elsize = (int)size;
+        }
+    }
+
+    static inline npy_uint64
+    PyDataType_FLAGS(const PyArray_Descr *dtype)
+    {
+        if (PyArray_RUNTIME_VERSION >= NPY_2_0_API_VERSION) {
+            return ((_PyArray_DescrNumPy2 *)dtype)->flags;
+        }
+        else {
+            return (unsigned char)((PyArray_DescrProto *)dtype)->flags;
+        }
+    }
+
+    /* Cast to LegacyDescr always fine but needed when `legacy_only` */
+    #define DESCR_ACCESSOR(FIELD, field, type, legacy_only)        \
+        static inline type                                         \
+        PyDataType_##FIELD(const PyArray_Descr *dtype) {           \
+            if (legacy_only && !PyDataType_ISLEGACY(dtype)) {      \
+                return (type)0;                                    \
+            }                                                      \
+            if (PyArray_RUNTIME_VERSION >= NPY_2_0_API_VERSION) {  \
+                return ((_PyArray_LegacyDescr *)dtype)->field;     \
+            }                                                      \
+            else {                                                 \
+                return ((PyArray_DescrProto *)dtype)->field;       \
+            }                                                      \
+        }
+#endif
+
+DESCR_ACCESSOR(ELSIZE, elsize, npy_intp, 0)
+DESCR_ACCESSOR(ALIGNMENT, alignment, npy_intp, 0)
+DESCR_ACCESSOR(METADATA, metadata, PyObject *, 1)
+DESCR_ACCESSOR(SUBARRAY, subarray, PyArray_ArrayDescr *, 1)
+DESCR_ACCESSOR(NAMES, names, PyObject *, 1)
+DESCR_ACCESSOR(FIELDS, fields, PyObject *, 1)
+DESCR_ACCESSOR(C_METADATA, c_metadata, NpyAuxData *, 1)
+
+#undef DESCR_ACCESSOR
+
+
+#if !(defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD)
+#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION
+    static inline PyArray_ArrFuncs *
+    PyDataType_GetArrFuncs(const PyArray_Descr *descr)
+    {
+        return _PyDataType_GetArrFuncs(descr);
+    }
+#elif NPY_ABI_VERSION < 0x02000000
+    static inline PyArray_ArrFuncs *
+    PyDataType_GetArrFuncs(const PyArray_Descr *descr)
+    {
+        return descr->f;
+    }
+#else
+    static inline PyArray_ArrFuncs *
+    PyDataType_GetArrFuncs(const PyArray_Descr *descr)
+    {
+        if (PyArray_RUNTIME_VERSION >= NPY_2_0_API_VERSION) {
+            return _PyDataType_GetArrFuncs(descr);
+        }
+        else {
+            return ((PyArray_DescrProto *)descr)->f;
+        }
+    }
+#endif
+
+
+#endif  /* not internal build */
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NPY_2_COMPAT_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_2_complexcompat.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_2_complexcompat.h
new file mode 100644
index 0000000..0b50901
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_2_complexcompat.h
@@ -0,0 +1,28 @@
+/* This header is designed to be copy-pasted into downstream packages, since it provides
+   a compatibility layer between the old C struct complex types and the new native C99
+   complex types. The new macros are in numpy/npy_math.h, which is why it is included here. */
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_2_COMPLEXCOMPAT_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NPY_2_COMPLEXCOMPAT_H_
+
+#include <numpy/npy_math.h>
+
+#ifndef NPY_CSETREALF
+#define NPY_CSETREALF(c, r) (c)->real = (r)
+#endif
+#ifndef NPY_CSETIMAGF
+#define NPY_CSETIMAGF(c, i) (c)->imag = (i)
+#endif
+#ifndef NPY_CSETREAL
+#define NPY_CSETREAL(c, r)  (c)->real = (r)
+#endif
+#ifndef NPY_CSETIMAG
+#define NPY_CSETIMAG(c, i)  (c)->imag = (i)
+#endif
+#ifndef NPY_CSETREALL
+#define NPY_CSETREALL(c, r) (c)->real = (r)
+#endif
+#ifndef NPY_CSETIMAGL
+#define NPY_CSETIMAGL(c, i) (c)->imag = (i)
+#endif
+
+#endif
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_3kcompat.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_3kcompat.h
new file mode 100644
index 0000000..c2bf74f
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_3kcompat.h
@@ -0,0 +1,374 @@
+/*
+ * This is a convenience header file providing compatibility utilities
+ * for supporting different minor versions of Python 3.
+ * It was originally used to support the transition from Python 2,
+ * hence the "3k" naming.
+ *
+ * If you want to use this for your own projects, it's recommended to make a
+ * copy of it. We don't provide backwards compatibility guarantees.
+ */
+
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_3KCOMPAT_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NPY_3KCOMPAT_H_
+
+#include <Python.h>
+#include <stdio.h>
+
+#include "npy_common.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* Python13 removes _PyLong_AsInt */
+static inline int
+Npy__PyLong_AsInt(PyObject *obj)
+{
+    int overflow;
+    long result = PyLong_AsLongAndOverflow(obj, &overflow);
+
+    /* INT_MAX and INT_MIN are defined in Python.h */
+    if (overflow || result > INT_MAX || result < INT_MIN) {
+        /* XXX: could be cute and give a different
+           message for overflow == -1 */
+        PyErr_SetString(PyExc_OverflowError,
+                        "Python int too large to convert to C int");
+        return -1;
+    }
+    return (int)result;
+}
+
+#if defined _MSC_VER && _MSC_VER >= 1900
+
+#include <stdlib.h>
+
+/*
+ * Macros to protect CRT calls against instant termination when passed an
+ * invalid parameter (https://bugs.python.org/issue23524).
+ */
+extern _invalid_parameter_handler _Py_silent_invalid_parameter_handler;
+#define NPY_BEGIN_SUPPRESS_IPH { _invalid_parameter_handler _Py_old_handler = \
+    _set_thread_local_invalid_parameter_handler(_Py_silent_invalid_parameter_handler);
+#define NPY_END_SUPPRESS_IPH _set_thread_local_invalid_parameter_handler(_Py_old_handler); }
+
+#else
+
+#define NPY_BEGIN_SUPPRESS_IPH
+#define NPY_END_SUPPRESS_IPH
+
+#endif /* _MSC_VER >= 1900 */
+
+/*
+ * PyFile_* compatibility
+ */
+
+/*
+ * Get a FILE* handle to the file represented by the Python object
+ */
+static inline FILE*
+npy_PyFile_Dup2(PyObject *file, char *mode, npy_off_t *orig_pos)
+{
+    int fd, fd2, unbuf;
+    Py_ssize_t fd2_tmp;
+    PyObject *ret, *os, *io, *io_raw;
+    npy_off_t pos;
+    FILE *handle;
+
+    /* Flush first to ensure things end up in the file in the correct order */
+    ret = PyObject_CallMethod(file, "flush", "");
+    if (ret == NULL) {
+        return NULL;
+    }
+    Py_DECREF(ret);
+    fd = PyObject_AsFileDescriptor(file);
+    if (fd == -1) {
+        return NULL;
+    }
+
+    /*
+     * The handle needs to be dup'd because we have to call fclose
+     * at the end
+     */
+    os = PyImport_ImportModule("os");
+    if (os == NULL) {
+        return NULL;
+    }
+    ret = PyObject_CallMethod(os, "dup", "i", fd);
+    Py_DECREF(os);
+    if (ret == NULL) {
+        return NULL;
+    }
+    fd2_tmp = PyNumber_AsSsize_t(ret, PyExc_IOError);
+    Py_DECREF(ret);
+    if (fd2_tmp == -1 && PyErr_Occurred()) {
+        return NULL;
+    }
+    if (fd2_tmp < INT_MIN || fd2_tmp > INT_MAX) {
+        PyErr_SetString(PyExc_IOError,
+                        "Getting an 'int' from os.dup() failed");
+        return NULL;
+    }
+    fd2 = (int)fd2_tmp;
+
+    /* Convert to FILE* handle */
+#ifdef _WIN32
+    NPY_BEGIN_SUPPRESS_IPH
+    handle = _fdopen(fd2, mode);
+    NPY_END_SUPPRESS_IPH
+#else
+    handle = fdopen(fd2, mode);
+#endif
+    if (handle == NULL) {
+        PyErr_SetString(PyExc_IOError,
+                        "Getting a FILE* from a Python file object via "
+                        "_fdopen failed. If you built NumPy, you probably "
+                        "linked with the wrong debug/release runtime");
+        return NULL;
+    }
+
+    /* Record the original raw file handle position */
+    *orig_pos = npy_ftell(handle);
+    if (*orig_pos == -1) {
+        /* The io module is needed to determine if buffering is used */
+        io = PyImport_ImportModule("io");
+        if (io == NULL) {
+            fclose(handle);
+            return NULL;
+        }
+        /* File object instances of RawIOBase are unbuffered */
+        io_raw = PyObject_GetAttrString(io, "RawIOBase");
+        Py_DECREF(io);
+        if (io_raw == NULL) {
+            fclose(handle);
+            return NULL;
+        }
+        unbuf = PyObject_IsInstance(file, io_raw);
+        Py_DECREF(io_raw);
+        if (unbuf == 1) {
+            /* Succeed if the IO is unbuffered */
+            return handle;
+        }
+        else {
+            PyErr_SetString(PyExc_IOError, "obtaining file position failed");
+            fclose(handle);
+            return NULL;
+        }
+    }
+
+    /* Seek raw handle to the Python-side position */
+    ret = PyObject_CallMethod(file, "tell", "");
+    if (ret == NULL) {
+        fclose(handle);
+        return NULL;
+    }
+    pos = PyLong_AsLongLong(ret);
+    Py_DECREF(ret);
+    if (PyErr_Occurred()) {
+        fclose(handle);
+        return NULL;
+    }
+    if (npy_fseek(handle, pos, SEEK_SET) == -1) {
+        PyErr_SetString(PyExc_IOError, "seeking file failed");
+        fclose(handle);
+        return NULL;
+    }
+    return handle;
+}
+
+/*
+ * Close the dup-ed file handle, and seek the Python one to the current position
+ */
+static inline int
+npy_PyFile_DupClose2(PyObject *file, FILE* handle, npy_off_t orig_pos)
+{
+    int fd, unbuf;
+    PyObject *ret, *io, *io_raw;
+    npy_off_t position;
+
+    position = npy_ftell(handle);
+
+    /* Close the FILE* handle */
+    fclose(handle);
+
+    /*
+     * Restore original file handle position, in order to not confuse
+     * Python-side data structures
+     */
+    fd = PyObject_AsFileDescriptor(file);
+    if (fd == -1) {
+        return -1;
+    }
+
+    if (npy_lseek(fd, orig_pos, SEEK_SET) == -1) {
+
+        /* The io module is needed to determine if buffering is used */
+        io = PyImport_ImportModule("io");
+        if (io == NULL) {
+            return -1;
+        }
+        /* File object instances of RawIOBase are unbuffered */
+        io_raw = PyObject_GetAttrString(io, "RawIOBase");
+        Py_DECREF(io);
+        if (io_raw == NULL) {
+            return -1;
+        }
+        unbuf = PyObject_IsInstance(file, io_raw);
+        Py_DECREF(io_raw);
+        if (unbuf == 1) {
+            /* Succeed if the IO is unbuffered */
+            return 0;
+        }
+        else {
+            PyErr_SetString(PyExc_IOError, "seeking file failed");
+            return -1;
+        }
+    }
+
+    if (position == -1) {
+        PyErr_SetString(PyExc_IOError, "obtaining file position failed");
+        return -1;
+    }
+
+    /* Seek Python-side handle to the FILE* handle position */
+    ret = PyObject_CallMethod(file, "seek", NPY_OFF_T_PYFMT "i", position, 0);
+    if (ret == NULL) {
+        return -1;
+    }
+    Py_DECREF(ret);
+    return 0;
+}
+
+static inline PyObject*
+npy_PyFile_OpenFile(PyObject *filename, const char *mode)
+{
+    PyObject *open;
+    open = PyDict_GetItemString(PyEval_GetBuiltins(), "open");
+    if (open == NULL) {
+        return NULL;
+    }
+    return PyObject_CallFunction(open, "Os", filename, mode);
+}
+
+static inline int
+npy_PyFile_CloseFile(PyObject *file)
+{
+    PyObject *ret;
+
+    ret = PyObject_CallMethod(file, "close", NULL);
+    if (ret == NULL) {
+        return -1;
+    }
+    Py_DECREF(ret);
+    return 0;
+}
+
+/* This is a copy of _PyErr_ChainExceptions, which
+ *  is no longer exported from Python3.12
+ */
+static inline void
+npy_PyErr_ChainExceptions(PyObject *exc, PyObject *val, PyObject *tb)
+{
+    if (exc == NULL)
+        return;
+
+    if (PyErr_Occurred()) {
+        PyObject *exc2, *val2, *tb2;
+        PyErr_Fetch(&exc2, &val2, &tb2);
+        PyErr_NormalizeException(&exc, &val, &tb);
+        if (tb != NULL) {
+            PyException_SetTraceback(val, tb);
+            Py_DECREF(tb);
+        }
+        Py_DECREF(exc);
+        PyErr_NormalizeException(&exc2, &val2, &tb2);
+        PyException_SetContext(val2, val);
+        PyErr_Restore(exc2, val2, tb2);
+    }
+    else {
+        PyErr_Restore(exc, val, tb);
+    }
+}
+
+/* This is a copy of _PyErr_ChainExceptions, with:
+ *  __cause__ used instead of __context__
+ */
+static inline void
+npy_PyErr_ChainExceptionsCause(PyObject *exc, PyObject *val, PyObject *tb)
+{
+    if (exc == NULL)
+        return;
+
+    if (PyErr_Occurred()) {
+        PyObject *exc2, *val2, *tb2;
+        PyErr_Fetch(&exc2, &val2, &tb2);
+        PyErr_NormalizeException(&exc, &val, &tb);
+        if (tb != NULL) {
+            PyException_SetTraceback(val, tb);
+            Py_DECREF(tb);
+        }
+        Py_DECREF(exc);
+        PyErr_NormalizeException(&exc2, &val2, &tb2);
+        PyException_SetCause(val2, val);
+        PyErr_Restore(exc2, val2, tb2);
+    }
+    else {
+        PyErr_Restore(exc, val, tb);
+    }
+}
+
+/*
+ * PyCObject functions adapted to PyCapsules.
+ *
+ * The main job here is to get rid of the improved error handling
+ * of PyCapsules. It's a shame...
+ */
+static inline PyObject *
+NpyCapsule_FromVoidPtr(void *ptr, void (*dtor)(PyObject *))
+{
+    PyObject *ret = PyCapsule_New(ptr, NULL, dtor);
+    if (ret == NULL) {
+        PyErr_Clear();
+    }
+    return ret;
+}
+
+static inline PyObject *
+NpyCapsule_FromVoidPtrAndDesc(void *ptr, void* context, void (*dtor)(PyObject *))
+{
+    PyObject *ret = NpyCapsule_FromVoidPtr(ptr, dtor);
+    if (ret != NULL && PyCapsule_SetContext(ret, context) != 0) {
+        PyErr_Clear();
+        Py_DECREF(ret);
+        ret = NULL;
+    }
+    return ret;
+}
+
+static inline void *
+NpyCapsule_AsVoidPtr(PyObject *obj)
+{
+    void *ret = PyCapsule_GetPointer(obj, NULL);
+    if (ret == NULL) {
+        PyErr_Clear();
+    }
+    return ret;
+}
+
+static inline void *
+NpyCapsule_GetDesc(PyObject *obj)
+{
+    return PyCapsule_GetContext(obj);
+}
+
+static inline int
+NpyCapsule_Check(PyObject *ptr)
+{
+    return PyCapsule_CheckExact(ptr);
+}
+
+#ifdef __cplusplus
+}
+#endif
+
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NPY_3KCOMPAT_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_common.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_common.h
new file mode 100644
index 0000000..e2556a0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_common.h
@@ -0,0 +1,977 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_COMMON_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NPY_COMMON_H_
+
+/* need Python.h for npy_intp, npy_uintp */
+#include <Python.h>
+
+/* numpconfig.h is auto-generated */
+#include "numpyconfig.h"
+#ifdef HAVE_NPY_CONFIG_H
+#include <npy_config.h>
+#endif
+
+/*
+ * using static inline modifiers when defining npy_math functions
+ * allows the compiler to make optimizations when possible
+ */
+#ifndef NPY_INLINE_MATH
+#if defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD
+    #define NPY_INLINE_MATH 1
+#else
+    #define NPY_INLINE_MATH 0
+#endif
+#endif
+
+/*
+ * gcc does not unroll even with -O3
+ * use with care, unrolling on modern cpus rarely speeds things up
+ */
+#ifdef HAVE_ATTRIBUTE_OPTIMIZE_UNROLL_LOOPS
+#define NPY_GCC_UNROLL_LOOPS \
+    __attribute__((optimize("unroll-loops")))
+#else
+#define NPY_GCC_UNROLL_LOOPS
+#endif
+
+/* highest gcc optimization level, enabled autovectorizer */
+#ifdef HAVE_ATTRIBUTE_OPTIMIZE_OPT_3
+#define NPY_GCC_OPT_3 __attribute__((optimize("O3")))
+#else
+#define NPY_GCC_OPT_3
+#endif
+
+/*
+ * mark an argument (starting from 1) that must not be NULL and is not checked
+ * DO NOT USE IF FUNCTION CHECKS FOR NULL!! the compiler will remove the check
+ */
+#ifdef HAVE_ATTRIBUTE_NONNULL
+#define NPY_GCC_NONNULL(n) __attribute__((nonnull(n)))
+#else
+#define NPY_GCC_NONNULL(n)
+#endif
+
+/*
+ * give a hint to the compiler which branch is more likely or unlikely
+ * to occur, e.g. rare error cases:
+ *
+ * if (NPY_UNLIKELY(failure == 0))
+ *    return NULL;
+ *
+ * the double !! is to cast the expression (e.g. NULL) to a boolean required by
+ * the intrinsic
+ */
+#ifdef HAVE___BUILTIN_EXPECT
+#define NPY_LIKELY(x) __builtin_expect(!!(x), 1)
+#define NPY_UNLIKELY(x) __builtin_expect(!!(x), 0)
+#else
+#define NPY_LIKELY(x) (x)
+#define NPY_UNLIKELY(x) (x)
+#endif
+
+#ifdef HAVE___BUILTIN_PREFETCH
+/* unlike _mm_prefetch also works on non-x86 */
+#define NPY_PREFETCH(x, rw, loc) __builtin_prefetch((x), (rw), (loc))
+#else
+#ifdef NPY_HAVE_SSE
+/* _MM_HINT_ET[01] (rw = 1) unsupported, only available in gcc >= 4.9 */
+#define NPY_PREFETCH(x, rw, loc) _mm_prefetch((x), loc == 0 ? _MM_HINT_NTA : \
+                                             (loc == 1 ? _MM_HINT_T2 : \
+                                              (loc == 2 ? _MM_HINT_T1 : \
+                                               (loc == 3 ? _MM_HINT_T0 : -1))))
+#else
+#define NPY_PREFETCH(x, rw,loc)
+#endif
+#endif
+
+/* `NPY_INLINE` kept for backwards compatibility; use `inline` instead */
+#if defined(_MSC_VER) && !defined(__clang__)
+    #define NPY_INLINE __inline
+/* clang included here to handle clang-cl on Windows */
+#elif defined(__GNUC__) || defined(__clang__)
+    #if defined(__STRICT_ANSI__)
+         #define NPY_INLINE __inline__
+    #else
+         #define NPY_INLINE inline
+    #endif
+#else
+    #define NPY_INLINE
+#endif
+
+#ifdef _MSC_VER
+    #define NPY_FINLINE static __forceinline
+#elif defined(__GNUC__)
+    #define NPY_FINLINE static inline __attribute__((always_inline))
+#else
+    #define NPY_FINLINE static
+#endif
+
+#if defined(_MSC_VER)
+    #define NPY_NOINLINE static __declspec(noinline)
+#elif defined(__GNUC__) || defined(__clang__)
+    #define NPY_NOINLINE static __attribute__((noinline))
+#else
+    #define NPY_NOINLINE static
+#endif
+
+#ifdef __cplusplus
+    #define NPY_TLS thread_local
+#elif defined(HAVE_THREAD_LOCAL)
+    #define NPY_TLS thread_local
+#elif defined(HAVE__THREAD_LOCAL)
+    #define NPY_TLS _Thread_local
+#elif defined(HAVE___THREAD)
+    #define NPY_TLS __thread
+#elif defined(HAVE___DECLSPEC_THREAD_)
+    #define NPY_TLS __declspec(thread)
+#else
+    #define NPY_TLS
+#endif
+
+#ifdef WITH_CPYCHECKER_RETURNS_BORROWED_REF_ATTRIBUTE
+  #define NPY_RETURNS_BORROWED_REF \
+    __attribute__((cpychecker_returns_borrowed_ref))
+#else
+  #define NPY_RETURNS_BORROWED_REF
+#endif
+
+#ifdef WITH_CPYCHECKER_STEALS_REFERENCE_TO_ARG_ATTRIBUTE
+  #define NPY_STEALS_REF_TO_ARG(n) \
+   __attribute__((cpychecker_steals_reference_to_arg(n)))
+#else
+ #define NPY_STEALS_REF_TO_ARG(n)
+#endif
+
+/* 64 bit file position support, also on win-amd64. Issue gh-2256 */
+#if defined(_MSC_VER) && defined(_WIN64) && (_MSC_VER > 1400) || \
+    defined(__MINGW32__) || defined(__MINGW64__)
+    #include <io.h>
+
+    #define npy_fseek _fseeki64
+    #define npy_ftell _ftelli64
+    #define npy_lseek _lseeki64
+    #define npy_off_t npy_int64
+
+    #if NPY_SIZEOF_INT == 8
+        #define NPY_OFF_T_PYFMT "i"
+    #elif NPY_SIZEOF_LONG == 8
+        #define NPY_OFF_T_PYFMT "l"
+    #elif NPY_SIZEOF_LONGLONG == 8
+        #define NPY_OFF_T_PYFMT "L"
+    #else
+        #error Unsupported size for type off_t
+    #endif
+#else
+#ifdef HAVE_FSEEKO
+    #define npy_fseek fseeko
+#else
+    #define npy_fseek fseek
+#endif
+#ifdef HAVE_FTELLO
+    #define npy_ftell ftello
+#else
+    #define npy_ftell ftell
+#endif
+    #include <sys/types.h>
+    #ifndef _WIN32
+        #include <unistd.h>
+    #endif
+    #define npy_lseek lseek
+    #define npy_off_t off_t
+
+    #if NPY_SIZEOF_OFF_T == NPY_SIZEOF_SHORT
+        #define NPY_OFF_T_PYFMT "h"
+    #elif NPY_SIZEOF_OFF_T == NPY_SIZEOF_INT
+        #define NPY_OFF_T_PYFMT "i"
+    #elif NPY_SIZEOF_OFF_T == NPY_SIZEOF_LONG
+        #define NPY_OFF_T_PYFMT "l"
+    #elif NPY_SIZEOF_OFF_T == NPY_SIZEOF_LONGLONG
+        #define NPY_OFF_T_PYFMT "L"
+    #else
+        #error Unsupported size for type off_t
+    #endif
+#endif
+
+/* enums for detected endianness */
+enum {
+        NPY_CPU_UNKNOWN_ENDIAN,
+        NPY_CPU_LITTLE,
+        NPY_CPU_BIG
+};
+
+/*
+ * This is to typedef npy_intp to the appropriate size for Py_ssize_t.
+ * (Before NumPy 2.0 we used Py_intptr_t and Py_uintptr_t from `pyport.h`.)
+ */
+typedef Py_ssize_t npy_intp;
+typedef size_t npy_uintp;
+
+/*
+ * Define sizes that were not defined in numpyconfig.h.
+ */
+#define NPY_SIZEOF_CHAR 1
+#define NPY_SIZEOF_BYTE 1
+#define NPY_SIZEOF_DATETIME 8
+#define NPY_SIZEOF_TIMEDELTA 8
+#define NPY_SIZEOF_HALF 2
+#define NPY_SIZEOF_CFLOAT NPY_SIZEOF_COMPLEX_FLOAT
+#define NPY_SIZEOF_CDOUBLE NPY_SIZEOF_COMPLEX_DOUBLE
+#define NPY_SIZEOF_CLONGDOUBLE NPY_SIZEOF_COMPLEX_LONGDOUBLE
+
+#ifdef constchar
+#undef constchar
+#endif
+
+#define NPY_SSIZE_T_PYFMT "n"
+#define constchar char
+
+/* NPY_INTP_FMT Note:
+ *      Unlike the other NPY_*_FMT macros, which are used with PyOS_snprintf,
+ *      NPY_INTP_FMT is used with PyErr_Format and PyUnicode_FromFormat. Those
+ *      functions use different formatting codes that are portably specified
+ *      according to the Python documentation. See issue gh-2388.
+ */
+#if NPY_SIZEOF_INTP == NPY_SIZEOF_LONG
+        #define NPY_INTP NPY_LONG
+        #define NPY_UINTP NPY_ULONG
+        #define PyIntpArrType_Type PyLongArrType_Type
+        #define PyUIntpArrType_Type PyULongArrType_Type
+        #define NPY_MAX_INTP NPY_MAX_LONG
+        #define NPY_MIN_INTP NPY_MIN_LONG
+        #define NPY_MAX_UINTP NPY_MAX_ULONG
+        #define NPY_INTP_FMT "ld"
+#elif NPY_SIZEOF_INTP == NPY_SIZEOF_INT
+        #define NPY_INTP NPY_INT
+        #define NPY_UINTP NPY_UINT
+        #define PyIntpArrType_Type PyIntArrType_Type
+        #define PyUIntpArrType_Type PyUIntArrType_Type
+        #define NPY_MAX_INTP NPY_MAX_INT
+        #define NPY_MIN_INTP NPY_MIN_INT
+        #define NPY_MAX_UINTP NPY_MAX_UINT
+        #define NPY_INTP_FMT "d"
+#elif defined(PY_LONG_LONG) && (NPY_SIZEOF_INTP == NPY_SIZEOF_LONGLONG)
+        #define NPY_INTP NPY_LONGLONG
+        #define NPY_UINTP NPY_ULONGLONG
+        #define PyIntpArrType_Type PyLongLongArrType_Type
+        #define PyUIntpArrType_Type PyULongLongArrType_Type
+        #define NPY_MAX_INTP NPY_MAX_LONGLONG
+        #define NPY_MIN_INTP NPY_MIN_LONGLONG
+        #define NPY_MAX_UINTP NPY_MAX_ULONGLONG
+        #define NPY_INTP_FMT "lld"
+#else
+    #error "Failed to correctly define NPY_INTP and NPY_UINTP"
+#endif
+
+
+/*
+ * Some platforms don't define bool, long long, or long double.
+ * Handle that here.
+ */
+#define NPY_BYTE_FMT "hhd"
+#define NPY_UBYTE_FMT "hhu"
+#define NPY_SHORT_FMT "hd"
+#define NPY_USHORT_FMT "hu"
+#define NPY_INT_FMT "d"
+#define NPY_UINT_FMT "u"
+#define NPY_LONG_FMT "ld"
+#define NPY_ULONG_FMT "lu"
+#define NPY_HALF_FMT "g"
+#define NPY_FLOAT_FMT "g"
+#define NPY_DOUBLE_FMT "g"
+
+
+#ifdef PY_LONG_LONG
+typedef PY_LONG_LONG npy_longlong;
+typedef unsigned PY_LONG_LONG npy_ulonglong;
+#  ifdef _MSC_VER
+#    define NPY_LONGLONG_FMT         "I64d"
+#    define NPY_ULONGLONG_FMT        "I64u"
+#  else
+#    define NPY_LONGLONG_FMT         "lld"
+#    define NPY_ULONGLONG_FMT        "llu"
+#  endif
+#  ifdef _MSC_VER
+#    define NPY_LONGLONG_SUFFIX(x)   (x##i64)
+#    define NPY_ULONGLONG_SUFFIX(x)  (x##Ui64)
+#  else
+#    define NPY_LONGLONG_SUFFIX(x)   (x##LL)
+#    define NPY_ULONGLONG_SUFFIX(x)  (x##ULL)
+#  endif
+#else
+typedef long npy_longlong;
+typedef unsigned long npy_ulonglong;
+#  define NPY_LONGLONG_SUFFIX(x)  (x##L)
+#  define NPY_ULONGLONG_SUFFIX(x) (x##UL)
+#endif
+
+
+typedef unsigned char npy_bool;
+#define NPY_FALSE 0
+#define NPY_TRUE 1
+/*
+ * `NPY_SIZEOF_LONGDOUBLE` isn't usually equal to sizeof(long double).
+ * In some certain cases, it may forced to be equal to sizeof(double)
+ * even against the compiler implementation and the same goes for
+ * `complex long double`.
+ *
+ * Therefore, avoid `long double`, use `npy_longdouble` instead,
+ * and when it comes to standard math functions make sure of using
+ * the double version when `NPY_SIZEOF_LONGDOUBLE` == `NPY_SIZEOF_DOUBLE`.
+ * For example:
+ *   npy_longdouble *ptr, x;
+ *   #if NPY_SIZEOF_LONGDOUBLE == NPY_SIZEOF_DOUBLE
+ *       npy_longdouble r = modf(x, ptr);
+ *   #else
+ *       npy_longdouble r = modfl(x, ptr);
+ *   #endif
+ *
+ * See https://github.com/numpy/numpy/issues/20348
+ */
+#if NPY_SIZEOF_LONGDOUBLE == NPY_SIZEOF_DOUBLE
+    #define NPY_LONGDOUBLE_FMT "g"
+    #define longdouble_t double
+    typedef double npy_longdouble;
+#else
+    #define NPY_LONGDOUBLE_FMT "Lg"
+    #define longdouble_t long double
+    typedef long double npy_longdouble;
+#endif
+
+#ifndef Py_USING_UNICODE
+#error Must use Python with unicode enabled.
+#endif
+
+
+typedef signed char npy_byte;
+typedef unsigned char npy_ubyte;
+typedef unsigned short npy_ushort;
+typedef unsigned int npy_uint;
+typedef unsigned long npy_ulong;
+
+/* These are for completeness */
+typedef char npy_char;
+typedef short npy_short;
+typedef int npy_int;
+typedef long npy_long;
+typedef float npy_float;
+typedef double npy_double;
+
+typedef Py_hash_t npy_hash_t;
+#define NPY_SIZEOF_HASH_T NPY_SIZEOF_INTP
+
+#if defined(__cplusplus)
+
+typedef struct
+{
+    double _Val[2];
+} npy_cdouble;
+
+typedef struct
+{
+    float _Val[2];
+} npy_cfloat;
+
+typedef struct
+{
+    long double _Val[2];
+} npy_clongdouble;
+
+#else
+
+#include <complex.h>
+
+
+#if defined(_MSC_VER) && !defined(__INTEL_COMPILER)
+typedef _Dcomplex npy_cdouble;
+typedef _Fcomplex npy_cfloat;
+typedef _Lcomplex npy_clongdouble;
+#else /* !defined(_MSC_VER) || defined(__INTEL_COMPILER) */
+typedef double _Complex npy_cdouble;
+typedef float _Complex npy_cfloat;
+typedef longdouble_t _Complex npy_clongdouble;
+#endif
+
+#endif
+
+/*
+ * numarray-style bit-width typedefs
+ */
+#define NPY_MAX_INT8 127
+#define NPY_MIN_INT8 -128
+#define NPY_MAX_UINT8 255
+#define NPY_MAX_INT16 32767
+#define NPY_MIN_INT16 -32768
+#define NPY_MAX_UINT16 65535
+#define NPY_MAX_INT32 2147483647
+#define NPY_MIN_INT32 (-NPY_MAX_INT32 - 1)
+#define NPY_MAX_UINT32 4294967295U
+#define NPY_MAX_INT64 NPY_LONGLONG_SUFFIX(9223372036854775807)
+#define NPY_MIN_INT64 (-NPY_MAX_INT64 - NPY_LONGLONG_SUFFIX(1))
+#define NPY_MAX_UINT64 NPY_ULONGLONG_SUFFIX(18446744073709551615)
+#define NPY_MAX_INT128 NPY_LONGLONG_SUFFIX(85070591730234615865843651857942052864)
+#define NPY_MIN_INT128 (-NPY_MAX_INT128 - NPY_LONGLONG_SUFFIX(1))
+#define NPY_MAX_UINT128 NPY_ULONGLONG_SUFFIX(170141183460469231731687303715884105728)
+#define NPY_MIN_DATETIME NPY_MIN_INT64
+#define NPY_MAX_DATETIME NPY_MAX_INT64
+#define NPY_MIN_TIMEDELTA NPY_MIN_INT64
+#define NPY_MAX_TIMEDELTA NPY_MAX_INT64
+
+        /* Need to find the number of bits for each type and
+           make definitions accordingly.
+
+           C states that sizeof(char) == 1 by definition
+
+           So, just using the sizeof keyword won't help.
+
+           It also looks like Python itself uses sizeof(char) quite a
+           bit, which by definition should be 1 all the time.
+
+           Idea: Make Use of CHAR_BIT which should tell us how many
+           BITS per CHARACTER
+        */
+
+        /* Include platform definitions -- These are in the C89/90 standard */
+#include <limits.h>
+#define NPY_MAX_BYTE SCHAR_MAX
+#define NPY_MIN_BYTE SCHAR_MIN
+#define NPY_MAX_UBYTE UCHAR_MAX
+#define NPY_MAX_SHORT SHRT_MAX
+#define NPY_MIN_SHORT SHRT_MIN
+#define NPY_MAX_USHORT USHRT_MAX
+#define NPY_MAX_INT   INT_MAX
+#ifndef INT_MIN
+#define INT_MIN (-INT_MAX - 1)
+#endif
+#define NPY_MIN_INT   INT_MIN
+#define NPY_MAX_UINT  UINT_MAX
+#define NPY_MAX_LONG  LONG_MAX
+#define NPY_MIN_LONG  LONG_MIN
+#define NPY_MAX_ULONG  ULONG_MAX
+
+#define NPY_BITSOF_BOOL (sizeof(npy_bool) * CHAR_BIT)
+#define NPY_BITSOF_CHAR CHAR_BIT
+#define NPY_BITSOF_BYTE (NPY_SIZEOF_BYTE * CHAR_BIT)
+#define NPY_BITSOF_SHORT (NPY_SIZEOF_SHORT * CHAR_BIT)
+#define NPY_BITSOF_INT (NPY_SIZEOF_INT * CHAR_BIT)
+#define NPY_BITSOF_LONG (NPY_SIZEOF_LONG * CHAR_BIT)
+#define NPY_BITSOF_LONGLONG (NPY_SIZEOF_LONGLONG * CHAR_BIT)
+#define NPY_BITSOF_INTP (NPY_SIZEOF_INTP * CHAR_BIT)
+#define NPY_BITSOF_HALF (NPY_SIZEOF_HALF * CHAR_BIT)
+#define NPY_BITSOF_FLOAT (NPY_SIZEOF_FLOAT * CHAR_BIT)
+#define NPY_BITSOF_DOUBLE (NPY_SIZEOF_DOUBLE * CHAR_BIT)
+#define NPY_BITSOF_LONGDOUBLE (NPY_SIZEOF_LONGDOUBLE * CHAR_BIT)
+#define NPY_BITSOF_CFLOAT (NPY_SIZEOF_CFLOAT * CHAR_BIT)
+#define NPY_BITSOF_CDOUBLE (NPY_SIZEOF_CDOUBLE * CHAR_BIT)
+#define NPY_BITSOF_CLONGDOUBLE (NPY_SIZEOF_CLONGDOUBLE * CHAR_BIT)
+#define NPY_BITSOF_DATETIME (NPY_SIZEOF_DATETIME * CHAR_BIT)
+#define NPY_BITSOF_TIMEDELTA (NPY_SIZEOF_TIMEDELTA * CHAR_BIT)
+
+#if NPY_BITSOF_LONG == 8
+#define NPY_INT8 NPY_LONG
+#define NPY_UINT8 NPY_ULONG
+        typedef long npy_int8;
+        typedef unsigned long npy_uint8;
+#define PyInt8ScalarObject PyLongScalarObject
+#define PyInt8ArrType_Type PyLongArrType_Type
+#define PyUInt8ScalarObject PyULongScalarObject
+#define PyUInt8ArrType_Type PyULongArrType_Type
+#define NPY_INT8_FMT NPY_LONG_FMT
+#define NPY_UINT8_FMT NPY_ULONG_FMT
+#elif NPY_BITSOF_LONG == 16
+#define NPY_INT16 NPY_LONG
+#define NPY_UINT16 NPY_ULONG
+        typedef long npy_int16;
+        typedef unsigned long npy_uint16;
+#define PyInt16ScalarObject PyLongScalarObject
+#define PyInt16ArrType_Type PyLongArrType_Type
+#define PyUInt16ScalarObject PyULongScalarObject
+#define PyUInt16ArrType_Type PyULongArrType_Type
+#define NPY_INT16_FMT NPY_LONG_FMT
+#define NPY_UINT16_FMT NPY_ULONG_FMT
+#elif NPY_BITSOF_LONG == 32
+#define NPY_INT32 NPY_LONG
+#define NPY_UINT32 NPY_ULONG
+        typedef long npy_int32;
+        typedef unsigned long npy_uint32;
+        typedef unsigned long npy_ucs4;
+#define PyInt32ScalarObject PyLongScalarObject
+#define PyInt32ArrType_Type PyLongArrType_Type
+#define PyUInt32ScalarObject PyULongScalarObject
+#define PyUInt32ArrType_Type PyULongArrType_Type
+#define NPY_INT32_FMT NPY_LONG_FMT
+#define NPY_UINT32_FMT NPY_ULONG_FMT
+#elif NPY_BITSOF_LONG == 64
+#define NPY_INT64 NPY_LONG
+#define NPY_UINT64 NPY_ULONG
+        typedef long npy_int64;
+        typedef unsigned long npy_uint64;
+#define PyInt64ScalarObject PyLongScalarObject
+#define PyInt64ArrType_Type PyLongArrType_Type
+#define PyUInt64ScalarObject PyULongScalarObject
+#define PyUInt64ArrType_Type PyULongArrType_Type
+#define NPY_INT64_FMT NPY_LONG_FMT
+#define NPY_UINT64_FMT NPY_ULONG_FMT
+#define MyPyLong_FromInt64 PyLong_FromLong
+#define MyPyLong_AsInt64 PyLong_AsLong
+#endif
+
+#if NPY_BITSOF_LONGLONG == 8
+#  ifndef NPY_INT8
+#    define NPY_INT8 NPY_LONGLONG
+#    define NPY_UINT8 NPY_ULONGLONG
+        typedef npy_longlong npy_int8;
+        typedef npy_ulonglong npy_uint8;
+#    define PyInt8ScalarObject PyLongLongScalarObject
+#    define PyInt8ArrType_Type PyLongLongArrType_Type
+#    define PyUInt8ScalarObject PyULongLongScalarObject
+#    define PyUInt8ArrType_Type PyULongLongArrType_Type
+#define NPY_INT8_FMT NPY_LONGLONG_FMT
+#define NPY_UINT8_FMT NPY_ULONGLONG_FMT
+#  endif
+#  define NPY_MAX_LONGLONG NPY_MAX_INT8
+#  define NPY_MIN_LONGLONG NPY_MIN_INT8
+#  define NPY_MAX_ULONGLONG NPY_MAX_UINT8
+#elif NPY_BITSOF_LONGLONG == 16
+#  ifndef NPY_INT16
+#    define NPY_INT16 NPY_LONGLONG
+#    define NPY_UINT16 NPY_ULONGLONG
+        typedef npy_longlong npy_int16;
+        typedef npy_ulonglong npy_uint16;
+#    define PyInt16ScalarObject PyLongLongScalarObject
+#    define PyInt16ArrType_Type PyLongLongArrType_Type
+#    define PyUInt16ScalarObject PyULongLongScalarObject
+#    define PyUInt16ArrType_Type PyULongLongArrType_Type
+#define NPY_INT16_FMT NPY_LONGLONG_FMT
+#define NPY_UINT16_FMT NPY_ULONGLONG_FMT
+#  endif
+#  define NPY_MAX_LONGLONG NPY_MAX_INT16
+#  define NPY_MIN_LONGLONG NPY_MIN_INT16
+#  define NPY_MAX_ULONGLONG NPY_MAX_UINT16
+#elif NPY_BITSOF_LONGLONG == 32
+#  ifndef NPY_INT32
+#    define NPY_INT32 NPY_LONGLONG
+#    define NPY_UINT32 NPY_ULONGLONG
+        typedef npy_longlong npy_int32;
+        typedef npy_ulonglong npy_uint32;
+        typedef npy_ulonglong npy_ucs4;
+#    define PyInt32ScalarObject PyLongLongScalarObject
+#    define PyInt32ArrType_Type PyLongLongArrType_Type
+#    define PyUInt32ScalarObject PyULongLongScalarObject
+#    define PyUInt32ArrType_Type PyULongLongArrType_Type
+#define NPY_INT32_FMT NPY_LONGLONG_FMT
+#define NPY_UINT32_FMT NPY_ULONGLONG_FMT
+#  endif
+#  define NPY_MAX_LONGLONG NPY_MAX_INT32
+#  define NPY_MIN_LONGLONG NPY_MIN_INT32
+#  define NPY_MAX_ULONGLONG NPY_MAX_UINT32
+#elif NPY_BITSOF_LONGLONG == 64
+#  ifndef NPY_INT64
+#    define NPY_INT64 NPY_LONGLONG
+#    define NPY_UINT64 NPY_ULONGLONG
+        typedef npy_longlong npy_int64;
+        typedef npy_ulonglong npy_uint64;
+#    define PyInt64ScalarObject PyLongLongScalarObject
+#    define PyInt64ArrType_Type PyLongLongArrType_Type
+#    define PyUInt64ScalarObject PyULongLongScalarObject
+#    define PyUInt64ArrType_Type PyULongLongArrType_Type
+#define NPY_INT64_FMT NPY_LONGLONG_FMT
+#define NPY_UINT64_FMT NPY_ULONGLONG_FMT
+#    define MyPyLong_FromInt64 PyLong_FromLongLong
+#    define MyPyLong_AsInt64 PyLong_AsLongLong
+#  endif
+#  define NPY_MAX_LONGLONG NPY_MAX_INT64
+#  define NPY_MIN_LONGLONG NPY_MIN_INT64
+#  define NPY_MAX_ULONGLONG NPY_MAX_UINT64
+#endif
+
+#if NPY_BITSOF_INT == 8
+#ifndef NPY_INT8
+#define NPY_INT8 NPY_INT
+#define NPY_UINT8 NPY_UINT
+        typedef int npy_int8;
+        typedef unsigned int npy_uint8;
+#    define PyInt8ScalarObject PyIntScalarObject
+#    define PyInt8ArrType_Type PyIntArrType_Type
+#    define PyUInt8ScalarObject PyUIntScalarObject
+#    define PyUInt8ArrType_Type PyUIntArrType_Type
+#define NPY_INT8_FMT NPY_INT_FMT
+#define NPY_UINT8_FMT NPY_UINT_FMT
+#endif
+#elif NPY_BITSOF_INT == 16
+#ifndef NPY_INT16
+#define NPY_INT16 NPY_INT
+#define NPY_UINT16 NPY_UINT
+        typedef int npy_int16;
+        typedef unsigned int npy_uint16;
+#    define PyInt16ScalarObject PyIntScalarObject
+#    define PyInt16ArrType_Type PyIntArrType_Type
+#    define PyUInt16ScalarObject PyIntUScalarObject
+#    define PyUInt16ArrType_Type PyIntUArrType_Type
+#define NPY_INT16_FMT NPY_INT_FMT
+#define NPY_UINT16_FMT NPY_UINT_FMT
+#endif
+#elif NPY_BITSOF_INT == 32
+#ifndef NPY_INT32
+#define NPY_INT32 NPY_INT
+#define NPY_UINT32 NPY_UINT
+        typedef int npy_int32;
+        typedef unsigned int npy_uint32;
+        typedef unsigned int npy_ucs4;
+#    define PyInt32ScalarObject PyIntScalarObject
+#    define PyInt32ArrType_Type PyIntArrType_Type
+#    define PyUInt32ScalarObject PyUIntScalarObject
+#    define PyUInt32ArrType_Type PyUIntArrType_Type
+#define NPY_INT32_FMT NPY_INT_FMT
+#define NPY_UINT32_FMT NPY_UINT_FMT
+#endif
+#elif NPY_BITSOF_INT == 64
+#ifndef NPY_INT64
+#define NPY_INT64 NPY_INT
+#define NPY_UINT64 NPY_UINT
+        typedef int npy_int64;
+        typedef unsigned int npy_uint64;
+#    define PyInt64ScalarObject PyIntScalarObject
+#    define PyInt64ArrType_Type PyIntArrType_Type
+#    define PyUInt64ScalarObject PyUIntScalarObject
+#    define PyUInt64ArrType_Type PyUIntArrType_Type
+#define NPY_INT64_FMT NPY_INT_FMT
+#define NPY_UINT64_FMT NPY_UINT_FMT
+#    define MyPyLong_FromInt64 PyLong_FromLong
+#    define MyPyLong_AsInt64 PyLong_AsLong
+#endif
+#endif
+
+#if NPY_BITSOF_SHORT == 8
+#ifndef NPY_INT8
+#define NPY_INT8 NPY_SHORT
+#define NPY_UINT8 NPY_USHORT
+        typedef short npy_int8;
+        typedef unsigned short npy_uint8;
+#    define PyInt8ScalarObject PyShortScalarObject
+#    define PyInt8ArrType_Type PyShortArrType_Type
+#    define PyUInt8ScalarObject PyUShortScalarObject
+#    define PyUInt8ArrType_Type PyUShortArrType_Type
+#define NPY_INT8_FMT NPY_SHORT_FMT
+#define NPY_UINT8_FMT NPY_USHORT_FMT
+#endif
+#elif NPY_BITSOF_SHORT == 16
+#ifndef NPY_INT16
+#define NPY_INT16 NPY_SHORT
+#define NPY_UINT16 NPY_USHORT
+        typedef short npy_int16;
+        typedef unsigned short npy_uint16;
+#    define PyInt16ScalarObject PyShortScalarObject
+#    define PyInt16ArrType_Type PyShortArrType_Type
+#    define PyUInt16ScalarObject PyUShortScalarObject
+#    define PyUInt16ArrType_Type PyUShortArrType_Type
+#define NPY_INT16_FMT NPY_SHORT_FMT
+#define NPY_UINT16_FMT NPY_USHORT_FMT
+#endif
+#elif NPY_BITSOF_SHORT == 32
+#ifndef NPY_INT32
+#define NPY_INT32 NPY_SHORT
+#define NPY_UINT32 NPY_USHORT
+        typedef short npy_int32;
+        typedef unsigned short npy_uint32;
+        typedef unsigned short npy_ucs4;
+#    define PyInt32ScalarObject PyShortScalarObject
+#    define PyInt32ArrType_Type PyShortArrType_Type
+#    define PyUInt32ScalarObject PyUShortScalarObject
+#    define PyUInt32ArrType_Type PyUShortArrType_Type
+#define NPY_INT32_FMT NPY_SHORT_FMT
+#define NPY_UINT32_FMT NPY_USHORT_FMT
+#endif
+#elif NPY_BITSOF_SHORT == 64
+#ifndef NPY_INT64
+#define NPY_INT64 NPY_SHORT
+#define NPY_UINT64 NPY_USHORT
+        typedef short npy_int64;
+        typedef unsigned short npy_uint64;
+#    define PyInt64ScalarObject PyShortScalarObject
+#    define PyInt64ArrType_Type PyShortArrType_Type
+#    define PyUInt64ScalarObject PyUShortScalarObject
+#    define PyUInt64ArrType_Type PyUShortArrType_Type
+#define NPY_INT64_FMT NPY_SHORT_FMT
+#define NPY_UINT64_FMT NPY_USHORT_FMT
+#    define MyPyLong_FromInt64 PyLong_FromLong
+#    define MyPyLong_AsInt64 PyLong_AsLong
+#endif
+#endif
+
+
+#if NPY_BITSOF_CHAR == 8
+#ifndef NPY_INT8
+#define NPY_INT8 NPY_BYTE
+#define NPY_UINT8 NPY_UBYTE
+        typedef signed char npy_int8;
+        typedef unsigned char npy_uint8;
+#    define PyInt8ScalarObject PyByteScalarObject
+#    define PyInt8ArrType_Type PyByteArrType_Type
+#    define PyUInt8ScalarObject PyUByteScalarObject
+#    define PyUInt8ArrType_Type PyUByteArrType_Type
+#define NPY_INT8_FMT NPY_BYTE_FMT
+#define NPY_UINT8_FMT NPY_UBYTE_FMT
+#endif
+#elif NPY_BITSOF_CHAR == 16
+#ifndef NPY_INT16
+#define NPY_INT16 NPY_BYTE
+#define NPY_UINT16 NPY_UBYTE
+        typedef signed char npy_int16;
+        typedef unsigned char npy_uint16;
+#    define PyInt16ScalarObject PyByteScalarObject
+#    define PyInt16ArrType_Type PyByteArrType_Type
+#    define PyUInt16ScalarObject PyUByteScalarObject
+#    define PyUInt16ArrType_Type PyUByteArrType_Type
+#define NPY_INT16_FMT NPY_BYTE_FMT
+#define NPY_UINT16_FMT NPY_UBYTE_FMT
+#endif
+#elif NPY_BITSOF_CHAR == 32
+#ifndef NPY_INT32
+#define NPY_INT32 NPY_BYTE
+#define NPY_UINT32 NPY_UBYTE
+        typedef signed char npy_int32;
+        typedef unsigned char npy_uint32;
+        typedef unsigned char npy_ucs4;
+#    define PyInt32ScalarObject PyByteScalarObject
+#    define PyInt32ArrType_Type PyByteArrType_Type
+#    define PyUInt32ScalarObject PyUByteScalarObject
+#    define PyUInt32ArrType_Type PyUByteArrType_Type
+#define NPY_INT32_FMT NPY_BYTE_FMT
+#define NPY_UINT32_FMT NPY_UBYTE_FMT
+#endif
+#elif NPY_BITSOF_CHAR == 64
+#ifndef NPY_INT64
+#define NPY_INT64 NPY_BYTE
+#define NPY_UINT64 NPY_UBYTE
+        typedef signed char npy_int64;
+        typedef unsigned char npy_uint64;
+#    define PyInt64ScalarObject PyByteScalarObject
+#    define PyInt64ArrType_Type PyByteArrType_Type
+#    define PyUInt64ScalarObject PyUByteScalarObject
+#    define PyUInt64ArrType_Type PyUByteArrType_Type
+#define NPY_INT64_FMT NPY_BYTE_FMT
+#define NPY_UINT64_FMT NPY_UBYTE_FMT
+#    define MyPyLong_FromInt64 PyLong_FromLong
+#    define MyPyLong_AsInt64 PyLong_AsLong
+#endif
+#elif NPY_BITSOF_CHAR == 128
+#endif
+
+
+
+#if NPY_BITSOF_DOUBLE == 32
+#ifndef NPY_FLOAT32
+#define NPY_FLOAT32 NPY_DOUBLE
+#define NPY_COMPLEX64 NPY_CDOUBLE
+        typedef double npy_float32;
+        typedef npy_cdouble npy_complex64;
+#    define PyFloat32ScalarObject PyDoubleScalarObject
+#    define PyComplex64ScalarObject PyCDoubleScalarObject
+#    define PyFloat32ArrType_Type PyDoubleArrType_Type
+#    define PyComplex64ArrType_Type PyCDoubleArrType_Type
+#define NPY_FLOAT32_FMT NPY_DOUBLE_FMT
+#define NPY_COMPLEX64_FMT NPY_CDOUBLE_FMT
+#endif
+#elif NPY_BITSOF_DOUBLE == 64
+#ifndef NPY_FLOAT64
+#define NPY_FLOAT64 NPY_DOUBLE
+#define NPY_COMPLEX128 NPY_CDOUBLE
+        typedef double npy_float64;
+        typedef npy_cdouble npy_complex128;
+#    define PyFloat64ScalarObject PyDoubleScalarObject
+#    define PyComplex128ScalarObject PyCDoubleScalarObject
+#    define PyFloat64ArrType_Type PyDoubleArrType_Type
+#    define PyComplex128ArrType_Type PyCDoubleArrType_Type
+#define NPY_FLOAT64_FMT NPY_DOUBLE_FMT
+#define NPY_COMPLEX128_FMT NPY_CDOUBLE_FMT
+#endif
+#elif NPY_BITSOF_DOUBLE == 80
+#ifndef NPY_FLOAT80
+#define NPY_FLOAT80 NPY_DOUBLE
+#define NPY_COMPLEX160 NPY_CDOUBLE
+        typedef double npy_float80;
+        typedef npy_cdouble npy_complex160;
+#    define PyFloat80ScalarObject PyDoubleScalarObject
+#    define PyComplex160ScalarObject PyCDoubleScalarObject
+#    define PyFloat80ArrType_Type PyDoubleArrType_Type
+#    define PyComplex160ArrType_Type PyCDoubleArrType_Type
+#define NPY_FLOAT80_FMT NPY_DOUBLE_FMT
+#define NPY_COMPLEX160_FMT NPY_CDOUBLE_FMT
+#endif
+#elif NPY_BITSOF_DOUBLE == 96
+#ifndef NPY_FLOAT96
+#define NPY_FLOAT96 NPY_DOUBLE
+#define NPY_COMPLEX192 NPY_CDOUBLE
+        typedef double npy_float96;
+        typedef npy_cdouble npy_complex192;
+#    define PyFloat96ScalarObject PyDoubleScalarObject
+#    define PyComplex192ScalarObject PyCDoubleScalarObject
+#    define PyFloat96ArrType_Type PyDoubleArrType_Type
+#    define PyComplex192ArrType_Type PyCDoubleArrType_Type
+#define NPY_FLOAT96_FMT NPY_DOUBLE_FMT
+#define NPY_COMPLEX192_FMT NPY_CDOUBLE_FMT
+#endif
+#elif NPY_BITSOF_DOUBLE == 128
+#ifndef NPY_FLOAT128
+#define NPY_FLOAT128 NPY_DOUBLE
+#define NPY_COMPLEX256 NPY_CDOUBLE
+        typedef double npy_float128;
+        typedef npy_cdouble npy_complex256;
+#    define PyFloat128ScalarObject PyDoubleScalarObject
+#    define PyComplex256ScalarObject PyCDoubleScalarObject
+#    define PyFloat128ArrType_Type PyDoubleArrType_Type
+#    define PyComplex256ArrType_Type PyCDoubleArrType_Type
+#define NPY_FLOAT128_FMT NPY_DOUBLE_FMT
+#define NPY_COMPLEX256_FMT NPY_CDOUBLE_FMT
+#endif
+#endif
+
+
+
+#if NPY_BITSOF_FLOAT == 32
+#ifndef NPY_FLOAT32
+#define NPY_FLOAT32 NPY_FLOAT
+#define NPY_COMPLEX64 NPY_CFLOAT
+        typedef float npy_float32;
+        typedef npy_cfloat npy_complex64;
+#    define PyFloat32ScalarObject PyFloatScalarObject
+#    define PyComplex64ScalarObject PyCFloatScalarObject
+#    define PyFloat32ArrType_Type PyFloatArrType_Type
+#    define PyComplex64ArrType_Type PyCFloatArrType_Type
+#define NPY_FLOAT32_FMT NPY_FLOAT_FMT
+#define NPY_COMPLEX64_FMT NPY_CFLOAT_FMT
+#endif
+#elif NPY_BITSOF_FLOAT == 64
+#ifndef NPY_FLOAT64
+#define NPY_FLOAT64 NPY_FLOAT
+#define NPY_COMPLEX128 NPY_CFLOAT
+        typedef float npy_float64;
+        typedef npy_cfloat npy_complex128;
+#    define PyFloat64ScalarObject PyFloatScalarObject
+#    define PyComplex128ScalarObject PyCFloatScalarObject
+#    define PyFloat64ArrType_Type PyFloatArrType_Type
+#    define PyComplex128ArrType_Type PyCFloatArrType_Type
+#define NPY_FLOAT64_FMT NPY_FLOAT_FMT
+#define NPY_COMPLEX128_FMT NPY_CFLOAT_FMT
+#endif
+#elif NPY_BITSOF_FLOAT == 80
+#ifndef NPY_FLOAT80
+#define NPY_FLOAT80 NPY_FLOAT
+#define NPY_COMPLEX160 NPY_CFLOAT
+        typedef float npy_float80;
+        typedef npy_cfloat npy_complex160;
+#    define PyFloat80ScalarObject PyFloatScalarObject
+#    define PyComplex160ScalarObject PyCFloatScalarObject
+#    define PyFloat80ArrType_Type PyFloatArrType_Type
+#    define PyComplex160ArrType_Type PyCFloatArrType_Type
+#define NPY_FLOAT80_FMT NPY_FLOAT_FMT
+#define NPY_COMPLEX160_FMT NPY_CFLOAT_FMT
+#endif
+#elif NPY_BITSOF_FLOAT == 96
+#ifndef NPY_FLOAT96
+#define NPY_FLOAT96 NPY_FLOAT
+#define NPY_COMPLEX192 NPY_CFLOAT
+        typedef float npy_float96;
+        typedef npy_cfloat npy_complex192;
+#    define PyFloat96ScalarObject PyFloatScalarObject
+#    define PyComplex192ScalarObject PyCFloatScalarObject
+#    define PyFloat96ArrType_Type PyFloatArrType_Type
+#    define PyComplex192ArrType_Type PyCFloatArrType_Type
+#define NPY_FLOAT96_FMT NPY_FLOAT_FMT
+#define NPY_COMPLEX192_FMT NPY_CFLOAT_FMT
+#endif
+#elif NPY_BITSOF_FLOAT == 128
+#ifndef NPY_FLOAT128
+#define NPY_FLOAT128 NPY_FLOAT
+#define NPY_COMPLEX256 NPY_CFLOAT
+        typedef float npy_float128;
+        typedef npy_cfloat npy_complex256;
+#    define PyFloat128ScalarObject PyFloatScalarObject
+#    define PyComplex256ScalarObject PyCFloatScalarObject
+#    define PyFloat128ArrType_Type PyFloatArrType_Type
+#    define PyComplex256ArrType_Type PyCFloatArrType_Type
+#define NPY_FLOAT128_FMT NPY_FLOAT_FMT
+#define NPY_COMPLEX256_FMT NPY_CFLOAT_FMT
+#endif
+#endif
+
+/* half/float16 isn't a floating-point type in C */
+#define NPY_FLOAT16 NPY_HALF
+typedef npy_uint16 npy_half;
+typedef npy_half npy_float16;
+
+#if NPY_BITSOF_LONGDOUBLE == 32
+#ifndef NPY_FLOAT32
+#define NPY_FLOAT32 NPY_LONGDOUBLE
+#define NPY_COMPLEX64 NPY_CLONGDOUBLE
+        typedef npy_longdouble npy_float32;
+        typedef npy_clongdouble npy_complex64;
+#    define PyFloat32ScalarObject PyLongDoubleScalarObject
+#    define PyComplex64ScalarObject PyCLongDoubleScalarObject
+#    define PyFloat32ArrType_Type PyLongDoubleArrType_Type
+#    define PyComplex64ArrType_Type PyCLongDoubleArrType_Type
+#define NPY_FLOAT32_FMT NPY_LONGDOUBLE_FMT
+#define NPY_COMPLEX64_FMT NPY_CLONGDOUBLE_FMT
+#endif
+#elif NPY_BITSOF_LONGDOUBLE == 64
+#ifndef NPY_FLOAT64
+#define NPY_FLOAT64 NPY_LONGDOUBLE
+#define NPY_COMPLEX128 NPY_CLONGDOUBLE
+        typedef npy_longdouble npy_float64;
+        typedef npy_clongdouble npy_complex128;
+#    define PyFloat64ScalarObject PyLongDoubleScalarObject
+#    define PyComplex128ScalarObject PyCLongDoubleScalarObject
+#    define PyFloat64ArrType_Type PyLongDoubleArrType_Type
+#    define PyComplex128ArrType_Type PyCLongDoubleArrType_Type
+#define NPY_FLOAT64_FMT NPY_LONGDOUBLE_FMT
+#define NPY_COMPLEX128_FMT NPY_CLONGDOUBLE_FMT
+#endif
+#elif NPY_BITSOF_LONGDOUBLE == 80
+#ifndef NPY_FLOAT80
+#define NPY_FLOAT80 NPY_LONGDOUBLE
+#define NPY_COMPLEX160 NPY_CLONGDOUBLE
+        typedef npy_longdouble npy_float80;
+        typedef npy_clongdouble npy_complex160;
+#    define PyFloat80ScalarObject PyLongDoubleScalarObject
+#    define PyComplex160ScalarObject PyCLongDoubleScalarObject
+#    define PyFloat80ArrType_Type PyLongDoubleArrType_Type
+#    define PyComplex160ArrType_Type PyCLongDoubleArrType_Type
+#define NPY_FLOAT80_FMT NPY_LONGDOUBLE_FMT
+#define NPY_COMPLEX160_FMT NPY_CLONGDOUBLE_FMT
+#endif
+#elif NPY_BITSOF_LONGDOUBLE == 96
+#ifndef NPY_FLOAT96
+#define NPY_FLOAT96 NPY_LONGDOUBLE
+#define NPY_COMPLEX192 NPY_CLONGDOUBLE
+        typedef npy_longdouble npy_float96;
+        typedef npy_clongdouble npy_complex192;
+#    define PyFloat96ScalarObject PyLongDoubleScalarObject
+#    define PyComplex192ScalarObject PyCLongDoubleScalarObject
+#    define PyFloat96ArrType_Type PyLongDoubleArrType_Type
+#    define PyComplex192ArrType_Type PyCLongDoubleArrType_Type
+#define NPY_FLOAT96_FMT NPY_LONGDOUBLE_FMT
+#define NPY_COMPLEX192_FMT NPY_CLONGDOUBLE_FMT
+#endif
+#elif NPY_BITSOF_LONGDOUBLE == 128
+#ifndef NPY_FLOAT128
+#define NPY_FLOAT128 NPY_LONGDOUBLE
+#define NPY_COMPLEX256 NPY_CLONGDOUBLE
+        typedef npy_longdouble npy_float128;
+        typedef npy_clongdouble npy_complex256;
+#    define PyFloat128ScalarObject PyLongDoubleScalarObject
+#    define PyComplex256ScalarObject PyCLongDoubleScalarObject
+#    define PyFloat128ArrType_Type PyLongDoubleArrType_Type
+#    define PyComplex256ArrType_Type PyCLongDoubleArrType_Type
+#define NPY_FLOAT128_FMT NPY_LONGDOUBLE_FMT
+#define NPY_COMPLEX256_FMT NPY_CLONGDOUBLE_FMT
+#endif
+#endif
+
+/* datetime typedefs */
+typedef npy_int64 npy_timedelta;
+typedef npy_int64 npy_datetime;
+#define NPY_DATETIME_FMT NPY_INT64_FMT
+#define NPY_TIMEDELTA_FMT NPY_INT64_FMT
+
+/* End of typedefs for numarray style bit-width names */
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NPY_COMMON_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_cpu.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_cpu.h
new file mode 100644
index 0000000..91cf2d8
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_cpu.h
@@ -0,0 +1,124 @@
+/*
+ * This set (target) cpu specific macros:
+ *      - Possible values:
+ *              NPY_CPU_X86
+ *              NPY_CPU_AMD64
+ *              NPY_CPU_PPC
+ *              NPY_CPU_PPC64
+ *              NPY_CPU_PPC64LE
+ *              NPY_CPU_SPARC
+ *              NPY_CPU_S390
+ *              NPY_CPU_IA64
+ *              NPY_CPU_HPPA
+ *              NPY_CPU_ALPHA
+ *              NPY_CPU_ARMEL
+ *              NPY_CPU_ARMEB
+ *              NPY_CPU_SH_LE
+ *              NPY_CPU_SH_BE
+ *              NPY_CPU_ARCEL
+ *              NPY_CPU_ARCEB
+ *              NPY_CPU_RISCV64
+ *              NPY_CPU_RISCV32
+ *              NPY_CPU_LOONGARCH
+ *              NPY_CPU_WASM
+ */
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_CPU_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NPY_CPU_H_
+
+#include "numpyconfig.h"
+
+#if defined( __i386__ ) || defined(i386) || defined(_M_IX86)
+    /*
+     * __i386__ is defined by gcc and Intel compiler on Linux,
+     * _M_IX86 by VS compiler,
+     * i386 by Sun compilers on opensolaris at least
+     */
+    #define NPY_CPU_X86
+#elif defined(__x86_64__) || defined(__amd64__) || defined(__x86_64) || defined(_M_AMD64)
+    /*
+     * both __x86_64__ and __amd64__ are defined by gcc
+     * __x86_64 defined by sun compiler on opensolaris at least
+     * _M_AMD64 defined by MS compiler
+     */
+    #define NPY_CPU_AMD64
+#elif defined(__powerpc64__) && defined(__LITTLE_ENDIAN__)
+    #define NPY_CPU_PPC64LE
+#elif defined(__powerpc64__) && defined(__BIG_ENDIAN__)
+    #define NPY_CPU_PPC64
+#elif defined(__ppc__) || defined(__powerpc__) || defined(_ARCH_PPC)
+    /*
+     * __ppc__ is defined by gcc, I remember having seen __powerpc__ once,
+     * but can't find it ATM
+     * _ARCH_PPC is used by at least gcc on AIX
+     * As __powerpc__ and _ARCH_PPC are also defined by PPC64 check
+     * for those specifically first before defaulting to ppc
+     */
+    #define NPY_CPU_PPC
+#elif defined(__sparc__) || defined(__sparc)
+    /* __sparc__ is defined by gcc and Forte (e.g. Sun) compilers */
+    #define NPY_CPU_SPARC
+#elif defined(__s390__)
+    #define NPY_CPU_S390
+#elif defined(__ia64)
+    #define NPY_CPU_IA64
+#elif defined(__hppa)
+    #define NPY_CPU_HPPA
+#elif defined(__alpha__)
+    #define NPY_CPU_ALPHA
+#elif defined(__arm__) || defined(__aarch64__) || defined(_M_ARM64)
+    /* _M_ARM64 is defined in MSVC for ARM64 compilation on Windows */
+    #if defined(__ARMEB__) || defined(__AARCH64EB__)
+        #if defined(__ARM_32BIT_STATE)
+            #define NPY_CPU_ARMEB_AARCH32
+        #elif defined(__ARM_64BIT_STATE)
+            #define NPY_CPU_ARMEB_AARCH64
+        #else
+            #define NPY_CPU_ARMEB
+        #endif
+    #elif defined(__ARMEL__) || defined(__AARCH64EL__) || defined(_M_ARM64)
+        #if defined(__ARM_32BIT_STATE)
+            #define NPY_CPU_ARMEL_AARCH32
+        #elif defined(__ARM_64BIT_STATE) || defined(_M_ARM64) || defined(__AARCH64EL__)
+            #define NPY_CPU_ARMEL_AARCH64
+        #else
+            #define NPY_CPU_ARMEL
+        #endif
+    #else
+        # error Unknown ARM CPU, please report this to numpy maintainers with \
+	information about your platform (OS, CPU and compiler)
+    #endif
+#elif defined(__sh__) && defined(__LITTLE_ENDIAN__)
+    #define NPY_CPU_SH_LE
+#elif defined(__sh__) && defined(__BIG_ENDIAN__)
+    #define NPY_CPU_SH_BE
+#elif defined(__MIPSEL__)
+    #define NPY_CPU_MIPSEL
+#elif defined(__MIPSEB__)
+    #define NPY_CPU_MIPSEB
+#elif defined(__or1k__)
+    #define NPY_CPU_OR1K
+#elif defined(__mc68000__)
+    #define NPY_CPU_M68K
+#elif defined(__arc__) && defined(__LITTLE_ENDIAN__)
+    #define NPY_CPU_ARCEL
+#elif defined(__arc__) && defined(__BIG_ENDIAN__)
+    #define NPY_CPU_ARCEB
+#elif defined(__riscv)
+    #if __riscv_xlen == 64
+	#define NPY_CPU_RISCV64
+    #elif __riscv_xlen == 32
+	#define NPY_CPU_RISCV32
+    #endif
+#elif defined(__loongarch_lp64)
+    #define NPY_CPU_LOONGARCH64
+#elif defined(__EMSCRIPTEN__)
+    /* __EMSCRIPTEN__ is defined by emscripten: an LLVM-to-Web compiler */
+    #define NPY_CPU_WASM
+#else
+    #error Unknown CPU, please report this to numpy maintainers with \
+    information about your platform (OS, CPU and compiler)
+#endif
+
+#define NPY_ALIGNMENT_REQUIRED 1
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NPY_CPU_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_endian.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_endian.h
new file mode 100644
index 0000000..0926212
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_endian.h
@@ -0,0 +1,78 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_ENDIAN_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NPY_ENDIAN_H_
+
+/*
+ * NPY_BYTE_ORDER is set to the same value as BYTE_ORDER set by glibc in
+ * endian.h
+ */
+
+#if defined(NPY_HAVE_ENDIAN_H) || defined(NPY_HAVE_SYS_ENDIAN_H)
+    /* Use endian.h if available */
+
+    #if defined(NPY_HAVE_ENDIAN_H)
+    #include <endian.h>
+    #elif defined(NPY_HAVE_SYS_ENDIAN_H)
+    #include <sys/endian.h>
+    #endif
+
+    #if defined(BYTE_ORDER) && defined(BIG_ENDIAN) && defined(LITTLE_ENDIAN)
+        #define NPY_BYTE_ORDER    BYTE_ORDER
+        #define NPY_LITTLE_ENDIAN LITTLE_ENDIAN
+        #define NPY_BIG_ENDIAN    BIG_ENDIAN
+    #elif defined(_BYTE_ORDER) && defined(_BIG_ENDIAN) && defined(_LITTLE_ENDIAN)
+        #define NPY_BYTE_ORDER    _BYTE_ORDER
+        #define NPY_LITTLE_ENDIAN _LITTLE_ENDIAN
+        #define NPY_BIG_ENDIAN    _BIG_ENDIAN
+    #elif defined(__BYTE_ORDER) && defined(__BIG_ENDIAN) && defined(__LITTLE_ENDIAN)
+        #define NPY_BYTE_ORDER    __BYTE_ORDER
+        #define NPY_LITTLE_ENDIAN __LITTLE_ENDIAN
+        #define NPY_BIG_ENDIAN    __BIG_ENDIAN
+    #endif
+#endif
+
+#ifndef NPY_BYTE_ORDER
+    /* Set endianness info using target CPU */
+    #include "npy_cpu.h"
+
+    #define NPY_LITTLE_ENDIAN 1234
+    #define NPY_BIG_ENDIAN 4321
+
+    #if defined(NPY_CPU_X86)                  \
+            || defined(NPY_CPU_AMD64)         \
+            || defined(NPY_CPU_IA64)          \
+            || defined(NPY_CPU_ALPHA)         \
+            || defined(NPY_CPU_ARMEL)         \
+            || defined(NPY_CPU_ARMEL_AARCH32) \
+            || defined(NPY_CPU_ARMEL_AARCH64) \
+            || defined(NPY_CPU_SH_LE)         \
+            || defined(NPY_CPU_MIPSEL)        \
+            || defined(NPY_CPU_PPC64LE)       \
+            || defined(NPY_CPU_ARCEL)         \
+            || defined(NPY_CPU_RISCV64)       \
+            || defined(NPY_CPU_RISCV32)       \
+            || defined(NPY_CPU_LOONGARCH)     \
+            || defined(NPY_CPU_WASM)
+        #define NPY_BYTE_ORDER NPY_LITTLE_ENDIAN
+
+    #elif defined(NPY_CPU_PPC)                \
+            || defined(NPY_CPU_SPARC)         \
+            || defined(NPY_CPU_S390)          \
+            || defined(NPY_CPU_HPPA)          \
+            || defined(NPY_CPU_PPC64)         \
+            || defined(NPY_CPU_ARMEB)         \
+            || defined(NPY_CPU_ARMEB_AARCH32) \
+            || defined(NPY_CPU_ARMEB_AARCH64) \
+            || defined(NPY_CPU_SH_BE)         \
+            || defined(NPY_CPU_MIPSEB)        \
+            || defined(NPY_CPU_OR1K)          \
+            || defined(NPY_CPU_M68K)          \
+            || defined(NPY_CPU_ARCEB)
+        #define NPY_BYTE_ORDER NPY_BIG_ENDIAN
+
+    #else
+        #error Unknown CPU: can not set endianness
+    #endif
+
+#endif
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NPY_ENDIAN_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_math.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_math.h
new file mode 100644
index 0000000..abc784b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_math.h
@@ -0,0 +1,602 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_MATH_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NPY_MATH_H_
+
+#include <numpy/npy_common.h>
+
+#include <math.h>
+
+/* By adding static inline specifiers to npy_math function definitions when
+   appropriate, compiler is given the opportunity to optimize */
+#if NPY_INLINE_MATH
+#define NPY_INPLACE static inline
+#else
+#define NPY_INPLACE
+#endif
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#define PyArray_MAX(a,b) (((a)>(b))?(a):(b))
+#define PyArray_MIN(a,b) (((a)<(b))?(a):(b))
+
+/*
+ * NAN and INFINITY like macros (same behavior as glibc for NAN, same as C99
+ * for INFINITY)
+ *
+ * XXX: I should test whether INFINITY and NAN are available on the platform
+ */
+static inline float __npy_inff(void)
+{
+    const union { npy_uint32 __i; float __f;} __bint = {0x7f800000UL};
+    return __bint.__f;
+}
+
+static inline float __npy_nanf(void)
+{
+    const union { npy_uint32 __i; float __f;} __bint = {0x7fc00000UL};
+    return __bint.__f;
+}
+
+static inline float __npy_pzerof(void)
+{
+    const union { npy_uint32 __i; float __f;} __bint = {0x00000000UL};
+    return __bint.__f;
+}
+
+static inline float __npy_nzerof(void)
+{
+    const union { npy_uint32 __i; float __f;} __bint = {0x80000000UL};
+    return __bint.__f;
+}
+
+#define NPY_INFINITYF __npy_inff()
+#define NPY_NANF __npy_nanf()
+#define NPY_PZEROF __npy_pzerof()
+#define NPY_NZEROF __npy_nzerof()
+
+#define NPY_INFINITY ((npy_double)NPY_INFINITYF)
+#define NPY_NAN ((npy_double)NPY_NANF)
+#define NPY_PZERO ((npy_double)NPY_PZEROF)
+#define NPY_NZERO ((npy_double)NPY_NZEROF)
+
+#define NPY_INFINITYL ((npy_longdouble)NPY_INFINITYF)
+#define NPY_NANL ((npy_longdouble)NPY_NANF)
+#define NPY_PZEROL ((npy_longdouble)NPY_PZEROF)
+#define NPY_NZEROL ((npy_longdouble)NPY_NZEROF)
+
+/*
+ * Useful constants
+ */
+#define NPY_E         2.718281828459045235360287471352662498  /* e */
+#define NPY_LOG2E     1.442695040888963407359924681001892137  /* log_2 e */
+#define NPY_LOG10E    0.434294481903251827651128918916605082  /* log_10 e */
+#define NPY_LOGE2     0.693147180559945309417232121458176568  /* log_e 2 */
+#define NPY_LOGE10    2.302585092994045684017991454684364208  /* log_e 10 */
+#define NPY_PI        3.141592653589793238462643383279502884  /* pi */
+#define NPY_PI_2      1.570796326794896619231321691639751442  /* pi/2 */
+#define NPY_PI_4      0.785398163397448309615660845819875721  /* pi/4 */
+#define NPY_1_PI      0.318309886183790671537767526745028724  /* 1/pi */
+#define NPY_2_PI      0.636619772367581343075535053490057448  /* 2/pi */
+#define NPY_EULER     0.577215664901532860606512090082402431  /* Euler constant */
+#define NPY_SQRT2     1.414213562373095048801688724209698079  /* sqrt(2) */
+#define NPY_SQRT1_2   0.707106781186547524400844362104849039  /* 1/sqrt(2) */
+
+#define NPY_Ef        2.718281828459045235360287471352662498F /* e */
+#define NPY_LOG2Ef    1.442695040888963407359924681001892137F /* log_2 e */
+#define NPY_LOG10Ef   0.434294481903251827651128918916605082F /* log_10 e */
+#define NPY_LOGE2f    0.693147180559945309417232121458176568F /* log_e 2 */
+#define NPY_LOGE10f   2.302585092994045684017991454684364208F /* log_e 10 */
+#define NPY_PIf       3.141592653589793238462643383279502884F /* pi */
+#define NPY_PI_2f     1.570796326794896619231321691639751442F /* pi/2 */
+#define NPY_PI_4f     0.785398163397448309615660845819875721F /* pi/4 */
+#define NPY_1_PIf     0.318309886183790671537767526745028724F /* 1/pi */
+#define NPY_2_PIf     0.636619772367581343075535053490057448F /* 2/pi */
+#define NPY_EULERf    0.577215664901532860606512090082402431F /* Euler constant */
+#define NPY_SQRT2f    1.414213562373095048801688724209698079F /* sqrt(2) */
+#define NPY_SQRT1_2f  0.707106781186547524400844362104849039F /* 1/sqrt(2) */
+
+#define NPY_El        2.718281828459045235360287471352662498L /* e */
+#define NPY_LOG2El    1.442695040888963407359924681001892137L /* log_2 e */
+#define NPY_LOG10El   0.434294481903251827651128918916605082L /* log_10 e */
+#define NPY_LOGE2l    0.693147180559945309417232121458176568L /* log_e 2 */
+#define NPY_LOGE10l   2.302585092994045684017991454684364208L /* log_e 10 */
+#define NPY_PIl       3.141592653589793238462643383279502884L /* pi */
+#define NPY_PI_2l     1.570796326794896619231321691639751442L /* pi/2 */
+#define NPY_PI_4l     0.785398163397448309615660845819875721L /* pi/4 */
+#define NPY_1_PIl     0.318309886183790671537767526745028724L /* 1/pi */
+#define NPY_2_PIl     0.636619772367581343075535053490057448L /* 2/pi */
+#define NPY_EULERl    0.577215664901532860606512090082402431L /* Euler constant */
+#define NPY_SQRT2l    1.414213562373095048801688724209698079L /* sqrt(2) */
+#define NPY_SQRT1_2l  0.707106781186547524400844362104849039L /* 1/sqrt(2) */
+
+/*
+ * Integer functions.
+ */
+NPY_INPLACE npy_uint npy_gcdu(npy_uint a, npy_uint b);
+NPY_INPLACE npy_uint npy_lcmu(npy_uint a, npy_uint b);
+NPY_INPLACE npy_ulong npy_gcdul(npy_ulong a, npy_ulong b);
+NPY_INPLACE npy_ulong npy_lcmul(npy_ulong a, npy_ulong b);
+NPY_INPLACE npy_ulonglong npy_gcdull(npy_ulonglong a, npy_ulonglong b);
+NPY_INPLACE npy_ulonglong npy_lcmull(npy_ulonglong a, npy_ulonglong b);
+
+NPY_INPLACE npy_int npy_gcd(npy_int a, npy_int b);
+NPY_INPLACE npy_int npy_lcm(npy_int a, npy_int b);
+NPY_INPLACE npy_long npy_gcdl(npy_long a, npy_long b);
+NPY_INPLACE npy_long npy_lcml(npy_long a, npy_long b);
+NPY_INPLACE npy_longlong npy_gcdll(npy_longlong a, npy_longlong b);
+NPY_INPLACE npy_longlong npy_lcmll(npy_longlong a, npy_longlong b);
+
+NPY_INPLACE npy_ubyte npy_rshiftuhh(npy_ubyte a, npy_ubyte b);
+NPY_INPLACE npy_ubyte npy_lshiftuhh(npy_ubyte a, npy_ubyte b);
+NPY_INPLACE npy_ushort npy_rshiftuh(npy_ushort a, npy_ushort b);
+NPY_INPLACE npy_ushort npy_lshiftuh(npy_ushort a, npy_ushort b);
+NPY_INPLACE npy_uint npy_rshiftu(npy_uint a, npy_uint b);
+NPY_INPLACE npy_uint npy_lshiftu(npy_uint a, npy_uint b);
+NPY_INPLACE npy_ulong npy_rshiftul(npy_ulong a, npy_ulong b);
+NPY_INPLACE npy_ulong npy_lshiftul(npy_ulong a, npy_ulong b);
+NPY_INPLACE npy_ulonglong npy_rshiftull(npy_ulonglong a, npy_ulonglong b);
+NPY_INPLACE npy_ulonglong npy_lshiftull(npy_ulonglong a, npy_ulonglong b);
+
+NPY_INPLACE npy_byte npy_rshifthh(npy_byte a, npy_byte b);
+NPY_INPLACE npy_byte npy_lshifthh(npy_byte a, npy_byte b);
+NPY_INPLACE npy_short npy_rshifth(npy_short a, npy_short b);
+NPY_INPLACE npy_short npy_lshifth(npy_short a, npy_short b);
+NPY_INPLACE npy_int npy_rshift(npy_int a, npy_int b);
+NPY_INPLACE npy_int npy_lshift(npy_int a, npy_int b);
+NPY_INPLACE npy_long npy_rshiftl(npy_long a, npy_long b);
+NPY_INPLACE npy_long npy_lshiftl(npy_long a, npy_long b);
+NPY_INPLACE npy_longlong npy_rshiftll(npy_longlong a, npy_longlong b);
+NPY_INPLACE npy_longlong npy_lshiftll(npy_longlong a, npy_longlong b);
+
+NPY_INPLACE uint8_t npy_popcountuhh(npy_ubyte a);
+NPY_INPLACE uint8_t npy_popcountuh(npy_ushort a);
+NPY_INPLACE uint8_t npy_popcountu(npy_uint a);
+NPY_INPLACE uint8_t npy_popcountul(npy_ulong a);
+NPY_INPLACE uint8_t npy_popcountull(npy_ulonglong a);
+NPY_INPLACE uint8_t npy_popcounthh(npy_byte a);
+NPY_INPLACE uint8_t npy_popcounth(npy_short a);
+NPY_INPLACE uint8_t npy_popcount(npy_int a);
+NPY_INPLACE uint8_t npy_popcountl(npy_long a);
+NPY_INPLACE uint8_t npy_popcountll(npy_longlong a);
+
+/*
+ * C99 double math funcs that need fixups or are blocklist-able
+ */
+NPY_INPLACE double npy_sin(double x);
+NPY_INPLACE double npy_cos(double x);
+NPY_INPLACE double npy_tan(double x);
+NPY_INPLACE double npy_hypot(double x, double y);
+NPY_INPLACE double npy_log2(double x);
+NPY_INPLACE double npy_atan2(double x, double y);
+
+/* Mandatory C99 double math funcs, no blocklisting or fixups */
+/* defined for legacy reasons, should be deprecated at some point */
+#define npy_sinh sinh
+#define npy_cosh cosh
+#define npy_tanh tanh
+#define npy_asin asin
+#define npy_acos acos
+#define npy_atan atan
+#define npy_log log
+#define npy_log10 log10
+#define npy_cbrt cbrt
+#define npy_fabs fabs
+#define npy_ceil ceil
+#define npy_fmod fmod
+#define npy_floor floor
+#define npy_expm1 expm1
+#define npy_log1p log1p
+#define npy_acosh acosh
+#define npy_asinh asinh
+#define npy_atanh atanh
+#define npy_rint rint
+#define npy_trunc trunc
+#define npy_exp2 exp2
+#define npy_frexp frexp
+#define npy_ldexp ldexp
+#define npy_copysign copysign
+#define npy_exp exp
+#define npy_sqrt sqrt
+#define npy_pow pow
+#define npy_modf modf
+#define npy_nextafter nextafter
+
+double npy_spacing(double x);
+
+/*
+ * IEEE 754 fpu handling
+ */
+
+/* use builtins to avoid function calls in tight loops
+ * only available if npy_config.h is available (= numpys own build) */
+#ifdef HAVE___BUILTIN_ISNAN
+    #define npy_isnan(x) __builtin_isnan(x)
+#else
+    #define npy_isnan(x) isnan(x)
+#endif
+
+
+/* only available if npy_config.h is available (= numpys own build) */
+#ifdef HAVE___BUILTIN_ISFINITE
+    #define npy_isfinite(x) __builtin_isfinite(x)
+#else
+    #define npy_isfinite(x) isfinite((x))
+#endif
+
+/* only available if npy_config.h is available (= numpys own build) */
+#ifdef HAVE___BUILTIN_ISINF
+    #define npy_isinf(x) __builtin_isinf(x)
+#else
+    #define npy_isinf(x) isinf((x))
+#endif
+
+#define npy_signbit(x) signbit((x))
+
+/*
+ * float C99 math funcs that need fixups or are blocklist-able
+ */
+NPY_INPLACE float npy_sinf(float x);
+NPY_INPLACE float npy_cosf(float x);
+NPY_INPLACE float npy_tanf(float x);
+NPY_INPLACE float npy_expf(float x);
+NPY_INPLACE float npy_sqrtf(float x);
+NPY_INPLACE float npy_hypotf(float x, float y);
+NPY_INPLACE float npy_log2f(float x);
+NPY_INPLACE float npy_atan2f(float x, float y);
+NPY_INPLACE float npy_powf(float x, float y);
+NPY_INPLACE float npy_modff(float x, float* y);
+
+/* Mandatory C99 float math funcs, no blocklisting or fixups */
+/* defined for legacy reasons, should be deprecated at some point */
+
+#define npy_sinhf sinhf
+#define npy_coshf coshf
+#define npy_tanhf tanhf
+#define npy_asinf asinf
+#define npy_acosf acosf
+#define npy_atanf atanf
+#define npy_logf logf
+#define npy_log10f log10f
+#define npy_cbrtf cbrtf
+#define npy_fabsf fabsf
+#define npy_ceilf ceilf
+#define npy_fmodf fmodf
+#define npy_floorf floorf
+#define npy_expm1f expm1f
+#define npy_log1pf log1pf
+#define npy_asinhf asinhf
+#define npy_acoshf acoshf
+#define npy_atanhf atanhf
+#define npy_rintf rintf
+#define npy_truncf truncf
+#define npy_exp2f exp2f
+#define npy_frexpf frexpf
+#define npy_ldexpf ldexpf
+#define npy_copysignf copysignf
+#define npy_nextafterf nextafterf
+
+float npy_spacingf(float x);
+
+/*
+ * long double C99 double math funcs that need fixups or are blocklist-able
+ */
+NPY_INPLACE npy_longdouble npy_sinl(npy_longdouble x);
+NPY_INPLACE npy_longdouble npy_cosl(npy_longdouble x);
+NPY_INPLACE npy_longdouble npy_tanl(npy_longdouble x);
+NPY_INPLACE npy_longdouble npy_expl(npy_longdouble x);
+NPY_INPLACE npy_longdouble npy_sqrtl(npy_longdouble x);
+NPY_INPLACE npy_longdouble npy_hypotl(npy_longdouble x, npy_longdouble y);
+NPY_INPLACE npy_longdouble npy_log2l(npy_longdouble x);
+NPY_INPLACE npy_longdouble npy_atan2l(npy_longdouble x, npy_longdouble y);
+NPY_INPLACE npy_longdouble npy_powl(npy_longdouble x, npy_longdouble y);
+NPY_INPLACE npy_longdouble npy_modfl(npy_longdouble x, npy_longdouble* y);
+
+/* Mandatory C99 double math funcs, no blocklisting or fixups */
+/* defined for legacy reasons, should be deprecated at some point */
+#define npy_sinhl sinhl
+#define npy_coshl coshl
+#define npy_tanhl tanhl
+#define npy_fabsl fabsl
+#define npy_floorl floorl
+#define npy_ceill ceill
+#define npy_rintl rintl
+#define npy_truncl truncl
+#define npy_cbrtl cbrtl
+#define npy_log10l log10l
+#define npy_logl logl
+#define npy_expm1l expm1l
+#define npy_asinl asinl
+#define npy_acosl acosl
+#define npy_atanl atanl
+#define npy_asinhl asinhl
+#define npy_acoshl acoshl
+#define npy_atanhl atanhl
+#define npy_log1pl log1pl
+#define npy_exp2l exp2l
+#define npy_fmodl fmodl
+#define npy_frexpl frexpl
+#define npy_ldexpl ldexpl
+#define npy_copysignl copysignl
+#define npy_nextafterl nextafterl
+
+npy_longdouble npy_spacingl(npy_longdouble x);
+
+/*
+ * Non standard functions
+ */
+NPY_INPLACE double npy_deg2rad(double x);
+NPY_INPLACE double npy_rad2deg(double x);
+NPY_INPLACE double npy_logaddexp(double x, double y);
+NPY_INPLACE double npy_logaddexp2(double x, double y);
+NPY_INPLACE double npy_divmod(double x, double y, double *modulus);
+NPY_INPLACE double npy_heaviside(double x, double h0);
+
+NPY_INPLACE float npy_deg2radf(float x);
+NPY_INPLACE float npy_rad2degf(float x);
+NPY_INPLACE float npy_logaddexpf(float x, float y);
+NPY_INPLACE float npy_logaddexp2f(float x, float y);
+NPY_INPLACE float npy_divmodf(float x, float y, float *modulus);
+NPY_INPLACE float npy_heavisidef(float x, float h0);
+
+NPY_INPLACE npy_longdouble npy_deg2radl(npy_longdouble x);
+NPY_INPLACE npy_longdouble npy_rad2degl(npy_longdouble x);
+NPY_INPLACE npy_longdouble npy_logaddexpl(npy_longdouble x, npy_longdouble y);
+NPY_INPLACE npy_longdouble npy_logaddexp2l(npy_longdouble x, npy_longdouble y);
+NPY_INPLACE npy_longdouble npy_divmodl(npy_longdouble x, npy_longdouble y,
+                           npy_longdouble *modulus);
+NPY_INPLACE npy_longdouble npy_heavisidel(npy_longdouble x, npy_longdouble h0);
+
+#define npy_degrees npy_rad2deg
+#define npy_degreesf npy_rad2degf
+#define npy_degreesl npy_rad2degl
+
+#define npy_radians npy_deg2rad
+#define npy_radiansf npy_deg2radf
+#define npy_radiansl npy_deg2radl
+
+/*
+ * Complex declarations
+ */
+
+static inline double npy_creal(const npy_cdouble z)
+{
+#if defined(__cplusplus)
+    return z._Val[0];
+#else
+    return creal(z);
+#endif
+}
+
+static inline void npy_csetreal(npy_cdouble *z, const double r)
+{
+    ((double *) z)[0] = r;
+}
+
+static inline double npy_cimag(const npy_cdouble z)
+{
+#if defined(__cplusplus)
+    return z._Val[1];
+#else
+    return cimag(z);
+#endif
+}
+
+static inline void npy_csetimag(npy_cdouble *z, const double i)
+{
+    ((double *) z)[1] = i;
+}
+
+static inline float npy_crealf(const npy_cfloat z)
+{
+#if defined(__cplusplus)
+    return z._Val[0];
+#else
+    return crealf(z);
+#endif
+}
+
+static inline void npy_csetrealf(npy_cfloat *z, const float r)
+{
+    ((float *) z)[0] = r;
+}
+
+static inline float npy_cimagf(const npy_cfloat z)
+{
+#if defined(__cplusplus)
+    return z._Val[1];
+#else
+    return cimagf(z);
+#endif
+}
+
+static inline void npy_csetimagf(npy_cfloat *z, const float i)
+{
+    ((float *) z)[1] = i;
+}
+
+static inline npy_longdouble npy_creall(const npy_clongdouble z)
+{
+#if defined(__cplusplus)
+    return (npy_longdouble)z._Val[0];
+#else
+    return creall(z);
+#endif
+}
+
+static inline void npy_csetreall(npy_clongdouble *z, const longdouble_t r)
+{
+    ((longdouble_t *) z)[0] = r;
+}
+
+static inline npy_longdouble npy_cimagl(const npy_clongdouble z)
+{
+#if defined(__cplusplus)
+    return (npy_longdouble)z._Val[1];
+#else
+    return cimagl(z);
+#endif
+}
+
+static inline void npy_csetimagl(npy_clongdouble *z, const longdouble_t i)
+{
+    ((longdouble_t *) z)[1] = i;
+}
+
+#define NPY_CSETREAL(z, r) npy_csetreal(z, r)
+#define NPY_CSETIMAG(z, i) npy_csetimag(z, i)
+#define NPY_CSETREALF(z, r) npy_csetrealf(z, r)
+#define NPY_CSETIMAGF(z, i) npy_csetimagf(z, i)
+#define NPY_CSETREALL(z, r) npy_csetreall(z, r)
+#define NPY_CSETIMAGL(z, i) npy_csetimagl(z, i)
+
+static inline npy_cdouble npy_cpack(double x, double y)
+{
+    npy_cdouble z;
+    npy_csetreal(&z, x);
+    npy_csetimag(&z, y);
+    return z;
+}
+
+static inline npy_cfloat npy_cpackf(float x, float y)
+{
+    npy_cfloat z;
+    npy_csetrealf(&z, x);
+    npy_csetimagf(&z, y);
+    return z;
+}
+
+static inline npy_clongdouble npy_cpackl(npy_longdouble x, npy_longdouble y)
+{
+    npy_clongdouble z;
+    npy_csetreall(&z, x);
+    npy_csetimagl(&z, y);
+    return z;
+}
+
+/*
+ * Double precision complex functions
+ */
+double npy_cabs(npy_cdouble z);
+double npy_carg(npy_cdouble z);
+
+npy_cdouble npy_cexp(npy_cdouble z);
+npy_cdouble npy_clog(npy_cdouble z);
+npy_cdouble npy_cpow(npy_cdouble x, npy_cdouble y);
+
+npy_cdouble npy_csqrt(npy_cdouble z);
+
+npy_cdouble npy_ccos(npy_cdouble z);
+npy_cdouble npy_csin(npy_cdouble z);
+npy_cdouble npy_ctan(npy_cdouble z);
+
+npy_cdouble npy_ccosh(npy_cdouble z);
+npy_cdouble npy_csinh(npy_cdouble z);
+npy_cdouble npy_ctanh(npy_cdouble z);
+
+npy_cdouble npy_cacos(npy_cdouble z);
+npy_cdouble npy_casin(npy_cdouble z);
+npy_cdouble npy_catan(npy_cdouble z);
+
+npy_cdouble npy_cacosh(npy_cdouble z);
+npy_cdouble npy_casinh(npy_cdouble z);
+npy_cdouble npy_catanh(npy_cdouble z);
+
+/*
+ * Single precision complex functions
+ */
+float npy_cabsf(npy_cfloat z);
+float npy_cargf(npy_cfloat z);
+
+npy_cfloat npy_cexpf(npy_cfloat z);
+npy_cfloat npy_clogf(npy_cfloat z);
+npy_cfloat npy_cpowf(npy_cfloat x, npy_cfloat y);
+
+npy_cfloat npy_csqrtf(npy_cfloat z);
+
+npy_cfloat npy_ccosf(npy_cfloat z);
+npy_cfloat npy_csinf(npy_cfloat z);
+npy_cfloat npy_ctanf(npy_cfloat z);
+
+npy_cfloat npy_ccoshf(npy_cfloat z);
+npy_cfloat npy_csinhf(npy_cfloat z);
+npy_cfloat npy_ctanhf(npy_cfloat z);
+
+npy_cfloat npy_cacosf(npy_cfloat z);
+npy_cfloat npy_casinf(npy_cfloat z);
+npy_cfloat npy_catanf(npy_cfloat z);
+
+npy_cfloat npy_cacoshf(npy_cfloat z);
+npy_cfloat npy_casinhf(npy_cfloat z);
+npy_cfloat npy_catanhf(npy_cfloat z);
+
+
+/*
+ * Extended precision complex functions
+ */
+npy_longdouble npy_cabsl(npy_clongdouble z);
+npy_longdouble npy_cargl(npy_clongdouble z);
+
+npy_clongdouble npy_cexpl(npy_clongdouble z);
+npy_clongdouble npy_clogl(npy_clongdouble z);
+npy_clongdouble npy_cpowl(npy_clongdouble x, npy_clongdouble y);
+
+npy_clongdouble npy_csqrtl(npy_clongdouble z);
+
+npy_clongdouble npy_ccosl(npy_clongdouble z);
+npy_clongdouble npy_csinl(npy_clongdouble z);
+npy_clongdouble npy_ctanl(npy_clongdouble z);
+
+npy_clongdouble npy_ccoshl(npy_clongdouble z);
+npy_clongdouble npy_csinhl(npy_clongdouble z);
+npy_clongdouble npy_ctanhl(npy_clongdouble z);
+
+npy_clongdouble npy_cacosl(npy_clongdouble z);
+npy_clongdouble npy_casinl(npy_clongdouble z);
+npy_clongdouble npy_catanl(npy_clongdouble z);
+
+npy_clongdouble npy_cacoshl(npy_clongdouble z);
+npy_clongdouble npy_casinhl(npy_clongdouble z);
+npy_clongdouble npy_catanhl(npy_clongdouble z);
+
+
+/*
+ * Functions that set the floating point error
+ * status word.
+ */
+
+/*
+ * platform-dependent code translates floating point
+ * status to an integer sum of these values
+ */
+#define NPY_FPE_DIVIDEBYZERO  1
+#define NPY_FPE_OVERFLOW      2
+#define NPY_FPE_UNDERFLOW     4
+#define NPY_FPE_INVALID       8
+
+int npy_clear_floatstatus_barrier(char*);
+int npy_get_floatstatus_barrier(char*);
+/*
+ * use caution with these - clang and gcc8.1 are known to reorder calls
+ * to this form of the function which can defeat the check. The _barrier
+ * form of the call is preferable, where the argument is
+ * (char*)&local_variable
+ */
+int npy_clear_floatstatus(void);
+int npy_get_floatstatus(void);
+
+void npy_set_floatstatus_divbyzero(void);
+void npy_set_floatstatus_overflow(void);
+void npy_set_floatstatus_underflow(void);
+void npy_set_floatstatus_invalid(void);
+
+#ifdef __cplusplus
+}
+#endif
+
+#if NPY_INLINE_MATH
+#include "npy_math_internal.h"
+#endif
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NPY_MATH_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_no_deprecated_api.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_no_deprecated_api.h
new file mode 100644
index 0000000..39658c0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_no_deprecated_api.h
@@ -0,0 +1,20 @@
+/*
+ * This include file is provided for inclusion in Cython *.pyd files where
+ * one would like to define the NPY_NO_DEPRECATED_API macro. It can be
+ * included by
+ *
+ * cdef extern from "npy_no_deprecated_api.h": pass
+ *
+ */
+#ifndef NPY_NO_DEPRECATED_API
+
+/* put this check here since there may be multiple includes in C extensions. */
+#if defined(NUMPY_CORE_INCLUDE_NUMPY_NDARRAYTYPES_H_) || \
+    defined(NUMPY_CORE_INCLUDE_NUMPY_NPY_DEPRECATED_API_H) || \
+    defined(NUMPY_CORE_INCLUDE_NUMPY_OLD_DEFINES_H_)
+#error "npy_no_deprecated_api.h" must be first among numpy includes.
+#else
+#define NPY_NO_DEPRECATED_API NPY_API_VERSION
+#endif
+
+#endif  /* NPY_NO_DEPRECATED_API */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_os.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_os.h
new file mode 100644
index 0000000..0ce5d78
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/npy_os.h
@@ -0,0 +1,42 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_OS_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NPY_OS_H_
+
+#if defined(linux) || defined(__linux) || defined(__linux__)
+    #define NPY_OS_LINUX
+#elif defined(__FreeBSD__) || defined(__NetBSD__) || \
+            defined(__OpenBSD__) || defined(__DragonFly__)
+    #define NPY_OS_BSD
+    #ifdef __FreeBSD__
+        #define NPY_OS_FREEBSD
+    #elif defined(__NetBSD__)
+        #define NPY_OS_NETBSD
+    #elif defined(__OpenBSD__)
+        #define NPY_OS_OPENBSD
+    #elif defined(__DragonFly__)
+        #define NPY_OS_DRAGONFLY
+    #endif
+#elif defined(sun) || defined(__sun)
+    #define NPY_OS_SOLARIS
+#elif defined(__CYGWIN__)
+    #define NPY_OS_CYGWIN
+/* We are on Windows.*/
+#elif defined(_WIN32)
+  /* We are using MinGW (64-bit or 32-bit)*/
+  #if defined(__MINGW32__) || defined(__MINGW64__)
+    #define NPY_OS_MINGW
+  /* Otherwise, if _WIN64 is defined, we are targeting 64-bit Windows*/
+  #elif defined(_WIN64)
+    #define NPY_OS_WIN64
+  /* Otherwise assume we are targeting 32-bit Windows*/
+  #else
+    #define NPY_OS_WIN32
+  #endif
+#elif defined(__APPLE__)
+    #define NPY_OS_DARWIN
+#elif defined(__HAIKU__)
+    #define NPY_OS_HAIKU
+#else
+    #define NPY_OS_UNKNOWN
+#endif
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NPY_OS_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/numpyconfig.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/numpyconfig.h
new file mode 100644
index 0000000..ba44c28
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/numpyconfig.h
@@ -0,0 +1,182 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_NUMPYCONFIG_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_NPY_NUMPYCONFIG_H_
+
+#include "_numpyconfig.h"
+
+/*
+ * On Mac OS X, because there is only one configuration stage for all the archs
+ * in universal builds, any macro which depends on the arch needs to be
+ * hardcoded.
+ *
+ * Note that distutils/pip will attempt a universal2 build when Python itself
+ * is built as universal2, hence this hardcoding is needed even if we do not
+ * support universal2 wheels anymore (see gh-22796).
+ * This code block can be removed after we have dropped the setup.py based
+ * build completely.
+ */
+#ifdef __APPLE__
+    #undef NPY_SIZEOF_LONG
+
+    #ifdef __LP64__
+        #define NPY_SIZEOF_LONG         8
+    #else
+        #define NPY_SIZEOF_LONG         4
+    #endif
+
+    #undef NPY_SIZEOF_LONGDOUBLE
+    #undef NPY_SIZEOF_COMPLEX_LONGDOUBLE
+    #ifdef HAVE_LDOUBLE_IEEE_DOUBLE_LE
+      #undef HAVE_LDOUBLE_IEEE_DOUBLE_LE
+    #endif
+    #ifdef HAVE_LDOUBLE_INTEL_EXTENDED_16_BYTES_LE
+      #undef HAVE_LDOUBLE_INTEL_EXTENDED_16_BYTES_LE
+    #endif
+
+    #if defined(__arm64__)
+        #define NPY_SIZEOF_LONGDOUBLE         8
+        #define NPY_SIZEOF_COMPLEX_LONGDOUBLE 16
+        #define HAVE_LDOUBLE_IEEE_DOUBLE_LE 1
+    #elif defined(__x86_64)
+        #define NPY_SIZEOF_LONGDOUBLE         16
+        #define NPY_SIZEOF_COMPLEX_LONGDOUBLE 32
+        #define HAVE_LDOUBLE_INTEL_EXTENDED_16_BYTES_LE 1
+    #elif defined (__i386)
+        #define NPY_SIZEOF_LONGDOUBLE         12
+        #define NPY_SIZEOF_COMPLEX_LONGDOUBLE 24
+    #elif defined(__ppc__) || defined (__ppc64__)
+        #define NPY_SIZEOF_LONGDOUBLE         16
+        #define NPY_SIZEOF_COMPLEX_LONGDOUBLE 32
+    #else
+        #error "unknown architecture"
+    #endif
+#endif
+
+
+/**
+ * To help with both NPY_TARGET_VERSION and the NPY_NO_DEPRECATED_API macro,
+ * we include API version numbers for specific versions of NumPy.
+ * To exclude all API that was deprecated as of 1.7, add the following before
+ * #including any NumPy headers:
+ *   #define NPY_NO_DEPRECATED_API  NPY_1_7_API_VERSION
+ * The same is true for NPY_TARGET_VERSION, although NumPy will default to
+ * a backwards compatible build anyway.
+ */
+#define NPY_1_7_API_VERSION 0x00000007
+#define NPY_1_8_API_VERSION 0x00000008
+#define NPY_1_9_API_VERSION 0x00000009
+#define NPY_1_10_API_VERSION 0x0000000a
+#define NPY_1_11_API_VERSION 0x0000000a
+#define NPY_1_12_API_VERSION 0x0000000a
+#define NPY_1_13_API_VERSION 0x0000000b
+#define NPY_1_14_API_VERSION 0x0000000c
+#define NPY_1_15_API_VERSION 0x0000000c
+#define NPY_1_16_API_VERSION 0x0000000d
+#define NPY_1_17_API_VERSION 0x0000000d
+#define NPY_1_18_API_VERSION 0x0000000d
+#define NPY_1_19_API_VERSION 0x0000000d
+#define NPY_1_20_API_VERSION 0x0000000e
+#define NPY_1_21_API_VERSION 0x0000000e
+#define NPY_1_22_API_VERSION 0x0000000f
+#define NPY_1_23_API_VERSION 0x00000010
+#define NPY_1_24_API_VERSION 0x00000010
+#define NPY_1_25_API_VERSION 0x00000011
+#define NPY_2_0_API_VERSION 0x00000012
+#define NPY_2_1_API_VERSION 0x00000013
+#define NPY_2_2_API_VERSION 0x00000013
+#define NPY_2_3_API_VERSION 0x00000014
+
+
+/*
+ * Binary compatibility version number.  This number is increased
+ * whenever the C-API is changed such that binary compatibility is
+ * broken, i.e. whenever a recompile of extension modules is needed.
+ */
+#define NPY_VERSION NPY_ABI_VERSION
+
+/*
+ * Minor API version we are compiling to be compatible with.  The version
+ * Number is always increased when the API changes via: `NPY_API_VERSION`
+ * (and should maybe just track the NumPy version).
+ *
+ * If we have an internal build, we always target the current version of
+ * course.
+ *
+ * For downstream users, we default to an older version to provide them with
+ * maximum compatibility by default.  Downstream can choose to extend that
+ * default, or narrow it down if they wish to use newer API.  If you adjust
+ * this, consider the Python version support (example for 1.25.x):
+ *
+ * NumPy 1.25.x supports Python:                     3.9  3.10  3.11  (3.12)
+ * NumPy 1.19.x supports Python:      3.6  3.7  3.8  3.9
+ * NumPy 1.17.x supports Python: 3.5  3.6  3.7  3.8
+ * NumPy 1.15.x supports Python: ...  3.6  3.7
+ *
+ * Users of the stable ABI may wish to target the last Python that is not
+ * end of life.  This would be 3.8 at NumPy 1.25 release time.
+ * 1.17 as default was the choice of oldest-support-numpy at the time and
+ * has in practice no limit (compared to 1.19).  Even earlier becomes legacy.
+ */
+#if defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD
+    /* NumPy internal build, always use current version. */
+    #define NPY_FEATURE_VERSION NPY_API_VERSION
+#elif defined(NPY_TARGET_VERSION) && NPY_TARGET_VERSION
+    /* user provided a target version, use it */
+    #define NPY_FEATURE_VERSION NPY_TARGET_VERSION
+#else
+    /* Use the default (increase when dropping Python 3.11 support) */
+    #define NPY_FEATURE_VERSION NPY_1_23_API_VERSION
+#endif
+
+/* Sanity check the (requested) feature version */
+#if NPY_FEATURE_VERSION > NPY_API_VERSION
+    #error "NPY_TARGET_VERSION higher than NumPy headers!"
+#elif NPY_FEATURE_VERSION < NPY_1_15_API_VERSION
+    /* No support for irrelevant old targets, no need for error, but warn. */
+    #ifndef _MSC_VER
+        #warning "Requested NumPy target lower than supported NumPy 1.15."
+    #else
+        #define _WARN___STR2__(x) #x
+        #define _WARN___STR1__(x) _WARN___STR2__(x)
+        #define _WARN___LOC__ __FILE__ "(" _WARN___STR1__(__LINE__) ") : Warning Msg: "
+        #pragma message(_WARN___LOC__"Requested NumPy target lower than supported NumPy 1.15.")
+    #endif
+#endif
+
+/*
+ * We define a human readable translation to the Python version of NumPy
+ * for error messages (and also to allow grepping the binaries for conda).
+ */
+#if NPY_FEATURE_VERSION == NPY_1_7_API_VERSION
+    #define NPY_FEATURE_VERSION_STRING "1.7"
+#elif NPY_FEATURE_VERSION == NPY_1_8_API_VERSION
+    #define NPY_FEATURE_VERSION_STRING "1.8"
+#elif NPY_FEATURE_VERSION == NPY_1_9_API_VERSION
+    #define NPY_FEATURE_VERSION_STRING "1.9"
+#elif NPY_FEATURE_VERSION == NPY_1_10_API_VERSION  /* also 1.11, 1.12 */
+    #define NPY_FEATURE_VERSION_STRING "1.10"
+#elif NPY_FEATURE_VERSION == NPY_1_13_API_VERSION
+    #define NPY_FEATURE_VERSION_STRING "1.13"
+#elif NPY_FEATURE_VERSION == NPY_1_14_API_VERSION  /* also 1.15 */
+    #define NPY_FEATURE_VERSION_STRING "1.14"
+#elif NPY_FEATURE_VERSION == NPY_1_16_API_VERSION  /* also 1.17, 1.18, 1.19 */
+    #define NPY_FEATURE_VERSION_STRING "1.16"
+#elif NPY_FEATURE_VERSION == NPY_1_20_API_VERSION  /* also 1.21 */
+    #define NPY_FEATURE_VERSION_STRING "1.20"
+#elif NPY_FEATURE_VERSION == NPY_1_22_API_VERSION
+    #define NPY_FEATURE_VERSION_STRING "1.22"
+#elif NPY_FEATURE_VERSION == NPY_1_23_API_VERSION  /* also 1.24 */
+    #define NPY_FEATURE_VERSION_STRING "1.23"
+#elif NPY_FEATURE_VERSION == NPY_1_25_API_VERSION
+    #define NPY_FEATURE_VERSION_STRING "1.25"
+#elif NPY_FEATURE_VERSION == NPY_2_0_API_VERSION
+    #define NPY_FEATURE_VERSION_STRING "2.0"
+#elif NPY_FEATURE_VERSION == NPY_2_1_API_VERSION
+    #define NPY_FEATURE_VERSION_STRING "2.1"
+#elif NPY_FEATURE_VERSION == NPY_2_3_API_VERSION
+    #define NPY_FEATURE_VERSION_STRING "2.3"
+#else
+    #error "Missing version string define for new NumPy version."
+#endif
+
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_NPY_NUMPYCONFIG_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/LICENSE.txt b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/LICENSE.txt
new file mode 100644
index 0000000..d72a7c3
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/LICENSE.txt
@@ -0,0 +1,21 @@
+  zlib License
+  ------------
+
+  Copyright (C) 2010 - 2019 ridiculous_fish, <libdivide@ridiculousfish.com>
+  Copyright (C) 2016 - 2019 Kim Walisch, <kim.walisch@gmail.com>
+
+  This software is provided 'as-is', without any express or implied
+  warranty.  In no event will the authors be held liable for any damages
+  arising from the use of this software.
+
+  Permission is granted to anyone to use this software for any purpose,
+  including commercial applications, and to alter it and redistribute it
+  freely, subject to the following restrictions:
+
+  1. The origin of this software must not be misrepresented; you must not
+     claim that you wrote the original software. If you use this software
+     in a product, an acknowledgment in the product documentation would be
+     appreciated but is not required.
+  2. Altered source versions must be plainly marked as such, and must not be
+     misrepresented as being the original software.
+  3. This notice may not be removed or altered from any source distribution.
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/bitgen.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/bitgen.h
new file mode 100644
index 0000000..162dd5c
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/bitgen.h
@@ -0,0 +1,20 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_RANDOM_BITGEN_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_RANDOM_BITGEN_H_
+
+#pragma once
+#include <stddef.h>
+#include <stdbool.h>
+#include <stdint.h>
+
+/* Must match the declaration in numpy/random/<any>.pxd */
+
+typedef struct bitgen {
+  void *state;
+  uint64_t (*next_uint64)(void *st);
+  uint32_t (*next_uint32)(void *st);
+  double (*next_double)(void *st);
+  uint64_t (*next_raw)(void *st);
+} bitgen_t;
+
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_RANDOM_BITGEN_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/distributions.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/distributions.h
new file mode 100644
index 0000000..e7fa4bd
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/distributions.h
@@ -0,0 +1,209 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_RANDOM_DISTRIBUTIONS_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_RANDOM_DISTRIBUTIONS_H_
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <Python.h>
+#include "numpy/npy_common.h"
+#include <stddef.h>
+#include <stdbool.h>
+#include <stdint.h>
+
+#include "numpy/npy_math.h"
+#include "numpy/random/bitgen.h"
+
+/*
+ * RAND_INT_TYPE is used to share integer generators with RandomState which
+ * used long in place of int64_t. If changing a distribution that uses
+ * RAND_INT_TYPE, then the original unmodified copy must be retained for
+ * use in RandomState by copying to the legacy distributions source file.
+ */
+#ifdef NP_RANDOM_LEGACY
+#define RAND_INT_TYPE long
+#define RAND_INT_MAX LONG_MAX
+#else
+#define RAND_INT_TYPE int64_t
+#define RAND_INT_MAX INT64_MAX
+#endif
+
+#ifdef _MSC_VER
+#define DECLDIR __declspec(dllexport)
+#else
+#define DECLDIR extern
+#endif
+
+#ifndef MIN
+#define MIN(x, y) (((x) < (y)) ? x : y)
+#define MAX(x, y) (((x) > (y)) ? x : y)
+#endif
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846264338328
+#endif
+
+typedef struct s_binomial_t {
+  int has_binomial; /* !=0: following parameters initialized for binomial */
+  double psave;
+  RAND_INT_TYPE nsave;
+  double r;
+  double q;
+  double fm;
+  RAND_INT_TYPE m;
+  double p1;
+  double xm;
+  double xl;
+  double xr;
+  double c;
+  double laml;
+  double lamr;
+  double p2;
+  double p3;
+  double p4;
+} binomial_t;
+
+DECLDIR float random_standard_uniform_f(bitgen_t *bitgen_state);
+DECLDIR double random_standard_uniform(bitgen_t *bitgen_state);
+DECLDIR void random_standard_uniform_fill(bitgen_t *, npy_intp, double *);
+DECLDIR void random_standard_uniform_fill_f(bitgen_t *, npy_intp, float *);
+
+DECLDIR int64_t random_positive_int64(bitgen_t *bitgen_state);
+DECLDIR int32_t random_positive_int32(bitgen_t *bitgen_state);
+DECLDIR int64_t random_positive_int(bitgen_t *bitgen_state);
+DECLDIR uint64_t random_uint(bitgen_t *bitgen_state);
+
+DECLDIR double random_standard_exponential(bitgen_t *bitgen_state);
+DECLDIR float random_standard_exponential_f(bitgen_t *bitgen_state);
+DECLDIR void random_standard_exponential_fill(bitgen_t *, npy_intp, double *);
+DECLDIR void random_standard_exponential_fill_f(bitgen_t *, npy_intp, float *);
+DECLDIR void random_standard_exponential_inv_fill(bitgen_t *, npy_intp, double *);
+DECLDIR void random_standard_exponential_inv_fill_f(bitgen_t *, npy_intp, float *);
+
+DECLDIR double random_standard_normal(bitgen_t *bitgen_state);
+DECLDIR float random_standard_normal_f(bitgen_t *bitgen_state);
+DECLDIR void random_standard_normal_fill(bitgen_t *, npy_intp, double *);
+DECLDIR void random_standard_normal_fill_f(bitgen_t *, npy_intp, float *);
+DECLDIR double random_standard_gamma(bitgen_t *bitgen_state, double shape);
+DECLDIR float random_standard_gamma_f(bitgen_t *bitgen_state, float shape);
+
+DECLDIR double random_normal(bitgen_t *bitgen_state, double loc, double scale);
+
+DECLDIR double random_gamma(bitgen_t *bitgen_state, double shape, double scale);
+DECLDIR float random_gamma_f(bitgen_t *bitgen_state, float shape, float scale);
+
+DECLDIR double random_exponential(bitgen_t *bitgen_state, double scale);
+DECLDIR double random_uniform(bitgen_t *bitgen_state, double lower, double range);
+DECLDIR double random_beta(bitgen_t *bitgen_state, double a, double b);
+DECLDIR double random_chisquare(bitgen_t *bitgen_state, double df);
+DECLDIR double random_f(bitgen_t *bitgen_state, double dfnum, double dfden);
+DECLDIR double random_standard_cauchy(bitgen_t *bitgen_state);
+DECLDIR double random_pareto(bitgen_t *bitgen_state, double a);
+DECLDIR double random_weibull(bitgen_t *bitgen_state, double a);
+DECLDIR double random_power(bitgen_t *bitgen_state, double a);
+DECLDIR double random_laplace(bitgen_t *bitgen_state, double loc, double scale);
+DECLDIR double random_gumbel(bitgen_t *bitgen_state, double loc, double scale);
+DECLDIR double random_logistic(bitgen_t *bitgen_state, double loc, double scale);
+DECLDIR double random_lognormal(bitgen_t *bitgen_state, double mean, double sigma);
+DECLDIR double random_rayleigh(bitgen_t *bitgen_state, double mode);
+DECLDIR double random_standard_t(bitgen_t *bitgen_state, double df);
+DECLDIR double random_noncentral_chisquare(bitgen_t *bitgen_state, double df,
+                                           double nonc);
+DECLDIR double random_noncentral_f(bitgen_t *bitgen_state, double dfnum,
+                                   double dfden, double nonc);
+DECLDIR double random_wald(bitgen_t *bitgen_state, double mean, double scale);
+DECLDIR double random_vonmises(bitgen_t *bitgen_state, double mu, double kappa);
+DECLDIR double random_triangular(bitgen_t *bitgen_state, double left, double mode,
+                                 double right);
+
+DECLDIR RAND_INT_TYPE random_poisson(bitgen_t *bitgen_state, double lam);
+DECLDIR RAND_INT_TYPE random_negative_binomial(bitgen_t *bitgen_state, double n,
+                                 double p);
+
+DECLDIR int64_t random_binomial(bitgen_t *bitgen_state, double p,
+                                int64_t n, binomial_t *binomial);
+
+DECLDIR int64_t random_logseries(bitgen_t *bitgen_state, double p);
+DECLDIR int64_t random_geometric(bitgen_t *bitgen_state, double p);
+DECLDIR RAND_INT_TYPE random_geometric_search(bitgen_t *bitgen_state, double p);
+DECLDIR RAND_INT_TYPE random_zipf(bitgen_t *bitgen_state, double a);
+DECLDIR int64_t random_hypergeometric(bitgen_t *bitgen_state,
+                                      int64_t good, int64_t bad, int64_t sample);
+DECLDIR uint64_t random_interval(bitgen_t *bitgen_state, uint64_t max);
+
+/* Generate random uint64 numbers in closed interval [off, off + rng]. */
+DECLDIR uint64_t random_bounded_uint64(bitgen_t *bitgen_state, uint64_t off,
+                                       uint64_t rng, uint64_t mask,
+                                       bool use_masked);
+
+/* Generate random uint32 numbers in closed interval [off, off + rng]. */
+DECLDIR uint32_t random_buffered_bounded_uint32(bitgen_t *bitgen_state,
+                                                uint32_t off, uint32_t rng,
+                                                uint32_t mask, bool use_masked,
+                                                int *bcnt, uint32_t *buf);
+DECLDIR uint16_t random_buffered_bounded_uint16(bitgen_t *bitgen_state,
+                                                uint16_t off, uint16_t rng,
+                                                uint16_t mask, bool use_masked,
+                                                int *bcnt, uint32_t *buf);
+DECLDIR uint8_t random_buffered_bounded_uint8(bitgen_t *bitgen_state, uint8_t off,
+                                              uint8_t rng, uint8_t mask,
+                                              bool use_masked, int *bcnt,
+                                              uint32_t *buf);
+DECLDIR npy_bool random_buffered_bounded_bool(bitgen_t *bitgen_state, npy_bool off,
+                                              npy_bool rng, npy_bool mask,
+                                              bool use_masked, int *bcnt,
+                                              uint32_t *buf);
+
+DECLDIR void random_bounded_uint64_fill(bitgen_t *bitgen_state, uint64_t off,
+                                        uint64_t rng, npy_intp cnt,
+                                        bool use_masked, uint64_t *out);
+DECLDIR void random_bounded_uint32_fill(bitgen_t *bitgen_state, uint32_t off,
+                                        uint32_t rng, npy_intp cnt,
+                                        bool use_masked, uint32_t *out);
+DECLDIR void random_bounded_uint16_fill(bitgen_t *bitgen_state, uint16_t off,
+                                        uint16_t rng, npy_intp cnt,
+                                        bool use_masked, uint16_t *out);
+DECLDIR void random_bounded_uint8_fill(bitgen_t *bitgen_state, uint8_t off,
+                                       uint8_t rng, npy_intp cnt,
+                                       bool use_masked, uint8_t *out);
+DECLDIR void random_bounded_bool_fill(bitgen_t *bitgen_state, npy_bool off,
+                                      npy_bool rng, npy_intp cnt,
+                                      bool use_masked, npy_bool *out);
+
+DECLDIR void random_multinomial(bitgen_t *bitgen_state, RAND_INT_TYPE n, RAND_INT_TYPE *mnix,
+                                double *pix, npy_intp d, binomial_t *binomial);
+
+/* multivariate hypergeometric, "count" method */
+DECLDIR int random_multivariate_hypergeometric_count(bitgen_t *bitgen_state,
+                              int64_t total,
+                              size_t num_colors, int64_t *colors,
+                              int64_t nsample,
+                              size_t num_variates, int64_t *variates);
+
+/* multivariate hypergeometric, "marginals" method */
+DECLDIR void random_multivariate_hypergeometric_marginals(bitgen_t *bitgen_state,
+                                   int64_t total,
+                                   size_t num_colors, int64_t *colors,
+                                   int64_t nsample,
+                                   size_t num_variates, int64_t *variates);
+
+/* Common to legacy-distributions.c and distributions.c but not exported */
+
+RAND_INT_TYPE random_binomial_btpe(bitgen_t *bitgen_state,
+                                   RAND_INT_TYPE n,
+                                   double p,
+                                   binomial_t *binomial);
+RAND_INT_TYPE random_binomial_inversion(bitgen_t *bitgen_state,
+                                        RAND_INT_TYPE n,
+                                        double p,
+                                        binomial_t *binomial);
+double random_loggam(double x);
+static inline double next_double(bitgen_t *bitgen_state) {
+    return bitgen_state->next_double(bitgen_state->state);
+}
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_RANDOM_DISTRIBUTIONS_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/libdivide.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/libdivide.h
new file mode 100644
index 0000000..f4eb803
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/random/libdivide.h
@@ -0,0 +1,2079 @@
+// libdivide.h - Optimized integer division
+// https://libdivide.com
+//
+// Copyright (C) 2010 - 2019 ridiculous_fish, <libdivide@ridiculousfish.com>
+// Copyright (C) 2016 - 2019 Kim Walisch, <kim.walisch@gmail.com>
+//
+// libdivide is dual-licensed under the Boost or zlib licenses.
+// You may use libdivide under the terms of either of these.
+// See LICENSE.txt for more details.
+
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_LIBDIVIDE_LIBDIVIDE_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_LIBDIVIDE_LIBDIVIDE_H_
+
+#define LIBDIVIDE_VERSION "3.0"
+#define LIBDIVIDE_VERSION_MAJOR 3
+#define LIBDIVIDE_VERSION_MINOR 0
+
+#include <stdint.h>
+
+#if defined(__cplusplus)
+    #include <cstdlib>
+    #include <cstdio>
+    #include <type_traits>
+#else
+    #include <stdlib.h>
+    #include <stdio.h>
+#endif
+
+#if defined(LIBDIVIDE_AVX512)
+    #include <immintrin.h>
+#elif defined(LIBDIVIDE_AVX2)
+    #include <immintrin.h>
+#elif defined(LIBDIVIDE_SSE2)
+    #include <emmintrin.h>
+#endif
+
+#if defined(_MSC_VER)
+    #include <intrin.h>
+    // disable warning C4146: unary minus operator applied
+    // to unsigned type, result still unsigned
+    #pragma warning(disable: 4146)
+    #define LIBDIVIDE_VC
+#endif
+
+#if !defined(__has_builtin)
+    #define __has_builtin(x) 0
+#endif
+
+#if defined(__SIZEOF_INT128__)
+    #define HAS_INT128_T
+    // clang-cl on Windows does not yet support 128-bit division
+    #if !(defined(__clang__) && defined(LIBDIVIDE_VC))
+        #define HAS_INT128_DIV
+    #endif
+#endif
+
+#if defined(__x86_64__) || defined(_M_X64)
+    #define LIBDIVIDE_X86_64
+#endif
+
+#if defined(__i386__)
+    #define LIBDIVIDE_i386
+#endif
+
+#if defined(__GNUC__) || defined(__clang__)
+    #define LIBDIVIDE_GCC_STYLE_ASM
+#endif
+
+#if defined(__cplusplus) || defined(LIBDIVIDE_VC)
+    #define LIBDIVIDE_FUNCTION __FUNCTION__
+#else
+    #define LIBDIVIDE_FUNCTION __func__
+#endif
+
+#define LIBDIVIDE_ERROR(msg) \
+    do { \
+        fprintf(stderr, "libdivide.h:%d: %s(): Error: %s\n", \
+            __LINE__, LIBDIVIDE_FUNCTION, msg); \
+        abort(); \
+    } while (0)
+
+#if defined(LIBDIVIDE_ASSERTIONS_ON)
+    #define LIBDIVIDE_ASSERT(x) \
+        do { \
+            if (!(x)) { \
+                fprintf(stderr, "libdivide.h:%d: %s(): Assertion failed: %s\n", \
+                    __LINE__, LIBDIVIDE_FUNCTION, #x); \
+                abort(); \
+            } \
+        } while (0)
+#else
+    #define LIBDIVIDE_ASSERT(x)
+#endif
+
+#ifdef __cplusplus
+namespace libdivide {
+#endif
+
+// pack divider structs to prevent compilers from padding.
+// This reduces memory usage by up to 43% when using a large
+// array of libdivide dividers and improves performance
+// by up to 10% because of reduced memory bandwidth.
+#pragma pack(push, 1)
+
+struct libdivide_u32_t {
+    uint32_t magic;
+    uint8_t more;
+};
+
+struct libdivide_s32_t {
+    int32_t magic;
+    uint8_t more;
+};
+
+struct libdivide_u64_t {
+    uint64_t magic;
+    uint8_t more;
+};
+
+struct libdivide_s64_t {
+    int64_t magic;
+    uint8_t more;
+};
+
+struct libdivide_u32_branchfree_t {
+    uint32_t magic;
+    uint8_t more;
+};
+
+struct libdivide_s32_branchfree_t {
+    int32_t magic;
+    uint8_t more;
+};
+
+struct libdivide_u64_branchfree_t {
+    uint64_t magic;
+    uint8_t more;
+};
+
+struct libdivide_s64_branchfree_t {
+    int64_t magic;
+    uint8_t more;
+};
+
+#pragma pack(pop)
+
+// Explanation of the "more" field:
+//
+// * Bits 0-5 is the shift value (for shift path or mult path).
+// * Bit 6 is the add indicator for mult path.
+// * Bit 7 is set if the divisor is negative. We use bit 7 as the negative
+//   divisor indicator so that we can efficiently use sign extension to
+//   create a bitmask with all bits set to 1 (if the divisor is negative)
+//   or 0 (if the divisor is positive).
+//
+// u32: [0-4] shift value
+//      [5] ignored
+//      [6] add indicator
+//      magic number of 0 indicates shift path
+//
+// s32: [0-4] shift value
+//      [5] ignored
+//      [6] add indicator
+//      [7] indicates negative divisor
+//      magic number of 0 indicates shift path
+//
+// u64: [0-5] shift value
+//      [6] add indicator
+//      magic number of 0 indicates shift path
+//
+// s64: [0-5] shift value
+//      [6] add indicator
+//      [7] indicates negative divisor
+//      magic number of 0 indicates shift path
+//
+// In s32 and s64 branchfree modes, the magic number is negated according to
+// whether the divisor is negated. In branchfree strategy, it is not negated.
+
+enum {
+    LIBDIVIDE_32_SHIFT_MASK = 0x1F,
+    LIBDIVIDE_64_SHIFT_MASK = 0x3F,
+    LIBDIVIDE_ADD_MARKER = 0x40,
+    LIBDIVIDE_NEGATIVE_DIVISOR = 0x80
+};
+
+static inline struct libdivide_s32_t libdivide_s32_gen(int32_t d);
+static inline struct libdivide_u32_t libdivide_u32_gen(uint32_t d);
+static inline struct libdivide_s64_t libdivide_s64_gen(int64_t d);
+static inline struct libdivide_u64_t libdivide_u64_gen(uint64_t d);
+
+static inline struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d);
+static inline struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d);
+static inline struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d);
+static inline struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d);
+
+static inline int32_t  libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom);
+static inline uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom);
+static inline int64_t  libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom);
+static inline uint64_t libdivide_u64_do(uint64_t numer, const struct libdivide_u64_t *denom);
+
+static inline int32_t  libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom);
+static inline uint32_t libdivide_u32_branchfree_do(uint32_t numer, const struct libdivide_u32_branchfree_t *denom);
+static inline int64_t  libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom);
+static inline uint64_t libdivide_u64_branchfree_do(uint64_t numer, const struct libdivide_u64_branchfree_t *denom);
+
+static inline int32_t  libdivide_s32_recover(const struct libdivide_s32_t *denom);
+static inline uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom);
+static inline int64_t  libdivide_s64_recover(const struct libdivide_s64_t *denom);
+static inline uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom);
+
+static inline int32_t  libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom);
+static inline uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom);
+static inline int64_t  libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom);
+static inline uint64_t libdivide_u64_branchfree_recover(const struct libdivide_u64_branchfree_t *denom);
+
+//////// Internal Utility Functions
+
+static inline uint32_t libdivide_mullhi_u32(uint32_t x, uint32_t y) {
+    uint64_t xl = x, yl = y;
+    uint64_t rl = xl * yl;
+    return (uint32_t)(rl >> 32);
+}
+
+static inline int32_t libdivide_mullhi_s32(int32_t x, int32_t y) {
+    int64_t xl = x, yl = y;
+    int64_t rl = xl * yl;
+    // needs to be arithmetic shift
+    return (int32_t)(rl >> 32);
+}
+
+static inline uint64_t libdivide_mullhi_u64(uint64_t x, uint64_t y) {
+#if defined(LIBDIVIDE_VC) && \
+    defined(LIBDIVIDE_X86_64)
+    return __umulh(x, y);
+#elif defined(HAS_INT128_T)
+    __uint128_t xl = x, yl = y;
+    __uint128_t rl = xl * yl;
+    return (uint64_t)(rl >> 64);
+#else
+    // full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64)
+    uint32_t mask = 0xFFFFFFFF;
+    uint32_t x0 = (uint32_t)(x & mask);
+    uint32_t x1 = (uint32_t)(x >> 32);
+    uint32_t y0 = (uint32_t)(y & mask);
+    uint32_t y1 = (uint32_t)(y >> 32);
+    uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0);
+    uint64_t x0y1 = x0 * (uint64_t)y1;
+    uint64_t x1y0 = x1 * (uint64_t)y0;
+    uint64_t x1y1 = x1 * (uint64_t)y1;
+    uint64_t temp = x1y0 + x0y0_hi;
+    uint64_t temp_lo = temp & mask;
+    uint64_t temp_hi = temp >> 32;
+
+    return x1y1 + temp_hi + ((temp_lo + x0y1) >> 32);
+#endif
+}
+
+static inline int64_t libdivide_mullhi_s64(int64_t x, int64_t y) {
+#if defined(LIBDIVIDE_VC) && \
+    defined(LIBDIVIDE_X86_64)
+    return __mulh(x, y);
+#elif defined(HAS_INT128_T)
+    __int128_t xl = x, yl = y;
+    __int128_t rl = xl * yl;
+    return (int64_t)(rl >> 64);
+#else
+    // full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64)
+    uint32_t mask = 0xFFFFFFFF;
+    uint32_t x0 = (uint32_t)(x & mask);
+    uint32_t y0 = (uint32_t)(y & mask);
+    int32_t x1 = (int32_t)(x >> 32);
+    int32_t y1 = (int32_t)(y >> 32);
+    uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0);
+    int64_t t = x1 * (int64_t)y0 + x0y0_hi;
+    int64_t w1 = x0 * (int64_t)y1 + (t & mask);
+
+    return x1 * (int64_t)y1 + (t >> 32) + (w1 >> 32);
+#endif
+}
+
+static inline int32_t libdivide_count_leading_zeros32(uint32_t val) {
+#if defined(__GNUC__) || \
+    __has_builtin(__builtin_clz)
+    // Fast way to count leading zeros
+    return __builtin_clz(val);
+#elif defined(LIBDIVIDE_VC)
+    unsigned long result;
+    if (_BitScanReverse(&result, val)) {
+        return 31 - result;
+    }
+    return 0;
+#else
+    if (val == 0)
+        return 32;
+    int32_t result = 8;
+    uint32_t hi = 0xFFU << 24;
+    while ((val & hi) == 0) {
+        hi >>= 8;
+        result += 8;
+    }
+    while (val & hi) {
+        result -= 1;
+        hi <<= 1;
+    }
+    return result;
+#endif
+}
+
+static inline int32_t libdivide_count_leading_zeros64(uint64_t val) {
+#if defined(__GNUC__) || \
+    __has_builtin(__builtin_clzll)
+    // Fast way to count leading zeros
+    return __builtin_clzll(val);
+#elif defined(LIBDIVIDE_VC) && defined(_WIN64)
+    unsigned long result;
+    if (_BitScanReverse64(&result, val)) {
+        return 63 - result;
+    }
+    return 0;
+#else
+    uint32_t hi = val >> 32;
+    uint32_t lo = val & 0xFFFFFFFF;
+    if (hi != 0) return libdivide_count_leading_zeros32(hi);
+    return 32 + libdivide_count_leading_zeros32(lo);
+#endif
+}
+
+// libdivide_64_div_32_to_32: divides a 64-bit uint {u1, u0} by a 32-bit
+// uint {v}. The result must fit in 32 bits.
+// Returns the quotient directly and the remainder in *r
+static inline uint32_t libdivide_64_div_32_to_32(uint32_t u1, uint32_t u0, uint32_t v, uint32_t *r) {
+#if (defined(LIBDIVIDE_i386) || defined(LIBDIVIDE_X86_64)) && \
+     defined(LIBDIVIDE_GCC_STYLE_ASM)
+    uint32_t result;
+    __asm__("divl %[v]"
+            : "=a"(result), "=d"(*r)
+            : [v] "r"(v), "a"(u0), "d"(u1)
+            );
+    return result;
+#else
+    uint64_t n = ((uint64_t)u1 << 32) | u0;
+    uint32_t result = (uint32_t)(n / v);
+    *r = (uint32_t)(n - result * (uint64_t)v);
+    return result;
+#endif
+}
+
+// libdivide_128_div_64_to_64: divides a 128-bit uint {u1, u0} by a 64-bit
+// uint {v}. The result must fit in 64 bits.
+// Returns the quotient directly and the remainder in *r
+static uint64_t libdivide_128_div_64_to_64(uint64_t u1, uint64_t u0, uint64_t v, uint64_t *r) {
+#if defined(LIBDIVIDE_X86_64) && \
+    defined(LIBDIVIDE_GCC_STYLE_ASM)
+    uint64_t result;
+    __asm__("divq %[v]"
+            : "=a"(result), "=d"(*r)
+            : [v] "r"(v), "a"(u0), "d"(u1)
+            );
+    return result;
+#elif defined(HAS_INT128_T) && \
+      defined(HAS_INT128_DIV)
+    __uint128_t n = ((__uint128_t)u1 << 64) | u0;
+    uint64_t result = (uint64_t)(n / v);
+    *r = (uint64_t)(n - result * (__uint128_t)v);
+    return result;
+#else
+    // Code taken from Hacker's Delight:
+    // http://www.hackersdelight.org/HDcode/divlu.c.
+    // License permits inclusion here per:
+    // http://www.hackersdelight.org/permissions.htm
+
+    const uint64_t b = (1ULL << 32); // Number base (32 bits)
+    uint64_t un1, un0; // Norm. dividend LSD's
+    uint64_t vn1, vn0; // Norm. divisor digits
+    uint64_t q1, q0; // Quotient digits
+    uint64_t un64, un21, un10; // Dividend digit pairs
+    uint64_t rhat; // A remainder
+    int32_t s; // Shift amount for norm
+
+    // If overflow, set rem. to an impossible value,
+    // and return the largest possible quotient
+    if (u1 >= v) {
+        *r = (uint64_t) -1;
+        return (uint64_t) -1;
+    }
+
+    // count leading zeros
+    s = libdivide_count_leading_zeros64(v);
+    if (s > 0) {
+        // Normalize divisor
+        v = v << s;
+        un64 = (u1 << s) | (u0 >> (64 - s));
+        un10 = u0 << s; // Shift dividend left
+    } else {
+        // Avoid undefined behavior of (u0 >> 64).
+        // The behavior is undefined if the right operand is
+        // negative, or greater than or equal to the length
+        // in bits of the promoted left operand.
+        un64 = u1;
+        un10 = u0;
+    }
+
+    // Break divisor up into two 32-bit digits
+    vn1 = v >> 32;
+    vn0 = v & 0xFFFFFFFF;
+
+    // Break right half of dividend into two digits
+    un1 = un10 >> 32;
+    un0 = un10 & 0xFFFFFFFF;
+
+    // Compute the first quotient digit, q1
+    q1 = un64 / vn1;
+    rhat = un64 - q1 * vn1;
+
+    while (q1 >= b || q1 * vn0 > b * rhat + un1) {
+        q1 = q1 - 1;
+        rhat = rhat + vn1;
+        if (rhat >= b)
+            break;
+    }
+
+     // Multiply and subtract
+    un21 = un64 * b + un1 - q1 * v;
+
+    // Compute the second quotient digit
+    q0 = un21 / vn1;
+    rhat = un21 - q0 * vn1;
+
+    while (q0 >= b || q0 * vn0 > b * rhat + un0) {
+        q0 = q0 - 1;
+        rhat = rhat + vn1;
+        if (rhat >= b)
+            break;
+    }
+
+    *r = (un21 * b + un0 - q0 * v) >> s;
+    return q1 * b + q0;
+#endif
+}
+
+// Bitshift a u128 in place, left (signed_shift > 0) or right (signed_shift < 0)
+static inline void libdivide_u128_shift(uint64_t *u1, uint64_t *u0, int32_t signed_shift) {
+    if (signed_shift > 0) {
+        uint32_t shift = signed_shift;
+        *u1 <<= shift;
+        *u1 |= *u0 >> (64 - shift);
+        *u0 <<= shift;
+    }
+    else if (signed_shift < 0) {
+        uint32_t shift = -signed_shift;
+        *u0 >>= shift;
+        *u0 |= *u1 << (64 - shift);
+        *u1 >>= shift;
+    }
+}
+
+// Computes a 128 / 128 -> 64 bit division, with a 128 bit remainder.
+static uint64_t libdivide_128_div_128_to_64(uint64_t u_hi, uint64_t u_lo, uint64_t v_hi, uint64_t v_lo, uint64_t *r_hi, uint64_t *r_lo) {
+#if defined(HAS_INT128_T) && \
+    defined(HAS_INT128_DIV)
+    __uint128_t ufull = u_hi;
+    __uint128_t vfull = v_hi;
+    ufull = (ufull << 64) | u_lo;
+    vfull = (vfull << 64) | v_lo;
+    uint64_t res = (uint64_t)(ufull / vfull);
+    __uint128_t remainder = ufull - (vfull * res);
+    *r_lo = (uint64_t)remainder;
+    *r_hi = (uint64_t)(remainder >> 64);
+    return res;
+#else
+    // Adapted from "Unsigned Doubleword Division" in Hacker's Delight
+    // We want to compute u / v
+    typedef struct { uint64_t hi; uint64_t lo; } u128_t;
+    u128_t u = {u_hi, u_lo};
+    u128_t v = {v_hi, v_lo};
+
+    if (v.hi == 0) {
+        // divisor v is a 64 bit value, so we just need one 128/64 division
+        // Note that we are simpler than Hacker's Delight here, because we know
+        // the quotient fits in 64 bits whereas Hacker's Delight demands a full
+        // 128 bit quotient
+        *r_hi = 0;
+        return libdivide_128_div_64_to_64(u.hi, u.lo, v.lo, r_lo);
+    }
+    // Here v >= 2**64
+    // We know that v.hi != 0, so count leading zeros is OK
+    // We have 0 <= n <= 63
+    uint32_t n = libdivide_count_leading_zeros64(v.hi);
+
+    // Normalize the divisor so its MSB is 1
+    u128_t v1t = v;
+    libdivide_u128_shift(&v1t.hi, &v1t.lo, n);
+    uint64_t v1 = v1t.hi; // i.e. v1 = v1t >> 64
+
+    // To ensure no overflow
+    u128_t u1 = u;
+    libdivide_u128_shift(&u1.hi, &u1.lo, -1);
+
+    // Get quotient from divide unsigned insn.
+    uint64_t rem_ignored;
+    uint64_t q1 = libdivide_128_div_64_to_64(u1.hi, u1.lo, v1, &rem_ignored);
+
+    // Undo normalization and division of u by 2.
+    u128_t q0 = {0, q1};
+    libdivide_u128_shift(&q0.hi, &q0.lo, n);
+    libdivide_u128_shift(&q0.hi, &q0.lo, -63);
+
+    // Make q0 correct or too small by 1
+    // Equivalent to `if (q0 != 0) q0 = q0 - 1;`
+    if (q0.hi != 0 || q0.lo != 0) {
+        q0.hi -= (q0.lo == 0); // borrow
+        q0.lo -= 1;
+    }
+
+    // Now q0 is correct.
+    // Compute q0 * v as q0v
+    // = (q0.hi << 64 + q0.lo) * (v.hi << 64 + v.lo)
+    // = (q0.hi * v.hi << 128) + (q0.hi * v.lo << 64) +
+    //   (q0.lo * v.hi <<  64) + q0.lo * v.lo)
+    // Each term is 128 bit
+    // High half of full product (upper 128 bits!) are dropped
+    u128_t q0v = {0, 0};
+    q0v.hi = q0.hi*v.lo + q0.lo*v.hi + libdivide_mullhi_u64(q0.lo, v.lo);
+    q0v.lo = q0.lo*v.lo;
+
+    // Compute u - q0v as u_q0v
+    // This is the remainder
+    u128_t u_q0v = u;
+    u_q0v.hi -= q0v.hi + (u.lo < q0v.lo); // second term is borrow
+    u_q0v.lo -= q0v.lo;
+
+    // Check if u_q0v >= v
+    // This checks if our remainder is larger than the divisor
+    if ((u_q0v.hi > v.hi) ||
+        (u_q0v.hi == v.hi && u_q0v.lo >= v.lo)) {
+        // Increment q0
+        q0.lo += 1;
+        q0.hi += (q0.lo == 0); // carry
+
+        // Subtract v from remainder
+        u_q0v.hi -= v.hi + (u_q0v.lo < v.lo);
+        u_q0v.lo -= v.lo;
+    }
+
+    *r_hi = u_q0v.hi;
+    *r_lo = u_q0v.lo;
+
+    LIBDIVIDE_ASSERT(q0.hi == 0);
+    return q0.lo;
+#endif
+}
+
+////////// UINT32
+
+static inline struct libdivide_u32_t libdivide_internal_u32_gen(uint32_t d, int branchfree) {
+    if (d == 0) {
+        LIBDIVIDE_ERROR("divider must be != 0");
+    }
+
+    struct libdivide_u32_t result;
+    uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(d);
+
+    // Power of 2
+    if ((d & (d - 1)) == 0) {
+        // We need to subtract 1 from the shift value in case of an unsigned
+        // branchfree divider because there is a hardcoded right shift by 1
+        // in its division algorithm. Because of this we also need to add back
+        // 1 in its recovery algorithm.
+        result.magic = 0;
+        result.more = (uint8_t)(floor_log_2_d - (branchfree != 0));
+    } else {
+        uint8_t more;
+        uint32_t rem, proposed_m;
+        proposed_m = libdivide_64_div_32_to_32(1U << floor_log_2_d, 0, d, &rem);
+
+        LIBDIVIDE_ASSERT(rem > 0 && rem < d);
+        const uint32_t e = d - rem;
+
+        // This power works if e < 2**floor_log_2_d.
+        if (!branchfree && (e < (1U << floor_log_2_d))) {
+            // This power works
+            more = floor_log_2_d;
+        } else {
+            // We have to use the general 33-bit algorithm.  We need to compute
+            // (2**power) / d. However, we already have (2**(power-1))/d and
+            // its remainder.  By doubling both, and then correcting the
+            // remainder, we can compute the larger division.
+            // don't care about overflow here - in fact, we expect it
+            proposed_m += proposed_m;
+            const uint32_t twice_rem = rem + rem;
+            if (twice_rem >= d || twice_rem < rem) proposed_m += 1;
+            more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
+        }
+        result.magic = 1 + proposed_m;
+        result.more = more;
+        // result.more's shift should in general be ceil_log_2_d. But if we
+        // used the smaller power, we subtract one from the shift because we're
+        // using the smaller power. If we're using the larger power, we
+        // subtract one from the shift because it's taken care of by the add
+        // indicator. So floor_log_2_d happens to be correct in both cases.
+    }
+    return result;
+}
+
+struct libdivide_u32_t libdivide_u32_gen(uint32_t d) {
+    return libdivide_internal_u32_gen(d, 0);
+}
+
+struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d) {
+    if (d == 1) {
+        LIBDIVIDE_ERROR("branchfree divider must be != 1");
+    }
+    struct libdivide_u32_t tmp = libdivide_internal_u32_gen(d, 1);
+    struct libdivide_u32_branchfree_t ret = {tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_32_SHIFT_MASK)};
+    return ret;
+}
+
+uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        return numer >> more;
+    }
+    else {
+        uint32_t q = libdivide_mullhi_u32(denom->magic, numer);
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            uint32_t t = ((numer - q) >> 1) + q;
+            return t >> (more & LIBDIVIDE_32_SHIFT_MASK);
+        }
+        else {
+            // All upper bits are 0,
+            // don't need to mask them off.
+            return q >> more;
+        }
+    }
+}
+
+uint32_t libdivide_u32_branchfree_do(uint32_t numer, const struct libdivide_u32_branchfree_t *denom) {
+    uint32_t q = libdivide_mullhi_u32(denom->magic, numer);
+    uint32_t t = ((numer - q) >> 1) + q;
+    return t >> denom->more;
+}
+
+uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+
+    if (!denom->magic) {
+        return 1U << shift;
+    } else if (!(more & LIBDIVIDE_ADD_MARKER)) {
+        // We compute q = n/d = n*m / 2^(32 + shift)
+        // Therefore we have d = 2^(32 + shift) / m
+        // We need to ceil it.
+        // We know d is not a power of 2, so m is not a power of 2,
+        // so we can just add 1 to the floor
+        uint32_t hi_dividend = 1U << shift;
+        uint32_t rem_ignored;
+        return 1 + libdivide_64_div_32_to_32(hi_dividend, 0, denom->magic, &rem_ignored);
+    } else {
+        // Here we wish to compute d = 2^(32+shift+1)/(m+2^32).
+        // Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now
+        // Also note that shift may be as high as 31, so shift + 1 will
+        // overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and
+        // then double the quotient and remainder.
+        uint64_t half_n = 1ULL << (32 + shift);
+        uint64_t d = (1ULL << 32) | denom->magic;
+        // Note that the quotient is guaranteed <= 32 bits, but the remainder
+        // may need 33!
+        uint32_t half_q = (uint32_t)(half_n / d);
+        uint64_t rem = half_n % d;
+        // We computed 2^(32+shift)/(m+2^32)
+        // Need to double it, and then add 1 to the quotient if doubling th
+        // remainder would increase the quotient.
+        // Note that rem<<1 cannot overflow, since rem < d and d is 33 bits
+        uint32_t full_q = half_q + half_q + ((rem<<1) >= d);
+
+        // We rounded down in gen (hence +1)
+        return full_q + 1;
+    }
+}
+
+uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+
+    if (!denom->magic) {
+        return 1U << (shift + 1);
+    } else {
+        // Here we wish to compute d = 2^(32+shift+1)/(m+2^32).
+        // Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now
+        // Also note that shift may be as high as 31, so shift + 1 will
+        // overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and
+        // then double the quotient and remainder.
+        uint64_t half_n = 1ULL << (32 + shift);
+        uint64_t d = (1ULL << 32) | denom->magic;
+        // Note that the quotient is guaranteed <= 32 bits, but the remainder
+        // may need 33!
+        uint32_t half_q = (uint32_t)(half_n / d);
+        uint64_t rem = half_n % d;
+        // We computed 2^(32+shift)/(m+2^32)
+        // Need to double it, and then add 1 to the quotient if doubling th
+        // remainder would increase the quotient.
+        // Note that rem<<1 cannot overflow, since rem < d and d is 33 bits
+        uint32_t full_q = half_q + half_q + ((rem<<1) >= d);
+
+        // We rounded down in gen (hence +1)
+        return full_q + 1;
+    }
+}
+
+/////////// UINT64
+
+static inline struct libdivide_u64_t libdivide_internal_u64_gen(uint64_t d, int branchfree) {
+    if (d == 0) {
+        LIBDIVIDE_ERROR("divider must be != 0");
+    }
+
+    struct libdivide_u64_t result;
+    uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(d);
+
+    // Power of 2
+    if ((d & (d - 1)) == 0) {
+        // We need to subtract 1 from the shift value in case of an unsigned
+        // branchfree divider because there is a hardcoded right shift by 1
+        // in its division algorithm. Because of this we also need to add back
+        // 1 in its recovery algorithm.
+        result.magic = 0;
+        result.more = (uint8_t)(floor_log_2_d - (branchfree != 0));
+    } else {
+        uint64_t proposed_m, rem;
+        uint8_t more;
+        // (1 << (64 + floor_log_2_d)) / d
+        proposed_m = libdivide_128_div_64_to_64(1ULL << floor_log_2_d, 0, d, &rem);
+
+        LIBDIVIDE_ASSERT(rem > 0 && rem < d);
+        const uint64_t e = d - rem;
+
+        // This power works if e < 2**floor_log_2_d.
+        if (!branchfree && e < (1ULL << floor_log_2_d)) {
+            // This power works
+            more = floor_log_2_d;
+        } else {
+            // We have to use the general 65-bit algorithm.  We need to compute
+            // (2**power) / d. However, we already have (2**(power-1))/d and
+            // its remainder. By doubling both, and then correcting the
+            // remainder, we can compute the larger division.
+            // don't care about overflow here - in fact, we expect it
+            proposed_m += proposed_m;
+            const uint64_t twice_rem = rem + rem;
+            if (twice_rem >= d || twice_rem < rem) proposed_m += 1;
+                more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
+        }
+        result.magic = 1 + proposed_m;
+        result.more = more;
+        // result.more's shift should in general be ceil_log_2_d. But if we
+        // used the smaller power, we subtract one from the shift because we're
+        // using the smaller power. If we're using the larger power, we
+        // subtract one from the shift because it's taken care of by the add
+        // indicator. So floor_log_2_d happens to be correct in both cases,
+        // which is why we do it outside of the if statement.
+    }
+    return result;
+}
+
+struct libdivide_u64_t libdivide_u64_gen(uint64_t d) {
+    return libdivide_internal_u64_gen(d, 0);
+}
+
+struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d) {
+    if (d == 1) {
+        LIBDIVIDE_ERROR("branchfree divider must be != 1");
+    }
+    struct libdivide_u64_t tmp = libdivide_internal_u64_gen(d, 1);
+    struct libdivide_u64_branchfree_t ret = {tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_64_SHIFT_MASK)};
+    return ret;
+}
+
+uint64_t libdivide_u64_do(uint64_t numer, const struct libdivide_u64_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        return numer >> more;
+    }
+    else {
+        uint64_t q = libdivide_mullhi_u64(denom->magic, numer);
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            uint64_t t = ((numer - q) >> 1) + q;
+            return t >> (more & LIBDIVIDE_64_SHIFT_MASK);
+        }
+        else {
+             // All upper bits are 0,
+             // don't need to mask them off.
+            return q >> more;
+        }
+    }
+}
+
+uint64_t libdivide_u64_branchfree_do(uint64_t numer, const struct libdivide_u64_branchfree_t *denom) {
+    uint64_t q = libdivide_mullhi_u64(denom->magic, numer);
+    uint64_t t = ((numer - q) >> 1) + q;
+    return t >> denom->more;
+}
+
+uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+
+    if (!denom->magic) {
+        return 1ULL << shift;
+    } else if (!(more & LIBDIVIDE_ADD_MARKER)) {
+        // We compute q = n/d = n*m / 2^(64 + shift)
+        // Therefore we have d = 2^(64 + shift) / m
+        // We need to ceil it.
+        // We know d is not a power of 2, so m is not a power of 2,
+        // so we can just add 1 to the floor
+        uint64_t hi_dividend = 1ULL << shift;
+        uint64_t rem_ignored;
+        return 1 + libdivide_128_div_64_to_64(hi_dividend, 0, denom->magic, &rem_ignored);
+    } else {
+        // Here we wish to compute d = 2^(64+shift+1)/(m+2^64).
+        // Notice (m + 2^64) is a 65 bit number. This gets hairy. See
+        // libdivide_u32_recover for more on what we do here.
+        // TODO: do something better than 128 bit math
+
+        // Full n is a (potentially) 129 bit value
+        // half_n is a 128 bit value
+        // Compute the hi half of half_n. Low half is 0.
+        uint64_t half_n_hi = 1ULL << shift, half_n_lo = 0;
+        // d is a 65 bit value. The high bit is always set to 1.
+        const uint64_t d_hi = 1, d_lo = denom->magic;
+        // Note that the quotient is guaranteed <= 64 bits,
+        // but the remainder may need 65!
+        uint64_t r_hi, r_lo;
+        uint64_t half_q = libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo);
+        // We computed 2^(64+shift)/(m+2^64)
+        // Double the remainder ('dr') and check if that is larger than d
+        // Note that d is a 65 bit value, so r1 is small and so r1 + r1
+        // cannot overflow
+        uint64_t dr_lo = r_lo + r_lo;
+        uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo); // last term is carry
+        int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo);
+        uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0);
+        return full_q + 1;
+    }
+}
+
+uint64_t libdivide_u64_branchfree_recover(const struct libdivide_u64_branchfree_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+
+    if (!denom->magic) {
+        return 1ULL << (shift + 1);
+    } else {
+        // Here we wish to compute d = 2^(64+shift+1)/(m+2^64).
+        // Notice (m + 2^64) is a 65 bit number. This gets hairy. See
+        // libdivide_u32_recover for more on what we do here.
+        // TODO: do something better than 128 bit math
+
+        // Full n is a (potentially) 129 bit value
+        // half_n is a 128 bit value
+        // Compute the hi half of half_n. Low half is 0.
+        uint64_t half_n_hi = 1ULL << shift, half_n_lo = 0;
+        // d is a 65 bit value. The high bit is always set to 1.
+        const uint64_t d_hi = 1, d_lo = denom->magic;
+        // Note that the quotient is guaranteed <= 64 bits,
+        // but the remainder may need 65!
+        uint64_t r_hi, r_lo;
+        uint64_t half_q = libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo);
+        // We computed 2^(64+shift)/(m+2^64)
+        // Double the remainder ('dr') and check if that is larger than d
+        // Note that d is a 65 bit value, so r1 is small and so r1 + r1
+        // cannot overflow
+        uint64_t dr_lo = r_lo + r_lo;
+        uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo); // last term is carry
+        int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo);
+        uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0);
+        return full_q + 1;
+    }
+}
+
+/////////// SINT32
+
+static inline struct libdivide_s32_t libdivide_internal_s32_gen(int32_t d, int branchfree) {
+    if (d == 0) {
+        LIBDIVIDE_ERROR("divider must be != 0");
+    }
+
+    struct libdivide_s32_t result;
+
+    // If d is a power of 2, or negative a power of 2, we have to use a shift.
+    // This is especially important because the magic algorithm fails for -1.
+    // To check if d is a power of 2 or its inverse, it suffices to check
+    // whether its absolute value has exactly one bit set. This works even for
+    // INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set
+    // and is a power of 2.
+    uint32_t ud = (uint32_t)d;
+    uint32_t absD = (d < 0) ? -ud : ud;
+    uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(absD);
+    // check if exactly one bit is set,
+    // don't care if absD is 0 since that's divide by zero
+    if ((absD & (absD - 1)) == 0) {
+        // Branchfree and normal paths are exactly the same
+        result.magic = 0;
+        result.more = floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0);
+    } else {
+        LIBDIVIDE_ASSERT(floor_log_2_d >= 1);
+
+        uint8_t more;
+        // the dividend here is 2**(floor_log_2_d + 31), so the low 32 bit word
+        // is 0 and the high word is floor_log_2_d - 1
+        uint32_t rem, proposed_m;
+        proposed_m = libdivide_64_div_32_to_32(1U << (floor_log_2_d - 1), 0, absD, &rem);
+        const uint32_t e = absD - rem;
+
+        // We are going to start with a power of floor_log_2_d - 1.
+        // This works if works if e < 2**floor_log_2_d.
+        if (!branchfree && e < (1U << floor_log_2_d)) {
+            // This power works
+            more = floor_log_2_d - 1;
+        } else {
+            // We need to go one higher. This should not make proposed_m
+            // overflow, but it will make it negative when interpreted as an
+            // int32_t.
+            proposed_m += proposed_m;
+            const uint32_t twice_rem = rem + rem;
+            if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
+            more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
+        }
+
+        proposed_m += 1;
+        int32_t magic = (int32_t)proposed_m;
+
+        // Mark if we are negative. Note we only negate the magic number in the
+        // branchfull case.
+        if (d < 0) {
+            more |= LIBDIVIDE_NEGATIVE_DIVISOR;
+            if (!branchfree) {
+                magic = -magic;
+            }
+        }
+
+        result.more = more;
+        result.magic = magic;
+    }
+    return result;
+}
+
+struct libdivide_s32_t libdivide_s32_gen(int32_t d) {
+    return libdivide_internal_s32_gen(d, 0);
+}
+
+struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d) {
+    struct libdivide_s32_t tmp = libdivide_internal_s32_gen(d, 1);
+    struct libdivide_s32_branchfree_t result = {tmp.magic, tmp.more};
+    return result;
+}
+
+int32_t libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+
+    if (!denom->magic) {
+        uint32_t sign = (int8_t)more >> 7;
+        uint32_t mask = (1U << shift) - 1;
+        uint32_t uq = numer + ((numer >> 31) & mask);
+        int32_t q = (int32_t)uq;
+        q >>= shift;
+        q = (q ^ sign) - sign;
+        return q;
+    } else {
+        uint32_t uq = (uint32_t)libdivide_mullhi_s32(denom->magic, numer);
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // must be arithmetic shift and then sign extend
+            int32_t sign = (int8_t)more >> 7;
+            // q += (more < 0 ? -numer : numer)
+            // cast required to avoid UB
+            uq += ((uint32_t)numer ^ sign) - sign;
+        }
+        int32_t q = (int32_t)uq;
+        q >>= shift;
+        q += (q < 0);
+        return q;
+    }
+}
+
+int32_t libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+    // must be arithmetic shift and then sign extend
+    int32_t sign = (int8_t)more >> 7;
+    int32_t magic = denom->magic;
+    int32_t q = libdivide_mullhi_s32(magic, numer);
+    q += numer;
+
+    // If q is non-negative, we have nothing to do
+    // If q is negative, we want to add either (2**shift)-1 if d is a power of
+    // 2, or (2**shift) if it is not a power of 2
+    uint32_t is_power_of_2 = (magic == 0);
+    uint32_t q_sign = (uint32_t)(q >> 31);
+    q += q_sign & ((1U << shift) - is_power_of_2);
+
+    // Now arithmetic right shift
+    q >>= shift;
+    // Negate if needed
+    q = (q ^ sign) - sign;
+
+    return q;
+}
+
+int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+    if (!denom->magic) {
+        uint32_t absD = 1U << shift;
+        if (more & LIBDIVIDE_NEGATIVE_DIVISOR) {
+            absD = -absD;
+        }
+        return (int32_t)absD;
+    } else {
+        // Unsigned math is much easier
+        // We negate the magic number only in the branchfull case, and we don't
+        // know which case we're in. However we have enough information to
+        // determine the correct sign of the magic number. The divisor was
+        // negative if LIBDIVIDE_NEGATIVE_DIVISOR is set. If ADD_MARKER is set,
+        // the magic number's sign is opposite that of the divisor.
+        // We want to compute the positive magic number.
+        int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR);
+        int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER)
+            ? denom->magic > 0 : denom->magic < 0;
+
+        // Handle the power of 2 case (including branchfree)
+        if (denom->magic == 0) {
+            int32_t result = 1U << shift;
+            return negative_divisor ? -result : result;
+        }
+
+        uint32_t d = (uint32_t)(magic_was_negated ? -denom->magic : denom->magic);
+        uint64_t n = 1ULL << (32 + shift); // this shift cannot exceed 30
+        uint32_t q = (uint32_t)(n / d);
+        int32_t result = (int32_t)q;
+        result += 1;
+        return negative_divisor ? -result : result;
+    }
+}
+
+int32_t libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom) {
+    return libdivide_s32_recover((const struct libdivide_s32_t *)denom);
+}
+
+///////////// SINT64
+
+static inline struct libdivide_s64_t libdivide_internal_s64_gen(int64_t d, int branchfree) {
+    if (d == 0) {
+        LIBDIVIDE_ERROR("divider must be != 0");
+    }
+
+    struct libdivide_s64_t result;
+
+    // If d is a power of 2, or negative a power of 2, we have to use a shift.
+    // This is especially important because the magic algorithm fails for -1.
+    // To check if d is a power of 2 or its inverse, it suffices to check
+    // whether its absolute value has exactly one bit set.  This works even for
+    // INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set
+    // and is a power of 2.
+    uint64_t ud = (uint64_t)d;
+    uint64_t absD = (d < 0) ? -ud : ud;
+    uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(absD);
+    // check if exactly one bit is set,
+    // don't care if absD is 0 since that's divide by zero
+    if ((absD & (absD - 1)) == 0) {
+        // Branchfree and non-branchfree cases are the same
+        result.magic = 0;
+        result.more = floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0);
+    } else {
+        // the dividend here is 2**(floor_log_2_d + 63), so the low 64 bit word
+        // is 0 and the high word is floor_log_2_d - 1
+        uint8_t more;
+        uint64_t rem, proposed_m;
+        proposed_m = libdivide_128_div_64_to_64(1ULL << (floor_log_2_d - 1), 0, absD, &rem);
+        const uint64_t e = absD - rem;
+
+        // We are going to start with a power of floor_log_2_d - 1.
+        // This works if works if e < 2**floor_log_2_d.
+        if (!branchfree && e < (1ULL << floor_log_2_d)) {
+            // This power works
+            more = floor_log_2_d - 1;
+        } else {
+            // We need to go one higher. This should not make proposed_m
+            // overflow, but it will make it negative when interpreted as an
+            // int32_t.
+            proposed_m += proposed_m;
+            const uint64_t twice_rem = rem + rem;
+            if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
+            // note that we only set the LIBDIVIDE_NEGATIVE_DIVISOR bit if we
+            // also set ADD_MARKER this is an annoying optimization that
+            // enables algorithm #4 to avoid the mask. However we always set it
+            // in the branchfree case
+            more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
+        }
+        proposed_m += 1;
+        int64_t magic = (int64_t)proposed_m;
+
+        // Mark if we are negative
+        if (d < 0) {
+            more |= LIBDIVIDE_NEGATIVE_DIVISOR;
+            if (!branchfree) {
+                magic = -magic;
+            }
+        }
+
+        result.more = more;
+        result.magic = magic;
+    }
+    return result;
+}
+
+struct libdivide_s64_t libdivide_s64_gen(int64_t d) {
+    return libdivide_internal_s64_gen(d, 0);
+}
+
+struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d) {
+    struct libdivide_s64_t tmp = libdivide_internal_s64_gen(d, 1);
+    struct libdivide_s64_branchfree_t ret = {tmp.magic, tmp.more};
+    return ret;
+}
+
+int64_t libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+
+    if (!denom->magic) { // shift path
+        uint64_t mask = (1ULL << shift) - 1;
+        uint64_t uq = numer + ((numer >> 63) & mask);
+        int64_t q = (int64_t)uq;
+        q >>= shift;
+        // must be arithmetic shift and then sign-extend
+        int64_t sign = (int8_t)more >> 7;
+        q = (q ^ sign) - sign;
+        return q;
+    } else {
+        uint64_t uq = (uint64_t)libdivide_mullhi_s64(denom->magic, numer);
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // must be arithmetic shift and then sign extend
+            int64_t sign = (int8_t)more >> 7;
+            // q += (more < 0 ? -numer : numer)
+            // cast required to avoid UB
+            uq += ((uint64_t)numer ^ sign) - sign;
+        }
+        int64_t q = (int64_t)uq;
+        q >>= shift;
+        q += (q < 0);
+        return q;
+    }
+}
+
+int64_t libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+    // must be arithmetic shift and then sign extend
+    int64_t sign = (int8_t)more >> 7;
+    int64_t magic = denom->magic;
+    int64_t q = libdivide_mullhi_s64(magic, numer);
+    q += numer;
+
+    // If q is non-negative, we have nothing to do.
+    // If q is negative, we want to add either (2**shift)-1 if d is a power of
+    // 2, or (2**shift) if it is not a power of 2.
+    uint64_t is_power_of_2 = (magic == 0);
+    uint64_t q_sign = (uint64_t)(q >> 63);
+    q += q_sign & ((1ULL << shift) - is_power_of_2);
+
+    // Arithmetic right shift
+    q >>= shift;
+    // Negate if needed
+    q = (q ^ sign) - sign;
+
+    return q;
+}
+
+int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom) {
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+    if (denom->magic == 0) { // shift path
+        uint64_t absD = 1ULL << shift;
+        if (more & LIBDIVIDE_NEGATIVE_DIVISOR) {
+            absD = -absD;
+        }
+        return (int64_t)absD;
+    } else {
+        // Unsigned math is much easier
+        int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR);
+        int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER)
+            ? denom->magic > 0 : denom->magic < 0;
+
+        uint64_t d = (uint64_t)(magic_was_negated ? -denom->magic : denom->magic);
+        uint64_t n_hi = 1ULL << shift, n_lo = 0;
+        uint64_t rem_ignored;
+        uint64_t q = libdivide_128_div_64_to_64(n_hi, n_lo, d, &rem_ignored);
+        int64_t result = (int64_t)(q + 1);
+        if (negative_divisor) {
+            result = -result;
+        }
+        return result;
+    }
+}
+
+int64_t libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom) {
+    return libdivide_s64_recover((const struct libdivide_s64_t *)denom);
+}
+
+#if defined(LIBDIVIDE_AVX512)
+
+static inline __m512i libdivide_u32_do_vector(__m512i numers, const struct libdivide_u32_t *denom);
+static inline __m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom);
+static inline __m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom);
+static inline __m512i libdivide_s64_do_vector(__m512i numers, const struct libdivide_s64_t *denom);
+
+static inline __m512i libdivide_u32_branchfree_do_vector(__m512i numers, const struct libdivide_u32_branchfree_t *denom);
+static inline __m512i libdivide_s32_branchfree_do_vector(__m512i numers, const struct libdivide_s32_branchfree_t *denom);
+static inline __m512i libdivide_u64_branchfree_do_vector(__m512i numers, const struct libdivide_u64_branchfree_t *denom);
+static inline __m512i libdivide_s64_branchfree_do_vector(__m512i numers, const struct libdivide_s64_branchfree_t *denom);
+
+//////// Internal Utility Functions
+
+static inline __m512i libdivide_s64_signbits(__m512i v) {;
+    return _mm512_srai_epi64(v, 63);
+}
+
+static inline __m512i libdivide_s64_shift_right_vector(__m512i v, int amt) {
+    return _mm512_srai_epi64(v, amt);
+}
+
+// Here, b is assumed to contain one 32-bit value repeated.
+static inline __m512i libdivide_mullhi_u32_vector(__m512i a, __m512i b) {
+    __m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epu32(a, b), 32);
+    __m512i a1X3X = _mm512_srli_epi64(a, 32);
+    __m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0);
+    __m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epu32(a1X3X, b), mask);
+    return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3);
+}
+
+// b is one 32-bit value repeated.
+static inline __m512i libdivide_mullhi_s32_vector(__m512i a, __m512i b) {
+    __m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epi32(a, b), 32);
+    __m512i a1X3X = _mm512_srli_epi64(a, 32);
+    __m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0);
+    __m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epi32(a1X3X, b), mask);
+    return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3);
+}
+
+// Here, y is assumed to contain one 64-bit value repeated.
+// https://stackoverflow.com/a/28827013
+static inline __m512i libdivide_mullhi_u64_vector(__m512i x, __m512i y) {
+    __m512i lomask = _mm512_set1_epi64(0xffffffff);
+    __m512i xh = _mm512_shuffle_epi32(x, (_MM_PERM_ENUM) 0xB1);
+    __m512i yh = _mm512_shuffle_epi32(y, (_MM_PERM_ENUM) 0xB1);
+    __m512i w0 = _mm512_mul_epu32(x, y);
+    __m512i w1 = _mm512_mul_epu32(x, yh);
+    __m512i w2 = _mm512_mul_epu32(xh, y);
+    __m512i w3 = _mm512_mul_epu32(xh, yh);
+    __m512i w0h = _mm512_srli_epi64(w0, 32);
+    __m512i s1 = _mm512_add_epi64(w1, w0h);
+    __m512i s1l = _mm512_and_si512(s1, lomask);
+    __m512i s1h = _mm512_srli_epi64(s1, 32);
+    __m512i s2 = _mm512_add_epi64(w2, s1l);
+    __m512i s2h = _mm512_srli_epi64(s2, 32);
+    __m512i hi = _mm512_add_epi64(w3, s1h);
+            hi = _mm512_add_epi64(hi, s2h);
+
+    return hi;
+}
+
+// y is one 64-bit value repeated.
+static inline __m512i libdivide_mullhi_s64_vector(__m512i x, __m512i y) {
+    __m512i p = libdivide_mullhi_u64_vector(x, y);
+    __m512i t1 = _mm512_and_si512(libdivide_s64_signbits(x), y);
+    __m512i t2 = _mm512_and_si512(libdivide_s64_signbits(y), x);
+    p = _mm512_sub_epi64(p, t1);
+    p = _mm512_sub_epi64(p, t2);
+    return p;
+}
+
+////////// UINT32
+
+__m512i libdivide_u32_do_vector(__m512i numers, const struct libdivide_u32_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        return _mm512_srli_epi32(numers, more);
+    }
+    else {
+        __m512i q = libdivide_mullhi_u32_vector(numers, _mm512_set1_epi32(denom->magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // uint32_t t = ((numer - q) >> 1) + q;
+            // return t >> denom->shift;
+            uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+            __m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q);
+            return _mm512_srli_epi32(t, shift);
+        }
+        else {
+            return _mm512_srli_epi32(q, more);
+        }
+    }
+}
+
+__m512i libdivide_u32_branchfree_do_vector(__m512i numers, const struct libdivide_u32_branchfree_t *denom) {
+    __m512i q = libdivide_mullhi_u32_vector(numers, _mm512_set1_epi32(denom->magic));
+    __m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q);
+    return _mm512_srli_epi32(t, denom->more);
+}
+
+////////// UINT64
+
+__m512i libdivide_u64_do_vector(__m512i numers, const struct libdivide_u64_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        return _mm512_srli_epi64(numers, more);
+    }
+    else {
+        __m512i q = libdivide_mullhi_u64_vector(numers, _mm512_set1_epi64(denom->magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // uint32_t t = ((numer - q) >> 1) + q;
+            // return t >> denom->shift;
+            uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+            __m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q);
+            return _mm512_srli_epi64(t, shift);
+        }
+        else {
+            return _mm512_srli_epi64(q, more);
+        }
+    }
+}
+
+__m512i libdivide_u64_branchfree_do_vector(__m512i numers, const struct libdivide_u64_branchfree_t *denom) {
+    __m512i q = libdivide_mullhi_u64_vector(numers, _mm512_set1_epi64(denom->magic));
+    __m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q);
+    return _mm512_srli_epi64(t, denom->more);
+}
+
+////////// SINT32
+
+__m512i libdivide_s32_do_vector(__m512i numers, const struct libdivide_s32_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+        uint32_t mask = (1U << shift) - 1;
+        __m512i roundToZeroTweak = _mm512_set1_epi32(mask);
+        // q = numer + ((numer >> 31) & roundToZeroTweak);
+        __m512i q = _mm512_add_epi32(numers, _mm512_and_si512(_mm512_srai_epi32(numers, 31), roundToZeroTweak));
+        q = _mm512_srai_epi32(q, shift);
+        __m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
+        // q = (q ^ sign) - sign;
+        q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign);
+        return q;
+    }
+    else {
+        __m512i q = libdivide_mullhi_s32_vector(numers, _mm512_set1_epi32(denom->magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+             // must be arithmetic shift
+            __m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
+             // q += ((numer ^ sign) - sign);
+            q = _mm512_add_epi32(q, _mm512_sub_epi32(_mm512_xor_si512(numers, sign), sign));
+        }
+        // q >>= shift
+        q = _mm512_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
+        q = _mm512_add_epi32(q, _mm512_srli_epi32(q, 31)); // q += (q < 0)
+        return q;
+    }
+}
+
+__m512i libdivide_s32_branchfree_do_vector(__m512i numers, const struct libdivide_s32_branchfree_t *denom) {
+    int32_t magic = denom->magic;
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+     // must be arithmetic shift
+    __m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
+    __m512i q = libdivide_mullhi_s32_vector(numers, _mm512_set1_epi32(magic));
+    q = _mm512_add_epi32(q, numers); // q += numers
+
+    // If q is non-negative, we have nothing to do
+    // If q is negative, we want to add either (2**shift)-1 if d is
+    // a power of 2, or (2**shift) if it is not a power of 2
+    uint32_t is_power_of_2 = (magic == 0);
+    __m512i q_sign = _mm512_srai_epi32(q, 31); // q_sign = q >> 31
+    __m512i mask = _mm512_set1_epi32((1U << shift) - is_power_of_2);
+    q = _mm512_add_epi32(q, _mm512_and_si512(q_sign, mask)); // q = q + (q_sign & mask)
+    q = _mm512_srai_epi32(q, shift); // q >>= shift
+    q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign); // q = (q ^ sign) - sign
+    return q;
+}
+
+////////// SINT64
+
+__m512i libdivide_s64_do_vector(__m512i numers, const struct libdivide_s64_t *denom) {
+    uint8_t more = denom->more;
+    int64_t magic = denom->magic;
+    if (magic == 0) { // shift path
+        uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+        uint64_t mask = (1ULL << shift) - 1;
+        __m512i roundToZeroTweak = _mm512_set1_epi64(mask);
+        // q = numer + ((numer >> 63) & roundToZeroTweak);
+        __m512i q = _mm512_add_epi64(numers, _mm512_and_si512(libdivide_s64_signbits(numers), roundToZeroTweak));
+        q = libdivide_s64_shift_right_vector(q, shift);
+        __m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
+         // q = (q ^ sign) - sign;
+        q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign);
+        return q;
+    }
+    else {
+        __m512i q = libdivide_mullhi_s64_vector(numers, _mm512_set1_epi64(magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // must be arithmetic shift
+            __m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
+            // q += ((numer ^ sign) - sign);
+            q = _mm512_add_epi64(q, _mm512_sub_epi64(_mm512_xor_si512(numers, sign), sign));
+        }
+        // q >>= denom->mult_path.shift
+        q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK);
+        q = _mm512_add_epi64(q, _mm512_srli_epi64(q, 63)); // q += (q < 0)
+        return q;
+    }
+}
+
+__m512i libdivide_s64_branchfree_do_vector(__m512i numers, const struct libdivide_s64_branchfree_t *denom) {
+    int64_t magic = denom->magic;
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+    // must be arithmetic shift
+    __m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
+
+     // libdivide_mullhi_s64(numers, magic);
+    __m512i q = libdivide_mullhi_s64_vector(numers, _mm512_set1_epi64(magic));
+    q = _mm512_add_epi64(q, numers); // q += numers
+
+    // If q is non-negative, we have nothing to do.
+    // If q is negative, we want to add either (2**shift)-1 if d is
+    // a power of 2, or (2**shift) if it is not a power of 2.
+    uint32_t is_power_of_2 = (magic == 0);
+    __m512i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
+    __m512i mask = _mm512_set1_epi64((1ULL << shift) - is_power_of_2);
+    q = _mm512_add_epi64(q, _mm512_and_si512(q_sign, mask)); // q = q + (q_sign & mask)
+    q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift
+    q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign); // q = (q ^ sign) - sign
+    return q;
+}
+
+#elif defined(LIBDIVIDE_AVX2)
+
+static inline __m256i libdivide_u32_do_vector(__m256i numers, const struct libdivide_u32_t *denom);
+static inline __m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom);
+static inline __m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom);
+static inline __m256i libdivide_s64_do_vector(__m256i numers, const struct libdivide_s64_t *denom);
+
+static inline __m256i libdivide_u32_branchfree_do_vector(__m256i numers, const struct libdivide_u32_branchfree_t *denom);
+static inline __m256i libdivide_s32_branchfree_do_vector(__m256i numers, const struct libdivide_s32_branchfree_t *denom);
+static inline __m256i libdivide_u64_branchfree_do_vector(__m256i numers, const struct libdivide_u64_branchfree_t *denom);
+static inline __m256i libdivide_s64_branchfree_do_vector(__m256i numers, const struct libdivide_s64_branchfree_t *denom);
+
+//////// Internal Utility Functions
+
+// Implementation of _mm256_srai_epi64(v, 63) (from AVX512).
+static inline __m256i libdivide_s64_signbits(__m256i v) {
+    __m256i hiBitsDuped = _mm256_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1));
+    __m256i signBits = _mm256_srai_epi32(hiBitsDuped, 31);
+    return signBits;
+}
+
+// Implementation of _mm256_srai_epi64 (from AVX512).
+static inline __m256i libdivide_s64_shift_right_vector(__m256i v, int amt) {
+    const int b = 64 - amt;
+    __m256i m = _mm256_set1_epi64x(1ULL << (b - 1));
+    __m256i x = _mm256_srli_epi64(v, amt);
+    __m256i result = _mm256_sub_epi64(_mm256_xor_si256(x, m), m);
+    return result;
+}
+
+// Here, b is assumed to contain one 32-bit value repeated.
+static inline __m256i libdivide_mullhi_u32_vector(__m256i a, __m256i b) {
+    __m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epu32(a, b), 32);
+    __m256i a1X3X = _mm256_srli_epi64(a, 32);
+    __m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0);
+    __m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epu32(a1X3X, b), mask);
+    return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3);
+}
+
+// b is one 32-bit value repeated.
+static inline __m256i libdivide_mullhi_s32_vector(__m256i a, __m256i b) {
+    __m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epi32(a, b), 32);
+    __m256i a1X3X = _mm256_srli_epi64(a, 32);
+    __m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0);
+    __m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epi32(a1X3X, b), mask);
+    return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3);
+}
+
+// Here, y is assumed to contain one 64-bit value repeated.
+// https://stackoverflow.com/a/28827013
+static inline __m256i libdivide_mullhi_u64_vector(__m256i x, __m256i y) {
+    __m256i lomask = _mm256_set1_epi64x(0xffffffff);
+    __m256i xh = _mm256_shuffle_epi32(x, 0xB1);        // x0l, x0h, x1l, x1h
+    __m256i yh = _mm256_shuffle_epi32(y, 0xB1);        // y0l, y0h, y1l, y1h
+    __m256i w0 = _mm256_mul_epu32(x, y);               // x0l*y0l, x1l*y1l
+    __m256i w1 = _mm256_mul_epu32(x, yh);              // x0l*y0h, x1l*y1h
+    __m256i w2 = _mm256_mul_epu32(xh, y);              // x0h*y0l, x1h*y0l
+    __m256i w3 = _mm256_mul_epu32(xh, yh);             // x0h*y0h, x1h*y1h
+    __m256i w0h = _mm256_srli_epi64(w0, 32);
+    __m256i s1 = _mm256_add_epi64(w1, w0h);
+    __m256i s1l = _mm256_and_si256(s1, lomask);
+    __m256i s1h = _mm256_srli_epi64(s1, 32);
+    __m256i s2 = _mm256_add_epi64(w2, s1l);
+    __m256i s2h = _mm256_srli_epi64(s2, 32);
+    __m256i hi = _mm256_add_epi64(w3, s1h);
+            hi = _mm256_add_epi64(hi, s2h);
+
+    return hi;
+}
+
+// y is one 64-bit value repeated.
+static inline __m256i libdivide_mullhi_s64_vector(__m256i x, __m256i y) {
+    __m256i p = libdivide_mullhi_u64_vector(x, y);
+    __m256i t1 = _mm256_and_si256(libdivide_s64_signbits(x), y);
+    __m256i t2 = _mm256_and_si256(libdivide_s64_signbits(y), x);
+    p = _mm256_sub_epi64(p, t1);
+    p = _mm256_sub_epi64(p, t2);
+    return p;
+}
+
+////////// UINT32
+
+__m256i libdivide_u32_do_vector(__m256i numers, const struct libdivide_u32_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        return _mm256_srli_epi32(numers, more);
+    }
+    else {
+        __m256i q = libdivide_mullhi_u32_vector(numers, _mm256_set1_epi32(denom->magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // uint32_t t = ((numer - q) >> 1) + q;
+            // return t >> denom->shift;
+            uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+            __m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q);
+            return _mm256_srli_epi32(t, shift);
+        }
+        else {
+            return _mm256_srli_epi32(q, more);
+        }
+    }
+}
+
+__m256i libdivide_u32_branchfree_do_vector(__m256i numers, const struct libdivide_u32_branchfree_t *denom) {
+    __m256i q = libdivide_mullhi_u32_vector(numers, _mm256_set1_epi32(denom->magic));
+    __m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q);
+    return _mm256_srli_epi32(t, denom->more);
+}
+
+////////// UINT64
+
+__m256i libdivide_u64_do_vector(__m256i numers, const struct libdivide_u64_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        return _mm256_srli_epi64(numers, more);
+    }
+    else {
+        __m256i q = libdivide_mullhi_u64_vector(numers, _mm256_set1_epi64x(denom->magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // uint32_t t = ((numer - q) >> 1) + q;
+            // return t >> denom->shift;
+            uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+            __m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q);
+            return _mm256_srli_epi64(t, shift);
+        }
+        else {
+            return _mm256_srli_epi64(q, more);
+        }
+    }
+}
+
+__m256i libdivide_u64_branchfree_do_vector(__m256i numers, const struct libdivide_u64_branchfree_t *denom) {
+    __m256i q = libdivide_mullhi_u64_vector(numers, _mm256_set1_epi64x(denom->magic));
+    __m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q);
+    return _mm256_srli_epi64(t, denom->more);
+}
+
+////////// SINT32
+
+__m256i libdivide_s32_do_vector(__m256i numers, const struct libdivide_s32_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+        uint32_t mask = (1U << shift) - 1;
+        __m256i roundToZeroTweak = _mm256_set1_epi32(mask);
+        // q = numer + ((numer >> 31) & roundToZeroTweak);
+        __m256i q = _mm256_add_epi32(numers, _mm256_and_si256(_mm256_srai_epi32(numers, 31), roundToZeroTweak));
+        q = _mm256_srai_epi32(q, shift);
+        __m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
+        // q = (q ^ sign) - sign;
+        q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign);
+        return q;
+    }
+    else {
+        __m256i q = libdivide_mullhi_s32_vector(numers, _mm256_set1_epi32(denom->magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+             // must be arithmetic shift
+            __m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
+             // q += ((numer ^ sign) - sign);
+            q = _mm256_add_epi32(q, _mm256_sub_epi32(_mm256_xor_si256(numers, sign), sign));
+        }
+        // q >>= shift
+        q = _mm256_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
+        q = _mm256_add_epi32(q, _mm256_srli_epi32(q, 31)); // q += (q < 0)
+        return q;
+    }
+}
+
+__m256i libdivide_s32_branchfree_do_vector(__m256i numers, const struct libdivide_s32_branchfree_t *denom) {
+    int32_t magic = denom->magic;
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+     // must be arithmetic shift
+    __m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
+    __m256i q = libdivide_mullhi_s32_vector(numers, _mm256_set1_epi32(magic));
+    q = _mm256_add_epi32(q, numers); // q += numers
+
+    // If q is non-negative, we have nothing to do
+    // If q is negative, we want to add either (2**shift)-1 if d is
+    // a power of 2, or (2**shift) if it is not a power of 2
+    uint32_t is_power_of_2 = (magic == 0);
+    __m256i q_sign = _mm256_srai_epi32(q, 31); // q_sign = q >> 31
+    __m256i mask = _mm256_set1_epi32((1U << shift) - is_power_of_2);
+    q = _mm256_add_epi32(q, _mm256_and_si256(q_sign, mask)); // q = q + (q_sign & mask)
+    q = _mm256_srai_epi32(q, shift); // q >>= shift
+    q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign); // q = (q ^ sign) - sign
+    return q;
+}
+
+////////// SINT64
+
+__m256i libdivide_s64_do_vector(__m256i numers, const struct libdivide_s64_t *denom) {
+    uint8_t more = denom->more;
+    int64_t magic = denom->magic;
+    if (magic == 0) { // shift path
+        uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+        uint64_t mask = (1ULL << shift) - 1;
+        __m256i roundToZeroTweak = _mm256_set1_epi64x(mask);
+        // q = numer + ((numer >> 63) & roundToZeroTweak);
+        __m256i q = _mm256_add_epi64(numers, _mm256_and_si256(libdivide_s64_signbits(numers), roundToZeroTweak));
+        q = libdivide_s64_shift_right_vector(q, shift);
+        __m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
+         // q = (q ^ sign) - sign;
+        q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign);
+        return q;
+    }
+    else {
+        __m256i q = libdivide_mullhi_s64_vector(numers, _mm256_set1_epi64x(magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // must be arithmetic shift
+            __m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
+            // q += ((numer ^ sign) - sign);
+            q = _mm256_add_epi64(q, _mm256_sub_epi64(_mm256_xor_si256(numers, sign), sign));
+        }
+        // q >>= denom->mult_path.shift
+        q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK);
+        q = _mm256_add_epi64(q, _mm256_srli_epi64(q, 63)); // q += (q < 0)
+        return q;
+    }
+}
+
+__m256i libdivide_s64_branchfree_do_vector(__m256i numers, const struct libdivide_s64_branchfree_t *denom) {
+    int64_t magic = denom->magic;
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+    // must be arithmetic shift
+    __m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
+
+     // libdivide_mullhi_s64(numers, magic);
+    __m256i q = libdivide_mullhi_s64_vector(numers, _mm256_set1_epi64x(magic));
+    q = _mm256_add_epi64(q, numers); // q += numers
+
+    // If q is non-negative, we have nothing to do.
+    // If q is negative, we want to add either (2**shift)-1 if d is
+    // a power of 2, or (2**shift) if it is not a power of 2.
+    uint32_t is_power_of_2 = (magic == 0);
+    __m256i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
+    __m256i mask = _mm256_set1_epi64x((1ULL << shift) - is_power_of_2);
+    q = _mm256_add_epi64(q, _mm256_and_si256(q_sign, mask)); // q = q + (q_sign & mask)
+    q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift
+    q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign); // q = (q ^ sign) - sign
+    return q;
+}
+
+#elif defined(LIBDIVIDE_SSE2)
+
+static inline __m128i libdivide_u32_do_vector(__m128i numers, const struct libdivide_u32_t *denom);
+static inline __m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom);
+static inline __m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom);
+static inline __m128i libdivide_s64_do_vector(__m128i numers, const struct libdivide_s64_t *denom);
+
+static inline __m128i libdivide_u32_branchfree_do_vector(__m128i numers, const struct libdivide_u32_branchfree_t *denom);
+static inline __m128i libdivide_s32_branchfree_do_vector(__m128i numers, const struct libdivide_s32_branchfree_t *denom);
+static inline __m128i libdivide_u64_branchfree_do_vector(__m128i numers, const struct libdivide_u64_branchfree_t *denom);
+static inline __m128i libdivide_s64_branchfree_do_vector(__m128i numers, const struct libdivide_s64_branchfree_t *denom);
+
+//////// Internal Utility Functions
+
+// Implementation of _mm_srai_epi64(v, 63) (from AVX512).
+static inline __m128i libdivide_s64_signbits(__m128i v) {
+    __m128i hiBitsDuped = _mm_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1));
+    __m128i signBits = _mm_srai_epi32(hiBitsDuped, 31);
+    return signBits;
+}
+
+// Implementation of _mm_srai_epi64 (from AVX512).
+static inline __m128i libdivide_s64_shift_right_vector(__m128i v, int amt) {
+    const int b = 64 - amt;
+    __m128i m = _mm_set1_epi64x(1ULL << (b - 1));
+    __m128i x = _mm_srli_epi64(v, amt);
+    __m128i result = _mm_sub_epi64(_mm_xor_si128(x, m), m);
+    return result;
+}
+
+// Here, b is assumed to contain one 32-bit value repeated.
+static inline __m128i libdivide_mullhi_u32_vector(__m128i a, __m128i b) {
+    __m128i hi_product_0Z2Z = _mm_srli_epi64(_mm_mul_epu32(a, b), 32);
+    __m128i a1X3X = _mm_srli_epi64(a, 32);
+    __m128i mask = _mm_set_epi32(-1, 0, -1, 0);
+    __m128i hi_product_Z1Z3 = _mm_and_si128(_mm_mul_epu32(a1X3X, b), mask);
+    return _mm_or_si128(hi_product_0Z2Z, hi_product_Z1Z3);
+}
+
+// SSE2 does not have a signed multiplication instruction, but we can convert
+// unsigned to signed pretty efficiently. Again, b is just a 32 bit value
+// repeated four times.
+static inline __m128i libdivide_mullhi_s32_vector(__m128i a, __m128i b) {
+    __m128i p = libdivide_mullhi_u32_vector(a, b);
+    // t1 = (a >> 31) & y, arithmetic shift
+    __m128i t1 = _mm_and_si128(_mm_srai_epi32(a, 31), b);
+    __m128i t2 = _mm_and_si128(_mm_srai_epi32(b, 31), a);
+    p = _mm_sub_epi32(p, t1);
+    p = _mm_sub_epi32(p, t2);
+    return p;
+}
+
+// Here, y is assumed to contain one 64-bit value repeated.
+// https://stackoverflow.com/a/28827013
+static inline __m128i libdivide_mullhi_u64_vector(__m128i x, __m128i y) {
+    __m128i lomask = _mm_set1_epi64x(0xffffffff);
+    __m128i xh = _mm_shuffle_epi32(x, 0xB1);        // x0l, x0h, x1l, x1h
+    __m128i yh = _mm_shuffle_epi32(y, 0xB1);        // y0l, y0h, y1l, y1h
+    __m128i w0 = _mm_mul_epu32(x, y);               // x0l*y0l, x1l*y1l
+    __m128i w1 = _mm_mul_epu32(x, yh);              // x0l*y0h, x1l*y1h
+    __m128i w2 = _mm_mul_epu32(xh, y);              // x0h*y0l, x1h*y0l
+    __m128i w3 = _mm_mul_epu32(xh, yh);             // x0h*y0h, x1h*y1h
+    __m128i w0h = _mm_srli_epi64(w0, 32);
+    __m128i s1 = _mm_add_epi64(w1, w0h);
+    __m128i s1l = _mm_and_si128(s1, lomask);
+    __m128i s1h = _mm_srli_epi64(s1, 32);
+    __m128i s2 = _mm_add_epi64(w2, s1l);
+    __m128i s2h = _mm_srli_epi64(s2, 32);
+    __m128i hi = _mm_add_epi64(w3, s1h);
+            hi = _mm_add_epi64(hi, s2h);
+
+    return hi;
+}
+
+// y is one 64-bit value repeated.
+static inline __m128i libdivide_mullhi_s64_vector(__m128i x, __m128i y) {
+    __m128i p = libdivide_mullhi_u64_vector(x, y);
+    __m128i t1 = _mm_and_si128(libdivide_s64_signbits(x), y);
+    __m128i t2 = _mm_and_si128(libdivide_s64_signbits(y), x);
+    p = _mm_sub_epi64(p, t1);
+    p = _mm_sub_epi64(p, t2);
+    return p;
+}
+
+////////// UINT32
+
+__m128i libdivide_u32_do_vector(__m128i numers, const struct libdivide_u32_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        return _mm_srli_epi32(numers, more);
+    }
+    else {
+        __m128i q = libdivide_mullhi_u32_vector(numers, _mm_set1_epi32(denom->magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // uint32_t t = ((numer - q) >> 1) + q;
+            // return t >> denom->shift;
+            uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+            __m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q);
+            return _mm_srli_epi32(t, shift);
+        }
+        else {
+            return _mm_srli_epi32(q, more);
+        }
+    }
+}
+
+__m128i libdivide_u32_branchfree_do_vector(__m128i numers, const struct libdivide_u32_branchfree_t *denom) {
+    __m128i q = libdivide_mullhi_u32_vector(numers, _mm_set1_epi32(denom->magic));
+    __m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q);
+    return _mm_srli_epi32(t, denom->more);
+}
+
+////////// UINT64
+
+__m128i libdivide_u64_do_vector(__m128i numers, const struct libdivide_u64_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        return _mm_srli_epi64(numers, more);
+    }
+    else {
+        __m128i q = libdivide_mullhi_u64_vector(numers, _mm_set1_epi64x(denom->magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // uint32_t t = ((numer - q) >> 1) + q;
+            // return t >> denom->shift;
+            uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+            __m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q);
+            return _mm_srli_epi64(t, shift);
+        }
+        else {
+            return _mm_srli_epi64(q, more);
+        }
+    }
+}
+
+__m128i libdivide_u64_branchfree_do_vector(__m128i numers, const struct libdivide_u64_branchfree_t *denom) {
+    __m128i q = libdivide_mullhi_u64_vector(numers, _mm_set1_epi64x(denom->magic));
+    __m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q);
+    return _mm_srli_epi64(t, denom->more);
+}
+
+////////// SINT32
+
+__m128i libdivide_s32_do_vector(__m128i numers, const struct libdivide_s32_t *denom) {
+    uint8_t more = denom->more;
+    if (!denom->magic) {
+        uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+        uint32_t mask = (1U << shift) - 1;
+        __m128i roundToZeroTweak = _mm_set1_epi32(mask);
+        // q = numer + ((numer >> 31) & roundToZeroTweak);
+        __m128i q = _mm_add_epi32(numers, _mm_and_si128(_mm_srai_epi32(numers, 31), roundToZeroTweak));
+        q = _mm_srai_epi32(q, shift);
+        __m128i sign = _mm_set1_epi32((int8_t)more >> 7);
+        // q = (q ^ sign) - sign;
+        q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign);
+        return q;
+    }
+    else {
+        __m128i q = libdivide_mullhi_s32_vector(numers, _mm_set1_epi32(denom->magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+             // must be arithmetic shift
+            __m128i sign = _mm_set1_epi32((int8_t)more >> 7);
+             // q += ((numer ^ sign) - sign);
+            q = _mm_add_epi32(q, _mm_sub_epi32(_mm_xor_si128(numers, sign), sign));
+        }
+        // q >>= shift
+        q = _mm_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
+        q = _mm_add_epi32(q, _mm_srli_epi32(q, 31)); // q += (q < 0)
+        return q;
+    }
+}
+
+__m128i libdivide_s32_branchfree_do_vector(__m128i numers, const struct libdivide_s32_branchfree_t *denom) {
+    int32_t magic = denom->magic;
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
+     // must be arithmetic shift
+    __m128i sign = _mm_set1_epi32((int8_t)more >> 7);
+    __m128i q = libdivide_mullhi_s32_vector(numers, _mm_set1_epi32(magic));
+    q = _mm_add_epi32(q, numers); // q += numers
+
+    // If q is non-negative, we have nothing to do
+    // If q is negative, we want to add either (2**shift)-1 if d is
+    // a power of 2, or (2**shift) if it is not a power of 2
+    uint32_t is_power_of_2 = (magic == 0);
+    __m128i q_sign = _mm_srai_epi32(q, 31); // q_sign = q >> 31
+    __m128i mask = _mm_set1_epi32((1U << shift) - is_power_of_2);
+    q = _mm_add_epi32(q, _mm_and_si128(q_sign, mask)); // q = q + (q_sign & mask)
+    q = _mm_srai_epi32(q, shift); // q >>= shift
+    q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign); // q = (q ^ sign) - sign
+    return q;
+}
+
+////////// SINT64
+
+__m128i libdivide_s64_do_vector(__m128i numers, const struct libdivide_s64_t *denom) {
+    uint8_t more = denom->more;
+    int64_t magic = denom->magic;
+    if (magic == 0) { // shift path
+        uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+        uint64_t mask = (1ULL << shift) - 1;
+        __m128i roundToZeroTweak = _mm_set1_epi64x(mask);
+        // q = numer + ((numer >> 63) & roundToZeroTweak);
+        __m128i q = _mm_add_epi64(numers, _mm_and_si128(libdivide_s64_signbits(numers), roundToZeroTweak));
+        q = libdivide_s64_shift_right_vector(q, shift);
+        __m128i sign = _mm_set1_epi32((int8_t)more >> 7);
+         // q = (q ^ sign) - sign;
+        q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign);
+        return q;
+    }
+    else {
+        __m128i q = libdivide_mullhi_s64_vector(numers, _mm_set1_epi64x(magic));
+        if (more & LIBDIVIDE_ADD_MARKER) {
+            // must be arithmetic shift
+            __m128i sign = _mm_set1_epi32((int8_t)more >> 7);
+            // q += ((numer ^ sign) - sign);
+            q = _mm_add_epi64(q, _mm_sub_epi64(_mm_xor_si128(numers, sign), sign));
+        }
+        // q >>= denom->mult_path.shift
+        q = libdivide_s64_shift_right_vector(q, more & LIBDIVIDE_64_SHIFT_MASK);
+        q = _mm_add_epi64(q, _mm_srli_epi64(q, 63)); // q += (q < 0)
+        return q;
+    }
+}
+
+__m128i libdivide_s64_branchfree_do_vector(__m128i numers, const struct libdivide_s64_branchfree_t *denom) {
+    int64_t magic = denom->magic;
+    uint8_t more = denom->more;
+    uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
+    // must be arithmetic shift
+    __m128i sign = _mm_set1_epi32((int8_t)more >> 7);
+
+     // libdivide_mullhi_s64(numers, magic);
+    __m128i q = libdivide_mullhi_s64_vector(numers, _mm_set1_epi64x(magic));
+    q = _mm_add_epi64(q, numers); // q += numers
+
+    // If q is non-negative, we have nothing to do.
+    // If q is negative, we want to add either (2**shift)-1 if d is
+    // a power of 2, or (2**shift) if it is not a power of 2.
+    uint32_t is_power_of_2 = (magic == 0);
+    __m128i q_sign = libdivide_s64_signbits(q); // q_sign = q >> 63
+    __m128i mask = _mm_set1_epi64x((1ULL << shift) - is_power_of_2);
+    q = _mm_add_epi64(q, _mm_and_si128(q_sign, mask)); // q = q + (q_sign & mask)
+    q = libdivide_s64_shift_right_vector(q, shift); // q >>= shift
+    q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign); // q = (q ^ sign) - sign
+    return q;
+}
+
+#endif
+
+/////////// C++ stuff
+
+#ifdef __cplusplus
+
+// The C++ divider class is templated on both an integer type
+// (like uint64_t) and an algorithm type.
+// * BRANCHFULL is the default algorithm type.
+// * BRANCHFREE is the branchfree algorithm type.
+enum {
+    BRANCHFULL,
+    BRANCHFREE
+};
+
+#if defined(LIBDIVIDE_AVX512)
+    #define LIBDIVIDE_VECTOR_TYPE __m512i
+#elif defined(LIBDIVIDE_AVX2)
+    #define LIBDIVIDE_VECTOR_TYPE __m256i
+#elif defined(LIBDIVIDE_SSE2)
+    #define LIBDIVIDE_VECTOR_TYPE __m128i
+#endif
+
+#if !defined(LIBDIVIDE_VECTOR_TYPE)
+    #define LIBDIVIDE_DIVIDE_VECTOR(ALGO)
+#else
+    #define LIBDIVIDE_DIVIDE_VECTOR(ALGO) \
+        LIBDIVIDE_VECTOR_TYPE divide(LIBDIVIDE_VECTOR_TYPE n) const { \
+            return libdivide_##ALGO##_do_vector(n, &denom); \
+        }
+#endif
+
+// The DISPATCHER_GEN() macro generates C++ methods (for the given integer
+// and algorithm types) that redirect to libdivide's C API.
+#define DISPATCHER_GEN(T, ALGO) \
+    libdivide_##ALGO##_t denom; \
+    dispatcher() { } \
+    dispatcher(T d) \
+        : denom(libdivide_##ALGO##_gen(d)) \
+    { } \
+    T divide(T n) const { \
+        return libdivide_##ALGO##_do(n, &denom); \
+    } \
+    LIBDIVIDE_DIVIDE_VECTOR(ALGO) \
+    T recover() const { \
+        return libdivide_##ALGO##_recover(&denom); \
+    }
+
+// The dispatcher selects a specific division algorithm for a given
+// type and ALGO using partial template specialization.
+template<bool IS_INTEGRAL, bool IS_SIGNED, int SIZEOF, int ALGO> struct dispatcher { };
+
+template<> struct dispatcher<true, true, sizeof(int32_t), BRANCHFULL> { DISPATCHER_GEN(int32_t, s32) };
+template<> struct dispatcher<true, true, sizeof(int32_t), BRANCHFREE> { DISPATCHER_GEN(int32_t, s32_branchfree) };
+template<> struct dispatcher<true, false, sizeof(uint32_t), BRANCHFULL> { DISPATCHER_GEN(uint32_t, u32) };
+template<> struct dispatcher<true, false, sizeof(uint32_t), BRANCHFREE> { DISPATCHER_GEN(uint32_t, u32_branchfree) };
+template<> struct dispatcher<true, true, sizeof(int64_t), BRANCHFULL> { DISPATCHER_GEN(int64_t, s64) };
+template<> struct dispatcher<true, true, sizeof(int64_t), BRANCHFREE> { DISPATCHER_GEN(int64_t, s64_branchfree) };
+template<> struct dispatcher<true, false, sizeof(uint64_t), BRANCHFULL> { DISPATCHER_GEN(uint64_t, u64) };
+template<> struct dispatcher<true, false, sizeof(uint64_t), BRANCHFREE> { DISPATCHER_GEN(uint64_t, u64_branchfree) };
+
+// This is the main divider class for use by the user (C++ API).
+// The actual division algorithm is selected using the dispatcher struct
+// based on the integer and algorithm template parameters.
+template<typename T, int ALGO = BRANCHFULL>
+class divider {
+public:
+    // We leave the default constructor empty so that creating
+    // an array of dividers and then initializing them
+    // later doesn't slow us down.
+    divider() { }
+
+    // Constructor that takes the divisor as a parameter
+    divider(T d) : div(d) { }
+
+    // Divides n by the divisor
+    T divide(T n) const {
+        return div.divide(n);
+    }
+
+    // Recovers the divisor, returns the value that was
+    // used to initialize this divider object.
+    T recover() const {
+        return div.recover();
+    }
+
+    bool operator==(const divider<T, ALGO>& other) const {
+        return div.denom.magic == other.denom.magic &&
+               div.denom.more == other.denom.more;
+    }
+
+    bool operator!=(const divider<T, ALGO>& other) const {
+        return !(*this == other);
+    }
+
+#if defined(LIBDIVIDE_VECTOR_TYPE)
+    // Treats the vector as packed integer values with the same type as
+    // the divider (e.g. s32, u32, s64, u64) and divides each of
+    // them by the divider, returning the packed quotients.
+    LIBDIVIDE_VECTOR_TYPE divide(LIBDIVIDE_VECTOR_TYPE n) const {
+        return div.divide(n);
+    }
+#endif
+
+private:
+    // Storage for the actual divisor
+    dispatcher<std::is_integral<T>::value,
+               std::is_signed<T>::value, sizeof(T), ALGO> div;
+};
+
+// Overload of operator / for scalar division
+template<typename T, int ALGO>
+T operator/(T n, const divider<T, ALGO>& div) {
+    return div.divide(n);
+}
+
+// Overload of operator /= for scalar division
+template<typename T, int ALGO>
+T& operator/=(T& n, const divider<T, ALGO>& div) {
+    n = div.divide(n);
+    return n;
+}
+
+#if defined(LIBDIVIDE_VECTOR_TYPE)
+    // Overload of operator / for vector division
+    template<typename T, int ALGO>
+    LIBDIVIDE_VECTOR_TYPE operator/(LIBDIVIDE_VECTOR_TYPE n, const divider<T, ALGO>& div) {
+        return div.divide(n);
+    }
+    // Overload of operator /= for vector division
+    template<typename T, int ALGO>
+    LIBDIVIDE_VECTOR_TYPE& operator/=(LIBDIVIDE_VECTOR_TYPE& n, const divider<T, ALGO>& div) {
+        n = div.divide(n);
+        return n;
+    }
+#endif
+
+// libdivdie::branchfree_divider<T>
+template <typename T>
+using branchfree_divider = divider<T, BRANCHFREE>;
+
+}  // namespace libdivide
+
+#endif  // __cplusplus
+
+#endif  // NUMPY_CORE_INCLUDE_NUMPY_LIBDIVIDE_LIBDIVIDE_H_
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/ufuncobject.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/ufuncobject.h
new file mode 100644
index 0000000..f5f82b5
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/ufuncobject.h
@@ -0,0 +1,343 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_UFUNCOBJECT_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_UFUNCOBJECT_H_
+
+#include <numpy/npy_math.h>
+#include <numpy/npy_common.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/*
+ * The legacy generic inner loop for a standard element-wise or
+ * generalized ufunc.
+ */
+typedef void (*PyUFuncGenericFunction)
+            (char **args,
+             npy_intp const *dimensions,
+             npy_intp const *strides,
+             void *innerloopdata);
+
+/*
+ * The most generic one-dimensional inner loop for
+ * a masked standard element-wise ufunc. "Masked" here means that it skips
+ * doing calculations on any items for which the maskptr array has a true
+ * value.
+ */
+typedef void (PyUFunc_MaskedStridedInnerLoopFunc)(
+                char **dataptrs, npy_intp *strides,
+                char *maskptr, npy_intp mask_stride,
+                npy_intp count,
+                NpyAuxData *innerloopdata);
+
+/* Forward declaration for the type resolver and loop selector typedefs */
+struct _tagPyUFuncObject;
+
+/*
+ * Given the operands for calling a ufunc, should determine the
+ * calculation input and output data types and return an inner loop function.
+ * This function should validate that the casting rule is being followed,
+ * and fail if it is not.
+ *
+ * For backwards compatibility, the regular type resolution function does not
+ * support auxiliary data with object semantics. The type resolution call
+ * which returns a masked generic function returns a standard NpyAuxData
+ * object, for which the NPY_AUXDATA_FREE and NPY_AUXDATA_CLONE macros
+ * work.
+ *
+ * ufunc:             The ufunc object.
+ * casting:           The 'casting' parameter provided to the ufunc.
+ * operands:          An array of length (ufunc->nin + ufunc->nout),
+ *                    with the output parameters possibly NULL.
+ * type_tup:          Either NULL, or the type_tup passed to the ufunc.
+ * out_dtypes:        An array which should be populated with new
+ *                    references to (ufunc->nin + ufunc->nout) new
+ *                    dtypes, one for each input and output. These
+ *                    dtypes should all be in native-endian format.
+ *
+ * Should return 0 on success, -1 on failure (with exception set),
+ * or -2 if Py_NotImplemented should be returned.
+ */
+typedef int (PyUFunc_TypeResolutionFunc)(
+                                struct _tagPyUFuncObject *ufunc,
+                                NPY_CASTING casting,
+                                PyArrayObject **operands,
+                                PyObject *type_tup,
+                                PyArray_Descr **out_dtypes);
+
+/*
+ * This is the signature for the functions that may be assigned to the
+ * `process_core_dims_func` field of the PyUFuncObject structure.
+ * Implementation of this function is optional.  This function is only used
+ * by generalized ufuncs (i.e. those with the field `core_enabled` set to 1).
+ * The function is called by the ufunc during the processing of the arguments
+ * of a call of the ufunc. The function can check the core dimensions of the
+ * input and output arrays and return -1 with an exception set if any
+ * requirements are not satisfied. If the caller of the ufunc didn't provide
+ * output arrays, the core dimensions associated with the output arrays (i.e.
+ * those that are not also used in input arrays) will have the value -1 in
+ * `core_dim_sizes`.  This function can replace any output core dimensions
+ * that are -1 with a value that is appropriate for the ufunc.
+ *
+ * Parameter       Description
+ * --------------- ------------------------------------------------------
+ * ufunc           The ufunc object
+ * core_dim_sizes  An array with length `ufunc->core_num_dim_ix`.
+ *                 The core dimensions of the arrays passed to the ufunc
+ *                 will have been set.  If the caller of the ufunc didn't
+ *                 provide the output array(s), the output-only core
+ *                 dimensions will have the value -1.
+ *
+ * The function must not change any element in `core_dim_sizes` that is
+ * not -1 on input. Doing so will result in incorrect output from the
+ * ufunc, and could result in a crash of the Python interpreter.
+ *
+ * The function must return 0 on success, -1 on failure (with an exception
+ * set).
+ */
+typedef int (PyUFunc_ProcessCoreDimsFunc)(
+                                struct _tagPyUFuncObject *ufunc,
+                                npy_intp *core_dim_sizes);
+
+typedef struct _tagPyUFuncObject {
+        PyObject_HEAD
+        /*
+         * nin: Number of inputs
+         * nout: Number of outputs
+         * nargs: Always nin + nout (Why is it stored?)
+         */
+        int nin, nout, nargs;
+
+        /*
+         * Identity for reduction, any of PyUFunc_One, PyUFunc_Zero
+         * PyUFunc_MinusOne, PyUFunc_None, PyUFunc_ReorderableNone,
+         * PyUFunc_IdentityValue.
+         */
+        int identity;
+
+        /* Array of one-dimensional core loops */
+        PyUFuncGenericFunction *functions;
+        /* Array of funcdata that gets passed into the functions */
+        void *const *data;
+        /* The number of elements in 'functions' and 'data' */
+        int ntypes;
+
+        /* Used to be unused field 'check_return' */
+        int reserved1;
+
+        /* The name of the ufunc */
+        const char *name;
+
+        /* Array of type numbers, of size ('nargs' * 'ntypes') */
+        const char *types;
+
+        /* Documentation string */
+        const char *doc;
+
+        void *ptr;
+        PyObject *obj;
+        PyObject *userloops;
+
+        /* generalized ufunc parameters */
+
+        /* 0 for scalar ufunc; 1 for generalized ufunc */
+        int core_enabled;
+        /* number of distinct dimension names in signature */
+        int core_num_dim_ix;
+
+        /*
+         * dimension indices of input/output argument k are stored in
+         * core_dim_ixs[core_offsets[k]..core_offsets[k]+core_num_dims[k]-1]
+         */
+
+        /* numbers of core dimensions of each argument */
+        int *core_num_dims;
+        /*
+         * dimension indices in a flatted form; indices
+         * are in the range of [0,core_num_dim_ix)
+         */
+        int *core_dim_ixs;
+        /*
+         * positions of 1st core dimensions of each
+         * argument in core_dim_ixs, equivalent to cumsum(core_num_dims)
+         */
+        int *core_offsets;
+        /* signature string for printing purpose */
+        char *core_signature;
+
+        /*
+         * A function which resolves the types and fills an array
+         * with the dtypes for the inputs and outputs.
+         */
+        PyUFunc_TypeResolutionFunc *type_resolver;
+
+        /* A dictionary to monkeypatch ufuncs */
+        PyObject *dict;
+
+        /*
+         * This was blocked off to be the "new" inner loop selector in 1.7,
+         * but this was never implemented. (This is also why the above
+         * selector is called the "legacy" selector.)
+         */
+        #ifndef Py_LIMITED_API
+            vectorcallfunc vectorcall;
+        #else
+            void *vectorcall;
+        #endif
+
+        /* Was previously the `PyUFunc_MaskedInnerLoopSelectionFunc` */
+        void *reserved3;
+
+        /*
+         * List of flags for each operand when ufunc is called by nditer object.
+         * These flags will be used in addition to the default flags for each
+         * operand set by nditer object.
+         */
+        npy_uint32 *op_flags;
+
+        /*
+         * List of global flags used when ufunc is called by nditer object.
+         * These flags will be used in addition to the default global flags
+         * set by nditer object.
+         */
+        npy_uint32 iter_flags;
+
+        /* New in NPY_API_VERSION 0x0000000D and above */
+    #if NPY_FEATURE_VERSION >= NPY_1_16_API_VERSION
+        /*
+         * for each core_num_dim_ix distinct dimension names,
+         * the possible "frozen" size (-1 if not frozen).
+         */
+        npy_intp *core_dim_sizes;
+
+        /*
+         * for each distinct core dimension, a set of UFUNC_CORE_DIM* flags
+         */
+        npy_uint32 *core_dim_flags;
+
+        /* Identity for reduction, when identity == PyUFunc_IdentityValue */
+        PyObject *identity_value;
+    #endif  /* NPY_FEATURE_VERSION >= NPY_1_16_API_VERSION */
+
+        /* New in NPY_API_VERSION 0x0000000F and above */
+    #if NPY_FEATURE_VERSION >= NPY_1_22_API_VERSION
+        /* New private fields related to dispatching */
+        void *_dispatch_cache;
+        /* A PyListObject of `(tuple of DTypes, ArrayMethod/Promoter)` */
+        PyObject *_loops;
+    #endif
+    #if NPY_FEATURE_VERSION >= NPY_2_1_API_VERSION
+        /*
+         * Optional function to process core dimensions of a gufunc.
+         */
+        PyUFunc_ProcessCoreDimsFunc *process_core_dims_func;
+    #endif
+} PyUFuncObject;
+
+#include "arrayobject.h"
+/* Generalized ufunc; 0x0001 reserved for possible use as CORE_ENABLED */
+/* the core dimension's size will be determined by the operands. */
+#define UFUNC_CORE_DIM_SIZE_INFERRED 0x0002
+/* the core dimension may be absent */
+#define UFUNC_CORE_DIM_CAN_IGNORE 0x0004
+/* flags inferred during execution */
+#define UFUNC_CORE_DIM_MISSING 0x00040000
+
+
+#define UFUNC_OBJ_ISOBJECT      1
+#define UFUNC_OBJ_NEEDS_API     2
+
+
+#if NPY_ALLOW_THREADS
+#define NPY_LOOP_BEGIN_THREADS do {if (!(loop->obj & UFUNC_OBJ_NEEDS_API)) _save = PyEval_SaveThread();} while (0);
+#define NPY_LOOP_END_THREADS   do {if (!(loop->obj & UFUNC_OBJ_NEEDS_API)) PyEval_RestoreThread(_save);} while (0);
+#else
+#define NPY_LOOP_BEGIN_THREADS
+#define NPY_LOOP_END_THREADS
+#endif
+
+/*
+ * UFunc has unit of 0, and the order of operations can be reordered
+ * This case allows reduction with multiple axes at once.
+ */
+#define PyUFunc_Zero 0
+/*
+ * UFunc has unit of 1, and the order of operations can be reordered
+ * This case allows reduction with multiple axes at once.
+ */
+#define PyUFunc_One 1
+/*
+ * UFunc has unit of -1, and the order of operations can be reordered
+ * This case allows reduction with multiple axes at once. Intended for
+ * bitwise_and reduction.
+ */
+#define PyUFunc_MinusOne 2
+/*
+ * UFunc has no unit, and the order of operations cannot be reordered.
+ * This case does not allow reduction with multiple axes at once.
+ */
+#define PyUFunc_None -1
+/*
+ * UFunc has no unit, and the order of operations can be reordered
+ * This case allows reduction with multiple axes at once.
+ */
+#define PyUFunc_ReorderableNone -2
+/*
+ * UFunc unit is an identity_value, and the order of operations can be reordered
+ * This case allows reduction with multiple axes at once.
+ */
+#define PyUFunc_IdentityValue -3
+
+
+#define UFUNC_REDUCE 0
+#define UFUNC_ACCUMULATE 1
+#define UFUNC_REDUCEAT 2
+#define UFUNC_OUTER 3
+
+
+typedef struct {
+        int nin;
+        int nout;
+        PyObject *callable;
+} PyUFunc_PyFuncData;
+
+/* A linked-list of function information for
+   user-defined 1-d loops.
+ */
+typedef struct _loop1d_info {
+        PyUFuncGenericFunction func;
+        void *data;
+        int *arg_types;
+        struct _loop1d_info *next;
+        int nargs;
+        PyArray_Descr **arg_dtypes;
+} PyUFunc_Loop1d;
+
+
+#define UFUNC_PYVALS_NAME "UFUNC_PYVALS"
+
+/* THESE MACROS ARE DEPRECATED.
+ * Use npy_set_floatstatus_* in the npymath library.
+ */
+#define UFUNC_FPE_DIVIDEBYZERO  NPY_FPE_DIVIDEBYZERO
+#define UFUNC_FPE_OVERFLOW      NPY_FPE_OVERFLOW
+#define UFUNC_FPE_UNDERFLOW     NPY_FPE_UNDERFLOW
+#define UFUNC_FPE_INVALID       NPY_FPE_INVALID
+
+/* Make sure it gets defined if it isn't already */
+#ifndef UFUNC_NOFPE
+/* Clear the floating point exception default of Borland C++ */
+#if defined(__BORLANDC__)
+#define UFUNC_NOFPE _control87(MCW_EM, MCW_EM);
+#else
+#define UFUNC_NOFPE
+#endif
+#endif
+
+#include "__ufunc_api.h"
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_UFUNCOBJECT_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/utils.h b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/utils.h
new file mode 100644
index 0000000..97f0609
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/include/numpy/utils.h
@@ -0,0 +1,37 @@
+#ifndef NUMPY_CORE_INCLUDE_NUMPY_UTILS_H_
+#define NUMPY_CORE_INCLUDE_NUMPY_UTILS_H_
+
+#ifndef __COMP_NPY_UNUSED
+    #if defined(__GNUC__)
+        #define __COMP_NPY_UNUSED __attribute__ ((__unused__))
+    #elif defined(__ICC)
+        #define __COMP_NPY_UNUSED __attribute__ ((__unused__))
+    #elif defined(__clang__)
+        #define __COMP_NPY_UNUSED __attribute__ ((unused))
+    #else
+        #define __COMP_NPY_UNUSED
+    #endif
+#endif
+
+#if defined(__GNUC__) || defined(__ICC) || defined(__clang__)
+    #define NPY_DECL_ALIGNED(x) __attribute__ ((aligned (x)))
+#elif defined(_MSC_VER)
+    #define NPY_DECL_ALIGNED(x) __declspec(align(x))
+#else
+    #define NPY_DECL_ALIGNED(x)
+#endif
+
+/* Use this to tag a variable as not used. It will remove unused variable
+ * warning on support platforms (see __COM_NPY_UNUSED) and mangle the variable
+ * to avoid accidental use */
+#define NPY_UNUSED(x) __NPY_UNUSED_TAGGED ## x __COMP_NPY_UNUSED
+#define NPY_EXPAND(x) x
+
+#define NPY_STRINGIFY(x) #x
+#define NPY_TOSTRING(x) NPY_STRINGIFY(x)
+
+#define NPY_CAT__(a, b) a ## b
+#define NPY_CAT_(a, b) NPY_CAT__(a, b)
+#define NPY_CAT(a, b) NPY_CAT_(a, b)
+
+#endif  /* NUMPY_CORE_INCLUDE_NUMPY_UTILS_H_ */
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/lib/libnpymath.a b/.venv/lib/python3.12/site-packages/numpy/_core/lib/libnpymath.a
new file mode 100644
index 0000000..f8d561d
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/lib/libnpymath.a
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/lib/npy-pkg-config/mlib.ini b/.venv/lib/python3.12/site-packages/numpy/_core/lib/npy-pkg-config/mlib.ini
new file mode 100644
index 0000000..5840f5e
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/lib/npy-pkg-config/mlib.ini
@@ -0,0 +1,12 @@
+[meta]
+Name = mlib
+Description = Math library used with this version of numpy
+Version = 1.0
+
+[default]
+Libs=-lm
+Cflags=
+
+[msvc]
+Libs=m.lib
+Cflags=
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/lib/npy-pkg-config/npymath.ini b/.venv/lib/python3.12/site-packages/numpy/_core/lib/npy-pkg-config/npymath.ini
new file mode 100644
index 0000000..8d879e3
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/lib/npy-pkg-config/npymath.ini
@@ -0,0 +1,20 @@
+[meta]
+Name=npymath
+Description=Portable, core math library implementing C99 standard
+Version=0.1
+
+[variables]
+pkgname=numpy._core
+prefix=${pkgdir}
+libdir=${prefix}/lib
+includedir=${prefix}/include
+
+[default]
+Libs=-L${libdir} -lnpymath
+Cflags=-I${includedir}
+Requires=mlib
+
+[msvc]
+Libs=/LIBPATH:${libdir} npymath.lib
+Cflags=/INCLUDE:${includedir}
+Requires=mlib
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/lib/pkgconfig/numpy.pc b/.venv/lib/python3.12/site-packages/numpy/_core/lib/pkgconfig/numpy.pc
new file mode 100644
index 0000000..3a4fdbc
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/lib/pkgconfig/numpy.pc
@@ -0,0 +1,7 @@
+prefix=${pcfiledir}/../..
+includedir=${prefix}/include
+
+Name: numpy
+Description: NumPy is the fundamental package for scientific computing with Python.
+Version: 2.3.2
+Cflags: -I${includedir}
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/memmap.py b/.venv/lib/python3.12/site-packages/numpy/_core/memmap.py
new file mode 100644
index 0000000..8cfa7f9
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/memmap.py
@@ -0,0 +1,363 @@
+import operator
+from contextlib import nullcontext
+
+import numpy as np
+from numpy._utils import set_module
+
+from .numeric import dtype, ndarray, uint8
+
+__all__ = ['memmap']
+
+dtypedescr = dtype
+valid_filemodes = ["r", "c", "r+", "w+"]
+writeable_filemodes = ["r+", "w+"]
+
+mode_equivalents = {
+    "readonly": "r",
+    "copyonwrite": "c",
+    "readwrite": "r+",
+    "write": "w+"
+    }
+
+
+@set_module('numpy')
+class memmap(ndarray):
+    """Create a memory-map to an array stored in a *binary* file on disk.
+
+    Memory-mapped files are used for accessing small segments of large files
+    on disk, without reading the entire file into memory.  NumPy's
+    memmap's are array-like objects.  This differs from Python's ``mmap``
+    module, which uses file-like objects.
+
+    This subclass of ndarray has some unpleasant interactions with
+    some operations, because it doesn't quite fit properly as a subclass.
+    An alternative to using this subclass is to create the ``mmap``
+    object yourself, then create an ndarray with ndarray.__new__ directly,
+    passing the object created in its 'buffer=' parameter.
+
+    This class may at some point be turned into a factory function
+    which returns a view into an mmap buffer.
+
+    Flush the memmap instance to write the changes to the file. Currently there
+    is no API to close the underlying ``mmap``. It is tricky to ensure the
+    resource is actually closed, since it may be shared between different
+    memmap instances.
+
+
+    Parameters
+    ----------
+    filename : str, file-like object, or pathlib.Path instance
+        The file name or file object to be used as the array data buffer.
+    dtype : data-type, optional
+        The data-type used to interpret the file contents.
+        Default is `uint8`.
+    mode : {'r+', 'r', 'w+', 'c'}, optional
+        The file is opened in this mode:
+
+        +------+-------------------------------------------------------------+
+        | 'r'  | Open existing file for reading only.                        |
+        +------+-------------------------------------------------------------+
+        | 'r+' | Open existing file for reading and writing.                 |
+        +------+-------------------------------------------------------------+
+        | 'w+' | Create or overwrite existing file for reading and writing.  |
+        |      | If ``mode == 'w+'`` then `shape` must also be specified.    |
+        +------+-------------------------------------------------------------+
+        | 'c'  | Copy-on-write: assignments affect data in memory, but       |
+        |      | changes are not saved to disk.  The file on disk is         |
+        |      | read-only.                                                  |
+        +------+-------------------------------------------------------------+
+
+        Default is 'r+'.
+    offset : int, optional
+        In the file, array data starts at this offset. Since `offset` is
+        measured in bytes, it should normally be a multiple of the byte-size
+        of `dtype`. When ``mode != 'r'``, even positive offsets beyond end of
+        file are valid; The file will be extended to accommodate the
+        additional data. By default, ``memmap`` will start at the beginning of
+        the file, even if ``filename`` is a file pointer ``fp`` and
+        ``fp.tell() != 0``.
+    shape : int or sequence of ints, optional
+        The desired shape of the array. If ``mode == 'r'`` and the number
+        of remaining bytes after `offset` is not a multiple of the byte-size
+        of `dtype`, you must specify `shape`. By default, the returned array
+        will be 1-D with the number of elements determined by file size
+        and data-type.
+
+        .. versionchanged:: 2.0
+         The shape parameter can now be any integer sequence type, previously
+         types were limited to tuple and int.
+
+    order : {'C', 'F'}, optional
+        Specify the order of the ndarray memory layout:
+        :term:`row-major`, C-style or :term:`column-major`,
+        Fortran-style.  This only has an effect if the shape is
+        greater than 1-D.  The default order is 'C'.
+
+    Attributes
+    ----------
+    filename : str or pathlib.Path instance
+        Path to the mapped file.
+    offset : int
+        Offset position in the file.
+    mode : str
+        File mode.
+
+    Methods
+    -------
+    flush
+        Flush any changes in memory to file on disk.
+        When you delete a memmap object, flush is called first to write
+        changes to disk.
+
+
+    See also
+    --------
+    lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file.
+
+    Notes
+    -----
+    The memmap object can be used anywhere an ndarray is accepted.
+    Given a memmap ``fp``, ``isinstance(fp, numpy.ndarray)`` returns
+    ``True``.
+
+    Memory-mapped files cannot be larger than 2GB on 32-bit systems.
+
+    When a memmap causes a file to be created or extended beyond its
+    current size in the filesystem, the contents of the new part are
+    unspecified. On systems with POSIX filesystem semantics, the extended
+    part will be filled with zero bytes.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> data = np.arange(12, dtype='float32')
+    >>> data.resize((3,4))
+
+    This example uses a temporary file so that doctest doesn't write
+    files to your directory. You would use a 'normal' filename.
+
+    >>> from tempfile import mkdtemp
+    >>> import os.path as path
+    >>> filename = path.join(mkdtemp(), 'newfile.dat')
+
+    Create a memmap with dtype and shape that matches our data:
+
+    >>> fp = np.memmap(filename, dtype='float32', mode='w+', shape=(3,4))
+    >>> fp
+    memmap([[0., 0., 0., 0.],
+            [0., 0., 0., 0.],
+            [0., 0., 0., 0.]], dtype=float32)
+
+    Write data to memmap array:
+
+    >>> fp[:] = data[:]
+    >>> fp
+    memmap([[  0.,   1.,   2.,   3.],
+            [  4.,   5.,   6.,   7.],
+            [  8.,   9.,  10.,  11.]], dtype=float32)
+
+    >>> fp.filename == path.abspath(filename)
+    True
+
+    Flushes memory changes to disk in order to read them back
+
+    >>> fp.flush()
+
+    Load the memmap and verify data was stored:
+
+    >>> newfp = np.memmap(filename, dtype='float32', mode='r', shape=(3,4))
+    >>> newfp
+    memmap([[  0.,   1.,   2.,   3.],
+            [  4.,   5.,   6.,   7.],
+            [  8.,   9.,  10.,  11.]], dtype=float32)
+
+    Read-only memmap:
+
+    >>> fpr = np.memmap(filename, dtype='float32', mode='r', shape=(3,4))
+    >>> fpr.flags.writeable
+    False
+
+    Copy-on-write memmap:
+
+    >>> fpc = np.memmap(filename, dtype='float32', mode='c', shape=(3,4))
+    >>> fpc.flags.writeable
+    True
+
+    It's possible to assign to copy-on-write array, but values are only
+    written into the memory copy of the array, and not written to disk:
+
+    >>> fpc
+    memmap([[  0.,   1.,   2.,   3.],
+            [  4.,   5.,   6.,   7.],
+            [  8.,   9.,  10.,  11.]], dtype=float32)
+    >>> fpc[0,:] = 0
+    >>> fpc
+    memmap([[  0.,   0.,   0.,   0.],
+            [  4.,   5.,   6.,   7.],
+            [  8.,   9.,  10.,  11.]], dtype=float32)
+
+    File on disk is unchanged:
+
+    >>> fpr
+    memmap([[  0.,   1.,   2.,   3.],
+            [  4.,   5.,   6.,   7.],
+            [  8.,   9.,  10.,  11.]], dtype=float32)
+
+    Offset into a memmap:
+
+    >>> fpo = np.memmap(filename, dtype='float32', mode='r', offset=16)
+    >>> fpo
+    memmap([  4.,   5.,   6.,   7.,   8.,   9.,  10.,  11.], dtype=float32)
+
+    """
+
+    __array_priority__ = -100.0
+
+    def __new__(subtype, filename, dtype=uint8, mode='r+', offset=0,
+                shape=None, order='C'):
+        # Import here to minimize 'import numpy' overhead
+        import mmap
+        import os.path
+        try:
+            mode = mode_equivalents[mode]
+        except KeyError as e:
+            if mode not in valid_filemodes:
+                all_modes = valid_filemodes + list(mode_equivalents.keys())
+                raise ValueError(
+                    f"mode must be one of {all_modes!r} (got {mode!r})"
+                ) from None
+
+        if mode == 'w+' and shape is None:
+            raise ValueError("shape must be given if mode == 'w+'")
+
+        if hasattr(filename, 'read'):
+            f_ctx = nullcontext(filename)
+        else:
+            f_ctx = open(
+                os.fspath(filename),
+                ('r' if mode == 'c' else mode) + 'b'
+            )
+
+        with f_ctx as fid:
+            fid.seek(0, 2)
+            flen = fid.tell()
+            descr = dtypedescr(dtype)
+            _dbytes = descr.itemsize
+
+            if shape is None:
+                bytes = flen - offset
+                if bytes % _dbytes:
+                    raise ValueError("Size of available data is not a "
+                            "multiple of the data-type size.")
+                size = bytes // _dbytes
+                shape = (size,)
+            else:
+                if not isinstance(shape, (tuple, list)):
+                    try:
+                        shape = [operator.index(shape)]
+                    except TypeError:
+                        pass
+                shape = tuple(shape)
+                size = np.intp(1)  # avoid overflows
+                for k in shape:
+                    size *= k
+
+            bytes = int(offset + size * _dbytes)
+
+            if mode in ('w+', 'r+'):
+                # gh-27723
+                # if bytes == 0, we write out 1 byte to allow empty memmap.
+                bytes = max(bytes, 1)
+                if flen < bytes:
+                    fid.seek(bytes - 1, 0)
+                    fid.write(b'\0')
+                    fid.flush()
+
+            if mode == 'c':
+                acc = mmap.ACCESS_COPY
+            elif mode == 'r':
+                acc = mmap.ACCESS_READ
+            else:
+                acc = mmap.ACCESS_WRITE
+
+            start = offset - offset % mmap.ALLOCATIONGRANULARITY
+            bytes -= start
+            # bytes == 0 is problematic as in mmap length=0 maps the full file.
+            # See PR gh-27723 for a more detailed explanation.
+            if bytes == 0 and start > 0:
+                bytes += mmap.ALLOCATIONGRANULARITY
+                start -= mmap.ALLOCATIONGRANULARITY
+            array_offset = offset - start
+            mm = mmap.mmap(fid.fileno(), bytes, access=acc, offset=start)
+
+            self = ndarray.__new__(subtype, shape, dtype=descr, buffer=mm,
+                                   offset=array_offset, order=order)
+            self._mmap = mm
+            self.offset = offset
+            self.mode = mode
+
+            if isinstance(filename, os.PathLike):
+                # special case - if we were constructed with a pathlib.path,
+                # then filename is a path object, not a string
+                self.filename = filename.resolve()
+            elif hasattr(fid, "name") and isinstance(fid.name, str):
+                # py3 returns int for TemporaryFile().name
+                self.filename = os.path.abspath(fid.name)
+            # same as memmap copies (e.g. memmap + 1)
+            else:
+                self.filename = None
+
+        return self
+
+    def __array_finalize__(self, obj):
+        if hasattr(obj, '_mmap') and np.may_share_memory(self, obj):
+            self._mmap = obj._mmap
+            self.filename = obj.filename
+            self.offset = obj.offset
+            self.mode = obj.mode
+        else:
+            self._mmap = None
+            self.filename = None
+            self.offset = None
+            self.mode = None
+
+    def flush(self):
+        """
+        Write any changes in the array to the file on disk.
+
+        For further information, see `memmap`.
+
+        Parameters
+        ----------
+        None
+
+        See Also
+        --------
+        memmap
+
+        """
+        if self.base is not None and hasattr(self.base, 'flush'):
+            self.base.flush()
+
+    def __array_wrap__(self, arr, context=None, return_scalar=False):
+        arr = super().__array_wrap__(arr, context)
+
+        # Return a memmap if a memmap was given as the output of the
+        # ufunc. Leave the arr class unchanged if self is not a memmap
+        # to keep original memmap subclasses behavior
+        if self is arr or type(self) is not memmap:
+            return arr
+
+        # Return scalar instead of 0d memmap, e.g. for np.sum with
+        # axis=None (note that subclasses will not reach here)
+        if return_scalar:
+            return arr[()]
+
+        # Return ndarray otherwise
+        return arr.view(np.ndarray)
+
+    def __getitem__(self, index):
+        res = super().__getitem__(index)
+        if type(res) is memmap and res._mmap is None:
+            return res.view(type=ndarray)
+        return res
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/memmap.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/memmap.pyi
new file mode 100644
index 0000000..0b31328
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/memmap.pyi
@@ -0,0 +1,3 @@
+from numpy import memmap
+
+__all__ = ["memmap"]
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/multiarray.py b/.venv/lib/python3.12/site-packages/numpy/_core/multiarray.py
new file mode 100644
index 0000000..236ca7e
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/multiarray.py
@@ -0,0 +1,1762 @@
+"""
+Create the numpy._core.multiarray namespace for backward compatibility.
+In v1.16 the multiarray and umath c-extension modules were merged into
+a single _multiarray_umath extension module. So we replicate the old
+namespace by importing from the extension module.
+
+"""
+
+import functools
+
+from . import _multiarray_umath, overrides
+from ._multiarray_umath import *  # noqa: F403
+
+# These imports are needed for backward compatibility,
+# do not change them. issue gh-15518
+# _get_ndarray_c_version is semi-public, on purpose not added to __all__
+from ._multiarray_umath import (  # noqa: F401
+    _ARRAY_API,
+    _flagdict,
+    _get_madvise_hugepage,
+    _get_ndarray_c_version,
+    _monotonicity,
+    _place,
+    _reconstruct,
+    _set_madvise_hugepage,
+    _vec_string,
+    from_dlpack,
+)
+
+__all__ = [
+    '_ARRAY_API', 'ALLOW_THREADS', 'BUFSIZE', 'CLIP', 'DATETIMEUNITS',
+    'ITEM_HASOBJECT', 'ITEM_IS_POINTER', 'LIST_PICKLE', 'MAXDIMS',
+    'MAY_SHARE_BOUNDS', 'MAY_SHARE_EXACT', 'NEEDS_INIT', 'NEEDS_PYAPI',
+    'RAISE', 'USE_GETITEM', 'USE_SETITEM', 'WRAP',
+    '_flagdict', 'from_dlpack', '_place', '_reconstruct', '_vec_string',
+    '_monotonicity', 'add_docstring', 'arange', 'array', 'asarray',
+    'asanyarray', 'ascontiguousarray', 'asfortranarray', 'bincount',
+    'broadcast', 'busday_count', 'busday_offset', 'busdaycalendar', 'can_cast',
+    'compare_chararrays', 'concatenate', 'copyto', 'correlate', 'correlate2',
+    'count_nonzero', 'c_einsum', 'datetime_as_string', 'datetime_data',
+    'dot', 'dragon4_positional', 'dragon4_scientific', 'dtype',
+    'empty', 'empty_like', 'error', 'flagsobj', 'flatiter', 'format_longfloat',
+    'frombuffer', 'fromfile', 'fromiter', 'fromstring',
+    'get_handler_name', 'get_handler_version', 'inner', 'interp',
+    'interp_complex', 'is_busday', 'lexsort', 'matmul', 'vecdot',
+    'may_share_memory', 'min_scalar_type', 'ndarray', 'nditer', 'nested_iters',
+    'normalize_axis_index', 'packbits', 'promote_types', 'putmask',
+    'ravel_multi_index', 'result_type', 'scalar', 'set_datetimeparse_function',
+    'set_typeDict', 'shares_memory', 'typeinfo',
+    'unpackbits', 'unravel_index', 'vdot', 'where', 'zeros']
+
+# For backward compatibility, make sure pickle imports
+# these functions from here
+_reconstruct.__module__ = 'numpy._core.multiarray'
+scalar.__module__ = 'numpy._core.multiarray'
+
+
+from_dlpack.__module__ = 'numpy'
+arange.__module__ = 'numpy'
+array.__module__ = 'numpy'
+asarray.__module__ = 'numpy'
+asanyarray.__module__ = 'numpy'
+ascontiguousarray.__module__ = 'numpy'
+asfortranarray.__module__ = 'numpy'
+datetime_data.__module__ = 'numpy'
+empty.__module__ = 'numpy'
+frombuffer.__module__ = 'numpy'
+fromfile.__module__ = 'numpy'
+fromiter.__module__ = 'numpy'
+frompyfunc.__module__ = 'numpy'
+fromstring.__module__ = 'numpy'
+may_share_memory.__module__ = 'numpy'
+nested_iters.__module__ = 'numpy'
+promote_types.__module__ = 'numpy'
+zeros.__module__ = 'numpy'
+normalize_axis_index.__module__ = 'numpy.lib.array_utils'
+add_docstring.__module__ = 'numpy.lib'
+compare_chararrays.__module__ = 'numpy.char'
+
+
+def _override___module__():
+    namespace_names = globals()
+    for ufunc_name in [
+        'absolute', 'arccos', 'arccosh', 'add', 'arcsin', 'arcsinh', 'arctan',
+        'arctan2', 'arctanh', 'bitwise_and', 'bitwise_count', 'invert',
+        'left_shift', 'bitwise_or', 'right_shift', 'bitwise_xor', 'cbrt',
+        'ceil', 'conjugate', 'copysign', 'cos', 'cosh', 'deg2rad', 'degrees',
+        'divide', 'divmod', 'equal', 'exp', 'exp2', 'expm1', 'fabs',
+        'float_power', 'floor', 'floor_divide', 'fmax', 'fmin', 'fmod',
+        'frexp', 'gcd', 'greater', 'greater_equal', 'heaviside', 'hypot',
+        'isfinite', 'isinf', 'isnan', 'isnat', 'lcm', 'ldexp', 'less',
+        'less_equal', 'log', 'log10', 'log1p', 'log2', 'logaddexp',
+        'logaddexp2', 'logical_and', 'logical_not', 'logical_or',
+        'logical_xor', 'matmul', 'matvec', 'maximum', 'minimum', 'remainder',
+        'modf', 'multiply', 'negative', 'nextafter', 'not_equal', 'positive',
+        'power', 'rad2deg', 'radians', 'reciprocal', 'rint', 'sign', 'signbit',
+        'sin', 'sinh', 'spacing', 'sqrt', 'square', 'subtract', 'tan', 'tanh',
+        'trunc', 'vecdot', 'vecmat',
+    ]:
+        ufunc = namespace_names[ufunc_name]
+        ufunc.__module__ = "numpy"
+        ufunc.__qualname__ = ufunc_name
+
+
+_override___module__()
+
+
+# We can't verify dispatcher signatures because NumPy's C functions don't
+# support introspection.
+array_function_from_c_func_and_dispatcher = functools.partial(
+    overrides.array_function_from_dispatcher,
+    module='numpy', docs_from_dispatcher=True, verify=False)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.empty_like)
+def empty_like(
+    prototype, dtype=None, order=None, subok=None, shape=None, *, device=None
+):
+    """
+    empty_like(prototype, dtype=None, order='K', subok=True, shape=None, *,
+               device=None)
+
+    Return a new array with the same shape and type as a given array.
+
+    Parameters
+    ----------
+    prototype : array_like
+        The shape and data-type of `prototype` define these same attributes
+        of the returned array.
+    dtype : data-type, optional
+        Overrides the data type of the result.
+    order : {'C', 'F', 'A', or 'K'}, optional
+        Overrides the memory layout of the result. 'C' means C-order,
+        'F' means F-order, 'A' means 'F' if `prototype` is Fortran
+        contiguous, 'C' otherwise. 'K' means match the layout of `prototype`
+        as closely as possible.
+    subok : bool, optional.
+        If True, then the newly created array will use the sub-class
+        type of `prototype`, otherwise it will be a base-class array. Defaults
+        to True.
+    shape : int or sequence of ints, optional.
+        Overrides the shape of the result. If order='K' and the number of
+        dimensions is unchanged, will try to keep order, otherwise,
+        order='C' is implied.
+    device : str, optional
+        The device on which to place the created array. Default: None.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    out : ndarray
+        Array of uninitialized (arbitrary) data with the same
+        shape and type as `prototype`.
+
+    See Also
+    --------
+    ones_like : Return an array of ones with shape and type of input.
+    zeros_like : Return an array of zeros with shape and type of input.
+    full_like : Return a new array with shape of input filled with value.
+    empty : Return a new uninitialized array.
+
+    Notes
+    -----
+    Unlike other array creation functions (e.g. `zeros_like`, `ones_like`,
+    `full_like`), `empty_like` does not initialize the values of the array,
+    and may therefore be marginally faster. However, the values stored in the
+    newly allocated array are arbitrary. For reproducible behavior, be sure
+    to set each element of the array before reading.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = ([1,2,3], [4,5,6])                         # a is array-like
+    >>> np.empty_like(a)
+    array([[-1073741821, -1073741821,           3],    # uninitialized
+           [          0,           0, -1073741821]])
+    >>> a = np.array([[1., 2., 3.],[4.,5.,6.]])
+    >>> np.empty_like(a)
+    array([[ -2.00000715e+000,   1.48219694e-323,  -2.00000572e+000], # uninitialized
+           [  4.38791518e-305,  -2.00000715e+000,   4.17269252e-309]])
+
+    """
+    return (prototype,)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.concatenate)
+def concatenate(arrays, axis=None, out=None, *, dtype=None, casting=None):
+    """
+    concatenate(
+        (a1, a2, ...),
+        axis=0,
+        out=None,
+        dtype=None,
+        casting="same_kind"
+    )
+
+    Join a sequence of arrays along an existing axis.
+
+    Parameters
+    ----------
+    a1, a2, ... : sequence of array_like
+        The arrays must have the same shape, except in the dimension
+        corresponding to `axis` (the first, by default).
+    axis : int, optional
+        The axis along which the arrays will be joined.  If axis is None,
+        arrays are flattened before use.  Default is 0.
+    out : ndarray, optional
+        If provided, the destination to place the result. The shape must be
+        correct, matching that of what concatenate would have returned if no
+        out argument were specified.
+    dtype : str or dtype
+        If provided, the destination array will have this dtype. Cannot be
+        provided together with `out`.
+
+        .. versionadded:: 1.20.0
+
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur. Defaults to 'same_kind'.
+        For a description of the options, please see :term:`casting`.
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    res : ndarray
+        The concatenated array.
+
+    See Also
+    --------
+    ma.concatenate : Concatenate function that preserves input masks.
+    array_split : Split an array into multiple sub-arrays of equal or
+                  near-equal size.
+    split : Split array into a list of multiple sub-arrays of equal size.
+    hsplit : Split array into multiple sub-arrays horizontally (column wise).
+    vsplit : Split array into multiple sub-arrays vertically (row wise).
+    dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).
+    stack : Stack a sequence of arrays along a new axis.
+    block : Assemble arrays from blocks.
+    hstack : Stack arrays in sequence horizontally (column wise).
+    vstack : Stack arrays in sequence vertically (row wise).
+    dstack : Stack arrays in sequence depth wise (along third dimension).
+    column_stack : Stack 1-D arrays as columns into a 2-D array.
+
+    Notes
+    -----
+    When one or more of the arrays to be concatenated is a MaskedArray,
+    this function will return a MaskedArray object instead of an ndarray,
+    but the input masks are *not* preserved. In cases where a MaskedArray
+    is expected as input, use the ma.concatenate function from the masked
+    array module instead.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[1, 2], [3, 4]])
+    >>> b = np.array([[5, 6]])
+    >>> np.concatenate((a, b), axis=0)
+    array([[1, 2],
+           [3, 4],
+           [5, 6]])
+    >>> np.concatenate((a, b.T), axis=1)
+    array([[1, 2, 5],
+           [3, 4, 6]])
+    >>> np.concatenate((a, b), axis=None)
+    array([1, 2, 3, 4, 5, 6])
+
+    This function will not preserve masking of MaskedArray inputs.
+
+    >>> a = np.ma.arange(3)
+    >>> a[1] = np.ma.masked
+    >>> b = np.arange(2, 5)
+    >>> a
+    masked_array(data=[0, --, 2],
+                 mask=[False,  True, False],
+           fill_value=999999)
+    >>> b
+    array([2, 3, 4])
+    >>> np.concatenate([a, b])
+    masked_array(data=[0, 1, 2, 2, 3, 4],
+                 mask=False,
+           fill_value=999999)
+    >>> np.ma.concatenate([a, b])
+    masked_array(data=[0, --, 2, 2, 3, 4],
+                 mask=[False,  True, False, False, False, False],
+           fill_value=999999)
+
+    """
+    if out is not None:
+        # optimize for the typical case where only arrays is provided
+        arrays = list(arrays)
+        arrays.append(out)
+    return arrays
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.inner)
+def inner(a, b):
+    """
+    inner(a, b, /)
+
+    Inner product of two arrays.
+
+    Ordinary inner product of vectors for 1-D arrays (without complex
+    conjugation), in higher dimensions a sum product over the last axes.
+
+    Parameters
+    ----------
+    a, b : array_like
+        If `a` and `b` are nonscalar, their last dimensions must match.
+
+    Returns
+    -------
+    out : ndarray
+        If `a` and `b` are both
+        scalars or both 1-D arrays then a scalar is returned; otherwise
+        an array is returned.
+        ``out.shape = (*a.shape[:-1], *b.shape[:-1])``
+
+    Raises
+    ------
+    ValueError
+        If both `a` and `b` are nonscalar and their last dimensions have
+        different sizes.
+
+    See Also
+    --------
+    tensordot : Sum products over arbitrary axes.
+    dot : Generalised matrix product, using second last dimension of `b`.
+    vecdot : Vector dot product of two arrays.
+    einsum : Einstein summation convention.
+
+    Notes
+    -----
+    For vectors (1-D arrays) it computes the ordinary inner-product::
+
+        np.inner(a, b) = sum(a[:]*b[:])
+
+    More generally, if ``ndim(a) = r > 0`` and ``ndim(b) = s > 0``::
+
+        np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))
+
+    or explicitly::
+
+        np.inner(a, b)[i0,...,ir-2,j0,...,js-2]
+             = sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:])
+
+    In addition `a` or `b` may be scalars, in which case::
+
+       np.inner(a,b) = a*b
+
+    Examples
+    --------
+    Ordinary inner product for vectors:
+
+    >>> import numpy as np
+    >>> a = np.array([1,2,3])
+    >>> b = np.array([0,1,0])
+    >>> np.inner(a, b)
+    2
+
+    Some multidimensional examples:
+
+    >>> a = np.arange(24).reshape((2,3,4))
+    >>> b = np.arange(4)
+    >>> c = np.inner(a, b)
+    >>> c.shape
+    (2, 3)
+    >>> c
+    array([[ 14,  38,  62],
+           [ 86, 110, 134]])
+
+    >>> a = np.arange(2).reshape((1,1,2))
+    >>> b = np.arange(6).reshape((3,2))
+    >>> c = np.inner(a, b)
+    >>> c.shape
+    (1, 1, 3)
+    >>> c
+    array([[[1, 3, 5]]])
+
+    An example where `b` is a scalar:
+
+    >>> np.inner(np.eye(2), 7)
+    array([[7., 0.],
+           [0., 7.]])
+
+    """
+    return (a, b)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.where)
+def where(condition, x=None, y=None):
+    """
+    where(condition, [x, y], /)
+
+    Return elements chosen from `x` or `y` depending on `condition`.
+
+    .. note::
+        When only `condition` is provided, this function is a shorthand for
+        ``np.asarray(condition).nonzero()``. Using `nonzero` directly should be
+        preferred, as it behaves correctly for subclasses. The rest of this
+        documentation covers only the case where all three arguments are
+        provided.
+
+    Parameters
+    ----------
+    condition : array_like, bool
+        Where True, yield `x`, otherwise yield `y`.
+    x, y : array_like
+        Values from which to choose. `x`, `y` and `condition` need to be
+        broadcastable to some shape.
+
+    Returns
+    -------
+    out : ndarray
+        An array with elements from `x` where `condition` is True, and elements
+        from `y` elsewhere.
+
+    See Also
+    --------
+    choose
+    nonzero : The function that is called when x and y are omitted
+
+    Notes
+    -----
+    If all the arrays are 1-D, `where` is equivalent to::
+
+        [xv if c else yv
+         for c, xv, yv in zip(condition, x, y)]
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.arange(10)
+    >>> a
+    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+    >>> np.where(a < 5, a, 10*a)
+    array([ 0,  1,  2,  3,  4, 50, 60, 70, 80, 90])
+
+    This can be used on multidimensional arrays too:
+
+    >>> np.where([[True, False], [True, True]],
+    ...          [[1, 2], [3, 4]],
+    ...          [[9, 8], [7, 6]])
+    array([[1, 8],
+           [3, 4]])
+
+    The shapes of x, y, and the condition are broadcast together:
+
+    >>> x, y = np.ogrid[:3, :4]
+    >>> np.where(x < y, x, 10 + y)  # both x and 10+y are broadcast
+    array([[10,  0,  0,  0],
+           [10, 11,  1,  1],
+           [10, 11, 12,  2]])
+
+    >>> a = np.array([[0, 1, 2],
+    ...               [0, 2, 4],
+    ...               [0, 3, 6]])
+    >>> np.where(a < 4, a, -1)  # -1 is broadcast
+    array([[ 0,  1,  2],
+           [ 0,  2, -1],
+           [ 0,  3, -1]])
+    """
+    return (condition, x, y)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.lexsort)
+def lexsort(keys, axis=None):
+    """
+    lexsort(keys, axis=-1)
+
+    Perform an indirect stable sort using a sequence of keys.
+
+    Given multiple sorting keys, lexsort returns an array of integer indices
+    that describes the sort order by multiple keys. The last key in the
+    sequence is used for the primary sort order, ties are broken by the
+    second-to-last key, and so on.
+
+    Parameters
+    ----------
+    keys : (k, m, n, ...) array-like
+        The `k` keys to be sorted. The *last* key (e.g, the last
+        row if `keys` is a 2D array) is the primary sort key.
+        Each element of `keys` along the zeroth axis must be
+        an array-like object of the same shape.
+    axis : int, optional
+        Axis to be indirectly sorted. By default, sort over the last axis
+        of each sequence. Separate slices along `axis` sorted over
+        independently; see last example.
+
+    Returns
+    -------
+    indices : (m, n, ...) ndarray of ints
+        Array of indices that sort the keys along the specified axis.
+
+    See Also
+    --------
+    argsort : Indirect sort.
+    ndarray.sort : In-place sort.
+    sort : Return a sorted copy of an array.
+
+    Examples
+    --------
+    Sort names: first by surname, then by name.
+
+    >>> import numpy as np
+    >>> surnames =    ('Hertz',    'Galilei', 'Hertz')
+    >>> first_names = ('Heinrich', 'Galileo', 'Gustav')
+    >>> ind = np.lexsort((first_names, surnames))
+    >>> ind
+    array([1, 2, 0])
+
+    >>> [surnames[i] + ", " + first_names[i] for i in ind]
+    ['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich']
+
+    Sort according to two numerical keys, first by elements
+    of ``a``, then breaking ties according to elements of ``b``:
+
+    >>> a = [1, 5, 1, 4, 3, 4, 4]  # First sequence
+    >>> b = [9, 4, 0, 4, 0, 2, 1]  # Second sequence
+    >>> ind = np.lexsort((b, a))  # Sort by `a`, then by `b`
+    >>> ind
+    array([2, 0, 4, 6, 5, 3, 1])
+    >>> [(a[i], b[i]) for i in ind]
+    [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)]
+
+    Compare against `argsort`, which would sort each key independently.
+
+    >>> np.argsort((b, a), kind='stable')
+    array([[2, 4, 6, 5, 1, 3, 0],
+           [0, 2, 4, 3, 5, 6, 1]])
+
+    To sort lexicographically with `argsort`, we would need to provide a
+    structured array.
+
+    >>> x = np.array([(ai, bi) for ai, bi in zip(a, b)],
+    ...              dtype = np.dtype([('x', int), ('y', int)]))
+    >>> np.argsort(x)  # or np.argsort(x, order=('x', 'y'))
+    array([2, 0, 4, 6, 5, 3, 1])
+
+    The zeroth axis of `keys` always corresponds with the sequence of keys,
+    so 2D arrays are treated just like other sequences of keys.
+
+    >>> arr = np.asarray([b, a])
+    >>> ind2 = np.lexsort(arr)
+    >>> np.testing.assert_equal(ind2, ind)
+
+    Accordingly, the `axis` parameter refers to an axis of *each* key, not of
+    the `keys` argument itself. For instance, the array ``arr`` is treated as
+    a sequence of two 1-D keys, so specifying ``axis=0`` is equivalent to
+    using the default axis, ``axis=-1``.
+
+    >>> np.testing.assert_equal(np.lexsort(arr, axis=0),
+    ...                         np.lexsort(arr, axis=-1))
+
+    For higher-dimensional arrays, the axis parameter begins to matter. The
+    resulting array has the same shape as each key, and the values are what
+    we would expect if `lexsort` were performed on corresponding slices
+    of the keys independently. For instance,
+
+    >>> x = [[1, 2, 3, 4],
+    ...      [4, 3, 2, 1],
+    ...      [2, 1, 4, 3]]
+    >>> y = [[2, 2, 1, 1],
+    ...      [1, 2, 1, 2],
+    ...      [1, 1, 2, 1]]
+    >>> np.lexsort((x, y), axis=1)
+    array([[2, 3, 0, 1],
+           [2, 0, 3, 1],
+           [1, 0, 3, 2]])
+
+    Each row of the result is what we would expect if we were to perform
+    `lexsort` on the corresponding row of the keys:
+
+    >>> for i in range(3):
+    ...     print(np.lexsort((x[i], y[i])))
+    [2 3 0 1]
+    [2 0 3 1]
+    [1 0 3 2]
+
+    """
+    if isinstance(keys, tuple):
+        return keys
+    else:
+        return (keys,)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.can_cast)
+def can_cast(from_, to, casting=None):
+    """
+    can_cast(from_, to, casting='safe')
+
+    Returns True if cast between data types can occur according to the
+    casting rule.
+
+    Parameters
+    ----------
+    from_ : dtype, dtype specifier, NumPy scalar, or array
+        Data type, NumPy scalar, or array to cast from.
+    to : dtype or dtype specifier
+        Data type to cast to.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur.
+
+        * 'no' means the data types should not be cast at all.
+        * 'equiv' means only byte-order changes are allowed.
+        * 'safe' means only casts which can preserve values are allowed.
+        * 'same_kind' means only safe casts or casts within a kind,
+          like float64 to float32, are allowed.
+        * 'unsafe' means any data conversions may be done.
+
+    Returns
+    -------
+    out : bool
+        True if cast can occur according to the casting rule.
+
+    Notes
+    -----
+    .. versionchanged:: 2.0
+       This function does not support Python scalars anymore and does not
+       apply any value-based logic for 0-D arrays and NumPy scalars.
+
+    See also
+    --------
+    dtype, result_type
+
+    Examples
+    --------
+    Basic examples
+
+    >>> import numpy as np
+    >>> np.can_cast(np.int32, np.int64)
+    True
+    >>> np.can_cast(np.float64, complex)
+    True
+    >>> np.can_cast(complex, float)
+    False
+
+    >>> np.can_cast('i8', 'f8')
+    True
+    >>> np.can_cast('i8', 'f4')
+    False
+    >>> np.can_cast('i4', 'S4')
+    False
+
+    """
+    return (from_,)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.min_scalar_type)
+def min_scalar_type(a):
+    """
+    min_scalar_type(a, /)
+
+    For scalar ``a``, returns the data type with the smallest size
+    and smallest scalar kind which can hold its value.  For non-scalar
+    array ``a``, returns the vector's dtype unmodified.
+
+    Floating point values are not demoted to integers,
+    and complex values are not demoted to floats.
+
+    Parameters
+    ----------
+    a : scalar or array_like
+        The value whose minimal data type is to be found.
+
+    Returns
+    -------
+    out : dtype
+        The minimal data type.
+
+    See Also
+    --------
+    result_type, promote_types, dtype, can_cast
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.min_scalar_type(10)
+    dtype('uint8')
+
+    >>> np.min_scalar_type(-260)
+    dtype('int16')
+
+    >>> np.min_scalar_type(3.1)
+    dtype('float16')
+
+    >>> np.min_scalar_type(1e50)
+    dtype('float64')
+
+    >>> np.min_scalar_type(np.arange(4,dtype='f8'))
+    dtype('float64')
+
+    """
+    return (a,)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.result_type)
+def result_type(*arrays_and_dtypes):
+    """
+    result_type(*arrays_and_dtypes)
+
+    Returns the type that results from applying the NumPy
+    type promotion rules to the arguments.
+
+    Type promotion in NumPy works similarly to the rules in languages
+    like C++, with some slight differences.  When both scalars and
+    arrays are used, the array's type takes precedence and the actual value
+    of the scalar is taken into account.
+
+    For example, calculating 3*a, where a is an array of 32-bit floats,
+    intuitively should result in a 32-bit float output.  If the 3 is a
+    32-bit integer, the NumPy rules indicate it can't convert losslessly
+    into a 32-bit float, so a 64-bit float should be the result type.
+    By examining the value of the constant, '3', we see that it fits in
+    an 8-bit integer, which can be cast losslessly into the 32-bit float.
+
+    Parameters
+    ----------
+    arrays_and_dtypes : list of arrays and dtypes
+        The operands of some operation whose result type is needed.
+
+    Returns
+    -------
+    out : dtype
+        The result type.
+
+    See also
+    --------
+    dtype, promote_types, min_scalar_type, can_cast
+
+    Notes
+    -----
+    The specific algorithm used is as follows.
+
+    Categories are determined by first checking which of boolean,
+    integer (int/uint), or floating point (float/complex) the maximum
+    kind of all the arrays and the scalars are.
+
+    If there are only scalars or the maximum category of the scalars
+    is higher than the maximum category of the arrays,
+    the data types are combined with :func:`promote_types`
+    to produce the return value.
+
+    Otherwise, `min_scalar_type` is called on each scalar, and
+    the resulting data types are all combined with :func:`promote_types`
+    to produce the return value.
+
+    The set of int values is not a subset of the uint values for types
+    with the same number of bits, something not reflected in
+    :func:`min_scalar_type`, but handled as a special case in `result_type`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.result_type(3, np.arange(7, dtype='i1'))
+    dtype('int8')
+
+    >>> np.result_type('i4', 'c8')
+    dtype('complex128')
+
+    >>> np.result_type(3.0, -2)
+    dtype('float64')
+
+    """
+    return arrays_and_dtypes
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.dot)
+def dot(a, b, out=None):
+    """
+    dot(a, b, out=None)
+
+    Dot product of two arrays. Specifically,
+
+    - If both `a` and `b` are 1-D arrays, it is inner product of vectors
+      (without complex conjugation).
+
+    - If both `a` and `b` are 2-D arrays, it is matrix multiplication,
+      but using :func:`matmul` or ``a @ b`` is preferred.
+
+    - If either `a` or `b` is 0-D (scalar), it is equivalent to
+      :func:`multiply` and using ``numpy.multiply(a, b)`` or ``a * b`` is
+      preferred.
+
+    - If `a` is an N-D array and `b` is a 1-D array, it is a sum product over
+      the last axis of `a` and `b`.
+
+    - If `a` is an N-D array and `b` is an M-D array (where ``M>=2``), it is a
+      sum product over the last axis of `a` and the second-to-last axis of
+      `b`::
+
+        dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
+
+    It uses an optimized BLAS library when possible (see `numpy.linalg`).
+
+    Parameters
+    ----------
+    a : array_like
+        First argument.
+    b : array_like
+        Second argument.
+    out : ndarray, optional
+        Output argument. This must have the exact kind that would be returned
+        if it was not used. In particular, it must have the right type, must be
+        C-contiguous, and its dtype must be the dtype that would be returned
+        for `dot(a,b)`. This is a performance feature. Therefore, if these
+        conditions are not met, an exception is raised, instead of attempting
+        to be flexible.
+
+    Returns
+    -------
+    output : ndarray
+        Returns the dot product of `a` and `b`.  If `a` and `b` are both
+        scalars or both 1-D arrays then a scalar is returned; otherwise
+        an array is returned.
+        If `out` is given, then it is returned.
+
+    Raises
+    ------
+    ValueError
+        If the last dimension of `a` is not the same size as
+        the second-to-last dimension of `b`.
+
+    See Also
+    --------
+    vdot : Complex-conjugating dot product.
+    vecdot : Vector dot product of two arrays.
+    tensordot : Sum products over arbitrary axes.
+    einsum : Einstein summation convention.
+    matmul : '@' operator as method with out parameter.
+    linalg.multi_dot : Chained dot product.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.dot(3, 4)
+    12
+
+    Neither argument is complex-conjugated:
+
+    >>> np.dot([2j, 3j], [2j, 3j])
+    (-13+0j)
+
+    For 2-D arrays it is the matrix product:
+
+    >>> a = [[1, 0], [0, 1]]
+    >>> b = [[4, 1], [2, 2]]
+    >>> np.dot(a, b)
+    array([[4, 1],
+           [2, 2]])
+
+    >>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
+    >>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
+    >>> np.dot(a, b)[2,3,2,1,2,2]
+    499128
+    >>> sum(a[2,3,2,:] * b[1,2,:,2])
+    499128
+
+    """
+    return (a, b, out)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.vdot)
+def vdot(a, b):
+    r"""
+    vdot(a, b, /)
+
+    Return the dot product of two vectors.
+
+    The `vdot` function handles complex numbers differently than `dot`:
+    if the first argument is complex, it is replaced by its complex conjugate
+    in the dot product calculation. `vdot` also handles multidimensional
+    arrays differently than `dot`: it does not perform a matrix product, but
+    flattens the arguments to 1-D arrays before taking a vector dot product.
+
+    Consequently, when the arguments are 2-D arrays of the same shape, this
+    function effectively returns their
+    `Frobenius inner product <https://en.wikipedia.org/wiki/Frobenius_inner_product>`_
+    (also known as the *trace inner product* or the *standard inner product*
+    on a vector space of matrices).
+
+    Parameters
+    ----------
+    a : array_like
+        If `a` is complex the complex conjugate is taken before calculation
+        of the dot product.
+    b : array_like
+        Second argument to the dot product.
+
+    Returns
+    -------
+    output : ndarray
+        Dot product of `a` and `b`.  Can be an int, float, or
+        complex depending on the types of `a` and `b`.
+
+    See Also
+    --------
+    dot : Return the dot product without using the complex conjugate of the
+          first argument.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([1+2j,3+4j])
+    >>> b = np.array([5+6j,7+8j])
+    >>> np.vdot(a, b)
+    (70-8j)
+    >>> np.vdot(b, a)
+    (70+8j)
+
+    Note that higher-dimensional arrays are flattened!
+
+    >>> a = np.array([[1, 4], [5, 6]])
+    >>> b = np.array([[4, 1], [2, 2]])
+    >>> np.vdot(a, b)
+    30
+    >>> np.vdot(b, a)
+    30
+    >>> 1*4 + 4*1 + 5*2 + 6*2
+    30
+
+    """  # noqa: E501
+    return (a, b)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.bincount)
+def bincount(x, weights=None, minlength=None):
+    """
+    bincount(x, /, weights=None, minlength=0)
+
+    Count number of occurrences of each value in array of non-negative ints.
+
+    The number of bins (of size 1) is one larger than the largest value in
+    `x`. If `minlength` is specified, there will be at least this number
+    of bins in the output array (though it will be longer if necessary,
+    depending on the contents of `x`).
+    Each bin gives the number of occurrences of its index value in `x`.
+    If `weights` is specified the input array is weighted by it, i.e. if a
+    value ``n`` is found at position ``i``, ``out[n] += weight[i]`` instead
+    of ``out[n] += 1``.
+
+    Parameters
+    ----------
+    x : array_like, 1 dimension, nonnegative ints
+        Input array.
+    weights : array_like, optional
+        Weights, array of the same shape as `x`.
+    minlength : int, optional
+        A minimum number of bins for the output array.
+
+    Returns
+    -------
+    out : ndarray of ints
+        The result of binning the input array.
+        The length of `out` is equal to ``np.amax(x)+1``.
+
+    Raises
+    ------
+    ValueError
+        If the input is not 1-dimensional, or contains elements with negative
+        values, or if `minlength` is negative.
+    TypeError
+        If the type of the input is float or complex.
+
+    See Also
+    --------
+    histogram, digitize, unique
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.bincount(np.arange(5))
+    array([1, 1, 1, 1, 1])
+    >>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7]))
+    array([1, 3, 1, 1, 0, 0, 0, 1])
+
+    >>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23])
+    >>> np.bincount(x).size == np.amax(x)+1
+    True
+
+    The input array needs to be of integer dtype, otherwise a
+    TypeError is raised:
+
+    >>> np.bincount(np.arange(5, dtype=float))
+    Traceback (most recent call last):
+      ...
+    TypeError: Cannot cast array data from dtype('float64') to dtype('int64')
+    according to the rule 'safe'
+
+    A possible use of ``bincount`` is to perform sums over
+    variable-size chunks of an array, using the ``weights`` keyword.
+
+    >>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights
+    >>> x = np.array([0, 1, 1, 2, 2, 2])
+    >>> np.bincount(x,  weights=w)
+    array([ 0.3,  0.7,  1.1])
+
+    """
+    return (x, weights)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.ravel_multi_index)
+def ravel_multi_index(multi_index, dims, mode=None, order=None):
+    """
+    ravel_multi_index(multi_index, dims, mode='raise', order='C')
+
+    Converts a tuple of index arrays into an array of flat
+    indices, applying boundary modes to the multi-index.
+
+    Parameters
+    ----------
+    multi_index : tuple of array_like
+        A tuple of integer arrays, one array for each dimension.
+    dims : tuple of ints
+        The shape of array into which the indices from ``multi_index`` apply.
+    mode : {'raise', 'wrap', 'clip'}, optional
+        Specifies how out-of-bounds indices are handled.  Can specify
+        either one mode or a tuple of modes, one mode per index.
+
+        * 'raise' -- raise an error (default)
+        * 'wrap' -- wrap around
+        * 'clip' -- clip to the range
+
+        In 'clip' mode, a negative index which would normally
+        wrap will clip to 0 instead.
+    order : {'C', 'F'}, optional
+        Determines whether the multi-index should be viewed as
+        indexing in row-major (C-style) or column-major
+        (Fortran-style) order.
+
+    Returns
+    -------
+    raveled_indices : ndarray
+        An array of indices into the flattened version of an array
+        of dimensions ``dims``.
+
+    See Also
+    --------
+    unravel_index
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> arr = np.array([[3,6,6],[4,5,1]])
+    >>> np.ravel_multi_index(arr, (7,6))
+    array([22, 41, 37])
+    >>> np.ravel_multi_index(arr, (7,6), order='F')
+    array([31, 41, 13])
+    >>> np.ravel_multi_index(arr, (4,6), mode='clip')
+    array([22, 23, 19])
+    >>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap'))
+    array([12, 13, 13])
+
+    >>> np.ravel_multi_index((3,1,4,1), (6,7,8,9))
+    1621
+    """
+    return multi_index
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.unravel_index)
+def unravel_index(indices, shape=None, order=None):
+    """
+    unravel_index(indices, shape, order='C')
+
+    Converts a flat index or array of flat indices into a tuple
+    of coordinate arrays.
+
+    Parameters
+    ----------
+    indices : array_like
+        An integer array whose elements are indices into the flattened
+        version of an array of dimensions ``shape``. Before version 1.6.0,
+        this function accepted just one index value.
+    shape : tuple of ints
+        The shape of the array to use for unraveling ``indices``.
+    order : {'C', 'F'}, optional
+        Determines whether the indices should be viewed as indexing in
+        row-major (C-style) or column-major (Fortran-style) order.
+
+    Returns
+    -------
+    unraveled_coords : tuple of ndarray
+        Each array in the tuple has the same shape as the ``indices``
+        array.
+
+    See Also
+    --------
+    ravel_multi_index
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.unravel_index([22, 41, 37], (7,6))
+    (array([3, 6, 6]), array([4, 5, 1]))
+    >>> np.unravel_index([31, 41, 13], (7,6), order='F')
+    (array([3, 6, 6]), array([4, 5, 1]))
+
+    >>> np.unravel_index(1621, (6,7,8,9))
+    (3, 1, 4, 1)
+
+    """
+    return (indices,)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.copyto)
+def copyto(dst, src, casting=None, where=None):
+    """
+    copyto(dst, src, casting='same_kind', where=True)
+
+    Copies values from one array to another, broadcasting as necessary.
+
+    Raises a TypeError if the `casting` rule is violated, and if
+    `where` is provided, it selects which elements to copy.
+
+    Parameters
+    ----------
+    dst : ndarray
+        The array into which values are copied.
+    src : array_like
+        The array from which values are copied.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur when copying.
+
+        * 'no' means the data types should not be cast at all.
+        * 'equiv' means only byte-order changes are allowed.
+        * 'safe' means only casts which can preserve values are allowed.
+        * 'same_kind' means only safe casts or casts within a kind,
+          like float64 to float32, are allowed.
+        * 'unsafe' means any data conversions may be done.
+    where : array_like of bool, optional
+        A boolean array which is broadcasted to match the dimensions
+        of `dst`, and selects elements to copy from `src` to `dst`
+        wherever it contains the value True.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> A = np.array([4, 5, 6])
+    >>> B = [1, 2, 3]
+    >>> np.copyto(A, B)
+    >>> A
+    array([1, 2, 3])
+
+    >>> A = np.array([[1, 2, 3], [4, 5, 6]])
+    >>> B = [[4, 5, 6], [7, 8, 9]]
+    >>> np.copyto(A, B)
+    >>> A
+    array([[4, 5, 6],
+           [7, 8, 9]])
+
+    """
+    return (dst, src, where)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.putmask)
+def putmask(a, /, mask, values):
+    """
+    putmask(a, mask, values)
+
+    Changes elements of an array based on conditional and input values.
+
+    Sets ``a.flat[n] = values[n]`` for each n where ``mask.flat[n]==True``.
+
+    If `values` is not the same size as `a` and `mask` then it will repeat.
+    This gives behavior different from ``a[mask] = values``.
+
+    Parameters
+    ----------
+    a : ndarray
+        Target array.
+    mask : array_like
+        Boolean mask array. It has to be the same shape as `a`.
+    values : array_like
+        Values to put into `a` where `mask` is True. If `values` is smaller
+        than `a` it will be repeated.
+
+    See Also
+    --------
+    place, put, take, copyto
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6).reshape(2, 3)
+    >>> np.putmask(x, x>2, x**2)
+    >>> x
+    array([[ 0,  1,  2],
+           [ 9, 16, 25]])
+
+    If `values` is smaller than `a` it is repeated:
+
+    >>> x = np.arange(5)
+    >>> np.putmask(x, x>1, [-33, -44])
+    >>> x
+    array([  0,   1, -33, -44, -33])
+
+    """
+    return (a, mask, values)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.packbits)
+def packbits(a, axis=None, bitorder='big'):
+    """
+    packbits(a, /, axis=None, bitorder='big')
+
+    Packs the elements of a binary-valued array into bits in a uint8 array.
+
+    The result is padded to full bytes by inserting zero bits at the end.
+
+    Parameters
+    ----------
+    a : array_like
+        An array of integers or booleans whose elements should be packed to
+        bits.
+    axis : int, optional
+        The dimension over which bit-packing is done.
+        ``None`` implies packing the flattened array.
+    bitorder : {'big', 'little'}, optional
+        The order of the input bits. 'big' will mimic bin(val),
+        ``[0, 0, 0, 0, 0, 0, 1, 1] => 3 = 0b00000011``, 'little' will
+        reverse the order so ``[1, 1, 0, 0, 0, 0, 0, 0] => 3``.
+        Defaults to 'big'.
+
+    Returns
+    -------
+    packed : ndarray
+        Array of type uint8 whose elements represent bits corresponding to the
+        logical (0 or nonzero) value of the input elements. The shape of
+        `packed` has the same number of dimensions as the input (unless `axis`
+        is None, in which case the output is 1-D).
+
+    See Also
+    --------
+    unpackbits: Unpacks elements of a uint8 array into a binary-valued output
+                array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[[1,0,1],
+    ...                [0,1,0]],
+    ...               [[1,1,0],
+    ...                [0,0,1]]])
+    >>> b = np.packbits(a, axis=-1)
+    >>> b
+    array([[[160],
+            [ 64]],
+           [[192],
+            [ 32]]], dtype=uint8)
+
+    Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000,
+    and 32 = 0010 0000.
+
+    """
+    return (a,)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.unpackbits)
+def unpackbits(a, axis=None, count=None, bitorder='big'):
+    """
+    unpackbits(a, /, axis=None, count=None, bitorder='big')
+
+    Unpacks elements of a uint8 array into a binary-valued output array.
+
+    Each element of `a` represents a bit-field that should be unpacked
+    into a binary-valued output array. The shape of the output array is
+    either 1-D (if `axis` is ``None``) or the same shape as the input
+    array with unpacking done along the axis specified.
+
+    Parameters
+    ----------
+    a : ndarray, uint8 type
+       Input array.
+    axis : int, optional
+        The dimension over which bit-unpacking is done.
+        ``None`` implies unpacking the flattened array.
+    count : int or None, optional
+        The number of elements to unpack along `axis`, provided as a way
+        of undoing the effect of packing a size that is not a multiple
+        of eight. A non-negative number means to only unpack `count`
+        bits. A negative number means to trim off that many bits from
+        the end. ``None`` means to unpack the entire array (the
+        default). Counts larger than the available number of bits will
+        add zero padding to the output. Negative counts must not
+        exceed the available number of bits.
+    bitorder : {'big', 'little'}, optional
+        The order of the returned bits. 'big' will mimic bin(val),
+        ``3 = 0b00000011 => [0, 0, 0, 0, 0, 0, 1, 1]``, 'little' will reverse
+        the order to ``[1, 1, 0, 0, 0, 0, 0, 0]``.
+        Defaults to 'big'.
+
+    Returns
+    -------
+    unpacked : ndarray, uint8 type
+       The elements are binary-valued (0 or 1).
+
+    See Also
+    --------
+    packbits : Packs the elements of a binary-valued array into bits in
+               a uint8 array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([[2], [7], [23]], dtype=np.uint8)
+    >>> a
+    array([[ 2],
+           [ 7],
+           [23]], dtype=uint8)
+    >>> b = np.unpackbits(a, axis=1)
+    >>> b
+    array([[0, 0, 0, 0, 0, 0, 1, 0],
+           [0, 0, 0, 0, 0, 1, 1, 1],
+           [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8)
+    >>> c = np.unpackbits(a, axis=1, count=-3)
+    >>> c
+    array([[0, 0, 0, 0, 0],
+           [0, 0, 0, 0, 0],
+           [0, 0, 0, 1, 0]], dtype=uint8)
+
+    >>> p = np.packbits(b, axis=0)
+    >>> np.unpackbits(p, axis=0)
+    array([[0, 0, 0, 0, 0, 0, 1, 0],
+           [0, 0, 0, 0, 0, 1, 1, 1],
+           [0, 0, 0, 1, 0, 1, 1, 1],
+           [0, 0, 0, 0, 0, 0, 0, 0],
+           [0, 0, 0, 0, 0, 0, 0, 0],
+           [0, 0, 0, 0, 0, 0, 0, 0],
+           [0, 0, 0, 0, 0, 0, 0, 0],
+           [0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
+    >>> np.array_equal(b, np.unpackbits(p, axis=0, count=b.shape[0]))
+    True
+
+    """
+    return (a,)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.shares_memory)
+def shares_memory(a, b, max_work=None):
+    """
+    shares_memory(a, b, /, max_work=None)
+
+    Determine if two arrays share memory.
+
+    .. warning::
+
+       This function can be exponentially slow for some inputs, unless
+       `max_work` is set to zero or a positive integer.
+       If in doubt, use `numpy.may_share_memory` instead.
+
+    Parameters
+    ----------
+    a, b : ndarray
+        Input arrays
+    max_work : int, optional
+        Effort to spend on solving the overlap problem (maximum number
+        of candidate solutions to consider). The following special
+        values are recognized:
+
+        max_work=-1 (default)
+            The problem is solved exactly. In this case, the function returns
+            True only if there is an element shared between the arrays. Finding
+            the exact solution may take extremely long in some cases.
+        max_work=0
+            Only the memory bounds of a and b are checked.
+            This is equivalent to using ``may_share_memory()``.
+
+    Raises
+    ------
+    numpy.exceptions.TooHardError
+        Exceeded max_work.
+
+    Returns
+    -------
+    out : bool
+
+    See Also
+    --------
+    may_share_memory
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array([1, 2, 3, 4])
+    >>> np.shares_memory(x, np.array([5, 6, 7]))
+    False
+    >>> np.shares_memory(x[::2], x)
+    True
+    >>> np.shares_memory(x[::2], x[1::2])
+    False
+
+    Checking whether two arrays share memory is NP-complete, and
+    runtime may increase exponentially in the number of
+    dimensions. Hence, `max_work` should generally be set to a finite
+    number, as it is possible to construct examples that take
+    extremely long to run:
+
+    >>> from numpy.lib.stride_tricks import as_strided
+    >>> x = np.zeros([192163377], dtype=np.int8)
+    >>> x1 = as_strided(
+    ...     x, strides=(36674, 61119, 85569), shape=(1049, 1049, 1049))
+    >>> x2 = as_strided(
+    ...     x[64023025:], strides=(12223, 12224, 1), shape=(1049, 1049, 1))
+    >>> np.shares_memory(x1, x2, max_work=1000)
+    Traceback (most recent call last):
+    ...
+    numpy.exceptions.TooHardError: Exceeded max_work
+
+    Running ``np.shares_memory(x1, x2)`` without `max_work` set takes
+    around 1 minute for this case. It is possible to find problems
+    that take still significantly longer.
+
+    """
+    return (a, b)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.may_share_memory)
+def may_share_memory(a, b, max_work=None):
+    """
+    may_share_memory(a, b, /, max_work=None)
+
+    Determine if two arrays might share memory
+
+    A return of True does not necessarily mean that the two arrays
+    share any element.  It just means that they *might*.
+
+    Only the memory bounds of a and b are checked by default.
+
+    Parameters
+    ----------
+    a, b : ndarray
+        Input arrays
+    max_work : int, optional
+        Effort to spend on solving the overlap problem.  See
+        `shares_memory` for details.  Default for ``may_share_memory``
+        is to do a bounds check.
+
+    Returns
+    -------
+    out : bool
+
+    See Also
+    --------
+    shares_memory
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9]))
+    False
+    >>> x = np.zeros([3, 4])
+    >>> np.may_share_memory(x[:,0], x[:,1])
+    True
+
+    """
+    return (a, b)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.is_busday)
+def is_busday(dates, weekmask=None, holidays=None, busdaycal=None, out=None):
+    """
+    is_busday(
+        dates,
+        weekmask='1111100',
+        holidays=None,
+        busdaycal=None,
+        out=None
+    )
+
+    Calculates which of the given dates are valid days, and which are not.
+
+    Parameters
+    ----------
+    dates : array_like of datetime64[D]
+        The array of dates to process.
+    weekmask : str or array_like of bool, optional
+        A seven-element array indicating which of Monday through Sunday are
+        valid days. May be specified as a length-seven list or array, like
+        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
+        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
+        weekdays, optionally separated by white space. Valid abbreviations
+        are: Mon Tue Wed Thu Fri Sat Sun
+    holidays : array_like of datetime64[D], optional
+        An array of dates to consider as invalid dates.  They may be
+        specified in any order, and NaT (not-a-time) dates are ignored.
+        This list is saved in a normalized form that is suited for
+        fast calculations of valid days.
+    busdaycal : busdaycalendar, optional
+        A `busdaycalendar` object which specifies the valid days. If this
+        parameter is provided, neither weekmask nor holidays may be
+        provided.
+    out : array of bool, optional
+        If provided, this array is filled with the result.
+
+    Returns
+    -------
+    out : array of bool
+        An array with the same shape as ``dates``, containing True for
+        each valid day, and False for each invalid day.
+
+    See Also
+    --------
+    busdaycalendar : An object that specifies a custom set of valid days.
+    busday_offset : Applies an offset counted in valid days.
+    busday_count : Counts how many valid days are in a half-open date range.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> # The weekdays are Friday, Saturday, and Monday
+    ... np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'],
+    ...                 holidays=['2011-07-01', '2011-07-04', '2011-07-17'])
+    array([False, False,  True])
+    """
+    return (dates, weekmask, holidays, out)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.busday_offset)
+def busday_offset(dates, offsets, roll=None, weekmask=None, holidays=None,
+                  busdaycal=None, out=None):
+    """
+    busday_offset(
+        dates,
+        offsets,
+        roll='raise',
+        weekmask='1111100',
+        holidays=None,
+        busdaycal=None,
+        out=None
+    )
+
+    First adjusts the date to fall on a valid day according to
+    the ``roll`` rule, then applies offsets to the given dates
+    counted in valid days.
+
+    Parameters
+    ----------
+    dates : array_like of datetime64[D]
+        The array of dates to process.
+    offsets : array_like of int
+        The array of offsets, which is broadcast with ``dates``.
+    roll : {'raise', 'nat', 'forward', 'following', 'backward', 'preceding', \
+        'modifiedfollowing', 'modifiedpreceding'}, optional
+        How to treat dates that do not fall on a valid day. The default
+        is 'raise'.
+
+        * 'raise' means to raise an exception for an invalid day.
+        * 'nat' means to return a NaT (not-a-time) for an invalid day.
+        * 'forward' and 'following' mean to take the first valid day
+          later in time.
+        * 'backward' and 'preceding' mean to take the first valid day
+          earlier in time.
+        * 'modifiedfollowing' means to take the first valid day
+          later in time unless it is across a Month boundary, in which
+          case to take the first valid day earlier in time.
+        * 'modifiedpreceding' means to take the first valid day
+          earlier in time unless it is across a Month boundary, in which
+          case to take the first valid day later in time.
+    weekmask : str or array_like of bool, optional
+        A seven-element array indicating which of Monday through Sunday are
+        valid days. May be specified as a length-seven list or array, like
+        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
+        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
+        weekdays, optionally separated by white space. Valid abbreviations
+        are: Mon Tue Wed Thu Fri Sat Sun
+    holidays : array_like of datetime64[D], optional
+        An array of dates to consider as invalid dates.  They may be
+        specified in any order, and NaT (not-a-time) dates are ignored.
+        This list is saved in a normalized form that is suited for
+        fast calculations of valid days.
+    busdaycal : busdaycalendar, optional
+        A `busdaycalendar` object which specifies the valid days. If this
+        parameter is provided, neither weekmask nor holidays may be
+        provided.
+    out : array of datetime64[D], optional
+        If provided, this array is filled with the result.
+
+    Returns
+    -------
+    out : array of datetime64[D]
+        An array with a shape from broadcasting ``dates`` and ``offsets``
+        together, containing the dates with offsets applied.
+
+    See Also
+    --------
+    busdaycalendar : An object that specifies a custom set of valid days.
+    is_busday : Returns a boolean array indicating valid days.
+    busday_count : Counts how many valid days are in a half-open date range.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> # First business day in October 2011 (not accounting for holidays)
+    ... np.busday_offset('2011-10', 0, roll='forward')
+    np.datetime64('2011-10-03')
+    >>> # Last business day in February 2012 (not accounting for holidays)
+    ... np.busday_offset('2012-03', -1, roll='forward')
+    np.datetime64('2012-02-29')
+    >>> # Third Wednesday in January 2011
+    ... np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed')
+    np.datetime64('2011-01-19')
+    >>> # 2012 Mother's Day in Canada and the U.S.
+    ... np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun')
+    np.datetime64('2012-05-13')
+
+    >>> # First business day on or after a date
+    ... np.busday_offset('2011-03-20', 0, roll='forward')
+    np.datetime64('2011-03-21')
+    >>> np.busday_offset('2011-03-22', 0, roll='forward')
+    np.datetime64('2011-03-22')
+    >>> # First business day after a date
+    ... np.busday_offset('2011-03-20', 1, roll='backward')
+    np.datetime64('2011-03-21')
+    >>> np.busday_offset('2011-03-22', 1, roll='backward')
+    np.datetime64('2011-03-23')
+    """
+    return (dates, offsets, weekmask, holidays, out)
+
+
+@array_function_from_c_func_and_dispatcher(_multiarray_umath.busday_count)
+def busday_count(begindates, enddates, weekmask=None, holidays=None,
+                 busdaycal=None, out=None):
+    """
+    busday_count(
+        begindates,
+        enddates,
+        weekmask='1111100',
+        holidays=[],
+        busdaycal=None,
+        out=None
+    )
+
+    Counts the number of valid days between `begindates` and
+    `enddates`, not including the day of `enddates`.
+
+    If ``enddates`` specifies a date value that is earlier than the
+    corresponding ``begindates`` date value, the count will be negative.
+
+    Parameters
+    ----------
+    begindates : array_like of datetime64[D]
+        The array of the first dates for counting.
+    enddates : array_like of datetime64[D]
+        The array of the end dates for counting, which are excluded
+        from the count themselves.
+    weekmask : str or array_like of bool, optional
+        A seven-element array indicating which of Monday through Sunday are
+        valid days. May be specified as a length-seven list or array, like
+        [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
+        like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
+        weekdays, optionally separated by white space. Valid abbreviations
+        are: Mon Tue Wed Thu Fri Sat Sun
+    holidays : array_like of datetime64[D], optional
+        An array of dates to consider as invalid dates.  They may be
+        specified in any order, and NaT (not-a-time) dates are ignored.
+        This list is saved in a normalized form that is suited for
+        fast calculations of valid days.
+    busdaycal : busdaycalendar, optional
+        A `busdaycalendar` object which specifies the valid days. If this
+        parameter is provided, neither weekmask nor holidays may be
+        provided.
+    out : array of int, optional
+        If provided, this array is filled with the result.
+
+    Returns
+    -------
+    out : array of int
+        An array with a shape from broadcasting ``begindates`` and ``enddates``
+        together, containing the number of valid days between
+        the begin and end dates.
+
+    See Also
+    --------
+    busdaycalendar : An object that specifies a custom set of valid days.
+    is_busday : Returns a boolean array indicating valid days.
+    busday_offset : Applies an offset counted in valid days.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> # Number of weekdays in January 2011
+    ... np.busday_count('2011-01', '2011-02')
+    21
+    >>> # Number of weekdays in 2011
+    >>> np.busday_count('2011', '2012')
+    260
+    >>> # Number of Saturdays in 2011
+    ... np.busday_count('2011', '2012', weekmask='Sat')
+    53
+    """
+    return (begindates, enddates, weekmask, holidays, out)
+
+
+@array_function_from_c_func_and_dispatcher(
+    _multiarray_umath.datetime_as_string)
+def datetime_as_string(arr, unit=None, timezone=None, casting=None):
+    """
+    datetime_as_string(arr, unit=None, timezone='naive', casting='same_kind')
+
+    Convert an array of datetimes into an array of strings.
+
+    Parameters
+    ----------
+    arr : array_like of datetime64
+        The array of UTC timestamps to format.
+    unit : str
+        One of None, 'auto', or
+        a :ref:`datetime unit <arrays.dtypes.dateunits>`.
+    timezone : {'naive', 'UTC', 'local'} or tzinfo
+        Timezone information to use when displaying the datetime. If 'UTC',
+        end with a Z to indicate UTC time. If 'local', convert to the local
+        timezone first, and suffix with a +-#### timezone offset. If a tzinfo
+        object, then do as with 'local', but use the specified timezone.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}
+        Casting to allow when changing between datetime units.
+
+    Returns
+    -------
+    str_arr : ndarray
+        An array of strings the same shape as `arr`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> import pytz
+    >>> d = np.arange('2002-10-27T04:30', 4*60, 60, dtype='M8[m]')
+    >>> d
+    array(['2002-10-27T04:30', '2002-10-27T05:30', '2002-10-27T06:30',
+           '2002-10-27T07:30'], dtype='datetime64[m]')
+
+    Setting the timezone to UTC shows the same information, but with a Z suffix
+
+    >>> np.datetime_as_string(d, timezone='UTC')
+    array(['2002-10-27T04:30Z', '2002-10-27T05:30Z', '2002-10-27T06:30Z',
+           '2002-10-27T07:30Z'], dtype='<U35')
+
+    Note that we picked datetimes that cross a DST boundary. Passing in a
+    ``pytz`` timezone object will print the appropriate offset
+
+    >>> np.datetime_as_string(d, timezone=pytz.timezone('US/Eastern'))
+    array(['2002-10-27T00:30-0400', '2002-10-27T01:30-0400',
+           '2002-10-27T01:30-0500', '2002-10-27T02:30-0500'], dtype='<U39')
+
+    Passing in a unit will change the precision
+
+    >>> np.datetime_as_string(d, unit='h')
+    array(['2002-10-27T04', '2002-10-27T05', '2002-10-27T06', '2002-10-27T07'],
+          dtype='<U32')
+    >>> np.datetime_as_string(d, unit='s')
+    array(['2002-10-27T04:30:00', '2002-10-27T05:30:00', '2002-10-27T06:30:00',
+           '2002-10-27T07:30:00'], dtype='<U38')
+
+    'casting' can be used to specify whether precision can be changed
+
+    >>> np.datetime_as_string(d, unit='h', casting='safe')
+    Traceback (most recent call last):
+        ...
+    TypeError: Cannot create a datetime string as units 'h' from a NumPy
+    datetime with units 'm' according to the rule 'safe'
+    """
+    return (arr,)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/multiarray.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/multiarray.pyi
new file mode 100644
index 0000000..13a3f00
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/multiarray.pyi
@@ -0,0 +1,1285 @@
+# TODO: Sort out any and all missing functions in this namespace
+import datetime as dt
+from collections.abc import Callable, Iterable, Sequence
+from typing import (
+    Any,
+    ClassVar,
+    Final,
+    Protocol,
+    SupportsIndex,
+    TypeAlias,
+    TypedDict,
+    TypeVar,
+    Unpack,
+    final,
+    overload,
+    type_check_only,
+)
+from typing import (
+    Literal as L,
+)
+
+from _typeshed import StrOrBytesPath, SupportsLenAndGetItem
+from typing_extensions import CapsuleType
+
+import numpy as np
+from numpy import (  # type: ignore[attr-defined]
+    _AnyShapeT,
+    _CastingKind,
+    _CopyMode,
+    _ModeKind,
+    _NDIterFlagsKind,
+    _NDIterFlagsOp,
+    _OrderCF,
+    _OrderKACF,
+    _SupportsBuffer,
+    _SupportsFileMethods,
+    broadcast,
+    # Re-exports
+    busdaycalendar,
+    complexfloating,
+    correlate,
+    count_nonzero,
+    datetime64,
+    dtype,
+    flatiter,
+    float64,
+    floating,
+    from_dlpack,
+    generic,
+    int_,
+    interp,
+    intp,
+    matmul,
+    ndarray,
+    nditer,
+    signedinteger,
+    str_,
+    timedelta64,
+    # The rest
+    ufunc,
+    uint8,
+    unsignedinteger,
+    vecdot,
+)
+from numpy import (
+    einsum as c_einsum,
+)
+from numpy._typing import (
+    ArrayLike,
+    # DTypes
+    DTypeLike,
+    # Arrays
+    NDArray,
+    _ArrayLike,
+    _ArrayLikeBool_co,
+    _ArrayLikeBytes_co,
+    _ArrayLikeComplex_co,
+    _ArrayLikeDT64_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeInt_co,
+    _ArrayLikeObject_co,
+    _ArrayLikeStr_co,
+    _ArrayLikeTD64_co,
+    _ArrayLikeUInt_co,
+    _DTypeLike,
+    _FloatLike_co,
+    _IntLike_co,
+    _NestedSequence,
+    _ScalarLike_co,
+    # Shapes
+    _Shape,
+    _ShapeLike,
+    _SupportsArrayFunc,
+    _SupportsDType,
+    _TD64Like_co,
+)
+from numpy._typing._ufunc import (
+    _2PTuple,
+    _PyFunc_Nin1_Nout1,
+    _PyFunc_Nin1P_Nout2P,
+    _PyFunc_Nin2_Nout1,
+    _PyFunc_Nin3P_Nout1,
+)
+from numpy.lib._array_utils_impl import normalize_axis_index
+
+__all__ = [
+    "_ARRAY_API",
+    "ALLOW_THREADS",
+    "BUFSIZE",
+    "CLIP",
+    "DATETIMEUNITS",
+    "ITEM_HASOBJECT",
+    "ITEM_IS_POINTER",
+    "LIST_PICKLE",
+    "MAXDIMS",
+    "MAY_SHARE_BOUNDS",
+    "MAY_SHARE_EXACT",
+    "NEEDS_INIT",
+    "NEEDS_PYAPI",
+    "RAISE",
+    "USE_GETITEM",
+    "USE_SETITEM",
+    "WRAP",
+    "_flagdict",
+    "from_dlpack",
+    "_place",
+    "_reconstruct",
+    "_vec_string",
+    "_monotonicity",
+    "add_docstring",
+    "arange",
+    "array",
+    "asarray",
+    "asanyarray",
+    "ascontiguousarray",
+    "asfortranarray",
+    "bincount",
+    "broadcast",
+    "busday_count",
+    "busday_offset",
+    "busdaycalendar",
+    "can_cast",
+    "compare_chararrays",
+    "concatenate",
+    "copyto",
+    "correlate",
+    "correlate2",
+    "count_nonzero",
+    "c_einsum",
+    "datetime_as_string",
+    "datetime_data",
+    "dot",
+    "dragon4_positional",
+    "dragon4_scientific",
+    "dtype",
+    "empty",
+    "empty_like",
+    "error",
+    "flagsobj",
+    "flatiter",
+    "format_longfloat",
+    "frombuffer",
+    "fromfile",
+    "fromiter",
+    "fromstring",
+    "get_handler_name",
+    "get_handler_version",
+    "inner",
+    "interp",
+    "interp_complex",
+    "is_busday",
+    "lexsort",
+    "matmul",
+    "vecdot",
+    "may_share_memory",
+    "min_scalar_type",
+    "ndarray",
+    "nditer",
+    "nested_iters",
+    "normalize_axis_index",
+    "packbits",
+    "promote_types",
+    "putmask",
+    "ravel_multi_index",
+    "result_type",
+    "scalar",
+    "set_datetimeparse_function",
+    "set_typeDict",
+    "shares_memory",
+    "typeinfo",
+    "unpackbits",
+    "unravel_index",
+    "vdot",
+    "where",
+    "zeros",
+]
+
+_ScalarT = TypeVar("_ScalarT", bound=generic)
+_DTypeT = TypeVar("_DTypeT", bound=np.dtype)
+_ArrayT = TypeVar("_ArrayT", bound=ndarray[Any, Any])
+_ArrayT_co = TypeVar(
+    "_ArrayT_co",
+    bound=ndarray[Any, Any],
+    covariant=True,
+)
+_ReturnType = TypeVar("_ReturnType")
+_IDType = TypeVar("_IDType")
+_Nin = TypeVar("_Nin", bound=int)
+_Nout = TypeVar("_Nout", bound=int)
+
+_ShapeT = TypeVar("_ShapeT", bound=_Shape)
+_Array: TypeAlias = ndarray[_ShapeT, dtype[_ScalarT]]
+_Array1D: TypeAlias = ndarray[tuple[int], dtype[_ScalarT]]
+
+# Valid time units
+_UnitKind: TypeAlias = L[
+    "Y",
+    "M",
+    "D",
+    "h",
+    "m",
+    "s",
+    "ms",
+    "us", "μs",
+    "ns",
+    "ps",
+    "fs",
+    "as",
+]
+_RollKind: TypeAlias = L[  # `raise` is deliberately excluded
+    "nat",
+    "forward",
+    "following",
+    "backward",
+    "preceding",
+    "modifiedfollowing",
+    "modifiedpreceding",
+]
+
+@type_check_only
+class _SupportsArray(Protocol[_ArrayT_co]):
+    def __array__(self, /) -> _ArrayT_co: ...
+
+@type_check_only
+class _KwargsEmpty(TypedDict, total=False):
+    device: L["cpu"] | None
+    like: _SupportsArrayFunc | None
+
+@type_check_only
+class _ConstructorEmpty(Protocol):
+    # 1-D shape
+    @overload
+    def __call__(
+        self,
+        /,
+        shape: SupportsIndex,
+        dtype: None = ...,
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> _Array1D[float64]: ...
+    @overload
+    def __call__(
+        self,
+        /,
+        shape: SupportsIndex,
+        dtype: _DTypeT | _SupportsDType[_DTypeT],
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> ndarray[tuple[int], _DTypeT]: ...
+    @overload
+    def __call__(
+        self,
+        /,
+        shape: SupportsIndex,
+        dtype: type[_ScalarT],
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> _Array1D[_ScalarT]: ...
+    @overload
+    def __call__(
+        self,
+        /,
+        shape: SupportsIndex,
+        dtype: DTypeLike | None = ...,
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> _Array1D[Any]: ...
+
+    # known shape
+    @overload
+    def __call__(
+        self,
+        /,
+        shape: _AnyShapeT,
+        dtype: None = ...,
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> _Array[_AnyShapeT, float64]: ...
+    @overload
+    def __call__(
+        self,
+        /,
+        shape: _AnyShapeT,
+        dtype: _DTypeT | _SupportsDType[_DTypeT],
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> ndarray[_AnyShapeT, _DTypeT]: ...
+    @overload
+    def __call__(
+        self,
+        /,
+        shape: _AnyShapeT,
+        dtype: type[_ScalarT],
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> _Array[_AnyShapeT, _ScalarT]: ...
+    @overload
+    def __call__(
+        self,
+        /,
+        shape: _AnyShapeT,
+        dtype: DTypeLike | None = ...,
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> _Array[_AnyShapeT, Any]: ...
+
+    # unknown shape
+    @overload
+    def __call__(
+        self, /,
+        shape: _ShapeLike,
+        dtype: None = ...,
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> NDArray[float64]: ...
+    @overload
+    def __call__(
+        self, /,
+        shape: _ShapeLike,
+        dtype: _DTypeT | _SupportsDType[_DTypeT],
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> ndarray[Any, _DTypeT]: ...
+    @overload
+    def __call__(
+        self, /,
+        shape: _ShapeLike,
+        dtype: type[_ScalarT],
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> NDArray[_ScalarT]: ...
+    @overload
+    def __call__(
+        self,
+        /,
+        shape: _ShapeLike,
+        dtype: DTypeLike | None = ...,
+        order: _OrderCF = ...,
+        **kwargs: Unpack[_KwargsEmpty],
+    ) -> NDArray[Any]: ...
+
+# using `Final` or `TypeAlias` will break stubtest
+error = Exception
+
+# from ._multiarray_umath
+ITEM_HASOBJECT: Final = 1
+LIST_PICKLE: Final = 2
+ITEM_IS_POINTER: Final = 4
+NEEDS_INIT: Final = 8
+NEEDS_PYAPI: Final = 16
+USE_GETITEM: Final = 32
+USE_SETITEM: Final = 64
+DATETIMEUNITS: Final[CapsuleType]
+_ARRAY_API: Final[CapsuleType]
+_flagdict: Final[dict[str, int]]
+_monotonicity: Final[Callable[..., object]]
+_place: Final[Callable[..., object]]
+_reconstruct: Final[Callable[..., object]]
+_vec_string: Final[Callable[..., object]]
+correlate2: Final[Callable[..., object]]
+dragon4_positional: Final[Callable[..., object]]
+dragon4_scientific: Final[Callable[..., object]]
+interp_complex: Final[Callable[..., object]]
+set_datetimeparse_function: Final[Callable[..., object]]
+def get_handler_name(a: NDArray[Any] = ..., /) -> str | None: ...
+def get_handler_version(a: NDArray[Any] = ..., /) -> int | None: ...
+def format_longfloat(x: np.longdouble, precision: int) -> str: ...
+def scalar(dtype: _DTypeT, object: bytes | object = ...) -> ndarray[tuple[()], _DTypeT]: ...
+def set_typeDict(dict_: dict[str, np.dtype], /) -> None: ...
+typeinfo: Final[dict[str, np.dtype[np.generic]]]
+
+ALLOW_THREADS: Final[int]  # 0 or 1 (system-specific)
+BUFSIZE: L[8192]
+CLIP: L[0]
+WRAP: L[1]
+RAISE: L[2]
+MAXDIMS: L[32]
+MAY_SHARE_BOUNDS: L[0]
+MAY_SHARE_EXACT: L[-1]
+tracemalloc_domain: L[389047]
+
+zeros: Final[_ConstructorEmpty]
+empty: Final[_ConstructorEmpty]
+
+@overload
+def empty_like(
+    prototype: _ArrayT,
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> _ArrayT: ...
+@overload
+def empty_like(
+    prototype: _ArrayLike[_ScalarT],
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def empty_like(
+    prototype: Any,
+    dtype: _DTypeLike[_ScalarT],
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def empty_like(
+    prototype: Any,
+    dtype: DTypeLike | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def array(
+    object: _ArrayT,
+    dtype: None = ...,
+    *,
+    copy: bool | _CopyMode | None = ...,
+    order: _OrderKACF = ...,
+    subok: L[True],
+    ndmin: int = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _ArrayT: ...
+@overload
+def array(
+    object: _SupportsArray[_ArrayT],
+    dtype: None = ...,
+    *,
+    copy: bool | _CopyMode | None = ...,
+    order: _OrderKACF = ...,
+    subok: L[True],
+    ndmin: L[0] = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _ArrayT: ...
+@overload
+def array(
+    object: _ArrayLike[_ScalarT],
+    dtype: None = ...,
+    *,
+    copy: bool | _CopyMode | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    ndmin: int = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def array(
+    object: Any,
+    dtype: _DTypeLike[_ScalarT],
+    *,
+    copy: bool | _CopyMode | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    ndmin: int = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def array(
+    object: Any,
+    dtype: DTypeLike | None = ...,
+    *,
+    copy: bool | _CopyMode | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    ndmin: int = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+#
+@overload
+def ravel_multi_index(
+    multi_index: SupportsLenAndGetItem[_IntLike_co],
+    dims: _ShapeLike,
+    mode: _ModeKind | tuple[_ModeKind, ...] = "raise",
+    order: _OrderCF = "C",
+) -> intp: ...
+@overload
+def ravel_multi_index(
+    multi_index: SupportsLenAndGetItem[_ArrayLikeInt_co],
+    dims: _ShapeLike,
+    mode: _ModeKind | tuple[_ModeKind, ...] = "raise",
+    order: _OrderCF = "C",
+) -> NDArray[intp]: ...
+
+#
+@overload
+def unravel_index(indices: _IntLike_co, shape: _ShapeLike, order: _OrderCF = "C") -> tuple[intp, ...]: ...
+@overload
+def unravel_index(indices: _ArrayLikeInt_co, shape: _ShapeLike, order: _OrderCF = "C") -> tuple[NDArray[intp], ...]: ...
+
+# NOTE: Allow any sequence of array-like objects
+@overload
+def concatenate(  # type: ignore[misc]
+    arrays: _ArrayLike[_ScalarT],
+    /,
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+    *,
+    dtype: None = ...,
+    casting: _CastingKind | None = ...
+) -> NDArray[_ScalarT]: ...
+@overload
+@overload
+def concatenate(  # type: ignore[misc]
+    arrays: SupportsLenAndGetItem[ArrayLike],
+    /,
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    casting: _CastingKind | None = ...
+) -> NDArray[_ScalarT]: ...
+@overload
+def concatenate(  # type: ignore[misc]
+    arrays: SupportsLenAndGetItem[ArrayLike],
+    /,
+    axis: SupportsIndex | None = ...,
+    out: None = ...,
+    *,
+    dtype: DTypeLike | None = None,
+    casting: _CastingKind | None = ...
+) -> NDArray[Any]: ...
+@overload
+def concatenate(
+    arrays: SupportsLenAndGetItem[ArrayLike],
+    /,
+    axis: SupportsIndex | None = ...,
+    out: _ArrayT = ...,
+    *,
+    dtype: DTypeLike = ...,
+    casting: _CastingKind | None = ...
+) -> _ArrayT: ...
+
+def inner(
+    a: ArrayLike,
+    b: ArrayLike,
+    /,
+) -> Any: ...
+
+@overload
+def where(
+    condition: ArrayLike,
+    /,
+) -> tuple[NDArray[intp], ...]: ...
+@overload
+def where(
+    condition: ArrayLike,
+    x: ArrayLike,
+    y: ArrayLike,
+    /,
+) -> NDArray[Any]: ...
+
+def lexsort(
+    keys: ArrayLike,
+    axis: SupportsIndex | None = ...,
+) -> Any: ...
+
+def can_cast(
+    from_: ArrayLike | DTypeLike,
+    to: DTypeLike,
+    casting: _CastingKind | None = ...,
+) -> bool: ...
+
+def min_scalar_type(a: ArrayLike, /) -> dtype: ...
+
+def result_type(*arrays_and_dtypes: ArrayLike | DTypeLike) -> dtype: ...
+
+@overload
+def dot(a: ArrayLike, b: ArrayLike, out: None = ...) -> Any: ...
+@overload
+def dot(a: ArrayLike, b: ArrayLike, out: _ArrayT) -> _ArrayT: ...
+
+@overload
+def vdot(a: _ArrayLikeBool_co, b: _ArrayLikeBool_co, /) -> np.bool: ...  # type: ignore[misc]
+@overload
+def vdot(a: _ArrayLikeUInt_co, b: _ArrayLikeUInt_co, /) -> unsignedinteger: ...  # type: ignore[misc]
+@overload
+def vdot(a: _ArrayLikeInt_co, b: _ArrayLikeInt_co, /) -> signedinteger: ...  # type: ignore[misc]
+@overload
+def vdot(a: _ArrayLikeFloat_co, b: _ArrayLikeFloat_co, /) -> floating: ...  # type: ignore[misc]
+@overload
+def vdot(a: _ArrayLikeComplex_co, b: _ArrayLikeComplex_co, /) -> complexfloating: ...  # type: ignore[misc]
+@overload
+def vdot(a: _ArrayLikeTD64_co, b: _ArrayLikeTD64_co, /) -> timedelta64: ...
+@overload
+def vdot(a: _ArrayLikeObject_co, b: Any, /) -> Any: ...
+@overload
+def vdot(a: Any, b: _ArrayLikeObject_co, /) -> Any: ...
+
+def bincount(
+    x: ArrayLike,
+    /,
+    weights: ArrayLike | None = ...,
+    minlength: SupportsIndex = ...,
+) -> NDArray[intp]: ...
+
+def copyto(
+    dst: NDArray[Any],
+    src: ArrayLike,
+    casting: _CastingKind | None = ...,
+    where: _ArrayLikeBool_co | None = ...,
+) -> None: ...
+
+def putmask(
+    a: NDArray[Any],
+    /,
+    mask: _ArrayLikeBool_co,
+    values: ArrayLike,
+) -> None: ...
+
+def packbits(
+    a: _ArrayLikeInt_co,
+    /,
+    axis: SupportsIndex | None = ...,
+    bitorder: L["big", "little"] = ...,
+) -> NDArray[uint8]: ...
+
+def unpackbits(
+    a: _ArrayLike[uint8],
+    /,
+    axis: SupportsIndex | None = ...,
+    count: SupportsIndex | None = ...,
+    bitorder: L["big", "little"] = ...,
+) -> NDArray[uint8]: ...
+
+def shares_memory(
+    a: object,
+    b: object,
+    /,
+    max_work: int | None = ...,
+) -> bool: ...
+
+def may_share_memory(
+    a: object,
+    b: object,
+    /,
+    max_work: int | None = ...,
+) -> bool: ...
+
+@overload
+def asarray(
+    a: _ArrayLike[_ScalarT],
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    copy: bool | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def asarray(
+    a: Any,
+    dtype: _DTypeLike[_ScalarT],
+    order: _OrderKACF = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    copy: bool | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def asarray(
+    a: Any,
+    dtype: DTypeLike | None = ...,
+    order: _OrderKACF = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    copy: bool | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def asanyarray(
+    a: _ArrayT,  # Preserve subclass-information
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    copy: bool | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _ArrayT: ...
+@overload
+def asanyarray(
+    a: _ArrayLike[_ScalarT],
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    copy: bool | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def asanyarray(
+    a: Any,
+    dtype: _DTypeLike[_ScalarT],
+    order: _OrderKACF = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    copy: bool | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def asanyarray(
+    a: Any,
+    dtype: DTypeLike | None = ...,
+    order: _OrderKACF = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    copy: bool | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def ascontiguousarray(
+    a: _ArrayLike[_ScalarT],
+    dtype: None = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def ascontiguousarray(
+    a: Any,
+    dtype: _DTypeLike[_ScalarT],
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def ascontiguousarray(
+    a: Any,
+    dtype: DTypeLike | None = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def asfortranarray(
+    a: _ArrayLike[_ScalarT],
+    dtype: None = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def asfortranarray(
+    a: Any,
+    dtype: _DTypeLike[_ScalarT],
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def asfortranarray(
+    a: Any,
+    dtype: DTypeLike | None = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+def promote_types(__type1: DTypeLike, __type2: DTypeLike) -> dtype: ...
+
+# `sep` is a de facto mandatory argument, as its default value is deprecated
+@overload
+def fromstring(
+    string: str | bytes,
+    dtype: None = ...,
+    count: SupportsIndex = ...,
+    *,
+    sep: str,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[float64]: ...
+@overload
+def fromstring(
+    string: str | bytes,
+    dtype: _DTypeLike[_ScalarT],
+    count: SupportsIndex = ...,
+    *,
+    sep: str,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def fromstring(
+    string: str | bytes,
+    dtype: DTypeLike | None = ...,
+    count: SupportsIndex = ...,
+    *,
+    sep: str,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def frompyfunc(  # type: ignore[overload-overlap]
+    func: Callable[[Any], _ReturnType], /,
+    nin: L[1],
+    nout: L[1],
+    *,
+    identity: None = ...,
+) -> _PyFunc_Nin1_Nout1[_ReturnType, None]: ...
+@overload
+def frompyfunc(  # type: ignore[overload-overlap]
+    func: Callable[[Any], _ReturnType], /,
+    nin: L[1],
+    nout: L[1],
+    *,
+    identity: _IDType,
+) -> _PyFunc_Nin1_Nout1[_ReturnType, _IDType]: ...
+@overload
+def frompyfunc(  # type: ignore[overload-overlap]
+    func: Callable[[Any, Any], _ReturnType], /,
+    nin: L[2],
+    nout: L[1],
+    *,
+    identity: None = ...,
+) -> _PyFunc_Nin2_Nout1[_ReturnType, None]: ...
+@overload
+def frompyfunc(  # type: ignore[overload-overlap]
+    func: Callable[[Any, Any], _ReturnType], /,
+    nin: L[2],
+    nout: L[1],
+    *,
+    identity: _IDType,
+) -> _PyFunc_Nin2_Nout1[_ReturnType, _IDType]: ...
+@overload
+def frompyfunc(  # type: ignore[overload-overlap]
+    func: Callable[..., _ReturnType], /,
+    nin: _Nin,
+    nout: L[1],
+    *,
+    identity: None = ...,
+) -> _PyFunc_Nin3P_Nout1[_ReturnType, None, _Nin]: ...
+@overload
+def frompyfunc(  # type: ignore[overload-overlap]
+    func: Callable[..., _ReturnType], /,
+    nin: _Nin,
+    nout: L[1],
+    *,
+    identity: _IDType,
+) -> _PyFunc_Nin3P_Nout1[_ReturnType, _IDType, _Nin]: ...
+@overload
+def frompyfunc(
+    func: Callable[..., _2PTuple[_ReturnType]], /,
+    nin: _Nin,
+    nout: _Nout,
+    *,
+    identity: None = ...,
+) -> _PyFunc_Nin1P_Nout2P[_ReturnType, None, _Nin, _Nout]: ...
+@overload
+def frompyfunc(
+    func: Callable[..., _2PTuple[_ReturnType]], /,
+    nin: _Nin,
+    nout: _Nout,
+    *,
+    identity: _IDType,
+) -> _PyFunc_Nin1P_Nout2P[_ReturnType, _IDType, _Nin, _Nout]: ...
+@overload
+def frompyfunc(
+    func: Callable[..., Any], /,
+    nin: SupportsIndex,
+    nout: SupportsIndex,
+    *,
+    identity: object | None = ...,
+) -> ufunc: ...
+
+@overload
+def fromfile(
+    file: StrOrBytesPath | _SupportsFileMethods,
+    dtype: None = ...,
+    count: SupportsIndex = ...,
+    sep: str = ...,
+    offset: SupportsIndex = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[float64]: ...
+@overload
+def fromfile(
+    file: StrOrBytesPath | _SupportsFileMethods,
+    dtype: _DTypeLike[_ScalarT],
+    count: SupportsIndex = ...,
+    sep: str = ...,
+    offset: SupportsIndex = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def fromfile(
+    file: StrOrBytesPath | _SupportsFileMethods,
+    dtype: DTypeLike | None = ...,
+    count: SupportsIndex = ...,
+    sep: str = ...,
+    offset: SupportsIndex = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def fromiter(
+    iter: Iterable[Any],
+    dtype: _DTypeLike[_ScalarT],
+    count: SupportsIndex = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def fromiter(
+    iter: Iterable[Any],
+    dtype: DTypeLike,
+    count: SupportsIndex = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def frombuffer(
+    buffer: _SupportsBuffer,
+    dtype: None = ...,
+    count: SupportsIndex = ...,
+    offset: SupportsIndex = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[float64]: ...
+@overload
+def frombuffer(
+    buffer: _SupportsBuffer,
+    dtype: _DTypeLike[_ScalarT],
+    count: SupportsIndex = ...,
+    offset: SupportsIndex = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def frombuffer(
+    buffer: _SupportsBuffer,
+    dtype: DTypeLike | None = ...,
+    count: SupportsIndex = ...,
+    offset: SupportsIndex = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def arange(  # type: ignore[misc]
+    stop: _IntLike_co,
+    /, *,
+    dtype: None = ...,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[signedinteger]: ...
+@overload
+def arange(  # type: ignore[misc]
+    start: _IntLike_co,
+    stop: _IntLike_co,
+    step: _IntLike_co = ...,
+    dtype: None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[signedinteger]: ...
+@overload
+def arange(  # type: ignore[misc]
+    stop: _FloatLike_co,
+    /, *,
+    dtype: None = ...,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[floating]: ...
+@overload
+def arange(  # type: ignore[misc]
+    start: _FloatLike_co,
+    stop: _FloatLike_co,
+    step: _FloatLike_co = ...,
+    dtype: None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[floating]: ...
+@overload
+def arange(
+    stop: _TD64Like_co,
+    /, *,
+    dtype: None = ...,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[timedelta64]: ...
+@overload
+def arange(
+    start: _TD64Like_co,
+    stop: _TD64Like_co,
+    step: _TD64Like_co = ...,
+    dtype: None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[timedelta64]: ...
+@overload
+def arange(  # both start and stop must always be specified for datetime64
+    start: datetime64,
+    stop: datetime64,
+    step: datetime64 = ...,
+    dtype: None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[datetime64]: ...
+@overload
+def arange(
+    stop: Any,
+    /, *,
+    dtype: _DTypeLike[_ScalarT],
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[_ScalarT]: ...
+@overload
+def arange(
+    start: Any,
+    stop: Any,
+    step: Any = ...,
+    dtype: _DTypeLike[_ScalarT] = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[_ScalarT]: ...
+@overload
+def arange(
+    stop: Any, /,
+    *,
+    dtype: DTypeLike | None = ...,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[Any]: ...
+@overload
+def arange(
+    start: Any,
+    stop: Any,
+    step: Any = ...,
+    dtype: DTypeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+    like: _SupportsArrayFunc | None = ...,
+) -> _Array1D[Any]: ...
+
+def datetime_data(
+    dtype: str | _DTypeLike[datetime64] | _DTypeLike[timedelta64], /,
+) -> tuple[str, int]: ...
+
+# The datetime functions perform unsafe casts to `datetime64[D]`,
+# so a lot of different argument types are allowed here
+
+@overload
+def busday_count(  # type: ignore[misc]
+    begindates: _ScalarLike_co | dt.date,
+    enddates: _ScalarLike_co | dt.date,
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: None = ...,
+) -> int_: ...
+@overload
+def busday_count(  # type: ignore[misc]
+    begindates: ArrayLike | dt.date | _NestedSequence[dt.date],
+    enddates: ArrayLike | dt.date | _NestedSequence[dt.date],
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: None = ...,
+) -> NDArray[int_]: ...
+@overload
+def busday_count(
+    begindates: ArrayLike | dt.date | _NestedSequence[dt.date],
+    enddates: ArrayLike | dt.date | _NestedSequence[dt.date],
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: _ArrayT = ...,
+) -> _ArrayT: ...
+
+# `roll="raise"` is (more or less?) equivalent to `casting="safe"`
+@overload
+def busday_offset(  # type: ignore[misc]
+    dates: datetime64 | dt.date,
+    offsets: _TD64Like_co | dt.timedelta,
+    roll: L["raise"] = ...,
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: None = ...,
+) -> datetime64: ...
+@overload
+def busday_offset(  # type: ignore[misc]
+    dates: _ArrayLike[datetime64] | dt.date | _NestedSequence[dt.date],
+    offsets: _ArrayLikeTD64_co | dt.timedelta | _NestedSequence[dt.timedelta],
+    roll: L["raise"] = ...,
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: None = ...,
+) -> NDArray[datetime64]: ...
+@overload
+def busday_offset(  # type: ignore[misc]
+    dates: _ArrayLike[datetime64] | dt.date | _NestedSequence[dt.date],
+    offsets: _ArrayLikeTD64_co | dt.timedelta | _NestedSequence[dt.timedelta],
+    roll: L["raise"] = ...,
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: _ArrayT = ...,
+) -> _ArrayT: ...
+@overload
+def busday_offset(  # type: ignore[misc]
+    dates: _ScalarLike_co | dt.date,
+    offsets: _ScalarLike_co | dt.timedelta,
+    roll: _RollKind,
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: None = ...,
+) -> datetime64: ...
+@overload
+def busday_offset(  # type: ignore[misc]
+    dates: ArrayLike | dt.date | _NestedSequence[dt.date],
+    offsets: ArrayLike | dt.timedelta | _NestedSequence[dt.timedelta],
+    roll: _RollKind,
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: None = ...,
+) -> NDArray[datetime64]: ...
+@overload
+def busday_offset(
+    dates: ArrayLike | dt.date | _NestedSequence[dt.date],
+    offsets: ArrayLike | dt.timedelta | _NestedSequence[dt.timedelta],
+    roll: _RollKind,
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: _ArrayT = ...,
+) -> _ArrayT: ...
+
+@overload
+def is_busday(  # type: ignore[misc]
+    dates: _ScalarLike_co | dt.date,
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: None = ...,
+) -> np.bool: ...
+@overload
+def is_busday(  # type: ignore[misc]
+    dates: ArrayLike | _NestedSequence[dt.date],
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def is_busday(
+    dates: ArrayLike | _NestedSequence[dt.date],
+    weekmask: ArrayLike = ...,
+    holidays: ArrayLike | dt.date | _NestedSequence[dt.date] | None = ...,
+    busdaycal: busdaycalendar | None = ...,
+    out: _ArrayT = ...,
+) -> _ArrayT: ...
+
+@overload
+def datetime_as_string(  # type: ignore[misc]
+    arr: datetime64 | dt.date,
+    unit: L["auto"] | _UnitKind | None = ...,
+    timezone: L["naive", "UTC", "local"] | dt.tzinfo = ...,
+    casting: _CastingKind = ...,
+) -> str_: ...
+@overload
+def datetime_as_string(
+    arr: _ArrayLikeDT64_co | _NestedSequence[dt.date],
+    unit: L["auto"] | _UnitKind | None = ...,
+    timezone: L["naive", "UTC", "local"] | dt.tzinfo = ...,
+    casting: _CastingKind = ...,
+) -> NDArray[str_]: ...
+
+@overload
+def compare_chararrays(
+    a1: _ArrayLikeStr_co,
+    a2: _ArrayLikeStr_co,
+    cmp: L["<", "<=", "==", ">=", ">", "!="],
+    rstrip: bool,
+) -> NDArray[np.bool]: ...
+@overload
+def compare_chararrays(
+    a1: _ArrayLikeBytes_co,
+    a2: _ArrayLikeBytes_co,
+    cmp: L["<", "<=", "==", ">=", ">", "!="],
+    rstrip: bool,
+) -> NDArray[np.bool]: ...
+
+def add_docstring(obj: Callable[..., Any], docstring: str, /) -> None: ...
+
+_GetItemKeys: TypeAlias = L[
+    "C", "CONTIGUOUS", "C_CONTIGUOUS",
+    "F", "FORTRAN", "F_CONTIGUOUS",
+    "W", "WRITEABLE",
+    "B", "BEHAVED",
+    "O", "OWNDATA",
+    "A", "ALIGNED",
+    "X", "WRITEBACKIFCOPY",
+    "CA", "CARRAY",
+    "FA", "FARRAY",
+    "FNC",
+    "FORC",
+]
+_SetItemKeys: TypeAlias = L[
+    "A", "ALIGNED",
+    "W", "WRITEABLE",
+    "X", "WRITEBACKIFCOPY",
+]
+
+@final
+class flagsobj:
+    __hash__: ClassVar[None]  # type: ignore[assignment]
+    aligned: bool
+    # NOTE: deprecated
+    # updateifcopy: bool
+    writeable: bool
+    writebackifcopy: bool
+    @property
+    def behaved(self) -> bool: ...
+    @property
+    def c_contiguous(self) -> bool: ...
+    @property
+    def carray(self) -> bool: ...
+    @property
+    def contiguous(self) -> bool: ...
+    @property
+    def f_contiguous(self) -> bool: ...
+    @property
+    def farray(self) -> bool: ...
+    @property
+    def fnc(self) -> bool: ...
+    @property
+    def forc(self) -> bool: ...
+    @property
+    def fortran(self) -> bool: ...
+    @property
+    def num(self) -> int: ...
+    @property
+    def owndata(self) -> bool: ...
+    def __getitem__(self, key: _GetItemKeys) -> bool: ...
+    def __setitem__(self, key: _SetItemKeys, value: bool) -> None: ...
+
+def nested_iters(
+    op: ArrayLike | Sequence[ArrayLike],
+    axes: Sequence[Sequence[SupportsIndex]],
+    flags: Sequence[_NDIterFlagsKind] | None = ...,
+    op_flags: Sequence[Sequence[_NDIterFlagsOp]] | None = ...,
+    op_dtypes: DTypeLike | Sequence[DTypeLike] = ...,
+    order: _OrderKACF = ...,
+    casting: _CastingKind = ...,
+    buffersize: SupportsIndex = ...,
+) -> tuple[nditer, ...]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/numeric.py b/.venv/lib/python3.12/site-packages/numpy/_core/numeric.py
new file mode 100644
index 0000000..964447f
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/numeric.py
@@ -0,0 +1,2760 @@
+import builtins
+import functools
+import itertools
+import math
+import numbers
+import operator
+import sys
+import warnings
+
+import numpy as np
+from numpy.exceptions import AxisError
+
+from . import multiarray, numerictypes, overrides, shape_base, umath
+from . import numerictypes as nt
+from ._ufunc_config import errstate
+from .multiarray import (  # noqa: F401
+    ALLOW_THREADS,
+    BUFSIZE,
+    CLIP,
+    MAXDIMS,
+    MAY_SHARE_BOUNDS,
+    MAY_SHARE_EXACT,
+    RAISE,
+    WRAP,
+    arange,
+    array,
+    asanyarray,
+    asarray,
+    ascontiguousarray,
+    asfortranarray,
+    broadcast,
+    can_cast,
+    concatenate,
+    copyto,
+    dot,
+    dtype,
+    empty,
+    empty_like,
+    flatiter,
+    from_dlpack,
+    frombuffer,
+    fromfile,
+    fromiter,
+    fromstring,
+    inner,
+    lexsort,
+    matmul,
+    may_share_memory,
+    min_scalar_type,
+    ndarray,
+    nditer,
+    nested_iters,
+    normalize_axis_index,
+    promote_types,
+    putmask,
+    result_type,
+    shares_memory,
+    vdot,
+    vecdot,
+    where,
+    zeros,
+)
+from .overrides import finalize_array_function_like, set_module
+from .umath import NAN, PINF, invert, multiply, sin
+
+bitwise_not = invert
+ufunc = type(sin)
+newaxis = None
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+__all__ = [
+    'newaxis', 'ndarray', 'flatiter', 'nditer', 'nested_iters', 'ufunc',
+    'arange', 'array', 'asarray', 'asanyarray', 'ascontiguousarray',
+    'asfortranarray', 'zeros', 'count_nonzero', 'empty', 'broadcast', 'dtype',
+    'fromstring', 'fromfile', 'frombuffer', 'from_dlpack', 'where',
+    'argwhere', 'copyto', 'concatenate', 'lexsort', 'astype',
+    'can_cast', 'promote_types', 'min_scalar_type',
+    'result_type', 'isfortran', 'empty_like', 'zeros_like', 'ones_like',
+    'correlate', 'convolve', 'inner', 'dot', 'outer', 'vdot', 'roll',
+    'rollaxis', 'moveaxis', 'cross', 'tensordot', 'little_endian',
+    'fromiter', 'array_equal', 'array_equiv', 'indices', 'fromfunction',
+    'isclose', 'isscalar', 'binary_repr', 'base_repr', 'ones',
+    'identity', 'allclose', 'putmask',
+    'flatnonzero', 'inf', 'nan', 'False_', 'True_', 'bitwise_not',
+    'full', 'full_like', 'matmul', 'vecdot', 'shares_memory',
+    'may_share_memory']
+
+
+def _zeros_like_dispatcher(
+    a, dtype=None, order=None, subok=None, shape=None, *, device=None
+):
+    return (a,)
+
+
+@array_function_dispatch(_zeros_like_dispatcher)
+def zeros_like(
+    a, dtype=None, order='K', subok=True, shape=None, *, device=None
+):
+    """
+    Return an array of zeros with the same shape and type as a given array.
+
+    Parameters
+    ----------
+    a : array_like
+        The shape and data-type of `a` define these same attributes of
+        the returned array.
+    dtype : data-type, optional
+        Overrides the data type of the result.
+    order : {'C', 'F', 'A', or 'K'}, optional
+        Overrides the memory layout of the result. 'C' means C-order,
+        'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
+        'C' otherwise. 'K' means match the layout of `a` as closely
+        as possible.
+    subok : bool, optional.
+        If True, then the newly created array will use the sub-class
+        type of `a`, otherwise it will be a base-class array. Defaults
+        to True.
+    shape : int or sequence of ints, optional.
+        Overrides the shape of the result. If order='K' and the number of
+        dimensions is unchanged, will try to keep order, otherwise,
+        order='C' is implied.
+    device : str, optional
+        The device on which to place the created array. Default: None.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    out : ndarray
+        Array of zeros with the same shape and type as `a`.
+
+    See Also
+    --------
+    empty_like : Return an empty array with shape and type of input.
+    ones_like : Return an array of ones with shape and type of input.
+    full_like : Return a new array with shape of input filled with value.
+    zeros : Return a new array setting values to zero.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6)
+    >>> x = x.reshape((2, 3))
+    >>> x
+    array([[0, 1, 2],
+           [3, 4, 5]])
+    >>> np.zeros_like(x)
+    array([[0, 0, 0],
+           [0, 0, 0]])
+
+    >>> y = np.arange(3, dtype=float)
+    >>> y
+    array([0., 1., 2.])
+    >>> np.zeros_like(y)
+    array([0.,  0.,  0.])
+
+    """
+    res = empty_like(
+        a, dtype=dtype, order=order, subok=subok, shape=shape, device=device
+    )
+    # needed instead of a 0 to get same result as zeros for string dtypes
+    z = zeros(1, dtype=res.dtype)
+    multiarray.copyto(res, z, casting='unsafe')
+    return res
+
+
+@finalize_array_function_like
+@set_module('numpy')
+def ones(shape, dtype=None, order='C', *, device=None, like=None):
+    """
+    Return a new array of given shape and type, filled with ones.
+
+    Parameters
+    ----------
+    shape : int or sequence of ints
+        Shape of the new array, e.g., ``(2, 3)`` or ``2``.
+    dtype : data-type, optional
+        The desired data-type for the array, e.g., `numpy.int8`.  Default is
+        `numpy.float64`.
+    order : {'C', 'F'}, optional, default: C
+        Whether to store multi-dimensional data in row-major
+        (C-style) or column-major (Fortran-style) order in
+        memory.
+    device : str, optional
+        The device on which to place the created array. Default: None.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        Array of ones with the given shape, dtype, and order.
+
+    See Also
+    --------
+    ones_like : Return an array of ones with shape and type of input.
+    empty : Return a new uninitialized array.
+    zeros : Return a new array setting values to zero.
+    full : Return a new array of given shape filled with value.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.ones(5)
+    array([1., 1., 1., 1., 1.])
+
+    >>> np.ones((5,), dtype=int)
+    array([1, 1, 1, 1, 1])
+
+    >>> np.ones((2, 1))
+    array([[1.],
+           [1.]])
+
+    >>> s = (2,2)
+    >>> np.ones(s)
+    array([[1.,  1.],
+           [1.,  1.]])
+
+    """
+    if like is not None:
+        return _ones_with_like(
+            like, shape, dtype=dtype, order=order, device=device
+        )
+
+    a = empty(shape, dtype, order, device=device)
+    multiarray.copyto(a, 1, casting='unsafe')
+    return a
+
+
+_ones_with_like = array_function_dispatch()(ones)
+
+
+def _ones_like_dispatcher(
+    a, dtype=None, order=None, subok=None, shape=None, *, device=None
+):
+    return (a,)
+
+
+@array_function_dispatch(_ones_like_dispatcher)
+def ones_like(
+    a, dtype=None, order='K', subok=True, shape=None, *, device=None
+):
+    """
+    Return an array of ones with the same shape and type as a given array.
+
+    Parameters
+    ----------
+    a : array_like
+        The shape and data-type of `a` define these same attributes of
+        the returned array.
+    dtype : data-type, optional
+        Overrides the data type of the result.
+    order : {'C', 'F', 'A', or 'K'}, optional
+        Overrides the memory layout of the result. 'C' means C-order,
+        'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
+        'C' otherwise. 'K' means match the layout of `a` as closely
+        as possible.
+    subok : bool, optional.
+        If True, then the newly created array will use the sub-class
+        type of `a`, otherwise it will be a base-class array. Defaults
+        to True.
+    shape : int or sequence of ints, optional.
+        Overrides the shape of the result. If order='K' and the number of
+        dimensions is unchanged, will try to keep order, otherwise,
+        order='C' is implied.
+    device : str, optional
+        The device on which to place the created array. Default: None.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    out : ndarray
+        Array of ones with the same shape and type as `a`.
+
+    See Also
+    --------
+    empty_like : Return an empty array with shape and type of input.
+    zeros_like : Return an array of zeros with shape and type of input.
+    full_like : Return a new array with shape of input filled with value.
+    ones : Return a new array setting values to one.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6)
+    >>> x = x.reshape((2, 3))
+    >>> x
+    array([[0, 1, 2],
+           [3, 4, 5]])
+    >>> np.ones_like(x)
+    array([[1, 1, 1],
+           [1, 1, 1]])
+
+    >>> y = np.arange(3, dtype=float)
+    >>> y
+    array([0., 1., 2.])
+    >>> np.ones_like(y)
+    array([1.,  1.,  1.])
+
+    """
+    res = empty_like(
+        a, dtype=dtype, order=order, subok=subok, shape=shape, device=device
+    )
+    multiarray.copyto(res, 1, casting='unsafe')
+    return res
+
+
+def _full_dispatcher(
+    shape, fill_value, dtype=None, order=None, *, device=None, like=None
+):
+    return (like,)
+
+
+@finalize_array_function_like
+@set_module('numpy')
+def full(shape, fill_value, dtype=None, order='C', *, device=None, like=None):
+    """
+    Return a new array of given shape and type, filled with `fill_value`.
+
+    Parameters
+    ----------
+    shape : int or sequence of ints
+        Shape of the new array, e.g., ``(2, 3)`` or ``2``.
+    fill_value : scalar or array_like
+        Fill value.
+    dtype : data-type, optional
+        The desired data-type for the array  The default, None, means
+         ``np.array(fill_value).dtype``.
+    order : {'C', 'F'}, optional
+        Whether to store multidimensional data in C- or Fortran-contiguous
+        (row- or column-wise) order in memory.
+    device : str, optional
+        The device on which to place the created array. Default: None.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        Array of `fill_value` with the given shape, dtype, and order.
+
+    See Also
+    --------
+    full_like : Return a new array with shape of input filled with value.
+    empty : Return a new uninitialized array.
+    ones : Return a new array setting values to one.
+    zeros : Return a new array setting values to zero.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.full((2, 2), np.inf)
+    array([[inf, inf],
+           [inf, inf]])
+    >>> np.full((2, 2), 10)
+    array([[10, 10],
+           [10, 10]])
+
+    >>> np.full((2, 2), [1, 2])
+    array([[1, 2],
+           [1, 2]])
+
+    """
+    if like is not None:
+        return _full_with_like(
+            like, shape, fill_value, dtype=dtype, order=order, device=device
+        )
+
+    if dtype is None:
+        fill_value = asarray(fill_value)
+        dtype = fill_value.dtype
+    a = empty(shape, dtype, order, device=device)
+    multiarray.copyto(a, fill_value, casting='unsafe')
+    return a
+
+
+_full_with_like = array_function_dispatch()(full)
+
+
+def _full_like_dispatcher(
+    a, fill_value, dtype=None, order=None, subok=None, shape=None,
+    *, device=None
+):
+    return (a,)
+
+
+@array_function_dispatch(_full_like_dispatcher)
+def full_like(
+    a, fill_value, dtype=None, order='K', subok=True, shape=None,
+    *, device=None
+):
+    """
+    Return a full array with the same shape and type as a given array.
+
+    Parameters
+    ----------
+    a : array_like
+        The shape and data-type of `a` define these same attributes of
+        the returned array.
+    fill_value : array_like
+        Fill value.
+    dtype : data-type, optional
+        Overrides the data type of the result.
+    order : {'C', 'F', 'A', or 'K'}, optional
+        Overrides the memory layout of the result. 'C' means C-order,
+        'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
+        'C' otherwise. 'K' means match the layout of `a` as closely
+        as possible.
+    subok : bool, optional.
+        If True, then the newly created array will use the sub-class
+        type of `a`, otherwise it will be a base-class array. Defaults
+        to True.
+    shape : int or sequence of ints, optional.
+        Overrides the shape of the result. If order='K' and the number of
+        dimensions is unchanged, will try to keep order, otherwise,
+        order='C' is implied.
+    device : str, optional
+        The device on which to place the created array. Default: None.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.0.0
+
+    Returns
+    -------
+    out : ndarray
+        Array of `fill_value` with the same shape and type as `a`.
+
+    See Also
+    --------
+    empty_like : Return an empty array with shape and type of input.
+    ones_like : Return an array of ones with shape and type of input.
+    zeros_like : Return an array of zeros with shape and type of input.
+    full : Return a new array of given shape filled with value.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6, dtype=int)
+    >>> np.full_like(x, 1)
+    array([1, 1, 1, 1, 1, 1])
+    >>> np.full_like(x, 0.1)
+    array([0, 0, 0, 0, 0, 0])
+    >>> np.full_like(x, 0.1, dtype=np.double)
+    array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
+    >>> np.full_like(x, np.nan, dtype=np.double)
+    array([nan, nan, nan, nan, nan, nan])
+
+    >>> y = np.arange(6, dtype=np.double)
+    >>> np.full_like(y, 0.1)
+    array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
+
+    >>> y = np.zeros([2, 2, 3], dtype=int)
+    >>> np.full_like(y, [0, 0, 255])
+    array([[[  0,   0, 255],
+            [  0,   0, 255]],
+           [[  0,   0, 255],
+            [  0,   0, 255]]])
+    """
+    res = empty_like(
+        a, dtype=dtype, order=order, subok=subok, shape=shape, device=device
+    )
+    multiarray.copyto(res, fill_value, casting='unsafe')
+    return res
+
+
+def _count_nonzero_dispatcher(a, axis=None, *, keepdims=None):
+    return (a,)
+
+
+@array_function_dispatch(_count_nonzero_dispatcher)
+def count_nonzero(a, axis=None, *, keepdims=False):
+    """
+    Counts the number of non-zero values in the array ``a``.
+
+    The word "non-zero" is in reference to the Python 2.x
+    built-in method ``__nonzero__()`` (renamed ``__bool__()``
+    in Python 3.x) of Python objects that tests an object's
+    "truthfulness". For example, any number is considered
+    truthful if it is nonzero, whereas any string is considered
+    truthful if it is not the empty string. Thus, this function
+    (recursively) counts how many elements in ``a`` (and in
+    sub-arrays thereof) have their ``__nonzero__()`` or ``__bool__()``
+    method evaluated to ``True``.
+
+    Parameters
+    ----------
+    a : array_like
+        The array for which to count non-zeros.
+    axis : int or tuple, optional
+        Axis or tuple of axes along which to count non-zeros.
+        Default is None, meaning that non-zeros will be counted
+        along a flattened version of ``a``.
+    keepdims : bool, optional
+        If this is set to True, the axes that are counted are left
+        in the result as dimensions with size one. With this option,
+        the result will broadcast correctly against the input array.
+
+    Returns
+    -------
+    count : int or array of int
+        Number of non-zero values in the array along a given axis.
+        Otherwise, the total number of non-zero values in the array
+        is returned.
+
+    See Also
+    --------
+    nonzero : Return the coordinates of all the non-zero values.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.count_nonzero(np.eye(4))
+    4
+    >>> a = np.array([[0, 1, 7, 0],
+    ...               [3, 0, 2, 19]])
+    >>> np.count_nonzero(a)
+    5
+    >>> np.count_nonzero(a, axis=0)
+    array([1, 1, 2, 1])
+    >>> np.count_nonzero(a, axis=1)
+    array([2, 3])
+    >>> np.count_nonzero(a, axis=1, keepdims=True)
+    array([[2],
+           [3]])
+    """
+    if axis is None and not keepdims:
+        return multiarray.count_nonzero(a)
+
+    a = asanyarray(a)
+
+    # TODO: this works around .astype(bool) not working properly (gh-9847)
+    if np.issubdtype(a.dtype, np.character):
+        a_bool = a != a.dtype.type()
+    else:
+        a_bool = a.astype(np.bool, copy=False)
+
+    return a_bool.sum(axis=axis, dtype=np.intp, keepdims=keepdims)
+
+
+@set_module('numpy')
+def isfortran(a):
+    """
+    Check if the array is Fortran contiguous but *not* C contiguous.
+
+    This function is obsolete. If you only want to check if an array is Fortran
+    contiguous use ``a.flags.f_contiguous`` instead.
+
+    Parameters
+    ----------
+    a : ndarray
+        Input array.
+
+    Returns
+    -------
+    isfortran : bool
+        Returns True if the array is Fortran contiguous but *not* C contiguous.
+
+
+    Examples
+    --------
+
+    np.array allows to specify whether the array is written in C-contiguous
+    order (last index varies the fastest), or FORTRAN-contiguous order in
+    memory (first index varies the fastest).
+
+    >>> import numpy as np
+    >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
+    >>> a
+    array([[1, 2, 3],
+           [4, 5, 6]])
+    >>> np.isfortran(a)
+    False
+
+    >>> b = np.array([[1, 2, 3], [4, 5, 6]], order='F')
+    >>> b
+    array([[1, 2, 3],
+           [4, 5, 6]])
+    >>> np.isfortran(b)
+    True
+
+
+    The transpose of a C-ordered array is a FORTRAN-ordered array.
+
+    >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
+    >>> a
+    array([[1, 2, 3],
+           [4, 5, 6]])
+    >>> np.isfortran(a)
+    False
+    >>> b = a.T
+    >>> b
+    array([[1, 4],
+           [2, 5],
+           [3, 6]])
+    >>> np.isfortran(b)
+    True
+
+    C-ordered arrays evaluate as False even if they are also FORTRAN-ordered.
+
+    >>> np.isfortran(np.array([1, 2], order='F'))
+    False
+
+    """
+    return a.flags.fnc
+
+
+def _argwhere_dispatcher(a):
+    return (a,)
+
+
+@array_function_dispatch(_argwhere_dispatcher)
+def argwhere(a):
+    """
+    Find the indices of array elements that are non-zero, grouped by element.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+
+    Returns
+    -------
+    index_array : (N, a.ndim) ndarray
+        Indices of elements that are non-zero. Indices are grouped by element.
+        This array will have shape ``(N, a.ndim)`` where ``N`` is the number of
+        non-zero items.
+
+    See Also
+    --------
+    where, nonzero
+
+    Notes
+    -----
+    ``np.argwhere(a)`` is almost the same as ``np.transpose(np.nonzero(a))``,
+    but produces a result of the correct shape for a 0D array.
+
+    The output of ``argwhere`` is not suitable for indexing arrays.
+    For this purpose use ``nonzero(a)`` instead.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(6).reshape(2,3)
+    >>> x
+    array([[0, 1, 2],
+           [3, 4, 5]])
+    >>> np.argwhere(x>1)
+    array([[0, 2],
+           [1, 0],
+           [1, 1],
+           [1, 2]])
+
+    """
+    # nonzero does not behave well on 0d, so promote to 1d
+    if np.ndim(a) == 0:
+        a = shape_base.atleast_1d(a)
+        # then remove the added dimension
+        return argwhere(a)[:, :0]
+    return transpose(nonzero(a))
+
+
+def _flatnonzero_dispatcher(a):
+    return (a,)
+
+
+@array_function_dispatch(_flatnonzero_dispatcher)
+def flatnonzero(a):
+    """
+    Return indices that are non-zero in the flattened version of a.
+
+    This is equivalent to ``np.nonzero(np.ravel(a))[0]``.
+
+    Parameters
+    ----------
+    a : array_like
+        Input data.
+
+    Returns
+    -------
+    res : ndarray
+        Output array, containing the indices of the elements of ``a.ravel()``
+        that are non-zero.
+
+    See Also
+    --------
+    nonzero : Return the indices of the non-zero elements of the input array.
+    ravel : Return a 1-D array containing the elements of the input array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(-2, 3)
+    >>> x
+    array([-2, -1,  0,  1,  2])
+    >>> np.flatnonzero(x)
+    array([0, 1, 3, 4])
+
+    Use the indices of the non-zero elements as an index array to extract
+    these elements:
+
+    >>> x.ravel()[np.flatnonzero(x)]
+    array([-2, -1,  1,  2])
+
+    """
+    return np.nonzero(np.ravel(a))[0]
+
+
+def _correlate_dispatcher(a, v, mode=None):
+    return (a, v)
+
+
+@array_function_dispatch(_correlate_dispatcher)
+def correlate(a, v, mode='valid'):
+    r"""
+    Cross-correlation of two 1-dimensional sequences.
+
+    This function computes the correlation as generally defined in signal
+    processing texts [1]_:
+
+    .. math:: c_k = \sum_n a_{n+k} \cdot \overline{v}_n
+
+    with a and v sequences being zero-padded where necessary and
+    :math:`\overline v` denoting complex conjugation.
+
+    Parameters
+    ----------
+    a, v : array_like
+        Input sequences.
+    mode : {'valid', 'same', 'full'}, optional
+        Refer to the `convolve` docstring.  Note that the default
+        is 'valid', unlike `convolve`, which uses 'full'.
+
+    Returns
+    -------
+    out : ndarray
+        Discrete cross-correlation of `a` and `v`.
+
+    See Also
+    --------
+    convolve : Discrete, linear convolution of two one-dimensional sequences.
+    scipy.signal.correlate : uses FFT which has superior performance
+        on large arrays.
+
+    Notes
+    -----
+    The definition of correlation above is not unique and sometimes
+    correlation may be defined differently. Another common definition is [1]_:
+
+    .. math:: c'_k = \sum_n a_{n} \cdot \overline{v_{n+k}}
+
+    which is related to :math:`c_k` by :math:`c'_k = c_{-k}`.
+
+    `numpy.correlate` may perform slowly in large arrays (i.e. n = 1e5)
+    because it does not use the FFT to compute the convolution; in that case,
+    `scipy.signal.correlate` might be preferable.
+
+    References
+    ----------
+    .. [1] Wikipedia, "Cross-correlation",
+           https://en.wikipedia.org/wiki/Cross-correlation
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.correlate([1, 2, 3], [0, 1, 0.5])
+    array([3.5])
+    >>> np.correlate([1, 2, 3], [0, 1, 0.5], "same")
+    array([2. ,  3.5,  3. ])
+    >>> np.correlate([1, 2, 3], [0, 1, 0.5], "full")
+    array([0.5,  2. ,  3.5,  3. ,  0. ])
+
+    Using complex sequences:
+
+    >>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full')
+    array([ 0.5-0.5j,  1.0+0.j ,  1.5-1.5j,  3.0-1.j ,  0.0+0.j ])
+
+    Note that you get the time reversed, complex conjugated result
+    (:math:`\overline{c_{-k}}`) when the two input sequences a and v change
+    places:
+
+    >>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')
+    array([ 0.0+0.j ,  3.0+1.j ,  1.5+1.5j,  1.0+0.j ,  0.5+0.5j])
+
+    """
+    return multiarray.correlate2(a, v, mode)
+
+
+def _convolve_dispatcher(a, v, mode=None):
+    return (a, v)
+
+
+@array_function_dispatch(_convolve_dispatcher)
+def convolve(a, v, mode='full'):
+    """
+    Returns the discrete, linear convolution of two one-dimensional sequences.
+
+    The convolution operator is often seen in signal processing, where it
+    models the effect of a linear time-invariant system on a signal [1]_.  In
+    probability theory, the sum of two independent random variables is
+    distributed according to the convolution of their individual
+    distributions.
+
+    If `v` is longer than `a`, the arrays are swapped before computation.
+
+    Parameters
+    ----------
+    a : (N,) array_like
+        First one-dimensional input array.
+    v : (M,) array_like
+        Second one-dimensional input array.
+    mode : {'full', 'valid', 'same'}, optional
+        'full':
+          By default, mode is 'full'.  This returns the convolution
+          at each point of overlap, with an output shape of (N+M-1,). At
+          the end-points of the convolution, the signals do not overlap
+          completely, and boundary effects may be seen.
+
+        'same':
+          Mode 'same' returns output of length ``max(M, N)``.  Boundary
+          effects are still visible.
+
+        'valid':
+          Mode 'valid' returns output of length
+          ``max(M, N) - min(M, N) + 1``.  The convolution product is only given
+          for points where the signals overlap completely.  Values outside
+          the signal boundary have no effect.
+
+    Returns
+    -------
+    out : ndarray
+        Discrete, linear convolution of `a` and `v`.
+
+    See Also
+    --------
+    scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier
+                               Transform.
+    scipy.linalg.toeplitz : Used to construct the convolution operator.
+    polymul : Polynomial multiplication. Same output as convolve, but also
+              accepts poly1d objects as input.
+
+    Notes
+    -----
+    The discrete convolution operation is defined as
+
+    .. math:: (a * v)_n = \\sum_{m = -\\infty}^{\\infty} a_m v_{n - m}
+
+    It can be shown that a convolution :math:`x(t) * y(t)` in time/space
+    is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier
+    domain, after appropriate padding (padding is necessary to prevent
+    circular convolution).  Since multiplication is more efficient (faster)
+    than convolution, the function `scipy.signal.fftconvolve` exploits the
+    FFT to calculate the convolution of large data-sets.
+
+    References
+    ----------
+    .. [1] Wikipedia, "Convolution",
+        https://en.wikipedia.org/wiki/Convolution
+
+    Examples
+    --------
+    Note how the convolution operator flips the second array
+    before "sliding" the two across one another:
+
+    >>> import numpy as np
+    >>> np.convolve([1, 2, 3], [0, 1, 0.5])
+    array([0. , 1. , 2.5, 4. , 1.5])
+
+    Only return the middle values of the convolution.
+    Contains boundary effects, where zeros are taken
+    into account:
+
+    >>> np.convolve([1,2,3],[0,1,0.5], 'same')
+    array([1. ,  2.5,  4. ])
+
+    The two arrays are of the same length, so there
+    is only one position where they completely overlap:
+
+    >>> np.convolve([1,2,3],[0,1,0.5], 'valid')
+    array([2.5])
+
+    """
+    a, v = array(a, copy=None, ndmin=1), array(v, copy=None, ndmin=1)
+    if (len(v) > len(a)):
+        a, v = v, a
+    if len(a) == 0:
+        raise ValueError('a cannot be empty')
+    if len(v) == 0:
+        raise ValueError('v cannot be empty')
+    return multiarray.correlate(a, v[::-1], mode)
+
+
+def _outer_dispatcher(a, b, out=None):
+    return (a, b, out)
+
+
+@array_function_dispatch(_outer_dispatcher)
+def outer(a, b, out=None):
+    """
+    Compute the outer product of two vectors.
+
+    Given two vectors `a` and `b` of length ``M`` and ``N``, respectively,
+    the outer product [1]_ is::
+
+      [[a_0*b_0  a_0*b_1 ... a_0*b_{N-1} ]
+       [a_1*b_0    .
+       [ ...          .
+       [a_{M-1}*b_0            a_{M-1}*b_{N-1} ]]
+
+    Parameters
+    ----------
+    a : (M,) array_like
+        First input vector.  Input is flattened if
+        not already 1-dimensional.
+    b : (N,) array_like
+        Second input vector.  Input is flattened if
+        not already 1-dimensional.
+    out : (M, N) ndarray, optional
+        A location where the result is stored
+
+    Returns
+    -------
+    out : (M, N) ndarray
+        ``out[i, j] = a[i] * b[j]``
+
+    See also
+    --------
+    inner
+    einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent.
+    ufunc.outer : A generalization to dimensions other than 1D and other
+                  operations. ``np.multiply.outer(a.ravel(), b.ravel())``
+                  is the equivalent.
+    linalg.outer : An Array API compatible variation of ``np.outer``,
+                   which accepts 1-dimensional inputs only.
+    tensordot : ``np.tensordot(a.ravel(), b.ravel(), axes=((), ()))``
+                is the equivalent.
+
+    References
+    ----------
+    .. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd
+           ed., Baltimore, MD, Johns Hopkins University Press, 1996,
+           pg. 8.
+
+    Examples
+    --------
+    Make a (*very* coarse) grid for computing a Mandelbrot set:
+
+    >>> import numpy as np
+    >>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
+    >>> rl
+    array([[-2., -1.,  0.,  1.,  2.],
+           [-2., -1.,  0.,  1.,  2.],
+           [-2., -1.,  0.,  1.,  2.],
+           [-2., -1.,  0.,  1.,  2.],
+           [-2., -1.,  0.,  1.,  2.]])
+    >>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
+    >>> im
+    array([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],
+           [0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],
+           [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
+           [0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],
+           [0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])
+    >>> grid = rl + im
+    >>> grid
+    array([[-2.+2.j, -1.+2.j,  0.+2.j,  1.+2.j,  2.+2.j],
+           [-2.+1.j, -1.+1.j,  0.+1.j,  1.+1.j,  2.+1.j],
+           [-2.+0.j, -1.+0.j,  0.+0.j,  1.+0.j,  2.+0.j],
+           [-2.-1.j, -1.-1.j,  0.-1.j,  1.-1.j,  2.-1.j],
+           [-2.-2.j, -1.-2.j,  0.-2.j,  1.-2.j,  2.-2.j]])
+
+    An example using a "vector" of letters:
+
+    >>> x = np.array(['a', 'b', 'c'], dtype=object)
+    >>> np.outer(x, [1, 2, 3])
+    array([['a', 'aa', 'aaa'],
+           ['b', 'bb', 'bbb'],
+           ['c', 'cc', 'ccc']], dtype=object)
+
+    """
+    a = asarray(a)
+    b = asarray(b)
+    return multiply(a.ravel()[:, newaxis], b.ravel()[newaxis, :], out)
+
+
+def _tensordot_dispatcher(a, b, axes=None):
+    return (a, b)
+
+
+@array_function_dispatch(_tensordot_dispatcher)
+def tensordot(a, b, axes=2):
+    """
+    Compute tensor dot product along specified axes.
+
+    Given two tensors, `a` and `b`, and an array_like object containing
+    two array_like objects, ``(a_axes, b_axes)``, sum the products of
+    `a`'s and `b`'s elements (components) over the axes specified by
+    ``a_axes`` and ``b_axes``. The third argument can be a single non-negative
+    integer_like scalar, ``N``; if it is such, then the last ``N`` dimensions
+    of `a` and the first ``N`` dimensions of `b` are summed over.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Tensors to "dot".
+
+    axes : int or (2,) array_like
+        * integer_like
+          If an int N, sum over the last N axes of `a` and the first N axes
+          of `b` in order. The sizes of the corresponding axes must match.
+        * (2,) array_like
+          Or, a list of axes to be summed over, first sequence applying to `a`,
+          second to `b`. Both elements array_like must be of the same length.
+
+    Returns
+    -------
+    output : ndarray
+        The tensor dot product of the input.
+
+    See Also
+    --------
+    dot, einsum
+
+    Notes
+    -----
+    Three common use cases are:
+        * ``axes = 0`` : tensor product :math:`a\\otimes b`
+        * ``axes = 1`` : tensor dot product :math:`a\\cdot b`
+        * ``axes = 2`` : (default) tensor double contraction :math:`a:b`
+
+    When `axes` is integer_like, the sequence of axes for evaluation
+    will be: from the -Nth axis to the -1th axis in `a`,
+    and from the 0th axis to (N-1)th axis in `b`.
+    For example, ``axes = 2`` is the equal to
+    ``axes = [[-2, -1], [0, 1]]``.
+    When N-1 is smaller than 0, or when -N is larger than -1,
+    the element of `a` and `b` are defined as the `axes`.
+
+    When there is more than one axis to sum over - and they are not the last
+    (first) axes of `a` (`b`) - the argument `axes` should consist of
+    two sequences of the same length, with the first axis to sum over given
+    first in both sequences, the second axis second, and so forth.
+    The calculation can be referred to ``numpy.einsum``.
+
+    The shape of the result consists of the non-contracted axes of the
+    first tensor, followed by the non-contracted axes of the second.
+
+    Examples
+    --------
+    An example on integer_like:
+
+    >>> a_0 = np.array([[1, 2], [3, 4]])
+    >>> b_0 = np.array([[5, 6], [7, 8]])
+    >>> c_0 = np.tensordot(a_0, b_0, axes=0)
+    >>> c_0.shape
+    (2, 2, 2, 2)
+    >>> c_0
+    array([[[[ 5,  6],
+             [ 7,  8]],
+            [[10, 12],
+             [14, 16]]],
+           [[[15, 18],
+             [21, 24]],
+            [[20, 24],
+             [28, 32]]]])
+
+    An example on array_like:
+
+    >>> a = np.arange(60.).reshape(3,4,5)
+    >>> b = np.arange(24.).reshape(4,3,2)
+    >>> c = np.tensordot(a,b, axes=([1,0],[0,1]))
+    >>> c.shape
+    (5, 2)
+    >>> c
+    array([[4400., 4730.],
+           [4532., 4874.],
+           [4664., 5018.],
+           [4796., 5162.],
+           [4928., 5306.]])
+
+    A slower but equivalent way of computing the same...
+
+    >>> d = np.zeros((5,2))
+    >>> for i in range(5):
+    ...   for j in range(2):
+    ...     for k in range(3):
+    ...       for n in range(4):
+    ...         d[i,j] += a[k,n,i] * b[n,k,j]
+    >>> c == d
+    array([[ True,  True],
+           [ True,  True],
+           [ True,  True],
+           [ True,  True],
+           [ True,  True]])
+
+    An extended example taking advantage of the overloading of + and \\*:
+
+    >>> a = np.array(range(1, 9))
+    >>> a.shape = (2, 2, 2)
+    >>> A = np.array(('a', 'b', 'c', 'd'), dtype=object)
+    >>> A.shape = (2, 2)
+    >>> a; A
+    array([[[1, 2],
+            [3, 4]],
+           [[5, 6],
+            [7, 8]]])
+    array([['a', 'b'],
+           ['c', 'd']], dtype=object)
+
+    >>> np.tensordot(a, A) # third argument default is 2 for double-contraction
+    array(['abbcccdddd', 'aaaaabbbbbbcccccccdddddddd'], dtype=object)
+
+    >>> np.tensordot(a, A, 1)
+    array([[['acc', 'bdd'],
+            ['aaacccc', 'bbbdddd']],
+           [['aaaaacccccc', 'bbbbbdddddd'],
+            ['aaaaaaacccccccc', 'bbbbbbbdddddddd']]], dtype=object)
+
+    >>> np.tensordot(a, A, 0) # tensor product (result too long to incl.)
+    array([[[[['a', 'b'],
+              ['c', 'd']],
+              ...
+
+    >>> np.tensordot(a, A, (0, 1))
+    array([[['abbbbb', 'cddddd'],
+            ['aabbbbbb', 'ccdddddd']],
+           [['aaabbbbbbb', 'cccddddddd'],
+            ['aaaabbbbbbbb', 'ccccdddddddd']]], dtype=object)
+
+    >>> np.tensordot(a, A, (2, 1))
+    array([[['abb', 'cdd'],
+            ['aaabbbb', 'cccdddd']],
+           [['aaaaabbbbbb', 'cccccdddddd'],
+            ['aaaaaaabbbbbbbb', 'cccccccdddddddd']]], dtype=object)
+
+    >>> np.tensordot(a, A, ((0, 1), (0, 1)))
+    array(['abbbcccccddddddd', 'aabbbbccccccdddddddd'], dtype=object)
+
+    >>> np.tensordot(a, A, ((2, 1), (1, 0)))
+    array(['acccbbdddd', 'aaaaacccccccbbbbbbdddddddd'], dtype=object)
+
+    """
+    try:
+        iter(axes)
+    except Exception:
+        axes_a = list(range(-axes, 0))
+        axes_b = list(range(axes))
+    else:
+        axes_a, axes_b = axes
+    try:
+        na = len(axes_a)
+        axes_a = list(axes_a)
+    except TypeError:
+        axes_a = [axes_a]
+        na = 1
+    try:
+        nb = len(axes_b)
+        axes_b = list(axes_b)
+    except TypeError:
+        axes_b = [axes_b]
+        nb = 1
+
+    a, b = asarray(a), asarray(b)
+    as_ = a.shape
+    nda = a.ndim
+    bs = b.shape
+    ndb = b.ndim
+    equal = True
+    if na != nb:
+        equal = False
+    else:
+        for k in range(na):
+            if as_[axes_a[k]] != bs[axes_b[k]]:
+                equal = False
+                break
+            if axes_a[k] < 0:
+                axes_a[k] += nda
+            if axes_b[k] < 0:
+                axes_b[k] += ndb
+    if not equal:
+        raise ValueError("shape-mismatch for sum")
+
+    # Move the axes to sum over to the end of "a"
+    # and to the front of "b"
+    notin = [k for k in range(nda) if k not in axes_a]
+    newaxes_a = notin + axes_a
+    N2 = math.prod(as_[axis] for axis in axes_a)
+    newshape_a = (math.prod(as_[ax] for ax in notin), N2)
+    olda = [as_[axis] for axis in notin]
+
+    notin = [k for k in range(ndb) if k not in axes_b]
+    newaxes_b = axes_b + notin
+    N2 = math.prod(bs[axis] for axis in axes_b)
+    newshape_b = (N2, math.prod(bs[ax] for ax in notin))
+    oldb = [bs[axis] for axis in notin]
+
+    at = a.transpose(newaxes_a).reshape(newshape_a)
+    bt = b.transpose(newaxes_b).reshape(newshape_b)
+    res = dot(at, bt)
+    return res.reshape(olda + oldb)
+
+
+def _roll_dispatcher(a, shift, axis=None):
+    return (a,)
+
+
+@array_function_dispatch(_roll_dispatcher)
+def roll(a, shift, axis=None):
+    """
+    Roll array elements along a given axis.
+
+    Elements that roll beyond the last position are re-introduced at
+    the first.
+
+    Parameters
+    ----------
+    a : array_like
+        Input array.
+    shift : int or tuple of ints
+        The number of places by which elements are shifted.  If a tuple,
+        then `axis` must be a tuple of the same size, and each of the
+        given axes is shifted by the corresponding number.  If an int
+        while `axis` is a tuple of ints, then the same value is used for
+        all given axes.
+    axis : int or tuple of ints, optional
+        Axis or axes along which elements are shifted.  By default, the
+        array is flattened before shifting, after which the original
+        shape is restored.
+
+    Returns
+    -------
+    res : ndarray
+        Output array, with the same shape as `a`.
+
+    See Also
+    --------
+    rollaxis : Roll the specified axis backwards, until it lies in a
+               given position.
+
+    Notes
+    -----
+    Supports rolling over multiple dimensions simultaneously.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.arange(10)
+    >>> np.roll(x, 2)
+    array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7])
+    >>> np.roll(x, -2)
+    array([2, 3, 4, 5, 6, 7, 8, 9, 0, 1])
+
+    >>> x2 = np.reshape(x, (2, 5))
+    >>> x2
+    array([[0, 1, 2, 3, 4],
+           [5, 6, 7, 8, 9]])
+    >>> np.roll(x2, 1)
+    array([[9, 0, 1, 2, 3],
+           [4, 5, 6, 7, 8]])
+    >>> np.roll(x2, -1)
+    array([[1, 2, 3, 4, 5],
+           [6, 7, 8, 9, 0]])
+    >>> np.roll(x2, 1, axis=0)
+    array([[5, 6, 7, 8, 9],
+           [0, 1, 2, 3, 4]])
+    >>> np.roll(x2, -1, axis=0)
+    array([[5, 6, 7, 8, 9],
+           [0, 1, 2, 3, 4]])
+    >>> np.roll(x2, 1, axis=1)
+    array([[4, 0, 1, 2, 3],
+           [9, 5, 6, 7, 8]])
+    >>> np.roll(x2, -1, axis=1)
+    array([[1, 2, 3, 4, 0],
+           [6, 7, 8, 9, 5]])
+    >>> np.roll(x2, (1, 1), axis=(1, 0))
+    array([[9, 5, 6, 7, 8],
+           [4, 0, 1, 2, 3]])
+    >>> np.roll(x2, (2, 1), axis=(1, 0))
+    array([[8, 9, 5, 6, 7],
+           [3, 4, 0, 1, 2]])
+
+    """
+    a = asanyarray(a)
+    if axis is None:
+        return roll(a.ravel(), shift, 0).reshape(a.shape)
+
+    else:
+        axis = normalize_axis_tuple(axis, a.ndim, allow_duplicate=True)
+        broadcasted = broadcast(shift, axis)
+        if broadcasted.ndim > 1:
+            raise ValueError(
+                "'shift' and 'axis' should be scalars or 1D sequences")
+        shifts = dict.fromkeys(range(a.ndim), 0)
+        for sh, ax in broadcasted:
+            shifts[ax] += int(sh)
+
+        rolls = [((slice(None), slice(None)),)] * a.ndim
+        for ax, offset in shifts.items():
+            offset %= a.shape[ax] or 1  # If `a` is empty, nothing matters.
+            if offset:
+                # (original, result), (original, result)
+                rolls[ax] = ((slice(None, -offset), slice(offset, None)),
+                             (slice(-offset, None), slice(None, offset)))
+
+        result = empty_like(a)
+        for indices in itertools.product(*rolls):
+            arr_index, res_index = zip(*indices)
+            result[res_index] = a[arr_index]
+
+        return result
+
+
+def _rollaxis_dispatcher(a, axis, start=None):
+    return (a,)
+
+
+@array_function_dispatch(_rollaxis_dispatcher)
+def rollaxis(a, axis, start=0):
+    """
+    Roll the specified axis backwards, until it lies in a given position.
+
+    This function continues to be supported for backward compatibility, but you
+    should prefer `moveaxis`. The `moveaxis` function was added in NumPy
+    1.11.
+
+    Parameters
+    ----------
+    a : ndarray
+        Input array.
+    axis : int
+        The axis to be rolled. The positions of the other axes do not
+        change relative to one another.
+    start : int, optional
+        When ``start <= axis``, the axis is rolled back until it lies in
+        this position. When ``start > axis``, the axis is rolled until it
+        lies before this position. The default, 0, results in a "complete"
+        roll. The following table describes how negative values of ``start``
+        are interpreted:
+
+        .. table::
+           :align: left
+
+           +-------------------+----------------------+
+           |     ``start``     | Normalized ``start`` |
+           +===================+======================+
+           | ``-(arr.ndim+1)`` | raise ``AxisError``  |
+           +-------------------+----------------------+
+           | ``-arr.ndim``     | 0                    |
+           +-------------------+----------------------+
+           | |vdots|           | |vdots|              |
+           +-------------------+----------------------+
+           | ``-1``            | ``arr.ndim-1``       |
+           +-------------------+----------------------+
+           | ``0``             | ``0``                |
+           +-------------------+----------------------+
+           | |vdots|           | |vdots|              |
+           +-------------------+----------------------+
+           | ``arr.ndim``      | ``arr.ndim``         |
+           +-------------------+----------------------+
+           | ``arr.ndim + 1``  | raise ``AxisError``  |
+           +-------------------+----------------------+
+
+        .. |vdots|   unicode:: U+22EE .. Vertical Ellipsis
+
+    Returns
+    -------
+    res : ndarray
+        For NumPy >= 1.10.0 a view of `a` is always returned. For earlier
+        NumPy versions a view of `a` is returned only if the order of the
+        axes is changed, otherwise the input array is returned.
+
+    See Also
+    --------
+    moveaxis : Move array axes to new positions.
+    roll : Roll the elements of an array by a number of positions along a
+        given axis.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.ones((3,4,5,6))
+    >>> np.rollaxis(a, 3, 1).shape
+    (3, 6, 4, 5)
+    >>> np.rollaxis(a, 2).shape
+    (5, 3, 4, 6)
+    >>> np.rollaxis(a, 1, 4).shape
+    (3, 5, 6, 4)
+
+    """
+    n = a.ndim
+    axis = normalize_axis_index(axis, n)
+    if start < 0:
+        start += n
+    msg = "'%s' arg requires %d <= %s < %d, but %d was passed in"
+    if not (0 <= start < n + 1):
+        raise AxisError(msg % ('start', -n, 'start', n + 1, start))
+    if axis < start:
+        # it's been removed
+        start -= 1
+    if axis == start:
+        return a[...]
+    axes = list(range(n))
+    axes.remove(axis)
+    axes.insert(start, axis)
+    return a.transpose(axes)
+
+
+@set_module("numpy.lib.array_utils")
+def normalize_axis_tuple(axis, ndim, argname=None, allow_duplicate=False):
+    """
+    Normalizes an axis argument into a tuple of non-negative integer axes.
+
+    This handles shorthands such as ``1`` and converts them to ``(1,)``,
+    as well as performing the handling of negative indices covered by
+    `normalize_axis_index`.
+
+    By default, this forbids axes from being specified multiple times.
+
+    Used internally by multi-axis-checking logic.
+
+    Parameters
+    ----------
+    axis : int, iterable of int
+        The un-normalized index or indices of the axis.
+    ndim : int
+        The number of dimensions of the array that `axis` should be normalized
+        against.
+    argname : str, optional
+        A prefix to put before the error message, typically the name of the
+        argument.
+    allow_duplicate : bool, optional
+        If False, the default, disallow an axis from being specified twice.
+
+    Returns
+    -------
+    normalized_axes : tuple of int
+        The normalized axis index, such that `0 <= normalized_axis < ndim`
+
+    Raises
+    ------
+    AxisError
+        If any axis provided is out of range
+    ValueError
+        If an axis is repeated
+
+    See also
+    --------
+    normalize_axis_index : normalizing a single scalar axis
+    """
+    # Optimization to speed-up the most common cases.
+    if not isinstance(axis, (tuple, list)):
+        try:
+            axis = [operator.index(axis)]
+        except TypeError:
+            pass
+    # Going via an iterator directly is slower than via list comprehension.
+    axis = tuple(normalize_axis_index(ax, ndim, argname) for ax in axis)
+    if not allow_duplicate and len(set(axis)) != len(axis):
+        if argname:
+            raise ValueError(f'repeated axis in `{argname}` argument')
+        else:
+            raise ValueError('repeated axis')
+    return axis
+
+
+def _moveaxis_dispatcher(a, source, destination):
+    return (a,)
+
+
+@array_function_dispatch(_moveaxis_dispatcher)
+def moveaxis(a, source, destination):
+    """
+    Move axes of an array to new positions.
+
+    Other axes remain in their original order.
+
+    Parameters
+    ----------
+    a : np.ndarray
+        The array whose axes should be reordered.
+    source : int or sequence of int
+        Original positions of the axes to move. These must be unique.
+    destination : int or sequence of int
+        Destination positions for each of the original axes. These must also be
+        unique.
+
+    Returns
+    -------
+    result : np.ndarray
+        Array with moved axes. This array is a view of the input array.
+
+    See Also
+    --------
+    transpose : Permute the dimensions of an array.
+    swapaxes : Interchange two axes of an array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.zeros((3, 4, 5))
+    >>> np.moveaxis(x, 0, -1).shape
+    (4, 5, 3)
+    >>> np.moveaxis(x, -1, 0).shape
+    (5, 3, 4)
+
+    These all achieve the same result:
+
+    >>> np.transpose(x).shape
+    (5, 4, 3)
+    >>> np.swapaxes(x, 0, -1).shape
+    (5, 4, 3)
+    >>> np.moveaxis(x, [0, 1], [-1, -2]).shape
+    (5, 4, 3)
+    >>> np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape
+    (5, 4, 3)
+
+    """
+    try:
+        # allow duck-array types if they define transpose
+        transpose = a.transpose
+    except AttributeError:
+        a = asarray(a)
+        transpose = a.transpose
+
+    source = normalize_axis_tuple(source, a.ndim, 'source')
+    destination = normalize_axis_tuple(destination, a.ndim, 'destination')
+    if len(source) != len(destination):
+        raise ValueError('`source` and `destination` arguments must have '
+                         'the same number of elements')
+
+    order = [n for n in range(a.ndim) if n not in source]
+
+    for dest, src in sorted(zip(destination, source)):
+        order.insert(dest, src)
+
+    result = transpose(order)
+    return result
+
+
+def _cross_dispatcher(a, b, axisa=None, axisb=None, axisc=None, axis=None):
+    return (a, b)
+
+
+@array_function_dispatch(_cross_dispatcher)
+def cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None):
+    """
+    Return the cross product of two (arrays of) vectors.
+
+    The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular
+    to both `a` and `b`.  If `a` and `b` are arrays of vectors, the vectors
+    are defined by the last axis of `a` and `b` by default, and these axes
+    can have dimensions 2 or 3.  Where the dimension of either `a` or `b` is
+    2, the third component of the input vector is assumed to be zero and the
+    cross product calculated accordingly.  In cases where both input vectors
+    have dimension 2, the z-component of the cross product is returned.
+
+    Parameters
+    ----------
+    a : array_like
+        Components of the first vector(s).
+    b : array_like
+        Components of the second vector(s).
+    axisa : int, optional
+        Axis of `a` that defines the vector(s).  By default, the last axis.
+    axisb : int, optional
+        Axis of `b` that defines the vector(s).  By default, the last axis.
+    axisc : int, optional
+        Axis of `c` containing the cross product vector(s).  Ignored if
+        both input vectors have dimension 2, as the return is scalar.
+        By default, the last axis.
+    axis : int, optional
+        If defined, the axis of `a`, `b` and `c` that defines the vector(s)
+        and cross product(s).  Overrides `axisa`, `axisb` and `axisc`.
+
+    Returns
+    -------
+    c : ndarray
+        Vector cross product(s).
+
+    Raises
+    ------
+    ValueError
+        When the dimension of the vector(s) in `a` and/or `b` does not
+        equal 2 or 3.
+
+    See Also
+    --------
+    inner : Inner product
+    outer : Outer product.
+    linalg.cross : An Array API compatible variation of ``np.cross``,
+                   which accepts (arrays of) 3-element vectors only.
+    ix_ : Construct index arrays.
+
+    Notes
+    -----
+    Supports full broadcasting of the inputs.
+
+    Dimension-2 input arrays were deprecated in 2.0.0. If you do need this
+    functionality, you can use::
+
+        def cross2d(x, y):
+            return x[..., 0] * y[..., 1] - x[..., 1] * y[..., 0]
+
+    Examples
+    --------
+    Vector cross-product.
+
+    >>> import numpy as np
+    >>> x = [1, 2, 3]
+    >>> y = [4, 5, 6]
+    >>> np.cross(x, y)
+    array([-3,  6, -3])
+
+    One vector with dimension 2.
+
+    >>> x = [1, 2]
+    >>> y = [4, 5, 6]
+    >>> np.cross(x, y)
+    array([12, -6, -3])
+
+    Equivalently:
+
+    >>> x = [1, 2, 0]
+    >>> y = [4, 5, 6]
+    >>> np.cross(x, y)
+    array([12, -6, -3])
+
+    Both vectors with dimension 2.
+
+    >>> x = [1,2]
+    >>> y = [4,5]
+    >>> np.cross(x, y)
+    array(-3)
+
+    Multiple vector cross-products. Note that the direction of the cross
+    product vector is defined by the *right-hand rule*.
+
+    >>> x = np.array([[1,2,3], [4,5,6]])
+    >>> y = np.array([[4,5,6], [1,2,3]])
+    >>> np.cross(x, y)
+    array([[-3,  6, -3],
+           [ 3, -6,  3]])
+
+    The orientation of `c` can be changed using the `axisc` keyword.
+
+    >>> np.cross(x, y, axisc=0)
+    array([[-3,  3],
+           [ 6, -6],
+           [-3,  3]])
+
+    Change the vector definition of `x` and `y` using `axisa` and `axisb`.
+
+    >>> x = np.array([[1,2,3], [4,5,6], [7, 8, 9]])
+    >>> y = np.array([[7, 8, 9], [4,5,6], [1,2,3]])
+    >>> np.cross(x, y)
+    array([[ -6,  12,  -6],
+           [  0,   0,   0],
+           [  6, -12,   6]])
+    >>> np.cross(x, y, axisa=0, axisb=0)
+    array([[-24,  48, -24],
+           [-30,  60, -30],
+           [-36,  72, -36]])
+
+    """
+    if axis is not None:
+        axisa, axisb, axisc = (axis,) * 3
+    a = asarray(a)
+    b = asarray(b)
+
+    if (a.ndim < 1) or (b.ndim < 1):
+        raise ValueError("At least one array has zero dimension")
+
+    # Check axisa and axisb are within bounds
+    axisa = normalize_axis_index(axisa, a.ndim, msg_prefix='axisa')
+    axisb = normalize_axis_index(axisb, b.ndim, msg_prefix='axisb')
+
+    # Move working axis to the end of the shape
+    a = moveaxis(a, axisa, -1)
+    b = moveaxis(b, axisb, -1)
+    msg = ("incompatible dimensions for cross product\n"
+           "(dimension must be 2 or 3)")
+    if a.shape[-1] not in (2, 3) or b.shape[-1] not in (2, 3):
+        raise ValueError(msg)
+    if a.shape[-1] == 2 or b.shape[-1] == 2:
+        # Deprecated in NumPy 2.0, 2023-09-26
+        warnings.warn(
+            "Arrays of 2-dimensional vectors are deprecated. Use arrays of "
+            "3-dimensional vectors instead. (deprecated in NumPy 2.0)",
+            DeprecationWarning, stacklevel=2
+        )
+
+    # Create the output array
+    shape = broadcast(a[..., 0], b[..., 0]).shape
+    if a.shape[-1] == 3 or b.shape[-1] == 3:
+        shape += (3,)
+        # Check axisc is within bounds
+        axisc = normalize_axis_index(axisc, len(shape), msg_prefix='axisc')
+    dtype = promote_types(a.dtype, b.dtype)
+    cp = empty(shape, dtype)
+
+    # recast arrays as dtype
+    a = a.astype(dtype)
+    b = b.astype(dtype)
+
+    # create local aliases for readability
+    a0 = a[..., 0]
+    a1 = a[..., 1]
+    if a.shape[-1] == 3:
+        a2 = a[..., 2]
+    b0 = b[..., 0]
+    b1 = b[..., 1]
+    if b.shape[-1] == 3:
+        b2 = b[..., 2]
+    if cp.ndim != 0 and cp.shape[-1] == 3:
+        cp0 = cp[..., 0]
+        cp1 = cp[..., 1]
+        cp2 = cp[..., 2]
+
+    if a.shape[-1] == 2:
+        if b.shape[-1] == 2:
+            # a0 * b1 - a1 * b0
+            multiply(a0, b1, out=cp)
+            cp -= a1 * b0
+            return cp
+        else:
+            assert b.shape[-1] == 3
+            # cp0 = a1 * b2 - 0  (a2 = 0)
+            # cp1 = 0 - a0 * b2  (a2 = 0)
+            # cp2 = a0 * b1 - a1 * b0
+            multiply(a1, b2, out=cp0)
+            multiply(a0, b2, out=cp1)
+            negative(cp1, out=cp1)
+            multiply(a0, b1, out=cp2)
+            cp2 -= a1 * b0
+    else:
+        assert a.shape[-1] == 3
+        if b.shape[-1] == 3:
+            # cp0 = a1 * b2 - a2 * b1
+            # cp1 = a2 * b0 - a0 * b2
+            # cp2 = a0 * b1 - a1 * b0
+            multiply(a1, b2, out=cp0)
+            tmp = np.multiply(a2, b1, out=...)
+            cp0 -= tmp
+            multiply(a2, b0, out=cp1)
+            multiply(a0, b2, out=tmp)
+            cp1 -= tmp
+            multiply(a0, b1, out=cp2)
+            multiply(a1, b0, out=tmp)
+            cp2 -= tmp
+        else:
+            assert b.shape[-1] == 2
+            # cp0 = 0 - a2 * b1  (b2 = 0)
+            # cp1 = a2 * b0 - 0  (b2 = 0)
+            # cp2 = a0 * b1 - a1 * b0
+            multiply(a2, b1, out=cp0)
+            negative(cp0, out=cp0)
+            multiply(a2, b0, out=cp1)
+            multiply(a0, b1, out=cp2)
+            cp2 -= a1 * b0
+
+    return moveaxis(cp, -1, axisc)
+
+
+little_endian = (sys.byteorder == 'little')
+
+
+@set_module('numpy')
+def indices(dimensions, dtype=int, sparse=False):
+    """
+    Return an array representing the indices of a grid.
+
+    Compute an array where the subarrays contain index values 0, 1, ...
+    varying only along the corresponding axis.
+
+    Parameters
+    ----------
+    dimensions : sequence of ints
+        The shape of the grid.
+    dtype : dtype, optional
+        Data type of the result.
+    sparse : boolean, optional
+        Return a sparse representation of the grid instead of a dense
+        representation. Default is False.
+
+    Returns
+    -------
+    grid : one ndarray or tuple of ndarrays
+        If sparse is False:
+            Returns one array of grid indices,
+            ``grid.shape = (len(dimensions),) + tuple(dimensions)``.
+        If sparse is True:
+            Returns a tuple of arrays, with
+            ``grid[i].shape = (1, ..., 1, dimensions[i], 1, ..., 1)`` with
+            dimensions[i] in the ith place
+
+    See Also
+    --------
+    mgrid, ogrid, meshgrid
+
+    Notes
+    -----
+    The output shape in the dense case is obtained by prepending the number
+    of dimensions in front of the tuple of dimensions, i.e. if `dimensions`
+    is a tuple ``(r0, ..., rN-1)`` of length ``N``, the output shape is
+    ``(N, r0, ..., rN-1)``.
+
+    The subarrays ``grid[k]`` contains the N-D array of indices along the
+    ``k-th`` axis. Explicitly::
+
+        grid[k, i0, i1, ..., iN-1] = ik
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> grid = np.indices((2, 3))
+    >>> grid.shape
+    (2, 2, 3)
+    >>> grid[0]        # row indices
+    array([[0, 0, 0],
+           [1, 1, 1]])
+    >>> grid[1]        # column indices
+    array([[0, 1, 2],
+           [0, 1, 2]])
+
+    The indices can be used as an index into an array.
+
+    >>> x = np.arange(20).reshape(5, 4)
+    >>> row, col = np.indices((2, 3))
+    >>> x[row, col]
+    array([[0, 1, 2],
+           [4, 5, 6]])
+
+    Note that it would be more straightforward in the above example to
+    extract the required elements directly with ``x[:2, :3]``.
+
+    If sparse is set to true, the grid will be returned in a sparse
+    representation.
+
+    >>> i, j = np.indices((2, 3), sparse=True)
+    >>> i.shape
+    (2, 1)
+    >>> j.shape
+    (1, 3)
+    >>> i        # row indices
+    array([[0],
+           [1]])
+    >>> j        # column indices
+    array([[0, 1, 2]])
+
+    """
+    dimensions = tuple(dimensions)
+    N = len(dimensions)
+    shape = (1,) * N
+    if sparse:
+        res = ()
+    else:
+        res = empty((N,) + dimensions, dtype=dtype)
+    for i, dim in enumerate(dimensions):
+        idx = arange(dim, dtype=dtype).reshape(
+            shape[:i] + (dim,) + shape[i + 1:]
+        )
+        if sparse:
+            res = res + (idx,)
+        else:
+            res[i] = idx
+    return res
+
+
+@finalize_array_function_like
+@set_module('numpy')
+def fromfunction(function, shape, *, dtype=float, like=None, **kwargs):
+    """
+    Construct an array by executing a function over each coordinate.
+
+    The resulting array therefore has a value ``fn(x, y, z)`` at
+    coordinate ``(x, y, z)``.
+
+    Parameters
+    ----------
+    function : callable
+        The function is called with N parameters, where N is the rank of
+        `shape`.  Each parameter represents the coordinates of the array
+        varying along a specific axis.  For example, if `shape`
+        were ``(2, 2)``, then the parameters would be
+        ``array([[0, 0], [1, 1]])`` and ``array([[0, 1], [0, 1]])``
+    shape : (N,) tuple of ints
+        Shape of the output array, which also determines the shape of
+        the coordinate arrays passed to `function`.
+    dtype : data-type, optional
+        Data-type of the coordinate arrays passed to `function`.
+        By default, `dtype` is float.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    fromfunction : any
+        The result of the call to `function` is passed back directly.
+        Therefore the shape of `fromfunction` is completely determined by
+        `function`.  If `function` returns a scalar value, the shape of
+        `fromfunction` would not match the `shape` parameter.
+
+    See Also
+    --------
+    indices, meshgrid
+
+    Notes
+    -----
+    Keywords other than `dtype` and `like` are passed to `function`.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.fromfunction(lambda i, j: i, (2, 2), dtype=float)
+    array([[0., 0.],
+           [1., 1.]])
+
+    >>> np.fromfunction(lambda i, j: j, (2, 2), dtype=float)
+    array([[0., 1.],
+           [0., 1.]])
+
+    >>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int)
+    array([[ True, False, False],
+           [False,  True, False],
+           [False, False,  True]])
+
+    >>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int)
+    array([[0, 1, 2],
+           [1, 2, 3],
+           [2, 3, 4]])
+
+    """
+    if like is not None:
+        return _fromfunction_with_like(
+                like, function, shape, dtype=dtype, **kwargs)
+
+    args = indices(shape, dtype=dtype)
+    return function(*args, **kwargs)
+
+
+_fromfunction_with_like = array_function_dispatch()(fromfunction)
+
+
+def _frombuffer(buf, dtype, shape, order, axis_order=None):
+    array = frombuffer(buf, dtype=dtype)
+    if order == 'K' and axis_order is not None:
+        return array.reshape(shape, order='C').transpose(axis_order)
+    return array.reshape(shape, order=order)
+
+
+@set_module('numpy')
+def isscalar(element):
+    """
+    Returns True if the type of `element` is a scalar type.
+
+    Parameters
+    ----------
+    element : any
+        Input argument, can be of any type and shape.
+
+    Returns
+    -------
+    val : bool
+        True if `element` is a scalar type, False if it is not.
+
+    See Also
+    --------
+    ndim : Get the number of dimensions of an array
+
+    Notes
+    -----
+    If you need a stricter way to identify a *numerical* scalar, use
+    ``isinstance(x, numbers.Number)``, as that returns ``False`` for most
+    non-numerical elements such as strings.
+
+    In most cases ``np.ndim(x) == 0`` should be used instead of this function,
+    as that will also return true for 0d arrays. This is how numpy overloads
+    functions in the style of the ``dx`` arguments to `gradient` and
+    the ``bins`` argument to `histogram`. Some key differences:
+
+    +------------------------------------+---------------+-------------------+
+    | x                                  |``isscalar(x)``|``np.ndim(x) == 0``|
+    +====================================+===============+===================+
+    | PEP 3141 numeric objects           | ``True``      | ``True``          |
+    | (including builtins)               |               |                   |
+    +------------------------------------+---------------+-------------------+
+    | builtin string and buffer objects  | ``True``      | ``True``          |
+    +------------------------------------+---------------+-------------------+
+    | other builtin objects, like        | ``False``     | ``True``          |
+    | `pathlib.Path`, `Exception`,       |               |                   |
+    | the result of `re.compile`         |               |                   |
+    +------------------------------------+---------------+-------------------+
+    | third-party objects like           | ``False``     | ``True``          |
+    | `matplotlib.figure.Figure`         |               |                   |
+    +------------------------------------+---------------+-------------------+
+    | zero-dimensional numpy arrays      | ``False``     | ``True``          |
+    +------------------------------------+---------------+-------------------+
+    | other numpy arrays                 | ``False``     | ``False``         |
+    +------------------------------------+---------------+-------------------+
+    | `list`, `tuple`, and other         | ``False``     | ``False``         |
+    | sequence objects                   |               |                   |
+    +------------------------------------+---------------+-------------------+
+
+    Examples
+    --------
+    >>> import numpy as np
+
+    >>> np.isscalar(3.1)
+    True
+
+    >>> np.isscalar(np.array(3.1))
+    False
+
+    >>> np.isscalar([3.1])
+    False
+
+    >>> np.isscalar(False)
+    True
+
+    >>> np.isscalar('numpy')
+    True
+
+    NumPy supports PEP 3141 numbers:
+
+    >>> from fractions import Fraction
+    >>> np.isscalar(Fraction(5, 17))
+    True
+    >>> from numbers import Number
+    >>> np.isscalar(Number())
+    True
+
+    """
+    return (isinstance(element, generic)
+            or type(element) in ScalarType
+            or isinstance(element, numbers.Number))
+
+
+@set_module('numpy')
+def binary_repr(num, width=None):
+    """
+    Return the binary representation of the input number as a string.
+
+    For negative numbers, if width is not given, a minus sign is added to the
+    front. If width is given, the two's complement of the number is
+    returned, with respect to that width.
+
+    In a two's-complement system negative numbers are represented by the two's
+    complement of the absolute value. This is the most common method of
+    representing signed integers on computers [1]_. A N-bit two's-complement
+    system can represent every integer in the range
+    :math:`-2^{N-1}` to :math:`+2^{N-1}-1`.
+
+    Parameters
+    ----------
+    num : int
+        Only an integer decimal number can be used.
+    width : int, optional
+        The length of the returned string if `num` is positive, or the length
+        of the two's complement if `num` is negative, provided that `width` is
+        at least a sufficient number of bits for `num` to be represented in
+        the designated form. If the `width` value is insufficient, an error is
+        raised.
+
+    Returns
+    -------
+    bin : str
+        Binary representation of `num` or two's complement of `num`.
+
+    See Also
+    --------
+    base_repr: Return a string representation of a number in the given base
+               system.
+    bin: Python's built-in binary representation generator of an integer.
+
+    Notes
+    -----
+    `binary_repr` is equivalent to using `base_repr` with base 2, but about 25x
+    faster.
+
+    References
+    ----------
+    .. [1] Wikipedia, "Two's complement",
+        https://en.wikipedia.org/wiki/Two's_complement
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.binary_repr(3)
+    '11'
+    >>> np.binary_repr(-3)
+    '-11'
+    >>> np.binary_repr(3, width=4)
+    '0011'
+
+    The two's complement is returned when the input number is negative and
+    width is specified:
+
+    >>> np.binary_repr(-3, width=3)
+    '101'
+    >>> np.binary_repr(-3, width=5)
+    '11101'
+
+    """
+    def err_if_insufficient(width, binwidth):
+        if width is not None and width < binwidth:
+            raise ValueError(
+                f"Insufficient bit {width=} provided for {binwidth=}"
+            )
+
+    # Ensure that num is a Python integer to avoid overflow or unwanted
+    # casts to floating point.
+    num = operator.index(num)
+
+    if num == 0:
+        return '0' * (width or 1)
+
+    elif num > 0:
+        binary = f'{num:b}'
+        binwidth = len(binary)
+        outwidth = (binwidth if width is None
+                    else builtins.max(binwidth, width))
+        err_if_insufficient(width, binwidth)
+        return binary.zfill(outwidth)
+
+    elif width is None:
+        return f'-{-num:b}'
+
+    else:
+        poswidth = len(f'{-num:b}')
+
+        # See gh-8679: remove extra digit
+        # for numbers at boundaries.
+        if 2**(poswidth - 1) == -num:
+            poswidth -= 1
+
+        twocomp = 2**(poswidth + 1) + num
+        binary = f'{twocomp:b}'
+        binwidth = len(binary)
+
+        outwidth = builtins.max(binwidth, width)
+        err_if_insufficient(width, binwidth)
+        return '1' * (outwidth - binwidth) + binary
+
+
+@set_module('numpy')
+def base_repr(number, base=2, padding=0):
+    """
+    Return a string representation of a number in the given base system.
+
+    Parameters
+    ----------
+    number : int
+        The value to convert. Positive and negative values are handled.
+    base : int, optional
+        Convert `number` to the `base` number system. The valid range is 2-36,
+        the default value is 2.
+    padding : int, optional
+        Number of zeros padded on the left. Default is 0 (no padding).
+
+    Returns
+    -------
+    out : str
+        String representation of `number` in `base` system.
+
+    See Also
+    --------
+    binary_repr : Faster version of `base_repr` for base 2.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.base_repr(5)
+    '101'
+    >>> np.base_repr(6, 5)
+    '11'
+    >>> np.base_repr(7, base=5, padding=3)
+    '00012'
+
+    >>> np.base_repr(10, base=16)
+    'A'
+    >>> np.base_repr(32, base=16)
+    '20'
+
+    """
+    digits = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'
+    if base > len(digits):
+        raise ValueError("Bases greater than 36 not handled in base_repr.")
+    elif base < 2:
+        raise ValueError("Bases less than 2 not handled in base_repr.")
+
+    num = abs(int(number))
+    res = []
+    while num:
+        res.append(digits[num % base])
+        num //= base
+    if padding:
+        res.append('0' * padding)
+    if number < 0:
+        res.append('-')
+    return ''.join(reversed(res or '0'))
+
+
+# These are all essentially abbreviations
+# These might wind up in a special abbreviations module
+
+
+def _maketup(descr, val):
+    dt = dtype(descr)
+    # Place val in all scalar tuples:
+    fields = dt.fields
+    if fields is None:
+        return val
+    else:
+        res = [_maketup(fields[name][0], val) for name in dt.names]
+        return tuple(res)
+
+
+@finalize_array_function_like
+@set_module('numpy')
+def identity(n, dtype=None, *, like=None):
+    """
+    Return the identity array.
+
+    The identity array is a square array with ones on
+    the main diagonal.
+
+    Parameters
+    ----------
+    n : int
+        Number of rows (and columns) in `n` x `n` output.
+    dtype : data-type, optional
+        Data-type of the output.  Defaults to ``float``.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. versionadded:: 1.20.0
+
+    Returns
+    -------
+    out : ndarray
+        `n` x `n` array with its main diagonal set to one,
+        and all other elements 0.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.identity(3)
+    array([[1.,  0.,  0.],
+           [0.,  1.,  0.],
+           [0.,  0.,  1.]])
+
+    """
+    if like is not None:
+        return _identity_with_like(like, n, dtype=dtype)
+
+    from numpy import eye
+    return eye(n, dtype=dtype, like=like)
+
+
+_identity_with_like = array_function_dispatch()(identity)
+
+
+def _allclose_dispatcher(a, b, rtol=None, atol=None, equal_nan=None):
+    return (a, b, rtol, atol)
+
+
+@array_function_dispatch(_allclose_dispatcher)
+def allclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):
+    """
+    Returns True if two arrays are element-wise equal within a tolerance.
+
+    The tolerance values are positive, typically very small numbers.  The
+    relative difference (`rtol` * abs(`b`)) and the absolute difference
+    `atol` are added together to compare against the absolute difference
+    between `a` and `b`.
+
+    .. warning:: The default `atol` is not appropriate for comparing numbers
+                 with magnitudes much smaller than one (see Notes).
+
+    NaNs are treated as equal if they are in the same place and if
+    ``equal_nan=True``.  Infs are treated as equal if they are in the same
+    place and of the same sign in both arrays.
+
+    Parameters
+    ----------
+    a, b : array_like
+        Input arrays to compare.
+    rtol : array_like
+        The relative tolerance parameter (see Notes).
+    atol : array_like
+        The absolute tolerance parameter (see Notes).
+    equal_nan : bool
+        Whether to compare NaN's as equal.  If True, NaN's in `a` will be
+        considered equal to NaN's in `b` in the output array.
+
+    Returns
+    -------
+    allclose : bool
+        Returns True if the two arrays are equal within the given
+        tolerance; False otherwise.
+
+    See Also
+    --------
+    isclose, all, any, equal
+
+    Notes
+    -----
+    If the following equation is element-wise True, then allclose returns
+    True.::
+
+     absolute(a - b) <= (atol + rtol * absolute(b))
+
+    The above equation is not symmetric in `a` and `b`, so that
+    ``allclose(a, b)`` might be different from ``allclose(b, a)`` in
+    some rare cases.
+
+    The default value of `atol` is not appropriate when the reference value
+    `b` has magnitude smaller than one. For example, it is unlikely that
+    ``a = 1e-9`` and ``b = 2e-9`` should be considered "close", yet
+    ``allclose(1e-9, 2e-9)`` is ``True`` with default settings. Be sure
+    to select `atol` for the use case at hand, especially for defining the
+    threshold below which a non-zero value in `a` will be considered "close"
+    to a very small or zero value in `b`.
+
+    The comparison of `a` and `b` uses standard broadcasting, which
+    means that `a` and `b` need not have the same shape in order for
+    ``allclose(a, b)`` to evaluate to True.  The same is true for
+    `equal` but not `array_equal`.
+
+    `allclose` is not defined for non-numeric data types.
+    `bool` is considered a numeric data-type for this purpose.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.allclose([1e10,1e-7], [1.00001e10,1e-8])
+    False
+
+    >>> np.allclose([1e10,1e-8], [1.00001e10,1e-9])
+    True
+
+    >>> np.allclose([1e10,1e-8], [1.0001e10,1e-9])
+    False
+
+    >>> np.allclose([1.0, np.nan], [1.0, np.nan])
+    False
+
+    >>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
+    True
+
+
+    """
+    res = all(isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan))
+    return builtins.bool(res)
+
+
+def _isclose_dispatcher(a, b, rtol=None, atol=None, equal_nan=None):
+    return (a, b, rtol, atol)
+
+
+@array_function_dispatch(_isclose_dispatcher)
+def isclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):
+    """
+    Returns a boolean array where two arrays are element-wise equal within a
+    tolerance.
+
+    The tolerance values are positive, typically very small numbers.  The
+    relative difference (`rtol` * abs(`b`)) and the absolute difference
+    `atol` are added together to compare against the absolute difference
+    between `a` and `b`.
+
+    .. warning:: The default `atol` is not appropriate for comparing numbers
+                 with magnitudes much smaller than one (see Notes).
+
+    Parameters
+    ----------
+    a, b : array_like
+        Input arrays to compare.
+    rtol : array_like
+        The relative tolerance parameter (see Notes).
+    atol : array_like
+        The absolute tolerance parameter (see Notes).
+    equal_nan : bool
+        Whether to compare NaN's as equal.  If True, NaN's in `a` will be
+        considered equal to NaN's in `b` in the output array.
+
+    Returns
+    -------
+    y : array_like
+        Returns a boolean array of where `a` and `b` are equal within the
+        given tolerance. If both `a` and `b` are scalars, returns a single
+        boolean value.
+
+    See Also
+    --------
+    allclose
+    math.isclose
+
+    Notes
+    -----
+    For finite values, isclose uses the following equation to test whether
+    two floating point values are equivalent.::
+
+     absolute(a - b) <= (atol + rtol * absolute(b))
+
+    Unlike the built-in `math.isclose`, the above equation is not symmetric
+    in `a` and `b` -- it assumes `b` is the reference value -- so that
+    `isclose(a, b)` might be different from `isclose(b, a)`.
+
+    The default value of `atol` is not appropriate when the reference value
+    `b` has magnitude smaller than one. For example, it is unlikely that
+    ``a = 1e-9`` and ``b = 2e-9`` should be considered "close", yet
+    ``isclose(1e-9, 2e-9)`` is ``True`` with default settings. Be sure
+    to select `atol` for the use case at hand, especially for defining the
+    threshold below which a non-zero value in `a` will be considered "close"
+    to a very small or zero value in `b`.
+
+    `isclose` is not defined for non-numeric data types.
+    :class:`bool` is considered a numeric data-type for this purpose.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.isclose([1e10,1e-7], [1.00001e10,1e-8])
+    array([ True, False])
+
+    >>> np.isclose([1e10,1e-8], [1.00001e10,1e-9])
+    array([ True, True])
+
+    >>> np.isclose([1e10,1e-8], [1.0001e10,1e-9])
+    array([False,  True])
+
+    >>> np.isclose([1.0, np.nan], [1.0, np.nan])
+    array([ True, False])
+
+    >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
+    array([ True, True])
+
+    >>> np.isclose([1e-8, 1e-7], [0.0, 0.0])
+    array([ True, False])
+
+    >>> np.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0)
+    array([False, False])
+
+    >>> np.isclose([1e-10, 1e-10], [1e-20, 0.0])
+    array([ True,  True])
+
+    >>> np.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], atol=0.0)
+    array([False,  True])
+
+    """
+    # Turn all but python scalars into arrays.
+    x, y, atol, rtol = (
+        a if isinstance(a, (int, float, complex)) else asanyarray(a)
+        for a in (a, b, atol, rtol))
+
+    # Make sure y is an inexact type to avoid bad behavior on abs(MIN_INT).
+    # This will cause casting of x later. Also, make sure to allow subclasses
+    # (e.g., for numpy.ma).
+    # NOTE: We explicitly allow timedelta, which used to work. This could
+    #       possibly be deprecated. See also gh-18286.
+    #       timedelta works if `atol` is an integer or also a timedelta.
+    #       Although, the default tolerances are unlikely to be useful
+    if (dtype := getattr(y, "dtype", None)) is not None and dtype.kind != "m":
+        dt = multiarray.result_type(y, 1.)
+        y = asanyarray(y, dtype=dt)
+    elif isinstance(y, int):
+        y = float(y)
+
+    # atol and rtol can be arrays
+    if not (np.all(np.isfinite(atol)) and np.all(np.isfinite(rtol))):
+        err_s = np.geterr()["invalid"]
+        err_msg = f"One of rtol or atol is not valid, atol: {atol}, rtol: {rtol}"
+
+        if err_s == "warn":
+            warnings.warn(err_msg, RuntimeWarning, stacklevel=2)
+        elif err_s == "raise":
+            raise FloatingPointError(err_msg)
+        elif err_s == "print":
+            print(err_msg)
+
+    with errstate(invalid='ignore'):
+
+        result = (less_equal(abs(x - y), atol + rtol * abs(y))
+                  & isfinite(y)
+                  | (x == y))
+        if equal_nan:
+            result |= isnan(x) & isnan(y)
+
+    return result[()]  # Flatten 0d arrays to scalars
+
+
+def _array_equal_dispatcher(a1, a2, equal_nan=None):
+    return (a1, a2)
+
+
+_no_nan_types = {
+    # should use np.dtype.BoolDType, but as of writing
+    # that fails the reloading test.
+    type(dtype(nt.bool)),
+    type(dtype(nt.int8)),
+    type(dtype(nt.int16)),
+    type(dtype(nt.int32)),
+    type(dtype(nt.int64)),
+}
+
+
+def _dtype_cannot_hold_nan(dtype):
+    return type(dtype) in _no_nan_types
+
+
+@array_function_dispatch(_array_equal_dispatcher)
+def array_equal(a1, a2, equal_nan=False):
+    """
+    True if two arrays have the same shape and elements, False otherwise.
+
+    Parameters
+    ----------
+    a1, a2 : array_like
+        Input arrays.
+    equal_nan : bool
+        Whether to compare NaN's as equal. If the dtype of a1 and a2 is
+        complex, values will be considered equal if either the real or the
+        imaginary component of a given value is ``nan``.
+
+    Returns
+    -------
+    b : bool
+        Returns True if the arrays are equal.
+
+    See Also
+    --------
+    allclose: Returns True if two arrays are element-wise equal within a
+              tolerance.
+    array_equiv: Returns True if input arrays are shape consistent and all
+                 elements equal.
+
+    Examples
+    --------
+    >>> import numpy as np
+
+    >>> np.array_equal([1, 2], [1, 2])
+    True
+
+    >>> np.array_equal(np.array([1, 2]), np.array([1, 2]))
+    True
+
+    >>> np.array_equal([1, 2], [1, 2, 3])
+    False
+
+    >>> np.array_equal([1, 2], [1, 4])
+    False
+
+    >>> a = np.array([1, np.nan])
+    >>> np.array_equal(a, a)
+    False
+
+    >>> np.array_equal(a, a, equal_nan=True)
+    True
+
+    When ``equal_nan`` is True, complex values with nan components are
+    considered equal if either the real *or* the imaginary components are nan.
+
+    >>> a = np.array([1 + 1j])
+    >>> b = a.copy()
+    >>> a.real = np.nan
+    >>> b.imag = np.nan
+    >>> np.array_equal(a, b, equal_nan=True)
+    True
+    """
+    try:
+        a1, a2 = asarray(a1), asarray(a2)
+    except Exception:
+        return False
+    if a1.shape != a2.shape:
+        return False
+    if not equal_nan:
+        return builtins.bool((asanyarray(a1 == a2)).all())
+
+    if a1 is a2:
+        # nan will compare equal so an array will compare equal to itself.
+        return True
+
+    cannot_have_nan = (_dtype_cannot_hold_nan(a1.dtype)
+                       and _dtype_cannot_hold_nan(a2.dtype))
+    if cannot_have_nan:
+        return builtins.bool(asarray(a1 == a2).all())
+
+    # Handling NaN values if equal_nan is True
+    a1nan, a2nan = isnan(a1), isnan(a2)
+    # NaN's occur at different locations
+    if not (a1nan == a2nan).all():
+        return False
+    # Shapes of a1, a2 and masks are guaranteed to be consistent by this point
+    return builtins.bool((a1[~a1nan] == a2[~a1nan]).all())
+
+
+def _array_equiv_dispatcher(a1, a2):
+    return (a1, a2)
+
+
+@array_function_dispatch(_array_equiv_dispatcher)
+def array_equiv(a1, a2):
+    """
+    Returns True if input arrays are shape consistent and all elements equal.
+
+    Shape consistent means they are either the same shape, or one input array
+    can be broadcasted to create the same shape as the other one.
+
+    Parameters
+    ----------
+    a1, a2 : array_like
+        Input arrays.
+
+    Returns
+    -------
+    out : bool
+        True if equivalent, False otherwise.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.array_equiv([1, 2], [1, 2])
+    True
+    >>> np.array_equiv([1, 2], [1, 3])
+    False
+
+    Showing the shape equivalence:
+
+    >>> np.array_equiv([1, 2], [[1, 2], [1, 2]])
+    True
+    >>> np.array_equiv([1, 2], [[1, 2, 1, 2], [1, 2, 1, 2]])
+    False
+
+    >>> np.array_equiv([1, 2], [[1, 2], [1, 3]])
+    False
+
+    """
+    try:
+        a1, a2 = asarray(a1), asarray(a2)
+    except Exception:
+        return False
+    try:
+        multiarray.broadcast(a1, a2)
+    except Exception:
+        return False
+
+    return builtins.bool(asanyarray(a1 == a2).all())
+
+
+def _astype_dispatcher(x, dtype, /, *, copy=None, device=None):
+    return (x, dtype)
+
+
+@array_function_dispatch(_astype_dispatcher)
+def astype(x, dtype, /, *, copy=True, device=None):
+    """
+    Copies an array to a specified data type.
+
+    This function is an Array API compatible alternative to
+    `numpy.ndarray.astype`.
+
+    Parameters
+    ----------
+    x : ndarray
+        Input NumPy array to cast. ``array_likes`` are explicitly not
+        supported here.
+    dtype : dtype
+        Data type of the result.
+    copy : bool, optional
+        Specifies whether to copy an array when the specified dtype matches
+        the data type of the input array ``x``. If ``True``, a newly allocated
+        array must always be returned. If ``False`` and the specified dtype
+        matches the data type of the input array, the input array must be
+        returned; otherwise, a newly allocated array must be returned.
+        Defaults to ``True``.
+    device : str, optional
+        The device on which to place the returned array. Default: None.
+        For Array-API interoperability only, so must be ``"cpu"`` if passed.
+
+        .. versionadded:: 2.1.0
+
+    Returns
+    -------
+    out : ndarray
+        An array having the specified data type.
+
+    See Also
+    --------
+    ndarray.astype
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> arr = np.array([1, 2, 3]); arr
+    array([1, 2, 3])
+    >>> np.astype(arr, np.float64)
+    array([1., 2., 3.])
+
+    Non-copy case:
+
+    >>> arr = np.array([1, 2, 3])
+    >>> arr_noncpy = np.astype(arr, arr.dtype, copy=False)
+    >>> np.shares_memory(arr, arr_noncpy)
+    True
+
+    """
+    if not (isinstance(x, np.ndarray) or isscalar(x)):
+        raise TypeError(
+            "Input should be a NumPy array or scalar. "
+            f"It is a {type(x)} instead."
+        )
+    if device is not None and device != "cpu":
+        raise ValueError(
+            'Device not understood. Only "cpu" is allowed, but received:'
+            f' {device}'
+        )
+    return x.astype(dtype, copy=copy)
+
+
+inf = PINF
+nan = NAN
+False_ = nt.bool(False)
+True_ = nt.bool(True)
+
+
+def extend_all(module):
+    existing = set(__all__)
+    mall = module.__all__
+    for a in mall:
+        if a not in existing:
+            __all__.append(a)
+
+
+from . import _asarray, _ufunc_config, arrayprint, fromnumeric
+from ._asarray import *
+from ._ufunc_config import *
+from .arrayprint import *
+from .fromnumeric import *
+from .numerictypes import *
+from .umath import *
+
+extend_all(fromnumeric)
+extend_all(umath)
+extend_all(numerictypes)
+extend_all(arrayprint)
+extend_all(_asarray)
+extend_all(_ufunc_config)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/numeric.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/numeric.pyi
new file mode 100644
index 0000000..919fe19
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/numeric.pyi
@@ -0,0 +1,882 @@
+from collections.abc import Callable, Sequence
+from typing import (
+    Any,
+    Final,
+    Never,
+    NoReturn,
+    SupportsAbs,
+    SupportsIndex,
+    TypeAlias,
+    TypeGuard,
+    TypeVar,
+    Unpack,
+    overload,
+)
+from typing import Literal as L
+
+import numpy as np
+from numpy import (
+    False_,
+    True_,
+    _OrderCF,
+    _OrderKACF,
+    # re-exports
+    bitwise_not,
+    broadcast,
+    complexfloating,
+    dtype,
+    flatiter,
+    float64,
+    floating,
+    from_dlpack,
+    # other
+    generic,
+    inf,
+    int_,
+    intp,
+    little_endian,
+    matmul,
+    nan,
+    ndarray,
+    nditer,
+    newaxis,
+    object_,
+    signedinteger,
+    timedelta64,
+    ufunc,
+    unsignedinteger,
+    vecdot,
+)
+from numpy._typing import (
+    ArrayLike,
+    DTypeLike,
+    NDArray,
+    _ArrayLike,
+    _ArrayLikeBool_co,
+    _ArrayLikeComplex_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeInt_co,
+    _ArrayLikeObject_co,
+    _ArrayLikeTD64_co,
+    _ArrayLikeUInt_co,
+    _DTypeLike,
+    _NestedSequence,
+    _ScalarLike_co,
+    _Shape,
+    _ShapeLike,
+    _SupportsArrayFunc,
+    _SupportsDType,
+)
+
+from .fromnumeric import all as all
+from .fromnumeric import any as any
+from .fromnumeric import argpartition as argpartition
+from .fromnumeric import matrix_transpose as matrix_transpose
+from .fromnumeric import mean as mean
+from .multiarray import (
+    # other
+    _Array,
+    _ConstructorEmpty,
+    _KwargsEmpty,
+    # re-exports
+    arange,
+    array,
+    asanyarray,
+    asarray,
+    ascontiguousarray,
+    asfortranarray,
+    can_cast,
+    concatenate,
+    copyto,
+    dot,
+    empty,
+    empty_like,
+    frombuffer,
+    fromfile,
+    fromiter,
+    fromstring,
+    inner,
+    lexsort,
+    may_share_memory,
+    min_scalar_type,
+    nested_iters,
+    promote_types,
+    putmask,
+    result_type,
+    shares_memory,
+    vdot,
+    where,
+    zeros,
+)
+
+__all__ = [
+    "newaxis",
+    "ndarray",
+    "flatiter",
+    "nditer",
+    "nested_iters",
+    "ufunc",
+    "arange",
+    "array",
+    "asarray",
+    "asanyarray",
+    "ascontiguousarray",
+    "asfortranarray",
+    "zeros",
+    "count_nonzero",
+    "empty",
+    "broadcast",
+    "dtype",
+    "fromstring",
+    "fromfile",
+    "frombuffer",
+    "from_dlpack",
+    "where",
+    "argwhere",
+    "copyto",
+    "concatenate",
+    "lexsort",
+    "astype",
+    "can_cast",
+    "promote_types",
+    "min_scalar_type",
+    "result_type",
+    "isfortran",
+    "empty_like",
+    "zeros_like",
+    "ones_like",
+    "correlate",
+    "convolve",
+    "inner",
+    "dot",
+    "outer",
+    "vdot",
+    "roll",
+    "rollaxis",
+    "moveaxis",
+    "cross",
+    "tensordot",
+    "little_endian",
+    "fromiter",
+    "array_equal",
+    "array_equiv",
+    "indices",
+    "fromfunction",
+    "isclose",
+    "isscalar",
+    "binary_repr",
+    "base_repr",
+    "ones",
+    "identity",
+    "allclose",
+    "putmask",
+    "flatnonzero",
+    "inf",
+    "nan",
+    "False_",
+    "True_",
+    "bitwise_not",
+    "full",
+    "full_like",
+    "matmul",
+    "vecdot",
+    "shares_memory",
+    "may_share_memory",
+]
+
+_T = TypeVar("_T")
+_ScalarT = TypeVar("_ScalarT", bound=generic)
+_DTypeT = TypeVar("_DTypeT", bound=np.dtype)
+_ArrayT = TypeVar("_ArrayT", bound=np.ndarray[Any, Any])
+_ShapeT = TypeVar("_ShapeT", bound=_Shape)
+_AnyShapeT = TypeVar(
+    "_AnyShapeT",
+    tuple[()],
+    tuple[int],
+    tuple[int, int],
+    tuple[int, int, int],
+    tuple[int, int, int, int],
+    tuple[int, ...],
+)
+
+_CorrelateMode: TypeAlias = L["valid", "same", "full"]
+
+@overload
+def zeros_like(
+    a: _ArrayT,
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    subok: L[True] = ...,
+    shape: None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> _ArrayT: ...
+@overload
+def zeros_like(
+    a: _ArrayLike[_ScalarT],
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def zeros_like(
+    a: Any,
+    dtype: _DTypeLike[_ScalarT],
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def zeros_like(
+    a: Any,
+    dtype: DTypeLike | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[Any]: ...
+
+ones: Final[_ConstructorEmpty]
+
+@overload
+def ones_like(
+    a: _ArrayT,
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    subok: L[True] = ...,
+    shape: None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> _ArrayT: ...
+@overload
+def ones_like(
+    a: _ArrayLike[_ScalarT],
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def ones_like(
+    a: Any,
+    dtype: _DTypeLike[_ScalarT],
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def ones_like(
+    a: Any,
+    dtype: DTypeLike | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[Any]: ...
+
+# TODO: Add overloads for bool, int, float, complex, str, bytes, and memoryview
+# 1-D shape
+@overload
+def full(
+    shape: SupportsIndex,
+    fill_value: _ScalarT,
+    dtype: None = ...,
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> _Array[tuple[int], _ScalarT]: ...
+@overload
+def full(
+    shape: SupportsIndex,
+    fill_value: Any,
+    dtype: _DTypeT | _SupportsDType[_DTypeT],
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> np.ndarray[tuple[int], _DTypeT]: ...
+@overload
+def full(
+    shape: SupportsIndex,
+    fill_value: Any,
+    dtype: type[_ScalarT],
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> _Array[tuple[int], _ScalarT]: ...
+@overload
+def full(
+    shape: SupportsIndex,
+    fill_value: Any,
+    dtype: DTypeLike | None = ...,
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> _Array[tuple[int], Any]: ...
+# known shape
+@overload
+def full(
+    shape: _AnyShapeT,
+    fill_value: _ScalarT,
+    dtype: None = ...,
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> _Array[_AnyShapeT, _ScalarT]: ...
+@overload
+def full(
+    shape: _AnyShapeT,
+    fill_value: Any,
+    dtype: _DTypeT | _SupportsDType[_DTypeT],
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> np.ndarray[_AnyShapeT, _DTypeT]: ...
+@overload
+def full(
+    shape: _AnyShapeT,
+    fill_value: Any,
+    dtype: type[_ScalarT],
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> _Array[_AnyShapeT, _ScalarT]: ...
+@overload
+def full(
+    shape: _AnyShapeT,
+    fill_value: Any,
+    dtype: DTypeLike | None = ...,
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> _Array[_AnyShapeT, Any]: ...
+# unknown shape
+@overload
+def full(
+    shape: _ShapeLike,
+    fill_value: _ScalarT,
+    dtype: None = ...,
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> NDArray[_ScalarT]: ...
+@overload
+def full(
+    shape: _ShapeLike,
+    fill_value: Any,
+    dtype: _DTypeT | _SupportsDType[_DTypeT],
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> np.ndarray[Any, _DTypeT]: ...
+@overload
+def full(
+    shape: _ShapeLike,
+    fill_value: Any,
+    dtype: type[_ScalarT],
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> NDArray[_ScalarT]: ...
+@overload
+def full(
+    shape: _ShapeLike,
+    fill_value: Any,
+    dtype: DTypeLike | None = ...,
+    order: _OrderCF = ...,
+    **kwargs: Unpack[_KwargsEmpty],
+) -> NDArray[Any]: ...
+
+@overload
+def full_like(
+    a: _ArrayT,
+    fill_value: Any,
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    subok: L[True] = ...,
+    shape: None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> _ArrayT: ...
+@overload
+def full_like(
+    a: _ArrayLike[_ScalarT],
+    fill_value: Any,
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def full_like(
+    a: Any,
+    fill_value: Any,
+    dtype: _DTypeLike[_ScalarT],
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def full_like(
+    a: Any,
+    fill_value: Any,
+    dtype: DTypeLike | None = ...,
+    order: _OrderKACF = ...,
+    subok: bool = ...,
+    shape: _ShapeLike | None = ...,
+    *,
+    device: L["cpu"] | None = ...,
+) -> NDArray[Any]: ...
+
+#
+@overload
+def count_nonzero(a: ArrayLike, axis: None = None, *, keepdims: L[False] = False) -> np.intp: ...
+@overload
+def count_nonzero(a: _ScalarLike_co, axis: _ShapeLike | None = None, *, keepdims: L[True]) -> np.intp: ...
+@overload
+def count_nonzero(
+    a: NDArray[Any] | _NestedSequence[ArrayLike], axis: _ShapeLike | None = None, *, keepdims: L[True]
+) -> NDArray[np.intp]: ...
+@overload
+def count_nonzero(a: ArrayLike, axis: _ShapeLike | None = None, *, keepdims: bool = False) -> Any: ...
+
+#
+def isfortran(a: NDArray[Any] | generic) -> bool: ...
+
+def argwhere(a: ArrayLike) -> NDArray[intp]: ...
+
+def flatnonzero(a: ArrayLike) -> NDArray[intp]: ...
+
+@overload
+def correlate(
+    a: _ArrayLike[Never],
+    v: _ArrayLike[Never],
+    mode: _CorrelateMode = ...,
+) -> NDArray[Any]: ...
+@overload
+def correlate(
+    a: _ArrayLikeBool_co,
+    v: _ArrayLikeBool_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def correlate(
+    a: _ArrayLikeUInt_co,
+    v: _ArrayLikeUInt_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[unsignedinteger]: ...
+@overload
+def correlate(
+    a: _ArrayLikeInt_co,
+    v: _ArrayLikeInt_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[signedinteger]: ...
+@overload
+def correlate(
+    a: _ArrayLikeFloat_co,
+    v: _ArrayLikeFloat_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[floating]: ...
+@overload
+def correlate(
+    a: _ArrayLikeComplex_co,
+    v: _ArrayLikeComplex_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[complexfloating]: ...
+@overload
+def correlate(
+    a: _ArrayLikeTD64_co,
+    v: _ArrayLikeTD64_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[timedelta64]: ...
+@overload
+def correlate(
+    a: _ArrayLikeObject_co,
+    v: _ArrayLikeObject_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def convolve(
+    a: _ArrayLike[Never],
+    v: _ArrayLike[Never],
+    mode: _CorrelateMode = ...,
+) -> NDArray[Any]: ...
+@overload
+def convolve(
+    a: _ArrayLikeBool_co,
+    v: _ArrayLikeBool_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def convolve(
+    a: _ArrayLikeUInt_co,
+    v: _ArrayLikeUInt_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[unsignedinteger]: ...
+@overload
+def convolve(
+    a: _ArrayLikeInt_co,
+    v: _ArrayLikeInt_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[signedinteger]: ...
+@overload
+def convolve(
+    a: _ArrayLikeFloat_co,
+    v: _ArrayLikeFloat_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[floating]: ...
+@overload
+def convolve(
+    a: _ArrayLikeComplex_co,
+    v: _ArrayLikeComplex_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[complexfloating]: ...
+@overload
+def convolve(
+    a: _ArrayLikeTD64_co,
+    v: _ArrayLikeTD64_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[timedelta64]: ...
+@overload
+def convolve(
+    a: _ArrayLikeObject_co,
+    v: _ArrayLikeObject_co,
+    mode: _CorrelateMode = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def outer(
+    a: _ArrayLike[Never],
+    b: _ArrayLike[Never],
+    out: None = ...,
+) -> NDArray[Any]: ...
+@overload
+def outer(
+    a: _ArrayLikeBool_co,
+    b: _ArrayLikeBool_co,
+    out: None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def outer(
+    a: _ArrayLikeUInt_co,
+    b: _ArrayLikeUInt_co,
+    out: None = ...,
+) -> NDArray[unsignedinteger]: ...
+@overload
+def outer(
+    a: _ArrayLikeInt_co,
+    b: _ArrayLikeInt_co,
+    out: None = ...,
+) -> NDArray[signedinteger]: ...
+@overload
+def outer(
+    a: _ArrayLikeFloat_co,
+    b: _ArrayLikeFloat_co,
+    out: None = ...,
+) -> NDArray[floating]: ...
+@overload
+def outer(
+    a: _ArrayLikeComplex_co,
+    b: _ArrayLikeComplex_co,
+    out: None = ...,
+) -> NDArray[complexfloating]: ...
+@overload
+def outer(
+    a: _ArrayLikeTD64_co,
+    b: _ArrayLikeTD64_co,
+    out: None = ...,
+) -> NDArray[timedelta64]: ...
+@overload
+def outer(
+    a: _ArrayLikeObject_co,
+    b: _ArrayLikeObject_co,
+    out: None = ...,
+) -> NDArray[object_]: ...
+@overload
+def outer(
+    a: _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeObject_co,
+    b: _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeObject_co,
+    out: _ArrayT,
+) -> _ArrayT: ...
+
+@overload
+def tensordot(
+    a: _ArrayLike[Never],
+    b: _ArrayLike[Never],
+    axes: int | tuple[_ShapeLike, _ShapeLike] = ...,
+) -> NDArray[Any]: ...
+@overload
+def tensordot(
+    a: _ArrayLikeBool_co,
+    b: _ArrayLikeBool_co,
+    axes: int | tuple[_ShapeLike, _ShapeLike] = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def tensordot(
+    a: _ArrayLikeUInt_co,
+    b: _ArrayLikeUInt_co,
+    axes: int | tuple[_ShapeLike, _ShapeLike] = ...,
+) -> NDArray[unsignedinteger]: ...
+@overload
+def tensordot(
+    a: _ArrayLikeInt_co,
+    b: _ArrayLikeInt_co,
+    axes: int | tuple[_ShapeLike, _ShapeLike] = ...,
+) -> NDArray[signedinteger]: ...
+@overload
+def tensordot(
+    a: _ArrayLikeFloat_co,
+    b: _ArrayLikeFloat_co,
+    axes: int | tuple[_ShapeLike, _ShapeLike] = ...,
+) -> NDArray[floating]: ...
+@overload
+def tensordot(
+    a: _ArrayLikeComplex_co,
+    b: _ArrayLikeComplex_co,
+    axes: int | tuple[_ShapeLike, _ShapeLike] = ...,
+) -> NDArray[complexfloating]: ...
+@overload
+def tensordot(
+    a: _ArrayLikeTD64_co,
+    b: _ArrayLikeTD64_co,
+    axes: int | tuple[_ShapeLike, _ShapeLike] = ...,
+) -> NDArray[timedelta64]: ...
+@overload
+def tensordot(
+    a: _ArrayLikeObject_co,
+    b: _ArrayLikeObject_co,
+    axes: int | tuple[_ShapeLike, _ShapeLike] = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def roll(
+    a: _ArrayLike[_ScalarT],
+    shift: _ShapeLike,
+    axis: _ShapeLike | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def roll(
+    a: ArrayLike,
+    shift: _ShapeLike,
+    axis: _ShapeLike | None = ...,
+) -> NDArray[Any]: ...
+
+def rollaxis(
+    a: NDArray[_ScalarT],
+    axis: int,
+    start: int = ...,
+) -> NDArray[_ScalarT]: ...
+
+def moveaxis(
+    a: NDArray[_ScalarT],
+    source: _ShapeLike,
+    destination: _ShapeLike,
+) -> NDArray[_ScalarT]: ...
+
+@overload
+def cross(
+    a: _ArrayLike[Never],
+    b: _ArrayLike[Never],
+    axisa: int = ...,
+    axisb: int = ...,
+    axisc: int = ...,
+    axis: int | None = ...,
+) -> NDArray[Any]: ...
+@overload
+def cross(
+    a: _ArrayLikeBool_co,
+    b: _ArrayLikeBool_co,
+    axisa: int = ...,
+    axisb: int = ...,
+    axisc: int = ...,
+    axis: int | None = ...,
+) -> NoReturn: ...
+@overload
+def cross(
+    a: _ArrayLikeUInt_co,
+    b: _ArrayLikeUInt_co,
+    axisa: int = ...,
+    axisb: int = ...,
+    axisc: int = ...,
+    axis: int | None = ...,
+) -> NDArray[unsignedinteger]: ...
+@overload
+def cross(
+    a: _ArrayLikeInt_co,
+    b: _ArrayLikeInt_co,
+    axisa: int = ...,
+    axisb: int = ...,
+    axisc: int = ...,
+    axis: int | None = ...,
+) -> NDArray[signedinteger]: ...
+@overload
+def cross(
+    a: _ArrayLikeFloat_co,
+    b: _ArrayLikeFloat_co,
+    axisa: int = ...,
+    axisb: int = ...,
+    axisc: int = ...,
+    axis: int | None = ...,
+) -> NDArray[floating]: ...
+@overload
+def cross(
+    a: _ArrayLikeComplex_co,
+    b: _ArrayLikeComplex_co,
+    axisa: int = ...,
+    axisb: int = ...,
+    axisc: int = ...,
+    axis: int | None = ...,
+) -> NDArray[complexfloating]: ...
+@overload
+def cross(
+    a: _ArrayLikeObject_co,
+    b: _ArrayLikeObject_co,
+    axisa: int = ...,
+    axisb: int = ...,
+    axisc: int = ...,
+    axis: int | None = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def indices(
+    dimensions: Sequence[int],
+    dtype: type[int] = ...,
+    sparse: L[False] = ...,
+) -> NDArray[int_]: ...
+@overload
+def indices(
+    dimensions: Sequence[int],
+    dtype: type[int],
+    sparse: L[True],
+) -> tuple[NDArray[int_], ...]: ...
+@overload
+def indices(
+    dimensions: Sequence[int],
+    dtype: type[int] = ...,
+    *,
+    sparse: L[True],
+) -> tuple[NDArray[int_], ...]: ...
+@overload
+def indices(
+    dimensions: Sequence[int],
+    dtype: _DTypeLike[_ScalarT],
+    sparse: L[False] = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def indices(
+    dimensions: Sequence[int],
+    dtype: _DTypeLike[_ScalarT],
+    sparse: L[True],
+) -> tuple[NDArray[_ScalarT], ...]: ...
+@overload
+def indices(
+    dimensions: Sequence[int],
+    dtype: DTypeLike = ...,
+    sparse: L[False] = ...,
+) -> NDArray[Any]: ...
+@overload
+def indices(
+    dimensions: Sequence[int],
+    dtype: DTypeLike,
+    sparse: L[True],
+) -> tuple[NDArray[Any], ...]: ...
+@overload
+def indices(
+    dimensions: Sequence[int],
+    dtype: DTypeLike = ...,
+    *,
+    sparse: L[True],
+) -> tuple[NDArray[Any], ...]: ...
+
+def fromfunction(
+    function: Callable[..., _T],
+    shape: Sequence[int],
+    *,
+    dtype: DTypeLike = ...,
+    like: _SupportsArrayFunc | None = ...,
+    **kwargs: Any,
+) -> _T: ...
+
+def isscalar(element: object) -> TypeGuard[generic | complex | str | bytes | memoryview]: ...
+
+def binary_repr(num: SupportsIndex, width: int | None = ...) -> str: ...
+
+def base_repr(
+    number: SupportsAbs[float],
+    base: float = ...,
+    padding: SupportsIndex | None = ...,
+) -> str: ...
+
+@overload
+def identity(
+    n: int,
+    dtype: None = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[float64]: ...
+@overload
+def identity(
+    n: int,
+    dtype: _DTypeLike[_ScalarT],
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[_ScalarT]: ...
+@overload
+def identity(
+    n: int,
+    dtype: DTypeLike | None = ...,
+    *,
+    like: _SupportsArrayFunc | None = ...,
+) -> NDArray[Any]: ...
+
+def allclose(
+    a: ArrayLike,
+    b: ArrayLike,
+    rtol: ArrayLike = ...,
+    atol: ArrayLike = ...,
+    equal_nan: bool = ...,
+) -> bool: ...
+
+@overload
+def isclose(
+    a: _ScalarLike_co,
+    b: _ScalarLike_co,
+    rtol: ArrayLike = ...,
+    atol: ArrayLike = ...,
+    equal_nan: bool = ...,
+) -> np.bool: ...
+@overload
+def isclose(
+    a: ArrayLike,
+    b: ArrayLike,
+    rtol: ArrayLike = ...,
+    atol: ArrayLike = ...,
+    equal_nan: bool = ...,
+) -> NDArray[np.bool]: ...
+
+def array_equal(a1: ArrayLike, a2: ArrayLike, equal_nan: bool = ...) -> bool: ...
+
+def array_equiv(a1: ArrayLike, a2: ArrayLike) -> bool: ...
+
+@overload
+def astype(
+    x: ndarray[_ShapeT, dtype],
+    dtype: _DTypeLike[_ScalarT],
+    /,
+    *,
+    copy: bool = ...,
+    device: L["cpu"] | None = ...,
+) -> ndarray[_ShapeT, dtype[_ScalarT]]: ...
+@overload
+def astype(
+    x: ndarray[_ShapeT, dtype],
+    dtype: DTypeLike,
+    /,
+    *,
+    copy: bool = ...,
+    device: L["cpu"] | None = ...,
+) -> ndarray[_ShapeT, dtype]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/numerictypes.py b/.venv/lib/python3.12/site-packages/numpy/_core/numerictypes.py
new file mode 100644
index 0000000..135dc1b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/numerictypes.py
@@ -0,0 +1,633 @@
+"""
+numerictypes: Define the numeric type objects
+
+This module is designed so "from numerictypes import \\*" is safe.
+Exported symbols include:
+
+  Dictionary with all registered number types (including aliases):
+    sctypeDict
+
+  Type objects (not all will be available, depends on platform):
+      see variable sctypes for which ones you have
+
+    Bit-width names
+
+    int8 int16 int32 int64
+    uint8 uint16 uint32 uint64
+    float16 float32 float64 float96 float128
+    complex64 complex128 complex192 complex256
+    datetime64 timedelta64
+
+    c-based names
+
+    bool
+
+    object_
+
+    void, str_
+
+    byte, ubyte,
+    short, ushort
+    intc, uintc,
+    intp, uintp,
+    int_, uint,
+    longlong, ulonglong,
+
+    single, csingle,
+    double, cdouble,
+    longdouble, clongdouble,
+
+   As part of the type-hierarchy:    xx -- is bit-width
+
+   generic
+     +-> bool                                   (kind=b)
+     +-> number
+     |   +-> integer
+     |   |   +-> signedinteger     (intxx)      (kind=i)
+     |   |   |     byte
+     |   |   |     short
+     |   |   |     intc
+     |   |   |     intp
+     |   |   |     int_
+     |   |   |     longlong
+     |   |   \\-> unsignedinteger  (uintxx)     (kind=u)
+     |   |         ubyte
+     |   |         ushort
+     |   |         uintc
+     |   |         uintp
+     |   |         uint
+     |   |         ulonglong
+     |   +-> inexact
+     |       +-> floating          (floatxx)    (kind=f)
+     |       |     half
+     |       |     single
+     |       |     double
+     |       |     longdouble
+     |       \\-> complexfloating  (complexxx)  (kind=c)
+     |             csingle
+     |             cdouble
+     |             clongdouble
+     +-> flexible
+     |   +-> character
+     |   |     bytes_                           (kind=S)
+     |   |     str_                             (kind=U)
+     |   |
+     |   \\-> void                              (kind=V)
+     \\-> object_ (not used much)               (kind=O)
+
+"""
+import numbers
+import warnings
+
+from numpy._utils import set_module
+
+from . import multiarray as ma
+from .multiarray import (
+    busday_count,
+    busday_offset,
+    busdaycalendar,
+    datetime_as_string,
+    datetime_data,
+    dtype,
+    is_busday,
+    ndarray,
+)
+
+# we add more at the bottom
+__all__ = [
+    'ScalarType', 'typecodes', 'issubdtype', 'datetime_data',
+    'datetime_as_string', 'busday_offset', 'busday_count',
+    'is_busday', 'busdaycalendar', 'isdtype'
+]
+
+# we don't need all these imports, but we need to keep them for compatibility
+# for users using np._core.numerictypes.UPPER_TABLE
+# we don't export these for import *, but we do want them accessible
+# as numerictypes.bool, etc.
+from builtins import bool, bytes, complex, float, int, object, str  # noqa: F401, UP029
+
+from ._dtype import _kind_name
+from ._string_helpers import (  # noqa: F401
+    LOWER_TABLE,
+    UPPER_TABLE,
+    english_capitalize,
+    english_lower,
+    english_upper,
+)
+from ._type_aliases import allTypes, sctypeDict, sctypes
+
+# We use this later
+generic = allTypes['generic']
+
+genericTypeRank = ['bool', 'int8', 'uint8', 'int16', 'uint16',
+                   'int32', 'uint32', 'int64', 'uint64',
+                   'float16', 'float32', 'float64', 'float96', 'float128',
+                   'complex64', 'complex128', 'complex192', 'complex256',
+                   'object']
+
+@set_module('numpy')
+def maximum_sctype(t):
+    """
+    Return the scalar type of highest precision of the same kind as the input.
+
+    .. deprecated:: 2.0
+        Use an explicit dtype like int64 or float64 instead.
+
+    Parameters
+    ----------
+    t : dtype or dtype specifier
+        The input data type. This can be a `dtype` object or an object that
+        is convertible to a `dtype`.
+
+    Returns
+    -------
+    out : dtype
+        The highest precision data type of the same kind (`dtype.kind`) as `t`.
+
+    See Also
+    --------
+    obj2sctype, mintypecode, sctype2char
+    dtype
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import maximum_sctype
+    >>> maximum_sctype(int)
+    <class 'numpy.int64'>
+    >>> maximum_sctype(np.uint8)
+    <class 'numpy.uint64'>
+    >>> maximum_sctype(complex)
+    <class 'numpy.complex256'> # may vary
+
+    >>> maximum_sctype(str)
+    <class 'numpy.str_'>
+
+    >>> maximum_sctype('i2')
+    <class 'numpy.int64'>
+    >>> maximum_sctype('f4')
+    <class 'numpy.float128'> # may vary
+
+    """
+
+    # Deprecated in NumPy 2.0, 2023-07-11
+    warnings.warn(
+        "`maximum_sctype` is deprecated. Use an explicit dtype like int64 "
+        "or float64 instead. (deprecated in NumPy 2.0)",
+        DeprecationWarning,
+        stacklevel=2
+    )
+
+    g = obj2sctype(t)
+    if g is None:
+        return t
+    t = g
+    base = _kind_name(dtype(t))
+    if base in sctypes:
+        return sctypes[base][-1]
+    else:
+        return t
+
+
+@set_module('numpy')
+def issctype(rep):
+    """
+    Determines whether the given object represents a scalar data-type.
+
+    Parameters
+    ----------
+    rep : any
+        If `rep` is an instance of a scalar dtype, True is returned. If not,
+        False is returned.
+
+    Returns
+    -------
+    out : bool
+        Boolean result of check whether `rep` is a scalar dtype.
+
+    See Also
+    --------
+    issubsctype, issubdtype, obj2sctype, sctype2char
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import issctype
+    >>> issctype(np.int32)
+    True
+    >>> issctype(list)
+    False
+    >>> issctype(1.1)
+    False
+
+    Strings are also a scalar type:
+
+    >>> issctype(np.dtype('str'))
+    True
+
+    """
+    if not isinstance(rep, (type, dtype)):
+        return False
+    try:
+        res = obj2sctype(rep)
+        if res and res != object_:
+            return True
+        else:
+            return False
+    except Exception:
+        return False
+
+
+def obj2sctype(rep, default=None):
+    """
+    Return the scalar dtype or NumPy equivalent of Python type of an object.
+
+    Parameters
+    ----------
+    rep : any
+        The object of which the type is returned.
+    default : any, optional
+        If given, this is returned for objects whose types can not be
+        determined. If not given, None is returned for those objects.
+
+    Returns
+    -------
+    dtype : dtype or Python type
+        The data type of `rep`.
+
+    See Also
+    --------
+    sctype2char, issctype, issubsctype, issubdtype
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import obj2sctype
+    >>> obj2sctype(np.int32)
+    <class 'numpy.int32'>
+    >>> obj2sctype(np.array([1., 2.]))
+    <class 'numpy.float64'>
+    >>> obj2sctype(np.array([1.j]))
+    <class 'numpy.complex128'>
+
+    >>> obj2sctype(dict)
+    <class 'numpy.object_'>
+    >>> obj2sctype('string')
+
+    >>> obj2sctype(1, default=list)
+    <class 'list'>
+
+    """
+    # prevent abstract classes being upcast
+    if isinstance(rep, type) and issubclass(rep, generic):
+        return rep
+    # extract dtype from arrays
+    if isinstance(rep, ndarray):
+        return rep.dtype.type
+    # fall back on dtype to convert
+    try:
+        res = dtype(rep)
+    except Exception:
+        return default
+    else:
+        return res.type
+
+
+@set_module('numpy')
+def issubclass_(arg1, arg2):
+    """
+    Determine if a class is a subclass of a second class.
+
+    `issubclass_` is equivalent to the Python built-in ``issubclass``,
+    except that it returns False instead of raising a TypeError if one
+    of the arguments is not a class.
+
+    Parameters
+    ----------
+    arg1 : class
+        Input class. True is returned if `arg1` is a subclass of `arg2`.
+    arg2 : class or tuple of classes.
+        Input class. If a tuple of classes, True is returned if `arg1` is a
+        subclass of any of the tuple elements.
+
+    Returns
+    -------
+    out : bool
+        Whether `arg1` is a subclass of `arg2` or not.
+
+    See Also
+    --------
+    issubsctype, issubdtype, issctype
+
+    Examples
+    --------
+    >>> np.issubclass_(np.int32, int)
+    False
+    >>> np.issubclass_(np.int32, float)
+    False
+    >>> np.issubclass_(np.float64, float)
+    True
+
+    """
+    try:
+        return issubclass(arg1, arg2)
+    except TypeError:
+        return False
+
+
+@set_module('numpy')
+def issubsctype(arg1, arg2):
+    """
+    Determine if the first argument is a subclass of the second argument.
+
+    Parameters
+    ----------
+    arg1, arg2 : dtype or dtype specifier
+        Data-types.
+
+    Returns
+    -------
+    out : bool
+        The result.
+
+    See Also
+    --------
+    issctype, issubdtype, obj2sctype
+
+    Examples
+    --------
+    >>> from numpy._core import issubsctype
+    >>> issubsctype('S8', str)
+    False
+    >>> issubsctype(np.array([1]), int)
+    True
+    >>> issubsctype(np.array([1]), float)
+    False
+
+    """
+    return issubclass(obj2sctype(arg1), obj2sctype(arg2))
+
+
+class _PreprocessDTypeError(Exception):
+    pass
+
+
+def _preprocess_dtype(dtype):
+    """
+    Preprocess dtype argument by:
+      1. fetching type from a data type
+      2. verifying that types are built-in NumPy dtypes
+    """
+    if isinstance(dtype, ma.dtype):
+        dtype = dtype.type
+    if isinstance(dtype, ndarray) or dtype not in allTypes.values():
+        raise _PreprocessDTypeError
+    return dtype
+
+
+@set_module('numpy')
+def isdtype(dtype, kind):
+    """
+    Determine if a provided dtype is of a specified data type ``kind``.
+
+    This function only supports built-in NumPy's data types.
+    Third-party dtypes are not yet supported.
+
+    Parameters
+    ----------
+    dtype : dtype
+        The input dtype.
+    kind : dtype or str or tuple of dtypes/strs.
+        dtype or dtype kind. Allowed dtype kinds are:
+        * ``'bool'`` : boolean kind
+        * ``'signed integer'`` : signed integer data types
+        * ``'unsigned integer'`` : unsigned integer data types
+        * ``'integral'`` : integer data types
+        * ``'real floating'`` : real-valued floating-point data types
+        * ``'complex floating'`` : complex floating-point data types
+        * ``'numeric'`` : numeric data types
+
+    Returns
+    -------
+    out : bool
+
+    See Also
+    --------
+    issubdtype
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.isdtype(np.float32, np.float64)
+    False
+    >>> np.isdtype(np.float32, "real floating")
+    True
+    >>> np.isdtype(np.complex128, ("real floating", "complex floating"))
+    True
+
+    """
+    try:
+        dtype = _preprocess_dtype(dtype)
+    except _PreprocessDTypeError:
+        raise TypeError(
+            "dtype argument must be a NumPy dtype, "
+            f"but it is a {type(dtype)}."
+        ) from None
+
+    input_kinds = kind if isinstance(kind, tuple) else (kind,)
+
+    processed_kinds = set()
+
+    for kind in input_kinds:
+        if kind == "bool":
+            processed_kinds.add(allTypes["bool"])
+        elif kind == "signed integer":
+            processed_kinds.update(sctypes["int"])
+        elif kind == "unsigned integer":
+            processed_kinds.update(sctypes["uint"])
+        elif kind == "integral":
+            processed_kinds.update(sctypes["int"] + sctypes["uint"])
+        elif kind == "real floating":
+            processed_kinds.update(sctypes["float"])
+        elif kind == "complex floating":
+            processed_kinds.update(sctypes["complex"])
+        elif kind == "numeric":
+            processed_kinds.update(
+                sctypes["int"] + sctypes["uint"] +
+                sctypes["float"] + sctypes["complex"]
+            )
+        elif isinstance(kind, str):
+            raise ValueError(
+                "kind argument is a string, but"
+                f" {kind!r} is not a known kind name."
+            )
+        else:
+            try:
+                kind = _preprocess_dtype(kind)
+            except _PreprocessDTypeError:
+                raise TypeError(
+                    "kind argument must be comprised of "
+                    "NumPy dtypes or strings only, "
+                    f"but is a {type(kind)}."
+                ) from None
+            processed_kinds.add(kind)
+
+    return dtype in processed_kinds
+
+
+@set_module('numpy')
+def issubdtype(arg1, arg2):
+    r"""
+    Returns True if first argument is a typecode lower/equal in type hierarchy.
+
+    This is like the builtin :func:`issubclass`, but for `dtype`\ s.
+
+    Parameters
+    ----------
+    arg1, arg2 : dtype_like
+        `dtype` or object coercible to one
+
+    Returns
+    -------
+    out : bool
+
+    See Also
+    --------
+    :ref:`arrays.scalars` : Overview of the numpy type hierarchy.
+
+    Examples
+    --------
+    `issubdtype` can be used to check the type of arrays:
+
+    >>> ints = np.array([1, 2, 3], dtype=np.int32)
+    >>> np.issubdtype(ints.dtype, np.integer)
+    True
+    >>> np.issubdtype(ints.dtype, np.floating)
+    False
+
+    >>> floats = np.array([1, 2, 3], dtype=np.float32)
+    >>> np.issubdtype(floats.dtype, np.integer)
+    False
+    >>> np.issubdtype(floats.dtype, np.floating)
+    True
+
+    Similar types of different sizes are not subdtypes of each other:
+
+    >>> np.issubdtype(np.float64, np.float32)
+    False
+    >>> np.issubdtype(np.float32, np.float64)
+    False
+
+    but both are subtypes of `floating`:
+
+    >>> np.issubdtype(np.float64, np.floating)
+    True
+    >>> np.issubdtype(np.float32, np.floating)
+    True
+
+    For convenience, dtype-like objects are allowed too:
+
+    >>> np.issubdtype('S1', np.bytes_)
+    True
+    >>> np.issubdtype('i4', np.signedinteger)
+    True
+
+    """
+    if not issubclass_(arg1, generic):
+        arg1 = dtype(arg1).type
+    if not issubclass_(arg2, generic):
+        arg2 = dtype(arg2).type
+
+    return issubclass(arg1, arg2)
+
+
+@set_module('numpy')
+def sctype2char(sctype):
+    """
+    Return the string representation of a scalar dtype.
+
+    Parameters
+    ----------
+    sctype : scalar dtype or object
+        If a scalar dtype, the corresponding string character is
+        returned. If an object, `sctype2char` tries to infer its scalar type
+        and then return the corresponding string character.
+
+    Returns
+    -------
+    typechar : str
+        The string character corresponding to the scalar type.
+
+    Raises
+    ------
+    ValueError
+        If `sctype` is an object for which the type can not be inferred.
+
+    See Also
+    --------
+    obj2sctype, issctype, issubsctype, mintypecode
+
+    Examples
+    --------
+    >>> from numpy._core.numerictypes import sctype2char
+    >>> for sctype in [np.int32, np.double, np.cdouble, np.bytes_, np.ndarray]:
+    ...     print(sctype2char(sctype))
+    l # may vary
+    d
+    D
+    S
+    O
+
+    >>> x = np.array([1., 2-1.j])
+    >>> sctype2char(x)
+    'D'
+    >>> sctype2char(list)
+    'O'
+
+    """
+    sctype = obj2sctype(sctype)
+    if sctype is None:
+        raise ValueError("unrecognized type")
+    if sctype not in sctypeDict.values():
+        # for compatibility
+        raise KeyError(sctype)
+    return dtype(sctype).char
+
+
+def _scalar_type_key(typ):
+    """A ``key`` function for `sorted`."""
+    dt = dtype(typ)
+    return (dt.kind.lower(), dt.itemsize)
+
+
+ScalarType = [int, float, complex, bool, bytes, str, memoryview]
+ScalarType += sorted(set(sctypeDict.values()), key=_scalar_type_key)
+ScalarType = tuple(ScalarType)
+
+
+# Now add the types we've determined to this module
+for key in allTypes:
+    globals()[key] = allTypes[key]
+    __all__.append(key)
+
+del key
+
+typecodes = {'Character': 'c',
+             'Integer': 'bhilqnp',
+             'UnsignedInteger': 'BHILQNP',
+             'Float': 'efdg',
+             'Complex': 'FDG',
+             'AllInteger': 'bBhHiIlLqQnNpP',
+             'AllFloat': 'efdgFDG',
+             'Datetime': 'Mm',
+             'All': '?bhilqnpBHILQNPefdgFDGSUVOMm'}
+
+# backwards compatibility --- deprecated name
+# Formal deprecation: Numpy 1.20.0, 2020-10-19 (see numpy/__init__.py)
+typeDict = sctypeDict
+
+def _register_types():
+    numbers.Integral.register(integer)
+    numbers.Complex.register(inexact)
+    numbers.Real.register(floating)
+    numbers.Number.register(number)
+
+
+_register_types()
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/numerictypes.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/numerictypes.pyi
new file mode 100644
index 0000000..753fe34
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/numerictypes.pyi
@@ -0,0 +1,192 @@
+import builtins
+from typing import Any, TypedDict, type_check_only
+from typing import Literal as L
+
+import numpy as np
+from numpy import (
+    bool,
+    bool_,
+    byte,
+    bytes_,
+    cdouble,
+    character,
+    clongdouble,
+    complex64,
+    complex128,
+    complexfloating,
+    csingle,
+    datetime64,
+    double,
+    dtype,
+    flexible,
+    float16,
+    float32,
+    float64,
+    floating,
+    generic,
+    half,
+    inexact,
+    int8,
+    int16,
+    int32,
+    int64,
+    int_,
+    intc,
+    integer,
+    intp,
+    long,
+    longdouble,
+    longlong,
+    number,
+    object_,
+    short,
+    signedinteger,
+    single,
+    str_,
+    timedelta64,
+    ubyte,
+    uint,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+    uintc,
+    uintp,
+    ulong,
+    ulonglong,
+    unsignedinteger,
+    ushort,
+    void,
+)
+from numpy._typing import DTypeLike
+from numpy._typing._extended_precision import complex192, complex256, float96, float128
+
+from ._type_aliases import sctypeDict  # noqa: F401
+from .multiarray import (
+    busday_count,
+    busday_offset,
+    busdaycalendar,
+    datetime_as_string,
+    datetime_data,
+    is_busday,
+)
+
+__all__ = [
+    "ScalarType",
+    "typecodes",
+    "issubdtype",
+    "datetime_data",
+    "datetime_as_string",
+    "busday_offset",
+    "busday_count",
+    "is_busday",
+    "busdaycalendar",
+    "isdtype",
+    "generic",
+    "unsignedinteger",
+    "character",
+    "inexact",
+    "number",
+    "integer",
+    "flexible",
+    "complexfloating",
+    "signedinteger",
+    "floating",
+    "bool",
+    "float16",
+    "float32",
+    "float64",
+    "longdouble",
+    "complex64",
+    "complex128",
+    "clongdouble",
+    "bytes_",
+    "str_",
+    "void",
+    "object_",
+    "datetime64",
+    "timedelta64",
+    "int8",
+    "byte",
+    "uint8",
+    "ubyte",
+    "int16",
+    "short",
+    "uint16",
+    "ushort",
+    "int32",
+    "intc",
+    "uint32",
+    "uintc",
+    "int64",
+    "long",
+    "uint64",
+    "ulong",
+    "longlong",
+    "ulonglong",
+    "intp",
+    "uintp",
+    "double",
+    "cdouble",
+    "single",
+    "csingle",
+    "half",
+    "bool_",
+    "int_",
+    "uint",
+    "float96",
+    "float128",
+    "complex192",
+    "complex256",
+]
+
+@type_check_only
+class _TypeCodes(TypedDict):
+    Character: L['c']
+    Integer: L['bhilqnp']
+    UnsignedInteger: L['BHILQNP']
+    Float: L['efdg']
+    Complex: L['FDG']
+    AllInteger: L['bBhHiIlLqQnNpP']
+    AllFloat: L['efdgFDG']
+    Datetime: L['Mm']
+    All: L['?bhilqnpBHILQNPefdgFDGSUVOMm']
+
+def isdtype(dtype: dtype | type[Any], kind: DTypeLike | tuple[DTypeLike, ...]) -> builtins.bool: ...
+
+def issubdtype(arg1: DTypeLike, arg2: DTypeLike) -> builtins.bool: ...
+
+typecodes: _TypeCodes
+ScalarType: tuple[
+    type[int],
+    type[float],
+    type[complex],
+    type[builtins.bool],
+    type[bytes],
+    type[str],
+    type[memoryview],
+    type[np.bool],
+    type[csingle],
+    type[cdouble],
+    type[clongdouble],
+    type[half],
+    type[single],
+    type[double],
+    type[longdouble],
+    type[byte],
+    type[short],
+    type[intc],
+    type[long],
+    type[longlong],
+    type[timedelta64],
+    type[datetime64],
+    type[object_],
+    type[bytes_],
+    type[str_],
+    type[ubyte],
+    type[ushort],
+    type[uintc],
+    type[ulong],
+    type[ulonglong],
+    type[void],
+]
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/overrides.py b/.venv/lib/python3.12/site-packages/numpy/_core/overrides.py
new file mode 100644
index 0000000..6414710
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/overrides.py
@@ -0,0 +1,183 @@
+"""Implementation of __array_function__ overrides from NEP-18."""
+import collections
+import functools
+
+from numpy._core._multiarray_umath import (
+    _ArrayFunctionDispatcher,
+    _get_implementing_args,
+    add_docstring,
+)
+from numpy._utils import set_module  # noqa: F401
+from numpy._utils._inspect import getargspec
+
+ARRAY_FUNCTIONS = set()
+
+array_function_like_doc = (
+    """like : array_like, optional
+        Reference object to allow the creation of arrays which are not
+        NumPy arrays. If an array-like passed in as ``like`` supports
+        the ``__array_function__`` protocol, the result will be defined
+        by it. In this case, it ensures the creation of an array object
+        compatible with that passed in via this argument."""
+)
+
+def get_array_function_like_doc(public_api, docstring_template=""):
+    ARRAY_FUNCTIONS.add(public_api)
+    docstring = public_api.__doc__ or docstring_template
+    return docstring.replace("${ARRAY_FUNCTION_LIKE}", array_function_like_doc)
+
+def finalize_array_function_like(public_api):
+    public_api.__doc__ = get_array_function_like_doc(public_api)
+    return public_api
+
+
+add_docstring(
+    _ArrayFunctionDispatcher,
+    """
+    Class to wrap functions with checks for __array_function__ overrides.
+
+    All arguments are required, and can only be passed by position.
+
+    Parameters
+    ----------
+    dispatcher : function or None
+        The dispatcher function that returns a single sequence-like object
+        of all arguments relevant.  It must have the same signature (except
+        the default values) as the actual implementation.
+        If ``None``, this is a ``like=`` dispatcher and the
+        ``_ArrayFunctionDispatcher`` must be called with ``like`` as the
+        first (additional and positional) argument.
+    implementation : function
+        Function that implements the operation on NumPy arrays without
+        overrides.  Arguments passed calling the ``_ArrayFunctionDispatcher``
+        will be forwarded to this (and the ``dispatcher``) as if using
+        ``*args, **kwargs``.
+
+    Attributes
+    ----------
+    _implementation : function
+        The original implementation passed in.
+    """)
+
+
+# exposed for testing purposes; used internally by _ArrayFunctionDispatcher
+add_docstring(
+    _get_implementing_args,
+    """
+    Collect arguments on which to call __array_function__.
+
+    Parameters
+    ----------
+    relevant_args : iterable of array-like
+        Iterable of possibly array-like arguments to check for
+        __array_function__ methods.
+
+    Returns
+    -------
+    Sequence of arguments with __array_function__ methods, in the order in
+    which they should be called.
+    """)
+
+
+ArgSpec = collections.namedtuple('ArgSpec', 'args varargs keywords defaults')
+
+
+def verify_matching_signatures(implementation, dispatcher):
+    """Verify that a dispatcher function has the right signature."""
+    implementation_spec = ArgSpec(*getargspec(implementation))
+    dispatcher_spec = ArgSpec(*getargspec(dispatcher))
+
+    if (implementation_spec.args != dispatcher_spec.args or
+            implementation_spec.varargs != dispatcher_spec.varargs or
+            implementation_spec.keywords != dispatcher_spec.keywords or
+            (bool(implementation_spec.defaults) !=
+             bool(dispatcher_spec.defaults)) or
+            (implementation_spec.defaults is not None and
+             len(implementation_spec.defaults) !=
+             len(dispatcher_spec.defaults))):
+        raise RuntimeError('implementation and dispatcher for %s have '
+                           'different function signatures' % implementation)
+
+    if implementation_spec.defaults is not None:
+        if dispatcher_spec.defaults != (None,) * len(dispatcher_spec.defaults):
+            raise RuntimeError('dispatcher functions can only use None for '
+                               'default argument values')
+
+
+def array_function_dispatch(dispatcher=None, module=None, verify=True,
+                            docs_from_dispatcher=False):
+    """Decorator for adding dispatch with the __array_function__ protocol.
+
+    See NEP-18 for example usage.
+
+    Parameters
+    ----------
+    dispatcher : callable or None
+        Function that when called like ``dispatcher(*args, **kwargs)`` with
+        arguments from the NumPy function call returns an iterable of
+        array-like arguments to check for ``__array_function__``.
+
+        If `None`, the first argument is used as the single `like=` argument
+        and not passed on.  A function implementing `like=` must call its
+        dispatcher with `like` as the first non-keyword argument.
+    module : str, optional
+        __module__ attribute to set on new function, e.g., ``module='numpy'``.
+        By default, module is copied from the decorated function.
+    verify : bool, optional
+        If True, verify the that the signature of the dispatcher and decorated
+        function signatures match exactly: all required and optional arguments
+        should appear in order with the same names, but the default values for
+        all optional arguments should be ``None``. Only disable verification
+        if the dispatcher's signature needs to deviate for some particular
+        reason, e.g., because the function has a signature like
+        ``func(*args, **kwargs)``.
+    docs_from_dispatcher : bool, optional
+        If True, copy docs from the dispatcher function onto the dispatched
+        function, rather than from the implementation. This is useful for
+        functions defined in C, which otherwise don't have docstrings.
+
+    Returns
+    -------
+    Function suitable for decorating the implementation of a NumPy function.
+
+    """
+    def decorator(implementation):
+        if verify:
+            if dispatcher is not None:
+                verify_matching_signatures(implementation, dispatcher)
+            else:
+                # Using __code__ directly similar to verify_matching_signature
+                co = implementation.__code__
+                last_arg = co.co_argcount + co.co_kwonlyargcount - 1
+                last_arg = co.co_varnames[last_arg]
+                if last_arg != "like" or co.co_kwonlyargcount == 0:
+                    raise RuntimeError(
+                        "__array_function__ expects `like=` to be the last "
+                        "argument and a keyword-only argument. "
+                        f"{implementation} does not seem to comply.")
+
+        if docs_from_dispatcher:
+            add_docstring(implementation, dispatcher.__doc__)
+
+        public_api = _ArrayFunctionDispatcher(dispatcher, implementation)
+        public_api = functools.wraps(implementation)(public_api)
+
+        if module is not None:
+            public_api.__module__ = module
+
+        ARRAY_FUNCTIONS.add(public_api)
+
+        return public_api
+
+    return decorator
+
+
+def array_function_from_dispatcher(
+        implementation, module=None, verify=True, docs_from_dispatcher=True):
+    """Like array_function_dispatcher, but with function arguments flipped."""
+
+    def decorator(dispatcher):
+        return array_function_dispatch(
+            dispatcher, module, verify=verify,
+            docs_from_dispatcher=docs_from_dispatcher)(implementation)
+    return decorator
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/overrides.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/overrides.pyi
new file mode 100644
index 0000000..0545319
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/overrides.pyi
@@ -0,0 +1,48 @@
+from collections.abc import Callable, Iterable
+from typing import Any, Final, NamedTuple, ParamSpec, TypeVar
+
+from numpy._typing import _SupportsArrayFunc
+
+_T = TypeVar("_T")
+_Tss = ParamSpec("_Tss")
+_FuncT = TypeVar("_FuncT", bound=Callable[..., object])
+
+###
+
+ARRAY_FUNCTIONS: set[Callable[..., Any]] = ...
+array_function_like_doc: Final[str] = ...
+
+class ArgSpec(NamedTuple):
+    args: list[str]
+    varargs: str | None
+    keywords: str | None
+    defaults: tuple[Any, ...]
+
+def get_array_function_like_doc(public_api: Callable[..., Any], docstring_template: str = "") -> str: ...
+def finalize_array_function_like(public_api: _FuncT) -> _FuncT: ...
+
+#
+def verify_matching_signatures(
+    implementation: Callable[_Tss, object],
+    dispatcher: Callable[_Tss, Iterable[_SupportsArrayFunc]],
+) -> None: ...
+
+# NOTE: This actually returns a `_ArrayFunctionDispatcher` callable wrapper object, with
+# the original wrapped callable stored in the `._implementation` attribute. It checks
+# for any `__array_function__` of the values of specific arguments that the dispatcher
+# specifies. Since the dispatcher only returns an iterable of passed array-like args,
+# this overridable behaviour is impossible to annotate.
+def array_function_dispatch(
+    dispatcher: Callable[_Tss, Iterable[_SupportsArrayFunc]] | None = None,
+    module: str | None = None,
+    verify: bool = True,
+    docs_from_dispatcher: bool = False,
+) -> Callable[[_FuncT], _FuncT]: ...
+
+#
+def array_function_from_dispatcher(
+    implementation: Callable[_Tss, _T],
+    module: str | None = None,
+    verify: bool = True,
+    docs_from_dispatcher: bool = True,
+) -> Callable[[Callable[_Tss, Iterable[_SupportsArrayFunc]]], Callable[_Tss, _T]]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/printoptions.py b/.venv/lib/python3.12/site-packages/numpy/_core/printoptions.py
new file mode 100644
index 0000000..5d6f963
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/printoptions.py
@@ -0,0 +1,32 @@
+"""
+Stores and defines the low-level format_options context variable.
+
+This is defined in its own file outside of the arrayprint module
+so we can import it from C while initializing the multiarray
+C module during import without introducing circular dependencies.
+"""
+
+import sys
+from contextvars import ContextVar
+
+__all__ = ["format_options"]
+
+default_format_options_dict = {
+    "edgeitems": 3,  # repr N leading and trailing items of each dimension
+    "threshold": 1000,  # total items > triggers array summarization
+    "floatmode": "maxprec",
+    "precision": 8,  # precision of floating point representations
+    "suppress": False,  # suppress printing small floating values in exp format
+    "linewidth": 75,
+    "nanstr": "nan",
+    "infstr": "inf",
+    "sign": "-",
+    "formatter": None,
+    # Internally stored as an int to simplify comparisons; converted from/to
+    # str/False on the way in/out.
+    'legacy': sys.maxsize,
+    'override_repr': None,
+}
+
+format_options = ContextVar(
+    "format_options", default=default_format_options_dict)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/printoptions.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/printoptions.pyi
new file mode 100644
index 0000000..bd7c7b4
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/printoptions.pyi
@@ -0,0 +1,28 @@
+from collections.abc import Callable
+from contextvars import ContextVar
+from typing import Any, Final, TypedDict
+
+from .arrayprint import _FormatDict
+
+__all__ = ["format_options"]
+
+###
+
+class _FormatOptionsDict(TypedDict):
+    edgeitems: int
+    threshold: int
+    floatmode: str
+    precision: int
+    suppress: bool
+    linewidth: int
+    nanstr: str
+    infstr: str
+    sign: str
+    formatter: _FormatDict | None
+    legacy: int
+    override_repr: Callable[[Any], str] | None
+
+###
+
+default_format_options_dict: Final[_FormatOptionsDict] = ...
+format_options: ContextVar[_FormatOptionsDict]
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/records.py b/.venv/lib/python3.12/site-packages/numpy/_core/records.py
new file mode 100644
index 0000000..39bcf4b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/records.py
@@ -0,0 +1,1089 @@
+"""
+This module contains a set of functions for record arrays.
+"""
+import os
+import warnings
+from collections import Counter
+from contextlib import nullcontext
+
+from numpy._utils import set_module
+
+from . import numeric as sb
+from . import numerictypes as nt
+from .arrayprint import _get_legacy_print_mode
+
+# All of the functions allow formats to be a dtype
+__all__ = [
+    'record', 'recarray', 'format_parser', 'fromarrays', 'fromrecords',
+    'fromstring', 'fromfile', 'array', 'find_duplicate',
+]
+
+
+ndarray = sb.ndarray
+
+_byteorderconv = {'b': '>',
+                  'l': '<',
+                  'n': '=',
+                  'B': '>',
+                  'L': '<',
+                  'N': '=',
+                  'S': 's',
+                  's': 's',
+                  '>': '>',
+                  '<': '<',
+                  '=': '=',
+                  '|': '|',
+                  'I': '|',
+                  'i': '|'}
+
+# formats regular expression
+# allows multidimensional spec with a tuple syntax in front
+# of the letter code '(2,3)f4' and ' (  2 ,  3  )  f4  '
+# are equally allowed
+
+numfmt = nt.sctypeDict
+
+
+@set_module('numpy.rec')
+def find_duplicate(list):
+    """Find duplication in a list, return a list of duplicated elements"""
+    return [
+        item
+        for item, counts in Counter(list).items()
+        if counts > 1
+    ]
+
+
+@set_module('numpy.rec')
+class format_parser:
+    """
+    Class to convert formats, names, titles description to a dtype.
+
+    After constructing the format_parser object, the dtype attribute is
+    the converted data-type:
+    ``dtype = format_parser(formats, names, titles).dtype``
+
+    Attributes
+    ----------
+    dtype : dtype
+        The converted data-type.
+
+    Parameters
+    ----------
+    formats : str or list of str
+        The format description, either specified as a string with
+        comma-separated format descriptions in the form ``'f8, i4, S5'``, or
+        a list of format description strings  in the form
+        ``['f8', 'i4', 'S5']``.
+    names : str or list/tuple of str
+        The field names, either specified as a comma-separated string in the
+        form ``'col1, col2, col3'``, or as a list or tuple of strings in the
+        form ``['col1', 'col2', 'col3']``.
+        An empty list can be used, in that case default field names
+        ('f0', 'f1', ...) are used.
+    titles : sequence
+        Sequence of title strings. An empty list can be used to leave titles
+        out.
+    aligned : bool, optional
+        If True, align the fields by padding as the C-compiler would.
+        Default is False.
+    byteorder : str, optional
+        If specified, all the fields will be changed to the
+        provided byte-order.  Otherwise, the default byte-order is
+        used. For all available string specifiers, see `dtype.newbyteorder`.
+
+    See Also
+    --------
+    numpy.dtype, numpy.typename
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.rec.format_parser(['<f8', '<i4'], ['col1', 'col2'],
+    ...                      ['T1', 'T2']).dtype
+    dtype([(('T1', 'col1'), '<f8'), (('T2', 'col2'), '<i4')])
+
+    `names` and/or `titles` can be empty lists. If `titles` is an empty list,
+    titles will simply not appear. If `names` is empty, default field names
+    will be used.
+
+    >>> np.rec.format_parser(['f8', 'i4', 'a5'], ['col1', 'col2', 'col3'],
+    ...                      []).dtype
+    dtype([('col1', '<f8'), ('col2', '<i4'), ('col3', '<S5')])
+    >>> np.rec.format_parser(['<f8', '<i4', '<a5'], [], []).dtype
+    dtype([('f0', '<f8'), ('f1', '<i4'), ('f2', 'S5')])
+
+    """
+
+    def __init__(self, formats, names, titles, aligned=False, byteorder=None):
+        self._parseFormats(formats, aligned)
+        self._setfieldnames(names, titles)
+        self._createdtype(byteorder)
+
+    def _parseFormats(self, formats, aligned=False):
+        """ Parse the field formats """
+
+        if formats is None:
+            raise ValueError("Need formats argument")
+        if isinstance(formats, list):
+            dtype = sb.dtype(
+                [
+                    (f'f{i}', format_)
+                    for i, format_ in enumerate(formats)
+                ],
+                aligned,
+            )
+        else:
+            dtype = sb.dtype(formats, aligned)
+        fields = dtype.fields
+        if fields is None:
+            dtype = sb.dtype([('f1', dtype)], aligned)
+            fields = dtype.fields
+        keys = dtype.names
+        self._f_formats = [fields[key][0] for key in keys]
+        self._offsets = [fields[key][1] for key in keys]
+        self._nfields = len(keys)
+
+    def _setfieldnames(self, names, titles):
+        """convert input field names into a list and assign to the _names
+        attribute """
+
+        if names:
+            if type(names) in [list, tuple]:
+                pass
+            elif isinstance(names, str):
+                names = names.split(',')
+            else:
+                raise NameError(f"illegal input names {repr(names)}")
+
+            self._names = [n.strip() for n in names[:self._nfields]]
+        else:
+            self._names = []
+
+        # if the names are not specified, they will be assigned as
+        #  "f0, f1, f2,..."
+        # if not enough names are specified, they will be assigned as "f[n],
+        # f[n+1],..." etc. where n is the number of specified names..."
+        self._names += ['f%d' % i for i in range(len(self._names),
+                                                 self._nfields)]
+        # check for redundant names
+        _dup = find_duplicate(self._names)
+        if _dup:
+            raise ValueError(f"Duplicate field names: {_dup}")
+
+        if titles:
+            self._titles = [n.strip() for n in titles[:self._nfields]]
+        else:
+            self._titles = []
+            titles = []
+
+        if self._nfields > len(titles):
+            self._titles += [None] * (self._nfields - len(titles))
+
+    def _createdtype(self, byteorder):
+        dtype = sb.dtype({
+            'names': self._names,
+            'formats': self._f_formats,
+            'offsets': self._offsets,
+            'titles': self._titles,
+        })
+        if byteorder is not None:
+            byteorder = _byteorderconv[byteorder[0]]
+            dtype = dtype.newbyteorder(byteorder)
+
+        self.dtype = dtype
+
+
+class record(nt.void):
+    """A data-type scalar that allows field access as attribute lookup.
+    """
+
+    # manually set name and module so that this class's type shows up
+    # as numpy.record when printed
+    __name__ = 'record'
+    __module__ = 'numpy'
+
+    def __repr__(self):
+        if _get_legacy_print_mode() <= 113:
+            return self.__str__()
+        return super().__repr__()
+
+    def __str__(self):
+        if _get_legacy_print_mode() <= 113:
+            return str(self.item())
+        return super().__str__()
+
+    def __getattribute__(self, attr):
+        if attr in ('setfield', 'getfield', 'dtype'):
+            return nt.void.__getattribute__(self, attr)
+        try:
+            return nt.void.__getattribute__(self, attr)
+        except AttributeError:
+            pass
+        fielddict = nt.void.__getattribute__(self, 'dtype').fields
+        res = fielddict.get(attr, None)
+        if res:
+            obj = self.getfield(*res[:2])
+            # if it has fields return a record,
+            # otherwise return the object
+            try:
+                dt = obj.dtype
+            except AttributeError:
+                # happens if field is Object type
+                return obj
+            if dt.names is not None:
+                return obj.view((self.__class__, obj.dtype))
+            return obj
+        else:
+            raise AttributeError(f"'record' object has no attribute '{attr}'")
+
+    def __setattr__(self, attr, val):
+        if attr in ('setfield', 'getfield', 'dtype'):
+            raise AttributeError(f"Cannot set '{attr}' attribute")
+        fielddict = nt.void.__getattribute__(self, 'dtype').fields
+        res = fielddict.get(attr, None)
+        if res:
+            return self.setfield(val, *res[:2])
+        elif getattr(self, attr, None):
+            return nt.void.__setattr__(self, attr, val)
+        else:
+            raise AttributeError(f"'record' object has no attribute '{attr}'")
+
+    def __getitem__(self, indx):
+        obj = nt.void.__getitem__(self, indx)
+
+        # copy behavior of record.__getattribute__,
+        if isinstance(obj, nt.void) and obj.dtype.names is not None:
+            return obj.view((self.__class__, obj.dtype))
+        else:
+            # return a single element
+            return obj
+
+    def pprint(self):
+        """Pretty-print all fields."""
+        # pretty-print all fields
+        names = self.dtype.names
+        maxlen = max(len(name) for name in names)
+        fmt = '%% %ds: %%s' % maxlen
+        rows = [fmt % (name, getattr(self, name)) for name in names]
+        return "\n".join(rows)
+
+# The recarray is almost identical to a standard array (which supports
+#   named fields already)  The biggest difference is that it can use
+#   attribute-lookup to find the fields and it is constructed using
+#   a record.
+
+# If byteorder is given it forces a particular byteorder on all
+#  the fields (and any subfields)
+
+
+@set_module("numpy.rec")
+class recarray(ndarray):
+    """Construct an ndarray that allows field access using attributes.
+
+    Arrays may have a data-types containing fields, analogous
+    to columns in a spread sheet.  An example is ``[(x, int), (y, float)]``,
+    where each entry in the array is a pair of ``(int, float)``.  Normally,
+    these attributes are accessed using dictionary lookups such as ``arr['x']``
+    and ``arr['y']``.  Record arrays allow the fields to be accessed as members
+    of the array, using ``arr.x`` and ``arr.y``.
+
+    Parameters
+    ----------
+    shape : tuple
+        Shape of output array.
+    dtype : data-type, optional
+        The desired data-type.  By default, the data-type is determined
+        from `formats`, `names`, `titles`, `aligned` and `byteorder`.
+    formats : list of data-types, optional
+        A list containing the data-types for the different columns, e.g.
+        ``['i4', 'f8', 'i4']``.  `formats` does *not* support the new
+        convention of using types directly, i.e. ``(int, float, int)``.
+        Note that `formats` must be a list, not a tuple.
+        Given that `formats` is somewhat limited, we recommend specifying
+        `dtype` instead.
+    names : tuple of str, optional
+        The name of each column, e.g. ``('x', 'y', 'z')``.
+    buf : buffer, optional
+        By default, a new array is created of the given shape and data-type.
+        If `buf` is specified and is an object exposing the buffer interface,
+        the array will use the memory from the existing buffer.  In this case,
+        the `offset` and `strides` keywords are available.
+
+    Other Parameters
+    ----------------
+    titles : tuple of str, optional
+        Aliases for column names.  For example, if `names` were
+        ``('x', 'y', 'z')`` and `titles` is
+        ``('x_coordinate', 'y_coordinate', 'z_coordinate')``, then
+        ``arr['x']`` is equivalent to both ``arr.x`` and ``arr.x_coordinate``.
+    byteorder : {'<', '>', '='}, optional
+        Byte-order for all fields.
+    aligned : bool, optional
+        Align the fields in memory as the C-compiler would.
+    strides : tuple of ints, optional
+        Buffer (`buf`) is interpreted according to these strides (strides
+        define how many bytes each array element, row, column, etc.
+        occupy in memory).
+    offset : int, optional
+        Start reading buffer (`buf`) from this offset onwards.
+    order : {'C', 'F'}, optional
+        Row-major (C-style) or column-major (Fortran-style) order.
+
+    Returns
+    -------
+    rec : recarray
+        Empty array of the given shape and type.
+
+    See Also
+    --------
+    numpy.rec.fromrecords : Construct a record array from data.
+    numpy.record : fundamental data-type for `recarray`.
+    numpy.rec.format_parser : determine data-type from formats, names, titles.
+
+    Notes
+    -----
+    This constructor can be compared to ``empty``: it creates a new record
+    array but does not fill it with data.  To create a record array from data,
+    use one of the following methods:
+
+    1. Create a standard ndarray and convert it to a record array,
+       using ``arr.view(np.recarray)``
+    2. Use the `buf` keyword.
+    3. Use `np.rec.fromrecords`.
+
+    Examples
+    --------
+    Create an array with two fields, ``x`` and ``y``:
+
+    >>> import numpy as np
+    >>> x = np.array([(1.0, 2), (3.0, 4)], dtype=[('x', '<f8'), ('y', '<i8')])
+    >>> x
+    array([(1., 2), (3., 4)], dtype=[('x', '<f8'), ('y', '<i8')])
+
+    >>> x['x']
+    array([1., 3.])
+
+    View the array as a record array:
+
+    >>> x = x.view(np.recarray)
+
+    >>> x.x
+    array([1., 3.])
+
+    >>> x.y
+    array([2, 4])
+
+    Create a new, empty record array:
+
+    >>> np.recarray((2,),
+    ... dtype=[('x', int), ('y', float), ('z', int)]) #doctest: +SKIP
+    rec.array([(-1073741821, 1.2249118382103472e-301, 24547520),
+           (3471280, 1.2134086255804012e-316, 0)],
+          dtype=[('x', '<i4'), ('y', '<f8'), ('z', '<i4')])
+
+    """
+
+    def __new__(subtype, shape, dtype=None, buf=None, offset=0, strides=None,
+                formats=None, names=None, titles=None,
+                byteorder=None, aligned=False, order='C'):
+
+        if dtype is not None:
+            descr = sb.dtype(dtype)
+        else:
+            descr = format_parser(
+                formats, names, titles, aligned, byteorder
+            ).dtype
+
+        if buf is None:
+            self = ndarray.__new__(
+                subtype, shape, (record, descr), order=order
+            )
+        else:
+            self = ndarray.__new__(
+                subtype, shape, (record, descr), buffer=buf,
+                offset=offset, strides=strides, order=order
+            )
+        return self
+
+    def __array_finalize__(self, obj):
+        if self.dtype.type is not record and self.dtype.names is not None:
+            # if self.dtype is not np.record, invoke __setattr__ which will
+            # convert it to a record if it is a void dtype.
+            self.dtype = self.dtype
+
+    def __getattribute__(self, attr):
+        # See if ndarray has this attr, and return it if so. (note that this
+        # means a field with the same name as an ndarray attr cannot be
+        # accessed by attribute).
+        try:
+            return object.__getattribute__(self, attr)
+        except AttributeError:  # attr must be a fieldname
+            pass
+
+        # look for a field with this name
+        fielddict = ndarray.__getattribute__(self, 'dtype').fields
+        try:
+            res = fielddict[attr][:2]
+        except (TypeError, KeyError) as e:
+            raise AttributeError(f"recarray has no attribute {attr}") from e
+        obj = self.getfield(*res)
+
+        # At this point obj will always be a recarray, since (see
+        # PyArray_GetField) the type of obj is inherited. Next, if obj.dtype is
+        # non-structured, convert it to an ndarray. Then if obj is structured
+        # with void type convert it to the same dtype.type (eg to preserve
+        # numpy.record type if present), since nested structured fields do not
+        # inherit type. Don't do this for non-void structures though.
+        if obj.dtype.names is not None:
+            if issubclass(obj.dtype.type, nt.void):
+                return obj.view(dtype=(self.dtype.type, obj.dtype))
+            return obj
+        else:
+            return obj.view(ndarray)
+
+    # Save the dictionary.
+    # If the attr is a field name and not in the saved dictionary
+    # Undo any "setting" of the attribute and do a setfield
+    # Thus, you can't create attributes on-the-fly that are field names.
+    def __setattr__(self, attr, val):
+
+        # Automatically convert (void) structured types to records
+        # (but not non-void structures, subarrays, or non-structured voids)
+        if (
+            attr == 'dtype' and
+            issubclass(val.type, nt.void) and
+            val.names is not None
+        ):
+            val = sb.dtype((record, val))
+
+        newattr = attr not in self.__dict__
+        try:
+            ret = object.__setattr__(self, attr, val)
+        except Exception:
+            fielddict = ndarray.__getattribute__(self, 'dtype').fields or {}
+            if attr not in fielddict:
+                raise
+        else:
+            fielddict = ndarray.__getattribute__(self, 'dtype').fields or {}
+            if attr not in fielddict:
+                return ret
+            if newattr:
+                # We just added this one or this setattr worked on an
+                # internal attribute.
+                try:
+                    object.__delattr__(self, attr)
+                except Exception:
+                    return ret
+        try:
+            res = fielddict[attr][:2]
+        except (TypeError, KeyError) as e:
+            raise AttributeError(
+                f"record array has no attribute {attr}"
+            ) from e
+        return self.setfield(val, *res)
+
+    def __getitem__(self, indx):
+        obj = super().__getitem__(indx)
+
+        # copy behavior of getattr, except that here
+        # we might also be returning a single element
+        if isinstance(obj, ndarray):
+            if obj.dtype.names is not None:
+                obj = obj.view(type(self))
+                if issubclass(obj.dtype.type, nt.void):
+                    return obj.view(dtype=(self.dtype.type, obj.dtype))
+                return obj
+            else:
+                return obj.view(type=ndarray)
+        else:
+            # return a single element
+            return obj
+
+    def __repr__(self):
+
+        repr_dtype = self.dtype
+        if (
+            self.dtype.type is record or
+            not issubclass(self.dtype.type, nt.void)
+        ):
+            # If this is a full record array (has numpy.record dtype),
+            # or if it has a scalar (non-void) dtype with no records,
+            # represent it using the rec.array function. Since rec.array
+            # converts dtype to a numpy.record for us, convert back
+            # to non-record before printing
+            if repr_dtype.type is record:
+                repr_dtype = sb.dtype((nt.void, repr_dtype))
+            prefix = "rec.array("
+            fmt = 'rec.array(%s,%sdtype=%s)'
+        else:
+            # otherwise represent it using np.array plus a view
+            # This should only happen if the user is playing
+            # strange games with dtypes.
+            prefix = "array("
+            fmt = 'array(%s,%sdtype=%s).view(numpy.recarray)'
+
+        # get data/shape string. logic taken from numeric.array_repr
+        if self.size > 0 or self.shape == (0,):
+            lst = sb.array2string(
+                self, separator=', ', prefix=prefix, suffix=',')
+        else:
+            # show zero-length shape unless it is (0,)
+            lst = f"[], shape={repr(self.shape)}"
+
+        lf = '\n' + ' ' * len(prefix)
+        if _get_legacy_print_mode() <= 113:
+            lf = ' ' + lf  # trailing space
+        return fmt % (lst, lf, repr_dtype)
+
+    def field(self, attr, val=None):
+        if isinstance(attr, int):
+            names = ndarray.__getattribute__(self, 'dtype').names
+            attr = names[attr]
+
+        fielddict = ndarray.__getattribute__(self, 'dtype').fields
+
+        res = fielddict[attr][:2]
+
+        if val is None:
+            obj = self.getfield(*res)
+            if obj.dtype.names is not None:
+                return obj
+            return obj.view(ndarray)
+        else:
+            return self.setfield(val, *res)
+
+
+def _deprecate_shape_0_as_None(shape):
+    if shape == 0:
+        warnings.warn(
+            "Passing `shape=0` to have the shape be inferred is deprecated, "
+            "and in future will be equivalent to `shape=(0,)`. To infer "
+            "the shape and suppress this warning, pass `shape=None` instead.",
+            FutureWarning, stacklevel=3)
+        return None
+    else:
+        return shape
+
+
+@set_module("numpy.rec")
+def fromarrays(arrayList, dtype=None, shape=None, formats=None,
+               names=None, titles=None, aligned=False, byteorder=None):
+    """Create a record array from a (flat) list of arrays
+
+    Parameters
+    ----------
+    arrayList : list or tuple
+        List of array-like objects (such as lists, tuples,
+        and ndarrays).
+    dtype : data-type, optional
+        valid dtype for all arrays
+    shape : int or tuple of ints, optional
+        Shape of the resulting array. If not provided, inferred from
+        ``arrayList[0]``.
+    formats, names, titles, aligned, byteorder :
+        If `dtype` is ``None``, these arguments are passed to
+        `numpy.rec.format_parser` to construct a dtype. See that function for
+        detailed documentation.
+
+    Returns
+    -------
+    np.recarray
+        Record array consisting of given arrayList columns.
+
+    Examples
+    --------
+    >>> x1=np.array([1,2,3,4])
+    >>> x2=np.array(['a','dd','xyz','12'])
+    >>> x3=np.array([1.1,2,3,4])
+    >>> r = np.rec.fromarrays([x1,x2,x3],names='a,b,c')
+    >>> print(r[1])
+    (2, 'dd', 2.0) # may vary
+    >>> x1[1]=34
+    >>> r.a
+    array([1, 2, 3, 4])
+
+    >>> x1 = np.array([1, 2, 3, 4])
+    >>> x2 = np.array(['a', 'dd', 'xyz', '12'])
+    >>> x3 = np.array([1.1, 2, 3,4])
+    >>> r = np.rec.fromarrays(
+    ...     [x1, x2, x3],
+    ...     dtype=np.dtype([('a', np.int32), ('b', 'S3'), ('c', np.float32)]))
+    >>> r
+    rec.array([(1, b'a', 1.1), (2, b'dd', 2. ), (3, b'xyz', 3. ),
+               (4, b'12', 4. )],
+              dtype=[('a', '<i4'), ('b', 'S3'), ('c', '<f4')])
+    """
+
+    arrayList = [sb.asarray(x) for x in arrayList]
+
+    # NumPy 1.19.0, 2020-01-01
+    shape = _deprecate_shape_0_as_None(shape)
+
+    if shape is None:
+        shape = arrayList[0].shape
+    elif isinstance(shape, int):
+        shape = (shape,)
+
+    if formats is None and dtype is None:
+        # go through each object in the list to see if it is an ndarray
+        # and determine the formats.
+        formats = [obj.dtype for obj in arrayList]
+
+    if dtype is not None:
+        descr = sb.dtype(dtype)
+    else:
+        descr = format_parser(formats, names, titles, aligned, byteorder).dtype
+    _names = descr.names
+
+    # Determine shape from data-type.
+    if len(descr) != len(arrayList):
+        raise ValueError("mismatch between the number of fields "
+                "and the number of arrays")
+
+    d0 = descr[0].shape
+    nn = len(d0)
+    if nn > 0:
+        shape = shape[:-nn]
+
+    _array = recarray(shape, descr)
+
+    # populate the record array (makes a copy)
+    for k, obj in enumerate(arrayList):
+        nn = descr[k].ndim
+        testshape = obj.shape[:obj.ndim - nn]
+        name = _names[k]
+        if testshape != shape:
+            raise ValueError(f'array-shape mismatch in array {k} ("{name}")')
+
+        _array[name] = obj
+
+    return _array
+
+
+@set_module("numpy.rec")
+def fromrecords(recList, dtype=None, shape=None, formats=None, names=None,
+                titles=None, aligned=False, byteorder=None):
+    """Create a recarray from a list of records in text form.
+
+    Parameters
+    ----------
+    recList : sequence
+        data in the same field may be heterogeneous - they will be promoted
+        to the highest data type.
+    dtype : data-type, optional
+        valid dtype for all arrays
+    shape : int or tuple of ints, optional
+        shape of each array.
+    formats, names, titles, aligned, byteorder :
+        If `dtype` is ``None``, these arguments are passed to
+        `numpy.format_parser` to construct a dtype. See that function for
+        detailed documentation.
+
+        If both `formats` and `dtype` are None, then this will auto-detect
+        formats. Use list of tuples rather than list of lists for faster
+        processing.
+
+    Returns
+    -------
+    np.recarray
+        record array consisting of given recList rows.
+
+    Examples
+    --------
+    >>> r=np.rec.fromrecords([(456,'dbe',1.2),(2,'de',1.3)],
+    ... names='col1,col2,col3')
+    >>> print(r[0])
+    (456, 'dbe', 1.2)
+    >>> r.col1
+    array([456,   2])
+    >>> r.col2
+    array(['dbe', 'de'], dtype='<U3')
+    >>> import pickle
+    >>> pickle.loads(pickle.dumps(r))
+    rec.array([(456, 'dbe', 1.2), (  2, 'de', 1.3)],
+              dtype=[('col1', '<i8'), ('col2', '<U3'), ('col3', '<f8')])
+    """
+
+    if formats is None and dtype is None:  # slower
+        obj = sb.array(recList, dtype=object)
+        arrlist = [
+            sb.array(obj[..., i].tolist()) for i in range(obj.shape[-1])
+        ]
+        return fromarrays(arrlist, formats=formats, shape=shape, names=names,
+                          titles=titles, aligned=aligned, byteorder=byteorder)
+
+    if dtype is not None:
+        descr = sb.dtype((record, dtype))
+    else:
+        descr = format_parser(
+            formats, names, titles, aligned, byteorder
+        ).dtype
+
+    try:
+        retval = sb.array(recList, dtype=descr)
+    except (TypeError, ValueError):
+        # NumPy 1.19.0, 2020-01-01
+        shape = _deprecate_shape_0_as_None(shape)
+        if shape is None:
+            shape = len(recList)
+        if isinstance(shape, int):
+            shape = (shape,)
+        if len(shape) > 1:
+            raise ValueError("Can only deal with 1-d array.")
+        _array = recarray(shape, descr)
+        for k in range(_array.size):
+            _array[k] = tuple(recList[k])
+        # list of lists instead of list of tuples ?
+        # 2018-02-07, 1.14.1
+        warnings.warn(
+            "fromrecords expected a list of tuples, may have received a list "
+            "of lists instead. In the future that will raise an error",
+            FutureWarning, stacklevel=2)
+        return _array
+    else:
+        if shape is not None and retval.shape != shape:
+            retval.shape = shape
+
+    res = retval.view(recarray)
+
+    return res
+
+
+@set_module("numpy.rec")
+def fromstring(datastring, dtype=None, shape=None, offset=0, formats=None,
+               names=None, titles=None, aligned=False, byteorder=None):
+    r"""Create a record array from binary data
+
+    Note that despite the name of this function it does not accept `str`
+    instances.
+
+    Parameters
+    ----------
+    datastring : bytes-like
+        Buffer of binary data
+    dtype : data-type, optional
+        Valid dtype for all arrays
+    shape : int or tuple of ints, optional
+        Shape of each array.
+    offset : int, optional
+        Position in the buffer to start reading from.
+    formats, names, titles, aligned, byteorder :
+        If `dtype` is ``None``, these arguments are passed to
+        `numpy.format_parser` to construct a dtype. See that function for
+        detailed documentation.
+
+
+    Returns
+    -------
+    np.recarray
+        Record array view into the data in datastring. This will be readonly
+        if `datastring` is readonly.
+
+    See Also
+    --------
+    numpy.frombuffer
+
+    Examples
+    --------
+    >>> a = b'\x01\x02\x03abc'
+    >>> np.rec.fromstring(a, dtype='u1,u1,u1,S3')
+    rec.array([(1, 2, 3, b'abc')],
+            dtype=[('f0', 'u1'), ('f1', 'u1'), ('f2', 'u1'), ('f3', 'S3')])
+
+    >>> grades_dtype = [('Name', (np.str_, 10)), ('Marks', np.float64),
+    ...                 ('GradeLevel', np.int32)]
+    >>> grades_array = np.array([('Sam', 33.3, 3), ('Mike', 44.4, 5),
+    ...                         ('Aadi', 66.6, 6)], dtype=grades_dtype)
+    >>> np.rec.fromstring(grades_array.tobytes(), dtype=grades_dtype)
+    rec.array([('Sam', 33.3, 3), ('Mike', 44.4, 5), ('Aadi', 66.6, 6)],
+            dtype=[('Name', '<U10'), ('Marks', '<f8'), ('GradeLevel', '<i4')])
+
+    >>> s = '\x01\x02\x03abc'
+    >>> np.rec.fromstring(s, dtype='u1,u1,u1,S3')
+    Traceback (most recent call last):
+       ...
+    TypeError: a bytes-like object is required, not 'str'
+    """
+
+    if dtype is None and formats is None:
+        raise TypeError("fromstring() needs a 'dtype' or 'formats' argument")
+
+    if dtype is not None:
+        descr = sb.dtype(dtype)
+    else:
+        descr = format_parser(formats, names, titles, aligned, byteorder).dtype
+
+    itemsize = descr.itemsize
+
+    # NumPy 1.19.0, 2020-01-01
+    shape = _deprecate_shape_0_as_None(shape)
+
+    if shape in (None, -1):
+        shape = (len(datastring) - offset) // itemsize
+
+    _array = recarray(shape, descr, buf=datastring, offset=offset)
+    return _array
+
+def get_remaining_size(fd):
+    pos = fd.tell()
+    try:
+        fd.seek(0, 2)
+        return fd.tell() - pos
+    finally:
+        fd.seek(pos, 0)
+
+
+@set_module("numpy.rec")
+def fromfile(fd, dtype=None, shape=None, offset=0, formats=None,
+             names=None, titles=None, aligned=False, byteorder=None):
+    """Create an array from binary file data
+
+    Parameters
+    ----------
+    fd : str or file type
+        If file is a string or a path-like object then that file is opened,
+        else it is assumed to be a file object. The file object must
+        support random access (i.e. it must have tell and seek methods).
+    dtype : data-type, optional
+        valid dtype for all arrays
+    shape : int or tuple of ints, optional
+        shape of each array.
+    offset : int, optional
+        Position in the file to start reading from.
+    formats, names, titles, aligned, byteorder :
+        If `dtype` is ``None``, these arguments are passed to
+        `numpy.format_parser` to construct a dtype. See that function for
+        detailed documentation
+
+    Returns
+    -------
+    np.recarray
+        record array consisting of data enclosed in file.
+
+    Examples
+    --------
+    >>> from tempfile import TemporaryFile
+    >>> a = np.empty(10,dtype='f8,i4,a5')
+    >>> a[5] = (0.5,10,'abcde')
+    >>>
+    >>> fd=TemporaryFile()
+    >>> a = a.view(a.dtype.newbyteorder('<'))
+    >>> a.tofile(fd)
+    >>>
+    >>> _ = fd.seek(0)
+    >>> r=np.rec.fromfile(fd, formats='f8,i4,a5', shape=10,
+    ... byteorder='<')
+    >>> print(r[5])
+    (0.5, 10, b'abcde')
+    >>> r.shape
+    (10,)
+    """
+
+    if dtype is None and formats is None:
+        raise TypeError("fromfile() needs a 'dtype' or 'formats' argument")
+
+    # NumPy 1.19.0, 2020-01-01
+    shape = _deprecate_shape_0_as_None(shape)
+
+    if shape is None:
+        shape = (-1,)
+    elif isinstance(shape, int):
+        shape = (shape,)
+
+    if hasattr(fd, 'readinto'):
+        # GH issue 2504. fd supports io.RawIOBase or io.BufferedIOBase
+        # interface. Example of fd: gzip, BytesIO, BufferedReader
+        # file already opened
+        ctx = nullcontext(fd)
+    else:
+        # open file
+        ctx = open(os.fspath(fd), 'rb')
+
+    with ctx as fd:
+        if offset > 0:
+            fd.seek(offset, 1)
+        size = get_remaining_size(fd)
+
+        if dtype is not None:
+            descr = sb.dtype(dtype)
+        else:
+            descr = format_parser(
+                formats, names, titles, aligned, byteorder
+            ).dtype
+
+        itemsize = descr.itemsize
+
+        shapeprod = sb.array(shape).prod(dtype=nt.intp)
+        shapesize = shapeprod * itemsize
+        if shapesize < 0:
+            shape = list(shape)
+            shape[shape.index(-1)] = size // -shapesize
+            shape = tuple(shape)
+            shapeprod = sb.array(shape).prod(dtype=nt.intp)
+
+        nbytes = shapeprod * itemsize
+
+        if nbytes > size:
+            raise ValueError(
+                    "Not enough bytes left in file for specified "
+                    "shape and type."
+                )
+
+        # create the array
+        _array = recarray(shape, descr)
+        nbytesread = fd.readinto(_array.data)
+        if nbytesread != nbytes:
+            raise OSError("Didn't read as many bytes as expected")
+
+    return _array
+
+
+@set_module("numpy.rec")
+def array(obj, dtype=None, shape=None, offset=0, strides=None, formats=None,
+          names=None, titles=None, aligned=False, byteorder=None, copy=True):
+    """
+    Construct a record array from a wide-variety of objects.
+
+    A general-purpose record array constructor that dispatches to the
+    appropriate `recarray` creation function based on the inputs (see Notes).
+
+    Parameters
+    ----------
+    obj : any
+        Input object. See Notes for details on how various input types are
+        treated.
+    dtype : data-type, optional
+        Valid dtype for array.
+    shape : int or tuple of ints, optional
+        Shape of each array.
+    offset : int, optional
+        Position in the file or buffer to start reading from.
+    strides : tuple of ints, optional
+        Buffer (`buf`) is interpreted according to these strides (strides
+        define how many bytes each array element, row, column, etc.
+        occupy in memory).
+    formats, names, titles, aligned, byteorder :
+        If `dtype` is ``None``, these arguments are passed to
+        `numpy.format_parser` to construct a dtype. See that function for
+        detailed documentation.
+    copy : bool, optional
+        Whether to copy the input object (True), or to use a reference instead.
+        This option only applies when the input is an ndarray or recarray.
+        Defaults to True.
+
+    Returns
+    -------
+    np.recarray
+        Record array created from the specified object.
+
+    Notes
+    -----
+    If `obj` is ``None``, then call the `~numpy.recarray` constructor. If
+    `obj` is a string, then call the `fromstring` constructor. If `obj` is a
+    list or a tuple, then if the first object is an `~numpy.ndarray`, call
+    `fromarrays`, otherwise call `fromrecords`. If `obj` is a
+    `~numpy.recarray`, then make a copy of the data in the recarray
+    (if ``copy=True``) and use the new formats, names, and titles. If `obj`
+    is a file, then call `fromfile`. Finally, if obj is an `ndarray`, then
+    return ``obj.view(recarray)``, making a copy of the data if ``copy=True``.
+
+    Examples
+    --------
+    >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> a
+    array([[1, 2, 3],
+           [4, 5, 6],
+           [7, 8, 9]])
+
+    >>> np.rec.array(a)
+    rec.array([[1, 2, 3],
+               [4, 5, 6],
+               [7, 8, 9]],
+              dtype=int64)
+
+    >>> b = [(1, 1), (2, 4), (3, 9)]
+    >>> c = np.rec.array(b, formats = ['i2', 'f2'], names = ('x', 'y'))
+    >>> c
+    rec.array([(1, 1.), (2, 4.), (3, 9.)],
+              dtype=[('x', '<i2'), ('y', '<f2')])
+
+    >>> c.x
+    array([1, 2, 3], dtype=int16)
+
+    >>> c.y
+    array([1.,  4.,  9.], dtype=float16)
+
+    >>> r = np.rec.array(['abc','def'], names=['col1','col2'])
+    >>> print(r.col1)
+    abc
+
+    >>> r.col1
+    array('abc', dtype='<U3')
+
+    >>> r.col2
+    array('def', dtype='<U3')
+    """
+
+    if ((isinstance(obj, (type(None), str)) or hasattr(obj, 'readinto')) and
+           formats is None and dtype is None):
+        raise ValueError("Must define formats (or dtype) if object is "
+                         "None, string, or an open file")
+
+    kwds = {}
+    if dtype is not None:
+        dtype = sb.dtype(dtype)
+    elif formats is not None:
+        dtype = format_parser(formats, names, titles,
+                              aligned, byteorder).dtype
+    else:
+        kwds = {'formats': formats,
+                'names': names,
+                'titles': titles,
+                'aligned': aligned,
+                'byteorder': byteorder
+                }
+
+    if obj is None:
+        if shape is None:
+            raise ValueError("Must define a shape if obj is None")
+        return recarray(shape, dtype, buf=obj, offset=offset, strides=strides)
+
+    elif isinstance(obj, bytes):
+        return fromstring(obj, dtype, shape=shape, offset=offset, **kwds)
+
+    elif isinstance(obj, (list, tuple)):
+        if isinstance(obj[0], (tuple, list)):
+            return fromrecords(obj, dtype=dtype, shape=shape, **kwds)
+        else:
+            return fromarrays(obj, dtype=dtype, shape=shape, **kwds)
+
+    elif isinstance(obj, recarray):
+        if dtype is not None and (obj.dtype != dtype):
+            new = obj.view(dtype)
+        else:
+            new = obj
+        if copy:
+            new = new.copy()
+        return new
+
+    elif hasattr(obj, 'readinto'):
+        return fromfile(obj, dtype=dtype, shape=shape, offset=offset)
+
+    elif isinstance(obj, ndarray):
+        if dtype is not None and (obj.dtype != dtype):
+            new = obj.view(dtype)
+        else:
+            new = obj
+        if copy:
+            new = new.copy()
+        return new.view(recarray)
+
+    else:
+        interface = getattr(obj, "__array_interface__", None)
+        if interface is None or not isinstance(interface, dict):
+            raise ValueError("Unknown input type")
+        obj = sb.array(obj)
+        if dtype is not None and (obj.dtype != dtype):
+            obj = obj.view(dtype)
+        return obj.view(recarray)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/records.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/records.pyi
new file mode 100644
index 0000000..93177b2
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/records.pyi
@@ -0,0 +1,333 @@
+# ruff: noqa: ANN401
+# pyright: reportSelfClsParameterName=false
+from collections.abc import Iterable, Sequence
+from typing import (
+    Any,
+    ClassVar,
+    Literal,
+    Protocol,
+    SupportsIndex,
+    TypeAlias,
+    overload,
+    type_check_only,
+)
+
+from _typeshed import StrOrBytesPath
+from typing_extensions import TypeVar
+
+import numpy as np
+from numpy import _ByteOrder, _OrderKACF, _SupportsBuffer
+from numpy._typing import (
+    ArrayLike,
+    DTypeLike,
+    NDArray,
+    _AnyShape,
+    _ArrayLikeVoid_co,
+    _NestedSequence,
+    _Shape,
+    _ShapeLike,
+)
+
+__all__ = [
+    "array",
+    "find_duplicate",
+    "format_parser",
+    "fromarrays",
+    "fromfile",
+    "fromrecords",
+    "fromstring",
+    "recarray",
+    "record",
+]
+
+_T = TypeVar("_T")
+_ScalarT = TypeVar("_ScalarT", bound=np.generic)
+_DTypeT_co = TypeVar("_DTypeT_co", bound=np.dtype, default=np.dtype, covariant=True)
+_ShapeT_co = TypeVar("_ShapeT_co", bound=_Shape, default=_AnyShape, covariant=True)
+
+_RecArray: TypeAlias = recarray[_AnyShape, np.dtype[_ScalarT]]
+
+@type_check_only
+class _SupportsReadInto(Protocol):
+    def seek(self, offset: int, whence: int, /) -> object: ...
+    def tell(self, /) -> int: ...
+    def readinto(self, buffer: memoryview, /) -> int: ...
+
+###
+
+# exported in `numpy.rec`
+class record(np.void):
+    def __getattribute__(self, attr: str) -> Any: ...
+    def __setattr__(self, attr: str, val: ArrayLike) -> None: ...
+    def pprint(self) -> str: ...
+    @overload
+    def __getitem__(self, key: str | SupportsIndex) -> Any: ...
+    @overload
+    def __getitem__(self, key: list[str]) -> record: ...
+
+# exported in `numpy.rec`
+class recarray(np.ndarray[_ShapeT_co, _DTypeT_co]):
+    __name__: ClassVar[Literal["record"]] = "record"
+    __module__: Literal["numpy"] = "numpy"
+    @overload
+    def __new__(
+        subtype,
+        shape: _ShapeLike,
+        dtype: None = None,
+        buf: _SupportsBuffer | None = None,
+        offset: SupportsIndex = 0,
+        strides: _ShapeLike | None = None,
+        *,
+        formats: DTypeLike,
+        names: str | Sequence[str] | None = None,
+        titles: str | Sequence[str] | None = None,
+        byteorder: _ByteOrder | None = None,
+        aligned: bool = False,
+        order: _OrderKACF = "C",
+    ) -> _RecArray[record]: ...
+    @overload
+    def __new__(
+        subtype,
+        shape: _ShapeLike,
+        dtype: DTypeLike,
+        buf: _SupportsBuffer | None = None,
+        offset: SupportsIndex = 0,
+        strides: _ShapeLike | None = None,
+        formats: None = None,
+        names: None = None,
+        titles: None = None,
+        byteorder: None = None,
+        aligned: Literal[False] = False,
+        order: _OrderKACF = "C",
+    ) -> _RecArray[Any]: ...
+    def __array_finalize__(self, /, obj: object) -> None: ...
+    def __getattribute__(self, attr: str, /) -> Any: ...
+    def __setattr__(self, attr: str, val: ArrayLike, /) -> None: ...
+
+    #
+    @overload
+    def field(self, /, attr: int | str, val: ArrayLike) -> None: ...
+    @overload
+    def field(self, /, attr: int | str, val: None = None) -> Any: ...
+
+# exported in `numpy.rec`
+class format_parser:
+    dtype: np.dtype[np.void]
+    def __init__(
+        self,
+        /,
+        formats: DTypeLike,
+        names: str | Sequence[str] | None,
+        titles: str | Sequence[str] | None,
+        aligned: bool = False,
+        byteorder: _ByteOrder | None = None,
+    ) -> None: ...
+
+# exported in `numpy.rec`
+@overload
+def fromarrays(
+    arrayList: Iterable[ArrayLike],
+    dtype: DTypeLike | None = None,
+    shape: _ShapeLike | None = None,
+    formats: None = None,
+    names: None = None,
+    titles: None = None,
+    aligned: bool = False,
+    byteorder: None = None,
+) -> _RecArray[Any]: ...
+@overload
+def fromarrays(
+    arrayList: Iterable[ArrayLike],
+    dtype: None = None,
+    shape: _ShapeLike | None = None,
+    *,
+    formats: DTypeLike,
+    names: str | Sequence[str] | None = None,
+    titles: str | Sequence[str] | None = None,
+    aligned: bool = False,
+    byteorder: _ByteOrder | None = None,
+) -> _RecArray[record]: ...
+
+@overload
+def fromrecords(
+    recList: _ArrayLikeVoid_co | tuple[object, ...] | _NestedSequence[tuple[object, ...]],
+    dtype: DTypeLike | None = None,
+    shape: _ShapeLike | None = None,
+    formats: None = None,
+    names: None = None,
+    titles: None = None,
+    aligned: bool = False,
+    byteorder: None = None,
+) -> _RecArray[record]: ...
+@overload
+def fromrecords(
+    recList: _ArrayLikeVoid_co | tuple[object, ...] | _NestedSequence[tuple[object, ...]],
+    dtype: None = None,
+    shape: _ShapeLike | None = None,
+    *,
+    formats: DTypeLike,
+    names: str | Sequence[str] | None = None,
+    titles: str | Sequence[str] | None = None,
+    aligned: bool = False,
+    byteorder: _ByteOrder | None = None,
+) -> _RecArray[record]: ...
+
+# exported in `numpy.rec`
+@overload
+def fromstring(
+    datastring: _SupportsBuffer,
+    dtype: DTypeLike,
+    shape: _ShapeLike | None = None,
+    offset: int = 0,
+    formats: None = None,
+    names: None = None,
+    titles: None = None,
+    aligned: bool = False,
+    byteorder: None = None,
+) -> _RecArray[record]: ...
+@overload
+def fromstring(
+    datastring: _SupportsBuffer,
+    dtype: None = None,
+    shape: _ShapeLike | None = None,
+    offset: int = 0,
+    *,
+    formats: DTypeLike,
+    names: str | Sequence[str] | None = None,
+    titles: str | Sequence[str] | None = None,
+    aligned: bool = False,
+    byteorder: _ByteOrder | None = None,
+) -> _RecArray[record]: ...
+
+# exported in `numpy.rec`
+@overload
+def fromfile(
+    fd: StrOrBytesPath | _SupportsReadInto,
+    dtype: DTypeLike,
+    shape: _ShapeLike | None = None,
+    offset: int = 0,
+    formats: None = None,
+    names: None = None,
+    titles: None = None,
+    aligned: bool = False,
+    byteorder: None = None,
+) -> _RecArray[Any]: ...
+@overload
+def fromfile(
+    fd: StrOrBytesPath | _SupportsReadInto,
+    dtype: None = None,
+    shape: _ShapeLike | None = None,
+    offset: int = 0,
+    *,
+    formats: DTypeLike,
+    names: str | Sequence[str] | None = None,
+    titles: str | Sequence[str] | None = None,
+    aligned: bool = False,
+    byteorder: _ByteOrder | None = None,
+) -> _RecArray[record]: ...
+
+# exported in `numpy.rec`
+@overload
+def array(
+    obj: _ScalarT | NDArray[_ScalarT],
+    dtype: None = None,
+    shape: _ShapeLike | None = None,
+    offset: int = 0,
+    strides: tuple[int, ...] | None = None,
+    formats: None = None,
+    names: None = None,
+    titles: None = None,
+    aligned: bool = False,
+    byteorder: None = None,
+    copy: bool = True,
+) -> _RecArray[_ScalarT]: ...
+@overload
+def array(
+    obj: ArrayLike,
+    dtype: DTypeLike,
+    shape: _ShapeLike | None = None,
+    offset: int = 0,
+    strides: tuple[int, ...] | None = None,
+    formats: None = None,
+    names: None = None,
+    titles: None = None,
+    aligned: bool = False,
+    byteorder: None = None,
+    copy: bool = True,
+) -> _RecArray[Any]: ...
+@overload
+def array(
+    obj: ArrayLike,
+    dtype: None = None,
+    shape: _ShapeLike | None = None,
+    offset: int = 0,
+    strides: tuple[int, ...] | None = None,
+    *,
+    formats: DTypeLike,
+    names: str | Sequence[str] | None = None,
+    titles: str | Sequence[str] | None = None,
+    aligned: bool = False,
+    byteorder: _ByteOrder | None = None,
+    copy: bool = True,
+) -> _RecArray[record]: ...
+@overload
+def array(
+    obj: None,
+    dtype: DTypeLike,
+    shape: _ShapeLike,
+    offset: int = 0,
+    strides: tuple[int, ...] | None = None,
+    formats: None = None,
+    names: None = None,
+    titles: None = None,
+    aligned: bool = False,
+    byteorder: None = None,
+    copy: bool = True,
+) -> _RecArray[Any]: ...
+@overload
+def array(
+    obj: None,
+    dtype: None = None,
+    *,
+    shape: _ShapeLike,
+    offset: int = 0,
+    strides: tuple[int, ...] | None = None,
+    formats: DTypeLike,
+    names: str | Sequence[str] | None = None,
+    titles: str | Sequence[str] | None = None,
+    aligned: bool = False,
+    byteorder: _ByteOrder | None = None,
+    copy: bool = True,
+) -> _RecArray[record]: ...
+@overload
+def array(
+    obj: _SupportsReadInto,
+    dtype: DTypeLike,
+    shape: _ShapeLike | None = None,
+    offset: int = 0,
+    strides: tuple[int, ...] | None = None,
+    formats: None = None,
+    names: None = None,
+    titles: None = None,
+    aligned: bool = False,
+    byteorder: None = None,
+    copy: bool = True,
+) -> _RecArray[Any]: ...
+@overload
+def array(
+    obj: _SupportsReadInto,
+    dtype: None = None,
+    shape: _ShapeLike | None = None,
+    offset: int = 0,
+    strides: tuple[int, ...] | None = None,
+    *,
+    formats: DTypeLike,
+    names: str | Sequence[str] | None = None,
+    titles: str | Sequence[str] | None = None,
+    aligned: bool = False,
+    byteorder: _ByteOrder | None = None,
+    copy: bool = True,
+) -> _RecArray[record]: ...
+
+# exported in `numpy.rec`
+def find_duplicate(list: Iterable[_T]) -> list[_T]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/shape_base.py b/.venv/lib/python3.12/site-packages/numpy/_core/shape_base.py
new file mode 100644
index 0000000..c2a0f0d
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/shape_base.py
@@ -0,0 +1,998 @@
+__all__ = ['atleast_1d', 'atleast_2d', 'atleast_3d', 'block', 'hstack',
+           'stack', 'unstack', 'vstack']
+
+import functools
+import itertools
+import operator
+
+from . import fromnumeric as _from_nx
+from . import numeric as _nx
+from . import overrides
+from .multiarray import array, asanyarray, normalize_axis_index
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+def _atleast_1d_dispatcher(*arys):
+    return arys
+
+
+@array_function_dispatch(_atleast_1d_dispatcher)
+def atleast_1d(*arys):
+    """
+    Convert inputs to arrays with at least one dimension.
+
+    Scalar inputs are converted to 1-dimensional arrays, whilst
+    higher-dimensional inputs are preserved.
+
+    Parameters
+    ----------
+    arys1, arys2, ... : array_like
+        One or more input arrays.
+
+    Returns
+    -------
+    ret : ndarray
+        An array, or tuple of arrays, each with ``a.ndim >= 1``.
+        Copies are made only if necessary.
+
+    See Also
+    --------
+    atleast_2d, atleast_3d
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.atleast_1d(1.0)
+    array([1.])
+
+    >>> x = np.arange(9.0).reshape(3,3)
+    >>> np.atleast_1d(x)
+    array([[0., 1., 2.],
+           [3., 4., 5.],
+           [6., 7., 8.]])
+    >>> np.atleast_1d(x) is x
+    True
+
+    >>> np.atleast_1d(1, [3, 4])
+    (array([1]), array([3, 4]))
+
+    """
+    if len(arys) == 1:
+        result = asanyarray(arys[0])
+        if result.ndim == 0:
+            result = result.reshape(1)
+        return result
+    res = []
+    for ary in arys:
+        result = asanyarray(ary)
+        if result.ndim == 0:
+            result = result.reshape(1)
+        res.append(result)
+    return tuple(res)
+
+
+def _atleast_2d_dispatcher(*arys):
+    return arys
+
+
+@array_function_dispatch(_atleast_2d_dispatcher)
+def atleast_2d(*arys):
+    """
+    View inputs as arrays with at least two dimensions.
+
+    Parameters
+    ----------
+    arys1, arys2, ... : array_like
+        One or more array-like sequences.  Non-array inputs are converted
+        to arrays.  Arrays that already have two or more dimensions are
+        preserved.
+
+    Returns
+    -------
+    res, res2, ... : ndarray
+        An array, or tuple of arrays, each with ``a.ndim >= 2``.
+        Copies are avoided where possible, and views with two or more
+        dimensions are returned.
+
+    See Also
+    --------
+    atleast_1d, atleast_3d
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.atleast_2d(3.0)
+    array([[3.]])
+
+    >>> x = np.arange(3.0)
+    >>> np.atleast_2d(x)
+    array([[0., 1., 2.]])
+    >>> np.atleast_2d(x).base is x
+    True
+
+    >>> np.atleast_2d(1, [1, 2], [[1, 2]])
+    (array([[1]]), array([[1, 2]]), array([[1, 2]]))
+
+    """
+    res = []
+    for ary in arys:
+        ary = asanyarray(ary)
+        if ary.ndim == 0:
+            result = ary.reshape(1, 1)
+        elif ary.ndim == 1:
+            result = ary[_nx.newaxis, :]
+        else:
+            result = ary
+        res.append(result)
+    if len(res) == 1:
+        return res[0]
+    else:
+        return tuple(res)
+
+
+def _atleast_3d_dispatcher(*arys):
+    return arys
+
+
+@array_function_dispatch(_atleast_3d_dispatcher)
+def atleast_3d(*arys):
+    """
+    View inputs as arrays with at least three dimensions.
+
+    Parameters
+    ----------
+    arys1, arys2, ... : array_like
+        One or more array-like sequences.  Non-array inputs are converted to
+        arrays.  Arrays that already have three or more dimensions are
+        preserved.
+
+    Returns
+    -------
+    res1, res2, ... : ndarray
+        An array, or tuple of arrays, each with ``a.ndim >= 3``.  Copies are
+        avoided where possible, and views with three or more dimensions are
+        returned.  For example, a 1-D array of shape ``(N,)`` becomes a view
+        of shape ``(1, N, 1)``, and a 2-D array of shape ``(M, N)`` becomes a
+        view of shape ``(M, N, 1)``.
+
+    See Also
+    --------
+    atleast_1d, atleast_2d
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.atleast_3d(3.0)
+    array([[[3.]]])
+
+    >>> x = np.arange(3.0)
+    >>> np.atleast_3d(x).shape
+    (1, 3, 1)
+
+    >>> x = np.arange(12.0).reshape(4,3)
+    >>> np.atleast_3d(x).shape
+    (4, 3, 1)
+    >>> np.atleast_3d(x).base is x.base  # x is a reshape, so not base itself
+    True
+
+    >>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]):
+    ...     print(arr, arr.shape) # doctest: +SKIP
+    ...
+    [[[1]
+      [2]]] (1, 2, 1)
+    [[[1]
+      [2]]] (1, 2, 1)
+    [[[1 2]]] (1, 1, 2)
+
+    """
+    res = []
+    for ary in arys:
+        ary = asanyarray(ary)
+        if ary.ndim == 0:
+            result = ary.reshape(1, 1, 1)
+        elif ary.ndim == 1:
+            result = ary[_nx.newaxis, :, _nx.newaxis]
+        elif ary.ndim == 2:
+            result = ary[:, :, _nx.newaxis]
+        else:
+            result = ary
+        res.append(result)
+    if len(res) == 1:
+        return res[0]
+    else:
+        return tuple(res)
+
+
+def _arrays_for_stack_dispatcher(arrays):
+    if not hasattr(arrays, "__getitem__"):
+        raise TypeError('arrays to stack must be passed as a "sequence" type '
+                        'such as list or tuple.')
+
+    return tuple(arrays)
+
+
+def _vhstack_dispatcher(tup, *, dtype=None, casting=None):
+    return _arrays_for_stack_dispatcher(tup)
+
+
+@array_function_dispatch(_vhstack_dispatcher)
+def vstack(tup, *, dtype=None, casting="same_kind"):
+    """
+    Stack arrays in sequence vertically (row wise).
+
+    This is equivalent to concatenation along the first axis after 1-D arrays
+    of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by
+    `vsplit`.
+
+    This function makes most sense for arrays with up to 3 dimensions. For
+    instance, for pixel-data with a height (first axis), width (second axis),
+    and r/g/b channels (third axis). The functions `concatenate`, `stack` and
+    `block` provide more general stacking and concatenation operations.
+
+    Parameters
+    ----------
+    tup : sequence of ndarrays
+        The arrays must have the same shape along all but the first axis.
+        1-D arrays must have the same length. In the case of a single
+        array_like input, it will be treated as a sequence of arrays; i.e.,
+        each element along the zeroth axis is treated as a separate array.
+
+    dtype : str or dtype
+        If provided, the destination array will have this dtype. Cannot be
+        provided together with `out`.
+
+        .. versionadded:: 1.24
+
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur. Defaults to 'same_kind'.
+
+        .. versionadded:: 1.24
+
+    Returns
+    -------
+    stacked : ndarray
+        The array formed by stacking the given arrays, will be at least 2-D.
+
+    See Also
+    --------
+    concatenate : Join a sequence of arrays along an existing axis.
+    stack : Join a sequence of arrays along a new axis.
+    block : Assemble an nd-array from nested lists of blocks.
+    hstack : Stack arrays in sequence horizontally (column wise).
+    dstack : Stack arrays in sequence depth wise (along third axis).
+    column_stack : Stack 1-D arrays as columns into a 2-D array.
+    vsplit : Split an array into multiple sub-arrays vertically (row-wise).
+    unstack : Split an array into a tuple of sub-arrays along an axis.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array([1, 2, 3])
+    >>> b = np.array([4, 5, 6])
+    >>> np.vstack((a,b))
+    array([[1, 2, 3],
+           [4, 5, 6]])
+
+    >>> a = np.array([[1], [2], [3]])
+    >>> b = np.array([[4], [5], [6]])
+    >>> np.vstack((a,b))
+    array([[1],
+           [2],
+           [3],
+           [4],
+           [5],
+           [6]])
+
+    """
+    arrs = atleast_2d(*tup)
+    if not isinstance(arrs, tuple):
+        arrs = (arrs,)
+    return _nx.concatenate(arrs, 0, dtype=dtype, casting=casting)
+
+
+@array_function_dispatch(_vhstack_dispatcher)
+def hstack(tup, *, dtype=None, casting="same_kind"):
+    """
+    Stack arrays in sequence horizontally (column wise).
+
+    This is equivalent to concatenation along the second axis, except for 1-D
+    arrays where it concatenates along the first axis. Rebuilds arrays divided
+    by `hsplit`.
+
+    This function makes most sense for arrays with up to 3 dimensions. For
+    instance, for pixel-data with a height (first axis), width (second axis),
+    and r/g/b channels (third axis). The functions `concatenate`, `stack` and
+    `block` provide more general stacking and concatenation operations.
+
+    Parameters
+    ----------
+    tup : sequence of ndarrays
+        The arrays must have the same shape along all but the second axis,
+        except 1-D arrays which can be any length. In the case of a single
+        array_like input, it will be treated as a sequence of arrays; i.e.,
+        each element along the zeroth axis is treated as a separate array.
+
+    dtype : str or dtype
+        If provided, the destination array will have this dtype. Cannot be
+        provided together with `out`.
+
+        .. versionadded:: 1.24
+
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur. Defaults to 'same_kind'.
+
+        .. versionadded:: 1.24
+
+    Returns
+    -------
+    stacked : ndarray
+        The array formed by stacking the given arrays.
+
+    See Also
+    --------
+    concatenate : Join a sequence of arrays along an existing axis.
+    stack : Join a sequence of arrays along a new axis.
+    block : Assemble an nd-array from nested lists of blocks.
+    vstack : Stack arrays in sequence vertically (row wise).
+    dstack : Stack arrays in sequence depth wise (along third axis).
+    column_stack : Stack 1-D arrays as columns into a 2-D array.
+    hsplit : Split an array into multiple sub-arrays
+             horizontally (column-wise).
+    unstack : Split an array into a tuple of sub-arrays along an axis.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array((1,2,3))
+    >>> b = np.array((4,5,6))
+    >>> np.hstack((a,b))
+    array([1, 2, 3, 4, 5, 6])
+    >>> a = np.array([[1],[2],[3]])
+    >>> b = np.array([[4],[5],[6]])
+    >>> np.hstack((a,b))
+    array([[1, 4],
+           [2, 5],
+           [3, 6]])
+
+    """
+    arrs = atleast_1d(*tup)
+    if not isinstance(arrs, tuple):
+        arrs = (arrs,)
+    # As a special case, dimension 0 of 1-dimensional arrays is "horizontal"
+    if arrs and arrs[0].ndim == 1:
+        return _nx.concatenate(arrs, 0, dtype=dtype, casting=casting)
+    else:
+        return _nx.concatenate(arrs, 1, dtype=dtype, casting=casting)
+
+
+def _stack_dispatcher(arrays, axis=None, out=None, *,
+                      dtype=None, casting=None):
+    arrays = _arrays_for_stack_dispatcher(arrays)
+    if out is not None:
+        # optimize for the typical case where only arrays is provided
+        arrays = list(arrays)
+        arrays.append(out)
+    return arrays
+
+
+@array_function_dispatch(_stack_dispatcher)
+def stack(arrays, axis=0, out=None, *, dtype=None, casting="same_kind"):
+    """
+    Join a sequence of arrays along a new axis.
+
+    The ``axis`` parameter specifies the index of the new axis in the
+    dimensions of the result. For example, if ``axis=0`` it will be the first
+    dimension and if ``axis=-1`` it will be the last dimension.
+
+    Parameters
+    ----------
+    arrays : sequence of ndarrays
+        Each array must have the same shape. In the case of a single ndarray
+        array_like input, it will be treated as a sequence of arrays; i.e.,
+        each element along the zeroth axis is treated as a separate array.
+
+    axis : int, optional
+        The axis in the result array along which the input arrays are stacked.
+
+    out : ndarray, optional
+        If provided, the destination to place the result. The shape must be
+        correct, matching that of what stack would have returned if no
+        out argument were specified.
+
+    dtype : str or dtype
+        If provided, the destination array will have this dtype. Cannot be
+        provided together with `out`.
+
+        .. versionadded:: 1.24
+
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        Controls what kind of data casting may occur. Defaults to 'same_kind'.
+
+        .. versionadded:: 1.24
+
+
+    Returns
+    -------
+    stacked : ndarray
+        The stacked array has one more dimension than the input arrays.
+
+    See Also
+    --------
+    concatenate : Join a sequence of arrays along an existing axis.
+    block : Assemble an nd-array from nested lists of blocks.
+    split : Split array into a list of multiple sub-arrays of equal size.
+    unstack : Split an array into a tuple of sub-arrays along an axis.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> rng = np.random.default_rng()
+    >>> arrays = [rng.normal(size=(3,4)) for _ in range(10)]
+    >>> np.stack(arrays, axis=0).shape
+    (10, 3, 4)
+
+    >>> np.stack(arrays, axis=1).shape
+    (3, 10, 4)
+
+    >>> np.stack(arrays, axis=2).shape
+    (3, 4, 10)
+
+    >>> a = np.array([1, 2, 3])
+    >>> b = np.array([4, 5, 6])
+    >>> np.stack((a, b))
+    array([[1, 2, 3],
+           [4, 5, 6]])
+
+    >>> np.stack((a, b), axis=-1)
+    array([[1, 4],
+           [2, 5],
+           [3, 6]])
+
+    """
+    arrays = [asanyarray(arr) for arr in arrays]
+    if not arrays:
+        raise ValueError('need at least one array to stack')
+
+    shapes = {arr.shape for arr in arrays}
+    if len(shapes) != 1:
+        raise ValueError('all input arrays must have the same shape')
+
+    result_ndim = arrays[0].ndim + 1
+    axis = normalize_axis_index(axis, result_ndim)
+
+    sl = (slice(None),) * axis + (_nx.newaxis,)
+    expanded_arrays = [arr[sl] for arr in arrays]
+    return _nx.concatenate(expanded_arrays, axis=axis, out=out,
+                           dtype=dtype, casting=casting)
+
+def _unstack_dispatcher(x, /, *, axis=None):
+    return (x,)
+
+@array_function_dispatch(_unstack_dispatcher)
+def unstack(x, /, *, axis=0):
+    """
+    Split an array into a sequence of arrays along the given axis.
+
+    The ``axis`` parameter specifies the dimension along which the array will
+    be split. For example, if ``axis=0`` (the default) it will be the first
+    dimension and if ``axis=-1`` it will be the last dimension.
+
+    The result is a tuple of arrays split along ``axis``.
+
+    .. versionadded:: 2.1.0
+
+    Parameters
+    ----------
+    x : ndarray
+        The array to be unstacked.
+    axis : int, optional
+        Axis along which the array will be split. Default: ``0``.
+
+    Returns
+    -------
+    unstacked : tuple of ndarrays
+        The unstacked arrays.
+
+    See Also
+    --------
+    stack : Join a sequence of arrays along a new axis.
+    concatenate : Join a sequence of arrays along an existing axis.
+    block : Assemble an nd-array from nested lists of blocks.
+    split : Split array into a list of multiple sub-arrays of equal size.
+
+    Notes
+    -----
+    ``unstack`` serves as the reverse operation of :py:func:`stack`, i.e.,
+    ``stack(unstack(x, axis=axis), axis=axis) == x``.
+
+    This function is equivalent to ``tuple(np.moveaxis(x, axis, 0))``, since
+    iterating on an array iterates along the first axis.
+
+    Examples
+    --------
+    >>> arr = np.arange(24).reshape((2, 3, 4))
+    >>> np.unstack(arr)
+    (array([[ 0,  1,  2,  3],
+            [ 4,  5,  6,  7],
+            [ 8,  9, 10, 11]]),
+     array([[12, 13, 14, 15],
+            [16, 17, 18, 19],
+            [20, 21, 22, 23]]))
+    >>> np.unstack(arr, axis=1)
+    (array([[ 0,  1,  2,  3],
+            [12, 13, 14, 15]]),
+     array([[ 4,  5,  6,  7],
+            [16, 17, 18, 19]]),
+     array([[ 8,  9, 10, 11],
+            [20, 21, 22, 23]]))
+    >>> arr2 = np.stack(np.unstack(arr, axis=1), axis=1)
+    >>> arr2.shape
+    (2, 3, 4)
+    >>> np.all(arr == arr2)
+    np.True_
+
+    """
+    if x.ndim == 0:
+        raise ValueError("Input array must be at least 1-d.")
+    return tuple(_nx.moveaxis(x, axis, 0))
+
+
+# Internal functions to eliminate the overhead of repeated dispatch in one of
+# the two possible paths inside np.block.
+# Use getattr to protect against __array_function__ being disabled.
+_size = getattr(_from_nx.size, '__wrapped__', _from_nx.size)
+_ndim = getattr(_from_nx.ndim, '__wrapped__', _from_nx.ndim)
+_concatenate = getattr(_from_nx.concatenate,
+                       '__wrapped__', _from_nx.concatenate)
+
+
+def _block_format_index(index):
+    """
+    Convert a list of indices ``[0, 1, 2]`` into ``"arrays[0][1][2]"``.
+    """
+    idx_str = ''.join(f'[{i}]' for i in index if i is not None)
+    return 'arrays' + idx_str
+
+
+def _block_check_depths_match(arrays, parent_index=[]):
+    """
+    Recursive function checking that the depths of nested lists in `arrays`
+    all match. Mismatch raises a ValueError as described in the block
+    docstring below.
+
+    The entire index (rather than just the depth) needs to be calculated
+    for each innermost list, in case an error needs to be raised, so that
+    the index of the offending list can be printed as part of the error.
+
+    Parameters
+    ----------
+    arrays : nested list of arrays
+        The arrays to check
+    parent_index : list of int
+        The full index of `arrays` within the nested lists passed to
+        `_block_check_depths_match` at the top of the recursion.
+
+    Returns
+    -------
+    first_index : list of int
+        The full index of an element from the bottom of the nesting in
+        `arrays`. If any element at the bottom is an empty list, this will
+        refer to it, and the last index along the empty axis will be None.
+    max_arr_ndim : int
+        The maximum of the ndims of the arrays nested in `arrays`.
+    final_size: int
+        The number of elements in the final array. This is used the motivate
+        the choice of algorithm used using benchmarking wisdom.
+
+    """
+    if isinstance(arrays, tuple):
+        # not strictly necessary, but saves us from:
+        #  - more than one way to do things - no point treating tuples like
+        #    lists
+        #  - horribly confusing behaviour that results when tuples are
+        #    treated like ndarray
+        raise TypeError(
+            f'{_block_format_index(parent_index)} is a tuple. '
+            'Only lists can be used to arrange blocks, and np.block does '
+            'not allow implicit conversion from tuple to ndarray.'
+        )
+    elif isinstance(arrays, list) and len(arrays) > 0:
+        idxs_ndims = (_block_check_depths_match(arr, parent_index + [i])
+                      for i, arr in enumerate(arrays))
+
+        first_index, max_arr_ndim, final_size = next(idxs_ndims)
+        for index, ndim, size in idxs_ndims:
+            final_size += size
+            if ndim > max_arr_ndim:
+                max_arr_ndim = ndim
+            if len(index) != len(first_index):
+                raise ValueError(
+                    "List depths are mismatched. First element was at "
+                    f"depth {len(first_index)}, but there is an element at "
+                    f"depth {len(index)} ({_block_format_index(index)})"
+                )
+            # propagate our flag that indicates an empty list at the bottom
+            if index[-1] is None:
+                first_index = index
+
+        return first_index, max_arr_ndim, final_size
+    elif isinstance(arrays, list) and len(arrays) == 0:
+        # We've 'bottomed out' on an empty list
+        return parent_index + [None], 0, 0
+    else:
+        # We've 'bottomed out' - arrays is either a scalar or an array
+        size = _size(arrays)
+        return parent_index, _ndim(arrays), size
+
+
+def _atleast_nd(a, ndim):
+    # Ensures `a` has at least `ndim` dimensions by prepending
+    # ones to `a.shape` as necessary
+    return array(a, ndmin=ndim, copy=None, subok=True)
+
+
+def _accumulate(values):
+    return list(itertools.accumulate(values))
+
+
+def _concatenate_shapes(shapes, axis):
+    """Given array shapes, return the resulting shape and slices prefixes.
+
+    These help in nested concatenation.
+
+    Returns
+    -------
+    shape: tuple of int
+        This tuple satisfies::
+
+            shape, _ = _concatenate_shapes([arr.shape for shape in arrs], axis)
+            shape == concatenate(arrs, axis).shape
+
+    slice_prefixes: tuple of (slice(start, end), )
+        For a list of arrays being concatenated, this returns the slice
+        in the larger array at axis that needs to be sliced into.
+
+        For example, the following holds::
+
+            ret = concatenate([a, b, c], axis)
+            _, (sl_a, sl_b, sl_c) = concatenate_slices([a, b, c], axis)
+
+            ret[(slice(None),) * axis + sl_a] == a
+            ret[(slice(None),) * axis + sl_b] == b
+            ret[(slice(None),) * axis + sl_c] == c
+
+        These are called slice prefixes since they are used in the recursive
+        blocking algorithm to compute the left-most slices during the
+        recursion. Therefore, they must be prepended to rest of the slice
+        that was computed deeper in the recursion.
+
+        These are returned as tuples to ensure that they can quickly be added
+        to existing slice tuple without creating a new tuple every time.
+
+    """
+    # Cache a result that will be reused.
+    shape_at_axis = [shape[axis] for shape in shapes]
+
+    # Take a shape, any shape
+    first_shape = shapes[0]
+    first_shape_pre = first_shape[:axis]
+    first_shape_post = first_shape[axis + 1:]
+
+    if any(shape[:axis] != first_shape_pre or
+           shape[axis + 1:] != first_shape_post for shape in shapes):
+        raise ValueError(
+            f'Mismatched array shapes in block along axis {axis}.')
+
+    shape = (first_shape_pre + (sum(shape_at_axis),) + first_shape[axis + 1:])
+
+    offsets_at_axis = _accumulate(shape_at_axis)
+    slice_prefixes = [(slice(start, end),)
+                      for start, end in zip([0] + offsets_at_axis,
+                                            offsets_at_axis)]
+    return shape, slice_prefixes
+
+
+def _block_info_recursion(arrays, max_depth, result_ndim, depth=0):
+    """
+    Returns the shape of the final array, along with a list
+    of slices and a list of arrays that can be used for assignment inside the
+    new array
+
+    Parameters
+    ----------
+    arrays : nested list of arrays
+        The arrays to check
+    max_depth : list of int
+        The number of nested lists
+    result_ndim : int
+        The number of dimensions in thefinal array.
+
+    Returns
+    -------
+    shape : tuple of int
+        The shape that the final array will take on.
+    slices: list of tuple of slices
+        The slices into the full array required for assignment. These are
+        required to be prepended with ``(Ellipsis, )`` to obtain to correct
+        final index.
+    arrays: list of ndarray
+        The data to assign to each slice of the full array
+
+    """
+    if depth < max_depth:
+        shapes, slices, arrays = zip(
+            *[_block_info_recursion(arr, max_depth, result_ndim, depth + 1)
+              for arr in arrays])
+
+        axis = result_ndim - max_depth + depth
+        shape, slice_prefixes = _concatenate_shapes(shapes, axis)
+
+        # Prepend the slice prefix and flatten the slices
+        slices = [slice_prefix + the_slice
+                  for slice_prefix, inner_slices in zip(slice_prefixes, slices)
+                  for the_slice in inner_slices]
+
+        # Flatten the array list
+        arrays = functools.reduce(operator.add, arrays)
+
+        return shape, slices, arrays
+    else:
+        # We've 'bottomed out' - arrays is either a scalar or an array
+        # type(arrays) is not list
+        # Return the slice and the array inside a list to be consistent with
+        # the recursive case.
+        arr = _atleast_nd(arrays, result_ndim)
+        return arr.shape, [()], [arr]
+
+
+def _block(arrays, max_depth, result_ndim, depth=0):
+    """
+    Internal implementation of block based on repeated concatenation.
+    `arrays` is the argument passed to
+    block. `max_depth` is the depth of nested lists within `arrays` and
+    `result_ndim` is the greatest of the dimensions of the arrays in
+    `arrays` and the depth of the lists in `arrays` (see block docstring
+    for details).
+    """
+    if depth < max_depth:
+        arrs = [_block(arr, max_depth, result_ndim, depth + 1)
+                for arr in arrays]
+        return _concatenate(arrs, axis=-(max_depth - depth))
+    else:
+        # We've 'bottomed out' - arrays is either a scalar or an array
+        # type(arrays) is not list
+        return _atleast_nd(arrays, result_ndim)
+
+
+def _block_dispatcher(arrays):
+    # Use type(...) is list to match the behavior of np.block(), which special
+    # cases list specifically rather than allowing for generic iterables or
+    # tuple. Also, we know that list.__array_function__ will never exist.
+    if isinstance(arrays, list):
+        for subarrays in arrays:
+            yield from _block_dispatcher(subarrays)
+    else:
+        yield arrays
+
+
+@array_function_dispatch(_block_dispatcher)
+def block(arrays):
+    """
+    Assemble an nd-array from nested lists of blocks.
+
+    Blocks in the innermost lists are concatenated (see `concatenate`) along
+    the last dimension (-1), then these are concatenated along the
+    second-last dimension (-2), and so on until the outermost list is reached.
+
+    Blocks can be of any dimension, but will not be broadcasted using
+    the normal rules. Instead, leading axes of size 1 are inserted,
+    to make ``block.ndim`` the same for all blocks. This is primarily useful
+    for working with scalars, and means that code like ``np.block([v, 1])``
+    is valid, where ``v.ndim == 1``.
+
+    When the nested list is two levels deep, this allows block matrices to be
+    constructed from their components.
+
+    Parameters
+    ----------
+    arrays : nested list of array_like or scalars (but not tuples)
+        If passed a single ndarray or scalar (a nested list of depth 0), this
+        is returned unmodified (and not copied).
+
+        Elements shapes must match along the appropriate axes (without
+        broadcasting), but leading 1s will be prepended to the shape as
+        necessary to make the dimensions match.
+
+    Returns
+    -------
+    block_array : ndarray
+        The array assembled from the given blocks.
+
+        The dimensionality of the output is equal to the greatest of:
+
+        * the dimensionality of all the inputs
+        * the depth to which the input list is nested
+
+    Raises
+    ------
+    ValueError
+        * If list depths are mismatched - for instance, ``[[a, b], c]`` is
+          illegal, and should be spelt ``[[a, b], [c]]``
+        * If lists are empty - for instance, ``[[a, b], []]``
+
+    See Also
+    --------
+    concatenate : Join a sequence of arrays along an existing axis.
+    stack : Join a sequence of arrays along a new axis.
+    vstack : Stack arrays in sequence vertically (row wise).
+    hstack : Stack arrays in sequence horizontally (column wise).
+    dstack : Stack arrays in sequence depth wise (along third axis).
+    column_stack : Stack 1-D arrays as columns into a 2-D array.
+    vsplit : Split an array into multiple sub-arrays vertically (row-wise).
+    unstack : Split an array into a tuple of sub-arrays along an axis.
+
+    Notes
+    -----
+    When called with only scalars, ``np.block`` is equivalent to an ndarray
+    call. So ``np.block([[1, 2], [3, 4]])`` is equivalent to
+    ``np.array([[1, 2], [3, 4]])``.
+
+    This function does not enforce that the blocks lie on a fixed grid.
+    ``np.block([[a, b], [c, d]])`` is not restricted to arrays of the form::
+
+        AAAbb
+        AAAbb
+        cccDD
+
+    But is also allowed to produce, for some ``a, b, c, d``::
+
+        AAAbb
+        AAAbb
+        cDDDD
+
+    Since concatenation happens along the last axis first, `block` is *not*
+    capable of producing the following directly::
+
+        AAAbb
+        cccbb
+        cccDD
+
+    Matlab's "square bracket stacking", ``[A, B, ...; p, q, ...]``, is
+    equivalent to ``np.block([[A, B, ...], [p, q, ...]])``.
+
+    Examples
+    --------
+    The most common use of this function is to build a block matrix:
+
+    >>> import numpy as np
+    >>> A = np.eye(2) * 2
+    >>> B = np.eye(3) * 3
+    >>> np.block([
+    ...     [A,               np.zeros((2, 3))],
+    ...     [np.ones((3, 2)), B               ]
+    ... ])
+    array([[2., 0., 0., 0., 0.],
+           [0., 2., 0., 0., 0.],
+           [1., 1., 3., 0., 0.],
+           [1., 1., 0., 3., 0.],
+           [1., 1., 0., 0., 3.]])
+
+    With a list of depth 1, `block` can be used as `hstack`:
+
+    >>> np.block([1, 2, 3])              # hstack([1, 2, 3])
+    array([1, 2, 3])
+
+    >>> a = np.array([1, 2, 3])
+    >>> b = np.array([4, 5, 6])
+    >>> np.block([a, b, 10])             # hstack([a, b, 10])
+    array([ 1,  2,  3,  4,  5,  6, 10])
+
+    >>> A = np.ones((2, 2), int)
+    >>> B = 2 * A
+    >>> np.block([A, B])                 # hstack([A, B])
+    array([[1, 1, 2, 2],
+           [1, 1, 2, 2]])
+
+    With a list of depth 2, `block` can be used in place of `vstack`:
+
+    >>> a = np.array([1, 2, 3])
+    >>> b = np.array([4, 5, 6])
+    >>> np.block([[a], [b]])             # vstack([a, b])
+    array([[1, 2, 3],
+           [4, 5, 6]])
+
+    >>> A = np.ones((2, 2), int)
+    >>> B = 2 * A
+    >>> np.block([[A], [B]])             # vstack([A, B])
+    array([[1, 1],
+           [1, 1],
+           [2, 2],
+           [2, 2]])
+
+    It can also be used in place of `atleast_1d` and `atleast_2d`:
+
+    >>> a = np.array(0)
+    >>> b = np.array([1])
+    >>> np.block([a])                    # atleast_1d(a)
+    array([0])
+    >>> np.block([b])                    # atleast_1d(b)
+    array([1])
+
+    >>> np.block([[a]])                  # atleast_2d(a)
+    array([[0]])
+    >>> np.block([[b]])                  # atleast_2d(b)
+    array([[1]])
+
+
+    """
+    arrays, list_ndim, result_ndim, final_size = _block_setup(arrays)
+
+    # It was found through benchmarking that making an array of final size
+    # around 256x256 was faster by straight concatenation on a
+    # i7-7700HQ processor and dual channel ram 2400MHz.
+    # It didn't seem to matter heavily on the dtype used.
+    #
+    # A 2D array using repeated concatenation requires 2 copies of the array.
+    #
+    # The fastest algorithm will depend on the ratio of CPU power to memory
+    # speed.
+    # One can monitor the results of the benchmark
+    # https://pv.github.io/numpy-bench/#bench_shape_base.Block2D.time_block2d
+    # to tune this parameter until a C version of the `_block_info_recursion`
+    # algorithm is implemented which would likely be faster than the python
+    # version.
+    if list_ndim * final_size > (2 * 512 * 512):
+        return _block_slicing(arrays, list_ndim, result_ndim)
+    else:
+        return _block_concatenate(arrays, list_ndim, result_ndim)
+
+
+# These helper functions are mostly used for testing.
+# They allow us to write tests that directly call `_block_slicing`
+# or `_block_concatenate` without blocking large arrays to force the wisdom
+# to trigger the desired path.
+def _block_setup(arrays):
+    """
+    Returns
+    (`arrays`, list_ndim, result_ndim, final_size)
+    """
+    bottom_index, arr_ndim, final_size = _block_check_depths_match(arrays)
+    list_ndim = len(bottom_index)
+    if bottom_index and bottom_index[-1] is None:
+        raise ValueError(
+            f'List at {_block_format_index(bottom_index)} cannot be empty'
+        )
+    result_ndim = max(arr_ndim, list_ndim)
+    return arrays, list_ndim, result_ndim, final_size
+
+
+def _block_slicing(arrays, list_ndim, result_ndim):
+    shape, slices, arrays = _block_info_recursion(
+        arrays, list_ndim, result_ndim)
+    dtype = _nx.result_type(*[arr.dtype for arr in arrays])
+
+    # Test preferring F only in the case that all input arrays are F
+    F_order = all(arr.flags['F_CONTIGUOUS'] for arr in arrays)
+    C_order = all(arr.flags['C_CONTIGUOUS'] for arr in arrays)
+    order = 'F' if F_order and not C_order else 'C'
+    result = _nx.empty(shape=shape, dtype=dtype, order=order)
+    # Note: In a c implementation, the function
+    # PyArray_CreateMultiSortedStridePerm could be used for more advanced
+    # guessing of the desired order.
+
+    for the_slice, arr in zip(slices, arrays):
+        result[(Ellipsis,) + the_slice] = arr
+    return result
+
+
+def _block_concatenate(arrays, list_ndim, result_ndim):
+    result = _block(arrays, list_ndim, result_ndim)
+    if list_ndim == 0:
+        # Catch an edge case where _block returns a view because
+        # `arrays` is a single numpy array and not a list of numpy arrays.
+        # This might copy scalars or lists twice, but this isn't a likely
+        # usecase for those interested in performance
+        result = result.copy()
+    return result
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/shape_base.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/shape_base.pyi
new file mode 100644
index 0000000..c2c9c96
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/shape_base.pyi
@@ -0,0 +1,175 @@
+from collections.abc import Sequence
+from typing import Any, SupportsIndex, TypeVar, overload
+
+from numpy import _CastingKind, generic
+from numpy._typing import ArrayLike, DTypeLike, NDArray, _ArrayLike, _DTypeLike
+
+__all__ = [
+    "atleast_1d",
+    "atleast_2d",
+    "atleast_3d",
+    "block",
+    "hstack",
+    "stack",
+    "unstack",
+    "vstack",
+]
+
+_ScalarT = TypeVar("_ScalarT", bound=generic)
+_ScalarT1 = TypeVar("_ScalarT1", bound=generic)
+_ScalarT2 = TypeVar("_ScalarT2", bound=generic)
+_ArrayT = TypeVar("_ArrayT", bound=NDArray[Any])
+
+###
+
+@overload
+def atleast_1d(a0: _ArrayLike[_ScalarT], /) -> NDArray[_ScalarT]: ...
+@overload
+def atleast_1d(a0: _ArrayLike[_ScalarT1], a1: _ArrayLike[_ScalarT2], /) -> tuple[NDArray[_ScalarT1], NDArray[_ScalarT2]]: ...
+@overload
+def atleast_1d(a0: _ArrayLike[_ScalarT], a1: _ArrayLike[_ScalarT], /, *arys: _ArrayLike[_ScalarT]) -> tuple[NDArray[_ScalarT], ...]: ...
+@overload
+def atleast_1d(a0: ArrayLike, /) -> NDArray[Any]: ...
+@overload
+def atleast_1d(a0: ArrayLike, a1: ArrayLike, /) -> tuple[NDArray[Any], NDArray[Any]]: ...
+@overload
+def atleast_1d(a0: ArrayLike, a1: ArrayLike, /, *ai: ArrayLike) -> tuple[NDArray[Any], ...]: ...
+
+#
+@overload
+def atleast_2d(a0: _ArrayLike[_ScalarT], /) -> NDArray[_ScalarT]: ...
+@overload
+def atleast_2d(a0: _ArrayLike[_ScalarT1], a1: _ArrayLike[_ScalarT2], /) -> tuple[NDArray[_ScalarT1], NDArray[_ScalarT2]]: ...
+@overload
+def atleast_2d(a0: _ArrayLike[_ScalarT], a1: _ArrayLike[_ScalarT], /, *arys: _ArrayLike[_ScalarT]) -> tuple[NDArray[_ScalarT], ...]: ...
+@overload
+def atleast_2d(a0: ArrayLike, /) -> NDArray[Any]: ...
+@overload
+def atleast_2d(a0: ArrayLike, a1: ArrayLike, /) -> tuple[NDArray[Any], NDArray[Any]]: ...
+@overload
+def atleast_2d(a0: ArrayLike, a1: ArrayLike, /, *ai: ArrayLike) -> tuple[NDArray[Any], ...]: ...
+
+#
+@overload
+def atleast_3d(a0: _ArrayLike[_ScalarT], /) -> NDArray[_ScalarT]: ...
+@overload
+def atleast_3d(a0: _ArrayLike[_ScalarT1], a1: _ArrayLike[_ScalarT2], /) -> tuple[NDArray[_ScalarT1], NDArray[_ScalarT2]]: ...
+@overload
+def atleast_3d(a0: _ArrayLike[_ScalarT], a1: _ArrayLike[_ScalarT], /, *arys: _ArrayLike[_ScalarT]) -> tuple[NDArray[_ScalarT], ...]: ...
+@overload
+def atleast_3d(a0: ArrayLike, /) -> NDArray[Any]: ...
+@overload
+def atleast_3d(a0: ArrayLike, a1: ArrayLike, /) -> tuple[NDArray[Any], NDArray[Any]]: ...
+@overload
+def atleast_3d(a0: ArrayLike, a1: ArrayLike, /, *ai: ArrayLike) -> tuple[NDArray[Any], ...]: ...
+
+#
+@overload
+def vstack(
+    tup: Sequence[_ArrayLike[_ScalarT]],
+    *,
+    dtype: None = ...,
+    casting: _CastingKind = ...
+) -> NDArray[_ScalarT]: ...
+@overload
+def vstack(
+    tup: Sequence[ArrayLike],
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    casting: _CastingKind = ...
+) -> NDArray[_ScalarT]: ...
+@overload
+def vstack(
+    tup: Sequence[ArrayLike],
+    *,
+    dtype: DTypeLike = ...,
+    casting: _CastingKind = ...
+) -> NDArray[Any]: ...
+
+@overload
+def hstack(
+    tup: Sequence[_ArrayLike[_ScalarT]],
+    *,
+    dtype: None = ...,
+    casting: _CastingKind = ...
+) -> NDArray[_ScalarT]: ...
+@overload
+def hstack(
+    tup: Sequence[ArrayLike],
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    casting: _CastingKind = ...
+) -> NDArray[_ScalarT]: ...
+@overload
+def hstack(
+    tup: Sequence[ArrayLike],
+    *,
+    dtype: DTypeLike = ...,
+    casting: _CastingKind = ...
+) -> NDArray[Any]: ...
+
+@overload
+def stack(
+    arrays: Sequence[_ArrayLike[_ScalarT]],
+    axis: SupportsIndex = ...,
+    out: None = ...,
+    *,
+    dtype: None = ...,
+    casting: _CastingKind = ...
+) -> NDArray[_ScalarT]: ...
+@overload
+def stack(
+    arrays: Sequence[ArrayLike],
+    axis: SupportsIndex = ...,
+    out: None = ...,
+    *,
+    dtype: _DTypeLike[_ScalarT],
+    casting: _CastingKind = ...
+) -> NDArray[_ScalarT]: ...
+@overload
+def stack(
+    arrays: Sequence[ArrayLike],
+    axis: SupportsIndex = ...,
+    out: None = ...,
+    *,
+    dtype: DTypeLike = ...,
+    casting: _CastingKind = ...
+) -> NDArray[Any]: ...
+@overload
+def stack(
+    arrays: Sequence[ArrayLike],
+    axis: SupportsIndex,
+    out: _ArrayT,
+    *,
+    dtype: DTypeLike | None = None,
+    casting: _CastingKind = "same_kind",
+) -> _ArrayT: ...
+@overload
+def stack(
+    arrays: Sequence[ArrayLike],
+    axis: SupportsIndex = 0,
+    *,
+    out: _ArrayT,
+    dtype: DTypeLike | None = None,
+    casting: _CastingKind = "same_kind",
+) -> _ArrayT: ...
+
+@overload
+def unstack(
+    array: _ArrayLike[_ScalarT],
+    /,
+    *,
+    axis: int = ...,
+) -> tuple[NDArray[_ScalarT], ...]: ...
+@overload
+def unstack(
+    array: ArrayLike,
+    /,
+    *,
+    axis: int = ...,
+) -> tuple[NDArray[Any], ...]: ...
+
+@overload
+def block(arrays: _ArrayLike[_ScalarT]) -> NDArray[_ScalarT]: ...
+@overload
+def block(arrays: ArrayLike) -> NDArray[Any]: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/strings.py b/.venv/lib/python3.12/site-packages/numpy/_core/strings.py
new file mode 100644
index 0000000..b4dc165
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/strings.py
@@ -0,0 +1,1823 @@
+"""
+This module contains a set of functions for vectorized string
+operations.
+"""
+
+import functools
+import sys
+
+import numpy as np
+from numpy import (
+    add,
+    equal,
+    greater,
+    greater_equal,
+    less,
+    less_equal,
+    not_equal,
+)
+from numpy import (
+    multiply as _multiply_ufunc,
+)
+from numpy._core.multiarray import _vec_string
+from numpy._core.overrides import array_function_dispatch, set_module
+from numpy._core.umath import (
+    _center,
+    _expandtabs,
+    _expandtabs_length,
+    _ljust,
+    _lstrip_chars,
+    _lstrip_whitespace,
+    _partition,
+    _partition_index,
+    _replace,
+    _rjust,
+    _rpartition,
+    _rpartition_index,
+    _rstrip_chars,
+    _rstrip_whitespace,
+    _slice,
+    _strip_chars,
+    _strip_whitespace,
+    _zfill,
+    isalnum,
+    isalpha,
+    isdecimal,
+    isdigit,
+    islower,
+    isnumeric,
+    isspace,
+    istitle,
+    isupper,
+    str_len,
+)
+from numpy._core.umath import (
+    count as _count_ufunc,
+)
+from numpy._core.umath import (
+    endswith as _endswith_ufunc,
+)
+from numpy._core.umath import (
+    find as _find_ufunc,
+)
+from numpy._core.umath import (
+    index as _index_ufunc,
+)
+from numpy._core.umath import (
+    rfind as _rfind_ufunc,
+)
+from numpy._core.umath import (
+    rindex as _rindex_ufunc,
+)
+from numpy._core.umath import (
+    startswith as _startswith_ufunc,
+)
+
+
+def _override___module__():
+    for ufunc in [
+        isalnum, isalpha, isdecimal, isdigit, islower, isnumeric, isspace,
+        istitle, isupper, str_len,
+    ]:
+        ufunc.__module__ = "numpy.strings"
+        ufunc.__qualname__ = ufunc.__name__
+
+
+_override___module__()
+
+
+__all__ = [
+    # UFuncs
+    "equal", "not_equal", "less", "less_equal", "greater", "greater_equal",
+    "add", "multiply", "isalpha", "isdigit", "isspace", "isalnum", "islower",
+    "isupper", "istitle", "isdecimal", "isnumeric", "str_len", "find",
+    "rfind", "index", "rindex", "count", "startswith", "endswith", "lstrip",
+    "rstrip", "strip", "replace", "expandtabs", "center", "ljust", "rjust",
+    "zfill", "partition", "rpartition", "slice",
+
+    # _vec_string - Will gradually become ufuncs as well
+    "upper", "lower", "swapcase", "capitalize", "title",
+
+    # _vec_string - Will probably not become ufuncs
+    "mod", "decode", "encode", "translate",
+
+    # Removed from namespace until behavior has been crystallized
+    # "join", "split", "rsplit", "splitlines",
+]
+
+
+MAX = np.iinfo(np.int64).max
+
+array_function_dispatch = functools.partial(
+    array_function_dispatch, module='numpy.strings')
+
+
+def _get_num_chars(a):
+    """
+    Helper function that returns the number of characters per field in
+    a string or unicode array.  This is to abstract out the fact that
+    for a unicode array this is itemsize / 4.
+    """
+    if issubclass(a.dtype.type, np.str_):
+        return a.itemsize // 4
+    return a.itemsize
+
+
+def _to_bytes_or_str_array(result, output_dtype_like):
+    """
+    Helper function to cast a result back into an array
+    with the appropriate dtype if an object array must be used
+    as an intermediary.
+    """
+    output_dtype_like = np.asarray(output_dtype_like)
+    if result.size == 0:
+        # Calling asarray & tolist in an empty array would result
+        # in losing shape information
+        return result.astype(output_dtype_like.dtype)
+    ret = np.asarray(result.tolist())
+    if isinstance(output_dtype_like.dtype, np.dtypes.StringDType):
+        return ret.astype(type(output_dtype_like.dtype))
+    return ret.astype(type(output_dtype_like.dtype)(_get_num_chars(ret)))
+
+
+def _clean_args(*args):
+    """
+    Helper function for delegating arguments to Python string
+    functions.
+
+    Many of the Python string operations that have optional arguments
+    do not use 'None' to indicate a default value.  In these cases,
+    we need to remove all None arguments, and those following them.
+    """
+    newargs = []
+    for chk in args:
+        if chk is None:
+            break
+        newargs.append(chk)
+    return newargs
+
+
+def _multiply_dispatcher(a, i):
+    return (a,)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_multiply_dispatcher)
+def multiply(a, i):
+    """
+    Return (a * i), that is string multiple concatenation,
+    element-wise.
+
+    Values in ``i`` of less than 0 are treated as 0 (which yields an
+    empty string).
+
+    Parameters
+    ----------
+    a : array_like, with ``StringDType``, ``bytes_`` or ``str_`` dtype
+
+    i : array_like, with any integer dtype
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(["a", "b", "c"])
+    >>> np.strings.multiply(a, 3)
+    array(['aaa', 'bbb', 'ccc'], dtype='<U3')
+    >>> i = np.array([1, 2, 3])
+    >>> np.strings.multiply(a, i)
+    array(['a', 'bb', 'ccc'], dtype='<U3')
+    >>> np.strings.multiply(np.array(['a']), i)
+    array(['a', 'aa', 'aaa'], dtype='<U3')
+    >>> a = np.array(['a', 'b', 'c', 'd', 'e', 'f']).reshape((2, 3))
+    >>> np.strings.multiply(a, 3)
+    array([['aaa', 'bbb', 'ccc'],
+           ['ddd', 'eee', 'fff']], dtype='<U3')
+    >>> np.strings.multiply(a, i)
+    array([['a', 'bb', 'ccc'],
+           ['d', 'ee', 'fff']], dtype='<U3')
+
+    """
+    a = np.asanyarray(a)
+
+    i = np.asanyarray(i)
+    if not np.issubdtype(i.dtype, np.integer):
+        raise TypeError(f"unsupported type {i.dtype} for operand 'i'")
+    i = np.maximum(i, 0)
+
+    # delegate to stringdtype loops that also do overflow checking
+    if a.dtype.char == "T":
+        return a * i
+
+    a_len = str_len(a)
+
+    # Ensure we can do a_len * i without overflow.
+    if np.any(a_len > sys.maxsize / np.maximum(i, 1)):
+        raise OverflowError("Overflow encountered in string multiply")
+
+    buffersizes = a_len * i
+    out_dtype = f"{a.dtype.char}{buffersizes.max()}"
+    out = np.empty_like(a, shape=buffersizes.shape, dtype=out_dtype)
+    return _multiply_ufunc(a, i, out=out)
+
+
+def _mod_dispatcher(a, values):
+    return (a, values)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_mod_dispatcher)
+def mod(a, values):
+    """
+    Return (a % i), that is pre-Python 2.6 string formatting
+    (interpolation), element-wise for a pair of array_likes of str
+    or unicode.
+
+    Parameters
+    ----------
+    a : array_like, with `np.bytes_` or `np.str_` dtype
+
+    values : array_like of values
+       These values will be element-wise interpolated into the string.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(["NumPy is a %s library"])
+    >>> np.strings.mod(a, values=["Python"])
+    array(['NumPy is a Python library'], dtype='<U25')
+
+    >>> a = np.array([b'%d bytes', b'%d bits'])
+    >>> values = np.array([8, 64])
+    >>> np.strings.mod(a, values)
+    array([b'8 bytes', b'64 bits'], dtype='|S7')
+
+    """
+    return _to_bytes_or_str_array(
+        _vec_string(a, np.object_, '__mod__', (values,)), a)
+
+
+@set_module("numpy.strings")
+def find(a, sub, start=0, end=None):
+    """
+    For each element, return the lowest index in the string where
+    substring ``sub`` is found, such that ``sub`` is contained in the
+    range [``start``, ``end``).
+
+    Parameters
+    ----------
+    a : array_like, with ``StringDType``, ``bytes_`` or ``str_`` dtype
+
+    sub : array_like, with `np.bytes_` or `np.str_` dtype
+        The substring to search for.
+
+    start, end : array_like, with any integer dtype
+        The range to look in, interpreted as in slice notation.
+
+    Returns
+    -------
+    y : ndarray
+        Output array of ints
+
+    See Also
+    --------
+    str.find
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(["NumPy is a Python library"])
+    >>> np.strings.find(a, "Python")
+    array([11])
+
+    """
+    end = end if end is not None else MAX
+    return _find_ufunc(a, sub, start, end)
+
+
+@set_module("numpy.strings")
+def rfind(a, sub, start=0, end=None):
+    """
+    For each element, return the highest index in the string where
+    substring ``sub`` is found, such that ``sub`` is contained in the
+    range [``start``, ``end``).
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    sub : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        The substring to search for.
+
+    start, end : array_like, with any integer dtype
+        The range to look in, interpreted as in slice notation.
+
+    Returns
+    -------
+    y : ndarray
+        Output array of ints
+
+    See Also
+    --------
+    str.rfind
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(["Computer Science"])
+    >>> np.strings.rfind(a, "Science", start=0, end=None)
+    array([9])
+    >>> np.strings.rfind(a, "Science", start=0, end=8)
+    array([-1])
+    >>> b = np.array(["Computer Science", "Science"])
+    >>> np.strings.rfind(b, "Science", start=0, end=None)
+    array([9, 0])
+
+    """
+    end = end if end is not None else MAX
+    return _rfind_ufunc(a, sub, start, end)
+
+
+@set_module("numpy.strings")
+def index(a, sub, start=0, end=None):
+    """
+    Like `find`, but raises :exc:`ValueError` when the substring is not found.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    sub : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    start, end : array_like, with any integer dtype, optional
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ints.
+
+    See Also
+    --------
+    find, str.index
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(["Computer Science"])
+    >>> np.strings.index(a, "Science", start=0, end=None)
+    array([9])
+
+    """
+    end = end if end is not None else MAX
+    return _index_ufunc(a, sub, start, end)
+
+
+@set_module("numpy.strings")
+def rindex(a, sub, start=0, end=None):
+    """
+    Like `rfind`, but raises :exc:`ValueError` when the substring `sub` is
+    not found.
+
+    Parameters
+    ----------
+    a : array-like, with `np.bytes_` or `np.str_` dtype
+
+    sub : array-like, with `np.bytes_` or `np.str_` dtype
+
+    start, end : array-like, with any integer dtype, optional
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ints.
+
+    See Also
+    --------
+    rfind, str.rindex
+
+    Examples
+    --------
+    >>> a = np.array(["Computer Science"])
+    >>> np.strings.rindex(a, "Science", start=0, end=None)
+    array([9])
+
+    """
+    end = end if end is not None else MAX
+    return _rindex_ufunc(a, sub, start, end)
+
+
+@set_module("numpy.strings")
+def count(a, sub, start=0, end=None):
+    """
+    Returns an array with the number of non-overlapping occurrences of
+    substring ``sub`` in the range [``start``, ``end``).
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    sub : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+       The substring to search for.
+
+    start, end : array_like, with any integer dtype
+        The range to look in, interpreted as in slice notation.
+
+    Returns
+    -------
+    y : ndarray
+        Output array of ints
+
+    See Also
+    --------
+    str.count
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array(['aAaAaA', '  aA  ', 'abBABba'])
+    >>> c
+    array(['aAaAaA', '  aA  ', 'abBABba'], dtype='<U7')
+    >>> np.strings.count(c, 'A')
+    array([3, 1, 1])
+    >>> np.strings.count(c, 'aA')
+    array([3, 1, 0])
+    >>> np.strings.count(c, 'A', start=1, end=4)
+    array([2, 1, 1])
+    >>> np.strings.count(c, 'A', start=1, end=3)
+    array([1, 0, 0])
+
+    """
+    end = end if end is not None else MAX
+    return _count_ufunc(a, sub, start, end)
+
+
+@set_module("numpy.strings")
+def startswith(a, prefix, start=0, end=None):
+    """
+    Returns a boolean array which is `True` where the string element
+    in ``a`` starts with ``prefix``, otherwise `False`.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    prefix : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    start, end : array_like, with any integer dtype
+        With ``start``, test beginning at that position. With ``end``,
+        stop comparing at that position.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools
+
+    See Also
+    --------
+    str.startswith
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> s = np.array(['foo', 'bar'])
+    >>> s
+    array(['foo', 'bar'], dtype='<U3')
+    >>> np.strings.startswith(s, 'fo')
+    array([True,  False])
+    >>> np.strings.startswith(s, 'o', start=1, end=2)
+    array([True,  False])
+
+    """
+    end = end if end is not None else MAX
+    return _startswith_ufunc(a, prefix, start, end)
+
+
+@set_module("numpy.strings")
+def endswith(a, suffix, start=0, end=None):
+    """
+    Returns a boolean array which is `True` where the string element
+    in ``a`` ends with ``suffix``, otherwise `False`.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    suffix : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    start, end : array_like, with any integer dtype
+        With ``start``, test beginning at that position. With ``end``,
+        stop comparing at that position.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of bools
+
+    See Also
+    --------
+    str.endswith
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> s = np.array(['foo', 'bar'])
+    >>> s
+    array(['foo', 'bar'], dtype='<U3')
+    >>> np.strings.endswith(s, 'ar')
+    array([False,  True])
+    >>> np.strings.endswith(s, 'a', start=1, end=2)
+    array([False,  True])
+
+    """
+    end = end if end is not None else MAX
+    return _endswith_ufunc(a, suffix, start, end)
+
+
+def _code_dispatcher(a, encoding=None, errors=None):
+    return (a,)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_code_dispatcher)
+def decode(a, encoding=None, errors=None):
+    r"""
+    Calls :meth:`bytes.decode` element-wise.
+
+    The set of available codecs comes from the Python standard library,
+    and may be extended at runtime.  For more information, see the
+    :mod:`codecs` module.
+
+    Parameters
+    ----------
+    a : array_like, with ``bytes_`` dtype
+
+    encoding : str, optional
+       The name of an encoding
+
+    errors : str, optional
+       Specifies how to handle encoding errors
+
+    Returns
+    -------
+    out : ndarray
+
+    See Also
+    --------
+    :py:meth:`bytes.decode`
+
+    Notes
+    -----
+    The type of the result will depend on the encoding specified.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array([b'\x81\xc1\x81\xc1\x81\xc1', b'@@\x81\xc1@@',
+    ...               b'\x81\x82\xc2\xc1\xc2\x82\x81'])
+    >>> c
+    array([b'\x81\xc1\x81\xc1\x81\xc1', b'@@\x81\xc1@@',
+           b'\x81\x82\xc2\xc1\xc2\x82\x81'], dtype='|S7')
+    >>> np.strings.decode(c, encoding='cp037')
+    array(['aAaAaA', '  aA  ', 'abBABba'], dtype='<U7')
+
+    """
+    return _to_bytes_or_str_array(
+        _vec_string(a, np.object_, 'decode', _clean_args(encoding, errors)),
+        np.str_(''))
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_code_dispatcher)
+def encode(a, encoding=None, errors=None):
+    """
+    Calls :meth:`str.encode` element-wise.
+
+    The set of available codecs comes from the Python standard library,
+    and may be extended at runtime. For more information, see the
+    :mod:`codecs` module.
+
+    Parameters
+    ----------
+    a : array_like, with ``StringDType`` or ``str_`` dtype
+
+    encoding : str, optional
+       The name of an encoding
+
+    errors : str, optional
+       Specifies how to handle encoding errors
+
+    Returns
+    -------
+    out : ndarray
+
+    See Also
+    --------
+    str.encode
+
+    Notes
+    -----
+    The type of the result will depend on the encoding specified.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(['aAaAaA', '  aA  ', 'abBABba'])
+    >>> np.strings.encode(a, encoding='cp037')
+    array([b'\x81\xc1\x81\xc1\x81\xc1', b'@@\x81\xc1@@',
+       b'\x81\x82\xc2\xc1\xc2\x82\x81'], dtype='|S7')
+
+    """
+    return _to_bytes_or_str_array(
+        _vec_string(a, np.object_, 'encode', _clean_args(encoding, errors)),
+        np.bytes_(b''))
+
+
+def _expandtabs_dispatcher(a, tabsize=None):
+    return (a,)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_expandtabs_dispatcher)
+def expandtabs(a, tabsize=8):
+    """
+    Return a copy of each string element where all tab characters are
+    replaced by one or more spaces.
+
+    Calls :meth:`str.expandtabs` element-wise.
+
+    Return a copy of each string element where all tab characters are
+    replaced by one or more spaces, depending on the current column
+    and the given `tabsize`. The column number is reset to zero after
+    each newline occurring in the string. This doesn't understand other
+    non-printing characters or escape sequences.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array
+    tabsize : int, optional
+        Replace tabs with `tabsize` number of spaces.  If not given defaults
+        to 8 spaces.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input type
+
+    See Also
+    --------
+    str.expandtabs
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(['\t\tHello\tworld'])
+    >>> np.strings.expandtabs(a, tabsize=4)  # doctest: +SKIP
+    array(['        Hello   world'], dtype='<U21')  # doctest: +SKIP
+
+    """
+    a = np.asanyarray(a)
+    tabsize = np.asanyarray(tabsize)
+
+    if a.dtype.char == "T":
+        return _expandtabs(a, tabsize)
+
+    buffersizes = _expandtabs_length(a, tabsize)
+    out_dtype = f"{a.dtype.char}{buffersizes.max()}"
+    out = np.empty_like(a, shape=buffersizes.shape, dtype=out_dtype)
+    return _expandtabs(a, tabsize, out=out)
+
+
+def _just_dispatcher(a, width, fillchar=None):
+    return (a,)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_just_dispatcher)
+def center(a, width, fillchar=' '):
+    """
+    Return a copy of `a` with its elements centered in a string of
+    length `width`.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    width : array_like, with any integer dtype
+        The length of the resulting strings, unless ``width < str_len(a)``.
+    fillchar : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Optional padding character to use (default is space).
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.center
+
+    Notes
+    -----
+    While it is possible for ``a`` and ``fillchar`` to have different dtypes,
+    passing a non-ASCII character in ``fillchar`` when ``a`` is of dtype "S"
+    is not allowed, and a ``ValueError`` is raised.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array(['a1b2','1b2a','b2a1','2a1b']); c
+    array(['a1b2', '1b2a', 'b2a1', '2a1b'], dtype='<U4')
+    >>> np.strings.center(c, width=9)
+    array(['   a1b2  ', '   1b2a  ', '   b2a1  ', '   2a1b  '], dtype='<U9')
+    >>> np.strings.center(c, width=9, fillchar='*')
+    array(['***a1b2**', '***1b2a**', '***b2a1**', '***2a1b**'], dtype='<U9')
+    >>> np.strings.center(c, width=1)
+    array(['a1b2', '1b2a', 'b2a1', '2a1b'], dtype='<U4')
+
+    """
+    width = np.asanyarray(width)
+
+    if not np.issubdtype(width.dtype, np.integer):
+        raise TypeError(f"unsupported type {width.dtype} for operand 'width'")
+
+    a = np.asanyarray(a)
+    fillchar = np.asanyarray(fillchar)
+
+    if np.any(str_len(fillchar) != 1):
+        raise TypeError(
+            "The fill character must be exactly one character long")
+
+    if np.result_type(a, fillchar).char == "T":
+        return _center(a, width, fillchar)
+
+    fillchar = fillchar.astype(a.dtype, copy=False)
+    width = np.maximum(str_len(a), width)
+    out_dtype = f"{a.dtype.char}{width.max()}"
+    shape = np.broadcast_shapes(a.shape, width.shape, fillchar.shape)
+    out = np.empty_like(a, shape=shape, dtype=out_dtype)
+
+    return _center(a, width, fillchar, out=out)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_just_dispatcher)
+def ljust(a, width, fillchar=' '):
+    """
+    Return an array with the elements of `a` left-justified in a
+    string of length `width`.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    width : array_like, with any integer dtype
+        The length of the resulting strings, unless ``width < str_len(a)``.
+    fillchar : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Optional character to use for padding (default is space).
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.ljust
+
+    Notes
+    -----
+    While it is possible for ``a`` and ``fillchar`` to have different dtypes,
+    passing a non-ASCII character in ``fillchar`` when ``a`` is of dtype "S"
+    is not allowed, and a ``ValueError`` is raised.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array(['aAaAaA', '  aA  ', 'abBABba'])
+    >>> np.strings.ljust(c, width=3)
+    array(['aAaAaA', '  aA  ', 'abBABba'], dtype='<U7')
+    >>> np.strings.ljust(c, width=9)
+    array(['aAaAaA   ', '  aA     ', 'abBABba  '], dtype='<U9')
+
+    """
+    width = np.asanyarray(width)
+    if not np.issubdtype(width.dtype, np.integer):
+        raise TypeError(f"unsupported type {width.dtype} for operand 'width'")
+
+    a = np.asanyarray(a)
+    fillchar = np.asanyarray(fillchar)
+
+    if np.any(str_len(fillchar) != 1):
+        raise TypeError(
+            "The fill character must be exactly one character long")
+
+    if np.result_type(a, fillchar).char == "T":
+        return _ljust(a, width, fillchar)
+
+    fillchar = fillchar.astype(a.dtype, copy=False)
+    width = np.maximum(str_len(a), width)
+    shape = np.broadcast_shapes(a.shape, width.shape, fillchar.shape)
+    out_dtype = f"{a.dtype.char}{width.max()}"
+    out = np.empty_like(a, shape=shape, dtype=out_dtype)
+
+    return _ljust(a, width, fillchar, out=out)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_just_dispatcher)
+def rjust(a, width, fillchar=' '):
+    """
+    Return an array with the elements of `a` right-justified in a
+    string of length `width`.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    width : array_like, with any integer dtype
+        The length of the resulting strings, unless ``width < str_len(a)``.
+    fillchar : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Optional padding character to use (default is space).
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.rjust
+
+    Notes
+    -----
+    While it is possible for ``a`` and ``fillchar`` to have different dtypes,
+    passing a non-ASCII character in ``fillchar`` when ``a`` is of dtype "S"
+    is not allowed, and a ``ValueError`` is raised.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(['aAaAaA', '  aA  ', 'abBABba'])
+    >>> np.strings.rjust(a, width=3)
+    array(['aAaAaA', '  aA  ', 'abBABba'], dtype='<U7')
+    >>> np.strings.rjust(a, width=9)
+    array(['   aAaAaA', '     aA  ', '  abBABba'], dtype='<U9')
+
+    """
+    width = np.asanyarray(width)
+    if not np.issubdtype(width.dtype, np.integer):
+        raise TypeError(f"unsupported type {width.dtype} for operand 'width'")
+
+    a = np.asanyarray(a)
+    fillchar = np.asanyarray(fillchar)
+
+    if np.any(str_len(fillchar) != 1):
+        raise TypeError(
+            "The fill character must be exactly one character long")
+
+    if np.result_type(a, fillchar).char == "T":
+        return _rjust(a, width, fillchar)
+
+    fillchar = fillchar.astype(a.dtype, copy=False)
+    width = np.maximum(str_len(a), width)
+    shape = np.broadcast_shapes(a.shape, width.shape, fillchar.shape)
+    out_dtype = f"{a.dtype.char}{width.max()}"
+    out = np.empty_like(a, shape=shape, dtype=out_dtype)
+
+    return _rjust(a, width, fillchar, out=out)
+
+
+def _zfill_dispatcher(a, width):
+    return (a,)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_zfill_dispatcher)
+def zfill(a, width):
+    """
+    Return the numeric string left-filled with zeros. A leading
+    sign prefix (``+``/``-``) is handled by inserting the padding
+    after the sign character rather than before.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    width : array_like, with any integer dtype
+        Width of string to left-fill elements in `a`.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input type
+
+    See Also
+    --------
+    str.zfill
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.strings.zfill(['1', '-1', '+1'], 3)
+    array(['001', '-01', '+01'], dtype='<U3')
+
+    """
+    width = np.asanyarray(width)
+    if not np.issubdtype(width.dtype, np.integer):
+        raise TypeError(f"unsupported type {width.dtype} for operand 'width'")
+
+    a = np.asanyarray(a)
+
+    if a.dtype.char == "T":
+        return _zfill(a, width)
+
+    width = np.maximum(str_len(a), width)
+    shape = np.broadcast_shapes(a.shape, width.shape)
+    out_dtype = f"{a.dtype.char}{width.max()}"
+    out = np.empty_like(a, shape=shape, dtype=out_dtype)
+    return _zfill(a, width, out=out)
+
+
+@set_module("numpy.strings")
+def lstrip(a, chars=None):
+    """
+    For each element in `a`, return a copy with the leading characters
+    removed.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+    chars : scalar with the same dtype as ``a``, optional
+       The ``chars`` argument is a string specifying the set of
+       characters to be removed. If ``None``, the ``chars``
+       argument defaults to removing whitespace. The ``chars`` argument
+       is not a prefix or suffix; rather, all combinations of its
+       values are stripped.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.lstrip
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array(['aAaAaA', '  aA  ', 'abBABba'])
+    >>> c
+    array(['aAaAaA', '  aA  ', 'abBABba'], dtype='<U7')
+    # The 'a' variable is unstripped from c[1] because of leading whitespace.
+    >>> np.strings.lstrip(c, 'a')
+    array(['AaAaA', '  aA  ', 'bBABba'], dtype='<U7')
+    >>> np.strings.lstrip(c, 'A') # leaves c unchanged
+    array(['aAaAaA', '  aA  ', 'abBABba'], dtype='<U7')
+    >>> (np.strings.lstrip(c, ' ') == np.strings.lstrip(c, '')).all()
+    np.False_
+    >>> (np.strings.lstrip(c, ' ') == np.strings.lstrip(c)).all()
+    np.True_
+
+    """
+    if chars is None:
+        return _lstrip_whitespace(a)
+    return _lstrip_chars(a, chars)
+
+
+@set_module("numpy.strings")
+def rstrip(a, chars=None):
+    """
+    For each element in `a`, return a copy with the trailing characters
+    removed.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+    chars : scalar with the same dtype as ``a``, optional
+       The ``chars`` argument is a string specifying the set of
+       characters to be removed. If ``None``, the ``chars``
+       argument defaults to removing whitespace. The ``chars`` argument
+       is not a prefix or suffix; rather, all combinations of its
+       values are stripped.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.rstrip
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array(['aAaAaA', 'abBABba'])
+    >>> c
+    array(['aAaAaA', 'abBABba'], dtype='<U7')
+    >>> np.strings.rstrip(c, 'a')
+    array(['aAaAaA', 'abBABb'], dtype='<U7')
+    >>> np.strings.rstrip(c, 'A')
+    array(['aAaAa', 'abBABba'], dtype='<U7')
+
+    """
+    if chars is None:
+        return _rstrip_whitespace(a)
+    return _rstrip_chars(a, chars)
+
+
+@set_module("numpy.strings")
+def strip(a, chars=None):
+    """
+    For each element in `a`, return a copy with the leading and
+    trailing characters removed.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+    chars : scalar with the same dtype as ``a``, optional
+       The ``chars`` argument is a string specifying the set of
+       characters to be removed. If ``None``, the ``chars``
+       argument defaults to removing whitespace. The ``chars`` argument
+       is not a prefix or suffix; rather, all combinations of its
+       values are stripped.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.strip
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array(['aAaAaA', '  aA  ', 'abBABba'])
+    >>> c
+    array(['aAaAaA', '  aA  ', 'abBABba'], dtype='<U7')
+    >>> np.strings.strip(c)
+    array(['aAaAaA', 'aA', 'abBABba'], dtype='<U7')
+    # 'a' unstripped from c[1] because of leading whitespace.
+    >>> np.strings.strip(c, 'a')
+    array(['AaAaA', '  aA  ', 'bBABb'], dtype='<U7')
+    # 'A' unstripped from c[1] because of trailing whitespace.
+    >>> np.strings.strip(c, 'A')
+    array(['aAaAa', '  aA  ', 'abBABba'], dtype='<U7')
+
+    """
+    if chars is None:
+        return _strip_whitespace(a)
+    return _strip_chars(a, chars)
+
+
+def _unary_op_dispatcher(a):
+    return (a,)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_unary_op_dispatcher)
+def upper(a):
+    """
+    Return an array with the elements converted to uppercase.
+
+    Calls :meth:`str.upper` element-wise.
+
+    For 8-bit strings, this method is locale-dependent.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.upper
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array(['a1b c', '1bca', 'bca1']); c
+    array(['a1b c', '1bca', 'bca1'], dtype='<U5')
+    >>> np.strings.upper(c)
+    array(['A1B C', '1BCA', 'BCA1'], dtype='<U5')
+
+    """
+    a_arr = np.asarray(a)
+    return _vec_string(a_arr, a_arr.dtype, 'upper')
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_unary_op_dispatcher)
+def lower(a):
+    """
+    Return an array with the elements converted to lowercase.
+
+    Call :meth:`str.lower` element-wise.
+
+    For 8-bit strings, this method is locale-dependent.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.lower
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array(['A1B C', '1BCA', 'BCA1']); c
+    array(['A1B C', '1BCA', 'BCA1'], dtype='<U5')
+    >>> np.strings.lower(c)
+    array(['a1b c', '1bca', 'bca1'], dtype='<U5')
+
+    """
+    a_arr = np.asarray(a)
+    return _vec_string(a_arr, a_arr.dtype, 'lower')
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_unary_op_dispatcher)
+def swapcase(a):
+    """
+    Return element-wise a copy of the string with
+    uppercase characters converted to lowercase and vice versa.
+
+    Calls :meth:`str.swapcase` element-wise.
+
+    For 8-bit strings, this method is locale-dependent.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.swapcase
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c=np.array(['a1B c','1b Ca','b Ca1','cA1b'],'S5'); c
+    array(['a1B c', '1b Ca', 'b Ca1', 'cA1b'],
+        dtype='|S5')
+    >>> np.strings.swapcase(c)
+    array(['A1b C', '1B cA', 'B cA1', 'Ca1B'],
+        dtype='|S5')
+
+    """
+    a_arr = np.asarray(a)
+    return _vec_string(a_arr, a_arr.dtype, 'swapcase')
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_unary_op_dispatcher)
+def capitalize(a):
+    """
+    Return a copy of ``a`` with only the first character of each element
+    capitalized.
+
+    Calls :meth:`str.capitalize` element-wise.
+
+    For byte strings, this method is locale-dependent.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array of strings to capitalize.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.capitalize
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c = np.array(['a1b2','1b2a','b2a1','2a1b'],'S4'); c
+    array(['a1b2', '1b2a', 'b2a1', '2a1b'],
+        dtype='|S4')
+    >>> np.strings.capitalize(c)
+    array(['A1b2', '1b2a', 'B2a1', '2a1b'],
+        dtype='|S4')
+
+    """
+    a_arr = np.asarray(a)
+    return _vec_string(a_arr, a_arr.dtype, 'capitalize')
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_unary_op_dispatcher)
+def title(a):
+    """
+    Return element-wise title cased version of string or unicode.
+
+    Title case words start with uppercase characters, all remaining cased
+    characters are lowercase.
+
+    Calls :meth:`str.title` element-wise.
+
+    For 8-bit strings, this method is locale-dependent.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.title
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> c=np.array(['a1b c','1b ca','b ca1','ca1b'],'S5'); c
+    array(['a1b c', '1b ca', 'b ca1', 'ca1b'],
+        dtype='|S5')
+    >>> np.strings.title(c)
+    array(['A1B C', '1B Ca', 'B Ca1', 'Ca1B'],
+        dtype='|S5')
+
+    """
+    a_arr = np.asarray(a)
+    return _vec_string(a_arr, a_arr.dtype, 'title')
+
+
+def _replace_dispatcher(a, old, new, count=None):
+    return (a,)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_replace_dispatcher)
+def replace(a, old, new, count=-1):
+    """
+    For each element in ``a``, return a copy of the string with
+    occurrences of substring ``old`` replaced by ``new``.
+
+    Parameters
+    ----------
+    a : array_like, with ``bytes_`` or ``str_`` dtype
+
+    old, new : array_like, with ``bytes_`` or ``str_`` dtype
+
+    count : array_like, with ``int_`` dtype
+        If the optional argument ``count`` is given, only the first
+        ``count`` occurrences are replaced.
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.replace
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(["That is a mango", "Monkeys eat mangos"])
+    >>> np.strings.replace(a, 'mango', 'banana')
+    array(['That is a banana', 'Monkeys eat bananas'], dtype='<U19')
+
+    >>> a = np.array(["The dish is fresh", "This is it"])
+    >>> np.strings.replace(a, 'is', 'was')
+    array(['The dwash was fresh', 'Thwas was it'], dtype='<U19')
+
+    """
+    count = np.asanyarray(count)
+    if not np.issubdtype(count.dtype, np.integer):
+        raise TypeError(f"unsupported type {count.dtype} for operand 'count'")
+
+    arr = np.asanyarray(a)
+    old_dtype = getattr(old, 'dtype', None)
+    old = np.asanyarray(old)
+    new_dtype = getattr(new, 'dtype', None)
+    new = np.asanyarray(new)
+
+    if np.result_type(arr, old, new).char == "T":
+        return _replace(arr, old, new, count)
+
+    a_dt = arr.dtype
+    old = old.astype(old_dtype or a_dt, copy=False)
+    new = new.astype(new_dtype or a_dt, copy=False)
+    max_int64 = np.iinfo(np.int64).max
+    counts = _count_ufunc(arr, old, 0, max_int64)
+    counts = np.where(count < 0, counts, np.minimum(counts, count))
+    buffersizes = str_len(arr) + counts * (str_len(new) - str_len(old))
+    out_dtype = f"{arr.dtype.char}{buffersizes.max()}"
+    out = np.empty_like(arr, shape=buffersizes.shape, dtype=out_dtype)
+
+    return _replace(arr, old, new, counts, out=out)
+
+
+def _join_dispatcher(sep, seq):
+    return (sep, seq)
+
+
+@array_function_dispatch(_join_dispatcher)
+def _join(sep, seq):
+    """
+    Return a string which is the concatenation of the strings in the
+    sequence `seq`.
+
+    Calls :meth:`str.join` element-wise.
+
+    Parameters
+    ----------
+    sep : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+    seq : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input types
+
+    See Also
+    --------
+    str.join
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> np.strings.join('-', 'osd')  # doctest: +SKIP
+    array('o-s-d', dtype='<U5')  # doctest: +SKIP
+
+    >>> np.strings.join(['-', '.'], ['ghc', 'osd'])  # doctest: +SKIP
+    array(['g-h-c', 'o.s.d'], dtype='<U5')  # doctest: +SKIP
+
+    """
+    return _to_bytes_or_str_array(
+        _vec_string(sep, np.object_, 'join', (seq,)), seq)
+
+
+def _split_dispatcher(a, sep=None, maxsplit=None):
+    return (a,)
+
+
+@array_function_dispatch(_split_dispatcher)
+def _split(a, sep=None, maxsplit=None):
+    """
+    For each element in `a`, return a list of the words in the
+    string, using `sep` as the delimiter string.
+
+    Calls :meth:`str.split` element-wise.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    sep : str or unicode, optional
+       If `sep` is not specified or None, any whitespace string is a
+       separator.
+
+    maxsplit : int, optional
+        If `maxsplit` is given, at most `maxsplit` splits are done.
+
+    Returns
+    -------
+    out : ndarray
+        Array of list objects
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array("Numpy is nice!")
+    >>> np.strings.split(x, " ")  # doctest: +SKIP
+    array(list(['Numpy', 'is', 'nice!']), dtype=object)  # doctest: +SKIP
+
+    >>> np.strings.split(x, " ", 1)  # doctest: +SKIP
+    array(list(['Numpy', 'is nice!']), dtype=object)  # doctest: +SKIP
+
+    See Also
+    --------
+    str.split, rsplit
+
+    """
+    # This will return an array of lists of different sizes, so we
+    # leave it as an object array
+    return _vec_string(
+        a, np.object_, 'split', [sep] + _clean_args(maxsplit))
+
+
+@array_function_dispatch(_split_dispatcher)
+def _rsplit(a, sep=None, maxsplit=None):
+    """
+    For each element in `a`, return a list of the words in the
+    string, using `sep` as the delimiter string.
+
+    Calls :meth:`str.rsplit` element-wise.
+
+    Except for splitting from the right, `rsplit`
+    behaves like `split`.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    sep : str or unicode, optional
+        If `sep` is not specified or None, any whitespace string
+        is a separator.
+    maxsplit : int, optional
+        If `maxsplit` is given, at most `maxsplit` splits are done,
+        the rightmost ones.
+
+    Returns
+    -------
+    out : ndarray
+        Array of list objects
+
+    See Also
+    --------
+    str.rsplit, split
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(['aAaAaA', 'abBABba'])
+    >>> np.strings.rsplit(a, 'A')  # doctest: +SKIP
+    array([list(['a', 'a', 'a', '']),  # doctest: +SKIP
+           list(['abB', 'Bba'])], dtype=object)  # doctest: +SKIP
+
+    """
+    # This will return an array of lists of different sizes, so we
+    # leave it as an object array
+    return _vec_string(
+        a, np.object_, 'rsplit', [sep] + _clean_args(maxsplit))
+
+
+def _splitlines_dispatcher(a, keepends=None):
+    return (a,)
+
+
+@array_function_dispatch(_splitlines_dispatcher)
+def _splitlines(a, keepends=None):
+    """
+    For each element in `a`, return a list of the lines in the
+    element, breaking at line boundaries.
+
+    Calls :meth:`str.splitlines` element-wise.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+
+    keepends : bool, optional
+        Line breaks are not included in the resulting list unless
+        keepends is given and true.
+
+    Returns
+    -------
+    out : ndarray
+        Array of list objects
+
+    See Also
+    --------
+    str.splitlines
+
+    Examples
+    --------
+    >>> np.char.splitlines("first line\\nsecond line")
+    array(list(['first line', 'second line']), dtype=object)
+    >>> a = np.array(["first\\nsecond", "third\\nfourth"])
+    >>> np.char.splitlines(a)
+    array([list(['first', 'second']), list(['third', 'fourth'])], dtype=object)
+
+    """
+    return _vec_string(
+        a, np.object_, 'splitlines', _clean_args(keepends))
+
+
+def _partition_dispatcher(a, sep):
+    return (a,)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_partition_dispatcher)
+def partition(a, sep):
+    """
+    Partition each element in ``a`` around ``sep``.
+
+    For each element in ``a``, split the element at the first
+    occurrence of ``sep``, and return a 3-tuple containing the part
+    before the separator, the separator itself, and the part after
+    the separator. If the separator is not found, the first item of
+    the tuple will contain the whole string, and the second and third
+    ones will be the empty string.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array
+    sep : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Separator to split each string element in ``a``.
+
+    Returns
+    -------
+    out : 3-tuple:
+        - array with ``StringDType``, ``bytes_`` or ``str_`` dtype with the
+          part before the separator
+        - array with ``StringDType``, ``bytes_`` or ``str_`` dtype with the
+          separator
+        - array with ``StringDType``, ``bytes_`` or ``str_`` dtype with the
+          part after the separator
+
+    See Also
+    --------
+    str.partition
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> x = np.array(["Numpy is nice!"])
+    >>> np.strings.partition(x, " ")
+    (array(['Numpy'], dtype='<U5'),
+     array([' '], dtype='<U1'),
+     array(['is nice!'], dtype='<U8'))
+
+    """
+    a = np.asanyarray(a)
+    sep = np.asanyarray(sep)
+
+    if np.result_type(a, sep).char == "T":
+        return _partition(a, sep)
+
+    sep = sep.astype(a.dtype, copy=False)
+    pos = _find_ufunc(a, sep, 0, MAX)
+    a_len = str_len(a)
+    sep_len = str_len(sep)
+
+    not_found = pos < 0
+    buffersizes1 = np.where(not_found, a_len, pos)
+    buffersizes3 = np.where(not_found, 0, a_len - pos - sep_len)
+
+    out_dtype = ",".join([f"{a.dtype.char}{n}" for n in (
+        buffersizes1.max(),
+        1 if np.all(not_found) else sep_len.max(),
+        buffersizes3.max(),
+    )])
+    shape = np.broadcast_shapes(a.shape, sep.shape)
+    out = np.empty_like(a, shape=shape, dtype=out_dtype)
+    return _partition_index(a, sep, pos, out=(out["f0"], out["f1"], out["f2"]))
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_partition_dispatcher)
+def rpartition(a, sep):
+    """
+    Partition (split) each element around the right-most separator.
+
+    For each element in ``a``, split the element at the last
+    occurrence of ``sep``, and return a 3-tuple containing the part
+    before the separator, the separator itself, and the part after
+    the separator. If the separator is not found, the third item of
+    the tuple will contain the whole string, and the first and second
+    ones will be the empty string.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array
+    sep : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Separator to split each string element in ``a``.
+
+    Returns
+    -------
+    out : 3-tuple:
+        - array with ``StringDType``, ``bytes_`` or ``str_`` dtype with the
+          part before the separator
+        - array with ``StringDType``, ``bytes_`` or ``str_`` dtype with the
+          separator
+        - array with ``StringDType``, ``bytes_`` or ``str_`` dtype with the
+          part after the separator
+
+    See Also
+    --------
+    str.rpartition
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(['aAaAaA', '  aA  ', 'abBABba'])
+    >>> np.strings.rpartition(a, 'A')
+    (array(['aAaAa', '  a', 'abB'], dtype='<U5'),
+     array(['A', 'A', 'A'], dtype='<U1'),
+     array(['', '  ', 'Bba'], dtype='<U3'))
+
+    """
+    a = np.asanyarray(a)
+    sep = np.asanyarray(sep)
+
+    if np.result_type(a, sep).char == "T":
+        return _rpartition(a, sep)
+
+    sep = sep.astype(a.dtype, copy=False)
+    pos = _rfind_ufunc(a, sep, 0, MAX)
+    a_len = str_len(a)
+    sep_len = str_len(sep)
+
+    not_found = pos < 0
+    buffersizes1 = np.where(not_found, 0, pos)
+    buffersizes3 = np.where(not_found, a_len, a_len - pos - sep_len)
+
+    out_dtype = ",".join([f"{a.dtype.char}{n}" for n in (
+        buffersizes1.max(),
+        1 if np.all(not_found) else sep_len.max(),
+        buffersizes3.max(),
+    )])
+    shape = np.broadcast_shapes(a.shape, sep.shape)
+    out = np.empty_like(a, shape=shape, dtype=out_dtype)
+    return _rpartition_index(
+        a, sep, pos, out=(out["f0"], out["f1"], out["f2"]))
+
+
+def _translate_dispatcher(a, table, deletechars=None):
+    return (a,)
+
+
+@set_module("numpy.strings")
+@array_function_dispatch(_translate_dispatcher)
+def translate(a, table, deletechars=None):
+    """
+    For each element in `a`, return a copy of the string where all
+    characters occurring in the optional argument `deletechars` are
+    removed, and the remaining characters have been mapped through the
+    given translation table.
+
+    Calls :meth:`str.translate` element-wise.
+
+    Parameters
+    ----------
+    a : array-like, with `np.bytes_` or `np.str_` dtype
+
+    table : str of length 256
+
+    deletechars : str
+
+    Returns
+    -------
+    out : ndarray
+        Output array of str or unicode, depending on input type
+
+    See Also
+    --------
+    str.translate
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(['a1b c', '1bca', 'bca1'])
+    >>> table = a[0].maketrans('abc', '123')
+    >>> deletechars = ' '
+    >>> np.char.translate(a, table, deletechars)
+    array(['112 3', '1231', '2311'], dtype='<U5')
+
+    """
+    a_arr = np.asarray(a)
+    if issubclass(a_arr.dtype.type, np.str_):
+        return _vec_string(
+            a_arr, a_arr.dtype, 'translate', (table,))
+    else:
+        return _vec_string(
+            a_arr,
+            a_arr.dtype,
+            'translate',
+            [table] + _clean_args(deletechars)
+        )
+
+@set_module("numpy.strings")
+def slice(a, start=None, stop=None, step=None, /):
+    """
+    Slice the strings in `a` by slices specified by `start`, `stop`, `step`.
+    Like in the regular Python `slice` object, if only `start` is
+    specified then it is interpreted as the `stop`.
+
+    Parameters
+    ----------
+    a : array-like, with ``StringDType``, ``bytes_``, or ``str_`` dtype
+        Input array
+
+    start : None, an integer or an array of integers
+        The start of the slice, broadcasted to `a`'s shape
+
+    stop : None, an integer or an array of integers
+        The end of the slice, broadcasted to `a`'s shape
+
+    step : None, an integer or an array of integers
+        The step for the slice, broadcasted to `a`'s shape
+
+    Returns
+    -------
+    out : ndarray
+        Output array of ``StringDType``, ``bytes_`` or ``str_`` dtype,
+        depending on input type
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> a = np.array(['hello', 'world'])
+    >>> np.strings.slice(a, 2)
+    array(['he', 'wo'], dtype='<U5')
+
+    >>> np.strings.slice(a, 1, 5, 2)
+    array(['el', 'ol'], dtype='<U5')
+
+    One can specify different start/stop/step for different array entries:
+
+    >>> np.strings.slice(a, np.array([1, 2]), np.array([4, 5]))
+    array(['ell', 'rld'], dtype='<U5')
+
+    Negative slices have the same meaning as in regular Python:
+
+    >>> b = np.array(['hello world', 'γεια σου κόσμε', '你好世界', '👋 🌍'],
+    ...              dtype=np.dtypes.StringDType())
+    >>> np.strings.slice(b, -2)
+    array(['hello wor', 'γεια σου κόσ', '你好', '👋'], dtype=StringDType())
+
+    >>> np.strings.slice(b, [3, -10, 2, -3], [-1, -2, -1, 3])
+    array(['lo worl', ' σου κόσ', '世', '👋 🌍'], dtype=StringDType())
+
+    >>> np.strings.slice(b, None, None, -1)
+    array(['dlrow olleh', 'εμσόκ υοσ αιεγ', '界世好你', '🌍 👋'],
+          dtype=StringDType())
+
+    """
+    # Just like in the construction of a regular slice object, if only start
+    # is specified then start will become stop, see logic in slice_new.
+    if stop is None:
+        stop = start
+        start = None
+
+    # adjust start, stop, step to be integers, see logic in PySlice_Unpack
+    if step is None:
+        step = 1
+    step = np.asanyarray(step)
+    if not np.issubdtype(step.dtype, np.integer):
+        raise TypeError(f"unsupported type {step.dtype} for operand 'step'")
+    if np.any(step == 0):
+        raise ValueError("slice step cannot be zero")
+
+    if start is None:
+        start = np.where(step < 0, np.iinfo(np.intp).max, 0)
+
+    if stop is None:
+        stop = np.where(step < 0, np.iinfo(np.intp).min, np.iinfo(np.intp).max)
+
+    return _slice(a, start, stop, step)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/strings.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/strings.pyi
new file mode 100644
index 0000000..b187ce7
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/strings.pyi
@@ -0,0 +1,511 @@
+from typing import TypeAlias, overload
+
+import numpy as np
+from numpy._typing import NDArray, _AnyShape, _SupportsArray
+from numpy._typing import _ArrayLikeAnyString_co as UST_co
+from numpy._typing import _ArrayLikeBytes_co as S_co
+from numpy._typing import _ArrayLikeInt_co as i_co
+from numpy._typing import _ArrayLikeStr_co as U_co
+from numpy._typing import _ArrayLikeString_co as T_co
+
+__all__ = [
+    "add",
+    "capitalize",
+    "center",
+    "count",
+    "decode",
+    "encode",
+    "endswith",
+    "equal",
+    "expandtabs",
+    "find",
+    "greater",
+    "greater_equal",
+    "index",
+    "isalnum",
+    "isalpha",
+    "isdecimal",
+    "isdigit",
+    "islower",
+    "isnumeric",
+    "isspace",
+    "istitle",
+    "isupper",
+    "less",
+    "less_equal",
+    "ljust",
+    "lower",
+    "lstrip",
+    "mod",
+    "multiply",
+    "not_equal",
+    "partition",
+    "replace",
+    "rfind",
+    "rindex",
+    "rjust",
+    "rpartition",
+    "rstrip",
+    "startswith",
+    "str_len",
+    "strip",
+    "swapcase",
+    "title",
+    "translate",
+    "upper",
+    "zfill",
+    "slice",
+]
+
+_StringDTypeArray: TypeAlias = np.ndarray[_AnyShape, np.dtypes.StringDType]
+_StringDTypeSupportsArray: TypeAlias = _SupportsArray[np.dtypes.StringDType]
+_StringDTypeOrUnicodeArray: TypeAlias = np.ndarray[_AnyShape, np.dtype[np.str_]] | _StringDTypeArray
+
+@overload
+def equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def not_equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def not_equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def not_equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def greater_equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def greater_equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def greater_equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def less_equal(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def less_equal(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def less_equal(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def greater(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def greater(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def greater(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def less(x1: U_co, x2: U_co) -> NDArray[np.bool]: ...
+@overload
+def less(x1: S_co, x2: S_co) -> NDArray[np.bool]: ...
+@overload
+def less(x1: T_co, x2: T_co) -> NDArray[np.bool]: ...
+
+@overload
+def add(x1: U_co, x2: U_co) -> NDArray[np.str_]: ...
+@overload
+def add(x1: S_co, x2: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def add(x1: _StringDTypeSupportsArray, x2: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def add(x1: T_co, x2: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def multiply(a: U_co, i: i_co) -> NDArray[np.str_]: ...
+@overload
+def multiply(a: S_co, i: i_co) -> NDArray[np.bytes_]: ...
+@overload
+def multiply(a: _StringDTypeSupportsArray, i: i_co) -> _StringDTypeArray: ...
+@overload
+def multiply(a: T_co, i: i_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def mod(a: U_co, value: object) -> NDArray[np.str_]: ...
+@overload
+def mod(a: S_co, value: object) -> NDArray[np.bytes_]: ...
+@overload
+def mod(a: _StringDTypeSupportsArray, value: object) -> _StringDTypeArray: ...
+@overload
+def mod(a: T_co, value: object) -> _StringDTypeOrUnicodeArray: ...
+
+def isalpha(x: UST_co) -> NDArray[np.bool]: ...
+def isalnum(a: UST_co) -> NDArray[np.bool]: ...
+def isdigit(x: UST_co) -> NDArray[np.bool]: ...
+def isspace(x: UST_co) -> NDArray[np.bool]: ...
+def isdecimal(x: U_co | T_co) -> NDArray[np.bool]: ...
+def isnumeric(x: U_co | T_co) -> NDArray[np.bool]: ...
+def islower(a: UST_co) -> NDArray[np.bool]: ...
+def istitle(a: UST_co) -> NDArray[np.bool]: ...
+def isupper(a: UST_co) -> NDArray[np.bool]: ...
+
+def str_len(x: UST_co) -> NDArray[np.int_]: ...
+
+@overload
+def find(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def find(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def find(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+@overload
+def rfind(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def rfind(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def rfind(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+@overload
+def index(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def index(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def index(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+@overload
+def rindex(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def rindex(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def rindex(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+@overload
+def count(
+    a: U_co,
+    sub: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def count(
+    a: S_co,
+    sub: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+@overload
+def count(
+    a: T_co,
+    sub: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.int_]: ...
+
+@overload
+def startswith(
+    a: U_co,
+    prefix: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def startswith(
+    a: S_co,
+    prefix: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def startswith(
+    a: T_co,
+    prefix: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+
+@overload
+def endswith(
+    a: U_co,
+    suffix: U_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def endswith(
+    a: S_co,
+    suffix: S_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+@overload
+def endswith(
+    a: T_co,
+    suffix: T_co,
+    start: i_co = ...,
+    end: i_co | None = ...,
+) -> NDArray[np.bool]: ...
+
+def decode(
+    a: S_co,
+    encoding: str | None = None,
+    errors: str | None = None,
+) -> NDArray[np.str_]: ...
+def encode(
+    a: U_co | T_co,
+    encoding: str | None = None,
+    errors: str | None = None,
+) -> NDArray[np.bytes_]: ...
+
+@overload
+def expandtabs(a: U_co, tabsize: i_co = ...) -> NDArray[np.str_]: ...
+@overload
+def expandtabs(a: S_co, tabsize: i_co = ...) -> NDArray[np.bytes_]: ...
+@overload
+def expandtabs(a: _StringDTypeSupportsArray, tabsize: i_co = ...) -> _StringDTypeArray: ...
+@overload
+def expandtabs(a: T_co, tabsize: i_co = ...) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def center(a: U_co, width: i_co, fillchar: UST_co = " ") -> NDArray[np.str_]: ...
+@overload
+def center(a: S_co, width: i_co, fillchar: UST_co = " ") -> NDArray[np.bytes_]: ...
+@overload
+def center(a: _StringDTypeSupportsArray, width: i_co, fillchar: UST_co = " ") -> _StringDTypeArray: ...
+@overload
+def center(a: T_co, width: i_co, fillchar: UST_co = " ") -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def ljust(a: U_co, width: i_co, fillchar: UST_co = " ") -> NDArray[np.str_]: ...
+@overload
+def ljust(a: S_co, width: i_co, fillchar: UST_co = " ") -> NDArray[np.bytes_]: ...
+@overload
+def ljust(a: _StringDTypeSupportsArray, width: i_co, fillchar: UST_co = " ") -> _StringDTypeArray: ...
+@overload
+def ljust(a: T_co, width: i_co, fillchar: UST_co = " ") -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def rjust(a: U_co, width: i_co, fillchar: UST_co = " ") -> NDArray[np.str_]: ...
+@overload
+def rjust(a: S_co, width: i_co, fillchar: UST_co = " ") -> NDArray[np.bytes_]: ...
+@overload
+def rjust(a: _StringDTypeSupportsArray, width: i_co, fillchar: UST_co = " ") -> _StringDTypeArray: ...
+@overload
+def rjust(a: T_co, width: i_co, fillchar: UST_co = " ") -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def lstrip(a: U_co, chars: U_co | None = None) -> NDArray[np.str_]: ...
+@overload
+def lstrip(a: S_co, chars: S_co | None = None) -> NDArray[np.bytes_]: ...
+@overload
+def lstrip(a: _StringDTypeSupportsArray, chars: T_co | None = None) -> _StringDTypeArray: ...
+@overload
+def lstrip(a: T_co, chars: T_co | None = None) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def rstrip(a: U_co, chars: U_co | None = None) -> NDArray[np.str_]: ...
+@overload
+def rstrip(a: S_co, chars: S_co | None = None) -> NDArray[np.bytes_]: ...
+@overload
+def rstrip(a: _StringDTypeSupportsArray, chars: T_co | None = None) -> _StringDTypeArray: ...
+@overload
+def rstrip(a: T_co, chars: T_co | None = None) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def strip(a: U_co, chars: U_co | None = None) -> NDArray[np.str_]: ...
+@overload
+def strip(a: S_co, chars: S_co | None = None) -> NDArray[np.bytes_]: ...
+@overload
+def strip(a: _StringDTypeSupportsArray, chars: T_co | None = None) -> _StringDTypeArray: ...
+@overload
+def strip(a: T_co, chars: T_co | None = None) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def zfill(a: U_co, width: i_co) -> NDArray[np.str_]: ...
+@overload
+def zfill(a: S_co, width: i_co) -> NDArray[np.bytes_]: ...
+@overload
+def zfill(a: _StringDTypeSupportsArray, width: i_co) -> _StringDTypeArray: ...
+@overload
+def zfill(a: T_co, width: i_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def upper(a: U_co) -> NDArray[np.str_]: ...
+@overload
+def upper(a: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def upper(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def upper(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def lower(a: U_co) -> NDArray[np.str_]: ...
+@overload
+def lower(a: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def lower(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def lower(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def swapcase(a: U_co) -> NDArray[np.str_]: ...
+@overload
+def swapcase(a: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def swapcase(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def swapcase(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def capitalize(a: U_co) -> NDArray[np.str_]: ...
+@overload
+def capitalize(a: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def capitalize(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def capitalize(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def title(a: U_co) -> NDArray[np.str_]: ...
+@overload
+def title(a: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def title(a: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def title(a: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def replace(
+    a: U_co,
+    old: U_co,
+    new: U_co,
+    count: i_co = ...,
+) -> NDArray[np.str_]: ...
+@overload
+def replace(
+    a: S_co,
+    old: S_co,
+    new: S_co,
+    count: i_co = ...,
+) -> NDArray[np.bytes_]: ...
+@overload
+def replace(
+    a: _StringDTypeSupportsArray,
+    old: _StringDTypeSupportsArray,
+    new: _StringDTypeSupportsArray,
+    count: i_co = ...,
+) -> _StringDTypeArray: ...
+@overload
+def replace(
+    a: T_co,
+    old: T_co,
+    new: T_co,
+    count: i_co = ...,
+) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def partition(a: U_co, sep: U_co) -> NDArray[np.str_]: ...
+@overload
+def partition(a: S_co, sep: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def partition(a: _StringDTypeSupportsArray, sep: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def partition(a: T_co, sep: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def rpartition(a: U_co, sep: U_co) -> NDArray[np.str_]: ...
+@overload
+def rpartition(a: S_co, sep: S_co) -> NDArray[np.bytes_]: ...
+@overload
+def rpartition(a: _StringDTypeSupportsArray, sep: _StringDTypeSupportsArray) -> _StringDTypeArray: ...
+@overload
+def rpartition(a: T_co, sep: T_co) -> _StringDTypeOrUnicodeArray: ...
+
+@overload
+def translate(
+    a: U_co,
+    table: str,
+    deletechars: str | None = None,
+) -> NDArray[np.str_]: ...
+@overload
+def translate(
+    a: S_co,
+    table: str,
+    deletechars: str | None = None,
+) -> NDArray[np.bytes_]: ...
+@overload
+def translate(
+    a: _StringDTypeSupportsArray,
+    table: str,
+    deletechars: str | None = None,
+) -> _StringDTypeArray: ...
+@overload
+def translate(
+    a: T_co,
+    table: str,
+    deletechars: str | None = None,
+) -> _StringDTypeOrUnicodeArray: ...
+
+#
+@overload
+def slice(a: U_co, start: i_co | None = None, stop: i_co | None = None, step: i_co | None = None, /) -> NDArray[np.str_]: ...  # type: ignore[overload-overlap]
+@overload
+def slice(a: S_co, start: i_co | None = None, stop: i_co | None = None, step: i_co | None = None, /) -> NDArray[np.bytes_]: ...
+@overload
+def slice(
+    a: _StringDTypeSupportsArray, start: i_co | None = None, stop: i_co | None = None, step: i_co | None = None, /
+) -> _StringDTypeArray: ...
+@overload
+def slice(
+    a: T_co, start: i_co | None = None, stop: i_co | None = None, step: i_co | None = None, /
+) -> _StringDTypeOrUnicodeArray: ...
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/_locales.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/_locales.cpython-312.pyc
new file mode 100644
index 0000000..2ff2bc1
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/_locales.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/_natype.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/_natype.cpython-312.pyc
new file mode 100644
index 0000000..3c399d9
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/_natype.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test__exceptions.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test__exceptions.cpython-312.pyc
new file mode 100644
index 0000000..c699888
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test__exceptions.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_abc.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_abc.cpython-312.pyc
new file mode 100644
index 0000000..40e9375
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_abc.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_api.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_api.cpython-312.pyc
new file mode 100644
index 0000000..a58ff81
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_api.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_argparse.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_argparse.cpython-312.pyc
new file mode 100644
index 0000000..7719c19
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_argparse.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_array_api_info.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_array_api_info.cpython-312.pyc
new file mode 100644
index 0000000..51fb4f5
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_simd_module.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_simd_module.cpython-312.pyc
new file mode 100644
index 0000000..b05f5f9
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_simd_module.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_stringdtype.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_stringdtype.cpython-312.pyc
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index 0000000..5484abe
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_stringdtype.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_strings.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_strings.cpython-312.pyc
new file mode 100644
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+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_strings.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_ufunc.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_ufunc.cpython-312.pyc
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index 0000000..168a209
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+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_ufunc.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_umath.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_umath.cpython-312.pyc
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+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_umath.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_umath_accuracy.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_umath_accuracy.cpython-312.pyc
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+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_umath_accuracy.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_umath_complex.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_umath_complex.cpython-312.pyc
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--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_umath_complex.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_unicode.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_unicode.cpython-312.pyc
new file mode 100644
index 0000000..0fcf3c8
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/__pycache__/test_unicode.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/_locales.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/_locales.py
new file mode 100644
index 0000000..debda96
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/_locales.py
@@ -0,0 +1,72 @@
+"""Provide class for testing in French locale
+
+"""
+import locale
+import sys
+
+import pytest
+
+__ALL__ = ['CommaDecimalPointLocale']
+
+
+def find_comma_decimal_point_locale():
+    """See if platform has a decimal point as comma locale.
+
+    Find a locale that uses a comma instead of a period as the
+    decimal point.
+
+    Returns
+    -------
+    old_locale: str
+        Locale when the function was called.
+    new_locale: {str, None)
+        First French locale found, None if none found.
+
+    """
+    if sys.platform == 'win32':
+        locales = ['FRENCH']
+    else:
+        locales = ['fr_FR', 'fr_FR.UTF-8', 'fi_FI', 'fi_FI.UTF-8']
+
+    old_locale = locale.getlocale(locale.LC_NUMERIC)
+    new_locale = None
+    try:
+        for loc in locales:
+            try:
+                locale.setlocale(locale.LC_NUMERIC, loc)
+                new_locale = loc
+                break
+            except locale.Error:
+                pass
+    finally:
+        locale.setlocale(locale.LC_NUMERIC, locale=old_locale)
+    return old_locale, new_locale
+
+
+class CommaDecimalPointLocale:
+    """Sets LC_NUMERIC to a locale with comma as decimal point.
+
+    Classes derived from this class have setup and teardown methods that run
+    tests with locale.LC_NUMERIC set to a locale where commas (',') are used as
+    the decimal point instead of periods ('.'). On exit the locale is restored
+    to the initial locale. It also serves as context manager with the same
+    effect. If no such locale is available, the test is skipped.
+
+    """
+    (cur_locale, tst_locale) = find_comma_decimal_point_locale()
+
+    def setup_method(self):
+        if self.tst_locale is None:
+            pytest.skip("No French locale available")
+        locale.setlocale(locale.LC_NUMERIC, locale=self.tst_locale)
+
+    def teardown_method(self):
+        locale.setlocale(locale.LC_NUMERIC, locale=self.cur_locale)
+
+    def __enter__(self):
+        if self.tst_locale is None:
+            pytest.skip("No French locale available")
+        locale.setlocale(locale.LC_NUMERIC, locale=self.tst_locale)
+
+    def __exit__(self, type, value, traceback):
+        locale.setlocale(locale.LC_NUMERIC, locale=self.cur_locale)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/_natype.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/_natype.py
new file mode 100644
index 0000000..1c2175b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/_natype.py
@@ -0,0 +1,205 @@
+# Vendored implementation of pandas.NA, adapted from pandas/_libs/missing.pyx
+#
+# This is vendored to avoid adding pandas as a test dependency.
+
+__all__ = ["pd_NA"]
+
+import numbers
+
+import numpy as np
+
+
+def _create_binary_propagating_op(name, is_divmod=False):
+    is_cmp = name.strip("_") in ["eq", "ne", "le", "lt", "ge", "gt"]
+
+    def method(self, other):
+        if (
+            other is pd_NA
+            or isinstance(other, (str, bytes, numbers.Number, np.bool))
+            or (isinstance(other, np.ndarray) and not other.shape)
+        ):
+            # Need the other.shape clause to handle NumPy scalars,
+            # since we do a setitem on `out` below, which
+            # won't work for NumPy scalars.
+            if is_divmod:
+                return pd_NA, pd_NA
+            else:
+                return pd_NA
+
+        elif isinstance(other, np.ndarray):
+            out = np.empty(other.shape, dtype=object)
+            out[:] = pd_NA
+
+            if is_divmod:
+                return out, out.copy()
+            else:
+                return out
+
+        elif is_cmp and isinstance(other, (np.datetime64, np.timedelta64)):
+            return pd_NA
+
+        elif isinstance(other, np.datetime64):
+            if name in ["__sub__", "__rsub__"]:
+                return pd_NA
+
+        elif isinstance(other, np.timedelta64):
+            if name in ["__sub__", "__rsub__", "__add__", "__radd__"]:
+                return pd_NA
+
+        return NotImplemented
+
+    method.__name__ = name
+    return method
+
+
+def _create_unary_propagating_op(name: str):
+    def method(self):
+        return pd_NA
+
+    method.__name__ = name
+    return method
+
+
+class NAType:
+    def __repr__(self) -> str:
+        return "<NA>"
+
+    def __format__(self, format_spec) -> str:
+        try:
+            return self.__repr__().__format__(format_spec)
+        except ValueError:
+            return self.__repr__()
+
+    def __bool__(self):
+        raise TypeError("boolean value of NA is ambiguous")
+
+    def __hash__(self):
+        exponent = 31 if is_32bit else 61
+        return 2**exponent - 1
+
+    def __reduce__(self):
+        return "pd_NA"
+
+    # Binary arithmetic and comparison ops -> propagate
+
+    __add__ = _create_binary_propagating_op("__add__")
+    __radd__ = _create_binary_propagating_op("__radd__")
+    __sub__ = _create_binary_propagating_op("__sub__")
+    __rsub__ = _create_binary_propagating_op("__rsub__")
+    __mul__ = _create_binary_propagating_op("__mul__")
+    __rmul__ = _create_binary_propagating_op("__rmul__")
+    __matmul__ = _create_binary_propagating_op("__matmul__")
+    __rmatmul__ = _create_binary_propagating_op("__rmatmul__")
+    __truediv__ = _create_binary_propagating_op("__truediv__")
+    __rtruediv__ = _create_binary_propagating_op("__rtruediv__")
+    __floordiv__ = _create_binary_propagating_op("__floordiv__")
+    __rfloordiv__ = _create_binary_propagating_op("__rfloordiv__")
+    __mod__ = _create_binary_propagating_op("__mod__")
+    __rmod__ = _create_binary_propagating_op("__rmod__")
+    __divmod__ = _create_binary_propagating_op("__divmod__", is_divmod=True)
+    __rdivmod__ = _create_binary_propagating_op("__rdivmod__", is_divmod=True)
+    # __lshift__ and __rshift__ are not implemented
+
+    __eq__ = _create_binary_propagating_op("__eq__")
+    __ne__ = _create_binary_propagating_op("__ne__")
+    __le__ = _create_binary_propagating_op("__le__")
+    __lt__ = _create_binary_propagating_op("__lt__")
+    __gt__ = _create_binary_propagating_op("__gt__")
+    __ge__ = _create_binary_propagating_op("__ge__")
+
+    # Unary ops
+
+    __neg__ = _create_unary_propagating_op("__neg__")
+    __pos__ = _create_unary_propagating_op("__pos__")
+    __abs__ = _create_unary_propagating_op("__abs__")
+    __invert__ = _create_unary_propagating_op("__invert__")
+
+    # pow has special
+    def __pow__(self, other):
+        if other is pd_NA:
+            return pd_NA
+        elif isinstance(other, (numbers.Number, np.bool)):
+            if other == 0:
+                # returning positive is correct for +/- 0.
+                return type(other)(1)
+            else:
+                return pd_NA
+        elif util.is_array(other):
+            return np.where(other == 0, other.dtype.type(1), pd_NA)
+
+        return NotImplemented
+
+    def __rpow__(self, other):
+        if other is pd_NA:
+            return pd_NA
+        elif isinstance(other, (numbers.Number, np.bool)):
+            if other == 1:
+                return other
+            else:
+                return pd_NA
+        elif util.is_array(other):
+            return np.where(other == 1, other, pd_NA)
+        return NotImplemented
+
+    # Logical ops using Kleene logic
+
+    def __and__(self, other):
+        if other is False:
+            return False
+        elif other is True or other is pd_NA:
+            return pd_NA
+        return NotImplemented
+
+    __rand__ = __and__
+
+    def __or__(self, other):
+        if other is True:
+            return True
+        elif other is False or other is pd_NA:
+            return pd_NA
+        return NotImplemented
+
+    __ror__ = __or__
+
+    def __xor__(self, other):
+        if other is False or other is True or other is pd_NA:
+            return pd_NA
+        return NotImplemented
+
+    __rxor__ = __xor__
+
+    __array_priority__ = 1000
+    _HANDLED_TYPES = (np.ndarray, numbers.Number, str, np.bool)
+
+    def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+        types = self._HANDLED_TYPES + (NAType,)
+        for x in inputs:
+            if not isinstance(x, types):
+                return NotImplemented
+
+        if method != "__call__":
+            raise ValueError(f"ufunc method '{method}' not supported for NA")
+        result = maybe_dispatch_ufunc_to_dunder_op(
+            self, ufunc, method, *inputs, **kwargs
+        )
+        if result is NotImplemented:
+            # For a NumPy ufunc that's not a binop, like np.logaddexp
+            index = next(i for i, x in enumerate(inputs) if x is pd_NA)
+            result = np.broadcast_arrays(*inputs)[index]
+            if result.ndim == 0:
+                result = result.item()
+            if ufunc.nout > 1:
+                result = (pd_NA,) * ufunc.nout
+
+        return result
+
+
+pd_NA = NAType()
+
+
+def get_stringdtype_dtype(na_object, coerce=True):
+    # explicit is check for pd_NA because != with pd_NA returns pd_NA
+    if na_object is pd_NA or na_object != "unset":
+        return np.dtypes.StringDType(na_object=na_object, coerce=coerce)
+    else:
+        return np.dtypes.StringDType(coerce=coerce)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/astype_copy.pkl b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/astype_copy.pkl
new file mode 100644
index 0000000..7397c97
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/astype_copy.pkl
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/generate_umath_validation_data.cpp b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/generate_umath_validation_data.cpp
new file mode 100644
index 0000000..88ff45e
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/generate_umath_validation_data.cpp
@@ -0,0 +1,170 @@
+#include <algorithm>
+#include <fstream>
+#include <iostream>
+#include <math.h>
+#include <random>
+#include <cstdio>
+#include <ctime>
+#include <vector>
+
+struct ufunc {
+    std::string name;
+    double (*f32func)(double);
+    long double (*f64func)(long double);
+    float f32ulp;
+    float f64ulp;
+};
+
+template <typename T>
+T
+RandomFloat(T a, T b)
+{
+    T random = ((T)rand()) / (T)RAND_MAX;
+    T diff = b - a;
+    T r = random * diff;
+    return a + r;
+}
+
+template <typename T>
+void
+append_random_array(std::vector<T> &arr, T min, T max, size_t N)
+{
+    for (size_t ii = 0; ii < N; ++ii)
+        arr.emplace_back(RandomFloat<T>(min, max));
+}
+
+template <typename T1, typename T2>
+std::vector<T1>
+computeTrueVal(const std::vector<T1> &in, T2 (*mathfunc)(T2))
+{
+    std::vector<T1> out;
+    for (T1 elem : in) {
+        T2 elem_d = (T2)elem;
+        T1 out_elem = (T1)mathfunc(elem_d);
+        out.emplace_back(out_elem);
+    }
+    return out;
+}
+
+/*
+ * FP range:
+ * [-inf, -maxflt, -1., -minflt, -minden, 0., minden, minflt, 1., maxflt, inf]
+ */
+
+#define MINDEN std::numeric_limits<T>::denorm_min()
+#define MINFLT std::numeric_limits<T>::min()
+#define MAXFLT std::numeric_limits<T>::max()
+#define INF std::numeric_limits<T>::infinity()
+#define qNAN std::numeric_limits<T>::quiet_NaN()
+#define sNAN std::numeric_limits<T>::signaling_NaN()
+
+template <typename T>
+std::vector<T>
+generate_input_vector(std::string func)
+{
+    std::vector<T> input = {MINDEN,  -MINDEN, MINFLT, -MINFLT, MAXFLT,
+                            -MAXFLT, INF,     -INF,   qNAN,    sNAN,
+                            -1.0,    1.0,     0.0,    -0.0};
+
+    // [-1.0, 1.0]
+    if ((func == "arcsin") || (func == "arccos") || (func == "arctanh")) {
+        append_random_array<T>(input, -1.0, 1.0, 700);
+    }
+    // (0.0, INF]
+    else if ((func == "log2") || (func == "log10")) {
+        append_random_array<T>(input, 0.0, 1.0, 200);
+        append_random_array<T>(input, MINDEN, MINFLT, 200);
+        append_random_array<T>(input, MINFLT, 1.0, 200);
+        append_random_array<T>(input, 1.0, MAXFLT, 200);
+    }
+    // (-1.0, INF]
+    else if (func == "log1p") {
+        append_random_array<T>(input, -1.0, 1.0, 200);
+        append_random_array<T>(input, -MINFLT, -MINDEN, 100);
+        append_random_array<T>(input, -1.0, -MINFLT, 100);
+        append_random_array<T>(input, MINDEN, MINFLT, 100);
+        append_random_array<T>(input, MINFLT, 1.0, 100);
+        append_random_array<T>(input, 1.0, MAXFLT, 100);
+    }
+    // [1.0, INF]
+    else if (func == "arccosh") {
+        append_random_array<T>(input, 1.0, 2.0, 400);
+        append_random_array<T>(input, 2.0, MAXFLT, 300);
+    }
+    // [-INF, INF]
+    else {
+        append_random_array<T>(input, -1.0, 1.0, 100);
+        append_random_array<T>(input, MINDEN, MINFLT, 100);
+        append_random_array<T>(input, -MINFLT, -MINDEN, 100);
+        append_random_array<T>(input, MINFLT, 1.0, 100);
+        append_random_array<T>(input, -1.0, -MINFLT, 100);
+        append_random_array<T>(input, 1.0, MAXFLT, 100);
+        append_random_array<T>(input, -MAXFLT, -100.0, 100);
+    }
+
+    std::random_shuffle(input.begin(), input.end());
+    return input;
+}
+
+int
+main()
+{
+    srand(42);
+    std::vector<struct ufunc> umathfunc = {
+            {"sin", sin, sin, 1.49, 1.00},
+            {"cos", cos, cos, 1.49, 1.00},
+            {"tan", tan, tan, 3.91, 1.00},
+            {"arcsin", asin, asin, 3.12, 1.00},
+            {"arccos", acos, acos, 2.1, 1.00},
+            {"arctan", atan, atan, 2.3, 1.00},
+            {"sinh", sinh, sinh, 1.55, 1.00},
+            {"cosh", cosh, cosh, 2.48, 1.00},
+            {"tanh", tanh, tanh, 1.38, 2.00},
+            {"arcsinh", asinh, asinh, 1.01, 1.00},
+            {"arccosh", acosh, acosh, 1.16, 1.00},
+            {"arctanh", atanh, atanh, 1.45, 1.00},
+            {"cbrt", cbrt, cbrt, 1.94, 2.00},
+            //{"exp",exp,exp,3.76,1.00},
+            {"exp2", exp2, exp2, 1.01, 1.00},
+            {"expm1", expm1, expm1, 2.62, 1.00},
+            //{"log",log,log,1.84,1.00},
+            {"log10", log10, log10, 3.5, 1.00},
+            {"log1p", log1p, log1p, 1.96, 1.0},
+            {"log2", log2, log2, 2.12, 1.00},
+    };
+
+    for (int ii = 0; ii < umathfunc.size(); ++ii) {
+        // ignore sin/cos
+        if ((umathfunc[ii].name != "sin") && (umathfunc[ii].name != "cos")) {
+            std::string fileName =
+                    "umath-validation-set-" + umathfunc[ii].name + ".csv";
+            std::ofstream txtOut;
+            txtOut.open(fileName, std::ofstream::trunc);
+            txtOut << "dtype,input,output,ulperrortol" << std::endl;
+
+            // Single Precision
+            auto f32in = generate_input_vector<float>(umathfunc[ii].name);
+            auto f32out = computeTrueVal<float, double>(f32in,
+                                                        umathfunc[ii].f32func);
+            for (int jj = 0; jj < f32in.size(); ++jj) {
+                txtOut << "np.float32" << std::hex << ",0x"
+                       << *reinterpret_cast<uint32_t *>(&f32in[jj]) << ",0x"
+                       << *reinterpret_cast<uint32_t *>(&f32out[jj]) << ","
+                       << ceil(umathfunc[ii].f32ulp) << std::endl;
+            }
+
+            // Double Precision
+            auto f64in = generate_input_vector<double>(umathfunc[ii].name);
+            auto f64out = computeTrueVal<double, long double>(
+                    f64in, umathfunc[ii].f64func);
+            for (int jj = 0; jj < f64in.size(); ++jj) {
+                txtOut << "np.float64" << std::hex << ",0x"
+                       << *reinterpret_cast<uint64_t *>(&f64in[jj]) << ",0x"
+                       << *reinterpret_cast<uint64_t *>(&f64out[jj]) << ","
+                       << ceil(umathfunc[ii].f64ulp) << std::endl;
+            }
+            txtOut.close();
+        }
+    }
+    return 0;
+}
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/recarray_from_file.fits b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/recarray_from_file.fits
new file mode 100644
index 0000000..ca48ee8
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/recarray_from_file.fits
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-README.txt b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-README.txt
new file mode 100644
index 0000000..cfc9e41
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-README.txt
@@ -0,0 +1,15 @@
+Steps to validate transcendental functions:
+1) Add a file 'umath-validation-set-<ufuncname>.txt', where ufuncname is name of
+   the function in NumPy you want to validate
+2) The file should contain 4 columns: dtype,input,expected output,ulperror
+    a. dtype: one of np.float16, np.float32, np.float64
+    b. input: floating point input to ufunc in hex. Example: 0x414570a4
+       represents 12.340000152587890625
+    c. expected output: floating point output for the corresponding input in hex.
+       This should be computed using a high(er) precision library and then rounded to
+       same format as the input.
+    d. ulperror: expected maximum ulp error of the function. This
+       should be same across all rows of the same dtype. Otherwise, the function is
+       tested for the maximum ulp error among all entries of that dtype.
+3) Add file umath-validation-set-<ufuncname>.txt to the test file test_umath_accuracy.py
+   which will then validate your ufunc.
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arccos.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arccos.csv
new file mode 100644
index 0000000..82c8595
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arccos.csv
@@ -0,0 +1,1429 @@
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arccosh.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arccosh.csv
new file mode 100644
index 0000000..1b3eda4
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arccosh.csv
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arcsinh.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arcsinh.csv
new file mode 100644
index 0000000..9eedb1a
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new file mode 100644
index 0000000..c03e144
--- /dev/null
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arctanh.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arctanh.csv
new file mode 100644
index 0000000..68ecaab
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-arctanh.csv
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-cbrt.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-cbrt.csv
new file mode 100644
index 0000000..ad141cb
--- /dev/null
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+np.float64,0xffe6c1fc93ad83f8,0xd541fe6a6a716756,2
+np.float64,0xbfd7b9c1d32f7384,0xbfe6fcdae563d638,2
+np.float64,0x800e1bea06fc37d4,0xaaa354c0bf61449c,2
+np.float64,0xbfd78f097aaf1e12,0xbfe6ef068329bdf4,2
+np.float64,0x7fea6a400874d47f,0x5542e905978ad722,2
+np.float64,0x8008b4377cb1686f,0xaaa074c87eee29f9,2
+np.float64,0x8002f3fb8d45e7f8,0xaa96f47ac539b614,2
+np.float64,0xbfcf2b3fd13e5680,0xbfe3fb91c0cc66ad,2
+np.float64,0xffecca2f5279945e,0xd54375f361075927,2
+np.float64,0x7ff0000000000000,0x7ff0000000000000,2
+np.float64,0x7f84d5a5a029ab4a,0x552178d1d4e8640e,2
+np.float64,0x3fea8a4b64351497,0x3fee10c332440eb2,2
+np.float64,0x800fe01ac1dfc036,0xaaa41b34d91a4bee,2
+np.float64,0x3fc0b3d8872167b1,0x3fe03b178d354f8d,2
+np.float64,0x5ee8b0acbdd17,0x2a9cf69f2e317729,2
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+np.float64,0x49663f9c92cc9,0x2a9a95e0affe5108,2
+np.float64,0x7fd9b87e79b370fc,0x553dc0b5cff3dc7d,2
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+np.float64,0x7fcc246bcb3848d7,0x5538557309449bba,2
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+np.float64,0xd2a6e995a54dd,0x2aa2e3e9c0fdd6c0,2
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+np.float64,0x3fe858f1c470b1e4,0x3fed36ab90557d89,2
+np.float64,0x800e857278fd0ae5,0xaaa3847d13220545,2
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+np.float64,0xffeb4500f1768a01,0xd5431cab828e254a,2
+np.float64,0xffccca8fc6399520,0xd53884f8b505e79e,2
+np.float64,0xffeee9406b7dd280,0xd543ed6d27a1a899,2
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+np.float64,0xe6b54005cd6a8,0x2aa378c25938dfda,2
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-cos.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-cos.csv
new file mode 100644
index 0000000..258ae48
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-cos.csv
@@ -0,0 +1,1375 @@
+dtype,input,output,ulperrortol
+## +ve denormals ##
+np.float32,0x004b4716,0x3f800000,2
+np.float32,0x007b2490,0x3f800000,2
+np.float32,0x007c99fa,0x3f800000,2
+np.float32,0x00734a0c,0x3f800000,2
+np.float32,0x0070de24,0x3f800000,2
+np.float32,0x007fffff,0x3f800000,2
+np.float32,0x00000001,0x3f800000,2
+## -ve denormals ##
+np.float32,0x80495d65,0x3f800000,2
+np.float32,0x806894f6,0x3f800000,2
+np.float32,0x80555a76,0x3f800000,2
+np.float32,0x804e1fb8,0x3f800000,2
+np.float32,0x80687de9,0x3f800000,2
+np.float32,0x807fffff,0x3f800000,2
+np.float32,0x80000001,0x3f800000,2
+## +/-0.0f, +/-FLT_MIN +/-FLT_MAX ##
+np.float32,0x00000000,0x3f800000,2
+np.float32,0x80000000,0x3f800000,2
+np.float32,0x00800000,0x3f800000,2
+np.float32,0x80800000,0x3f800000,2
+## 1.00f + 0x00000001 ##
+np.float32,0x3f800000,0x3f0a5140,2
+np.float32,0x3f800001,0x3f0a513f,2
+np.float32,0x3f800002,0x3f0a513d,2
+np.float32,0xc090a8b0,0xbe4332ce,2
+np.float32,0x41ce3184,0x3f4d1de1,2
+np.float32,0xc1d85848,0xbeaa8980,2
+np.float32,0x402b8820,0xbf653aa3,2
+np.float32,0x42b4e454,0xbf4a338b,2
+np.float32,0x42a67a60,0x3c58202e,2
+np.float32,0x41d92388,0xbed987c7,2
+np.float32,0x422dd66c,0x3f5dcab3,2
+np.float32,0xc28f5be6,0xbf5688d8,2
+np.float32,0x41ab2674,0xbf53aa3b,2
+np.float32,0x3f490fdb,0x3f3504f3,2
+np.float32,0xbf490fdb,0x3f3504f3,2
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-cosh.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-cosh.csv
new file mode 100644
index 0000000..af14d84
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-cosh.csv
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-exp.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-exp.csv
new file mode 100644
index 0000000..7c5ef3b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-exp.csv
@@ -0,0 +1,412 @@
+dtype,input,output,ulperrortol
+## +ve denormals ##
+np.float32,0x004b4716,0x3f800000,3
+np.float32,0x007b2490,0x3f800000,3
+np.float32,0x007c99fa,0x3f800000,3
+np.float32,0x00734a0c,0x3f800000,3
+np.float32,0x0070de24,0x3f800000,3
+np.float32,0x00495d65,0x3f800000,3
+np.float32,0x006894f6,0x3f800000,3
+np.float32,0x00555a76,0x3f800000,3
+np.float32,0x004e1fb8,0x3f800000,3
+np.float32,0x00687de9,0x3f800000,3
+## -ve denormals ##
+np.float32,0x805b59af,0x3f800000,3
+np.float32,0x807ed8ed,0x3f800000,3
+np.float32,0x807142ad,0x3f800000,3
+np.float32,0x80772002,0x3f800000,3
+np.float32,0x8062abcb,0x3f800000,3
+np.float32,0x8045e31c,0x3f800000,3
+np.float32,0x805f01c2,0x3f800000,3
+np.float32,0x80506432,0x3f800000,3
+np.float32,0x8060089d,0x3f800000,3
+np.float32,0x8071292f,0x3f800000,3
+## floats that output a denormal ##
+np.float32,0xc2cf3fc1,0x00000001,3
+np.float32,0xc2c79726,0x00000021,3
+np.float32,0xc2cb295d,0x00000005,3
+np.float32,0xc2b49e6b,0x00068c4c,3
+np.float32,0xc2ca8116,0x00000008,3
+np.float32,0xc2c23f82,0x000001d7,3
+np.float32,0xc2cb69c0,0x00000005,3
+np.float32,0xc2cc1f4d,0x00000003,3
+np.float32,0xc2ae094e,0x00affc4c,3
+np.float32,0xc2c86c44,0x00000015,3
+## random floats between -87.0f and 88.0f ##
+np.float32,0x4030d7e0,0x417d9a05,3
+np.float32,0x426f60e8,0x6aa1be2c,3
+np.float32,0x41a1b220,0x4e0efc11,3
+np.float32,0xc20cc722,0x26159da7,3
+np.float32,0x41c492bc,0x512ec79d,3
+np.float32,0x40980210,0x42e73a0e,3
+np.float32,0xbf1f7b80,0x3f094de3,3
+np.float32,0x42a678a4,0x7b87a383,3
+np.float32,0xc20f3cfd,0x25a1c304,3
+np.float32,0x423ff34c,0x6216467f,3
+np.float32,0x00000000,0x3f800000,3
+## floats that cause an overflow ##
+np.float32,0x7f06d8c1,0x7f800000,3
+np.float32,0x7f451912,0x7f800000,3
+np.float32,0x7ecceac3,0x7f800000,3
+np.float32,0x7f643b45,0x7f800000,3
+np.float32,0x7e910ea0,0x7f800000,3
+np.float32,0x7eb4756b,0x7f800000,3
+np.float32,0x7f4ec708,0x7f800000,3
+np.float32,0x7f6b4551,0x7f800000,3
+np.float32,0x7d8edbda,0x7f800000,3
+np.float32,0x7f730718,0x7f800000,3
+np.float32,0x42b17217,0x7f7fff84,3
+np.float32,0x42b17218,0x7f800000,3
+np.float32,0x42b17219,0x7f800000,3
+np.float32,0xfef2b0bc,0x00000000,3
+np.float32,0xff69f83e,0x00000000,3
+np.float32,0xff4ecb12,0x00000000,3
+np.float32,0xfeac6d86,0x00000000,3
+np.float32,0xfde0cdb8,0x00000000,3
+np.float32,0xff26aef4,0x00000000,3
+np.float32,0xff6f9277,0x00000000,3
+np.float32,0xff7adfc4,0x00000000,3
+np.float32,0xff0ad40e,0x00000000,3
+np.float32,0xff6fd8f3,0x00000000,3
+np.float32,0xc2cff1b4,0x00000001,3
+np.float32,0xc2cff1b5,0x00000000,3
+np.float32,0xc2cff1b6,0x00000000,3
+np.float32,0x7f800000,0x7f800000,3
+np.float32,0xff800000,0x00000000,3
+np.float32,0x4292f27c,0x7480000a,3
+np.float32,0x42a920be,0x7c7fff94,3
+np.float32,0x41c214c9,0x50ffffd9,3
+np.float32,0x41abe686,0x4effffd9,3
+np.float32,0x4287db5a,0x707fffd3,3
+np.float32,0x41902cbb,0x4c800078,3
+np.float32,0x42609466,0x67ffffeb,3
+np.float32,0x41a65af5,0x4e7fffd1,3
+np.float32,0x417f13ff,0x4affffc9,3
+np.float32,0x426d0e6c,0x6a3504f2,3
+np.float32,0x41bc8934,0x507fff51,3
+np.float32,0x42a7bdde,0x7c0000d6,3
+np.float32,0x4120cf66,0x46b504f6,3
+np.float32,0x4244da8f,0x62ffff1a,3
+np.float32,0x41a0cf69,0x4e000034,3
+np.float32,0x41cd2bec,0x52000005,3
+np.float32,0x42893e41,0x7100009e,3
+np.float32,0x41b437e1,0x4fb50502,3
+np.float32,0x41d8430f,0x5300001d,3
+np.float32,0x4244da92,0x62ffffda,3
+np.float32,0x41a0cf63,0x4dffffa9,3
+np.float32,0x3eb17218,0x3fb504f3,3
+np.float32,0x428729e8,0x703504dc,3
+np.float32,0x41a0cf67,0x4e000014,3
+np.float32,0x4252b77d,0x65800011,3
+np.float32,0x41902cb9,0x4c800058,3
+np.float32,0x42a0cf67,0x79800052,3
+np.float32,0x4152b77b,0x48ffffe9,3
+np.float32,0x41265af3,0x46ffffc8,3
+np.float32,0x42187e0b,0x5affff9a,3
+np.float32,0xc0d2b77c,0x3ab504f6,3
+np.float32,0xc283b2ac,0x10000072,3
+np.float32,0xc1cff1b4,0x2cb504f5,3
+np.float32,0xc05dce9e,0x3d000000,3
+np.float32,0xc28ec9d2,0x0bfffea5,3
+np.float32,0xc23c893a,0x1d7fffde,3
+np.float32,0xc2a920c0,0x027fff6c,3
+np.float32,0xc1f9886f,0x2900002b,3
+np.float32,0xc2c42920,0x000000b5,3
+np.float32,0xc2893e41,0x0dfffec5,3
+np.float32,0xc2c4da93,0x00000080,3
+np.float32,0xc17f1401,0x3400000c,3
+np.float32,0xc1902cb6,0x327fffaf,3
+np.float32,0xc27c4e3b,0x11ffffc5,3
+np.float32,0xc268e5c5,0x157ffe9d,3
+np.float32,0xc2b4e953,0x0005a826,3
+np.float32,0xc287db5a,0x0e800016,3
+np.float32,0xc207db5a,0x2700000b,3
+np.float32,0xc2b2d4fe,0x000ffff1,3
+np.float32,0xc268e5c0,0x157fffdd,3
+np.float32,0xc22920bd,0x2100003b,3
+np.float32,0xc2902caf,0x0b80011e,3
+np.float32,0xc1902cba,0x327fff2f,3
+np.float32,0xc2ca6625,0x00000008,3
+np.float32,0xc280ece8,0x10fffeb5,3
+np.float32,0xc2918f94,0x0b0000ea,3
+np.float32,0xc29b43d5,0x077ffffc,3
+np.float32,0xc1e61ff7,0x2ab504f5,3
+np.float32,0xc2867878,0x0effff15,3
+np.float32,0xc2a2324a,0x04fffff4,3
+#float64
+## near zero ##
+np.float64,0x8000000000000000,0x3ff0000000000000,1
+np.float64,0x8010000000000000,0x3ff0000000000000,1
+np.float64,0x8000000000000001,0x3ff0000000000000,1
+np.float64,0x8360000000000000,0x3ff0000000000000,1
+np.float64,0x9a70000000000000,0x3ff0000000000000,1
+np.float64,0xb9b0000000000000,0x3ff0000000000000,1
+np.float64,0xb810000000000000,0x3ff0000000000000,1
+np.float64,0xbc30000000000000,0x3ff0000000000000,1
+np.float64,0xb6a0000000000000,0x3ff0000000000000,1
+np.float64,0x0000000000000000,0x3ff0000000000000,1
+np.float64,0x0010000000000000,0x3ff0000000000000,1
+np.float64,0x0000000000000001,0x3ff0000000000000,1
+np.float64,0x0360000000000000,0x3ff0000000000000,1
+np.float64,0x1a70000000000000,0x3ff0000000000000,1
+np.float64,0x3c30000000000000,0x3ff0000000000000,1
+np.float64,0x36a0000000000000,0x3ff0000000000000,1
+np.float64,0x39b0000000000000,0x3ff0000000000000,1
+np.float64,0x3810000000000000,0x3ff0000000000000,1
+## underflow ##
+np.float64,0xc0c6276800000000,0x0000000000000000,1
+np.float64,0xc0c62d918ce2421d,0x0000000000000000,1
+np.float64,0xc0c62d918ce2421e,0x0000000000000000,1
+np.float64,0xc0c62d91a0000000,0x0000000000000000,1
+np.float64,0xc0c62d9180000000,0x0000000000000000,1
+np.float64,0xc0c62dea45ee3e06,0x0000000000000000,1
+np.float64,0xc0c62dea45ee3e07,0x0000000000000000,1
+np.float64,0xc0c62dea40000000,0x0000000000000000,1
+np.float64,0xc0c62dea60000000,0x0000000000000000,1
+np.float64,0xc0875f1120000000,0x0000000000000000,1
+np.float64,0xc0875f113c30b1c8,0x0000000000000000,1
+np.float64,0xc0875f1140000000,0x0000000000000000,1
+np.float64,0xc093480000000000,0x0000000000000000,1
+np.float64,0xffefffffffffffff,0x0000000000000000,1
+np.float64,0xc7efffffe0000000,0x0000000000000000,1
+## overflow ##
+np.float64,0x40862e52fefa39ef,0x7ff0000000000000,1
+np.float64,0x40872e42fefa39ef,0x7ff0000000000000,1
+## +/- INF, +/- NAN ##
+np.float64,0x7ff0000000000000,0x7ff0000000000000,1
+np.float64,0xfff0000000000000,0x0000000000000000,1
+np.float64,0x7ff8000000000000,0x7ff8000000000000,1
+np.float64,0xfff8000000000000,0xfff8000000000000,1
+## output denormal ##
+np.float64,0xc087438520000000,0x0000000000000001,1
+np.float64,0xc08743853f2f4461,0x0000000000000001,1
+np.float64,0xc08743853f2f4460,0x0000000000000001,1
+np.float64,0xc087438540000000,0x0000000000000001,1
+## between -745.13321910 and 709.78271289 ##
+np.float64,0xbff760cd14774bd9,0x3fcdb14ced00ceb6,1
+np.float64,0xbff760cd20000000,0x3fcdb14cd7993879,1
+np.float64,0xbff760cd00000000,0x3fcdb14d12fbd264,1
+np.float64,0xc07f1cf360000000,0x130c1b369af14fda,1
+np.float64,0xbeb0000000000000,0x3feffffe00001000,1
+np.float64,0xbd70000000000000,0x3fefffffffffe000,1
+np.float64,0xc084fd46e5c84952,0x0360000000000139,1
+np.float64,0xc084fd46e5c84953,0x035ffffffffffe71,1
+np.float64,0xc084fd46e0000000,0x0360000b9096d32c,1
+np.float64,0xc084fd4700000000,0x035fff9721d12104,1
+np.float64,0xc086232bc0000000,0x0010003af5e64635,1
+np.float64,0xc086232bdd7abcd2,0x001000000000007c,1
+np.float64,0xc086232bdd7abcd3,0x000ffffffffffe7c,1
+np.float64,0xc086232be0000000,0x000ffffaf57a6fc9,1
+np.float64,0xc086233920000000,0x000fe590e3b45eb0,1
+np.float64,0xc086233938000000,0x000fe56133493c57,1
+np.float64,0xc086233940000000,0x000fe5514deffbbc,1
+np.float64,0xc086234c98000000,0x000fbf1024c32ccb,1
+np.float64,0xc086234ca0000000,0x000fbf0065bae78d,1
+np.float64,0xc086234c80000000,0x000fbf3f623a7724,1
+np.float64,0xc086234ec0000000,0x000fbad237c846f9,1
+np.float64,0xc086234ec8000000,0x000fbac27cfdec97,1
+np.float64,0xc086234ee0000000,0x000fba934cfd3dc2,1
+np.float64,0xc086234ef0000000,0x000fba73d7f618d9,1
+np.float64,0xc086234f00000000,0x000fba54632dddc0,1
+np.float64,0xc0862356e0000000,0x000faae0945b761a,1
+np.float64,0xc0862356f0000000,0x000faac13eb9a310,1
+np.float64,0xc086235700000000,0x000faaa1e9567b0a,1
+np.float64,0xc086236020000000,0x000f98cd75c11ed7,1
+np.float64,0xc086236ca0000000,0x000f8081b4d93f89,1
+np.float64,0xc086236cb0000000,0x000f8062b3f4d6c5,1
+np.float64,0xc086236cc0000000,0x000f8043b34e6f8c,1
+np.float64,0xc086238d98000000,0x000f41220d9b0d2c,1
+np.float64,0xc086238da0000000,0x000f4112cc80a01f,1
+np.float64,0xc086238d80000000,0x000f414fd145db5b,1
+np.float64,0xc08624fd00000000,0x000cbfce8ea1e6c4,1
+np.float64,0xc086256080000000,0x000c250747fcd46e,1
+np.float64,0xc08626c480000000,0x000a34f4bd975193,1
+np.float64,0xbf50000000000000,0x3feff800ffeaac00,1
+np.float64,0xbe10000000000000,0x3fefffffff800000,1
+np.float64,0xbcd0000000000000,0x3feffffffffffff8,1
+np.float64,0xc055d589e0000000,0x38100004bf94f63e,1
+np.float64,0xc055d58a00000000,0x380ffff97f292ce8,1
+np.float64,0xbfd962d900000000,0x3fe585a4b00110e1,1
+np.float64,0x3ff4bed280000000,0x400d411e7a58a303,1
+np.float64,0x3fff0b3620000000,0x401bd7737ffffcf3,1
+np.float64,0x3ff0000000000000,0x4005bf0a8b145769,1
+np.float64,0x3eb0000000000000,0x3ff0000100000800,1
+np.float64,0x3d70000000000000,0x3ff0000000001000,1
+np.float64,0x40862e42e0000000,0x7fefff841808287f,1
+np.float64,0x40862e42fefa39ef,0x7fefffffffffff2a,1
+np.float64,0x40862e0000000000,0x7feef85a11e73f2d,1
+np.float64,0x4000000000000000,0x401d8e64b8d4ddae,1
+np.float64,0x4009242920000000,0x40372a52c383a488,1
+np.float64,0x4049000000000000,0x44719103e4080b45,1
+np.float64,0x4008000000000000,0x403415e5bf6fb106,1
+np.float64,0x3f50000000000000,0x3ff00400800aab55,1
+np.float64,0x3e10000000000000,0x3ff0000000400000,1
+np.float64,0x3cd0000000000000,0x3ff0000000000004,1
+np.float64,0x40562e40a0000000,0x47effed088821c3f,1
+np.float64,0x40562e42e0000000,0x47effff082e6c7ff,1
+np.float64,0x40562e4300000000,0x47f00000417184b8,1
+np.float64,0x3fe8000000000000,0x4000ef9db467dcf8,1
+np.float64,0x402b12e8d4f33589,0x412718f68c71a6fe,1
+np.float64,0x402b12e8d4f3358a,0x412718f68c71a70a,1
+np.float64,0x402b12e8c0000000,0x412718f59a7f472e,1
+np.float64,0x402b12e8e0000000,0x412718f70c0eac62,1
+##use 1th entry
+np.float64,0x40631659AE147CB4,0x4db3a95025a4890f,1
+np.float64,0xC061B87D2E85A4E2,0x332640c8e2de2c51,1
+np.float64,0x405A4A50BE243AF4,0x496a45e4b7f0339a,1
+np.float64,0xC0839898B98EC5C6,0x0764027828830df4,1
+#use 2th entry
+np.float64,0xC072428C44B6537C,0x2596ade838b96f3e,1
+np.float64,0xC053057C5E1AE9BF,0x3912c8fad18fdadf,1
+np.float64,0x407E89C78328BAA3,0x6bfe35d5b9a1a194,1
+np.float64,0x4083501B6DD87112,0x77a855503a38924e,1
+#use 3th entry
+np.float64,0x40832C6195F24540,0x7741e73c80e5eb2f,1
+np.float64,0xC083D4CD557C2EC9,0x06b61727c2d2508e,1
+np.float64,0x400C48F5F67C99BD,0x404128820f02b92e,1
+np.float64,0x4056E36D9B2DF26A,0x4830f52ff34a8242,1
+#use 4th entry
+np.float64,0x4080FF700D8CBD06,0x70fa70df9bc30f20,1
+np.float64,0x406C276D39E53328,0x543eb8e20a8f4741,1
+np.float64,0xC070D6159BBD8716,0x27a4a0548c904a75,1
+np.float64,0xC052EBCF8ED61F83,0x391c0e92368d15e4,1
+#use 5th entry
+np.float64,0xC061F892A8AC5FBE,0x32f807a89efd3869,1
+np.float64,0x4021D885D2DBA085,0x40bd4dc86d3e3270,1
+np.float64,0x40767AEEEE7D4FCF,0x605e22851ee2afb7,1
+np.float64,0xC0757C5D75D08C80,0x20f0751599b992a2,1
+#use 6th entry
+np.float64,0x405ACF7A284C4CE3,0x499a4e0b7a27027c,1
+np.float64,0xC085A6C9E80D7AF5,0x0175914009d62ec2,1
+np.float64,0xC07E4C02F86F1DAE,0x1439269b29a9231e,1
+np.float64,0x4080D80F9691CC87,0x7088a6cdafb041de,1
+#use 7th entry
+np.float64,0x407FDFD84FBA0AC1,0x6deb1ae6f9bc4767,1
+np.float64,0x40630C06A1A2213D,0x4dac7a9d51a838b7,1
+np.float64,0x40685FDB30BB8B4F,0x5183f5cc2cac9e79,1
+np.float64,0x408045A2208F77F4,0x6ee299e08e2aa2f0,1
+#use 8th entry
+np.float64,0xC08104E391F5078B,0x0ed397b7cbfbd230,1
+np.float64,0xC031501CAEFAE395,0x3e6040fd1ea35085,1
+np.float64,0xC079229124F6247C,0x1babf4f923306b1e,1
+np.float64,0x407FB65F44600435,0x6db03beaf2512b8a,1
+#use 9th entry
+np.float64,0xC07EDEE8E8E8A5AC,0x136536cec9cbef48,1
+np.float64,0x4072BB4086099A14,0x5af4d3c3008b56cc,1
+np.float64,0x4050442A2EC42CB4,0x45cd393bd8fad357,1
+np.float64,0xC06AC28FB3D419B4,0x2ca1b9d3437df85f,1
+#use 10th entry
+np.float64,0x40567FC6F0A68076,0x480c977fd5f3122e,1
+np.float64,0x40620A2F7EDA59BB,0x4cf278e96f4ce4d7,1
+np.float64,0xC085044707CD557C,0x034aad6c968a045a,1
+np.float64,0xC07374EA5AC516AA,0x23dd6afdc03e83d5,1
+#use 11th entry
+np.float64,0x4073CC95332619C1,0x5c804b1498bbaa54,1
+np.float64,0xC0799FEBBE257F31,0x1af6a954c43b87d2,1
+np.float64,0x408159F19EA424F6,0x7200858efcbfc84d,1
+np.float64,0x404A81F6F24C0792,0x44b664a07ce5bbfa,1
+#use 12th entry
+np.float64,0x40295FF1EFB9A741,0x4113c0e74c52d7b0,1
+np.float64,0x4073975F4CC411DA,0x5c32be40b4fec2c1,1
+np.float64,0x406E9DE52E82A77E,0x56049c9a3f1ae089,1
+np.float64,0x40748C2F52560ED9,0x5d93bc14fd4cd23b,1
+#use 13th entry
+np.float64,0x4062A553CDC4D04C,0x4d6266bfde301318,1
+np.float64,0xC079EC1D63598AB7,0x1a88cb184dab224c,1
+np.float64,0xC0725C1CB3167427,0x25725b46f8a081f6,1
+np.float64,0x407888771D9B45F9,0x6353b1ec6bd7ce80,1
+#use 14th entry
+np.float64,0xC082CBA03AA89807,0x09b383723831ce56,1
+np.float64,0xC083A8961BB67DD7,0x0735b118d5275552,1
+np.float64,0xC076BC6ECA12E7E3,0x1f2222679eaef615,1
+np.float64,0xC072752503AA1A5B,0x254eb832242c77e1,1
+#use 15th entry
+np.float64,0xC058800792125DEC,0x371882372a0b48d4,1
+np.float64,0x4082909FD863E81C,0x7580d5f386920142,1
+np.float64,0xC071616F8FB534F9,0x26dbe20ef64a412b,1
+np.float64,0x406D1AB571CAA747,0x54ee0d55cb38ac20,1
+#use 16th entry
+np.float64,0x406956428B7DAD09,0x52358682c271237f,1
+np.float64,0xC07EFC2D9D17B621,0x133b3e77c27a4d45,1
+np.float64,0xC08469BAC5BA3CCA,0x050863e5f42cc52f,1
+np.float64,0x407189D9626386A5,0x593cb1c0b3b5c1d3,1
+#use 17th entry
+np.float64,0x4077E652E3DEB8C6,0x6269a10dcbd3c752,1
+np.float64,0x407674C97DB06878,0x605485dcc2426ec2,1
+np.float64,0xC07CE9969CF4268D,0x16386cf8996669f2,1
+np.float64,0x40780EE32D5847C4,0x62a436bd1abe108d,1
+#use 18th entry
+np.float64,0x4076C3AA5E1E8DA1,0x60c62f56a5e72e24,1
+np.float64,0xC0730AFC7239B9BE,0x24758ead095cec1e,1
+np.float64,0xC085CC2B9C420DDB,0x0109cdaa2e5694c1,1
+np.float64,0x406D0765CB6D7AA4,0x54e06f8dd91bd945,1
+#use 19th entry
+np.float64,0xC082D011F3B495E7,0x09a6647661d279c2,1
+np.float64,0xC072826AF8F6AFBC,0x253acd3cd224507e,1
+np.float64,0x404EB9C4810CEA09,0x457933dbf07e8133,1
+np.float64,0x408284FBC97C58CE,0x755f6eb234aa4b98,1
+#use 20th entry
+np.float64,0x40856008CF6EDC63,0x7d9c0b3c03f4f73c,1
+np.float64,0xC077CB2E9F013B17,0x1d9b3d3a166a55db,1
+np.float64,0xC0479CA3C20AD057,0x3bad40e081555b99,1
+np.float64,0x40844CD31107332A,0x7a821d70aea478e2,1
+#use 21th entry
+np.float64,0xC07C8FCC0BFCC844,0x16ba1cc8c539d19b,1
+np.float64,0xC085C4E9A3ABA488,0x011ff675ba1a2217,1
+np.float64,0x4074D538B32966E5,0x5dfd9d78043c6ad9,1
+np.float64,0xC0630CA16902AD46,0x3231a446074cede6,1
+#use 22th entry
+np.float64,0xC06C826733D7D0B7,0x2b5f1078314d41e1,1
+np.float64,0xC0520DF55B2B907F,0x396c13a6ce8e833e,1
+np.float64,0xC080712072B0F437,0x107eae02d11d98ea,1
+np.float64,0x40528A6150E19EFB,0x469fdabda02228c5,1
+#use 23th entry
+np.float64,0xC07B1D74B6586451,0x18d1253883ae3b48,1
+np.float64,0x4045AFD7867DAEC0,0x43d7d634fc4c5d98,1
+np.float64,0xC07A08B91F9ED3E2,0x1a60973e6397fc37,1
+np.float64,0x407B3ECF0AE21C8C,0x673e03e9d98d7235,1
+#use 24th entry
+np.float64,0xC078AEB6F30CEABF,0x1c530b93ab54a1b3,1
+np.float64,0x4084495006A41672,0x7a775b6dc7e63064,1
+np.float64,0x40830B1C0EBF95DD,0x76e1e6eed77cfb89,1
+np.float64,0x407D93E8F33D8470,0x6a9adbc9e1e4f1e5,1
+#use 25th entry
+np.float64,0x4066B11A09EFD9E8,0x504dd528065c28a7,1
+np.float64,0x408545823723AEEB,0x7d504a9b1844f594,1
+np.float64,0xC068C711F2CA3362,0x2e104f3496ea118e,1
+np.float64,0x407F317FCC3CA873,0x6cf0732c9948ebf4,1
+#use 26th entry
+np.float64,0x407AFB3EBA2ED50F,0x66dc28a129c868d5,1
+np.float64,0xC075377037708ADE,0x21531a329f3d793e,1
+np.float64,0xC07C30066A1F3246,0x174448baa16ded2b,1
+np.float64,0xC06689A75DE2ABD3,0x2fad70662fae230b,1
+#use 27th entry
+np.float64,0x4081514E9FCCF1E0,0x71e673b9efd15f44,1
+np.float64,0xC0762C710AF68460,0x1ff1ed7d8947fe43,1
+np.float64,0xC0468102FF70D9C4,0x3be0c3a8ff3419a3,1
+np.float64,0xC07EA4CEEF02A83E,0x13b908f085102c61,1
+#use 28th entry
+np.float64,0xC06290B04AE823C4,0x328a83da3c2e3351,1
+np.float64,0xC0770EB1D1C395FB,0x1eab281c1f1db5fe,1
+np.float64,0xC06F5D4D838A5BAE,0x29500ea32fb474ea,1
+np.float64,0x40723B3133B54C5D,0x5a3c82c7c3a2b848,1
+#use 29th entry
+np.float64,0x4085E6454CE3B4AA,0x7f20319b9638d06a,1
+np.float64,0x408389F2A0585D4B,0x7850667c58aab3d0,1
+np.float64,0xC0382798F9C8AE69,0x3dc1c79fe8739d6d,1
+np.float64,0xC08299D827608418,0x0a4335f76cdbaeb5,1
+#use 30th entry
+np.float64,0xC06F3DED43301BF1,0x2965670ae46750a8,1
+np.float64,0xC070CAF6BDD577D9,0x27b4aa4ffdd29981,1
+np.float64,0x4078529AD4B2D9F2,0x6305c12755d5e0a6,1
+np.float64,0xC055B14E75A31B96,0x381c2eda6d111e5d,1
+#use 31th entry
+np.float64,0x407B13EE414FA931,0x6700772c7544564d,1
+np.float64,0x407EAFDE9DE3EC54,0x6c346a0e49724a3c,1
+np.float64,0xC08362F398B9530D,0x07ffeddbadf980cb,1
+np.float64,0x407E865CDD9EEB86,0x6bf866cac5e0d126,1
+#use 32th entry
+np.float64,0x407FB62DBC794C86,0x6db009f708ac62cb,1
+np.float64,0xC063D0BAA68CDDDE,0x31a3b2a51ce50430,1
+np.float64,0xC05E7706A2231394,0x34f24bead6fab5c9,1
+np.float64,0x4083E3A06FDE444E,0x79527b7a386d1937,1
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-exp2.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-exp2.csv
new file mode 100644
index 0000000..4e0a63e
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-exp2.csv
@@ -0,0 +1,1429 @@
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-expm1.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-expm1.csv
new file mode 100644
index 0000000..dcbc7cd
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-expm1.csv
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log.csv
new file mode 100644
index 0000000..b8f6b08
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log.csv
@@ -0,0 +1,271 @@
+dtype,input,output,ulperrortol
+## +ve denormals ##
+np.float32,0x004b4716,0xc2afbc1b,4
+np.float32,0x007b2490,0xc2aec01e,4
+np.float32,0x007c99fa,0xc2aeba17,4
+np.float32,0x00734a0c,0xc2aee1dc,4
+np.float32,0x0070de24,0xc2aeecba,4
+np.float32,0x007fffff,0xc2aeac50,4
+np.float32,0x00000001,0xc2ce8ed0,4
+## -ve denormals ##
+np.float32,0x80495d65,0xffc00000,4
+np.float32,0x806894f6,0xffc00000,4
+np.float32,0x80555a76,0xffc00000,4
+np.float32,0x804e1fb8,0xffc00000,4
+np.float32,0x80687de9,0xffc00000,4
+np.float32,0x807fffff,0xffc00000,4
+np.float32,0x80000001,0xffc00000,4
+## +/-0.0f, +/-FLT_MIN +/-FLT_MAX ##
+np.float32,0x00000000,0xff800000,4
+np.float32,0x80000000,0xff800000,4
+np.float32,0x7f7fffff,0x42b17218,4
+np.float32,0x80800000,0xffc00000,4
+np.float32,0xff7fffff,0xffc00000,4
+## 1.00f + 0x00000001 ##
+np.float32,0x3f800000,0x00000000,4
+np.float32,0x3f800001,0x33ffffff,4
+np.float32,0x3f800002,0x347ffffe,4
+np.float32,0x3f7fffff,0xb3800000,4
+np.float32,0x3f7ffffe,0xb4000000,4
+np.float32,0x3f7ffffd,0xb4400001,4
+np.float32,0x402df853,0x3f7ffffe,4
+np.float32,0x402df854,0x3f7fffff,4
+np.float32,0x402df855,0x3f800000,4
+np.float32,0x402df856,0x3f800001,4
+np.float32,0x3ebc5ab0,0xbf800001,4
+np.float32,0x3ebc5ab1,0xbf800000,4
+np.float32,0x3ebc5ab2,0xbf800000,4
+np.float32,0x3ebc5ab3,0xbf7ffffe,4
+np.float32,0x423ef575,0x407768ab,4
+np.float32,0x427b8c61,0x408485dd,4
+np.float32,0x4211e9ee,0x406630b0,4
+np.float32,0x424d5c41,0x407c0fed,4
+np.float32,0x42be722a,0x4091cc91,4
+np.float32,0x42b73d30,0x4090908b,4
+np.float32,0x427e48e2,0x4084de7f,4
+np.float32,0x428f759b,0x4088bba3,4
+np.float32,0x41629069,0x4029a0cc,4
+np.float32,0x4272c99d,0x40836379,4
+np.float32,0x4d1b7458,0x4197463d,4
+np.float32,0x4f10c594,0x41ace2b2,4
+np.float32,0x4ea397c2,0x41a85171,4
+np.float32,0x4fefa9d1,0x41b6769c,4
+np.float32,0x4ebac6ab,0x41a960dc,4
+np.float32,0x4f6efb42,0x41b0e535,4
+np.float32,0x4e9ab8e7,0x41a7df44,4
+np.float32,0x4e81b5d1,0x41a67625,4
+np.float32,0x5014d9f2,0x41b832bd,4
+np.float32,0x4f02175c,0x41ac07b8,4
+np.float32,0x7f034f89,0x42b01c47,4
+np.float32,0x7f56d00e,0x42b11849,4
+np.float32,0x7f1cd5f6,0x42b0773a,4
+np.float32,0x7e979174,0x42af02d7,4
+np.float32,0x7f23369f,0x42b08ba2,4
+np.float32,0x7f0637ae,0x42b0277d,4
+np.float32,0x7efcb6e8,0x42b00897,4
+np.float32,0x7f7907c8,0x42b163f6,4
+np.float32,0x7e95c4c2,0x42aefcba,4
+np.float32,0x7f4577b2,0x42b0ed2d,4
+np.float32,0x3f49c92e,0xbe73ae84,4
+np.float32,0x3f4a23d1,0xbe71e2f8,4
+np.float32,0x3f4abb67,0xbe6ee430,4
+np.float32,0x3f48169a,0xbe7c5532,4
+np.float32,0x3f47f5fa,0xbe7cfc37,4
+np.float32,0x3f488309,0xbe7a2ad8,4
+np.float32,0x3f479df4,0xbe7ebf5f,4
+np.float32,0x3f47cfff,0xbe7dbec9,4
+np.float32,0x3f496704,0xbe75a125,4
+np.float32,0x3f478ee8,0xbe7f0c92,4
+np.float32,0x3f4a763b,0xbe7041ce,4
+np.float32,0x3f47a108,0xbe7eaf94,4
+np.float32,0x3f48136c,0xbe7c6578,4
+np.float32,0x3f481c17,0xbe7c391c,4
+np.float32,0x3f47cd28,0xbe7dcd56,4
+np.float32,0x3f478be8,0xbe7f1bf7,4
+np.float32,0x3f4c1f8e,0xbe67e367,4
+np.float32,0x3f489b0c,0xbe79b03f,4
+np.float32,0x3f4934cf,0xbe76a08a,4
+np.float32,0x3f4954df,0xbe75fd6a,4
+np.float32,0x3f47a3f5,0xbe7ea093,4
+np.float32,0x3f4ba4fc,0xbe6a4b02,4
+np.float32,0x3f47a0e1,0xbe7eb05c,4
+np.float32,0x3f48c30a,0xbe78e42f,4
+np.float32,0x3f48cab8,0xbe78bd05,4
+np.float32,0x3f4b0569,0xbe6d6ea4,4
+np.float32,0x3f47de32,0xbe7d7607,4
+np.float32,0x3f477328,0xbe7f9b00,4
+np.float32,0x3f496dab,0xbe757f52,4
+np.float32,0x3f47662c,0xbe7fddac,4
+np.float32,0x3f48ddd8,0xbe785b80,4
+np.float32,0x3f481866,0xbe7c4bff,4
+np.float32,0x3f48b119,0xbe793fb6,4
+np.float32,0x3f48c7e8,0xbe78cb5c,4
+np.float32,0x3f4985f6,0xbe7503da,4
+np.float32,0x3f483fdf,0xbe7b8212,4
+np.float32,0x3f4b1c76,0xbe6cfa67,4
+np.float32,0x3f480b2e,0xbe7c8fa8,4
+np.float32,0x3f48745f,0xbe7a75bf,4
+np.float32,0x3f485bda,0xbe7af308,4
+np.float32,0x3f47a660,0xbe7e942c,4
+np.float32,0x3f47d4d5,0xbe7da600,4
+np.float32,0x3f4b0a26,0xbe6d56be,4
+np.float32,0x3f4a4883,0xbe712924,4
+np.float32,0x3f4769e7,0xbe7fca84,4
+np.float32,0x3f499702,0xbe74ad3f,4
+np.float32,0x3f494ab1,0xbe763131,4
+np.float32,0x3f476b69,0xbe7fc2c6,4
+np.float32,0x3f4884e8,0xbe7a214a,4
+np.float32,0x3f486945,0xbe7aae76,4
+#float64
+## +ve denormal ##
+np.float64,0x0000000000000001,0xc0874385446d71c3,1
+np.float64,0x0001000000000000,0xc086395a2079b70c,1
+np.float64,0x000fffffffffffff,0xc086232bdd7abcd2,1
+np.float64,0x0007ad63e2168cb6,0xc086290bc0b2980f,1
+## -ve denormal ##
+np.float64,0x8000000000000001,0xfff8000000000001,1
+np.float64,0x8001000000000000,0xfff8000000000001,1
+np.float64,0x800fffffffffffff,0xfff8000000000001,1
+np.float64,0x8007ad63e2168cb6,0xfff8000000000001,1
+## +/-0.0f, MAX, MIN##
+np.float64,0x0000000000000000,0xfff0000000000000,1
+np.float64,0x8000000000000000,0xfff0000000000000,1
+np.float64,0x7fefffffffffffff,0x40862e42fefa39ef,1
+np.float64,0xffefffffffffffff,0xfff8000000000001,1
+## near 1.0f ##
+np.float64,0x3ff0000000000000,0x0000000000000000,1
+np.float64,0x3fe8000000000000,0xbfd269621134db92,1
+np.float64,0x3ff0000000000001,0x3cafffffffffffff,1
+np.float64,0x3ff0000020000000,0x3e7fffffe000002b,1
+np.float64,0x3ff0000000000001,0x3cafffffffffffff,1
+np.float64,0x3fefffffe0000000,0xbe70000008000005,1
+np.float64,0x3fefffffffffffff,0xbca0000000000000,1
+## random numbers ##
+np.float64,0x02500186f3d9da56,0xc0855b8abf135773,1
+np.float64,0x09200815a3951173,0xc082ff1ad7131bdc,1
+np.float64,0x0da029623b0243d4,0xc0816fc994695bb5,1
+np.float64,0x48703b8ac483a382,0x40579213a313490b,1
+np.float64,0x09207b74c87c9860,0xc082fee20ff349ef,1
+np.float64,0x62c077698e8df947,0x407821c996d110f0,1
+np.float64,0x2350b45e87c3cfb0,0xc073d6b16b51d072,1
+np.float64,0x3990a23f9ff2b623,0xc051aa60eadd8c61,1
+np.float64,0x0d011386a116c348,0xc081a6cc7ea3b8fb,1
+np.float64,0x1fe0f0303ebe273a,0xc0763870b78a81ca,1
+np.float64,0x0cd1260121d387da,0xc081b7668d61a9d1,1
+np.float64,0x1e6135a8f581d422,0xc077425ac10f08c2,1
+np.float64,0x622168db5fe52d30,0x4077b3c669b9fadb,1
+np.float64,0x69f188e1ec6d1718,0x407d1e2f18c63889,1
+np.float64,0x3aa1bf1d9c4dd1a3,0xc04d682e24bde479,1
+np.float64,0x6c81c4011ce4f683,0x407ee5190e8a8e6a,1
+np.float64,0x2191fa55aa5a5095,0xc0750c0c318b5e2d,1
+np.float64,0x32a1f602a32bf360,0xc06270caa493fc17,1
+np.float64,0x16023c90ba93249b,0xc07d0f88e0801638,1
+np.float64,0x1c525fe6d71fa9ff,0xc078af49c66a5d63,1
+np.float64,0x1a927675815d65b7,0xc079e5bdd7fe376e,1
+np.float64,0x41227b8fe70da028,0x402aa0c9f9a84c71,1
+np.float64,0x4962bb6e853fe87d,0x405a34aa04c83747,1
+np.float64,0x23d2cda00b26b5a4,0xc0737c13a06d00ea,1
+np.float64,0x2d13083fd62987fa,0xc06a25055aeb474e,1
+np.float64,0x10e31e4c9b4579a1,0xc0804e181929418e,1
+np.float64,0x26d3247d556a86a9,0xc0716774171da7e8,1
+np.float64,0x6603379398d0d4ac,0x407a64f51f8a887b,1
+np.float64,0x02d38af17d9442ba,0xc0852d955ac9dd68,1
+np.float64,0x6a2382b4818dd967,0x407d4129d688e5d4,1
+np.float64,0x2ee3c403c79b3934,0xc067a091fefaf8b6,1
+np.float64,0x6493a699acdbf1a4,0x4079663c8602bfc5,1
+np.float64,0x1c8413c4f0de3100,0xc0788c99697059b6,1
+np.float64,0x4573f1ed350d9622,0x404e9bd1e4c08920,1
+np.float64,0x2f34265c9200b69c,0xc067310cfea4e986,1
+np.float64,0x19b43e65fa22029b,0xc07a7f8877de22d6,1
+np.float64,0x0af48ab7925ed6bc,0xc0825c4fbc0e5ade,1
+np.float64,0x4fa49699cad82542,0x4065c76d2a318235,1
+np.float64,0x7204a15e56ade492,0x40815bb87484dffb,1
+np.float64,0x4734aa08a230982d,0x40542a4bf7a361a9,1
+np.float64,0x1ae4ed296c2fd749,0xc079ac4921f20abb,1
+np.float64,0x472514ea4370289c,0x4053ff372bd8f18f,1
+np.float64,0x53a54b3f73820430,0x406b5411fc5f2e33,1
+np.float64,0x64754de5a15684fa,0x407951592e99a5ab,1
+np.float64,0x69358e279868a7c3,0x407c9c671a882c31,1
+np.float64,0x284579ec61215945,0xc0706688e55f0927,1
+np.float64,0x68b5c58806447adc,0x407c43d6f4eff760,1
+np.float64,0x1945a83f98b0e65d,0xc07acc15eeb032cc,1
+np.float64,0x0fc5eb98a16578bf,0xc080b0d02eddca0e,1
+np.float64,0x6a75e208f5784250,0x407d7a7383bf8f05,1
+np.float64,0x0fe63a029c47645d,0xc080a59ca1e98866,1
+np.float64,0x37963ac53f065510,0xc057236281f7bdb6,1
+np.float64,0x135661bb07067ff7,0xc07ee924930c21e4,1
+np.float64,0x4b4699469d458422,0x405f73843756e887,1
+np.float64,0x1a66d73e4bf4881b,0xc07a039ba1c63adf,1
+np.float64,0x12a6b9b119a7da59,0xc07f62e49c6431f3,1
+np.float64,0x24c719aa8fd1bdb5,0xc072d26da4bf84d3,1
+np.float64,0x0fa6ff524ffef314,0xc080bb8514662e77,1
+np.float64,0x1db751d66fdd4a9a,0xc077b77cb50d7c92,1
+np.float64,0x4947374c516da82c,0x4059e9acfc7105bf,1
+np.float64,0x1b1771ab98f3afc8,0xc07989326b8e1f66,1
+np.float64,0x25e78805baac8070,0xc0720a818e6ef080,1
+np.float64,0x4bd7a148225d3687,0x406082d004ea3ee7,1
+np.float64,0x53d7d6b2bbbda00a,0x406b9a398967cbd5,1
+np.float64,0x6997fb9f4e1c685f,0x407ce0a703413eba,1
+np.float64,0x069802c2ff71b951,0xc083df39bf7acddc,1
+np.float64,0x4d683ac9890f66d8,0x4062ae21d8c2acf0,1
+np.float64,0x5a2825863ec14f4c,0x40722d718d549552,1
+np.float64,0x0398799a88f4db80,0xc084e93dab8e2158,1
+np.float64,0x5ed87a8b77e135a5,0x40756d7051777b33,1
+np.float64,0x5828cd6d79b9bede,0x4070cafb22fc6ca1,1
+np.float64,0x7b18ba2a5ec6f068,0x408481386b3ed6fe,1
+np.float64,0x4938fd60922198fe,0x4059c206b762ea7e,1
+np.float64,0x31b8f44fcdd1a46e,0xc063b2faa8b6434e,1
+np.float64,0x5729341c0d918464,0x407019cac0c4a7d7,1
+np.float64,0x13595e9228ee878e,0xc07ee7235a7d8088,1
+np.float64,0x17698b0dc9dd4135,0xc07c1627e3a5ad5f,1
+np.float64,0x63b977c283abb0cc,0x4078cf1ec6ed65be,1
+np.float64,0x7349cc0d4dc16943,0x4081cc697ce4cb53,1
+np.float64,0x4e49a80b732fb28d,0x4063e67e3c5cbe90,1
+np.float64,0x07ba14b848a8ae02,0xc0837ac032a094e0,1
+np.float64,0x3da9f17b691bfddc,0xc03929c25366acda,1
+np.float64,0x02ea39aa6c3ac007,0xc08525af6f21e1c4,1
+np.float64,0x3a6a42f04ed9563d,0xc04e98e825dca46b,1
+np.float64,0x1afa877cd7900be7,0xc0799d6648cb34a9,1
+np.float64,0x58ea986649e052c6,0x4071512e939ad790,1
+np.float64,0x691abbc04647f536,0x407c89aaae0fcb83,1
+np.float64,0x43aabc5063e6f284,0x4044b45d18106fd2,1
+np.float64,0x488b003c893e0bea,0x4057df012a2dafbe,1
+np.float64,0x77eb076ed67caee5,0x40836720de94769e,1
+np.float64,0x5c1b46974aba46f4,0x40738731ba256007,1
+np.float64,0x1a5b29ecb5d3c261,0xc07a0becc77040d6,1
+np.float64,0x5d8b6ccf868c6032,0x4074865c1865e2db,1
+np.float64,0x4cfb6690b4aaf5af,0x406216cd8c7e8ddb,1
+np.float64,0x76cbd8eb5c5fc39e,0x4083038dc66d682b,1
+np.float64,0x28bbd1fec5012814,0xc07014c2dd1b9711,1
+np.float64,0x33dc1b3a4fd6bf7a,0xc060bd0756e07d8a,1
+np.float64,0x52bbe89b37de99f3,0x406a10041aa7d343,1
+np.float64,0x07bc479d15eb2dd3,0xc0837a1a6e3a3b61,1
+np.float64,0x18fc5275711a901d,0xc07aff3e9d62bc93,1
+np.float64,0x114c9758e247dc71,0xc080299a7cf15b05,1
+np.float64,0x25ac8f6d60755148,0xc07233c4c0c511d4,1
+np.float64,0x260cae2bb9e9fd7e,0xc071f128c7e82eac,1
+np.float64,0x572ccdfe0241de82,0x40701bedc84bb504,1
+np.float64,0x0ddcef6c8d41f5ee,0xc0815a7e16d07084,1
+np.float64,0x6dad1d59c988af68,0x407fb4a0bc0142b1,1
+np.float64,0x025d200580d8b6d1,0xc08556c0bc32b1b2,1
+np.float64,0x7aad344b6aa74c18,0x40845bbc453f22be,1
+np.float64,0x5b5d9d6ad9d14429,0x4073036d2d21f382,1
+np.float64,0x49cd8d8dcdf19954,0x405b5c034f5c7353,1
+np.float64,0x63edb9483335c1e6,0x4078f2dd21378786,1
+np.float64,0x7b1dd64c9d2c26bd,0x408482b922017bc9,1
+np.float64,0x782e13e0b574be5f,0x40837e2a0090a5ad,1
+np.float64,0x592dfe18b9d6db2f,0x40717f777fbcb1ec,1
+np.float64,0x654e3232ac60d72c,0x4079e71a95a70446,1
+np.float64,0x7b8e42ad22091456,0x4084a9a6f1e61722,1
+np.float64,0x570e88dfd5860ae6,0x407006ae6c0d137a,1
+np.float64,0x294e98346cb98ef1,0xc06f5edaac12bd44,1
+np.float64,0x1adeaa4ab792e642,0xc079b1431d5e2633,1
+np.float64,0x7b6ead3377529ac8,0x40849eabc8c7683c,1
+np.float64,0x2b8eedae8a9b2928,0xc06c400054deef11,1
+np.float64,0x65defb45b2dcf660,0x407a4b53f181c05a,1
+np.float64,0x1baf582d475e7701,0xc07920bcad4a502c,1
+np.float64,0x461f39cf05a0f15a,0x405126368f984fa1,1
+np.float64,0x7e5f6f5dcfff005b,0x4085a37d610439b4,1
+np.float64,0x136f66e4d09bd662,0xc07ed8a2719f2511,1
+np.float64,0x65afd8983fb6ca1f,0x407a2a7f48bf7fc1,1
+np.float64,0x572fa7f95ed22319,0x40701d706cf82e6f,1
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log10.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log10.csv
new file mode 100644
index 0000000..c765777
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log10.csv
@@ -0,0 +1,1629 @@
+dtype,input,output,ulperrortol
+np.float32,0x3f6fd5c8,0xbce80e8e,4
+np.float32,0x3ea4ab17,0xbefc3deb,4
+np.float32,0x3e87a133,0xbf13b0b7,4
+np.float32,0x3f0d9069,0xbe83bb19,4
+np.float32,0x3f7b9269,0xbbf84f47,4
+np.float32,0x3f7a9ffa,0xbc16fd97,4
+np.float32,0x7f535d34,0x4219cb66,4
+np.float32,0x3e79ad7c,0xbf1ce857,4
+np.float32,0x7e8bfd3b,0x4217dfe9,4
+np.float32,0x3f2d2ee9,0xbe2dcec6,4
+np.float32,0x572e04,0xc21862e4,4
+np.float32,0x7f36f8,0xc217bad5,4
+np.float32,0x3f7982fb,0xbc36aaed,4
+np.float32,0x45b019,0xc218c67c,4
+np.float32,0x3f521c46,0xbdafb3e3,4
+np.float32,0x80000001,0x7fc00000,4
+np.float32,0x3f336c81,0xbe1e107f,4
+np.float32,0x3eac92d7,0xbef1d0bb,4
+np.float32,0x47bdfc,0xc218b990,4
+np.float32,0x7f2d94c8,0x421973d1,4
+np.float32,0x7d53ff8d,0x4214fbb6,4
+np.float32,0x3f581e4e,0xbd96a079,4
+np.float32,0x7ddaf20d,0x42163e4e,4
+np.float32,0x3f341d3c,0xbe1c5b4c,4
+np.float32,0x7ef04ba9,0x4218d032,4
+np.float32,0x620ed2,0xc2182e99,4
+np.float32,0x507850,0xc2188682,4
+np.float32,0x7d08f9,0xc217c284,4
+np.float32,0x7f0cf2aa,0x42191734,4
+np.float32,0x3f109a17,0xbe7e04fe,4
+np.float32,0x7f426152,0x4219a625,4
+np.float32,0x7f32d5a3,0x42198113,4
+np.float32,0x2e14b2,0xc2197e6f,4
+np.float32,0x3a5acd,0xc219156a,4
+np.float32,0x50a565,0xc2188589,4
+np.float32,0x5b751c,0xc2184d97,4
+np.float32,0x7e4149f6,0x42173b22,4
+np.float32,0x3dc34bf9,0xbf82a42a,4
+np.float32,0x3d12bc28,0xbfb910d6,4
+np.float32,0x7ebd2584,0x421865c1,4
+np.float32,0x7f6b3375,0x4219faeb,4
+np.float32,0x7fa00000,0x7fe00000,4
+np.float32,0x3f35fe7d,0xbe17bd33,4
+np.float32,0x7db45c87,0x4215e818,4
+np.float32,0x3efff366,0xbe9a2b8d,4
+np.float32,0x3eb331d0,0xbee971a3,4
+np.float32,0x3f259d5f,0xbe41ae2e,4
+np.float32,0x3eab85ec,0xbef32c4a,4
+np.float32,0x7f194b8a,0x42193c8c,4
+np.float32,0x3f11a614,0xbe7acfc7,4
+np.float32,0x5b17,0xc221f16b,4
+np.float32,0x3f33dadc,0xbe1cff4d,4
+np.float32,0x3cda1506,0xbfc9920f,4
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log1p.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log1p.csv
new file mode 100644
index 0000000..094e052
--- /dev/null
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log2.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-log2.csv
new file mode 100644
index 0000000..26921ef
--- /dev/null
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-sin.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-sin.csv
new file mode 100644
index 0000000..03e76ff
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-sin.csv
@@ -0,0 +1,1370 @@
+dtype,input,output,ulperrortol
+## +ve denormals ##
+np.float32,0x004b4716,0x004b4716,2
+np.float32,0x007b2490,0x007b2490,2
+np.float32,0x007c99fa,0x007c99fa,2
+np.float32,0x00734a0c,0x00734a0c,2
+np.float32,0x0070de24,0x0070de24,2
+np.float32,0x007fffff,0x007fffff,2
+np.float32,0x00000001,0x00000001,2
+## -ve denormals ##
+np.float32,0x80495d65,0x80495d65,2
+np.float32,0x806894f6,0x806894f6,2
+np.float32,0x80555a76,0x80555a76,2
+np.float32,0x804e1fb8,0x804e1fb8,2
+np.float32,0x80687de9,0x80687de9,2
+np.float32,0x807fffff,0x807fffff,2
+np.float32,0x80000001,0x80000001,2
+## +/-0.0f, +/-FLT_MIN +/-FLT_MAX ##
+np.float32,0x00000000,0x00000000,2
+np.float32,0x80000000,0x80000000,2
+np.float32,0x00800000,0x00800000,2
+np.float32,0x80800000,0x80800000,2
+## 1.00f ##
+np.float32,0x3f800000,0x3f576aa4,2
+np.float32,0x3f800001,0x3f576aa6,2
+np.float32,0x3f800002,0x3f576aa7,2
+np.float32,0xc090a8b0,0x3f7b4e48,2
+np.float32,0x41ce3184,0x3f192d43,2
+np.float32,0xc1d85848,0xbf7161cb,2
+np.float32,0x402b8820,0x3ee3f29f,2
+np.float32,0x42b4e454,0x3f1d0151,2
+np.float32,0x42a67a60,0x3f7ffa4c,2
+np.float32,0x41d92388,0x3f67beef,2
+np.float32,0x422dd66c,0xbeffb0c1,2
+np.float32,0xc28f5be6,0xbf0bae79,2
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-sinh.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-sinh.csv
new file mode 100644
index 0000000..1ef7b6e
--- /dev/null
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-tan.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-tan.csv
new file mode 100644
index 0000000..ac97624
--- /dev/null
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diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-tanh.csv b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-tanh.csv
new file mode 100644
index 0000000..9e3ddc6
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/data/umath-validation-set-tanh.csv
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+np.float64,0xbfe846b420f08d68,0xbfe47d1709e43937,2
+np.float64,0x7fe8e87043f1d0e0,0x3ff0000000000000,2
+np.float64,0x3fcfb718453f6e31,0x3fcf14ecee7b32b4,2
+np.float64,0x7fe4306b71a860d6,0x3ff0000000000000,2
+np.float64,0x7fee08459f7c108a,0x3ff0000000000000,2
+np.float64,0x3fed705165fae0a3,0x3fe73a66369c5700,2
+np.float64,0x7fd0e63f4da1cc7e,0x3ff0000000000000,2
+np.float64,0xffd1a40c2ea34818,0xbff0000000000000,2
+np.float64,0xbfa369795c26d2f0,0xbfa36718218d46b3,2
+np.float64,0xef70b9f5dee17,0xef70b9f5dee17,2
+np.float64,0x3fb50a0a6e2a1410,0x3fb4fdf27724560a,2
+np.float64,0x7fe30a0f6166141e,0x3ff0000000000000,2
+np.float64,0xbfd7b3ca7daf6794,0xbfd6accb81032b2d,2
+np.float64,0x3fc21dceb3243b9d,0x3fc1ff15d5d277a3,2
+np.float64,0x3fe483e445a907c9,0x3fe219ca0e269552,2
+np.float64,0x3fb2b1e2a22563c0,0x3fb2a96554900eaf,2
+np.float64,0x4b1ff6409641,0x4b1ff6409641,2
+np.float64,0xbfd92eabc9b25d58,0xbfd7f55d7776d64e,2
+np.float64,0x8003b8604c8770c1,0x8003b8604c8770c1,2
+np.float64,0x800d20a9df1a4154,0x800d20a9df1a4154,2
+np.float64,0xecf8a535d9f15,0xecf8a535d9f15,2
+np.float64,0x3fe92d15bab25a2b,0x3fe50296aa15ae85,2
+np.float64,0x800239c205a47385,0x800239c205a47385,2
+np.float64,0x3fc48664a9290cc8,0x3fc459d126320ef6,2
+np.float64,0x3fe7620625eec40c,0x3fe3f3bcbee3e8c6,2
+np.float64,0x3fd242ff4ca48600,0x3fd1c81ed7a971c8,2
+np.float64,0xbfe39bafcfa73760,0xbfe17959c7a279db,2
+np.float64,0x7fdcd2567239a4ac,0x3ff0000000000000,2
+np.float64,0x3fe5f2f292ebe5e6,0x3fe30d12f05e2752,2
+np.float64,0x7fda3819d1347033,0x3ff0000000000000,2
+np.float64,0xffca5b4d4334b69c,0xbff0000000000000,2
+np.float64,0xb8a2b7cd71457,0xb8a2b7cd71457,2
+np.float64,0x3fee689603fcd12c,0x3fe7ad4ace26d6dd,2
+np.float64,0x7fe26541a564ca82,0x3ff0000000000000,2
+np.float64,0x3fe6912ee66d225e,0x3fe3720d242c4d82,2
+np.float64,0xffe6580c75ecb018,0xbff0000000000000,2
+np.float64,0x7fe01a3370603466,0x3ff0000000000000,2
+np.float64,0xffe84e3f84b09c7e,0xbff0000000000000,2
+np.float64,0x3ff0000000000000,0x3fe85efab514f394,2
+np.float64,0x3fe214d4266429a8,0x3fe05fec03a3c247,2
+np.float64,0x3fd00aec5da015d8,0x3fcf6e070ad4ad62,2
+np.float64,0x800aac8631f5590d,0x800aac8631f5590d,2
+np.float64,0xbfe7c4f5f76f89ec,0xbfe42fc1c57b4a13,2
+np.float64,0xaf146c7d5e28e,0xaf146c7d5e28e,2
+np.float64,0xbfe57188b66ae312,0xbfe2b8be4615ef75,2
+np.float64,0xffef8cb8e1ff1971,0xbff0000000000000,2
+np.float64,0x8001daf8aa63b5f2,0x8001daf8aa63b5f2,2
+np.float64,0x3fdddcc339bbb986,0x3fdbde5f3783538b,2
+np.float64,0xdd8c92c3bb193,0xdd8c92c3bb193,2
+np.float64,0xbfe861a148f0c342,0xbfe48cf1d228a336,2
+np.float64,0xffe260a32e24c146,0xbff0000000000000,2
+np.float64,0x1f7474b43ee8f,0x1f7474b43ee8f,2
+np.float64,0x3fe81dbd89703b7c,0x3fe464d78df92b7b,2
+np.float64,0x7fed0101177a0201,0x3ff0000000000000,2
+np.float64,0x7fd8b419a8316832,0x3ff0000000000000,2
+np.float64,0x3fe93debccf27bd8,0x3fe50c27727917f0,2
+np.float64,0xe5ead05bcbd5a,0xe5ead05bcbd5a,2
+np.float64,0xbfebbbc4cff7778a,0xbfe663c4ca003bbf,2
+np.float64,0xbfea343eb474687e,0xbfe59529f73ea151,2
+np.float64,0x3fbe74a5963ce94b,0x3fbe50123ed05d8d,2
+np.float64,0x3fd31d3a5d263a75,0x3fd290c026cb38a5,2
+np.float64,0xbfd79908acaf3212,0xbfd695620e31c3c6,2
+np.float64,0xbfc26a350324d46c,0xbfc249f335f3e465,2
+np.float64,0xbfac38d5583871b0,0xbfac31866d12a45e,2
+np.float64,0x3fe40cea672819d5,0x3fe1c83754e72c92,2
+np.float64,0xbfa74770642e8ee0,0xbfa74355fcf67332,2
+np.float64,0x7fc60942d32c1285,0x3ff0000000000000,2
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/__pycache__/setup.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/__pycache__/setup.cpython-312.pyc
new file mode 100644
index 0000000..c26db55
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/__pycache__/setup.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/checks.pyx b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/checks.pyx
new file mode 100644
index 0000000..57df05c
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/checks.pyx
@@ -0,0 +1,373 @@
+#cython: language_level=3
+
+"""
+Functions in this module give python-space wrappers for cython functions
+exposed in numpy/__init__.pxd, so they can be tested in test_cython.py
+"""
+cimport numpy as cnp
+cnp.import_array()
+
+
+def is_td64(obj):
+    return cnp.is_timedelta64_object(obj)
+
+
+def is_dt64(obj):
+    return cnp.is_datetime64_object(obj)
+
+
+def get_dt64_value(obj):
+    return cnp.get_datetime64_value(obj)
+
+
+def get_td64_value(obj):
+    return cnp.get_timedelta64_value(obj)
+
+
+def get_dt64_unit(obj):
+    return cnp.get_datetime64_unit(obj)
+
+
+def is_integer(obj):
+    return isinstance(obj, (cnp.integer, int))
+
+
+def get_datetime_iso_8601_strlen():
+    return cnp.get_datetime_iso_8601_strlen(0, cnp.NPY_FR_ns)
+
+
+def convert_datetime64_to_datetimestruct():
+    cdef:
+        cnp.npy_datetimestruct dts
+        cnp.PyArray_DatetimeMetaData meta
+        cnp.int64_t value = 1647374515260292
+        # i.e. (time.time() * 10**6) at 2022-03-15 20:01:55.260292 UTC
+
+    meta.base = cnp.NPY_FR_us
+    meta.num = 1
+    cnp.convert_datetime64_to_datetimestruct(&meta, value, &dts)
+    return dts
+
+
+def make_iso_8601_datetime(dt: "datetime"):
+    cdef:
+        cnp.npy_datetimestruct dts
+        char result[36]  # 36 corresponds to NPY_FR_s passed below
+        int local = 0
+        int utc = 0
+        int tzoffset = 0
+
+    dts.year = dt.year
+    dts.month = dt.month
+    dts.day = dt.day
+    dts.hour = dt.hour
+    dts.min = dt.minute
+    dts.sec = dt.second
+    dts.us = dt.microsecond
+    dts.ps = dts.as = 0
+
+    cnp.make_iso_8601_datetime(
+        &dts,
+        result,
+        sizeof(result),
+        local,
+        utc,
+        cnp.NPY_FR_s,
+        tzoffset,
+        cnp.NPY_NO_CASTING,
+    )
+    return result
+
+
+cdef cnp.broadcast multiiter_from_broadcast_obj(object bcast):
+    cdef dict iter_map = {
+        1: cnp.PyArray_MultiIterNew1,
+        2: cnp.PyArray_MultiIterNew2,
+        3: cnp.PyArray_MultiIterNew3,
+        4: cnp.PyArray_MultiIterNew4,
+        5: cnp.PyArray_MultiIterNew5,
+    }
+    arrays = [x.base for x in bcast.iters]
+    cdef cnp.broadcast result = iter_map[len(arrays)](*arrays)
+    return result
+
+
+def get_multiiter_size(bcast: "broadcast"):
+    cdef cnp.broadcast multi = multiiter_from_broadcast_obj(bcast)
+    return multi.size
+
+
+def get_multiiter_number_of_dims(bcast: "broadcast"):
+    cdef cnp.broadcast multi = multiiter_from_broadcast_obj(bcast)
+    return multi.nd
+
+
+def get_multiiter_current_index(bcast: "broadcast"):
+    cdef cnp.broadcast multi = multiiter_from_broadcast_obj(bcast)
+    return multi.index
+
+
+def get_multiiter_num_of_iterators(bcast: "broadcast"):
+    cdef cnp.broadcast multi = multiiter_from_broadcast_obj(bcast)
+    return multi.numiter
+
+
+def get_multiiter_shape(bcast: "broadcast"):
+    cdef cnp.broadcast multi = multiiter_from_broadcast_obj(bcast)
+    return tuple([multi.dimensions[i] for i in range(bcast.nd)])
+
+
+def get_multiiter_iters(bcast: "broadcast"):
+    cdef cnp.broadcast multi = multiiter_from_broadcast_obj(bcast)
+    return tuple([<cnp.flatiter>multi.iters[i] for i in range(bcast.numiter)])
+
+
+def get_default_integer():
+    if cnp.NPY_DEFAULT_INT == cnp.NPY_LONG:
+        return cnp.dtype("long")
+    if cnp.NPY_DEFAULT_INT == cnp.NPY_INTP:
+        return cnp.dtype("intp")
+    return None
+
+def get_ravel_axis():
+    return cnp.NPY_RAVEL_AXIS
+
+
+def conv_intp(cnp.intp_t val):
+    return val
+
+
+def get_dtype_flags(cnp.dtype dtype):
+    return dtype.flags
+
+
+cdef cnp.NpyIter* npyiter_from_nditer_obj(object it):
+    """A function to create a NpyIter struct from a nditer object.
+
+    This function is only meant for testing purposes and only extracts the
+    necessary info from nditer to test the functionality of NpyIter methods
+    """
+    cdef:
+        cnp.NpyIter* cit
+        cnp.PyArray_Descr* op_dtypes[3]
+        cnp.npy_uint32 op_flags[3]
+        cnp.PyArrayObject* ops[3]
+        cnp.npy_uint32 flags = 0
+
+    if it.has_index:
+        flags |= cnp.NPY_ITER_C_INDEX
+    if it.has_delayed_bufalloc:
+        flags |= cnp.NPY_ITER_BUFFERED | cnp.NPY_ITER_DELAY_BUFALLOC
+    if it.has_multi_index:
+        flags |= cnp.NPY_ITER_MULTI_INDEX
+
+    # one of READWRITE, READONLY and WRTIEONLY at the minimum must be specified for op_flags
+    for i in range(it.nop):
+        op_flags[i] = cnp.NPY_ITER_READONLY
+
+    for i in range(it.nop):
+        op_dtypes[i] = cnp.PyArray_DESCR(it.operands[i])
+        ops[i] = <cnp.PyArrayObject*>it.operands[i]
+
+    cit = cnp.NpyIter_MultiNew(it.nop, &ops[0], flags, cnp.NPY_KEEPORDER,
+                               cnp.NPY_NO_CASTING, &op_flags[0],
+                               <cnp.PyArray_Descr**>NULL)
+    return cit
+
+
+def get_npyiter_size(it: "nditer"):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    result = cnp.NpyIter_GetIterSize(cit)
+    cnp.NpyIter_Deallocate(cit)
+    return result
+
+
+def get_npyiter_ndim(it: "nditer"):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    result = cnp.NpyIter_GetNDim(cit)
+    cnp.NpyIter_Deallocate(cit)
+    return result
+
+
+def get_npyiter_nop(it: "nditer"):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    result = cnp.NpyIter_GetNOp(cit)
+    cnp.NpyIter_Deallocate(cit)
+    return result
+
+
+def get_npyiter_operands(it: "nditer"):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    try:
+        arr = cnp.NpyIter_GetOperandArray(cit)
+        return tuple([<cnp.ndarray>arr[i] for i in range(it.nop)])
+    finally:
+        cnp.NpyIter_Deallocate(cit)
+
+
+def get_npyiter_itviews(it: "nditer"):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    result = tuple([cnp.NpyIter_GetIterView(cit, i) for i in range(it.nop)])
+    cnp.NpyIter_Deallocate(cit)
+    return result
+
+
+def get_npyiter_dtypes(it: "nditer"):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    try:
+        arr = cnp.NpyIter_GetDescrArray(cit)
+        return tuple([<cnp.dtype>arr[i] for i in range(it.nop)])
+    finally:
+        cnp.NpyIter_Deallocate(cit)
+
+
+def npyiter_has_delayed_bufalloc(it: "nditer"):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    result = cnp.NpyIter_HasDelayedBufAlloc(cit)
+    cnp.NpyIter_Deallocate(cit)
+    return result
+
+
+def npyiter_has_index(it: "nditer"):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    result = cnp.NpyIter_HasIndex(cit)
+    cnp.NpyIter_Deallocate(cit)
+    return result
+
+
+def npyiter_has_multi_index(it: "nditer"):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    result = cnp.NpyIter_HasMultiIndex(cit)
+    cnp.NpyIter_Deallocate(cit)
+    return result
+
+
+def test_get_multi_index_iter_next(it: "nditer", cnp.ndarray[cnp.float64_t, ndim=2] arr):
+    cdef cnp.NpyIter* cit = npyiter_from_nditer_obj(it)
+    cdef cnp.NpyIter_GetMultiIndexFunc get_multi_index = \
+        cnp.NpyIter_GetGetMultiIndex(cit, NULL)
+    cdef cnp.NpyIter_IterNextFunc iternext = \
+        cnp.NpyIter_GetIterNext(cit, NULL)
+    return 1
+
+
+def npyiter_has_finished(it: "nditer"):
+    cdef cnp.NpyIter* cit
+    try:
+        cit = npyiter_from_nditer_obj(it)
+        cnp.NpyIter_GotoIterIndex(cit, it.index)
+        return not (cnp.NpyIter_GetIterIndex(cit) < cnp.NpyIter_GetIterSize(cit))
+    finally:
+        cnp.NpyIter_Deallocate(cit)
+
+def compile_fillwithbyte():
+    # Regression test for gh-25878, mostly checks it compiles.
+    cdef cnp.npy_intp dims[2]
+    dims = (1, 2)
+    pos = cnp.PyArray_ZEROS(2, dims, cnp.NPY_UINT8, 0)
+    cnp.PyArray_FILLWBYTE(pos, 1)
+    return pos
+
+def inc2_cfloat_struct(cnp.ndarray[cnp.cfloat_t] arr):
+    # This works since we compile in C mode, it will fail in cpp mode
+    arr[1].real += 1
+    arr[1].imag += 1
+    # This works in both modes
+    arr[1].real = arr[1].real + 1
+    arr[1].imag = arr[1].imag + 1
+
+
+def npystring_pack(arr):
+    cdef char *string = "Hello world"
+    cdef size_t size = 11
+
+    allocator = cnp.NpyString_acquire_allocator(
+        <cnp.PyArray_StringDTypeObject *>cnp.PyArray_DESCR(arr)
+    )
+
+    # copy string->packed_string, the pointer to the underlying array buffer
+    ret = cnp.NpyString_pack(
+        allocator, <cnp.npy_packed_static_string *>cnp.PyArray_DATA(arr), string, size,
+    )
+
+    cnp.NpyString_release_allocator(allocator)
+    return ret
+
+
+def npystring_load(arr):
+    allocator = cnp.NpyString_acquire_allocator(
+        <cnp.PyArray_StringDTypeObject *>cnp.PyArray_DESCR(arr)
+    )
+
+    cdef cnp.npy_static_string sdata
+    sdata.size = 0
+    sdata.buf = NULL
+
+    cdef cnp.npy_packed_static_string *packed_string = <cnp.npy_packed_static_string *>cnp.PyArray_DATA(arr)
+    cdef int is_null = cnp.NpyString_load(allocator, packed_string, &sdata)
+    cnp.NpyString_release_allocator(allocator)
+    if is_null == -1:
+        raise ValueError("String unpacking failed.")
+    elif is_null == 1:
+        # String in the array buffer is the null string
+        return ""
+    else:
+        # Cython syntax for copying a c string to python bytestring:
+        # slice the char * by the length of the string
+        return sdata.buf[:sdata.size].decode('utf-8')
+
+
+def npystring_pack_multiple(arr1, arr2):
+    cdef cnp.npy_string_allocator *allocators[2]
+    cdef cnp.PyArray_Descr *descrs[2]
+    descrs[0] = cnp.PyArray_DESCR(arr1)
+    descrs[1] = cnp.PyArray_DESCR(arr2)
+
+    cnp.NpyString_acquire_allocators(2, descrs, allocators)
+
+    # Write into the first element of each array
+    cdef int ret1 = cnp.NpyString_pack(
+        allocators[0], <cnp.npy_packed_static_string *>cnp.PyArray_DATA(arr1), "Hello world", 11,
+    )
+    cdef int ret2 = cnp.NpyString_pack(
+        allocators[1], <cnp.npy_packed_static_string *>cnp.PyArray_DATA(arr2), "test this", 9,
+    )
+
+    # Write a null string into the last element
+    cdef cnp.npy_intp elsize = cnp.PyArray_ITEMSIZE(arr1)
+    cdef int ret3 = cnp.NpyString_pack_null(
+        allocators[0],
+        <cnp.npy_packed_static_string *>(<char *>cnp.PyArray_DATA(arr1) + 2*elsize),
+    )
+
+    cnp.NpyString_release_allocators(2, allocators)
+    if ret1 == -1 or ret2 == -1 or ret3 == -1:
+        return -1
+
+    return 0
+
+
+def npystring_allocators_other_types(arr1, arr2):
+    cdef cnp.npy_string_allocator *allocators[2]
+    cdef cnp.PyArray_Descr *descrs[2]
+    descrs[0] = cnp.PyArray_DESCR(arr1)
+    descrs[1] = cnp.PyArray_DESCR(arr2)
+
+    cnp.NpyString_acquire_allocators(2, descrs, allocators)
+
+    # None of the dtypes here are StringDType, so every allocator
+    # should be NULL upon acquisition.
+    cdef int ret = 0
+    for allocator in allocators:
+        if allocator != NULL:
+            ret = -1
+            break
+
+    cnp.NpyString_release_allocators(2, allocators)
+    return ret
+
+
+def check_npy_uintp_type_enum():
+    # Regression test for gh-27890: cnp.NPY_UINTP was not defined.
+    # Cython would fail to compile this before gh-27890 was fixed.
+    return cnp.NPY_UINTP > 0
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/meson.build b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/meson.build
new file mode 100644
index 0000000..8362c33
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/meson.build
@@ -0,0 +1,43 @@
+project('checks', 'c', 'cython')
+
+py = import('python').find_installation(pure: false)
+
+cc = meson.get_compiler('c')
+cy = meson.get_compiler('cython')
+
+# Keep synced with pyproject.toml
+if not cy.version().version_compare('>=3.0.6')
+  error('tests requires Cython >= 3.0.6')
+endif
+
+cython_args = []
+if cy.version().version_compare('>=3.1.0')
+  cython_args += ['-Xfreethreading_compatible=True']
+endif
+
+npy_include_path = run_command(py, [
+    '-c',
+    'import os; os.chdir(".."); import numpy; print(os.path.abspath(numpy.get_include()))'
+    ], check: true).stdout().strip()
+
+npy_path = run_command(py, [
+    '-c',
+    'import os; os.chdir(".."); import numpy; print(os.path.dirname(numpy.__file__).removesuffix("numpy"))'
+    ], check: true).stdout().strip()
+
+# TODO: This is a hack due to gh-25135, where cython may not find the right
+#       __init__.pyd file.
+add_project_arguments('-I', npy_path, language : 'cython')
+
+py.extension_module(
+    'checks',
+    'checks.pyx',
+    install: false,
+    c_args: [
+      '-DNPY_NO_DEPRECATED_API=0',  # Cython still uses old NumPy C API
+      # Require 1.25+ to test datetime additions
+      '-DNPY_TARGET_VERSION=NPY_2_0_API_VERSION',
+    ],
+    include_directories: [npy_include_path],
+    cython_args: cython_args,
+)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/setup.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/setup.py
new file mode 100644
index 0000000..eb57477
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/cython/setup.py
@@ -0,0 +1,39 @@
+"""
+Provide python-space access to the functions exposed in numpy/__init__.pxd
+for testing.
+"""
+
+import os
+from distutils.core import setup
+
+import Cython
+from Cython.Build import cythonize
+from setuptools.extension import Extension
+
+import numpy as np
+from numpy._utils import _pep440
+
+macros = [
+    ("NPY_NO_DEPRECATED_API", 0),
+    # Require 1.25+ to test datetime additions
+    ("NPY_TARGET_VERSION", "NPY_2_0_API_VERSION"),
+]
+
+checks = Extension(
+    "checks",
+    sources=[os.path.join('.', "checks.pyx")],
+    include_dirs=[np.get_include()],
+    define_macros=macros,
+)
+
+extensions = [checks]
+
+compiler_directives = {}
+if _pep440.parse(Cython.__version__) >= _pep440.parse("3.1.0a0"):
+    compiler_directives['freethreading_compatible'] = True
+
+setup(
+    ext_modules=cythonize(
+        extensions,
+        compiler_directives=compiler_directives)
+)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/__pycache__/setup.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/__pycache__/setup.cpython-312.pyc
new file mode 100644
index 0000000..0783909
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/__pycache__/setup.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/limited_api1.c b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/limited_api1.c
new file mode 100644
index 0000000..3dbf569
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/limited_api1.c
@@ -0,0 +1,17 @@
+#define Py_LIMITED_API 0x03060000
+
+#include <Python.h>
+#include <numpy/arrayobject.h>
+#include <numpy/ufuncobject.h>
+
+static PyModuleDef moduledef = {
+    .m_base = PyModuleDef_HEAD_INIT,
+    .m_name = "limited_api1"
+};
+
+PyMODINIT_FUNC PyInit_limited_api1(void)
+{
+    import_array();
+    import_umath();
+    return PyModule_Create(&moduledef);
+}
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/limited_api2.pyx b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/limited_api2.pyx
new file mode 100644
index 0000000..327d5b0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/limited_api2.pyx
@@ -0,0 +1,11 @@
+#cython: language_level=3
+
+"""
+Make sure cython can compile in limited API mode (see meson.build)
+"""
+
+cdef extern from "numpy/arrayobject.h":
+    pass
+cdef extern from "numpy/arrayscalars.h":
+    pass
+
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/limited_api_latest.c b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/limited_api_latest.c
new file mode 100644
index 0000000..13668f2
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/limited_api_latest.c
@@ -0,0 +1,19 @@
+#if Py_LIMITED_API != PY_VERSION_HEX & 0xffff0000
+    # error "Py_LIMITED_API not defined to Python major+minor version"
+#endif
+
+#include <Python.h>
+#include <numpy/arrayobject.h>
+#include <numpy/ufuncobject.h>
+
+static PyModuleDef moduledef = {
+    .m_base = PyModuleDef_HEAD_INIT,
+    .m_name = "limited_api_latest"
+};
+
+PyMODINIT_FUNC PyInit_limited_api_latest(void)
+{
+    import_array();
+    import_umath();
+    return PyModule_Create(&moduledef);
+}
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/meson.build b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/meson.build
new file mode 100644
index 0000000..65287d8
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/meson.build
@@ -0,0 +1,59 @@
+project('checks', 'c', 'cython')
+
+py = import('python').find_installation(pure: false)
+
+cc = meson.get_compiler('c')
+cy = meson.get_compiler('cython')
+
+# Keep synced with pyproject.toml
+if not cy.version().version_compare('>=3.0.6')
+  error('tests requires Cython >= 3.0.6')
+endif
+
+npy_include_path = run_command(py, [
+    '-c',
+    'import os; os.chdir(".."); import numpy; print(os.path.abspath(numpy.get_include()))'
+    ], check: true).stdout().strip()
+
+npy_path = run_command(py, [
+    '-c',
+    'import os; os.chdir(".."); import numpy; print(os.path.dirname(numpy.__file__).removesuffix("numpy"))'
+    ], check: true).stdout().strip()
+
+# TODO: This is a hack due to https://github.com/cython/cython/issues/5820,
+# where cython may not find the right __init__.pyd file.
+add_project_arguments('-I', npy_path, language : 'cython')
+
+py.extension_module(
+    'limited_api1',
+    'limited_api1.c',
+    c_args: [
+      '-DNPY_NO_DEPRECATED_API=NPY_1_21_API_VERSION',
+    ],
+    include_directories: [npy_include_path],
+    limited_api: '3.6',
+)
+
+py.extension_module(
+    'limited_api_latest',
+    'limited_api_latest.c',
+    c_args: [
+      '-DNPY_NO_DEPRECATED_API=NPY_1_21_API_VERSION',
+    ],
+    include_directories: [npy_include_path],
+    limited_api: py.language_version(),
+)
+
+py.extension_module(
+    'limited_api2',
+    'limited_api2.pyx',
+    install: false,
+    c_args: [
+      '-DNPY_NO_DEPRECATED_API=0',
+      # Require 1.25+ to test datetime additions
+      '-DNPY_TARGET_VERSION=NPY_2_0_API_VERSION',
+      '-DCYTHON_LIMITED_API=1',
+    ],
+    include_directories: [npy_include_path],
+    limited_api: '3.7',
+)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/setup.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/setup.py
new file mode 100644
index 0000000..16adcd1
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/examples/limited_api/setup.py
@@ -0,0 +1,24 @@
+"""
+Build an example package using the limited Python C API.
+"""
+
+import os
+
+from setuptools import Extension, setup
+
+import numpy as np
+
+macros = [("NPY_NO_DEPRECATED_API", 0), ("Py_LIMITED_API", "0x03060000")]
+
+limited_api = Extension(
+    "limited_api",
+    sources=[os.path.join('.', "limited_api.c")],
+    include_dirs=[np.get_include()],
+    define_macros=macros,
+)
+
+extensions = [limited_api]
+
+setup(
+    ext_modules=extensions
+)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test__exceptions.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test__exceptions.py
new file mode 100644
index 0000000..35782e7
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test__exceptions.py
@@ -0,0 +1,90 @@
+"""
+Tests of the ._exceptions module. Primarily for exercising the __str__ methods.
+"""
+
+import pickle
+
+import pytest
+
+import numpy as np
+from numpy.exceptions import AxisError
+
+_ArrayMemoryError = np._core._exceptions._ArrayMemoryError
+_UFuncNoLoopError = np._core._exceptions._UFuncNoLoopError
+
+class TestArrayMemoryError:
+    def test_pickling(self):
+        """ Test that _ArrayMemoryError can be pickled """
+        error = _ArrayMemoryError((1023,), np.dtype(np.uint8))
+        res = pickle.loads(pickle.dumps(error))
+        assert res._total_size == error._total_size
+
+    def test_str(self):
+        e = _ArrayMemoryError((1023,), np.dtype(np.uint8))
+        str(e)  # not crashing is enough
+
+    # testing these properties is easier than testing the full string repr
+    def test__size_to_string(self):
+        """ Test e._size_to_string """
+        f = _ArrayMemoryError._size_to_string
+        Ki = 1024
+        assert f(0) == '0 bytes'
+        assert f(1) == '1 bytes'
+        assert f(1023) == '1023 bytes'
+        assert f(Ki) == '1.00 KiB'
+        assert f(Ki + 1) == '1.00 KiB'
+        assert f(10 * Ki) == '10.0 KiB'
+        assert f(int(999.4 * Ki)) == '999. KiB'
+        assert f(int(1023.4 * Ki)) == '1023. KiB'
+        assert f(int(1023.5 * Ki)) == '1.00 MiB'
+        assert f(Ki * Ki) == '1.00 MiB'
+
+        # 1023.9999 Mib should round to 1 GiB
+        assert f(int(Ki * Ki * Ki * 0.9999)) == '1.00 GiB'
+        assert f(Ki * Ki * Ki * Ki * Ki * Ki) == '1.00 EiB'
+        # larger than sys.maxsize, adding larger prefixes isn't going to help
+        # anyway.
+        assert f(Ki * Ki * Ki * Ki * Ki * Ki * 123456) == '123456. EiB'
+
+    def test__total_size(self):
+        """ Test e._total_size """
+        e = _ArrayMemoryError((1,), np.dtype(np.uint8))
+        assert e._total_size == 1
+
+        e = _ArrayMemoryError((2, 4), np.dtype((np.uint64, 16)))
+        assert e._total_size == 1024
+
+
+class TestUFuncNoLoopError:
+    def test_pickling(self):
+        """ Test that _UFuncNoLoopError can be pickled """
+        assert isinstance(pickle.dumps(_UFuncNoLoopError), bytes)
+
+
+@pytest.mark.parametrize("args", [
+    (2, 1, None),
+    (2, 1, "test_prefix"),
+    ("test message",),
+])
+class TestAxisError:
+    def test_attr(self, args):
+        """Validate attribute types."""
+        exc = AxisError(*args)
+        if len(args) == 1:
+            assert exc.axis is None
+            assert exc.ndim is None
+        else:
+            axis, ndim, *_ = args
+            assert exc.axis == axis
+            assert exc.ndim == ndim
+
+    def test_pickling(self, args):
+        """Test that `AxisError` can be pickled."""
+        exc = AxisError(*args)
+        exc2 = pickle.loads(pickle.dumps(exc))
+
+        assert type(exc) is type(exc2)
+        for name in ("axis", "ndim", "args"):
+            attr1 = getattr(exc, name)
+            attr2 = getattr(exc2, name)
+            assert attr1 == attr2, name
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_abc.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_abc.py
new file mode 100644
index 0000000..aee1904
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_abc.py
@@ -0,0 +1,54 @@
+import numbers
+
+import numpy as np
+from numpy._core.numerictypes import sctypes
+from numpy.testing import assert_
+
+
+class TestABC:
+    def test_abstract(self):
+        assert_(issubclass(np.number, numbers.Number))
+
+        assert_(issubclass(np.inexact, numbers.Complex))
+        assert_(issubclass(np.complexfloating, numbers.Complex))
+        assert_(issubclass(np.floating, numbers.Real))
+
+        assert_(issubclass(np.integer, numbers.Integral))
+        assert_(issubclass(np.signedinteger, numbers.Integral))
+        assert_(issubclass(np.unsignedinteger, numbers.Integral))
+
+    def test_floats(self):
+        for t in sctypes['float']:
+            assert_(isinstance(t(), numbers.Real),
+                    f"{t.__name__} is not instance of Real")
+            assert_(issubclass(t, numbers.Real),
+                    f"{t.__name__} is not subclass of Real")
+            assert_(not isinstance(t(), numbers.Rational),
+                    f"{t.__name__} is instance of Rational")
+            assert_(not issubclass(t, numbers.Rational),
+                    f"{t.__name__} is subclass of Rational")
+
+    def test_complex(self):
+        for t in sctypes['complex']:
+            assert_(isinstance(t(), numbers.Complex),
+                    f"{t.__name__} is not instance of Complex")
+            assert_(issubclass(t, numbers.Complex),
+                    f"{t.__name__} is not subclass of Complex")
+            assert_(not isinstance(t(), numbers.Real),
+                    f"{t.__name__} is instance of Real")
+            assert_(not issubclass(t, numbers.Real),
+                    f"{t.__name__} is subclass of Real")
+
+    def test_int(self):
+        for t in sctypes['int']:
+            assert_(isinstance(t(), numbers.Integral),
+                    f"{t.__name__} is not instance of Integral")
+            assert_(issubclass(t, numbers.Integral),
+                    f"{t.__name__} is not subclass of Integral")
+
+    def test_uint(self):
+        for t in sctypes['uint']:
+            assert_(isinstance(t(), numbers.Integral),
+                    f"{t.__name__} is not instance of Integral")
+            assert_(issubclass(t, numbers.Integral),
+                    f"{t.__name__} is not subclass of Integral")
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_api.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_api.py
new file mode 100644
index 0000000..2599053
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_api.py
@@ -0,0 +1,621 @@
+import sys
+
+import pytest
+from numpy._core._rational_tests import rational
+
+import numpy as np
+import numpy._core.umath as ncu
+from numpy.testing import (
+    HAS_REFCOUNT,
+    assert_,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    assert_warns,
+)
+
+
+def test_array_array():
+    tobj = type(object)
+    ones11 = np.ones((1, 1), np.float64)
+    tndarray = type(ones11)
+    # Test is_ndarray
+    assert_equal(np.array(ones11, dtype=np.float64), ones11)
+    if HAS_REFCOUNT:
+        old_refcount = sys.getrefcount(tndarray)
+        np.array(ones11)
+        assert_equal(old_refcount, sys.getrefcount(tndarray))
+
+    # test None
+    assert_equal(np.array(None, dtype=np.float64),
+                 np.array(np.nan, dtype=np.float64))
+    if HAS_REFCOUNT:
+        old_refcount = sys.getrefcount(tobj)
+        np.array(None, dtype=np.float64)
+        assert_equal(old_refcount, sys.getrefcount(tobj))
+
+    # test scalar
+    assert_equal(np.array(1.0, dtype=np.float64),
+                 np.ones((), dtype=np.float64))
+    if HAS_REFCOUNT:
+        old_refcount = sys.getrefcount(np.float64)
+        np.array(np.array(1.0, dtype=np.float64), dtype=np.float64)
+        assert_equal(old_refcount, sys.getrefcount(np.float64))
+
+    # test string
+    S2 = np.dtype((bytes, 2))
+    S3 = np.dtype((bytes, 3))
+    S5 = np.dtype((bytes, 5))
+    assert_equal(np.array(b"1.0", dtype=np.float64),
+                 np.ones((), dtype=np.float64))
+    assert_equal(np.array(b"1.0").dtype, S3)
+    assert_equal(np.array(b"1.0", dtype=bytes).dtype, S3)
+    assert_equal(np.array(b"1.0", dtype=S2), np.array(b"1."))
+    assert_equal(np.array(b"1", dtype=S5), np.ones((), dtype=S5))
+
+    # test string
+    U2 = np.dtype((str, 2))
+    U3 = np.dtype((str, 3))
+    U5 = np.dtype((str, 5))
+    assert_equal(np.array("1.0", dtype=np.float64),
+                 np.ones((), dtype=np.float64))
+    assert_equal(np.array("1.0").dtype, U3)
+    assert_equal(np.array("1.0", dtype=str).dtype, U3)
+    assert_equal(np.array("1.0", dtype=U2), np.array("1."))
+    assert_equal(np.array("1", dtype=U5), np.ones((), dtype=U5))
+
+    builtins = getattr(__builtins__, '__dict__', __builtins__)
+    assert_(hasattr(builtins, 'get'))
+
+    # test memoryview
+    dat = np.array(memoryview(b'1.0'), dtype=np.float64)
+    assert_equal(dat, [49.0, 46.0, 48.0])
+    assert_(dat.dtype.type is np.float64)
+
+    dat = np.array(memoryview(b'1.0'))
+    assert_equal(dat, [49, 46, 48])
+    assert_(dat.dtype.type is np.uint8)
+
+    # test array interface
+    a = np.array(100.0, dtype=np.float64)
+    o = type("o", (object,),
+             {"__array_interface__": a.__array_interface__})
+    assert_equal(np.array(o, dtype=np.float64), a)
+
+    # test array_struct interface
+    a = np.array([(1, 4.0, 'Hello'), (2, 6.0, 'World')],
+                 dtype=[('f0', int), ('f1', float), ('f2', str)])
+    o = type("o", (object,),
+             {"__array_struct__": a.__array_struct__})
+    # wasn't what I expected... is np.array(o) supposed to equal a ?
+    # instead we get a array([...], dtype=">V18")
+    assert_equal(bytes(np.array(o).data), bytes(a.data))
+
+    # test array
+    def custom__array__(self, dtype=None, copy=None):
+        return np.array(100.0, dtype=dtype, copy=copy)
+
+    o = type("o", (object,), {"__array__": custom__array__})()
+    assert_equal(np.array(o, dtype=np.float64), np.array(100.0, np.float64))
+
+    # test recursion
+    nested = 1.5
+    for i in range(ncu.MAXDIMS):
+        nested = [nested]
+
+    # no error
+    np.array(nested)
+
+    # Exceeds recursion limit
+    assert_raises(ValueError, np.array, [nested], dtype=np.float64)
+
+    # Try with lists...
+    # float32
+    assert_equal(np.array([None] * 10, dtype=np.float32),
+                 np.full((10,), np.nan, dtype=np.float32))
+    assert_equal(np.array([[None]] * 10, dtype=np.float32),
+                 np.full((10, 1), np.nan, dtype=np.float32))
+    assert_equal(np.array([[None] * 10], dtype=np.float32),
+                 np.full((1, 10), np.nan, dtype=np.float32))
+    assert_equal(np.array([[None] * 10] * 10, dtype=np.float32),
+                 np.full((10, 10), np.nan, dtype=np.float32))
+    # float64
+    assert_equal(np.array([None] * 10, dtype=np.float64),
+                 np.full((10,), np.nan, dtype=np.float64))
+    assert_equal(np.array([[None]] * 10, dtype=np.float64),
+                 np.full((10, 1), np.nan, dtype=np.float64))
+    assert_equal(np.array([[None] * 10], dtype=np.float64),
+                 np.full((1, 10), np.nan, dtype=np.float64))
+    assert_equal(np.array([[None] * 10] * 10, dtype=np.float64),
+                 np.full((10, 10), np.nan, dtype=np.float64))
+
+    assert_equal(np.array([1.0] * 10, dtype=np.float64),
+                 np.ones((10,), dtype=np.float64))
+    assert_equal(np.array([[1.0]] * 10, dtype=np.float64),
+                 np.ones((10, 1), dtype=np.float64))
+    assert_equal(np.array([[1.0] * 10], dtype=np.float64),
+                 np.ones((1, 10), dtype=np.float64))
+    assert_equal(np.array([[1.0] * 10] * 10, dtype=np.float64),
+                 np.ones((10, 10), dtype=np.float64))
+
+    # Try with tuples
+    assert_equal(np.array((None,) * 10, dtype=np.float64),
+                 np.full((10,), np.nan, dtype=np.float64))
+    assert_equal(np.array([(None,)] * 10, dtype=np.float64),
+                 np.full((10, 1), np.nan, dtype=np.float64))
+    assert_equal(np.array([(None,) * 10], dtype=np.float64),
+                 np.full((1, 10), np.nan, dtype=np.float64))
+    assert_equal(np.array([(None,) * 10] * 10, dtype=np.float64),
+                 np.full((10, 10), np.nan, dtype=np.float64))
+
+    assert_equal(np.array((1.0,) * 10, dtype=np.float64),
+                 np.ones((10,), dtype=np.float64))
+    assert_equal(np.array([(1.0,)] * 10, dtype=np.float64),
+                 np.ones((10, 1), dtype=np.float64))
+    assert_equal(np.array([(1.0,) * 10], dtype=np.float64),
+                 np.ones((1, 10), dtype=np.float64))
+    assert_equal(np.array([(1.0,) * 10] * 10, dtype=np.float64),
+                 np.ones((10, 10), dtype=np.float64))
+
+@pytest.mark.parametrize("array", [True, False])
+def test_array_impossible_casts(array):
+    # All builtin types can be forcibly cast, at least theoretically,
+    # but user dtypes cannot necessarily.
+    rt = rational(1, 2)
+    if array:
+        rt = np.array(rt)
+    with assert_raises(TypeError):
+        np.array(rt, dtype="M8")
+
+
+def test_array_astype():
+    a = np.arange(6, dtype='f4').reshape(2, 3)
+    # Default behavior: allows unsafe casts, keeps memory layout,
+    #                   always copies.
+    b = a.astype('i4')
+    assert_equal(a, b)
+    assert_equal(b.dtype, np.dtype('i4'))
+    assert_equal(a.strides, b.strides)
+    b = a.T.astype('i4')
+    assert_equal(a.T, b)
+    assert_equal(b.dtype, np.dtype('i4'))
+    assert_equal(a.T.strides, b.strides)
+    b = a.astype('f4')
+    assert_equal(a, b)
+    assert_(not (a is b))
+
+    # copy=False parameter skips a copy
+    b = a.astype('f4', copy=False)
+    assert_(a is b)
+
+    # order parameter allows overriding of the memory layout,
+    # forcing a copy if the layout is wrong
+    b = a.astype('f4', order='F', copy=False)
+    assert_equal(a, b)
+    assert_(not (a is b))
+    assert_(b.flags.f_contiguous)
+
+    b = a.astype('f4', order='C', copy=False)
+    assert_equal(a, b)
+    assert_(a is b)
+    assert_(b.flags.c_contiguous)
+
+    # casting parameter allows catching bad casts
+    b = a.astype('c8', casting='safe')
+    assert_equal(a, b)
+    assert_equal(b.dtype, np.dtype('c8'))
+
+    assert_raises(TypeError, a.astype, 'i4', casting='safe')
+
+    # subok=False passes through a non-subclassed array
+    b = a.astype('f4', subok=0, copy=False)
+    assert_(a is b)
+
+    class MyNDArray(np.ndarray):
+        pass
+
+    a = np.array([[0, 1, 2], [3, 4, 5]], dtype='f4').view(MyNDArray)
+
+    # subok=True passes through a subclass
+    b = a.astype('f4', subok=True, copy=False)
+    assert_(a is b)
+
+    # subok=True is default, and creates a subtype on a cast
+    b = a.astype('i4', copy=False)
+    assert_equal(a, b)
+    assert_equal(type(b), MyNDArray)
+
+    # subok=False never returns a subclass
+    b = a.astype('f4', subok=False, copy=False)
+    assert_equal(a, b)
+    assert_(not (a is b))
+    assert_(type(b) is not MyNDArray)
+
+    # Make sure converting from string object to fixed length string
+    # does not truncate.
+    a = np.array([b'a' * 100], dtype='O')
+    b = a.astype('S')
+    assert_equal(a, b)
+    assert_equal(b.dtype, np.dtype('S100'))
+    a = np.array(['a' * 100], dtype='O')
+    b = a.astype('U')
+    assert_equal(a, b)
+    assert_equal(b.dtype, np.dtype('U100'))
+
+    # Same test as above but for strings shorter than 64 characters
+    a = np.array([b'a' * 10], dtype='O')
+    b = a.astype('S')
+    assert_equal(a, b)
+    assert_equal(b.dtype, np.dtype('S10'))
+    a = np.array(['a' * 10], dtype='O')
+    b = a.astype('U')
+    assert_equal(a, b)
+    assert_equal(b.dtype, np.dtype('U10'))
+
+    a = np.array(123456789012345678901234567890, dtype='O').astype('S')
+    assert_array_equal(a, np.array(b'1234567890' * 3, dtype='S30'))
+    a = np.array(123456789012345678901234567890, dtype='O').astype('U')
+    assert_array_equal(a, np.array('1234567890' * 3, dtype='U30'))
+
+    a = np.array([123456789012345678901234567890], dtype='O').astype('S')
+    assert_array_equal(a, np.array(b'1234567890' * 3, dtype='S30'))
+    a = np.array([123456789012345678901234567890], dtype='O').astype('U')
+    assert_array_equal(a, np.array('1234567890' * 3, dtype='U30'))
+
+    a = np.array(123456789012345678901234567890, dtype='S')
+    assert_array_equal(a, np.array(b'1234567890' * 3, dtype='S30'))
+    a = np.array(123456789012345678901234567890, dtype='U')
+    assert_array_equal(a, np.array('1234567890' * 3, dtype='U30'))
+
+    a = np.array('a\u0140', dtype='U')
+    b = np.ndarray(buffer=a, dtype='uint32', shape=2)
+    assert_(b.size == 2)
+
+    a = np.array([1000], dtype='i4')
+    assert_raises(TypeError, a.astype, 'S1', casting='safe')
+
+    a = np.array(1000, dtype='i4')
+    assert_raises(TypeError, a.astype, 'U1', casting='safe')
+
+    # gh-24023
+    assert_raises(TypeError, a.astype)
+
+@pytest.mark.parametrize("dt", ["S", "U"])
+def test_array_astype_to_string_discovery_empty(dt):
+    # See also gh-19085
+    arr = np.array([""], dtype=object)
+    # Note, the itemsize is the `0 -> 1` logic, which should change.
+    # The important part the test is rather that it does not error.
+    assert arr.astype(dt).dtype.itemsize == np.dtype(f"{dt}1").itemsize
+
+    # check the same thing for `np.can_cast` (since it accepts arrays)
+    assert np.can_cast(arr, dt, casting="unsafe")
+    assert not np.can_cast(arr, dt, casting="same_kind")
+    # as well as for the object as a descriptor:
+    assert np.can_cast("O", dt, casting="unsafe")
+
+@pytest.mark.parametrize("dt", ["d", "f", "S13", "U32"])
+def test_array_astype_to_void(dt):
+    dt = np.dtype(dt)
+    arr = np.array([], dtype=dt)
+    assert arr.astype("V").dtype.itemsize == dt.itemsize
+
+def test_object_array_astype_to_void():
+    # This is different to `test_array_astype_to_void` as object arrays
+    # are inspected.  The default void is "V8" (8 is the length of double)
+    arr = np.array([], dtype="O").astype("V")
+    assert arr.dtype == "V8"
+
+@pytest.mark.parametrize("t",
+    np._core.sctypes['uint'] +
+    np._core.sctypes['int'] +
+    np._core.sctypes['float']
+)
+def test_array_astype_warning(t):
+    # test ComplexWarning when casting from complex to float or int
+    a = np.array(10, dtype=np.complex128)
+    assert_warns(np.exceptions.ComplexWarning, a.astype, t)
+
+@pytest.mark.parametrize(["dtype", "out_dtype"],
+        [(np.bytes_, np.bool),
+         (np.str_, np.bool),
+         (np.dtype("S10,S9"), np.dtype("?,?")),
+         # The following also checks unaligned unicode access:
+         (np.dtype("S7,U9"), np.dtype("?,?"))])
+def test_string_to_boolean_cast(dtype, out_dtype):
+    # Only the last two (empty) strings are falsy (the `\0` is stripped):
+    arr = np.array(
+            ["10", "10\0\0\0", "0\0\0", "0", "False", " ", "", "\0"],
+            dtype=dtype)
+    expected = np.array(
+            [True, True, True, True, True, True, False, False],
+            dtype=out_dtype)
+    assert_array_equal(arr.astype(out_dtype), expected)
+    # As it's similar, check that nonzero behaves the same (structs are
+    # nonzero if all entries are)
+    assert_array_equal(np.nonzero(arr), np.nonzero(expected))
+
+@pytest.mark.parametrize("str_type", [str, bytes, np.str_])
+@pytest.mark.parametrize("scalar_type",
+        [np.complex64, np.complex128, np.clongdouble])
+def test_string_to_complex_cast(str_type, scalar_type):
+    value = scalar_type(b"1+3j")
+    assert scalar_type(value) == 1 + 3j
+    assert np.array([value], dtype=object).astype(scalar_type)[()] == 1 + 3j
+    assert np.array(value).astype(scalar_type)[()] == 1 + 3j
+    arr = np.zeros(1, dtype=scalar_type)
+    arr[0] = value
+    assert arr[0] == 1 + 3j
+
+@pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
+def test_none_to_nan_cast(dtype):
+    # Note that at the time of writing this test, the scalar constructors
+    # reject None
+    arr = np.zeros(1, dtype=dtype)
+    arr[0] = None
+    assert np.isnan(arr)[0]
+    assert np.isnan(np.array(None, dtype=dtype))[()]
+    assert np.isnan(np.array([None], dtype=dtype))[0]
+    assert np.isnan(np.array(None).astype(dtype))[()]
+
+def test_copyto_fromscalar():
+    a = np.arange(6, dtype='f4').reshape(2, 3)
+
+    # Simple copy
+    np.copyto(a, 1.5)
+    assert_equal(a, 1.5)
+    np.copyto(a.T, 2.5)
+    assert_equal(a, 2.5)
+
+    # Where-masked copy
+    mask = np.array([[0, 1, 0], [0, 0, 1]], dtype='?')
+    np.copyto(a, 3.5, where=mask)
+    assert_equal(a, [[2.5, 3.5, 2.5], [2.5, 2.5, 3.5]])
+    mask = np.array([[0, 1], [1, 1], [1, 0]], dtype='?')
+    np.copyto(a.T, 4.5, where=mask)
+    assert_equal(a, [[2.5, 4.5, 4.5], [4.5, 4.5, 3.5]])
+
+def test_copyto():
+    a = np.arange(6, dtype='i4').reshape(2, 3)
+
+    # Simple copy
+    np.copyto(a, [[3, 1, 5], [6, 2, 1]])
+    assert_equal(a, [[3, 1, 5], [6, 2, 1]])
+
+    # Overlapping copy should work
+    np.copyto(a[:, :2], a[::-1, 1::-1])
+    assert_equal(a, [[2, 6, 5], [1, 3, 1]])
+
+    # Defaults to 'same_kind' casting
+    assert_raises(TypeError, np.copyto, a, 1.5)
+
+    # Force a copy with 'unsafe' casting, truncating 1.5 to 1
+    np.copyto(a, 1.5, casting='unsafe')
+    assert_equal(a, 1)
+
+    # Copying with a mask
+    np.copyto(a, 3, where=[True, False, True])
+    assert_equal(a, [[3, 1, 3], [3, 1, 3]])
+
+    # Casting rule still applies with a mask
+    assert_raises(TypeError, np.copyto, a, 3.5, where=[True, False, True])
+
+    # Lists of integer 0's and 1's is ok too
+    np.copyto(a, 4.0, casting='unsafe', where=[[0, 1, 1], [1, 0, 0]])
+    assert_equal(a, [[3, 4, 4], [4, 1, 3]])
+
+    # Overlapping copy with mask should work
+    np.copyto(a[:, :2], a[::-1, 1::-1], where=[[0, 1], [1, 1]])
+    assert_equal(a, [[3, 4, 4], [4, 3, 3]])
+
+    # 'dst' must be an array
+    assert_raises(TypeError, np.copyto, [1, 2, 3], [2, 3, 4])
+
+
+def test_copyto_cast_safety():
+    with pytest.raises(TypeError):
+        np.copyto(np.arange(3), 3., casting="safe")
+
+    # Can put integer and float scalars safely (and equiv):
+    np.copyto(np.arange(3), 3, casting="equiv")
+    np.copyto(np.arange(3.), 3., casting="equiv")
+    # And also with less precision safely:
+    np.copyto(np.arange(3, dtype="uint8"), 3, casting="safe")
+    np.copyto(np.arange(3., dtype="float32"), 3., casting="safe")
+
+    # But not equiv:
+    with pytest.raises(TypeError):
+        np.copyto(np.arange(3, dtype="uint8"), 3, casting="equiv")
+
+    with pytest.raises(TypeError):
+        np.copyto(np.arange(3., dtype="float32"), 3., casting="equiv")
+
+    # As a special thing, object is equiv currently:
+    np.copyto(np.arange(3, dtype=object), 3, casting="equiv")
+
+    # The following raises an overflow error/gives a warning but not
+    # type error (due to casting), though:
+    with pytest.raises(OverflowError):
+        np.copyto(np.arange(3), 2**80, casting="safe")
+
+    with pytest.warns(RuntimeWarning):
+        np.copyto(np.arange(3, dtype=np.float32), 2e300, casting="safe")
+
+
+def test_copyto_permut():
+    # test explicit overflow case
+    pad = 500
+    l = [True] * pad + [True, True, True, True]
+    r = np.zeros(len(l) - pad)
+    d = np.ones(len(l) - pad)
+    mask = np.array(l)[pad:]
+    np.copyto(r, d, where=mask[::-1])
+
+    # test all permutation of possible masks, 9 should be sufficient for
+    # current 4 byte unrolled code
+    power = 9
+    d = np.ones(power)
+    for i in range(2**power):
+        r = np.zeros(power)
+        l = [(i & x) != 0 for x in range(power)]
+        mask = np.array(l)
+        np.copyto(r, d, where=mask)
+        assert_array_equal(r == 1, l)
+        assert_equal(r.sum(), sum(l))
+
+        r = np.zeros(power)
+        np.copyto(r, d, where=mask[::-1])
+        assert_array_equal(r == 1, l[::-1])
+        assert_equal(r.sum(), sum(l))
+
+        r = np.zeros(power)
+        np.copyto(r[::2], d[::2], where=mask[::2])
+        assert_array_equal(r[::2] == 1, l[::2])
+        assert_equal(r[::2].sum(), sum(l[::2]))
+
+        r = np.zeros(power)
+        np.copyto(r[::2], d[::2], where=mask[::-2])
+        assert_array_equal(r[::2] == 1, l[::-2])
+        assert_equal(r[::2].sum(), sum(l[::-2]))
+
+        for c in [0xFF, 0x7F, 0x02, 0x10]:
+            r = np.zeros(power)
+            mask = np.array(l)
+            imask = np.array(l).view(np.uint8)
+            imask[mask != 0] = c
+            np.copyto(r, d, where=mask)
+            assert_array_equal(r == 1, l)
+            assert_equal(r.sum(), sum(l))
+
+    r = np.zeros(power)
+    np.copyto(r, d, where=True)
+    assert_equal(r.sum(), r.size)
+    r = np.ones(power)
+    d = np.zeros(power)
+    np.copyto(r, d, where=False)
+    assert_equal(r.sum(), r.size)
+
+def test_copy_order():
+    a = np.arange(24).reshape(2, 1, 3, 4)
+    b = a.copy(order='F')
+    c = np.arange(24).reshape(2, 1, 4, 3).swapaxes(2, 3)
+
+    def check_copy_result(x, y, ccontig, fcontig, strides=False):
+        assert_(not (x is y))
+        assert_equal(x, y)
+        assert_equal(res.flags.c_contiguous, ccontig)
+        assert_equal(res.flags.f_contiguous, fcontig)
+
+    # Validate the initial state of a, b, and c
+    assert_(a.flags.c_contiguous)
+    assert_(not a.flags.f_contiguous)
+    assert_(not b.flags.c_contiguous)
+    assert_(b.flags.f_contiguous)
+    assert_(not c.flags.c_contiguous)
+    assert_(not c.flags.f_contiguous)
+
+    # Copy with order='C'
+    res = a.copy(order='C')
+    check_copy_result(res, a, ccontig=True, fcontig=False, strides=True)
+    res = b.copy(order='C')
+    check_copy_result(res, b, ccontig=True, fcontig=False, strides=False)
+    res = c.copy(order='C')
+    check_copy_result(res, c, ccontig=True, fcontig=False, strides=False)
+    res = np.copy(a, order='C')
+    check_copy_result(res, a, ccontig=True, fcontig=False, strides=True)
+    res = np.copy(b, order='C')
+    check_copy_result(res, b, ccontig=True, fcontig=False, strides=False)
+    res = np.copy(c, order='C')
+    check_copy_result(res, c, ccontig=True, fcontig=False, strides=False)
+
+    # Copy with order='F'
+    res = a.copy(order='F')
+    check_copy_result(res, a, ccontig=False, fcontig=True, strides=False)
+    res = b.copy(order='F')
+    check_copy_result(res, b, ccontig=False, fcontig=True, strides=True)
+    res = c.copy(order='F')
+    check_copy_result(res, c, ccontig=False, fcontig=True, strides=False)
+    res = np.copy(a, order='F')
+    check_copy_result(res, a, ccontig=False, fcontig=True, strides=False)
+    res = np.copy(b, order='F')
+    check_copy_result(res, b, ccontig=False, fcontig=True, strides=True)
+    res = np.copy(c, order='F')
+    check_copy_result(res, c, ccontig=False, fcontig=True, strides=False)
+
+    # Copy with order='K'
+    res = a.copy(order='K')
+    check_copy_result(res, a, ccontig=True, fcontig=False, strides=True)
+    res = b.copy(order='K')
+    check_copy_result(res, b, ccontig=False, fcontig=True, strides=True)
+    res = c.copy(order='K')
+    check_copy_result(res, c, ccontig=False, fcontig=False, strides=True)
+    res = np.copy(a, order='K')
+    check_copy_result(res, a, ccontig=True, fcontig=False, strides=True)
+    res = np.copy(b, order='K')
+    check_copy_result(res, b, ccontig=False, fcontig=True, strides=True)
+    res = np.copy(c, order='K')
+    check_copy_result(res, c, ccontig=False, fcontig=False, strides=True)
+
+def test_contiguous_flags():
+    a = np.ones((4, 4, 1))[::2, :, :]
+    a.strides = a.strides[:2] + (-123,)
+    b = np.ones((2, 2, 1, 2, 2)).swapaxes(3, 4)
+
+    def check_contig(a, ccontig, fcontig):
+        assert_(a.flags.c_contiguous == ccontig)
+        assert_(a.flags.f_contiguous == fcontig)
+
+    # Check if new arrays are correct:
+    check_contig(a, False, False)
+    check_contig(b, False, False)
+    check_contig(np.empty((2, 2, 0, 2, 2)), True, True)
+    check_contig(np.array([[[1], [2]]], order='F'), True, True)
+    check_contig(np.empty((2, 2)), True, False)
+    check_contig(np.empty((2, 2), order='F'), False, True)
+
+    # Check that np.array creates correct contiguous flags:
+    check_contig(np.array(a, copy=None), False, False)
+    check_contig(np.array(a, copy=None, order='C'), True, False)
+    check_contig(np.array(a, ndmin=4, copy=None, order='F'), False, True)
+
+    # Check slicing update of flags and :
+    check_contig(a[0], True, True)
+    check_contig(a[None, ::4, ..., None], True, True)
+    check_contig(b[0, 0, ...], False, True)
+    check_contig(b[:, :, 0:0, :, :], True, True)
+
+    # Test ravel and squeeze.
+    check_contig(a.ravel(), True, True)
+    check_contig(np.ones((1, 3, 1)).squeeze(), True, True)
+
+def test_broadcast_arrays():
+    # Test user defined dtypes
+    a = np.array([(1, 2, 3)], dtype='u4,u4,u4')
+    b = np.array([(1, 2, 3), (4, 5, 6), (7, 8, 9)], dtype='u4,u4,u4')
+    result = np.broadcast_arrays(a, b)
+    assert_equal(result[0], np.array([(1, 2, 3), (1, 2, 3), (1, 2, 3)], dtype='u4,u4,u4'))
+    assert_equal(result[1], np.array([(1, 2, 3), (4, 5, 6), (7, 8, 9)], dtype='u4,u4,u4'))
+
+@pytest.mark.parametrize(["shape", "fill_value", "expected_output"],
+        [((2, 2), [5.0,  6.0], np.array([[5.0, 6.0], [5.0, 6.0]])),
+         ((3, 2), [1.0,  2.0], np.array([[1.0, 2.0], [1.0, 2.0], [1.0,  2.0]]))])
+def test_full_from_list(shape, fill_value, expected_output):
+    output = np.full(shape, fill_value)
+    assert_equal(output, expected_output)
+
+def test_astype_copyflag():
+    # test the various copyflag options
+    arr = np.arange(10, dtype=np.intp)
+
+    res_true = arr.astype(np.intp, copy=True)
+    assert not np.shares_memory(arr, res_true)
+
+    res_false = arr.astype(np.intp, copy=False)
+    assert np.shares_memory(arr, res_false)
+
+    res_false_float = arr.astype(np.float64, copy=False)
+    assert not np.shares_memory(arr, res_false_float)
+
+    # _CopyMode enum isn't allowed
+    assert_raises(ValueError, arr.astype, np.float64,
+                  copy=np._CopyMode.NEVER)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_argparse.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_argparse.py
new file mode 100644
index 0000000..7f949c1
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_argparse.py
@@ -0,0 +1,92 @@
+"""
+Tests for the private NumPy argument parsing functionality.
+They mainly exists to ensure good test coverage without having to try the
+weirder cases on actual numpy functions but test them in one place.
+
+The test function is defined in C to be equivalent to (errors may not always
+match exactly, and could be adjusted):
+
+    def func(arg1, /, arg2, *, arg3):
+        i = integer(arg1)  # reproducing the 'i' parsing in Python.
+        return None
+"""
+
+import threading
+
+import pytest
+from numpy._core._multiarray_tests import (
+    argparse_example_function as func,
+)
+from numpy._core._multiarray_tests import (
+    threaded_argparse_example_function as thread_func,
+)
+
+import numpy as np
+from numpy.testing import IS_WASM
+
+
+@pytest.mark.skipif(IS_WASM, reason="wasm doesn't have support for threads")
+def test_thread_safe_argparse_cache():
+    b = threading.Barrier(8)
+
+    def call_thread_func():
+        b.wait()
+        thread_func(arg1=3, arg2=None)
+
+    tasks = [threading.Thread(target=call_thread_func) for _ in range(8)]
+    [t.start() for t in tasks]
+    [t.join() for t in tasks]
+
+
+def test_invalid_integers():
+    with pytest.raises(TypeError,
+            match="integer argument expected, got float"):
+        func(1.)
+    with pytest.raises(OverflowError):
+        func(2**100)
+
+
+def test_missing_arguments():
+    with pytest.raises(TypeError,
+            match="missing required positional argument 0"):
+        func()
+    with pytest.raises(TypeError,
+            match="missing required positional argument 0"):
+        func(arg2=1, arg3=4)
+    with pytest.raises(TypeError,
+            match=r"missing required argument \'arg2\' \(pos 1\)"):
+        func(1, arg3=5)
+
+
+def test_too_many_positional():
+    # the second argument is positional but can be passed as keyword.
+    with pytest.raises(TypeError,
+            match="takes from 2 to 3 positional arguments but 4 were given"):
+        func(1, 2, 3, 4)
+
+
+def test_multiple_values():
+    with pytest.raises(TypeError,
+            match=r"given by name \('arg2'\) and position \(position 1\)"):
+        func(1, 2, arg2=3)
+
+
+def test_string_fallbacks():
+    # We can (currently?) use numpy strings to test the "slow" fallbacks
+    # that should normally not be taken due to string interning.
+    arg2 = np.str_("arg2")
+    missing_arg = np.str_("missing_arg")
+    func(1, **{arg2: 3})
+    with pytest.raises(TypeError,
+            match="got an unexpected keyword argument 'missing_arg'"):
+        func(2, **{missing_arg: 3})
+
+
+def test_too_many_arguments_method_forwarding():
+    # Not directly related to the standard argument parsing, but we sometimes
+    # forward methods to Python: arr.mean() calls np._core._methods._mean()
+    # This adds code coverage for this `npy_forward_method`.
+    arr = np.arange(3)
+    args = range(1000)
+    with pytest.raises(TypeError):
+        arr.mean(*args)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_array_api_info.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_array_api_info.py
new file mode 100644
index 0000000..4842dbf
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_array_api_info.py
@@ -0,0 +1,113 @@
+import pytest
+
+import numpy as np
+
+info = np.__array_namespace_info__()
+
+
+def test_capabilities():
+    caps = info.capabilities()
+    assert caps["boolean indexing"] is True
+    assert caps["data-dependent shapes"] is True
+
+    # This will be added in the 2024.12 release of the array API standard.
+
+    # assert caps["max rank"] == 64
+    # np.zeros((1,)*64)
+    # with pytest.raises(ValueError):
+    #     np.zeros((1,)*65)
+
+
+def test_default_device():
+    assert info.default_device() == "cpu" == np.asarray(0).device
+
+
+def test_default_dtypes():
+    dtypes = info.default_dtypes()
+    assert dtypes["real floating"] == np.float64 == np.asarray(0.0).dtype
+    assert dtypes["complex floating"] == np.complex128 == \
+        np.asarray(0.0j).dtype
+    assert dtypes["integral"] == np.intp == np.asarray(0).dtype
+    assert dtypes["indexing"] == np.intp == np.argmax(np.zeros(10)).dtype
+
+    with pytest.raises(ValueError, match="Device not understood"):
+        info.default_dtypes(device="gpu")
+
+
+def test_dtypes_all():
+    dtypes = info.dtypes()
+    assert dtypes == {
+        "bool": np.bool_,
+        "int8": np.int8,
+        "int16": np.int16,
+        "int32": np.int32,
+        "int64": np.int64,
+        "uint8": np.uint8,
+        "uint16": np.uint16,
+        "uint32": np.uint32,
+        "uint64": np.uint64,
+        "float32": np.float32,
+        "float64": np.float64,
+        "complex64": np.complex64,
+        "complex128": np.complex128,
+    }
+
+
+dtype_categories = {
+    "bool": {"bool": np.bool_},
+    "signed integer": {
+        "int8": np.int8,
+        "int16": np.int16,
+        "int32": np.int32,
+        "int64": np.int64,
+    },
+    "unsigned integer": {
+        "uint8": np.uint8,
+        "uint16": np.uint16,
+        "uint32": np.uint32,
+        "uint64": np.uint64,
+    },
+    "integral": ("signed integer", "unsigned integer"),
+    "real floating": {"float32": np.float32, "float64": np.float64},
+    "complex floating": {"complex64": np.complex64, "complex128":
+                         np.complex128},
+    "numeric": ("integral", "real floating", "complex floating"),
+}
+
+
+@pytest.mark.parametrize("kind", dtype_categories)
+def test_dtypes_kind(kind):
+    expected = dtype_categories[kind]
+    if isinstance(expected, tuple):
+        assert info.dtypes(kind=kind) == info.dtypes(kind=expected)
+    else:
+        assert info.dtypes(kind=kind) == expected
+
+
+def test_dtypes_tuple():
+    dtypes = info.dtypes(kind=("bool", "integral"))
+    assert dtypes == {
+        "bool": np.bool_,
+        "int8": np.int8,
+        "int16": np.int16,
+        "int32": np.int32,
+        "int64": np.int64,
+        "uint8": np.uint8,
+        "uint16": np.uint16,
+        "uint32": np.uint32,
+        "uint64": np.uint64,
+    }
+
+
+def test_dtypes_invalid_kind():
+    with pytest.raises(ValueError, match="unsupported kind"):
+        info.dtypes(kind="invalid")
+
+
+def test_dtypes_invalid_device():
+    with pytest.raises(ValueError, match="Device not understood"):
+        info.dtypes(device="gpu")
+
+
+def test_devices():
+    assert info.devices() == ["cpu"]
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_array_coercion.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_array_coercion.py
new file mode 100644
index 0000000..883aee6
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_array_coercion.py
@@ -0,0 +1,911 @@
+"""
+Tests for array coercion, mainly through testing `np.array` results directly.
+Note that other such tests exist, e.g., in `test_api.py` and many corner-cases
+are tested (sometimes indirectly) elsewhere.
+"""
+
+from itertools import permutations, product
+
+import numpy._core._multiarray_umath as ncu
+import pytest
+from numpy._core._rational_tests import rational
+from pytest import param
+
+import numpy as np
+from numpy.testing import IS_64BIT, IS_PYPY, assert_array_equal
+
+
+def arraylikes():
+    """
+    Generator for functions converting an array into various array-likes.
+    If full is True (default) it includes array-likes not capable of handling
+    all dtypes.
+    """
+    # base array:
+    def ndarray(a):
+        return a
+
+    yield param(ndarray, id="ndarray")
+
+    # subclass:
+    class MyArr(np.ndarray):
+        pass
+
+    def subclass(a):
+        return a.view(MyArr)
+
+    yield subclass
+
+    class _SequenceLike:
+        # Older NumPy versions, sometimes cared whether a protocol array was
+        # also _SequenceLike.  This shouldn't matter, but keep it for now
+        # for __array__ and not the others.
+        def __len__(self):
+            raise TypeError
+
+        def __getitem__(self, _, /):
+            raise TypeError
+
+    # Array-interface
+    class ArrayDunder(_SequenceLike):
+        def __init__(self, a):
+            self.a = a
+
+        def __array__(self, dtype=None, copy=None):
+            if dtype is None:
+                return self.a
+            return self.a.astype(dtype)
+
+    yield param(ArrayDunder, id="__array__")
+
+    # memory-view
+    yield param(memoryview, id="memoryview")
+
+    # Array-interface
+    class ArrayInterface:
+        def __init__(self, a):
+            self.a = a  # need to hold on to keep interface valid
+            self.__array_interface__ = a.__array_interface__
+
+    yield param(ArrayInterface, id="__array_interface__")
+
+    # Array-Struct
+    class ArrayStruct:
+        def __init__(self, a):
+            self.a = a  # need to hold on to keep struct valid
+            self.__array_struct__ = a.__array_struct__
+
+    yield param(ArrayStruct, id="__array_struct__")
+
+
+def scalar_instances(times=True, extended_precision=True, user_dtype=True):
+    # Hard-coded list of scalar instances.
+    # Floats:
+    yield param(np.sqrt(np.float16(5)), id="float16")
+    yield param(np.sqrt(np.float32(5)), id="float32")
+    yield param(np.sqrt(np.float64(5)), id="float64")
+    if extended_precision:
+        yield param(np.sqrt(np.longdouble(5)), id="longdouble")
+
+    # Complex:
+    yield param(np.sqrt(np.complex64(2 + 3j)), id="complex64")
+    yield param(np.sqrt(np.complex128(2 + 3j)), id="complex128")
+    if extended_precision:
+        yield param(np.sqrt(np.clongdouble(2 + 3j)), id="clongdouble")
+
+    # Bool:
+    # XFAIL: Bool should be added, but has some bad properties when it
+    # comes to strings, see also gh-9875
+    # yield param(np.bool(0), id="bool")
+
+    # Integers:
+    yield param(np.int8(2), id="int8")
+    yield param(np.int16(2), id="int16")
+    yield param(np.int32(2), id="int32")
+    yield param(np.int64(2), id="int64")
+
+    yield param(np.uint8(2), id="uint8")
+    yield param(np.uint16(2), id="uint16")
+    yield param(np.uint32(2), id="uint32")
+    yield param(np.uint64(2), id="uint64")
+
+    # Rational:
+    if user_dtype:
+        yield param(rational(1, 2), id="rational")
+
+    # Cannot create a structured void scalar directly:
+    structured = np.array([(1, 3)], "i,i")[0]
+    assert isinstance(structured, np.void)
+    assert structured.dtype == np.dtype("i,i")
+    yield param(structured, id="structured")
+
+    if times:
+        # Datetimes and timedelta
+        yield param(np.timedelta64(2), id="timedelta64[generic]")
+        yield param(np.timedelta64(23, "s"), id="timedelta64[s]")
+        yield param(np.timedelta64("NaT", "s"), id="timedelta64[s](NaT)")
+
+        yield param(np.datetime64("NaT"), id="datetime64[generic](NaT)")
+        yield param(np.datetime64("2020-06-07 12:43", "ms"), id="datetime64[ms]")
+
+    # Strings and unstructured void:
+    yield param(np.bytes_(b"1234"), id="bytes")
+    yield param(np.str_("2345"), id="unicode")
+    yield param(np.void(b"4321"), id="unstructured_void")
+
+
+def is_parametric_dtype(dtype):
+    """Returns True if the dtype is a parametric legacy dtype (itemsize
+    is 0, or a datetime without units)
+    """
+    if dtype.itemsize == 0:
+        return True
+    if issubclass(dtype.type, (np.datetime64, np.timedelta64)):
+        if dtype.name.endswith("64"):
+            # Generic time units
+            return True
+    return False
+
+
+class TestStringDiscovery:
+    @pytest.mark.parametrize("obj",
+            [object(), 1.2, 10**43, None, "string"],
+            ids=["object", "1.2", "10**43", "None", "string"])
+    def test_basic_stringlength(self, obj):
+        length = len(str(obj))
+        expected = np.dtype(f"S{length}")
+
+        assert np.array(obj, dtype="S").dtype == expected
+        assert np.array([obj], dtype="S").dtype == expected
+
+        # A nested array is also discovered correctly
+        arr = np.array(obj, dtype="O")
+        assert np.array(arr, dtype="S").dtype == expected
+        # Also if we use the dtype class
+        assert np.array(arr, dtype=type(expected)).dtype == expected
+        # Check that .astype() behaves identical
+        assert arr.astype("S").dtype == expected
+        # The DType class is accepted by `.astype()`
+        assert arr.astype(type(np.dtype("S"))).dtype == expected
+
+    @pytest.mark.parametrize("obj",
+            [object(), 1.2, 10**43, None, "string"],
+            ids=["object", "1.2", "10**43", "None", "string"])
+    def test_nested_arrays_stringlength(self, obj):
+        length = len(str(obj))
+        expected = np.dtype(f"S{length}")
+        arr = np.array(obj, dtype="O")
+        assert np.array([arr, arr], dtype="S").dtype == expected
+
+    @pytest.mark.parametrize("arraylike", arraylikes())
+    def test_unpack_first_level(self, arraylike):
+        # We unpack exactly one level of array likes
+        obj = np.array([None])
+        obj[0] = np.array(1.2)
+        # the length of the included item, not of the float dtype
+        length = len(str(obj[0]))
+        expected = np.dtype(f"S{length}")
+
+        obj = arraylike(obj)
+        # casting to string usually calls str(obj)
+        arr = np.array([obj], dtype="S")
+        assert arr.shape == (1, 1)
+        assert arr.dtype == expected
+
+
+class TestScalarDiscovery:
+    def test_void_special_case(self):
+        # Void dtypes with structures discover tuples as elements
+        arr = np.array((1, 2, 3), dtype="i,i,i")
+        assert arr.shape == ()
+        arr = np.array([(1, 2, 3)], dtype="i,i,i")
+        assert arr.shape == (1,)
+
+    def test_char_special_case(self):
+        arr = np.array("string", dtype="c")
+        assert arr.shape == (6,)
+        assert arr.dtype.char == "c"
+        arr = np.array(["string"], dtype="c")
+        assert arr.shape == (1, 6)
+        assert arr.dtype.char == "c"
+
+    def test_char_special_case_deep(self):
+        # Check that the character special case errors correctly if the
+        # array is too deep:
+        nested = ["string"]  # 2 dimensions (due to string being sequence)
+        for i in range(ncu.MAXDIMS - 2):
+            nested = [nested]
+
+        arr = np.array(nested, dtype='c')
+        assert arr.shape == (1,) * (ncu.MAXDIMS - 1) + (6,)
+        with pytest.raises(ValueError):
+            np.array([nested], dtype="c")
+
+    def test_unknown_object(self):
+        arr = np.array(object())
+        assert arr.shape == ()
+        assert arr.dtype == np.dtype("O")
+
+    @pytest.mark.parametrize("scalar", scalar_instances())
+    def test_scalar(self, scalar):
+        arr = np.array(scalar)
+        assert arr.shape == ()
+        assert arr.dtype == scalar.dtype
+
+        arr = np.array([[scalar, scalar]])
+        assert arr.shape == (1, 2)
+        assert arr.dtype == scalar.dtype
+
+    # Additionally to string this test also runs into a corner case
+    # with datetime promotion (the difference is the promotion order).
+    @pytest.mark.filterwarnings("ignore:Promotion of numbers:FutureWarning")
+    def test_scalar_promotion(self):
+        for sc1, sc2 in product(scalar_instances(), scalar_instances()):
+            sc1, sc2 = sc1.values[0], sc2.values[0]
+            # test all combinations:
+            try:
+                arr = np.array([sc1, sc2])
+            except (TypeError, ValueError):
+                # The promotion between two times can fail
+                # XFAIL (ValueError): Some object casts are currently undefined
+                continue
+            assert arr.shape == (2,)
+            try:
+                dt1, dt2 = sc1.dtype, sc2.dtype
+                expected_dtype = np.promote_types(dt1, dt2)
+                assert arr.dtype == expected_dtype
+            except TypeError as e:
+                # Will currently always go to object dtype
+                assert arr.dtype == np.dtype("O")
+
+    @pytest.mark.parametrize("scalar", scalar_instances())
+    def test_scalar_coercion(self, scalar):
+        # This tests various scalar coercion paths, mainly for the numerical
+        # types. It includes some paths not directly related to `np.array`.
+        if isinstance(scalar, np.inexact):
+            # Ensure we have a full-precision number if available
+            scalar = type(scalar)((scalar * 2)**0.5)
+
+        if type(scalar) is rational:
+            # Rational generally fails due to a missing cast. In the future
+            # object casts should automatically be defined based on `setitem`.
+            pytest.xfail("Rational to object cast is undefined currently.")
+
+        # Use casting from object:
+        arr = np.array(scalar, dtype=object).astype(scalar.dtype)
+
+        # Test various ways to create an array containing this scalar:
+        arr1 = np.array(scalar).reshape(1)
+        arr2 = np.array([scalar])
+        arr3 = np.empty(1, dtype=scalar.dtype)
+        arr3[0] = scalar
+        arr4 = np.empty(1, dtype=scalar.dtype)
+        arr4[:] = [scalar]
+        # All of these methods should yield the same results
+        assert_array_equal(arr, arr1)
+        assert_array_equal(arr, arr2)
+        assert_array_equal(arr, arr3)
+        assert_array_equal(arr, arr4)
+
+    @pytest.mark.xfail(IS_PYPY, reason="`int(np.complex128(3))` fails on PyPy")
+    @pytest.mark.filterwarnings("ignore::numpy.exceptions.ComplexWarning")
+    @pytest.mark.parametrize("cast_to", scalar_instances())
+    def test_scalar_coercion_same_as_cast_and_assignment(self, cast_to):
+        """
+        Test that in most cases:
+           * `np.array(scalar, dtype=dtype)`
+           * `np.empty((), dtype=dtype)[()] = scalar`
+           * `np.array(scalar).astype(dtype)`
+        should behave the same.  The only exceptions are parametric dtypes
+        (mainly datetime/timedelta without unit) and void without fields.
+        """
+        dtype = cast_to.dtype  # use to parametrize only the target dtype
+
+        for scalar in scalar_instances(times=False):
+            scalar = scalar.values[0]
+
+            if dtype.type == np.void:
+                if scalar.dtype.fields is not None and dtype.fields is None:
+                    # Here, coercion to "V6" works, but the cast fails.
+                    # Since the types are identical, SETITEM takes care of
+                    # this, but has different rules than the cast.
+                    with pytest.raises(TypeError):
+                        np.array(scalar).astype(dtype)
+                    np.array(scalar, dtype=dtype)
+                    np.array([scalar], dtype=dtype)
+                    continue
+
+            # The main test, we first try to use casting and if it succeeds
+            # continue below testing that things are the same, otherwise
+            # test that the alternative paths at least also fail.
+            try:
+                cast = np.array(scalar).astype(dtype)
+            except (TypeError, ValueError, RuntimeError):
+                # coercion should also raise (error type may change)
+                with pytest.raises(Exception):  # noqa: B017
+                    np.array(scalar, dtype=dtype)
+
+                if (isinstance(scalar, rational) and
+                        np.issubdtype(dtype, np.signedinteger)):
+                    return
+
+                with pytest.raises(Exception):  # noqa: B017
+                    np.array([scalar], dtype=dtype)
+                # assignment should also raise
+                res = np.zeros((), dtype=dtype)
+                with pytest.raises(Exception):  # noqa: B017
+                    res[()] = scalar
+
+                return
+
+            # Non error path:
+            arr = np.array(scalar, dtype=dtype)
+            assert_array_equal(arr, cast)
+            # assignment behaves the same
+            ass = np.zeros((), dtype=dtype)
+            ass[()] = scalar
+            assert_array_equal(ass, cast)
+
+    @pytest.mark.parametrize("pyscalar", [10, 10.32, 10.14j, 10**100])
+    def test_pyscalar_subclasses(self, pyscalar):
+        """NumPy arrays are read/write which means that anything but invariant
+        behaviour is on thin ice.  However, we currently are happy to discover
+        subclasses of Python float, int, complex the same as the base classes.
+        This should potentially be deprecated.
+        """
+        class MyScalar(type(pyscalar)):
+            pass
+
+        res = np.array(MyScalar(pyscalar))
+        expected = np.array(pyscalar)
+        assert_array_equal(res, expected)
+
+    @pytest.mark.parametrize("dtype_char", np.typecodes["All"])
+    def test_default_dtype_instance(self, dtype_char):
+        if dtype_char in "SU":
+            dtype = np.dtype(dtype_char + "1")
+        elif dtype_char == "V":
+            # Legacy behaviour was to use V8. The reason was float64 being the
+            # default dtype and that having 8 bytes.
+            dtype = np.dtype("V8")
+        else:
+            dtype = np.dtype(dtype_char)
+
+        discovered_dtype, _ = ncu._discover_array_parameters([], type(dtype))
+
+        assert discovered_dtype == dtype
+        assert discovered_dtype.itemsize == dtype.itemsize
+
+    @pytest.mark.parametrize("dtype", np.typecodes["Integer"])
+    @pytest.mark.parametrize(["scalar", "error"],
+            [(np.float64(np.nan), ValueError),
+             (np.array(-1).astype(np.ulonglong)[()], OverflowError)])
+    def test_scalar_to_int_coerce_does_not_cast(self, dtype, scalar, error):
+        """
+        Signed integers are currently different in that they do not cast other
+        NumPy scalar, but instead use scalar.__int__(). The hardcoded
+        exception to this rule is `np.array(scalar, dtype=integer)`.
+        """
+        dtype = np.dtype(dtype)
+
+        # This is a special case using casting logic. It warns for the NaN
+        # but allows the cast (giving undefined behaviour).
+        with np.errstate(invalid="ignore"):
+            coerced = np.array(scalar, dtype=dtype)
+            cast = np.array(scalar).astype(dtype)
+        assert_array_equal(coerced, cast)
+
+        # However these fail:
+        with pytest.raises(error):
+            np.array([scalar], dtype=dtype)
+        with pytest.raises(error):
+            cast[()] = scalar
+
+
+class TestTimeScalars:
+    @pytest.mark.parametrize("dtype", [np.int64, np.float32])
+    @pytest.mark.parametrize("scalar",
+            [param(np.timedelta64("NaT", "s"), id="timedelta64[s](NaT)"),
+             param(np.timedelta64(123, "s"), id="timedelta64[s]"),
+             param(np.datetime64("NaT", "generic"), id="datetime64[generic](NaT)"),
+             param(np.datetime64(1, "D"), id="datetime64[D]")],)
+    def test_coercion_basic(self, dtype, scalar):
+        # Note the `[scalar]` is there because np.array(scalar) uses stricter
+        # `scalar.__int__()` rules for backward compatibility right now.
+        arr = np.array(scalar, dtype=dtype)
+        cast = np.array(scalar).astype(dtype)
+        assert_array_equal(arr, cast)
+
+        ass = np.ones((), dtype=dtype)
+        if issubclass(dtype, np.integer):
+            with pytest.raises(TypeError):
+                # raises, as would np.array([scalar], dtype=dtype), this is
+                # conversion from times, but behaviour of integers.
+                ass[()] = scalar
+        else:
+            ass[()] = scalar
+            assert_array_equal(ass, cast)
+
+    @pytest.mark.parametrize("dtype", [np.int64, np.float32])
+    @pytest.mark.parametrize("scalar",
+            [param(np.timedelta64(123, "ns"), id="timedelta64[ns]"),
+             param(np.timedelta64(12, "generic"), id="timedelta64[generic]")])
+    def test_coercion_timedelta_convert_to_number(self, dtype, scalar):
+        # Only "ns" and "generic" timedeltas can be converted to numbers
+        # so these are slightly special.
+        arr = np.array(scalar, dtype=dtype)
+        cast = np.array(scalar).astype(dtype)
+        ass = np.ones((), dtype=dtype)
+        ass[()] = scalar  # raises, as would np.array([scalar], dtype=dtype)
+
+        assert_array_equal(arr, cast)
+        assert_array_equal(cast, cast)
+
+    @pytest.mark.parametrize("dtype", ["S6", "U6"])
+    @pytest.mark.parametrize(["val", "unit"],
+            [param(123, "s", id="[s]"), param(123, "D", id="[D]")])
+    def test_coercion_assignment_datetime(self, val, unit, dtype):
+        # String from datetime64 assignment is currently special cased to
+        # never use casting.  This is because casting will error in this
+        # case, and traditionally in most cases the behaviour is maintained
+        # like this.  (`np.array(scalar, dtype="U6")` would have failed before)
+        # TODO: This discrepancy _should_ be resolved, either by relaxing the
+        #       cast, or by deprecating the first part.
+        scalar = np.datetime64(val, unit)
+        dtype = np.dtype(dtype)
+        cut_string = dtype.type(str(scalar)[:6])
+
+        arr = np.array(scalar, dtype=dtype)
+        assert arr[()] == cut_string
+        ass = np.ones((), dtype=dtype)
+        ass[()] = scalar
+        assert ass[()] == cut_string
+
+        with pytest.raises(RuntimeError):
+            # However, unlike the above assignment using `str(scalar)[:6]`
+            # due to being handled by the string DType and not be casting
+            # the explicit cast fails:
+            np.array(scalar).astype(dtype)
+
+    @pytest.mark.parametrize(["val", "unit"],
+            [param(123, "s", id="[s]"), param(123, "D", id="[D]")])
+    def test_coercion_assignment_timedelta(self, val, unit):
+        scalar = np.timedelta64(val, unit)
+
+        # Unlike datetime64, timedelta allows the unsafe cast:
+        np.array(scalar, dtype="S6")
+        cast = np.array(scalar).astype("S6")
+        ass = np.ones((), dtype="S6")
+        ass[()] = scalar
+        expected = scalar.astype("S")[:6]
+        assert cast[()] == expected
+        assert ass[()] == expected
+
+class TestNested:
+    def test_nested_simple(self):
+        initial = [1.2]
+        nested = initial
+        for i in range(ncu.MAXDIMS - 1):
+            nested = [nested]
+
+        arr = np.array(nested, dtype="float64")
+        assert arr.shape == (1,) * ncu.MAXDIMS
+        with pytest.raises(ValueError):
+            np.array([nested], dtype="float64")
+
+        with pytest.raises(ValueError, match=".*would exceed the maximum"):
+            np.array([nested])  # user must ask for `object` explicitly
+
+        arr = np.array([nested], dtype=object)
+        assert arr.dtype == np.dtype("O")
+        assert arr.shape == (1,) * ncu.MAXDIMS
+        assert arr.item() is initial
+
+    def test_pathological_self_containing(self):
+        # Test that this also works for two nested sequences
+        l = []
+        l.append(l)
+        arr = np.array([l, l, l], dtype=object)
+        assert arr.shape == (3,) + (1,) * (ncu.MAXDIMS - 1)
+
+        # Also check a ragged case:
+        arr = np.array([l, [None], l], dtype=object)
+        assert arr.shape == (3, 1)
+
+    @pytest.mark.parametrize("arraylike", arraylikes())
+    def test_nested_arraylikes(self, arraylike):
+        # We try storing an array like into an array, but the array-like
+        # will have too many dimensions.  This means the shape discovery
+        # decides that the array-like must be treated as an object (a special
+        # case of ragged discovery).  The result will be an array with one
+        # dimension less than the maximum dimensions, and the array being
+        # assigned to it (which does work for object or if `float(arraylike)`
+        # works).
+        initial = arraylike(np.ones((1, 1)))
+
+        nested = initial
+        for i in range(ncu.MAXDIMS - 1):
+            nested = [nested]
+
+        with pytest.raises(ValueError, match=".*would exceed the maximum"):
+            # It will refuse to assign the array into
+            np.array(nested, dtype="float64")
+
+        # If this is object, we end up assigning a (1, 1) array into (1,)
+        # (due to running out of dimensions), this is currently supported but
+        # a special case which is not ideal.
+        arr = np.array(nested, dtype=object)
+        assert arr.shape == (1,) * ncu.MAXDIMS
+        assert arr.item() == np.array(initial).item()
+
+    @pytest.mark.parametrize("arraylike", arraylikes())
+    def test_uneven_depth_ragged(self, arraylike):
+        arr = np.arange(4).reshape((2, 2))
+        arr = arraylike(arr)
+
+        # Array is ragged in the second dimension already:
+        out = np.array([arr, [arr]], dtype=object)
+        assert out.shape == (2,)
+        assert out[0] is arr
+        assert type(out[1]) is list
+
+        # Array is ragged in the third dimension:
+        with pytest.raises(ValueError):
+            # This is a broadcast error during assignment, because
+            # the array shape would be (2, 2, 2) but `arr[0, 0] = arr` fails.
+            np.array([arr, [arr, arr]], dtype=object)
+
+    def test_empty_sequence(self):
+        arr = np.array([[], [1], [[1]]], dtype=object)
+        assert arr.shape == (3,)
+
+        # The empty sequence stops further dimension discovery, so the
+        # result shape will be (0,) which leads to an error during:
+        with pytest.raises(ValueError):
+            np.array([[], np.empty((0, 1))], dtype=object)
+
+    def test_array_of_different_depths(self):
+        # When multiple arrays (or array-likes) are included in a
+        # sequences and have different depth, we currently discover
+        # as many dimensions as they share. (see also gh-17224)
+        arr = np.zeros((3, 2))
+        mismatch_first_dim = np.zeros((1, 2))
+        mismatch_second_dim = np.zeros((3, 3))
+
+        dtype, shape = ncu._discover_array_parameters(
+            [arr, mismatch_second_dim], dtype=np.dtype("O"))
+        assert shape == (2, 3)
+
+        dtype, shape = ncu._discover_array_parameters(
+            [arr, mismatch_first_dim], dtype=np.dtype("O"))
+        assert shape == (2,)
+        # The second case is currently supported because the arrays
+        # can be stored as objects:
+        res = np.asarray([arr, mismatch_first_dim], dtype=np.dtype("O"))
+        assert res[0] is arr
+        assert res[1] is mismatch_first_dim
+
+
+class TestBadSequences:
+    # These are tests for bad objects passed into `np.array`, in general
+    # these have undefined behaviour.  In the old code they partially worked
+    # when now they will fail.  We could (and maybe should) create a copy
+    # of all sequences to be safe against bad-actors.
+
+    def test_growing_list(self):
+        # List to coerce, `mylist` will append to it during coercion
+        obj = []
+
+        class mylist(list):
+            def __len__(self):
+                obj.append([1, 2])
+                return super().__len__()
+
+        obj.append(mylist([1, 2]))
+
+        with pytest.raises(RuntimeError):
+            np.array(obj)
+
+    # Note: We do not test a shrinking list.  These do very evil things
+    #       and the only way to fix them would be to copy all sequences.
+    #       (which may be a real option in the future).
+
+    def test_mutated_list(self):
+        # List to coerce, `mylist` will mutate the first element
+        obj = []
+
+        class mylist(list):
+            def __len__(self):
+                obj[0] = [2, 3]  # replace with a different list.
+                return super().__len__()
+
+        obj.append([2, 3])
+        obj.append(mylist([1, 2]))
+        # Does not crash:
+        np.array(obj)
+
+    def test_replace_0d_array(self):
+        # List to coerce, `mylist` will mutate the first element
+        obj = []
+
+        class baditem:
+            def __len__(self):
+                obj[0][0] = 2  # replace with a different list.
+                raise ValueError("not actually a sequence!")
+
+            def __getitem__(self, _, /):
+                pass
+
+        # Runs into a corner case in the new code, the `array(2)` is cached
+        # so replacing it invalidates the cache.
+        obj.append([np.array(2), baditem()])
+        with pytest.raises(RuntimeError):
+            np.array(obj)
+
+
+class TestArrayLikes:
+    @pytest.mark.parametrize("arraylike", arraylikes())
+    def test_0d_object_special_case(self, arraylike):
+        arr = np.array(0.)
+        obj = arraylike(arr)
+        # A single array-like is always converted:
+        res = np.array(obj, dtype=object)
+        assert_array_equal(arr, res)
+
+        # But a single 0-D nested array-like never:
+        res = np.array([obj], dtype=object)
+        assert res[0] is obj
+
+    @pytest.mark.parametrize("arraylike", arraylikes())
+    @pytest.mark.parametrize("arr", [np.array(0.), np.arange(4)])
+    def test_object_assignment_special_case(self, arraylike, arr):
+        obj = arraylike(arr)
+        empty = np.arange(1, dtype=object)
+        empty[:] = [obj]
+        assert empty[0] is obj
+
+    def test_0d_generic_special_case(self):
+        class ArraySubclass(np.ndarray):
+            def __float__(self):
+                raise TypeError("e.g. quantities raise on this")
+
+        arr = np.array(0.)
+        obj = arr.view(ArraySubclass)
+        res = np.array(obj)
+        # The subclass is simply cast:
+        assert_array_equal(arr, res)
+
+        # If the 0-D array-like is included, __float__ is currently
+        # guaranteed to be used.  We may want to change that, quantities
+        # and masked arrays half make use of this.
+        with pytest.raises(TypeError):
+            np.array([obj])
+
+        # The same holds for memoryview:
+        obj = memoryview(arr)
+        res = np.array(obj)
+        assert_array_equal(arr, res)
+        with pytest.raises(ValueError):
+            # The error type does not matter much here.
+            np.array([obj])
+
+    def test_arraylike_classes(self):
+        # The classes of array-likes should generally be acceptable to be
+        # stored inside a numpy (object) array.  This tests all of the
+        # special attributes (since all are checked during coercion).
+        arr = np.array(np.int64)
+        assert arr[()] is np.int64
+        arr = np.array([np.int64])
+        assert arr[0] is np.int64
+
+        # This also works for properties/unbound methods:
+        class ArrayLike:
+            @property
+            def __array_interface__(self):
+                pass
+
+            @property
+            def __array_struct__(self):
+                pass
+
+            def __array__(self, dtype=None, copy=None):
+                pass
+
+        arr = np.array(ArrayLike)
+        assert arr[()] is ArrayLike
+        arr = np.array([ArrayLike])
+        assert arr[0] is ArrayLike
+
+    @pytest.mark.skipif(not IS_64BIT, reason="Needs 64bit platform")
+    def test_too_large_array_error_paths(self):
+        """Test the error paths, including for memory leaks"""
+        arr = np.array(0, dtype="uint8")
+        # Guarantees that a contiguous copy won't work:
+        arr = np.broadcast_to(arr, 2**62)
+
+        for i in range(5):
+            # repeat, to ensure caching cannot have an effect:
+            with pytest.raises(MemoryError):
+                np.array(arr)
+            with pytest.raises(MemoryError):
+                np.array([arr])
+
+    @pytest.mark.parametrize("attribute",
+        ["__array_interface__", "__array__", "__array_struct__"])
+    @pytest.mark.parametrize("error", [RecursionError, MemoryError])
+    def test_bad_array_like_attributes(self, attribute, error):
+        # RecursionError and MemoryError are considered fatal. All errors
+        # (except AttributeError) should probably be raised in the future,
+        # but shapely made use of it, so it will require a deprecation.
+
+        class BadInterface:
+            def __getattr__(self, attr):
+                if attr == attribute:
+                    raise error
+                super().__getattr__(attr)
+
+        with pytest.raises(error):
+            np.array(BadInterface())
+
+    @pytest.mark.parametrize("error", [RecursionError, MemoryError])
+    def test_bad_array_like_bad_length(self, error):
+        # RecursionError and MemoryError are considered "critical" in
+        # sequences. We could expand this more generally though. (NumPy 1.20)
+        class BadSequence:
+            def __len__(self):
+                raise error
+
+            def __getitem__(self, _, /):
+                # must have getitem to be a Sequence
+                return 1
+
+        with pytest.raises(error):
+            np.array(BadSequence())
+
+    def test_array_interface_descr_optional(self):
+        # The descr should be optional regression test for gh-27249
+        arr = np.ones(10, dtype="V10")
+        iface = arr.__array_interface__
+        iface.pop("descr")
+
+        class MyClass:
+            __array_interface__ = iface
+
+        assert_array_equal(np.asarray(MyClass), arr)
+
+
+class TestAsArray:
+    """Test expected behaviors of ``asarray``."""
+
+    def test_dtype_identity(self):
+        """Confirm the intended behavior for *dtype* kwarg.
+
+        The result of ``asarray()`` should have the dtype provided through the
+        keyword argument, when used. This forces unique array handles to be
+        produced for unique np.dtype objects, but (for equivalent dtypes), the
+        underlying data (the base object) is shared with the original array
+        object.
+
+        Ref https://github.com/numpy/numpy/issues/1468
+        """
+        int_array = np.array([1, 2, 3], dtype='i')
+        assert np.asarray(int_array) is int_array
+
+        # The character code resolves to the singleton dtype object provided
+        # by the numpy package.
+        assert np.asarray(int_array, dtype='i') is int_array
+
+        # Derive a dtype from n.dtype('i'), but add a metadata object to force
+        # the dtype to be distinct.
+        unequal_type = np.dtype('i', metadata={'spam': True})
+        annotated_int_array = np.asarray(int_array, dtype=unequal_type)
+        assert annotated_int_array is not int_array
+        assert annotated_int_array.base is int_array
+        # Create an equivalent descriptor with a new and distinct dtype
+        # instance.
+        equivalent_requirement = np.dtype('i', metadata={'spam': True})
+        annotated_int_array_alt = np.asarray(annotated_int_array,
+                                             dtype=equivalent_requirement)
+        assert unequal_type == equivalent_requirement
+        assert unequal_type is not equivalent_requirement
+        assert annotated_int_array_alt is not annotated_int_array
+        assert annotated_int_array_alt.dtype is equivalent_requirement
+
+        # Check the same logic for a pair of C types whose equivalence may vary
+        # between computing environments.
+        # Find an equivalent pair.
+        integer_type_codes = ('i', 'l', 'q')
+        integer_dtypes = [np.dtype(code) for code in integer_type_codes]
+        typeA = None
+        typeB = None
+        for typeA, typeB in permutations(integer_dtypes, r=2):
+            if typeA == typeB:
+                assert typeA is not typeB
+                break
+        assert isinstance(typeA, np.dtype) and isinstance(typeB, np.dtype)
+
+        # These ``asarray()`` calls may produce a new view or a copy,
+        # but never the same object.
+        long_int_array = np.asarray(int_array, dtype='l')
+        long_long_int_array = np.asarray(int_array, dtype='q')
+        assert long_int_array is not int_array
+        assert long_long_int_array is not int_array
+        assert np.asarray(long_int_array, dtype='q') is not long_int_array
+        array_a = np.asarray(int_array, dtype=typeA)
+        assert typeA == typeB
+        assert typeA is not typeB
+        assert array_a.dtype is typeA
+        assert array_a is not np.asarray(array_a, dtype=typeB)
+        assert np.asarray(array_a, dtype=typeB).dtype is typeB
+        assert array_a is np.asarray(array_a, dtype=typeB).base
+
+
+class TestSpecialAttributeLookupFailure:
+    # An exception was raised while fetching the attribute
+
+    class WeirdArrayLike:
+        @property
+        def __array__(self, dtype=None, copy=None):  # noqa: PLR0206
+            raise RuntimeError("oops!")
+
+    class WeirdArrayInterface:
+        @property
+        def __array_interface__(self):
+            raise RuntimeError("oops!")
+
+    def test_deprecated(self):
+        with pytest.raises(RuntimeError):
+            np.array(self.WeirdArrayLike())
+        with pytest.raises(RuntimeError):
+            np.array(self.WeirdArrayInterface())
+
+
+def test_subarray_from_array_construction():
+    # Arrays are more complex, since they "broadcast" on success:
+    arr = np.array([1, 2])
+
+    res = arr.astype("2i")
+    assert_array_equal(res, [[1, 1], [2, 2]])
+
+    res = np.array(arr, dtype="(2,)i")
+
+    assert_array_equal(res, [[1, 1], [2, 2]])
+
+    res = np.array([[(1,), (2,)], arr], dtype="2i")
+    assert_array_equal(res, [[[1, 1], [2, 2]], [[1, 1], [2, 2]]])
+
+    # Also try a multi-dimensional example:
+    arr = np.arange(5 * 2).reshape(5, 2)
+    expected = np.broadcast_to(arr[:, :, np.newaxis, np.newaxis], (5, 2, 2, 2))
+
+    res = arr.astype("(2,2)f")
+    assert_array_equal(res, expected)
+
+    res = np.array(arr, dtype="(2,2)f")
+    assert_array_equal(res, expected)
+
+
+def test_empty_string():
+    # Empty strings are unfortunately often converted to S1 and we need to
+    # make sure we are filling the S1 and not the (possibly) detected S0
+    # result.  This should likely just return S0 and if not maybe the decision
+    # to return S1 should be moved.
+    res = np.array([""] * 10, dtype="S")
+    assert_array_equal(res, np.array("\0", "S1"))
+    assert res.dtype == "S1"
+
+    arr = np.array([""] * 10, dtype=object)
+
+    res = arr.astype("S")
+    assert_array_equal(res, b"")
+    assert res.dtype == "S1"
+
+    res = np.array(arr, dtype="S")
+    assert_array_equal(res, b"")
+    # TODO: This is arguably weird/wrong, but seems old:
+    assert res.dtype == f"S{np.dtype('O').itemsize}"
+
+    res = np.array([[""] * 10, arr], dtype="S")
+    assert_array_equal(res, b"")
+    assert res.shape == (2, 10)
+    assert res.dtype == "S1"
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_array_interface.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_array_interface.py
new file mode 100644
index 0000000..afb19f4
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_array_interface.py
@@ -0,0 +1,222 @@
+import sys
+import sysconfig
+
+import pytest
+
+import numpy as np
+from numpy.testing import IS_EDITABLE, IS_WASM, extbuild
+
+
+@pytest.fixture
+def get_module(tmp_path):
+    """ Some codes to generate data and manage temporary buffers use when
+    sharing with numpy via the array interface protocol.
+    """
+    if sys.platform.startswith('cygwin'):
+        pytest.skip('link fails on cygwin')
+    if IS_WASM:
+        pytest.skip("Can't build module inside Wasm")
+    if IS_EDITABLE:
+        pytest.skip("Can't build module for editable install")
+
+    prologue = '''
+        #include <Python.h>
+        #define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION
+        #include <numpy/arrayobject.h>
+        #include <stdio.h>
+        #include <math.h>
+
+        NPY_NO_EXPORT
+        void delete_array_struct(PyObject *cap) {
+
+            /* get the array interface structure */
+            PyArrayInterface *inter = (PyArrayInterface*)
+                PyCapsule_GetPointer(cap, NULL);
+
+            /* get the buffer by which data was shared */
+            double *ptr = (double*)PyCapsule_GetContext(cap);
+
+            /* for the purposes of the regression test set the elements
+               to nan */
+            for (npy_intp i = 0; i < inter->shape[0]; ++i)
+                ptr[i] = nan("");
+
+            /* free the shared buffer */
+            free(ptr);
+
+            /* free the array interface structure */
+            free(inter->shape);
+            free(inter);
+
+            fprintf(stderr, "delete_array_struct\\ncap = %ld inter = %ld"
+                " ptr = %ld\\n", (long)cap, (long)inter, (long)ptr);
+        }
+        '''
+
+    functions = [
+        ("new_array_struct", "METH_VARARGS", """
+
+            long long n_elem = 0;
+            double value = 0.0;
+
+            if (!PyArg_ParseTuple(args, "Ld", &n_elem, &value)) {
+                Py_RETURN_NONE;
+            }
+
+            /* allocate and initialize the data to share with numpy */
+            long long n_bytes = n_elem*sizeof(double);
+            double *data = (double*)malloc(n_bytes);
+
+            if (!data) {
+                PyErr_Format(PyExc_MemoryError,
+                    "Failed to malloc %lld bytes", n_bytes);
+
+                Py_RETURN_NONE;
+            }
+
+            for (long long i = 0; i < n_elem; ++i) {
+                data[i] = value;
+            }
+
+            /* calculate the shape and stride */
+            int nd = 1;
+
+            npy_intp *ss = (npy_intp*)malloc(2*nd*sizeof(npy_intp));
+            npy_intp *shape = ss;
+            npy_intp *stride = ss + nd;
+
+            shape[0] = n_elem;
+            stride[0] = sizeof(double);
+
+            /* construct the array interface */
+            PyArrayInterface *inter = (PyArrayInterface*)
+                malloc(sizeof(PyArrayInterface));
+
+            memset(inter, 0, sizeof(PyArrayInterface));
+
+            inter->two = 2;
+            inter->nd = nd;
+            inter->typekind = 'f';
+            inter->itemsize = sizeof(double);
+            inter->shape = shape;
+            inter->strides = stride;
+            inter->data = data;
+            inter->flags = NPY_ARRAY_WRITEABLE | NPY_ARRAY_NOTSWAPPED |
+                           NPY_ARRAY_ALIGNED | NPY_ARRAY_C_CONTIGUOUS;
+
+            /* package into a capsule */
+            PyObject *cap = PyCapsule_New(inter, NULL, delete_array_struct);
+
+            /* save the pointer to the data */
+            PyCapsule_SetContext(cap, data);
+
+            fprintf(stderr, "new_array_struct\\ncap = %ld inter = %ld"
+                " ptr = %ld\\n", (long)cap, (long)inter, (long)data);
+
+            return cap;
+        """)
+        ]
+
+    more_init = "import_array();"
+
+    try:
+        import array_interface_testing
+        return array_interface_testing
+    except ImportError:
+        pass
+
+    # if it does not exist, build and load it
+    if sysconfig.get_platform() == "win-arm64":
+        pytest.skip("Meson unable to find MSVC linker on win-arm64")
+    return extbuild.build_and_import_extension('array_interface_testing',
+                                               functions,
+                                               prologue=prologue,
+                                               include_dirs=[np.get_include()],
+                                               build_dir=tmp_path,
+                                               more_init=more_init)
+
+
+@pytest.mark.slow
+def test_cstruct(get_module):
+
+    class data_source:
+        """
+        This class is for testing the timing of the PyCapsule destructor
+        invoked when numpy release its reference to the shared data as part of
+        the numpy array interface protocol. If the PyCapsule destructor is
+        called early the shared data is freed and invalid memory accesses will
+        occur.
+        """
+
+        def __init__(self, size, value):
+            self.size = size
+            self.value = value
+
+        @property
+        def __array_struct__(self):
+            return get_module.new_array_struct(self.size, self.value)
+
+    # write to the same stream as the C code
+    stderr = sys.__stderr__
+
+    # used to validate the shared data.
+    expected_value = -3.1415
+    multiplier = -10000.0
+
+    # create some data to share with numpy via the array interface
+    # assign the data an expected value.
+    stderr.write(' ---- create an object to share data ---- \n')
+    buf = data_source(256, expected_value)
+    stderr.write(' ---- OK!\n\n')
+
+    # share the data
+    stderr.write(' ---- share data via the array interface protocol ---- \n')
+    arr = np.array(buf, copy=False)
+    stderr.write(f'arr.__array_interface___ = {str(arr.__array_interface__)}\n')
+    stderr.write(f'arr.base = {str(arr.base)}\n')
+    stderr.write(' ---- OK!\n\n')
+
+    # release the source of the shared data. this will not release the data
+    # that was shared with numpy, that is done in the PyCapsule destructor.
+    stderr.write(' ---- destroy the object that shared data ---- \n')
+    buf = None
+    stderr.write(' ---- OK!\n\n')
+
+    # check that we got the expected data. If the PyCapsule destructor we
+    # defined was prematurely called then this test will fail because our
+    # destructor sets the elements of the array to NaN before free'ing the
+    # buffer. Reading the values here may also cause a SEGV
+    assert np.allclose(arr, expected_value)
+
+    # read the data. If the PyCapsule destructor we defined was prematurely
+    # called then reading the values here may cause a SEGV and will be reported
+    # as invalid reads by valgrind
+    stderr.write(' ---- read shared data ---- \n')
+    stderr.write(f'arr = {str(arr)}\n')
+    stderr.write(' ---- OK!\n\n')
+
+    # write to the shared buffer. If the shared data was prematurely deleted
+    # this will may cause a SEGV and valgrind will report invalid writes
+    stderr.write(' ---- modify shared data ---- \n')
+    arr *= multiplier
+    expected_value *= multiplier
+    stderr.write(f'arr.__array_interface___ = {str(arr.__array_interface__)}\n')
+    stderr.write(f'arr.base = {str(arr.base)}\n')
+    stderr.write(' ---- OK!\n\n')
+
+    # read the data. If the shared data was prematurely deleted this
+    # will may cause a SEGV and valgrind will report invalid reads
+    stderr.write(' ---- read modified shared data ---- \n')
+    stderr.write(f'arr = {str(arr)}\n')
+    stderr.write(' ---- OK!\n\n')
+
+    # check that we got the expected data. If the PyCapsule destructor we
+    # defined was prematurely called then this test will fail because our
+    # destructor sets the elements of the array to NaN before free'ing the
+    # buffer. Reading the values here may also cause a SEGV
+    assert np.allclose(arr, expected_value)
+
+    # free the shared data, the PyCapsule destructor should run here
+    stderr.write(' ---- free shared data ---- \n')
+    arr = None
+    stderr.write(' ---- OK!\n\n')
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_arraymethod.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_arraymethod.py
new file mode 100644
index 0000000..d8baef7
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_arraymethod.py
@@ -0,0 +1,84 @@
+"""
+This file tests the generic aspects of ArrayMethod.  At the time of writing
+this is private API, but when added, public API may be added here.
+"""
+
+import types
+from typing import Any
+
+import pytest
+from numpy._core._multiarray_umath import _get_castingimpl as get_castingimpl
+
+import numpy as np
+
+
+class TestResolveDescriptors:
+    # Test mainly error paths of the resolve_descriptors function,
+    # note that the `casting_unittests` tests exercise this non-error paths.
+
+    # Casting implementations are the main/only current user:
+    method = get_castingimpl(type(np.dtype("d")), type(np.dtype("f")))
+
+    @pytest.mark.parametrize("args", [
+        (True,),  # Not a tuple.
+        ((None,)),  # Too few elements
+        ((None, None, None),),  # Too many
+        ((None, None),),  # Input dtype is None, which is invalid.
+        ((np.dtype("d"), True),),  # Output dtype is not a dtype
+        ((np.dtype("f"), None),),  # Input dtype does not match method
+    ])
+    def test_invalid_arguments(self, args):
+        with pytest.raises(TypeError):
+            self.method._resolve_descriptors(*args)
+
+
+class TestSimpleStridedCall:
+    # Test mainly error paths of the resolve_descriptors function,
+    # note that the `casting_unittests` tests exercise this non-error paths.
+
+    # Casting implementations are the main/only current user:
+    method = get_castingimpl(type(np.dtype("d")), type(np.dtype("f")))
+
+    @pytest.mark.parametrize(["args", "error"], [
+        ((True,), TypeError),  # Not a tuple
+        (((None,),), TypeError),  # Too few elements
+        ((None, None), TypeError),  # Inputs are not arrays.
+        (((None, None, None),), TypeError),  # Too many
+        (((np.arange(3), np.arange(3)),), TypeError),  # Incorrect dtypes
+        (((np.ones(3, dtype=">d"), np.ones(3, dtype="<f")),),
+         TypeError),  # Does not support byte-swapping
+        (((np.ones((2, 2), dtype="d"), np.ones((2, 2), dtype="f")),),
+         ValueError),  # not 1-D
+        (((np.ones(3, dtype="d"), np.ones(4, dtype="f")),),
+          ValueError),  # different length
+        (((np.frombuffer(b"\0x00" * 3 * 2, dtype="d"),
+           np.frombuffer(b"\0x00" * 3, dtype="f")),),
+         ValueError),  # output not writeable
+    ])
+    def test_invalid_arguments(self, args, error):
+        # This is private API, which may be modified freely
+        with pytest.raises(error):
+            self.method._simple_strided_call(*args)
+
+
+@pytest.mark.parametrize(
+    "cls", [
+        np.ndarray, np.recarray, np.char.chararray, np.matrix, np.memmap
+    ]
+)
+class TestClassGetItem:
+    def test_class_getitem(self, cls: type[np.ndarray]) -> None:
+        """Test `ndarray.__class_getitem__`."""
+        alias = cls[Any, Any]
+        assert isinstance(alias, types.GenericAlias)
+        assert alias.__origin__ is cls
+
+    @pytest.mark.parametrize("arg_len", range(4))
+    def test_subscript_tup(self, cls: type[np.ndarray], arg_len: int) -> None:
+        arg_tup = (Any,) * arg_len
+        if arg_len in (1, 2):
+            assert cls[arg_tup]
+        else:
+            match = f"Too {'few' if arg_len == 0 else 'many'} arguments"
+            with pytest.raises(TypeError, match=match):
+                cls[arg_tup]
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_arrayobject.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_arrayobject.py
new file mode 100644
index 0000000..ffa1ba0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_arrayobject.py
@@ -0,0 +1,75 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_array_equal
+
+
+def test_matrix_transpose_raises_error_for_1d():
+    msg = "matrix transpose with ndim < 2 is undefined"
+    arr = np.arange(48)
+    with pytest.raises(ValueError, match=msg):
+        arr.mT
+
+
+def test_matrix_transpose_equals_transpose_2d():
+    arr = np.arange(48).reshape((6, 8))
+    assert_array_equal(arr.T, arr.mT)
+
+
+ARRAY_SHAPES_TO_TEST = (
+    (5, 2),
+    (5, 2, 3),
+    (5, 2, 3, 4),
+)
+
+
+@pytest.mark.parametrize("shape", ARRAY_SHAPES_TO_TEST)
+def test_matrix_transpose_equals_swapaxes(shape):
+    num_of_axes = len(shape)
+    vec = np.arange(shape[-1])
+    arr = np.broadcast_to(vec, shape)
+    tgt = np.swapaxes(arr, num_of_axes - 2, num_of_axes - 1)
+    mT = arr.mT
+    assert_array_equal(tgt, mT)
+
+
+class MyArr(np.ndarray):
+    def __array_wrap__(self, arr, context=None, return_scalar=None):
+        return super().__array_wrap__(arr, context, return_scalar)
+
+
+class MyArrNoWrap(np.ndarray):
+    pass
+
+
+@pytest.mark.parametrize("subclass_self", [np.ndarray, MyArr, MyArrNoWrap])
+@pytest.mark.parametrize("subclass_arr", [np.ndarray, MyArr, MyArrNoWrap])
+def test_array_wrap(subclass_self, subclass_arr):
+    # NumPy should allow `__array_wrap__` to be called on arrays, it's logic
+    # is designed in a way that:
+    #
+    # * Subclasses never return scalars by default (to preserve their
+    #   information).  They can choose to if they wish.
+    # * NumPy returns scalars, if `return_scalar` is passed as True to allow
+    #   manual calls to `arr.__array_wrap__` to do the right thing.
+    # * The type of the input should be ignored (it should be a base-class
+    #   array, but I am not sure this is guaranteed).
+
+    arr = np.arange(3).view(subclass_self)
+
+    arr0d = np.array(3, dtype=np.int8).view(subclass_arr)
+    # With third argument True, ndarray allows "decay" to scalar.
+    # (I don't think NumPy would pass `None`, but it seems clear to support)
+    if subclass_self is np.ndarray:
+        assert type(arr.__array_wrap__(arr0d, None, True)) is np.int8
+    else:
+        assert type(arr.__array_wrap__(arr0d, None, True)) is type(arr)
+
+    # Otherwise, result should be viewed as the subclass
+    assert type(arr.__array_wrap__(arr0d)) is type(arr)
+    assert type(arr.__array_wrap__(arr0d, None, None)) is type(arr)
+    assert type(arr.__array_wrap__(arr0d, None, False)) is type(arr)
+
+    # Non 0-D array can't be converted to scalar, so we ignore that
+    arr1d = np.array([3], dtype=np.int8).view(subclass_arr)
+    assert type(arr.__array_wrap__(arr1d, None, True)) is type(arr)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_arrayprint.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_arrayprint.py
new file mode 100644
index 0000000..1fd4ac2
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_arrayprint.py
@@ -0,0 +1,1328 @@
+import gc
+import sys
+import textwrap
+
+import pytest
+from hypothesis import given
+from hypothesis.extra import numpy as hynp
+
+import numpy as np
+from numpy._core.arrayprint import _typelessdata
+from numpy.testing import (
+    HAS_REFCOUNT,
+    IS_WASM,
+    assert_,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+    assert_warns,
+)
+from numpy.testing._private.utils import run_threaded
+
+
+class TestArrayRepr:
+    def test_nan_inf(self):
+        x = np.array([np.nan, np.inf])
+        assert_equal(repr(x), 'array([nan, inf])')
+
+    def test_subclass(self):
+        class sub(np.ndarray):
+            pass
+
+        # one dimensional
+        x1d = np.array([1, 2]).view(sub)
+        assert_equal(repr(x1d), 'sub([1, 2])')
+
+        # two dimensional
+        x2d = np.array([[1, 2], [3, 4]]).view(sub)
+        assert_equal(repr(x2d),
+            'sub([[1, 2],\n'
+            '     [3, 4]])')
+
+        # two dimensional with flexible dtype
+        xstruct = np.ones((2, 2), dtype=[('a', '<i4')]).view(sub)
+        assert_equal(repr(xstruct),
+            "sub([[(1,), (1,)],\n"
+            "     [(1,), (1,)]], dtype=[('a', '<i4')])"
+        )
+
+    @pytest.mark.xfail(reason="See gh-10544")
+    def test_object_subclass(self):
+        class sub(np.ndarray):
+            def __new__(cls, inp):
+                obj = np.asarray(inp).view(cls)
+                return obj
+
+            def __getitem__(self, ind):
+                ret = super().__getitem__(ind)
+                return sub(ret)
+
+        # test that object + subclass is OK:
+        x = sub([None, None])
+        assert_equal(repr(x), 'sub([None, None], dtype=object)')
+        assert_equal(str(x), '[None None]')
+
+        x = sub([None, sub([None, None])])
+        assert_equal(repr(x),
+            'sub([None, sub([None, None], dtype=object)], dtype=object)')
+        assert_equal(str(x), '[None sub([None, None], dtype=object)]')
+
+    def test_0d_object_subclass(self):
+        # make sure that subclasses which return 0ds instead
+        # of scalars don't cause infinite recursion in str
+        class sub(np.ndarray):
+            def __new__(cls, inp):
+                obj = np.asarray(inp).view(cls)
+                return obj
+
+            def __getitem__(self, ind):
+                ret = super().__getitem__(ind)
+                return sub(ret)
+
+        x = sub(1)
+        assert_equal(repr(x), 'sub(1)')
+        assert_equal(str(x), '1')
+
+        x = sub([1, 1])
+        assert_equal(repr(x), 'sub([1, 1])')
+        assert_equal(str(x), '[1 1]')
+
+        # check it works properly with object arrays too
+        x = sub(None)
+        assert_equal(repr(x), 'sub(None, dtype=object)')
+        assert_equal(str(x), 'None')
+
+        # plus recursive object arrays (even depth > 1)
+        y = sub(None)
+        x[()] = y
+        y[()] = x
+        assert_equal(repr(x),
+            'sub(sub(sub(..., dtype=object), dtype=object), dtype=object)')
+        assert_equal(str(x), '...')
+        x[()] = 0  # resolve circular references for garbage collector
+
+        # nested 0d-subclass-object
+        x = sub(None)
+        x[()] = sub(None)
+        assert_equal(repr(x), 'sub(sub(None, dtype=object), dtype=object)')
+        assert_equal(str(x), 'None')
+
+        # gh-10663
+        class DuckCounter(np.ndarray):
+            def __getitem__(self, item):
+                result = super().__getitem__(item)
+                if not isinstance(result, DuckCounter):
+                    result = result[...].view(DuckCounter)
+                return result
+
+            def to_string(self):
+                return {0: 'zero', 1: 'one', 2: 'two'}.get(self.item(), 'many')
+
+            def __str__(self):
+                if self.shape == ():
+                    return self.to_string()
+                else:
+                    fmt = {'all': lambda x: x.to_string()}
+                    return np.array2string(self, formatter=fmt)
+
+        dc = np.arange(5).view(DuckCounter)
+        assert_equal(str(dc), "[zero one two many many]")
+        assert_equal(str(dc[0]), "zero")
+
+    def test_self_containing(self):
+        arr0d = np.array(None)
+        arr0d[()] = arr0d
+        assert_equal(repr(arr0d),
+            'array(array(..., dtype=object), dtype=object)')
+        arr0d[()] = 0  # resolve recursion for garbage collector
+
+        arr1d = np.array([None, None])
+        arr1d[1] = arr1d
+        assert_equal(repr(arr1d),
+            'array([None, array(..., dtype=object)], dtype=object)')
+        arr1d[1] = 0  # resolve recursion for garbage collector
+
+        first = np.array(None)
+        second = np.array(None)
+        first[()] = second
+        second[()] = first
+        assert_equal(repr(first),
+            'array(array(array(..., dtype=object), dtype=object), dtype=object)')
+        first[()] = 0  # resolve circular references for garbage collector
+
+    def test_containing_list(self):
+        # printing square brackets directly would be ambiguous
+        arr1d = np.array([None, None])
+        arr1d[0] = [1, 2]
+        arr1d[1] = [3]
+        assert_equal(repr(arr1d),
+            'array([list([1, 2]), list([3])], dtype=object)')
+
+    def test_void_scalar_recursion(self):
+        # gh-9345
+        repr(np.void(b'test'))  # RecursionError ?
+
+    def test_fieldless_structured(self):
+        # gh-10366
+        no_fields = np.dtype([])
+        arr_no_fields = np.empty(4, dtype=no_fields)
+        assert_equal(repr(arr_no_fields), 'array([(), (), (), ()], dtype=[])')
+
+
+class TestComplexArray:
+    def test_str(self):
+        rvals = [0, 1, -1, np.inf, -np.inf, np.nan]
+        cvals = [complex(rp, ip) for rp in rvals for ip in rvals]
+        dtypes = [np.complex64, np.cdouble, np.clongdouble]
+        actual = [str(np.array([c], dt)) for c in cvals for dt in dtypes]
+        wanted = [
+            '[0.+0.j]',    '[0.+0.j]',    '[0.+0.j]',
+            '[0.+1.j]',    '[0.+1.j]',    '[0.+1.j]',
+            '[0.-1.j]',    '[0.-1.j]',    '[0.-1.j]',
+            '[0.+infj]',   '[0.+infj]',   '[0.+infj]',
+            '[0.-infj]',   '[0.-infj]',   '[0.-infj]',
+            '[0.+nanj]',   '[0.+nanj]',   '[0.+nanj]',
+            '[1.+0.j]',    '[1.+0.j]',    '[1.+0.j]',
+            '[1.+1.j]',    '[1.+1.j]',    '[1.+1.j]',
+            '[1.-1.j]',    '[1.-1.j]',    '[1.-1.j]',
+            '[1.+infj]',   '[1.+infj]',   '[1.+infj]',
+            '[1.-infj]',   '[1.-infj]',   '[1.-infj]',
+            '[1.+nanj]',   '[1.+nanj]',   '[1.+nanj]',
+            '[-1.+0.j]',   '[-1.+0.j]',   '[-1.+0.j]',
+            '[-1.+1.j]',   '[-1.+1.j]',   '[-1.+1.j]',
+            '[-1.-1.j]',   '[-1.-1.j]',   '[-1.-1.j]',
+            '[-1.+infj]',  '[-1.+infj]',  '[-1.+infj]',
+            '[-1.-infj]',  '[-1.-infj]',  '[-1.-infj]',
+            '[-1.+nanj]',  '[-1.+nanj]',  '[-1.+nanj]',
+            '[inf+0.j]',   '[inf+0.j]',   '[inf+0.j]',
+            '[inf+1.j]',   '[inf+1.j]',   '[inf+1.j]',
+            '[inf-1.j]',   '[inf-1.j]',   '[inf-1.j]',
+            '[inf+infj]',  '[inf+infj]',  '[inf+infj]',
+            '[inf-infj]',  '[inf-infj]',  '[inf-infj]',
+            '[inf+nanj]',  '[inf+nanj]',  '[inf+nanj]',
+            '[-inf+0.j]',  '[-inf+0.j]',  '[-inf+0.j]',
+            '[-inf+1.j]',  '[-inf+1.j]',  '[-inf+1.j]',
+            '[-inf-1.j]',  '[-inf-1.j]',  '[-inf-1.j]',
+            '[-inf+infj]', '[-inf+infj]', '[-inf+infj]',
+            '[-inf-infj]', '[-inf-infj]', '[-inf-infj]',
+            '[-inf+nanj]', '[-inf+nanj]', '[-inf+nanj]',
+            '[nan+0.j]',   '[nan+0.j]',   '[nan+0.j]',
+            '[nan+1.j]',   '[nan+1.j]',   '[nan+1.j]',
+            '[nan-1.j]',   '[nan-1.j]',   '[nan-1.j]',
+            '[nan+infj]',  '[nan+infj]',  '[nan+infj]',
+            '[nan-infj]',  '[nan-infj]',  '[nan-infj]',
+            '[nan+nanj]',  '[nan+nanj]',  '[nan+nanj]']
+
+        for res, val in zip(actual, wanted):
+            assert_equal(res, val)
+
+class TestArray2String:
+    def test_basic(self):
+        """Basic test of array2string."""
+        a = np.arange(3)
+        assert_(np.array2string(a) == '[0 1 2]')
+        assert_(np.array2string(a, max_line_width=4, legacy='1.13') == '[0 1\n 2]')
+        assert_(np.array2string(a, max_line_width=4) == '[0\n 1\n 2]')
+
+    def test_unexpected_kwarg(self):
+        # ensure than an appropriate TypeError
+        # is raised when array2string receives
+        # an unexpected kwarg
+
+        with assert_raises_regex(TypeError, 'nonsense'):
+            np.array2string(np.array([1, 2, 3]),
+                            nonsense=None)
+
+    def test_format_function(self):
+        """Test custom format function for each element in array."""
+        def _format_function(x):
+            if np.abs(x) < 1:
+                return '.'
+            elif np.abs(x) < 2:
+                return 'o'
+            else:
+                return 'O'
+
+        x = np.arange(3)
+        x_hex = "[0x0 0x1 0x2]"
+        x_oct = "[0o0 0o1 0o2]"
+        assert_(np.array2string(x, formatter={'all': _format_function}) ==
+                "[. o O]")
+        assert_(np.array2string(x, formatter={'int_kind': _format_function}) ==
+                "[. o O]")
+        assert_(np.array2string(x, formatter={'all': lambda x: f"{x:.4f}"}) ==
+                "[0.0000 1.0000 2.0000]")
+        assert_equal(np.array2string(x, formatter={'int': hex}),
+                x_hex)
+        assert_equal(np.array2string(x, formatter={'int': oct}),
+                x_oct)
+
+        x = np.arange(3.)
+        assert_(np.array2string(x, formatter={'float_kind': lambda x: f"{x:.2f}"}) ==
+                "[0.00 1.00 2.00]")
+        assert_(np.array2string(x, formatter={'float': lambda x: f"{x:.2f}"}) ==
+                "[0.00 1.00 2.00]")
+
+        s = np.array(['abc', 'def'])
+        assert_(np.array2string(s, formatter={'numpystr': lambda s: s * 2}) ==
+                '[abcabc defdef]')
+
+    def test_structure_format_mixed(self):
+        dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
+        x = np.array([('Sarah', (8.0, 7.0)), ('John', (6.0, 7.0))], dtype=dt)
+        assert_equal(np.array2string(x),
+                "[('Sarah', [8., 7.]) ('John', [6., 7.])]")
+
+        np.set_printoptions(legacy='1.13')
+        try:
+            # for issue #5692
+            A = np.zeros(shape=10, dtype=[("A", "M8[s]")])
+            A[5:].fill(np.datetime64('NaT'))
+            assert_equal(
+                np.array2string(A),
+                textwrap.dedent("""\
+                [('1970-01-01T00:00:00',) ('1970-01-01T00:00:00',) ('1970-01-01T00:00:00',)
+                 ('1970-01-01T00:00:00',) ('1970-01-01T00:00:00',) ('NaT',) ('NaT',)
+                 ('NaT',) ('NaT',) ('NaT',)]""")
+            )
+        finally:
+            np.set_printoptions(legacy=False)
+
+        # same again, but with non-legacy behavior
+        assert_equal(
+            np.array2string(A),
+            textwrap.dedent("""\
+            [('1970-01-01T00:00:00',) ('1970-01-01T00:00:00',)
+             ('1970-01-01T00:00:00',) ('1970-01-01T00:00:00',)
+             ('1970-01-01T00:00:00',) (                'NaT',)
+             (                'NaT',) (                'NaT',)
+             (                'NaT',) (                'NaT',)]""")
+        )
+
+        # and again, with timedeltas
+        A = np.full(10, 123456, dtype=[("A", "m8[s]")])
+        A[5:].fill(np.datetime64('NaT'))
+        assert_equal(
+            np.array2string(A),
+            textwrap.dedent("""\
+            [(123456,) (123456,) (123456,) (123456,) (123456,) ( 'NaT',) ( 'NaT',)
+             ( 'NaT',) ( 'NaT',) ( 'NaT',)]""")
+        )
+
+    def test_structure_format_int(self):
+        # See #8160
+        struct_int = np.array([([1, -1],), ([123, 1],)],
+                dtype=[('B', 'i4', 2)])
+        assert_equal(np.array2string(struct_int),
+                "[([  1,  -1],) ([123,   1],)]")
+        struct_2dint = np.array([([[0, 1], [2, 3]],), ([[12, 0], [0, 0]],)],
+                dtype=[('B', 'i4', (2, 2))])
+        assert_equal(np.array2string(struct_2dint),
+                "[([[ 0,  1], [ 2,  3]],) ([[12,  0], [ 0,  0]],)]")
+
+    def test_structure_format_float(self):
+        # See #8172
+        array_scalar = np.array(
+                (1., 2.1234567890123456789, 3.), dtype=('f8,f8,f8'))
+        assert_equal(np.array2string(array_scalar), "(1., 2.12345679, 3.)")
+
+    def test_unstructured_void_repr(self):
+        a = np.array([27, 91, 50, 75, 7, 65, 10, 8, 27, 91, 51, 49, 109, 82, 101, 100],
+                      dtype='u1').view('V8')
+        assert_equal(repr(a[0]),
+            r"np.void(b'\x1B\x5B\x32\x4B\x07\x41\x0A\x08')")
+        assert_equal(str(a[0]), r"b'\x1B\x5B\x32\x4B\x07\x41\x0A\x08'")
+        assert_equal(repr(a),
+            r"array([b'\x1B\x5B\x32\x4B\x07\x41\x0A\x08',"
+            "\n"
+            r"       b'\x1B\x5B\x33\x31\x6D\x52\x65\x64'], dtype='|V8')")
+
+        assert_equal(eval(repr(a), vars(np)), a)
+        assert_equal(eval(repr(a[0]), {'np': np}), a[0])
+
+    def test_edgeitems_kwarg(self):
+        # previously the global print options would be taken over the kwarg
+        arr = np.zeros(3, int)
+        assert_equal(
+            np.array2string(arr, edgeitems=1, threshold=0),
+            "[0 ... 0]"
+        )
+
+    def test_summarize_1d(self):
+        A = np.arange(1001)
+        strA = '[   0    1    2 ...  998  999 1000]'
+        assert_equal(str(A), strA)
+
+        reprA = 'array([   0,    1,    2, ...,  998,  999, 1000])'
+        try:
+            np.set_printoptions(legacy='2.1')
+            assert_equal(repr(A), reprA)
+        finally:
+            np.set_printoptions(legacy=False)
+
+        assert_equal(repr(A), reprA.replace(')', ', shape=(1001,))'))
+
+    def test_summarize_2d(self):
+        A = np.arange(1002).reshape(2, 501)
+        strA = '[[   0    1    2 ...  498  499  500]\n' \
+               ' [ 501  502  503 ...  999 1000 1001]]'
+        assert_equal(str(A), strA)
+
+        reprA = 'array([[   0,    1,    2, ...,  498,  499,  500],\n' \
+                '       [ 501,  502,  503, ...,  999, 1000, 1001]])'
+        try:
+            np.set_printoptions(legacy='2.1')
+            assert_equal(repr(A), reprA)
+        finally:
+            np.set_printoptions(legacy=False)
+
+        assert_equal(repr(A), reprA.replace(')', ', shape=(2, 501))'))
+
+    def test_summarize_2d_dtype(self):
+        A = np.arange(1002, dtype='i2').reshape(2, 501)
+        strA = '[[   0    1    2 ...  498  499  500]\n' \
+               ' [ 501  502  503 ...  999 1000 1001]]'
+        assert_equal(str(A), strA)
+
+        reprA = ('array([[   0,    1,    2, ...,  498,  499,  500],\n'
+                 '       [ 501,  502,  503, ...,  999, 1000, 1001]],\n'
+                 '      shape=(2, 501), dtype=int16)')
+        assert_equal(repr(A), reprA)
+
+    def test_summarize_structure(self):
+        A = (np.arange(2002, dtype="<i8").reshape(2, 1001)
+             .view([('i', "<i8", (1001,))]))
+        strA = ("[[([   0,    1,    2, ...,  998,  999, 1000],)]\n"
+                " [([1001, 1002, 1003, ..., 1999, 2000, 2001],)]]")
+        assert_equal(str(A), strA)
+
+        reprA = ("array([[([   0,    1,    2, ...,  998,  999, 1000],)],\n"
+                 "       [([1001, 1002, 1003, ..., 1999, 2000, 2001],)]],\n"
+                 "      dtype=[('i', '<i8', (1001,))])")
+        assert_equal(repr(A), reprA)
+
+        B = np.ones(2002, dtype=">i8").view([('i', ">i8", (2, 1001))])
+        strB = "[([[1, 1, 1, ..., 1, 1, 1], [1, 1, 1, ..., 1, 1, 1]],)]"
+        assert_equal(str(B), strB)
+
+        reprB = (
+            "array([([[1, 1, 1, ..., 1, 1, 1], [1, 1, 1, ..., 1, 1, 1]],)],\n"
+            "      dtype=[('i', '>i8', (2, 1001))])"
+        )
+        assert_equal(repr(B), reprB)
+
+        C = (np.arange(22, dtype="<i8").reshape(2, 11)
+             .view([('i1', "<i8"), ('i10', "<i8", (10,))]))
+        strC = "[[( 0, [ 1, ..., 10])]\n [(11, [12, ..., 21])]]"
+        assert_equal(np.array2string(C, threshold=1, edgeitems=1), strC)
+
+    def test_linewidth(self):
+        a = np.full(6, 1)
+
+        def make_str(a, width, **kw):
+            return np.array2string(a, separator="", max_line_width=width, **kw)
+
+        assert_equal(make_str(a, 8, legacy='1.13'), '[111111]')
+        assert_equal(make_str(a, 7, legacy='1.13'), '[111111]')
+        assert_equal(make_str(a, 5, legacy='1.13'), '[1111\n'
+                                                    ' 11]')
+
+        assert_equal(make_str(a, 8), '[111111]')
+        assert_equal(make_str(a, 7), '[11111\n'
+                                     ' 1]')
+        assert_equal(make_str(a, 5), '[111\n'
+                                     ' 111]')
+
+        b = a[None, None, :]
+
+        assert_equal(make_str(b, 12, legacy='1.13'), '[[[111111]]]')
+        assert_equal(make_str(b,  9, legacy='1.13'), '[[[111111]]]')
+        assert_equal(make_str(b,  8, legacy='1.13'), '[[[11111\n'
+                                                     '   1]]]')
+
+        assert_equal(make_str(b, 12), '[[[111111]]]')
+        assert_equal(make_str(b,  9), '[[[111\n'
+                                      '   111]]]')
+        assert_equal(make_str(b,  8), '[[[11\n'
+                                      '   11\n'
+                                      '   11]]]')
+
+    def test_wide_element(self):
+        a = np.array(['xxxxx'])
+        assert_equal(
+            np.array2string(a, max_line_width=5),
+            "['xxxxx']"
+        )
+        assert_equal(
+            np.array2string(a, max_line_width=5, legacy='1.13'),
+            "[ 'xxxxx']"
+        )
+
+    def test_multiline_repr(self):
+        class MultiLine:
+            def __repr__(self):
+                return "Line 1\nLine 2"
+
+        a = np.array([[None, MultiLine()], [MultiLine(), None]])
+
+        assert_equal(
+            np.array2string(a),
+            '[[None Line 1\n'
+            '       Line 2]\n'
+            ' [Line 1\n'
+            '  Line 2 None]]'
+        )
+        assert_equal(
+            np.array2string(a, max_line_width=5),
+            '[[None\n'
+            '  Line 1\n'
+            '  Line 2]\n'
+            ' [Line 1\n'
+            '  Line 2\n'
+            '  None]]'
+        )
+        assert_equal(
+            repr(a),
+            'array([[None, Line 1\n'
+            '              Line 2],\n'
+            '       [Line 1\n'
+            '        Line 2, None]], dtype=object)'
+        )
+
+        class MultiLineLong:
+            def __repr__(self):
+                return "Line 1\nLooooooooooongestLine2\nLongerLine 3"
+
+        a = np.array([[None, MultiLineLong()], [MultiLineLong(), None]])
+        assert_equal(
+            repr(a),
+            'array([[None, Line 1\n'
+            '              LooooooooooongestLine2\n'
+            '              LongerLine 3          ],\n'
+            '       [Line 1\n'
+            '        LooooooooooongestLine2\n'
+            '        LongerLine 3          , None]], dtype=object)'
+        )
+        assert_equal(
+            np.array_repr(a, 20),
+            'array([[None,\n'
+            '        Line 1\n'
+            '        LooooooooooongestLine2\n'
+            '        LongerLine 3          ],\n'
+            '       [Line 1\n'
+            '        LooooooooooongestLine2\n'
+            '        LongerLine 3          ,\n'
+            '        None]],\n'
+            '      dtype=object)'
+        )
+
+    def test_nested_array_repr(self):
+        a = np.empty((2, 2), dtype=object)
+        a[0, 0] = np.eye(2)
+        a[0, 1] = np.eye(3)
+        a[1, 0] = None
+        a[1, 1] = np.ones((3, 1))
+        assert_equal(
+            repr(a),
+            'array([[array([[1., 0.],\n'
+            '               [0., 1.]]), array([[1., 0., 0.],\n'
+            '                                  [0., 1., 0.],\n'
+            '                                  [0., 0., 1.]])],\n'
+            '       [None, array([[1.],\n'
+            '                     [1.],\n'
+            '                     [1.]])]], dtype=object)'
+        )
+
+    @given(hynp.from_dtype(np.dtype("U")))
+    def test_any_text(self, text):
+        # This test checks that, given any value that can be represented in an
+        # array of dtype("U") (i.e. unicode string), ...
+        a = np.array([text, text, text])
+        # casting a list of them to an array does not e.g. truncate the value
+        assert_equal(a[0], text)
+        text = text.item()  # use raw python strings for repr below
+        # and that np.array2string puts a newline in the expected location
+        expected_repr = f"[{text!r} {text!r}\n {text!r}]"
+        result = np.array2string(a, max_line_width=len(repr(text)) * 2 + 3)
+        assert_equal(result, expected_repr)
+
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test_refcount(self):
+        # make sure we do not hold references to the array due to a recursive
+        # closure (gh-10620)
+        gc.disable()
+        a = np.arange(2)
+        r1 = sys.getrefcount(a)
+        np.array2string(a)
+        np.array2string(a)
+        r2 = sys.getrefcount(a)
+        gc.collect()
+        gc.enable()
+        assert_(r1 == r2)
+
+    def test_with_sign(self):
+        # mixed negative and positive value array
+        a = np.array([-2, 0, 3])
+        assert_equal(
+            np.array2string(a, sign='+'),
+            '[-2 +0 +3]'
+        )
+        assert_equal(
+            np.array2string(a, sign='-'),
+            '[-2  0  3]'
+        )
+        assert_equal(
+            np.array2string(a, sign=' '),
+            '[-2  0  3]'
+        )
+        # all non-negative array
+        a = np.array([2, 0, 3])
+        assert_equal(
+            np.array2string(a, sign='+'),
+            '[+2 +0 +3]'
+        )
+        assert_equal(
+            np.array2string(a, sign='-'),
+            '[2 0 3]'
+        )
+        assert_equal(
+            np.array2string(a, sign=' '),
+            '[ 2  0  3]'
+        )
+        # all negative array
+        a = np.array([-2, -1, -3])
+        assert_equal(
+            np.array2string(a, sign='+'),
+            '[-2 -1 -3]'
+        )
+        assert_equal(
+            np.array2string(a, sign='-'),
+            '[-2 -1 -3]'
+        )
+        assert_equal(
+            np.array2string(a, sign=' '),
+            '[-2 -1 -3]'
+        )
+        # 2d array mixed negative and positive
+        a = np.array([[10, -1, 1, 1], [10, 10, 10, 10]])
+        assert_equal(
+            np.array2string(a, sign='+'),
+            '[[+10  -1  +1  +1]\n [+10 +10 +10 +10]]'
+        )
+        assert_equal(
+            np.array2string(a, sign='-'),
+            '[[10 -1  1  1]\n [10 10 10 10]]'
+        )
+        assert_equal(
+            np.array2string(a, sign=' '),
+            '[[10 -1  1  1]\n [10 10 10 10]]'
+        )
+        # 2d array all positive
+        a = np.array([[10, 0, 1, 1], [10, 10, 10, 10]])
+        assert_equal(
+            np.array2string(a, sign='+'),
+            '[[+10  +0  +1  +1]\n [+10 +10 +10 +10]]'
+        )
+        assert_equal(
+            np.array2string(a, sign='-'),
+            '[[10  0  1  1]\n [10 10 10 10]]'
+        )
+        assert_equal(
+            np.array2string(a, sign=' '),
+            '[[ 10   0   1   1]\n [ 10  10  10  10]]'
+        )
+        # 2d array all negative
+        a = np.array([[-10, -1, -1, -1], [-10, -10, -10, -10]])
+        assert_equal(
+            np.array2string(a, sign='+'),
+            '[[-10  -1  -1  -1]\n [-10 -10 -10 -10]]'
+        )
+        assert_equal(
+            np.array2string(a, sign='-'),
+            '[[-10  -1  -1  -1]\n [-10 -10 -10 -10]]'
+        )
+        assert_equal(
+            np.array2string(a, sign=' '),
+            '[[-10  -1  -1  -1]\n [-10 -10 -10 -10]]'
+        )
+
+
+class TestPrintOptions:
+    """Test getting and setting global print options."""
+
+    def setup_method(self):
+        self.oldopts = np.get_printoptions()
+
+    def teardown_method(self):
+        np.set_printoptions(**self.oldopts)
+
+    def test_basic(self):
+        x = np.array([1.5, 0, 1.234567890])
+        assert_equal(repr(x), "array([1.5       , 0.        , 1.23456789])")
+        ret = np.set_printoptions(precision=4)
+        assert_equal(repr(x), "array([1.5   , 0.    , 1.2346])")
+        assert ret is None
+
+    def test_precision_zero(self):
+        np.set_printoptions(precision=0)
+        for values, string in (
+                ([0.], "0."), ([.3], "0."), ([-.3], "-0."), ([.7], "1."),
+                ([1.5], "2."), ([-1.5], "-2."), ([-15.34], "-15."),
+                ([100.], "100."), ([.2, -1, 122.51], "  0.,  -1., 123."),
+                ([0], "0"), ([-12], "-12"), ([complex(.3, -.7)], "0.-1.j")):
+            x = np.array(values)
+            assert_equal(repr(x), f"array([{string}])")
+
+    def test_formatter(self):
+        x = np.arange(3)
+        np.set_printoptions(formatter={'all': lambda x: str(x - 1)})
+        assert_equal(repr(x), "array([-1, 0, 1])")
+
+    def test_formatter_reset(self):
+        x = np.arange(3)
+        np.set_printoptions(formatter={'all': lambda x: str(x - 1)})
+        assert_equal(repr(x), "array([-1, 0, 1])")
+        np.set_printoptions(formatter={'int': None})
+        assert_equal(repr(x), "array([0, 1, 2])")
+
+        np.set_printoptions(formatter={'all': lambda x: str(x - 1)})
+        assert_equal(repr(x), "array([-1, 0, 1])")
+        np.set_printoptions(formatter={'all': None})
+        assert_equal(repr(x), "array([0, 1, 2])")
+
+        np.set_printoptions(formatter={'int': lambda x: str(x - 1)})
+        assert_equal(repr(x), "array([-1, 0, 1])")
+        np.set_printoptions(formatter={'int_kind': None})
+        assert_equal(repr(x), "array([0, 1, 2])")
+
+        x = np.arange(3.)
+        np.set_printoptions(formatter={'float': lambda x: str(x - 1)})
+        assert_equal(repr(x), "array([-1.0, 0.0, 1.0])")
+        np.set_printoptions(formatter={'float_kind': None})
+        assert_equal(repr(x), "array([0., 1., 2.])")
+
+    def test_override_repr(self):
+        x = np.arange(3)
+        np.set_printoptions(override_repr=lambda x: "FOO")
+        assert_equal(repr(x), "FOO")
+        np.set_printoptions(override_repr=None)
+        assert_equal(repr(x), "array([0, 1, 2])")
+
+        with np.printoptions(override_repr=lambda x: "BAR"):
+            assert_equal(repr(x), "BAR")
+        assert_equal(repr(x), "array([0, 1, 2])")
+
+    def test_0d_arrays(self):
+        assert_equal(str(np.array('café', '<U4')), 'café')
+
+        assert_equal(repr(np.array('café', '<U4')),
+                     "array('café', dtype='<U4')")
+        assert_equal(str(np.array('test', np.str_)), 'test')
+
+        a = np.zeros(1, dtype=[('a', '<i4', (3,))])
+        assert_equal(str(a[0]), '([0, 0, 0],)')
+
+        assert_equal(repr(np.datetime64('2005-02-25')[...]),
+                     "array('2005-02-25', dtype='datetime64[D]')")
+
+        assert_equal(repr(np.timedelta64('10', 'Y')[...]),
+                     "array(10, dtype='timedelta64[Y]')")
+
+        # repr of 0d arrays is affected by printoptions
+        x = np.array(1)
+        np.set_printoptions(formatter={'all': lambda x: "test"})
+        assert_equal(repr(x), "array(test)")
+        # str is unaffected
+        assert_equal(str(x), "1")
+
+        # check `style` arg raises
+        assert_warns(DeprecationWarning, np.array2string,
+                                         np.array(1.), style=repr)
+        # but not in legacy mode
+        np.array2string(np.array(1.), style=repr, legacy='1.13')
+        # gh-10934 style was broken in legacy mode, check it works
+        np.array2string(np.array(1.), legacy='1.13')
+
+    def test_float_spacing(self):
+        x = np.array([1., 2., 3.])
+        y = np.array([1., 2., -10.])
+        z = np.array([100., 2., -1.])
+        w = np.array([-100., 2., 1.])
+
+        assert_equal(repr(x), 'array([1., 2., 3.])')
+        assert_equal(repr(y), 'array([  1.,   2., -10.])')
+        assert_equal(repr(np.array(y[0])), 'array(1.)')
+        assert_equal(repr(np.array(y[-1])), 'array(-10.)')
+        assert_equal(repr(z), 'array([100.,   2.,  -1.])')
+        assert_equal(repr(w), 'array([-100.,    2.,    1.])')
+
+        assert_equal(repr(np.array([np.nan, np.inf])), 'array([nan, inf])')
+        assert_equal(repr(np.array([np.nan, -np.inf])), 'array([ nan, -inf])')
+
+        x = np.array([np.inf, 100000, 1.1234])
+        y = np.array([np.inf, 100000, -1.1234])
+        z = np.array([np.inf, 1.1234, -1e120])
+        np.set_printoptions(precision=2)
+        assert_equal(repr(x), 'array([     inf, 1.00e+05, 1.12e+00])')
+        assert_equal(repr(y), 'array([      inf,  1.00e+05, -1.12e+00])')
+        assert_equal(repr(z), 'array([       inf,  1.12e+000, -1.00e+120])')
+
+    def test_bool_spacing(self):
+        assert_equal(repr(np.array([True, True])),
+                     'array([ True,  True])')
+        assert_equal(repr(np.array([True, False])),
+                     'array([ True, False])')
+        assert_equal(repr(np.array([True])),
+                     'array([ True])')
+        assert_equal(repr(np.array(True)),
+                     'array(True)')
+        assert_equal(repr(np.array(False)),
+                     'array(False)')
+
+    def test_sign_spacing(self):
+        a = np.arange(4.)
+        b = np.array([1.234e9])
+        c = np.array([1.0 + 1.0j, 1.123456789 + 1.123456789j], dtype='c16')
+
+        assert_equal(repr(a), 'array([0., 1., 2., 3.])')
+        assert_equal(repr(np.array(1.)), 'array(1.)')
+        assert_equal(repr(b), 'array([1.234e+09])')
+        assert_equal(repr(np.array([0.])), 'array([0.])')
+        assert_equal(repr(c),
+            "array([1.        +1.j        , 1.12345679+1.12345679j])")
+        assert_equal(repr(np.array([0., -0.])), 'array([ 0., -0.])')
+
+        np.set_printoptions(sign=' ')
+        assert_equal(repr(a), 'array([ 0.,  1.,  2.,  3.])')
+        assert_equal(repr(np.array(1.)), 'array( 1.)')
+        assert_equal(repr(b), 'array([ 1.234e+09])')
+        assert_equal(repr(c),
+            "array([ 1.        +1.j        ,  1.12345679+1.12345679j])")
+        assert_equal(repr(np.array([0., -0.])), 'array([ 0., -0.])')
+
+        np.set_printoptions(sign='+')
+        assert_equal(repr(a), 'array([+0., +1., +2., +3.])')
+        assert_equal(repr(np.array(1.)), 'array(+1.)')
+        assert_equal(repr(b), 'array([+1.234e+09])')
+        assert_equal(repr(c),
+            "array([+1.        +1.j        , +1.12345679+1.12345679j])")
+
+        np.set_printoptions(legacy='1.13')
+        assert_equal(repr(a), 'array([ 0.,  1.,  2.,  3.])')
+        assert_equal(repr(b),  'array([  1.23400000e+09])')
+        assert_equal(repr(-b), 'array([ -1.23400000e+09])')
+        assert_equal(repr(np.array(1.)), 'array(1.0)')
+        assert_equal(repr(np.array([0.])), 'array([ 0.])')
+        assert_equal(repr(c),
+            "array([ 1.00000000+1.j        ,  1.12345679+1.12345679j])")
+        # gh-10383
+        assert_equal(str(np.array([-1., 10])), "[ -1.  10.]")
+
+        assert_raises(TypeError, np.set_printoptions, wrongarg=True)
+
+    def test_float_overflow_nowarn(self):
+        # make sure internal computations in FloatingFormat don't
+        # warn about overflow
+        repr(np.array([1e4, 0.1], dtype='f2'))
+
+    def test_sign_spacing_structured(self):
+        a = np.ones(2, dtype='<f,<f')
+        assert_equal(repr(a),
+            "array([(1., 1.), (1., 1.)], dtype=[('f0', '<f4'), ('f1', '<f4')])")
+        assert_equal(repr(a[0]),
+            "np.void((1.0, 1.0), dtype=[('f0', '<f4'), ('f1', '<f4')])")
+
+    def test_floatmode(self):
+        x = np.array([0.6104, 0.922, 0.457, 0.0906, 0.3733, 0.007244,
+                      0.5933, 0.947, 0.2383, 0.4226], dtype=np.float16)
+        y = np.array([0.2918820979355541, 0.5064172631089138,
+                      0.2848750619642916, 0.4342965294660567,
+                      0.7326538397312751, 0.3459503329096204,
+                      0.0862072768214508, 0.39112753029631175],
+                      dtype=np.float64)
+        z = np.arange(6, dtype=np.float16) / 10
+        c = np.array([1.0 + 1.0j, 1.123456789 + 1.123456789j], dtype='c16')
+
+        # also make sure 1e23 is right (is between two fp numbers)
+        w = np.array([f'1e{i}' for i in range(25)], dtype=np.float64)
+        # note: we construct w from the strings `1eXX` instead of doing
+        # `10.**arange(24)` because it turns out the two are not equivalent in
+        # python. On some architectures `1e23 != 10.**23`.
+        wp = np.array([1.234e1, 1e2, 1e123])
+
+        # unique mode
+        np.set_printoptions(floatmode='unique')
+        assert_equal(repr(x),
+            "array([0.6104  , 0.922   , 0.457   , 0.0906  , 0.3733  , 0.007244,\n"
+            "       0.5933  , 0.947   , 0.2383  , 0.4226  ], dtype=float16)")
+        assert_equal(repr(y),
+            "array([0.2918820979355541 , 0.5064172631089138 , 0.2848750619642916 ,\n"
+            "       0.4342965294660567 , 0.7326538397312751 , 0.3459503329096204 ,\n"
+            "       0.0862072768214508 , 0.39112753029631175])")
+        assert_equal(repr(z),
+            "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5], dtype=float16)")
+        assert_equal(repr(w),
+            "array([1.e+00, 1.e+01, 1.e+02, 1.e+03, 1.e+04, 1.e+05, 1.e+06, 1.e+07,\n"
+            "       1.e+08, 1.e+09, 1.e+10, 1.e+11, 1.e+12, 1.e+13, 1.e+14, 1.e+15,\n"
+            "       1.e+16, 1.e+17, 1.e+18, 1.e+19, 1.e+20, 1.e+21, 1.e+22, 1.e+23,\n"
+            "       1.e+24])")
+        assert_equal(repr(wp), "array([1.234e+001, 1.000e+002, 1.000e+123])")
+        assert_equal(repr(c),
+            "array([1.         +1.j         , 1.123456789+1.123456789j])")
+
+        # maxprec mode, precision=8
+        np.set_printoptions(floatmode='maxprec', precision=8)
+        assert_equal(repr(x),
+            "array([0.6104  , 0.922   , 0.457   , 0.0906  , 0.3733  , 0.007244,\n"
+            "       0.5933  , 0.947   , 0.2383  , 0.4226  ], dtype=float16)")
+        assert_equal(repr(y),
+            "array([0.2918821 , 0.50641726, 0.28487506, 0.43429653, 0.73265384,\n"
+            "       0.34595033, 0.08620728, 0.39112753])")
+        assert_equal(repr(z),
+            "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5], dtype=float16)")
+        assert_equal(repr(w[::5]),
+            "array([1.e+00, 1.e+05, 1.e+10, 1.e+15, 1.e+20])")
+        assert_equal(repr(wp), "array([1.234e+001, 1.000e+002, 1.000e+123])")
+        assert_equal(repr(c),
+            "array([1.        +1.j        , 1.12345679+1.12345679j])")
+
+        # fixed mode, precision=4
+        np.set_printoptions(floatmode='fixed', precision=4)
+        assert_equal(repr(x),
+            "array([0.6104, 0.9219, 0.4570, 0.0906, 0.3733, 0.0072, 0.5933, 0.9468,\n"
+            "       0.2383, 0.4226], dtype=float16)")
+        assert_equal(repr(y),
+            "array([0.2919, 0.5064, 0.2849, 0.4343, 0.7327, 0.3460, 0.0862, 0.3911])")
+        assert_equal(repr(z),
+            "array([0.0000, 0.1000, 0.2000, 0.3000, 0.3999, 0.5000], dtype=float16)")
+        assert_equal(repr(w[::5]),
+            "array([1.0000e+00, 1.0000e+05, 1.0000e+10, 1.0000e+15, 1.0000e+20])")
+        assert_equal(repr(wp), "array([1.2340e+001, 1.0000e+002, 1.0000e+123])")
+        assert_equal(repr(np.zeros(3)), "array([0.0000, 0.0000, 0.0000])")
+        assert_equal(repr(c),
+            "array([1.0000+1.0000j, 1.1235+1.1235j])")
+        # for larger precision, representation error becomes more apparent:
+        np.set_printoptions(floatmode='fixed', precision=8)
+        assert_equal(repr(z),
+            "array([0.00000000, 0.09997559, 0.19995117, 0.30004883, 0.39990234,\n"
+            "       0.50000000], dtype=float16)")
+
+        # maxprec_equal  mode, precision=8
+        np.set_printoptions(floatmode='maxprec_equal', precision=8)
+        assert_equal(repr(x),
+            "array([0.610352, 0.921875, 0.457031, 0.090576, 0.373291, 0.007244,\n"
+            "       0.593262, 0.946777, 0.238281, 0.422607], dtype=float16)")
+        assert_equal(repr(y),
+            "array([0.29188210, 0.50641726, 0.28487506, 0.43429653, 0.73265384,\n"
+            "       0.34595033, 0.08620728, 0.39112753])")
+        assert_equal(repr(z),
+            "array([0.0, 0.1, 0.2, 0.3, 0.4, 0.5], dtype=float16)")
+        assert_equal(repr(w[::5]),
+            "array([1.e+00, 1.e+05, 1.e+10, 1.e+15, 1.e+20])")
+        assert_equal(repr(wp), "array([1.234e+001, 1.000e+002, 1.000e+123])")
+        assert_equal(repr(c),
+            "array([1.00000000+1.00000000j, 1.12345679+1.12345679j])")
+
+        # test unique special case (gh-18609)
+        a = np.float64.fromhex('-1p-97')
+        assert_equal(np.float64(np.array2string(a, floatmode='unique')), a)
+
+    test_cases_gh_28679 = [
+        (np.half([999, 999]), "[999. 999.]"),
+        (np.half([999, 1000]), "[9.99e+02 1.00e+03]"),
+        (np.single([999999, 999999]), "[999999. 999999.]"),
+        (np.single([999999, -1000000]), "[ 9.99999e+05 -1.00000e+06]"),
+        (
+            np.complex64([999999 + 999999j, 999999 + 999999j]),
+            "[999999.+999999.j 999999.+999999.j]"
+        ),
+        (
+            np.complex64([999999 + 999999j, 999999 + -1000000j]),
+            "[999999.+9.99999e+05j 999999.-1.00000e+06j]"
+        ),
+    ]
+
+    @pytest.mark.parametrize("input_array, expected_str", test_cases_gh_28679)
+    def test_gh_28679(self, input_array, expected_str):
+        # test cutoff to exponent notation for half, single, and complex64
+        assert_equal(str(input_array), expected_str)
+
+    test_cases_legacy_2_2 = [
+        (np.half([1.e3, 1.e4, 65504]), "[ 1000. 10000. 65504.]"),
+        (np.single([1.e6, 1.e7]), "[ 1000000. 10000000.]"),
+        (np.single([1.e7, 1.e8]), "[1.e+07 1.e+08]"),
+    ]
+
+    @pytest.mark.parametrize("input_array, expected_str", test_cases_legacy_2_2)
+    def test_legacy_2_2_mode(self, input_array, expected_str):
+        # test legacy cutoff to exponent notation for half and single
+        with np.printoptions(legacy='2.2'):
+            assert_equal(str(input_array), expected_str)
+
+    @pytest.mark.parametrize("legacy", ['1.13', '1.21', '1.25', '2.1', '2.2'])
+    def test_legacy_get_options(self, legacy):
+        # test legacy get options works okay
+        with np.printoptions(legacy=legacy):
+            p_opt = np.get_printoptions()
+            assert_equal(p_opt["legacy"], legacy)
+
+    def test_legacy_mode_scalars(self):
+        # in legacy mode, str of floats get truncated, and complex scalars
+        # use * for non-finite imaginary part
+        np.set_printoptions(legacy='1.13')
+        assert_equal(str(np.float64(1.123456789123456789)), '1.12345678912')
+        assert_equal(str(np.complex128(complex(1, np.nan))), '(1+nan*j)')
+
+        np.set_printoptions(legacy=False)
+        assert_equal(str(np.float64(1.123456789123456789)),
+                     '1.1234567891234568')
+        assert_equal(str(np.complex128(complex(1, np.nan))), '(1+nanj)')
+
+    def test_legacy_stray_comma(self):
+        np.set_printoptions(legacy='1.13')
+        assert_equal(str(np.arange(10000)), '[   0    1    2 ..., 9997 9998 9999]')
+
+        np.set_printoptions(legacy=False)
+        assert_equal(str(np.arange(10000)), '[   0    1    2 ... 9997 9998 9999]')
+
+    def test_dtype_linewidth_wrapping(self):
+        np.set_printoptions(linewidth=75)
+        assert_equal(repr(np.arange(10, 20., dtype='f4')),
+            "array([10., 11., 12., 13., 14., 15., 16., 17., 18., 19.], dtype=float32)")
+        assert_equal(repr(np.arange(10, 23., dtype='f4')), textwrap.dedent("""\
+            array([10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.],
+                  dtype=float32)"""))
+
+        styp = '<U4'
+        assert_equal(repr(np.ones(3, dtype=styp)),
+            f"array(['1', '1', '1'], dtype='{styp}')")
+        assert_equal(repr(np.ones(12, dtype=styp)), textwrap.dedent(f"""\
+            array(['1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1'],
+                  dtype='{styp}')"""))
+
+    @pytest.mark.parametrize(
+        ['native'],
+        [
+            ('bool',),
+            ('uint8',),
+            ('uint16',),
+            ('uint32',),
+            ('uint64',),
+            ('int8',),
+            ('int16',),
+            ('int32',),
+            ('int64',),
+            ('float16',),
+            ('float32',),
+            ('float64',),
+            ('U1',),     # 4-byte width string
+        ],
+    )
+    def test_dtype_endianness_repr(self, native):
+        '''
+        there was an issue where
+        repr(array([0], dtype='<u2')) and repr(array([0], dtype='>u2'))
+        both returned the same thing:
+        array([0], dtype=uint16)
+        even though their dtypes have different endianness.
+        '''
+        native_dtype = np.dtype(native)
+        non_native_dtype = native_dtype.newbyteorder()
+        non_native_repr = repr(np.array([1], non_native_dtype))
+        native_repr = repr(np.array([1], native_dtype))
+        # preserve the sensible default of only showing dtype if nonstandard
+        assert ('dtype' in native_repr) ^ (native_dtype in _typelessdata),\
+                ("an array's repr should show dtype if and only if the type "
+                 'of the array is NOT one of the standard types '
+                 '(e.g., int32, bool, float64).')
+        if non_native_dtype.itemsize > 1:
+            # if the type is >1 byte, the non-native endian version
+            # must show endianness.
+            assert non_native_repr != native_repr
+            assert f"dtype='{non_native_dtype.byteorder}" in non_native_repr
+
+    def test_linewidth_repr(self):
+        a = np.full(7, fill_value=2)
+        np.set_printoptions(linewidth=17)
+        assert_equal(
+            repr(a),
+            textwrap.dedent("""\
+            array([2, 2, 2,
+                   2, 2, 2,
+                   2])""")
+        )
+        np.set_printoptions(linewidth=17, legacy='1.13')
+        assert_equal(
+            repr(a),
+            textwrap.dedent("""\
+            array([2, 2, 2,
+                   2, 2, 2, 2])""")
+        )
+
+        a = np.full(8, fill_value=2)
+
+        np.set_printoptions(linewidth=18, legacy=False)
+        assert_equal(
+            repr(a),
+            textwrap.dedent("""\
+            array([2, 2, 2,
+                   2, 2, 2,
+                   2, 2])""")
+        )
+
+        np.set_printoptions(linewidth=18, legacy='1.13')
+        assert_equal(
+            repr(a),
+            textwrap.dedent("""\
+            array([2, 2, 2, 2,
+                   2, 2, 2, 2])""")
+        )
+
+    def test_linewidth_str(self):
+        a = np.full(18, fill_value=2)
+        np.set_printoptions(linewidth=18)
+        assert_equal(
+            str(a),
+            textwrap.dedent("""\
+            [2 2 2 2 2 2 2 2
+             2 2 2 2 2 2 2 2
+             2 2]""")
+        )
+        np.set_printoptions(linewidth=18, legacy='1.13')
+        assert_equal(
+            str(a),
+            textwrap.dedent("""\
+            [2 2 2 2 2 2 2 2 2
+             2 2 2 2 2 2 2 2 2]""")
+        )
+
+    def test_edgeitems(self):
+        np.set_printoptions(edgeitems=1, threshold=1)
+        a = np.arange(27).reshape((3, 3, 3))
+        assert_equal(
+            repr(a),
+            textwrap.dedent("""\
+            array([[[ 0, ...,  2],
+                    ...,
+                    [ 6, ...,  8]],
+
+                   ...,
+
+                   [[18, ..., 20],
+                    ...,
+                    [24, ..., 26]]], shape=(3, 3, 3))""")
+        )
+
+        b = np.zeros((3, 3, 1, 1))
+        assert_equal(
+            repr(b),
+            textwrap.dedent("""\
+            array([[[[0.]],
+
+                    ...,
+
+                    [[0.]]],
+
+
+                   ...,
+
+
+                   [[[0.]],
+
+                    ...,
+
+                    [[0.]]]], shape=(3, 3, 1, 1))""")
+        )
+
+        # 1.13 had extra trailing spaces, and was missing newlines
+        try:
+            np.set_printoptions(legacy='1.13')
+            assert_equal(repr(a), (
+                "array([[[ 0, ...,  2],\n"
+                "        ..., \n"
+                "        [ 6, ...,  8]],\n"
+                "\n"
+                "       ..., \n"
+                "       [[18, ..., 20],\n"
+                "        ..., \n"
+                "        [24, ..., 26]]])")
+            )
+            assert_equal(repr(b), (
+                "array([[[[ 0.]],\n"
+                "\n"
+                "        ..., \n"
+                "        [[ 0.]]],\n"
+                "\n"
+                "\n"
+                "       ..., \n"
+                "       [[[ 0.]],\n"
+                "\n"
+                "        ..., \n"
+                "        [[ 0.]]]])")
+            )
+        finally:
+            np.set_printoptions(legacy=False)
+
+    def test_edgeitems_structured(self):
+        np.set_printoptions(edgeitems=1, threshold=1)
+        A = np.arange(5 * 2 * 3, dtype="<i8").view([('i', "<i8", (5, 2, 3))])
+        reprA = (
+            "array([([[[ 0, ...,  2], [ 3, ...,  5]], ..., "
+            "[[24, ..., 26], [27, ..., 29]]],)],\n"
+            "      dtype=[('i', '<i8', (5, 2, 3))])"
+        )
+        assert_equal(repr(A), reprA)
+
+    def test_bad_args(self):
+        assert_raises(ValueError, np.set_printoptions, threshold=float('nan'))
+        assert_raises(TypeError, np.set_printoptions, threshold='1')
+        assert_raises(TypeError, np.set_printoptions, threshold=b'1')
+
+        assert_raises(TypeError, np.set_printoptions, precision='1')
+        assert_raises(TypeError, np.set_printoptions, precision=1.5)
+
+def test_unicode_object_array():
+    expected = "array(['é'], dtype=object)"
+    x = np.array(['\xe9'], dtype=object)
+    assert_equal(repr(x), expected)
+
+
+class TestContextManager:
+    def test_ctx_mgr(self):
+        # test that context manager actually works
+        with np.printoptions(precision=2):
+            s = str(np.array([2.0]) / 3)
+        assert_equal(s, '[0.67]')
+
+    def test_ctx_mgr_restores(self):
+        # test that print options are actually restored
+        opts = np.get_printoptions()
+        with np.printoptions(precision=opts['precision'] - 1,
+                             linewidth=opts['linewidth'] - 4):
+            pass
+        assert_equal(np.get_printoptions(), opts)
+
+    def test_ctx_mgr_exceptions(self):
+        # test that print options are restored even if an exception is raised
+        opts = np.get_printoptions()
+        try:
+            with np.printoptions(precision=2, linewidth=11):
+                raise ValueError
+        except ValueError:
+            pass
+        assert_equal(np.get_printoptions(), opts)
+
+    def test_ctx_mgr_as_smth(self):
+        opts = {"precision": 2}
+        with np.printoptions(**opts) as ctx:
+            saved_opts = ctx.copy()
+        assert_equal({k: saved_opts[k] for k in opts}, opts)
+
+
+@pytest.mark.parametrize("dtype", "bhilqpBHILQPefdgFDG")
+@pytest.mark.parametrize("value", [0, 1])
+def test_scalar_repr_numbers(dtype, value):
+    # Test NEP 51 scalar repr (and legacy option) for numeric types
+    dtype = np.dtype(dtype)
+    scalar = np.array(value, dtype=dtype)[()]
+    assert isinstance(scalar, np.generic)
+
+    string = str(scalar)
+    repr_string = string.strip("()")  # complex may have extra brackets
+    representation = repr(scalar)
+    if dtype.char == "g":
+        assert representation == f"np.longdouble('{repr_string}')"
+    elif dtype.char == 'G':
+        assert representation == f"np.clongdouble('{repr_string}')"
+    else:
+        normalized_name = np.dtype(f"{dtype.kind}{dtype.itemsize}").type.__name__
+        assert representation == f"np.{normalized_name}({repr_string})"
+
+    with np.printoptions(legacy="1.25"):
+        assert repr(scalar) == string
+
+
+@pytest.mark.parametrize("scalar, legacy_repr, representation", [
+        (np.True_, "True", "np.True_"),
+        (np.bytes_(b'a'), "b'a'", "np.bytes_(b'a')"),
+        (np.str_('a'), "'a'", "np.str_('a')"),
+        (np.datetime64("2012"),
+            "numpy.datetime64('2012')", "np.datetime64('2012')"),
+        (np.timedelta64(1), "numpy.timedelta64(1)", "np.timedelta64(1)"),
+        (np.void((True, 2), dtype="?,<i8"),
+            "(True, 2)",
+            "np.void((True, 2), dtype=[('f0', '?'), ('f1', '<i8')])"),
+        (np.void((1, 2), dtype="<f8,>f4"),
+            "(1., 2.)",
+            "np.void((1.0, 2.0), dtype=[('f0', '<f8'), ('f1', '>f4')])"),
+        (np.void(b'a'), r"void(b'\x61')", r"np.void(b'\x61')"),
+    ])
+def test_scalar_repr_special(scalar, legacy_repr, representation):
+    # Test NEP 51 scalar repr (and legacy option) for numeric types
+    assert repr(scalar) == representation
+
+    with np.printoptions(legacy="1.25"):
+        assert repr(scalar) == legacy_repr
+
+def test_scalar_void_float_str():
+    # Note that based on this currently we do not print the same as a tuple
+    # would, since the tuple would include the repr() inside for floats, but
+    # we do not do that.
+    scalar = np.void((1.0, 2.0), dtype=[('f0', '<f8'), ('f1', '>f4')])
+    assert str(scalar) == "(1.0, 2.0)"
+
+@pytest.mark.skipif(IS_WASM, reason="wasm doesn't support asyncio")
+@pytest.mark.skipif(sys.version_info < (3, 11),
+                    reason="asyncio.barrier was added in Python 3.11")
+def test_printoptions_asyncio_safe():
+    asyncio = pytest.importorskip("asyncio")
+
+    b = asyncio.Barrier(2)
+
+    async def legacy_113():
+        np.set_printoptions(legacy='1.13', precision=12)
+        await b.wait()
+        po = np.get_printoptions()
+        assert po['legacy'] == '1.13'
+        assert po['precision'] == 12
+        orig_linewidth = po['linewidth']
+        with np.printoptions(linewidth=34, legacy='1.21'):
+            po = np.get_printoptions()
+            assert po['legacy'] == '1.21'
+            assert po['precision'] == 12
+            assert po['linewidth'] == 34
+        po = np.get_printoptions()
+        assert po['linewidth'] == orig_linewidth
+        assert po['legacy'] == '1.13'
+        assert po['precision'] == 12
+
+    async def legacy_125():
+        np.set_printoptions(legacy='1.25', precision=7)
+        await b.wait()
+        po = np.get_printoptions()
+        assert po['legacy'] == '1.25'
+        assert po['precision'] == 7
+        orig_linewidth = po['linewidth']
+        with np.printoptions(linewidth=6, legacy='1.13'):
+            po = np.get_printoptions()
+            assert po['legacy'] == '1.13'
+            assert po['precision'] == 7
+            assert po['linewidth'] == 6
+        po = np.get_printoptions()
+        assert po['linewidth'] == orig_linewidth
+        assert po['legacy'] == '1.25'
+        assert po['precision'] == 7
+
+    async def main():
+        await asyncio.gather(legacy_125(), legacy_125())
+
+    loop = asyncio.new_event_loop()
+    asyncio.run(main())
+    loop.close()
+
+@pytest.mark.skipif(IS_WASM, reason="wasm doesn't support threads")
+def test_multithreaded_array_printing():
+    # the dragon4 implementation uses a static scratch space for performance
+    # reasons this test makes sure it is set up in a thread-safe manner
+
+    run_threaded(TestPrintOptions().test_floatmode, 500)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_casting_floatingpoint_errors.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_casting_floatingpoint_errors.py
new file mode 100644
index 0000000..2f9c01f
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_casting_floatingpoint_errors.py
@@ -0,0 +1,154 @@
+import pytest
+from pytest import param
+
+import numpy as np
+from numpy.testing import IS_WASM
+
+
+def values_and_dtypes():
+    """
+    Generate value+dtype pairs that generate floating point errors during
+    casts.  The invalid casts to integers will generate "invalid" value
+    warnings, the float casts all generate "overflow".
+
+    (The Python int/float paths don't need to get tested in all the same
+    situations, but it does not hurt.)
+    """
+    # Casting to float16:
+    yield param(70000, "float16", id="int-to-f2")
+    yield param("70000", "float16", id="str-to-f2")
+    yield param(70000.0, "float16", id="float-to-f2")
+    yield param(np.longdouble(70000.), "float16", id="longdouble-to-f2")
+    yield param(np.float64(70000.), "float16", id="double-to-f2")
+    yield param(np.float32(70000.), "float16", id="float-to-f2")
+    # Casting to float32:
+    yield param(10**100, "float32", id="int-to-f4")
+    yield param(1e100, "float32", id="float-to-f2")
+    yield param(np.longdouble(1e300), "float32", id="longdouble-to-f2")
+    yield param(np.float64(1e300), "float32", id="double-to-f2")
+    # Casting to float64:
+    # If longdouble is double-double, its max can be rounded down to the double
+    # max.  So we correct the double spacing (a bit weird, admittedly):
+    max_ld = np.finfo(np.longdouble).max
+    spacing = np.spacing(np.nextafter(np.finfo("f8").max, 0))
+    if max_ld - spacing > np.finfo("f8").max:
+        yield param(np.finfo(np.longdouble).max, "float64",
+                    id="longdouble-to-f8")
+
+    # Cast to complex32:
+    yield param(2e300, "complex64", id="float-to-c8")
+    yield param(2e300 + 0j, "complex64", id="complex-to-c8")
+    yield param(2e300j, "complex64", id="complex-to-c8")
+    yield param(np.longdouble(2e300), "complex64", id="longdouble-to-c8")
+
+    # Invalid float to integer casts:
+    with np.errstate(over="ignore"):
+        for to_dt in np.typecodes["AllInteger"]:
+            for value in [np.inf, np.nan]:
+                for from_dt in np.typecodes["AllFloat"]:
+                    from_dt = np.dtype(from_dt)
+                    from_val = from_dt.type(value)
+
+                    yield param(from_val, to_dt, id=f"{from_val}-to-{to_dt}")
+
+
+def check_operations(dtype, value):
+    """
+    There are many dedicated paths in NumPy which cast and should check for
+    floating point errors which occurred during those casts.
+    """
+    if dtype.kind != 'i':
+        # These assignments use the stricter setitem logic:
+        def assignment():
+            arr = np.empty(3, dtype=dtype)
+            arr[0] = value
+
+        yield assignment
+
+        def fill():
+            arr = np.empty(3, dtype=dtype)
+            arr.fill(value)
+
+        yield fill
+
+    def copyto_scalar():
+        arr = np.empty(3, dtype=dtype)
+        np.copyto(arr, value, casting="unsafe")
+
+    yield copyto_scalar
+
+    def copyto():
+        arr = np.empty(3, dtype=dtype)
+        np.copyto(arr, np.array([value, value, value]), casting="unsafe")
+
+    yield copyto
+
+    def copyto_scalar_masked():
+        arr = np.empty(3, dtype=dtype)
+        np.copyto(arr, value, casting="unsafe",
+                  where=[True, False, True])
+
+    yield copyto_scalar_masked
+
+    def copyto_masked():
+        arr = np.empty(3, dtype=dtype)
+        np.copyto(arr, np.array([value, value, value]), casting="unsafe",
+                  where=[True, False, True])
+
+    yield copyto_masked
+
+    def direct_cast():
+        np.array([value, value, value]).astype(dtype)
+
+    yield direct_cast
+
+    def direct_cast_nd_strided():
+        arr = np.full((5, 5, 5), fill_value=value)[:, ::2, :]
+        arr.astype(dtype)
+
+    yield direct_cast_nd_strided
+
+    def boolean_array_assignment():
+        arr = np.empty(3, dtype=dtype)
+        arr[[True, False, True]] = np.array([value, value])
+
+    yield boolean_array_assignment
+
+    def integer_array_assignment():
+        arr = np.empty(3, dtype=dtype)
+        values = np.array([value, value])
+
+        arr[[0, 1]] = values
+
+    yield integer_array_assignment
+
+    def integer_array_assignment_with_subspace():
+        arr = np.empty((5, 3), dtype=dtype)
+        values = np.array([value, value, value])
+
+        arr[[0, 2]] = values
+
+    yield integer_array_assignment_with_subspace
+
+    def flat_assignment():
+        arr = np.empty((3,), dtype=dtype)
+        values = np.array([value, value, value])
+        arr.flat[:] = values
+
+    yield flat_assignment
+
+@pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support")
+@pytest.mark.parametrize(["value", "dtype"], values_and_dtypes())
+@pytest.mark.filterwarnings("ignore::numpy.exceptions.ComplexWarning")
+def test_floatingpoint_errors_casting(dtype, value):
+    dtype = np.dtype(dtype)
+    for operation in check_operations(dtype, value):
+        dtype = np.dtype(dtype)
+
+        match = "invalid" if dtype.kind in 'iu' else "overflow"
+        with pytest.warns(RuntimeWarning, match=match):
+            operation()
+
+        with np.errstate(all="raise"):
+            with pytest.raises(FloatingPointError, match=match):
+                operation()
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_casting_unittests.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_casting_unittests.py
new file mode 100644
index 0000000..f8441ea
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_casting_unittests.py
@@ -0,0 +1,817 @@
+"""
+The tests exercise the casting machinery in a more low-level manner.
+The reason is mostly to test a new implementation of the casting machinery.
+
+Unlike most tests in NumPy, these are closer to unit-tests rather
+than integration tests.
+"""
+
+import ctypes
+import enum
+import random
+import textwrap
+
+import pytest
+from numpy._core._multiarray_umath import _get_castingimpl as get_castingimpl
+
+import numpy as np
+from numpy.lib.stride_tricks import as_strided
+from numpy.testing import assert_array_equal
+
+# Simple skips object, parametric and long double (unsupported by struct)
+simple_dtypes = "?bhilqBHILQefdFD"
+if np.dtype("l").itemsize != np.dtype("q").itemsize:
+    # Remove l and L, the table was generated with 64bit linux in mind.
+    simple_dtypes = simple_dtypes.replace("l", "").replace("L", "")
+simple_dtypes = [type(np.dtype(c)) for c in simple_dtypes]
+
+
+def simple_dtype_instances():
+    for dtype_class in simple_dtypes:
+        dt = dtype_class()
+        yield pytest.param(dt, id=str(dt))
+        if dt.byteorder != "|":
+            dt = dt.newbyteorder()
+            yield pytest.param(dt, id=str(dt))
+
+
+def get_expected_stringlength(dtype):
+    """Returns the string length when casting the basic dtypes to strings.
+    """
+    if dtype == np.bool:
+        return 5
+    if dtype.kind in "iu":
+        if dtype.itemsize == 1:
+            length = 3
+        elif dtype.itemsize == 2:
+            length = 5
+        elif dtype.itemsize == 4:
+            length = 10
+        elif dtype.itemsize == 8:
+            length = 20
+        else:
+            raise AssertionError(f"did not find expected length for {dtype}")
+
+        if dtype.kind == "i":
+            length += 1  # adds one character for the sign
+
+        return length
+
+    # Note: Can't do dtype comparison for longdouble on windows
+    if dtype.char == "g":
+        return 48
+    elif dtype.char == "G":
+        return 48 * 2
+    elif dtype.kind == "f":
+        return 32  # also for half apparently.
+    elif dtype.kind == "c":
+        return 32 * 2
+
+    raise AssertionError(f"did not find expected length for {dtype}")
+
+
+class Casting(enum.IntEnum):
+    no = 0
+    equiv = 1
+    safe = 2
+    same_kind = 3
+    unsafe = 4
+
+
+def _get_cancast_table():
+    table = textwrap.dedent("""
+        X ? b h i l q B H I L Q e f d g F D G S U V O M m
+        ? # = = = = = = = = = = = = = = = = = = = = = . =
+        b . # = = = = . . . . . = = = = = = = = = = = . =
+        h . ~ # = = = . . . . . ~ = = = = = = = = = = . =
+        i . ~ ~ # = = . . . . . ~ ~ = = ~ = = = = = = . =
+        l . ~ ~ ~ # # . . . . . ~ ~ = = ~ = = = = = = . =
+        q . ~ ~ ~ # # . . . . . ~ ~ = = ~ = = = = = = . =
+        B . ~ = = = = # = = = = = = = = = = = = = = = . =
+        H . ~ ~ = = = ~ # = = = ~ = = = = = = = = = = . =
+        I . ~ ~ ~ = = ~ ~ # = = ~ ~ = = ~ = = = = = = . =
+        L . ~ ~ ~ ~ ~ ~ ~ ~ # # ~ ~ = = ~ = = = = = = . ~
+        Q . ~ ~ ~ ~ ~ ~ ~ ~ # # ~ ~ = = ~ = = = = = = . ~
+        e . . . . . . . . . . . # = = = = = = = = = = . .
+        f . . . . . . . . . . . ~ # = = = = = = = = = . .
+        d . . . . . . . . . . . ~ ~ # = ~ = = = = = = . .
+        g . . . . . . . . . . . ~ ~ ~ # ~ ~ = = = = = . .
+        F . . . . . . . . . . . . . . . # = = = = = = . .
+        D . . . . . . . . . . . . . . . ~ # = = = = = . .
+        G . . . . . . . . . . . . . . . ~ ~ # = = = = . .
+        S . . . . . . . . . . . . . . . . . . # = = = . .
+        U . . . . . . . . . . . . . . . . . . . # = = . .
+        V . . . . . . . . . . . . . . . . . . . . # = . .
+        O . . . . . . . . . . . . . . . . . . . . = # . .
+        M . . . . . . . . . . . . . . . . . . . . = = # .
+        m . . . . . . . . . . . . . . . . . . . . = = . #
+        """).strip().split("\n")
+    dtypes = [type(np.dtype(c)) for c in table[0][2::2]]
+
+    convert_cast = {".": Casting.unsafe, "~": Casting.same_kind,
+                    "=": Casting.safe, "#": Casting.equiv,
+                    " ": -1}
+
+    cancast = {}
+    for from_dt, row in zip(dtypes, table[1:]):
+        cancast[from_dt] = {}
+        for to_dt, c in zip(dtypes, row[2::2]):
+            cancast[from_dt][to_dt] = convert_cast[c]
+
+    return cancast
+
+
+CAST_TABLE = _get_cancast_table()
+
+
+class TestChanges:
+    """
+    These test cases exercise some behaviour changes
+    """
+    @pytest.mark.parametrize("string", ["S", "U"])
+    @pytest.mark.parametrize("floating", ["e", "f", "d", "g"])
+    def test_float_to_string(self, floating, string):
+        assert np.can_cast(floating, string)
+        # 100 is long enough to hold any formatted floating
+        assert np.can_cast(floating, f"{string}100")
+
+    def test_to_void(self):
+        # But in general, we do consider these safe:
+        assert np.can_cast("d", "V")
+        assert np.can_cast("S20", "V")
+
+        # Do not consider it a safe cast if the void is too smaller:
+        assert not np.can_cast("d", "V1")
+        assert not np.can_cast("S20", "V1")
+        assert not np.can_cast("U1", "V1")
+        # Structured to unstructured is just like any other:
+        assert np.can_cast("d,i", "V", casting="same_kind")
+        # Unstructured void to unstructured is actually no cast at all:
+        assert np.can_cast("V3", "V", casting="no")
+        assert np.can_cast("V0", "V", casting="no")
+
+
+class TestCasting:
+    size = 1500  # Best larger than NPY_LOWLEVEL_BUFFER_BLOCKSIZE * itemsize
+
+    def get_data(self, dtype1, dtype2):
+        if dtype2 is None or dtype1.itemsize >= dtype2.itemsize:
+            length = self.size // dtype1.itemsize
+        else:
+            length = self.size // dtype2.itemsize
+
+        # Assume that the base array is well enough aligned for all inputs.
+        arr1 = np.empty(length, dtype=dtype1)
+        assert arr1.flags.c_contiguous
+        assert arr1.flags.aligned
+
+        values = [random.randrange(-128, 128) for _ in range(length)]
+
+        for i, value in enumerate(values):
+            # Use item assignment to ensure this is not using casting:
+            if value < 0 and dtype1.kind == "u":
+                # Manually rollover unsigned integers (-1 -> int.max)
+                value = value + np.iinfo(dtype1).max + 1
+            arr1[i] = value
+
+        if dtype2 is None:
+            if dtype1.char == "?":
+                values = [bool(v) for v in values]
+            return arr1, values
+
+        if dtype2.char == "?":
+            values = [bool(v) for v in values]
+
+        arr2 = np.empty(length, dtype=dtype2)
+        assert arr2.flags.c_contiguous
+        assert arr2.flags.aligned
+
+        for i, value in enumerate(values):
+            # Use item assignment to ensure this is not using casting:
+            if value < 0 and dtype2.kind == "u":
+                # Manually rollover unsigned integers (-1 -> int.max)
+                value = value + np.iinfo(dtype2).max + 1
+            arr2[i] = value
+
+        return arr1, arr2, values
+
+    def get_data_variation(self, arr1, arr2, aligned=True, contig=True):
+        """
+        Returns a copy of arr1 that may be non-contiguous or unaligned, and a
+        matching array for arr2 (although not a copy).
+        """
+        if contig:
+            stride1 = arr1.dtype.itemsize
+            stride2 = arr2.dtype.itemsize
+        elif aligned:
+            stride1 = 2 * arr1.dtype.itemsize
+            stride2 = 2 * arr2.dtype.itemsize
+        else:
+            stride1 = arr1.dtype.itemsize + 1
+            stride2 = arr2.dtype.itemsize + 1
+
+        max_size1 = len(arr1) * 3 * arr1.dtype.itemsize + 1
+        max_size2 = len(arr2) * 3 * arr2.dtype.itemsize + 1
+        from_bytes = np.zeros(max_size1, dtype=np.uint8)
+        to_bytes = np.zeros(max_size2, dtype=np.uint8)
+
+        # Sanity check that the above is large enough:
+        assert stride1 * len(arr1) <= from_bytes.nbytes
+        assert stride2 * len(arr2) <= to_bytes.nbytes
+
+        if aligned:
+            new1 = as_strided(from_bytes[:-1].view(arr1.dtype),
+                              arr1.shape, (stride1,))
+            new2 = as_strided(to_bytes[:-1].view(arr2.dtype),
+                              arr2.shape, (stride2,))
+        else:
+            new1 = as_strided(from_bytes[1:].view(arr1.dtype),
+                              arr1.shape, (stride1,))
+            new2 = as_strided(to_bytes[1:].view(arr2.dtype),
+                              arr2.shape, (stride2,))
+
+        new1[...] = arr1
+
+        if not contig:
+            # Ensure we did not overwrite bytes that should not be written:
+            offset = arr1.dtype.itemsize if aligned else 0
+            buf = from_bytes[offset::stride1].tobytes()
+            assert buf.count(b"\0") == len(buf)
+
+        if contig:
+            assert new1.flags.c_contiguous
+            assert new2.flags.c_contiguous
+        else:
+            assert not new1.flags.c_contiguous
+            assert not new2.flags.c_contiguous
+
+        if aligned:
+            assert new1.flags.aligned
+            assert new2.flags.aligned
+        else:
+            assert not new1.flags.aligned or new1.dtype.alignment == 1
+            assert not new2.flags.aligned or new2.dtype.alignment == 1
+
+        return new1, new2
+
+    @pytest.mark.parametrize("from_Dt", simple_dtypes)
+    def test_simple_cancast(self, from_Dt):
+        for to_Dt in simple_dtypes:
+            cast = get_castingimpl(from_Dt, to_Dt)
+
+            for from_dt in [from_Dt(), from_Dt().newbyteorder()]:
+                default = cast._resolve_descriptors((from_dt, None))[1][1]
+                assert default == to_Dt()
+                del default
+
+                for to_dt in [to_Dt(), to_Dt().newbyteorder()]:
+                    casting, (from_res, to_res), view_off = (
+                            cast._resolve_descriptors((from_dt, to_dt)))
+                    assert type(from_res) == from_Dt
+                    assert type(to_res) == to_Dt
+                    if view_off is not None:
+                        # If a view is acceptable, this is "no" casting
+                        # and byte order must be matching.
+                        assert casting == Casting.no
+                        # The above table lists this as "equivalent"
+                        assert Casting.equiv == CAST_TABLE[from_Dt][to_Dt]
+                        # Note that to_res may not be the same as from_dt
+                        assert from_res.isnative == to_res.isnative
+                    else:
+                        if from_Dt == to_Dt:
+                            # Note that to_res may not be the same as from_dt
+                            assert from_res.isnative != to_res.isnative
+                        assert casting == CAST_TABLE[from_Dt][to_Dt]
+
+                    if from_Dt is to_Dt:
+                        assert from_dt is from_res
+                        assert to_dt is to_res
+
+    @pytest.mark.filterwarnings("ignore::numpy.exceptions.ComplexWarning")
+    @pytest.mark.parametrize("from_dt", simple_dtype_instances())
+    def test_simple_direct_casts(self, from_dt):
+        """
+        This test checks numeric direct casts for dtypes supported also by the
+        struct module (plus complex).  It tries to be test a wide range of
+        inputs, but skips over possibly undefined behaviour (e.g. int rollover).
+        Longdouble and CLongdouble are tested, but only using double precision.
+
+        If this test creates issues, it should possibly just be simplified
+        or even removed (checking whether unaligned/non-contiguous casts give
+        the same results is useful, though).
+        """
+        for to_dt in simple_dtype_instances():
+            to_dt = to_dt.values[0]
+            cast = get_castingimpl(type(from_dt), type(to_dt))
+
+            casting, (from_res, to_res), view_off = cast._resolve_descriptors(
+                (from_dt, to_dt))
+
+            if from_res is not from_dt or to_res is not to_dt:
+                # Do not test this case, it is handled in multiple steps,
+                # each of which should is tested individually.
+                return
+
+            safe = casting <= Casting.safe
+            del from_res, to_res, casting
+
+            arr1, arr2, values = self.get_data(from_dt, to_dt)
+
+            cast._simple_strided_call((arr1, arr2))
+
+            # Check via python list
+            assert arr2.tolist() == values
+
+            # Check that the same results are achieved for strided loops
+            arr1_o, arr2_o = self.get_data_variation(arr1, arr2, True, False)
+            cast._simple_strided_call((arr1_o, arr2_o))
+
+            assert_array_equal(arr2_o, arr2)
+            assert arr2_o.tobytes() == arr2.tobytes()
+
+            # Check if alignment makes a difference, but only if supported
+            # and only if the alignment can be wrong
+            if ((from_dt.alignment == 1 and to_dt.alignment == 1) or
+                    not cast._supports_unaligned):
+                return
+
+            arr1_o, arr2_o = self.get_data_variation(arr1, arr2, False, True)
+            cast._simple_strided_call((arr1_o, arr2_o))
+
+            assert_array_equal(arr2_o, arr2)
+            assert arr2_o.tobytes() == arr2.tobytes()
+
+            arr1_o, arr2_o = self.get_data_variation(arr1, arr2, False, False)
+            cast._simple_strided_call((arr1_o, arr2_o))
+
+            assert_array_equal(arr2_o, arr2)
+            assert arr2_o.tobytes() == arr2.tobytes()
+
+            del arr1_o, arr2_o, cast
+
+    @pytest.mark.parametrize("from_Dt", simple_dtypes)
+    def test_numeric_to_times(self, from_Dt):
+        # We currently only implement contiguous loops, so only need to
+        # test those.
+        from_dt = from_Dt()
+
+        time_dtypes = [np.dtype("M8"), np.dtype("M8[ms]"), np.dtype("M8[4D]"),
+                       np.dtype("m8"), np.dtype("m8[ms]"), np.dtype("m8[4D]")]
+        for time_dt in time_dtypes:
+            cast = get_castingimpl(type(from_dt), type(time_dt))
+
+            casting, (from_res, to_res), view_off = cast._resolve_descriptors(
+                (from_dt, time_dt))
+
+            assert from_res is from_dt
+            assert to_res is time_dt
+            del from_res, to_res
+
+            assert casting & CAST_TABLE[from_Dt][type(time_dt)]
+            assert view_off is None
+
+            int64_dt = np.dtype(np.int64)
+            arr1, arr2, values = self.get_data(from_dt, int64_dt)
+            arr2 = arr2.view(time_dt)
+            arr2[...] = np.datetime64("NaT")
+
+            if time_dt == np.dtype("M8"):
+                # This is a bit of a strange path, and could probably be removed
+                arr1[-1] = 0  # ensure at least one value is not NaT
+
+                # The cast currently succeeds, but the values are invalid:
+                cast._simple_strided_call((arr1, arr2))
+                with pytest.raises(ValueError):
+                    str(arr2[-1])  # e.g. conversion to string fails
+                return
+
+            cast._simple_strided_call((arr1, arr2))
+
+            assert [int(v) for v in arr2.tolist()] == values
+
+            # Check that the same results are achieved for strided loops
+            arr1_o, arr2_o = self.get_data_variation(arr1, arr2, True, False)
+            cast._simple_strided_call((arr1_o, arr2_o))
+
+            assert_array_equal(arr2_o, arr2)
+            assert arr2_o.tobytes() == arr2.tobytes()
+
+    @pytest.mark.parametrize(
+            ["from_dt", "to_dt", "expected_casting", "expected_view_off",
+             "nom", "denom"],
+            [("M8[ns]", None, Casting.no, 0, 1, 1),
+             (str(np.dtype("M8[ns]").newbyteorder()), None,
+                  Casting.equiv, None, 1, 1),
+             ("M8", "M8[ms]", Casting.safe, 0, 1, 1),
+             # should be invalid cast:
+             ("M8[ms]", "M8", Casting.unsafe, None, 1, 1),
+             ("M8[5ms]", "M8[5ms]", Casting.no, 0, 1, 1),
+             ("M8[ns]", "M8[ms]", Casting.same_kind, None, 1, 10**6),
+             ("M8[ms]", "M8[ns]", Casting.safe, None, 10**6, 1),
+             ("M8[ms]", "M8[7ms]", Casting.same_kind, None, 1, 7),
+             ("M8[4D]", "M8[1M]", Casting.same_kind, None, None,
+                  # give full values based on NumPy 1.19.x
+                  [-2**63, 0, -1, 1314, -1315, 564442610]),
+             ("m8[ns]", None, Casting.no, 0, 1, 1),
+             (str(np.dtype("m8[ns]").newbyteorder()), None,
+                  Casting.equiv, None, 1, 1),
+             ("m8", "m8[ms]", Casting.safe, 0, 1, 1),
+             # should be invalid cast:
+             ("m8[ms]", "m8", Casting.unsafe, None, 1, 1),
+             ("m8[5ms]", "m8[5ms]", Casting.no, 0, 1, 1),
+             ("m8[ns]", "m8[ms]", Casting.same_kind, None, 1, 10**6),
+             ("m8[ms]", "m8[ns]", Casting.safe, None, 10**6, 1),
+             ("m8[ms]", "m8[7ms]", Casting.same_kind, None, 1, 7),
+             ("m8[4D]", "m8[1M]", Casting.unsafe, None, None,
+                  # give full values based on NumPy 1.19.x
+                  [-2**63, 0, 0, 1314, -1315, 564442610])])
+    def test_time_to_time(self, from_dt, to_dt,
+                          expected_casting, expected_view_off,
+                          nom, denom):
+        from_dt = np.dtype(from_dt)
+        if to_dt is not None:
+            to_dt = np.dtype(to_dt)
+
+        # Test a few values for casting (results generated with NumPy 1.19)
+        values = np.array([-2**63, 1, 2**63 - 1, 10000, -10000, 2**32])
+        values = values.astype(np.dtype("int64").newbyteorder(from_dt.byteorder))
+        assert values.dtype.byteorder == from_dt.byteorder
+        assert np.isnat(values.view(from_dt)[0])
+
+        DType = type(from_dt)
+        cast = get_castingimpl(DType, DType)
+        casting, (from_res, to_res), view_off = cast._resolve_descriptors(
+                (from_dt, to_dt))
+        assert from_res is from_dt
+        assert to_res is to_dt or to_dt is None
+        assert casting == expected_casting
+        assert view_off == expected_view_off
+
+        if nom is not None:
+            expected_out = (values * nom // denom).view(to_res)
+            expected_out[0] = "NaT"
+        else:
+            expected_out = np.empty_like(values)
+            expected_out[...] = denom
+            expected_out = expected_out.view(to_dt)
+
+        orig_arr = values.view(from_dt)
+        orig_out = np.empty_like(expected_out)
+
+        if casting == Casting.unsafe and (to_dt == "m8" or to_dt == "M8"):  # noqa: PLR1714
+            # Casting from non-generic to generic units is an error and should
+            # probably be reported as an invalid cast earlier.
+            with pytest.raises(ValueError):
+                cast._simple_strided_call((orig_arr, orig_out))
+            return
+
+        for aligned in [True, True]:
+            for contig in [True, True]:
+                arr, out = self.get_data_variation(
+                        orig_arr, orig_out, aligned, contig)
+                out[...] = 0
+                cast._simple_strided_call((arr, out))
+                assert_array_equal(out.view("int64"), expected_out.view("int64"))
+
+    def string_with_modified_length(self, dtype, change_length):
+        fact = 1 if dtype.char == "S" else 4
+        length = dtype.itemsize // fact + change_length
+        return np.dtype(f"{dtype.byteorder}{dtype.char}{length}")
+
+    @pytest.mark.parametrize("other_DT", simple_dtypes)
+    @pytest.mark.parametrize("string_char", ["S", "U"])
+    def test_string_cancast(self, other_DT, string_char):
+        fact = 1 if string_char == "S" else 4
+
+        string_DT = type(np.dtype(string_char))
+        cast = get_castingimpl(other_DT, string_DT)
+
+        other_dt = other_DT()
+        expected_length = get_expected_stringlength(other_dt)
+        string_dt = np.dtype(f"{string_char}{expected_length}")
+
+        safety, (res_other_dt, res_dt), view_off = cast._resolve_descriptors(
+                (other_dt, None))
+        assert res_dt.itemsize == expected_length * fact
+        assert safety == Casting.safe  # we consider to string casts "safe"
+        assert view_off is None
+        assert isinstance(res_dt, string_DT)
+
+        # These casts currently implement changing the string length, so
+        # check the cast-safety for too long/fixed string lengths:
+        for change_length in [-1, 0, 1]:
+            if change_length >= 0:
+                expected_safety = Casting.safe
+            else:
+                expected_safety = Casting.same_kind
+
+            to_dt = self.string_with_modified_length(string_dt, change_length)
+            safety, (_, res_dt), view_off = cast._resolve_descriptors(
+                    (other_dt, to_dt))
+            assert res_dt is to_dt
+            assert safety == expected_safety
+            assert view_off is None
+
+        # The opposite direction is always considered unsafe:
+        cast = get_castingimpl(string_DT, other_DT)
+
+        safety, _, view_off = cast._resolve_descriptors((string_dt, other_dt))
+        assert safety == Casting.unsafe
+        assert view_off is None
+
+        cast = get_castingimpl(string_DT, other_DT)
+        safety, (_, res_dt), view_off = cast._resolve_descriptors(
+            (string_dt, None))
+        assert safety == Casting.unsafe
+        assert view_off is None
+        assert other_dt is res_dt  # returns the singleton for simple dtypes
+
+    @pytest.mark.parametrize("string_char", ["S", "U"])
+    @pytest.mark.parametrize("other_dt", simple_dtype_instances())
+    def test_simple_string_casts_roundtrip(self, other_dt, string_char):
+        """
+        Tests casts from and to string by checking the roundtripping property.
+
+        The test also covers some string to string casts (but not all).
+
+        If this test creates issues, it should possibly just be simplified
+        or even removed (checking whether unaligned/non-contiguous casts give
+        the same results is useful, though).
+        """
+        string_DT = type(np.dtype(string_char))
+
+        cast = get_castingimpl(type(other_dt), string_DT)
+        cast_back = get_castingimpl(string_DT, type(other_dt))
+        _, (res_other_dt, string_dt), _ = cast._resolve_descriptors(
+                (other_dt, None))
+
+        if res_other_dt is not other_dt:
+            # do not support non-native byteorder, skip test in that case
+            assert other_dt.byteorder != res_other_dt.byteorder
+            return
+
+        orig_arr, values = self.get_data(other_dt, None)
+        str_arr = np.zeros(len(orig_arr), dtype=string_dt)
+        string_dt_short = self.string_with_modified_length(string_dt, -1)
+        str_arr_short = np.zeros(len(orig_arr), dtype=string_dt_short)
+        string_dt_long = self.string_with_modified_length(string_dt, 1)
+        str_arr_long = np.zeros(len(orig_arr), dtype=string_dt_long)
+
+        assert not cast._supports_unaligned  # if support is added, should test
+        assert not cast_back._supports_unaligned
+
+        for contig in [True, False]:
+            other_arr, str_arr = self.get_data_variation(
+                orig_arr, str_arr, True, contig)
+            _, str_arr_short = self.get_data_variation(
+                orig_arr, str_arr_short.copy(), True, contig)
+            _, str_arr_long = self.get_data_variation(
+                orig_arr, str_arr_long, True, contig)
+
+            cast._simple_strided_call((other_arr, str_arr))
+
+            cast._simple_strided_call((other_arr, str_arr_short))
+            assert_array_equal(str_arr.astype(string_dt_short), str_arr_short)
+
+            cast._simple_strided_call((other_arr, str_arr_long))
+            assert_array_equal(str_arr, str_arr_long)
+
+            if other_dt.kind == "b":
+                # Booleans do not roundtrip
+                continue
+
+            other_arr[...] = 0
+            cast_back._simple_strided_call((str_arr, other_arr))
+            assert_array_equal(orig_arr, other_arr)
+
+            other_arr[...] = 0
+            cast_back._simple_strided_call((str_arr_long, other_arr))
+            assert_array_equal(orig_arr, other_arr)
+
+    @pytest.mark.parametrize("other_dt", ["S8", "<U8", ">U8"])
+    @pytest.mark.parametrize("string_char", ["S", "U"])
+    def test_string_to_string_cancast(self, other_dt, string_char):
+        other_dt = np.dtype(other_dt)
+
+        fact = 1 if string_char == "S" else 4
+        div = 1 if other_dt.char == "S" else 4
+
+        string_DT = type(np.dtype(string_char))
+        cast = get_castingimpl(type(other_dt), string_DT)
+
+        expected_length = other_dt.itemsize // div
+        string_dt = np.dtype(f"{string_char}{expected_length}")
+
+        safety, (res_other_dt, res_dt), view_off = cast._resolve_descriptors(
+                (other_dt, None))
+        assert res_dt.itemsize == expected_length * fact
+        assert isinstance(res_dt, string_DT)
+
+        expected_view_off = None
+        if other_dt.char == string_char:
+            if other_dt.isnative:
+                expected_safety = Casting.no
+                expected_view_off = 0
+            else:
+                expected_safety = Casting.equiv
+        elif string_char == "U":
+            expected_safety = Casting.safe
+        else:
+            expected_safety = Casting.unsafe
+
+        assert view_off == expected_view_off
+        assert expected_safety == safety
+
+        for change_length in [-1, 0, 1]:
+            to_dt = self.string_with_modified_length(string_dt, change_length)
+            safety, (_, res_dt), view_off = cast._resolve_descriptors(
+                    (other_dt, to_dt))
+
+            assert res_dt is to_dt
+            if change_length <= 0:
+                assert view_off == expected_view_off
+            else:
+                assert view_off is None
+            if expected_safety == Casting.unsafe:
+                assert safety == expected_safety
+            elif change_length < 0:
+                assert safety == Casting.same_kind
+            elif change_length == 0:
+                assert safety == expected_safety
+            elif change_length > 0:
+                assert safety == Casting.safe
+
+    @pytest.mark.parametrize("order1", [">", "<"])
+    @pytest.mark.parametrize("order2", [">", "<"])
+    def test_unicode_byteswapped_cast(self, order1, order2):
+        # Very specific tests (not using the castingimpl directly)
+        # that tests unicode bytedwaps including for unaligned array data.
+        dtype1 = np.dtype(f"{order1}U30")
+        dtype2 = np.dtype(f"{order2}U30")
+        data1 = np.empty(30 * 4 + 1, dtype=np.uint8)[1:].view(dtype1)
+        data2 = np.empty(30 * 4 + 1, dtype=np.uint8)[1:].view(dtype2)
+        if dtype1.alignment != 1:
+            # alignment should always be >1, but skip the check if not
+            assert not data1.flags.aligned
+            assert not data2.flags.aligned
+
+        element = "this is a ünicode string‽"
+        data1[()] = element
+        # Test both `data1` and `data1.copy()`  (which should be aligned)
+        for data in [data1, data1.copy()]:
+            data2[...] = data1
+            assert data2[()] == element
+            assert data2.copy()[()] == element
+
+    def test_void_to_string_special_case(self):
+        # Cover a small special case in void to string casting that could
+        # probably just as well be turned into an error (compare
+        # `test_object_to_parametric_internal_error` below).
+        assert np.array([], dtype="V5").astype("S").dtype.itemsize == 5
+        assert np.array([], dtype="V5").astype("U").dtype.itemsize == 4 * 5
+
+    def test_object_to_parametric_internal_error(self):
+        # We reject casting from object to a parametric type, without
+        # figuring out the correct instance first.
+        object_dtype = type(np.dtype(object))
+        other_dtype = type(np.dtype(str))
+        cast = get_castingimpl(object_dtype, other_dtype)
+        with pytest.raises(TypeError,
+                    match="casting from object to the parametric DType"):
+            cast._resolve_descriptors((np.dtype("O"), None))
+
+    @pytest.mark.parametrize("dtype", simple_dtype_instances())
+    def test_object_and_simple_resolution(self, dtype):
+        # Simple test to exercise the cast when no instance is specified
+        object_dtype = type(np.dtype(object))
+        cast = get_castingimpl(object_dtype, type(dtype))
+
+        safety, (_, res_dt), view_off = cast._resolve_descriptors(
+                (np.dtype("O"), dtype))
+        assert safety == Casting.unsafe
+        assert view_off is None
+        assert res_dt is dtype
+
+        safety, (_, res_dt), view_off = cast._resolve_descriptors(
+                (np.dtype("O"), None))
+        assert safety == Casting.unsafe
+        assert view_off is None
+        assert res_dt == dtype.newbyteorder("=")
+
+    @pytest.mark.parametrize("dtype", simple_dtype_instances())
+    def test_simple_to_object_resolution(self, dtype):
+        # Simple test to exercise the cast when no instance is specified
+        object_dtype = type(np.dtype(object))
+        cast = get_castingimpl(type(dtype), object_dtype)
+
+        safety, (_, res_dt), view_off = cast._resolve_descriptors(
+                (dtype, None))
+        assert safety == Casting.safe
+        assert view_off is None
+        assert res_dt is np.dtype("O")
+
+    @pytest.mark.parametrize("casting", ["no", "unsafe"])
+    def test_void_and_structured_with_subarray(self, casting):
+        # test case corresponding to gh-19325
+        dtype = np.dtype([("foo", "<f4", (3, 2))])
+        expected = casting == "unsafe"
+        assert np.can_cast("V4", dtype, casting=casting) == expected
+        assert np.can_cast(dtype, "V4", casting=casting) == expected
+
+    @pytest.mark.parametrize(["to_dt", "expected_off"],
+            [  # Same as `from_dt` but with both fields shifted:
+             (np.dtype({"names": ["a", "b"], "formats": ["i4", "f4"],
+                        "offsets": [0, 4]}), 2),
+             # Additional change of the names
+             (np.dtype({"names": ["b", "a"], "formats": ["i4", "f4"],
+                        "offsets": [0, 4]}), 2),
+             # Incompatible field offset change
+             (np.dtype({"names": ["b", "a"], "formats": ["i4", "f4"],
+                        "offsets": [0, 6]}), None)])
+    def test_structured_field_offsets(self, to_dt, expected_off):
+        # This checks the cast-safety and view offset for swapped and "shifted"
+        # fields which are viewable
+        from_dt = np.dtype({"names": ["a", "b"],
+                            "formats": ["i4", "f4"],
+                            "offsets": [2, 6]})
+        cast = get_castingimpl(type(from_dt), type(to_dt))
+        safety, _, view_off = cast._resolve_descriptors((from_dt, to_dt))
+        if from_dt.names == to_dt.names:
+            assert safety == Casting.equiv
+        else:
+            assert safety == Casting.safe
+        # Shifting the original data pointer by -2 will align both by
+        # effectively adding 2 bytes of spacing before `from_dt`.
+        assert view_off == expected_off
+
+    @pytest.mark.parametrize(("from_dt", "to_dt", "expected_off"), [
+            # Subarray cases:
+            ("i", "(1,1)i", 0),
+            ("(1,1)i", "i", 0),
+            ("(2,1)i", "(2,1)i", 0),
+            # field cases (field to field is tested explicitly also):
+            # Not considered viewable, because a negative offset would allow
+            # may structured dtype to indirectly access invalid memory.
+            ("i", {"names": ["a"], "formats": ["i"], "offsets": [2]}, None),
+            ({"names": ["a"], "formats": ["i"], "offsets": [2]}, "i", 2),
+            # Currently considered not viewable, due to multiple fields
+            # even though they overlap (maybe we should not allow that?)
+            ("i", {"names": ["a", "b"], "formats": ["i", "i"], "offsets": [2, 2]},
+             None),
+            # different number of fields can't work, should probably just fail
+            # so it never reports "viewable":
+            ("i,i", "i,i,i", None),
+            # Unstructured void cases:
+            ("i4", "V3", 0),  # void smaller or equal
+            ("i4", "V4", 0),  # void smaller or equal
+            ("i4", "V10", None),  # void is larger (no view)
+            ("O", "V4", None),  # currently reject objects for view here.
+            ("O", "V8", None),  # currently reject objects for view here.
+            ("V4", "V3", 0),
+            ("V4", "V4", 0),
+            ("V3", "V4", None),
+            # Note that currently void-to-other cast goes via byte-strings
+            # and is not a "view" based cast like the opposite direction:
+            ("V4", "i4", None),
+            # completely invalid/impossible cast:
+            ("i,i", "i,i,i", None),
+        ])
+    def test_structured_view_offsets_parametric(
+            self, from_dt, to_dt, expected_off):
+        # TODO: While this test is fairly thorough, right now, it does not
+        # really test some paths that may have nonzero offsets (they don't
+        # really exists).
+        from_dt = np.dtype(from_dt)
+        to_dt = np.dtype(to_dt)
+        cast = get_castingimpl(type(from_dt), type(to_dt))
+        _, _, view_off = cast._resolve_descriptors((from_dt, to_dt))
+        assert view_off == expected_off
+
+    @pytest.mark.parametrize("dtype", np.typecodes["All"])
+    def test_object_casts_NULL_None_equivalence(self, dtype):
+        # None to <other> casts may succeed or fail, but a NULL'ed array must
+        # behave the same as one filled with None's.
+        arr_normal = np.array([None] * 5)
+        arr_NULLs = np.empty_like(arr_normal)
+        ctypes.memset(arr_NULLs.ctypes.data, 0, arr_NULLs.nbytes)
+        # If the check fails (maybe it should) the test would lose its purpose:
+        assert arr_NULLs.tobytes() == b"\x00" * arr_NULLs.nbytes
+
+        try:
+            expected = arr_normal.astype(dtype)
+        except TypeError:
+            with pytest.raises(TypeError):
+                arr_NULLs.astype(dtype)
+        else:
+            assert_array_equal(expected, arr_NULLs.astype(dtype))
+
+    @pytest.mark.parametrize("dtype",
+            np.typecodes["AllInteger"] + np.typecodes["AllFloat"])
+    def test_nonstandard_bool_to_other(self, dtype):
+        # simple test for casting bool_ to numeric types, which should not
+        # expose the detail that NumPy bools can sometimes take values other
+        # than 0 and 1.  See also gh-19514.
+        nonstandard_bools = np.array([0, 3, -7], dtype=np.int8).view(bool)
+        res = nonstandard_bools.astype(dtype)
+        expected = [0, 1, 1]
+        assert_array_equal(res, expected)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_conversion_utils.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_conversion_utils.py
new file mode 100644
index 0000000..03ba339
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_conversion_utils.py
@@ -0,0 +1,206 @@
+"""
+Tests for numpy/_core/src/multiarray/conversion_utils.c
+"""
+import re
+
+import numpy._core._multiarray_tests as mt
+import pytest
+
+from numpy._core.multiarray import CLIP, RAISE, WRAP
+from numpy.testing import assert_raises
+
+
+class StringConverterTestCase:
+    allow_bytes = True
+    case_insensitive = True
+    exact_match = False
+    warn = True
+
+    def _check_value_error(self, val):
+        pattern = fr'\(got {re.escape(repr(val))}\)'
+        with pytest.raises(ValueError, match=pattern) as exc:
+            self.conv(val)
+
+    def _check_conv_assert_warn(self, val, expected):
+        if self.warn:
+            with assert_raises(ValueError) as exc:
+                assert self.conv(val) == expected
+        else:
+            assert self.conv(val) == expected
+
+    def _check(self, val, expected):
+        """Takes valid non-deprecated inputs for converters,
+        runs converters on inputs, checks correctness of outputs,
+        warnings and errors"""
+        assert self.conv(val) == expected
+
+        if self.allow_bytes:
+            assert self.conv(val.encode('ascii')) == expected
+        else:
+            with pytest.raises(TypeError):
+                self.conv(val.encode('ascii'))
+
+        if len(val) != 1:
+            if self.exact_match:
+                self._check_value_error(val[:1])
+                self._check_value_error(val + '\0')
+            else:
+                self._check_conv_assert_warn(val[:1], expected)
+
+        if self.case_insensitive:
+            if val != val.lower():
+                self._check_conv_assert_warn(val.lower(), expected)
+            if val != val.upper():
+                self._check_conv_assert_warn(val.upper(), expected)
+        else:
+            if val != val.lower():
+                self._check_value_error(val.lower())
+            if val != val.upper():
+                self._check_value_error(val.upper())
+
+    def test_wrong_type(self):
+        # common cases which apply to all the below
+        with pytest.raises(TypeError):
+            self.conv({})
+        with pytest.raises(TypeError):
+            self.conv([])
+
+    def test_wrong_value(self):
+        # nonsense strings
+        self._check_value_error('')
+        self._check_value_error('\N{greek small letter pi}')
+
+        if self.allow_bytes:
+            self._check_value_error(b'')
+            # bytes which can't be converted to strings via utf8
+            self._check_value_error(b"\xFF")
+        if self.exact_match:
+            self._check_value_error("there's no way this is supported")
+
+
+class TestByteorderConverter(StringConverterTestCase):
+    """ Tests of PyArray_ByteorderConverter """
+    conv = mt.run_byteorder_converter
+    warn = False
+
+    def test_valid(self):
+        for s in ['big', '>']:
+            self._check(s, 'NPY_BIG')
+        for s in ['little', '<']:
+            self._check(s, 'NPY_LITTLE')
+        for s in ['native', '=']:
+            self._check(s, 'NPY_NATIVE')
+        for s in ['ignore', '|']:
+            self._check(s, 'NPY_IGNORE')
+        for s in ['swap']:
+            self._check(s, 'NPY_SWAP')
+
+
+class TestSortkindConverter(StringConverterTestCase):
+    """ Tests of PyArray_SortkindConverter """
+    conv = mt.run_sortkind_converter
+    warn = False
+
+    def test_valid(self):
+        self._check('quicksort', 'NPY_QUICKSORT')
+        self._check('heapsort', 'NPY_HEAPSORT')
+        self._check('mergesort', 'NPY_STABLESORT')  # alias
+        self._check('stable', 'NPY_STABLESORT')
+
+
+class TestSelectkindConverter(StringConverterTestCase):
+    """ Tests of PyArray_SelectkindConverter """
+    conv = mt.run_selectkind_converter
+    case_insensitive = False
+    exact_match = True
+
+    def test_valid(self):
+        self._check('introselect', 'NPY_INTROSELECT')
+
+
+class TestSearchsideConverter(StringConverterTestCase):
+    """ Tests of PyArray_SearchsideConverter """
+    conv = mt.run_searchside_converter
+
+    def test_valid(self):
+        self._check('left', 'NPY_SEARCHLEFT')
+        self._check('right', 'NPY_SEARCHRIGHT')
+
+
+class TestOrderConverter(StringConverterTestCase):
+    """ Tests of PyArray_OrderConverter """
+    conv = mt.run_order_converter
+    warn = False
+
+    def test_valid(self):
+        self._check('c', 'NPY_CORDER')
+        self._check('f', 'NPY_FORTRANORDER')
+        self._check('a', 'NPY_ANYORDER')
+        self._check('k', 'NPY_KEEPORDER')
+
+    def test_flatten_invalid_order(self):
+        # invalid after gh-14596
+        with pytest.raises(ValueError):
+            self.conv('Z')
+        for order in [False, True, 0, 8]:
+            with pytest.raises(TypeError):
+                self.conv(order)
+
+
+class TestClipmodeConverter(StringConverterTestCase):
+    """ Tests of PyArray_ClipmodeConverter """
+    conv = mt.run_clipmode_converter
+
+    def test_valid(self):
+        self._check('clip', 'NPY_CLIP')
+        self._check('wrap', 'NPY_WRAP')
+        self._check('raise', 'NPY_RAISE')
+
+        # integer values allowed here
+        assert self.conv(CLIP) == 'NPY_CLIP'
+        assert self.conv(WRAP) == 'NPY_WRAP'
+        assert self.conv(RAISE) == 'NPY_RAISE'
+
+
+class TestCastingConverter(StringConverterTestCase):
+    """ Tests of PyArray_CastingConverter """
+    conv = mt.run_casting_converter
+    case_insensitive = False
+    exact_match = True
+
+    def test_valid(self):
+        self._check("no", "NPY_NO_CASTING")
+        self._check("equiv", "NPY_EQUIV_CASTING")
+        self._check("safe", "NPY_SAFE_CASTING")
+        self._check("same_kind", "NPY_SAME_KIND_CASTING")
+        self._check("unsafe", "NPY_UNSAFE_CASTING")
+
+
+class TestIntpConverter:
+    """ Tests of PyArray_IntpConverter """
+    conv = mt.run_intp_converter
+
+    def test_basic(self):
+        assert self.conv(1) == (1,)
+        assert self.conv((1, 2)) == (1, 2)
+        assert self.conv([1, 2]) == (1, 2)
+        assert self.conv(()) == ()
+
+    def test_none(self):
+        with pytest.raises(TypeError):
+            assert self.conv(None) == ()
+
+    def test_float(self):
+        with pytest.raises(TypeError):
+            self.conv(1.0)
+        with pytest.raises(TypeError):
+            self.conv([1, 1.0])
+
+    def test_too_large(self):
+        with pytest.raises(ValueError):
+            self.conv(2**64)
+
+    def test_too_many_dims(self):
+        assert self.conv([1] * 64) == (1,) * 64
+        with pytest.raises(ValueError):
+            self.conv([1] * 65)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_cpu_dispatcher.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_cpu_dispatcher.py
new file mode 100644
index 0000000..0a47685
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_cpu_dispatcher.py
@@ -0,0 +1,49 @@
+from numpy._core._multiarray_umath import (
+    __cpu_baseline__,
+    __cpu_dispatch__,
+    __cpu_features__,
+)
+
+from numpy._core import _umath_tests
+from numpy.testing import assert_equal
+
+
+def test_dispatcher():
+    """
+    Testing the utilities of the CPU dispatcher
+    """
+    targets = (
+        "SSE2", "SSE41", "AVX2",
+        "VSX", "VSX2", "VSX3",
+        "NEON", "ASIMD", "ASIMDHP",
+        "VX", "VXE", "LSX"
+    )
+    highest_sfx = ""  # no suffix for the baseline
+    all_sfx = []
+    for feature in reversed(targets):
+        # skip baseline features, by the default `CCompilerOpt` do not generate separated objects
+        # for the baseline,  just one object combined all of them via 'baseline' option
+        # within the configuration statements.
+        if feature in __cpu_baseline__:
+            continue
+        # check compiler and running machine support
+        if feature not in __cpu_dispatch__ or not __cpu_features__[feature]:
+            continue
+
+        if not highest_sfx:
+            highest_sfx = "_" + feature
+        all_sfx.append("func" + "_" + feature)
+
+    test = _umath_tests.test_dispatch()
+    assert_equal(test["func"], "func" + highest_sfx)
+    assert_equal(test["var"], "var" + highest_sfx)
+
+    if highest_sfx:
+        assert_equal(test["func_xb"], "func" + highest_sfx)
+        assert_equal(test["var_xb"], "var" + highest_sfx)
+    else:
+        assert_equal(test["func_xb"], "nobase")
+        assert_equal(test["var_xb"], "nobase")
+
+    all_sfx.append("func")  # add the baseline
+    assert_equal(test["all"], all_sfx)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_cpu_features.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_cpu_features.py
new file mode 100644
index 0000000..d1e3dc6
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_cpu_features.py
@@ -0,0 +1,432 @@
+import os
+import pathlib
+import platform
+import re
+import subprocess
+import sys
+
+import pytest
+from numpy._core._multiarray_umath import (
+    __cpu_baseline__,
+    __cpu_dispatch__,
+    __cpu_features__,
+)
+
+
+def assert_features_equal(actual, desired, fname):
+    __tracebackhide__ = True  # Hide traceback for py.test
+    actual, desired = str(actual), str(desired)
+    if actual == desired:
+        return
+    detected = str(__cpu_features__).replace("'", "")
+    try:
+        with open("/proc/cpuinfo") as fd:
+            cpuinfo = fd.read(2048)
+    except Exception as err:
+        cpuinfo = str(err)
+
+    try:
+        import subprocess
+        auxv = subprocess.check_output(['/bin/true'], env={"LD_SHOW_AUXV": "1"})
+        auxv = auxv.decode()
+    except Exception as err:
+        auxv = str(err)
+
+    import textwrap
+    error_report = textwrap.indent(
+f"""
+###########################################
+### Extra debugging information
+###########################################
+-------------------------------------------
+--- NumPy Detections
+-------------------------------------------
+{detected}
+-------------------------------------------
+--- SYS / CPUINFO
+-------------------------------------------
+{cpuinfo}....
+-------------------------------------------
+--- SYS / AUXV
+-------------------------------------------
+{auxv}
+""", prefix='\r')
+
+    raise AssertionError((
+        "Failure Detection\n"
+        " NAME: '%s'\n"
+        " ACTUAL: %s\n"
+        " DESIRED: %s\n"
+        "%s"
+    ) % (fname, actual, desired, error_report))
+
+def _text_to_list(txt):
+    out = txt.strip("][\n").replace("'", "").split(', ')
+    return None if out[0] == "" else out
+
+class AbstractTest:
+    features = []
+    features_groups = {}
+    features_map = {}
+    features_flags = set()
+
+    def load_flags(self):
+        # a hook
+        pass
+
+    def test_features(self):
+        self.load_flags()
+        for gname, features in self.features_groups.items():
+            test_features = [self.cpu_have(f) for f in features]
+            assert_features_equal(__cpu_features__.get(gname), all(test_features), gname)
+
+        for feature_name in self.features:
+            cpu_have = self.cpu_have(feature_name)
+            npy_have = __cpu_features__.get(feature_name)
+            assert_features_equal(npy_have, cpu_have, feature_name)
+
+    def cpu_have(self, feature_name):
+        map_names = self.features_map.get(feature_name, feature_name)
+        if isinstance(map_names, str):
+            return map_names in self.features_flags
+        return any(f in self.features_flags for f in map_names)
+
+    def load_flags_cpuinfo(self, magic_key):
+        self.features_flags = self.get_cpuinfo_item(magic_key)
+
+    def get_cpuinfo_item(self, magic_key):
+        values = set()
+        with open('/proc/cpuinfo') as fd:
+            for line in fd:
+                if not line.startswith(magic_key):
+                    continue
+                flags_value = [s.strip() for s in line.split(':', 1)]
+                if len(flags_value) == 2:
+                    values = values.union(flags_value[1].upper().split())
+        return values
+
+    def load_flags_auxv(self):
+        auxv = subprocess.check_output(['/bin/true'], env={"LD_SHOW_AUXV": "1"})
+        for at in auxv.split(b'\n'):
+            if not at.startswith(b"AT_HWCAP"):
+                continue
+            hwcap_value = [s.strip() for s in at.split(b':', 1)]
+            if len(hwcap_value) == 2:
+                self.features_flags = self.features_flags.union(
+                    hwcap_value[1].upper().decode().split()
+                )
+
+@pytest.mark.skipif(
+    sys.platform == 'emscripten',
+    reason=(
+        "The subprocess module is not available on WASM platforms and"
+        " therefore this test class cannot be properly executed."
+    ),
+)
+class TestEnvPrivation:
+    cwd = pathlib.Path(__file__).parent.resolve()
+    env = os.environ.copy()
+    _enable = os.environ.pop('NPY_ENABLE_CPU_FEATURES', None)
+    _disable = os.environ.pop('NPY_DISABLE_CPU_FEATURES', None)
+    SUBPROCESS_ARGS = {"cwd": cwd, "capture_output": True, "text": True, "check": True}
+    unavailable_feats = [
+        feat for feat in __cpu_dispatch__ if not __cpu_features__[feat]
+    ]
+    UNAVAILABLE_FEAT = (
+        None if len(unavailable_feats) == 0
+        else unavailable_feats[0]
+    )
+    BASELINE_FEAT = None if len(__cpu_baseline__) == 0 else __cpu_baseline__[0]
+    SCRIPT = """
+def main():
+    from numpy._core._multiarray_umath import (
+        __cpu_features__,
+        __cpu_dispatch__
+    )
+
+    detected = [feat for feat in __cpu_dispatch__ if __cpu_features__[feat]]
+    print(detected)
+
+if __name__ == "__main__":
+    main()
+    """
+
+    @pytest.fixture(autouse=True)
+    def setup_class(self, tmp_path_factory):
+        file = tmp_path_factory.mktemp("runtime_test_script")
+        file /= "_runtime_detect.py"
+        file.write_text(self.SCRIPT)
+        self.file = file
+
+    def _run(self):
+        return subprocess.run(
+            [sys.executable, self.file],
+            env=self.env,
+            **self.SUBPROCESS_ARGS,
+            )
+
+    # Helper function mimicking pytest.raises for subprocess call
+    def _expect_error(
+        self,
+        msg,
+        err_type,
+        no_error_msg="Failed to generate error"
+    ):
+        try:
+            self._run()
+        except subprocess.CalledProcessError as e:
+            assertion_message = f"Expected: {msg}\nGot: {e.stderr}"
+            assert re.search(msg, e.stderr), assertion_message
+
+            assertion_message = (
+                f"Expected error of type: {err_type}; see full "
+                f"error:\n{e.stderr}"
+            )
+            assert re.search(err_type, e.stderr), assertion_message
+        else:
+            assert False, no_error_msg
+
+    def setup_method(self):
+        """Ensure that the environment is reset"""
+        self.env = os.environ.copy()
+
+    def test_runtime_feature_selection(self):
+        """
+        Ensure that when selecting `NPY_ENABLE_CPU_FEATURES`, only the
+        features exactly specified are dispatched.
+        """
+
+        # Capture runtime-enabled features
+        out = self._run()
+        non_baseline_features = _text_to_list(out.stdout)
+
+        if non_baseline_features is None:
+            pytest.skip(
+                "No dispatchable features outside of baseline detected."
+            )
+        feature = non_baseline_features[0]
+
+        # Capture runtime-enabled features when `NPY_ENABLE_CPU_FEATURES` is
+        # specified
+        self.env['NPY_ENABLE_CPU_FEATURES'] = feature
+        out = self._run()
+        enabled_features = _text_to_list(out.stdout)
+
+        # Ensure that only one feature is enabled, and it is exactly the one
+        # specified by `NPY_ENABLE_CPU_FEATURES`
+        assert set(enabled_features) == {feature}
+
+        if len(non_baseline_features) < 2:
+            pytest.skip("Only one non-baseline feature detected.")
+        # Capture runtime-enabled features when `NPY_ENABLE_CPU_FEATURES` is
+        # specified
+        self.env['NPY_ENABLE_CPU_FEATURES'] = ",".join(non_baseline_features)
+        out = self._run()
+        enabled_features = _text_to_list(out.stdout)
+
+        # Ensure that both features are enabled, and they are exactly the ones
+        # specified by `NPY_ENABLE_CPU_FEATURES`
+        assert set(enabled_features) == set(non_baseline_features)
+
+    @pytest.mark.parametrize("enabled, disabled",
+    [
+        ("feature", "feature"),
+        ("feature", "same"),
+    ])
+    def test_both_enable_disable_set(self, enabled, disabled):
+        """
+        Ensure that when both environment variables are set then an
+        ImportError is thrown
+        """
+        self.env['NPY_ENABLE_CPU_FEATURES'] = enabled
+        self.env['NPY_DISABLE_CPU_FEATURES'] = disabled
+        msg = "Both NPY_DISABLE_CPU_FEATURES and NPY_ENABLE_CPU_FEATURES"
+        err_type = "ImportError"
+        self._expect_error(msg, err_type)
+
+    @pytest.mark.skipif(
+        not __cpu_dispatch__,
+        reason=(
+            "NPY_*_CPU_FEATURES only parsed if "
+            "`__cpu_dispatch__` is non-empty"
+        )
+    )
+    @pytest.mark.parametrize("action", ["ENABLE", "DISABLE"])
+    def test_variable_too_long(self, action):
+        """
+        Test that an error is thrown if the environment variables are too long
+        to be processed. Current limit is 1024, but this may change later.
+        """
+        MAX_VAR_LENGTH = 1024
+        # Actual length is MAX_VAR_LENGTH + 1 due to null-termination
+        self.env[f'NPY_{action}_CPU_FEATURES'] = "t" * MAX_VAR_LENGTH
+        msg = (
+            f"Length of environment variable 'NPY_{action}_CPU_FEATURES' is "
+            f"{MAX_VAR_LENGTH + 1}, only {MAX_VAR_LENGTH} accepted"
+        )
+        err_type = "RuntimeError"
+        self._expect_error(msg, err_type)
+
+    @pytest.mark.skipif(
+        not __cpu_dispatch__,
+        reason=(
+            "NPY_*_CPU_FEATURES only parsed if "
+            "`__cpu_dispatch__` is non-empty"
+        )
+    )
+    def test_impossible_feature_disable(self):
+        """
+        Test that a RuntimeError is thrown if an impossible feature-disabling
+        request is made. This includes disabling a baseline feature.
+        """
+
+        if self.BASELINE_FEAT is None:
+            pytest.skip("There are no unavailable features to test with")
+        bad_feature = self.BASELINE_FEAT
+        self.env['NPY_DISABLE_CPU_FEATURES'] = bad_feature
+        msg = (
+            f"You cannot disable CPU feature '{bad_feature}', since it is "
+            "part of the baseline optimizations"
+        )
+        err_type = "RuntimeError"
+        self._expect_error(msg, err_type)
+
+    def test_impossible_feature_enable(self):
+        """
+        Test that a RuntimeError is thrown if an impossible feature-enabling
+        request is made. This includes enabling a feature not supported by the
+        machine, or disabling a baseline optimization.
+        """
+
+        if self.UNAVAILABLE_FEAT is None:
+            pytest.skip("There are no unavailable features to test with")
+        bad_feature = self.UNAVAILABLE_FEAT
+        self.env['NPY_ENABLE_CPU_FEATURES'] = bad_feature
+        msg = (
+            f"You cannot enable CPU features \\({bad_feature}\\), since "
+            "they are not supported by your machine."
+        )
+        err_type = "RuntimeError"
+        self._expect_error(msg, err_type)
+
+        # Ensure that it fails even when providing garbage in addition
+        feats = f"{bad_feature}, Foobar"
+        self.env['NPY_ENABLE_CPU_FEATURES'] = feats
+        msg = (
+            f"You cannot enable CPU features \\({bad_feature}\\), since they "
+            "are not supported by your machine."
+        )
+        self._expect_error(msg, err_type)
+
+        if self.BASELINE_FEAT is not None:
+            # Ensure that only the bad feature gets reported
+            feats = f"{bad_feature}, {self.BASELINE_FEAT}"
+            self.env['NPY_ENABLE_CPU_FEATURES'] = feats
+            msg = (
+                f"You cannot enable CPU features \\({bad_feature}\\), since "
+                "they are not supported by your machine."
+            )
+            self._expect_error(msg, err_type)
+
+
+is_linux = sys.platform.startswith('linux')
+is_cygwin = sys.platform.startswith('cygwin')
+machine = platform.machine()
+is_x86 = re.match(r"^(amd64|x86|i386|i686)", machine, re.IGNORECASE)
+@pytest.mark.skipif(
+    not (is_linux or is_cygwin) or not is_x86, reason="Only for Linux and x86"
+)
+class Test_X86_Features(AbstractTest):
+    features = [
+        "MMX", "SSE", "SSE2", "SSE3", "SSSE3", "SSE41", "POPCNT", "SSE42",
+        "AVX", "F16C", "XOP", "FMA4", "FMA3", "AVX2", "AVX512F", "AVX512CD",
+        "AVX512ER", "AVX512PF", "AVX5124FMAPS", "AVX5124VNNIW", "AVX512VPOPCNTDQ",
+        "AVX512VL", "AVX512BW", "AVX512DQ", "AVX512VNNI", "AVX512IFMA",
+        "AVX512VBMI", "AVX512VBMI2", "AVX512BITALG", "AVX512FP16",
+    ]
+    features_groups = {
+        "AVX512_KNL": ["AVX512F", "AVX512CD", "AVX512ER", "AVX512PF"],
+        "AVX512_KNM": ["AVX512F", "AVX512CD", "AVX512ER", "AVX512PF", "AVX5124FMAPS",
+                      "AVX5124VNNIW", "AVX512VPOPCNTDQ"],
+        "AVX512_SKX": ["AVX512F", "AVX512CD", "AVX512BW", "AVX512DQ", "AVX512VL"],
+        "AVX512_CLX": ["AVX512F", "AVX512CD", "AVX512BW", "AVX512DQ", "AVX512VL", "AVX512VNNI"],
+        "AVX512_CNL": ["AVX512F", "AVX512CD", "AVX512BW", "AVX512DQ", "AVX512VL", "AVX512IFMA",
+                      "AVX512VBMI"],
+        "AVX512_ICL": ["AVX512F", "AVX512CD", "AVX512BW", "AVX512DQ", "AVX512VL", "AVX512IFMA",
+                      "AVX512VBMI", "AVX512VNNI", "AVX512VBMI2", "AVX512BITALG", "AVX512VPOPCNTDQ"],
+        "AVX512_SPR": ["AVX512F", "AVX512CD", "AVX512BW", "AVX512DQ",
+                      "AVX512VL", "AVX512IFMA", "AVX512VBMI", "AVX512VNNI",
+                      "AVX512VBMI2", "AVX512BITALG", "AVX512VPOPCNTDQ",
+                      "AVX512FP16"],
+    }
+    features_map = {
+        "SSE3": "PNI", "SSE41": "SSE4_1", "SSE42": "SSE4_2", "FMA3": "FMA",
+        "AVX512VNNI": "AVX512_VNNI", "AVX512BITALG": "AVX512_BITALG",
+        "AVX512VBMI2": "AVX512_VBMI2", "AVX5124FMAPS": "AVX512_4FMAPS",
+        "AVX5124VNNIW": "AVX512_4VNNIW", "AVX512VPOPCNTDQ": "AVX512_VPOPCNTDQ",
+        "AVX512FP16": "AVX512_FP16",
+    }
+
+    def load_flags(self):
+        self.load_flags_cpuinfo("flags")
+
+
+is_power = re.match(r"^(powerpc|ppc)64", machine, re.IGNORECASE)
+@pytest.mark.skipif(not is_linux or not is_power, reason="Only for Linux and Power")
+class Test_POWER_Features(AbstractTest):
+    features = ["VSX", "VSX2", "VSX3", "VSX4"]
+    features_map = {"VSX2": "ARCH_2_07", "VSX3": "ARCH_3_00", "VSX4": "ARCH_3_1"}
+
+    def load_flags(self):
+        self.load_flags_auxv()
+
+
+is_zarch = re.match(r"^(s390x)", machine, re.IGNORECASE)
+@pytest.mark.skipif(not is_linux or not is_zarch,
+                    reason="Only for Linux and IBM Z")
+class Test_ZARCH_Features(AbstractTest):
+    features = ["VX", "VXE", "VXE2"]
+
+    def load_flags(self):
+        self.load_flags_auxv()
+
+
+is_arm = re.match(r"^(arm|aarch64)", machine, re.IGNORECASE)
+@pytest.mark.skipif(not is_linux or not is_arm, reason="Only for Linux and ARM")
+class Test_ARM_Features(AbstractTest):
+    features = [
+        "SVE", "NEON", "ASIMD", "FPHP", "ASIMDHP", "ASIMDDP", "ASIMDFHM"
+    ]
+    features_groups = {
+        "NEON_FP16":  ["NEON", "HALF"],
+        "NEON_VFPV4": ["NEON", "VFPV4"],
+    }
+
+    def load_flags(self):
+        self.load_flags_cpuinfo("Features")
+        arch = self.get_cpuinfo_item("CPU architecture")
+        # in case of mounting virtual filesystem of aarch64 kernel without linux32
+        is_rootfs_v8 = (
+            not re.match(r"^armv[0-9]+l$", machine) and
+            (int('0' + next(iter(arch))) > 7 if arch else 0)
+        )
+        if re.match(r"^(aarch64|AARCH64)", machine) or is_rootfs_v8:
+            self.features_map = {
+                "NEON": "ASIMD", "HALF": "ASIMD", "VFPV4": "ASIMD"
+            }
+        else:
+            self.features_map = {
+                # ELF auxiliary vector and /proc/cpuinfo on Linux kernel(armv8 aarch32)
+                # doesn't provide information about ASIMD, so we assume that ASIMD is supported
+                # if the kernel reports any one of the following ARM8 features.
+                "ASIMD": ("AES", "SHA1", "SHA2", "PMULL", "CRC32")
+            }
+
+
+is_loongarch = re.match(r"^(loongarch)", machine, re.IGNORECASE)
+@pytest.mark.skipif(not is_linux or not is_loongarch, reason="Only for Linux and LoongArch")
+class Test_LOONGARCH_Features(AbstractTest):
+    features = ["LSX"]
+
+    def load_flags(self):
+        self.load_flags_cpuinfo("Features")
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_custom_dtypes.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_custom_dtypes.py
new file mode 100644
index 0000000..66e6de3
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_custom_dtypes.py
@@ -0,0 +1,315 @@
+from tempfile import NamedTemporaryFile
+
+import pytest
+from numpy._core._multiarray_umath import (
+    _discover_array_parameters as discover_array_params,
+)
+from numpy._core._multiarray_umath import _get_sfloat_dtype
+
+import numpy as np
+from numpy.testing import assert_array_equal
+
+SF = _get_sfloat_dtype()
+
+
+class TestSFloat:
+    def _get_array(self, scaling, aligned=True):
+        if not aligned:
+            a = np.empty(3 * 8 + 1, dtype=np.uint8)[1:]
+            a = a.view(np.float64)
+            a[:] = [1., 2., 3.]
+        else:
+            a = np.array([1., 2., 3.])
+
+        a *= 1. / scaling  # the casting code also uses the reciprocal.
+        return a.view(SF(scaling))
+
+    def test_sfloat_rescaled(self):
+        sf = SF(1.)
+        sf2 = sf.scaled_by(2.)
+        assert sf2.get_scaling() == 2.
+        sf6 = sf2.scaled_by(3.)
+        assert sf6.get_scaling() == 6.
+
+    def test_class_discovery(self):
+        # This does not test much, since we always discover the scaling as 1.
+        # But most of NumPy (when writing) does not understand DType classes
+        dt, _ = discover_array_params([1., 2., 3.], dtype=SF)
+        assert dt == SF(1.)
+
+    @pytest.mark.parametrize("scaling", [1., -1., 2.])
+    def test_scaled_float_from_floats(self, scaling):
+        a = np.array([1., 2., 3.], dtype=SF(scaling))
+
+        assert a.dtype.get_scaling() == scaling
+        assert_array_equal(scaling * a.view(np.float64), [1., 2., 3.])
+
+    def test_repr(self):
+        # Check the repr, mainly to cover the code paths:
+        assert repr(SF(scaling=1.)) == "_ScaledFloatTestDType(scaling=1.0)"
+
+    def test_dtype_str(self):
+        assert SF(1.).str == "_ScaledFloatTestDType(scaling=1.0)"
+
+    def test_dtype_name(self):
+        assert SF(1.).name == "_ScaledFloatTestDType64"
+
+    def test_sfloat_structured_dtype_printing(self):
+        dt = np.dtype([("id", int), ("value", SF(0.5))])
+        # repr of structured dtypes need special handling because the
+        # implementation bypasses the object repr
+        assert "('value', '_ScaledFloatTestDType64')" in repr(dt)
+
+    @pytest.mark.parametrize("scaling", [1., -1., 2.])
+    def test_sfloat_from_float(self, scaling):
+        a = np.array([1., 2., 3.]).astype(dtype=SF(scaling))
+
+        assert a.dtype.get_scaling() == scaling
+        assert_array_equal(scaling * a.view(np.float64), [1., 2., 3.])
+
+    @pytest.mark.parametrize("aligned", [True, False])
+    @pytest.mark.parametrize("scaling", [1., -1., 2.])
+    def test_sfloat_getitem(self, aligned, scaling):
+        a = self._get_array(1., aligned)
+        assert a.tolist() == [1., 2., 3.]
+
+    @pytest.mark.parametrize("aligned", [True, False])
+    def test_sfloat_casts(self, aligned):
+        a = self._get_array(1., aligned)
+
+        assert np.can_cast(a, SF(-1.), casting="equiv")
+        assert not np.can_cast(a, SF(-1.), casting="no")
+        na = a.astype(SF(-1.))
+        assert_array_equal(-1 * na.view(np.float64), a.view(np.float64))
+
+        assert np.can_cast(a, SF(2.), casting="same_kind")
+        assert not np.can_cast(a, SF(2.), casting="safe")
+        a2 = a.astype(SF(2.))
+        assert_array_equal(2 * a2.view(np.float64), a.view(np.float64))
+
+    @pytest.mark.parametrize("aligned", [True, False])
+    def test_sfloat_cast_internal_errors(self, aligned):
+        a = self._get_array(2e300, aligned)
+
+        with pytest.raises(TypeError,
+                match="error raised inside the core-loop: non-finite factor!"):
+            a.astype(SF(2e-300))
+
+    def test_sfloat_promotion(self):
+        assert np.result_type(SF(2.), SF(3.)) == SF(3.)
+        assert np.result_type(SF(3.), SF(2.)) == SF(3.)
+        # Float64 -> SF(1.) and then promotes normally, so both of this work:
+        assert np.result_type(SF(3.), np.float64) == SF(3.)
+        assert np.result_type(np.float64, SF(0.5)) == SF(1.)
+
+        # Test an undefined promotion:
+        with pytest.raises(TypeError):
+            np.result_type(SF(1.), np.int64)
+
+    def test_basic_multiply(self):
+        a = self._get_array(2.)
+        b = self._get_array(4.)
+
+        res = a * b
+        # multiplies dtype scaling and content separately:
+        assert res.dtype.get_scaling() == 8.
+        expected_view = a.view(np.float64) * b.view(np.float64)
+        assert_array_equal(res.view(np.float64), expected_view)
+
+    def test_possible_and_impossible_reduce(self):
+        # For reductions to work, the first and last operand must have the
+        # same dtype.  For this parametric DType that is not necessarily true.
+        a = self._get_array(2.)
+        # Addition reduction works (as of writing requires to pass initial
+        # because setting a scaled-float from the default `0` fails).
+        res = np.add.reduce(a, initial=0.)
+        assert res == a.astype(np.float64).sum()
+
+        # But each multiplication changes the factor, so a reduction is not
+        # possible (the relaxed version of the old refusal to handle any
+        # flexible dtype).
+        with pytest.raises(TypeError,
+                match="the resolved dtypes are not compatible"):
+            np.multiply.reduce(a)
+
+    def test_basic_ufunc_at(self):
+        float_a = np.array([1., 2., 3.])
+        b = self._get_array(2.)
+
+        float_b = b.view(np.float64).copy()
+        np.multiply.at(float_b, [1, 1, 1], float_a)
+        np.multiply.at(b, [1, 1, 1], float_a)
+
+        assert_array_equal(b.view(np.float64), float_b)
+
+    def test_basic_multiply_promotion(self):
+        float_a = np.array([1., 2., 3.])
+        b = self._get_array(2.)
+
+        res1 = float_a * b
+        res2 = b * float_a
+
+        # one factor is one, so we get the factor of b:
+        assert res1.dtype == res2.dtype == b.dtype
+        expected_view = float_a * b.view(np.float64)
+        assert_array_equal(res1.view(np.float64), expected_view)
+        assert_array_equal(res2.view(np.float64), expected_view)
+
+        # Check that promotion works when `out` is used:
+        np.multiply(b, float_a, out=res2)
+        with pytest.raises(TypeError):
+            # The promoter accepts this (maybe it should not), but the SFloat
+            # result cannot be cast to integer:
+            np.multiply(b, float_a, out=np.arange(3))
+
+    def test_basic_addition(self):
+        a = self._get_array(2.)
+        b = self._get_array(4.)
+
+        res = a + b
+        # addition uses the type promotion rules for the result:
+        assert res.dtype == np.result_type(a.dtype, b.dtype)
+        expected_view = (a.astype(res.dtype).view(np.float64) +
+                         b.astype(res.dtype).view(np.float64))
+        assert_array_equal(res.view(np.float64), expected_view)
+
+    def test_addition_cast_safety(self):
+        """The addition method is special for the scaled float, because it
+        includes the "cast" between different factors, thus cast-safety
+        is influenced by the implementation.
+        """
+        a = self._get_array(2.)
+        b = self._get_array(-2.)
+        c = self._get_array(3.)
+
+        # sign change is "equiv":
+        np.add(a, b, casting="equiv")
+        with pytest.raises(TypeError):
+            np.add(a, b, casting="no")
+
+        # Different factor is "same_kind" (default) so check that "safe" fails
+        with pytest.raises(TypeError):
+            np.add(a, c, casting="safe")
+
+        # Check that casting the output fails also (done by the ufunc here)
+        with pytest.raises(TypeError):
+            np.add(a, a, out=c, casting="safe")
+
+    @pytest.mark.parametrize("ufunc",
+            [np.logical_and, np.logical_or, np.logical_xor])
+    def test_logical_ufuncs_casts_to_bool(self, ufunc):
+        a = self._get_array(2.)
+        a[0] = 0.  # make sure first element is considered False.
+
+        float_equiv = a.astype(float)
+        expected = ufunc(float_equiv, float_equiv)
+        res = ufunc(a, a)
+        assert_array_equal(res, expected)
+
+        # also check that the same works for reductions:
+        expected = ufunc.reduce(float_equiv)
+        res = ufunc.reduce(a)
+        assert_array_equal(res, expected)
+
+        # The output casting does not match the bool, bool -> bool loop:
+        with pytest.raises(TypeError):
+            ufunc(a, a, out=np.empty(a.shape, dtype=int), casting="equiv")
+
+    def test_wrapped_and_wrapped_reductions(self):
+        a = self._get_array(2.)
+        float_equiv = a.astype(float)
+
+        expected = np.hypot(float_equiv, float_equiv)
+        res = np.hypot(a, a)
+        assert res.dtype == a.dtype
+        res_float = res.view(np.float64) * 2
+        assert_array_equal(res_float, expected)
+
+        # Also check reduction (keepdims, due to incorrect getitem)
+        res = np.hypot.reduce(a, keepdims=True)
+        assert res.dtype == a.dtype
+        expected = np.hypot.reduce(float_equiv, keepdims=True)
+        assert res.view(np.float64) * 2 == expected
+
+    def test_astype_class(self):
+        # Very simple test that we accept `.astype()` also on the class.
+        # ScaledFloat always returns the default descriptor, but it does
+        # check the relevant code paths.
+        arr = np.array([1., 2., 3.], dtype=object)
+
+        res = arr.astype(SF)  # passing the class class
+        expected = arr.astype(SF(1.))  # above will have discovered 1. scaling
+        assert_array_equal(res.view(np.float64), expected.view(np.float64))
+
+    def test_creation_class(self):
+        # passing in a dtype class should return
+        # the default descriptor
+        arr1 = np.array([1., 2., 3.], dtype=SF)
+        assert arr1.dtype == SF(1.)
+        arr2 = np.array([1., 2., 3.], dtype=SF(1.))
+        assert_array_equal(arr1.view(np.float64), arr2.view(np.float64))
+        assert arr1.dtype == arr2.dtype
+
+        assert np.empty(3, dtype=SF).dtype == SF(1.)
+        assert np.empty_like(arr1, dtype=SF).dtype == SF(1.)
+        assert np.zeros(3, dtype=SF).dtype == SF(1.)
+        assert np.zeros_like(arr1, dtype=SF).dtype == SF(1.)
+
+    def test_np_save_load(self):
+        # this monkeypatch is needed because pickle
+        # uses the repr of a type to reconstruct it
+        np._ScaledFloatTestDType = SF
+
+        arr = np.array([1.0, 2.0, 3.0], dtype=SF(1.0))
+
+        # adapted from RoundtripTest.roundtrip in np.save tests
+        with NamedTemporaryFile("wb", delete=False, suffix=".npz") as f:
+            with pytest.warns(UserWarning) as record:
+                np.savez(f.name, arr)
+
+        assert len(record) == 1
+
+        with np.load(f.name, allow_pickle=True) as data:
+            larr = data["arr_0"]
+        assert_array_equal(arr.view(np.float64), larr.view(np.float64))
+        assert larr.dtype == arr.dtype == SF(1.0)
+
+        del np._ScaledFloatTestDType
+
+    def test_flatiter(self):
+        arr = np.array([1.0, 2.0, 3.0], dtype=SF(1.0))
+
+        for i, val in enumerate(arr.flat):
+            assert arr[i] == val
+
+    @pytest.mark.parametrize(
+        "index", [
+            [1, 2], ..., slice(None, 2, None),
+            np.array([True, True, False]), np.array([0, 1])
+        ], ids=["int_list", "ellipsis", "slice", "bool_array", "int_array"])
+    def test_flatiter_index(self, index):
+        arr = np.array([1.0, 2.0, 3.0], dtype=SF(1.0))
+        np.testing.assert_array_equal(
+            arr[index].view(np.float64), arr.flat[index].view(np.float64))
+
+        arr2 = arr.copy()
+        arr[index] = 5.0
+        arr2.flat[index] = 5.0
+        np.testing.assert_array_equal(
+            arr.view(np.float64), arr2.view(np.float64))
+
+def test_type_pickle():
+    # can't actually unpickle, but we can pickle (if in namespace)
+    import pickle
+
+    np._ScaledFloatTestDType = SF
+
+    s = pickle.dumps(SF)
+    res = pickle.loads(s)
+    assert res is SF
+
+    del np._ScaledFloatTestDType
+
+
+def test_is_numeric():
+    assert SF._is_numeric
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_cython.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_cython.py
new file mode 100644
index 0000000..fb3839f
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_cython.py
@@ -0,0 +1,351 @@
+import os
+import subprocess
+import sys
+import sysconfig
+from datetime import datetime
+
+import pytest
+
+import numpy as np
+from numpy.testing import IS_EDITABLE, IS_WASM, assert_array_equal
+
+# This import is copied from random.tests.test_extending
+try:
+    import cython
+    from Cython.Compiler.Version import version as cython_version
+except ImportError:
+    cython = None
+else:
+    from numpy._utils import _pep440
+
+    # Note: keep in sync with the one in pyproject.toml
+    required_version = "3.0.6"
+    if _pep440.parse(cython_version) < _pep440.Version(required_version):
+        # too old or wrong cython, skip the test
+        cython = None
+
+pytestmark = pytest.mark.skipif(cython is None, reason="requires cython")
+
+
+if IS_EDITABLE:
+    pytest.skip(
+        "Editable install doesn't support tests with a compile step",
+        allow_module_level=True
+    )
+
+
+@pytest.fixture(scope='module')
+def install_temp(tmpdir_factory):
+    # Based in part on test_cython from random.tests.test_extending
+    if IS_WASM:
+        pytest.skip("No subprocess")
+
+    srcdir = os.path.join(os.path.dirname(__file__), 'examples', 'cython')
+    build_dir = tmpdir_factory.mktemp("cython_test") / "build"
+    os.makedirs(build_dir, exist_ok=True)
+    # Ensure we use the correct Python interpreter even when `meson` is
+    # installed in a different Python environment (see gh-24956)
+    native_file = str(build_dir / 'interpreter-native-file.ini')
+    with open(native_file, 'w') as f:
+        f.write("[binaries]\n")
+        f.write(f"python = '{sys.executable}'\n")
+        f.write(f"python3 = '{sys.executable}'")
+
+    try:
+        subprocess.check_call(["meson", "--version"])
+    except FileNotFoundError:
+        pytest.skip("No usable 'meson' found")
+    if sysconfig.get_platform() == "win-arm64":
+        pytest.skip("Meson unable to find MSVC linker on win-arm64")
+    if sys.platform == "win32":
+        subprocess.check_call(["meson", "setup",
+                               "--buildtype=release",
+                               "--vsenv", "--native-file", native_file,
+                               str(srcdir)],
+                              cwd=build_dir,
+                              )
+    else:
+        subprocess.check_call(["meson", "setup",
+                               "--native-file", native_file, str(srcdir)],
+                              cwd=build_dir
+                              )
+    try:
+        subprocess.check_call(["meson", "compile", "-vv"], cwd=build_dir)
+    except subprocess.CalledProcessError:
+        print("----------------")
+        print("meson build failed when doing")
+        print(f"'meson setup --native-file {native_file} {srcdir}'")
+        print("'meson compile -vv'")
+        print(f"in {build_dir}")
+        print("----------------")
+        raise
+
+    sys.path.append(str(build_dir))
+
+
+def test_is_timedelta64_object(install_temp):
+    import checks
+
+    assert checks.is_td64(np.timedelta64(1234))
+    assert checks.is_td64(np.timedelta64(1234, "ns"))
+    assert checks.is_td64(np.timedelta64("NaT", "ns"))
+
+    assert not checks.is_td64(1)
+    assert not checks.is_td64(None)
+    assert not checks.is_td64("foo")
+    assert not checks.is_td64(np.datetime64("now", "s"))
+
+
+def test_is_datetime64_object(install_temp):
+    import checks
+
+    assert checks.is_dt64(np.datetime64(1234, "ns"))
+    assert checks.is_dt64(np.datetime64("NaT", "ns"))
+
+    assert not checks.is_dt64(1)
+    assert not checks.is_dt64(None)
+    assert not checks.is_dt64("foo")
+    assert not checks.is_dt64(np.timedelta64(1234))
+
+
+def test_get_datetime64_value(install_temp):
+    import checks
+
+    dt64 = np.datetime64("2016-01-01", "ns")
+
+    result = checks.get_dt64_value(dt64)
+    expected = dt64.view("i8")
+
+    assert result == expected
+
+
+def test_get_timedelta64_value(install_temp):
+    import checks
+
+    td64 = np.timedelta64(12345, "h")
+
+    result = checks.get_td64_value(td64)
+    expected = td64.view("i8")
+
+    assert result == expected
+
+
+def test_get_datetime64_unit(install_temp):
+    import checks
+
+    dt64 = np.datetime64("2016-01-01", "ns")
+    result = checks.get_dt64_unit(dt64)
+    expected = 10
+    assert result == expected
+
+    td64 = np.timedelta64(12345, "h")
+    result = checks.get_dt64_unit(td64)
+    expected = 5
+    assert result == expected
+
+
+def test_abstract_scalars(install_temp):
+    import checks
+
+    assert checks.is_integer(1)
+    assert checks.is_integer(np.int8(1))
+    assert checks.is_integer(np.uint64(1))
+
+def test_default_int(install_temp):
+    import checks
+
+    assert checks.get_default_integer() is np.dtype(int)
+
+
+def test_ravel_axis(install_temp):
+    import checks
+
+    assert checks.get_ravel_axis() == np.iinfo("intc").min
+
+
+def test_convert_datetime64_to_datetimestruct(install_temp):
+    # GH#21199
+    import checks
+
+    res = checks.convert_datetime64_to_datetimestruct()
+
+    exp = {
+        "year": 2022,
+        "month": 3,
+        "day": 15,
+        "hour": 20,
+        "min": 1,
+        "sec": 55,
+        "us": 260292,
+        "ps": 0,
+        "as": 0,
+    }
+
+    assert res == exp
+
+
+class TestDatetimeStrings:
+    def test_make_iso_8601_datetime(self, install_temp):
+        # GH#21199
+        import checks
+        dt = datetime(2016, 6, 2, 10, 45, 19)
+        # uses NPY_FR_s
+        result = checks.make_iso_8601_datetime(dt)
+        assert result == b"2016-06-02T10:45:19"
+
+    def test_get_datetime_iso_8601_strlen(self, install_temp):
+        # GH#21199
+        import checks
+        # uses NPY_FR_ns
+        res = checks.get_datetime_iso_8601_strlen()
+        assert res == 48
+
+
+@pytest.mark.parametrize(
+    "arrays",
+    [
+        [np.random.rand(2)],
+        [np.random.rand(2), np.random.rand(3, 1)],
+        [np.random.rand(2), np.random.rand(2, 3, 2), np.random.rand(1, 3, 2)],
+        [np.random.rand(2, 1)] * 4 + [np.random.rand(1, 1, 1)],
+    ]
+)
+def test_multiiter_fields(install_temp, arrays):
+    import checks
+    bcast = np.broadcast(*arrays)
+
+    assert bcast.ndim == checks.get_multiiter_number_of_dims(bcast)
+    assert bcast.size == checks.get_multiiter_size(bcast)
+    assert bcast.numiter == checks.get_multiiter_num_of_iterators(bcast)
+    assert bcast.shape == checks.get_multiiter_shape(bcast)
+    assert bcast.index == checks.get_multiiter_current_index(bcast)
+    assert all(
+        x.base is y.base
+        for x, y in zip(bcast.iters, checks.get_multiiter_iters(bcast))
+    )
+
+
+def test_dtype_flags(install_temp):
+    import checks
+    dtype = np.dtype("i,O")  # dtype with somewhat interesting flags
+    assert dtype.flags == checks.get_dtype_flags(dtype)
+
+
+def test_conv_intp(install_temp):
+    import checks
+
+    class myint:
+        def __int__(self):
+            return 3
+
+    # These conversion passes via `__int__`, not `__index__`:
+    assert checks.conv_intp(3.) == 3
+    assert checks.conv_intp(myint()) == 3
+
+
+def test_npyiter_api(install_temp):
+    import checks
+    arr = np.random.rand(3, 2)
+
+    it = np.nditer(arr)
+    assert checks.get_npyiter_size(it) == it.itersize == np.prod(arr.shape)
+    assert checks.get_npyiter_ndim(it) == it.ndim == 1
+    assert checks.npyiter_has_index(it) == it.has_index == False
+
+    it = np.nditer(arr, flags=["c_index"])
+    assert checks.npyiter_has_index(it) == it.has_index == True
+    assert (
+        checks.npyiter_has_delayed_bufalloc(it)
+        == it.has_delayed_bufalloc
+        == False
+    )
+
+    it = np.nditer(arr, flags=["buffered", "delay_bufalloc"])
+    assert (
+        checks.npyiter_has_delayed_bufalloc(it)
+        == it.has_delayed_bufalloc
+        == True
+    )
+
+    it = np.nditer(arr, flags=["multi_index"])
+    assert checks.get_npyiter_size(it) == it.itersize == np.prod(arr.shape)
+    assert checks.npyiter_has_multi_index(it) == it.has_multi_index == True
+    assert checks.get_npyiter_ndim(it) == it.ndim == 2
+    assert checks.test_get_multi_index_iter_next(it, arr)
+
+    arr2 = np.random.rand(2, 1, 2)
+    it = np.nditer([arr, arr2])
+    assert checks.get_npyiter_nop(it) == it.nop == 2
+    assert checks.get_npyiter_size(it) == it.itersize == 12
+    assert checks.get_npyiter_ndim(it) == it.ndim == 3
+    assert all(
+        x is y for x, y in zip(checks.get_npyiter_operands(it), it.operands)
+    )
+    assert all(
+        np.allclose(x, y)
+        for x, y in zip(checks.get_npyiter_itviews(it), it.itviews)
+    )
+
+
+def test_fillwithbytes(install_temp):
+    import checks
+
+    arr = checks.compile_fillwithbyte()
+    assert_array_equal(arr, np.ones((1, 2)))
+
+
+def test_complex(install_temp):
+    from checks import inc2_cfloat_struct
+
+    arr = np.array([0, 10 + 10j], dtype="F")
+    inc2_cfloat_struct(arr)
+    assert arr[1] == (12 + 12j)
+
+
+def test_npystring_pack(install_temp):
+    """Check that the cython API can write to a vstring array."""
+    import checks
+
+    arr = np.array(['a', 'b', 'c'], dtype='T')
+    assert checks.npystring_pack(arr) == 0
+
+    # checks.npystring_pack writes to the beginning of the array
+    assert arr[0] == "Hello world"
+
+def test_npystring_load(install_temp):
+    """Check that the cython API can load strings from a vstring array."""
+    import checks
+
+    arr = np.array(['abcd', 'b', 'c'], dtype='T')
+    result = checks.npystring_load(arr)
+    assert result == 'abcd'
+
+
+def test_npystring_multiple_allocators(install_temp):
+    """Check that the cython API can acquire/release multiple vstring allocators."""
+    import checks
+
+    dt = np.dtypes.StringDType(na_object=None)
+    arr1 = np.array(['abcd', 'b', 'c'], dtype=dt)
+    arr2 = np.array(['a', 'b', 'c'], dtype=dt)
+
+    assert checks.npystring_pack_multiple(arr1, arr2) == 0
+    assert arr1[0] == "Hello world"
+    assert arr1[-1] is None
+    assert arr2[0] == "test this"
+
+
+def test_npystring_allocators_other_dtype(install_temp):
+    """Check that allocators for non-StringDType arrays is NULL."""
+    import checks
+
+    arr1 = np.array([1, 2, 3], dtype='i')
+    arr2 = np.array([4, 5, 6], dtype='i')
+
+    assert checks.npystring_allocators_other_types(arr1, arr2) == 0
+
+
+@pytest.mark.skipif(sysconfig.get_platform() == 'win-arm64', reason='no checks module on win-arm64')
+def test_npy_uintp_type_enum():
+    import checks
+    assert checks.check_npy_uintp_type_enum()
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_datetime.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_datetime.py
new file mode 100644
index 0000000..1cbacb8
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_datetime.py
@@ -0,0 +1,2710 @@
+import datetime
+import pickle
+
+import pytest
+
+import numpy
+import numpy as np
+from numpy.testing import (
+    IS_WASM,
+    assert_,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+    assert_warns,
+    suppress_warnings,
+)
+
+# Use pytz to test out various time zones if available
+try:
+    from pytz import timezone as tz
+    _has_pytz = True
+except ImportError:
+    _has_pytz = False
+
+try:
+    RecursionError
+except NameError:
+    RecursionError = RuntimeError  # python < 3.5
+
+
+def _assert_equal_hash(v1, v2):
+    assert v1 == v2
+    assert hash(v1) == hash(v2)
+    assert v2 in {v1}
+
+
+class TestDateTime:
+
+    def test_string(self):
+        msg = "no explicit representation of timezones available for " \
+              "np.datetime64"
+        with pytest.warns(UserWarning, match=msg):
+            np.datetime64('2000-01-01T00+01')
+
+    def test_datetime(self):
+        msg = "no explicit representation of timezones available for " \
+              "np.datetime64"
+        with pytest.warns(UserWarning, match=msg):
+            t0 = np.datetime64('2023-06-09T12:18:40Z', 'ns')
+
+        t0 = np.datetime64('2023-06-09T12:18:40', 'ns')
+
+    def test_datetime_dtype_creation(self):
+        for unit in ['Y', 'M', 'W', 'D',
+                     'h', 'm', 's', 'ms', 'us',
+                     'μs',  # alias for us
+                     'ns', 'ps', 'fs', 'as']:
+            dt1 = np.dtype(f'M8[750{unit}]')
+            assert_(dt1 == np.dtype(f'datetime64[750{unit}]'))
+            dt2 = np.dtype(f'm8[{unit}]')
+            assert_(dt2 == np.dtype(f'timedelta64[{unit}]'))
+
+        # Generic units shouldn't add [] to the end
+        assert_equal(str(np.dtype("M8")), "datetime64")
+
+        # Should be possible to specify the endianness
+        assert_equal(np.dtype("=M8"), np.dtype("M8"))
+        assert_equal(np.dtype("=M8[s]"), np.dtype("M8[s]"))
+        assert_(np.dtype(">M8") == np.dtype("M8") or
+                np.dtype("<M8") == np.dtype("M8"))
+        assert_(np.dtype(">M8[D]") == np.dtype("M8[D]") or
+                np.dtype("<M8[D]") == np.dtype("M8[D]"))
+        assert_(np.dtype(">M8") != np.dtype("<M8"))
+
+        assert_equal(np.dtype("=m8"), np.dtype("m8"))
+        assert_equal(np.dtype("=m8[s]"), np.dtype("m8[s]"))
+        assert_(np.dtype(">m8") == np.dtype("m8") or
+                np.dtype("<m8") == np.dtype("m8"))
+        assert_(np.dtype(">m8[D]") == np.dtype("m8[D]") or
+                np.dtype("<m8[D]") == np.dtype("m8[D]"))
+        assert_(np.dtype(">m8") != np.dtype("<m8"))
+
+        # Check that the parser rejects bad datetime types
+        assert_raises(TypeError, np.dtype, 'M8[badunit]')
+        assert_raises(TypeError, np.dtype, 'm8[badunit]')
+        assert_raises(TypeError, np.dtype, 'M8[YY]')
+        assert_raises(TypeError, np.dtype, 'm8[YY]')
+        assert_raises(TypeError, np.dtype, 'm4')
+        assert_raises(TypeError, np.dtype, 'M7')
+        assert_raises(TypeError, np.dtype, 'm7')
+        assert_raises(TypeError, np.dtype, 'M16')
+        assert_raises(TypeError, np.dtype, 'm16')
+        assert_raises(TypeError, np.dtype, 'M8[3000000000ps]')
+
+    def test_datetime_casting_rules(self):
+        # Cannot cast safely/same_kind between timedelta and datetime
+        assert_(not np.can_cast('m8', 'M8', casting='same_kind'))
+        assert_(not np.can_cast('M8', 'm8', casting='same_kind'))
+        assert_(not np.can_cast('m8', 'M8', casting='safe'))
+        assert_(not np.can_cast('M8', 'm8', casting='safe'))
+
+        # Can cast safely/same_kind from integer to timedelta
+        assert_(np.can_cast('i8', 'm8', casting='same_kind'))
+        assert_(np.can_cast('i8', 'm8', casting='safe'))
+        assert_(np.can_cast('i4', 'm8', casting='same_kind'))
+        assert_(np.can_cast('i4', 'm8', casting='safe'))
+        assert_(np.can_cast('u4', 'm8', casting='same_kind'))
+        assert_(np.can_cast('u4', 'm8', casting='safe'))
+
+        # Cannot cast safely from unsigned integer of the same size, which
+        # could overflow
+        assert_(np.can_cast('u8', 'm8', casting='same_kind'))
+        assert_(not np.can_cast('u8', 'm8', casting='safe'))
+
+        # Cannot cast safely/same_kind from float to timedelta
+        assert_(not np.can_cast('f4', 'm8', casting='same_kind'))
+        assert_(not np.can_cast('f4', 'm8', casting='safe'))
+
+        # Cannot cast safely/same_kind from integer to datetime
+        assert_(not np.can_cast('i8', 'M8', casting='same_kind'))
+        assert_(not np.can_cast('i8', 'M8', casting='safe'))
+
+        # Cannot cast safely/same_kind from bool to datetime
+        assert_(not np.can_cast('b1', 'M8', casting='same_kind'))
+        assert_(not np.can_cast('b1', 'M8', casting='safe'))
+        # Can cast safely/same_kind from bool to timedelta
+        assert_(np.can_cast('b1', 'm8', casting='same_kind'))
+        assert_(np.can_cast('b1', 'm8', casting='safe'))
+
+        # Can cast datetime safely from months/years to days
+        assert_(np.can_cast('M8[M]', 'M8[D]', casting='safe'))
+        assert_(np.can_cast('M8[Y]', 'M8[D]', casting='safe'))
+        # Cannot cast timedelta safely from months/years to days
+        assert_(not np.can_cast('m8[M]', 'm8[D]', casting='safe'))
+        assert_(not np.can_cast('m8[Y]', 'm8[D]', casting='safe'))
+        # Can cast datetime same_kind from months/years to days
+        assert_(np.can_cast('M8[M]', 'M8[D]', casting='same_kind'))
+        assert_(np.can_cast('M8[Y]', 'M8[D]', casting='same_kind'))
+        # Can't cast timedelta same_kind from months/years to days
+        assert_(not np.can_cast('m8[M]', 'm8[D]', casting='same_kind'))
+        assert_(not np.can_cast('m8[Y]', 'm8[D]', casting='same_kind'))
+        # Can cast datetime same_kind across the date/time boundary
+        assert_(np.can_cast('M8[D]', 'M8[h]', casting='same_kind'))
+        # Can cast timedelta same_kind across the date/time boundary
+        assert_(np.can_cast('m8[D]', 'm8[h]', casting='same_kind'))
+        assert_(np.can_cast('m8[h]', 'm8[D]', casting='same_kind'))
+
+        # Cannot cast safely if the integer multiplier doesn't divide
+        assert_(not np.can_cast('M8[7h]', 'M8[3h]', casting='safe'))
+        assert_(not np.can_cast('M8[3h]', 'M8[6h]', casting='safe'))
+        # But can cast same_kind
+        assert_(np.can_cast('M8[7h]', 'M8[3h]', casting='same_kind'))
+        # Can cast safely if the integer multiplier does divide
+        assert_(np.can_cast('M8[6h]', 'M8[3h]', casting='safe'))
+
+        # We can always cast types with generic units (corresponding to NaT) to
+        # more specific types
+        assert_(np.can_cast('m8', 'm8[h]', casting='same_kind'))
+        assert_(np.can_cast('m8', 'm8[h]', casting='safe'))
+        assert_(np.can_cast('M8', 'M8[h]', casting='same_kind'))
+        assert_(np.can_cast('M8', 'M8[h]', casting='safe'))
+        # but not the other way around
+        assert_(not np.can_cast('m8[h]', 'm8', casting='same_kind'))
+        assert_(not np.can_cast('m8[h]', 'm8', casting='safe'))
+        assert_(not np.can_cast('M8[h]', 'M8', casting='same_kind'))
+        assert_(not np.can_cast('M8[h]', 'M8', casting='safe'))
+
+    def test_datetime_prefix_conversions(self):
+        # regression tests related to gh-19631;
+        # test metric prefixes from seconds down to
+        # attoseconds for bidirectional conversions
+        smaller_units = ['M8[7000ms]',
+                         'M8[2000us]',
+                         'M8[1000ns]',
+                         'M8[5000ns]',
+                         'M8[2000ps]',
+                         'M8[9000fs]',
+                         'M8[1000as]',
+                         'M8[2000000ps]',
+                         'M8[1000000as]',
+                         'M8[2000000000ps]',
+                         'M8[1000000000as]']
+        larger_units = ['M8[7s]',
+                        'M8[2ms]',
+                        'M8[us]',
+                        'M8[5us]',
+                        'M8[2ns]',
+                        'M8[9ps]',
+                        'M8[1fs]',
+                        'M8[2us]',
+                        'M8[1ps]',
+                        'M8[2ms]',
+                        'M8[1ns]']
+        for larger_unit, smaller_unit in zip(larger_units, smaller_units):
+            assert np.can_cast(larger_unit, smaller_unit, casting='safe')
+            assert np.can_cast(smaller_unit, larger_unit, casting='safe')
+
+    @pytest.mark.parametrize("unit", [
+        "s", "ms", "us", "ns", "ps", "fs", "as"])
+    def test_prohibit_negative_datetime(self, unit):
+        with assert_raises(TypeError):
+            np.array([1], dtype=f"M8[-1{unit}]")
+
+    def test_compare_generic_nat(self):
+        # regression tests for gh-6452
+        assert_(np.datetime64('NaT') !=
+                np.datetime64('2000') + np.timedelta64('NaT'))
+        assert_(np.datetime64('NaT') != np.datetime64('NaT', 'us'))
+        assert_(np.datetime64('NaT', 'us') != np.datetime64('NaT'))
+
+    @pytest.mark.parametrize("size", [
+        3, 21, 217, 1000])
+    def test_datetime_nat_argsort_stability(self, size):
+        # NaT < NaT should be False internally for
+        # sort stability
+        expected = np.arange(size)
+        arr = np.tile(np.datetime64('NaT'), size)
+        assert_equal(np.argsort(arr, kind='mergesort'), expected)
+
+    @pytest.mark.parametrize("size", [
+        3, 21, 217, 1000])
+    def test_timedelta_nat_argsort_stability(self, size):
+        # NaT < NaT should be False internally for
+        # sort stability
+        expected = np.arange(size)
+        arr = np.tile(np.timedelta64('NaT'), size)
+        assert_equal(np.argsort(arr, kind='mergesort'), expected)
+
+    @pytest.mark.parametrize("arr, expected", [
+        # the example provided in gh-12629
+        (['NaT', 1, 2, 3],
+         [1, 2, 3, 'NaT']),
+        # multiple NaTs
+        (['NaT', 9, 'NaT', -707],
+         [-707, 9, 'NaT', 'NaT']),
+        # this sort explores another code path for NaT
+        ([1, -2, 3, 'NaT'],
+         [-2, 1, 3, 'NaT']),
+        # 2-D array
+        ([[51, -220, 'NaT'],
+          [-17, 'NaT', -90]],
+         [[-220, 51, 'NaT'],
+          [-90, -17, 'NaT']]),
+        ])
+    @pytest.mark.parametrize("dtype", [
+        'M8[ns]', 'M8[us]',
+        'm8[ns]', 'm8[us]'])
+    def test_datetime_timedelta_sort_nat(self, arr, expected, dtype):
+        # fix for gh-12629 and gh-15063; NaT sorting to end of array
+        arr = np.array(arr, dtype=dtype)
+        expected = np.array(expected, dtype=dtype)
+        arr.sort()
+        assert_equal(arr, expected)
+
+    def test_datetime_scalar_construction(self):
+        # Construct with different units
+        assert_equal(np.datetime64('1950-03-12', 'D'),
+                     np.datetime64('1950-03-12'))
+        assert_equal(np.datetime64('1950-03-12T13', 's'),
+                     np.datetime64('1950-03-12T13', 'm'))
+
+        # Default construction means NaT
+        assert_equal(np.datetime64(), np.datetime64('NaT'))
+
+        # Some basic strings and repr
+        assert_equal(str(np.datetime64('NaT')), 'NaT')
+        assert_equal(repr(np.datetime64('NaT')),
+                     "np.datetime64('NaT')")
+        assert_equal(str(np.datetime64('2011-02')), '2011-02')
+        assert_equal(repr(np.datetime64('2011-02')),
+                     "np.datetime64('2011-02')")
+
+        # None gets constructed as NaT
+        assert_equal(np.datetime64(None), np.datetime64('NaT'))
+
+        # Default construction of NaT is in generic units
+        assert_equal(np.datetime64().dtype, np.dtype('M8'))
+        assert_equal(np.datetime64('NaT').dtype, np.dtype('M8'))
+
+        # Construction from integers requires a specified unit
+        assert_raises(ValueError, np.datetime64, 17)
+
+        # When constructing from a scalar or zero-dimensional array,
+        # it either keeps the units or you can override them.
+        a = np.datetime64('2000-03-18T16', 'h')
+        b = np.array('2000-03-18T16', dtype='M8[h]')
+
+        assert_equal(a.dtype, np.dtype('M8[h]'))
+        assert_equal(b.dtype, np.dtype('M8[h]'))
+
+        assert_equal(np.datetime64(a), a)
+        assert_equal(np.datetime64(a).dtype, np.dtype('M8[h]'))
+
+        assert_equal(np.datetime64(b), a)
+        assert_equal(np.datetime64(b).dtype, np.dtype('M8[h]'))
+
+        assert_equal(np.datetime64(a, 's'), a)
+        assert_equal(np.datetime64(a, 's').dtype, np.dtype('M8[s]'))
+
+        assert_equal(np.datetime64(b, 's'), a)
+        assert_equal(np.datetime64(b, 's').dtype, np.dtype('M8[s]'))
+
+        # Construction from datetime.date
+        assert_equal(np.datetime64('1945-03-25'),
+                     np.datetime64(datetime.date(1945, 3, 25)))
+        assert_equal(np.datetime64('2045-03-25', 'D'),
+                     np.datetime64(datetime.date(2045, 3, 25), 'D'))
+        # Construction from datetime.datetime
+        assert_equal(np.datetime64('1980-01-25T14:36:22.5'),
+                     np.datetime64(datetime.datetime(1980, 1, 25,
+                                                14, 36, 22, 500000)))
+
+        # Construction with time units from a date is okay
+        assert_equal(np.datetime64('1920-03-13', 'h'),
+                     np.datetime64('1920-03-13T00'))
+        assert_equal(np.datetime64('1920-03', 'm'),
+                     np.datetime64('1920-03-01T00:00'))
+        assert_equal(np.datetime64('1920', 's'),
+                     np.datetime64('1920-01-01T00:00:00'))
+        assert_equal(np.datetime64(datetime.date(2045, 3, 25), 'ms'),
+                     np.datetime64('2045-03-25T00:00:00.000'))
+
+        # Construction with date units from a datetime is also okay
+        assert_equal(np.datetime64('1920-03-13T18', 'D'),
+                     np.datetime64('1920-03-13'))
+        assert_equal(np.datetime64('1920-03-13T18:33:12', 'M'),
+                     np.datetime64('1920-03'))
+        assert_equal(np.datetime64('1920-03-13T18:33:12.5', 'Y'),
+                     np.datetime64('1920'))
+
+    def test_datetime_scalar_construction_timezone(self):
+        msg = "no explicit representation of timezones available for " \
+              "np.datetime64"
+        # verify that supplying an explicit timezone works, but is deprecated
+        with pytest.warns(UserWarning, match=msg):
+            assert_equal(np.datetime64('2000-01-01T00Z'),
+                         np.datetime64('2000-01-01T00'))
+        with pytest.warns(UserWarning, match=msg):
+            assert_equal(np.datetime64('2000-01-01T00-08'),
+                         np.datetime64('2000-01-01T08'))
+
+    def test_datetime_array_find_type(self):
+        dt = np.datetime64('1970-01-01', 'M')
+        arr = np.array([dt])
+        assert_equal(arr.dtype, np.dtype('M8[M]'))
+
+        # at the moment, we don't automatically convert these to datetime64
+
+        dt = datetime.date(1970, 1, 1)
+        arr = np.array([dt])
+        assert_equal(arr.dtype, np.dtype('O'))
+
+        dt = datetime.datetime(1970, 1, 1, 12, 30, 40)
+        arr = np.array([dt])
+        assert_equal(arr.dtype, np.dtype('O'))
+
+        # find "supertype" for non-dates and dates
+
+        b = np.bool(True)
+        dm = np.datetime64('1970-01-01', 'M')
+        d = datetime.date(1970, 1, 1)
+        dt = datetime.datetime(1970, 1, 1, 12, 30, 40)
+
+        arr = np.array([b, dm])
+        assert_equal(arr.dtype, np.dtype('O'))
+
+        arr = np.array([b, d])
+        assert_equal(arr.dtype, np.dtype('O'))
+
+        arr = np.array([b, dt])
+        assert_equal(arr.dtype, np.dtype('O'))
+
+        arr = np.array([d, d]).astype('datetime64')
+        assert_equal(arr.dtype, np.dtype('M8[D]'))
+
+        arr = np.array([dt, dt]).astype('datetime64')
+        assert_equal(arr.dtype, np.dtype('M8[us]'))
+
+    @pytest.mark.parametrize("unit", [
+    # test all date / time units and use
+    # "generic" to select generic unit
+    ("Y"), ("M"), ("W"), ("D"), ("h"), ("m"),
+    ("s"), ("ms"), ("us"), ("ns"), ("ps"),
+    ("fs"), ("as"), ("generic")])
+    def test_timedelta_np_int_construction(self, unit):
+        # regression test for gh-7617
+        if unit != "generic":
+            assert_equal(np.timedelta64(np.int64(123), unit),
+                         np.timedelta64(123, unit))
+        else:
+            assert_equal(np.timedelta64(np.int64(123)),
+                         np.timedelta64(123))
+
+    def test_timedelta_scalar_construction(self):
+        # Construct with different units
+        assert_equal(np.timedelta64(7, 'D'),
+                     np.timedelta64(1, 'W'))
+        assert_equal(np.timedelta64(120, 's'),
+                     np.timedelta64(2, 'm'))
+
+        # Default construction means 0
+        assert_equal(np.timedelta64(), np.timedelta64(0))
+
+        # None gets constructed as NaT
+        assert_equal(np.timedelta64(None), np.timedelta64('NaT'))
+
+        # Some basic strings and repr
+        assert_equal(str(np.timedelta64('NaT')), 'NaT')
+        assert_equal(repr(np.timedelta64('NaT')),
+                     "np.timedelta64('NaT')")
+        assert_equal(str(np.timedelta64(3, 's')), '3 seconds')
+        assert_equal(repr(np.timedelta64(-3, 's')),
+                     "np.timedelta64(-3,'s')")
+        assert_equal(repr(np.timedelta64(12)),
+                     "np.timedelta64(12)")
+
+        # Construction from an integer produces generic units
+        assert_equal(np.timedelta64(12).dtype, np.dtype('m8'))
+
+        # When constructing from a scalar or zero-dimensional array,
+        # it either keeps the units or you can override them.
+        a = np.timedelta64(2, 'h')
+        b = np.array(2, dtype='m8[h]')
+
+        assert_equal(a.dtype, np.dtype('m8[h]'))
+        assert_equal(b.dtype, np.dtype('m8[h]'))
+
+        assert_equal(np.timedelta64(a), a)
+        assert_equal(np.timedelta64(a).dtype, np.dtype('m8[h]'))
+
+        assert_equal(np.timedelta64(b), a)
+        assert_equal(np.timedelta64(b).dtype, np.dtype('m8[h]'))
+
+        assert_equal(np.timedelta64(a, 's'), a)
+        assert_equal(np.timedelta64(a, 's').dtype, np.dtype('m8[s]'))
+
+        assert_equal(np.timedelta64(b, 's'), a)
+        assert_equal(np.timedelta64(b, 's').dtype, np.dtype('m8[s]'))
+
+        # Construction from datetime.timedelta
+        assert_equal(np.timedelta64(5, 'D'),
+                     np.timedelta64(datetime.timedelta(days=5)))
+        assert_equal(np.timedelta64(102347621, 's'),
+                     np.timedelta64(datetime.timedelta(seconds=102347621)))
+        assert_equal(np.timedelta64(-10234760000, 'us'),
+                     np.timedelta64(datetime.timedelta(
+                                            microseconds=-10234760000)))
+        assert_equal(np.timedelta64(10234760000, 'us'),
+                     np.timedelta64(datetime.timedelta(
+                                            microseconds=10234760000)))
+        assert_equal(np.timedelta64(1023476, 'ms'),
+                     np.timedelta64(datetime.timedelta(milliseconds=1023476)))
+        assert_equal(np.timedelta64(10, 'm'),
+                     np.timedelta64(datetime.timedelta(minutes=10)))
+        assert_equal(np.timedelta64(281, 'h'),
+                     np.timedelta64(datetime.timedelta(hours=281)))
+        assert_equal(np.timedelta64(28, 'W'),
+                     np.timedelta64(datetime.timedelta(weeks=28)))
+
+        # Cannot construct across nonlinear time unit boundaries
+        a = np.timedelta64(3, 's')
+        assert_raises(TypeError, np.timedelta64, a, 'M')
+        assert_raises(TypeError, np.timedelta64, a, 'Y')
+        a = np.timedelta64(6, 'M')
+        assert_raises(TypeError, np.timedelta64, a, 'D')
+        assert_raises(TypeError, np.timedelta64, a, 'h')
+        a = np.timedelta64(1, 'Y')
+        assert_raises(TypeError, np.timedelta64, a, 'D')
+        assert_raises(TypeError, np.timedelta64, a, 'm')
+        a = datetime.timedelta(seconds=3)
+        assert_raises(TypeError, np.timedelta64, a, 'M')
+        assert_raises(TypeError, np.timedelta64, a, 'Y')
+        a = datetime.timedelta(weeks=3)
+        assert_raises(TypeError, np.timedelta64, a, 'M')
+        assert_raises(TypeError, np.timedelta64, a, 'Y')
+        a = datetime.timedelta()
+        assert_raises(TypeError, np.timedelta64, a, 'M')
+        assert_raises(TypeError, np.timedelta64, a, 'Y')
+
+    def test_timedelta_object_array_conversion(self):
+        # Regression test for gh-11096
+        inputs = [datetime.timedelta(28),
+                  datetime.timedelta(30),
+                  datetime.timedelta(31)]
+        expected = np.array([28, 30, 31], dtype='timedelta64[D]')
+        actual = np.array(inputs, dtype='timedelta64[D]')
+        assert_equal(expected, actual)
+
+    def test_timedelta_0_dim_object_array_conversion(self):
+        # Regression test for gh-11151
+        test = np.array(datetime.timedelta(seconds=20))
+        actual = test.astype(np.timedelta64)
+        # expected value from the array constructor workaround
+        # described in above issue
+        expected = np.array(datetime.timedelta(seconds=20),
+                            np.timedelta64)
+        assert_equal(actual, expected)
+
+    def test_timedelta_nat_format(self):
+        # gh-17552
+        assert_equal('NaT', f'{np.timedelta64("nat")}')
+
+    def test_timedelta_scalar_construction_units(self):
+        # String construction detecting units
+        assert_equal(np.datetime64('2010').dtype,
+                     np.dtype('M8[Y]'))
+        assert_equal(np.datetime64('2010-03').dtype,
+                     np.dtype('M8[M]'))
+        assert_equal(np.datetime64('2010-03-12').dtype,
+                     np.dtype('M8[D]'))
+        assert_equal(np.datetime64('2010-03-12T17').dtype,
+                     np.dtype('M8[h]'))
+        assert_equal(np.datetime64('2010-03-12T17:15').dtype,
+                     np.dtype('M8[m]'))
+        assert_equal(np.datetime64('2010-03-12T17:15:08').dtype,
+                     np.dtype('M8[s]'))
+
+        assert_equal(np.datetime64('2010-03-12T17:15:08.1').dtype,
+                     np.dtype('M8[ms]'))
+        assert_equal(np.datetime64('2010-03-12T17:15:08.12').dtype,
+                     np.dtype('M8[ms]'))
+        assert_equal(np.datetime64('2010-03-12T17:15:08.123').dtype,
+                     np.dtype('M8[ms]'))
+
+        assert_equal(np.datetime64('2010-03-12T17:15:08.1234').dtype,
+                     np.dtype('M8[us]'))
+        assert_equal(np.datetime64('2010-03-12T17:15:08.12345').dtype,
+                     np.dtype('M8[us]'))
+        assert_equal(np.datetime64('2010-03-12T17:15:08.123456').dtype,
+                     np.dtype('M8[us]'))
+
+        assert_equal(np.datetime64('1970-01-01T00:00:02.1234567').dtype,
+                     np.dtype('M8[ns]'))
+        assert_equal(np.datetime64('1970-01-01T00:00:02.12345678').dtype,
+                     np.dtype('M8[ns]'))
+        assert_equal(np.datetime64('1970-01-01T00:00:02.123456789').dtype,
+                     np.dtype('M8[ns]'))
+
+        assert_equal(np.datetime64('1970-01-01T00:00:02.1234567890').dtype,
+                     np.dtype('M8[ps]'))
+        assert_equal(np.datetime64('1970-01-01T00:00:02.12345678901').dtype,
+                     np.dtype('M8[ps]'))
+        assert_equal(np.datetime64('1970-01-01T00:00:02.123456789012').dtype,
+                     np.dtype('M8[ps]'))
+
+        assert_equal(np.datetime64(
+                     '1970-01-01T00:00:02.1234567890123').dtype,
+                     np.dtype('M8[fs]'))
+        assert_equal(np.datetime64(
+                     '1970-01-01T00:00:02.12345678901234').dtype,
+                     np.dtype('M8[fs]'))
+        assert_equal(np.datetime64(
+                     '1970-01-01T00:00:02.123456789012345').dtype,
+                     np.dtype('M8[fs]'))
+
+        assert_equal(np.datetime64(
+                    '1970-01-01T00:00:02.1234567890123456').dtype,
+                     np.dtype('M8[as]'))
+        assert_equal(np.datetime64(
+                    '1970-01-01T00:00:02.12345678901234567').dtype,
+                     np.dtype('M8[as]'))
+        assert_equal(np.datetime64(
+                    '1970-01-01T00:00:02.123456789012345678').dtype,
+                     np.dtype('M8[as]'))
+
+        # Python date object
+        assert_equal(np.datetime64(datetime.date(2010, 4, 16)).dtype,
+                     np.dtype('M8[D]'))
+
+        # Python datetime object
+        assert_equal(np.datetime64(
+                        datetime.datetime(2010, 4, 16, 13, 45, 18)).dtype,
+                     np.dtype('M8[us]'))
+
+        # 'today' special value
+        assert_equal(np.datetime64('today').dtype,
+                     np.dtype('M8[D]'))
+
+        # 'now' special value
+        assert_equal(np.datetime64('now').dtype,
+                     np.dtype('M8[s]'))
+
+    def test_datetime_nat_casting(self):
+        a = np.array('NaT', dtype='M8[D]')
+        b = np.datetime64('NaT', '[D]')
+
+        # Arrays
+        assert_equal(a.astype('M8[s]'), np.array('NaT', dtype='M8[s]'))
+        assert_equal(a.astype('M8[ms]'), np.array('NaT', dtype='M8[ms]'))
+        assert_equal(a.astype('M8[M]'), np.array('NaT', dtype='M8[M]'))
+        assert_equal(a.astype('M8[Y]'), np.array('NaT', dtype='M8[Y]'))
+        assert_equal(a.astype('M8[W]'), np.array('NaT', dtype='M8[W]'))
+
+        # Scalars -> Scalars
+        assert_equal(np.datetime64(b, '[s]'), np.datetime64('NaT', '[s]'))
+        assert_equal(np.datetime64(b, '[ms]'), np.datetime64('NaT', '[ms]'))
+        assert_equal(np.datetime64(b, '[M]'), np.datetime64('NaT', '[M]'))
+        assert_equal(np.datetime64(b, '[Y]'), np.datetime64('NaT', '[Y]'))
+        assert_equal(np.datetime64(b, '[W]'), np.datetime64('NaT', '[W]'))
+
+        # Arrays -> Scalars
+        assert_equal(np.datetime64(a, '[s]'), np.datetime64('NaT', '[s]'))
+        assert_equal(np.datetime64(a, '[ms]'), np.datetime64('NaT', '[ms]'))
+        assert_equal(np.datetime64(a, '[M]'), np.datetime64('NaT', '[M]'))
+        assert_equal(np.datetime64(a, '[Y]'), np.datetime64('NaT', '[Y]'))
+        assert_equal(np.datetime64(a, '[W]'), np.datetime64('NaT', '[W]'))
+
+        # NaN -> NaT
+        nan = np.array([np.nan] * 8 + [0])
+        fnan = nan.astype('f')
+        lnan = nan.astype('g')
+        cnan = nan.astype('D')
+        cfnan = nan.astype('F')
+        clnan = nan.astype('G')
+        hnan = nan.astype(np.half)
+
+        nat = np.array([np.datetime64('NaT')] * 8 + [np.datetime64(0, 'D')])
+        assert_equal(nan.astype('M8[ns]'), nat)
+        assert_equal(fnan.astype('M8[ns]'), nat)
+        assert_equal(lnan.astype('M8[ns]'), nat)
+        assert_equal(cnan.astype('M8[ns]'), nat)
+        assert_equal(cfnan.astype('M8[ns]'), nat)
+        assert_equal(clnan.astype('M8[ns]'), nat)
+        assert_equal(hnan.astype('M8[ns]'), nat)
+
+        nat = np.array([np.timedelta64('NaT')] * 8 + [np.timedelta64(0)])
+        assert_equal(nan.astype('timedelta64[ns]'), nat)
+        assert_equal(fnan.astype('timedelta64[ns]'), nat)
+        assert_equal(lnan.astype('timedelta64[ns]'), nat)
+        assert_equal(cnan.astype('timedelta64[ns]'), nat)
+        assert_equal(cfnan.astype('timedelta64[ns]'), nat)
+        assert_equal(clnan.astype('timedelta64[ns]'), nat)
+        assert_equal(hnan.astype('timedelta64[ns]'), nat)
+
+    def test_days_creation(self):
+        assert_equal(np.array('1599', dtype='M8[D]').astype('i8'),
+                (1600 - 1970) * 365 - (1972 - 1600) / 4 + 3 - 365)
+        assert_equal(np.array('1600', dtype='M8[D]').astype('i8'),
+                (1600 - 1970) * 365 - (1972 - 1600) / 4 + 3)
+        assert_equal(np.array('1601', dtype='M8[D]').astype('i8'),
+                (1600 - 1970) * 365 - (1972 - 1600) / 4 + 3 + 366)
+        assert_equal(np.array('1900', dtype='M8[D]').astype('i8'),
+                (1900 - 1970) * 365 - (1970 - 1900) // 4)
+        assert_equal(np.array('1901', dtype='M8[D]').astype('i8'),
+                (1900 - 1970) * 365 - (1970 - 1900) // 4 + 365)
+        assert_equal(np.array('1967', dtype='M8[D]').astype('i8'), -3 * 365 - 1)
+        assert_equal(np.array('1968', dtype='M8[D]').astype('i8'), -2 * 365 - 1)
+        assert_equal(np.array('1969', dtype='M8[D]').astype('i8'), -1 * 365)
+        assert_equal(np.array('1970', dtype='M8[D]').astype('i8'), 0 * 365)
+        assert_equal(np.array('1971', dtype='M8[D]').astype('i8'), 1 * 365)
+        assert_equal(np.array('1972', dtype='M8[D]').astype('i8'), 2 * 365)
+        assert_equal(np.array('1973', dtype='M8[D]').astype('i8'), 3 * 365 + 1)
+        assert_equal(np.array('1974', dtype='M8[D]').astype('i8'), 4 * 365 + 1)
+        assert_equal(np.array('2000', dtype='M8[D]').astype('i8'),
+                 (2000 - 1970) * 365 + (2000 - 1972) // 4)
+        assert_equal(np.array('2001', dtype='M8[D]').astype('i8'),
+                 (2000 - 1970) * 365 + (2000 - 1972) // 4 + 366)
+        assert_equal(np.array('2400', dtype='M8[D]').astype('i8'),
+                 (2400 - 1970) * 365 + (2400 - 1972) // 4 - 3)
+        assert_equal(np.array('2401', dtype='M8[D]').astype('i8'),
+                 (2400 - 1970) * 365 + (2400 - 1972) // 4 - 3 + 366)
+
+        assert_equal(np.array('1600-02-29', dtype='M8[D]').astype('i8'),
+                (1600 - 1970) * 365 - (1972 - 1600) // 4 + 3 + 31 + 28)
+        assert_equal(np.array('1600-03-01', dtype='M8[D]').astype('i8'),
+                (1600 - 1970) * 365 - (1972 - 1600) // 4 + 3 + 31 + 29)
+        assert_equal(np.array('2000-02-29', dtype='M8[D]').astype('i8'),
+                 (2000 - 1970) * 365 + (2000 - 1972) // 4 + 31 + 28)
+        assert_equal(np.array('2000-03-01', dtype='M8[D]').astype('i8'),
+                 (2000 - 1970) * 365 + (2000 - 1972) // 4 + 31 + 29)
+        assert_equal(np.array('2001-03-22', dtype='M8[D]').astype('i8'),
+                 (2000 - 1970) * 365 + (2000 - 1972) // 4 + 366 + 31 + 28 + 21)
+
+    def test_days_to_pydate(self):
+        assert_equal(np.array('1599', dtype='M8[D]').astype('O'),
+                    datetime.date(1599, 1, 1))
+        assert_equal(np.array('1600', dtype='M8[D]').astype('O'),
+                    datetime.date(1600, 1, 1))
+        assert_equal(np.array('1601', dtype='M8[D]').astype('O'),
+                    datetime.date(1601, 1, 1))
+        assert_equal(np.array('1900', dtype='M8[D]').astype('O'),
+                    datetime.date(1900, 1, 1))
+        assert_equal(np.array('1901', dtype='M8[D]').astype('O'),
+                    datetime.date(1901, 1, 1))
+        assert_equal(np.array('2000', dtype='M8[D]').astype('O'),
+                    datetime.date(2000, 1, 1))
+        assert_equal(np.array('2001', dtype='M8[D]').astype('O'),
+                    datetime.date(2001, 1, 1))
+        assert_equal(np.array('1600-02-29', dtype='M8[D]').astype('O'),
+                    datetime.date(1600, 2, 29))
+        assert_equal(np.array('1600-03-01', dtype='M8[D]').astype('O'),
+                    datetime.date(1600, 3, 1))
+        assert_equal(np.array('2001-03-22', dtype='M8[D]').astype('O'),
+                    datetime.date(2001, 3, 22))
+
+    def test_dtype_comparison(self):
+        assert_(not (np.dtype('M8[us]') == np.dtype('M8[ms]')))
+        assert_(np.dtype('M8[us]') != np.dtype('M8[ms]'))
+        assert_(np.dtype('M8[2D]') != np.dtype('M8[D]'))
+        assert_(np.dtype('M8[D]') != np.dtype('M8[2D]'))
+
+    def test_pydatetime_creation(self):
+        a = np.array(['1960-03-12', datetime.date(1960, 3, 12)], dtype='M8[D]')
+        assert_equal(a[0], a[1])
+        a = np.array(['1999-12-31', datetime.date(1999, 12, 31)], dtype='M8[D]')
+        assert_equal(a[0], a[1])
+        a = np.array(['2000-01-01', datetime.date(2000, 1, 1)], dtype='M8[D]')
+        assert_equal(a[0], a[1])
+        # Will fail if the date changes during the exact right moment
+        a = np.array(['today', datetime.date.today()], dtype='M8[D]')
+        assert_equal(a[0], a[1])
+        # datetime.datetime.now() returns local time, not UTC
+        #a = np.array(['now', datetime.datetime.now()], dtype='M8[s]')
+        #assert_equal(a[0], a[1])
+
+        # we can give a datetime.date time units
+        assert_equal(np.array(datetime.date(1960, 3, 12), dtype='M8[s]'),
+                     np.array(np.datetime64('1960-03-12T00:00:00')))
+
+    def test_datetime_string_conversion(self):
+        a = ['2011-03-16', '1920-01-01', '2013-05-19']
+        str_a = np.array(a, dtype='S')
+        uni_a = np.array(a, dtype='U')
+        dt_a = np.array(a, dtype='M')
+
+        # String to datetime
+        assert_equal(dt_a, str_a.astype('M'))
+        assert_equal(dt_a.dtype, str_a.astype('M').dtype)
+        dt_b = np.empty_like(dt_a)
+        dt_b[...] = str_a
+        assert_equal(dt_a, dt_b)
+
+        # Datetime to string
+        assert_equal(str_a, dt_a.astype('S0'))
+        str_b = np.empty_like(str_a)
+        str_b[...] = dt_a
+        assert_equal(str_a, str_b)
+
+        # Unicode to datetime
+        assert_equal(dt_a, uni_a.astype('M'))
+        assert_equal(dt_a.dtype, uni_a.astype('M').dtype)
+        dt_b = np.empty_like(dt_a)
+        dt_b[...] = uni_a
+        assert_equal(dt_a, dt_b)
+
+        # Datetime to unicode
+        assert_equal(uni_a, dt_a.astype('U'))
+        uni_b = np.empty_like(uni_a)
+        uni_b[...] = dt_a
+        assert_equal(uni_a, uni_b)
+
+        # Datetime to long string - gh-9712
+        assert_equal(str_a, dt_a.astype((np.bytes_, 128)))
+        str_b = np.empty(str_a.shape, dtype=(np.bytes_, 128))
+        str_b[...] = dt_a
+        assert_equal(str_a, str_b)
+
+    @pytest.mark.parametrize("time_dtype", ["m8[D]", "M8[Y]"])
+    def test_time_byteswapping(self, time_dtype):
+        times = np.array(["2017", "NaT"], dtype=time_dtype)
+        times_swapped = times.astype(times.dtype.newbyteorder())
+        assert_array_equal(times, times_swapped)
+
+        unswapped = times_swapped.view(np.dtype("int64").newbyteorder())
+        assert_array_equal(unswapped, times.view(np.int64))
+
+    @pytest.mark.parametrize(["time1", "time2"],
+            [("M8[s]", "M8[D]"), ("m8[s]", "m8[ns]")])
+    def test_time_byteswapped_cast(self, time1, time2):
+        dtype1 = np.dtype(time1)
+        dtype2 = np.dtype(time2)
+        times = np.array(["2017", "NaT"], dtype=dtype1)
+        expected = times.astype(dtype2)
+
+        # Test that every byte-swapping combination also returns the same
+        # results (previous tests check that this comparison works fine).
+        res = times.astype(dtype1.newbyteorder()).astype(dtype2)
+        assert_array_equal(res, expected)
+        res = times.astype(dtype2.newbyteorder())
+        assert_array_equal(res, expected)
+        res = times.astype(dtype1.newbyteorder()).astype(dtype2.newbyteorder())
+        assert_array_equal(res, expected)
+
+    @pytest.mark.parametrize("time_dtype", ["m8[D]", "M8[Y]"])
+    @pytest.mark.parametrize("str_dtype", ["U", "S"])
+    def test_datetime_conversions_byteorders(self, str_dtype, time_dtype):
+        times = np.array(["2017", "NaT"], dtype=time_dtype)
+        # Unfortunately, timedelta does not roundtrip:
+        from_strings = np.array(["2017", "NaT"], dtype=str_dtype)
+        to_strings = times.astype(str_dtype)  # assume this is correct
+
+        # Check that conversion from times to string works if src is swapped:
+        times_swapped = times.astype(times.dtype.newbyteorder())
+        res = times_swapped.astype(str_dtype)
+        assert_array_equal(res, to_strings)
+        # And also if both are swapped:
+        res = times_swapped.astype(to_strings.dtype.newbyteorder())
+        assert_array_equal(res, to_strings)
+        # only destination is swapped:
+        res = times.astype(to_strings.dtype.newbyteorder())
+        assert_array_equal(res, to_strings)
+
+        # Check that conversion from string to times works if src is swapped:
+        from_strings_swapped = from_strings.astype(
+                from_strings.dtype.newbyteorder())
+        res = from_strings_swapped.astype(time_dtype)
+        assert_array_equal(res, times)
+        # And if both are swapped:
+        res = from_strings_swapped.astype(times.dtype.newbyteorder())
+        assert_array_equal(res, times)
+        # Only destination is swapped:
+        res = from_strings.astype(times.dtype.newbyteorder())
+        assert_array_equal(res, times)
+
+    def test_datetime_array_str(self):
+        a = np.array(['2011-03-16', '1920-01-01', '2013-05-19'], dtype='M')
+        assert_equal(str(a), "['2011-03-16' '1920-01-01' '2013-05-19']")
+
+        a = np.array(['2011-03-16T13:55', '1920-01-01T03:12'], dtype='M')
+        assert_equal(np.array2string(a, separator=', ',
+                    formatter={'datetime': lambda x:
+                            f"'{np.datetime_as_string(x, timezone='UTC')}'"}),
+                     "['2011-03-16T13:55Z', '1920-01-01T03:12Z']")
+
+        # Check that one NaT doesn't corrupt subsequent entries
+        a = np.array(['2010', 'NaT', '2030']).astype('M')
+        assert_equal(str(a), "['2010'  'NaT' '2030']")
+
+    def test_timedelta_array_str(self):
+        a = np.array([-1, 0, 100], dtype='m')
+        assert_equal(str(a), "[ -1   0 100]")
+        a = np.array(['NaT', 'NaT'], dtype='m')
+        assert_equal(str(a), "['NaT' 'NaT']")
+        # Check right-alignment with NaTs
+        a = np.array([-1, 'NaT', 0], dtype='m')
+        assert_equal(str(a), "[   -1 'NaT'     0]")
+        a = np.array([-1, 'NaT', 1234567], dtype='m')
+        assert_equal(str(a), "[     -1   'NaT' 1234567]")
+
+        # Test with other byteorder:
+        a = np.array([-1, 'NaT', 1234567], dtype='>m')
+        assert_equal(str(a), "[     -1   'NaT' 1234567]")
+        a = np.array([-1, 'NaT', 1234567], dtype='<m')
+        assert_equal(str(a), "[     -1   'NaT' 1234567]")
+
+    def test_pickle(self):
+        # Check that pickle roundtripping works
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            dt = np.dtype('M8[7D]')
+            assert_equal(pickle.loads(pickle.dumps(dt, protocol=proto)), dt)
+            dt = np.dtype('M8[W]')
+            assert_equal(pickle.loads(pickle.dumps(dt, protocol=proto)), dt)
+            scalar = np.datetime64('2016-01-01T00:00:00.000000000')
+            assert_equal(pickle.loads(pickle.dumps(scalar, protocol=proto)),
+                         scalar)
+            delta = scalar - np.datetime64('2015-01-01T00:00:00.000000000')
+            assert_equal(pickle.loads(pickle.dumps(delta, protocol=proto)),
+                         delta)
+
+        # Check that loading pickles from 1.6 works
+        pkl = b"cnumpy\ndtype\np0\n(S'M8'\np1\nI0\nI1\ntp2\nRp3\n"\
+              b"(I4\nS'<'\np4\nNNNI-1\nI-1\nI0\n((dp5\n(S'D'\np6\n"\
+              b"I7\nI1\nI1\ntp7\ntp8\ntp9\nb."
+        assert_equal(pickle.loads(pkl), np.dtype('<M8[7D]'))
+        pkl = b"cnumpy\ndtype\np0\n(S'M8'\np1\nI0\nI1\ntp2\nRp3\n"\
+              b"(I4\nS'<'\np4\nNNNI-1\nI-1\nI0\n((dp5\n(S'W'\np6\n"\
+              b"I1\nI1\nI1\ntp7\ntp8\ntp9\nb."
+        assert_equal(pickle.loads(pkl), np.dtype('<M8[W]'))
+        pkl = b"cnumpy\ndtype\np0\n(S'M8'\np1\nI0\nI1\ntp2\nRp3\n"\
+              b"(I4\nS'>'\np4\nNNNI-1\nI-1\nI0\n((dp5\n(S'us'\np6\n"\
+              b"I1\nI1\nI1\ntp7\ntp8\ntp9\nb."
+        assert_equal(pickle.loads(pkl), np.dtype('>M8[us]'))
+
+    def test_setstate(self):
+        "Verify that datetime dtype __setstate__ can handle bad arguments"
+        dt = np.dtype('>M8[us]')
+        assert_raises(ValueError, dt.__setstate__, (4, '>', None, None, None, -1, -1, 0, 1))
+        assert_(dt.__reduce__()[2] == np.dtype('>M8[us]').__reduce__()[2])
+        assert_raises(TypeError, dt.__setstate__, (4, '>', None, None, None, -1, -1, 0, ({}, 'xxx')))
+        assert_(dt.__reduce__()[2] == np.dtype('>M8[us]').__reduce__()[2])
+
+    def test_dtype_promotion(self):
+        # datetime <op> datetime computes the metadata gcd
+        # timedelta <op> timedelta computes the metadata gcd
+        for mM in ['m', 'M']:
+            assert_equal(
+                np.promote_types(np.dtype(mM + '8[2Y]'), np.dtype(mM + '8[2Y]')),
+                np.dtype(mM + '8[2Y]'))
+            assert_equal(
+                np.promote_types(np.dtype(mM + '8[12Y]'), np.dtype(mM + '8[15Y]')),
+                np.dtype(mM + '8[3Y]'))
+            assert_equal(
+                np.promote_types(np.dtype(mM + '8[62M]'), np.dtype(mM + '8[24M]')),
+                np.dtype(mM + '8[2M]'))
+            assert_equal(
+                np.promote_types(np.dtype(mM + '8[1W]'), np.dtype(mM + '8[2D]')),
+                np.dtype(mM + '8[1D]'))
+            assert_equal(
+                np.promote_types(np.dtype(mM + '8[W]'), np.dtype(mM + '8[13s]')),
+                np.dtype(mM + '8[s]'))
+            assert_equal(
+                np.promote_types(np.dtype(mM + '8[13W]'), np.dtype(mM + '8[49s]')),
+                np.dtype(mM + '8[7s]'))
+        # timedelta <op> timedelta raises when there is no reasonable gcd
+        assert_raises(TypeError, np.promote_types,
+                            np.dtype('m8[Y]'), np.dtype('m8[D]'))
+        assert_raises(TypeError, np.promote_types,
+                            np.dtype('m8[M]'), np.dtype('m8[W]'))
+        # timedelta and float cannot be safely cast with each other
+        assert_raises(TypeError, np.promote_types, "float32", "m8")
+        assert_raises(TypeError, np.promote_types, "m8", "float32")
+        assert_raises(TypeError, np.promote_types, "uint64", "m8")
+        assert_raises(TypeError, np.promote_types, "m8", "uint64")
+
+        # timedelta <op> timedelta may overflow with big unit ranges
+        assert_raises(OverflowError, np.promote_types,
+                            np.dtype('m8[W]'), np.dtype('m8[fs]'))
+        assert_raises(OverflowError, np.promote_types,
+                            np.dtype('m8[s]'), np.dtype('m8[as]'))
+
+    def test_cast_overflow(self):
+        # gh-4486
+        def cast():
+            numpy.datetime64("1971-01-01 00:00:00.000000000000000").astype("<M8[D]")
+        assert_raises(OverflowError, cast)
+
+        def cast2():
+            numpy.datetime64("2014").astype("<M8[fs]")
+        assert_raises(OverflowError, cast2)
+
+    def test_pyobject_roundtrip(self):
+        # All datetime types should be able to roundtrip through object
+        a = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0,
+                      -1020040340, -2942398, -1, 0, 1, 234523453, 1199164176],
+                                                        dtype=np.int64)
+        # With date units
+        for unit in ['M8[D]', 'M8[W]', 'M8[M]', 'M8[Y]']:
+            b = a.copy().view(dtype=unit)
+            b[0] = '-0001-01-01'
+            b[1] = '-0001-12-31'
+            b[2] = '0000-01-01'
+            b[3] = '0001-01-01'
+            b[4] = '1969-12-31'
+            b[5] = '1970-01-01'
+            b[6] = '9999-12-31'
+            b[7] = '10000-01-01'
+            b[8] = 'NaT'
+
+            assert_equal(b.astype(object).astype(unit), b,
+                            f"Error roundtripping unit {unit}")
+        # With time units
+        for unit in ['M8[as]', 'M8[16fs]', 'M8[ps]', 'M8[us]',
+                     'M8[300as]', 'M8[20us]']:
+            b = a.copy().view(dtype=unit)
+            b[0] = '-0001-01-01T00'
+            b[1] = '-0001-12-31T00'
+            b[2] = '0000-01-01T00'
+            b[3] = '0001-01-01T00'
+            b[4] = '1969-12-31T23:59:59.999999'
+            b[5] = '1970-01-01T00'
+            b[6] = '9999-12-31T23:59:59.999999'
+            b[7] = '10000-01-01T00'
+            b[8] = 'NaT'
+
+            assert_equal(b.astype(object).astype(unit), b,
+                            f"Error roundtripping unit {unit}")
+
+    def test_month_truncation(self):
+        # Make sure that months are truncating correctly
+        assert_equal(np.array('1945-03-01', dtype='M8[M]'),
+                     np.array('1945-03-31', dtype='M8[M]'))
+        assert_equal(np.array('1969-11-01', dtype='M8[M]'),
+             np.array('1969-11-30T23:59:59.99999', dtype='M').astype('M8[M]'))
+        assert_equal(np.array('1969-12-01', dtype='M8[M]'),
+             np.array('1969-12-31T23:59:59.99999', dtype='M').astype('M8[M]'))
+        assert_equal(np.array('1970-01-01', dtype='M8[M]'),
+             np.array('1970-01-31T23:59:59.99999', dtype='M').astype('M8[M]'))
+        assert_equal(np.array('1980-02-01', dtype='M8[M]'),
+             np.array('1980-02-29T23:59:59.99999', dtype='M').astype('M8[M]'))
+
+    def test_different_unit_comparison(self):
+        # Check some years with date units
+        for unit1 in ['Y', 'M', 'D']:
+            dt1 = np.dtype(f'M8[{unit1}]')
+            for unit2 in ['Y', 'M', 'D']:
+                dt2 = np.dtype(f'M8[{unit2}]')
+                assert_equal(np.array('1945', dtype=dt1),
+                             np.array('1945', dtype=dt2))
+                assert_equal(np.array('1970', dtype=dt1),
+                             np.array('1970', dtype=dt2))
+                assert_equal(np.array('9999', dtype=dt1),
+                             np.array('9999', dtype=dt2))
+                assert_equal(np.array('10000', dtype=dt1),
+                             np.array('10000-01-01', dtype=dt2))
+                assert_equal(np.datetime64('1945', unit1),
+                             np.datetime64('1945', unit2))
+                assert_equal(np.datetime64('1970', unit1),
+                             np.datetime64('1970', unit2))
+                assert_equal(np.datetime64('9999', unit1),
+                             np.datetime64('9999', unit2))
+                assert_equal(np.datetime64('10000', unit1),
+                             np.datetime64('10000-01-01', unit2))
+        # Check some datetimes with time units
+        for unit1 in ['6h', 'h', 'm', 's', '10ms', 'ms', 'us']:
+            dt1 = np.dtype(f'M8[{unit1}]')
+            for unit2 in ['h', 'm', 's', 'ms', 'us']:
+                dt2 = np.dtype(f'M8[{unit2}]')
+                assert_equal(np.array('1945-03-12T18', dtype=dt1),
+                             np.array('1945-03-12T18', dtype=dt2))
+                assert_equal(np.array('1970-03-12T18', dtype=dt1),
+                             np.array('1970-03-12T18', dtype=dt2))
+                assert_equal(np.array('9999-03-12T18', dtype=dt1),
+                             np.array('9999-03-12T18', dtype=dt2))
+                assert_equal(np.array('10000-01-01T00', dtype=dt1),
+                             np.array('10000-01-01T00', dtype=dt2))
+                assert_equal(np.datetime64('1945-03-12T18', unit1),
+                             np.datetime64('1945-03-12T18', unit2))
+                assert_equal(np.datetime64('1970-03-12T18', unit1),
+                             np.datetime64('1970-03-12T18', unit2))
+                assert_equal(np.datetime64('9999-03-12T18', unit1),
+                             np.datetime64('9999-03-12T18', unit2))
+                assert_equal(np.datetime64('10000-01-01T00', unit1),
+                             np.datetime64('10000-01-01T00', unit2))
+        # Check some days with units that won't overflow
+        for unit1 in ['D', '12h', 'h', 'm', 's', '4s', 'ms', 'us']:
+            dt1 = np.dtype(f'M8[{unit1}]')
+            for unit2 in ['D', 'h', 'm', 's', 'ms', 'us']:
+                dt2 = np.dtype(f'M8[{unit2}]')
+                assert_(np.equal(np.array('1932-02-17', dtype='M').astype(dt1),
+                     np.array('1932-02-17T00:00:00', dtype='M').astype(dt2),
+                     casting='unsafe'))
+                assert_(np.equal(np.array('10000-04-27', dtype='M').astype(dt1),
+                     np.array('10000-04-27T00:00:00', dtype='M').astype(dt2),
+                     casting='unsafe'))
+
+        # Shouldn't be able to compare datetime and timedelta
+        a = np.array('2012-12-21', dtype='M8[D]')
+        b = np.array(3, dtype='m8[D]')
+        assert_raises(TypeError, np.less, a, b)
+        # not even if "unsafe"
+        assert_raises(TypeError, np.less, a, b, casting='unsafe')
+
+    def test_datetime_like(self):
+        a = np.array([3], dtype='m8[4D]')
+        b = np.array(['2012-12-21'], dtype='M8[D]')
+
+        assert_equal(np.ones_like(a).dtype, a.dtype)
+        assert_equal(np.zeros_like(a).dtype, a.dtype)
+        assert_equal(np.empty_like(a).dtype, a.dtype)
+        assert_equal(np.ones_like(b).dtype, b.dtype)
+        assert_equal(np.zeros_like(b).dtype, b.dtype)
+        assert_equal(np.empty_like(b).dtype, b.dtype)
+
+    def test_datetime_unary(self):
+        for tda, tdb, tdzero, tdone, tdmone in \
+                [
+                 # One-dimensional arrays
+                 (np.array([3], dtype='m8[D]'),
+                  np.array([-3], dtype='m8[D]'),
+                  np.array([0], dtype='m8[D]'),
+                  np.array([1], dtype='m8[D]'),
+                  np.array([-1], dtype='m8[D]')),
+                 # NumPy scalars
+                 (np.timedelta64(3, '[D]'),
+                  np.timedelta64(-3, '[D]'),
+                  np.timedelta64(0, '[D]'),
+                  np.timedelta64(1, '[D]'),
+                  np.timedelta64(-1, '[D]'))]:
+            # negative ufunc
+            assert_equal(-tdb, tda)
+            assert_equal((-tdb).dtype, tda.dtype)
+            assert_equal(np.negative(tdb), tda)
+            assert_equal(np.negative(tdb).dtype, tda.dtype)
+
+            # positive ufunc
+            assert_equal(np.positive(tda), tda)
+            assert_equal(np.positive(tda).dtype, tda.dtype)
+            assert_equal(np.positive(tdb), tdb)
+            assert_equal(np.positive(tdb).dtype, tdb.dtype)
+
+            # absolute ufunc
+            assert_equal(np.absolute(tdb), tda)
+            assert_equal(np.absolute(tdb).dtype, tda.dtype)
+
+            # sign ufunc
+            assert_equal(np.sign(tda), tdone)
+            assert_equal(np.sign(tdb), tdmone)
+            assert_equal(np.sign(tdzero), tdzero)
+            assert_equal(np.sign(tda).dtype, tda.dtype)
+
+            # The ufuncs always produce native-endian results
+            assert_
+
+    def test_datetime_add(self):
+        for dta, dtb, dtc, dtnat, tda, tdb, tdc in \
+                    [
+                     # One-dimensional arrays
+                     (np.array(['2012-12-21'], dtype='M8[D]'),
+                      np.array(['2012-12-24'], dtype='M8[D]'),
+                      np.array(['2012-12-21T11'], dtype='M8[h]'),
+                      np.array(['NaT'], dtype='M8[D]'),
+                      np.array([3], dtype='m8[D]'),
+                      np.array([11], dtype='m8[h]'),
+                      np.array([3 * 24 + 11], dtype='m8[h]')),
+                     # NumPy scalars
+                     (np.datetime64('2012-12-21', '[D]'),
+                      np.datetime64('2012-12-24', '[D]'),
+                      np.datetime64('2012-12-21T11', '[h]'),
+                      np.datetime64('NaT', '[D]'),
+                      np.timedelta64(3, '[D]'),
+                      np.timedelta64(11, '[h]'),
+                      np.timedelta64(3 * 24 + 11, '[h]'))]:
+            # m8 + m8
+            assert_equal(tda + tdb, tdc)
+            assert_equal((tda + tdb).dtype, np.dtype('m8[h]'))
+            # m8 + bool
+            assert_equal(tdb + True, tdb + 1)
+            assert_equal((tdb + True).dtype, np.dtype('m8[h]'))
+            # m8 + int
+            assert_equal(tdb + 3 * 24, tdc)
+            assert_equal((tdb + 3 * 24).dtype, np.dtype('m8[h]'))
+            # bool + m8
+            assert_equal(False + tdb, tdb)
+            assert_equal((False + tdb).dtype, np.dtype('m8[h]'))
+            # int + m8
+            assert_equal(3 * 24 + tdb, tdc)
+            assert_equal((3 * 24 + tdb).dtype, np.dtype('m8[h]'))
+            # M8 + bool
+            assert_equal(dta + True, dta + 1)
+            assert_equal(dtnat + True, dtnat)
+            assert_equal((dta + True).dtype, np.dtype('M8[D]'))
+            # M8 + int
+            assert_equal(dta + 3, dtb)
+            assert_equal(dtnat + 3, dtnat)
+            assert_equal((dta + 3).dtype, np.dtype('M8[D]'))
+            # bool + M8
+            assert_equal(False + dta, dta)
+            assert_equal(False + dtnat, dtnat)
+            assert_equal((False + dta).dtype, np.dtype('M8[D]'))
+            # int + M8
+            assert_equal(3 + dta, dtb)
+            assert_equal(3 + dtnat, dtnat)
+            assert_equal((3 + dta).dtype, np.dtype('M8[D]'))
+            # M8 + m8
+            assert_equal(dta + tda, dtb)
+            assert_equal(dtnat + tda, dtnat)
+            assert_equal((dta + tda).dtype, np.dtype('M8[D]'))
+            # m8 + M8
+            assert_equal(tda + dta, dtb)
+            assert_equal(tda + dtnat, dtnat)
+            assert_equal((tda + dta).dtype, np.dtype('M8[D]'))
+
+            # In M8 + m8, the result goes to higher precision
+            assert_equal(np.add(dta, tdb, casting='unsafe'), dtc)
+            assert_equal(np.add(dta, tdb, casting='unsafe').dtype,
+                         np.dtype('M8[h]'))
+            assert_equal(np.add(tdb, dta, casting='unsafe'), dtc)
+            assert_equal(np.add(tdb, dta, casting='unsafe').dtype,
+                         np.dtype('M8[h]'))
+
+            # M8 + M8
+            assert_raises(TypeError, np.add, dta, dtb)
+
+    def test_datetime_subtract(self):
+        for dta, dtb, dtc, dtd, dte, dtnat, tda, tdb, tdc in \
+                    [
+                     # One-dimensional arrays
+                     (np.array(['2012-12-21'], dtype='M8[D]'),
+                      np.array(['2012-12-24'], dtype='M8[D]'),
+                      np.array(['1940-12-24'], dtype='M8[D]'),
+                      np.array(['1940-12-24T00'], dtype='M8[h]'),
+                      np.array(['1940-12-23T13'], dtype='M8[h]'),
+                      np.array(['NaT'], dtype='M8[D]'),
+                      np.array([3], dtype='m8[D]'),
+                      np.array([11], dtype='m8[h]'),
+                      np.array([3 * 24 - 11], dtype='m8[h]')),
+                     # NumPy scalars
+                     (np.datetime64('2012-12-21', '[D]'),
+                      np.datetime64('2012-12-24', '[D]'),
+                      np.datetime64('1940-12-24', '[D]'),
+                      np.datetime64('1940-12-24T00', '[h]'),
+                      np.datetime64('1940-12-23T13', '[h]'),
+                      np.datetime64('NaT', '[D]'),
+                      np.timedelta64(3, '[D]'),
+                      np.timedelta64(11, '[h]'),
+                      np.timedelta64(3 * 24 - 11, '[h]'))]:
+            # m8 - m8
+            assert_equal(tda - tdb, tdc)
+            assert_equal((tda - tdb).dtype, np.dtype('m8[h]'))
+            assert_equal(tdb - tda, -tdc)
+            assert_equal((tdb - tda).dtype, np.dtype('m8[h]'))
+            # m8 - bool
+            assert_equal(tdc - True, tdc - 1)
+            assert_equal((tdc - True).dtype, np.dtype('m8[h]'))
+            # m8 - int
+            assert_equal(tdc - 3 * 24, -tdb)
+            assert_equal((tdc - 3 * 24).dtype, np.dtype('m8[h]'))
+            # int - m8
+            assert_equal(False - tdb, -tdb)
+            assert_equal((False - tdb).dtype, np.dtype('m8[h]'))
+            # int - m8
+            assert_equal(3 * 24 - tdb, tdc)
+            assert_equal((3 * 24 - tdb).dtype, np.dtype('m8[h]'))
+            # M8 - bool
+            assert_equal(dtb - True, dtb - 1)
+            assert_equal(dtnat - True, dtnat)
+            assert_equal((dtb - True).dtype, np.dtype('M8[D]'))
+            # M8 - int
+            assert_equal(dtb - 3, dta)
+            assert_equal(dtnat - 3, dtnat)
+            assert_equal((dtb - 3).dtype, np.dtype('M8[D]'))
+            # M8 - m8
+            assert_equal(dtb - tda, dta)
+            assert_equal(dtnat - tda, dtnat)
+            assert_equal((dtb - tda).dtype, np.dtype('M8[D]'))
+
+            # In M8 - m8, the result goes to higher precision
+            assert_equal(np.subtract(dtc, tdb, casting='unsafe'), dte)
+            assert_equal(np.subtract(dtc, tdb, casting='unsafe').dtype,
+                         np.dtype('M8[h]'))
+
+            # M8 - M8 with different goes to higher precision
+            assert_equal(np.subtract(dtc, dtd, casting='unsafe'),
+                         np.timedelta64(0, 'h'))
+            assert_equal(np.subtract(dtc, dtd, casting='unsafe').dtype,
+                         np.dtype('m8[h]'))
+            assert_equal(np.subtract(dtd, dtc, casting='unsafe'),
+                         np.timedelta64(0, 'h'))
+            assert_equal(np.subtract(dtd, dtc, casting='unsafe').dtype,
+                         np.dtype('m8[h]'))
+
+            # m8 - M8
+            assert_raises(TypeError, np.subtract, tda, dta)
+            # bool - M8
+            assert_raises(TypeError, np.subtract, False, dta)
+            # int - M8
+            assert_raises(TypeError, np.subtract, 3, dta)
+
+    def test_datetime_multiply(self):
+        for dta, tda, tdb, tdc in \
+                    [
+                     # One-dimensional arrays
+                     (np.array(['2012-12-21'], dtype='M8[D]'),
+                      np.array([6], dtype='m8[h]'),
+                      np.array([9], dtype='m8[h]'),
+                      np.array([12], dtype='m8[h]')),
+                     # NumPy scalars
+                     (np.datetime64('2012-12-21', '[D]'),
+                      np.timedelta64(6, '[h]'),
+                      np.timedelta64(9, '[h]'),
+                      np.timedelta64(12, '[h]'))]:
+            # m8 * int
+            assert_equal(tda * 2, tdc)
+            assert_equal((tda * 2).dtype, np.dtype('m8[h]'))
+            # int * m8
+            assert_equal(2 * tda, tdc)
+            assert_equal((2 * tda).dtype, np.dtype('m8[h]'))
+            # m8 * float
+            assert_equal(tda * 1.5, tdb)
+            assert_equal((tda * 1.5).dtype, np.dtype('m8[h]'))
+            # float * m8
+            assert_equal(1.5 * tda, tdb)
+            assert_equal((1.5 * tda).dtype, np.dtype('m8[h]'))
+
+            # m8 * m8
+            assert_raises(TypeError, np.multiply, tda, tdb)
+            # m8 * M8
+            assert_raises(TypeError, np.multiply, dta, tda)
+            # M8 * m8
+            assert_raises(TypeError, np.multiply, tda, dta)
+            # M8 * int
+            assert_raises(TypeError, np.multiply, dta, 2)
+            # int * M8
+            assert_raises(TypeError, np.multiply, 2, dta)
+            # M8 * float
+            assert_raises(TypeError, np.multiply, dta, 1.5)
+            # float * M8
+            assert_raises(TypeError, np.multiply, 1.5, dta)
+
+        # NaTs
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in multiply")
+            nat = np.timedelta64('NaT')
+
+            def check(a, b, res):
+                assert_equal(a * b, res)
+                assert_equal(b * a, res)
+            for tp in (int, float):
+                check(nat, tp(2), nat)
+                check(nat, tp(0), nat)
+            for f in (float('inf'), float('nan')):
+                check(np.timedelta64(1), f, nat)
+                check(np.timedelta64(0), f, nat)
+                check(nat, f, nat)
+
+    @pytest.mark.parametrize("op1, op2, exp", [
+        # m8 same units round down
+        (np.timedelta64(7, 's'),
+         np.timedelta64(4, 's'),
+         1),
+        # m8 same units round down with negative
+        (np.timedelta64(7, 's'),
+         np.timedelta64(-4, 's'),
+         -2),
+        # m8 same units negative no round down
+        (np.timedelta64(8, 's'),
+         np.timedelta64(-4, 's'),
+         -2),
+        # m8 different units
+        (np.timedelta64(1, 'm'),
+         np.timedelta64(31, 's'),
+         1),
+        # m8 generic units
+        (np.timedelta64(1890),
+         np.timedelta64(31),
+         60),
+        # Y // M works
+        (np.timedelta64(2, 'Y'),
+         np.timedelta64('13', 'M'),
+         1),
+        # handle 1D arrays
+        (np.array([1, 2, 3], dtype='m8'),
+         np.array([2], dtype='m8'),
+         np.array([0, 1, 1], dtype=np.int64)),
+        ])
+    def test_timedelta_floor_divide(self, op1, op2, exp):
+        assert_equal(op1 // op2, exp)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.parametrize("op1, op2", [
+        # div by 0
+        (np.timedelta64(10, 'us'),
+         np.timedelta64(0, 'us')),
+        # div with NaT
+        (np.timedelta64('NaT'),
+         np.timedelta64(50, 'us')),
+        # special case for int64 min
+        # in integer floor division
+        (np.timedelta64(np.iinfo(np.int64).min),
+         np.timedelta64(-1)),
+        ])
+    def test_timedelta_floor_div_warnings(self, op1, op2):
+        with assert_warns(RuntimeWarning):
+            actual = op1 // op2
+            assert_equal(actual, 0)
+            assert_equal(actual.dtype, np.int64)
+
+    @pytest.mark.parametrize("val1, val2", [
+        # the smallest integer that can't be represented
+        # exactly in a double should be preserved if we avoid
+        # casting to double in floordiv operation
+        (9007199254740993, 1),
+        # stress the alternate floordiv code path where
+        # operand signs don't match and remainder isn't 0
+        (9007199254740999, -2),
+        ])
+    def test_timedelta_floor_div_precision(self, val1, val2):
+        op1 = np.timedelta64(val1)
+        op2 = np.timedelta64(val2)
+        actual = op1 // op2
+        # Python reference integer floor
+        expected = val1 // val2
+        assert_equal(actual, expected)
+
+    @pytest.mark.parametrize("val1, val2", [
+        # years and months sometimes can't be unambiguously
+        # divided for floor division operation
+        (np.timedelta64(7, 'Y'),
+         np.timedelta64(3, 's')),
+        (np.timedelta64(7, 'M'),
+         np.timedelta64(1, 'D')),
+        ])
+    def test_timedelta_floor_div_error(self, val1, val2):
+        with assert_raises_regex(TypeError, "common metadata divisor"):
+            val1 // val2
+
+    @pytest.mark.parametrize("op1, op2", [
+        # reuse the test cases from floordiv
+        (np.timedelta64(7, 's'),
+         np.timedelta64(4, 's')),
+        # m8 same units round down with negative
+        (np.timedelta64(7, 's'),
+         np.timedelta64(-4, 's')),
+        # m8 same units negative no round down
+        (np.timedelta64(8, 's'),
+         np.timedelta64(-4, 's')),
+        # m8 different units
+        (np.timedelta64(1, 'm'),
+         np.timedelta64(31, 's')),
+        # m8 generic units
+        (np.timedelta64(1890),
+         np.timedelta64(31)),
+        # Y // M works
+        (np.timedelta64(2, 'Y'),
+         np.timedelta64('13', 'M')),
+        # handle 1D arrays
+        (np.array([1, 2, 3], dtype='m8'),
+         np.array([2], dtype='m8')),
+        ])
+    def test_timedelta_divmod(self, op1, op2):
+        expected = (op1 // op2, op1 % op2)
+        assert_equal(divmod(op1, op2), expected)
+
+    @pytest.mark.parametrize("op1, op2", [
+        # Y and M are incompatible with all units except Y and M
+        (np.timedelta64(1, 'Y'), np.timedelta64(1, 's')),
+        (np.timedelta64(1, 'D'), np.timedelta64(1, 'M')),
+        ])
+    def test_timedelta_divmod_typeerror(self, op1, op2):
+        assert_raises(TypeError, np.divmod, op1, op2)
+
+    @pytest.mark.skipif(IS_WASM, reason="does not work in wasm")
+    @pytest.mark.parametrize("op1, op2", [
+        # reuse cases from floordiv
+        # div by 0
+        (np.timedelta64(10, 'us'),
+         np.timedelta64(0, 'us')),
+        # div with NaT
+        (np.timedelta64('NaT'),
+         np.timedelta64(50, 'us')),
+        # special case for int64 min
+        # in integer floor division
+        (np.timedelta64(np.iinfo(np.int64).min),
+         np.timedelta64(-1)),
+        ])
+    def test_timedelta_divmod_warnings(self, op1, op2):
+        with assert_warns(RuntimeWarning):
+            expected = (op1 // op2, op1 % op2)
+        with assert_warns(RuntimeWarning):
+            actual = divmod(op1, op2)
+        assert_equal(actual, expected)
+
+    def test_datetime_divide(self):
+        for dta, tda, tdb, tdc, tdd in \
+                    [
+                     # One-dimensional arrays
+                     (np.array(['2012-12-21'], dtype='M8[D]'),
+                      np.array([6], dtype='m8[h]'),
+                      np.array([9], dtype='m8[h]'),
+                      np.array([12], dtype='m8[h]'),
+                      np.array([6], dtype='m8[m]')),
+                     # NumPy scalars
+                     (np.datetime64('2012-12-21', '[D]'),
+                      np.timedelta64(6, '[h]'),
+                      np.timedelta64(9, '[h]'),
+                      np.timedelta64(12, '[h]'),
+                      np.timedelta64(6, '[m]'))]:
+            # m8 / int
+            assert_equal(tdc / 2, tda)
+            assert_equal((tdc / 2).dtype, np.dtype('m8[h]'))
+            # m8 / float
+            assert_equal(tda / 0.5, tdc)
+            assert_equal((tda / 0.5).dtype, np.dtype('m8[h]'))
+            # m8 / m8
+            assert_equal(tda / tdb, 6 / 9)
+            assert_equal(np.divide(tda, tdb), 6 / 9)
+            assert_equal(np.true_divide(tda, tdb), 6 / 9)
+            assert_equal(tdb / tda, 9 / 6)
+            assert_equal((tda / tdb).dtype, np.dtype('f8'))
+            assert_equal(tda / tdd, 60)
+            assert_equal(tdd / tda, 1 / 60)
+
+            # int / m8
+            assert_raises(TypeError, np.divide, 2, tdb)
+            # float / m8
+            assert_raises(TypeError, np.divide, 0.5, tdb)
+            # m8 / M8
+            assert_raises(TypeError, np.divide, dta, tda)
+            # M8 / m8
+            assert_raises(TypeError, np.divide, tda, dta)
+            # M8 / int
+            assert_raises(TypeError, np.divide, dta, 2)
+            # int / M8
+            assert_raises(TypeError, np.divide, 2, dta)
+            # M8 / float
+            assert_raises(TypeError, np.divide, dta, 1.5)
+            # float / M8
+            assert_raises(TypeError, np.divide, 1.5, dta)
+
+        # NaTs
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning,  r".*encountered in divide")
+            nat = np.timedelta64('NaT')
+            for tp in (int, float):
+                assert_equal(np.timedelta64(1) / tp(0), nat)
+                assert_equal(np.timedelta64(0) / tp(0), nat)
+                assert_equal(nat / tp(0), nat)
+                assert_equal(nat / tp(2), nat)
+            # Division by inf
+            assert_equal(np.timedelta64(1) / float('inf'), np.timedelta64(0))
+            assert_equal(np.timedelta64(0) / float('inf'), np.timedelta64(0))
+            assert_equal(nat / float('inf'), nat)
+            # Division by nan
+            assert_equal(np.timedelta64(1) / float('nan'), nat)
+            assert_equal(np.timedelta64(0) / float('nan'), nat)
+            assert_equal(nat / float('nan'), nat)
+
+    def test_datetime_compare(self):
+        # Test all the comparison operators
+        a = np.datetime64('2000-03-12T18:00:00.000000')
+        b = np.array(['2000-03-12T18:00:00.000000',
+                      '2000-03-12T17:59:59.999999',
+                      '2000-03-12T18:00:00.000001',
+                      '1970-01-11T12:00:00.909090',
+                      '2016-01-11T12:00:00.909090'],
+                      dtype='datetime64[us]')
+        assert_equal(np.equal(a, b), [1, 0, 0, 0, 0])
+        assert_equal(np.not_equal(a, b), [0, 1, 1, 1, 1])
+        assert_equal(np.less(a, b), [0, 0, 1, 0, 1])
+        assert_equal(np.less_equal(a, b), [1, 0, 1, 0, 1])
+        assert_equal(np.greater(a, b), [0, 1, 0, 1, 0])
+        assert_equal(np.greater_equal(a, b), [1, 1, 0, 1, 0])
+
+    def test_datetime_compare_nat(self):
+        dt_nat = np.datetime64('NaT', 'D')
+        dt_other = np.datetime64('2000-01-01')
+        td_nat = np.timedelta64('NaT', 'h')
+        td_other = np.timedelta64(1, 'h')
+
+        for op in [np.equal, np.less, np.less_equal,
+                   np.greater, np.greater_equal]:
+            assert_(not op(dt_nat, dt_nat))
+            assert_(not op(dt_nat, dt_other))
+            assert_(not op(dt_other, dt_nat))
+
+            assert_(not op(td_nat, td_nat))
+            assert_(not op(td_nat, td_other))
+            assert_(not op(td_other, td_nat))
+
+        assert_(np.not_equal(dt_nat, dt_nat))
+        assert_(np.not_equal(dt_nat, dt_other))
+        assert_(np.not_equal(dt_other, dt_nat))
+
+        assert_(np.not_equal(td_nat, td_nat))
+        assert_(np.not_equal(td_nat, td_other))
+        assert_(np.not_equal(td_other, td_nat))
+
+    def test_datetime_minmax(self):
+        # The metadata of the result should become the GCD
+        # of the operand metadata
+        a = np.array('1999-03-12T13', dtype='M8[2m]')
+        b = np.array('1999-03-12T12', dtype='M8[s]')
+        assert_equal(np.minimum(a, b), b)
+        assert_equal(np.minimum(a, b).dtype, np.dtype('M8[s]'))
+        assert_equal(np.fmin(a, b), b)
+        assert_equal(np.fmin(a, b).dtype, np.dtype('M8[s]'))
+        assert_equal(np.maximum(a, b), a)
+        assert_equal(np.maximum(a, b).dtype, np.dtype('M8[s]'))
+        assert_equal(np.fmax(a, b), a)
+        assert_equal(np.fmax(a, b).dtype, np.dtype('M8[s]'))
+        # Viewed as integers, the comparison is opposite because
+        # of the units chosen
+        assert_equal(np.minimum(a.view('i8'), b.view('i8')), a.view('i8'))
+
+        # Interaction with NaT
+        a = np.array('1999-03-12T13', dtype='M8[2m]')
+        dtnat = np.array('NaT', dtype='M8[h]')
+        assert_equal(np.minimum(a, dtnat), dtnat)
+        assert_equal(np.minimum(dtnat, a), dtnat)
+        assert_equal(np.maximum(a, dtnat), dtnat)
+        assert_equal(np.maximum(dtnat, a), dtnat)
+        assert_equal(np.fmin(dtnat, a), a)
+        assert_equal(np.fmin(a, dtnat), a)
+        assert_equal(np.fmax(dtnat, a), a)
+        assert_equal(np.fmax(a, dtnat), a)
+
+        # Also do timedelta
+        a = np.array(3, dtype='m8[h]')
+        b = np.array(3 * 3600 - 3, dtype='m8[s]')
+        assert_equal(np.minimum(a, b), b)
+        assert_equal(np.minimum(a, b).dtype, np.dtype('m8[s]'))
+        assert_equal(np.fmin(a, b), b)
+        assert_equal(np.fmin(a, b).dtype, np.dtype('m8[s]'))
+        assert_equal(np.maximum(a, b), a)
+        assert_equal(np.maximum(a, b).dtype, np.dtype('m8[s]'))
+        assert_equal(np.fmax(a, b), a)
+        assert_equal(np.fmax(a, b).dtype, np.dtype('m8[s]'))
+        # Viewed as integers, the comparison is opposite because
+        # of the units chosen
+        assert_equal(np.minimum(a.view('i8'), b.view('i8')), a.view('i8'))
+
+        # should raise between datetime and timedelta
+        #
+        # TODO: Allowing unsafe casting by
+        #       default in ufuncs strikes again... :(
+        a = np.array(3, dtype='m8[h]')
+        b = np.array('1999-03-12T12', dtype='M8[s]')
+        #assert_raises(TypeError, np.minimum, a, b)
+        #assert_raises(TypeError, np.maximum, a, b)
+        #assert_raises(TypeError, np.fmin, a, b)
+        #assert_raises(TypeError, np.fmax, a, b)
+        assert_raises(TypeError, np.minimum, a, b, casting='same_kind')
+        assert_raises(TypeError, np.maximum, a, b, casting='same_kind')
+        assert_raises(TypeError, np.fmin, a, b, casting='same_kind')
+        assert_raises(TypeError, np.fmax, a, b, casting='same_kind')
+
+    def test_hours(self):
+        t = np.ones(3, dtype='M8[s]')
+        t[0] = 60 * 60 * 24 + 60 * 60 * 10
+        assert_(t[0].item().hour == 10)
+
+    def test_divisor_conversion_year(self):
+        assert_(np.dtype('M8[Y/4]') == np.dtype('M8[3M]'))
+        assert_(np.dtype('M8[Y/13]') == np.dtype('M8[4W]'))
+        assert_(np.dtype('M8[3Y/73]') == np.dtype('M8[15D]'))
+
+    def test_divisor_conversion_month(self):
+        assert_(np.dtype('M8[M/2]') == np.dtype('M8[2W]'))
+        assert_(np.dtype('M8[M/15]') == np.dtype('M8[2D]'))
+        assert_(np.dtype('M8[3M/40]') == np.dtype('M8[54h]'))
+
+    def test_divisor_conversion_week(self):
+        assert_(np.dtype('m8[W/7]') == np.dtype('m8[D]'))
+        assert_(np.dtype('m8[3W/14]') == np.dtype('m8[36h]'))
+        assert_(np.dtype('m8[5W/140]') == np.dtype('m8[360m]'))
+
+    def test_divisor_conversion_day(self):
+        assert_(np.dtype('M8[D/12]') == np.dtype('M8[2h]'))
+        assert_(np.dtype('M8[D/120]') == np.dtype('M8[12m]'))
+        assert_(np.dtype('M8[3D/960]') == np.dtype('M8[270s]'))
+
+    def test_divisor_conversion_hour(self):
+        assert_(np.dtype('m8[h/30]') == np.dtype('m8[2m]'))
+        assert_(np.dtype('m8[3h/300]') == np.dtype('m8[36s]'))
+
+    def test_divisor_conversion_minute(self):
+        assert_(np.dtype('m8[m/30]') == np.dtype('m8[2s]'))
+        assert_(np.dtype('m8[3m/300]') == np.dtype('m8[600ms]'))
+
+    def test_divisor_conversion_second(self):
+        assert_(np.dtype('m8[s/100]') == np.dtype('m8[10ms]'))
+        assert_(np.dtype('m8[3s/10000]') == np.dtype('m8[300us]'))
+
+    def test_divisor_conversion_fs(self):
+        assert_(np.dtype('M8[fs/100]') == np.dtype('M8[10as]'))
+        assert_raises(ValueError, lambda: np.dtype('M8[3fs/10000]'))
+
+    def test_divisor_conversion_as(self):
+        assert_raises(ValueError, lambda: np.dtype('M8[as/10]'))
+
+    def test_string_parser_variants(self):
+        msg = "no explicit representation of timezones available for " \
+              "np.datetime64"
+        # Allow space instead of 'T' between date and time
+        assert_equal(np.array(['1980-02-29T01:02:03'], np.dtype('M8[s]')),
+                     np.array(['1980-02-29 01:02:03'], np.dtype('M8[s]')))
+        # Allow positive years
+        assert_equal(np.array(['+1980-02-29T01:02:03'], np.dtype('M8[s]')),
+                     np.array(['+1980-02-29 01:02:03'], np.dtype('M8[s]')))
+        # Allow negative years
+        assert_equal(np.array(['-1980-02-29T01:02:03'], np.dtype('M8[s]')),
+                     np.array(['-1980-02-29 01:02:03'], np.dtype('M8[s]')))
+        # UTC specifier
+        with pytest.warns(UserWarning, match=msg):
+            assert_equal(
+                np.array(['+1980-02-29T01:02:03'], np.dtype('M8[s]')),
+                np.array(['+1980-02-29 01:02:03Z'], np.dtype('M8[s]')))
+        with pytest.warns(UserWarning, match=msg):
+            assert_equal(
+                np.array(['-1980-02-29T01:02:03'], np.dtype('M8[s]')),
+                np.array(['-1980-02-29 01:02:03Z'], np.dtype('M8[s]')))
+        # Time zone offset
+        with pytest.warns(UserWarning, match=msg):
+            assert_equal(
+                np.array(['1980-02-29T02:02:03'], np.dtype('M8[s]')),
+                np.array(['1980-02-29 00:32:03-0130'], np.dtype('M8[s]')))
+        with pytest.warns(UserWarning, match=msg):
+            assert_equal(
+                np.array(['1980-02-28T22:32:03'], np.dtype('M8[s]')),
+                np.array(['1980-02-29 00:02:03+01:30'], np.dtype('M8[s]')))
+        with pytest.warns(UserWarning, match=msg):
+            assert_equal(
+                np.array(['1980-02-29T02:32:03.506'], np.dtype('M8[s]')),
+                np.array(['1980-02-29 00:32:03.506-02'], np.dtype('M8[s]')))
+        with pytest.warns(UserWarning, match=msg):
+            assert_equal(np.datetime64('1977-03-02T12:30-0230'),
+                         np.datetime64('1977-03-02T15:00'))
+
+    def test_string_parser_error_check(self):
+        msg = "no explicit representation of timezones available for " \
+              "np.datetime64"
+        # Arbitrary bad string
+        assert_raises(ValueError, np.array, ['badvalue'], np.dtype('M8[us]'))
+        # Character after year must be '-'
+        assert_raises(ValueError, np.array, ['1980X'], np.dtype('M8[us]'))
+        # Cannot have trailing '-'
+        assert_raises(ValueError, np.array, ['1980-'], np.dtype('M8[us]'))
+        # Month must be in range [1,12]
+        assert_raises(ValueError, np.array, ['1980-00'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-13'], np.dtype('M8[us]'))
+        # Month must have two digits
+        assert_raises(ValueError, np.array, ['1980-1'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-1-02'], np.dtype('M8[us]'))
+        # 'Mor' is not a valid month
+        assert_raises(ValueError, np.array, ['1980-Mor'], np.dtype('M8[us]'))
+        # Cannot have trailing '-'
+        assert_raises(ValueError, np.array, ['1980-01-'], np.dtype('M8[us]'))
+        # Day must be in range [1,len(month)]
+        assert_raises(ValueError, np.array, ['1980-01-0'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-01-00'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-01-32'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1979-02-29'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-02-30'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-03-32'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-04-31'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-05-32'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-06-31'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-07-32'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-08-32'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-09-31'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-10-32'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-11-31'], np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-12-32'], np.dtype('M8[us]'))
+        # Cannot have trailing characters
+        assert_raises(ValueError, np.array, ['1980-02-03%'],
+                                                        np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-02-03 q'],
+                                                        np.dtype('M8[us]'))
+
+        # Hours must be in range [0, 23]
+        assert_raises(ValueError, np.array, ['1980-02-03 25'],
+                                                        np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-02-03T25'],
+                                                        np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-02-03 24:01'],
+                                                        np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-02-03T24:01'],
+                                                        np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-02-03 -1'],
+                                                        np.dtype('M8[us]'))
+        # No trailing ':'
+        assert_raises(ValueError, np.array, ['1980-02-03 01:'],
+                                                        np.dtype('M8[us]'))
+        # Minutes must be in range [0, 59]
+        assert_raises(ValueError, np.array, ['1980-02-03 01:-1'],
+                                                        np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-02-03 01:60'],
+                                                        np.dtype('M8[us]'))
+        # No trailing ':'
+        assert_raises(ValueError, np.array, ['1980-02-03 01:60:'],
+                                                        np.dtype('M8[us]'))
+        # Seconds must be in range [0, 59]
+        assert_raises(ValueError, np.array, ['1980-02-03 01:10:-1'],
+                                                        np.dtype('M8[us]'))
+        assert_raises(ValueError, np.array, ['1980-02-03 01:01:60'],
+                                                        np.dtype('M8[us]'))
+        # Timezone offset must within a reasonable range
+        with pytest.warns(UserWarning, match=msg):
+            assert_raises(ValueError, np.array, ['1980-02-03 01:01:00+0661'],
+                                                            np.dtype('M8[us]'))
+        with pytest.warns(UserWarning, match=msg):
+            assert_raises(ValueError, np.array, ['1980-02-03 01:01:00+2500'],
+                                                            np.dtype('M8[us]'))
+        with pytest.warns(UserWarning, match=msg):
+            assert_raises(ValueError, np.array, ['1980-02-03 01:01:00-0070'],
+                                                            np.dtype('M8[us]'))
+        with pytest.warns(UserWarning, match=msg):
+            assert_raises(ValueError, np.array, ['1980-02-03 01:01:00-3000'],
+                                                            np.dtype('M8[us]'))
+        with pytest.warns(UserWarning, match=msg):
+            assert_raises(ValueError, np.array, ['1980-02-03 01:01:00-25:00'],
+                                                            np.dtype('M8[us]'))
+
+    def test_creation_overflow(self):
+        date = '1980-03-23 20:00:00'
+        timesteps = np.array([date], dtype='datetime64[s]')[0].astype(np.int64)
+        for unit in ['ms', 'us', 'ns']:
+            timesteps *= 1000
+            x = np.array([date], dtype=f'datetime64[{unit}]')
+
+            assert_equal(timesteps, x[0].astype(np.int64),
+                         err_msg=f'Datetime conversion error for unit {unit}')
+
+        assert_equal(x[0].astype(np.int64), 322689600000000000)
+
+        # gh-13062
+        with pytest.raises(OverflowError):
+            np.datetime64(2**64, 'D')
+        with pytest.raises(OverflowError):
+            np.timedelta64(2**64, 'D')
+
+    def test_datetime_as_string(self):
+        # Check all the units with default string conversion
+        date = '1959-10-13'
+        datetime = '1959-10-13T12:34:56.789012345678901234'
+
+        assert_equal(np.datetime_as_string(np.datetime64(date, 'Y')),
+                     '1959')
+        assert_equal(np.datetime_as_string(np.datetime64(date, 'M')),
+                     '1959-10')
+        assert_equal(np.datetime_as_string(np.datetime64(date, 'D')),
+                     '1959-10-13')
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'h')),
+                     '1959-10-13T12')
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'm')),
+                     '1959-10-13T12:34')
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 's')),
+                     '1959-10-13T12:34:56')
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'ms')),
+                     '1959-10-13T12:34:56.789')
+        for us in ['us', 'μs', b'us']:  # check non-ascii and bytes too
+            assert_equal(np.datetime_as_string(np.datetime64(datetime, us)),
+                         '1959-10-13T12:34:56.789012')
+
+        datetime = '1969-12-31T23:34:56.789012345678901234'
+
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'ns')),
+                     '1969-12-31T23:34:56.789012345')
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'ps')),
+                     '1969-12-31T23:34:56.789012345678')
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'fs')),
+                     '1969-12-31T23:34:56.789012345678901')
+
+        datetime = '1969-12-31T23:59:57.789012345678901234'
+
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'as')),
+                     datetime)
+        datetime = '1970-01-01T00:34:56.789012345678901234'
+
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'ns')),
+                     '1970-01-01T00:34:56.789012345')
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'ps')),
+                     '1970-01-01T00:34:56.789012345678')
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'fs')),
+                     '1970-01-01T00:34:56.789012345678901')
+
+        datetime = '1970-01-01T00:00:05.789012345678901234'
+
+        assert_equal(np.datetime_as_string(np.datetime64(datetime, 'as')),
+                     datetime)
+
+        # String conversion with the unit= parameter
+        a = np.datetime64('2032-07-18T12:23:34.123456', 'us')
+        assert_equal(np.datetime_as_string(a, unit='Y', casting='unsafe'),
+                            '2032')
+        assert_equal(np.datetime_as_string(a, unit='M', casting='unsafe'),
+                            '2032-07')
+        assert_equal(np.datetime_as_string(a, unit='W', casting='unsafe'),
+                            '2032-07-18')
+        assert_equal(np.datetime_as_string(a, unit='D', casting='unsafe'),
+                            '2032-07-18')
+        assert_equal(np.datetime_as_string(a, unit='h'), '2032-07-18T12')
+        assert_equal(np.datetime_as_string(a, unit='m'),
+                            '2032-07-18T12:23')
+        assert_equal(np.datetime_as_string(a, unit='s'),
+                            '2032-07-18T12:23:34')
+        assert_equal(np.datetime_as_string(a, unit='ms'),
+                            '2032-07-18T12:23:34.123')
+        assert_equal(np.datetime_as_string(a, unit='us'),
+                            '2032-07-18T12:23:34.123456')
+        assert_equal(np.datetime_as_string(a, unit='ns'),
+                            '2032-07-18T12:23:34.123456000')
+        assert_equal(np.datetime_as_string(a, unit='ps'),
+                            '2032-07-18T12:23:34.123456000000')
+        assert_equal(np.datetime_as_string(a, unit='fs'),
+                            '2032-07-18T12:23:34.123456000000000')
+        assert_equal(np.datetime_as_string(a, unit='as'),
+                            '2032-07-18T12:23:34.123456000000000000')
+
+        # unit='auto' parameter
+        assert_equal(np.datetime_as_string(
+                np.datetime64('2032-07-18T12:23:34.123456', 'us'), unit='auto'),
+                '2032-07-18T12:23:34.123456')
+        assert_equal(np.datetime_as_string(
+                np.datetime64('2032-07-18T12:23:34.12', 'us'), unit='auto'),
+                '2032-07-18T12:23:34.120')
+        assert_equal(np.datetime_as_string(
+                np.datetime64('2032-07-18T12:23:34', 'us'), unit='auto'),
+                '2032-07-18T12:23:34')
+        assert_equal(np.datetime_as_string(
+                np.datetime64('2032-07-18T12:23:00', 'us'), unit='auto'),
+                '2032-07-18T12:23')
+        # 'auto' doesn't split up hour and minute
+        assert_equal(np.datetime_as_string(
+                np.datetime64('2032-07-18T12:00:00', 'us'), unit='auto'),
+                '2032-07-18T12:00')
+        assert_equal(np.datetime_as_string(
+                np.datetime64('2032-07-18T00:00:00', 'us'), unit='auto'),
+                '2032-07-18')
+        # 'auto' doesn't split up the date
+        assert_equal(np.datetime_as_string(
+                np.datetime64('2032-07-01T00:00:00', 'us'), unit='auto'),
+                '2032-07-01')
+        assert_equal(np.datetime_as_string(
+                np.datetime64('2032-01-01T00:00:00', 'us'), unit='auto'),
+                '2032-01-01')
+
+    @pytest.mark.skipif(not _has_pytz, reason="The pytz module is not available.")
+    def test_datetime_as_string_timezone(self):
+        # timezone='local' vs 'UTC'
+        a = np.datetime64('2010-03-15T06:30', 'm')
+        assert_equal(np.datetime_as_string(a),
+                '2010-03-15T06:30')
+        assert_equal(np.datetime_as_string(a, timezone='naive'),
+                '2010-03-15T06:30')
+        assert_equal(np.datetime_as_string(a, timezone='UTC'),
+                '2010-03-15T06:30Z')
+        assert_(np.datetime_as_string(a, timezone='local') !=
+                '2010-03-15T06:30')
+
+        b = np.datetime64('2010-02-15T06:30', 'm')
+
+        assert_equal(np.datetime_as_string(a, timezone=tz('US/Central')),
+                     '2010-03-15T01:30-0500')
+        assert_equal(np.datetime_as_string(a, timezone=tz('US/Eastern')),
+                     '2010-03-15T02:30-0400')
+        assert_equal(np.datetime_as_string(a, timezone=tz('US/Pacific')),
+                     '2010-03-14T23:30-0700')
+
+        assert_equal(np.datetime_as_string(b, timezone=tz('US/Central')),
+                     '2010-02-15T00:30-0600')
+        assert_equal(np.datetime_as_string(b, timezone=tz('US/Eastern')),
+                     '2010-02-15T01:30-0500')
+        assert_equal(np.datetime_as_string(b, timezone=tz('US/Pacific')),
+                     '2010-02-14T22:30-0800')
+
+        # Dates to strings with a timezone attached is disabled by default
+        assert_raises(TypeError, np.datetime_as_string, a, unit='D',
+                           timezone=tz('US/Pacific'))
+        # Check that we can print out the date in the specified time zone
+        assert_equal(np.datetime_as_string(a, unit='D',
+                           timezone=tz('US/Pacific'), casting='unsafe'),
+                     '2010-03-14')
+        assert_equal(np.datetime_as_string(b, unit='D',
+                           timezone=tz('US/Central'), casting='unsafe'),
+                     '2010-02-15')
+
+    def test_datetime_arange(self):
+        # With two datetimes provided as strings
+        a = np.arange('2010-01-05', '2010-01-10', dtype='M8[D]')
+        assert_equal(a.dtype, np.dtype('M8[D]'))
+        assert_equal(a,
+            np.array(['2010-01-05', '2010-01-06', '2010-01-07',
+                      '2010-01-08', '2010-01-09'], dtype='M8[D]'))
+
+        a = np.arange('1950-02-10', '1950-02-06', -1, dtype='M8[D]')
+        assert_equal(a.dtype, np.dtype('M8[D]'))
+        assert_equal(a,
+            np.array(['1950-02-10', '1950-02-09', '1950-02-08',
+                      '1950-02-07'], dtype='M8[D]'))
+
+        # Unit should be detected as months here
+        a = np.arange('1969-05', '1970-05', 2, dtype='M8')
+        assert_equal(a.dtype, np.dtype('M8[M]'))
+        assert_equal(a,
+            np.datetime64('1969-05') + np.arange(12, step=2))
+
+        # datetime, integer|timedelta works as well
+        # produces arange (start, start + stop) in this case
+        a = np.arange('1969', 18, 3, dtype='M8')
+        assert_equal(a.dtype, np.dtype('M8[Y]'))
+        assert_equal(a,
+            np.datetime64('1969') + np.arange(18, step=3))
+        a = np.arange('1969-12-19', 22, np.timedelta64(2), dtype='M8')
+        assert_equal(a.dtype, np.dtype('M8[D]'))
+        assert_equal(a,
+            np.datetime64('1969-12-19') + np.arange(22, step=2))
+
+        # Step of 0 is disallowed
+        assert_raises(ValueError, np.arange, np.datetime64('today'),
+                                np.datetime64('today') + 3, 0)
+        # Promotion across nonlinear unit boundaries is disallowed
+        assert_raises(TypeError, np.arange, np.datetime64('2011-03-01', 'D'),
+                                np.timedelta64(5, 'M'))
+        assert_raises(TypeError, np.arange,
+                                np.datetime64('2012-02-03T14', 's'),
+                                np.timedelta64(5, 'Y'))
+
+    def test_datetime_arange_no_dtype(self):
+        d = np.array('2010-01-04', dtype="M8[D]")
+        assert_equal(np.arange(d, d + 1), d)
+        assert_raises(ValueError, np.arange, d)
+
+    def test_timedelta_arange(self):
+        a = np.arange(3, 10, dtype='m8')
+        assert_equal(a.dtype, np.dtype('m8'))
+        assert_equal(a, np.timedelta64(0) + np.arange(3, 10))
+
+        a = np.arange(np.timedelta64(3, 's'), 10, 2, dtype='m8')
+        assert_equal(a.dtype, np.dtype('m8[s]'))
+        assert_equal(a, np.timedelta64(0, 's') + np.arange(3, 10, 2))
+
+        # Step of 0 is disallowed
+        assert_raises(ValueError, np.arange, np.timedelta64(0),
+                                np.timedelta64(5), 0)
+        # Promotion across nonlinear unit boundaries is disallowed
+        assert_raises(TypeError, np.arange, np.timedelta64(0, 'D'),
+                                np.timedelta64(5, 'M'))
+        assert_raises(TypeError, np.arange, np.timedelta64(0, 'Y'),
+                                np.timedelta64(5, 'D'))
+
+    @pytest.mark.parametrize("val1, val2, expected", [
+        # case from gh-12092
+        (np.timedelta64(7, 's'),
+         np.timedelta64(3, 's'),
+         np.timedelta64(1, 's')),
+        # negative value cases
+        (np.timedelta64(3, 's'),
+         np.timedelta64(-2, 's'),
+         np.timedelta64(-1, 's')),
+        (np.timedelta64(-3, 's'),
+         np.timedelta64(2, 's'),
+         np.timedelta64(1, 's')),
+        # larger value cases
+        (np.timedelta64(17, 's'),
+         np.timedelta64(22, 's'),
+         np.timedelta64(17, 's')),
+        (np.timedelta64(22, 's'),
+         np.timedelta64(17, 's'),
+         np.timedelta64(5, 's')),
+        # different units
+        (np.timedelta64(1, 'm'),
+         np.timedelta64(57, 's'),
+         np.timedelta64(3, 's')),
+        (np.timedelta64(1, 'us'),
+         np.timedelta64(727, 'ns'),
+         np.timedelta64(273, 'ns')),
+        # NaT is propagated
+        (np.timedelta64('NaT'),
+         np.timedelta64(50, 'ns'),
+         np.timedelta64('NaT')),
+        # Y % M works
+        (np.timedelta64(2, 'Y'),
+         np.timedelta64(22, 'M'),
+         np.timedelta64(2, 'M')),
+        ])
+    def test_timedelta_modulus(self, val1, val2, expected):
+        assert_equal(val1 % val2, expected)
+
+    @pytest.mark.parametrize("val1, val2", [
+        # years and months sometimes can't be unambiguously
+        # divided for modulus operation
+        (np.timedelta64(7, 'Y'),
+         np.timedelta64(3, 's')),
+        (np.timedelta64(7, 'M'),
+         np.timedelta64(1, 'D')),
+        ])
+    def test_timedelta_modulus_error(self, val1, val2):
+        with assert_raises_regex(TypeError, "common metadata divisor"):
+            val1 % val2
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_timedelta_modulus_div_by_zero(self):
+        with assert_warns(RuntimeWarning):
+            actual = np.timedelta64(10, 's') % np.timedelta64(0, 's')
+            assert_equal(actual, np.timedelta64('NaT'))
+
+    @pytest.mark.parametrize("val1, val2", [
+        # cases where one operand is not
+        # timedelta64
+        (np.timedelta64(7, 'Y'),
+         15,),
+        (7.5,
+         np.timedelta64(1, 'D')),
+        ])
+    def test_timedelta_modulus_type_resolution(self, val1, val2):
+        # NOTE: some of the operations may be supported
+        # in the future
+        with assert_raises_regex(TypeError,
+                                 "'remainder' cannot use operands with types"):
+            val1 % val2
+
+    def test_timedelta_arange_no_dtype(self):
+        d = np.array(5, dtype="m8[D]")
+        assert_equal(np.arange(d, d + 1), d)
+        assert_equal(np.arange(d), np.arange(0, d))
+
+    def test_datetime_maximum_reduce(self):
+        a = np.array(['2010-01-02', '1999-03-14', '1833-03'], dtype='M8[D]')
+        assert_equal(np.maximum.reduce(a).dtype, np.dtype('M8[D]'))
+        assert_equal(np.maximum.reduce(a),
+                     np.datetime64('2010-01-02'))
+
+        a = np.array([1, 4, 0, 7, 2], dtype='m8[s]')
+        assert_equal(np.maximum.reduce(a).dtype, np.dtype('m8[s]'))
+        assert_equal(np.maximum.reduce(a),
+                     np.timedelta64(7, 's'))
+
+    def test_timedelta_correct_mean(self):
+        # test mainly because it worked only via a bug in that allowed:
+        # `timedelta.sum(dtype="f8")` to ignore the dtype request.
+        a = np.arange(1000, dtype="m8[s]")
+        assert_array_equal(a.mean(), a.sum() / len(a))
+
+    def test_datetime_no_subtract_reducelike(self):
+        # subtracting two datetime64 works, but we cannot reduce it, since
+        # the result of that subtraction will have a different dtype.
+        arr = np.array(["2021-12-02", "2019-05-12"], dtype="M8[ms]")
+        msg = r"the resolved dtypes are not compatible"
+
+        with pytest.raises(TypeError, match=msg):
+            np.subtract.reduce(arr)
+
+        with pytest.raises(TypeError, match=msg):
+            np.subtract.accumulate(arr)
+
+        with pytest.raises(TypeError, match=msg):
+            np.subtract.reduceat(arr, [0])
+
+    def test_datetime_busday_offset(self):
+        # First Monday in June
+        assert_equal(
+            np.busday_offset('2011-06', 0, roll='forward', weekmask='Mon'),
+            np.datetime64('2011-06-06'))
+        # Last Monday in June
+        assert_equal(
+            np.busday_offset('2011-07', -1, roll='forward', weekmask='Mon'),
+            np.datetime64('2011-06-27'))
+        assert_equal(
+            np.busday_offset('2011-07', -1, roll='forward', weekmask='Mon'),
+            np.datetime64('2011-06-27'))
+
+        # Default M-F business days, different roll modes
+        assert_equal(np.busday_offset('2010-08', 0, roll='backward'),
+                     np.datetime64('2010-07-30'))
+        assert_equal(np.busday_offset('2010-08', 0, roll='preceding'),
+                     np.datetime64('2010-07-30'))
+        assert_equal(np.busday_offset('2010-08', 0, roll='modifiedpreceding'),
+                     np.datetime64('2010-08-02'))
+        assert_equal(np.busday_offset('2010-08', 0, roll='modifiedfollowing'),
+                     np.datetime64('2010-08-02'))
+        assert_equal(np.busday_offset('2010-08', 0, roll='forward'),
+                     np.datetime64('2010-08-02'))
+        assert_equal(np.busday_offset('2010-08', 0, roll='following'),
+                     np.datetime64('2010-08-02'))
+        assert_equal(np.busday_offset('2010-10-30', 0, roll='following'),
+                     np.datetime64('2010-11-01'))
+        assert_equal(
+                np.busday_offset('2010-10-30', 0, roll='modifiedfollowing'),
+                np.datetime64('2010-10-29'))
+        assert_equal(
+                np.busday_offset('2010-10-30', 0, roll='modifiedpreceding'),
+                np.datetime64('2010-10-29'))
+        assert_equal(
+                np.busday_offset('2010-10-16', 0, roll='modifiedfollowing'),
+                np.datetime64('2010-10-18'))
+        assert_equal(
+                np.busday_offset('2010-10-16', 0, roll='modifiedpreceding'),
+                np.datetime64('2010-10-15'))
+        # roll='raise' by default
+        assert_raises(ValueError, np.busday_offset, '2011-06-04', 0)
+
+        # Bigger offset values
+        assert_equal(np.busday_offset('2006-02-01', 25),
+                     np.datetime64('2006-03-08'))
+        assert_equal(np.busday_offset('2006-03-08', -25),
+                     np.datetime64('2006-02-01'))
+        assert_equal(np.busday_offset('2007-02-25', 11, weekmask='SatSun'),
+                     np.datetime64('2007-04-07'))
+        assert_equal(np.busday_offset('2007-04-07', -11, weekmask='SatSun'),
+                     np.datetime64('2007-02-25'))
+
+        # NaT values when roll is not raise
+        assert_equal(np.busday_offset(np.datetime64('NaT'), 1, roll='nat'),
+                     np.datetime64('NaT'))
+        assert_equal(np.busday_offset(np.datetime64('NaT'), 1, roll='following'),
+                     np.datetime64('NaT'))
+        assert_equal(np.busday_offset(np.datetime64('NaT'), 1, roll='preceding'),
+                     np.datetime64('NaT'))
+
+    def test_datetime_busdaycalendar(self):
+        # Check that it removes NaT, duplicates, and weekends
+        # and sorts the result.
+        bdd = np.busdaycalendar(
+            holidays=['NaT', '2011-01-17', '2011-03-06', 'NaT',
+                       '2011-12-26', '2011-05-30', '2011-01-17'])
+        assert_equal(bdd.holidays,
+            np.array(['2011-01-17', '2011-05-30', '2011-12-26'], dtype='M8'))
+        # Default M-F weekmask
+        assert_equal(bdd.weekmask, np.array([1, 1, 1, 1, 1, 0, 0], dtype='?'))
+
+        # Check string weekmask with varying whitespace.
+        bdd = np.busdaycalendar(weekmask="Sun TueWed  Thu\tFri")
+        assert_equal(bdd.weekmask, np.array([0, 1, 1, 1, 1, 0, 1], dtype='?'))
+
+        # Check length 7 0/1 string
+        bdd = np.busdaycalendar(weekmask="0011001")
+        assert_equal(bdd.weekmask, np.array([0, 0, 1, 1, 0, 0, 1], dtype='?'))
+
+        # Check length 7 string weekmask.
+        bdd = np.busdaycalendar(weekmask="Mon Tue")
+        assert_equal(bdd.weekmask, np.array([1, 1, 0, 0, 0, 0, 0], dtype='?'))
+
+        # All-zeros weekmask should raise
+        assert_raises(ValueError, np.busdaycalendar, weekmask=[0, 0, 0, 0, 0, 0, 0])
+        # weekday names must be correct case
+        assert_raises(ValueError, np.busdaycalendar, weekmask="satsun")
+        # All-zeros weekmask should raise
+        assert_raises(ValueError, np.busdaycalendar, weekmask="")
+        # Invalid weekday name codes should raise
+        assert_raises(ValueError, np.busdaycalendar, weekmask="Mon Tue We")
+        assert_raises(ValueError, np.busdaycalendar, weekmask="Max")
+        assert_raises(ValueError, np.busdaycalendar, weekmask="Monday Tue")
+
+    def test_datetime_busday_holidays_offset(self):
+        # With exactly one holiday
+        assert_equal(
+            np.busday_offset('2011-11-10', 1, holidays=['2011-11-11']),
+            np.datetime64('2011-11-14'))
+        assert_equal(
+            np.busday_offset('2011-11-04', 5, holidays=['2011-11-11']),
+            np.datetime64('2011-11-14'))
+        assert_equal(
+            np.busday_offset('2011-11-10', 5, holidays=['2011-11-11']),
+            np.datetime64('2011-11-18'))
+        assert_equal(
+            np.busday_offset('2011-11-14', -1, holidays=['2011-11-11']),
+            np.datetime64('2011-11-10'))
+        assert_equal(
+            np.busday_offset('2011-11-18', -5, holidays=['2011-11-11']),
+            np.datetime64('2011-11-10'))
+        assert_equal(
+            np.busday_offset('2011-11-14', -5, holidays=['2011-11-11']),
+            np.datetime64('2011-11-04'))
+        # With the holiday appearing twice
+        assert_equal(
+            np.busday_offset('2011-11-10', 1,
+                holidays=['2011-11-11', '2011-11-11']),
+            np.datetime64('2011-11-14'))
+        assert_equal(
+            np.busday_offset('2011-11-14', -1,
+                holidays=['2011-11-11', '2011-11-11']),
+            np.datetime64('2011-11-10'))
+        # With a NaT holiday
+        assert_equal(
+            np.busday_offset('2011-11-10', 1,
+                holidays=['2011-11-11', 'NaT']),
+            np.datetime64('2011-11-14'))
+        assert_equal(
+            np.busday_offset('2011-11-14', -1,
+                holidays=['NaT', '2011-11-11']),
+            np.datetime64('2011-11-10'))
+        # With another holiday after
+        assert_equal(
+            np.busday_offset('2011-11-10', 1,
+                holidays=['2011-11-11', '2011-11-24']),
+            np.datetime64('2011-11-14'))
+        assert_equal(
+            np.busday_offset('2011-11-14', -1,
+                holidays=['2011-11-11', '2011-11-24']),
+            np.datetime64('2011-11-10'))
+        # With another holiday before
+        assert_equal(
+            np.busday_offset('2011-11-10', 1,
+                holidays=['2011-10-10', '2011-11-11']),
+            np.datetime64('2011-11-14'))
+        assert_equal(
+            np.busday_offset('2011-11-14', -1,
+                holidays=['2011-10-10', '2011-11-11']),
+            np.datetime64('2011-11-10'))
+        # With another holiday before and after
+        assert_equal(
+            np.busday_offset('2011-11-10', 1,
+                holidays=['2011-10-10', '2011-11-11', '2011-11-24']),
+            np.datetime64('2011-11-14'))
+        assert_equal(
+            np.busday_offset('2011-11-14', -1,
+                holidays=['2011-10-10', '2011-11-11', '2011-11-24']),
+            np.datetime64('2011-11-10'))
+
+        # A bigger forward jump across more than one week/holiday
+        holidays = ['2011-10-10', '2011-11-11', '2011-11-24',
+                  '2011-12-25', '2011-05-30', '2011-02-21',
+                  '2011-12-26', '2012-01-02']
+        bdd = np.busdaycalendar(weekmask='1111100', holidays=holidays)
+        assert_equal(
+            np.busday_offset('2011-10-03', 4, holidays=holidays),
+            np.busday_offset('2011-10-03', 4))
+        assert_equal(
+            np.busday_offset('2011-10-03', 5, holidays=holidays),
+            np.busday_offset('2011-10-03', 5 + 1))
+        assert_equal(
+            np.busday_offset('2011-10-03', 27, holidays=holidays),
+            np.busday_offset('2011-10-03', 27 + 1))
+        assert_equal(
+            np.busday_offset('2011-10-03', 28, holidays=holidays),
+            np.busday_offset('2011-10-03', 28 + 2))
+        assert_equal(
+            np.busday_offset('2011-10-03', 35, holidays=holidays),
+            np.busday_offset('2011-10-03', 35 + 2))
+        assert_equal(
+            np.busday_offset('2011-10-03', 36, holidays=holidays),
+            np.busday_offset('2011-10-03', 36 + 3))
+        assert_equal(
+            np.busday_offset('2011-10-03', 56, holidays=holidays),
+            np.busday_offset('2011-10-03', 56 + 3))
+        assert_equal(
+            np.busday_offset('2011-10-03', 57, holidays=holidays),
+            np.busday_offset('2011-10-03', 57 + 4))
+        assert_equal(
+            np.busday_offset('2011-10-03', 60, holidays=holidays),
+            np.busday_offset('2011-10-03', 60 + 4))
+        assert_equal(
+            np.busday_offset('2011-10-03', 61, holidays=holidays),
+            np.busday_offset('2011-10-03', 61 + 5))
+        assert_equal(
+            np.busday_offset('2011-10-03', 61, busdaycal=bdd),
+            np.busday_offset('2011-10-03', 61 + 5))
+        # A bigger backward jump across more than one week/holiday
+        assert_equal(
+            np.busday_offset('2012-01-03', -1, holidays=holidays),
+            np.busday_offset('2012-01-03', -1 - 1))
+        assert_equal(
+            np.busday_offset('2012-01-03', -4, holidays=holidays),
+            np.busday_offset('2012-01-03', -4 - 1))
+        assert_equal(
+            np.busday_offset('2012-01-03', -5, holidays=holidays),
+            np.busday_offset('2012-01-03', -5 - 2))
+        assert_equal(
+            np.busday_offset('2012-01-03', -25, holidays=holidays),
+            np.busday_offset('2012-01-03', -25 - 2))
+        assert_equal(
+            np.busday_offset('2012-01-03', -26, holidays=holidays),
+            np.busday_offset('2012-01-03', -26 - 3))
+        assert_equal(
+            np.busday_offset('2012-01-03', -33, holidays=holidays),
+            np.busday_offset('2012-01-03', -33 - 3))
+        assert_equal(
+            np.busday_offset('2012-01-03', -34, holidays=holidays),
+            np.busday_offset('2012-01-03', -34 - 4))
+        assert_equal(
+            np.busday_offset('2012-01-03', -56, holidays=holidays),
+            np.busday_offset('2012-01-03', -56 - 4))
+        assert_equal(
+            np.busday_offset('2012-01-03', -57, holidays=holidays),
+            np.busday_offset('2012-01-03', -57 - 5))
+        assert_equal(
+            np.busday_offset('2012-01-03', -57, busdaycal=bdd),
+            np.busday_offset('2012-01-03', -57 - 5))
+
+        # Can't supply both a weekmask/holidays and busdaycal
+        assert_raises(ValueError, np.busday_offset, '2012-01-03', -15,
+                        weekmask='1111100', busdaycal=bdd)
+        assert_raises(ValueError, np.busday_offset, '2012-01-03', -15,
+                        holidays=holidays, busdaycal=bdd)
+
+        # Roll with the holidays
+        assert_equal(
+            np.busday_offset('2011-12-25', 0,
+                roll='forward', holidays=holidays),
+            np.datetime64('2011-12-27'))
+        assert_equal(
+            np.busday_offset('2011-12-26', 0,
+                roll='forward', holidays=holidays),
+            np.datetime64('2011-12-27'))
+        assert_equal(
+            np.busday_offset('2011-12-26', 0,
+                roll='backward', holidays=holidays),
+            np.datetime64('2011-12-23'))
+        assert_equal(
+            np.busday_offset('2012-02-27', 0,
+                roll='modifiedfollowing',
+                holidays=['2012-02-27', '2012-02-26', '2012-02-28',
+                          '2012-03-01', '2012-02-29']),
+            np.datetime64('2012-02-24'))
+        assert_equal(
+            np.busday_offset('2012-03-06', 0,
+                roll='modifiedpreceding',
+                holidays=['2012-03-02', '2012-03-03', '2012-03-01',
+                          '2012-03-05', '2012-03-07', '2012-03-06']),
+            np.datetime64('2012-03-08'))
+
+    def test_datetime_busday_holidays_count(self):
+        holidays = ['2011-01-01', '2011-10-10', '2011-11-11', '2011-11-24',
+                    '2011-12-25', '2011-05-30', '2011-02-21', '2011-01-17',
+                    '2011-12-26', '2012-01-02', '2011-02-21', '2011-05-30',
+                    '2011-07-01', '2011-07-04', '2011-09-05', '2011-10-10']
+        bdd = np.busdaycalendar(weekmask='1111100', holidays=holidays)
+
+        # Validate against busday_offset broadcast against
+        # a range of offsets
+        dates = np.busday_offset('2011-01-01', np.arange(366),
+                        roll='forward', busdaycal=bdd)
+        assert_equal(np.busday_count('2011-01-01', dates, busdaycal=bdd),
+                     np.arange(366))
+        # Returns negative value when reversed
+        # -1 since the '2011-01-01' is not a busday
+        assert_equal(np.busday_count(dates, '2011-01-01', busdaycal=bdd),
+                     -np.arange(366) - 1)
+
+        # 2011-12-31 is a saturday
+        dates = np.busday_offset('2011-12-31', -np.arange(366),
+                        roll='forward', busdaycal=bdd)
+        # only the first generated date is in the future of 2011-12-31
+        expected = np.arange(366)
+        expected[0] = -1
+        assert_equal(np.busday_count(dates, '2011-12-31', busdaycal=bdd),
+                     expected)
+        # Returns negative value when reversed
+        expected = -np.arange(366) + 1
+        expected[0] = 0
+        assert_equal(np.busday_count('2011-12-31', dates, busdaycal=bdd),
+                     expected)
+
+        # Can't supply both a weekmask/holidays and busdaycal
+        assert_raises(ValueError, np.busday_offset, '2012-01-03', '2012-02-03',
+                        weekmask='1111100', busdaycal=bdd)
+        assert_raises(ValueError, np.busday_offset, '2012-01-03', '2012-02-03',
+                        holidays=holidays, busdaycal=bdd)
+
+        # Number of Mondays in March 2011
+        assert_equal(np.busday_count('2011-03', '2011-04', weekmask='Mon'), 4)
+        # Returns negative value when reversed
+        assert_equal(np.busday_count('2011-04', '2011-03', weekmask='Mon'), -4)
+
+        sunday = np.datetime64('2023-03-05')
+        monday = sunday + 1
+        friday = sunday + 5
+        saturday = sunday + 6
+        assert_equal(np.busday_count(sunday, monday), 0)
+        assert_equal(np.busday_count(monday, sunday), -1)
+
+        assert_equal(np.busday_count(friday, saturday), 1)
+        assert_equal(np.busday_count(saturday, friday), 0)
+
+    def test_datetime_is_busday(self):
+        holidays = ['2011-01-01', '2011-10-10', '2011-11-11', '2011-11-24',
+                    '2011-12-25', '2011-05-30', '2011-02-21', '2011-01-17',
+                    '2011-12-26', '2012-01-02', '2011-02-21', '2011-05-30',
+                    '2011-07-01', '2011-07-04', '2011-09-05', '2011-10-10',
+                    'NaT']
+        bdd = np.busdaycalendar(weekmask='1111100', holidays=holidays)
+
+        # Weekend/weekday tests
+        assert_equal(np.is_busday('2011-01-01'), False)
+        assert_equal(np.is_busday('2011-01-02'), False)
+        assert_equal(np.is_busday('2011-01-03'), True)
+
+        # All the holidays are not business days
+        assert_equal(np.is_busday(holidays, busdaycal=bdd),
+                     np.zeros(len(holidays), dtype='?'))
+
+    def test_datetime_y2038(self):
+        msg = "no explicit representation of timezones available for " \
+              "np.datetime64"
+        # Test parsing on either side of the Y2038 boundary
+        a = np.datetime64('2038-01-19T03:14:07')
+        assert_equal(a.view(np.int64), 2**31 - 1)
+        a = np.datetime64('2038-01-19T03:14:08')
+        assert_equal(a.view(np.int64), 2**31)
+
+        # Test parsing on either side of the Y2038 boundary with
+        # a manually specified timezone offset
+        with pytest.warns(UserWarning, match=msg):
+            a = np.datetime64('2038-01-19T04:14:07+0100')
+            assert_equal(a.view(np.int64), 2**31 - 1)
+        with pytest.warns(UserWarning, match=msg):
+            a = np.datetime64('2038-01-19T04:14:08+0100')
+            assert_equal(a.view(np.int64), 2**31)
+
+        # Test parsing a date after Y2038
+        a = np.datetime64('2038-01-20T13:21:14')
+        assert_equal(str(a), '2038-01-20T13:21:14')
+
+    def test_isnat(self):
+        assert_(np.isnat(np.datetime64('NaT', 'ms')))
+        assert_(np.isnat(np.datetime64('NaT', 'ns')))
+        assert_(not np.isnat(np.datetime64('2038-01-19T03:14:07')))
+
+        assert_(np.isnat(np.timedelta64('NaT', "ms")))
+        assert_(not np.isnat(np.timedelta64(34, "ms")))
+
+        res = np.array([False, False, True])
+        for unit in ['Y', 'M', 'W', 'D',
+                     'h', 'm', 's', 'ms', 'us',
+                     'ns', 'ps', 'fs', 'as']:
+            arr = np.array([123, -321, "NaT"], dtype=f'<datetime64[{unit}]')
+            assert_equal(np.isnat(arr), res)
+            arr = np.array([123, -321, "NaT"], dtype=f'>datetime64[{unit}]')
+            assert_equal(np.isnat(arr), res)
+            arr = np.array([123, -321, "NaT"], dtype=f'<timedelta64[{unit}]')
+            assert_equal(np.isnat(arr), res)
+            arr = np.array([123, -321, "NaT"], dtype=f'>timedelta64[{unit}]')
+            assert_equal(np.isnat(arr), res)
+
+    def test_isnat_error(self):
+        # Test that only datetime dtype arrays are accepted
+        for t in np.typecodes["All"]:
+            if t in np.typecodes["Datetime"]:
+                continue
+            assert_raises(TypeError, np.isnat, np.zeros(10, t))
+
+    def test_isfinite_scalar(self):
+        assert_(not np.isfinite(np.datetime64('NaT', 'ms')))
+        assert_(not np.isfinite(np.datetime64('NaT', 'ns')))
+        assert_(np.isfinite(np.datetime64('2038-01-19T03:14:07')))
+
+        assert_(not np.isfinite(np.timedelta64('NaT', "ms")))
+        assert_(np.isfinite(np.timedelta64(34, "ms")))
+
+    @pytest.mark.parametrize('unit', ['Y', 'M', 'W', 'D', 'h', 'm', 's', 'ms',
+                                      'us', 'ns', 'ps', 'fs', 'as'])
+    @pytest.mark.parametrize('dstr', ['<datetime64[%s]', '>datetime64[%s]',
+                                      '<timedelta64[%s]', '>timedelta64[%s]'])
+    def test_isfinite_isinf_isnan_units(self, unit, dstr):
+        '''check isfinite, isinf, isnan for all units of <M, >M, <m, >m dtypes
+        '''
+        arr_val = [123, -321, "NaT"]
+        arr = np.array(arr_val, dtype=(dstr % unit))
+        pos = np.array([True, True, False])
+        neg = np.array([False, False, True])
+        false = np.array([False, False, False])
+        assert_equal(np.isfinite(arr), pos)
+        assert_equal(np.isinf(arr), false)
+        assert_equal(np.isnan(arr), neg)
+
+    def test_assert_equal(self):
+        assert_raises(AssertionError, assert_equal,
+                np.datetime64('nat'), np.timedelta64('nat'))
+
+    def test_corecursive_input(self):
+        # construct a co-recursive list
+        a, b = [], []
+        a.append(b)
+        b.append(a)
+        obj_arr = np.array([None])
+        obj_arr[0] = a
+
+        # At some point this caused a stack overflow (gh-11154). Now raises
+        # ValueError since the nested list cannot be converted to a datetime.
+        assert_raises(ValueError, obj_arr.astype, 'M8')
+        assert_raises(ValueError, obj_arr.astype, 'm8')
+
+    @pytest.mark.parametrize("shape", [(), (1,)])
+    def test_discovery_from_object_array(self, shape):
+        arr = np.array("2020-10-10", dtype=object).reshape(shape)
+        res = np.array("2020-10-10", dtype="M8").reshape(shape)
+        assert res.dtype == np.dtype("M8[D]")
+        assert_equal(arr.astype("M8"), res)
+        arr[...] = np.bytes_("2020-10-10")  # try a numpy string type
+        assert_equal(arr.astype("M8"), res)
+        arr = arr.astype("S")
+        assert_equal(arr.astype("S").astype("M8"), res)
+
+    @pytest.mark.parametrize("time_unit", [
+        "Y", "M", "W", "D", "h", "m", "s", "ms", "us", "ns", "ps", "fs", "as",
+        # compound units
+        "10D", "2M",
+    ])
+    def test_limit_symmetry(self, time_unit):
+        """
+        Dates should have symmetric limits around the unix epoch at +/-np.int64
+        """
+        epoch = np.datetime64(0, time_unit)
+        latest = np.datetime64(np.iinfo(np.int64).max, time_unit)
+        earliest = np.datetime64(-np.iinfo(np.int64).max, time_unit)
+
+        # above should not have overflowed
+        assert earliest < epoch < latest
+
+    @pytest.mark.parametrize("time_unit", [
+        "Y", "M",
+        pytest.param("W", marks=pytest.mark.xfail(reason="gh-13197")),
+        "D", "h", "m",
+        "s", "ms", "us", "ns", "ps", "fs", "as",
+        pytest.param("10D", marks=pytest.mark.xfail(reason="similar to gh-13197")),
+    ])
+    @pytest.mark.parametrize("sign", [-1, 1])
+    def test_limit_str_roundtrip(self, time_unit, sign):
+        """
+        Limits should roundtrip when converted to strings.
+
+        This tests the conversion to and from npy_datetimestruct.
+        """
+        # TODO: add absolute (gold standard) time span limit strings
+        limit = np.datetime64(np.iinfo(np.int64).max * sign, time_unit)
+
+        # Convert to string and back. Explicit unit needed since the day and
+        # week reprs are not distinguishable.
+        limit_via_str = np.datetime64(str(limit), time_unit)
+        assert limit_via_str == limit
+
+    def test_datetime_hash_nat(self):
+        nat1 = np.datetime64()
+        nat2 = np.datetime64()
+        assert nat1 is not nat2
+        assert nat1 != nat2
+        assert hash(nat1) != hash(nat2)
+
+    @pytest.mark.parametrize('unit', ('Y', 'M', 'W', 'D', 'h', 'm', 's', 'ms', 'us'))
+    def test_datetime_hash_weeks(self, unit):
+        dt = np.datetime64(2348, 'W')  # 2015-01-01
+        dt2 = np.datetime64(dt, unit)
+        _assert_equal_hash(dt, dt2)
+
+        dt3 = np.datetime64(int(dt2.astype(int)) + 1, unit)
+        assert hash(dt) != hash(dt3)  # doesn't collide
+
+    @pytest.mark.parametrize('unit', ('h', 'm', 's', 'ms', 'us'))
+    def test_datetime_hash_weeks_vs_pydatetime(self, unit):
+        dt = np.datetime64(2348, 'W')  # 2015-01-01
+        dt2 = np.datetime64(dt, unit)
+        pydt = dt2.astype(datetime.datetime)
+        assert isinstance(pydt, datetime.datetime)
+        _assert_equal_hash(pydt, dt2)
+
+    @pytest.mark.parametrize('unit', ('Y', 'M', 'W', 'D', 'h', 'm', 's', 'ms', 'us'))
+    def test_datetime_hash_big_negative(self, unit):
+        dt = np.datetime64(-102894, 'W')  # -002-01-01
+        dt2 = np.datetime64(dt, unit)
+        _assert_equal_hash(dt, dt2)
+
+    # can only go down to "fs" before integer overflow
+    @pytest.mark.parametrize('unit', ('m', 's', 'ms', 'us', 'ns', 'ps', 'fs'))
+    def test_datetime_hash_minutes(self, unit):
+        dt = np.datetime64(3, 'm')
+        dt2 = np.datetime64(dt, unit)
+        _assert_equal_hash(dt, dt2)
+
+    @pytest.mark.parametrize('unit', ('ns', 'ps', 'fs', 'as'))
+    def test_datetime_hash_ns(self, unit):
+        dt = np.datetime64(3, 'ns')
+        dt2 = np.datetime64(dt, unit)
+        _assert_equal_hash(dt, dt2)
+
+        dt3 = np.datetime64(int(dt2.astype(int)) + 1, unit)
+        assert hash(dt) != hash(dt3)  # doesn't collide
+
+    @pytest.mark.parametrize('wk', range(500000, 500010))  # 11552-09-04
+    @pytest.mark.parametrize('unit', ('W', 'D', 'h', 'm', 's', 'ms', 'us'))
+    def test_datetime_hash_big_positive(self, wk, unit):
+        dt = np.datetime64(wk, 'W')
+        dt2 = np.datetime64(dt, unit)
+        _assert_equal_hash(dt, dt2)
+
+    def test_timedelta_hash_generic(self):
+        assert_raises(ValueError, hash, np.timedelta64(123))  # generic
+
+    @pytest.mark.parametrize('unit', ('Y', 'M'))
+    def test_timedelta_hash_year_month(self, unit):
+        td = np.timedelta64(45, 'Y')
+        td2 = np.timedelta64(td, unit)
+        _assert_equal_hash(td, td2)
+
+    @pytest.mark.parametrize('unit', ('W', 'D', 'h', 'm', 's', 'ms', 'us'))
+    def test_timedelta_hash_weeks(self, unit):
+        td = np.timedelta64(10, 'W')
+        td2 = np.timedelta64(td, unit)
+        _assert_equal_hash(td, td2)
+
+        td3 = np.timedelta64(int(td2.astype(int)) + 1, unit)
+        assert hash(td) != hash(td3)  # doesn't collide
+
+    @pytest.mark.parametrize('unit', ('W', 'D', 'h', 'm', 's', 'ms', 'us'))
+    def test_timedelta_hash_weeks_vs_pydelta(self, unit):
+        td = np.timedelta64(10, 'W')
+        td2 = np.timedelta64(td, unit)
+        pytd = td2.astype(datetime.timedelta)
+        assert isinstance(pytd, datetime.timedelta)
+        _assert_equal_hash(pytd, td2)
+
+    @pytest.mark.parametrize('unit', ('ms', 'us', 'ns', 'ps', 'fs', 'as'))
+    def test_timedelta_hash_ms(self, unit):
+        td = np.timedelta64(3, 'ms')
+        td2 = np.timedelta64(td, unit)
+        _assert_equal_hash(td, td2)
+
+        td3 = np.timedelta64(int(td2.astype(int)) + 1, unit)
+        assert hash(td) != hash(td3)  # doesn't collide
+
+    @pytest.mark.parametrize('wk', range(500000, 500010))
+    @pytest.mark.parametrize('unit', ('W', 'D', 'h', 'm', 's', 'ms', 'us'))
+    def test_timedelta_hash_big_positive(self, wk, unit):
+        td = np.timedelta64(wk, 'W')
+        td2 = np.timedelta64(td, unit)
+        _assert_equal_hash(td, td2)
+
+
+class TestDateTimeData:
+
+    def test_basic(self):
+        a = np.array(['1980-03-23'], dtype=np.datetime64)
+        assert_equal(np.datetime_data(a.dtype), ('D', 1))
+
+    def test_bytes(self):
+        # byte units are converted to unicode
+        dt = np.datetime64('2000', (b'ms', 5))
+        assert np.datetime_data(dt.dtype) == ('ms', 5)
+
+        dt = np.datetime64('2000', b'5ms')
+        assert np.datetime_data(dt.dtype) == ('ms', 5)
+
+    def test_non_ascii(self):
+        # μs is normalized to μ
+        dt = np.datetime64('2000', ('μs', 5))
+        assert np.datetime_data(dt.dtype) == ('us', 5)
+
+        dt = np.datetime64('2000', '5μs')
+        assert np.datetime_data(dt.dtype) == ('us', 5)
+
+
+def test_comparisons_return_not_implemented():
+    # GH#17017
+
+    class custom:
+        __array_priority__ = 10000
+
+    obj = custom()
+
+    dt = np.datetime64('2000', 'ns')
+    td = dt - dt
+
+    for item in [dt, td]:
+        assert item.__eq__(obj) is NotImplemented
+        assert item.__ne__(obj) is NotImplemented
+        assert item.__le__(obj) is NotImplemented
+        assert item.__lt__(obj) is NotImplemented
+        assert item.__ge__(obj) is NotImplemented
+        assert item.__gt__(obj) is NotImplemented
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_defchararray.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_defchararray.py
new file mode 100644
index 0000000..2607953
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_defchararray.py
@@ -0,0 +1,825 @@
+import pytest
+
+import numpy as np
+from numpy._core.multiarray import _vec_string
+from numpy.testing import (
+    assert_,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+)
+
+kw_unicode_true = {'unicode': True}  # make 2to3 work properly
+kw_unicode_false = {'unicode': False}
+
+class TestBasic:
+    def test_from_object_array(self):
+        A = np.array([['abc', 2],
+                      ['long   ', '0123456789']], dtype='O')
+        B = np.char.array(A)
+        assert_equal(B.dtype.itemsize, 10)
+        assert_array_equal(B, [[b'abc', b'2'],
+                               [b'long', b'0123456789']])
+
+    def test_from_object_array_unicode(self):
+        A = np.array([['abc', 'Sigma \u03a3'],
+                      ['long   ', '0123456789']], dtype='O')
+        assert_raises(ValueError, np.char.array, (A,))
+        B = np.char.array(A, **kw_unicode_true)
+        assert_equal(B.dtype.itemsize, 10 * np.array('a', 'U').dtype.itemsize)
+        assert_array_equal(B, [['abc', 'Sigma \u03a3'],
+                               ['long', '0123456789']])
+
+    def test_from_string_array(self):
+        A = np.array([[b'abc', b'foo'],
+                      [b'long   ', b'0123456789']])
+        assert_equal(A.dtype.type, np.bytes_)
+        B = np.char.array(A)
+        assert_array_equal(B, A)
+        assert_equal(B.dtype, A.dtype)
+        assert_equal(B.shape, A.shape)
+        B[0, 0] = 'changed'
+        assert_(B[0, 0] != A[0, 0])
+        C = np.char.asarray(A)
+        assert_array_equal(C, A)
+        assert_equal(C.dtype, A.dtype)
+        C[0, 0] = 'changed again'
+        assert_(C[0, 0] != B[0, 0])
+        assert_(C[0, 0] == A[0, 0])
+
+    def test_from_unicode_array(self):
+        A = np.array([['abc', 'Sigma \u03a3'],
+                      ['long   ', '0123456789']])
+        assert_equal(A.dtype.type, np.str_)
+        B = np.char.array(A)
+        assert_array_equal(B, A)
+        assert_equal(B.dtype, A.dtype)
+        assert_equal(B.shape, A.shape)
+        B = np.char.array(A, **kw_unicode_true)
+        assert_array_equal(B, A)
+        assert_equal(B.dtype, A.dtype)
+        assert_equal(B.shape, A.shape)
+
+        def fail():
+            np.char.array(A, **kw_unicode_false)
+
+        assert_raises(UnicodeEncodeError, fail)
+
+    def test_unicode_upconvert(self):
+        A = np.char.array(['abc'])
+        B = np.char.array(['\u03a3'])
+        assert_(issubclass((A + B).dtype.type, np.str_))
+
+    def test_from_string(self):
+        A = np.char.array(b'abc')
+        assert_equal(len(A), 1)
+        assert_equal(len(A[0]), 3)
+        assert_(issubclass(A.dtype.type, np.bytes_))
+
+    def test_from_unicode(self):
+        A = np.char.array('\u03a3')
+        assert_equal(len(A), 1)
+        assert_equal(len(A[0]), 1)
+        assert_equal(A.itemsize, 4)
+        assert_(issubclass(A.dtype.type, np.str_))
+
+class TestVecString:
+    def test_non_existent_method(self):
+
+        def fail():
+            _vec_string('a', np.bytes_, 'bogus')
+
+        assert_raises(AttributeError, fail)
+
+    def test_non_string_array(self):
+
+        def fail():
+            _vec_string(1, np.bytes_, 'strip')
+
+        assert_raises(TypeError, fail)
+
+    def test_invalid_args_tuple(self):
+
+        def fail():
+            _vec_string(['a'], np.bytes_, 'strip', 1)
+
+        assert_raises(TypeError, fail)
+
+    def test_invalid_type_descr(self):
+
+        def fail():
+            _vec_string(['a'], 'BOGUS', 'strip')
+
+        assert_raises(TypeError, fail)
+
+    def test_invalid_function_args(self):
+
+        def fail():
+            _vec_string(['a'], np.bytes_, 'strip', (1,))
+
+        assert_raises(TypeError, fail)
+
+    def test_invalid_result_type(self):
+
+        def fail():
+            _vec_string(['a'], np.int_, 'strip')
+
+        assert_raises(TypeError, fail)
+
+    def test_broadcast_error(self):
+
+        def fail():
+            _vec_string([['abc', 'def']], np.int_, 'find', (['a', 'd', 'j'],))
+
+        assert_raises(ValueError, fail)
+
+
+class TestWhitespace:
+    def setup_method(self):
+        self.A = np.array([['abc ', '123  '],
+                           ['789 ', 'xyz ']]).view(np.char.chararray)
+        self.B = np.array([['abc', '123'],
+                           ['789', 'xyz']]).view(np.char.chararray)
+
+    def test1(self):
+        assert_(np.all(self.A == self.B))
+        assert_(np.all(self.A >= self.B))
+        assert_(np.all(self.A <= self.B))
+        assert_(not np.any(self.A > self.B))
+        assert_(not np.any(self.A < self.B))
+        assert_(not np.any(self.A != self.B))
+
+class TestChar:
+    def setup_method(self):
+        self.A = np.array('abc1', dtype='c').view(np.char.chararray)
+
+    def test_it(self):
+        assert_equal(self.A.shape, (4,))
+        assert_equal(self.A.upper()[:2].tobytes(), b'AB')
+
+class TestComparisons:
+    def setup_method(self):
+        self.A = np.array([['abc', 'abcc', '123'],
+                           ['789', 'abc', 'xyz']]).view(np.char.chararray)
+        self.B = np.array([['efg', 'efg', '123  '],
+                           ['051', 'efgg', 'tuv']]).view(np.char.chararray)
+
+    def test_not_equal(self):
+        assert_array_equal((self.A != self.B),
+                           [[True, True, False], [True, True, True]])
+
+    def test_equal(self):
+        assert_array_equal((self.A == self.B),
+                           [[False, False, True], [False, False, False]])
+
+    def test_greater_equal(self):
+        assert_array_equal((self.A >= self.B),
+                           [[False, False, True], [True, False, True]])
+
+    def test_less_equal(self):
+        assert_array_equal((self.A <= self.B),
+                           [[True, True, True], [False, True, False]])
+
+    def test_greater(self):
+        assert_array_equal((self.A > self.B),
+                           [[False, False, False], [True, False, True]])
+
+    def test_less(self):
+        assert_array_equal((self.A < self.B),
+                           [[True, True, False], [False, True, False]])
+
+    def test_type(self):
+        out1 = np.char.equal(self.A, self.B)
+        out2 = np.char.equal('a', 'a')
+        assert_(isinstance(out1, np.ndarray))
+        assert_(isinstance(out2, np.ndarray))
+
+class TestComparisonsMixed1(TestComparisons):
+    """Ticket #1276"""
+
+    def setup_method(self):
+        TestComparisons.setup_method(self)
+        self.B = np.array(
+            [['efg', 'efg', '123  '],
+             ['051', 'efgg', 'tuv']], np.str_).view(np.char.chararray)
+
+class TestComparisonsMixed2(TestComparisons):
+    """Ticket #1276"""
+
+    def setup_method(self):
+        TestComparisons.setup_method(self)
+        self.A = np.array(
+            [['abc', 'abcc', '123'],
+             ['789', 'abc', 'xyz']], np.str_).view(np.char.chararray)
+
+class TestInformation:
+    def setup_method(self):
+        self.A = np.array([[' abc ', ''],
+                           ['12345', 'MixedCase'],
+                           ['123 \t 345 \0 ', 'UPPER']]) \
+                            .view(np.char.chararray)
+        self.B = np.array([[' \u03a3 ', ''],
+                           ['12345', 'MixedCase'],
+                           ['123 \t 345 \0 ', 'UPPER']]) \
+                            .view(np.char.chararray)
+        # Array with longer strings, > MEMCHR_CUT_OFF in code.
+        self.C = (np.array(['ABCDEFGHIJKLMNOPQRSTUVWXYZ',
+                            '01234567890123456789012345'])
+                  .view(np.char.chararray))
+
+    def test_len(self):
+        assert_(issubclass(np.char.str_len(self.A).dtype.type, np.integer))
+        assert_array_equal(np.char.str_len(self.A), [[5, 0], [5, 9], [12, 5]])
+        assert_array_equal(np.char.str_len(self.B), [[3, 0], [5, 9], [12, 5]])
+
+    def test_count(self):
+        assert_(issubclass(self.A.count('').dtype.type, np.integer))
+        assert_array_equal(self.A.count('a'), [[1, 0], [0, 1], [0, 0]])
+        assert_array_equal(self.A.count('123'), [[0, 0], [1, 0], [1, 0]])
+        # Python doesn't seem to like counting NULL characters
+        # assert_array_equal(self.A.count('\0'), [[0, 0], [0, 0], [1, 0]])
+        assert_array_equal(self.A.count('a', 0, 2), [[1, 0], [0, 0], [0, 0]])
+        assert_array_equal(self.B.count('a'), [[0, 0], [0, 1], [0, 0]])
+        assert_array_equal(self.B.count('123'), [[0, 0], [1, 0], [1, 0]])
+        # assert_array_equal(self.B.count('\0'), [[0, 0], [0, 0], [1, 0]])
+
+    def test_endswith(self):
+        assert_(issubclass(self.A.endswith('').dtype.type, np.bool))
+        assert_array_equal(self.A.endswith(' '), [[1, 0], [0, 0], [1, 0]])
+        assert_array_equal(self.A.endswith('3', 0, 3), [[0, 0], [1, 0], [1, 0]])
+
+        def fail():
+            self.A.endswith('3', 'fdjk')
+
+        assert_raises(TypeError, fail)
+
+    @pytest.mark.parametrize(
+        "dtype, encode",
+        [("U", str),
+         ("S", lambda x: x.encode('ascii')),
+         ])
+    def test_find(self, dtype, encode):
+        A = self.A.astype(dtype)
+        assert_(issubclass(A.find(encode('a')).dtype.type, np.integer))
+        assert_array_equal(A.find(encode('a')),
+                           [[1, -1], [-1, 6], [-1, -1]])
+        assert_array_equal(A.find(encode('3')),
+                           [[-1, -1], [2, -1], [2, -1]])
+        assert_array_equal(A.find(encode('a'), 0, 2),
+                           [[1, -1], [-1, -1], [-1, -1]])
+        assert_array_equal(A.find([encode('1'), encode('P')]),
+                           [[-1, -1], [0, -1], [0, 1]])
+        C = self.C.astype(dtype)
+        assert_array_equal(C.find(encode('M')), [12, -1])
+
+    def test_index(self):
+
+        def fail():
+            self.A.index('a')
+
+        assert_raises(ValueError, fail)
+        assert_(np.char.index('abcba', 'b') == 1)
+        assert_(issubclass(np.char.index('abcba', 'b').dtype.type, np.integer))
+
+    def test_isalnum(self):
+        assert_(issubclass(self.A.isalnum().dtype.type, np.bool))
+        assert_array_equal(self.A.isalnum(), [[False, False], [True, True], [False, True]])
+
+    def test_isalpha(self):
+        assert_(issubclass(self.A.isalpha().dtype.type, np.bool))
+        assert_array_equal(self.A.isalpha(), [[False, False], [False, True], [False, True]])
+
+    def test_isdigit(self):
+        assert_(issubclass(self.A.isdigit().dtype.type, np.bool))
+        assert_array_equal(self.A.isdigit(), [[False, False], [True, False], [False, False]])
+
+    def test_islower(self):
+        assert_(issubclass(self.A.islower().dtype.type, np.bool))
+        assert_array_equal(self.A.islower(), [[True, False], [False, False], [False, False]])
+
+    def test_isspace(self):
+        assert_(issubclass(self.A.isspace().dtype.type, np.bool))
+        assert_array_equal(self.A.isspace(), [[False, False], [False, False], [False, False]])
+
+    def test_istitle(self):
+        assert_(issubclass(self.A.istitle().dtype.type, np.bool))
+        assert_array_equal(self.A.istitle(), [[False, False], [False, False], [False, False]])
+
+    def test_isupper(self):
+        assert_(issubclass(self.A.isupper().dtype.type, np.bool))
+        assert_array_equal(self.A.isupper(), [[False, False], [False, False], [False, True]])
+
+    def test_rfind(self):
+        assert_(issubclass(self.A.rfind('a').dtype.type, np.integer))
+        assert_array_equal(self.A.rfind('a'), [[1, -1], [-1, 6], [-1, -1]])
+        assert_array_equal(self.A.rfind('3'), [[-1, -1], [2, -1], [6, -1]])
+        assert_array_equal(self.A.rfind('a', 0, 2), [[1, -1], [-1, -1], [-1, -1]])
+        assert_array_equal(self.A.rfind(['1', 'P']), [[-1, -1], [0, -1], [0, 2]])
+
+    def test_rindex(self):
+
+        def fail():
+            self.A.rindex('a')
+
+        assert_raises(ValueError, fail)
+        assert_(np.char.rindex('abcba', 'b') == 3)
+        assert_(issubclass(np.char.rindex('abcba', 'b').dtype.type, np.integer))
+
+    def test_startswith(self):
+        assert_(issubclass(self.A.startswith('').dtype.type, np.bool))
+        assert_array_equal(self.A.startswith(' '), [[1, 0], [0, 0], [0, 0]])
+        assert_array_equal(self.A.startswith('1', 0, 3), [[0, 0], [1, 0], [1, 0]])
+
+        def fail():
+            self.A.startswith('3', 'fdjk')
+
+        assert_raises(TypeError, fail)
+
+
+class TestMethods:
+    def setup_method(self):
+        self.A = np.array([[' abc ', ''],
+                           ['12345', 'MixedCase'],
+                           ['123 \t 345 \0 ', 'UPPER']],
+                          dtype='S').view(np.char.chararray)
+        self.B = np.array([[' \u03a3 ', ''],
+                           ['12345', 'MixedCase'],
+                           ['123 \t 345 \0 ', 'UPPER']]).view(
+                                                            np.char.chararray)
+
+    def test_capitalize(self):
+        tgt = [[b' abc ', b''],
+               [b'12345', b'Mixedcase'],
+               [b'123 \t 345 \0 ', b'Upper']]
+        assert_(issubclass(self.A.capitalize().dtype.type, np.bytes_))
+        assert_array_equal(self.A.capitalize(), tgt)
+
+        tgt = [[' \u03c3 ', ''],
+               ['12345', 'Mixedcase'],
+               ['123 \t 345 \0 ', 'Upper']]
+        assert_(issubclass(self.B.capitalize().dtype.type, np.str_))
+        assert_array_equal(self.B.capitalize(), tgt)
+
+    def test_center(self):
+        assert_(issubclass(self.A.center(10).dtype.type, np.bytes_))
+        C = self.A.center([10, 20])
+        assert_array_equal(np.char.str_len(C), [[10, 20], [10, 20], [12, 20]])
+
+        C = self.A.center(20, b'#')
+        assert_(np.all(C.startswith(b'#')))
+        assert_(np.all(C.endswith(b'#')))
+
+        C = np.char.center(b'FOO', [[10, 20], [15, 8]])
+        tgt = [[b'   FOO    ', b'        FOO         '],
+               [b'      FOO      ', b'  FOO   ']]
+        assert_(issubclass(C.dtype.type, np.bytes_))
+        assert_array_equal(C, tgt)
+
+    def test_decode(self):
+        A = np.char.array([b'\\u03a3'])
+        assert_(A.decode('unicode-escape')[0] == '\u03a3')
+
+    def test_encode(self):
+        B = self.B.encode('unicode_escape')
+        assert_(B[0][0] == ' \\u03a3 '.encode('latin1'))
+
+    def test_expandtabs(self):
+        T = self.A.expandtabs()
+        assert_(T[2, 0] == b'123      345 \0')
+
+    def test_join(self):
+        # NOTE: list(b'123') == [49, 50, 51]
+        #       so that b','.join(b'123') results to an error on Py3
+        A0 = self.A.decode('ascii')
+
+        A = np.char.join([',', '#'], A0)
+        assert_(issubclass(A.dtype.type, np.str_))
+        tgt = np.array([[' ,a,b,c, ', ''],
+                        ['1,2,3,4,5', 'M#i#x#e#d#C#a#s#e'],
+                        ['1,2,3, ,\t, ,3,4,5, ,\x00, ', 'U#P#P#E#R']])
+        assert_array_equal(np.char.join([',', '#'], A0), tgt)
+
+    def test_ljust(self):
+        assert_(issubclass(self.A.ljust(10).dtype.type, np.bytes_))
+
+        C = self.A.ljust([10, 20])
+        assert_array_equal(np.char.str_len(C), [[10, 20], [10, 20], [12, 20]])
+
+        C = self.A.ljust(20, b'#')
+        assert_array_equal(C.startswith(b'#'), [
+                [False, True], [False, False], [False, False]])
+        assert_(np.all(C.endswith(b'#')))
+
+        C = np.char.ljust(b'FOO', [[10, 20], [15, 8]])
+        tgt = [[b'FOO       ', b'FOO                 '],
+               [b'FOO            ', b'FOO     ']]
+        assert_(issubclass(C.dtype.type, np.bytes_))
+        assert_array_equal(C, tgt)
+
+    def test_lower(self):
+        tgt = [[b' abc ', b''],
+               [b'12345', b'mixedcase'],
+               [b'123 \t 345 \0 ', b'upper']]
+        assert_(issubclass(self.A.lower().dtype.type, np.bytes_))
+        assert_array_equal(self.A.lower(), tgt)
+
+        tgt = [[' \u03c3 ', ''],
+               ['12345', 'mixedcase'],
+               ['123 \t 345 \0 ', 'upper']]
+        assert_(issubclass(self.B.lower().dtype.type, np.str_))
+        assert_array_equal(self.B.lower(), tgt)
+
+    def test_lstrip(self):
+        tgt = [[b'abc ', b''],
+               [b'12345', b'MixedCase'],
+               [b'123 \t 345 \0 ', b'UPPER']]
+        assert_(issubclass(self.A.lstrip().dtype.type, np.bytes_))
+        assert_array_equal(self.A.lstrip(), tgt)
+
+        tgt = [[b' abc', b''],
+               [b'2345', b'ixedCase'],
+               [b'23 \t 345 \x00', b'UPPER']]
+        assert_array_equal(self.A.lstrip([b'1', b'M']), tgt)
+
+        tgt = [['\u03a3 ', ''],
+               ['12345', 'MixedCase'],
+               ['123 \t 345 \0 ', 'UPPER']]
+        assert_(issubclass(self.B.lstrip().dtype.type, np.str_))
+        assert_array_equal(self.B.lstrip(), tgt)
+
+    def test_partition(self):
+        P = self.A.partition([b'3', b'M'])
+        tgt = [[(b' abc ', b'', b''), (b'', b'', b'')],
+               [(b'12', b'3', b'45'), (b'', b'M', b'ixedCase')],
+               [(b'12', b'3', b' \t 345 \0 '), (b'UPPER', b'', b'')]]
+        assert_(issubclass(P.dtype.type, np.bytes_))
+        assert_array_equal(P, tgt)
+
+    def test_replace(self):
+        R = self.A.replace([b'3', b'a'],
+                           [b'##########', b'@'])
+        tgt = [[b' abc ', b''],
+               [b'12##########45', b'MixedC@se'],
+               [b'12########## \t ##########45 \x00 ', b'UPPER']]
+        assert_(issubclass(R.dtype.type, np.bytes_))
+        assert_array_equal(R, tgt)
+        # Test special cases that should just return the input array,
+        # since replacements are not possible or do nothing.
+        S1 = self.A.replace(b'A very long byte string, longer than A', b'')
+        assert_array_equal(S1, self.A)
+        S2 = self.A.replace(b'', b'')
+        assert_array_equal(S2, self.A)
+        S3 = self.A.replace(b'3', b'3')
+        assert_array_equal(S3, self.A)
+        S4 = self.A.replace(b'3', b'', count=0)
+        assert_array_equal(S4, self.A)
+
+    def test_replace_count_and_size(self):
+        a = np.array(['0123456789' * i for i in range(4)]
+                     ).view(np.char.chararray)
+        r1 = a.replace('5', 'ABCDE')
+        assert r1.dtype.itemsize == (3 * 10 + 3 * 4) * 4
+        assert_array_equal(r1, np.array(['01234ABCDE6789' * i
+                                         for i in range(4)]))
+        r2 = a.replace('5', 'ABCDE', count=1)
+        assert r2.dtype.itemsize == (3 * 10 + 4) * 4
+        r3 = a.replace('5', 'ABCDE', count=0)
+        assert r3.dtype.itemsize == a.dtype.itemsize
+        assert_array_equal(r3, a)
+        # Negative values mean to replace all.
+        r4 = a.replace('5', 'ABCDE', count=-1)
+        assert r4.dtype.itemsize == (3 * 10 + 3 * 4) * 4
+        assert_array_equal(r4, r1)
+        # We can do count on an element-by-element basis.
+        r5 = a.replace('5', 'ABCDE', count=[-1, -1, -1, 1])
+        assert r5.dtype.itemsize == (3 * 10 + 4) * 4
+        assert_array_equal(r5, np.array(
+            ['01234ABCDE6789' * i for i in range(3)]
+            + ['01234ABCDE6789' + '0123456789' * 2]))
+
+    def test_replace_broadcasting(self):
+        a = np.array('0,0,0').view(np.char.chararray)
+        r1 = a.replace('0', '1', count=np.arange(3))
+        assert r1.dtype == a.dtype
+        assert_array_equal(r1, np.array(['0,0,0', '1,0,0', '1,1,0']))
+        r2 = a.replace('0', [['1'], ['2']], count=np.arange(1, 4))
+        assert_array_equal(r2, np.array([['1,0,0', '1,1,0', '1,1,1'],
+                                         ['2,0,0', '2,2,0', '2,2,2']]))
+        r3 = a.replace(['0', '0,0', '0,0,0'], 'X')
+        assert_array_equal(r3, np.array(['X,X,X', 'X,0', 'X']))
+
+    def test_rjust(self):
+        assert_(issubclass(self.A.rjust(10).dtype.type, np.bytes_))
+
+        C = self.A.rjust([10, 20])
+        assert_array_equal(np.char.str_len(C), [[10, 20], [10, 20], [12, 20]])
+
+        C = self.A.rjust(20, b'#')
+        assert_(np.all(C.startswith(b'#')))
+        assert_array_equal(C.endswith(b'#'),
+                           [[False, True], [False, False], [False, False]])
+
+        C = np.char.rjust(b'FOO', [[10, 20], [15, 8]])
+        tgt = [[b'       FOO', b'                 FOO'],
+               [b'            FOO', b'     FOO']]
+        assert_(issubclass(C.dtype.type, np.bytes_))
+        assert_array_equal(C, tgt)
+
+    def test_rpartition(self):
+        P = self.A.rpartition([b'3', b'M'])
+        tgt = [[(b'', b'', b' abc '), (b'', b'', b'')],
+               [(b'12', b'3', b'45'), (b'', b'M', b'ixedCase')],
+               [(b'123 \t ', b'3', b'45 \0 '), (b'', b'', b'UPPER')]]
+        assert_(issubclass(P.dtype.type, np.bytes_))
+        assert_array_equal(P, tgt)
+
+    def test_rsplit(self):
+        A = self.A.rsplit(b'3')
+        tgt = [[[b' abc '], [b'']],
+               [[b'12', b'45'], [b'MixedCase']],
+               [[b'12', b' \t ', b'45 \x00 '], [b'UPPER']]]
+        assert_(issubclass(A.dtype.type, np.object_))
+        assert_equal(A.tolist(), tgt)
+
+    def test_rstrip(self):
+        assert_(issubclass(self.A.rstrip().dtype.type, np.bytes_))
+
+        tgt = [[b' abc', b''],
+               [b'12345', b'MixedCase'],
+               [b'123 \t 345', b'UPPER']]
+        assert_array_equal(self.A.rstrip(), tgt)
+
+        tgt = [[b' abc ', b''],
+               [b'1234', b'MixedCase'],
+               [b'123 \t 345 \x00', b'UPP']
+               ]
+        assert_array_equal(self.A.rstrip([b'5', b'ER']), tgt)
+
+        tgt = [[' \u03a3', ''],
+               ['12345', 'MixedCase'],
+               ['123 \t 345', 'UPPER']]
+        assert_(issubclass(self.B.rstrip().dtype.type, np.str_))
+        assert_array_equal(self.B.rstrip(), tgt)
+
+    def test_strip(self):
+        tgt = [[b'abc', b''],
+               [b'12345', b'MixedCase'],
+               [b'123 \t 345', b'UPPER']]
+        assert_(issubclass(self.A.strip().dtype.type, np.bytes_))
+        assert_array_equal(self.A.strip(), tgt)
+
+        tgt = [[b' abc ', b''],
+               [b'234', b'ixedCas'],
+               [b'23 \t 345 \x00', b'UPP']]
+        assert_array_equal(self.A.strip([b'15', b'EReM']), tgt)
+
+        tgt = [['\u03a3', ''],
+               ['12345', 'MixedCase'],
+               ['123 \t 345', 'UPPER']]
+        assert_(issubclass(self.B.strip().dtype.type, np.str_))
+        assert_array_equal(self.B.strip(), tgt)
+
+    def test_split(self):
+        A = self.A.split(b'3')
+        tgt = [
+               [[b' abc '], [b'']],
+               [[b'12', b'45'], [b'MixedCase']],
+               [[b'12', b' \t ', b'45 \x00 '], [b'UPPER']]]
+        assert_(issubclass(A.dtype.type, np.object_))
+        assert_equal(A.tolist(), tgt)
+
+    def test_splitlines(self):
+        A = np.char.array(['abc\nfds\nwer']).splitlines()
+        assert_(issubclass(A.dtype.type, np.object_))
+        assert_(A.shape == (1,))
+        assert_(len(A[0]) == 3)
+
+    def test_swapcase(self):
+        tgt = [[b' ABC ', b''],
+               [b'12345', b'mIXEDcASE'],
+               [b'123 \t 345 \0 ', b'upper']]
+        assert_(issubclass(self.A.swapcase().dtype.type, np.bytes_))
+        assert_array_equal(self.A.swapcase(), tgt)
+
+        tgt = [[' \u03c3 ', ''],
+               ['12345', 'mIXEDcASE'],
+               ['123 \t 345 \0 ', 'upper']]
+        assert_(issubclass(self.B.swapcase().dtype.type, np.str_))
+        assert_array_equal(self.B.swapcase(), tgt)
+
+    def test_title(self):
+        tgt = [[b' Abc ', b''],
+               [b'12345', b'Mixedcase'],
+               [b'123 \t 345 \0 ', b'Upper']]
+        assert_(issubclass(self.A.title().dtype.type, np.bytes_))
+        assert_array_equal(self.A.title(), tgt)
+
+        tgt = [[' \u03a3 ', ''],
+               ['12345', 'Mixedcase'],
+               ['123 \t 345 \0 ', 'Upper']]
+        assert_(issubclass(self.B.title().dtype.type, np.str_))
+        assert_array_equal(self.B.title(), tgt)
+
+    def test_upper(self):
+        tgt = [[b' ABC ', b''],
+               [b'12345', b'MIXEDCASE'],
+               [b'123 \t 345 \0 ', b'UPPER']]
+        assert_(issubclass(self.A.upper().dtype.type, np.bytes_))
+        assert_array_equal(self.A.upper(), tgt)
+
+        tgt = [[' \u03a3 ', ''],
+               ['12345', 'MIXEDCASE'],
+               ['123 \t 345 \0 ', 'UPPER']]
+        assert_(issubclass(self.B.upper().dtype.type, np.str_))
+        assert_array_equal(self.B.upper(), tgt)
+
+    def test_isnumeric(self):
+
+        def fail():
+            self.A.isnumeric()
+
+        assert_raises(TypeError, fail)
+        assert_(issubclass(self.B.isnumeric().dtype.type, np.bool))
+        assert_array_equal(self.B.isnumeric(), [
+                [False, False], [True, False], [False, False]])
+
+    def test_isdecimal(self):
+
+        def fail():
+            self.A.isdecimal()
+
+        assert_raises(TypeError, fail)
+        assert_(issubclass(self.B.isdecimal().dtype.type, np.bool))
+        assert_array_equal(self.B.isdecimal(), [
+                [False, False], [True, False], [False, False]])
+
+
+class TestOperations:
+    def setup_method(self):
+        self.A = np.array([['abc', '123'],
+                           ['789', 'xyz']]).view(np.char.chararray)
+        self.B = np.array([['efg', '456'],
+                           ['051', 'tuv']]).view(np.char.chararray)
+
+    def test_add(self):
+        AB = np.array([['abcefg', '123456'],
+                       ['789051', 'xyztuv']]).view(np.char.chararray)
+        assert_array_equal(AB, (self.A + self.B))
+        assert_(len((self.A + self.B)[0][0]) == 6)
+
+    def test_radd(self):
+        QA = np.array([['qabc', 'q123'],
+                       ['q789', 'qxyz']]).view(np.char.chararray)
+        assert_array_equal(QA, ('q' + self.A))
+
+    def test_mul(self):
+        A = self.A
+        for r in (2, 3, 5, 7, 197):
+            Ar = np.array([[A[0, 0] * r, A[0, 1] * r],
+                           [A[1, 0] * r, A[1, 1] * r]]).view(np.char.chararray)
+
+            assert_array_equal(Ar, (self.A * r))
+
+        for ob in [object(), 'qrs']:
+            with assert_raises_regex(ValueError,
+                                     'Can only multiply by integers'):
+                A * ob
+
+    def test_rmul(self):
+        A = self.A
+        for r in (2, 3, 5, 7, 197):
+            Ar = np.array([[A[0, 0] * r, A[0, 1] * r],
+                           [A[1, 0] * r, A[1, 1] * r]]).view(np.char.chararray)
+            assert_array_equal(Ar, (r * self.A))
+
+        for ob in [object(), 'qrs']:
+            with assert_raises_regex(ValueError,
+                                     'Can only multiply by integers'):
+                ob * A
+
+    def test_mod(self):
+        """Ticket #856"""
+        F = np.array([['%d', '%f'], ['%s', '%r']]).view(np.char.chararray)
+        C = np.array([[3, 7], [19, 1]], dtype=np.int64)
+        FC = np.array([['3', '7.000000'],
+                       ['19', 'np.int64(1)']]).view(np.char.chararray)
+        assert_array_equal(FC, F % C)
+
+        A = np.array([['%.3f', '%d'], ['%s', '%r']]).view(np.char.chararray)
+        A1 = np.array([['1.000', '1'],
+                       ['1', repr(np.array(1)[()])]]).view(np.char.chararray)
+        assert_array_equal(A1, (A % 1))
+
+        A2 = np.array([['1.000', '2'],
+                       ['3', repr(np.array(4)[()])]]).view(np.char.chararray)
+        assert_array_equal(A2, (A % [[1, 2], [3, 4]]))
+
+    def test_rmod(self):
+        assert_(f"{self.A}" == str(self.A))
+        assert_(f"{self.A!r}" == repr(self.A))
+
+        for ob in [42, object()]:
+            with assert_raises_regex(
+                    TypeError, "unsupported operand type.* and 'chararray'"):
+                ob % self.A
+
+    def test_slice(self):
+        """Regression test for https://github.com/numpy/numpy/issues/5982"""
+
+        arr = np.array([['abc ', 'def '], ['geh ', 'ijk ']],
+                       dtype='S4').view(np.char.chararray)
+        sl1 = arr[:]
+        assert_array_equal(sl1, arr)
+        assert_(sl1.base is arr)
+        assert_(sl1.base.base is arr.base)
+
+        sl2 = arr[:, :]
+        assert_array_equal(sl2, arr)
+        assert_(sl2.base is arr)
+        assert_(sl2.base.base is arr.base)
+
+        assert_(arr[0, 0] == b'abc')
+
+    @pytest.mark.parametrize('data', [['plate', '   ', 'shrimp'],
+                                      [b'retro', b'  ', b'encabulator']])
+    def test_getitem_length_zero_item(self, data):
+        # Regression test for gh-26375.
+        a = np.char.array(data)
+        # a.dtype.type() will be an empty string or bytes instance.
+        # The equality test will fail if a[1] has the wrong type
+        # or does not have length 0.
+        assert_equal(a[1], a.dtype.type())
+
+
+class TestMethodsEmptyArray:
+    def setup_method(self):
+        self.U = np.array([], dtype='U')
+        self.S = np.array([], dtype='S')
+
+    def test_encode(self):
+        res = np.char.encode(self.U)
+        assert_array_equal(res, [])
+        assert_(res.dtype.char == 'S')
+
+    def test_decode(self):
+        res = np.char.decode(self.S)
+        assert_array_equal(res, [])
+        assert_(res.dtype.char == 'U')
+
+    def test_decode_with_reshape(self):
+        res = np.char.decode(self.S.reshape((1, 0, 1)))
+        assert_(res.shape == (1, 0, 1))
+
+
+class TestMethodsScalarValues:
+    def test_mod(self):
+        A = np.array([[' abc ', ''],
+                      ['12345', 'MixedCase'],
+                      ['123 \t 345 \0 ', 'UPPER']], dtype='S')
+        tgt = [[b'123 abc ', b'123'],
+               [b'12312345', b'123MixedCase'],
+               [b'123123 \t 345 \0 ', b'123UPPER']]
+        assert_array_equal(np.char.mod(b"123%s", A), tgt)
+
+    def test_decode(self):
+        bytestring = b'\x81\xc1\x81\xc1\x81\xc1'
+        assert_equal(np.char.decode(bytestring, encoding='cp037'),
+                     'aAaAaA')
+
+    def test_encode(self):
+        unicode = 'aAaAaA'
+        assert_equal(np.char.encode(unicode, encoding='cp037'),
+                     b'\x81\xc1\x81\xc1\x81\xc1')
+
+    def test_expandtabs(self):
+        s = "\tone level of indentation\n\t\ttwo levels of indentation"
+        assert_equal(
+            np.char.expandtabs(s, tabsize=2),
+            "  one level of indentation\n    two levels of indentation"
+        )
+
+    def test_join(self):
+        seps = np.array(['-', '_'])
+        assert_array_equal(np.char.join(seps, 'hello'),
+                           ['h-e-l-l-o', 'h_e_l_l_o'])
+
+    def test_partition(self):
+        assert_equal(np.char.partition('This string', ' '),
+                     ['This', ' ', 'string'])
+
+    def test_rpartition(self):
+        assert_equal(np.char.rpartition('This string here', ' '),
+                     ['This string', ' ', 'here'])
+
+    def test_replace(self):
+        assert_equal(np.char.replace('Python is good', 'good', 'great'),
+                     'Python is great')
+
+
+def test_empty_indexing():
+    """Regression test for ticket 1948."""
+    # Check that indexing a chararray with an empty list/array returns an
+    # empty chararray instead of a chararray with a single empty string in it.
+    s = np.char.chararray((4,))
+    assert_(s[[]].size == 0)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_deprecations.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_deprecations.py
new file mode 100644
index 0000000..d90c155
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_deprecations.py
@@ -0,0 +1,454 @@
+"""
+Tests related to deprecation warnings. Also a convenient place
+to document how deprecations should eventually be turned into errors.
+
+"""
+import contextlib
+import warnings
+
+import numpy._core._struct_ufunc_tests as struct_ufunc
+import pytest
+from numpy._core._multiarray_tests import fromstring_null_term_c_api  # noqa: F401
+
+import numpy as np
+from numpy.testing import assert_raises, temppath
+
+try:
+    import pytz  # noqa: F401
+    _has_pytz = True
+except ImportError:
+    _has_pytz = False
+
+
+class _DeprecationTestCase:
+    # Just as warning: warnings uses re.match, so the start of this message
+    # must match.
+    message = ''
+    warning_cls = DeprecationWarning
+
+    def setup_method(self):
+        self.warn_ctx = warnings.catch_warnings(record=True)
+        self.log = self.warn_ctx.__enter__()
+
+        # Do *not* ignore other DeprecationWarnings. Ignoring warnings
+        # can give very confusing results because of
+        # https://bugs.python.org/issue4180 and it is probably simplest to
+        # try to keep the tests cleanly giving only the right warning type.
+        # (While checking them set to "error" those are ignored anyway)
+        # We still have them show up, because otherwise they would be raised
+        warnings.filterwarnings("always", category=self.warning_cls)
+        warnings.filterwarnings("always", message=self.message,
+                                category=self.warning_cls)
+
+    def teardown_method(self):
+        self.warn_ctx.__exit__()
+
+    def assert_deprecated(self, function, num=1, ignore_others=False,
+                          function_fails=False,
+                          exceptions=np._NoValue,
+                          args=(), kwargs={}):
+        """Test if DeprecationWarnings are given and raised.
+
+        This first checks if the function when called gives `num`
+        DeprecationWarnings, after that it tries to raise these
+        DeprecationWarnings and compares them with `exceptions`.
+        The exceptions can be different for cases where this code path
+        is simply not anticipated and the exception is replaced.
+
+        Parameters
+        ----------
+        function : callable
+            The function to test
+        num : int
+            Number of DeprecationWarnings to expect. This should normally be 1.
+        ignore_others : bool
+            Whether warnings of the wrong type should be ignored (note that
+            the message is not checked)
+        function_fails : bool
+            If the function would normally fail, setting this will check for
+            warnings inside a try/except block.
+        exceptions : Exception or tuple of Exceptions
+            Exception to expect when turning the warnings into an error.
+            The default checks for DeprecationWarnings. If exceptions is
+            empty the function is expected to run successfully.
+        args : tuple
+            Arguments for `function`
+        kwargs : dict
+            Keyword arguments for `function`
+        """
+        __tracebackhide__ = True  # Hide traceback for py.test
+
+        # reset the log
+        self.log[:] = []
+
+        if exceptions is np._NoValue:
+            exceptions = (self.warning_cls,)
+
+        if function_fails:
+            context_manager = contextlib.suppress(Exception)
+        else:
+            context_manager = contextlib.nullcontext()
+        with context_manager:
+            function(*args, **kwargs)
+
+        # just in case, clear the registry
+        num_found = 0
+        for warning in self.log:
+            if warning.category is self.warning_cls:
+                num_found += 1
+            elif not ignore_others:
+                raise AssertionError(
+                        "expected %s but got: %s" %
+                        (self.warning_cls.__name__, warning.category))
+        if num is not None and num_found != num:
+            msg = f"{len(self.log)} warnings found but {num} expected."
+            lst = [str(w) for w in self.log]
+            raise AssertionError("\n".join([msg] + lst))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings("error", message=self.message,
+                                    category=self.warning_cls)
+            try:
+                function(*args, **kwargs)
+                if exceptions != ():
+                    raise AssertionError(
+                            "No error raised during function call")
+            except exceptions:
+                if exceptions == ():
+                    raise AssertionError(
+                            "Error raised during function call")
+
+    def assert_not_deprecated(self, function, args=(), kwargs={}):
+        """Test that warnings are not raised.
+
+        This is just a shorthand for:
+
+        self.assert_deprecated(function, num=0, ignore_others=True,
+                        exceptions=tuple(), args=args, kwargs=kwargs)
+        """
+        self.assert_deprecated(function, num=0, ignore_others=True,
+                        exceptions=(), args=args, kwargs=kwargs)
+
+
+class _VisibleDeprecationTestCase(_DeprecationTestCase):
+    warning_cls = np.exceptions.VisibleDeprecationWarning
+
+
+class TestTestDeprecated:
+    def test_assert_deprecated(self):
+        test_case_instance = _DeprecationTestCase()
+        test_case_instance.setup_method()
+        assert_raises(AssertionError,
+                      test_case_instance.assert_deprecated,
+                      lambda: None)
+
+        def foo():
+            warnings.warn("foo", category=DeprecationWarning, stacklevel=2)
+
+        test_case_instance.assert_deprecated(foo)
+        test_case_instance.teardown_method()
+
+
+class TestBincount(_DeprecationTestCase):
+    # 2024-07-29, 2.1.0
+    @pytest.mark.parametrize('badlist', [[0.5, 1.2, 1.5],
+                                         ['0', '1', '1']])
+    def test_bincount_bad_list(self, badlist):
+        self.assert_deprecated(lambda: np.bincount(badlist))
+
+
+class TestGeneratorSum(_DeprecationTestCase):
+    # 2018-02-25, 1.15.0
+    def test_generator_sum(self):
+        self.assert_deprecated(np.sum, args=((i for i in range(5)),))
+
+
+class BuiltInRoundComplexDType(_DeprecationTestCase):
+    # 2020-03-31 1.19.0
+    deprecated_types = [np.csingle, np.cdouble, np.clongdouble]
+    not_deprecated_types = [
+        np.int8, np.int16, np.int32, np.int64,
+        np.uint8, np.uint16, np.uint32, np.uint64,
+        np.float16, np.float32, np.float64,
+    ]
+
+    def test_deprecated(self):
+        for scalar_type in self.deprecated_types:
+            scalar = scalar_type(0)
+            self.assert_deprecated(round, args=(scalar,))
+            self.assert_deprecated(round, args=(scalar, 0))
+            self.assert_deprecated(round, args=(scalar,), kwargs={'ndigits': 0})
+
+    def test_not_deprecated(self):
+        for scalar_type in self.not_deprecated_types:
+            scalar = scalar_type(0)
+            self.assert_not_deprecated(round, args=(scalar,))
+            self.assert_not_deprecated(round, args=(scalar, 0))
+            self.assert_not_deprecated(round, args=(scalar,), kwargs={'ndigits': 0})
+
+
+class FlatteningConcatenateUnsafeCast(_DeprecationTestCase):
+    # NumPy 1.20, 2020-09-03
+    message = "concatenate with `axis=None` will use same-kind casting"
+
+    def test_deprecated(self):
+        self.assert_deprecated(np.concatenate,
+                args=(([0.], [1.]),),
+                kwargs={'axis': None, 'out': np.empty(2, dtype=np.int64)})
+
+    def test_not_deprecated(self):
+        self.assert_not_deprecated(np.concatenate,
+                args=(([0.], [1.]),),
+                kwargs={'axis': None, 'out': np.empty(2, dtype=np.int64),
+                        'casting': "unsafe"})
+
+        with assert_raises(TypeError):
+            # Tests should notice if the deprecation warning is given first...
+            np.concatenate(([0.], [1.]), out=np.empty(2, dtype=np.int64),
+                           casting="same_kind")
+
+
+class TestCtypesGetter(_DeprecationTestCase):
+    # Deprecated 2021-05-18, Numpy 1.21.0
+    warning_cls = DeprecationWarning
+    ctypes = np.array([1]).ctypes
+
+    @pytest.mark.parametrize(
+        "name", ["get_data", "get_shape", "get_strides", "get_as_parameter"]
+    )
+    def test_deprecated(self, name: str) -> None:
+        func = getattr(self.ctypes, name)
+        self.assert_deprecated(func)
+
+    @pytest.mark.parametrize(
+        "name", ["data", "shape", "strides", "_as_parameter_"]
+    )
+    def test_not_deprecated(self, name: str) -> None:
+        self.assert_not_deprecated(lambda: getattr(self.ctypes, name))
+
+
+class TestMachAr(_DeprecationTestCase):
+    # Deprecated 2022-11-22, NumPy 1.25
+    warning_cls = DeprecationWarning
+
+    def test_deprecated_module(self):
+        self.assert_deprecated(lambda: np._core.MachAr)
+
+
+class TestQuantileInterpolationDeprecation(_DeprecationTestCase):
+    # Deprecated 2021-11-08, NumPy 1.22
+    @pytest.mark.parametrize("func",
+        [np.percentile, np.quantile, np.nanpercentile, np.nanquantile])
+    def test_deprecated(self, func):
+        self.assert_deprecated(
+            lambda: func([0., 1.], 0., interpolation="linear"))
+        self.assert_deprecated(
+            lambda: func([0., 1.], 0., interpolation="nearest"))
+
+    @pytest.mark.parametrize("func",
+            [np.percentile, np.quantile, np.nanpercentile, np.nanquantile])
+    def test_both_passed(self, func):
+        with warnings.catch_warnings():
+            # catch the DeprecationWarning so that it does not raise:
+            warnings.simplefilter("always", DeprecationWarning)
+            with pytest.raises(TypeError):
+                func([0., 1.], 0., interpolation="nearest", method="nearest")
+
+
+class TestScalarConversion(_DeprecationTestCase):
+    # 2023-01-02, 1.25.0
+    def test_float_conversion(self):
+        self.assert_deprecated(float, args=(np.array([3.14]),))
+
+    def test_behaviour(self):
+        b = np.array([[3.14]])
+        c = np.zeros(5)
+        with pytest.warns(DeprecationWarning):
+            c[0] = b
+
+
+class TestPyIntConversion(_DeprecationTestCase):
+    message = r".*stop allowing conversion of out-of-bound.*"
+
+    @pytest.mark.parametrize("dtype", np.typecodes["AllInteger"])
+    def test_deprecated_scalar(self, dtype):
+        dtype = np.dtype(dtype)
+        info = np.iinfo(dtype)
+
+        # Cover the most common creation paths (all end up in the
+        # same place):
+        def scalar(value, dtype):
+            dtype.type(value)
+
+        def assign(value, dtype):
+            arr = np.array([0, 0, 0], dtype=dtype)
+            arr[2] = value
+
+        def create(value, dtype):
+            np.array([value], dtype=dtype)
+
+        for creation_func in [scalar, assign, create]:
+            try:
+                self.assert_deprecated(
+                        lambda: creation_func(info.min - 1, dtype))
+            except OverflowError:
+                pass  # OverflowErrors always happened also before and are OK.
+
+            try:
+                self.assert_deprecated(
+                        lambda: creation_func(info.max + 1, dtype))
+            except OverflowError:
+                pass  # OverflowErrors always happened also before and are OK.
+
+
+@pytest.mark.parametrize("name", ["str", "bytes", "object"])
+def test_future_scalar_attributes(name):
+    # FutureWarning added 2022-11-17, NumPy 1.24,
+    assert name not in dir(np)  # we may want to not add them
+    with pytest.warns(FutureWarning,
+            match=f"In the future .*{name}"):
+        assert not hasattr(np, name)
+
+    # Unfortunately, they are currently still valid via `np.dtype()`
+    np.dtype(name)
+    name in np._core.sctypeDict
+
+
+# Ignore the above future attribute warning for this test.
+@pytest.mark.filterwarnings("ignore:In the future:FutureWarning")
+class TestRemovedGlobals:
+    # Removed 2023-01-12, NumPy 1.24.0
+    # Not a deprecation, but the large error was added to aid those who missed
+    # the previous deprecation, and should be removed similarly to one
+    # (or faster).
+    @pytest.mark.parametrize("name",
+            ["object", "float", "complex", "str", "int"])
+    def test_attributeerror_includes_info(self, name):
+        msg = f".*\n`np.{name}` was a deprecated alias for the builtin"
+        with pytest.raises(AttributeError, match=msg):
+            getattr(np, name)
+
+
+class TestDeprecatedFinfo(_DeprecationTestCase):
+    # Deprecated in NumPy 1.25, 2023-01-16
+    def test_deprecated_none(self):
+        self.assert_deprecated(np.finfo, args=(None,))
+
+
+class TestMathAlias(_DeprecationTestCase):
+    def test_deprecated_np_lib_math(self):
+        self.assert_deprecated(lambda: np.lib.math)
+
+
+class TestLibImports(_DeprecationTestCase):
+    # Deprecated in Numpy 1.26.0, 2023-09
+    def test_lib_functions_deprecation_call(self):
+        from numpy import in1d, row_stack, trapz
+        from numpy._core.numerictypes import maximum_sctype
+        from numpy.lib._function_base_impl import disp
+        from numpy.lib._npyio_impl import recfromcsv, recfromtxt
+        from numpy.lib._shape_base_impl import get_array_wrap
+        from numpy.lib._utils_impl import safe_eval
+        from numpy.lib.tests.test_io import TextIO
+
+        self.assert_deprecated(lambda: safe_eval("None"))
+
+        data_gen = lambda: TextIO('A,B\n0,1\n2,3')
+        kwargs = {'delimiter': ",", 'missing_values': "N/A", 'names': True}
+        self.assert_deprecated(lambda: recfromcsv(data_gen()))
+        self.assert_deprecated(lambda: recfromtxt(data_gen(), **kwargs))
+
+        self.assert_deprecated(lambda: disp("test"))
+        self.assert_deprecated(get_array_wrap)
+        self.assert_deprecated(lambda: maximum_sctype(int))
+
+        self.assert_deprecated(lambda: in1d([1], [1]))
+        self.assert_deprecated(lambda: row_stack([[]]))
+        self.assert_deprecated(lambda: trapz([1], [1]))
+        self.assert_deprecated(lambda: np.chararray)
+
+
+class TestDeprecatedDTypeAliases(_DeprecationTestCase):
+
+    def _check_for_warning(self, func):
+        with warnings.catch_warnings(record=True) as caught_warnings:
+            func()
+        assert len(caught_warnings) == 1
+        w = caught_warnings[0]
+        assert w.category is DeprecationWarning
+        assert "alias 'a' was deprecated in NumPy 2.0" in str(w.message)
+
+    def test_a_dtype_alias(self):
+        for dtype in ["a", "a10"]:
+            f = lambda: np.dtype(dtype)
+            self._check_for_warning(f)
+            self.assert_deprecated(f)
+            f = lambda: np.array(["hello", "world"]).astype("a10")
+            self._check_for_warning(f)
+            self.assert_deprecated(f)
+
+
+class TestDeprecatedArrayWrap(_DeprecationTestCase):
+    message = "__array_wrap__.*"
+
+    def test_deprecated(self):
+        class Test1:
+            def __array__(self, dtype=None, copy=None):
+                return np.arange(4)
+
+            def __array_wrap__(self, arr, context=None):
+                self.called = True
+                return 'pass context'
+
+        class Test2(Test1):
+            def __array_wrap__(self, arr):
+                self.called = True
+                return 'pass'
+
+        test1 = Test1()
+        test2 = Test2()
+        self.assert_deprecated(lambda: np.negative(test1))
+        assert test1.called
+        self.assert_deprecated(lambda: np.negative(test2))
+        assert test2.called
+
+
+class TestDeprecatedDTypeParenthesizedRepeatCount(_DeprecationTestCase):
+    message = "Passing in a parenthesized single number"
+
+    @pytest.mark.parametrize("string", ["(2)i,", "(3)3S,", "f,(2)f"])
+    def test_parenthesized_repeat_count(self, string):
+        self.assert_deprecated(np.dtype, args=(string,))
+
+
+class TestDeprecatedSaveFixImports(_DeprecationTestCase):
+    # Deprecated in Numpy 2.1, 2024-05
+    message = "The 'fix_imports' flag is deprecated and has no effect."
+
+    def test_deprecated(self):
+        with temppath(suffix='.npy') as path:
+            sample_args = (path, np.array(np.zeros((1024, 10))))
+            self.assert_not_deprecated(np.save, args=sample_args)
+            self.assert_deprecated(np.save, args=sample_args,
+                                kwargs={'fix_imports': True})
+            self.assert_deprecated(np.save, args=sample_args,
+                                kwargs={'fix_imports': False})
+            for allow_pickle in [True, False]:
+                self.assert_not_deprecated(np.save, args=sample_args,
+                                        kwargs={'allow_pickle': allow_pickle})
+                self.assert_deprecated(np.save, args=sample_args,
+                                    kwargs={'allow_pickle': allow_pickle,
+                                            'fix_imports': True})
+                self.assert_deprecated(np.save, args=sample_args,
+                                    kwargs={'allow_pickle': allow_pickle,
+                                            'fix_imports': False})
+
+
+class TestAddNewdocUFunc(_DeprecationTestCase):
+    # Deprecated in Numpy 2.2, 2024-11
+    def test_deprecated(self):
+        self.assert_deprecated(
+            lambda: np._core.umath._add_newdoc_ufunc(
+                struct_ufunc.add_triplet, "new docs"
+            )
+        )
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_dlpack.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_dlpack.py
new file mode 100644
index 0000000..89c2403
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_dlpack.py
@@ -0,0 +1,190 @@
+import sys
+
+import pytest
+
+import numpy as np
+from numpy.testing import IS_PYPY, assert_array_equal
+
+
+def new_and_old_dlpack():
+    yield np.arange(5)
+
+    class OldDLPack(np.ndarray):
+        # Support only the "old" version
+        def __dlpack__(self, stream=None):
+            return super().__dlpack__(stream=None)
+
+    yield np.arange(5).view(OldDLPack)
+
+
+class TestDLPack:
+    @pytest.mark.skipif(IS_PYPY, reason="PyPy can't get refcounts.")
+    @pytest.mark.parametrize("max_version", [(0, 0), None, (1, 0), (100, 3)])
+    def test_dunder_dlpack_refcount(self, max_version):
+        x = np.arange(5)
+        y = x.__dlpack__(max_version=max_version)
+        startcount = sys.getrefcount(x)
+        del y
+        assert startcount - sys.getrefcount(x) == 1
+
+    def test_dunder_dlpack_stream(self):
+        x = np.arange(5)
+        x.__dlpack__(stream=None)
+
+        with pytest.raises(RuntimeError):
+            x.__dlpack__(stream=1)
+
+    def test_dunder_dlpack_copy(self):
+        # Checks the argument parsing of __dlpack__ explicitly.
+        # Honoring the flag is tested in the from_dlpack round-tripping test.
+        x = np.arange(5)
+        x.__dlpack__(copy=True)
+        x.__dlpack__(copy=None)
+        x.__dlpack__(copy=False)
+
+        with pytest.raises(ValueError):
+            # NOTE: The copy converter should be stricter, but not just here.
+            x.__dlpack__(copy=np.array([1, 2, 3]))
+
+    def test_strides_not_multiple_of_itemsize(self):
+        dt = np.dtype([('int', np.int32), ('char', np.int8)])
+        y = np.zeros((5,), dtype=dt)
+        z = y['int']
+
+        with pytest.raises(BufferError):
+            np.from_dlpack(z)
+
+    @pytest.mark.skipif(IS_PYPY, reason="PyPy can't get refcounts.")
+    @pytest.mark.parametrize("arr", new_and_old_dlpack())
+    def test_from_dlpack_refcount(self, arr):
+        arr = arr.copy()
+        y = np.from_dlpack(arr)
+        startcount = sys.getrefcount(arr)
+        del y
+        assert startcount - sys.getrefcount(arr) == 1
+
+    @pytest.mark.parametrize("dtype", [
+        np.bool,
+        np.int8, np.int16, np.int32, np.int64,
+        np.uint8, np.uint16, np.uint32, np.uint64,
+        np.float16, np.float32, np.float64,
+        np.complex64, np.complex128
+    ])
+    @pytest.mark.parametrize("arr", new_and_old_dlpack())
+    def test_dtype_passthrough(self, arr, dtype):
+        x = arr.astype(dtype)
+        y = np.from_dlpack(x)
+
+        assert y.dtype == x.dtype
+        assert_array_equal(x, y)
+
+    def test_invalid_dtype(self):
+        x = np.asarray(np.datetime64('2021-05-27'))
+
+        with pytest.raises(BufferError):
+            np.from_dlpack(x)
+
+    def test_invalid_byte_swapping(self):
+        dt = np.dtype('=i8').newbyteorder()
+        x = np.arange(5, dtype=dt)
+
+        with pytest.raises(BufferError):
+            np.from_dlpack(x)
+
+    def test_non_contiguous(self):
+        x = np.arange(25).reshape((5, 5))
+
+        y1 = x[0]
+        assert_array_equal(y1, np.from_dlpack(y1))
+
+        y2 = x[:, 0]
+        assert_array_equal(y2, np.from_dlpack(y2))
+
+        y3 = x[1, :]
+        assert_array_equal(y3, np.from_dlpack(y3))
+
+        y4 = x[1]
+        assert_array_equal(y4, np.from_dlpack(y4))
+
+        y5 = np.diagonal(x).copy()
+        assert_array_equal(y5, np.from_dlpack(y5))
+
+    @pytest.mark.parametrize("ndim", range(33))
+    def test_higher_dims(self, ndim):
+        shape = (1,) * ndim
+        x = np.zeros(shape, dtype=np.float64)
+
+        assert shape == np.from_dlpack(x).shape
+
+    def test_dlpack_device(self):
+        x = np.arange(5)
+        assert x.__dlpack_device__() == (1, 0)
+        y = np.from_dlpack(x)
+        assert y.__dlpack_device__() == (1, 0)
+        z = y[::2]
+        assert z.__dlpack_device__() == (1, 0)
+
+    def dlpack_deleter_exception(self, max_version):
+        x = np.arange(5)
+        _ = x.__dlpack__(max_version=max_version)
+        raise RuntimeError
+
+    @pytest.mark.parametrize("max_version", [None, (1, 0)])
+    def test_dlpack_destructor_exception(self, max_version):
+        with pytest.raises(RuntimeError):
+            self.dlpack_deleter_exception(max_version=max_version)
+
+    def test_readonly(self):
+        x = np.arange(5)
+        x.flags.writeable = False
+        # Raises without max_version
+        with pytest.raises(BufferError):
+            x.__dlpack__()
+
+        # But works fine if we try with version
+        y = np.from_dlpack(x)
+        assert not y.flags.writeable
+
+    def test_writeable(self):
+        x_new, x_old = new_and_old_dlpack()
+
+        # new dlpacks respect writeability
+        y = np.from_dlpack(x_new)
+        assert y.flags.writeable
+
+        # old dlpacks are not writeable for backwards compatibility
+        y = np.from_dlpack(x_old)
+        assert not y.flags.writeable
+
+    def test_ndim0(self):
+        x = np.array(1.0)
+        y = np.from_dlpack(x)
+        assert_array_equal(x, y)
+
+    def test_size1dims_arrays(self):
+        x = np.ndarray(dtype='f8', shape=(10, 5, 1), strides=(8, 80, 4),
+                       buffer=np.ones(1000, dtype=np.uint8), order='F')
+        y = np.from_dlpack(x)
+        assert_array_equal(x, y)
+
+    def test_copy(self):
+        x = np.arange(5)
+
+        y = np.from_dlpack(x)
+        assert np.may_share_memory(x, y)
+        y = np.from_dlpack(x, copy=False)
+        assert np.may_share_memory(x, y)
+        y = np.from_dlpack(x, copy=True)
+        assert not np.may_share_memory(x, y)
+
+    def test_device(self):
+        x = np.arange(5)
+        # requesting (1, 0), i.e. CPU device works in both calls:
+        x.__dlpack__(dl_device=(1, 0))
+        np.from_dlpack(x, device="cpu")
+        np.from_dlpack(x, device=None)
+
+        with pytest.raises(ValueError):
+            x.__dlpack__(dl_device=(10, 0))
+        with pytest.raises(ValueError):
+            np.from_dlpack(x, device="gpu")
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_dtype.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_dtype.py
new file mode 100644
index 0000000..684672a
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_dtype.py
@@ -0,0 +1,1995 @@
+import ctypes
+import gc
+import operator
+import pickle
+import random
+import sys
+import types
+from itertools import permutations
+from typing import Any
+
+import hypothesis
+import pytest
+from hypothesis.extra import numpy as hynp
+from numpy._core._multiarray_tests import create_custom_field_dtype
+from numpy._core._rational_tests import rational
+
+import numpy as np
+import numpy.dtypes
+from numpy.testing import (
+    HAS_REFCOUNT,
+    IS_PYSTON,
+    IS_WASM,
+    assert_,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+)
+
+
+def assert_dtype_equal(a, b):
+    assert_equal(a, b)
+    assert_equal(hash(a), hash(b),
+                 "two equivalent types do not hash to the same value !")
+
+def assert_dtype_not_equal(a, b):
+    assert_(a != b)
+    assert_(hash(a) != hash(b),
+            "two different types hash to the same value !")
+
+class TestBuiltin:
+    @pytest.mark.parametrize('t', [int, float, complex, np.int32, str, object])
+    def test_run(self, t):
+        """Only test hash runs at all."""
+        dt = np.dtype(t)
+        hash(dt)
+
+    @pytest.mark.parametrize('t', [int, float])
+    def test_dtype(self, t):
+        # Make sure equivalent byte order char hash the same (e.g. < and = on
+        # little endian)
+        dt = np.dtype(t)
+        dt2 = dt.newbyteorder("<")
+        dt3 = dt.newbyteorder(">")
+        if dt == dt2:
+            assert_(dt.byteorder != dt2.byteorder, "bogus test")
+            assert_dtype_equal(dt, dt2)
+        else:
+            assert_(dt.byteorder != dt3.byteorder, "bogus test")
+            assert_dtype_equal(dt, dt3)
+
+    def test_equivalent_dtype_hashing(self):
+        # Make sure equivalent dtypes with different type num hash equal
+        uintp = np.dtype(np.uintp)
+        if uintp.itemsize == 4:
+            left = uintp
+            right = np.dtype(np.uint32)
+        else:
+            left = uintp
+            right = np.dtype(np.ulonglong)
+        assert_(left == right)
+        assert_(hash(left) == hash(right))
+
+    def test_invalid_types(self):
+        # Make sure invalid type strings raise an error
+
+        assert_raises(TypeError, np.dtype, 'O3')
+        assert_raises(TypeError, np.dtype, 'O5')
+        assert_raises(TypeError, np.dtype, 'O7')
+        assert_raises(TypeError, np.dtype, 'b3')
+        assert_raises(TypeError, np.dtype, 'h4')
+        assert_raises(TypeError, np.dtype, 'I5')
+        assert_raises(TypeError, np.dtype, 'e3')
+        assert_raises(TypeError, np.dtype, 'f5')
+
+        if np.dtype('g').itemsize == 8 or np.dtype('g').itemsize == 16:
+            assert_raises(TypeError, np.dtype, 'g12')
+        elif np.dtype('g').itemsize == 12:
+            assert_raises(TypeError, np.dtype, 'g16')
+
+        if np.dtype('l').itemsize == 8:
+            assert_raises(TypeError, np.dtype, 'l4')
+            assert_raises(TypeError, np.dtype, 'L4')
+        else:
+            assert_raises(TypeError, np.dtype, 'l8')
+            assert_raises(TypeError, np.dtype, 'L8')
+
+        if np.dtype('q').itemsize == 8:
+            assert_raises(TypeError, np.dtype, 'q4')
+            assert_raises(TypeError, np.dtype, 'Q4')
+        else:
+            assert_raises(TypeError, np.dtype, 'q8')
+            assert_raises(TypeError, np.dtype, 'Q8')
+
+        # Make sure negative-sized dtype raises an error
+        assert_raises(TypeError, np.dtype, 'S-1')
+        assert_raises(TypeError, np.dtype, 'U-1')
+        assert_raises(TypeError, np.dtype, 'V-1')
+
+    def test_richcompare_invalid_dtype_equality(self):
+        # Make sure objects that cannot be converted to valid
+        # dtypes results in False/True when compared to valid dtypes.
+        # Here 7 cannot be converted to dtype. No exceptions should be raised
+
+        assert not np.dtype(np.int32) == 7, "dtype richcompare failed for =="
+        assert np.dtype(np.int32) != 7, "dtype richcompare failed for !="
+
+    @pytest.mark.parametrize(
+        'operation',
+        [operator.le, operator.lt, operator.ge, operator.gt])
+    def test_richcompare_invalid_dtype_comparison(self, operation):
+        # Make sure TypeError is raised for comparison operators
+        # for invalid dtypes. Here 7 is an invalid dtype.
+
+        with pytest.raises(TypeError):
+            operation(np.dtype(np.int32), 7)
+
+    @pytest.mark.parametrize("dtype",
+             ['Bool', 'Bytes0', 'Complex32', 'Complex64',
+              'Datetime64', 'Float16', 'Float32', 'Float64',
+              'Int8', 'Int16', 'Int32', 'Int64',
+              'Object0', 'Str0', 'Timedelta64',
+              'UInt8', 'UInt16', 'Uint32', 'UInt32',
+              'Uint64', 'UInt64', 'Void0',
+              "Float128", "Complex128"])
+    def test_numeric_style_types_are_invalid(self, dtype):
+        with assert_raises(TypeError):
+            np.dtype(dtype)
+
+    def test_expired_dtypes_with_bad_bytesize(self):
+        match: str = r".*removed in NumPy 2.0.*"
+        with pytest.raises(TypeError, match=match):
+            np.dtype("int0")
+        with pytest.raises(TypeError, match=match):
+            np.dtype("uint0")
+        with pytest.raises(TypeError, match=match):
+            np.dtype("bool8")
+        with pytest.raises(TypeError, match=match):
+            np.dtype("bytes0")
+        with pytest.raises(TypeError, match=match):
+            np.dtype("str0")
+        with pytest.raises(TypeError, match=match):
+            np.dtype("object0")
+        with pytest.raises(TypeError, match=match):
+            np.dtype("void0")
+
+    @pytest.mark.parametrize(
+        'value',
+        ['m8', 'M8', 'datetime64', 'timedelta64',
+         'i4, (2,3)f8, f4', 'S3, 3u8, (3,4)S10',
+         '>f', '<f', '=f', '|f',
+        ])
+    def test_dtype_bytes_str_equivalence(self, value):
+        bytes_value = value.encode('ascii')
+        from_bytes = np.dtype(bytes_value)
+        from_str = np.dtype(value)
+        assert_dtype_equal(from_bytes, from_str)
+
+    def test_dtype_from_bytes(self):
+        # Empty bytes object
+        assert_raises(TypeError, np.dtype, b'')
+        # Byte order indicator, but no type
+        assert_raises(TypeError, np.dtype, b'|')
+
+        # Single character with ordinal < NPY_NTYPES_LEGACY returns
+        # type by index into _builtin_descrs
+        assert_dtype_equal(np.dtype(bytes([0])), np.dtype('bool'))
+        assert_dtype_equal(np.dtype(bytes([17])), np.dtype(object))
+
+        # Single character where value is a valid type code
+        assert_dtype_equal(np.dtype(b'f'), np.dtype('float32'))
+
+        # Bytes with non-ascii values raise errors
+        assert_raises(TypeError, np.dtype, b'\xff')
+        assert_raises(TypeError, np.dtype, b's\xff')
+
+    def test_bad_param(self):
+        # Can't give a size that's too small
+        assert_raises(ValueError, np.dtype,
+                        {'names': ['f0', 'f1'],
+                         'formats': ['i4', 'i1'],
+                         'offsets': [0, 4],
+                         'itemsize': 4})
+        # If alignment is enabled, the alignment (4) must divide the itemsize
+        assert_raises(ValueError, np.dtype,
+                        {'names': ['f0', 'f1'],
+                         'formats': ['i4', 'i1'],
+                         'offsets': [0, 4],
+                         'itemsize': 9}, align=True)
+        # If alignment is enabled, the individual fields must be aligned
+        assert_raises(ValueError, np.dtype,
+                        {'names': ['f0', 'f1'],
+                         'formats': ['i1', 'f4'],
+                         'offsets': [0, 2]}, align=True)
+
+    def test_field_order_equality(self):
+        x = np.dtype({'names': ['A', 'B'],
+                      'formats': ['i4', 'f4'],
+                      'offsets': [0, 4]})
+        y = np.dtype({'names': ['B', 'A'],
+                      'formats': ['i4', 'f4'],
+                      'offsets': [4, 0]})
+        assert_equal(x == y, False)
+        # This is an safe cast (not equiv) due to the different names:
+        assert np.can_cast(x, y, casting="safe")
+
+    @pytest.mark.parametrize(
+        ["type_char", "char_size", "scalar_type"],
+        [["U", 4, np.str_],
+         ["S", 1, np.bytes_]])
+    def test_create_string_dtypes_directly(
+            self, type_char, char_size, scalar_type):
+        dtype_class = type(np.dtype(type_char))
+
+        dtype = dtype_class(8)
+        assert dtype.type is scalar_type
+        assert dtype.itemsize == 8 * char_size
+
+    def test_create_invalid_string_errors(self):
+        one_too_big = np.iinfo(np.intc).max + 1
+        with pytest.raises(TypeError):
+            type(np.dtype("U"))(one_too_big // 4)
+
+        with pytest.raises(TypeError):
+            # Code coverage for very large numbers:
+            type(np.dtype("U"))(np.iinfo(np.intp).max // 4 + 1)
+
+        if one_too_big < sys.maxsize:
+            with pytest.raises(TypeError):
+                type(np.dtype("S"))(one_too_big)
+
+        with pytest.raises(ValueError):
+            type(np.dtype("U"))(-1)
+
+        # OverflowError on 32 bit
+        with pytest.raises((TypeError, OverflowError)):
+            # see gh-26556
+            type(np.dtype("S"))(2**61)
+
+        with pytest.raises(TypeError):
+            np.dtype("S1234hello")
+
+    def test_leading_zero_parsing(self):
+        dt1 = np.dtype('S010')
+        dt2 = np.dtype('S10')
+
+        assert dt1 == dt2
+        assert repr(dt1) == "dtype('S10')"
+        assert dt1.itemsize == 10
+
+
+class TestRecord:
+    def test_equivalent_record(self):
+        """Test whether equivalent record dtypes hash the same."""
+        a = np.dtype([('yo', int)])
+        b = np.dtype([('yo', int)])
+        assert_dtype_equal(a, b)
+
+    def test_different_names(self):
+        # In theory, they may hash the same (collision) ?
+        a = np.dtype([('yo', int)])
+        b = np.dtype([('ye', int)])
+        assert_dtype_not_equal(a, b)
+
+    def test_different_titles(self):
+        # In theory, they may hash the same (collision) ?
+        a = np.dtype({'names': ['r', 'b'],
+                      'formats': ['u1', 'u1'],
+                      'titles': ['Red pixel', 'Blue pixel']})
+        b = np.dtype({'names': ['r', 'b'],
+                      'formats': ['u1', 'u1'],
+                      'titles': ['RRed pixel', 'Blue pixel']})
+        assert_dtype_not_equal(a, b)
+
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test_refcount_dictionary_setting(self):
+        names = ["name1"]
+        formats = ["f8"]
+        titles = ["t1"]
+        offsets = [0]
+        d = {"names": names, "formats": formats, "titles": titles, "offsets": offsets}
+        refcounts = {k: sys.getrefcount(i) for k, i in d.items()}
+        np.dtype(d)
+        refcounts_new = {k: sys.getrefcount(i) for k, i in d.items()}
+        assert refcounts == refcounts_new
+
+    def test_mutate(self):
+        # Mutating a dtype should reset the cached hash value.
+        # NOTE: Mutating should be deprecated, but new API added to replace it.
+        a = np.dtype([('yo', int)])
+        b = np.dtype([('yo', int)])
+        c = np.dtype([('ye', int)])
+        assert_dtype_equal(a, b)
+        assert_dtype_not_equal(a, c)
+        a.names = ['ye']
+        assert_dtype_equal(a, c)
+        assert_dtype_not_equal(a, b)
+        state = b.__reduce__()[2]
+        a.__setstate__(state)
+        assert_dtype_equal(a, b)
+        assert_dtype_not_equal(a, c)
+
+    def test_init_simple_structured(self):
+        dt1 = np.dtype("i, i")
+        assert dt1.names == ("f0", "f1")
+
+        dt2 = np.dtype("i,")
+        assert dt2.names == ("f0",)
+
+    def test_mutate_error(self):
+        # NOTE: Mutating should be deprecated, but new API added to replace it.
+        a = np.dtype("i,i")
+
+        with pytest.raises(ValueError, match="must replace all names at once"):
+            a.names = ["f0"]
+
+        with pytest.raises(ValueError, match=".*and not string"):
+            a.names = ["f0", b"not a unicode name"]
+
+    def test_not_lists(self):
+        """Test if an appropriate exception is raised when passing bad values to
+        the dtype constructor.
+        """
+        assert_raises(TypeError, np.dtype,
+                      {"names": {'A', 'B'}, "formats": ['f8', 'i4']})
+        assert_raises(TypeError, np.dtype,
+                      {"names": ['A', 'B'], "formats": {'f8', 'i4'}})
+
+    def test_aligned_size(self):
+        # Check that structured dtypes get padded to an aligned size
+        dt = np.dtype('i4, i1', align=True)
+        assert_equal(dt.itemsize, 8)
+        dt = np.dtype([('f0', 'i4'), ('f1', 'i1')], align=True)
+        assert_equal(dt.itemsize, 8)
+        dt = np.dtype({'names': ['f0', 'f1'],
+                       'formats': ['i4', 'u1'],
+                       'offsets': [0, 4]}, align=True)
+        assert_equal(dt.itemsize, 8)
+        dt = np.dtype({'f0': ('i4', 0), 'f1': ('u1', 4)}, align=True)
+        assert_equal(dt.itemsize, 8)
+        # Nesting should preserve that alignment
+        dt1 = np.dtype([('f0', 'i4'),
+                       ('f1', [('f1', 'i1'), ('f2', 'i4'), ('f3', 'i1')]),
+                       ('f2', 'i1')], align=True)
+        assert_equal(dt1.itemsize, 20)
+        dt2 = np.dtype({'names': ['f0', 'f1', 'f2'],
+                       'formats': ['i4',
+                                  [('f1', 'i1'), ('f2', 'i4'), ('f3', 'i1')],
+                                  'i1'],
+                       'offsets': [0, 4, 16]}, align=True)
+        assert_equal(dt2.itemsize, 20)
+        dt3 = np.dtype({'f0': ('i4', 0),
+                       'f1': ([('f1', 'i1'), ('f2', 'i4'), ('f3', 'i1')], 4),
+                       'f2': ('i1', 16)}, align=True)
+        assert_equal(dt3.itemsize, 20)
+        assert_equal(dt1, dt2)
+        assert_equal(dt2, dt3)
+        # Nesting should preserve packing
+        dt1 = np.dtype([('f0', 'i4'),
+                       ('f1', [('f1', 'i1'), ('f2', 'i4'), ('f3', 'i1')]),
+                       ('f2', 'i1')], align=False)
+        assert_equal(dt1.itemsize, 11)
+        dt2 = np.dtype({'names': ['f0', 'f1', 'f2'],
+                       'formats': ['i4',
+                                  [('f1', 'i1'), ('f2', 'i4'), ('f3', 'i1')],
+                                  'i1'],
+                       'offsets': [0, 4, 10]}, align=False)
+        assert_equal(dt2.itemsize, 11)
+        dt3 = np.dtype({'f0': ('i4', 0),
+                       'f1': ([('f1', 'i1'), ('f2', 'i4'), ('f3', 'i1')], 4),
+                       'f2': ('i1', 10)}, align=False)
+        assert_equal(dt3.itemsize, 11)
+        assert_equal(dt1, dt2)
+        assert_equal(dt2, dt3)
+        # Array of subtype should preserve alignment
+        dt1 = np.dtype([('a', '|i1'),
+                        ('b', [('f0', '<i2'),
+                        ('f1', '<f4')], 2)], align=True)
+        assert_equal(dt1.descr, [('a', '|i1'), ('', '|V3'),
+                                 ('b', [('f0', '<i2'), ('', '|V2'),
+                                 ('f1', '<f4')], (2,))])
+
+    def test_empty_struct_alignment(self):
+        # Empty dtypes should have an alignment of 1
+        dt = np.dtype([], align=True)
+        assert_equal(dt.alignment, 1)
+        dt = np.dtype([('f0', [])], align=True)
+        assert_equal(dt.alignment, 1)
+        dt = np.dtype({'names': [],
+                       'formats': [],
+                       'offsets': []}, align=True)
+        assert_equal(dt.alignment, 1)
+        dt = np.dtype({'names': ['f0'],
+                       'formats': [[]],
+                       'offsets': [0]}, align=True)
+        assert_equal(dt.alignment, 1)
+
+    def test_union_struct(self):
+        # Should be able to create union dtypes
+        dt = np.dtype({'names': ['f0', 'f1', 'f2'], 'formats': ['<u4', '<u2', '<u2'],
+                        'offsets': [0, 0, 2]}, align=True)
+        assert_equal(dt.itemsize, 4)
+        a = np.array([3], dtype='<u4').view(dt)
+        a['f1'] = 10
+        a['f2'] = 36
+        assert_equal(a['f0'], 10 + 36 * 256 * 256)
+        # Should be able to specify fields out of order
+        dt = np.dtype({'names': ['f0', 'f1', 'f2'], 'formats': ['<u4', '<u2', '<u2'],
+                        'offsets': [4, 0, 2]}, align=True)
+        assert_equal(dt.itemsize, 8)
+        # field name should not matter: assignment is by position
+        dt2 = np.dtype({'names': ['f2', 'f0', 'f1'],
+                        'formats': ['<u4', '<u2', '<u2'],
+                        'offsets': [4, 0, 2]}, align=True)
+        vals = [(0, 1, 2), (3, 2**15 - 1, 4)]
+        vals2 = [(0, 1, 2), (3, 2**15 - 1, 4)]
+        a = np.array(vals, dt)
+        b = np.array(vals2, dt2)
+        assert_equal(a.astype(dt2), b)
+        assert_equal(b.astype(dt), a)
+        assert_equal(a.view(dt2), b)
+        assert_equal(b.view(dt), a)
+        # Should not be able to overlap objects with other types
+        assert_raises(TypeError, np.dtype,
+                {'names': ['f0', 'f1'],
+                 'formats': ['O', 'i1'],
+                 'offsets': [0, 2]})
+        assert_raises(TypeError, np.dtype,
+                {'names': ['f0', 'f1'],
+                 'formats': ['i4', 'O'],
+                 'offsets': [0, 3]})
+        assert_raises(TypeError, np.dtype,
+                {'names': ['f0', 'f1'],
+                 'formats': [[('a', 'O')], 'i1'],
+                 'offsets': [0, 2]})
+        assert_raises(TypeError, np.dtype,
+                {'names': ['f0', 'f1'],
+                 'formats': ['i4', [('a', 'O')]],
+                 'offsets': [0, 3]})
+        # Out of order should still be ok, however
+        dt = np.dtype({'names': ['f0', 'f1'],
+                       'formats': ['i1', 'O'],
+                       'offsets': [np.dtype('intp').itemsize, 0]})
+
+    @pytest.mark.parametrize(["obj", "dtype", "expected"],
+        [([], ("2f4"), np.empty((0, 2), dtype="f4")),
+         (3, "(3,)f4", [3, 3, 3]),
+         (np.float64(2), "(2,)f4", [2, 2]),
+         ([((0, 1), (1, 2)), ((2,),)], '(2,2)f4', None),
+         (["1", "2"], "2i", None)])
+    def test_subarray_list(self, obj, dtype, expected):
+        dtype = np.dtype(dtype)
+        res = np.array(obj, dtype=dtype)
+
+        if expected is None:
+            # iterate the 1-d list to fill the array
+            expected = np.empty(len(obj), dtype=dtype)
+            for i in range(len(expected)):
+                expected[i] = obj[i]
+
+        assert_array_equal(res, expected)
+
+    def test_parenthesized_single_number(self):
+        with pytest.raises(TypeError, match="not understood"):
+            np.dtype("(2)f4")
+
+        # Deprecation also tested in
+        # test_deprecations.py::TestDeprecatedDTypeParenthesizedRepeatCount
+        # Left here to allow easy conversion to an exception check.
+        with pytest.warns(DeprecationWarning,
+                          match="parenthesized single number"):
+            np.dtype("(2)f4,")
+
+    def test_comma_datetime(self):
+        dt = np.dtype('M8[D],datetime64[Y],i8')
+        assert_equal(dt, np.dtype([('f0', 'M8[D]'),
+                                   ('f1', 'datetime64[Y]'),
+                                   ('f2', 'i8')]))
+
+    def test_from_dictproxy(self):
+        # Tests for PR #5920
+        dt = np.dtype({'names': ['a', 'b'], 'formats': ['i4', 'f4']})
+        assert_dtype_equal(dt, np.dtype(dt.fields))
+        dt2 = np.dtype((np.void, dt.fields))
+        assert_equal(dt2.fields, dt.fields)
+
+    def test_from_dict_with_zero_width_field(self):
+        # Regression test for #6430 / #2196
+        dt = np.dtype([('val1', np.float32, (0,)), ('val2', int)])
+        dt2 = np.dtype({'names': ['val1', 'val2'],
+                        'formats': [(np.float32, (0,)), int]})
+
+        assert_dtype_equal(dt, dt2)
+        assert_equal(dt.fields['val1'][0].itemsize, 0)
+        assert_equal(dt.itemsize, dt.fields['val2'][0].itemsize)
+
+    def test_bool_commastring(self):
+        d = np.dtype('?,?,?')  # raises?
+        assert_equal(len(d.names), 3)
+        for n in d.names:
+            assert_equal(d.fields[n][0], np.dtype('?'))
+
+    def test_nonint_offsets(self):
+        # gh-8059
+        def make_dtype(off):
+            return np.dtype({'names': ['A'], 'formats': ['i4'],
+                             'offsets': [off]})
+
+        assert_raises(TypeError, make_dtype, 'ASD')
+        assert_raises(OverflowError, make_dtype, 2**70)
+        assert_raises(TypeError, make_dtype, 2.3)
+        assert_raises(ValueError, make_dtype, -10)
+
+        # no errors here:
+        dt = make_dtype(np.uint32(0))
+        np.zeros(1, dtype=dt)[0].item()
+
+    def test_fields_by_index(self):
+        dt = np.dtype([('a', np.int8), ('b', np.float32, 3)])
+        assert_dtype_equal(dt[0], np.dtype(np.int8))
+        assert_dtype_equal(dt[1], np.dtype((np.float32, 3)))
+        assert_dtype_equal(dt[-1], dt[1])
+        assert_dtype_equal(dt[-2], dt[0])
+        assert_raises(IndexError, lambda: dt[-3])
+
+        assert_raises(TypeError, operator.getitem, dt, 3.0)
+
+        assert_equal(dt[1], dt[np.int8(1)])
+
+    @pytest.mark.parametrize('align_flag', [False, True])
+    def test_multifield_index(self, align_flag):
+        # indexing with a list produces subfields
+        # the align flag should be preserved
+        dt = np.dtype([
+            (('title', 'col1'), '<U20'), ('A', '<f8'), ('B', '<f8')
+        ], align=align_flag)
+
+        dt_sub = dt[['B', 'col1']]
+        assert_equal(
+            dt_sub,
+            np.dtype({
+                'names': ['B', 'col1'],
+                'formats': ['<f8', '<U20'],
+                'offsets': [88, 0],
+                'titles': [None, 'title'],
+                'itemsize': 96
+            })
+        )
+        assert_equal(dt_sub.isalignedstruct, align_flag)
+
+        dt_sub = dt[['B']]
+        assert_equal(
+            dt_sub,
+            np.dtype({
+                'names': ['B'],
+                'formats': ['<f8'],
+                'offsets': [88],
+                'itemsize': 96
+            })
+        )
+        assert_equal(dt_sub.isalignedstruct, align_flag)
+
+        dt_sub = dt[[]]
+        assert_equal(
+            dt_sub,
+            np.dtype({
+                'names': [],
+                'formats': [],
+                'offsets': [],
+                'itemsize': 96
+            })
+        )
+        assert_equal(dt_sub.isalignedstruct, align_flag)
+
+        assert_raises(TypeError, operator.getitem, dt, ())
+        assert_raises(TypeError, operator.getitem, dt, [1, 2, 3])
+        assert_raises(TypeError, operator.getitem, dt, ['col1', 2])
+        assert_raises(KeyError, operator.getitem, dt, ['fake'])
+        assert_raises(KeyError, operator.getitem, dt, ['title'])
+        assert_raises(ValueError, operator.getitem, dt, ['col1', 'col1'])
+
+    def test_partial_dict(self):
+        # 'names' is missing
+        assert_raises(ValueError, np.dtype,
+                {'formats': ['i4', 'i4'], 'f0': ('i4', 0), 'f1': ('i4', 4)})
+
+    def test_fieldless_views(self):
+        a = np.zeros(2, dtype={'names': [], 'formats': [], 'offsets': [],
+                               'itemsize': 8})
+        assert_raises(ValueError, a.view, np.dtype([]))
+
+        d = np.dtype((np.dtype([]), 10))
+        assert_equal(d.shape, (10,))
+        assert_equal(d.itemsize, 0)
+        assert_equal(d.base, np.dtype([]))
+
+        arr = np.fromiter((() for i in range(10)), [])
+        assert_equal(arr.dtype, np.dtype([]))
+        assert_raises(ValueError, np.frombuffer, b'', dtype=[])
+        assert_equal(np.frombuffer(b'', dtype=[], count=2),
+                     np.empty(2, dtype=[]))
+
+        assert_raises(ValueError, np.dtype, ([], 'f8'))
+        assert_raises(ValueError, np.zeros(1, dtype='i4').view, [])
+
+        assert_equal(np.zeros(2, dtype=[]) == np.zeros(2, dtype=[]),
+                     np.ones(2, dtype=bool))
+
+        assert_equal(np.zeros((1, 2), dtype=[]) == a,
+                     np.ones((1, 2), dtype=bool))
+
+    def test_nonstructured_with_object(self):
+        # See gh-23277, the dtype here thinks it contain objects, if the
+        # assert about that fails, the test becomes meaningless (which is OK)
+        arr = np.recarray((0,), dtype="O")
+        assert arr.dtype.names is None  # no fields
+        assert arr.dtype.hasobject  # but claims to contain objects
+        del arr  # the deletion failed previously.
+
+
+class TestSubarray:
+    def test_single_subarray(self):
+        a = np.dtype((int, (2)))
+        b = np.dtype((int, (2,)))
+        assert_dtype_equal(a, b)
+
+        assert_equal(type(a.subdtype[1]), tuple)
+        assert_equal(type(b.subdtype[1]), tuple)
+
+    def test_equivalent_record(self):
+        """Test whether equivalent subarray dtypes hash the same."""
+        a = np.dtype((int, (2, 3)))
+        b = np.dtype((int, (2, 3)))
+        assert_dtype_equal(a, b)
+
+    def test_nonequivalent_record(self):
+        """Test whether different subarray dtypes hash differently."""
+        a = np.dtype((int, (2, 3)))
+        b = np.dtype((int, (3, 2)))
+        assert_dtype_not_equal(a, b)
+
+        a = np.dtype((int, (2, 3)))
+        b = np.dtype((int, (2, 2)))
+        assert_dtype_not_equal(a, b)
+
+        a = np.dtype((int, (1, 2, 3)))
+        b = np.dtype((int, (1, 2)))
+        assert_dtype_not_equal(a, b)
+
+    def test_shape_equal(self):
+        """Test some data types that are equal"""
+        assert_dtype_equal(np.dtype('f8'), np.dtype(('f8', ())))
+        assert_dtype_equal(np.dtype('(1,)f8'), np.dtype(('f8', 1)))
+        assert np.dtype(('f8', 1)).shape == (1,)
+        assert_dtype_equal(np.dtype((int, 2)), np.dtype((int, (2,))))
+        assert_dtype_equal(np.dtype(('<f4', (3, 2))), np.dtype(('<f4', (3, 2))))
+        d = ([('a', 'f4', (1, 2)), ('b', 'f8', (3, 1))], (3, 2))
+        assert_dtype_equal(np.dtype(d), np.dtype(d))
+
+    def test_shape_simple(self):
+        """Test some simple cases that shouldn't be equal"""
+        assert_dtype_not_equal(np.dtype('f8'), np.dtype(('f8', (1,))))
+        assert_dtype_not_equal(np.dtype(('f8', (1,))), np.dtype(('f8', (1, 1))))
+        assert_dtype_not_equal(np.dtype(('f4', (3, 2))), np.dtype(('f4', (2, 3))))
+
+    def test_shape_monster(self):
+        """Test some more complicated cases that shouldn't be equal"""
+        assert_dtype_not_equal(
+            np.dtype(([('a', 'f4', (2, 1)), ('b', 'f8', (1, 3))], (2, 2))),
+            np.dtype(([('a', 'f4', (1, 2)), ('b', 'f8', (1, 3))], (2, 2))))
+        assert_dtype_not_equal(
+            np.dtype(([('a', 'f4', (2, 1)), ('b', 'f8', (1, 3))], (2, 2))),
+            np.dtype(([('a', 'f4', (2, 1)), ('b', 'i8', (1, 3))], (2, 2))))
+        assert_dtype_not_equal(
+            np.dtype(([('a', 'f4', (2, 1)), ('b', 'f8', (1, 3))], (2, 2))),
+            np.dtype(([('e', 'f8', (1, 3)), ('d', 'f4', (2, 1))], (2, 2))))
+        assert_dtype_not_equal(
+            np.dtype(([('a', [('a', 'i4', 6)], (2, 1)), ('b', 'f8', (1, 3))], (2, 2))),
+            np.dtype(([('a', [('a', 'u4', 6)], (2, 1)), ('b', 'f8', (1, 3))], (2, 2))))
+
+    def test_shape_sequence(self):
+        # Any sequence of integers should work as shape, but the result
+        # should be a tuple (immutable) of base type integers.
+        a = np.array([1, 2, 3], dtype=np.int16)
+        l = [1, 2, 3]
+        # Array gets converted
+        dt = np.dtype([('a', 'f4', a)])
+        assert_(isinstance(dt['a'].shape, tuple))
+        assert_(isinstance(dt['a'].shape[0], int))
+        # List gets converted
+        dt = np.dtype([('a', 'f4', l)])
+        assert_(isinstance(dt['a'].shape, tuple))
+        #
+
+        class IntLike:
+            def __index__(self):
+                return 3
+
+            def __int__(self):
+                # (a PyNumber_Check fails without __int__)
+                return 3
+
+        dt = np.dtype([('a', 'f4', IntLike())])
+        assert_(isinstance(dt['a'].shape, tuple))
+        assert_(isinstance(dt['a'].shape[0], int))
+        dt = np.dtype([('a', 'f4', (IntLike(),))])
+        assert_(isinstance(dt['a'].shape, tuple))
+        assert_(isinstance(dt['a'].shape[0], int))
+
+    def test_shape_matches_ndim(self):
+        dt = np.dtype([('a', 'f4', ())])
+        assert_equal(dt['a'].shape, ())
+        assert_equal(dt['a'].ndim, 0)
+
+        dt = np.dtype([('a', 'f4')])
+        assert_equal(dt['a'].shape, ())
+        assert_equal(dt['a'].ndim, 0)
+
+        dt = np.dtype([('a', 'f4', 4)])
+        assert_equal(dt['a'].shape, (4,))
+        assert_equal(dt['a'].ndim, 1)
+
+        dt = np.dtype([('a', 'f4', (1, 2, 3))])
+        assert_equal(dt['a'].shape, (1, 2, 3))
+        assert_equal(dt['a'].ndim, 3)
+
+    def test_shape_invalid(self):
+        # Check that the shape is valid.
+        max_int = np.iinfo(np.intc).max
+        max_intp = np.iinfo(np.intp).max
+        # Too large values (the datatype is part of this)
+        assert_raises(ValueError, np.dtype, [('a', 'f4', max_int // 4 + 1)])
+        assert_raises(ValueError, np.dtype, [('a', 'f4', max_int + 1)])
+        assert_raises(ValueError, np.dtype, [('a', 'f4', (max_int, 2))])
+        # Takes a different code path (fails earlier:
+        assert_raises(ValueError, np.dtype, [('a', 'f4', max_intp + 1)])
+        # Negative values
+        assert_raises(ValueError, np.dtype, [('a', 'f4', -1)])
+        assert_raises(ValueError, np.dtype, [('a', 'f4', (-1, -1))])
+
+    def test_alignment(self):
+        # Check that subarrays are aligned
+        t1 = np.dtype('(1,)i4', align=True)
+        t2 = np.dtype('2i4', align=True)
+        assert_equal(t1.alignment, t2.alignment)
+
+    def test_aligned_empty(self):
+        # Mainly regression test for gh-19696: construction failed completely
+        dt = np.dtype([], align=True)
+        assert dt == np.dtype([])
+        dt = np.dtype({"names": [], "formats": [], "itemsize": 0}, align=True)
+        assert dt == np.dtype([])
+
+    def test_subarray_base_item(self):
+        arr = np.ones(3, dtype=[("f", "i", 3)])
+        # Extracting the field "absorbs" the subarray into a view:
+        assert arr["f"].base is arr
+        # Extract the structured item, and then check the tuple component:
+        item = arr.item(0)
+        assert type(item) is tuple and len(item) == 1
+        assert item[0].base is arr
+
+    def test_subarray_cast_copies(self):
+        # Older versions of NumPy did NOT copy, but they got the ownership
+        # wrong (not actually knowing the correct base!).  Versions since 1.21
+        # (I think) crashed fairly reliable.  This defines the correct behavior
+        # as a copy.  Keeping the ownership would be possible (but harder)
+        arr = np.ones(3, dtype=[("f", "i", 3)])
+        cast = arr.astype(object)
+        for fields in cast:
+            assert type(fields) == tuple and len(fields) == 1
+            subarr = fields[0]
+            assert subarr.base is None
+            assert subarr.flags.owndata
+
+
+def iter_struct_object_dtypes():
+    """
+    Iterates over a few complex dtypes and object pattern which
+    fill the array with a given object (defaults to a singleton).
+
+    Yields
+    ------
+    dtype : dtype
+    pattern : tuple
+        Structured tuple for use with `np.array`.
+    count : int
+        Number of objects stored in the dtype.
+    singleton : object
+        A singleton object. The returned pattern is constructed so that
+        all objects inside the datatype are set to the singleton.
+    """
+    obj = object()
+
+    dt = np.dtype([('b', 'O', (2, 3))])
+    p = ([[obj] * 3] * 2,)
+    yield pytest.param(dt, p, 6, obj, id="<subarray>")
+
+    dt = np.dtype([('a', 'i4'), ('b', 'O', (2, 3))])
+    p = (0, [[obj] * 3] * 2)
+    yield pytest.param(dt, p, 6, obj, id="<subarray in field>")
+
+    dt = np.dtype([('a', 'i4'),
+                   ('b', [('ba', 'O'), ('bb', 'i1')], (2, 3))])
+    p = (0, [[(obj, 0)] * 3] * 2)
+    yield pytest.param(dt, p, 6, obj, id="<structured subarray 1>")
+
+    dt = np.dtype([('a', 'i4'),
+                   ('b', [('ba', 'O'), ('bb', 'O')], (2, 3))])
+    p = (0, [[(obj, obj)] * 3] * 2)
+    yield pytest.param(dt, p, 12, obj, id="<structured subarray 2>")
+
+
+@pytest.mark.skipif(
+    sys.version_info >= (3, 12),
+    reason="Python 3.12 has immortal refcounts, this test will no longer "
+           "work. See gh-23986"
+)
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+class TestStructuredObjectRefcounting:
+    """These tests cover various uses of complicated structured types which
+    include objects and thus require reference counting.
+    """
+    @pytest.mark.parametrize(['dt', 'pat', 'count', 'singleton'],
+                             iter_struct_object_dtypes())
+    @pytest.mark.parametrize(["creation_func", "creation_obj"], [
+        pytest.param(np.empty, None,
+             # None is probably used for too many things
+             marks=pytest.mark.skip("unreliable due to python's behaviour")),
+        (np.ones, 1),
+        (np.zeros, 0)])
+    def test_structured_object_create_delete(self, dt, pat, count, singleton,
+                                             creation_func, creation_obj):
+        """Structured object reference counting in creation and deletion"""
+        # The test assumes that 0, 1, and None are singletons.
+        gc.collect()
+        before = sys.getrefcount(creation_obj)
+        arr = creation_func(3, dt)
+
+        now = sys.getrefcount(creation_obj)
+        assert now - before == count * 3
+        del arr
+        now = sys.getrefcount(creation_obj)
+        assert now == before
+
+    @pytest.mark.parametrize(['dt', 'pat', 'count', 'singleton'],
+                             iter_struct_object_dtypes())
+    def test_structured_object_item_setting(self, dt, pat, count, singleton):
+        """Structured object reference counting for simple item setting"""
+        one = 1
+
+        gc.collect()
+        before = sys.getrefcount(singleton)
+        arr = np.array([pat] * 3, dt)
+        assert sys.getrefcount(singleton) - before == count * 3
+        # Fill with `1` and check that it was replaced correctly:
+        before2 = sys.getrefcount(one)
+        arr[...] = one
+        after2 = sys.getrefcount(one)
+        assert after2 - before2 == count * 3
+        del arr
+        gc.collect()
+        assert sys.getrefcount(one) == before2
+        assert sys.getrefcount(singleton) == before
+
+    @pytest.mark.parametrize(['dt', 'pat', 'count', 'singleton'],
+                             iter_struct_object_dtypes())
+    @pytest.mark.parametrize(
+        ['shape', 'index', 'items_changed'],
+        [((3,), ([0, 2],), 2),
+         ((3, 2), ([0, 2], slice(None)), 4),
+         ((3, 2), ([0, 2], [1]), 2),
+         ((3,), ([True, False, True]), 2)])
+    def test_structured_object_indexing(self, shape, index, items_changed,
+                                        dt, pat, count, singleton):
+        """Structured object reference counting for advanced indexing."""
+        # Use two small negative values (should be singletons, but less likely
+        # to run into race-conditions).  This failed in some threaded envs
+        # When using 0 and 1.  If it fails again, should remove all explicit
+        # checks, and rely on `pytest-leaks` reference count checker only.
+        val0 = -4
+        val1 = -5
+
+        arr = np.full(shape, val0, dt)
+
+        gc.collect()
+        before_val0 = sys.getrefcount(val0)
+        before_val1 = sys.getrefcount(val1)
+        # Test item getting:
+        part = arr[index]
+        after_val0 = sys.getrefcount(val0)
+        assert after_val0 - before_val0 == count * items_changed
+        del part
+        # Test item setting:
+        arr[index] = val1
+        gc.collect()
+        after_val0 = sys.getrefcount(val0)
+        after_val1 = sys.getrefcount(val1)
+        assert before_val0 - after_val0 == count * items_changed
+        assert after_val1 - before_val1 == count * items_changed
+
+    @pytest.mark.parametrize(['dt', 'pat', 'count', 'singleton'],
+                             iter_struct_object_dtypes())
+    def test_structured_object_take_and_repeat(self, dt, pat, count, singleton):
+        """Structured object reference counting for specialized functions.
+        The older functions such as take and repeat use different code paths
+        then item setting (when writing this).
+        """
+        indices = [0, 1]
+
+        arr = np.array([pat] * 3, dt)
+        gc.collect()
+        before = sys.getrefcount(singleton)
+        res = arr.take(indices)
+        after = sys.getrefcount(singleton)
+        assert after - before == count * 2
+        new = res.repeat(10)
+        gc.collect()
+        after_repeat = sys.getrefcount(singleton)
+        assert after_repeat - after == count * 2 * 10
+
+
+class TestStructuredDtypeSparseFields:
+    """Tests subarray fields which contain sparse dtypes so that
+    not all memory is used by the dtype work. Such dtype's should
+    leave the underlying memory unchanged.
+    """
+    dtype = np.dtype([('a', {'names': ['aa', 'ab'], 'formats': ['f', 'f'],
+                             'offsets': [0, 4]}, (2, 3))])
+    sparse_dtype = np.dtype([('a', {'names': ['ab'], 'formats': ['f'],
+                                    'offsets': [4]}, (2, 3))])
+
+    def test_sparse_field_assignment(self):
+        arr = np.zeros(3, self.dtype)
+        sparse_arr = arr.view(self.sparse_dtype)
+
+        sparse_arr[...] = np.finfo(np.float32).max
+        # dtype is reduced when accessing the field, so shape is (3, 2, 3):
+        assert_array_equal(arr["a"]["aa"], np.zeros((3, 2, 3)))
+
+    def test_sparse_field_assignment_fancy(self):
+        # Fancy assignment goes to the copyswap function for complex types:
+        arr = np.zeros(3, self.dtype)
+        sparse_arr = arr.view(self.sparse_dtype)
+
+        sparse_arr[[0, 1, 2]] = np.finfo(np.float32).max
+        # dtype is reduced when accessing the field, so shape is (3, 2, 3):
+        assert_array_equal(arr["a"]["aa"], np.zeros((3, 2, 3)))
+
+
+class TestMonsterType:
+    """Test deeply nested subtypes."""
+
+    def test1(self):
+        simple1 = np.dtype({'names': ['r', 'b'], 'formats': ['u1', 'u1'],
+            'titles': ['Red pixel', 'Blue pixel']})
+        a = np.dtype([('yo', int), ('ye', simple1),
+            ('yi', np.dtype((int, (3, 2))))])
+        b = np.dtype([('yo', int), ('ye', simple1),
+            ('yi', np.dtype((int, (3, 2))))])
+        assert_dtype_equal(a, b)
+
+        c = np.dtype([('yo', int), ('ye', simple1),
+            ('yi', np.dtype((a, (3, 2))))])
+        d = np.dtype([('yo', int), ('ye', simple1),
+            ('yi', np.dtype((a, (3, 2))))])
+        assert_dtype_equal(c, d)
+
+    @pytest.mark.skipif(IS_PYSTON, reason="Pyston disables recursion checking")
+    @pytest.mark.skipif(IS_WASM, reason="Pyodide/WASM has limited stack size")
+    def test_list_recursion(self):
+        l = []
+        l.append(('f', l))
+        with pytest.raises(RecursionError):
+            np.dtype(l)
+
+    @pytest.mark.skipif(IS_PYSTON, reason="Pyston disables recursion checking")
+    @pytest.mark.skipif(IS_WASM, reason="Pyodide/WASM has limited stack size")
+    def test_tuple_recursion(self):
+        d = np.int32
+        for i in range(100000):
+            d = (d, (1,))
+        with pytest.raises(RecursionError):
+            np.dtype(d)
+
+    @pytest.mark.skipif(IS_PYSTON, reason="Pyston disables recursion checking")
+    @pytest.mark.skipif(IS_WASM, reason="Pyodide/WASM has limited stack size")
+    def test_dict_recursion(self):
+        d = {"names": ['self'], "formats": [None], "offsets": [0]}
+        d['formats'][0] = d
+        with pytest.raises(RecursionError):
+            np.dtype(d)
+
+
+class TestMetadata:
+    def test_no_metadata(self):
+        d = np.dtype(int)
+        assert_(d.metadata is None)
+
+    def test_metadata_takes_dict(self):
+        d = np.dtype(int, metadata={'datum': 1})
+        assert_(d.metadata == {'datum': 1})
+
+    def test_metadata_rejects_nondict(self):
+        assert_raises(TypeError, np.dtype, int, metadata='datum')
+        assert_raises(TypeError, np.dtype, int, metadata=1)
+        assert_raises(TypeError, np.dtype, int, metadata=None)
+
+    def test_nested_metadata(self):
+        d = np.dtype([('a', np.dtype(int, metadata={'datum': 1}))])
+        assert_(d['a'].metadata == {'datum': 1})
+
+    def test_base_metadata_copied(self):
+        d = np.dtype((np.void, np.dtype('i4,i4', metadata={'datum': 1})))
+        assert_(d.metadata == {'datum': 1})
+
+class TestString:
+    def test_complex_dtype_str(self):
+        dt = np.dtype([('top', [('tiles', ('>f4', (64, 64)), (1,)),
+                                ('rtile', '>f4', (64, 36))], (3,)),
+                       ('bottom', [('bleft', ('>f4', (8, 64)), (1,)),
+                                   ('bright', '>f4', (8, 36))])])
+        assert_equal(str(dt),
+                     "[('top', [('tiles', ('>f4', (64, 64)), (1,)), "
+                     "('rtile', '>f4', (64, 36))], (3,)), "
+                     "('bottom', [('bleft', ('>f4', (8, 64)), (1,)), "
+                     "('bright', '>f4', (8, 36))])]")
+
+        # If the sticky aligned flag is set to True, it makes the
+        # str() function use a dict representation with an 'aligned' flag
+        dt = np.dtype([('top', [('tiles', ('>f4', (64, 64)), (1,)),
+                                ('rtile', '>f4', (64, 36))],
+                                (3,)),
+                       ('bottom', [('bleft', ('>f4', (8, 64)), (1,)),
+                                   ('bright', '>f4', (8, 36))])],
+                       align=True)
+        assert_equal(str(dt),
+                    "{'names': ['top', 'bottom'],"
+                    " 'formats': [([('tiles', ('>f4', (64, 64)), (1,)), "
+                                   "('rtile', '>f4', (64, 36))], (3,)), "
+                                  "[('bleft', ('>f4', (8, 64)), (1,)), "
+                                   "('bright', '>f4', (8, 36))]],"
+                    " 'offsets': [0, 76800],"
+                    " 'itemsize': 80000,"
+                    " 'aligned': True}")
+        with np.printoptions(legacy='1.21'):
+            assert_equal(str(dt),
+                        "{'names':['top','bottom'], "
+                         "'formats':[([('tiles', ('>f4', (64, 64)), (1,)), "
+                                      "('rtile', '>f4', (64, 36))], (3,)),"
+                                     "[('bleft', ('>f4', (8, 64)), (1,)), "
+                                      "('bright', '>f4', (8, 36))]], "
+                         "'offsets':[0,76800], "
+                         "'itemsize':80000, "
+                         "'aligned':True}")
+        assert_equal(np.dtype(eval(str(dt))), dt)
+
+        dt = np.dtype({'names': ['r', 'g', 'b'], 'formats': ['u1', 'u1', 'u1'],
+                        'offsets': [0, 1, 2],
+                        'titles': ['Red pixel', 'Green pixel', 'Blue pixel']})
+        assert_equal(str(dt),
+                    "[(('Red pixel', 'r'), 'u1'), "
+                    "(('Green pixel', 'g'), 'u1'), "
+                    "(('Blue pixel', 'b'), 'u1')]")
+
+        dt = np.dtype({'names': ['rgba', 'r', 'g', 'b'],
+                       'formats': ['<u4', 'u1', 'u1', 'u1'],
+                       'offsets': [0, 0, 1, 2],
+                       'titles': ['Color', 'Red pixel',
+                                  'Green pixel', 'Blue pixel']})
+        assert_equal(str(dt),
+                    "{'names': ['rgba', 'r', 'g', 'b'],"
+                    " 'formats': ['<u4', 'u1', 'u1', 'u1'],"
+                    " 'offsets': [0, 0, 1, 2],"
+                    " 'titles': ['Color', 'Red pixel', "
+                               "'Green pixel', 'Blue pixel'],"
+                    " 'itemsize': 4}")
+
+        dt = np.dtype({'names': ['r', 'b'], 'formats': ['u1', 'u1'],
+                        'offsets': [0, 2],
+                        'titles': ['Red pixel', 'Blue pixel']})
+        assert_equal(str(dt),
+                    "{'names': ['r', 'b'],"
+                    " 'formats': ['u1', 'u1'],"
+                    " 'offsets': [0, 2],"
+                    " 'titles': ['Red pixel', 'Blue pixel'],"
+                    " 'itemsize': 3}")
+
+        dt = np.dtype([('a', '<m8[D]'), ('b', '<M8[us]')])
+        assert_equal(str(dt),
+                    "[('a', '<m8[D]'), ('b', '<M8[us]')]")
+
+    def test_repr_structured(self):
+        dt = np.dtype([('top', [('tiles', ('>f4', (64, 64)), (1,)),
+                                ('rtile', '>f4', (64, 36))], (3,)),
+                       ('bottom', [('bleft', ('>f4', (8, 64)), (1,)),
+                                   ('bright', '>f4', (8, 36))])])
+        assert_equal(repr(dt),
+                     "dtype([('top', [('tiles', ('>f4', (64, 64)), (1,)), "
+                     "('rtile', '>f4', (64, 36))], (3,)), "
+                     "('bottom', [('bleft', ('>f4', (8, 64)), (1,)), "
+                     "('bright', '>f4', (8, 36))])])")
+
+        dt = np.dtype({'names': ['r', 'g', 'b'], 'formats': ['u1', 'u1', 'u1'],
+                        'offsets': [0, 1, 2],
+                        'titles': ['Red pixel', 'Green pixel', 'Blue pixel']},
+                        align=True)
+        assert_equal(repr(dt),
+                    "dtype([(('Red pixel', 'r'), 'u1'), "
+                    "(('Green pixel', 'g'), 'u1'), "
+                    "(('Blue pixel', 'b'), 'u1')], align=True)")
+
+    def test_repr_structured_not_packed(self):
+        dt = np.dtype({'names': ['rgba', 'r', 'g', 'b'],
+                       'formats': ['<u4', 'u1', 'u1', 'u1'],
+                       'offsets': [0, 0, 1, 2],
+                       'titles': ['Color', 'Red pixel',
+                                  'Green pixel', 'Blue pixel']}, align=True)
+        assert_equal(repr(dt),
+                    "dtype({'names': ['rgba', 'r', 'g', 'b'],"
+                    " 'formats': ['<u4', 'u1', 'u1', 'u1'],"
+                    " 'offsets': [0, 0, 1, 2],"
+                    " 'titles': ['Color', 'Red pixel', "
+                                "'Green pixel', 'Blue pixel'],"
+                    " 'itemsize': 4}, align=True)")
+
+        dt = np.dtype({'names': ['r', 'b'], 'formats': ['u1', 'u1'],
+                        'offsets': [0, 2],
+                        'titles': ['Red pixel', 'Blue pixel'],
+                        'itemsize': 4})
+        assert_equal(repr(dt),
+                    "dtype({'names': ['r', 'b'], "
+                    "'formats': ['u1', 'u1'], "
+                    "'offsets': [0, 2], "
+                    "'titles': ['Red pixel', 'Blue pixel'], "
+                    "'itemsize': 4})")
+
+    def test_repr_structured_datetime(self):
+        dt = np.dtype([('a', '<M8[D]'), ('b', '<m8[us]')])
+        assert_equal(repr(dt),
+                    "dtype([('a', '<M8[D]'), ('b', '<m8[us]')])")
+
+    def test_repr_str_subarray(self):
+        dt = np.dtype(('<i2', (1,)))
+        assert_equal(repr(dt), "dtype(('<i2', (1,)))")
+        assert_equal(str(dt), "('<i2', (1,))")
+
+    def test_base_dtype_with_object_type(self):
+        # Issue gh-2798, should not error.
+        np.array(['a'], dtype="O").astype(("O", [("name", "O")]))
+
+    def test_empty_string_to_object(self):
+        # Pull request #4722
+        np.array(["", ""]).astype(object)
+
+    def test_void_subclass_unsized(self):
+        dt = np.dtype(np.record)
+        assert_equal(repr(dt), "dtype('V')")
+        assert_equal(str(dt), '|V0')
+        assert_equal(dt.name, 'record')
+
+    def test_void_subclass_sized(self):
+        dt = np.dtype((np.record, 2))
+        assert_equal(repr(dt), "dtype('V2')")
+        assert_equal(str(dt), '|V2')
+        assert_equal(dt.name, 'record16')
+
+    def test_void_subclass_fields(self):
+        dt = np.dtype((np.record, [('a', '<u2')]))
+        assert_equal(repr(dt), "dtype((numpy.record, [('a', '<u2')]))")
+        assert_equal(str(dt), "(numpy.record, [('a', '<u2')])")
+        assert_equal(dt.name, 'record16')
+
+    def test_custom_dtype_str(self):
+        dt = np.dtypes.StringDType()
+        assert_equal(dt.str, "StringDType()")
+
+
+class TestDtypeAttributeDeletion:
+
+    def test_dtype_non_writable_attributes_deletion(self):
+        dt = np.dtype(np.double)
+        attr = ["subdtype", "descr", "str", "name", "base", "shape",
+                "isbuiltin", "isnative", "isalignedstruct", "fields",
+                "metadata", "hasobject"]
+
+        for s in attr:
+            assert_raises(AttributeError, delattr, dt, s)
+
+    def test_dtype_writable_attributes_deletion(self):
+        dt = np.dtype(np.double)
+        attr = ["names"]
+        for s in attr:
+            assert_raises(AttributeError, delattr, dt, s)
+
+
+class TestDtypeAttributes:
+    def test_descr_has_trailing_void(self):
+        # see gh-6359
+        dtype = np.dtype({
+            'names': ['A', 'B'],
+            'formats': ['f4', 'f4'],
+            'offsets': [0, 8],
+            'itemsize': 16})
+        new_dtype = np.dtype(dtype.descr)
+        assert_equal(new_dtype.itemsize, 16)
+
+    def test_name_dtype_subclass(self):
+        # Ticket #4357
+        class user_def_subcls(np.void):
+            pass
+        assert_equal(np.dtype(user_def_subcls).name, 'user_def_subcls')
+
+    def test_zero_stride(self):
+        arr = np.ones(1, dtype="i8")
+        arr = np.broadcast_to(arr, 10)
+        assert arr.strides == (0,)
+        with pytest.raises(ValueError):
+            arr.dtype = "i1"
+
+class TestDTypeMakeCanonical:
+    def check_canonical(self, dtype, canonical):
+        """
+        Check most properties relevant to "canonical" versions of a dtype,
+        which is mainly native byte order for datatypes supporting this.
+
+        The main work is checking structured dtypes with fields, where we
+        reproduce most the actual logic used in the C-code.
+        """
+        assert type(dtype) is type(canonical)
+
+        # a canonical DType should always have equivalent casting (both ways)
+        assert np.can_cast(dtype, canonical, casting="equiv")
+        assert np.can_cast(canonical, dtype, casting="equiv")
+        # a canonical dtype (and its fields) is always native (checks fields):
+        assert canonical.isnative
+
+        # Check that canonical of canonical is the same (no casting):
+        assert np.result_type(canonical) == canonical
+
+        if not dtype.names:
+            # The flags currently never change for unstructured dtypes
+            assert dtype.flags == canonical.flags
+            return
+
+        # Must have all the needs API flag set:
+        assert dtype.flags & 0b10000
+
+        # Check that the fields are identical (including titles):
+        assert dtype.fields.keys() == canonical.fields.keys()
+
+        def aligned_offset(offset, alignment):
+            # round up offset:
+            return - (-offset // alignment) * alignment
+
+        totalsize = 0
+        max_alignment = 1
+        for name in dtype.names:
+            # each field is also canonical:
+            new_field_descr = canonical.fields[name][0]
+            self.check_canonical(dtype.fields[name][0], new_field_descr)
+
+            # Must have the "inherited" object related flags:
+            expected = 0b11011 & new_field_descr.flags
+            assert (canonical.flags & expected) == expected
+
+            if canonical.isalignedstruct:
+                totalsize = aligned_offset(totalsize, new_field_descr.alignment)
+                max_alignment = max(new_field_descr.alignment, max_alignment)
+
+            assert canonical.fields[name][1] == totalsize
+            # if a title exists, they must match (otherwise empty tuple):
+            assert dtype.fields[name][2:] == canonical.fields[name][2:]
+
+            totalsize += new_field_descr.itemsize
+
+        if canonical.isalignedstruct:
+            totalsize = aligned_offset(totalsize, max_alignment)
+        assert canonical.itemsize == totalsize
+        assert canonical.alignment == max_alignment
+
+    def test_simple(self):
+        dt = np.dtype(">i4")
+        assert np.result_type(dt).isnative
+        assert np.result_type(dt).num == dt.num
+
+        # dtype with empty space:
+        struct_dt = np.dtype(">i4,<i1,i8,V3")[["f0", "f2"]]
+        canonical = np.result_type(struct_dt)
+        assert canonical.itemsize == 4 + 8
+        assert canonical.isnative
+
+        # aligned struct dtype with empty space:
+        struct_dt = np.dtype(">i1,<i4,i8,V3", align=True)[["f0", "f2"]]
+        canonical = np.result_type(struct_dt)
+        assert canonical.isalignedstruct
+        assert canonical.itemsize == np.dtype("i8").alignment + 8
+        assert canonical.isnative
+
+    def test_object_flag_not_inherited(self):
+        # The following dtype still indicates "object", because its included
+        # in the unaccessible space (maybe this could change at some point):
+        arr = np.ones(3, "i,O,i")[["f0", "f2"]]
+        assert arr.dtype.hasobject
+        canonical_dt = np.result_type(arr.dtype)
+        assert not canonical_dt.hasobject
+
+    @pytest.mark.slow
+    @hypothesis.given(dtype=hynp.nested_dtypes())
+    def test_make_canonical_hypothesis(self, dtype):
+        canonical = np.result_type(dtype)
+        self.check_canonical(dtype, canonical)
+        # result_type with two arguments should always give identical results:
+        two_arg_result = np.result_type(dtype, dtype)
+        assert np.can_cast(two_arg_result, canonical, casting="no")
+
+    @pytest.mark.slow
+    @hypothesis.given(
+            dtype=hypothesis.extra.numpy.array_dtypes(
+                subtype_strategy=hypothesis.extra.numpy.array_dtypes(),
+                min_size=5, max_size=10, allow_subarrays=True))
+    def test_structured(self, dtype):
+        # Pick 4 of the fields at random.  This will leave empty space in the
+        # dtype (since we do not canonicalize it here).
+        field_subset = random.sample(dtype.names, k=4)
+        dtype_with_empty_space = dtype[field_subset]
+        assert dtype_with_empty_space.itemsize == dtype.itemsize
+        canonicalized = np.result_type(dtype_with_empty_space)
+        self.check_canonical(dtype_with_empty_space, canonicalized)
+        # promotion with two arguments should always give identical results:
+        two_arg_result = np.promote_types(
+                dtype_with_empty_space, dtype_with_empty_space)
+        assert np.can_cast(two_arg_result, canonicalized, casting="no")
+
+        # Ensure that we also check aligned struct (check the opposite, in
+        # case hypothesis grows support for `align`.  Then repeat the test:
+        dtype_aligned = np.dtype(dtype.descr, align=not dtype.isalignedstruct)
+        dtype_with_empty_space = dtype_aligned[field_subset]
+        assert dtype_with_empty_space.itemsize == dtype_aligned.itemsize
+        canonicalized = np.result_type(dtype_with_empty_space)
+        self.check_canonical(dtype_with_empty_space, canonicalized)
+        # promotion with two arguments should always give identical results:
+        two_arg_result = np.promote_types(
+            dtype_with_empty_space, dtype_with_empty_space)
+        assert np.can_cast(two_arg_result, canonicalized, casting="no")
+
+
+class TestPickling:
+
+    def check_pickling(self, dtype):
+        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
+            buf = pickle.dumps(dtype, proto)
+            # The dtype pickling itself pickles `np.dtype` if it is pickled
+            # as a singleton `dtype` should be stored in the buffer:
+            assert b"_DType_reconstruct" not in buf
+            assert b"dtype" in buf
+            pickled = pickle.loads(buf)
+            assert_equal(pickled, dtype)
+            assert_equal(pickled.descr, dtype.descr)
+            if dtype.metadata is not None:
+                assert_equal(pickled.metadata, dtype.metadata)
+            # Check the reconstructed dtype is functional
+            x = np.zeros(3, dtype=dtype)
+            y = np.zeros(3, dtype=pickled)
+            assert_equal(x, y)
+            assert_equal(x[0], y[0])
+
+    @pytest.mark.parametrize('t', [int, float, complex, np.int32, str, object,
+                                   bool])
+    def test_builtin(self, t):
+        self.check_pickling(np.dtype(t))
+
+    def test_structured(self):
+        dt = np.dtype(([('a', '>f4', (2, 1)), ('b', '<f8', (1, 3))], (2, 2)))
+        self.check_pickling(dt)
+
+    def test_structured_aligned(self):
+        dt = np.dtype('i4, i1', align=True)
+        self.check_pickling(dt)
+
+    def test_structured_unaligned(self):
+        dt = np.dtype('i4, i1', align=False)
+        self.check_pickling(dt)
+
+    def test_structured_padded(self):
+        dt = np.dtype({
+            'names': ['A', 'B'],
+            'formats': ['f4', 'f4'],
+            'offsets': [0, 8],
+            'itemsize': 16})
+        self.check_pickling(dt)
+
+    def test_structured_titles(self):
+        dt = np.dtype({'names': ['r', 'b'],
+                       'formats': ['u1', 'u1'],
+                       'titles': ['Red pixel', 'Blue pixel']})
+        self.check_pickling(dt)
+
+    @pytest.mark.parametrize('base', ['m8', 'M8'])
+    @pytest.mark.parametrize('unit', ['', 'Y', 'M', 'W', 'D', 'h', 'm', 's',
+                                      'ms', 'us', 'ns', 'ps', 'fs', 'as'])
+    def test_datetime(self, base, unit):
+        dt = np.dtype(f'{base}[{unit}]' if unit else base)
+        self.check_pickling(dt)
+        if unit:
+            dt = np.dtype(f'{base}[7{unit}]')
+            self.check_pickling(dt)
+
+    def test_metadata(self):
+        dt = np.dtype(int, metadata={'datum': 1})
+        self.check_pickling(dt)
+
+    @pytest.mark.parametrize("DType",
+        [type(np.dtype(t)) for t in np.typecodes['All']] +
+        [type(np.dtype(rational)), np.dtype])
+    def test_pickle_dtype_class(self, DType):
+        # Check that DTypes (the classes/types) roundtrip when pickling
+        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
+            roundtrip_DType = pickle.loads(pickle.dumps(DType, proto))
+            assert roundtrip_DType is DType
+
+    @pytest.mark.parametrize("dt",
+        [np.dtype(t) for t in np.typecodes['All']] +
+        [np.dtype(rational)])
+    def test_pickle_dtype(self, dt):
+        # Check that dtype instances roundtrip when pickling and that pickling
+        # doesn't change the hash value
+        pre_pickle_hash = hash(dt)
+        for proto in range(pickle.HIGHEST_PROTOCOL + 1):
+            roundtrip_dt = pickle.loads(pickle.dumps(dt, proto))
+            assert roundtrip_dt == dt
+            assert hash(dt) == pre_pickle_hash
+
+
+class TestPromotion:
+    """Test cases related to more complex DType promotions.  Further promotion
+    tests are defined in `test_numeric.py`
+    """
+    @pytest.mark.parametrize(["other", "expected"],
+            [(2**16 - 1, np.complex64),
+             (2**32 - 1, np.complex64),
+             (np.float16(2), np.complex64),
+             (np.float32(2), np.complex64),
+             (np.longdouble(2), np.clongdouble),
+             # Base of the double value to sidestep any rounding issues:
+             (np.longdouble(np.nextafter(1.7e308, 0.)), np.clongdouble),
+             # Additionally use "nextafter" so the cast can't round down:
+             (np.longdouble(np.nextafter(1.7e308, np.inf)), np.clongdouble),
+             # repeat for complex scalars:
+             (np.complex64(2), np.complex64),
+             (np.clongdouble(2), np.clongdouble),
+             # Base of the double value to sidestep any rounding issues:
+             (np.clongdouble(np.nextafter(1.7e308, 0.) * 1j), np.clongdouble),
+             # Additionally use "nextafter" so the cast can't round down:
+             (np.clongdouble(np.nextafter(1.7e308, np.inf)), np.clongdouble),
+             ])
+    def test_complex_other_value_based(self, other, expected):
+        # This would change if we modify the value based promotion
+        min_complex = np.dtype(np.complex64)
+
+        res = np.result_type(other, min_complex)
+        assert res == expected
+        # Check the same for a simple ufunc call that uses the same logic:
+        res = np.minimum(other, np.ones(3, dtype=min_complex)).dtype
+        assert res == expected
+
+    @pytest.mark.parametrize(["other", "expected"],
+                 [(np.bool, np.complex128),
+                  (np.int64, np.complex128),
+                  (np.float16, np.complex64),
+                  (np.float32, np.complex64),
+                  (np.float64, np.complex128),
+                  (np.longdouble, np.clongdouble),
+                  (np.complex64, np.complex64),
+                  (np.complex128, np.complex128),
+                  (np.clongdouble, np.clongdouble),
+                  ])
+    def test_complex_scalar_value_based(self, other, expected):
+        # This would change if we modify the value based promotion
+        complex_scalar = 1j
+
+        res = np.result_type(other, complex_scalar)
+        assert res == expected
+        # Check the same for a simple ufunc call that uses the same logic:
+        res = np.minimum(np.ones(3, dtype=other), complex_scalar).dtype
+        assert res == expected
+
+    def test_complex_pyscalar_promote_rational(self):
+        with pytest.raises(TypeError,
+                match=r".* no common DType exists for the given inputs"):
+            np.result_type(1j, rational)
+
+        with pytest.raises(TypeError,
+                match=r".* no common DType exists for the given inputs"):
+            np.result_type(1j, rational(1, 2))
+
+    @pytest.mark.parametrize("val", [2, 2**32, 2**63, 2**64, 2 * 100])
+    def test_python_integer_promotion(self, val):
+        # If we only pass scalars (mainly python ones!), NEP 50 means
+        # that we get the default integer
+        expected_dtype = np.dtype(int)  # the default integer
+        assert np.result_type(val, 0) == expected_dtype
+        # With NEP 50, the NumPy scalar wins though:
+        assert np.result_type(val, np.int8(0)) == np.int8
+
+    @pytest.mark.parametrize(["other", "expected"],
+            [(1, rational), (1., np.float64)])
+    def test_float_int_pyscalar_promote_rational(self, other, expected):
+        # Note that rationals are a bit awkward as they promote with float64
+        # or default ints, but not float16 or uint8/int8 (which looks
+        # inconsistent here).  The new promotion fixed this (partially?)
+        assert np.result_type(other, rational) == expected
+        assert np.result_type(other, rational(1, 2)) == expected
+
+    @pytest.mark.parametrize(["dtypes", "expected"], [
+             # These promotions are not associative/commutative:
+             ([np.uint16, np.int16, np.float16], np.float32),
+             ([np.uint16, np.int8, np.float16], np.float32),
+             ([np.uint8, np.int16, np.float16], np.float32),
+             # The following promotions are not ambiguous, but cover code
+             # paths of abstract promotion (no particular logic being tested)
+             ([1, 1, np.float64], np.float64),
+             ([1, 1., np.complex128], np.complex128),
+             ([1, 1j, np.float64], np.complex128),
+             ([1., 1., np.int64], np.float64),
+             ([1., 1j, np.float64], np.complex128),
+             ([1j, 1j, np.float64], np.complex128),
+             ([1, True, np.bool], np.int_),
+            ])
+    def test_permutations_do_not_influence_result(self, dtypes, expected):
+        # Tests that most permutations do not influence the result.  In the
+        # above some uint and int combinations promote to a larger integer
+        # type, which would then promote to a larger than necessary float.
+        for perm in permutations(dtypes):
+            assert np.result_type(*perm) == expected
+
+
+def test_rational_dtype():
+    # test for bug gh-5719
+    a = np.array([1111], dtype=rational).astype
+    assert_raises(OverflowError, a, 'int8')
+
+    # test that dtype detection finds user-defined types
+    x = rational(1)
+    assert_equal(np.array([x, x]).dtype, np.dtype(rational))
+
+
+def test_dtypes_are_true():
+    # test for gh-6294
+    assert bool(np.dtype('f8'))
+    assert bool(np.dtype('i8'))
+    assert bool(np.dtype([('a', 'i8'), ('b', 'f4')]))
+
+
+def test_invalid_dtype_string():
+    # test for gh-10440
+    assert_raises(TypeError, np.dtype, 'f8,i8,[f8,i8]')
+    assert_raises(TypeError, np.dtype, 'Fl\xfcgel')
+
+
+def test_keyword_argument():
+    # test for https://github.com/numpy/numpy/pull/16574#issuecomment-642660971
+    assert np.dtype(dtype=np.float64) == np.dtype(np.float64)
+
+
+class TestFromDTypeAttribute:
+    def test_simple(self):
+        class dt:
+            dtype = np.dtype("f8")
+
+        assert np.dtype(dt) == np.float64
+        assert np.dtype(dt()) == np.float64
+
+    @pytest.mark.skipif(IS_PYSTON, reason="Pyston disables recursion checking")
+    @pytest.mark.skipif(IS_WASM, reason="Pyodide/WASM has limited stack size")
+    def test_recursion(self):
+        class dt:
+            pass
+
+        dt.dtype = dt
+        with pytest.raises(RecursionError):
+            np.dtype(dt)
+
+        dt_instance = dt()
+        dt_instance.dtype = dt
+        with pytest.raises(RecursionError):
+            np.dtype(dt_instance)
+
+    def test_void_subtype(self):
+        class dt(np.void):
+            # This code path is fully untested before, so it is unclear
+            # what this should be useful for. Note that if np.void is used
+            # numpy will think we are deallocating a base type [1.17, 2019-02].
+            dtype = np.dtype("f,f")
+
+        np.dtype(dt)
+        np.dtype(dt(1))
+
+    @pytest.mark.skipif(IS_PYSTON, reason="Pyston disables recursion checking")
+    @pytest.mark.skipif(IS_WASM, reason="Pyodide/WASM has limited stack size")
+    def test_void_subtype_recursion(self):
+        class vdt(np.void):
+            pass
+
+        vdt.dtype = vdt
+
+        with pytest.raises(RecursionError):
+            np.dtype(vdt)
+
+        with pytest.raises(RecursionError):
+            np.dtype(vdt(1))
+
+
+class TestDTypeClasses:
+    @pytest.mark.parametrize("dtype", list(np.typecodes['All']) + [rational])
+    def test_basic_dtypes_subclass_properties(self, dtype):
+        # Note: Except for the isinstance and type checks, these attributes
+        #       are considered currently private and may change.
+        dtype = np.dtype(dtype)
+        assert isinstance(dtype, np.dtype)
+        assert type(dtype) is not np.dtype
+        if dtype.type.__name__ != "rational":
+            dt_name = type(dtype).__name__.lower().removesuffix("dtype")
+            if dt_name in {"uint", "int"}:
+                # The scalar names has a `c` attached because "int" is Python
+                # int and that is long...
+                dt_name += "c"
+            sc_name = dtype.type.__name__
+            assert dt_name == sc_name.strip("_")
+            assert type(dtype).__module__ == "numpy.dtypes"
+
+            assert getattr(numpy.dtypes, type(dtype).__name__) is type(dtype)
+        else:
+            assert type(dtype).__name__ == "dtype[rational]"
+            assert type(dtype).__module__ == "numpy"
+
+        assert not type(dtype)._abstract
+
+        # the flexible dtypes and datetime/timedelta have additional parameters
+        # which are more than just storage information, these would need to be
+        # given when creating a dtype:
+        parametric = (np.void, np.str_, np.bytes_, np.datetime64, np.timedelta64)
+        if dtype.type not in parametric:
+            assert not type(dtype)._parametric
+            assert type(dtype)() is dtype
+        else:
+            assert type(dtype)._parametric
+            with assert_raises(TypeError):
+                type(dtype)()
+
+    def test_dtype_superclass(self):
+        assert type(np.dtype) is not type
+        assert isinstance(np.dtype, type)
+
+        assert type(np.dtype).__name__ == "_DTypeMeta"
+        assert type(np.dtype).__module__ == "numpy"
+        assert np.dtype._abstract
+
+    def test_is_numeric(self):
+        all_codes = set(np.typecodes['All'])
+        numeric_codes = set(np.typecodes['AllInteger'] +
+                            np.typecodes['AllFloat'] + '?')
+        non_numeric_codes = all_codes - numeric_codes
+
+        for code in numeric_codes:
+            assert type(np.dtype(code))._is_numeric
+
+        for code in non_numeric_codes:
+            assert not type(np.dtype(code))._is_numeric
+
+    @pytest.mark.parametrize("int_", ["UInt", "Int"])
+    @pytest.mark.parametrize("size", [8, 16, 32, 64])
+    def test_integer_alias_names(self, int_, size):
+        DType = getattr(numpy.dtypes, f"{int_}{size}DType")
+        sctype = getattr(numpy, f"{int_.lower()}{size}")
+        assert DType.type is sctype
+        assert DType.__name__.lower().removesuffix("dtype") == sctype.__name__
+
+    @pytest.mark.parametrize("name",
+            ["Half", "Float", "Double", "CFloat", "CDouble"])
+    def test_float_alias_names(self, name):
+        with pytest.raises(AttributeError):
+            getattr(numpy.dtypes, name + "DType") is numpy.dtypes.Float16DType
+
+    def test_scalar_helper_all_dtypes(self):
+        for dtype in np.dtypes.__all__:
+            dt_class = getattr(np.dtypes, dtype)
+            dt = np.dtype(dt_class)
+            if dt.char not in 'OTVM':
+                assert np._core.multiarray.scalar(dt) == dt.type()
+            elif dt.char == 'V':
+                assert np._core.multiarray.scalar(dt) == dt.type(b'\x00')
+            elif dt.char == 'M':
+                # can't do anything with this without generating ValueError
+                # because 'M' has no units
+                _ = np._core.multiarray.scalar(dt)
+            else:
+                with pytest.raises(TypeError):
+                    np._core.multiarray.scalar(dt)
+
+
+class TestFromCTypes:
+
+    @staticmethod
+    def check(ctype, dtype):
+        dtype = np.dtype(dtype)
+        assert np.dtype(ctype) == dtype
+        assert np.dtype(ctype()) == dtype
+        assert ctypes.sizeof(ctype) == dtype.itemsize
+
+    def test_array(self):
+        c8 = ctypes.c_uint8
+        self.check(     3 * c8,  (np.uint8, (3,)))
+        self.check(     1 * c8,  (np.uint8, (1,)))
+        self.check(     0 * c8,  (np.uint8, (0,)))
+        self.check(1 * (3 * c8), ((np.uint8, (3,)), (1,)))
+        self.check(3 * (1 * c8), ((np.uint8, (1,)), (3,)))
+
+    def test_padded_structure(self):
+        class PaddedStruct(ctypes.Structure):
+            _fields_ = [
+                ('a', ctypes.c_uint8),
+                ('b', ctypes.c_uint16)
+            ]
+        expected = np.dtype([
+            ('a', np.uint8),
+            ('b', np.uint16)
+        ], align=True)
+        self.check(PaddedStruct, expected)
+
+    def test_bit_fields(self):
+        class BitfieldStruct(ctypes.Structure):
+            _fields_ = [
+                ('a', ctypes.c_uint8, 7),
+                ('b', ctypes.c_uint8, 1)
+            ]
+        assert_raises(TypeError, np.dtype, BitfieldStruct)
+        assert_raises(TypeError, np.dtype, BitfieldStruct())
+
+    def test_pointer(self):
+        p_uint8 = ctypes.POINTER(ctypes.c_uint8)
+        assert_raises(TypeError, np.dtype, p_uint8)
+
+    def test_size_t(self):
+        assert np.dtype(np.uintp) is np.dtype("N")
+        self.check(ctypes.c_size_t, np.uintp)
+
+    def test_void_pointer(self):
+        self.check(ctypes.c_void_p, "P")
+
+    def test_union(self):
+        class Union(ctypes.Union):
+            _fields_ = [
+                ('a', ctypes.c_uint8),
+                ('b', ctypes.c_uint16),
+            ]
+        expected = np.dtype({
+            "names": ['a', 'b'],
+            "formats": [np.uint8, np.uint16],
+            "offsets": [0, 0],
+            "itemsize": 2
+        })
+        self.check(Union, expected)
+
+    def test_union_with_struct_packed(self):
+        class Struct(ctypes.Structure):
+            _pack_ = 1
+            _fields_ = [
+                ('one', ctypes.c_uint8),
+                ('two', ctypes.c_uint32)
+            ]
+
+        class Union(ctypes.Union):
+            _fields_ = [
+                ('a', ctypes.c_uint8),
+                ('b', ctypes.c_uint16),
+                ('c', ctypes.c_uint32),
+                ('d', Struct),
+            ]
+        expected = np.dtype({
+            "names": ['a', 'b', 'c', 'd'],
+            "formats": ['u1', np.uint16, np.uint32, [('one', 'u1'), ('two', np.uint32)]],
+            "offsets": [0, 0, 0, 0],
+            "itemsize": ctypes.sizeof(Union)
+        })
+        self.check(Union, expected)
+
+    def test_union_packed(self):
+        class Struct(ctypes.Structure):
+            _fields_ = [
+                ('one', ctypes.c_uint8),
+                ('two', ctypes.c_uint32)
+            ]
+            _pack_ = 1
+
+        class Union(ctypes.Union):
+            _pack_ = 1
+            _fields_ = [
+                ('a', ctypes.c_uint8),
+                ('b', ctypes.c_uint16),
+                ('c', ctypes.c_uint32),
+                ('d', Struct),
+            ]
+        expected = np.dtype({
+            "names": ['a', 'b', 'c', 'd'],
+            "formats": ['u1', np.uint16, np.uint32, [('one', 'u1'), ('two', np.uint32)]],
+            "offsets": [0, 0, 0, 0],
+            "itemsize": ctypes.sizeof(Union)
+        })
+        self.check(Union, expected)
+
+    def test_packed_structure(self):
+        class PackedStructure(ctypes.Structure):
+            _pack_ = 1
+            _fields_ = [
+                ('a', ctypes.c_uint8),
+                ('b', ctypes.c_uint16)
+            ]
+        expected = np.dtype([
+            ('a', np.uint8),
+            ('b', np.uint16)
+        ])
+        self.check(PackedStructure, expected)
+
+    def test_large_packed_structure(self):
+        class PackedStructure(ctypes.Structure):
+            _pack_ = 2
+            _fields_ = [
+                ('a', ctypes.c_uint8),
+                ('b', ctypes.c_uint16),
+                ('c', ctypes.c_uint8),
+                ('d', ctypes.c_uint16),
+                ('e', ctypes.c_uint32),
+                ('f', ctypes.c_uint32),
+                ('g', ctypes.c_uint8)
+                ]
+        expected = np.dtype({
+            "formats": [np.uint8, np.uint16, np.uint8, np.uint16, np.uint32, np.uint32, np.uint8],
+            "offsets": [0, 2, 4, 6, 8, 12, 16],
+            "names": ['a', 'b', 'c', 'd', 'e', 'f', 'g'],
+            "itemsize": 18})
+        self.check(PackedStructure, expected)
+
+    def test_big_endian_structure_packed(self):
+        class BigEndStruct(ctypes.BigEndianStructure):
+            _fields_ = [
+                ('one', ctypes.c_uint8),
+                ('two', ctypes.c_uint32)
+            ]
+            _pack_ = 1
+        expected = np.dtype([('one', 'u1'), ('two', '>u4')])
+        self.check(BigEndStruct, expected)
+
+    def test_little_endian_structure_packed(self):
+        class LittleEndStruct(ctypes.LittleEndianStructure):
+            _fields_ = [
+                ('one', ctypes.c_uint8),
+                ('two', ctypes.c_uint32)
+            ]
+            _pack_ = 1
+        expected = np.dtype([('one', 'u1'), ('two', '<u4')])
+        self.check(LittleEndStruct, expected)
+
+    def test_little_endian_structure(self):
+        class PaddedStruct(ctypes.LittleEndianStructure):
+            _fields_ = [
+                ('a', ctypes.c_uint8),
+                ('b', ctypes.c_uint16)
+            ]
+        expected = np.dtype([
+            ('a', '<B'),
+            ('b', '<H')
+        ], align=True)
+        self.check(PaddedStruct, expected)
+
+    def test_big_endian_structure(self):
+        class PaddedStruct(ctypes.BigEndianStructure):
+            _fields_ = [
+                ('a', ctypes.c_uint8),
+                ('b', ctypes.c_uint16)
+            ]
+        expected = np.dtype([
+            ('a', '>B'),
+            ('b', '>H')
+        ], align=True)
+        self.check(PaddedStruct, expected)
+
+    def test_simple_endian_types(self):
+        self.check(ctypes.c_uint16.__ctype_le__, np.dtype('<u2'))
+        self.check(ctypes.c_uint16.__ctype_be__, np.dtype('>u2'))
+        self.check(ctypes.c_uint8.__ctype_le__, np.dtype('u1'))
+        self.check(ctypes.c_uint8.__ctype_be__, np.dtype('u1'))
+
+    all_types = set(np.typecodes['All'])
+    all_pairs = permutations(all_types, 2)
+
+    @pytest.mark.parametrize("pair", all_pairs)
+    def test_pairs(self, pair):
+        """
+        Check that np.dtype('x,y') matches [np.dtype('x'), np.dtype('y')]
+        Example: np.dtype('d,I') -> dtype([('f0', '<f8'), ('f1', '<u4')])
+        """
+        # gh-5645: check that np.dtype('i,L') can be used
+        pair_type = np.dtype('{},{}'.format(*pair))
+        expected = np.dtype([('f0', pair[0]), ('f1', pair[1])])
+        assert_equal(pair_type, expected)
+
+
+class TestUserDType:
+    @pytest.mark.leaks_references(reason="dynamically creates custom dtype.")
+    def test_custom_structured_dtype(self):
+        class mytype:
+            pass
+
+        blueprint = np.dtype([("field", object)])
+        dt = create_custom_field_dtype(blueprint, mytype, 0)
+        assert dt.type == mytype
+        # We cannot (currently) *create* this dtype with `np.dtype` because
+        # mytype does not inherit from `np.generic`.  This seems like an
+        # unnecessary restriction, but one that has been around forever:
+        assert np.dtype(mytype) == np.dtype("O")
+
+        if HAS_REFCOUNT:
+            # Create an array and test that memory gets cleaned up (gh-25949)
+            o = object()
+            startcount = sys.getrefcount(o)
+            a = np.array([o], dtype=dt)
+            del a
+            assert sys.getrefcount(o) == startcount
+
+    def test_custom_structured_dtype_errors(self):
+        class mytype:
+            pass
+
+        blueprint = np.dtype([("field", object)])
+
+        with pytest.raises(ValueError):
+            # Tests what happens if fields are unset during creation
+            # which is currently rejected due to the containing object
+            # (see PyArray_RegisterDataType).
+            create_custom_field_dtype(blueprint, mytype, 1)
+
+        with pytest.raises(RuntimeError):
+            # Tests that a dtype must have its type field set up to np.dtype
+            # or in this case a builtin instance.
+            create_custom_field_dtype(blueprint, mytype, 2)
+
+
+class TestClassGetItem:
+    def test_dtype(self) -> None:
+        alias = np.dtype[Any]
+        assert isinstance(alias, types.GenericAlias)
+        assert alias.__origin__ is np.dtype
+
+    @pytest.mark.parametrize("code", np.typecodes["All"])
+    def test_dtype_subclass(self, code: str) -> None:
+        cls = type(np.dtype(code))
+        alias = cls[Any]
+        assert isinstance(alias, types.GenericAlias)
+        assert alias.__origin__ is cls
+
+    @pytest.mark.parametrize("arg_len", range(4))
+    def test_subscript_tuple(self, arg_len: int) -> None:
+        arg_tup = (Any,) * arg_len
+        if arg_len == 1:
+            assert np.dtype[arg_tup]
+        else:
+            with pytest.raises(TypeError):
+                np.dtype[arg_tup]
+
+    def test_subscript_scalar(self) -> None:
+        assert np.dtype[Any]
+
+
+def test_result_type_integers_and_unitless_timedelta64():
+    # Regression test for gh-20077.  The following call of `result_type`
+    # would cause a seg. fault.
+    td = np.timedelta64(4)
+    result = np.result_type(0, td)
+    assert_dtype_equal(result, td.dtype)
+
+
+def test_creating_dtype_with_dtype_class_errors():
+    # Regression test for #25031, calling `np.dtype` with itself segfaulted.
+    with pytest.raises(TypeError, match="Cannot convert np.dtype into a"):
+        np.array(np.ones(10), dtype=np.dtype)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_einsum.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_einsum.py
new file mode 100644
index 0000000..0bd180b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_einsum.py
@@ -0,0 +1,1317 @@
+import itertools
+
+import pytest
+
+import numpy as np
+from numpy.testing import (
+    assert_,
+    assert_allclose,
+    assert_almost_equal,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+    suppress_warnings,
+)
+
+# Setup for optimize einsum
+chars = 'abcdefghij'
+sizes = np.array([2, 3, 4, 5, 4, 3, 2, 6, 5, 4, 3])
+global_size_dict = dict(zip(chars, sizes))
+
+
+class TestEinsum:
+    @pytest.mark.parametrize("do_opt", [True, False])
+    @pytest.mark.parametrize("einsum_fn", [np.einsum, np.einsum_path])
+    def test_einsum_errors(self, do_opt, einsum_fn):
+        # Need enough arguments
+        assert_raises(ValueError, einsum_fn, optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "", optimize=do_opt)
+
+        # subscripts must be a string
+        assert_raises(TypeError, einsum_fn, 0, 0, optimize=do_opt)
+
+        # issue 4528 revealed a segfault with this call
+        assert_raises(TypeError, einsum_fn, *(None,) * 63, optimize=do_opt)
+
+        # number of operands must match count in subscripts string
+        assert_raises(ValueError, einsum_fn, "", 0, 0, optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, ",", 0, [0], [0],
+                      optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, ",", [0], optimize=do_opt)
+
+        # can't have more subscripts than dimensions in the operand
+        assert_raises(ValueError, einsum_fn, "i", 0, optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "ij", [0, 0], optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "...i", 0, optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "i...j", [0, 0], optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "i...", 0, optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "ij...", [0, 0], optimize=do_opt)
+
+        # invalid ellipsis
+        assert_raises(ValueError, einsum_fn, "i..", [0, 0], optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, ".i...", [0, 0], optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "j->..j", [0, 0], optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "j->.j...", [0, 0],
+                      optimize=do_opt)
+
+        # invalid subscript character
+        assert_raises(ValueError, einsum_fn, "i%...", [0, 0], optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "...j$", [0, 0], optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "i->&", [0, 0], optimize=do_opt)
+
+        # output subscripts must appear in input
+        assert_raises(ValueError, einsum_fn, "i->ij", [0, 0], optimize=do_opt)
+
+        # output subscripts may only be specified once
+        assert_raises(ValueError, einsum_fn, "ij->jij", [[0, 0], [0, 0]],
+                      optimize=do_opt)
+
+        # dimensions must match when being collapsed
+        assert_raises(ValueError, einsum_fn, "ii",
+                      np.arange(6).reshape(2, 3), optimize=do_opt)
+        assert_raises(ValueError, einsum_fn, "ii->i",
+                      np.arange(6).reshape(2, 3), optimize=do_opt)
+
+        with assert_raises_regex(ValueError, "'b'"):
+            # gh-11221 - 'c' erroneously appeared in the error message
+            a = np.ones((3, 3, 4, 5, 6))
+            b = np.ones((3, 4, 5))
+            einsum_fn('aabcb,abc', a, b)
+
+    def test_einsum_sorting_behavior(self):
+        # Case 1: 26 dimensions (all lowercase indices)
+        n1 = 26
+        x1 = np.random.random((1,) * n1)
+        path1 = np.einsum_path(x1, range(n1))[1]  # Get einsum path details
+        output_indices1 = path1.split("->")[-1].strip()  # Extract output indices
+        # Assert indices are only uppercase letters and sorted correctly
+        assert all(c.isupper() for c in output_indices1), (
+            "Output indices for n=26 should use uppercase letters only: "
+            f"{output_indices1}"
+        )
+        assert_equal(
+            output_indices1,
+            ''.join(sorted(output_indices1)),
+            err_msg=(
+                "Output indices for n=26 are not lexicographically sorted: "
+                f"{output_indices1}"
+            )
+        )
+
+        # Case 2: 27 dimensions (includes uppercase indices)
+        n2 = 27
+        x2 = np.random.random((1,) * n2)
+        path2 = np.einsum_path(x2, range(n2))[1]
+        output_indices2 = path2.split("->")[-1].strip()
+        # Assert indices include both uppercase and lowercase letters
+        assert any(c.islower() for c in output_indices2), (
+            "Output indices for n=27 should include uppercase letters: "
+            f"{output_indices2}"
+        )
+        # Assert output indices are sorted uppercase before lowercase
+        assert_equal(
+            output_indices2,
+            ''.join(sorted(output_indices2)),
+            err_msg=(
+                "Output indices for n=27 are not lexicographically sorted: "
+                f"{output_indices2}"
+            )
+        )
+
+        # Additional Check: Ensure dimensions correspond correctly to indices
+        # Generate expected mapping of dimensions to indices
+        expected_indices = [
+            chr(i + ord('A')) if i < 26 else chr(i - 26 + ord('a'))
+            for i in range(n2)
+        ]
+        assert_equal(
+            output_indices2,
+            ''.join(expected_indices),
+            err_msg=(
+                "Output indices do not map to the correct dimensions. Expected: "
+                f"{''.join(expected_indices)}, Got: {output_indices2}"
+            )
+        )
+
+    @pytest.mark.parametrize("do_opt", [True, False])
+    def test_einsum_specific_errors(self, do_opt):
+        # out parameter must be an array
+        assert_raises(TypeError, np.einsum, "", 0, out='test',
+                      optimize=do_opt)
+
+        # order parameter must be a valid order
+        assert_raises(ValueError, np.einsum, "", 0, order='W',
+                      optimize=do_opt)
+
+        # casting parameter must be a valid casting
+        assert_raises(ValueError, np.einsum, "", 0, casting='blah',
+                      optimize=do_opt)
+
+        # dtype parameter must be a valid dtype
+        assert_raises(TypeError, np.einsum, "", 0, dtype='bad_data_type',
+                      optimize=do_opt)
+
+        # other keyword arguments are rejected
+        assert_raises(TypeError, np.einsum, "", 0, bad_arg=0, optimize=do_opt)
+
+        # broadcasting to new dimensions must be enabled explicitly
+        assert_raises(ValueError, np.einsum, "i", np.arange(6).reshape(2, 3),
+                      optimize=do_opt)
+        assert_raises(ValueError, np.einsum, "i->i", [[0, 1], [0, 1]],
+                      out=np.arange(4).reshape(2, 2), optimize=do_opt)
+
+        # Check order kwarg, asanyarray allows 1d to pass through
+        assert_raises(ValueError, np.einsum, "i->i",
+                      np.arange(6).reshape(-1, 1), optimize=do_opt, order='d')
+
+    def test_einsum_object_errors(self):
+        # Exceptions created by object arithmetic should
+        # successfully propagate
+
+        class CustomException(Exception):
+            pass
+
+        class DestructoBox:
+
+            def __init__(self, value, destruct):
+                self._val = value
+                self._destruct = destruct
+
+            def __add__(self, other):
+                tmp = self._val + other._val
+                if tmp >= self._destruct:
+                    raise CustomException
+                else:
+                    self._val = tmp
+                    return self
+
+            def __radd__(self, other):
+                if other == 0:
+                    return self
+                else:
+                    return self.__add__(other)
+
+            def __mul__(self, other):
+                tmp = self._val * other._val
+                if tmp >= self._destruct:
+                    raise CustomException
+                else:
+                    self._val = tmp
+                    return self
+
+            def __rmul__(self, other):
+                if other == 0:
+                    return self
+                else:
+                    return self.__mul__(other)
+
+        a = np.array([DestructoBox(i, 5) for i in range(1, 10)],
+                     dtype='object').reshape(3, 3)
+
+        # raised from unbuffered_loop_nop1_ndim2
+        assert_raises(CustomException, np.einsum, "ij->i", a)
+
+        # raised from unbuffered_loop_nop1_ndim3
+        b = np.array([DestructoBox(i, 100) for i in range(27)],
+                     dtype='object').reshape(3, 3, 3)
+        assert_raises(CustomException, np.einsum, "i...k->...", b)
+
+        # raised from unbuffered_loop_nop2_ndim2
+        b = np.array([DestructoBox(i, 55) for i in range(1, 4)],
+                     dtype='object')
+        assert_raises(CustomException, np.einsum, "ij, j", a, b)
+
+        # raised from unbuffered_loop_nop2_ndim3
+        assert_raises(CustomException, np.einsum, "ij, jh", a, a)
+
+        # raised from PyArray_EinsteinSum
+        assert_raises(CustomException, np.einsum, "ij->", a)
+
+    def test_einsum_views(self):
+        # pass-through
+        for do_opt in [True, False]:
+            a = np.arange(6)
+            a.shape = (2, 3)
+
+            b = np.einsum("...", a, optimize=do_opt)
+            assert_(b.base is a)
+
+            b = np.einsum(a, [Ellipsis], optimize=do_opt)
+            assert_(b.base is a)
+
+            b = np.einsum("ij", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, a)
+
+            b = np.einsum(a, [0, 1], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, a)
+
+            # output is writeable whenever input is writeable
+            b = np.einsum("...", a, optimize=do_opt)
+            assert_(b.flags['WRITEABLE'])
+            a.flags['WRITEABLE'] = False
+            b = np.einsum("...", a, optimize=do_opt)
+            assert_(not b.flags['WRITEABLE'])
+
+            # transpose
+            a = np.arange(6)
+            a.shape = (2, 3)
+
+            b = np.einsum("ji", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, a.T)
+
+            b = np.einsum(a, [1, 0], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, a.T)
+
+            # diagonal
+            a = np.arange(9)
+            a.shape = (3, 3)
+
+            b = np.einsum("ii->i", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a[i, i] for i in range(3)])
+
+            b = np.einsum(a, [0, 0], [0], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a[i, i] for i in range(3)])
+
+            # diagonal with various ways of broadcasting an additional dimension
+            a = np.arange(27)
+            a.shape = (3, 3, 3)
+
+            b = np.einsum("...ii->...i", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [[x[i, i] for i in range(3)] for x in a])
+
+            b = np.einsum(a, [Ellipsis, 0, 0], [Ellipsis, 0], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [[x[i, i] for i in range(3)] for x in a])
+
+            b = np.einsum("ii...->...i", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [[x[i, i] for i in range(3)]
+                             for x in a.transpose(2, 0, 1)])
+
+            b = np.einsum(a, [0, 0, Ellipsis], [Ellipsis, 0], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [[x[i, i] for i in range(3)]
+                             for x in a.transpose(2, 0, 1)])
+
+            b = np.einsum("...ii->i...", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a[:, i, i] for i in range(3)])
+
+            b = np.einsum(a, [Ellipsis, 0, 0], [0, Ellipsis], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a[:, i, i] for i in range(3)])
+
+            b = np.einsum("jii->ij", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a[:, i, i] for i in range(3)])
+
+            b = np.einsum(a, [1, 0, 0], [0, 1], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a[:, i, i] for i in range(3)])
+
+            b = np.einsum("ii...->i...", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a.transpose(2, 0, 1)[:, i, i] for i in range(3)])
+
+            b = np.einsum(a, [0, 0, Ellipsis], [0, Ellipsis], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a.transpose(2, 0, 1)[:, i, i] for i in range(3)])
+
+            b = np.einsum("i...i->i...", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a.transpose(1, 0, 2)[:, i, i] for i in range(3)])
+
+            b = np.einsum(a, [0, Ellipsis, 0], [0, Ellipsis], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a.transpose(1, 0, 2)[:, i, i] for i in range(3)])
+
+            b = np.einsum("i...i->...i", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [[x[i, i] for i in range(3)]
+                             for x in a.transpose(1, 0, 2)])
+
+            b = np.einsum(a, [0, Ellipsis, 0], [Ellipsis, 0], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [[x[i, i] for i in range(3)]
+                             for x in a.transpose(1, 0, 2)])
+
+            # triple diagonal
+            a = np.arange(27)
+            a.shape = (3, 3, 3)
+
+            b = np.einsum("iii->i", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a[i, i, i] for i in range(3)])
+
+            b = np.einsum(a, [0, 0, 0], [0], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, [a[i, i, i] for i in range(3)])
+
+            # swap axes
+            a = np.arange(24)
+            a.shape = (2, 3, 4)
+
+            b = np.einsum("ijk->jik", a, optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, a.swapaxes(0, 1))
+
+            b = np.einsum(a, [0, 1, 2], [1, 0, 2], optimize=do_opt)
+            assert_(b.base is a)
+            assert_equal(b, a.swapaxes(0, 1))
+
+    def check_einsum_sums(self, dtype, do_opt=False):
+        dtype = np.dtype(dtype)
+        # Check various sums.  Does many sizes to exercise unrolled loops.
+
+        # sum(a, axis=-1)
+        for n in range(1, 17):
+            a = np.arange(n, dtype=dtype)
+            b = np.sum(a, axis=-1)
+            if hasattr(b, 'astype'):
+                b = b.astype(dtype)
+            assert_equal(np.einsum("i->", a, optimize=do_opt), b)
+            assert_equal(np.einsum(a, [0], [], optimize=do_opt), b)
+
+        for n in range(1, 17):
+            a = np.arange(2 * 3 * n, dtype=dtype).reshape(2, 3, n)
+            b = np.sum(a, axis=-1)
+            if hasattr(b, 'astype'):
+                b = b.astype(dtype)
+            assert_equal(np.einsum("...i->...", a, optimize=do_opt), b)
+            assert_equal(np.einsum(a, [Ellipsis, 0], [Ellipsis], optimize=do_opt), b)
+
+        # sum(a, axis=0)
+        for n in range(1, 17):
+            a = np.arange(2 * n, dtype=dtype).reshape(2, n)
+            b = np.sum(a, axis=0)
+            if hasattr(b, 'astype'):
+                b = b.astype(dtype)
+            assert_equal(np.einsum("i...->...", a, optimize=do_opt), b)
+            assert_equal(np.einsum(a, [0, Ellipsis], [Ellipsis], optimize=do_opt), b)
+
+        for n in range(1, 17):
+            a = np.arange(2 * 3 * n, dtype=dtype).reshape(2, 3, n)
+            b = np.sum(a, axis=0)
+            if hasattr(b, 'astype'):
+                b = b.astype(dtype)
+            assert_equal(np.einsum("i...->...", a, optimize=do_opt), b)
+            assert_equal(np.einsum(a, [0, Ellipsis], [Ellipsis], optimize=do_opt), b)
+
+        # trace(a)
+        for n in range(1, 17):
+            a = np.arange(n * n, dtype=dtype).reshape(n, n)
+            b = np.trace(a)
+            if hasattr(b, 'astype'):
+                b = b.astype(dtype)
+            assert_equal(np.einsum("ii", a, optimize=do_opt), b)
+            assert_equal(np.einsum(a, [0, 0], optimize=do_opt), b)
+
+            # gh-15961: should accept numpy int64 type in subscript list
+            np_array = np.asarray([0, 0])
+            assert_equal(np.einsum(a, np_array, optimize=do_opt), b)
+            assert_equal(np.einsum(a, list(np_array), optimize=do_opt), b)
+
+        # multiply(a, b)
+        assert_equal(np.einsum("..., ...", 3, 4), 12)  # scalar case
+        for n in range(1, 17):
+            a = np.arange(3 * n, dtype=dtype).reshape(3, n)
+            b = np.arange(2 * 3 * n, dtype=dtype).reshape(2, 3, n)
+            assert_equal(np.einsum("..., ...", a, b, optimize=do_opt),
+                         np.multiply(a, b))
+            assert_equal(np.einsum(a, [Ellipsis], b, [Ellipsis], optimize=do_opt),
+                         np.multiply(a, b))
+
+        # inner(a,b)
+        for n in range(1, 17):
+            a = np.arange(2 * 3 * n, dtype=dtype).reshape(2, 3, n)
+            b = np.arange(n, dtype=dtype)
+            assert_equal(np.einsum("...i, ...i", a, b, optimize=do_opt), np.inner(a, b))
+            assert_equal(np.einsum(a, [Ellipsis, 0], b, [Ellipsis, 0], optimize=do_opt),
+                         np.inner(a, b))
+
+        for n in range(1, 11):
+            a = np.arange(n * 3 * 2, dtype=dtype).reshape(n, 3, 2)
+            b = np.arange(n, dtype=dtype)
+            assert_equal(np.einsum("i..., i...", a, b, optimize=do_opt),
+                         np.inner(a.T, b.T).T)
+            assert_equal(np.einsum(a, [0, Ellipsis], b, [0, Ellipsis], optimize=do_opt),
+                         np.inner(a.T, b.T).T)
+
+        # outer(a,b)
+        for n in range(1, 17):
+            a = np.arange(3, dtype=dtype) + 1
+            b = np.arange(n, dtype=dtype) + 1
+            assert_equal(np.einsum("i,j", a, b, optimize=do_opt),
+                         np.outer(a, b))
+            assert_equal(np.einsum(a, [0], b, [1], optimize=do_opt),
+                         np.outer(a, b))
+
+        # Suppress the complex warnings for the 'as f8' tests
+        with suppress_warnings() as sup:
+            sup.filter(np.exceptions.ComplexWarning)
+
+            # matvec(a,b) / a.dot(b) where a is matrix, b is vector
+            for n in range(1, 17):
+                a = np.arange(4 * n, dtype=dtype).reshape(4, n)
+                b = np.arange(n, dtype=dtype)
+                assert_equal(np.einsum("ij, j", a, b, optimize=do_opt),
+                             np.dot(a, b))
+                assert_equal(np.einsum(a, [0, 1], b, [1], optimize=do_opt),
+                             np.dot(a, b))
+
+                c = np.arange(4, dtype=dtype)
+                np.einsum("ij,j", a, b, out=c,
+                          dtype='f8', casting='unsafe', optimize=do_opt)
+                assert_equal(c,
+                             np.dot(a.astype('f8'),
+                                    b.astype('f8')).astype(dtype))
+                c[...] = 0
+                np.einsum(a, [0, 1], b, [1], out=c,
+                          dtype='f8', casting='unsafe', optimize=do_opt)
+                assert_equal(c,
+                             np.dot(a.astype('f8'),
+                                    b.astype('f8')).astype(dtype))
+
+            for n in range(1, 17):
+                a = np.arange(4 * n, dtype=dtype).reshape(4, n)
+                b = np.arange(n, dtype=dtype)
+                assert_equal(np.einsum("ji,j", a.T, b.T, optimize=do_opt),
+                             np.dot(b.T, a.T))
+                assert_equal(np.einsum(a.T, [1, 0], b.T, [1], optimize=do_opt),
+                             np.dot(b.T, a.T))
+
+                c = np.arange(4, dtype=dtype)
+                np.einsum("ji,j", a.T, b.T, out=c,
+                          dtype='f8', casting='unsafe', optimize=do_opt)
+                assert_equal(c,
+                             np.dot(b.T.astype('f8'),
+                                    a.T.astype('f8')).astype(dtype))
+                c[...] = 0
+                np.einsum(a.T, [1, 0], b.T, [1], out=c,
+                          dtype='f8', casting='unsafe', optimize=do_opt)
+                assert_equal(c,
+                             np.dot(b.T.astype('f8'),
+                                    a.T.astype('f8')).astype(dtype))
+
+            # matmat(a,b) / a.dot(b) where a is matrix, b is matrix
+            for n in range(1, 17):
+                if n < 8 or dtype != 'f2':
+                    a = np.arange(4 * n, dtype=dtype).reshape(4, n)
+                    b = np.arange(n * 6, dtype=dtype).reshape(n, 6)
+                    assert_equal(np.einsum("ij,jk", a, b, optimize=do_opt),
+                                 np.dot(a, b))
+                    assert_equal(np.einsum(a, [0, 1], b, [1, 2], optimize=do_opt),
+                                 np.dot(a, b))
+
+            for n in range(1, 17):
+                a = np.arange(4 * n, dtype=dtype).reshape(4, n)
+                b = np.arange(n * 6, dtype=dtype).reshape(n, 6)
+                c = np.arange(24, dtype=dtype).reshape(4, 6)
+                np.einsum("ij,jk", a, b, out=c, dtype='f8', casting='unsafe',
+                          optimize=do_opt)
+                assert_equal(c,
+                             np.dot(a.astype('f8'),
+                                    b.astype('f8')).astype(dtype))
+                c[...] = 0
+                np.einsum(a, [0, 1], b, [1, 2], out=c,
+                          dtype='f8', casting='unsafe', optimize=do_opt)
+                assert_equal(c,
+                             np.dot(a.astype('f8'),
+                                    b.astype('f8')).astype(dtype))
+
+            # matrix triple product (note this is not currently an efficient
+            # way to multiply 3 matrices)
+            a = np.arange(12, dtype=dtype).reshape(3, 4)
+            b = np.arange(20, dtype=dtype).reshape(4, 5)
+            c = np.arange(30, dtype=dtype).reshape(5, 6)
+            if dtype != 'f2':
+                assert_equal(np.einsum("ij,jk,kl", a, b, c, optimize=do_opt),
+                             a.dot(b).dot(c))
+                assert_equal(np.einsum(a, [0, 1], b, [1, 2], c, [2, 3],
+                                       optimize=do_opt), a.dot(b).dot(c))
+
+            d = np.arange(18, dtype=dtype).reshape(3, 6)
+            np.einsum("ij,jk,kl", a, b, c, out=d,
+                      dtype='f8', casting='unsafe', optimize=do_opt)
+            tgt = a.astype('f8').dot(b.astype('f8'))
+            tgt = tgt.dot(c.astype('f8')).astype(dtype)
+            assert_equal(d, tgt)
+
+            d[...] = 0
+            np.einsum(a, [0, 1], b, [1, 2], c, [2, 3], out=d,
+                      dtype='f8', casting='unsafe', optimize=do_opt)
+            tgt = a.astype('f8').dot(b.astype('f8'))
+            tgt = tgt.dot(c.astype('f8')).astype(dtype)
+            assert_equal(d, tgt)
+
+            # tensordot(a, b)
+            if np.dtype(dtype) != np.dtype('f2'):
+                a = np.arange(60, dtype=dtype).reshape(3, 4, 5)
+                b = np.arange(24, dtype=dtype).reshape(4, 3, 2)
+                assert_equal(np.einsum("ijk, jil -> kl", a, b),
+                             np.tensordot(a, b, axes=([1, 0], [0, 1])))
+                assert_equal(np.einsum(a, [0, 1, 2], b, [1, 0, 3], [2, 3]),
+                             np.tensordot(a, b, axes=([1, 0], [0, 1])))
+
+                c = np.arange(10, dtype=dtype).reshape(5, 2)
+                np.einsum("ijk,jil->kl", a, b, out=c,
+                          dtype='f8', casting='unsafe', optimize=do_opt)
+                assert_equal(c, np.tensordot(a.astype('f8'), b.astype('f8'),
+                             axes=([1, 0], [0, 1])).astype(dtype))
+                c[...] = 0
+                np.einsum(a, [0, 1, 2], b, [1, 0, 3], [2, 3], out=c,
+                          dtype='f8', casting='unsafe', optimize=do_opt)
+                assert_equal(c, np.tensordot(a.astype('f8'), b.astype('f8'),
+                             axes=([1, 0], [0, 1])).astype(dtype))
+
+        # logical_and(logical_and(a!=0, b!=0), c!=0)
+        neg_val = -2 if dtype.kind != "u" else np.iinfo(dtype).max - 1
+        a = np.array([1,   3,   neg_val, 0,  12,  13,   0,   1], dtype=dtype)
+        b = np.array([0,   3.5, 0., neg_val,  0,   1,    3,   12], dtype=dtype)
+        c = np.array([True, True, False, True, True, False, True, True])
+
+        assert_equal(np.einsum("i,i,i->i", a, b, c,
+                     dtype='?', casting='unsafe', optimize=do_opt),
+                     np.logical_and(np.logical_and(a != 0, b != 0), c != 0))
+        assert_equal(np.einsum(a, [0], b, [0], c, [0], [0],
+                     dtype='?', casting='unsafe'),
+                     np.logical_and(np.logical_and(a != 0, b != 0), c != 0))
+
+        a = np.arange(9, dtype=dtype)
+        assert_equal(np.einsum(",i->", 3, a), 3 * np.sum(a))
+        assert_equal(np.einsum(3, [], a, [0], []), 3 * np.sum(a))
+        assert_equal(np.einsum("i,->", a, 3), 3 * np.sum(a))
+        assert_equal(np.einsum(a, [0], 3, [], []), 3 * np.sum(a))
+
+        # Various stride0, contiguous, and SSE aligned variants
+        for n in range(1, 25):
+            a = np.arange(n, dtype=dtype)
+            if np.dtype(dtype).itemsize > 1:
+                assert_equal(np.einsum("...,...", a, a, optimize=do_opt),
+                             np.multiply(a, a))
+                assert_equal(np.einsum("i,i", a, a, optimize=do_opt), np.dot(a, a))
+                assert_equal(np.einsum("i,->i", a, 2, optimize=do_opt), 2 * a)
+                assert_equal(np.einsum(",i->i", 2, a, optimize=do_opt), 2 * a)
+                assert_equal(np.einsum("i,->", a, 2, optimize=do_opt), 2 * np.sum(a))
+                assert_equal(np.einsum(",i->", 2, a, optimize=do_opt), 2 * np.sum(a))
+
+                assert_equal(np.einsum("...,...", a[1:], a[:-1], optimize=do_opt),
+                             np.multiply(a[1:], a[:-1]))
+                assert_equal(np.einsum("i,i", a[1:], a[:-1], optimize=do_opt),
+                             np.dot(a[1:], a[:-1]))
+                assert_equal(np.einsum("i,->i", a[1:], 2, optimize=do_opt), 2 * a[1:])
+                assert_equal(np.einsum(",i->i", 2, a[1:], optimize=do_opt), 2 * a[1:])
+                assert_equal(np.einsum("i,->", a[1:], 2, optimize=do_opt),
+                             2 * np.sum(a[1:]))
+                assert_equal(np.einsum(",i->", 2, a[1:], optimize=do_opt),
+                             2 * np.sum(a[1:]))
+
+        # An object array, summed as the data type
+        a = np.arange(9, dtype=object)
+
+        b = np.einsum("i->", a, dtype=dtype, casting='unsafe')
+        assert_equal(b, np.sum(a))
+        if hasattr(b, "dtype"):
+            # Can be a python object when dtype is object
+            assert_equal(b.dtype, np.dtype(dtype))
+
+        b = np.einsum(a, [0], [], dtype=dtype, casting='unsafe')
+        assert_equal(b, np.sum(a))
+        if hasattr(b, "dtype"):
+            # Can be a python object when dtype is object
+            assert_equal(b.dtype, np.dtype(dtype))
+
+        # A case which was failing (ticket #1885)
+        p = np.arange(2) + 1
+        q = np.arange(4).reshape(2, 2) + 3
+        r = np.arange(4).reshape(2, 2) + 7
+        assert_equal(np.einsum('z,mz,zm->', p, q, r), 253)
+
+        # singleton dimensions broadcast (gh-10343)
+        p = np.ones((10, 2))
+        q = np.ones((1, 2))
+        assert_array_equal(np.einsum('ij,ij->j', p, q, optimize=True),
+                           np.einsum('ij,ij->j', p, q, optimize=False))
+        assert_array_equal(np.einsum('ij,ij->j', p, q, optimize=True),
+                           [10.] * 2)
+
+        # a blas-compatible contraction broadcasting case which was failing
+        # for optimize=True (ticket #10930)
+        x = np.array([2., 3.])
+        y = np.array([4.])
+        assert_array_equal(np.einsum("i, i", x, y, optimize=False), 20.)
+        assert_array_equal(np.einsum("i, i", x, y, optimize=True), 20.)
+
+        # all-ones array was bypassing bug (ticket #10930)
+        p = np.ones((1, 5)) / 2
+        q = np.ones((5, 5)) / 2
+        for optimize in (True, False):
+            assert_array_equal(np.einsum("...ij,...jk->...ik", p, p,
+                                         optimize=optimize),
+                               np.einsum("...ij,...jk->...ik", p, q,
+                                         optimize=optimize))
+            assert_array_equal(np.einsum("...ij,...jk->...ik", p, q,
+                                         optimize=optimize),
+                               np.full((1, 5), 1.25))
+
+        # Cases which were failing (gh-10899)
+        x = np.eye(2, dtype=dtype)
+        y = np.ones(2, dtype=dtype)
+        assert_array_equal(np.einsum("ji,i->", x, y, optimize=optimize),
+                           [2.])  # contig_contig_outstride0_two
+        assert_array_equal(np.einsum("i,ij->", y, x, optimize=optimize),
+                           [2.])  # stride0_contig_outstride0_two
+        assert_array_equal(np.einsum("ij,i->", x, y, optimize=optimize),
+                           [2.])  # contig_stride0_outstride0_two
+
+    def test_einsum_sums_int8(self):
+        self.check_einsum_sums('i1')
+
+    def test_einsum_sums_uint8(self):
+        self.check_einsum_sums('u1')
+
+    def test_einsum_sums_int16(self):
+        self.check_einsum_sums('i2')
+
+    def test_einsum_sums_uint16(self):
+        self.check_einsum_sums('u2')
+
+    def test_einsum_sums_int32(self):
+        self.check_einsum_sums('i4')
+        self.check_einsum_sums('i4', True)
+
+    def test_einsum_sums_uint32(self):
+        self.check_einsum_sums('u4')
+        self.check_einsum_sums('u4', True)
+
+    def test_einsum_sums_int64(self):
+        self.check_einsum_sums('i8')
+
+    def test_einsum_sums_uint64(self):
+        self.check_einsum_sums('u8')
+
+    def test_einsum_sums_float16(self):
+        self.check_einsum_sums('f2')
+
+    def test_einsum_sums_float32(self):
+        self.check_einsum_sums('f4')
+
+    def test_einsum_sums_float64(self):
+        self.check_einsum_sums('f8')
+        self.check_einsum_sums('f8', True)
+
+    def test_einsum_sums_longdouble(self):
+        self.check_einsum_sums(np.longdouble)
+
+    def test_einsum_sums_cfloat64(self):
+        self.check_einsum_sums('c8')
+        self.check_einsum_sums('c8', True)
+
+    def test_einsum_sums_cfloat128(self):
+        self.check_einsum_sums('c16')
+
+    def test_einsum_sums_clongdouble(self):
+        self.check_einsum_sums(np.clongdouble)
+
+    def test_einsum_sums_object(self):
+        self.check_einsum_sums('object')
+        self.check_einsum_sums('object', True)
+
+    def test_einsum_misc(self):
+        # This call used to crash because of a bug in
+        # PyArray_AssignZero
+        a = np.ones((1, 2))
+        b = np.ones((2, 2, 1))
+        assert_equal(np.einsum('ij...,j...->i...', a, b), [[[2], [2]]])
+        assert_equal(np.einsum('ij...,j...->i...', a, b, optimize=True), [[[2], [2]]])
+
+        # Regression test for issue #10369 (test unicode inputs with Python 2)
+        assert_equal(np.einsum('ij...,j...->i...', a, b), [[[2], [2]]])
+        assert_equal(np.einsum('...i,...i', [1, 2, 3], [2, 3, 4]), 20)
+        assert_equal(np.einsum('...i,...i', [1, 2, 3], [2, 3, 4],
+                               optimize='greedy'), 20)
+
+        # The iterator had an issue with buffering this reduction
+        a = np.ones((5, 12, 4, 2, 3), np.int64)
+        b = np.ones((5, 12, 11), np.int64)
+        assert_equal(np.einsum('ijklm,ijn,ijn->', a, b, b),
+                     np.einsum('ijklm,ijn->', a, b))
+        assert_equal(np.einsum('ijklm,ijn,ijn->', a, b, b, optimize=True),
+                     np.einsum('ijklm,ijn->', a, b, optimize=True))
+
+        # Issue #2027, was a problem in the contiguous 3-argument
+        # inner loop implementation
+        a = np.arange(1, 3)
+        b = np.arange(1, 5).reshape(2, 2)
+        c = np.arange(1, 9).reshape(4, 2)
+        assert_equal(np.einsum('x,yx,zx->xzy', a, b, c),
+                     [[[1,  3], [3,  9], [5, 15], [7, 21]],
+                     [[8, 16], [16, 32], [24, 48], [32, 64]]])
+        assert_equal(np.einsum('x,yx,zx->xzy', a, b, c, optimize=True),
+                     [[[1,  3], [3,  9], [5, 15], [7, 21]],
+                     [[8, 16], [16, 32], [24, 48], [32, 64]]])
+
+        # Ensure explicitly setting out=None does not cause an error
+        # see issue gh-15776 and issue gh-15256
+        assert_equal(np.einsum('i,j', [1], [2], out=None), [[2]])
+
+    def test_object_loop(self):
+
+        class Mult:
+            def __mul__(self, other):
+                return 42
+
+        objMult = np.array([Mult()])
+        objNULL = np.ndarray(buffer=b'\0' * np.intp(0).itemsize, shape=1, dtype=object)
+
+        with pytest.raises(TypeError):
+            np.einsum("i,j", [1], objNULL)
+        with pytest.raises(TypeError):
+            np.einsum("i,j", objNULL, [1])
+        assert np.einsum("i,j", objMult, objMult) == 42
+
+    def test_subscript_range(self):
+        # Issue #7741, make sure that all letters of Latin alphabet (both uppercase & lowercase) can be used
+        # when creating a subscript from arrays
+        a = np.ones((2, 3))
+        b = np.ones((3, 4))
+        np.einsum(a, [0, 20], b, [20, 2], [0, 2], optimize=False)
+        np.einsum(a, [0, 27], b, [27, 2], [0, 2], optimize=False)
+        np.einsum(a, [0, 51], b, [51, 2], [0, 2], optimize=False)
+        assert_raises(ValueError, lambda: np.einsum(a, [0, 52], b, [52, 2], [0, 2], optimize=False))
+        assert_raises(ValueError, lambda: np.einsum(a, [-1, 5], b, [5, 2], [-1, 2], optimize=False))
+
+    def test_einsum_broadcast(self):
+        # Issue #2455 change in handling ellipsis
+        # remove the 'middle broadcast' error
+        # only use the 'RIGHT' iteration in prepare_op_axes
+        # adds auto broadcast on left where it belongs
+        # broadcast on right has to be explicit
+        # We need to test the optimized parsing as well
+
+        A = np.arange(2 * 3 * 4).reshape(2, 3, 4)
+        B = np.arange(3)
+        ref = np.einsum('ijk,j->ijk', A, B, optimize=False)
+        for opt in [True, False]:
+            assert_equal(np.einsum('ij...,j...->ij...', A, B, optimize=opt), ref)
+            assert_equal(np.einsum('ij...,...j->ij...', A, B, optimize=opt), ref)
+            assert_equal(np.einsum('ij...,j->ij...', A, B, optimize=opt), ref)  # used to raise error
+
+        A = np.arange(12).reshape((4, 3))
+        B = np.arange(6).reshape((3, 2))
+        ref = np.einsum('ik,kj->ij', A, B, optimize=False)
+        for opt in [True, False]:
+            assert_equal(np.einsum('ik...,k...->i...', A, B, optimize=opt), ref)
+            assert_equal(np.einsum('ik...,...kj->i...j', A, B, optimize=opt), ref)
+            assert_equal(np.einsum('...k,kj', A, B, optimize=opt), ref)  # used to raise error
+            assert_equal(np.einsum('ik,k...->i...', A, B, optimize=opt), ref)  # used to raise error
+
+        dims = [2, 3, 4, 5]
+        a = np.arange(np.prod(dims)).reshape(dims)
+        v = np.arange(dims[2])
+        ref = np.einsum('ijkl,k->ijl', a, v, optimize=False)
+        for opt in [True, False]:
+            assert_equal(np.einsum('ijkl,k', a, v, optimize=opt), ref)
+            assert_equal(np.einsum('...kl,k', a, v, optimize=opt), ref)  # used to raise error
+            assert_equal(np.einsum('...kl,k...', a, v, optimize=opt), ref)
+
+        J, K, M = 160, 160, 120
+        A = np.arange(J * K * M).reshape(1, 1, 1, J, K, M)
+        B = np.arange(J * K * M * 3).reshape(J, K, M, 3)
+        ref = np.einsum('...lmn,...lmno->...o', A, B, optimize=False)
+        for opt in [True, False]:
+            assert_equal(np.einsum('...lmn,lmno->...o', A, B,
+                                   optimize=opt), ref)  # used to raise error
+
+    def test_einsum_fixedstridebug(self):
+        # Issue #4485 obscure einsum bug
+        # This case revealed a bug in nditer where it reported a stride
+        # as 'fixed' (0) when it was in fact not fixed during processing
+        # (0 or 4). The reason for the bug was that the check for a fixed
+        # stride was using the information from the 2D inner loop reuse
+        # to restrict the iteration dimensions it had to validate to be
+        # the same, but that 2D inner loop reuse logic is only triggered
+        # during the buffer copying step, and hence it was invalid to
+        # rely on those values. The fix is to check all the dimensions
+        # of the stride in question, which in the test case reveals that
+        # the stride is not fixed.
+        #
+        # NOTE: This test is triggered by the fact that the default buffersize,
+        #       used by einsum, is 8192, and 3*2731 = 8193, is larger than that
+        #       and results in a mismatch between the buffering and the
+        #       striding for operand A.
+        A = np.arange(2 * 3).reshape(2, 3).astype(np.float32)
+        B = np.arange(2 * 3 * 2731).reshape(2, 3, 2731).astype(np.int16)
+        es = np.einsum('cl, cpx->lpx',  A,  B)
+        tp = np.tensordot(A,  B,  axes=(0,  0))
+        assert_equal(es,  tp)
+        # The following is the original test case from the bug report,
+        # made repeatable by changing random arrays to aranges.
+        A = np.arange(3 * 3).reshape(3, 3).astype(np.float64)
+        B = np.arange(3 * 3 * 64 * 64).reshape(3, 3, 64, 64).astype(np.float32)
+        es = np.einsum('cl, cpxy->lpxy',  A, B)
+        tp = np.tensordot(A, B,  axes=(0, 0))
+        assert_equal(es, tp)
+
+    def test_einsum_fixed_collapsingbug(self):
+        # Issue #5147.
+        # The bug only occurred when output argument of einssum was used.
+        x = np.random.normal(0, 1, (5, 5, 5, 5))
+        y1 = np.zeros((5, 5))
+        np.einsum('aabb->ab', x, out=y1)
+        idx = np.arange(5)
+        y2 = x[idx[:, None], idx[:, None], idx, idx]
+        assert_equal(y1, y2)
+
+    def test_einsum_failed_on_p9_and_s390x(self):
+        # Issues gh-14692 and gh-12689
+        # Bug with signed vs unsigned char errored on power9 and s390x Linux
+        tensor = np.random.random_sample((10, 10, 10, 10))
+        x = np.einsum('ijij->', tensor)
+        y = tensor.trace(axis1=0, axis2=2).trace()
+        assert_allclose(x, y)
+
+    def test_einsum_all_contig_non_contig_output(self):
+        # Issue gh-5907, tests that the all contiguous special case
+        # actually checks the contiguity of the output
+        x = np.ones((5, 5))
+        out = np.ones(10)[::2]
+        correct_base = np.ones(10)
+        correct_base[::2] = 5
+        # Always worked (inner iteration is done with 0-stride):
+        np.einsum('mi,mi,mi->m', x, x, x, out=out)
+        assert_array_equal(out.base, correct_base)
+        # Example 1:
+        out = np.ones(10)[::2]
+        np.einsum('im,im,im->m', x, x, x, out=out)
+        assert_array_equal(out.base, correct_base)
+        # Example 2, buffering causes x to be contiguous but
+        # special cases do not catch the operation before:
+        out = np.ones((2, 2, 2))[..., 0]
+        correct_base = np.ones((2, 2, 2))
+        correct_base[..., 0] = 2
+        x = np.ones((2, 2), np.float32)
+        np.einsum('ij,jk->ik', x, x, out=out)
+        assert_array_equal(out.base, correct_base)
+
+    @pytest.mark.parametrize("dtype",
+             np.typecodes["AllFloat"] + np.typecodes["AllInteger"])
+    def test_different_paths(self, dtype):
+        # Test originally added to cover broken float16 path: gh-20305
+        # Likely most are covered elsewhere, at least partially.
+        dtype = np.dtype(dtype)
+        # Simple test, designed to exercise most specialized code paths,
+        # note the +0.5 for floats.  This makes sure we use a float value
+        # where the results must be exact.
+        arr = (np.arange(7) + 0.5).astype(dtype)
+        scalar = np.array(2, dtype=dtype)
+
+        # contig -> scalar:
+        res = np.einsum('i->', arr)
+        assert res == arr.sum()
+        # contig, contig -> contig:
+        res = np.einsum('i,i->i', arr, arr)
+        assert_array_equal(res, arr * arr)
+        # noncontig, noncontig -> contig:
+        res = np.einsum('i,i->i', arr.repeat(2)[::2], arr.repeat(2)[::2])
+        assert_array_equal(res, arr * arr)
+        # contig + contig -> scalar
+        assert np.einsum('i,i->', arr, arr) == (arr * arr).sum()
+        # contig + scalar -> contig (with out)
+        out = np.ones(7, dtype=dtype)
+        res = np.einsum('i,->i', arr, dtype.type(2), out=out)
+        assert_array_equal(res, arr * dtype.type(2))
+        # scalar + contig -> contig (with out)
+        res = np.einsum(',i->i', scalar, arr)
+        assert_array_equal(res, arr * dtype.type(2))
+        # scalar + contig -> scalar
+        res = np.einsum(',i->', scalar, arr)
+        # Use einsum to compare to not have difference due to sum round-offs:
+        assert res == np.einsum('i->', scalar * arr)
+        # contig + scalar -> scalar
+        res = np.einsum('i,->', arr, scalar)
+        # Use einsum to compare to not have difference due to sum round-offs:
+        assert res == np.einsum('i->', scalar * arr)
+        # contig + contig + contig -> scalar
+        arr = np.array([0.5, 0.5, 0.25, 4.5, 3.], dtype=dtype)
+        res = np.einsum('i,i,i->', arr, arr, arr)
+        assert_array_equal(res, (arr * arr * arr).sum())
+        # four arrays:
+        res = np.einsum('i,i,i,i->', arr, arr, arr, arr)
+        assert_array_equal(res, (arr * arr * arr * arr).sum())
+
+    def test_small_boolean_arrays(self):
+        # See gh-5946.
+        # Use array of True embedded in False.
+        a = np.zeros((16, 1, 1), dtype=np.bool)[:2]
+        a[...] = True
+        out = np.zeros((16, 1, 1), dtype=np.bool)[:2]
+        tgt = np.ones((2, 1, 1), dtype=np.bool)
+        res = np.einsum('...ij,...jk->...ik', a, a, out=out)
+        assert_equal(res, tgt)
+
+    def test_out_is_res(self):
+        a = np.arange(9).reshape(3, 3)
+        res = np.einsum('...ij,...jk->...ik', a, a, out=a)
+        assert res is a
+
+    def optimize_compare(self, subscripts, operands=None):
+        # Tests all paths of the optimization function against
+        # conventional einsum
+        if operands is None:
+            args = [subscripts]
+            terms = subscripts.split('->')[0].split(',')
+            for term in terms:
+                dims = [global_size_dict[x] for x in term]
+                args.append(np.random.rand(*dims))
+        else:
+            args = [subscripts] + operands
+
+        noopt = np.einsum(*args, optimize=False)
+        opt = np.einsum(*args, optimize='greedy')
+        assert_almost_equal(opt, noopt)
+        opt = np.einsum(*args, optimize='optimal')
+        assert_almost_equal(opt, noopt)
+
+    def test_hadamard_like_products(self):
+        # Hadamard outer products
+        self.optimize_compare('a,ab,abc->abc')
+        self.optimize_compare('a,b,ab->ab')
+
+    def test_index_transformations(self):
+        # Simple index transformation cases
+        self.optimize_compare('ea,fb,gc,hd,abcd->efgh')
+        self.optimize_compare('ea,fb,abcd,gc,hd->efgh')
+        self.optimize_compare('abcd,ea,fb,gc,hd->efgh')
+
+    def test_complex(self):
+        # Long test cases
+        self.optimize_compare('acdf,jbje,gihb,hfac,gfac,gifabc,hfac')
+        self.optimize_compare('acdf,jbje,gihb,hfac,gfac,gifabc,hfac')
+        self.optimize_compare('cd,bdhe,aidb,hgca,gc,hgibcd,hgac')
+        self.optimize_compare('abhe,hidj,jgba,hiab,gab')
+        self.optimize_compare('bde,cdh,agdb,hica,ibd,hgicd,hiac')
+        self.optimize_compare('chd,bde,agbc,hiad,hgc,hgi,hiad')
+        self.optimize_compare('chd,bde,agbc,hiad,bdi,cgh,agdb')
+        self.optimize_compare('bdhe,acad,hiab,agac,hibd')
+
+    def test_collapse(self):
+        # Inner products
+        self.optimize_compare('ab,ab,c->')
+        self.optimize_compare('ab,ab,c->c')
+        self.optimize_compare('ab,ab,cd,cd->')
+        self.optimize_compare('ab,ab,cd,cd->ac')
+        self.optimize_compare('ab,ab,cd,cd->cd')
+        self.optimize_compare('ab,ab,cd,cd,ef,ef->')
+
+    def test_expand(self):
+        # Outer products
+        self.optimize_compare('ab,cd,ef->abcdef')
+        self.optimize_compare('ab,cd,ef->acdf')
+        self.optimize_compare('ab,cd,de->abcde')
+        self.optimize_compare('ab,cd,de->be')
+        self.optimize_compare('ab,bcd,cd->abcd')
+        self.optimize_compare('ab,bcd,cd->abd')
+
+    def test_edge_cases(self):
+        # Difficult edge cases for optimization
+        self.optimize_compare('eb,cb,fb->cef')
+        self.optimize_compare('dd,fb,be,cdb->cef')
+        self.optimize_compare('bca,cdb,dbf,afc->')
+        self.optimize_compare('dcc,fce,ea,dbf->ab')
+        self.optimize_compare('fdf,cdd,ccd,afe->ae')
+        self.optimize_compare('abcd,ad')
+        self.optimize_compare('ed,fcd,ff,bcf->be')
+        self.optimize_compare('baa,dcf,af,cde->be')
+        self.optimize_compare('bd,db,eac->ace')
+        self.optimize_compare('fff,fae,bef,def->abd')
+        self.optimize_compare('efc,dbc,acf,fd->abe')
+        self.optimize_compare('ba,ac,da->bcd')
+
+    def test_inner_product(self):
+        # Inner products
+        self.optimize_compare('ab,ab')
+        self.optimize_compare('ab,ba')
+        self.optimize_compare('abc,abc')
+        self.optimize_compare('abc,bac')
+        self.optimize_compare('abc,cba')
+
+    def test_random_cases(self):
+        # Randomly built test cases
+        self.optimize_compare('aab,fa,df,ecc->bde')
+        self.optimize_compare('ecb,fef,bad,ed->ac')
+        self.optimize_compare('bcf,bbb,fbf,fc->')
+        self.optimize_compare('bb,ff,be->e')
+        self.optimize_compare('bcb,bb,fc,fff->')
+        self.optimize_compare('fbb,dfd,fc,fc->')
+        self.optimize_compare('afd,ba,cc,dc->bf')
+        self.optimize_compare('adb,bc,fa,cfc->d')
+        self.optimize_compare('bbd,bda,fc,db->acf')
+        self.optimize_compare('dba,ead,cad->bce')
+        self.optimize_compare('aef,fbc,dca->bde')
+
+    def test_combined_views_mapping(self):
+        # gh-10792
+        a = np.arange(9).reshape(1, 1, 3, 1, 3)
+        b = np.einsum('bbcdc->d', a)
+        assert_equal(b, [12])
+
+    def test_broadcasting_dot_cases(self):
+        # Ensures broadcasting cases are not mistaken for GEMM
+
+        a = np.random.rand(1, 5, 4)
+        b = np.random.rand(4, 6)
+        c = np.random.rand(5, 6)
+        d = np.random.rand(10)
+
+        self.optimize_compare('ijk,kl,jl', operands=[a, b, c])
+        self.optimize_compare('ijk,kl,jl,i->i', operands=[a, b, c, d])
+
+        e = np.random.rand(1, 1, 5, 4)
+        f = np.random.rand(7, 7)
+        self.optimize_compare('abjk,kl,jl', operands=[e, b, c])
+        self.optimize_compare('abjk,kl,jl,ab->ab', operands=[e, b, c, f])
+
+        # Edge case found in gh-11308
+        g = np.arange(64).reshape(2, 4, 8)
+        self.optimize_compare('obk,ijk->ioj', operands=[g, g])
+
+    def test_output_order(self):
+        # Ensure output order is respected for optimize cases, the below
+        # contraction should yield a reshaped tensor view
+        # gh-16415
+
+        a = np.ones((2, 3, 5), order='F')
+        b = np.ones((4, 3), order='F')
+
+        for opt in [True, False]:
+            tmp = np.einsum('...ft,mf->...mt', a, b, order='a', optimize=opt)
+            assert_(tmp.flags.f_contiguous)
+
+            tmp = np.einsum('...ft,mf->...mt', a, b, order='f', optimize=opt)
+            assert_(tmp.flags.f_contiguous)
+
+            tmp = np.einsum('...ft,mf->...mt', a, b, order='c', optimize=opt)
+            assert_(tmp.flags.c_contiguous)
+
+            tmp = np.einsum('...ft,mf->...mt', a, b, order='k', optimize=opt)
+            assert_(tmp.flags.c_contiguous is False)
+            assert_(tmp.flags.f_contiguous is False)
+
+            tmp = np.einsum('...ft,mf->...mt', a, b, optimize=opt)
+            assert_(tmp.flags.c_contiguous is False)
+            assert_(tmp.flags.f_contiguous is False)
+
+        c = np.ones((4, 3), order='C')
+        for opt in [True, False]:
+            tmp = np.einsum('...ft,mf->...mt', a, c, order='a', optimize=opt)
+            assert_(tmp.flags.c_contiguous)
+
+        d = np.ones((2, 3, 5), order='C')
+        for opt in [True, False]:
+            tmp = np.einsum('...ft,mf->...mt', d, c, order='a', optimize=opt)
+            assert_(tmp.flags.c_contiguous)
+
+class TestEinsumPath:
+    def build_operands(self, string, size_dict=global_size_dict):
+
+        # Builds views based off initial operands
+        operands = [string]
+        terms = string.split('->')[0].split(',')
+        for term in terms:
+            dims = [size_dict[x] for x in term]
+            operands.append(np.random.rand(*dims))
+
+        return operands
+
+    def assert_path_equal(self, comp, benchmark):
+        # Checks if list of tuples are equivalent
+        ret = (len(comp) == len(benchmark))
+        assert_(ret)
+        for pos in range(len(comp) - 1):
+            ret &= isinstance(comp[pos + 1], tuple)
+            ret &= (comp[pos + 1] == benchmark[pos + 1])
+        assert_(ret)
+
+    def test_memory_contraints(self):
+        # Ensure memory constraints are satisfied
+
+        outer_test = self.build_operands('a,b,c->abc')
+
+        path, path_str = np.einsum_path(*outer_test, optimize=('greedy', 0))
+        self.assert_path_equal(path, ['einsum_path', (0, 1, 2)])
+
+        path, path_str = np.einsum_path(*outer_test, optimize=('optimal', 0))
+        self.assert_path_equal(path, ['einsum_path', (0, 1, 2)])
+
+        long_test = self.build_operands('acdf,jbje,gihb,hfac')
+        path, path_str = np.einsum_path(*long_test, optimize=('greedy', 0))
+        self.assert_path_equal(path, ['einsum_path', (0, 1, 2, 3)])
+
+        path, path_str = np.einsum_path(*long_test, optimize=('optimal', 0))
+        self.assert_path_equal(path, ['einsum_path', (0, 1, 2, 3)])
+
+    def test_long_paths(self):
+        # Long complex cases
+
+        # Long test 1
+        long_test1 = self.build_operands('acdf,jbje,gihb,hfac,gfac,gifabc,hfac')
+        path, path_str = np.einsum_path(*long_test1, optimize='greedy')
+        self.assert_path_equal(path, ['einsum_path',
+                                      (3, 6), (3, 4), (2, 4), (2, 3), (0, 2), (0, 1)])
+
+        path, path_str = np.einsum_path(*long_test1, optimize='optimal')
+        self.assert_path_equal(path, ['einsum_path',
+                                      (3, 6), (3, 4), (2, 4), (2, 3), (0, 2), (0, 1)])
+
+        # Long test 2
+        long_test2 = self.build_operands('chd,bde,agbc,hiad,bdi,cgh,agdb')
+        path, path_str = np.einsum_path(*long_test2, optimize='greedy')
+        self.assert_path_equal(path, ['einsum_path',
+                                      (3, 4), (0, 3), (3, 4), (1, 3), (1, 2), (0, 1)])
+
+        path, path_str = np.einsum_path(*long_test2, optimize='optimal')
+        self.assert_path_equal(path, ['einsum_path',
+                                      (0, 5), (1, 4), (3, 4), (1, 3), (1, 2), (0, 1)])
+
+    def test_edge_paths(self):
+        # Difficult edge cases
+
+        # Edge test1
+        edge_test1 = self.build_operands('eb,cb,fb->cef')
+        path, path_str = np.einsum_path(*edge_test1, optimize='greedy')
+        self.assert_path_equal(path, ['einsum_path', (0, 2), (0, 1)])
+
+        path, path_str = np.einsum_path(*edge_test1, optimize='optimal')
+        self.assert_path_equal(path, ['einsum_path', (0, 2), (0, 1)])
+
+        # Edge test2
+        edge_test2 = self.build_operands('dd,fb,be,cdb->cef')
+        path, path_str = np.einsum_path(*edge_test2, optimize='greedy')
+        self.assert_path_equal(path, ['einsum_path', (0, 3), (0, 1), (0, 1)])
+
+        path, path_str = np.einsum_path(*edge_test2, optimize='optimal')
+        self.assert_path_equal(path, ['einsum_path', (0, 3), (0, 1), (0, 1)])
+
+        # Edge test3
+        edge_test3 = self.build_operands('bca,cdb,dbf,afc->')
+        path, path_str = np.einsum_path(*edge_test3, optimize='greedy')
+        self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)])
+
+        path, path_str = np.einsum_path(*edge_test3, optimize='optimal')
+        self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)])
+
+        # Edge test4
+        edge_test4 = self.build_operands('dcc,fce,ea,dbf->ab')
+        path, path_str = np.einsum_path(*edge_test4, optimize='greedy')
+        self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 1), (0, 1)])
+
+        path, path_str = np.einsum_path(*edge_test4, optimize='optimal')
+        self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)])
+
+        # Edge test5
+        edge_test4 = self.build_operands('a,ac,ab,ad,cd,bd,bc->',
+                                         size_dict={"a": 20, "b": 20, "c": 20, "d": 20})
+        path, path_str = np.einsum_path(*edge_test4, optimize='greedy')
+        self.assert_path_equal(path, ['einsum_path', (0, 1), (0, 1, 2, 3, 4, 5)])
+
+        path, path_str = np.einsum_path(*edge_test4, optimize='optimal')
+        self.assert_path_equal(path, ['einsum_path', (0, 1), (0, 1, 2, 3, 4, 5)])
+
+    def test_path_type_input(self):
+        # Test explicit path handling
+        path_test = self.build_operands('dcc,fce,ea,dbf->ab')
+
+        path, path_str = np.einsum_path(*path_test, optimize=False)
+        self.assert_path_equal(path, ['einsum_path', (0, 1, 2, 3)])
+
+        path, path_str = np.einsum_path(*path_test, optimize=True)
+        self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 1), (0, 1)])
+
+        exp_path = ['einsum_path', (0, 2), (0, 2), (0, 1)]
+        path, path_str = np.einsum_path(*path_test, optimize=exp_path)
+        self.assert_path_equal(path, exp_path)
+
+        # Double check einsum works on the input path
+        noopt = np.einsum(*path_test, optimize=False)
+        opt = np.einsum(*path_test, optimize=exp_path)
+        assert_almost_equal(noopt, opt)
+
+    def test_path_type_input_internal_trace(self):
+        # gh-20962
+        path_test = self.build_operands('cab,cdd->ab')
+        exp_path = ['einsum_path', (1,), (0, 1)]
+
+        path, path_str = np.einsum_path(*path_test, optimize=exp_path)
+        self.assert_path_equal(path, exp_path)
+
+        # Double check einsum works on the input path
+        noopt = np.einsum(*path_test, optimize=False)
+        opt = np.einsum(*path_test, optimize=exp_path)
+        assert_almost_equal(noopt, opt)
+
+    def test_path_type_input_invalid(self):
+        path_test = self.build_operands('ab,bc,cd,de->ae')
+        exp_path = ['einsum_path', (2, 3), (0, 1)]
+        assert_raises(RuntimeError, np.einsum, *path_test, optimize=exp_path)
+        assert_raises(
+            RuntimeError, np.einsum_path, *path_test, optimize=exp_path)
+
+        path_test = self.build_operands('a,a,a->a')
+        exp_path = ['einsum_path', (1,), (0, 1)]
+        assert_raises(RuntimeError, np.einsum, *path_test, optimize=exp_path)
+        assert_raises(
+            RuntimeError, np.einsum_path, *path_test, optimize=exp_path)
+
+    def test_spaces(self):
+        # gh-10794
+        arr = np.array([[1]])
+        for sp in itertools.product(['', ' '], repeat=4):
+            # no error for any spacing
+            np.einsum('{}...a{}->{}...a{}'.format(*sp), arr)
+
+def test_overlap():
+    a = np.arange(9, dtype=int).reshape(3, 3)
+    b = np.arange(9, dtype=int).reshape(3, 3)
+    d = np.dot(a, b)
+    # sanity check
+    c = np.einsum('ij,jk->ik', a, b)
+    assert_equal(c, d)
+    # gh-10080, out overlaps one of the operands
+    c = np.einsum('ij,jk->ik', a, b, out=b)
+    assert_equal(c, d)
+
+def test_einsum_chunking_precision():
+    """Most einsum operations are reductions and until NumPy 2.3 reductions
+    never (or almost never?) used the `GROWINNER` mechanism to increase the
+    inner loop size when no buffers are needed.
+    Because einsum reductions work roughly:
+
+        def inner(*inputs, out):
+            accumulate = 0
+            for vals in zip(*inputs):
+                accumulate += prod(vals)
+            out[0] += accumulate
+
+    Calling the inner-loop more often actually improves accuracy slightly
+    (same effect as pairwise summation but much less).
+    Without adding pairwise summation to the inner-loop it seems best to just
+    not use GROWINNER, a quick tests suggest that is maybe 1% slowdown for
+    the simplest `einsum("i,i->i", x, x)` case.
+
+    (It is not clear that we should guarantee precision to this extend.)
+    """
+    num = 1_000_000
+    value = 1. + np.finfo(np.float64).eps * 8196
+    res = np.einsum("i->", np.broadcast_to(np.array(value), num)) / num
+
+    # At with GROWINNER 11 decimals succeed (larger will be less)
+    assert_almost_equal(res, value, decimal=15)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_errstate.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_errstate.py
new file mode 100644
index 0000000..b72fb65
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_errstate.py
@@ -0,0 +1,131 @@
+import sysconfig
+
+import pytest
+
+import numpy as np
+from numpy.testing import IS_WASM, assert_raises
+
+# The floating point emulation on ARM EABI systems lacking a hardware FPU is
+# known to be buggy. This is an attempt to identify these hosts. It may not
+# catch all possible cases, but it catches the known cases of gh-413 and
+# gh-15562.
+hosttype = sysconfig.get_config_var('HOST_GNU_TYPE')
+arm_softfloat = False if hosttype is None else hosttype.endswith('gnueabi')
+
+class TestErrstate:
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.skipif(arm_softfloat,
+                        reason='platform/cpu issue with FPU (gh-413,-15562)')
+    def test_invalid(self):
+        with np.errstate(all='raise', under='ignore'):
+            a = -np.arange(3)
+            # This should work
+            with np.errstate(invalid='ignore'):
+                np.sqrt(a)
+            # While this should fail!
+            with assert_raises(FloatingPointError):
+                np.sqrt(a)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.skipif(arm_softfloat,
+                        reason='platform/cpu issue with FPU (gh-15562)')
+    def test_divide(self):
+        with np.errstate(all='raise', under='ignore'):
+            a = -np.arange(3)
+            # This should work
+            with np.errstate(divide='ignore'):
+                a // 0
+            # While this should fail!
+            with assert_raises(FloatingPointError):
+                a // 0
+            # As should this, see gh-15562
+            with assert_raises(FloatingPointError):
+                a // a
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.skipif(arm_softfloat,
+                        reason='platform/cpu issue with FPU (gh-15562)')
+    def test_errcall(self):
+        count = 0
+
+        def foo(*args):
+            nonlocal count
+            count += 1
+
+        olderrcall = np.geterrcall()
+        with np.errstate(call=foo):
+            assert np.geterrcall() is foo
+            with np.errstate(call=None):
+                assert np.geterrcall() is None
+        assert np.geterrcall() is olderrcall
+        assert count == 0
+
+        with np.errstate(call=foo, invalid="call"):
+            np.array(np.inf) - np.array(np.inf)
+
+        assert count == 1
+
+    def test_errstate_decorator(self):
+        @np.errstate(all='ignore')
+        def foo():
+            a = -np.arange(3)
+            a // 0
+
+        foo()
+
+    def test_errstate_enter_once(self):
+        errstate = np.errstate(invalid="warn")
+        with errstate:
+            pass
+
+        # The errstate context cannot be entered twice as that would not be
+        # thread-safe
+        with pytest.raises(TypeError,
+                match="Cannot enter `np.errstate` twice"):
+            with errstate:
+                pass
+
+    @pytest.mark.skipif(IS_WASM, reason="wasm doesn't support asyncio")
+    def test_asyncio_safe(self):
+        # asyncio may not always work, lets assume its fine if missing
+        # Pyodide/wasm doesn't support it.  If this test makes problems,
+        # it should just be skipped liberally (or run differently).
+        asyncio = pytest.importorskip("asyncio")
+
+        @np.errstate(invalid="ignore")
+        def decorated():
+            # Decorated non-async function (it is not safe to decorate an
+            # async one)
+            assert np.geterr()["invalid"] == "ignore"
+
+        async def func1():
+            decorated()
+            await asyncio.sleep(0.1)
+            decorated()
+
+        async def func2():
+            with np.errstate(invalid="raise"):
+                assert np.geterr()["invalid"] == "raise"
+                await asyncio.sleep(0.125)
+                assert np.geterr()["invalid"] == "raise"
+
+        # for good sport, a third one with yet another state:
+        async def func3():
+            with np.errstate(invalid="print"):
+                assert np.geterr()["invalid"] == "print"
+                await asyncio.sleep(0.11)
+                assert np.geterr()["invalid"] == "print"
+
+        async def main():
+            # simply run all three function multiple times:
+            await asyncio.gather(
+                    func1(), func2(), func3(), func1(), func2(), func3(),
+                    func1(), func2(), func3(), func1(), func2(), func3())
+
+        loop = asyncio.new_event_loop()
+        with np.errstate(invalid="warn"):
+            asyncio.run(main())
+            assert np.geterr()["invalid"] == "warn"
+
+        assert np.geterr()["invalid"] == "warn"  # the default
+        loop.close()
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_extint128.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_extint128.py
new file mode 100644
index 0000000..1a05151
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_extint128.py
@@ -0,0 +1,217 @@
+import contextlib
+import itertools
+import operator
+
+import numpy._core._multiarray_tests as mt
+import pytest
+
+import numpy as np
+from numpy.testing import assert_equal, assert_raises
+
+INT64_MAX = np.iinfo(np.int64).max
+INT64_MIN = np.iinfo(np.int64).min
+INT64_MID = 2**32
+
+# int128 is not two's complement, the sign bit is separate
+INT128_MAX = 2**128 - 1
+INT128_MIN = -INT128_MAX
+INT128_MID = 2**64
+
+INT64_VALUES = (
+    [INT64_MIN + j for j in range(20)] +
+    [INT64_MAX - j for j in range(20)] +
+    [INT64_MID + j for j in range(-20, 20)] +
+    [2 * INT64_MID + j for j in range(-20, 20)] +
+    [INT64_MID // 2 + j for j in range(-20, 20)] +
+    list(range(-70, 70))
+)
+
+INT128_VALUES = (
+    [INT128_MIN + j for j in range(20)] +
+    [INT128_MAX - j for j in range(20)] +
+    [INT128_MID + j for j in range(-20, 20)] +
+    [2 * INT128_MID + j for j in range(-20, 20)] +
+    [INT128_MID // 2 + j for j in range(-20, 20)] +
+    list(range(-70, 70)) +
+    [False]  # negative zero
+)
+
+INT64_POS_VALUES = [x for x in INT64_VALUES if x > 0]
+
+
+@contextlib.contextmanager
+def exc_iter(*args):
+    """
+    Iterate over Cartesian product of *args, and if an exception is raised,
+    add information of the current iterate.
+    """
+
+    value = [None]
+
+    def iterate():
+        for v in itertools.product(*args):
+            value[0] = v
+            yield v
+
+    try:
+        yield iterate()
+    except Exception:
+        import traceback
+        msg = f"At: {repr(value[0])!r}\n{traceback.format_exc()}"
+        raise AssertionError(msg)
+
+
+def test_safe_binop():
+    # Test checked arithmetic routines
+
+    ops = [
+        (operator.add, 1),
+        (operator.sub, 2),
+        (operator.mul, 3)
+    ]
+
+    with exc_iter(ops, INT64_VALUES, INT64_VALUES) as it:
+        for xop, a, b in it:
+            pyop, op = xop
+            c = pyop(a, b)
+
+            if not (INT64_MIN <= c <= INT64_MAX):
+                assert_raises(OverflowError, mt.extint_safe_binop, a, b, op)
+            else:
+                d = mt.extint_safe_binop(a, b, op)
+                if c != d:
+                    # assert_equal is slow
+                    assert_equal(d, c)
+
+
+def test_to_128():
+    with exc_iter(INT64_VALUES) as it:
+        for a, in it:
+            b = mt.extint_to_128(a)
+            if a != b:
+                assert_equal(b, a)
+
+
+def test_to_64():
+    with exc_iter(INT128_VALUES) as it:
+        for a, in it:
+            if not (INT64_MIN <= a <= INT64_MAX):
+                assert_raises(OverflowError, mt.extint_to_64, a)
+            else:
+                b = mt.extint_to_64(a)
+                if a != b:
+                    assert_equal(b, a)
+
+
+def test_mul_64_64():
+    with exc_iter(INT64_VALUES, INT64_VALUES) as it:
+        for a, b in it:
+            c = a * b
+            d = mt.extint_mul_64_64(a, b)
+            if c != d:
+                assert_equal(d, c)
+
+
+def test_add_128():
+    with exc_iter(INT128_VALUES, INT128_VALUES) as it:
+        for a, b in it:
+            c = a + b
+            if not (INT128_MIN <= c <= INT128_MAX):
+                assert_raises(OverflowError, mt.extint_add_128, a, b)
+            else:
+                d = mt.extint_add_128(a, b)
+                if c != d:
+                    assert_equal(d, c)
+
+
+def test_sub_128():
+    with exc_iter(INT128_VALUES, INT128_VALUES) as it:
+        for a, b in it:
+            c = a - b
+            if not (INT128_MIN <= c <= INT128_MAX):
+                assert_raises(OverflowError, mt.extint_sub_128, a, b)
+            else:
+                d = mt.extint_sub_128(a, b)
+                if c != d:
+                    assert_equal(d, c)
+
+
+def test_neg_128():
+    with exc_iter(INT128_VALUES) as it:
+        for a, in it:
+            b = -a
+            c = mt.extint_neg_128(a)
+            if b != c:
+                assert_equal(c, b)
+
+
+def test_shl_128():
+    with exc_iter(INT128_VALUES) as it:
+        for a, in it:
+            if a < 0:
+                b = -(((-a) << 1) & (2**128 - 1))
+            else:
+                b = (a << 1) & (2**128 - 1)
+            c = mt.extint_shl_128(a)
+            if b != c:
+                assert_equal(c, b)
+
+
+def test_shr_128():
+    with exc_iter(INT128_VALUES) as it:
+        for a, in it:
+            if a < 0:
+                b = -((-a) >> 1)
+            else:
+                b = a >> 1
+            c = mt.extint_shr_128(a)
+            if b != c:
+                assert_equal(c, b)
+
+
+def test_gt_128():
+    with exc_iter(INT128_VALUES, INT128_VALUES) as it:
+        for a, b in it:
+            c = a > b
+            d = mt.extint_gt_128(a, b)
+            if c != d:
+                assert_equal(d, c)
+
+
+@pytest.mark.slow
+def test_divmod_128_64():
+    with exc_iter(INT128_VALUES, INT64_POS_VALUES) as it:
+        for a, b in it:
+            if a >= 0:
+                c, cr = divmod(a, b)
+            else:
+                c, cr = divmod(-a, b)
+                c = -c
+                cr = -cr
+
+            d, dr = mt.extint_divmod_128_64(a, b)
+
+            if c != d or d != dr or b * d + dr != a:
+                assert_equal(d, c)
+                assert_equal(dr, cr)
+                assert_equal(b * d + dr, a)
+
+
+def test_floordiv_128_64():
+    with exc_iter(INT128_VALUES, INT64_POS_VALUES) as it:
+        for a, b in it:
+            c = a // b
+            d = mt.extint_floordiv_128_64(a, b)
+
+            if c != d:
+                assert_equal(d, c)
+
+
+def test_ceildiv_128_64():
+    with exc_iter(INT128_VALUES, INT64_POS_VALUES) as it:
+        for a, b in it:
+            c = (a + b - 1) // b
+            d = mt.extint_ceildiv_128_64(a, b)
+
+            if c != d:
+                assert_equal(d, c)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_function_base.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_function_base.py
new file mode 100644
index 0000000..c925cf1
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_function_base.py
@@ -0,0 +1,503 @@
+import platform
+import sys
+
+import pytest
+
+import numpy as np
+from numpy import (
+    arange,
+    array,
+    dtype,
+    errstate,
+    geomspace,
+    isnan,
+    linspace,
+    logspace,
+    ndarray,
+    nextafter,
+    sqrt,
+    stack,
+)
+from numpy._core import sctypes
+from numpy._core.function_base import add_newdoc
+from numpy.testing import (
+    IS_PYPY,
+    assert_,
+    assert_allclose,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+)
+
+
+def _is_armhf():
+    # Check if the current platform is ARMHF (32-bit ARM architecture)
+    return platform.machine().startswith('arm') and platform.architecture()[0] == '32bit'
+
+class PhysicalQuantity(float):
+    def __new__(cls, value):
+        return float.__new__(cls, value)
+
+    def __add__(self, x):
+        assert_(isinstance(x, PhysicalQuantity))
+        return PhysicalQuantity(float(x) + float(self))
+    __radd__ = __add__
+
+    def __sub__(self, x):
+        assert_(isinstance(x, PhysicalQuantity))
+        return PhysicalQuantity(float(self) - float(x))
+
+    def __rsub__(self, x):
+        assert_(isinstance(x, PhysicalQuantity))
+        return PhysicalQuantity(float(x) - float(self))
+
+    def __mul__(self, x):
+        return PhysicalQuantity(float(x) * float(self))
+    __rmul__ = __mul__
+
+    def __truediv__(self, x):
+        return PhysicalQuantity(float(self) / float(x))
+
+    def __rtruediv__(self, x):
+        return PhysicalQuantity(float(x) / float(self))
+
+
+class PhysicalQuantity2(ndarray):
+    __array_priority__ = 10
+
+
+class TestLogspace:
+
+    def test_basic(self):
+        y = logspace(0, 6)
+        assert_(len(y) == 50)
+        y = logspace(0, 6, num=100)
+        assert_(y[-1] == 10 ** 6)
+        y = logspace(0, 6, endpoint=False)
+        assert_(y[-1] < 10 ** 6)
+        y = logspace(0, 6, num=7)
+        assert_array_equal(y, [1, 10, 100, 1e3, 1e4, 1e5, 1e6])
+
+    def test_start_stop_array(self):
+        start = array([0., 1.])
+        stop = array([6., 7.])
+        t1 = logspace(start, stop, 6)
+        t2 = stack([logspace(_start, _stop, 6)
+                    for _start, _stop in zip(start, stop)], axis=1)
+        assert_equal(t1, t2)
+        t3 = logspace(start, stop[0], 6)
+        t4 = stack([logspace(_start, stop[0], 6)
+                    for _start in start], axis=1)
+        assert_equal(t3, t4)
+        t5 = logspace(start, stop, 6, axis=-1)
+        assert_equal(t5, t2.T)
+
+    @pytest.mark.parametrize("axis", [0, 1, -1])
+    def test_base_array(self, axis: int):
+        start = 1
+        stop = 2
+        num = 6
+        base = array([1, 2])
+        t1 = logspace(start, stop, num=num, base=base, axis=axis)
+        t2 = stack(
+            [logspace(start, stop, num=num, base=_base) for _base in base],
+            axis=(axis + 1) % t1.ndim,
+        )
+        assert_equal(t1, t2)
+
+    @pytest.mark.parametrize("axis", [0, 1, -1])
+    def test_stop_base_array(self, axis: int):
+        start = 1
+        stop = array([2, 3])
+        num = 6
+        base = array([1, 2])
+        t1 = logspace(start, stop, num=num, base=base, axis=axis)
+        t2 = stack(
+            [logspace(start, _stop, num=num, base=_base)
+             for _stop, _base in zip(stop, base)],
+            axis=(axis + 1) % t1.ndim,
+        )
+        assert_equal(t1, t2)
+
+    def test_dtype(self):
+        y = logspace(0, 6, dtype='float32')
+        assert_equal(y.dtype, dtype('float32'))
+        y = logspace(0, 6, dtype='float64')
+        assert_equal(y.dtype, dtype('float64'))
+        y = logspace(0, 6, dtype='int32')
+        assert_equal(y.dtype, dtype('int32'))
+
+    def test_physical_quantities(self):
+        a = PhysicalQuantity(1.0)
+        b = PhysicalQuantity(5.0)
+        assert_equal(logspace(a, b), logspace(1.0, 5.0))
+
+    def test_subclass(self):
+        a = array(1).view(PhysicalQuantity2)
+        b = array(7).view(PhysicalQuantity2)
+        ls = logspace(a, b)
+        assert type(ls) is PhysicalQuantity2
+        assert_equal(ls, logspace(1.0, 7.0))
+        ls = logspace(a, b, 1)
+        assert type(ls) is PhysicalQuantity2
+        assert_equal(ls, logspace(1.0, 7.0, 1))
+
+
+class TestGeomspace:
+
+    def test_basic(self):
+        y = geomspace(1, 1e6)
+        assert_(len(y) == 50)
+        y = geomspace(1, 1e6, num=100)
+        assert_(y[-1] == 10 ** 6)
+        y = geomspace(1, 1e6, endpoint=False)
+        assert_(y[-1] < 10 ** 6)
+        y = geomspace(1, 1e6, num=7)
+        assert_array_equal(y, [1, 10, 100, 1e3, 1e4, 1e5, 1e6])
+
+        y = geomspace(8, 2, num=3)
+        assert_allclose(y, [8, 4, 2])
+        assert_array_equal(y.imag, 0)
+
+        y = geomspace(-1, -100, num=3)
+        assert_array_equal(y, [-1, -10, -100])
+        assert_array_equal(y.imag, 0)
+
+        y = geomspace(-100, -1, num=3)
+        assert_array_equal(y, [-100, -10, -1])
+        assert_array_equal(y.imag, 0)
+
+    def test_boundaries_match_start_and_stop_exactly(self):
+        # make sure that the boundaries of the returned array exactly
+        # equal 'start' and 'stop' - this isn't obvious because
+        # np.exp(np.log(x)) isn't necessarily exactly equal to x
+        start = 0.3
+        stop = 20.3
+
+        y = geomspace(start, stop, num=1)
+        assert_equal(y[0], start)
+
+        y = geomspace(start, stop, num=1, endpoint=False)
+        assert_equal(y[0], start)
+
+        y = geomspace(start, stop, num=3)
+        assert_equal(y[0], start)
+        assert_equal(y[-1], stop)
+
+        y = geomspace(start, stop, num=3, endpoint=False)
+        assert_equal(y[0], start)
+
+    def test_nan_interior(self):
+        with errstate(invalid='ignore'):
+            y = geomspace(-3, 3, num=4)
+
+        assert_equal(y[0], -3.0)
+        assert_(isnan(y[1:-1]).all())
+        assert_equal(y[3], 3.0)
+
+        with errstate(invalid='ignore'):
+            y = geomspace(-3, 3, num=4, endpoint=False)
+
+        assert_equal(y[0], -3.0)
+        assert_(isnan(y[1:]).all())
+
+    def test_complex(self):
+        # Purely imaginary
+        y = geomspace(1j, 16j, num=5)
+        assert_allclose(y, [1j, 2j, 4j, 8j, 16j])
+        assert_array_equal(y.real, 0)
+
+        y = geomspace(-4j, -324j, num=5)
+        assert_allclose(y, [-4j, -12j, -36j, -108j, -324j])
+        assert_array_equal(y.real, 0)
+
+        y = geomspace(1 + 1j, 1000 + 1000j, num=4)
+        assert_allclose(y, [1 + 1j, 10 + 10j, 100 + 100j, 1000 + 1000j])
+
+        y = geomspace(-1 + 1j, -1000 + 1000j, num=4)
+        assert_allclose(y, [-1 + 1j, -10 + 10j, -100 + 100j, -1000 + 1000j])
+
+        # Logarithmic spirals
+        y = geomspace(-1, 1, num=3, dtype=complex)
+        assert_allclose(y, [-1, 1j, +1])
+
+        y = geomspace(0 + 3j, -3 + 0j, 3)
+        assert_allclose(y, [0 + 3j, -3 / sqrt(2) + 3j / sqrt(2), -3 + 0j])
+        y = geomspace(0 + 3j, 3 + 0j, 3)
+        assert_allclose(y, [0 + 3j, 3 / sqrt(2) + 3j / sqrt(2), 3 + 0j])
+        y = geomspace(-3 + 0j, 0 - 3j, 3)
+        assert_allclose(y, [-3 + 0j, -3 / sqrt(2) - 3j / sqrt(2), 0 - 3j])
+        y = geomspace(0 + 3j, -3 + 0j, 3)
+        assert_allclose(y, [0 + 3j, -3 / sqrt(2) + 3j / sqrt(2), -3 + 0j])
+        y = geomspace(-2 - 3j, 5 + 7j, 7)
+        assert_allclose(y, [-2 - 3j, -0.29058977 - 4.15771027j,
+                            2.08885354 - 4.34146838j, 4.58345529 - 3.16355218j,
+                            6.41401745 - 0.55233457j, 6.75707386 + 3.11795092j,
+                            5 + 7j])
+
+        # Type promotion should prevent the -5 from becoming a NaN
+        y = geomspace(3j, -5, 2)
+        assert_allclose(y, [3j, -5])
+        y = geomspace(-5, 3j, 2)
+        assert_allclose(y, [-5, 3j])
+
+    def test_complex_shortest_path(self):
+        # test the shortest logarithmic spiral is used, see gh-25644
+        x = 1.2 + 3.4j
+        y = np.exp(1j * (np.pi - .1)) * x
+        z = np.geomspace(x, y, 5)
+        expected = np.array([1.2 + 3.4j, -1.47384 + 3.2905616j,
+                        -3.33577588 + 1.36842949j, -3.36011056 - 1.30753855j,
+                        -1.53343861 - 3.26321406j])
+        np.testing.assert_array_almost_equal(z, expected)
+
+    def test_dtype(self):
+        y = geomspace(1, 1e6, dtype='float32')
+        assert_equal(y.dtype, dtype('float32'))
+        y = geomspace(1, 1e6, dtype='float64')
+        assert_equal(y.dtype, dtype('float64'))
+        y = geomspace(1, 1e6, dtype='int32')
+        assert_equal(y.dtype, dtype('int32'))
+
+        # Native types
+        y = geomspace(1, 1e6, dtype=float)
+        assert_equal(y.dtype, dtype('float64'))
+        y = geomspace(1, 1e6, dtype=complex)
+        assert_equal(y.dtype, dtype('complex128'))
+
+    def test_start_stop_array_scalar(self):
+        lim1 = array([120, 100], dtype="int8")
+        lim2 = array([-120, -100], dtype="int8")
+        lim3 = array([1200, 1000], dtype="uint16")
+        t1 = geomspace(lim1[0], lim1[1], 5)
+        t2 = geomspace(lim2[0], lim2[1], 5)
+        t3 = geomspace(lim3[0], lim3[1], 5)
+        t4 = geomspace(120.0, 100.0, 5)
+        t5 = geomspace(-120.0, -100.0, 5)
+        t6 = geomspace(1200.0, 1000.0, 5)
+
+        # t3 uses float32, t6 uses float64
+        assert_allclose(t1, t4, rtol=1e-2)
+        assert_allclose(t2, t5, rtol=1e-2)
+        assert_allclose(t3, t6, rtol=1e-5)
+
+    def test_start_stop_array(self):
+        # Try to use all special cases.
+        start = array([1.e0, 32., 1j, -4j, 1 + 1j, -1])
+        stop = array([1.e4, 2., 16j, -324j, 10000 + 10000j, 1])
+        t1 = geomspace(start, stop, 5)
+        t2 = stack([geomspace(_start, _stop, 5)
+                    for _start, _stop in zip(start, stop)], axis=1)
+        assert_equal(t1, t2)
+        t3 = geomspace(start, stop[0], 5)
+        t4 = stack([geomspace(_start, stop[0], 5)
+                    for _start in start], axis=1)
+        assert_equal(t3, t4)
+        t5 = geomspace(start, stop, 5, axis=-1)
+        assert_equal(t5, t2.T)
+
+    def test_physical_quantities(self):
+        a = PhysicalQuantity(1.0)
+        b = PhysicalQuantity(5.0)
+        assert_equal(geomspace(a, b), geomspace(1.0, 5.0))
+
+    def test_subclass(self):
+        a = array(1).view(PhysicalQuantity2)
+        b = array(7).view(PhysicalQuantity2)
+        gs = geomspace(a, b)
+        assert type(gs) is PhysicalQuantity2
+        assert_equal(gs, geomspace(1.0, 7.0))
+        gs = geomspace(a, b, 1)
+        assert type(gs) is PhysicalQuantity2
+        assert_equal(gs, geomspace(1.0, 7.0, 1))
+
+    def test_bounds(self):
+        assert_raises(ValueError, geomspace, 0, 10)
+        assert_raises(ValueError, geomspace, 10, 0)
+        assert_raises(ValueError, geomspace, 0, 0)
+
+
+class TestLinspace:
+
+    def test_basic(self):
+        y = linspace(0, 10)
+        assert_(len(y) == 50)
+        y = linspace(2, 10, num=100)
+        assert_(y[-1] == 10)
+        y = linspace(2, 10, endpoint=False)
+        assert_(y[-1] < 10)
+        assert_raises(ValueError, linspace, 0, 10, num=-1)
+
+    def test_corner(self):
+        y = list(linspace(0, 1, 1))
+        assert_(y == [0.0], y)
+        assert_raises(TypeError, linspace, 0, 1, num=2.5)
+
+    def test_type(self):
+        t1 = linspace(0, 1, 0).dtype
+        t2 = linspace(0, 1, 1).dtype
+        t3 = linspace(0, 1, 2).dtype
+        assert_equal(t1, t2)
+        assert_equal(t2, t3)
+
+    def test_dtype(self):
+        y = linspace(0, 6, dtype='float32')
+        assert_equal(y.dtype, dtype('float32'))
+        y = linspace(0, 6, dtype='float64')
+        assert_equal(y.dtype, dtype('float64'))
+        y = linspace(0, 6, dtype='int32')
+        assert_equal(y.dtype, dtype('int32'))
+
+    def test_start_stop_array_scalar(self):
+        lim1 = array([-120, 100], dtype="int8")
+        lim2 = array([120, -100], dtype="int8")
+        lim3 = array([1200, 1000], dtype="uint16")
+        t1 = linspace(lim1[0], lim1[1], 5)
+        t2 = linspace(lim2[0], lim2[1], 5)
+        t3 = linspace(lim3[0], lim3[1], 5)
+        t4 = linspace(-120.0, 100.0, 5)
+        t5 = linspace(120.0, -100.0, 5)
+        t6 = linspace(1200.0, 1000.0, 5)
+        assert_equal(t1, t4)
+        assert_equal(t2, t5)
+        assert_equal(t3, t6)
+
+    def test_start_stop_array(self):
+        start = array([-120, 120], dtype="int8")
+        stop = array([100, -100], dtype="int8")
+        t1 = linspace(start, stop, 5)
+        t2 = stack([linspace(_start, _stop, 5)
+                    for _start, _stop in zip(start, stop)], axis=1)
+        assert_equal(t1, t2)
+        t3 = linspace(start, stop[0], 5)
+        t4 = stack([linspace(_start, stop[0], 5)
+                    for _start in start], axis=1)
+        assert_equal(t3, t4)
+        t5 = linspace(start, stop, 5, axis=-1)
+        assert_equal(t5, t2.T)
+
+    def test_complex(self):
+        lim1 = linspace(1 + 2j, 3 + 4j, 5)
+        t1 = array([1.0 + 2.j, 1.5 + 2.5j,  2.0 + 3j, 2.5 + 3.5j, 3.0 + 4j])
+        lim2 = linspace(1j, 10, 5)
+        t2 = array([0.0 + 1.j, 2.5 + 0.75j, 5.0 + 0.5j, 7.5 + 0.25j, 10.0 + 0j])
+        assert_equal(lim1, t1)
+        assert_equal(lim2, t2)
+
+    def test_physical_quantities(self):
+        a = PhysicalQuantity(0.0)
+        b = PhysicalQuantity(1.0)
+        assert_equal(linspace(a, b), linspace(0.0, 1.0))
+
+    def test_subclass(self):
+        a = array(0).view(PhysicalQuantity2)
+        b = array(1).view(PhysicalQuantity2)
+        ls = linspace(a, b)
+        assert type(ls) is PhysicalQuantity2
+        assert_equal(ls, linspace(0.0, 1.0))
+        ls = linspace(a, b, 1)
+        assert type(ls) is PhysicalQuantity2
+        assert_equal(ls, linspace(0.0, 1.0, 1))
+
+    def test_array_interface(self):
+        # Regression test for https://github.com/numpy/numpy/pull/6659
+        # Ensure that start/stop can be objects that implement
+        # __array_interface__ and are convertible to numeric scalars
+
+        class Arrayish:
+            """
+            A generic object that supports the __array_interface__ and hence
+            can in principle be converted to a numeric scalar, but is not
+            otherwise recognized as numeric, but also happens to support
+            multiplication by floats.
+
+            Data should be an object that implements the buffer interface,
+            and contains at least 4 bytes.
+            """
+
+            def __init__(self, data):
+                self._data = data
+
+            @property
+            def __array_interface__(self):
+                return {'shape': (), 'typestr': '<i4', 'data': self._data,
+                        'version': 3}
+
+            def __mul__(self, other):
+                # For the purposes of this test any multiplication is an
+                # identity operation :)
+                return self
+
+        one = Arrayish(array(1, dtype='<i4'))
+        five = Arrayish(array(5, dtype='<i4'))
+
+        assert_equal(linspace(one, five), linspace(1, 5))
+
+    # even when not explicitly enabled via FPSCR register
+    @pytest.mark.xfail(_is_armhf(),
+                       reason="ARMHF/AArch32 platforms seem to FTZ subnormals")
+    def test_denormal_numbers(self):
+        # Regression test for gh-5437. Will probably fail when compiled
+        # with ICC, which flushes denormals to zero
+        for ftype in sctypes['float']:
+            stop = nextafter(ftype(0), ftype(1)) * 5  # A denormal number
+            assert_(any(linspace(0, stop, 10, endpoint=False, dtype=ftype)))
+
+    def test_equivalent_to_arange(self):
+        for j in range(1000):
+            assert_equal(linspace(0, j, j + 1, dtype=int),
+                         arange(j + 1, dtype=int))
+
+    def test_retstep(self):
+        for num in [0, 1, 2]:
+            for ept in [False, True]:
+                y = linspace(0, 1, num, endpoint=ept, retstep=True)
+                assert isinstance(y, tuple) and len(y) == 2
+                if num == 2:
+                    y0_expect = [0.0, 1.0] if ept else [0.0, 0.5]
+                    assert_array_equal(y[0], y0_expect)
+                    assert_equal(y[1], y0_expect[1])
+                elif num == 1 and not ept:
+                    assert_array_equal(y[0], [0.0])
+                    assert_equal(y[1], 1.0)
+                else:
+                    assert_array_equal(y[0], [0.0][:num])
+                    assert isnan(y[1])
+
+    def test_object(self):
+        start = array(1, dtype='O')
+        stop = array(2, dtype='O')
+        y = linspace(start, stop, 3)
+        assert_array_equal(y, array([1., 1.5, 2.]))
+
+    def test_round_negative(self):
+        y = linspace(-1, 3, num=8, dtype=int)
+        t = array([-1, -1, 0, 0, 1, 1, 2, 3], dtype=int)
+        assert_array_equal(y, t)
+
+    def test_any_step_zero_and_not_mult_inplace(self):
+        # any_step_zero is True, _mult_inplace is False
+        start = array([0.0, 1.0])
+        stop = array([2.0, 1.0])
+        y = linspace(start, stop, 3)
+        assert_array_equal(y, array([[0.0, 1.0], [1.0, 1.0], [2.0, 1.0]]))
+
+
+class TestAdd_newdoc:
+
+    @pytest.mark.skipif(sys.flags.optimize == 2, reason="Python running -OO")
+    @pytest.mark.xfail(IS_PYPY, reason="PyPy does not modify tp_doc")
+    def test_add_doc(self):
+        # test that np.add_newdoc did attach a docstring successfully:
+        tgt = "Current flat index into the array."
+        assert_equal(np._core.flatiter.index.__doc__[:len(tgt)], tgt)
+        assert_(len(np._core.ufunc.identity.__doc__) > 300)
+        assert_(len(np.lib._index_tricks_impl.mgrid.__doc__) > 300)
+
+    @pytest.mark.skipif(sys.flags.optimize == 2, reason="Python running -OO")
+    def test_errors_are_ignored(self):
+        prev_doc = np._core.flatiter.index.__doc__
+        # nothing changed, but error ignored, this should probably
+        # give a warning (or even error) in the future.
+        add_newdoc("numpy._core", "flatiter", ("index", "bad docstring"))
+        assert prev_doc == np._core.flatiter.index.__doc__
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_getlimits.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_getlimits.py
new file mode 100644
index 0000000..721c6ac
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_getlimits.py
@@ -0,0 +1,205 @@
+""" Test functions for limits module.
+
+"""
+import types
+import warnings
+
+import pytest
+
+import numpy as np
+from numpy import double, half, longdouble, single
+from numpy._core import finfo, iinfo
+from numpy._core.getlimits import _discovered_machar, _float_ma
+from numpy.testing import assert_, assert_equal, assert_raises
+
+##################################################
+
+class TestPythonFloat:
+    def test_singleton(self):
+        ftype = finfo(float)
+        ftype2 = finfo(float)
+        assert_equal(id(ftype), id(ftype2))
+
+class TestHalf:
+    def test_singleton(self):
+        ftype = finfo(half)
+        ftype2 = finfo(half)
+        assert_equal(id(ftype), id(ftype2))
+
+class TestSingle:
+    def test_singleton(self):
+        ftype = finfo(single)
+        ftype2 = finfo(single)
+        assert_equal(id(ftype), id(ftype2))
+
+class TestDouble:
+    def test_singleton(self):
+        ftype = finfo(double)
+        ftype2 = finfo(double)
+        assert_equal(id(ftype), id(ftype2))
+
+class TestLongdouble:
+    def test_singleton(self):
+        ftype = finfo(longdouble)
+        ftype2 = finfo(longdouble)
+        assert_equal(id(ftype), id(ftype2))
+
+def assert_finfo_equal(f1, f2):
+    # assert two finfo instances have the same attributes
+    for attr in ('bits', 'eps', 'epsneg', 'iexp', 'machep',
+                 'max', 'maxexp', 'min', 'minexp', 'negep', 'nexp',
+                 'nmant', 'precision', 'resolution', 'tiny',
+                 'smallest_normal', 'smallest_subnormal'):
+        assert_equal(getattr(f1, attr), getattr(f2, attr),
+                     f'finfo instances {f1} and {f2} differ on {attr}')
+
+def assert_iinfo_equal(i1, i2):
+    # assert two iinfo instances have the same attributes
+    for attr in ('bits', 'min', 'max'):
+        assert_equal(getattr(i1, attr), getattr(i2, attr),
+                     f'iinfo instances {i1} and {i2} differ on {attr}')
+
+class TestFinfo:
+    def test_basic(self):
+        dts = list(zip(['f2', 'f4', 'f8', 'c8', 'c16'],
+                       [np.float16, np.float32, np.float64, np.complex64,
+                        np.complex128]))
+        for dt1, dt2 in dts:
+            assert_finfo_equal(finfo(dt1), finfo(dt2))
+
+        assert_raises(ValueError, finfo, 'i4')
+
+    def test_regression_gh23108(self):
+        # np.float32(1.0) and np.float64(1.0) have the same hash and are
+        # equal under the == operator
+        f1 = np.finfo(np.float32(1.0))
+        f2 = np.finfo(np.float64(1.0))
+        assert f1 != f2
+
+    def test_regression_gh23867(self):
+        class NonHashableWithDtype:
+            __hash__ = None
+            dtype = np.dtype('float32')
+
+        x = NonHashableWithDtype()
+        assert np.finfo(x) == np.finfo(x.dtype)
+
+
+class TestIinfo:
+    def test_basic(self):
+        dts = list(zip(['i1', 'i2', 'i4', 'i8',
+                   'u1', 'u2', 'u4', 'u8'],
+                  [np.int8, np.int16, np.int32, np.int64,
+                   np.uint8, np.uint16, np.uint32, np.uint64]))
+        for dt1, dt2 in dts:
+            assert_iinfo_equal(iinfo(dt1), iinfo(dt2))
+
+        assert_raises(ValueError, iinfo, 'f4')
+
+    def test_unsigned_max(self):
+        types = np._core.sctypes['uint']
+        for T in types:
+            with np.errstate(over="ignore"):
+                max_calculated = T(0) - T(1)
+            assert_equal(iinfo(T).max, max_calculated)
+
+class TestRepr:
+    def test_iinfo_repr(self):
+        expected = "iinfo(min=-32768, max=32767, dtype=int16)"
+        assert_equal(repr(np.iinfo(np.int16)), expected)
+
+    def test_finfo_repr(self):
+        expected = "finfo(resolution=1e-06, min=-3.4028235e+38,"\
+                   " max=3.4028235e+38, dtype=float32)"
+        assert_equal(repr(np.finfo(np.float32)), expected)
+
+
+def test_instances():
+    # Test the finfo and iinfo results on numeric instances agree with
+    # the results on the corresponding types
+
+    for c in [int, np.int16, np.int32, np.int64]:
+        class_iinfo = iinfo(c)
+        instance_iinfo = iinfo(c(12))
+
+        assert_iinfo_equal(class_iinfo, instance_iinfo)
+
+    for c in [float, np.float16, np.float32, np.float64]:
+        class_finfo = finfo(c)
+        instance_finfo = finfo(c(1.2))
+        assert_finfo_equal(class_finfo, instance_finfo)
+
+    with pytest.raises(ValueError):
+        iinfo(10.)
+
+    with pytest.raises(ValueError):
+        iinfo('hi')
+
+    with pytest.raises(ValueError):
+        finfo(np.int64(1))
+
+
+def assert_ma_equal(discovered, ma_like):
+    # Check MachAr-like objects same as calculated MachAr instances
+    for key, value in discovered.__dict__.items():
+        assert_equal(value, getattr(ma_like, key))
+        if hasattr(value, 'shape'):
+            assert_equal(value.shape, getattr(ma_like, key).shape)
+            assert_equal(value.dtype, getattr(ma_like, key).dtype)
+
+
+def test_known_types():
+    # Test we are correctly compiling parameters for known types
+    for ftype, ma_like in ((np.float16, _float_ma[16]),
+                           (np.float32, _float_ma[32]),
+                           (np.float64, _float_ma[64])):
+        assert_ma_equal(_discovered_machar(ftype), ma_like)
+    # Suppress warning for broken discovery of double double on PPC
+    with np.errstate(all='ignore'):
+        ld_ma = _discovered_machar(np.longdouble)
+    bytes = np.dtype(np.longdouble).itemsize
+    if (ld_ma.it, ld_ma.maxexp) == (63, 16384) and bytes in (12, 16):
+        # 80-bit extended precision
+        assert_ma_equal(ld_ma, _float_ma[80])
+    elif (ld_ma.it, ld_ma.maxexp) == (112, 16384) and bytes == 16:
+        # IEE 754 128-bit
+        assert_ma_equal(ld_ma, _float_ma[128])
+
+
+def test_subnormal_warning():
+    """Test that the subnormal is zero warning is not being raised."""
+    with np.errstate(all='ignore'):
+        ld_ma = _discovered_machar(np.longdouble)
+    bytes = np.dtype(np.longdouble).itemsize
+    with warnings.catch_warnings(record=True) as w:
+        warnings.simplefilter('always')
+        if (ld_ma.it, ld_ma.maxexp) == (63, 16384) and bytes in (12, 16):
+            # 80-bit extended precision
+            ld_ma.smallest_subnormal
+            assert len(w) == 0
+        elif (ld_ma.it, ld_ma.maxexp) == (112, 16384) and bytes == 16:
+            # IEE 754 128-bit
+            ld_ma.smallest_subnormal
+            assert len(w) == 0
+        else:
+            # Double double
+            ld_ma.smallest_subnormal
+            # This test may fail on some platforms
+            assert len(w) == 0
+
+
+def test_plausible_finfo():
+    # Assert that finfo returns reasonable results for all types
+    for ftype in np._core.sctypes['float'] + np._core.sctypes['complex']:
+        info = np.finfo(ftype)
+        assert_(info.nmant > 1)
+        assert_(info.minexp < -1)
+        assert_(info.maxexp > 1)
+
+
+class TestRuntimeSubscriptable:
+    def test_finfo_generic(self):
+        assert isinstance(np.finfo[np.float64], types.GenericAlias)
+
+    def test_iinfo_generic(self):
+        assert isinstance(np.iinfo[np.int_], types.GenericAlias)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_half.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_half.py
new file mode 100644
index 0000000..68f17b2
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_half.py
@@ -0,0 +1,568 @@
+import platform
+
+import pytest
+
+import numpy as np
+from numpy import float16, float32, float64, uint16
+from numpy.testing import IS_WASM, assert_, assert_equal
+
+
+def assert_raises_fpe(strmatch, callable, *args, **kwargs):
+    try:
+        callable(*args, **kwargs)
+    except FloatingPointError as exc:
+        assert_(str(exc).find(strmatch) >= 0,
+                f"Did not raise floating point {strmatch} error")
+    else:
+        assert_(False,
+                f"Did not raise floating point {strmatch} error")
+
+class TestHalf:
+    def setup_method(self):
+        # An array of all possible float16 values
+        self.all_f16 = np.arange(0x10000, dtype=uint16)
+        self.all_f16.dtype = float16
+
+        # NaN value can cause an invalid FP exception if HW is being used
+        with np.errstate(invalid='ignore'):
+            self.all_f32 = np.array(self.all_f16, dtype=float32)
+            self.all_f64 = np.array(self.all_f16, dtype=float64)
+
+        # An array of all non-NaN float16 values, in sorted order
+        self.nonan_f16 = np.concatenate(
+                                (np.arange(0xfc00, 0x7fff, -1, dtype=uint16),
+                                 np.arange(0x0000, 0x7c01, 1, dtype=uint16)))
+        self.nonan_f16.dtype = float16
+        self.nonan_f32 = np.array(self.nonan_f16, dtype=float32)
+        self.nonan_f64 = np.array(self.nonan_f16, dtype=float64)
+
+        # An array of all finite float16 values, in sorted order
+        self.finite_f16 = self.nonan_f16[1:-1]
+        self.finite_f32 = self.nonan_f32[1:-1]
+        self.finite_f64 = self.nonan_f64[1:-1]
+
+    def test_half_conversions(self):
+        """Checks that all 16-bit values survive conversion
+           to/from 32-bit and 64-bit float"""
+        # Because the underlying routines preserve the NaN bits, every
+        # value is preserved when converting to/from other floats.
+
+        # Convert from float32 back to float16
+        with np.errstate(invalid='ignore'):
+            b = np.array(self.all_f32, dtype=float16)
+        # avoid testing NaNs due to differing bit patterns in Q/S NaNs
+        b_nn = b == b
+        assert_equal(self.all_f16[b_nn].view(dtype=uint16),
+                     b[b_nn].view(dtype=uint16))
+
+        # Convert from float64 back to float16
+        with np.errstate(invalid='ignore'):
+            b = np.array(self.all_f64, dtype=float16)
+        b_nn = b == b
+        assert_equal(self.all_f16[b_nn].view(dtype=uint16),
+                     b[b_nn].view(dtype=uint16))
+
+        # Convert float16 to longdouble and back
+        # This doesn't necessarily preserve the extra NaN bits,
+        # so exclude NaNs.
+        a_ld = np.array(self.nonan_f16, dtype=np.longdouble)
+        b = np.array(a_ld, dtype=float16)
+        assert_equal(self.nonan_f16.view(dtype=uint16),
+                     b.view(dtype=uint16))
+
+        # Check the range for which all integers can be represented
+        i_int = np.arange(-2048, 2049)
+        i_f16 = np.array(i_int, dtype=float16)
+        j = np.array(i_f16, dtype=int)
+        assert_equal(i_int, j)
+
+    @pytest.mark.parametrize("string_dt", ["S", "U"])
+    def test_half_conversion_to_string(self, string_dt):
+        # Currently uses S/U32 (which is sufficient for float32)
+        expected_dt = np.dtype(f"{string_dt}32")
+        assert np.promote_types(np.float16, string_dt) == expected_dt
+        assert np.promote_types(string_dt, np.float16) == expected_dt
+
+        arr = np.ones(3, dtype=np.float16).astype(string_dt)
+        assert arr.dtype == expected_dt
+
+    @pytest.mark.parametrize("string_dt", ["S", "U"])
+    def test_half_conversion_from_string(self, string_dt):
+        string = np.array("3.1416", dtype=string_dt)
+        assert string.astype(np.float16) == np.array(3.1416, dtype=np.float16)
+
+    @pytest.mark.parametrize("offset", [None, "up", "down"])
+    @pytest.mark.parametrize("shift", [None, "up", "down"])
+    @pytest.mark.parametrize("float_t", [np.float32, np.float64])
+    def test_half_conversion_rounding(self, float_t, shift, offset):
+        # Assumes that round to even is used during casting.
+        max_pattern = np.float16(np.finfo(np.float16).max).view(np.uint16)
+
+        # Test all (positive) finite numbers, denormals are most interesting
+        # however:
+        f16s_patterns = np.arange(0, max_pattern + 1, dtype=np.uint16)
+        f16s_float = f16s_patterns.view(np.float16).astype(float_t)
+
+        # Shift the values by half a bit up or a down (or do not shift),
+        if shift == "up":
+            f16s_float = 0.5 * (f16s_float[:-1] + f16s_float[1:])[1:]
+        elif shift == "down":
+            f16s_float = 0.5 * (f16s_float[:-1] + f16s_float[1:])[:-1]
+        else:
+            f16s_float = f16s_float[1:-1]
+
+        # Increase the float by a minimal value:
+        if offset == "up":
+            f16s_float = np.nextafter(f16s_float, float_t(np.inf))
+        elif offset == "down":
+            f16s_float = np.nextafter(f16s_float, float_t(-np.inf))
+
+        # Convert back to float16 and its bit pattern:
+        res_patterns = f16s_float.astype(np.float16).view(np.uint16)
+
+        # The above calculation tries the original values, or the exact
+        # midpoints between the float16 values. It then further offsets them
+        # by as little as possible. If no offset occurs, "round to even"
+        # logic will be necessary, an arbitrarily small offset should cause
+        # normal up/down rounding always.
+
+        # Calculate the expected pattern:
+        cmp_patterns = f16s_patterns[1:-1].copy()
+
+        if shift == "down" and offset != "up":
+            shift_pattern = -1
+        elif shift == "up" and offset != "down":
+            shift_pattern = 1
+        else:
+            # There cannot be a shift, either shift is None, so all rounding
+            # will go back to original, or shift is reduced by offset too much.
+            shift_pattern = 0
+
+        # If rounding occurs, is it normal rounding or round to even?
+        if offset is None:
+            # Round to even occurs, modify only non-even, cast to allow + (-1)
+            cmp_patterns[0::2].view(np.int16)[...] += shift_pattern
+        else:
+            cmp_patterns.view(np.int16)[...] += shift_pattern
+
+        assert_equal(res_patterns, cmp_patterns)
+
+    @pytest.mark.parametrize(["float_t", "uint_t", "bits"],
+                             [(np.float32, np.uint32, 23),
+                              (np.float64, np.uint64, 52)])
+    def test_half_conversion_denormal_round_even(self, float_t, uint_t, bits):
+        # Test specifically that all bits are considered when deciding
+        # whether round to even should occur (i.e. no bits are lost at the
+        # end. Compare also gh-12721. The most bits can get lost for the
+        # smallest denormal:
+        smallest_value = np.uint16(1).view(np.float16).astype(float_t)
+        assert smallest_value == 2**-24
+
+        # Will be rounded to zero based on round to even rule:
+        rounded_to_zero = smallest_value / float_t(2)
+        assert rounded_to_zero.astype(np.float16) == 0
+
+        # The significand will be all 0 for the float_t, test that we do not
+        # lose the lower ones of these:
+        for i in range(bits):
+            # slightly increasing the value should make it round up:
+            larger_pattern = rounded_to_zero.view(uint_t) | uint_t(1 << i)
+            larger_value = larger_pattern.view(float_t)
+            assert larger_value.astype(np.float16) == smallest_value
+
+    def test_nans_infs(self):
+        with np.errstate(all='ignore'):
+            # Check some of the ufuncs
+            assert_equal(np.isnan(self.all_f16), np.isnan(self.all_f32))
+            assert_equal(np.isinf(self.all_f16), np.isinf(self.all_f32))
+            assert_equal(np.isfinite(self.all_f16), np.isfinite(self.all_f32))
+            assert_equal(np.signbit(self.all_f16), np.signbit(self.all_f32))
+            assert_equal(np.spacing(float16(65504)), np.inf)
+
+            # Check comparisons of all values with NaN
+            nan = float16(np.nan)
+
+            assert_(not (self.all_f16 == nan).any())
+            assert_(not (nan == self.all_f16).any())
+
+            assert_((self.all_f16 != nan).all())
+            assert_((nan != self.all_f16).all())
+
+            assert_(not (self.all_f16 < nan).any())
+            assert_(not (nan < self.all_f16).any())
+
+            assert_(not (self.all_f16 <= nan).any())
+            assert_(not (nan <= self.all_f16).any())
+
+            assert_(not (self.all_f16 > nan).any())
+            assert_(not (nan > self.all_f16).any())
+
+            assert_(not (self.all_f16 >= nan).any())
+            assert_(not (nan >= self.all_f16).any())
+
+    def test_half_values(self):
+        """Confirms a small number of known half values"""
+        a = np.array([1.0, -1.0,
+                      2.0, -2.0,
+                      0.0999755859375, 0.333251953125,  # 1/10, 1/3
+                      65504, -65504,           # Maximum magnitude
+                      2.0**(-14), -2.0**(-14),  # Minimum normal
+                      2.0**(-24), -2.0**(-24),  # Minimum subnormal
+                      0, -1 / 1e1000,            # Signed zeros
+                      np.inf, -np.inf])
+        b = np.array([0x3c00, 0xbc00,
+                      0x4000, 0xc000,
+                      0x2e66, 0x3555,
+                      0x7bff, 0xfbff,
+                      0x0400, 0x8400,
+                      0x0001, 0x8001,
+                      0x0000, 0x8000,
+                      0x7c00, 0xfc00], dtype=uint16)
+        b.dtype = float16
+        assert_equal(a, b)
+
+    def test_half_rounding(self):
+        """Checks that rounding when converting to half is correct"""
+        a = np.array([2.0**-25 + 2.0**-35,  # Rounds to minimum subnormal
+                      2.0**-25,       # Underflows to zero (nearest even mode)
+                      2.0**-26,       # Underflows to zero
+                      1.0 + 2.0**-11 + 2.0**-16,  # rounds to 1.0+2**(-10)
+                      1.0 + 2.0**-11,   # rounds to 1.0 (nearest even mode)
+                      1.0 + 2.0**-12,   # rounds to 1.0
+                      65519,          # rounds to 65504
+                      65520],         # rounds to inf
+                      dtype=float64)
+        rounded = [2.0**-24,
+                   0.0,
+                   0.0,
+                   1.0 + 2.0**(-10),
+                   1.0,
+                   1.0,
+                   65504,
+                   np.inf]
+
+        # Check float64->float16 rounding
+        with np.errstate(over="ignore"):
+            b = np.array(a, dtype=float16)
+        assert_equal(b, rounded)
+
+        # Check float32->float16 rounding
+        a = np.array(a, dtype=float32)
+        with np.errstate(over="ignore"):
+            b = np.array(a, dtype=float16)
+        assert_equal(b, rounded)
+
+    def test_half_correctness(self):
+        """Take every finite float16, and check the casting functions with
+           a manual conversion."""
+
+        # Create an array of all finite float16s
+        a_bits = self.finite_f16.view(dtype=uint16)
+
+        # Convert to 64-bit float manually
+        a_sgn = (-1.0)**((a_bits & 0x8000) >> 15)
+        a_exp = np.array((a_bits & 0x7c00) >> 10, dtype=np.int32) - 15
+        a_man = (a_bits & 0x03ff) * 2.0**(-10)
+        # Implicit bit of normalized floats
+        a_man[a_exp != -15] += 1
+        # Denormalized exponent is -14
+        a_exp[a_exp == -15] = -14
+
+        a_manual = a_sgn * a_man * 2.0**a_exp
+
+        a32_fail = np.nonzero(self.finite_f32 != a_manual)[0]
+        if len(a32_fail) != 0:
+            bad_index = a32_fail[0]
+            assert_equal(self.finite_f32, a_manual,
+                 "First non-equal is half value 0x%x -> %g != %g" %
+                            (a_bits[bad_index],
+                             self.finite_f32[bad_index],
+                             a_manual[bad_index]))
+
+        a64_fail = np.nonzero(self.finite_f64 != a_manual)[0]
+        if len(a64_fail) != 0:
+            bad_index = a64_fail[0]
+            assert_equal(self.finite_f64, a_manual,
+                 "First non-equal is half value 0x%x -> %g != %g" %
+                            (a_bits[bad_index],
+                             self.finite_f64[bad_index],
+                             a_manual[bad_index]))
+
+    def test_half_ordering(self):
+        """Make sure comparisons are working right"""
+
+        # All non-NaN float16 values in reverse order
+        a = self.nonan_f16[::-1].copy()
+
+        # 32-bit float copy
+        b = np.array(a, dtype=float32)
+
+        # Should sort the same
+        a.sort()
+        b.sort()
+        assert_equal(a, b)
+
+        # Comparisons should work
+        assert_((a[:-1] <= a[1:]).all())
+        assert_(not (a[:-1] > a[1:]).any())
+        assert_((a[1:] >= a[:-1]).all())
+        assert_(not (a[1:] < a[:-1]).any())
+        # All != except for +/-0
+        assert_equal(np.nonzero(a[:-1] < a[1:])[0].size, a.size - 2)
+        assert_equal(np.nonzero(a[1:] > a[:-1])[0].size, a.size - 2)
+
+    def test_half_funcs(self):
+        """Test the various ArrFuncs"""
+
+        # fill
+        assert_equal(np.arange(10, dtype=float16),
+                     np.arange(10, dtype=float32))
+
+        # fillwithscalar
+        a = np.zeros((5,), dtype=float16)
+        a.fill(1)
+        assert_equal(a, np.ones((5,), dtype=float16))
+
+        # nonzero and copyswap
+        a = np.array([0, 0, -1, -1 / 1e20, 0, 2.0**-24, 7.629e-6], dtype=float16)
+        assert_equal(a.nonzero()[0],
+                     [2, 5, 6])
+        a = a.byteswap()
+        a = a.view(a.dtype.newbyteorder())
+        assert_equal(a.nonzero()[0],
+                     [2, 5, 6])
+
+        # dot
+        a = np.arange(0, 10, 0.5, dtype=float16)
+        b = np.ones((20,), dtype=float16)
+        assert_equal(np.dot(a, b),
+                     95)
+
+        # argmax
+        a = np.array([0, -np.inf, -2, 0.5, 12.55, 7.3, 2.1, 12.4], dtype=float16)
+        assert_equal(a.argmax(),
+                     4)
+        a = np.array([0, -np.inf, -2, np.inf, 12.55, np.nan, 2.1, 12.4], dtype=float16)
+        assert_equal(a.argmax(),
+                     5)
+
+        # getitem
+        a = np.arange(10, dtype=float16)
+        for i in range(10):
+            assert_equal(a.item(i), i)
+
+    def test_spacing_nextafter(self):
+        """Test np.spacing and np.nextafter"""
+        # All non-negative finite #'s
+        a = np.arange(0x7c00, dtype=uint16)
+        hinf = np.array((np.inf,), dtype=float16)
+        hnan = np.array((np.nan,), dtype=float16)
+        a_f16 = a.view(dtype=float16)
+
+        assert_equal(np.spacing(a_f16[:-1]), a_f16[1:] - a_f16[:-1])
+
+        assert_equal(np.nextafter(a_f16[:-1], hinf), a_f16[1:])
+        assert_equal(np.nextafter(a_f16[0], -hinf), -a_f16[1])
+        assert_equal(np.nextafter(a_f16[1:], -hinf), a_f16[:-1])
+
+        assert_equal(np.nextafter(hinf, a_f16), a_f16[-1])
+        assert_equal(np.nextafter(-hinf, a_f16), -a_f16[-1])
+
+        assert_equal(np.nextafter(hinf, hinf), hinf)
+        assert_equal(np.nextafter(hinf, -hinf), a_f16[-1])
+        assert_equal(np.nextafter(-hinf, hinf), -a_f16[-1])
+        assert_equal(np.nextafter(-hinf, -hinf), -hinf)
+
+        assert_equal(np.nextafter(a_f16, hnan), hnan[0])
+        assert_equal(np.nextafter(hnan, a_f16), hnan[0])
+
+        assert_equal(np.nextafter(hnan, hnan), hnan)
+        assert_equal(np.nextafter(hinf, hnan), hnan)
+        assert_equal(np.nextafter(hnan, hinf), hnan)
+
+        # switch to negatives
+        a |= 0x8000
+
+        assert_equal(np.spacing(a_f16[0]), np.spacing(a_f16[1]))
+        assert_equal(np.spacing(a_f16[1:]), a_f16[:-1] - a_f16[1:])
+
+        assert_equal(np.nextafter(a_f16[0], hinf), -a_f16[1])
+        assert_equal(np.nextafter(a_f16[1:], hinf), a_f16[:-1])
+        assert_equal(np.nextafter(a_f16[:-1], -hinf), a_f16[1:])
+
+        assert_equal(np.nextafter(hinf, a_f16), -a_f16[-1])
+        assert_equal(np.nextafter(-hinf, a_f16), a_f16[-1])
+
+        assert_equal(np.nextafter(a_f16, hnan), hnan[0])
+        assert_equal(np.nextafter(hnan, a_f16), hnan[0])
+
+    def test_half_ufuncs(self):
+        """Test the various ufuncs"""
+
+        a = np.array([0, 1, 2, 4, 2], dtype=float16)
+        b = np.array([-2, 5, 1, 4, 3], dtype=float16)
+        c = np.array([0, -1, -np.inf, np.nan, 6], dtype=float16)
+
+        assert_equal(np.add(a, b), [-2, 6, 3, 8, 5])
+        assert_equal(np.subtract(a, b), [2, -4, 1, 0, -1])
+        assert_equal(np.multiply(a, b), [0, 5, 2, 16, 6])
+        assert_equal(np.divide(a, b), [0, 0.199951171875, 2, 1, 0.66650390625])
+
+        assert_equal(np.equal(a, b), [False, False, False, True, False])
+        assert_equal(np.not_equal(a, b), [True, True, True, False, True])
+        assert_equal(np.less(a, b), [False, True, False, False, True])
+        assert_equal(np.less_equal(a, b), [False, True, False, True, True])
+        assert_equal(np.greater(a, b), [True, False, True, False, False])
+        assert_equal(np.greater_equal(a, b), [True, False, True, True, False])
+        assert_equal(np.logical_and(a, b), [False, True, True, True, True])
+        assert_equal(np.logical_or(a, b), [True, True, True, True, True])
+        assert_equal(np.logical_xor(a, b), [True, False, False, False, False])
+        assert_equal(np.logical_not(a), [True, False, False, False, False])
+
+        assert_equal(np.isnan(c), [False, False, False, True, False])
+        assert_equal(np.isinf(c), [False, False, True, False, False])
+        assert_equal(np.isfinite(c), [True, True, False, False, True])
+        assert_equal(np.signbit(b), [True, False, False, False, False])
+
+        assert_equal(np.copysign(b, a), [2, 5, 1, 4, 3])
+
+        assert_equal(np.maximum(a, b), [0, 5, 2, 4, 3])
+
+        x = np.maximum(b, c)
+        assert_(np.isnan(x[3]))
+        x[3] = 0
+        assert_equal(x, [0, 5, 1, 0, 6])
+
+        assert_equal(np.minimum(a, b), [-2, 1, 1, 4, 2])
+
+        x = np.minimum(b, c)
+        assert_(np.isnan(x[3]))
+        x[3] = 0
+        assert_equal(x, [-2, -1, -np.inf, 0, 3])
+
+        assert_equal(np.fmax(a, b), [0, 5, 2, 4, 3])
+        assert_equal(np.fmax(b, c), [0, 5, 1, 4, 6])
+        assert_equal(np.fmin(a, b), [-2, 1, 1, 4, 2])
+        assert_equal(np.fmin(b, c), [-2, -1, -np.inf, 4, 3])
+
+        assert_equal(np.floor_divide(a, b), [0, 0, 2, 1, 0])
+        assert_equal(np.remainder(a, b), [0, 1, 0, 0, 2])
+        assert_equal(np.divmod(a, b), ([0, 0, 2, 1, 0], [0, 1, 0, 0, 2]))
+        assert_equal(np.square(b), [4, 25, 1, 16, 9])
+        assert_equal(np.reciprocal(b), [-0.5, 0.199951171875, 1, 0.25, 0.333251953125])
+        assert_equal(np.ones_like(b), [1, 1, 1, 1, 1])
+        assert_equal(np.conjugate(b), b)
+        assert_equal(np.absolute(b), [2, 5, 1, 4, 3])
+        assert_equal(np.negative(b), [2, -5, -1, -4, -3])
+        assert_equal(np.positive(b), b)
+        assert_equal(np.sign(b), [-1, 1, 1, 1, 1])
+        assert_equal(np.modf(b), ([0, 0, 0, 0, 0], b))
+        assert_equal(np.frexp(b), ([-0.5, 0.625, 0.5, 0.5, 0.75], [2, 3, 1, 3, 2]))
+        assert_equal(np.ldexp(b, [0, 1, 2, 4, 2]), [-2, 10, 4, 64, 12])
+
+    def test_half_coercion(self):
+        """Test that half gets coerced properly with the other types"""
+        a16 = np.array((1,), dtype=float16)
+        a32 = np.array((1,), dtype=float32)
+        b16 = float16(1)
+        b32 = float32(1)
+
+        assert np.power(a16, 2).dtype == float16
+        assert np.power(a16, 2.0).dtype == float16
+        assert np.power(a16, b16).dtype == float16
+        assert np.power(a16, b32).dtype == float32
+        assert np.power(a16, a16).dtype == float16
+        assert np.power(a16, a32).dtype == float32
+
+        assert np.power(b16, 2).dtype == float16
+        assert np.power(b16, 2.0).dtype == float16
+        assert np.power(b16, b16).dtype, float16
+        assert np.power(b16, b32).dtype, float32
+        assert np.power(b16, a16).dtype, float16
+        assert np.power(b16, a32).dtype, float32
+
+        assert np.power(a32, a16).dtype == float32
+        assert np.power(a32, b16).dtype == float32
+        assert np.power(b32, a16).dtype == float32
+        assert np.power(b32, b16).dtype == float32
+
+    @pytest.mark.skipif(platform.machine() == "armv5tel",
+                        reason="See gh-413.")
+    @pytest.mark.skipif(IS_WASM,
+                        reason="fp exceptions don't work in wasm.")
+    def test_half_fpe(self):
+        with np.errstate(all='raise'):
+            sx16 = np.array((1e-4,), dtype=float16)
+            bx16 = np.array((1e4,), dtype=float16)
+            sy16 = float16(1e-4)
+            by16 = float16(1e4)
+
+            # Underflow errors
+            assert_raises_fpe('underflow', lambda a, b: a * b, sx16, sx16)
+            assert_raises_fpe('underflow', lambda a, b: a * b, sx16, sy16)
+            assert_raises_fpe('underflow', lambda a, b: a * b, sy16, sx16)
+            assert_raises_fpe('underflow', lambda a, b: a * b, sy16, sy16)
+            assert_raises_fpe('underflow', lambda a, b: a / b, sx16, bx16)
+            assert_raises_fpe('underflow', lambda a, b: a / b, sx16, by16)
+            assert_raises_fpe('underflow', lambda a, b: a / b, sy16, bx16)
+            assert_raises_fpe('underflow', lambda a, b: a / b, sy16, by16)
+            assert_raises_fpe('underflow', lambda a, b: a / b,
+                                             float16(2.**-14), float16(2**11))
+            assert_raises_fpe('underflow', lambda a, b: a / b,
+                                             float16(-2.**-14), float16(2**11))
+            assert_raises_fpe('underflow', lambda a, b: a / b,
+                                             float16(2.**-14 + 2**-24), float16(2))
+            assert_raises_fpe('underflow', lambda a, b: a / b,
+                                             float16(-2.**-14 - 2**-24), float16(2))
+            assert_raises_fpe('underflow', lambda a, b: a / b,
+                                             float16(2.**-14 + 2**-23), float16(4))
+
+            # Overflow errors
+            assert_raises_fpe('overflow', lambda a, b: a * b, bx16, bx16)
+            assert_raises_fpe('overflow', lambda a, b: a * b, bx16, by16)
+            assert_raises_fpe('overflow', lambda a, b: a * b, by16, bx16)
+            assert_raises_fpe('overflow', lambda a, b: a * b, by16, by16)
+            assert_raises_fpe('overflow', lambda a, b: a / b, bx16, sx16)
+            assert_raises_fpe('overflow', lambda a, b: a / b, bx16, sy16)
+            assert_raises_fpe('overflow', lambda a, b: a / b, by16, sx16)
+            assert_raises_fpe('overflow', lambda a, b: a / b, by16, sy16)
+            assert_raises_fpe('overflow', lambda a, b: a + b,
+                                             float16(65504), float16(17))
+            assert_raises_fpe('overflow', lambda a, b: a - b,
+                                             float16(-65504), float16(17))
+            assert_raises_fpe('overflow', np.nextafter, float16(65504), float16(np.inf))
+            assert_raises_fpe('overflow', np.nextafter, float16(-65504), float16(-np.inf))
+            assert_raises_fpe('overflow', np.spacing, float16(65504))
+
+            # Invalid value errors
+            assert_raises_fpe('invalid', np.divide, float16(np.inf), float16(np.inf))
+            assert_raises_fpe('invalid', np.spacing, float16(np.inf))
+            assert_raises_fpe('invalid', np.spacing, float16(np.nan))
+
+            # These should not raise
+            float16(65472) + float16(32)
+            float16(2**-13) / float16(2)
+            float16(2**-14) / float16(2**10)
+            np.spacing(float16(-65504))
+            np.nextafter(float16(65504), float16(-np.inf))
+            np.nextafter(float16(-65504), float16(np.inf))
+            np.nextafter(float16(np.inf), float16(0))
+            np.nextafter(float16(-np.inf), float16(0))
+            np.nextafter(float16(0), float16(np.nan))
+            np.nextafter(float16(np.nan), float16(0))
+            float16(2**-14) / float16(2**10)
+            float16(-2**-14) / float16(2**10)
+            float16(2**-14 + 2**-23) / float16(2)
+            float16(-2**-14 - 2**-23) / float16(2)
+
+    def test_half_array_interface(self):
+        """Test that half is compatible with __array_interface__"""
+        class Dummy:
+            pass
+
+        a = np.ones((1,), dtype=float16)
+        b = Dummy()
+        b.__array_interface__ = a.__array_interface__
+        c = np.array(b)
+        assert_(c.dtype == float16)
+        assert_equal(a, c)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_hashtable.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_hashtable.py
new file mode 100644
index 0000000..74be521
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_hashtable.py
@@ -0,0 +1,35 @@
+import random
+
+import pytest
+from numpy._core._multiarray_tests import identityhash_tester
+
+
+@pytest.mark.parametrize("key_length", [1, 3, 6])
+@pytest.mark.parametrize("length", [1, 16, 2000])
+def test_identity_hashtable(key_length, length):
+    # use a 30 object pool for everything (duplicates will happen)
+    pool = [object() for i in range(20)]
+    keys_vals = []
+    for i in range(length):
+        keys = tuple(random.choices(pool, k=key_length))
+        keys_vals.append((keys, random.choice(pool)))
+
+    dictionary = dict(keys_vals)
+
+    # add a random item at the end:
+    keys_vals.append(random.choice(keys_vals))
+    # the expected one could be different with duplicates:
+    expected = dictionary[keys_vals[-1][0]]
+
+    res = identityhash_tester(key_length, keys_vals, replace=True)
+    assert res is expected
+
+    if length == 1:
+        return
+
+    # add a new item with a key that is already used and a new value, this
+    # should error if replace is False, see gh-26690
+    new_key = (keys_vals[1][0], object())
+    keys_vals[0] = new_key
+    with pytest.raises(RuntimeError):
+        identityhash_tester(key_length, keys_vals)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_indexerrors.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_indexerrors.py
new file mode 100644
index 0000000..02110c2
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_indexerrors.py
@@ -0,0 +1,125 @@
+import numpy as np
+from numpy.testing import (
+    assert_raises,
+    assert_raises_regex,
+)
+
+
+class TestIndexErrors:
+    '''Tests to exercise indexerrors not covered by other tests.'''
+
+    def test_arraytypes_fasttake(self):
+        'take from a 0-length dimension'
+        x = np.empty((2, 3, 0, 4))
+        assert_raises(IndexError, x.take, [0], axis=2)
+        assert_raises(IndexError, x.take, [1], axis=2)
+        assert_raises(IndexError, x.take, [0], axis=2, mode='wrap')
+        assert_raises(IndexError, x.take, [0], axis=2, mode='clip')
+
+    def test_take_from_object(self):
+        # Check exception taking from object array
+        d = np.zeros(5, dtype=object)
+        assert_raises(IndexError, d.take, [6])
+
+        # Check exception taking from 0-d array
+        d = np.zeros((5, 0), dtype=object)
+        assert_raises(IndexError, d.take, [1], axis=1)
+        assert_raises(IndexError, d.take, [0], axis=1)
+        assert_raises(IndexError, d.take, [0])
+        assert_raises(IndexError, d.take, [0], mode='wrap')
+        assert_raises(IndexError, d.take, [0], mode='clip')
+
+    def test_multiindex_exceptions(self):
+        a = np.empty(5, dtype=object)
+        assert_raises(IndexError, a.item, 20)
+        a = np.empty((5, 0), dtype=object)
+        assert_raises(IndexError, a.item, (0, 0))
+
+    def test_put_exceptions(self):
+        a = np.zeros((5, 5))
+        assert_raises(IndexError, a.put, 100, 0)
+        a = np.zeros((5, 5), dtype=object)
+        assert_raises(IndexError, a.put, 100, 0)
+        a = np.zeros((5, 5, 0))
+        assert_raises(IndexError, a.put, 100, 0)
+        a = np.zeros((5, 5, 0), dtype=object)
+        assert_raises(IndexError, a.put, 100, 0)
+
+    def test_iterators_exceptions(self):
+        "cases in iterators.c"
+        def assign(obj, ind, val):
+            obj[ind] = val
+
+        a = np.zeros([1, 2, 3])
+        assert_raises(IndexError, lambda: a[0, 5, None, 2])
+        assert_raises(IndexError, lambda: a[0, 5, 0, 2])
+        assert_raises(IndexError, lambda: assign(a, (0, 5, None, 2), 1))
+        assert_raises(IndexError, lambda: assign(a, (0, 5, 0, 2),  1))
+
+        a = np.zeros([1, 0, 3])
+        assert_raises(IndexError, lambda: a[0, 0, None, 2])
+        assert_raises(IndexError, lambda: assign(a, (0, 0, None, 2), 1))
+
+        a = np.zeros([1, 2, 3])
+        assert_raises(IndexError, lambda: a.flat[10])
+        assert_raises(IndexError, lambda: assign(a.flat, 10, 5))
+        a = np.zeros([1, 0, 3])
+        assert_raises(IndexError, lambda: a.flat[10])
+        assert_raises(IndexError, lambda: assign(a.flat, 10, 5))
+
+        a = np.zeros([1, 2, 3])
+        assert_raises(IndexError, lambda: a.flat[np.array(10)])
+        assert_raises(IndexError, lambda: assign(a.flat, np.array(10), 5))
+        a = np.zeros([1, 0, 3])
+        assert_raises(IndexError, lambda: a.flat[np.array(10)])
+        assert_raises(IndexError, lambda: assign(a.flat, np.array(10), 5))
+
+        a = np.zeros([1, 2, 3])
+        assert_raises(IndexError, lambda: a.flat[np.array([10])])
+        assert_raises(IndexError, lambda: assign(a.flat, np.array([10]), 5))
+        a = np.zeros([1, 0, 3])
+        assert_raises(IndexError, lambda: a.flat[np.array([10])])
+        assert_raises(IndexError, lambda: assign(a.flat, np.array([10]), 5))
+
+    def test_mapping(self):
+        "cases from mapping.c"
+
+        def assign(obj, ind, val):
+            obj[ind] = val
+
+        a = np.zeros((0, 10))
+        assert_raises(IndexError, lambda: a[12])
+
+        a = np.zeros((3, 5))
+        assert_raises(IndexError, lambda: a[(10, 20)])
+        assert_raises(IndexError, lambda: assign(a, (10, 20), 1))
+        a = np.zeros((3, 0))
+        assert_raises(IndexError, lambda: a[(1, 0)])
+        assert_raises(IndexError, lambda: assign(a, (1, 0), 1))
+
+        a = np.zeros((10,))
+        assert_raises(IndexError, lambda: assign(a, 10, 1))
+        a = np.zeros((0,))
+        assert_raises(IndexError, lambda: assign(a, 10, 1))
+
+        a = np.zeros((3, 5))
+        assert_raises(IndexError, lambda: a[(1, [1, 20])])
+        assert_raises(IndexError, lambda: assign(a, (1, [1, 20]), 1))
+        a = np.zeros((3, 0))
+        assert_raises(IndexError, lambda: a[(1, [0, 1])])
+        assert_raises(IndexError, lambda: assign(a, (1, [0, 1]), 1))
+
+    def test_mapping_error_message(self):
+        a = np.zeros((3, 5))
+        index = (1, 2, 3, 4, 5)
+        assert_raises_regex(
+                IndexError,
+                "too many indices for array: "
+                "array is 2-dimensional, but 5 were indexed",
+                lambda: a[index])
+
+    def test_methods(self):
+        "cases from methods.c"
+
+        a = np.zeros((3, 3))
+        assert_raises(IndexError, lambda: a.item(100))
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_indexing.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_indexing.py
new file mode 100644
index 0000000..e722d0c
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_indexing.py
@@ -0,0 +1,1455 @@
+import functools
+import operator
+import sys
+import warnings
+from itertools import product
+
+import pytest
+from numpy._core._multiarray_tests import array_indexing
+
+import numpy as np
+from numpy.exceptions import ComplexWarning, VisibleDeprecationWarning
+from numpy.testing import (
+    HAS_REFCOUNT,
+    assert_,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+    assert_warns,
+)
+
+
+class TestIndexing:
+    def test_index_no_floats(self):
+        a = np.array([[[5]]])
+
+        assert_raises(IndexError, lambda: a[0.0])
+        assert_raises(IndexError, lambda: a[0, 0.0])
+        assert_raises(IndexError, lambda: a[0.0, 0])
+        assert_raises(IndexError, lambda: a[0.0, :])
+        assert_raises(IndexError, lambda: a[:, 0.0])
+        assert_raises(IndexError, lambda: a[:, 0.0, :])
+        assert_raises(IndexError, lambda: a[0.0, :, :])
+        assert_raises(IndexError, lambda: a[0, 0, 0.0])
+        assert_raises(IndexError, lambda: a[0.0, 0, 0])
+        assert_raises(IndexError, lambda: a[0, 0.0, 0])
+        assert_raises(IndexError, lambda: a[-1.4])
+        assert_raises(IndexError, lambda: a[0, -1.4])
+        assert_raises(IndexError, lambda: a[-1.4, 0])
+        assert_raises(IndexError, lambda: a[-1.4, :])
+        assert_raises(IndexError, lambda: a[:, -1.4])
+        assert_raises(IndexError, lambda: a[:, -1.4, :])
+        assert_raises(IndexError, lambda: a[-1.4, :, :])
+        assert_raises(IndexError, lambda: a[0, 0, -1.4])
+        assert_raises(IndexError, lambda: a[-1.4, 0, 0])
+        assert_raises(IndexError, lambda: a[0, -1.4, 0])
+        assert_raises(IndexError, lambda: a[0.0:, 0.0])
+        assert_raises(IndexError, lambda: a[0.0:, 0.0, :])
+
+    def test_slicing_no_floats(self):
+        a = np.array([[5]])
+
+        # start as float.
+        assert_raises(TypeError, lambda: a[0.0:])
+        assert_raises(TypeError, lambda: a[0:, 0.0:2])
+        assert_raises(TypeError, lambda: a[0.0::2, :0])
+        assert_raises(TypeError, lambda: a[0.0:1:2, :])
+        assert_raises(TypeError, lambda: a[:, 0.0:])
+        # stop as float.
+        assert_raises(TypeError, lambda: a[:0.0])
+        assert_raises(TypeError, lambda: a[:0, 1:2.0])
+        assert_raises(TypeError, lambda: a[:0.0:2, :0])
+        assert_raises(TypeError, lambda: a[:0.0, :])
+        assert_raises(TypeError, lambda: a[:, 0:4.0:2])
+        # step as float.
+        assert_raises(TypeError, lambda: a[::1.0])
+        assert_raises(TypeError, lambda: a[0:, :2:2.0])
+        assert_raises(TypeError, lambda: a[1::4.0, :0])
+        assert_raises(TypeError, lambda: a[::5.0, :])
+        assert_raises(TypeError, lambda: a[:, 0:4:2.0])
+        # mixed.
+        assert_raises(TypeError, lambda: a[1.0:2:2.0])
+        assert_raises(TypeError, lambda: a[1.0::2.0])
+        assert_raises(TypeError, lambda: a[0:, :2.0:2.0])
+        assert_raises(TypeError, lambda: a[1.0:1:4.0, :0])
+        assert_raises(TypeError, lambda: a[1.0:5.0:5.0, :])
+        assert_raises(TypeError, lambda: a[:, 0.4:4.0:2.0])
+        # should still get the DeprecationWarning if step = 0.
+        assert_raises(TypeError, lambda: a[::0.0])
+
+    def test_index_no_array_to_index(self):
+        # No non-scalar arrays.
+        a = np.array([[[1]]])
+
+        assert_raises(TypeError, lambda: a[a:a:a])
+
+    def test_none_index(self):
+        # `None` index adds newaxis
+        a = np.array([1, 2, 3])
+        assert_equal(a[None], a[np.newaxis])
+        assert_equal(a[None].ndim, a.ndim + 1)
+
+    def test_empty_tuple_index(self):
+        # Empty tuple index creates a view
+        a = np.array([1, 2, 3])
+        assert_equal(a[()], a)
+        assert_(a[()].base is a)
+        a = np.array(0)
+        assert_(isinstance(a[()], np.int_))
+
+    def test_void_scalar_empty_tuple(self):
+        s = np.zeros((), dtype='V4')
+        assert_equal(s[()].dtype, s.dtype)
+        assert_equal(s[()], s)
+        assert_equal(type(s[...]), np.ndarray)
+
+    def test_same_kind_index_casting(self):
+        # Indexes should be cast with same-kind and not safe, even if that
+        # is somewhat unsafe. So test various different code paths.
+        index = np.arange(5)
+        u_index = index.astype(np.uintp)
+        arr = np.arange(10)
+
+        assert_array_equal(arr[index], arr[u_index])
+        arr[u_index] = np.arange(5)
+        assert_array_equal(arr, np.arange(10))
+
+        arr = np.arange(10).reshape(5, 2)
+        assert_array_equal(arr[index], arr[u_index])
+
+        arr[u_index] = np.arange(5)[:, None]
+        assert_array_equal(arr, np.arange(5)[:, None].repeat(2, axis=1))
+
+        arr = np.arange(25).reshape(5, 5)
+        assert_array_equal(arr[u_index, u_index], arr[index, index])
+
+    def test_empty_fancy_index(self):
+        # Empty list index creates an empty array
+        # with the same dtype (but with weird shape)
+        a = np.array([1, 2, 3])
+        assert_equal(a[[]], [])
+        assert_equal(a[[]].dtype, a.dtype)
+
+        b = np.array([], dtype=np.intp)
+        assert_equal(a[[]], [])
+        assert_equal(a[[]].dtype, a.dtype)
+
+        b = np.array([])
+        assert_raises(IndexError, a.__getitem__, b)
+
+    def test_gh_26542(self):
+        a = np.array([0, 1, 2])
+        idx = np.array([2, 1, 0])
+        a[idx] = a
+        expected = np.array([2, 1, 0])
+        assert_equal(a, expected)
+
+    def test_gh_26542_2d(self):
+        a = np.array([[0, 1, 2]])
+        idx_row = np.zeros(3, dtype=int)
+        idx_col = np.array([2, 1, 0])
+        a[idx_row, idx_col] = a
+        expected = np.array([[2, 1, 0]])
+        assert_equal(a, expected)
+
+    def test_gh_26542_index_overlap(self):
+        arr = np.arange(100)
+        expected_vals = np.copy(arr[:-10])
+        arr[10:] = arr[:-10]
+        actual_vals = arr[10:]
+        assert_equal(actual_vals, expected_vals)
+
+    def test_gh_26844(self):
+        expected = [0, 1, 3, 3, 3]
+        a = np.arange(5)
+        a[2:][a[:-2]] = 3
+        assert_equal(a, expected)
+
+    def test_gh_26844_segfault(self):
+        # check for absence of segfault for:
+        # https://github.com/numpy/numpy/pull/26958/files#r1854589178
+        a = np.arange(5)
+        expected = [0, 1, 3, 3, 3]
+        a[2:][None, a[:-2]] = 3
+        assert_equal(a, expected)
+
+    def test_ellipsis_index(self):
+        a = np.array([[1, 2, 3],
+                      [4, 5, 6],
+                      [7, 8, 9]])
+        assert_(a[...] is not a)
+        assert_equal(a[...], a)
+        # `a[...]` was `a` in numpy <1.9.
+        assert_(a[...].base is a)
+
+        # Slicing with ellipsis can skip an
+        # arbitrary number of dimensions
+        assert_equal(a[0, ...], a[0])
+        assert_equal(a[0, ...], a[0, :])
+        assert_equal(a[..., 0], a[:, 0])
+
+        # Slicing with ellipsis always results
+        # in an array, not a scalar
+        assert_equal(a[0, ..., 1], np.array(2))
+
+        # Assignment with `(Ellipsis,)` on 0-d arrays
+        b = np.array(1)
+        b[(Ellipsis,)] = 2
+        assert_equal(b, 2)
+
+    def test_single_int_index(self):
+        # Single integer index selects one row
+        a = np.array([[1, 2, 3],
+                      [4, 5, 6],
+                      [7, 8, 9]])
+
+        assert_equal(a[0], [1, 2, 3])
+        assert_equal(a[-1], [7, 8, 9])
+
+        # Index out of bounds produces IndexError
+        assert_raises(IndexError, a.__getitem__, 1 << 30)
+        # Index overflow produces IndexError
+        assert_raises(IndexError, a.__getitem__, 1 << 64)
+
+    def test_single_bool_index(self):
+        # Single boolean index
+        a = np.array([[1, 2, 3],
+                      [4, 5, 6],
+                      [7, 8, 9]])
+
+        assert_equal(a[np.array(True)], a[None])
+        assert_equal(a[np.array(False)], a[None][0:0])
+
+    def test_boolean_shape_mismatch(self):
+        arr = np.ones((5, 4, 3))
+
+        index = np.array([True])
+        assert_raises(IndexError, arr.__getitem__, index)
+
+        index = np.array([False] * 6)
+        assert_raises(IndexError, arr.__getitem__, index)
+
+        index = np.zeros((4, 4), dtype=bool)
+        assert_raises(IndexError, arr.__getitem__, index)
+
+        assert_raises(IndexError, arr.__getitem__, (slice(None), index))
+
+    def test_boolean_indexing_onedim(self):
+        # Indexing a 2-dimensional array with
+        # boolean array of length one
+        a = np.array([[0., 0., 0.]])
+        b = np.array([True], dtype=bool)
+        assert_equal(a[b], a)
+        # boolean assignment
+        a[b] = 1.
+        assert_equal(a, [[1., 1., 1.]])
+
+    def test_boolean_assignment_value_mismatch(self):
+        # A boolean assignment should fail when the shape of the values
+        # cannot be broadcast to the subscription. (see also gh-3458)
+        a = np.arange(4)
+
+        def f(a, v):
+            a[a > -1] = v
+
+        assert_raises(ValueError, f, a, [])
+        assert_raises(ValueError, f, a, [1, 2, 3])
+        assert_raises(ValueError, f, a[:1], [1, 2, 3])
+
+    def test_boolean_assignment_needs_api(self):
+        # See also gh-7666
+        # This caused a segfault on Python 2 due to the GIL not being
+        # held when the iterator does not need it, but the transfer function
+        # does
+        arr = np.zeros(1000)
+        indx = np.zeros(1000, dtype=bool)
+        indx[:100] = True
+        arr[indx] = np.ones(100, dtype=object)
+
+        expected = np.zeros(1000)
+        expected[:100] = 1
+        assert_array_equal(arr, expected)
+
+    def test_boolean_indexing_twodim(self):
+        # Indexing a 2-dimensional array with
+        # 2-dimensional boolean array
+        a = np.array([[1, 2, 3],
+                      [4, 5, 6],
+                      [7, 8, 9]])
+        b = np.array([[ True, False, True],
+                      [False, True, False],
+                      [ True, False, True]])
+        assert_equal(a[b], [1, 3, 5, 7, 9])
+        assert_equal(a[b[1]], [[4, 5, 6]])
+        assert_equal(a[b[0]], a[b[2]])
+
+        # boolean assignment
+        a[b] = 0
+        assert_equal(a, [[0, 2, 0],
+                         [4, 0, 6],
+                         [0, 8, 0]])
+
+    def test_boolean_indexing_list(self):
+        # Regression test for #13715. It's a use-after-free bug which the
+        # test won't directly catch, but it will show up in valgrind.
+        a = np.array([1, 2, 3])
+        b = [True, False, True]
+        # Two variants of the test because the first takes a fast path
+        assert_equal(a[b], [1, 3])
+        assert_equal(a[None, b], [[1, 3]])
+
+    def test_reverse_strides_and_subspace_bufferinit(self):
+        # This tests that the strides are not reversed for simple and
+        # subspace fancy indexing.
+        a = np.ones(5)
+        b = np.zeros(5, dtype=np.intp)[::-1]
+        c = np.arange(5)[::-1]
+
+        a[b] = c
+        # If the strides are not reversed, the 0 in the arange comes last.
+        assert_equal(a[0], 0)
+
+        # This also tests that the subspace buffer is initialized:
+        a = np.ones((5, 2))
+        c = np.arange(10).reshape(5, 2)[::-1]
+        a[b, :] = c
+        assert_equal(a[0], [0, 1])
+
+    def test_reversed_strides_result_allocation(self):
+        # Test a bug when calculating the output strides for a result array
+        # when the subspace size was 1 (and test other cases as well)
+        a = np.arange(10)[:, None]
+        i = np.arange(10)[::-1]
+        assert_array_equal(a[i], a[i.copy('C')])
+
+        a = np.arange(20).reshape(-1, 2)
+
+    def test_uncontiguous_subspace_assignment(self):
+        # During development there was a bug activating a skip logic
+        # based on ndim instead of size.
+        a = np.full((3, 4, 2), -1)
+        b = np.full((3, 4, 2), -1)
+
+        a[[0, 1]] = np.arange(2 * 4 * 2).reshape(2, 4, 2).T
+        b[[0, 1]] = np.arange(2 * 4 * 2).reshape(2, 4, 2).T.copy()
+
+        assert_equal(a, b)
+
+    def test_too_many_fancy_indices_special_case(self):
+        # Just documents behaviour, this is a small limitation.
+        a = np.ones((1,) * 64)  # 64 is NPY_MAXDIMS
+        assert_raises(IndexError, a.__getitem__, (np.array([0]),) * 64)
+
+    def test_scalar_array_bool(self):
+        # NumPy bools can be used as boolean index (python ones as of yet not)
+        a = np.array(1)
+        assert_equal(a[np.bool(True)], a[np.array(True)])
+        assert_equal(a[np.bool(False)], a[np.array(False)])
+
+        # After deprecating bools as integers:
+        #a = np.array([0,1,2])
+        #assert_equal(a[True, :], a[None, :])
+        #assert_equal(a[:, True], a[:, None])
+        #
+        #assert_(not np.may_share_memory(a, a[True, :]))
+
+    def test_everything_returns_views(self):
+        # Before `...` would return a itself.
+        a = np.arange(5)
+
+        assert_(a is not a[()])
+        assert_(a is not a[...])
+        assert_(a is not a[:])
+
+    def test_broaderrors_indexing(self):
+        a = np.zeros((5, 5))
+        assert_raises(IndexError, a.__getitem__, ([0, 1], [0, 1, 2]))
+        assert_raises(IndexError, a.__setitem__, ([0, 1], [0, 1, 2]), 0)
+
+    def test_trivial_fancy_out_of_bounds(self):
+        a = np.zeros(5)
+        ind = np.ones(20, dtype=np.intp)
+        ind[-1] = 10
+        assert_raises(IndexError, a.__getitem__, ind)
+        assert_raises(IndexError, a.__setitem__, ind, 0)
+        ind = np.ones(20, dtype=np.intp)
+        ind[0] = 11
+        assert_raises(IndexError, a.__getitem__, ind)
+        assert_raises(IndexError, a.__setitem__, ind, 0)
+
+    def test_trivial_fancy_not_possible(self):
+        # Test that the fast path for trivial assignment is not incorrectly
+        # used when the index is not contiguous or 1D, see also gh-11467.
+        a = np.arange(6)
+        idx = np.arange(6, dtype=np.intp).reshape(2, 1, 3)[:, :, 0]
+        assert_array_equal(a[idx], idx)
+
+        # this case must not go into the fast path, note that idx is
+        # a non-contiguous none 1D array here.
+        a[idx] = -1
+        res = np.arange(6)
+        res[0] = -1
+        res[3] = -1
+        assert_array_equal(a, res)
+
+    def test_nonbaseclass_values(self):
+        class SubClass(np.ndarray):
+            def __array_finalize__(self, old):
+                # Have array finalize do funny things
+                self.fill(99)
+
+        a = np.zeros((5, 5))
+        s = a.copy().view(type=SubClass)
+        s.fill(1)
+
+        a[[0, 1, 2, 3, 4], :] = s
+        assert_((a == 1).all())
+
+        # Subspace is last, so transposing might want to finalize
+        a[:, [0, 1, 2, 3, 4]] = s
+        assert_((a == 1).all())
+
+        a.fill(0)
+        a[...] = s
+        assert_((a == 1).all())
+
+    def test_array_like_values(self):
+        # Similar to the above test, but use a memoryview instead
+        a = np.zeros((5, 5))
+        s = np.arange(25, dtype=np.float64).reshape(5, 5)
+
+        a[[0, 1, 2, 3, 4], :] = memoryview(s)
+        assert_array_equal(a, s)
+
+        a[:, [0, 1, 2, 3, 4]] = memoryview(s)
+        assert_array_equal(a, s)
+
+        a[...] = memoryview(s)
+        assert_array_equal(a, s)
+
+    @pytest.mark.parametrize("writeable", [True, False])
+    def test_subclass_writeable(self, writeable):
+        d = np.rec.array([('NGC1001', 11), ('NGC1002', 1.), ('NGC1003', 1.)],
+                         dtype=[('target', 'S20'), ('V_mag', '>f4')])
+        d.flags.writeable = writeable
+        # Advanced indexing results are always writeable:
+        ind = np.array([False, True, True], dtype=bool)
+        assert d[ind].flags.writeable
+        ind = np.array([0, 1])
+        assert d[ind].flags.writeable
+        # Views should be writeable if the original array is:
+        assert d[...].flags.writeable == writeable
+        assert d[0].flags.writeable == writeable
+
+    def test_memory_order(self):
+        # This is not necessary to preserve. Memory layouts for
+        # more complex indices are not as simple.
+        a = np.arange(10)
+        b = np.arange(10).reshape(5, 2).T
+        assert_(a[b].flags.f_contiguous)
+
+        # Takes a different implementation branch:
+        a = a.reshape(-1, 1)
+        assert_(a[b, 0].flags.f_contiguous)
+
+    def test_scalar_return_type(self):
+        # Full scalar indices should return scalars and object
+        # arrays should not call PyArray_Return on their items
+        class Zero:
+            # The most basic valid indexing
+            def __index__(self):
+                return 0
+
+        z = Zero()
+
+        class ArrayLike:
+            # Simple array, should behave like the array
+            def __array__(self, dtype=None, copy=None):
+                return np.array(0)
+
+        a = np.zeros(())
+        assert_(isinstance(a[()], np.float64))
+        a = np.zeros(1)
+        assert_(isinstance(a[z], np.float64))
+        a = np.zeros((1, 1))
+        assert_(isinstance(a[z, np.array(0)], np.float64))
+        assert_(isinstance(a[z, ArrayLike()], np.float64))
+
+        # And object arrays do not call it too often:
+        b = np.array(0)
+        a = np.array(0, dtype=object)
+        a[()] = b
+        assert_(isinstance(a[()], np.ndarray))
+        a = np.array([b, None])
+        assert_(isinstance(a[z], np.ndarray))
+        a = np.array([[b, None]])
+        assert_(isinstance(a[z, np.array(0)], np.ndarray))
+        assert_(isinstance(a[z, ArrayLike()], np.ndarray))
+
+    def test_small_regressions(self):
+        # Reference count of intp for index checks
+        a = np.array([0])
+        if HAS_REFCOUNT:
+            refcount = sys.getrefcount(np.dtype(np.intp))
+        # item setting always checks indices in separate function:
+        a[np.array([0], dtype=np.intp)] = 1
+        a[np.array([0], dtype=np.uint8)] = 1
+        assert_raises(IndexError, a.__setitem__,
+                      np.array([1], dtype=np.intp), 1)
+        assert_raises(IndexError, a.__setitem__,
+                      np.array([1], dtype=np.uint8), 1)
+
+        if HAS_REFCOUNT:
+            assert_equal(sys.getrefcount(np.dtype(np.intp)), refcount)
+
+    def test_unaligned(self):
+        v = (np.zeros(64, dtype=np.int8) + ord('a'))[1:-7]
+        d = v.view(np.dtype("S8"))
+        # unaligned source
+        x = (np.zeros(16, dtype=np.int8) + ord('a'))[1:-7]
+        x = x.view(np.dtype("S8"))
+        x[...] = np.array("b" * 8, dtype="S")
+        b = np.arange(d.size)
+        # trivial
+        assert_equal(d[b], d)
+        d[b] = x
+        # nontrivial
+        # unaligned index array
+        b = np.zeros(d.size + 1).view(np.int8)[1:-(np.intp(0).itemsize - 1)]
+        b = b.view(np.intp)[:d.size]
+        b[...] = np.arange(d.size)
+        assert_equal(d[b.astype(np.int16)], d)
+        d[b.astype(np.int16)] = x
+        # boolean
+        d[b % 2 == 0]
+        d[b % 2 == 0] = x[::2]
+
+    def test_tuple_subclass(self):
+        arr = np.ones((5, 5))
+
+        # A tuple subclass should also be an nd-index
+        class TupleSubclass(tuple):
+            pass
+        index = ([1], [1])
+        index = TupleSubclass(index)
+        assert_(arr[index].shape == (1,))
+        # Unlike the non nd-index:
+        assert_(arr[index,].shape != (1,))
+
+    def test_broken_sequence_not_nd_index(self):
+        # See gh-5063:
+        # If we have an object which claims to be a sequence, but fails
+        # on item getting, this should not be converted to an nd-index (tuple)
+        # If this object happens to be a valid index otherwise, it should work
+        # This object here is very dubious and probably bad though:
+        class SequenceLike:
+            def __index__(self):
+                return 0
+
+            def __len__(self):
+                return 1
+
+            def __getitem__(self, item):
+                raise IndexError('Not possible')
+
+        arr = np.arange(10)
+        assert_array_equal(arr[SequenceLike()], arr[SequenceLike(),])
+
+        # also test that field indexing does not segfault
+        # for a similar reason, by indexing a structured array
+        arr = np.zeros((1,), dtype=[('f1', 'i8'), ('f2', 'i8')])
+        assert_array_equal(arr[SequenceLike()], arr[SequenceLike(),])
+
+    def test_indexing_array_weird_strides(self):
+        # See also gh-6221
+        # the shapes used here come from the issue and create the correct
+        # size for the iterator buffering size.
+        x = np.ones(10)
+        x2 = np.ones((10, 2))
+        ind = np.arange(10)[:, None, None, None]
+        ind = np.broadcast_to(ind, (10, 55, 4, 4))
+
+        # single advanced index case
+        assert_array_equal(x[ind], x[ind.copy()])
+        # higher dimensional advanced index
+        zind = np.zeros(4, dtype=np.intp)
+        assert_array_equal(x2[ind, zind], x2[ind.copy(), zind])
+
+    def test_indexing_array_negative_strides(self):
+        # From gh-8264,
+        # core dumps if negative strides are used in iteration
+        arro = np.zeros((4, 4))
+        arr = arro[::-1, ::-1]
+
+        slices = (slice(None), [0, 1, 2, 3])
+        arr[slices] = 10
+        assert_array_equal(arr, 10.)
+
+    def test_character_assignment(self):
+        # This is an example a function going through CopyObject which
+        # used to have an untested special path for scalars
+        # (the character special dtype case, should be deprecated probably)
+        arr = np.zeros((1, 5), dtype="c")
+        arr[0] = np.str_("asdfg")  # must assign as a sequence
+        assert_array_equal(arr[0], np.array("asdfg", dtype="c"))
+        assert arr[0, 1] == b"s"  # make sure not all were set to "a" for both
+
+    @pytest.mark.parametrize("index",
+            [True, False, np.array([0])])
+    @pytest.mark.parametrize("num", [64, 80])
+    @pytest.mark.parametrize("original_ndim", [1, 64])
+    def test_too_many_advanced_indices(self, index, num, original_ndim):
+        # These are limitations based on the number of arguments we can process.
+        # For `num=32` (and all boolean cases), the result is actually define;
+        # but the use of NpyIter (NPY_MAXARGS) limits it for technical reasons.
+        arr = np.ones((1,) * original_ndim)
+        with pytest.raises(IndexError):
+            arr[(index,) * num]
+        with pytest.raises(IndexError):
+            arr[(index,) * num] = 1.
+
+    def test_nontuple_ndindex(self):
+        a = np.arange(25).reshape((5, 5))
+        assert_equal(a[[0, 1]], np.array([a[0], a[1]]))
+        assert_equal(a[[0, 1], [0, 1]], np.array([0, 6]))
+        assert_raises(IndexError, a.__getitem__, [slice(None)])
+
+    def test_flat_index_on_flatiter(self):
+        a = np.arange(9).reshape((3, 3))
+        b = np.array([0, 5, 6])
+        assert_equal(a.flat[b.flat], np.array([0, 5, 6]))
+
+    def test_empty_string_flat_index_on_flatiter(self):
+        a = np.arange(9).reshape((3, 3))
+        b = np.array([], dtype="S")
+        assert_equal(a.flat[b.flat], np.array([]))
+
+    def test_nonempty_string_flat_index_on_flatiter(self):
+        a = np.arange(9).reshape((3, 3))
+        b = np.array(["a"], dtype="S")
+        with pytest.raises(IndexError, match="unsupported iterator index"):
+            a.flat[b.flat]
+
+
+class TestFieldIndexing:
+    def test_scalar_return_type(self):
+        # Field access on an array should return an array, even if it
+        # is 0-d.
+        a = np.zeros((), [('a', 'f8')])
+        assert_(isinstance(a['a'], np.ndarray))
+        assert_(isinstance(a[['a']], np.ndarray))
+
+
+class TestBroadcastedAssignments:
+    def assign(self, a, ind, val):
+        a[ind] = val
+        return a
+
+    def test_prepending_ones(self):
+        a = np.zeros((3, 2))
+
+        a[...] = np.ones((1, 3, 2))
+        # Fancy with subspace with and without transpose
+        a[[0, 1, 2], :] = np.ones((1, 3, 2))
+        a[:, [0, 1]] = np.ones((1, 3, 2))
+        # Fancy without subspace (with broadcasting)
+        a[[[0], [1], [2]], [0, 1]] = np.ones((1, 3, 2))
+
+    def test_prepend_not_one(self):
+        assign = self.assign
+        s_ = np.s_
+        a = np.zeros(5)
+
+        # Too large and not only ones.
+        assert_raises(ValueError, assign, a, s_[...], np.ones((2, 1)))
+        assert_raises(ValueError, assign, a, s_[[1, 2, 3],], np.ones((2, 1)))
+        assert_raises(ValueError, assign, a, s_[[[1], [2]],], np.ones((2, 2, 1)))
+
+    def test_simple_broadcasting_errors(self):
+        assign = self.assign
+        s_ = np.s_
+        a = np.zeros((5, 1))
+
+        assert_raises(ValueError, assign, a, s_[...], np.zeros((5, 2)))
+        assert_raises(ValueError, assign, a, s_[...], np.zeros((5, 0)))
+        assert_raises(ValueError, assign, a, s_[:, [0]], np.zeros((5, 2)))
+        assert_raises(ValueError, assign, a, s_[:, [0]], np.zeros((5, 0)))
+        assert_raises(ValueError, assign, a, s_[[0], :], np.zeros((2, 1)))
+
+    @pytest.mark.parametrize("index", [
+            (..., [1, 2], slice(None)),
+            ([0, 1], ..., 0),
+            (..., [1, 2], [1, 2])])
+    def test_broadcast_error_reports_correct_shape(self, index):
+        values = np.zeros((100, 100))  # will never broadcast below
+
+        arr = np.zeros((3, 4, 5, 6, 7))
+        # We currently report without any spaces (could be changed)
+        shape_str = str(arr[index].shape).replace(" ", "")
+
+        with pytest.raises(ValueError) as e:
+            arr[index] = values
+
+        assert str(e.value).endswith(shape_str)
+
+    def test_index_is_larger(self):
+        # Simple case of fancy index broadcasting of the index.
+        a = np.zeros((5, 5))
+        a[[[0], [1], [2]], [0, 1, 2]] = [2, 3, 4]
+
+        assert_((a[:3, :3] == [2, 3, 4]).all())
+
+    def test_broadcast_subspace(self):
+        a = np.zeros((100, 100))
+        v = np.arange(100)[:, None]
+        b = np.arange(100)[::-1]
+        a[b] = v
+        assert_((a[::-1] == v).all())
+
+
+class TestSubclasses:
+    def test_basic(self):
+        # Test that indexing in various ways produces SubClass instances,
+        # and that the base is set up correctly: the original subclass
+        # instance for views, and a new ndarray for advanced/boolean indexing
+        # where a copy was made (latter a regression test for gh-11983).
+        class SubClass(np.ndarray):
+            pass
+
+        a = np.arange(5)
+        s = a.view(SubClass)
+        s_slice = s[:3]
+        assert_(type(s_slice) is SubClass)
+        assert_(s_slice.base is s)
+        assert_array_equal(s_slice, a[:3])
+
+        s_fancy = s[[0, 1, 2]]
+        assert_(type(s_fancy) is SubClass)
+        assert_(s_fancy.base is not s)
+        assert_(type(s_fancy.base) is np.ndarray)
+        assert_array_equal(s_fancy, a[[0, 1, 2]])
+        assert_array_equal(s_fancy.base, a[[0, 1, 2]])
+
+        s_bool = s[s > 0]
+        assert_(type(s_bool) is SubClass)
+        assert_(s_bool.base is not s)
+        assert_(type(s_bool.base) is np.ndarray)
+        assert_array_equal(s_bool, a[a > 0])
+        assert_array_equal(s_bool.base, a[a > 0])
+
+    def test_fancy_on_read_only(self):
+        # Test that fancy indexing on read-only SubClass does not make a
+        # read-only copy (gh-14132)
+        class SubClass(np.ndarray):
+            pass
+
+        a = np.arange(5)
+        s = a.view(SubClass)
+        s.flags.writeable = False
+        s_fancy = s[[0, 1, 2]]
+        assert_(s_fancy.flags.writeable)
+
+    def test_finalize_gets_full_info(self):
+        # Array finalize should be called on the filled array.
+        class SubClass(np.ndarray):
+            def __array_finalize__(self, old):
+                self.finalize_status = np.array(self)
+                self.old = old
+
+        s = np.arange(10).view(SubClass)
+        new_s = s[:3]
+        assert_array_equal(new_s.finalize_status, new_s)
+        assert_array_equal(new_s.old, s)
+
+        new_s = s[[0, 1, 2, 3]]
+        assert_array_equal(new_s.finalize_status, new_s)
+        assert_array_equal(new_s.old, s)
+
+        new_s = s[s > 0]
+        assert_array_equal(new_s.finalize_status, new_s)
+        assert_array_equal(new_s.old, s)
+
+
+class TestFancyIndexingCast:
+    def test_boolean_index_cast_assign(self):
+        # Setup the boolean index and float arrays.
+        shape = (8, 63)
+        bool_index = np.zeros(shape).astype(bool)
+        bool_index[0, 1] = True
+        zero_array = np.zeros(shape)
+
+        # Assigning float is fine.
+        zero_array[bool_index] = np.array([1])
+        assert_equal(zero_array[0, 1], 1)
+
+        # Fancy indexing works, although we get a cast warning.
+        assert_warns(ComplexWarning,
+                     zero_array.__setitem__, ([0], [1]), np.array([2 + 1j]))
+        assert_equal(zero_array[0, 1], 2)  # No complex part
+
+        # Cast complex to float, throwing away the imaginary portion.
+        assert_warns(ComplexWarning,
+                     zero_array.__setitem__, bool_index, np.array([1j]))
+        assert_equal(zero_array[0, 1], 0)
+
+class TestFancyIndexingEquivalence:
+    def test_object_assign(self):
+        # Check that the field and object special case using copyto is active.
+        # The right hand side cannot be converted to an array here.
+        a = np.arange(5, dtype=object)
+        b = a.copy()
+        a[:3] = [1, (1, 2), 3]
+        b[[0, 1, 2]] = [1, (1, 2), 3]
+        assert_array_equal(a, b)
+
+        # test same for subspace fancy indexing
+        b = np.arange(5, dtype=object)[None, :]
+        b[[0], :3] = [[1, (1, 2), 3]]
+        assert_array_equal(a, b[0])
+
+        # Check that swapping of axes works.
+        # There was a bug that made the later assignment throw a ValueError
+        # do to an incorrectly transposed temporary right hand side (gh-5714)
+        b = b.T
+        b[:3, [0]] = [[1], [(1, 2)], [3]]
+        assert_array_equal(a, b[:, 0])
+
+        # Another test for the memory order of the subspace
+        arr = np.ones((3, 4, 5), dtype=object)
+        # Equivalent slicing assignment for comparison
+        cmp_arr = arr.copy()
+        cmp_arr[:1, ...] = [[[1], [2], [3], [4]]]
+        arr[[0], ...] = [[[1], [2], [3], [4]]]
+        assert_array_equal(arr, cmp_arr)
+        arr = arr.copy('F')
+        arr[[0], ...] = [[[1], [2], [3], [4]]]
+        assert_array_equal(arr, cmp_arr)
+
+    def test_cast_equivalence(self):
+        # Yes, normal slicing uses unsafe casting.
+        a = np.arange(5)
+        b = a.copy()
+
+        a[:3] = np.array(['2', '-3', '-1'])
+        b[[0, 2, 1]] = np.array(['2', '-1', '-3'])
+        assert_array_equal(a, b)
+
+        # test the same for subspace fancy indexing
+        b = np.arange(5)[None, :]
+        b[[0], :3] = np.array([['2', '-3', '-1']])
+        assert_array_equal(a, b[0])
+
+
+class TestMultiIndexingAutomated:
+    """
+    These tests use code to mimic the C-Code indexing for selection.
+
+    NOTE:
+
+        * This still lacks tests for complex item setting.
+        * If you change behavior of indexing, you might want to modify
+          these tests to try more combinations.
+        * Behavior was written to match numpy version 1.8. (though a
+          first version matched 1.7.)
+        * Only tuple indices are supported by the mimicking code.
+          (and tested as of writing this)
+        * Error types should match most of the time as long as there
+          is only one error. For multiple errors, what gets raised
+          will usually not be the same one. They are *not* tested.
+
+    Update 2016-11-30: It is probably not worth maintaining this test
+    indefinitely and it can be dropped if maintenance becomes a burden.
+
+    """
+
+    def setup_method(self):
+        self.a = np.arange(np.prod([3, 1, 5, 6])).reshape(3, 1, 5, 6)
+        self.b = np.empty((3, 0, 5, 6))
+        self.complex_indices = ['skip', Ellipsis,
+            0,
+            # Boolean indices, up to 3-d for some special cases of eating up
+            # dimensions, also need to test all False
+            np.array([True, False, False]),
+            np.array([[True, False], [False, True]]),
+            np.array([[[False, False], [False, False]]]),
+            # Some slices:
+            slice(-5, 5, 2),
+            slice(1, 1, 100),
+            slice(4, -1, -2),
+            slice(None, None, -3),
+            # Some Fancy indexes:
+            np.empty((0, 1, 1), dtype=np.intp),  # empty and can be broadcast
+            np.array([0, 1, -2]),
+            np.array([[2], [0], [1]]),
+            np.array([[0, -1], [0, 1]], dtype=np.dtype('intp').newbyteorder()),
+            np.array([2, -1], dtype=np.int8),
+            np.zeros([1] * 31, dtype=int),  # trigger too large array.
+            np.array([0., 1.])]  # invalid datatype
+        # Some simpler indices that still cover a bit more
+        self.simple_indices = [Ellipsis, None, -1, [1], np.array([True]),
+                               'skip']
+        # Very simple ones to fill the rest:
+        self.fill_indices = [slice(None, None), 0]
+
+    def _get_multi_index(self, arr, indices):
+        """Mimic multi dimensional indexing.
+
+        Parameters
+        ----------
+        arr : ndarray
+            Array to be indexed.
+        indices : tuple of index objects
+
+        Returns
+        -------
+        out : ndarray
+            An array equivalent to the indexing operation (but always a copy).
+            `arr[indices]` should be identical.
+        no_copy : bool
+            Whether the indexing operation requires a copy. If this is `True`,
+            `np.may_share_memory(arr, arr[indices])` should be `True` (with
+            some exceptions for scalars and possibly 0-d arrays).
+
+        Notes
+        -----
+        While the function may mostly match the errors of normal indexing this
+        is generally not the case.
+        """
+        in_indices = list(indices)
+        indices = []
+        # if False, this is a fancy or boolean index
+        no_copy = True
+        # number of fancy/scalar indexes that are not consecutive
+        num_fancy = 0
+        # number of dimensions indexed by a "fancy" index
+        fancy_dim = 0
+        # NOTE: This is a funny twist (and probably OK to change).
+        # The boolean array has illegal indexes, but this is
+        # allowed if the broadcast fancy-indices are 0-sized.
+        # This variable is to catch that case.
+        error_unless_broadcast_to_empty = False
+
+        # We need to handle Ellipsis and make arrays from indices, also
+        # check if this is fancy indexing (set no_copy).
+        ndim = 0
+        ellipsis_pos = None  # define here mostly to replace all but first.
+        for i, indx in enumerate(in_indices):
+            if indx is None:
+                continue
+            if isinstance(indx, np.ndarray) and indx.dtype == bool:
+                no_copy = False
+                if indx.ndim == 0:
+                    raise IndexError
+                # boolean indices can have higher dimensions
+                ndim += indx.ndim
+                fancy_dim += indx.ndim
+                continue
+            if indx is Ellipsis:
+                if ellipsis_pos is None:
+                    ellipsis_pos = i
+                    continue  # do not increment ndim counter
+                raise IndexError
+            if isinstance(indx, slice):
+                ndim += 1
+                continue
+            if not isinstance(indx, np.ndarray):
+                # This could be open for changes in numpy.
+                # numpy should maybe raise an error if casting to intp
+                # is not safe. It rejects np.array([1., 2.]) but not
+                # [1., 2.] as index (same for ie. np.take).
+                # (Note the importance of empty lists if changing this here)
+                try:
+                    indx = np.array(indx, dtype=np.intp)
+                except ValueError:
+                    raise IndexError
+                in_indices[i] = indx
+            elif indx.dtype.kind not in 'bi':
+                raise IndexError('arrays used as indices must be of '
+                                 'integer (or boolean) type')
+            if indx.ndim != 0:
+                no_copy = False
+            ndim += 1
+            fancy_dim += 1
+
+        if arr.ndim - ndim < 0:
+            # we can't take more dimensions then we have, not even for 0-d
+            # arrays.  since a[()] makes sense, but not a[(),]. We will
+            # raise an error later on, unless a broadcasting error occurs
+            # first.
+            raise IndexError
+
+        if ndim == 0 and None not in in_indices:
+            # Well we have no indexes or one Ellipsis. This is legal.
+            return arr.copy(), no_copy
+
+        if ellipsis_pos is not None:
+            in_indices[ellipsis_pos:ellipsis_pos + 1] = ([slice(None, None)] *
+                                                       (arr.ndim - ndim))
+
+        for ax, indx in enumerate(in_indices):
+            if isinstance(indx, slice):
+                # convert to an index array
+                indx = np.arange(*indx.indices(arr.shape[ax]))
+                indices.append(['s', indx])
+                continue
+            elif indx is None:
+                # this is like taking a slice with one element from a new axis:
+                indices.append(['n', np.array([0], dtype=np.intp)])
+                arr = arr.reshape(arr.shape[:ax] + (1,) + arr.shape[ax:])
+                continue
+            if isinstance(indx, np.ndarray) and indx.dtype == bool:
+                if indx.shape != arr.shape[ax:ax + indx.ndim]:
+                    raise IndexError
+
+                try:
+                    flat_indx = np.ravel_multi_index(np.nonzero(indx),
+                                    arr.shape[ax:ax + indx.ndim], mode='raise')
+                except Exception:
+                    error_unless_broadcast_to_empty = True
+                    # fill with 0s instead, and raise error later
+                    flat_indx = np.array([0] * indx.sum(), dtype=np.intp)
+                # concatenate axis into a single one:
+                if indx.ndim != 0:
+                    arr = arr.reshape(arr.shape[:ax]
+                                  + (np.prod(arr.shape[ax:ax + indx.ndim]),)
+                                  + arr.shape[ax + indx.ndim:])
+                    indx = flat_indx
+                else:
+                    # This could be changed, a 0-d boolean index can
+                    # make sense (even outside the 0-d indexed array case)
+                    # Note that originally this is could be interpreted as
+                    # integer in the full integer special case.
+                    raise IndexError
+            # If the index is a singleton, the bounds check is done
+            # before the broadcasting. This used to be different in <1.9
+            elif indx.ndim == 0 and not (
+                -arr.shape[ax] <= indx < arr.shape[ax]
+            ):
+                raise IndexError
+            if indx.ndim == 0:
+                # The index is a scalar. This used to be two fold, but if
+                # fancy indexing was active, the check was done later,
+                # possibly after broadcasting it away (1.7. or earlier).
+                # Now it is always done.
+                if indx >= arr.shape[ax] or indx < - arr.shape[ax]:
+                    raise IndexError
+            if (len(indices) > 0 and
+                    indices[-1][0] == 'f' and
+                    ax != ellipsis_pos):
+                # NOTE: There could still have been a 0-sized Ellipsis
+                # between them. Checked that with ellipsis_pos.
+                indices[-1].append(indx)
+            else:
+                # We have a fancy index that is not after an existing one.
+                # NOTE: A 0-d array triggers this as well, while one may
+                # expect it to not trigger it, since a scalar would not be
+                # considered fancy indexing.
+                num_fancy += 1
+                indices.append(['f', indx])
+
+        if num_fancy > 1 and not no_copy:
+            # We have to flush the fancy indexes left
+            new_indices = indices[:]
+            axes = list(range(arr.ndim))
+            fancy_axes = []
+            new_indices.insert(0, ['f'])
+            ni = 0
+            ai = 0
+            for indx in indices:
+                ni += 1
+                if indx[0] == 'f':
+                    new_indices[0].extend(indx[1:])
+                    del new_indices[ni]
+                    ni -= 1
+                    for ax in range(ai, ai + len(indx[1:])):
+                        fancy_axes.append(ax)
+                        axes.remove(ax)
+                ai += len(indx) - 1  # axis we are at
+            indices = new_indices
+            # and now we need to transpose arr:
+            arr = arr.transpose(*(fancy_axes + axes))
+
+        # We only have one 'f' index now and arr is transposed accordingly.
+        # Now handle newaxis by reshaping...
+        ax = 0
+        for indx in indices:
+            if indx[0] == 'f':
+                if len(indx) == 1:
+                    continue
+                # First of all, reshape arr to combine fancy axes into one:
+                orig_shape = arr.shape
+                orig_slice = orig_shape[ax:ax + len(indx[1:])]
+                arr = arr.reshape(arr.shape[:ax]
+                                    + (np.prod(orig_slice).astype(int),)
+                                    + arr.shape[ax + len(indx[1:]):])
+
+                # Check if broadcasting works
+                res = np.broadcast(*indx[1:])
+                # unfortunately the indices might be out of bounds. So check
+                # that first, and use mode='wrap' then. However only if
+                # there are any indices...
+                if res.size != 0:
+                    if error_unless_broadcast_to_empty:
+                        raise IndexError
+                    for _indx, _size in zip(indx[1:], orig_slice):
+                        if _indx.size == 0:
+                            continue
+                        if np.any(_indx >= _size) or np.any(_indx < -_size):
+                            raise IndexError
+                if len(indx[1:]) == len(orig_slice):
+                    if np.prod(orig_slice) == 0:
+                        # Work around for a crash or IndexError with 'wrap'
+                        # in some 0-sized cases.
+                        try:
+                            mi = np.ravel_multi_index(indx[1:], orig_slice,
+                                                      mode='raise')
+                        except Exception:
+                            # This happens with 0-sized orig_slice (sometimes?)
+                            # here it is a ValueError, but indexing gives a:
+                            raise IndexError('invalid index into 0-sized')
+                    else:
+                        mi = np.ravel_multi_index(indx[1:], orig_slice,
+                                                  mode='wrap')
+                else:
+                    # Maybe never happens...
+                    raise ValueError
+                arr = arr.take(mi.ravel(), axis=ax)
+                try:
+                    arr = arr.reshape(arr.shape[:ax]
+                                        + mi.shape
+                                        + arr.shape[ax + 1:])
+                except ValueError:
+                    # too many dimensions, probably
+                    raise IndexError
+                ax += mi.ndim
+                continue
+
+            # If we are here, we have a 1D array for take:
+            arr = arr.take(indx[1], axis=ax)
+            ax += 1
+
+        return arr, no_copy
+
+    def _check_multi_index(self, arr, index):
+        """Check a multi index item getting and simple setting.
+
+        Parameters
+        ----------
+        arr : ndarray
+            Array to be indexed, must be a reshaped arange.
+        index : tuple of indexing objects
+            Index being tested.
+        """
+        # Test item getting
+        try:
+            mimic_get, no_copy = self._get_multi_index(arr, index)
+        except Exception as e:
+            if HAS_REFCOUNT:
+                prev_refcount = sys.getrefcount(arr)
+            assert_raises(type(e), arr.__getitem__, index)
+            assert_raises(type(e), arr.__setitem__, index, 0)
+            if HAS_REFCOUNT:
+                assert_equal(prev_refcount, sys.getrefcount(arr))
+            return
+
+        self._compare_index_result(arr, index, mimic_get, no_copy)
+
+    def _check_single_index(self, arr, index):
+        """Check a single index item getting and simple setting.
+
+        Parameters
+        ----------
+        arr : ndarray
+            Array to be indexed, must be an arange.
+        index : indexing object
+            Index being tested. Must be a single index and not a tuple
+            of indexing objects (see also `_check_multi_index`).
+        """
+        try:
+            mimic_get, no_copy = self._get_multi_index(arr, (index,))
+        except Exception as e:
+            if HAS_REFCOUNT:
+                prev_refcount = sys.getrefcount(arr)
+            assert_raises(type(e), arr.__getitem__, index)
+            assert_raises(type(e), arr.__setitem__, index, 0)
+            if HAS_REFCOUNT:
+                assert_equal(prev_refcount, sys.getrefcount(arr))
+            return
+
+        self._compare_index_result(arr, index, mimic_get, no_copy)
+
+    def _compare_index_result(self, arr, index, mimic_get, no_copy):
+        """Compare mimicked result to indexing result.
+        """
+        arr = arr.copy()
+        if HAS_REFCOUNT:
+            startcount = sys.getrefcount(arr)
+        indexed_arr = arr[index]
+        assert_array_equal(indexed_arr, mimic_get)
+        # Check if we got a view, unless its a 0-sized or 0-d array.
+        # (then its not a view, and that does not matter)
+        if indexed_arr.size != 0 and indexed_arr.ndim != 0:
+            assert_(np.may_share_memory(indexed_arr, arr) == no_copy)
+            # Check reference count of the original array
+            if HAS_REFCOUNT:
+                if no_copy:
+                    # refcount increases by one:
+                    assert_equal(sys.getrefcount(arr), startcount + 1)
+                else:
+                    assert_equal(sys.getrefcount(arr), startcount)
+
+        # Test non-broadcast setitem:
+        b = arr.copy()
+        b[index] = mimic_get + 1000
+        if b.size == 0:
+            return  # nothing to compare here...
+        if no_copy and indexed_arr.ndim != 0:
+            # change indexed_arr in-place to manipulate original:
+            indexed_arr += 1000
+            assert_array_equal(arr, b)
+            return
+        # Use the fact that the array is originally an arange:
+        arr.flat[indexed_arr.ravel()] += 1000
+        assert_array_equal(arr, b)
+
+    def test_boolean(self):
+        a = np.array(5)
+        assert_equal(a[np.array(True)], 5)
+        a[np.array(True)] = 1
+        assert_equal(a, 1)
+        # NOTE: This is different from normal broadcasting, as
+        # arr[boolean_array] works like in a multi index. Which means
+        # it is aligned to the left. This is probably correct for
+        # consistency with arr[boolean_array,] also no broadcasting
+        # is done at all
+        self._check_multi_index(
+            self.a, (np.zeros_like(self.a, dtype=bool),))
+        self._check_multi_index(
+            self.a, (np.zeros_like(self.a, dtype=bool)[..., 0],))
+        self._check_multi_index(
+            self.a, (np.zeros_like(self.a, dtype=bool)[None, ...],))
+
+    def test_multidim(self):
+        # Automatically test combinations with complex indexes on 2nd (or 1st)
+        # spot and the simple ones in one other spot.
+        with warnings.catch_warnings():
+            # This is so that np.array(True) is not accepted in a full integer
+            # index, when running the file separately.
+            warnings.filterwarnings('error', '', DeprecationWarning)
+            warnings.filterwarnings('error', '', VisibleDeprecationWarning)
+
+            def isskip(idx):
+                return isinstance(idx, str) and idx == "skip"
+
+            for simple_pos in [0, 2, 3]:
+                tocheck = [self.fill_indices, self.complex_indices,
+                           self.fill_indices, self.fill_indices]
+                tocheck[simple_pos] = self.simple_indices
+                for index in product(*tocheck):
+                    index = tuple(i for i in index if not isskip(i))
+                    self._check_multi_index(self.a, index)
+                    self._check_multi_index(self.b, index)
+
+        # Check very simple item getting:
+        self._check_multi_index(self.a, (0, 0, 0, 0))
+        self._check_multi_index(self.b, (0, 0, 0, 0))
+        # Also check (simple cases of) too many indices:
+        assert_raises(IndexError, self.a.__getitem__, (0, 0, 0, 0, 0))
+        assert_raises(IndexError, self.a.__setitem__, (0, 0, 0, 0, 0), 0)
+        assert_raises(IndexError, self.a.__getitem__, (0, 0, [1], 0, 0))
+        assert_raises(IndexError, self.a.__setitem__, (0, 0, [1], 0, 0), 0)
+
+    def test_1d(self):
+        a = np.arange(10)
+        for index in self.complex_indices:
+            self._check_single_index(a, index)
+
+class TestFloatNonIntegerArgument:
+    """
+    These test that ``TypeError`` is raised when you try to use
+    non-integers as arguments to for indexing and slicing e.g. ``a[0.0:5]``
+    and ``a[0.5]``, or other functions like ``array.reshape(1., -1)``.
+
+    """
+    def test_valid_indexing(self):
+        # These should raise no errors.
+        a = np.array([[[5]]])
+
+        a[np.array([0])]
+        a[[0, 0]]
+        a[:, [0, 0]]
+        a[:, 0, :]
+        a[:, :, :]
+
+    def test_valid_slicing(self):
+        # These should raise no errors.
+        a = np.array([[[5]]])
+
+        a[::]
+        a[0:]
+        a[:2]
+        a[0:2]
+        a[::2]
+        a[1::2]
+        a[:2:2]
+        a[1:2:2]
+
+    def test_non_integer_argument_errors(self):
+        a = np.array([[5]])
+
+        assert_raises(TypeError, np.reshape, a, (1., 1., -1))
+        assert_raises(TypeError, np.reshape, a, (np.array(1.), -1))
+        assert_raises(TypeError, np.take, a, [0], 1.)
+        assert_raises(TypeError, np.take, a, [0], np.float64(1.))
+
+    def test_non_integer_sequence_multiplication(self):
+        # NumPy scalar sequence multiply should not work with non-integers
+        def mult(a, b):
+            return a * b
+
+        assert_raises(TypeError, mult, [1], np.float64(3))
+        # following should be OK
+        mult([1], np.int_(3))
+
+    def test_reduce_axis_float_index(self):
+        d = np.zeros((3, 3, 3))
+        assert_raises(TypeError, np.min, d, 0.5)
+        assert_raises(TypeError, np.min, d, (0.5, 1))
+        assert_raises(TypeError, np.min, d, (1, 2.2))
+        assert_raises(TypeError, np.min, d, (.2, 1.2))
+
+
+class TestBooleanIndexing:
+    # Using a boolean as integer argument/indexing is an error.
+    def test_bool_as_int_argument_errors(self):
+        a = np.array([[[1]]])
+
+        assert_raises(TypeError, np.reshape, a, (True, -1))
+        assert_raises(TypeError, np.reshape, a, (np.bool(True), -1))
+        # Note that operator.index(np.array(True)) does not work, a boolean
+        # array is thus also deprecated, but not with the same message:
+        assert_raises(TypeError, operator.index, np.array(True))
+        assert_raises(TypeError, operator.index, np.True_)
+        assert_raises(TypeError, np.take, args=(a, [0], False))
+
+    def test_boolean_indexing_weirdness(self):
+        # Weird boolean indexing things
+        a = np.ones((2, 3, 4))
+        assert a[False, True, ...].shape == (0, 2, 3, 4)
+        assert a[True, [0, 1], True, True, [1], [[2]]].shape == (1, 2)
+        assert_raises(IndexError, lambda: a[False, [0, 1], ...])
+
+    def test_boolean_indexing_fast_path(self):
+        # These used to either give the wrong error, or incorrectly give no
+        # error.
+        a = np.ones((3, 3))
+
+        # This used to incorrectly work (and give an array of shape (0,))
+        idx1 = np.array([[False] * 9])
+        assert_raises_regex(IndexError,
+            "boolean index did not match indexed array along axis 0; "
+            "size of axis is 3 but size of corresponding boolean axis is 1",
+            lambda: a[idx1])
+
+        # This used to incorrectly give a ValueError: operands could not be broadcast together
+        idx2 = np.array([[False] * 8 + [True]])
+        assert_raises_regex(IndexError,
+            "boolean index did not match indexed array along axis 0; "
+            "size of axis is 3 but size of corresponding boolean axis is 1",
+            lambda: a[idx2])
+
+        # This is the same as it used to be. The above two should work like this.
+        idx3 = np.array([[False] * 10])
+        assert_raises_regex(IndexError,
+            "boolean index did not match indexed array along axis 0; "
+            "size of axis is 3 but size of corresponding boolean axis is 1",
+            lambda: a[idx3])
+
+        # This used to give ValueError: non-broadcastable operand
+        a = np.ones((1, 1, 2))
+        idx = np.array([[[True], [False]]])
+        assert_raises_regex(IndexError,
+            "boolean index did not match indexed array along axis 1; "
+            "size of axis is 1 but size of corresponding boolean axis is 2",
+            lambda: a[idx])
+
+
+class TestArrayToIndexDeprecation:
+    """Creating an index from array not 0-D is an error.
+
+    """
+    def test_array_to_index_error(self):
+        # so no exception is expected. The raising is effectively tested above.
+        a = np.array([[[1]]])
+
+        assert_raises(TypeError, operator.index, np.array([1]))
+        assert_raises(TypeError, np.reshape, a, (a, -1))
+        assert_raises(TypeError, np.take, a, [0], a)
+
+
+class TestNonIntegerArrayLike:
+    """Tests that array_likes only valid if can safely cast to integer.
+
+    For instance, lists give IndexError when they cannot be safely cast to
+    an integer.
+
+    """
+    def test_basic(self):
+        a = np.arange(10)
+
+        assert_raises(IndexError, a.__getitem__, [0.5, 1.5])
+        assert_raises(IndexError, a.__getitem__, (['1', '2'],))
+
+        # The following is valid
+        a.__getitem__([])
+
+
+class TestMultipleEllipsisError:
+    """An index can only have a single ellipsis.
+
+    """
+    def test_basic(self):
+        a = np.arange(10)
+        assert_raises(IndexError, lambda: a[..., ...])
+        assert_raises(IndexError, a.__getitem__, ((Ellipsis,) * 2,))
+        assert_raises(IndexError, a.__getitem__, ((Ellipsis,) * 3,))
+
+
+class TestCApiAccess:
+    def test_getitem(self):
+        subscript = functools.partial(array_indexing, 0)
+
+        # 0-d arrays don't work:
+        assert_raises(IndexError, subscript, np.ones(()), 0)
+        # Out of bound values:
+        assert_raises(IndexError, subscript, np.ones(10), 11)
+        assert_raises(IndexError, subscript, np.ones(10), -11)
+        assert_raises(IndexError, subscript, np.ones((10, 10)), 11)
+        assert_raises(IndexError, subscript, np.ones((10, 10)), -11)
+
+        a = np.arange(10)
+        assert_array_equal(a[4], subscript(a, 4))
+        a = a.reshape(5, 2)
+        assert_array_equal(a[-4], subscript(a, -4))
+
+    def test_setitem(self):
+        assign = functools.partial(array_indexing, 1)
+
+        # Deletion is impossible:
+        assert_raises(ValueError, assign, np.ones(10), 0)
+        # 0-d arrays don't work:
+        assert_raises(IndexError, assign, np.ones(()), 0, 0)
+        # Out of bound values:
+        assert_raises(IndexError, assign, np.ones(10), 11, 0)
+        assert_raises(IndexError, assign, np.ones(10), -11, 0)
+        assert_raises(IndexError, assign, np.ones((10, 10)), 11, 0)
+        assert_raises(IndexError, assign, np.ones((10, 10)), -11, 0)
+
+        a = np.arange(10)
+        assign(a, 4, 10)
+        assert_(a[4] == 10)
+
+        a = a.reshape(5, 2)
+        assign(a, 4, 10)
+        assert_array_equal(a[-1], [10, 10])
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_item_selection.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_item_selection.py
new file mode 100644
index 0000000..79fb82d
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_item_selection.py
@@ -0,0 +1,167 @@
+import sys
+
+import pytest
+
+import numpy as np
+from numpy.testing import HAS_REFCOUNT, assert_, assert_array_equal, assert_raises
+
+
+class TestTake:
+    def test_simple(self):
+        a = [[1, 2], [3, 4]]
+        a_str = [[b'1', b'2'], [b'3', b'4']]
+        modes = ['raise', 'wrap', 'clip']
+        indices = [-1, 4]
+        index_arrays = [np.empty(0, dtype=np.intp),
+                        np.empty((), dtype=np.intp),
+                        np.empty((1, 1), dtype=np.intp)]
+        real_indices = {'raise': {-1: 1, 4: IndexError},
+                        'wrap': {-1: 1, 4: 0},
+                        'clip': {-1: 0, 4: 1}}
+        # Currently all types but object, use the same function generation.
+        # So it should not be necessary to test all. However test also a non
+        # refcounted struct on top of object, which has a size that hits the
+        # default (non-specialized) path.
+        types = int, object, np.dtype([('', 'i2', 3)])
+        for t in types:
+            # ta works, even if the array may be odd if buffer interface is used
+            ta = np.array(a if np.issubdtype(t, np.number) else a_str, dtype=t)
+            tresult = list(ta.T.copy())
+            for index_array in index_arrays:
+                if index_array.size != 0:
+                    tresult[0].shape = (2,) + index_array.shape
+                    tresult[1].shape = (2,) + index_array.shape
+                for mode in modes:
+                    for index in indices:
+                        real_index = real_indices[mode][index]
+                        if real_index is IndexError and index_array.size != 0:
+                            index_array.put(0, index)
+                            assert_raises(IndexError, ta.take, index_array,
+                                          mode=mode, axis=1)
+                        elif index_array.size != 0:
+                            index_array.put(0, index)
+                            res = ta.take(index_array, mode=mode, axis=1)
+                            assert_array_equal(res, tresult[real_index])
+                        else:
+                            res = ta.take(index_array, mode=mode, axis=1)
+                            assert_(res.shape == (2,) + index_array.shape)
+
+    def test_refcounting(self):
+        objects = [object() for i in range(10)]
+        if HAS_REFCOUNT:
+            orig_rcs = [sys.getrefcount(o) for o in objects]
+        for mode in ('raise', 'clip', 'wrap'):
+            a = np.array(objects)
+            b = np.array([2, 2, 4, 5, 3, 5])
+            a.take(b, out=a[:6], mode=mode)
+            del a
+            if HAS_REFCOUNT:
+                assert_(all(sys.getrefcount(o) == rc + 1
+                            for o, rc in zip(objects, orig_rcs)))
+            # not contiguous, example:
+            a = np.array(objects * 2)[::2]
+            a.take(b, out=a[:6], mode=mode)
+            del a
+            if HAS_REFCOUNT:
+                assert_(all(sys.getrefcount(o) == rc + 1
+                            for o, rc in zip(objects, orig_rcs)))
+
+    def test_unicode_mode(self):
+        d = np.arange(10)
+        k = b'\xc3\xa4'.decode("UTF8")
+        assert_raises(ValueError, d.take, 5, mode=k)
+
+    def test_empty_partition(self):
+        # In reference to github issue #6530
+        a_original = np.array([0, 2, 4, 6, 8, 10])
+        a = a_original.copy()
+
+        # An empty partition should be a successful no-op
+        a.partition(np.array([], dtype=np.int16))
+
+        assert_array_equal(a, a_original)
+
+    def test_empty_argpartition(self):
+        # In reference to github issue #6530
+        a = np.array([0, 2, 4, 6, 8, 10])
+        a = a.argpartition(np.array([], dtype=np.int16))
+
+        b = np.array([0, 1, 2, 3, 4, 5])
+        assert_array_equal(a, b)
+
+
+class TestPutMask:
+    @pytest.mark.parametrize("dtype", list(np.typecodes["All"]) + ["i,O"])
+    def test_simple(self, dtype):
+        if dtype.lower() == "m":
+            dtype += "8[ns]"
+
+        # putmask is weird and doesn't care about value length (even shorter)
+        vals = np.arange(1001).astype(dtype=dtype)
+
+        mask = np.random.randint(2, size=1000).astype(bool)
+        # Use vals.dtype in case of flexible dtype (i.e. string)
+        arr = np.zeros(1000, dtype=vals.dtype)
+        zeros = arr.copy()
+
+        np.putmask(arr, mask, vals)
+        assert_array_equal(arr[mask], vals[:len(mask)][mask])
+        assert_array_equal(arr[~mask], zeros[~mask])
+
+    @pytest.mark.parametrize("dtype", list(np.typecodes["All"])[1:] + ["i,O"])
+    @pytest.mark.parametrize("mode", ["raise", "wrap", "clip"])
+    def test_empty(self, dtype, mode):
+        arr = np.zeros(1000, dtype=dtype)
+        arr_copy = arr.copy()
+        mask = np.random.randint(2, size=1000).astype(bool)
+
+        # Allowing empty values like this is weird...
+        np.put(arr, mask, [])
+        assert_array_equal(arr, arr_copy)
+
+
+class TestPut:
+    @pytest.mark.parametrize("dtype", list(np.typecodes["All"])[1:] + ["i,O"])
+    @pytest.mark.parametrize("mode", ["raise", "wrap", "clip"])
+    def test_simple(self, dtype, mode):
+        if dtype.lower() == "m":
+            dtype += "8[ns]"
+
+        # put is weird and doesn't care about value length (even shorter)
+        vals = np.arange(1001).astype(dtype=dtype)
+
+        # Use vals.dtype in case of flexible dtype (i.e. string)
+        arr = np.zeros(1000, dtype=vals.dtype)
+        zeros = arr.copy()
+
+        if mode == "clip":
+            # Special because 0 and -1 value are "reserved" for clip test
+            indx = np.random.permutation(len(arr) - 2)[:-500] + 1
+
+            indx[-1] = 0
+            indx[-2] = len(arr) - 1
+            indx_put = indx.copy()
+            indx_put[-1] = -1389
+            indx_put[-2] = 1321
+        else:
+            # Avoid duplicates (for simplicity) and fill half only
+            indx = np.random.permutation(len(arr) - 3)[:-500]
+            indx_put = indx
+            if mode == "wrap":
+                indx_put = indx_put + len(arr)
+
+        np.put(arr, indx_put, vals, mode=mode)
+        assert_array_equal(arr[indx], vals[:len(indx)])
+        untouched = np.ones(len(arr), dtype=bool)
+        untouched[indx] = False
+        assert_array_equal(arr[untouched], zeros[:untouched.sum()])
+
+    @pytest.mark.parametrize("dtype", list(np.typecodes["All"])[1:] + ["i,O"])
+    @pytest.mark.parametrize("mode", ["raise", "wrap", "clip"])
+    def test_empty(self, dtype, mode):
+        arr = np.zeros(1000, dtype=dtype)
+        arr_copy = arr.copy()
+
+        # Allowing empty values like this is weird...
+        np.put(arr, [1, 2, 3], [])
+        assert_array_equal(arr, arr_copy)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_limited_api.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_limited_api.py
new file mode 100644
index 0000000..984210e
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_limited_api.py
@@ -0,0 +1,102 @@
+import os
+import subprocess
+import sys
+import sysconfig
+
+import pytest
+
+from numpy.testing import IS_EDITABLE, IS_PYPY, IS_WASM, NOGIL_BUILD
+
+# This import is copied from random.tests.test_extending
+try:
+    import cython
+    from Cython.Compiler.Version import version as cython_version
+except ImportError:
+    cython = None
+else:
+    from numpy._utils import _pep440
+
+    # Note: keep in sync with the one in pyproject.toml
+    required_version = "3.0.6"
+    if _pep440.parse(cython_version) < _pep440.Version(required_version):
+        # too old or wrong cython, skip the test
+        cython = None
+
+pytestmark = pytest.mark.skipif(cython is None, reason="requires cython")
+
+
+if IS_EDITABLE:
+    pytest.skip(
+        "Editable install doesn't support tests with a compile step",
+        allow_module_level=True
+    )
+
+
+@pytest.fixture(scope='module')
+def install_temp(tmpdir_factory):
+    # Based in part on test_cython from random.tests.test_extending
+    if IS_WASM:
+        pytest.skip("No subprocess")
+
+    srcdir = os.path.join(os.path.dirname(__file__), 'examples', 'limited_api')
+    build_dir = tmpdir_factory.mktemp("limited_api") / "build"
+    os.makedirs(build_dir, exist_ok=True)
+    # Ensure we use the correct Python interpreter even when `meson` is
+    # installed in a different Python environment (see gh-24956)
+    native_file = str(build_dir / 'interpreter-native-file.ini')
+    with open(native_file, 'w') as f:
+        f.write("[binaries]\n")
+        f.write(f"python = '{sys.executable}'\n")
+        f.write(f"python3 = '{sys.executable}'")
+
+    try:
+        subprocess.check_call(["meson", "--version"])
+    except FileNotFoundError:
+        pytest.skip("No usable 'meson' found")
+    if sysconfig.get_platform() == "win-arm64":
+        pytest.skip("Meson unable to find MSVC linker on win-arm64")
+    if sys.platform == "win32":
+        subprocess.check_call(["meson", "setup",
+                               "--werror",
+                               "--buildtype=release",
+                               "--vsenv", "--native-file", native_file,
+                               str(srcdir)],
+                              cwd=build_dir,
+                              )
+    else:
+        subprocess.check_call(["meson", "setup", "--werror",
+                               "--native-file", native_file, str(srcdir)],
+                              cwd=build_dir
+                              )
+    try:
+        subprocess.check_call(
+            ["meson", "compile", "-vv"], cwd=build_dir)
+    except subprocess.CalledProcessError as p:
+        print(f"{p.stdout=}")
+        print(f"{p.stderr=}")
+        raise
+
+    sys.path.append(str(build_dir))
+
+
+@pytest.mark.skipif(IS_WASM, reason="Can't start subprocess")
+@pytest.mark.xfail(
+    sysconfig.get_config_var("Py_DEBUG"),
+    reason=(
+        "Py_LIMITED_API is incompatible with Py_DEBUG, Py_TRACE_REFS, "
+        "and Py_REF_DEBUG"
+    ),
+)
+@pytest.mark.xfail(
+    NOGIL_BUILD,
+    reason="Py_GIL_DISABLED builds do not currently support the limited API",
+)
+@pytest.mark.skipif(IS_PYPY, reason="no support for limited API in PyPy")
+def test_limited_api(install_temp):
+    """Test building a third-party C extension with the limited API
+    and building a cython extension with the limited API
+    """
+
+    import limited_api1  # Earliest (3.6)  # noqa: F401
+    import limited_api2  # cython  # noqa: F401
+    import limited_api_latest  # Latest version (current Python)  # noqa: F401
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_longdouble.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_longdouble.py
new file mode 100644
index 0000000..f7edd97
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_longdouble.py
@@ -0,0 +1,369 @@
+import platform
+import warnings
+
+import pytest
+
+import numpy as np
+from numpy._core.tests._locales import CommaDecimalPointLocale
+from numpy.testing import (
+    IS_MUSL,
+    assert_,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    temppath,
+)
+
+LD_INFO = np.finfo(np.longdouble)
+longdouble_longer_than_double = (LD_INFO.eps < np.finfo(np.double).eps)
+
+
+_o = 1 + LD_INFO.eps
+string_to_longdouble_inaccurate = (_o != np.longdouble(str(_o)))
+del _o
+
+
+def test_scalar_extraction():
+    """Confirm that extracting a value doesn't convert to python float"""
+    o = 1 + LD_INFO.eps
+    a = np.array([o, o, o])
+    assert_equal(a[1], o)
+
+
+# Conversions string -> long double
+
+# 0.1 not exactly representable in base 2 floating point.
+repr_precision = len(repr(np.longdouble(0.1)))
+# +2 from macro block starting around line 842 in scalartypes.c.src.
+
+
+@pytest.mark.skipif(IS_MUSL,
+                    reason="test flaky on musllinux")
+@pytest.mark.skipif(LD_INFO.precision + 2 >= repr_precision,
+                    reason="repr precision not enough to show eps")
+def test_str_roundtrip():
+    # We will only see eps in repr if within printing precision.
+    o = 1 + LD_INFO.eps
+    assert_equal(np.longdouble(str(o)), o, f"str was {str(o)}")
+
+
+@pytest.mark.skipif(string_to_longdouble_inaccurate, reason="Need strtold_l")
+def test_str_roundtrip_bytes():
+    o = 1 + LD_INFO.eps
+    assert_equal(np.longdouble(str(o).encode("ascii")), o)
+
+
+@pytest.mark.skipif(string_to_longdouble_inaccurate, reason="Need strtold_l")
+@pytest.mark.parametrize("strtype", (np.str_, np.bytes_, str, bytes))
+def test_array_and_stringlike_roundtrip(strtype):
+    """
+    Test that string representations of long-double roundtrip both
+    for array casting and scalar coercion, see also gh-15608.
+    """
+    o = 1 + LD_INFO.eps
+
+    if strtype in (np.bytes_, bytes):
+        o_str = strtype(str(o).encode("ascii"))
+    else:
+        o_str = strtype(str(o))
+
+    # Test that `o` is correctly coerced from the string-like
+    assert o == np.longdouble(o_str)
+
+    # Test that arrays also roundtrip correctly:
+    o_strarr = np.asarray([o] * 3, dtype=strtype)
+    assert (o == o_strarr.astype(np.longdouble)).all()
+
+    # And array coercion and casting to string give the same as scalar repr:
+    assert (o_strarr == o_str).all()
+    assert (np.asarray([o] * 3).astype(strtype) == o_str).all()
+
+
+def test_bogus_string():
+    assert_raises(ValueError, np.longdouble, "spam")
+    assert_raises(ValueError, np.longdouble, "1.0 flub")
+
+
+@pytest.mark.skipif(string_to_longdouble_inaccurate, reason="Need strtold_l")
+def test_fromstring():
+    o = 1 + LD_INFO.eps
+    s = (" " + str(o)) * 5
+    a = np.array([o] * 5)
+    assert_equal(np.fromstring(s, sep=" ", dtype=np.longdouble), a,
+                 err_msg=f"reading '{s}'")
+
+
+def test_fromstring_complex():
+    for ctype in ["complex", "cdouble"]:
+        # Check spacing between separator
+        assert_equal(np.fromstring("1, 2 ,  3  ,4", sep=",", dtype=ctype),
+                     np.array([1., 2., 3., 4.]))
+        # Real component not specified
+        assert_equal(np.fromstring("1j, -2j,  3j, 4e1j", sep=",", dtype=ctype),
+                     np.array([1.j, -2.j, 3.j, 40.j]))
+        # Both components specified
+        assert_equal(np.fromstring("1+1j,2-2j, -3+3j,  -4e1+4j", sep=",", dtype=ctype),
+                     np.array([1. + 1.j, 2. - 2.j, - 3. + 3.j, - 40. + 4j]))
+        # Spaces at wrong places
+        with assert_raises(ValueError):
+            np.fromstring("1+2 j,3", dtype=ctype, sep=",")
+        with assert_raises(ValueError):
+            np.fromstring("1+ 2j,3", dtype=ctype, sep=",")
+        with assert_raises(ValueError):
+            np.fromstring("1 +2j,3", dtype=ctype, sep=",")
+        with assert_raises(ValueError):
+            np.fromstring("1+j", dtype=ctype, sep=",")
+        with assert_raises(ValueError):
+            np.fromstring("1+", dtype=ctype, sep=",")
+        with assert_raises(ValueError):
+            np.fromstring("1j+1", dtype=ctype, sep=",")
+
+
+def test_fromstring_bogus():
+    with assert_raises(ValueError):
+        np.fromstring("1. 2. 3. flop 4.", dtype=float, sep=" ")
+
+
+def test_fromstring_empty():
+    with assert_raises(ValueError):
+        np.fromstring("xxxxx", sep="x")
+
+
+def test_fromstring_missing():
+    with assert_raises(ValueError):
+        np.fromstring("1xx3x4x5x6", sep="x")
+
+
+class TestFileBased:
+
+    ldbl = 1 + LD_INFO.eps
+    tgt = np.array([ldbl] * 5)
+    out = ''.join([str(t) + '\n' for t in tgt])
+
+    def test_fromfile_bogus(self):
+        with temppath() as path:
+            with open(path, 'w') as f:
+                f.write("1. 2. 3. flop 4.\n")
+
+            with assert_raises(ValueError):
+                np.fromfile(path, dtype=float, sep=" ")
+
+    def test_fromfile_complex(self):
+        for ctype in ["complex", "cdouble"]:
+            # Check spacing between separator and only real component specified
+            with temppath() as path:
+                with open(path, 'w') as f:
+                    f.write("1, 2 ,  3  ,4\n")
+
+                res = np.fromfile(path, dtype=ctype, sep=",")
+            assert_equal(res, np.array([1., 2., 3., 4.]))
+
+            # Real component not specified
+            with temppath() as path:
+                with open(path, 'w') as f:
+                    f.write("1j, -2j,  3j, 4e1j\n")
+
+                res = np.fromfile(path, dtype=ctype, sep=",")
+            assert_equal(res, np.array([1.j, -2.j, 3.j, 40.j]))
+
+            # Both components specified
+            with temppath() as path:
+                with open(path, 'w') as f:
+                    f.write("1+1j,2-2j, -3+3j,  -4e1+4j\n")
+
+                res = np.fromfile(path, dtype=ctype, sep=",")
+            assert_equal(res, np.array([1. + 1.j, 2. - 2.j, - 3. + 3.j, - 40. + 4j]))
+
+            # Spaces at wrong places
+            with temppath() as path:
+                with open(path, 'w') as f:
+                    f.write("1+2 j,3\n")
+
+                with assert_raises(ValueError):
+                    np.fromfile(path, dtype=ctype, sep=",")
+
+            # Spaces at wrong places
+            with temppath() as path:
+                with open(path, 'w') as f:
+                    f.write("1+ 2j,3\n")
+
+                with assert_raises(ValueError):
+                    np.fromfile(path, dtype=ctype, sep=",")
+
+            # Spaces at wrong places
+            with temppath() as path:
+                with open(path, 'w') as f:
+                    f.write("1 +2j,3\n")
+
+                with assert_raises(ValueError):
+                    np.fromfile(path, dtype=ctype, sep=",")
+
+            # Wrong sep
+            with temppath() as path:
+                with open(path, 'w') as f:
+                    f.write("1+j\n")
+
+                with assert_raises(ValueError):
+                    np.fromfile(path, dtype=ctype, sep=",")
+
+            # Wrong sep
+            with temppath() as path:
+                with open(path, 'w') as f:
+                    f.write("1+\n")
+
+                with assert_raises(ValueError):
+                    np.fromfile(path, dtype=ctype, sep=",")
+
+            # Wrong sep
+            with temppath() as path:
+                with open(path, 'w') as f:
+                    f.write("1j+1\n")
+
+                with assert_raises(ValueError):
+                    np.fromfile(path, dtype=ctype, sep=",")
+
+    @pytest.mark.skipif(string_to_longdouble_inaccurate,
+                        reason="Need strtold_l")
+    def test_fromfile(self):
+        with temppath() as path:
+            with open(path, 'w') as f:
+                f.write(self.out)
+            res = np.fromfile(path, dtype=np.longdouble, sep="\n")
+        assert_equal(res, self.tgt)
+
+    @pytest.mark.skipif(string_to_longdouble_inaccurate,
+                        reason="Need strtold_l")
+    def test_genfromtxt(self):
+        with temppath() as path:
+            with open(path, 'w') as f:
+                f.write(self.out)
+            res = np.genfromtxt(path, dtype=np.longdouble)
+        assert_equal(res, self.tgt)
+
+    @pytest.mark.skipif(string_to_longdouble_inaccurate,
+                        reason="Need strtold_l")
+    def test_loadtxt(self):
+        with temppath() as path:
+            with open(path, 'w') as f:
+                f.write(self.out)
+            res = np.loadtxt(path, dtype=np.longdouble)
+        assert_equal(res, self.tgt)
+
+    @pytest.mark.skipif(string_to_longdouble_inaccurate,
+                        reason="Need strtold_l")
+    def test_tofile_roundtrip(self):
+        with temppath() as path:
+            self.tgt.tofile(path, sep=" ")
+            res = np.fromfile(path, dtype=np.longdouble, sep=" ")
+        assert_equal(res, self.tgt)
+
+
+# Conversions long double -> string
+
+
+def test_str_exact():
+    o = 1 + LD_INFO.eps
+    assert_(str(o) != '1')
+
+
+@pytest.mark.skipif(longdouble_longer_than_double, reason="BUG #2376")
+@pytest.mark.skipif(string_to_longdouble_inaccurate,
+                    reason="Need strtold_l")
+def test_format():
+    assert_(f"{1 + LD_INFO.eps:.40g}" != '1')
+
+
+@pytest.mark.skipif(longdouble_longer_than_double, reason="BUG #2376")
+@pytest.mark.skipif(string_to_longdouble_inaccurate,
+                    reason="Need strtold_l")
+def test_percent():
+    o = 1 + LD_INFO.eps
+    assert_(f"{o:.40g}" != '1')
+
+
+@pytest.mark.skipif(longdouble_longer_than_double,
+                    reason="array repr problem")
+@pytest.mark.skipif(string_to_longdouble_inaccurate,
+                    reason="Need strtold_l")
+def test_array_repr():
+    o = 1 + LD_INFO.eps
+    a = np.array([o])
+    b = np.array([1], dtype=np.longdouble)
+    if not np.all(a != b):
+        raise ValueError("precision loss creating arrays")
+    assert_(repr(a) != repr(b))
+
+#
+# Locale tests: scalar types formatting should be independent of the locale
+#
+
+class TestCommaDecimalPointLocale(CommaDecimalPointLocale):
+
+    def test_str_roundtrip_foreign(self):
+        o = 1.5
+        assert_equal(o, np.longdouble(str(o)))
+
+    def test_fromstring_foreign_repr(self):
+        f = 1.234
+        a = np.fromstring(repr(f), dtype=float, sep=" ")
+        assert_equal(a[0], f)
+
+    def test_fromstring_foreign(self):
+        s = "1.234"
+        a = np.fromstring(s, dtype=np.longdouble, sep=" ")
+        assert_equal(a[0], np.longdouble(s))
+
+    def test_fromstring_foreign_sep(self):
+        a = np.array([1, 2, 3, 4])
+        b = np.fromstring("1,2,3,4,", dtype=np.longdouble, sep=",")
+        assert_array_equal(a, b)
+
+    def test_fromstring_foreign_value(self):
+        with assert_raises(ValueError):
+            np.fromstring("1,234", dtype=np.longdouble, sep=" ")
+
+
+@pytest.mark.parametrize("int_val", [
+    # cases discussed in gh-10723
+    # and gh-9968
+    2 ** 1024, 0])
+def test_longdouble_from_int(int_val):
+    # for issue gh-9968
+    str_val = str(int_val)
+    # we'll expect a RuntimeWarning on platforms
+    # with np.longdouble equivalent to np.double
+    # for large integer input
+    with warnings.catch_warnings(record=True) as w:
+        warnings.filterwarnings('always', '', RuntimeWarning)
+        # can be inf==inf on some platforms
+        assert np.longdouble(int_val) == np.longdouble(str_val)
+        # we can't directly compare the int and
+        # max longdouble value on all platforms
+        if np.allclose(np.finfo(np.longdouble).max,
+                       np.finfo(np.double).max) and w:
+            assert w[0].category is RuntimeWarning
+
+@pytest.mark.parametrize("bool_val", [
+    True, False])
+def test_longdouble_from_bool(bool_val):
+    assert np.longdouble(bool_val) == np.longdouble(int(bool_val))
+
+
+@pytest.mark.skipif(
+    not (IS_MUSL and platform.machine() == "x86_64"),
+    reason="only need to run on musllinux_x86_64"
+)
+def test_musllinux_x86_64_signature():
+    # this test may fail if you're emulating musllinux_x86_64 on a different
+    # architecture, but should pass natively.
+    known_sigs = [b'\xcd\xcc\xcc\xcc\xcc\xcc\xcc\xcc\xfb\xbf']
+    sig = (np.longdouble(-1.0) / np.longdouble(10.0))
+    sig = sig.view(sig.dtype.newbyteorder('<')).tobytes()[:10]
+    assert sig in known_sigs
+
+
+def test_eps_positive():
+    # np.finfo('g').eps should be positive on all platforms. If this isn't true
+    # then something may have gone wrong with the MachArLike, e.g. if
+    # np._core.getlimits._discovered_machar didn't work properly
+    assert np.finfo(np.longdouble).eps > 0.
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_machar.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_machar.py
new file mode 100644
index 0000000..2d772dd
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_machar.py
@@ -0,0 +1,30 @@
+"""
+Test machar. Given recent changes to hardcode type data, we might want to get
+rid of both MachAr and this test at some point.
+
+"""
+import numpy._core.numerictypes as ntypes
+from numpy import array, errstate
+from numpy._core._machar import MachAr
+
+
+class TestMachAr:
+    def _run_machar_highprec(self):
+        # Instantiate MachAr instance with high enough precision to cause
+        # underflow
+        try:
+            hiprec = ntypes.float96
+            MachAr(lambda v: array(v, hiprec))
+        except AttributeError:
+            # Fixme, this needs to raise a 'skip' exception.
+            "Skipping test: no ntypes.float96 available on this platform."
+
+    def test_underlow(self):
+        # Regression test for #759:
+        # instantiating MachAr for dtype = np.float96 raises spurious warning.
+        with errstate(all='raise'):
+            try:
+                self._run_machar_highprec()
+            except FloatingPointError as e:
+                msg = f"Caught {e} exception, should not have been raised."
+                raise AssertionError(msg)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_mem_overlap.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_mem_overlap.py
new file mode 100644
index 0000000..d173567
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_mem_overlap.py
@@ -0,0 +1,930 @@
+import itertools
+
+import pytest
+from numpy._core._multiarray_tests import internal_overlap, solve_diophantine
+
+import numpy as np
+from numpy._core import _umath_tests
+from numpy.lib.stride_tricks import as_strided
+from numpy.testing import assert_, assert_array_equal, assert_equal, assert_raises
+
+ndims = 2
+size = 10
+shape = tuple([size] * ndims)
+
+MAY_SHARE_BOUNDS = 0
+MAY_SHARE_EXACT = -1
+
+
+def _indices_for_nelems(nelems):
+    """Returns slices of length nelems, from start onwards, in direction sign."""
+
+    if nelems == 0:
+        return [size // 2]  # int index
+
+    res = []
+    for step in (1, 2):
+        for sign in (-1, 1):
+            start = size // 2 - nelems * step * sign // 2
+            stop = start + nelems * step * sign
+            res.append(slice(start, stop, step * sign))
+
+    return res
+
+
+def _indices_for_axis():
+    """Returns (src, dst) pairs of indices."""
+
+    res = []
+    for nelems in (0, 2, 3):
+        ind = _indices_for_nelems(nelems)
+        res.extend(itertools.product(ind, ind))  # all assignments of size "nelems"
+
+    return res
+
+
+def _indices(ndims):
+    """Returns ((axis0_src, axis0_dst), (axis1_src, axis1_dst), ... ) index pairs."""
+
+    ind = _indices_for_axis()
+    return itertools.product(ind, repeat=ndims)
+
+
+def _check_assignment(srcidx, dstidx):
+    """Check assignment arr[dstidx] = arr[srcidx] works."""
+
+    arr = np.arange(np.prod(shape)).reshape(shape)
+
+    cpy = arr.copy()
+
+    cpy[dstidx] = arr[srcidx]
+    arr[dstidx] = arr[srcidx]
+
+    assert_(np.all(arr == cpy),
+            f'assigning arr[{dstidx}] = arr[{srcidx}]')
+
+
+def test_overlapping_assignments():
+    # Test automatically generated assignments which overlap in memory.
+
+    inds = _indices(ndims)
+
+    for ind in inds:
+        srcidx = tuple(a[0] for a in ind)
+        dstidx = tuple(a[1] for a in ind)
+
+        _check_assignment(srcidx, dstidx)
+
+
+@pytest.mark.slow
+def test_diophantine_fuzz():
+    # Fuzz test the diophantine solver
+    rng = np.random.RandomState(1234)
+
+    max_int = np.iinfo(np.intp).max
+
+    for ndim in range(10):
+        feasible_count = 0
+        infeasible_count = 0
+
+        min_count = 500 // (ndim + 1)
+
+        while min(feasible_count, infeasible_count) < min_count:
+            # Ensure big and small integer problems
+            A_max = 1 + rng.randint(0, 11, dtype=np.intp)**6
+            U_max = rng.randint(0, 11, dtype=np.intp)**6
+
+            A_max = min(max_int, A_max)
+            U_max = min(max_int - 1, U_max)
+
+            A = tuple(int(rng.randint(1, A_max + 1, dtype=np.intp))
+                      for j in range(ndim))
+            U = tuple(int(rng.randint(0, U_max + 2, dtype=np.intp))
+                      for j in range(ndim))
+
+            b_ub = min(max_int - 2, sum(a * ub for a, ub in zip(A, U)))
+            b = int(rng.randint(-1, b_ub + 2, dtype=np.intp))
+
+            if ndim == 0 and feasible_count < min_count:
+                b = 0
+
+            X = solve_diophantine(A, U, b)
+
+            if X is None:
+                # Check the simplified decision problem agrees
+                X_simplified = solve_diophantine(A, U, b, simplify=1)
+                assert_(X_simplified is None, (A, U, b, X_simplified))
+
+                # Check no solution exists (provided the problem is
+                # small enough so that brute force checking doesn't
+                # take too long)
+                ranges = tuple(range(0, a * ub + 1, a) for a, ub in zip(A, U))
+
+                size = 1
+                for r in ranges:
+                    size *= len(r)
+                if size < 100000:
+                    assert_(not any(sum(w) == b for w in itertools.product(*ranges)))
+                    infeasible_count += 1
+            else:
+                # Check the simplified decision problem agrees
+                X_simplified = solve_diophantine(A, U, b, simplify=1)
+                assert_(X_simplified is not None, (A, U, b, X_simplified))
+
+                # Check validity
+                assert_(sum(a * x for a, x in zip(A, X)) == b)
+                assert_(all(0 <= x <= ub for x, ub in zip(X, U)))
+                feasible_count += 1
+
+
+def test_diophantine_overflow():
+    # Smoke test integer overflow detection
+    max_intp = np.iinfo(np.intp).max
+    max_int64 = np.iinfo(np.int64).max
+
+    if max_int64 <= max_intp:
+        # Check that the algorithm works internally in 128-bit;
+        # solving this problem requires large intermediate numbers
+        A = (max_int64 // 2, max_int64 // 2 - 10)
+        U = (max_int64 // 2, max_int64 // 2 - 10)
+        b = 2 * (max_int64 // 2) - 10
+
+        assert_equal(solve_diophantine(A, U, b), (1, 1))
+
+
+def check_may_share_memory_exact(a, b):
+    got = np.may_share_memory(a, b, max_work=MAY_SHARE_EXACT)
+
+    assert_equal(np.may_share_memory(a, b),
+                 np.may_share_memory(a, b, max_work=MAY_SHARE_BOUNDS))
+
+    a.fill(0)
+    b.fill(0)
+    a.fill(1)
+    exact = b.any()
+
+    err_msg = ""
+    if got != exact:
+        err_msg = "    " + "\n    ".join([
+            f"base_a - base_b = {a.__array_interface__['data'][0] - b.__array_interface__['data'][0]!r}",
+            f"shape_a = {a.shape!r}",
+            f"shape_b = {b.shape!r}",
+            f"strides_a = {a.strides!r}",
+            f"strides_b = {b.strides!r}",
+            f"size_a = {a.size!r}",
+            f"size_b = {b.size!r}"
+        ])
+
+    assert_equal(got, exact, err_msg=err_msg)
+
+
+def test_may_share_memory_manual():
+    # Manual test cases for may_share_memory
+
+    # Base arrays
+    xs0 = [
+        np.zeros([13, 21, 23, 22], dtype=np.int8),
+        np.zeros([13, 21, 23 * 2, 22], dtype=np.int8)[:, :, ::2, :]
+    ]
+
+    # Generate all negative stride combinations
+    xs = []
+    for x in xs0:
+        for ss in itertools.product(*(([slice(None), slice(None, None, -1)],) * 4)):
+            xp = x[ss]
+            xs.append(xp)
+
+    for x in xs:
+        # The default is a simple extent check
+        assert_(np.may_share_memory(x[:, 0, :], x[:, 1, :]))
+        assert_(np.may_share_memory(x[:, 0, :], x[:, 1, :], max_work=None))
+
+        # Exact checks
+        check_may_share_memory_exact(x[:, 0, :], x[:, 1, :])
+        check_may_share_memory_exact(x[:, ::7], x[:, 3::3])
+
+        try:
+            xp = x.ravel()
+            if xp.flags.owndata:
+                continue
+            xp = xp.view(np.int16)
+        except ValueError:
+            continue
+
+        # 0-size arrays cannot overlap
+        check_may_share_memory_exact(x.ravel()[6:6],
+                                     xp.reshape(13, 21, 23, 11)[:, ::7])
+
+        # Test itemsize is dealt with
+        check_may_share_memory_exact(x[:, ::7],
+                                     xp.reshape(13, 21, 23, 11))
+        check_may_share_memory_exact(x[:, ::7],
+                                     xp.reshape(13, 21, 23, 11)[:, 3::3])
+        check_may_share_memory_exact(x.ravel()[6:7],
+                                     xp.reshape(13, 21, 23, 11)[:, ::7])
+
+    # Check unit size
+    x = np.zeros([1], dtype=np.int8)
+    check_may_share_memory_exact(x, x)
+    check_may_share_memory_exact(x, x.copy())
+
+
+def iter_random_view_pairs(x, same_steps=True, equal_size=False):
+    rng = np.random.RandomState(1234)
+
+    if equal_size and same_steps:
+        raise ValueError
+
+    def random_slice(n, step):
+        start = rng.randint(0, n + 1, dtype=np.intp)
+        stop = rng.randint(start, n + 1, dtype=np.intp)
+        if rng.randint(0, 2, dtype=np.intp) == 0:
+            stop, start = start, stop
+            step *= -1
+        return slice(start, stop, step)
+
+    def random_slice_fixed_size(n, step, size):
+        start = rng.randint(0, n + 1 - size * step)
+        stop = start + (size - 1) * step + 1
+        if rng.randint(0, 2) == 0:
+            stop, start = start - 1, stop - 1
+            if stop < 0:
+                stop = None
+            step *= -1
+        return slice(start, stop, step)
+
+    # First a few regular views
+    yield x, x
+    for j in range(1, 7, 3):
+        yield x[j:], x[:-j]
+        yield x[..., j:], x[..., :-j]
+
+    # An array with zero stride internal overlap
+    strides = list(x.strides)
+    strides[0] = 0
+    xp = as_strided(x, shape=x.shape, strides=strides)
+    yield x, xp
+    yield xp, xp
+
+    # An array with non-zero stride internal overlap
+    strides = list(x.strides)
+    if strides[0] > 1:
+        strides[0] = 1
+    xp = as_strided(x, shape=x.shape, strides=strides)
+    yield x, xp
+    yield xp, xp
+
+    # Then discontiguous views
+    while True:
+        steps = tuple(rng.randint(1, 11, dtype=np.intp)
+                      if rng.randint(0, 5, dtype=np.intp) == 0 else 1
+                      for j in range(x.ndim))
+        s1 = tuple(random_slice(p, s) for p, s in zip(x.shape, steps))
+
+        t1 = np.arange(x.ndim)
+        rng.shuffle(t1)
+
+        if equal_size:
+            t2 = t1
+        else:
+            t2 = np.arange(x.ndim)
+            rng.shuffle(t2)
+
+        a = x[s1]
+
+        if equal_size:
+            if a.size == 0:
+                continue
+
+            steps2 = tuple(rng.randint(1, max(2, p // (1 + pa)))
+                           if rng.randint(0, 5) == 0 else 1
+                           for p, s, pa in zip(x.shape, s1, a.shape))
+            s2 = tuple(random_slice_fixed_size(p, s, pa)
+                       for p, s, pa in zip(x.shape, steps2, a.shape))
+        elif same_steps:
+            steps2 = steps
+        else:
+            steps2 = tuple(rng.randint(1, 11, dtype=np.intp)
+                           if rng.randint(0, 5, dtype=np.intp) == 0 else 1
+                           for j in range(x.ndim))
+
+        if not equal_size:
+            s2 = tuple(random_slice(p, s) for p, s in zip(x.shape, steps2))
+
+        a = a.transpose(t1)
+        b = x[s2].transpose(t2)
+
+        yield a, b
+
+
+def check_may_share_memory_easy_fuzz(get_max_work, same_steps, min_count):
+    # Check that overlap problems with common strides are solved with
+    # little work.
+    x = np.zeros([17, 34, 71, 97], dtype=np.int16)
+
+    feasible = 0
+    infeasible = 0
+
+    pair_iter = iter_random_view_pairs(x, same_steps)
+
+    while min(feasible, infeasible) < min_count:
+        a, b = next(pair_iter)
+
+        bounds_overlap = np.may_share_memory(a, b)
+        may_share_answer = np.may_share_memory(a, b)
+        easy_answer = np.may_share_memory(a, b, max_work=get_max_work(a, b))
+        exact_answer = np.may_share_memory(a, b, max_work=MAY_SHARE_EXACT)
+
+        if easy_answer != exact_answer:
+            # assert_equal is slow...
+            assert_equal(easy_answer, exact_answer)
+
+        if may_share_answer != bounds_overlap:
+            assert_equal(may_share_answer, bounds_overlap)
+
+        if bounds_overlap:
+            if exact_answer:
+                feasible += 1
+            else:
+                infeasible += 1
+
+
+@pytest.mark.slow
+def test_may_share_memory_easy_fuzz():
+    # Check that overlap problems with common strides are always
+    # solved with little work.
+
+    check_may_share_memory_easy_fuzz(get_max_work=lambda a, b: 1,
+                                     same_steps=True,
+                                     min_count=2000)
+
+
+@pytest.mark.slow
+def test_may_share_memory_harder_fuzz():
+    # Overlap problems with not necessarily common strides take more
+    # work.
+    #
+    # The work bound below can't be reduced much. Harder problems can
+    # also exist but not be detected here, as the set of problems
+    # comes from RNG.
+
+    check_may_share_memory_easy_fuzz(get_max_work=lambda a, b: max(a.size, b.size) // 2,
+                                     same_steps=False,
+                                     min_count=2000)
+
+
+def test_shares_memory_api():
+    x = np.zeros([4, 5, 6], dtype=np.int8)
+
+    assert_equal(np.shares_memory(x, x), True)
+    assert_equal(np.shares_memory(x, x.copy()), False)
+
+    a = x[:, ::2, ::3]
+    b = x[:, ::3, ::2]
+    assert_equal(np.shares_memory(a, b), True)
+    assert_equal(np.shares_memory(a, b, max_work=None), True)
+    assert_raises(
+        np.exceptions.TooHardError, np.shares_memory, a, b, max_work=1
+    )
+
+
+def test_may_share_memory_bad_max_work():
+    x = np.zeros([1])
+    assert_raises(OverflowError, np.may_share_memory, x, x, max_work=10**100)
+    assert_raises(OverflowError, np.shares_memory, x, x, max_work=10**100)
+
+
+def test_internal_overlap_diophantine():
+    def check(A, U, exists=None):
+        X = solve_diophantine(A, U, 0, require_ub_nontrivial=1)
+
+        if exists is None:
+            exists = (X is not None)
+
+        if X is not None:
+            assert_(sum(a * x for a, x in zip(A, X)) == sum(a * u // 2 for a, u in zip(A, U)))
+            assert_(all(0 <= x <= u for x, u in zip(X, U)))
+            assert_(any(x != u // 2 for x, u in zip(X, U)))
+
+        if exists:
+            assert_(X is not None, repr(X))
+        else:
+            assert_(X is None, repr(X))
+
+    # Smoke tests
+    check((3, 2), (2 * 2, 3 * 2), exists=True)
+    check((3 * 2, 2), (15 * 2, (3 - 1) * 2), exists=False)
+
+
+def test_internal_overlap_slices():
+    # Slicing an array never generates internal overlap
+
+    x = np.zeros([17, 34, 71, 97], dtype=np.int16)
+
+    rng = np.random.RandomState(1234)
+
+    def random_slice(n, step):
+        start = rng.randint(0, n + 1, dtype=np.intp)
+        stop = rng.randint(start, n + 1, dtype=np.intp)
+        if rng.randint(0, 2, dtype=np.intp) == 0:
+            stop, start = start, stop
+            step *= -1
+        return slice(start, stop, step)
+
+    cases = 0
+    min_count = 5000
+
+    while cases < min_count:
+        steps = tuple(rng.randint(1, 11, dtype=np.intp)
+                      if rng.randint(0, 5, dtype=np.intp) == 0 else 1
+                      for j in range(x.ndim))
+        t1 = np.arange(x.ndim)
+        rng.shuffle(t1)
+        s1 = tuple(random_slice(p, s) for p, s in zip(x.shape, steps))
+        a = x[s1].transpose(t1)
+
+        assert_(not internal_overlap(a))
+        cases += 1
+
+
+def check_internal_overlap(a, manual_expected=None):
+    got = internal_overlap(a)
+
+    # Brute-force check
+    m = set()
+    ranges = tuple(range(n) for n in a.shape)
+    for v in itertools.product(*ranges):
+        offset = sum(s * w for s, w in zip(a.strides, v))
+        if offset in m:
+            expected = True
+            break
+        else:
+            m.add(offset)
+    else:
+        expected = False
+
+    # Compare
+    if got != expected:
+        assert_equal(got, expected, err_msg=repr((a.strides, a.shape)))
+    if manual_expected is not None and expected != manual_expected:
+        assert_equal(expected, manual_expected)
+    return got
+
+
+def test_internal_overlap_manual():
+    # Stride tricks can construct arrays with internal overlap
+
+    # We don't care about memory bounds, the array is not
+    # read/write accessed
+    x = np.arange(1).astype(np.int8)
+
+    # Check low-dimensional special cases
+
+    check_internal_overlap(x, False)  # 1-dim
+    check_internal_overlap(x.reshape([]), False)  # 0-dim
+
+    a = as_strided(x, strides=(3, 4), shape=(4, 4))
+    check_internal_overlap(a, False)
+
+    a = as_strided(x, strides=(3, 4), shape=(5, 4))
+    check_internal_overlap(a, True)
+
+    a = as_strided(x, strides=(0,), shape=(0,))
+    check_internal_overlap(a, False)
+
+    a = as_strided(x, strides=(0,), shape=(1,))
+    check_internal_overlap(a, False)
+
+    a = as_strided(x, strides=(0,), shape=(2,))
+    check_internal_overlap(a, True)
+
+    a = as_strided(x, strides=(0, -9993), shape=(87, 22))
+    check_internal_overlap(a, True)
+
+    a = as_strided(x, strides=(0, -9993), shape=(1, 22))
+    check_internal_overlap(a, False)
+
+    a = as_strided(x, strides=(0, -9993), shape=(0, 22))
+    check_internal_overlap(a, False)
+
+
+def test_internal_overlap_fuzz():
+    # Fuzz check; the brute-force check is fairly slow
+
+    x = np.arange(1).astype(np.int8)
+
+    overlap = 0
+    no_overlap = 0
+    min_count = 100
+
+    rng = np.random.RandomState(1234)
+
+    while min(overlap, no_overlap) < min_count:
+        ndim = rng.randint(1, 4, dtype=np.intp)
+
+        strides = tuple(rng.randint(-1000, 1000, dtype=np.intp)
+                        for j in range(ndim))
+        shape = tuple(rng.randint(1, 30, dtype=np.intp)
+                      for j in range(ndim))
+
+        a = as_strided(x, strides=strides, shape=shape)
+        result = check_internal_overlap(a)
+
+        if result:
+            overlap += 1
+        else:
+            no_overlap += 1
+
+
+def test_non_ndarray_inputs():
+    # Regression check for gh-5604
+
+    class MyArray:
+        def __init__(self, data):
+            self.data = data
+
+        @property
+        def __array_interface__(self):
+            return self.data.__array_interface__
+
+    class MyArray2:
+        def __init__(self, data):
+            self.data = data
+
+        def __array__(self, dtype=None, copy=None):
+            return self.data
+
+    for cls in [MyArray, MyArray2]:
+        x = np.arange(5)
+
+        assert_(np.may_share_memory(cls(x[::2]), x[1::2]))
+        assert_(not np.shares_memory(cls(x[::2]), x[1::2]))
+
+        assert_(np.shares_memory(cls(x[1::3]), x[::2]))
+        assert_(np.may_share_memory(cls(x[1::3]), x[::2]))
+
+
+def view_element_first_byte(x):
+    """Construct an array viewing the first byte of each element of `x`"""
+    from numpy.lib._stride_tricks_impl import DummyArray
+    interface = dict(x.__array_interface__)
+    interface['typestr'] = '|b1'
+    interface['descr'] = [('', '|b1')]
+    return np.asarray(DummyArray(interface, x))
+
+
+def assert_copy_equivalent(operation, args, out, **kwargs):
+    """
+    Check that operation(*args, out=out) produces results
+    equivalent to out[...] = operation(*args, out=out.copy())
+    """
+
+    kwargs['out'] = out
+    kwargs2 = dict(kwargs)
+    kwargs2['out'] = out.copy()
+
+    out_orig = out.copy()
+    out[...] = operation(*args, **kwargs2)
+    expected = out.copy()
+    out[...] = out_orig
+
+    got = operation(*args, **kwargs).copy()
+
+    if (got != expected).any():
+        assert_equal(got, expected)
+
+
+class TestUFunc:
+    """
+    Test ufunc call memory overlap handling
+    """
+
+    def check_unary_fuzz(self, operation, get_out_axis_size, dtype=np.int16,
+                             count=5000):
+        shapes = [7, 13, 8, 21, 29, 32]
+
+        rng = np.random.RandomState(1234)
+
+        for ndim in range(1, 6):
+            x = rng.randint(0, 2**16, size=shapes[:ndim]).astype(dtype)
+
+            it = iter_random_view_pairs(x, same_steps=False, equal_size=True)
+
+            min_count = count // (ndim + 1)**2
+
+            overlapping = 0
+            while overlapping < min_count:
+                a, b = next(it)
+
+                a_orig = a.copy()
+                b_orig = b.copy()
+
+                if get_out_axis_size is None:
+                    assert_copy_equivalent(operation, [a], out=b)
+
+                    if np.shares_memory(a, b):
+                        overlapping += 1
+                else:
+                    for axis in itertools.chain(range(ndim), [None]):
+                        a[...] = a_orig
+                        b[...] = b_orig
+
+                        # Determine size for reduction axis (None if scalar)
+                        outsize, scalarize = get_out_axis_size(a, b, axis)
+                        if outsize == 'skip':
+                            continue
+
+                        # Slice b to get an output array of the correct size
+                        sl = [slice(None)] * ndim
+                        if axis is None:
+                            if outsize is None:
+                                sl = [slice(0, 1)] + [0] * (ndim - 1)
+                            else:
+                                sl = [slice(0, outsize)] + [0] * (ndim - 1)
+                        elif outsize is None:
+                            k = b.shape[axis] // 2
+                            if ndim == 1:
+                                sl[axis] = slice(k, k + 1)
+                            else:
+                                sl[axis] = k
+                        else:
+                            assert b.shape[axis] >= outsize
+                            sl[axis] = slice(0, outsize)
+                        b_out = b[tuple(sl)]
+
+                        if scalarize:
+                            b_out = b_out.reshape([])
+
+                        if np.shares_memory(a, b_out):
+                            overlapping += 1
+
+                        # Check result
+                        assert_copy_equivalent(operation, [a], out=b_out, axis=axis)
+
+    @pytest.mark.slow
+    def test_unary_ufunc_call_fuzz(self):
+        self.check_unary_fuzz(np.invert, None, np.int16)
+
+    @pytest.mark.slow
+    def test_unary_ufunc_call_complex_fuzz(self):
+        # Complex typically has a smaller alignment than itemsize
+        self.check_unary_fuzz(np.negative, None, np.complex128, count=500)
+
+    def test_binary_ufunc_accumulate_fuzz(self):
+        def get_out_axis_size(a, b, axis):
+            if axis is None:
+                if a.ndim == 1:
+                    return a.size, False
+                else:
+                    return 'skip', False  # accumulate doesn't support this
+            else:
+                return a.shape[axis], False
+
+        self.check_unary_fuzz(np.add.accumulate, get_out_axis_size,
+                              dtype=np.int16, count=500)
+
+    def test_binary_ufunc_reduce_fuzz(self):
+        def get_out_axis_size(a, b, axis):
+            return None, (axis is None or a.ndim == 1)
+
+        self.check_unary_fuzz(np.add.reduce, get_out_axis_size,
+                              dtype=np.int16, count=500)
+
+    def test_binary_ufunc_reduceat_fuzz(self):
+        def get_out_axis_size(a, b, axis):
+            if axis is None:
+                if a.ndim == 1:
+                    return a.size, False
+                else:
+                    return 'skip', False  # reduceat doesn't support this
+            else:
+                return a.shape[axis], False
+
+        def do_reduceat(a, out, axis):
+            if axis is None:
+                size = len(a)
+                step = size // len(out)
+            else:
+                size = a.shape[axis]
+                step = a.shape[axis] // out.shape[axis]
+            idx = np.arange(0, size, step)
+            return np.add.reduceat(a, idx, out=out, axis=axis)
+
+        self.check_unary_fuzz(do_reduceat, get_out_axis_size,
+                              dtype=np.int16, count=500)
+
+    def test_binary_ufunc_reduceat_manual(self):
+        def check(ufunc, a, ind, out):
+            c1 = ufunc.reduceat(a.copy(), ind.copy(), out=out.copy())
+            c2 = ufunc.reduceat(a, ind, out=out)
+            assert_array_equal(c1, c2)
+
+        # Exactly same input/output arrays
+        a = np.arange(10000, dtype=np.int16)
+        check(np.add, a, a[::-1].copy(), a)
+
+        # Overlap with index
+        a = np.arange(10000, dtype=np.int16)
+        check(np.add, a, a[::-1], a)
+
+    @pytest.mark.slow
+    def test_unary_gufunc_fuzz(self):
+        shapes = [7, 13, 8, 21, 29, 32]
+        gufunc = _umath_tests.euclidean_pdist
+
+        rng = np.random.RandomState(1234)
+
+        for ndim in range(2, 6):
+            x = rng.rand(*shapes[:ndim])
+
+            it = iter_random_view_pairs(x, same_steps=False, equal_size=True)
+
+            min_count = 500 // (ndim + 1)**2
+
+            overlapping = 0
+            while overlapping < min_count:
+                a, b = next(it)
+
+                if min(a.shape[-2:]) < 2 or min(b.shape[-2:]) < 2 or a.shape[-1] < 2:
+                    continue
+
+                # Ensure the shapes are so that euclidean_pdist is happy
+                if b.shape[-1] > b.shape[-2]:
+                    b = b[..., 0, :]
+                else:
+                    b = b[..., :, 0]
+
+                n = a.shape[-2]
+                p = n * (n - 1) // 2
+                if p <= b.shape[-1] and p > 0:
+                    b = b[..., :p]
+                else:
+                    n = max(2, int(np.sqrt(b.shape[-1])) // 2)
+                    p = n * (n - 1) // 2
+                    a = a[..., :n, :]
+                    b = b[..., :p]
+
+                # Call
+                if np.shares_memory(a, b):
+                    overlapping += 1
+
+                with np.errstate(over='ignore', invalid='ignore'):
+                    assert_copy_equivalent(gufunc, [a], out=b)
+
+    def test_ufunc_at_manual(self):
+        def check(ufunc, a, ind, b=None):
+            a0 = a.copy()
+            if b is None:
+                ufunc.at(a0, ind.copy())
+                c1 = a0.copy()
+                ufunc.at(a, ind)
+                c2 = a.copy()
+            else:
+                ufunc.at(a0, ind.copy(), b.copy())
+                c1 = a0.copy()
+                ufunc.at(a, ind, b)
+                c2 = a.copy()
+            assert_array_equal(c1, c2)
+
+        # Overlap with index
+        a = np.arange(10000, dtype=np.int16)
+        check(np.invert, a[::-1], a)
+
+        # Overlap with second data array
+        a = np.arange(100, dtype=np.int16)
+        ind = np.arange(0, 100, 2, dtype=np.int16)
+        check(np.add, a, ind, a[25:75])
+
+    def test_unary_ufunc_1d_manual(self):
+        # Exercise ufunc fast-paths (that avoid creation of an `np.nditer`)
+
+        def check(a, b):
+            a_orig = a.copy()
+            b_orig = b.copy()
+
+            b0 = b.copy()
+            c1 = ufunc(a, out=b0)
+            c2 = ufunc(a, out=b)
+            assert_array_equal(c1, c2)
+
+            # Trigger "fancy ufunc loop" code path
+            mask = view_element_first_byte(b).view(np.bool)
+
+            a[...] = a_orig
+            b[...] = b_orig
+            c1 = ufunc(a, out=b.copy(), where=mask.copy()).copy()
+
+            a[...] = a_orig
+            b[...] = b_orig
+            c2 = ufunc(a, out=b, where=mask.copy()).copy()
+
+            # Also, mask overlapping with output
+            a[...] = a_orig
+            b[...] = b_orig
+            c3 = ufunc(a, out=b, where=mask).copy()
+
+            assert_array_equal(c1, c2)
+            assert_array_equal(c1, c3)
+
+        dtypes = [np.int8, np.int16, np.int32, np.int64, np.float32,
+                  np.float64, np.complex64, np.complex128]
+        dtypes = [np.dtype(x) for x in dtypes]
+
+        for dtype in dtypes:
+            if np.issubdtype(dtype, np.integer):
+                ufunc = np.invert
+            else:
+                ufunc = np.reciprocal
+
+            n = 1000
+            k = 10
+            indices = [
+                np.index_exp[:n],
+                np.index_exp[k:k + n],
+                np.index_exp[n - 1::-1],
+                np.index_exp[k + n - 1:k - 1:-1],
+                np.index_exp[:2 * n:2],
+                np.index_exp[k:k + 2 * n:2],
+                np.index_exp[2 * n - 1::-2],
+                np.index_exp[k + 2 * n - 1:k - 1:-2],
+            ]
+
+            for xi, yi in itertools.product(indices, indices):
+                v = np.arange(1, 1 + n * 2 + k, dtype=dtype)
+                x = v[xi]
+                y = v[yi]
+
+                with np.errstate(all='ignore'):
+                    check(x, y)
+
+                    # Scalar cases
+                    check(x[:1], y)
+                    check(x[-1:], y)
+                    check(x[:1].reshape([]), y)
+                    check(x[-1:].reshape([]), y)
+
+    def test_unary_ufunc_where_same(self):
+        # Check behavior at wheremask overlap
+        ufunc = np.invert
+
+        def check(a, out, mask):
+            c1 = ufunc(a, out=out.copy(), where=mask.copy())
+            c2 = ufunc(a, out=out, where=mask)
+            assert_array_equal(c1, c2)
+
+        # Check behavior with same input and output arrays
+        x = np.arange(100).astype(np.bool)
+        check(x, x, x)
+        check(x, x.copy(), x)
+        check(x, x, x.copy())
+
+    @pytest.mark.slow
+    def test_binary_ufunc_1d_manual(self):
+        ufunc = np.add
+
+        def check(a, b, c):
+            c0 = c.copy()
+            c1 = ufunc(a, b, out=c0)
+            c2 = ufunc(a, b, out=c)
+            assert_array_equal(c1, c2)
+
+        for dtype in [np.int8, np.int16, np.int32, np.int64,
+                      np.float32, np.float64, np.complex64, np.complex128]:
+            # Check different data dependency orders
+
+            n = 1000
+            k = 10
+
+            indices = []
+            for p in [1, 2]:
+                indices.extend([
+                    np.index_exp[:p * n:p],
+                    np.index_exp[k:k + p * n:p],
+                    np.index_exp[p * n - 1::-p],
+                    np.index_exp[k + p * n - 1:k - 1:-p],
+                ])
+
+            for x, y, z in itertools.product(indices, indices, indices):
+                v = np.arange(6 * n).astype(dtype)
+                x = v[x]
+                y = v[y]
+                z = v[z]
+
+                check(x, y, z)
+
+                # Scalar cases
+                check(x[:1], y, z)
+                check(x[-1:], y, z)
+                check(x[:1].reshape([]), y, z)
+                check(x[-1:].reshape([]), y, z)
+                check(x, y[:1], z)
+                check(x, y[-1:], z)
+                check(x, y[:1].reshape([]), z)
+                check(x, y[-1:].reshape([]), z)
+
+    def test_inplace_op_simple_manual(self):
+        rng = np.random.RandomState(1234)
+        x = rng.rand(200, 200)  # bigger than bufsize
+
+        x += x.T
+        assert_array_equal(x - x.T, 0)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_mem_policy.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_mem_policy.py
new file mode 100644
index 0000000..b9f971e
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_mem_policy.py
@@ -0,0 +1,452 @@
+import asyncio
+import gc
+import os
+import sys
+import sysconfig
+import threading
+
+import pytest
+
+import numpy as np
+from numpy._core.multiarray import get_handler_name
+from numpy.testing import IS_EDITABLE, IS_WASM, assert_warns, extbuild
+
+
+@pytest.fixture
+def get_module(tmp_path):
+    """ Add a memory policy that returns a false pointer 64 bytes into the
+    actual allocation, and fill the prefix with some text. Then check at each
+    memory manipulation that the prefix exists, to make sure all alloc/realloc/
+    free/calloc go via the functions here.
+    """
+    if sys.platform.startswith('cygwin'):
+        pytest.skip('link fails on cygwin')
+    if IS_WASM:
+        pytest.skip("Can't build module inside Wasm")
+    if IS_EDITABLE:
+        pytest.skip("Can't build module for editable install")
+
+    functions = [
+        ("get_default_policy", "METH_NOARGS", """
+             Py_INCREF(PyDataMem_DefaultHandler);
+             return PyDataMem_DefaultHandler;
+         """),
+        ("set_secret_data_policy", "METH_NOARGS", """
+             PyObject *secret_data =
+                 PyCapsule_New(&secret_data_handler, "mem_handler", NULL);
+             if (secret_data == NULL) {
+                 return NULL;
+             }
+             PyObject *old = PyDataMem_SetHandler(secret_data);
+             Py_DECREF(secret_data);
+             return old;
+         """),
+        ("set_wrong_capsule_name_data_policy", "METH_NOARGS", """
+             PyObject *wrong_name_capsule =
+                 PyCapsule_New(&secret_data_handler, "not_mem_handler", NULL);
+             if (wrong_name_capsule == NULL) {
+                 return NULL;
+             }
+             PyObject *old = PyDataMem_SetHandler(wrong_name_capsule);
+             Py_DECREF(wrong_name_capsule);
+             return old;
+         """),
+        ("set_old_policy", "METH_O", """
+             PyObject *old;
+             if (args != NULL && PyCapsule_CheckExact(args)) {
+                 old = PyDataMem_SetHandler(args);
+             }
+             else {
+                 old = PyDataMem_SetHandler(NULL);
+             }
+             return old;
+         """),
+        ("get_array", "METH_NOARGS", """
+            char *buf = (char *)malloc(20);
+            npy_intp dims[1];
+            dims[0] = 20;
+            PyArray_Descr *descr =  PyArray_DescrNewFromType(NPY_UINT8);
+            return PyArray_NewFromDescr(&PyArray_Type, descr, 1, dims, NULL,
+                                        buf, NPY_ARRAY_WRITEABLE, NULL);
+         """),
+        ("set_own", "METH_O", """
+            if (!PyArray_Check(args)) {
+                PyErr_SetString(PyExc_ValueError,
+                             "need an ndarray");
+                return NULL;
+            }
+            PyArray_ENABLEFLAGS((PyArrayObject*)args, NPY_ARRAY_OWNDATA);
+            // Maybe try this too?
+            // PyArray_BASE(PyArrayObject *)args) = NULL;
+            Py_RETURN_NONE;
+         """),
+        ("get_array_with_base", "METH_NOARGS", """
+            char *buf = (char *)malloc(20);
+            npy_intp dims[1];
+            dims[0] = 20;
+            PyArray_Descr *descr =  PyArray_DescrNewFromType(NPY_UINT8);
+            PyObject *arr = PyArray_NewFromDescr(&PyArray_Type, descr, 1, dims,
+                                                 NULL, buf,
+                                                 NPY_ARRAY_WRITEABLE, NULL);
+            if (arr == NULL) return NULL;
+            PyObject *obj = PyCapsule_New(buf, "buf capsule",
+                                          (PyCapsule_Destructor)&warn_on_free);
+            if (obj == NULL) {
+                Py_DECREF(arr);
+                return NULL;
+            }
+            if (PyArray_SetBaseObject((PyArrayObject *)arr, obj) < 0) {
+                Py_DECREF(arr);
+                Py_DECREF(obj);
+                return NULL;
+            }
+            return arr;
+
+         """),
+    ]
+    prologue = '''
+        #define NPY_TARGET_VERSION NPY_1_22_API_VERSION
+        #define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION
+        #include <numpy/arrayobject.h>
+        /*
+         * This struct allows the dynamic configuration of the allocator funcs
+         * of the `secret_data_allocator`. It is provided here for
+         * demonstration purposes, as a valid `ctx` use-case scenario.
+         */
+        typedef struct {
+            void *(*malloc)(size_t);
+            void *(*calloc)(size_t, size_t);
+            void *(*realloc)(void *, size_t);
+            void (*free)(void *);
+        } SecretDataAllocatorFuncs;
+
+        NPY_NO_EXPORT void *
+        shift_alloc(void *ctx, size_t sz) {
+            SecretDataAllocatorFuncs *funcs = (SecretDataAllocatorFuncs *)ctx;
+            char *real = (char *)funcs->malloc(sz + 64);
+            if (real == NULL) {
+                return NULL;
+            }
+            snprintf(real, 64, "originally allocated %ld", (unsigned long)sz);
+            return (void *)(real + 64);
+        }
+        NPY_NO_EXPORT void *
+        shift_zero(void *ctx, size_t sz, size_t cnt) {
+            SecretDataAllocatorFuncs *funcs = (SecretDataAllocatorFuncs *)ctx;
+            char *real = (char *)funcs->calloc(sz + 64, cnt);
+            if (real == NULL) {
+                return NULL;
+            }
+            snprintf(real, 64, "originally allocated %ld via zero",
+                     (unsigned long)sz);
+            return (void *)(real + 64);
+        }
+        NPY_NO_EXPORT void
+        shift_free(void *ctx, void * p, npy_uintp sz) {
+            SecretDataAllocatorFuncs *funcs = (SecretDataAllocatorFuncs *)ctx;
+            if (p == NULL) {
+                return ;
+            }
+            char *real = (char *)p - 64;
+            if (strncmp(real, "originally allocated", 20) != 0) {
+                fprintf(stdout, "uh-oh, unmatched shift_free, "
+                        "no appropriate prefix\\n");
+                /* Make C runtime crash by calling free on the wrong address */
+                funcs->free((char *)p + 10);
+                /* funcs->free(real); */
+            }
+            else {
+                npy_uintp i = (npy_uintp)atoi(real +20);
+                if (i != sz) {
+                    fprintf(stderr, "uh-oh, unmatched shift_free"
+                            "(ptr, %ld) but allocated %ld\\n", sz, i);
+                    /* This happens in some places, only print */
+                    funcs->free(real);
+                }
+                else {
+                    funcs->free(real);
+                }
+            }
+        }
+        NPY_NO_EXPORT void *
+        shift_realloc(void *ctx, void * p, npy_uintp sz) {
+            SecretDataAllocatorFuncs *funcs = (SecretDataAllocatorFuncs *)ctx;
+            if (p != NULL) {
+                char *real = (char *)p - 64;
+                if (strncmp(real, "originally allocated", 20) != 0) {
+                    fprintf(stdout, "uh-oh, unmatched shift_realloc\\n");
+                    return realloc(p, sz);
+                }
+                return (void *)((char *)funcs->realloc(real, sz + 64) + 64);
+            }
+            else {
+                char *real = (char *)funcs->realloc(p, sz + 64);
+                if (real == NULL) {
+                    return NULL;
+                }
+                snprintf(real, 64, "originally allocated "
+                         "%ld  via realloc", (unsigned long)sz);
+                return (void *)(real + 64);
+            }
+        }
+        /* As an example, we use the standard {m|c|re}alloc/free funcs. */
+        static SecretDataAllocatorFuncs secret_data_handler_ctx = {
+            malloc,
+            calloc,
+            realloc,
+            free
+        };
+        static PyDataMem_Handler secret_data_handler = {
+            "secret_data_allocator",
+            1,
+            {
+                &secret_data_handler_ctx, /* ctx */
+                shift_alloc,              /* malloc */
+                shift_zero,               /* calloc */
+                shift_realloc,            /* realloc */
+                shift_free                /* free */
+            }
+        };
+        void warn_on_free(void *capsule) {
+            PyErr_WarnEx(PyExc_UserWarning, "in warn_on_free", 1);
+            void * obj = PyCapsule_GetPointer(capsule,
+                                              PyCapsule_GetName(capsule));
+            free(obj);
+        };
+        '''
+    more_init = "import_array();"
+    try:
+        import mem_policy
+        return mem_policy
+    except ImportError:
+        pass
+    # if it does not exist, build and load it
+    if sysconfig.get_platform() == "win-arm64":
+        pytest.skip("Meson unable to find MSVC linker on win-arm64")
+    return extbuild.build_and_import_extension('mem_policy',
+                                               functions,
+                                               prologue=prologue,
+                                               include_dirs=[np.get_include()],
+                                               build_dir=tmp_path,
+                                               more_init=more_init)
+
+
+def test_set_policy(get_module):
+
+    get_handler_name = np._core.multiarray.get_handler_name
+    get_handler_version = np._core.multiarray.get_handler_version
+    orig_policy_name = get_handler_name()
+
+    a = np.arange(10).reshape((2, 5))  # a doesn't own its own data
+    assert get_handler_name(a) is None
+    assert get_handler_version(a) is None
+    assert get_handler_name(a.base) == orig_policy_name
+    assert get_handler_version(a.base) == 1
+
+    orig_policy = get_module.set_secret_data_policy()
+
+    b = np.arange(10).reshape((2, 5))  # b doesn't own its own data
+    assert get_handler_name(b) is None
+    assert get_handler_version(b) is None
+    assert get_handler_name(b.base) == 'secret_data_allocator'
+    assert get_handler_version(b.base) == 1
+
+    if orig_policy_name == 'default_allocator':
+        get_module.set_old_policy(None)  # tests PyDataMem_SetHandler(NULL)
+        assert get_handler_name() == 'default_allocator'
+    else:
+        get_module.set_old_policy(orig_policy)
+        assert get_handler_name() == orig_policy_name
+
+    with pytest.raises(ValueError,
+                       match="Capsule must be named 'mem_handler'"):
+        get_module.set_wrong_capsule_name_data_policy()
+
+
+def test_default_policy_singleton(get_module):
+    get_handler_name = np._core.multiarray.get_handler_name
+
+    # set the policy to default
+    orig_policy = get_module.set_old_policy(None)
+
+    assert get_handler_name() == 'default_allocator'
+
+    # re-set the policy to default
+    def_policy_1 = get_module.set_old_policy(None)
+
+    assert get_handler_name() == 'default_allocator'
+
+    # set the policy to original
+    def_policy_2 = get_module.set_old_policy(orig_policy)
+
+    # since default policy is a singleton,
+    # these should be the same object
+    assert def_policy_1 is def_policy_2 is get_module.get_default_policy()
+
+
+def test_policy_propagation(get_module):
+    # The memory policy goes hand-in-hand with flags.owndata
+
+    class MyArr(np.ndarray):
+        pass
+
+    get_handler_name = np._core.multiarray.get_handler_name
+    orig_policy_name = get_handler_name()
+    a = np.arange(10).view(MyArr).reshape((2, 5))
+    assert get_handler_name(a) is None
+    assert a.flags.owndata is False
+
+    assert get_handler_name(a.base) is None
+    assert a.base.flags.owndata is False
+
+    assert get_handler_name(a.base.base) == orig_policy_name
+    assert a.base.base.flags.owndata is True
+
+
+async def concurrent_context1(get_module, orig_policy_name, event):
+    if orig_policy_name == 'default_allocator':
+        get_module.set_secret_data_policy()
+        assert get_handler_name() == 'secret_data_allocator'
+    else:
+        get_module.set_old_policy(None)
+        assert get_handler_name() == 'default_allocator'
+    event.set()
+
+
+async def concurrent_context2(get_module, orig_policy_name, event):
+    await event.wait()
+    # the policy is not affected by changes in parallel contexts
+    assert get_handler_name() == orig_policy_name
+    # change policy in the child context
+    if orig_policy_name == 'default_allocator':
+        get_module.set_secret_data_policy()
+        assert get_handler_name() == 'secret_data_allocator'
+    else:
+        get_module.set_old_policy(None)
+        assert get_handler_name() == 'default_allocator'
+
+
+async def async_test_context_locality(get_module):
+    orig_policy_name = np._core.multiarray.get_handler_name()
+
+    event = asyncio.Event()
+    # the child contexts inherit the parent policy
+    concurrent_task1 = asyncio.create_task(
+        concurrent_context1(get_module, orig_policy_name, event))
+    concurrent_task2 = asyncio.create_task(
+        concurrent_context2(get_module, orig_policy_name, event))
+    await concurrent_task1
+    await concurrent_task2
+
+    # the parent context is not affected by child policy changes
+    assert np._core.multiarray.get_handler_name() == orig_policy_name
+
+
+def test_context_locality(get_module):
+    if (sys.implementation.name == 'pypy'
+            and sys.pypy_version_info[:3] < (7, 3, 6)):
+        pytest.skip('no context-locality support in PyPy < 7.3.6')
+    asyncio.run(async_test_context_locality(get_module))
+
+
+def concurrent_thread1(get_module, event):
+    get_module.set_secret_data_policy()
+    assert np._core.multiarray.get_handler_name() == 'secret_data_allocator'
+    event.set()
+
+
+def concurrent_thread2(get_module, event):
+    event.wait()
+    # the policy is not affected by changes in parallel threads
+    assert np._core.multiarray.get_handler_name() == 'default_allocator'
+    # change policy in the child thread
+    get_module.set_secret_data_policy()
+
+
+def test_thread_locality(get_module):
+    orig_policy_name = np._core.multiarray.get_handler_name()
+
+    event = threading.Event()
+    # the child threads do not inherit the parent policy
+    concurrent_task1 = threading.Thread(target=concurrent_thread1,
+                                        args=(get_module, event))
+    concurrent_task2 = threading.Thread(target=concurrent_thread2,
+                                        args=(get_module, event))
+    concurrent_task1.start()
+    concurrent_task2.start()
+    concurrent_task1.join()
+    concurrent_task2.join()
+
+    # the parent thread is not affected by child policy changes
+    assert np._core.multiarray.get_handler_name() == orig_policy_name
+
+
+@pytest.mark.skip(reason="too slow, see gh-23975")
+def test_new_policy(get_module):
+    a = np.arange(10)
+    orig_policy_name = np._core.multiarray.get_handler_name(a)
+
+    orig_policy = get_module.set_secret_data_policy()
+
+    b = np.arange(10)
+    assert np._core.multiarray.get_handler_name(b) == 'secret_data_allocator'
+
+    # test array manipulation. This is slow
+    if orig_policy_name == 'default_allocator':
+        # when the np._core.test tests recurse into this test, the
+        # policy will be set so this "if" will be false, preventing
+        # infinite recursion
+        #
+        # if needed, debug this by
+        # - running tests with -- -s (to not capture stdout/stderr
+        # - setting verbose=2
+        # - setting extra_argv=['-vv'] here
+        assert np._core.test('full', verbose=1, extra_argv=[])
+        # also try the ma tests, the pickling test is quite tricky
+        assert np.ma.test('full', verbose=1, extra_argv=[])
+
+    get_module.set_old_policy(orig_policy)
+
+    c = np.arange(10)
+    assert np._core.multiarray.get_handler_name(c) == orig_policy_name
+
+
+@pytest.mark.xfail(sys.implementation.name == "pypy",
+                   reason=("bad interaction between getenv and "
+                           "os.environ inside pytest"))
+@pytest.mark.parametrize("policy", ["0", "1", None])
+def test_switch_owner(get_module, policy):
+    a = get_module.get_array()
+    assert np._core.multiarray.get_handler_name(a) is None
+    get_module.set_own(a)
+
+    if policy is None:
+        # See what we expect to be set based on the env variable
+        policy = os.getenv("NUMPY_WARN_IF_NO_MEM_POLICY", "0") == "1"
+        oldval = None
+    else:
+        policy = policy == "1"
+        oldval = np._core._multiarray_umath._set_numpy_warn_if_no_mem_policy(
+            policy)
+    try:
+        # The policy should be NULL, so we have to assume we can call
+        # "free".  A warning is given if the policy == "1"
+        if policy:
+            with assert_warns(RuntimeWarning) as w:
+                del a
+                gc.collect()
+        else:
+            del a
+            gc.collect()
+
+    finally:
+        if oldval is not None:
+            np._core._multiarray_umath._set_numpy_warn_if_no_mem_policy(oldval)
+
+
+def test_owner_is_base(get_module):
+    a = get_module.get_array_with_base()
+    with pytest.warns(UserWarning, match='warn_on_free'):
+        del a
+        gc.collect()
+        gc.collect()
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_memmap.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_memmap.py
new file mode 100644
index 0000000..cbd8252
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_memmap.py
@@ -0,0 +1,246 @@
+import mmap
+import os
+import sys
+from pathlib import Path
+from tempfile import NamedTemporaryFile, TemporaryFile
+
+import pytest
+
+from numpy import (
+    add,
+    allclose,
+    arange,
+    asarray,
+    average,
+    isscalar,
+    memmap,
+    multiply,
+    ndarray,
+    prod,
+    subtract,
+    sum,
+)
+from numpy.testing import (
+    IS_PYPY,
+    assert_,
+    assert_array_equal,
+    assert_equal,
+    break_cycles,
+    suppress_warnings,
+)
+
+
+class TestMemmap:
+    def setup_method(self):
+        self.tmpfp = NamedTemporaryFile(prefix='mmap')
+        self.shape = (3, 4)
+        self.dtype = 'float32'
+        self.data = arange(12, dtype=self.dtype)
+        self.data.resize(self.shape)
+
+    def teardown_method(self):
+        self.tmpfp.close()
+        self.data = None
+        if IS_PYPY:
+            break_cycles()
+            break_cycles()
+
+    def test_roundtrip(self):
+        # Write data to file
+        fp = memmap(self.tmpfp, dtype=self.dtype, mode='w+',
+                    shape=self.shape)
+        fp[:] = self.data[:]
+        del fp  # Test __del__ machinery, which handles cleanup
+
+        # Read data back from file
+        newfp = memmap(self.tmpfp, dtype=self.dtype, mode='r',
+                       shape=self.shape)
+        assert_(allclose(self.data, newfp))
+        assert_array_equal(self.data, newfp)
+        assert_equal(newfp.flags.writeable, False)
+
+    def test_open_with_filename(self, tmp_path):
+        tmpname = tmp_path / 'mmap'
+        fp = memmap(tmpname, dtype=self.dtype, mode='w+',
+                       shape=self.shape)
+        fp[:] = self.data[:]
+        del fp
+
+    def test_unnamed_file(self):
+        with TemporaryFile() as f:
+            fp = memmap(f, dtype=self.dtype, shape=self.shape)
+            del fp
+
+    def test_attributes(self):
+        offset = 1
+        mode = "w+"
+        fp = memmap(self.tmpfp, dtype=self.dtype, mode=mode,
+                    shape=self.shape, offset=offset)
+        assert_equal(offset, fp.offset)
+        assert_equal(mode, fp.mode)
+        del fp
+
+    def test_filename(self, tmp_path):
+        tmpname = tmp_path / "mmap"
+        fp = memmap(tmpname, dtype=self.dtype, mode='w+',
+                       shape=self.shape)
+        abspath = Path(os.path.abspath(tmpname))
+        fp[:] = self.data[:]
+        assert_equal(abspath, fp.filename)
+        b = fp[:1]
+        assert_equal(abspath, b.filename)
+        del b
+        del fp
+
+    def test_path(self, tmp_path):
+        tmpname = tmp_path / "mmap"
+        fp = memmap(Path(tmpname), dtype=self.dtype, mode='w+',
+                       shape=self.shape)
+        # os.path.realpath does not resolve symlinks on Windows
+        # see: https://bugs.python.org/issue9949
+        # use Path.resolve, just as memmap class does internally
+        abspath = str(Path(tmpname).resolve())
+        fp[:] = self.data[:]
+        assert_equal(abspath, str(fp.filename.resolve()))
+        b = fp[:1]
+        assert_equal(abspath, str(b.filename.resolve()))
+        del b
+        del fp
+
+    def test_filename_fileobj(self):
+        fp = memmap(self.tmpfp, dtype=self.dtype, mode="w+",
+                    shape=self.shape)
+        assert_equal(fp.filename, self.tmpfp.name)
+
+    @pytest.mark.skipif(sys.platform == 'gnu0',
+                        reason="Known to fail on hurd")
+    def test_flush(self):
+        fp = memmap(self.tmpfp, dtype=self.dtype, mode='w+',
+                    shape=self.shape)
+        fp[:] = self.data[:]
+        assert_equal(fp[0], self.data[0])
+        fp.flush()
+
+    def test_del(self):
+        # Make sure a view does not delete the underlying mmap
+        fp_base = memmap(self.tmpfp, dtype=self.dtype, mode='w+',
+                    shape=self.shape)
+        fp_base[0] = 5
+        fp_view = fp_base[0:1]
+        assert_equal(fp_view[0], 5)
+        del fp_view
+        # Should still be able to access and assign values after
+        # deleting the view
+        assert_equal(fp_base[0], 5)
+        fp_base[0] = 6
+        assert_equal(fp_base[0], 6)
+
+    def test_arithmetic_drops_references(self):
+        fp = memmap(self.tmpfp, dtype=self.dtype, mode='w+',
+                    shape=self.shape)
+        tmp = (fp + 10)
+        if isinstance(tmp, memmap):
+            assert_(tmp._mmap is not fp._mmap)
+
+    def test_indexing_drops_references(self):
+        fp = memmap(self.tmpfp, dtype=self.dtype, mode='w+',
+                    shape=self.shape)
+        tmp = fp[(1, 2), (2, 3)]
+        if isinstance(tmp, memmap):
+            assert_(tmp._mmap is not fp._mmap)
+
+    def test_slicing_keeps_references(self):
+        fp = memmap(self.tmpfp, dtype=self.dtype, mode='w+',
+                    shape=self.shape)
+        assert_(fp[:2, :2]._mmap is fp._mmap)
+
+    def test_view(self):
+        fp = memmap(self.tmpfp, dtype=self.dtype, shape=self.shape)
+        new1 = fp.view()
+        new2 = new1.view()
+        assert_(new1.base is fp)
+        assert_(new2.base is fp)
+        new_array = asarray(fp)
+        assert_(new_array.base is fp)
+
+    def test_ufunc_return_ndarray(self):
+        fp = memmap(self.tmpfp, dtype=self.dtype, shape=self.shape)
+        fp[:] = self.data
+
+        with suppress_warnings() as sup:
+            sup.filter(FutureWarning, "np.average currently does not preserve")
+            for unary_op in [sum, average, prod]:
+                result = unary_op(fp)
+                assert_(isscalar(result))
+                assert_(result.__class__ is self.data[0, 0].__class__)
+
+                assert_(unary_op(fp, axis=0).__class__ is ndarray)
+                assert_(unary_op(fp, axis=1).__class__ is ndarray)
+
+        for binary_op in [add, subtract, multiply]:
+            assert_(binary_op(fp, self.data).__class__ is ndarray)
+            assert_(binary_op(self.data, fp).__class__ is ndarray)
+            assert_(binary_op(fp, fp).__class__ is ndarray)
+
+        fp += 1
+        assert fp.__class__ is memmap
+        add(fp, 1, out=fp)
+        assert fp.__class__ is memmap
+
+    def test_getitem(self):
+        fp = memmap(self.tmpfp, dtype=self.dtype, shape=self.shape)
+        fp[:] = self.data
+
+        assert_(fp[1:, :-1].__class__ is memmap)
+        # Fancy indexing returns a copy that is not memmapped
+        assert_(fp[[0, 1]].__class__ is ndarray)
+
+    def test_memmap_subclass(self):
+        class MemmapSubClass(memmap):
+            pass
+
+        fp = MemmapSubClass(self.tmpfp, dtype=self.dtype, shape=self.shape)
+        fp[:] = self.data
+
+        # We keep previous behavior for subclasses of memmap, i.e. the
+        # ufunc and __getitem__ output is never turned into a ndarray
+        assert_(sum(fp, axis=0).__class__ is MemmapSubClass)
+        assert_(sum(fp).__class__ is MemmapSubClass)
+        assert_(fp[1:, :-1].__class__ is MemmapSubClass)
+        assert fp[[0, 1]].__class__ is MemmapSubClass
+
+    def test_mmap_offset_greater_than_allocation_granularity(self):
+        size = 5 * mmap.ALLOCATIONGRANULARITY
+        offset = mmap.ALLOCATIONGRANULARITY + 1
+        fp = memmap(self.tmpfp, shape=size, mode='w+', offset=offset)
+        assert_(fp.offset == offset)
+
+    def test_empty_array_with_offset_multiple_of_allocation_granularity(self):
+        self.tmpfp.write(b'a' * mmap.ALLOCATIONGRANULARITY)
+        size = 0
+        offset = mmap.ALLOCATIONGRANULARITY
+        fp = memmap(self.tmpfp, shape=size, mode='w+', offset=offset)
+        assert_equal(fp.offset, offset)
+
+    def test_no_shape(self):
+        self.tmpfp.write(b'a' * 16)
+        mm = memmap(self.tmpfp, dtype='float64')
+        assert_equal(mm.shape, (2,))
+
+    def test_empty_array(self):
+        # gh-12653
+        with pytest.raises(ValueError, match='empty file'):
+            memmap(self.tmpfp, shape=(0, 4), mode='r')
+
+        # gh-27723
+        # empty memmap works with mode in ('w+','r+')
+        memmap(self.tmpfp, shape=(0, 4), mode='w+')
+
+        # ok now the file is not empty
+        memmap(self.tmpfp, shape=(0, 4), mode='w+')
+
+    def test_shape_type(self):
+        memmap(self.tmpfp, shape=3, mode='w+')
+        memmap(self.tmpfp, shape=self.shape, mode='w+')
+        memmap(self.tmpfp, shape=list(self.shape), mode='w+')
+        memmap(self.tmpfp, shape=asarray(self.shape), mode='w+')
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_multiarray.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_multiarray.py
new file mode 100644
index 0000000..26587b6
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_multiarray.py
@@ -0,0 +1,10563 @@
+import builtins
+import collections.abc
+import ctypes
+import functools
+import gc
+import io
+import itertools
+import mmap
+import operator
+import os
+import pathlib
+import pickle
+import re
+import sys
+import tempfile
+import warnings
+import weakref
+from contextlib import contextmanager
+
+# Need to test an object that does not fully implement math interface
+from datetime import datetime, timedelta
+from decimal import Decimal
+
+import numpy._core._multiarray_tests as _multiarray_tests
+import pytest
+from numpy._core._rational_tests import rational
+
+import numpy as np
+from numpy._core.multiarray import _get_ndarray_c_version, dot
+from numpy._core.tests._locales import CommaDecimalPointLocale
+from numpy.exceptions import AxisError, ComplexWarning
+from numpy.lib.recfunctions import repack_fields
+from numpy.testing import (
+    BLAS_SUPPORTS_FPE,
+    HAS_REFCOUNT,
+    IS_64BIT,
+    IS_PYPY,
+    IS_PYSTON,
+    IS_WASM,
+    assert_,
+    assert_allclose,
+    assert_almost_equal,
+    assert_array_almost_equal,
+    assert_array_compare,
+    assert_array_equal,
+    assert_array_less,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+    assert_warns,
+    break_cycles,
+    check_support_sve,
+    runstring,
+    suppress_warnings,
+    temppath,
+)
+from numpy.testing._private.utils import _no_tracing, requires_memory
+
+
+def assert_arg_sorted(arr, arg):
+    # resulting array should be sorted and arg values should be unique
+    assert_equal(arr[arg], np.sort(arr))
+    assert_equal(np.sort(arg), np.arange(len(arg)))
+
+
+def assert_arr_partitioned(kth, k, arr_part):
+    assert_equal(arr_part[k], kth)
+    assert_array_compare(operator.__le__, arr_part[:k], kth)
+    assert_array_compare(operator.__ge__, arr_part[k:], kth)
+
+
+def _aligned_zeros(shape, dtype=float, order="C", align=None):
+    """
+    Allocate a new ndarray with aligned memory.
+
+    The ndarray is guaranteed *not* aligned to twice the requested alignment.
+    Eg, if align=4, guarantees it is not aligned to 8. If align=None uses
+    dtype.alignment."""
+    dtype = np.dtype(dtype)
+    if dtype == np.dtype(object):
+        # Can't do this, fall back to standard allocation (which
+        # should always be sufficiently aligned)
+        if align is not None:
+            raise ValueError("object array alignment not supported")
+        return np.zeros(shape, dtype=dtype, order=order)
+    if align is None:
+        align = dtype.alignment
+    if not hasattr(shape, '__len__'):
+        shape = (shape,)
+    size = functools.reduce(operator.mul, shape) * dtype.itemsize
+    buf = np.empty(size + 2 * align + 1, np.uint8)
+
+    ptr = buf.__array_interface__['data'][0]
+    offset = ptr % align
+    if offset != 0:
+        offset = align - offset
+    if (ptr % (2 * align)) == 0:
+        offset += align
+
+    # Note: slices producing 0-size arrays do not necessarily change
+    # data pointer --- so we use and allocate size+1
+    buf = buf[offset:offset + size + 1][:-1]
+    buf.fill(0)
+    data = np.ndarray(shape, dtype, buf, order=order)
+    return data
+
+
+class TestFlags:
+    def setup_method(self):
+        self.a = np.arange(10)
+
+    def test_writeable(self):
+        mydict = locals()
+        self.a.flags.writeable = False
+        assert_raises(ValueError, runstring, 'self.a[0] = 3', mydict)
+        self.a.flags.writeable = True
+        self.a[0] = 5
+        self.a[0] = 0
+
+    def test_writeable_any_base(self):
+        # Ensure that any base being writeable is sufficient to change flag;
+        # this is especially interesting for arrays from an array interface.
+        arr = np.arange(10)
+
+        class subclass(np.ndarray):
+            pass
+
+        # Create subclass so base will not be collapsed, this is OK to change
+        view1 = arr.view(subclass)
+        view2 = view1[...]
+        arr.flags.writeable = False
+        view2.flags.writeable = False
+        view2.flags.writeable = True  # Can be set to True again.
+
+        arr = np.arange(10)
+
+        class frominterface:
+            def __init__(self, arr):
+                self.arr = arr
+                self.__array_interface__ = arr.__array_interface__
+
+        view1 = np.asarray(frominterface)
+        view2 = view1[...]
+        view2.flags.writeable = False
+        view2.flags.writeable = True
+
+        view1.flags.writeable = False
+        view2.flags.writeable = False
+        with assert_raises(ValueError):
+            # Must assume not writeable, since only base is not:
+            view2.flags.writeable = True
+
+    def test_writeable_from_readonly(self):
+        # gh-9440 - make sure fromstring, from buffer on readonly buffers
+        # set writeable False
+        data = b'\x00' * 100
+        vals = np.frombuffer(data, 'B')
+        assert_raises(ValueError, vals.setflags, write=True)
+        types = np.dtype([('vals', 'u1'), ('res3', 'S4')])
+        values = np._core.records.fromstring(data, types)
+        vals = values['vals']
+        assert_raises(ValueError, vals.setflags, write=True)
+
+    def test_writeable_from_buffer(self):
+        data = bytearray(b'\x00' * 100)
+        vals = np.frombuffer(data, 'B')
+        assert_(vals.flags.writeable)
+        vals.setflags(write=False)
+        assert_(vals.flags.writeable is False)
+        vals.setflags(write=True)
+        assert_(vals.flags.writeable)
+        types = np.dtype([('vals', 'u1'), ('res3', 'S4')])
+        values = np._core.records.fromstring(data, types)
+        vals = values['vals']
+        assert_(vals.flags.writeable)
+        vals.setflags(write=False)
+        assert_(vals.flags.writeable is False)
+        vals.setflags(write=True)
+        assert_(vals.flags.writeable)
+
+    @pytest.mark.skipif(IS_PYPY, reason="PyPy always copies")
+    def test_writeable_pickle(self):
+        import pickle
+        # Small arrays will be copied without setting base.
+        # See condition for using PyArray_SetBaseObject in
+        # array_setstate.
+        a = np.arange(1000)
+        for v in range(pickle.HIGHEST_PROTOCOL):
+            vals = pickle.loads(pickle.dumps(a, v))
+            assert_(vals.flags.writeable)
+            assert_(isinstance(vals.base, bytes))
+
+    def test_writeable_from_c_data(self):
+        # Test that the writeable flag can be changed for an array wrapping
+        # low level C-data, but not owning its data.
+        # Also see that this is deprecated to change from python.
+        from numpy._core._multiarray_tests import get_c_wrapping_array
+
+        arr_writeable = get_c_wrapping_array(True)
+        assert not arr_writeable.flags.owndata
+        assert arr_writeable.flags.writeable
+        view = arr_writeable[...]
+
+        # Toggling the writeable flag works on the view:
+        view.flags.writeable = False
+        assert not view.flags.writeable
+        view.flags.writeable = True
+        assert view.flags.writeable
+        # Flag can be unset on the arr_writeable:
+        arr_writeable.flags.writeable = False
+
+        arr_readonly = get_c_wrapping_array(False)
+        assert not arr_readonly.flags.owndata
+        assert not arr_readonly.flags.writeable
+
+        for arr in [arr_writeable, arr_readonly]:
+            view = arr[...]
+            view.flags.writeable = False  # make sure it is readonly
+            arr.flags.writeable = False
+            assert not arr.flags.writeable
+
+            with assert_raises(ValueError):
+                view.flags.writeable = True
+
+            with assert_raises(ValueError):
+                arr.flags.writeable = True
+
+    def test_warnonwrite(self):
+        a = np.arange(10)
+        a.flags._warn_on_write = True
+        with warnings.catch_warnings(record=True) as w:
+            warnings.filterwarnings('always')
+            a[1] = 10
+            a[2] = 10
+            # only warn once
+            assert_(len(w) == 1)
+
+    @pytest.mark.parametrize(["flag", "flag_value", "writeable"],
+            [("writeable", True, True),
+             # Delete _warn_on_write after deprecation and simplify
+             # the parameterization:
+             ("_warn_on_write", True, False),
+             ("writeable", False, False)])
+    def test_readonly_flag_protocols(self, flag, flag_value, writeable):
+        a = np.arange(10)
+        setattr(a.flags, flag, flag_value)
+
+        class MyArr:
+            __array_struct__ = a.__array_struct__
+
+        assert memoryview(a).readonly is not writeable
+        assert a.__array_interface__['data'][1] is not writeable
+        assert np.asarray(MyArr()).flags.writeable is writeable
+
+    def test_otherflags(self):
+        assert_equal(self.a.flags.carray, True)
+        assert_equal(self.a.flags['C'], True)
+        assert_equal(self.a.flags.farray, False)
+        assert_equal(self.a.flags.behaved, True)
+        assert_equal(self.a.flags.fnc, False)
+        assert_equal(self.a.flags.forc, True)
+        assert_equal(self.a.flags.owndata, True)
+        assert_equal(self.a.flags.writeable, True)
+        assert_equal(self.a.flags.aligned, True)
+        assert_equal(self.a.flags.writebackifcopy, False)
+        assert_equal(self.a.flags['X'], False)
+        assert_equal(self.a.flags['WRITEBACKIFCOPY'], False)
+
+    def test_string_align(self):
+        a = np.zeros(4, dtype=np.dtype('|S4'))
+        assert_(a.flags.aligned)
+        # not power of two are accessed byte-wise and thus considered aligned
+        a = np.zeros(5, dtype=np.dtype('|S4'))
+        assert_(a.flags.aligned)
+
+    def test_void_align(self):
+        a = np.zeros(4, dtype=np.dtype([("a", "i4"), ("b", "i4")]))
+        assert_(a.flags.aligned)
+
+    @pytest.mark.parametrize("row_size", [5, 1 << 16])
+    @pytest.mark.parametrize("row_count", [1, 5])
+    @pytest.mark.parametrize("ndmin", [0, 1, 2])
+    def test_xcontiguous_load_txt(self, row_size, row_count, ndmin):
+        s = io.StringIO('\n'.join(['1.0 ' * row_size] * row_count))
+        a = np.loadtxt(s, ndmin=ndmin)
+
+        assert a.flags.c_contiguous
+        x = [i for i in a.shape if i != 1]
+        assert a.flags.f_contiguous == (len(x) <= 1)
+
+
+class TestHash:
+    # see #3793
+    def test_int(self):
+        for st, ut, s in [(np.int8, np.uint8, 8),
+                          (np.int16, np.uint16, 16),
+                          (np.int32, np.uint32, 32),
+                          (np.int64, np.uint64, 64)]:
+            for i in range(1, s):
+                assert_equal(hash(st(-2**i)), hash(-2**i),
+                             err_msg="%r: -2**%d" % (st, i))
+                assert_equal(hash(st(2**(i - 1))), hash(2**(i - 1)),
+                             err_msg="%r: 2**%d" % (st, i - 1))
+                assert_equal(hash(st(2**i - 1)), hash(2**i - 1),
+                             err_msg="%r: 2**%d - 1" % (st, i))
+
+                i = max(i - 1, 1)
+                assert_equal(hash(ut(2**(i - 1))), hash(2**(i - 1)),
+                             err_msg="%r: 2**%d" % (ut, i - 1))
+                assert_equal(hash(ut(2**i - 1)), hash(2**i - 1),
+                             err_msg="%r: 2**%d - 1" % (ut, i))
+
+
+class TestAttributes:
+    def setup_method(self):
+        self.one = np.arange(10)
+        self.two = np.arange(20).reshape(4, 5)
+        self.three = np.arange(60, dtype=np.float64).reshape(2, 5, 6)
+
+    def test_attributes(self):
+        assert_equal(self.one.shape, (10,))
+        assert_equal(self.two.shape, (4, 5))
+        assert_equal(self.three.shape, (2, 5, 6))
+        self.three.shape = (10, 3, 2)
+        assert_equal(self.three.shape, (10, 3, 2))
+        self.three.shape = (2, 5, 6)
+        assert_equal(self.one.strides, (self.one.itemsize,))
+        num = self.two.itemsize
+        assert_equal(self.two.strides, (5 * num, num))
+        num = self.three.itemsize
+        assert_equal(self.three.strides, (30 * num, 6 * num, num))
+        assert_equal(self.one.ndim, 1)
+        assert_equal(self.two.ndim, 2)
+        assert_equal(self.three.ndim, 3)
+        num = self.two.itemsize
+        assert_equal(self.two.size, 20)
+        assert_equal(self.two.nbytes, 20 * num)
+        assert_equal(self.two.itemsize, self.two.dtype.itemsize)
+        assert_equal(self.two.base, np.arange(20))
+
+    def test_dtypeattr(self):
+        assert_equal(self.one.dtype, np.dtype(np.int_))
+        assert_equal(self.three.dtype, np.dtype(np.float64))
+        assert_equal(self.one.dtype.char, np.dtype(int).char)
+        assert self.one.dtype.char in "lq"
+        assert_equal(self.three.dtype.char, 'd')
+        assert_(self.three.dtype.str[0] in '<>')
+        assert_equal(self.one.dtype.str[1], 'i')
+        assert_equal(self.three.dtype.str[1], 'f')
+
+    def test_int_subclassing(self):
+        # Regression test for https://github.com/numpy/numpy/pull/3526
+
+        numpy_int = np.int_(0)
+
+        # int_ doesn't inherit from Python int, because it's not fixed-width
+        assert_(not isinstance(numpy_int, int))
+
+    def test_stridesattr(self):
+        x = self.one
+
+        def make_array(size, offset, strides):
+            return np.ndarray(size, buffer=x, dtype=int,
+                              offset=offset * x.itemsize,
+                              strides=strides * x.itemsize)
+
+        assert_equal(make_array(4, 4, -1), np.array([4, 3, 2, 1]))
+        assert_raises(ValueError, make_array, 4, 4, -2)
+        assert_raises(ValueError, make_array, 4, 2, -1)
+        assert_raises(ValueError, make_array, 8, 3, 1)
+        assert_equal(make_array(8, 3, 0), np.array([3] * 8))
+        # Check behavior reported in gh-2503:
+        assert_raises(ValueError, make_array, (2, 3), 5, np.array([-2, -3]))
+        make_array(0, 0, 10)
+
+    def test_set_stridesattr(self):
+        x = self.one
+
+        def make_array(size, offset, strides):
+            try:
+                r = np.ndarray([size], dtype=int, buffer=x,
+                               offset=offset * x.itemsize)
+            except Exception as e:
+                raise RuntimeError(e)
+            r.strides = strides = strides * x.itemsize
+            return r
+
+        assert_equal(make_array(4, 4, -1), np.array([4, 3, 2, 1]))
+        assert_equal(make_array(7, 3, 1), np.array([3, 4, 5, 6, 7, 8, 9]))
+        assert_raises(ValueError, make_array, 4, 4, -2)
+        assert_raises(ValueError, make_array, 4, 2, -1)
+        assert_raises(RuntimeError, make_array, 8, 3, 1)
+        # Check that the true extent of the array is used.
+        # Test relies on as_strided base not exposing a buffer.
+        x = np.lib.stride_tricks.as_strided(np.arange(1), (10, 10), (0, 0))
+
+        def set_strides(arr, strides):
+            arr.strides = strides
+
+        assert_raises(ValueError, set_strides, x, (10 * x.itemsize, x.itemsize))
+
+        # Test for offset calculations:
+        x = np.lib.stride_tricks.as_strided(np.arange(10, dtype=np.int8)[-1],
+                                                    shape=(10,), strides=(-1,))
+        assert_raises(ValueError, set_strides, x[::-1], -1)
+        a = x[::-1]
+        a.strides = 1
+        a[::2].strides = 2
+
+        # test 0d
+        arr_0d = np.array(0)
+        arr_0d.strides = ()
+        assert_raises(TypeError, set_strides, arr_0d, None)
+
+    def test_fill(self):
+        for t in "?bhilqpBHILQPfdgFDGO":
+            x = np.empty((3, 2, 1), t)
+            y = np.empty((3, 2, 1), t)
+            x.fill(1)
+            y[...] = 1
+            assert_equal(x, y)
+
+    def test_fill_max_uint64(self):
+        x = np.empty((3, 2, 1), dtype=np.uint64)
+        y = np.empty((3, 2, 1), dtype=np.uint64)
+        value = 2**64 - 1
+        y[...] = value
+        x.fill(value)
+        assert_array_equal(x, y)
+
+    def test_fill_struct_array(self):
+        # Filling from a scalar
+        x = np.array([(0, 0.0), (1, 1.0)], dtype='i4,f8')
+        x.fill(x[0])
+        assert_equal(x['f1'][1], x['f1'][0])
+        # Filling from a tuple that can be converted
+        # to a scalar
+        x = np.zeros(2, dtype=[('a', 'f8'), ('b', 'i4')])
+        x.fill((3.5, -2))
+        assert_array_equal(x['a'], [3.5, 3.5])
+        assert_array_equal(x['b'], [-2, -2])
+
+    def test_fill_readonly(self):
+        # gh-22922
+        a = np.zeros(11)
+        a.setflags(write=False)
+        with pytest.raises(ValueError, match=".*read-only"):
+            a.fill(0)
+
+    def test_fill_subarrays(self):
+        # NOTE:
+        # This is also a regression test for a crash with PYTHONMALLOC=debug
+
+        dtype = np.dtype("2<i8, 2<i8, 2<i8")
+        data = ([1, 2], [3, 4], [5, 6])
+
+        arr = np.empty(1, dtype=dtype)
+        arr.fill(data)
+
+        assert_equal(arr, np.array(data, dtype=dtype))
+
+
+class TestArrayConstruction:
+    def test_array(self):
+        d = np.ones(6)
+        r = np.array([d, d])
+        assert_equal(r, np.ones((2, 6)))
+
+        d = np.ones(6)
+        tgt = np.ones((2, 6))
+        r = np.array([d, d])
+        assert_equal(r, tgt)
+        tgt[1] = 2
+        r = np.array([d, d + 1])
+        assert_equal(r, tgt)
+
+        d = np.ones(6)
+        r = np.array([[d, d]])
+        assert_equal(r, np.ones((1, 2, 6)))
+
+        d = np.ones(6)
+        r = np.array([[d, d], [d, d]])
+        assert_equal(r, np.ones((2, 2, 6)))
+
+        d = np.ones((6, 6))
+        r = np.array([d, d])
+        assert_equal(r, np.ones((2, 6, 6)))
+
+        d = np.ones((6, ))
+        r = np.array([[d, d + 1], d + 2], dtype=object)
+        assert_equal(len(r), 2)
+        assert_equal(r[0], [d, d + 1])
+        assert_equal(r[1], d + 2)
+
+        tgt = np.ones((2, 3), dtype=bool)
+        tgt[0, 2] = False
+        tgt[1, 0:2] = False
+        r = np.array([[True, True, False], [False, False, True]])
+        assert_equal(r, tgt)
+        r = np.array([[True, False], [True, False], [False, True]])
+        assert_equal(r, tgt.T)
+
+    def test_array_empty(self):
+        assert_raises(TypeError, np.array)
+
+    def test_0d_array_shape(self):
+        assert np.ones(np.array(3)).shape == (3,)
+
+    def test_array_copy_false(self):
+        d = np.array([1, 2, 3])
+        e = np.array(d, copy=False)
+        d[1] = 3
+        assert_array_equal(e, [1, 3, 3])
+        np.array(d, copy=False, order='F')
+
+    def test_array_copy_if_needed(self):
+        d = np.array([1, 2, 3])
+        e = np.array(d, copy=None)
+        d[1] = 3
+        assert_array_equal(e, [1, 3, 3])
+        e = np.array(d, copy=None, order='F')
+        d[1] = 4
+        assert_array_equal(e, [1, 4, 3])
+        e[2] = 7
+        assert_array_equal(d, [1, 4, 7])
+
+    def test_array_copy_true(self):
+        d = np.array([[1, 2, 3], [1, 2, 3]])
+        e = np.array(d, copy=True)
+        d[0, 1] = 3
+        e[0, 2] = -7
+        assert_array_equal(e, [[1, 2, -7], [1, 2, 3]])
+        assert_array_equal(d, [[1, 3, 3], [1, 2, 3]])
+        e = np.array(d, copy=True, order='F')
+        d[0, 1] = 5
+        e[0, 2] = 7
+        assert_array_equal(e, [[1, 3, 7], [1, 2, 3]])
+        assert_array_equal(d, [[1, 5, 3], [1, 2, 3]])
+
+    def test_array_copy_str(self):
+        with pytest.raises(
+            ValueError,
+            match="strings are not allowed for 'copy' keyword. "
+                  "Use True/False/None instead."
+        ):
+            np.array([1, 2, 3], copy="always")
+
+    def test_array_cont(self):
+        d = np.ones(10)[::2]
+        assert_(np.ascontiguousarray(d).flags.c_contiguous)
+        assert_(np.ascontiguousarray(d).flags.f_contiguous)
+        assert_(np.asfortranarray(d).flags.c_contiguous)
+        assert_(np.asfortranarray(d).flags.f_contiguous)
+        d = np.ones((10, 10))[::2, ::2]
+        assert_(np.ascontiguousarray(d).flags.c_contiguous)
+        assert_(np.asfortranarray(d).flags.f_contiguous)
+
+    @pytest.mark.parametrize("func",
+            [np.array,
+             np.asarray,
+             np.asanyarray,
+             np.ascontiguousarray,
+             np.asfortranarray])
+    def test_bad_arguments_error(self, func):
+        with pytest.raises(TypeError):
+            func(3, dtype="bad dtype")
+        with pytest.raises(TypeError):
+            func()  # missing arguments
+        with pytest.raises(TypeError):
+            func(1, 2, 3, 4, 5, 6, 7, 8)  # too many arguments
+
+    @pytest.mark.parametrize("func",
+            [np.array,
+             np.asarray,
+             np.asanyarray,
+             np.ascontiguousarray,
+             np.asfortranarray])
+    def test_array_as_keyword(self, func):
+        # This should likely be made positional only, but do not change
+        # the name accidentally.
+        if func is np.array:
+            func(object=3)
+        else:
+            func(a=3)
+
+
+class TestAssignment:
+    def test_assignment_broadcasting(self):
+        a = np.arange(6).reshape(2, 3)
+
+        # Broadcasting the input to the output
+        a[...] = np.arange(3)
+        assert_equal(a, [[0, 1, 2], [0, 1, 2]])
+        a[...] = np.arange(2).reshape(2, 1)
+        assert_equal(a, [[0, 0, 0], [1, 1, 1]])
+
+        # For compatibility with <= 1.5, a limited version of broadcasting
+        # the output to the input.
+        #
+        # This behavior is inconsistent with NumPy broadcasting
+        # in general, because it only uses one of the two broadcasting
+        # rules (adding a new "1" dimension to the left of the shape),
+        # applied to the output instead of an input. In NumPy 2.0, this kind
+        # of broadcasting assignment will likely be disallowed.
+        a[...] = np.arange(6)[::-1].reshape(1, 2, 3)
+        assert_equal(a, [[5, 4, 3], [2, 1, 0]])
+        # The other type of broadcasting would require a reduction operation.
+
+        def assign(a, b):
+            a[...] = b
+
+        assert_raises(ValueError, assign, a, np.arange(12).reshape(2, 2, 3))
+
+    def test_assignment_errors(self):
+        # Address issue #2276
+        class C:
+            pass
+        a = np.zeros(1)
+
+        def assign(v):
+            a[0] = v
+
+        assert_raises((AttributeError, TypeError), assign, C())
+        assert_raises(ValueError, assign, [1])
+
+    @pytest.mark.filterwarnings(
+        "ignore:.*set_string_function.*:DeprecationWarning"
+    )
+    def test_unicode_assignment(self):
+        # gh-5049
+        from numpy._core.arrayprint import set_printoptions
+
+        @contextmanager
+        def inject_str(s):
+            """ replace ndarray.__str__ temporarily """
+            set_printoptions(formatter={"all": lambda x: s})
+            try:
+                yield
+            finally:
+                set_printoptions()
+
+        a1d = np.array(['test'])
+        a0d = np.array('done')
+        with inject_str('bad'):
+            a1d[0] = a0d  # previously this would invoke __str__
+        assert_equal(a1d[0], 'done')
+
+        # this would crash for the same reason
+        np.array([np.array('\xe5\xe4\xf6')])
+
+    def test_stringlike_empty_list(self):
+        # gh-8902
+        u = np.array(['done'])
+        b = np.array([b'done'])
+
+        class bad_sequence:
+            def __getitem__(self, _, /): pass
+            def __len__(self): raise RuntimeError
+
+        assert_raises(ValueError, operator.setitem, u, 0, [])
+        assert_raises(ValueError, operator.setitem, b, 0, [])
+
+        assert_raises(ValueError, operator.setitem, u, 0, bad_sequence())
+        assert_raises(ValueError, operator.setitem, b, 0, bad_sequence())
+
+    def test_longdouble_assignment(self):
+        # only relevant if longdouble is larger than float
+        # we're looking for loss of precision
+
+        for dtype in (np.longdouble, np.clongdouble):
+            # gh-8902
+            tinyb = np.nextafter(np.longdouble(0), 1).astype(dtype)
+            tinya = np.nextafter(np.longdouble(0), -1).astype(dtype)
+
+            # construction
+            tiny1d = np.array([tinya])
+            assert_equal(tiny1d[0], tinya)
+
+            # scalar = scalar
+            tiny1d[0] = tinyb
+            assert_equal(tiny1d[0], tinyb)
+
+            # 0d = scalar
+            tiny1d[0, ...] = tinya
+            assert_equal(tiny1d[0], tinya)
+
+            # 0d = 0d
+            tiny1d[0, ...] = tinyb[...]
+            assert_equal(tiny1d[0], tinyb)
+
+            # scalar = 0d
+            tiny1d[0] = tinyb[...]
+            assert_equal(tiny1d[0], tinyb)
+
+            arr = np.array([np.array(tinya)])
+            assert_equal(arr[0], tinya)
+
+    def test_cast_to_string(self):
+        # cast to str should do "str(scalar)", not "str(scalar.item())"
+        # When converting a float to a string via array assignment, we
+        # want to ensure that the conversion uses str(scalar) to preserve
+        # the expected precision.
+        a = np.zeros(1, dtype='S20')
+        a[:] = np.array(['1.12345678901234567890'], dtype='f8')
+        assert_equal(a[0], b"1.1234567890123457")
+
+
+class TestDtypedescr:
+    def test_construction(self):
+        d1 = np.dtype('i4')
+        assert_equal(d1, np.dtype(np.int32))
+        d2 = np.dtype('f8')
+        assert_equal(d2, np.dtype(np.float64))
+
+    def test_byteorders(self):
+        assert_(np.dtype('<i4') != np.dtype('>i4'))
+        assert_(np.dtype([('a', '<i4')]) != np.dtype([('a', '>i4')]))
+
+    def test_structured_non_void(self):
+        fields = [('a', '<i2'), ('b', '<i2')]
+        dt_int = np.dtype(('i4', fields))
+        assert_equal(str(dt_int), "(numpy.int32, [('a', '<i2'), ('b', '<i2')])")
+
+        # gh-9821
+        arr_int = np.zeros(4, dt_int)
+        assert_equal(repr(arr_int),
+            "array([0, 0, 0, 0], dtype=(numpy.int32, [('a', '<i2'), ('b', '<i2')]))")
+
+
+class TestZeroRank:
+    def setup_method(self):
+        self.d = np.array(0), np.array('x', object)
+
+    def test_ellipsis_subscript(self):
+        a, b = self.d
+        assert_equal(a[...], 0)
+        assert_equal(b[...], 'x')
+        assert_(a[...].base is a)  # `a[...] is a` in numpy <1.9.
+        assert_(b[...].base is b)  # `b[...] is b` in numpy <1.9.
+
+    def test_empty_subscript(self):
+        a, b = self.d
+        assert_equal(a[()], 0)
+        assert_equal(b[()], 'x')
+        assert_(type(a[()]) is a.dtype.type)
+        assert_(type(b[()]) is str)
+
+    def test_invalid_subscript(self):
+        a, b = self.d
+        assert_raises(IndexError, lambda x: x[0], a)
+        assert_raises(IndexError, lambda x: x[0], b)
+        assert_raises(IndexError, lambda x: x[np.array([], int)], a)
+        assert_raises(IndexError, lambda x: x[np.array([], int)], b)
+
+    def test_ellipsis_subscript_assignment(self):
+        a, b = self.d
+        a[...] = 42
+        assert_equal(a, 42)
+        b[...] = ''
+        assert_equal(b.item(), '')
+
+    def test_empty_subscript_assignment(self):
+        a, b = self.d
+        a[()] = 42
+        assert_equal(a, 42)
+        b[()] = ''
+        assert_equal(b.item(), '')
+
+    def test_invalid_subscript_assignment(self):
+        a, b = self.d
+
+        def assign(x, i, v):
+            x[i] = v
+
+        assert_raises(IndexError, assign, a, 0, 42)
+        assert_raises(IndexError, assign, b, 0, '')
+        assert_raises(ValueError, assign, a, (), '')
+
+    def test_newaxis(self):
+        a, b = self.d
+        assert_equal(a[np.newaxis].shape, (1,))
+        assert_equal(a[..., np.newaxis].shape, (1,))
+        assert_equal(a[np.newaxis, ...].shape, (1,))
+        assert_equal(a[..., np.newaxis].shape, (1,))
+        assert_equal(a[np.newaxis, ..., np.newaxis].shape, (1, 1))
+        assert_equal(a[..., np.newaxis, np.newaxis].shape, (1, 1))
+        assert_equal(a[np.newaxis, np.newaxis, ...].shape, (1, 1))
+        assert_equal(a[(np.newaxis,) * 10].shape, (1,) * 10)
+
+    def test_invalid_newaxis(self):
+        a, b = self.d
+
+        def subscript(x, i):
+            x[i]
+
+        assert_raises(IndexError, subscript, a, (np.newaxis, 0))
+        assert_raises(IndexError, subscript, a, (np.newaxis,) * 70)
+
+    def test_constructor(self):
+        x = np.ndarray(())
+        x[()] = 5
+        assert_equal(x[()], 5)
+        y = np.ndarray((), buffer=x)
+        y[()] = 6
+        assert_equal(x[()], 6)
+
+        # strides and shape must be the same length
+        with pytest.raises(ValueError):
+            np.ndarray((2,), strides=())
+        with pytest.raises(ValueError):
+            np.ndarray((), strides=(2,))
+
+    def test_output(self):
+        x = np.array(2)
+        assert_raises(ValueError, np.add, x, [1], x)
+
+    def test_real_imag(self):
+        # contiguity checks are for gh-11245
+        x = np.array(1j)
+        xr = x.real
+        xi = x.imag
+
+        assert_equal(xr, np.array(0))
+        assert_(type(xr) is np.ndarray)
+        assert_equal(xr.flags.contiguous, True)
+        assert_equal(xr.flags.f_contiguous, True)
+
+        assert_equal(xi, np.array(1))
+        assert_(type(xi) is np.ndarray)
+        assert_equal(xi.flags.contiguous, True)
+        assert_equal(xi.flags.f_contiguous, True)
+
+
+class TestScalarIndexing:
+    def setup_method(self):
+        self.d = np.array([0, 1])[0]
+
+    def test_ellipsis_subscript(self):
+        a = self.d
+        assert_equal(a[...], 0)
+        assert_equal(a[...].shape, ())
+
+    def test_empty_subscript(self):
+        a = self.d
+        assert_equal(a[()], 0)
+        assert_equal(a[()].shape, ())
+
+    def test_invalid_subscript(self):
+        a = self.d
+        assert_raises(IndexError, lambda x: x[0], a)
+        assert_raises(IndexError, lambda x: x[np.array([], int)], a)
+
+    def test_invalid_subscript_assignment(self):
+        a = self.d
+
+        def assign(x, i, v):
+            x[i] = v
+
+        assert_raises(TypeError, assign, a, 0, 42)
+
+    def test_newaxis(self):
+        a = self.d
+        assert_equal(a[np.newaxis].shape, (1,))
+        assert_equal(a[..., np.newaxis].shape, (1,))
+        assert_equal(a[np.newaxis, ...].shape, (1,))
+        assert_equal(a[..., np.newaxis].shape, (1,))
+        assert_equal(a[np.newaxis, ..., np.newaxis].shape, (1, 1))
+        assert_equal(a[..., np.newaxis, np.newaxis].shape, (1, 1))
+        assert_equal(a[np.newaxis, np.newaxis, ...].shape, (1, 1))
+        assert_equal(a[(np.newaxis,) * 10].shape, (1,) * 10)
+
+    def test_invalid_newaxis(self):
+        a = self.d
+
+        def subscript(x, i):
+            x[i]
+
+        assert_raises(IndexError, subscript, a, (np.newaxis, 0))
+        assert_raises(IndexError, subscript, a, (np.newaxis,) * 70)
+
+    def test_overlapping_assignment(self):
+        # With positive strides
+        a = np.arange(4)
+        a[:-1] = a[1:]
+        assert_equal(a, [1, 2, 3, 3])
+
+        a = np.arange(4)
+        a[1:] = a[:-1]
+        assert_equal(a, [0, 0, 1, 2])
+
+        # With positive and negative strides
+        a = np.arange(4)
+        a[:] = a[::-1]
+        assert_equal(a, [3, 2, 1, 0])
+
+        a = np.arange(6).reshape(2, 3)
+        a[::-1, :] = a[:, ::-1]
+        assert_equal(a, [[5, 4, 3], [2, 1, 0]])
+
+        a = np.arange(6).reshape(2, 3)
+        a[::-1, ::-1] = a[:, ::-1]
+        assert_equal(a, [[3, 4, 5], [0, 1, 2]])
+
+        # With just one element overlapping
+        a = np.arange(5)
+        a[:3] = a[2:]
+        assert_equal(a, [2, 3, 4, 3, 4])
+
+        a = np.arange(5)
+        a[2:] = a[:3]
+        assert_equal(a, [0, 1, 0, 1, 2])
+
+        a = np.arange(5)
+        a[2::-1] = a[2:]
+        assert_equal(a, [4, 3, 2, 3, 4])
+
+        a = np.arange(5)
+        a[2:] = a[2::-1]
+        assert_equal(a, [0, 1, 2, 1, 0])
+
+        a = np.arange(5)
+        a[2::-1] = a[:1:-1]
+        assert_equal(a, [2, 3, 4, 3, 4])
+
+        a = np.arange(5)
+        a[:1:-1] = a[2::-1]
+        assert_equal(a, [0, 1, 0, 1, 2])
+
+
+class TestCreation:
+    """
+    Test the np.array constructor
+    """
+    def test_from_attribute(self):
+        class x:
+            def __array__(self, dtype=None, copy=None):
+                pass
+
+        assert_raises(ValueError, np.array, x())
+
+    def test_from_string(self):
+        types = np.typecodes['AllInteger'] + np.typecodes['Float']
+        nstr = ['123', '123']
+        result = np.array([123, 123], dtype=int)
+        for type in types:
+            msg = f'String conversion for {type}'
+            assert_equal(np.array(nstr, dtype=type), result, err_msg=msg)
+
+    def test_void(self):
+        arr = np.array([], dtype='V')
+        assert arr.dtype == 'V8'  # current default
+        # Same length scalars (those that go to the same void) work:
+        arr = np.array([b"1234", b"1234"], dtype="V")
+        assert arr.dtype == "V4"
+
+        # Promoting different lengths will fail (pre 1.20 this worked)
+        # by going via S5 and casting to V5.
+        with pytest.raises(TypeError):
+            np.array([b"1234", b"12345"], dtype="V")
+        with pytest.raises(TypeError):
+            np.array([b"12345", b"1234"], dtype="V")
+
+        # Check the same for the casting path:
+        arr = np.array([b"1234", b"1234"], dtype="O").astype("V")
+        assert arr.dtype == "V4"
+        with pytest.raises(TypeError):
+            np.array([b"1234", b"12345"], dtype="O").astype("V")
+
+    @pytest.mark.parametrize("idx",
+            [pytest.param(Ellipsis, id="arr"), pytest.param((), id="scalar")])
+    def test_structured_void_promotion(self, idx):
+        arr = np.array(
+            [np.array(1, dtype="i,i")[idx], np.array(2, dtype='i,i')[idx]],
+            dtype="V")
+        assert_array_equal(arr, np.array([(1, 1), (2, 2)], dtype="i,i"))
+        # The following fails to promote the two dtypes, resulting in an error
+        with pytest.raises(TypeError):
+            np.array(
+                [np.array(1, dtype="i,i")[idx], np.array(2, dtype='i,i,i')[idx]],
+                dtype="V")
+
+    def test_too_big_error(self):
+        # 45341 is the smallest integer greater than sqrt(2**31 - 1).
+        # 3037000500 is the smallest integer greater than sqrt(2**63 - 1).
+        # We want to make sure that the square byte array with those dimensions
+        # is too big on 32 or 64 bit systems respectively.
+        if np.iinfo('intp').max == 2**31 - 1:
+            shape = (46341, 46341)
+        elif np.iinfo('intp').max == 2**63 - 1:
+            shape = (3037000500, 3037000500)
+        else:
+            return
+        assert_raises(ValueError, np.empty, shape, dtype=np.int8)
+        assert_raises(ValueError, np.zeros, shape, dtype=np.int8)
+        assert_raises(ValueError, np.ones, shape, dtype=np.int8)
+
+    @pytest.mark.skipif(not IS_64BIT,
+                        reason="malloc may not fail on 32 bit systems")
+    def test_malloc_fails(self):
+        # This test is guaranteed to fail due to a too large allocation
+        with assert_raises(np._core._exceptions._ArrayMemoryError):
+            np.empty(np.iinfo(np.intp).max, dtype=np.uint8)
+
+    def test_zeros(self):
+        types = np.typecodes['AllInteger'] + np.typecodes['AllFloat']
+        for dt in types:
+            d = np.zeros((13,), dtype=dt)
+            assert_equal(np.count_nonzero(d), 0)
+            # true for ieee floats
+            assert_equal(d.sum(), 0)
+            assert_(not d.any())
+
+            d = np.zeros(2, dtype='(2,4)i4')
+            assert_equal(np.count_nonzero(d), 0)
+            assert_equal(d.sum(), 0)
+            assert_(not d.any())
+
+            d = np.zeros(2, dtype='4i4')
+            assert_equal(np.count_nonzero(d), 0)
+            assert_equal(d.sum(), 0)
+            assert_(not d.any())
+
+            d = np.zeros(2, dtype='(2,4)i4, (2,4)i4')
+            assert_equal(np.count_nonzero(d), 0)
+
+    @pytest.mark.slow
+    def test_zeros_big(self):
+        # test big array as they might be allocated different by the system
+        types = np.typecodes['AllInteger'] + np.typecodes['AllFloat']
+        for dt in types:
+            d = np.zeros((30 * 1024**2,), dtype=dt)
+            assert_(not d.any())
+            # This test can fail on 32-bit systems due to insufficient
+            # contiguous memory. Deallocating the previous array increases the
+            # chance of success.
+            del d
+
+    def test_zeros_obj(self):
+        # test initialization from PyLong(0)
+        d = np.zeros((13,), dtype=object)
+        assert_array_equal(d, [0] * 13)
+        assert_equal(np.count_nonzero(d), 0)
+
+    def test_zeros_obj_obj(self):
+        d = np.zeros(10, dtype=[('k', object, 2)])
+        assert_array_equal(d['k'], 0)
+
+    def test_zeros_like_like_zeros(self):
+        # test zeros_like returns the same as zeros
+        for c in np.typecodes['All']:
+            if c == 'V':
+                continue
+            d = np.zeros((3, 3), dtype=c)
+            assert_array_equal(np.zeros_like(d), d)
+            assert_equal(np.zeros_like(d).dtype, d.dtype)
+        # explicitly check some special cases
+        d = np.zeros((3, 3), dtype='S5')
+        assert_array_equal(np.zeros_like(d), d)
+        assert_equal(np.zeros_like(d).dtype, d.dtype)
+        d = np.zeros((3, 3), dtype='U5')
+        assert_array_equal(np.zeros_like(d), d)
+        assert_equal(np.zeros_like(d).dtype, d.dtype)
+
+        d = np.zeros((3, 3), dtype='<i4')
+        assert_array_equal(np.zeros_like(d), d)
+        assert_equal(np.zeros_like(d).dtype, d.dtype)
+        d = np.zeros((3, 3), dtype='>i4')
+        assert_array_equal(np.zeros_like(d), d)
+        assert_equal(np.zeros_like(d).dtype, d.dtype)
+
+        d = np.zeros((3, 3), dtype='<M8[s]')
+        assert_array_equal(np.zeros_like(d), d)
+        assert_equal(np.zeros_like(d).dtype, d.dtype)
+        d = np.zeros((3, 3), dtype='>M8[s]')
+        assert_array_equal(np.zeros_like(d), d)
+        assert_equal(np.zeros_like(d).dtype, d.dtype)
+
+        d = np.zeros((3, 3), dtype='f4,f4')
+        assert_array_equal(np.zeros_like(d), d)
+        assert_equal(np.zeros_like(d).dtype, d.dtype)
+
+    def test_empty_unicode(self):
+        # don't throw decode errors on garbage memory
+        for i in range(5, 100, 5):
+            d = np.empty(i, dtype='U')
+            str(d)
+
+    def test_sequence_non_homogeneous(self):
+        assert_equal(np.array([4, 2**80]).dtype, object)
+        assert_equal(np.array([4, 2**80, 4]).dtype, object)
+        assert_equal(np.array([2**80, 4]).dtype, object)
+        assert_equal(np.array([2**80] * 3).dtype, object)
+        assert_equal(np.array([[1, 1], [1j, 1j]]).dtype, complex)
+        assert_equal(np.array([[1j, 1j], [1, 1]]).dtype, complex)
+        assert_equal(np.array([[1, 1, 1], [1, 1j, 1.], [1, 1, 1]]).dtype, complex)
+
+    def test_non_sequence_sequence(self):
+        """Should not segfault.
+
+        Class Fail breaks the sequence protocol for new style classes, i.e.,
+        those derived from object. Class Map is a mapping type indicated by
+        raising a ValueError. At some point we may raise a warning instead
+        of an error in the Fail case.
+
+        """
+        class Fail:
+            def __len__(self):
+                return 1
+
+            def __getitem__(self, index):
+                raise ValueError
+
+        class Map:
+            def __len__(self):
+                return 1
+
+            def __getitem__(self, index):
+                raise KeyError
+
+        a = np.array([Map()])
+        assert_(a.shape == (1,))
+        assert_(a.dtype == np.dtype(object))
+        assert_raises(ValueError, np.array, [Fail()])
+
+    def test_no_len_object_type(self):
+        # gh-5100, want object array from iterable object without len()
+        class Point2:
+            def __init__(self):
+                pass
+
+            def __getitem__(self, ind):
+                if ind in [0, 1]:
+                    return ind
+                else:
+                    raise IndexError
+        d = np.array([Point2(), Point2(), Point2()])
+        assert_equal(d.dtype, np.dtype(object))
+
+    def test_false_len_sequence(self):
+        # gh-7264, segfault for this example
+        class C:
+            def __getitem__(self, i):
+                raise IndexError
+
+            def __len__(self):
+                return 42
+
+        a = np.array(C())  # segfault?
+        assert_equal(len(a), 0)
+
+    def test_false_len_iterable(self):
+        # Special case where a bad __getitem__ makes us fall back on __iter__:
+        class C:
+            def __getitem__(self, x):
+                raise Exception
+
+            def __iter__(self):
+                return iter(())
+
+            def __len__(self):
+                return 2
+
+        a = np.empty(2)
+        with assert_raises(ValueError):
+            a[:] = C()  # Segfault!
+
+        np.array(C()) == list(C())
+
+    def test_failed_len_sequence(self):
+        # gh-7393
+        class A:
+            def __init__(self, data):
+                self._data = data
+
+            def __getitem__(self, item):
+                return type(self)(self._data[item])
+
+            def __len__(self):
+                return len(self._data)
+
+        # len(d) should give 3, but len(d[0]) will fail
+        d = A([1, 2, 3])
+        assert_equal(len(np.array(d)), 3)
+
+    def test_array_too_big(self):
+        # Test that array creation succeeds for arrays addressable by intp
+        # on the byte level and fails for too large arrays.
+        buf = np.zeros(100)
+
+        max_bytes = np.iinfo(np.intp).max
+        for dtype in ["intp", "S20", "b"]:
+            dtype = np.dtype(dtype)
+            itemsize = dtype.itemsize
+
+            np.ndarray(buffer=buf, strides=(0,),
+                       shape=(max_bytes // itemsize,), dtype=dtype)
+            assert_raises(ValueError, np.ndarray, buffer=buf, strides=(0,),
+                          shape=(max_bytes // itemsize + 1,), dtype=dtype)
+
+    def _ragged_creation(self, seq):
+        # without dtype=object, the ragged object raises
+        with pytest.raises(ValueError, match=".*detected shape was"):
+            a = np.array(seq)
+
+        return np.array(seq, dtype=object)
+
+    def test_ragged_ndim_object(self):
+        # Lists of mismatching depths are treated as object arrays
+        a = self._ragged_creation([[1], 2, 3])
+        assert_equal(a.shape, (3,))
+        assert_equal(a.dtype, object)
+
+        a = self._ragged_creation([1, [2], 3])
+        assert_equal(a.shape, (3,))
+        assert_equal(a.dtype, object)
+
+        a = self._ragged_creation([1, 2, [3]])
+        assert_equal(a.shape, (3,))
+        assert_equal(a.dtype, object)
+
+    def test_ragged_shape_object(self):
+        # The ragged dimension of a list is turned into an object array
+        a = self._ragged_creation([[1, 1], [2], [3]])
+        assert_equal(a.shape, (3,))
+        assert_equal(a.dtype, object)
+
+        a = self._ragged_creation([[1], [2, 2], [3]])
+        assert_equal(a.shape, (3,))
+        assert_equal(a.dtype, object)
+
+        a = self._ragged_creation([[1], [2], [3, 3]])
+        assert a.shape == (3,)
+        assert a.dtype == object
+
+    def test_array_of_ragged_array(self):
+        outer = np.array([None, None])
+        outer[0] = outer[1] = np.array([1, 2, 3])
+        assert np.array(outer).shape == (2,)
+        assert np.array([outer]).shape == (1, 2)
+
+        outer_ragged = np.array([None, None])
+        outer_ragged[0] = np.array([1, 2, 3])
+        outer_ragged[1] = np.array([1, 2, 3, 4])
+        # should both of these emit deprecation warnings?
+        assert np.array(outer_ragged).shape == (2,)
+        assert np.array([outer_ragged]).shape == (1, 2,)
+
+    def test_deep_nonragged_object(self):
+        # None of these should raise, even though they are missing dtype=object
+        a = np.array([[[Decimal(1)]]])
+        a = np.array([1, Decimal(1)])
+        a = np.array([[1], [Decimal(1)]])
+
+    @pytest.mark.parametrize("dtype", [object, "O,O", "O,(3,)O", "(2,3)O"])
+    @pytest.mark.parametrize("function", [
+            np.ndarray, np.empty,
+            lambda shape, dtype: np.empty_like(np.empty(shape, dtype=dtype))])
+    def test_object_initialized_to_None(self, function, dtype):
+        # NumPy has support for object fields to be NULL (meaning None)
+        # but generally, we should always fill with the proper None, and
+        # downstream may rely on that.  (For fully initialized arrays!)
+        arr = function(3, dtype=dtype)
+        # We expect a fill value of None, which is not NULL:
+        expected = np.array(None).tobytes()
+        expected = expected * (arr.nbytes // len(expected))
+        assert arr.tobytes() == expected
+
+    @pytest.mark.parametrize("func", [
+        np.array, np.asarray, np.asanyarray, np.ascontiguousarray,
+        np.asfortranarray])
+    def test_creation_from_dtypemeta(self, func):
+        dtype = np.dtype('i')
+        arr1 = func([1, 2, 3], dtype=dtype)
+        arr2 = func([1, 2, 3], dtype=type(dtype))
+        assert_array_equal(arr1, arr2)
+        assert arr2.dtype == dtype
+
+
+class TestStructured:
+    def test_subarray_field_access(self):
+        a = np.zeros((3, 5), dtype=[('a', ('i4', (2, 2)))])
+        a['a'] = np.arange(60).reshape(3, 5, 2, 2)
+
+        # Since the subarray is always in C-order, a transpose
+        # does not swap the subarray:
+        assert_array_equal(a.T['a'], a['a'].transpose(1, 0, 2, 3))
+
+        # In Fortran order, the subarray gets appended
+        # like in all other cases, not prepended as a special case
+        b = a.copy(order='F')
+        assert_equal(a['a'].shape, b['a'].shape)
+        assert_equal(a.T['a'].shape, a.T.copy()['a'].shape)
+
+    def test_subarray_comparison(self):
+        # Check that comparisons between record arrays with
+        # multi-dimensional field types work properly
+        a = np.rec.fromrecords(
+            [([1, 2, 3], 'a', [[1, 2], [3, 4]]), ([3, 3, 3], 'b', [[0, 0], [0, 0]])],
+            dtype=[('a', ('f4', 3)), ('b', object), ('c', ('i4', (2, 2)))])
+        b = a.copy()
+        assert_equal(a == b, [True, True])
+        assert_equal(a != b, [False, False])
+        b[1].b = 'c'
+        assert_equal(a == b, [True, False])
+        assert_equal(a != b, [False, True])
+        for i in range(3):
+            b[0].a = a[0].a
+            b[0].a[i] = 5
+            assert_equal(a == b, [False, False])
+            assert_equal(a != b, [True, True])
+        for i in range(2):
+            for j in range(2):
+                b = a.copy()
+                b[0].c[i, j] = 10
+                assert_equal(a == b, [False, True])
+                assert_equal(a != b, [True, False])
+
+        # Check that broadcasting with a subarray works, including cases that
+        # require promotion to work:
+        a = np.array([[(0,)], [(1,)]], dtype=[('a', 'f8')])
+        b = np.array([(0,), (0,), (1,)], dtype=[('a', 'f8')])
+        assert_equal(a == b, [[True, True, False], [False, False, True]])
+        assert_equal(b == a, [[True, True, False], [False, False, True]])
+        a = np.array([[(0,)], [(1,)]], dtype=[('a', 'f8', (1,))])
+        b = np.array([(0,), (0,), (1,)], dtype=[('a', 'f8', (1,))])
+        assert_equal(a == b, [[True, True, False], [False, False, True]])
+        assert_equal(b == a, [[True, True, False], [False, False, True]])
+        a = np.array([[([0, 0],)], [([1, 1],)]], dtype=[('a', 'f8', (2,))])
+        b = np.array([([0, 0],), ([0, 1],), ([1, 1],)], dtype=[('a', 'f8', (2,))])
+        assert_equal(a == b, [[True, False, False], [False, False, True]])
+        assert_equal(b == a, [[True, False, False], [False, False, True]])
+
+        # Check that broadcasting Fortran-style arrays with a subarray work
+        a = np.array([[([0, 0],)], [([1, 1],)]], dtype=[('a', 'f8', (2,))], order='F')
+        b = np.array([([0, 0],), ([0, 1],), ([1, 1],)], dtype=[('a', 'f8', (2,))])
+        assert_equal(a == b, [[True, False, False], [False, False, True]])
+        assert_equal(b == a, [[True, False, False], [False, False, True]])
+
+        # Check that incompatible sub-array shapes don't result to broadcasting
+        x = np.zeros((1,), dtype=[('a', ('f4', (1, 2))), ('b', 'i1')])
+        y = np.zeros((1,), dtype=[('a', ('f4', (2,))), ('b', 'i1')])
+        # The main importance is that it does not return True:
+        with pytest.raises(TypeError):
+            x == y
+
+        x = np.zeros((1,), dtype=[('a', ('f4', (2, 1))), ('b', 'i1')])
+        y = np.zeros((1,), dtype=[('a', ('f4', (2,))), ('b', 'i1')])
+        # The main importance is that it does not return True:
+        with pytest.raises(TypeError):
+            x == y
+
+    def test_empty_structured_array_comparison(self):
+        # Check that comparison works on empty arrays with nontrivially
+        # shaped fields
+        a = np.zeros(0, [('a', '<f8', (1, 1))])
+        assert_equal(a, a)
+        a = np.zeros(0, [('a', '<f8', (1,))])
+        assert_equal(a, a)
+        a = np.zeros((0, 0), [('a', '<f8', (1, 1))])
+        assert_equal(a, a)
+        a = np.zeros((1, 0, 1), [('a', '<f8', (1, 1))])
+        assert_equal(a, a)
+
+    @pytest.mark.parametrize("op", [operator.eq, operator.ne])
+    def test_structured_array_comparison_bad_broadcasts(self, op):
+        a = np.zeros(3, dtype='i,i')
+        b = np.array([], dtype="i,i")
+        with pytest.raises(ValueError):
+            op(a, b)
+
+    def test_structured_comparisons_with_promotion(self):
+        # Check that structured arrays can be compared so long as their
+        # dtypes promote fine:
+        a = np.array([(5, 42), (10, 1)], dtype=[('a', '>i8'), ('b', '<f8')])
+        b = np.array([(5, 43), (10, 1)], dtype=[('a', '<i8'), ('b', '>f8')])
+        assert_equal(a == b, [False, True])
+        assert_equal(a != b, [True, False])
+
+        a = np.array([(5, 42), (10, 1)], dtype=[('a', '>f8'), ('b', '<f8')])
+        b = np.array([(5, 43), (10, 1)], dtype=[('a', '<i8'), ('b', '>i8')])
+        assert_equal(a == b, [False, True])
+        assert_equal(a != b, [True, False])
+
+        # Including with embedded subarray dtype (although subarray comparison
+        # itself may still be a bit weird and compare the raw data)
+        a = np.array([(5, 42), (10, 1)], dtype=[('a', '10>f8'), ('b', '5<f8')])
+        b = np.array([(5, 43), (10, 1)], dtype=[('a', '10<i8'), ('b', '5>i8')])
+        assert_equal(a == b, [False, True])
+        assert_equal(a != b, [True, False])
+
+    @pytest.mark.parametrize("op", [
+            operator.eq, lambda x, y: operator.eq(y, x),
+            operator.ne, lambda x, y: operator.ne(y, x)])
+    def test_void_comparison_failures(self, op):
+        # In principle, one could decide to return an array of False for some
+        # if comparisons are impossible.  But right now we return TypeError
+        # when "void" dtype are involved.
+        x = np.zeros(3, dtype=[('a', 'i1')])
+        y = np.zeros(3)
+        # Cannot compare non-structured to structured:
+        with pytest.raises(TypeError):
+            op(x, y)
+
+        # Added title prevents promotion, but casts are OK:
+        y = np.zeros(3, dtype=[(('title', 'a'), 'i1')])
+        assert np.can_cast(y.dtype, x.dtype)
+        with pytest.raises(TypeError):
+            op(x, y)
+
+        x = np.zeros(3, dtype="V7")
+        y = np.zeros(3, dtype="V8")
+        with pytest.raises(TypeError):
+            op(x, y)
+
+    def test_casting(self):
+        # Check that casting a structured array to change its byte order
+        # works
+        a = np.array([(1,)], dtype=[('a', '<i4')])
+        assert_(np.can_cast(a.dtype, [('a', '>i4')], casting='unsafe'))
+        b = a.astype([('a', '>i4')])
+        a_tmp = a.byteswap()
+        a_tmp = a_tmp.view(a_tmp.dtype.newbyteorder())
+        assert_equal(b, a_tmp)
+        assert_equal(a['a'][0], b['a'][0])
+
+        # Check that equality comparison works on structured arrays if
+        # they are 'equiv'-castable
+        a = np.array([(5, 42), (10, 1)], dtype=[('a', '>i4'), ('b', '<f8')])
+        b = np.array([(5, 42), (10, 1)], dtype=[('a', '<i4'), ('b', '>f8')])
+        assert_(np.can_cast(a.dtype, b.dtype, casting='equiv'))
+        assert_equal(a == b, [True, True])
+
+        # Check that 'equiv' casting can change byte order
+        assert_(np.can_cast(a.dtype, b.dtype, casting='equiv'))
+        c = a.astype(b.dtype, casting='equiv')
+        assert_equal(a == c, [True, True])
+
+        # Check that 'safe' casting can change byte order and up-cast
+        # fields
+        t = [('a', '<i8'), ('b', '>f8')]
+        assert_(np.can_cast(a.dtype, t, casting='safe'))
+        c = a.astype(t, casting='safe')
+        assert_equal((c == np.array([(5, 42), (10, 1)], dtype=t)),
+                     [True, True])
+
+        # Check that 'same_kind' casting can change byte order and
+        # change field widths within a "kind"
+        t = [('a', '<i4'), ('b', '>f4')]
+        assert_(np.can_cast(a.dtype, t, casting='same_kind'))
+        c = a.astype(t, casting='same_kind')
+        assert_equal((c == np.array([(5, 42), (10, 1)], dtype=t)),
+                     [True, True])
+
+        # Check that casting fails if the casting rule should fail on
+        # any of the fields
+        t = [('a', '>i8'), ('b', '<f4')]
+        assert_(not np.can_cast(a.dtype, t, casting='safe'))
+        assert_raises(TypeError, a.astype, t, casting='safe')
+        t = [('a', '>i2'), ('b', '<f8')]
+        assert_(not np.can_cast(a.dtype, t, casting='equiv'))
+        assert_raises(TypeError, a.astype, t, casting='equiv')
+        t = [('a', '>i8'), ('b', '<i2')]
+        assert_(not np.can_cast(a.dtype, t, casting='same_kind'))
+        assert_raises(TypeError, a.astype, t, casting='same_kind')
+        assert_(not np.can_cast(a.dtype, b.dtype, casting='no'))
+        assert_raises(TypeError, a.astype, b.dtype, casting='no')
+
+        # Check that non-'unsafe' casting can't change the set of field names
+        for casting in ['no', 'safe', 'equiv', 'same_kind']:
+            t = [('a', '>i4')]
+            assert_(not np.can_cast(a.dtype, t, casting=casting))
+            t = [('a', '>i4'), ('b', '<f8'), ('c', 'i4')]
+            assert_(not np.can_cast(a.dtype, t, casting=casting))
+
+    def test_objview(self):
+        # https://github.com/numpy/numpy/issues/3286
+        a = np.array([], dtype=[('a', 'f'), ('b', 'f'), ('c', 'O')])
+        a[['a', 'b']]  # TypeError?
+
+        # https://github.com/numpy/numpy/issues/3253
+        dat2 = np.zeros(3, [('A', 'i'), ('B', '|O')])
+        dat2[['B', 'A']]  # TypeError?
+
+    def test_setfield(self):
+        # https://github.com/numpy/numpy/issues/3126
+        struct_dt = np.dtype([('elem', 'i4', 5),])
+        dt = np.dtype([('field', 'i4', 10), ('struct', struct_dt)])
+        x = np.zeros(1, dt)
+        x[0]['field'] = np.ones(10, dtype='i4')
+        x[0]['struct'] = np.ones(1, dtype=struct_dt)
+        assert_equal(x[0]['field'], np.ones(10, dtype='i4'))
+
+    def test_setfield_object(self):
+        # make sure object field assignment with ndarray value
+        # on void scalar mimics setitem behavior
+        b = np.zeros(1, dtype=[('x', 'O')])
+        # next line should work identically to b['x'][0] = np.arange(3)
+        b[0]['x'] = np.arange(3)
+        assert_equal(b[0]['x'], np.arange(3))
+
+        # check that broadcasting check still works
+        c = np.zeros(1, dtype=[('x', 'O', 5)])
+
+        def testassign():
+            c[0]['x'] = np.arange(3)
+
+        assert_raises(ValueError, testassign)
+
+    def test_zero_width_string(self):
+        # Test for PR #6430 / issues #473, #4955, #2585
+
+        dt = np.dtype([('I', int), ('S', 'S0')])
+
+        x = np.zeros(4, dtype=dt)
+
+        assert_equal(x['S'], [b'', b'', b'', b''])
+        assert_equal(x['S'].itemsize, 0)
+
+        x['S'] = ['a', 'b', 'c', 'd']
+        assert_equal(x['S'], [b'', b'', b'', b''])
+        assert_equal(x['I'], [0, 0, 0, 0])
+
+        # Variation on test case from #4955
+        x['S'][x['I'] == 0] = 'hello'
+        assert_equal(x['S'], [b'', b'', b'', b''])
+        assert_equal(x['I'], [0, 0, 0, 0])
+
+        # Variation on test case from #2585
+        x['S'] = 'A'
+        assert_equal(x['S'], [b'', b'', b'', b''])
+        assert_equal(x['I'], [0, 0, 0, 0])
+
+        # Allow zero-width dtypes in ndarray constructor
+        y = np.ndarray(4, dtype=x['S'].dtype)
+        assert_equal(y.itemsize, 0)
+        assert_equal(x['S'], y)
+
+        # More tests for indexing an array with zero-width fields
+        assert_equal(np.zeros(4, dtype=[('a', 'S0,S0'),
+                                        ('b', 'u1')])['a'].itemsize, 0)
+        assert_equal(np.empty(3, dtype='S0,S0').itemsize, 0)
+        assert_equal(np.zeros(4, dtype='S0,u1')['f0'].itemsize, 0)
+
+        xx = x['S'].reshape((2, 2))
+        assert_equal(xx.itemsize, 0)
+        assert_equal(xx, [[b'', b''], [b'', b'']])
+        # check for no uninitialized memory due to viewing S0 array
+        assert_equal(xx[:].dtype, xx.dtype)
+        assert_array_equal(eval(repr(xx), {"np": np, "array": np.array}), xx)
+
+        b = io.BytesIO()
+        np.save(b, xx)
+
+        b.seek(0)
+        yy = np.load(b)
+        assert_equal(yy.itemsize, 0)
+        assert_equal(xx, yy)
+
+        with temppath(suffix='.npy') as tmp:
+            np.save(tmp, xx)
+            yy = np.load(tmp)
+            assert_equal(yy.itemsize, 0)
+            assert_equal(xx, yy)
+
+    def test_base_attr(self):
+        a = np.zeros(3, dtype='i4,f4')
+        b = a[0]
+        assert_(b.base is a)
+
+    def test_assignment(self):
+        def testassign(arr, v):
+            c = arr.copy()
+            c[0] = v  # assign using setitem
+            c[1:] = v  # assign using "dtype_transfer" code paths
+            return c
+
+        dt = np.dtype([('foo', 'i8'), ('bar', 'i8')])
+        arr = np.ones(2, dt)
+        v1 = np.array([(2, 3)], dtype=[('foo', 'i8'), ('bar', 'i8')])
+        v2 = np.array([(2, 3)], dtype=[('bar', 'i8'), ('foo', 'i8')])
+        v3 = np.array([(2, 3)], dtype=[('bar', 'i8'), ('baz', 'i8')])
+        v4 = np.array([(2,)],  dtype=[('bar', 'i8')])
+        v5 = np.array([(2, 3)], dtype=[('foo', 'f8'), ('bar', 'f8')])
+        w = arr.view({'names': ['bar'], 'formats': ['i8'], 'offsets': [8]})
+
+        ans = np.array([(2, 3), (2, 3)], dtype=dt)
+        assert_equal(testassign(arr, v1), ans)
+        assert_equal(testassign(arr, v2), ans)
+        assert_equal(testassign(arr, v3), ans)
+        assert_raises(TypeError, lambda: testassign(arr, v4))
+        assert_equal(testassign(arr, v5), ans)
+        w[:] = 4
+        assert_equal(arr, np.array([(1, 4), (1, 4)], dtype=dt))
+
+        # test field-reordering, assignment by position, and self-assignment
+        a = np.array([(1, 2, 3)],
+                     dtype=[('foo', 'i8'), ('bar', 'i8'), ('baz', 'f4')])
+        a[['foo', 'bar']] = a[['bar', 'foo']]
+        assert_equal(a[0].item(), (2, 1, 3))
+
+        # test that this works even for 'simple_unaligned' structs
+        # (ie, that PyArray_EquivTypes cares about field order too)
+        a = np.array([(1, 2)], dtype=[('a', 'i4'), ('b', 'i4')])
+        a[['a', 'b']] = a[['b', 'a']]
+        assert_equal(a[0].item(), (2, 1))
+
+    def test_structuredscalar_indexing(self):
+        # test gh-7262
+        x = np.empty(shape=1, dtype="(2,)3S,(2,)3U")
+        assert_equal(x[["f0", "f1"]][0], x[0][["f0", "f1"]])
+        assert_equal(x[0], x[0][()])
+
+    def test_multiindex_titles(self):
+        a = np.zeros(4, dtype=[(('a', 'b'), 'i'), ('c', 'i'), ('d', 'i')])
+        assert_raises(KeyError, lambda: a[['a', 'c']])
+        assert_raises(KeyError, lambda: a[['a', 'a']])
+        assert_raises(ValueError, lambda: a[['b', 'b']])  # field exists, but repeated
+        a[['b', 'c']]  # no exception
+
+    def test_structured_cast_promotion_fieldorder(self):
+        # gh-15494
+        # dtypes with different field names are not promotable
+        A = ("a", "<i8")
+        B = ("b", ">i8")
+        ab = np.array([(1, 2)], dtype=[A, B])
+        ba = np.array([(1, 2)], dtype=[B, A])
+        assert_raises(TypeError, np.concatenate, ab, ba)
+        assert_raises(TypeError, np.result_type, ab.dtype, ba.dtype)
+        assert_raises(TypeError, np.promote_types, ab.dtype, ba.dtype)
+
+        # dtypes with same field names/order but different memory offsets
+        # and byte-order are promotable to packed nbo.
+        assert_equal(np.promote_types(ab.dtype, ba[['a', 'b']].dtype),
+                     repack_fields(ab.dtype.newbyteorder('N')))
+
+        # gh-13667
+        # dtypes with different fieldnames but castable field types are castable
+        assert_equal(np.can_cast(ab.dtype, ba.dtype), True)
+        assert_equal(ab.astype(ba.dtype).dtype, ba.dtype)
+        assert_equal(np.can_cast('f8,i8', [('f0', 'f8'), ('f1', 'i8')]), True)
+        assert_equal(np.can_cast('f8,i8', [('f1', 'f8'), ('f0', 'i8')]), True)
+        assert_equal(np.can_cast('f8,i8', [('f1', 'i8'), ('f0', 'f8')]), False)
+        assert_equal(np.can_cast('f8,i8', [('f1', 'i8'), ('f0', 'f8')],
+                                 casting='unsafe'), True)
+
+        ab[:] = ba  # make sure assignment still works
+
+        # tests of type-promotion of corresponding fields
+        dt1 = np.dtype([("", "i4")])
+        dt2 = np.dtype([("", "i8")])
+        assert_equal(np.promote_types(dt1, dt2), np.dtype([('f0', 'i8')]))
+        assert_equal(np.promote_types(dt2, dt1), np.dtype([('f0', 'i8')]))
+        assert_raises(TypeError, np.promote_types, dt1, np.dtype([("", "V3")]))
+        assert_equal(np.promote_types('i4,f8', 'i8,f4'),
+                     np.dtype([('f0', 'i8'), ('f1', 'f8')]))
+        # test nested case
+        dt1nest = np.dtype([("", dt1)])
+        dt2nest = np.dtype([("", dt2)])
+        assert_equal(np.promote_types(dt1nest, dt2nest),
+                     np.dtype([('f0', np.dtype([('f0', 'i8')]))]))
+
+        # note that offsets are lost when promoting:
+        dt = np.dtype({'names': ['x'], 'formats': ['i4'], 'offsets': [8]})
+        a = np.ones(3, dtype=dt)
+        assert_equal(np.concatenate([a, a]).dtype, np.dtype([('x', 'i4')]))
+
+    @pytest.mark.parametrize("dtype_dict", [
+            {"names": ["a", "b"], "formats": ["i4", "f"], "itemsize": 100},
+            {"names": ["a", "b"], "formats": ["i4", "f"],
+                 "offsets": [0, 12]}])
+    @pytest.mark.parametrize("align", [True, False])
+    def test_structured_promotion_packs(self, dtype_dict, align):
+        # Structured dtypes are packed when promoted (we consider the packed
+        # form to be "canonical"), so tere is no extra padding.
+        dtype = np.dtype(dtype_dict, align=align)
+        # Remove non "canonical" dtype options:
+        dtype_dict.pop("itemsize", None)
+        dtype_dict.pop("offsets", None)
+        expected = np.dtype(dtype_dict, align=align)
+
+        res = np.promote_types(dtype, dtype)
+        assert res.itemsize == expected.itemsize
+        assert res.fields == expected.fields
+
+        # But the "expected" one, should just be returned unchanged:
+        res = np.promote_types(expected, expected)
+        assert res is expected
+
+    def test_structured_asarray_is_view(self):
+        # A scalar viewing an array preserves its view even when creating a
+        # new array. This test documents behaviour, it may not be the best
+        # desired behaviour.
+        arr = np.array([1], dtype="i,i")
+        scalar = arr[0]
+        assert not scalar.flags.owndata  # view into the array
+        assert np.asarray(scalar).base is scalar
+        # But never when a dtype is passed in:
+        assert np.asarray(scalar, dtype=scalar.dtype).base is None
+        # A scalar which owns its data does not have this property.
+        # It is not easy to create one, one method is to use pickle:
+        scalar = pickle.loads(pickle.dumps(scalar))
+        assert scalar.flags.owndata
+        assert np.asarray(scalar).base is None
+
+class TestBool:
+    def test_test_interning(self):
+        a0 = np.bool(0)
+        b0 = np.bool(False)
+        assert_(a0 is b0)
+        a1 = np.bool(1)
+        b1 = np.bool(True)
+        assert_(a1 is b1)
+        assert_(np.array([True])[0] is a1)
+        assert_(np.array(True)[()] is a1)
+
+    def test_sum(self):
+        d = np.ones(101, dtype=bool)
+        assert_equal(d.sum(), d.size)
+        assert_equal(d[::2].sum(), d[::2].size)
+        assert_equal(d[::-2].sum(), d[::-2].size)
+
+        d = np.frombuffer(b'\xff\xff' * 100, dtype=bool)
+        assert_equal(d.sum(), d.size)
+        assert_equal(d[::2].sum(), d[::2].size)
+        assert_equal(d[::-2].sum(), d[::-2].size)
+
+    def check_count_nonzero(self, power, length):
+        powers = [2 ** i for i in range(length)]
+        for i in range(2**power):
+            l = [(i & x) != 0 for x in powers]
+            a = np.array(l, dtype=bool)
+            c = builtins.sum(l)
+            assert_equal(np.count_nonzero(a), c)
+            av = a.view(np.uint8)
+            av *= 3
+            assert_equal(np.count_nonzero(a), c)
+            av *= 4
+            assert_equal(np.count_nonzero(a), c)
+            av[av != 0] = 0xFF
+            assert_equal(np.count_nonzero(a), c)
+
+    def test_count_nonzero(self):
+        # check all 12 bit combinations in a length 17 array
+        # covers most cases of the 16 byte unrolled code
+        self.check_count_nonzero(12, 17)
+
+    @pytest.mark.slow
+    def test_count_nonzero_all(self):
+        # check all combinations in a length 17 array
+        # covers all cases of the 16 byte unrolled code
+        self.check_count_nonzero(17, 17)
+
+    def test_count_nonzero_unaligned(self):
+        # prevent mistakes as e.g. gh-4060
+        for o in range(7):
+            a = np.zeros((18,), dtype=bool)[o + 1:]
+            a[:o] = True
+            assert_equal(np.count_nonzero(a), builtins.sum(a.tolist()))
+            a = np.ones((18,), dtype=bool)[o + 1:]
+            a[:o] = False
+            assert_equal(np.count_nonzero(a), builtins.sum(a.tolist()))
+
+    def _test_cast_from_flexible(self, dtype):
+        # empty string -> false
+        for n in range(3):
+            v = np.array(b'', (dtype, n))
+            assert_equal(bool(v), False)
+            assert_equal(bool(v[()]), False)
+            assert_equal(v.astype(bool), False)
+            assert_(isinstance(v.astype(bool), np.ndarray))
+            assert_(v[()].astype(bool) is np.False_)
+
+        # anything else -> true
+        for n in range(1, 4):
+            for val in [b'a', b'0', b' ']:
+                v = np.array(val, (dtype, n))
+                assert_equal(bool(v), True)
+                assert_equal(bool(v[()]), True)
+                assert_equal(v.astype(bool), True)
+                assert_(isinstance(v.astype(bool), np.ndarray))
+                assert_(v[()].astype(bool) is np.True_)
+
+    def test_cast_from_void(self):
+        self._test_cast_from_flexible(np.void)
+
+    @pytest.mark.xfail(reason="See gh-9847")
+    def test_cast_from_unicode(self):
+        self._test_cast_from_flexible(np.str_)
+
+    @pytest.mark.xfail(reason="See gh-9847")
+    def test_cast_from_bytes(self):
+        self._test_cast_from_flexible(np.bytes_)
+
+
+class TestZeroSizeFlexible:
+    @staticmethod
+    def _zeros(shape, dtype=str):
+        dtype = np.dtype(dtype)
+        if dtype == np.void:
+            return np.zeros(shape, dtype=(dtype, 0))
+
+        # not constructable directly
+        dtype = np.dtype([('x', dtype, 0)])
+        return np.zeros(shape, dtype=dtype)['x']
+
+    def test_create(self):
+        zs = self._zeros(10, bytes)
+        assert_equal(zs.itemsize, 0)
+        zs = self._zeros(10, np.void)
+        assert_equal(zs.itemsize, 0)
+        zs = self._zeros(10, str)
+        assert_equal(zs.itemsize, 0)
+
+    def _test_sort_partition(self, name, kinds, **kwargs):
+        # Previously, these would all hang
+        for dt in [bytes, np.void, str]:
+            zs = self._zeros(10, dt)
+            sort_method = getattr(zs, name)
+            sort_func = getattr(np, name)
+            for kind in kinds:
+                sort_method(kind=kind, **kwargs)
+                sort_func(zs, kind=kind, **kwargs)
+
+    def test_sort(self):
+        self._test_sort_partition('sort', kinds='qhs')
+
+    def test_argsort(self):
+        self._test_sort_partition('argsort', kinds='qhs')
+
+    def test_partition(self):
+        self._test_sort_partition('partition', kinds=['introselect'], kth=2)
+
+    def test_argpartition(self):
+        self._test_sort_partition('argpartition', kinds=['introselect'], kth=2)
+
+    def test_resize(self):
+        # previously an error
+        for dt in [bytes, np.void, str]:
+            zs = self._zeros(10, dt)
+            zs.resize(25)
+            zs.resize((10, 10))
+
+    def test_view(self):
+        for dt in [bytes, np.void, str]:
+            zs = self._zeros(10, dt)
+
+            # viewing as itself should be allowed
+            assert_equal(zs.view(dt).dtype, np.dtype(dt))
+
+            # viewing as any non-empty type gives an empty result
+            assert_equal(zs.view((dt, 1)).shape, (0,))
+
+    def test_dumps(self):
+        zs = self._zeros(10, int)
+        assert_equal(zs, pickle.loads(zs.dumps()))
+
+    def test_pickle(self):
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            for dt in [bytes, np.void, str]:
+                zs = self._zeros(10, dt)
+                p = pickle.dumps(zs, protocol=proto)
+                zs2 = pickle.loads(p)
+
+                assert_equal(zs.dtype, zs2.dtype)
+
+    def test_pickle_empty(self):
+        """Checking if an empty array pickled and un-pickled will not cause a
+        segmentation fault"""
+        arr = np.array([]).reshape(999999, 0)
+        pk_dmp = pickle.dumps(arr)
+        pk_load = pickle.loads(pk_dmp)
+
+        assert pk_load.size == 0
+
+    @pytest.mark.skipif(pickle.HIGHEST_PROTOCOL < 5,
+                        reason="requires pickle protocol 5")
+    def test_pickle_with_buffercallback(self):
+        array = np.arange(10)
+        buffers = []
+        bytes_string = pickle.dumps(array, buffer_callback=buffers.append,
+                                    protocol=5)
+        array_from_buffer = pickle.loads(bytes_string, buffers=buffers)
+        # when using pickle protocol 5 with buffer callbacks,
+        # array_from_buffer is reconstructed from a buffer holding a view
+        # to the initial array's data, so modifying an element in array
+        # should modify it in array_from_buffer too.
+        array[0] = -1
+        assert array_from_buffer[0] == -1, array_from_buffer[0]
+
+
+class TestMethods:
+
+    sort_kinds = ['quicksort', 'heapsort', 'stable']
+
+    def test_all_where(self):
+        a = np.array([[True, False, True],
+                      [False, False, False],
+                      [True, True, True]])
+        wh_full = np.array([[True, False, True],
+                            [False, False, False],
+                            [True, False, True]])
+        wh_lower = np.array([[False],
+                             [False],
+                             [True]])
+        for _ax in [0, None]:
+            assert_equal(a.all(axis=_ax, where=wh_lower),
+                        np.all(a[wh_lower[:, 0], :], axis=_ax))
+            assert_equal(np.all(a, axis=_ax, where=wh_lower),
+                         a[wh_lower[:, 0], :].all(axis=_ax))
+
+        assert_equal(a.all(where=wh_full), True)
+        assert_equal(np.all(a, where=wh_full), True)
+        assert_equal(a.all(where=False), True)
+        assert_equal(np.all(a, where=False), True)
+
+    def test_any_where(self):
+        a = np.array([[True, False, True],
+                      [False, False, False],
+                      [True, True, True]])
+        wh_full = np.array([[False, True, False],
+                            [True, True, True],
+                            [False, False, False]])
+        wh_middle = np.array([[False],
+                              [True],
+                              [False]])
+        for _ax in [0, None]:
+            assert_equal(a.any(axis=_ax, where=wh_middle),
+                         np.any(a[wh_middle[:, 0], :], axis=_ax))
+            assert_equal(np.any(a, axis=_ax, where=wh_middle),
+                         a[wh_middle[:, 0], :].any(axis=_ax))
+        assert_equal(a.any(where=wh_full), False)
+        assert_equal(np.any(a, where=wh_full), False)
+        assert_equal(a.any(where=False), False)
+        assert_equal(np.any(a, where=False), False)
+
+    @pytest.mark.parametrize("dtype",
+            ["i8", "U10", "object", "datetime64[ms]"])
+    def test_any_and_all_result_dtype(self, dtype):
+        arr = np.ones(3, dtype=dtype)
+        assert arr.any().dtype == np.bool
+        assert arr.all().dtype == np.bool
+
+    def test_any_and_all_object_dtype(self):
+        # (seberg) Not sure we should even allow dtype here, but it is.
+        arr = np.ones(3, dtype=object)
+        # keepdims to prevent getting a scalar.
+        assert arr.any(dtype=object, keepdims=True).dtype == object
+        assert arr.all(dtype=object, keepdims=True).dtype == object
+
+    def test_compress(self):
+        tgt = [[5, 6, 7, 8, 9]]
+        arr = np.arange(10).reshape(2, 5)
+        out = arr.compress([0, 1], axis=0)
+        assert_equal(out, tgt)
+
+        tgt = [[1, 3], [6, 8]]
+        out = arr.compress([0, 1, 0, 1, 0], axis=1)
+        assert_equal(out, tgt)
+
+        tgt = [[1], [6]]
+        arr = np.arange(10).reshape(2, 5)
+        out = arr.compress([0, 1], axis=1)
+        assert_equal(out, tgt)
+
+        arr = np.arange(10).reshape(2, 5)
+        out = arr.compress([0, 1])
+        assert_equal(out, 1)
+
+    def test_choose(self):
+        x = 2 * np.ones((3,), dtype=int)
+        y = 3 * np.ones((3,), dtype=int)
+        x2 = 2 * np.ones((2, 3), dtype=int)
+        y2 = 3 * np.ones((2, 3), dtype=int)
+        ind = np.array([0, 0, 1])
+
+        A = ind.choose((x, y))
+        assert_equal(A, [2, 2, 3])
+
+        A = ind.choose((x2, y2))
+        assert_equal(A, [[2, 2, 3], [2, 2, 3]])
+
+        A = ind.choose((x, y2))
+        assert_equal(A, [[2, 2, 3], [2, 2, 3]])
+
+        oned = np.ones(1)
+        # gh-12031, caused SEGFAULT
+        assert_raises(TypeError, oned.choose, np.void(0), [oned])
+
+        out = np.array(0)
+        ret = np.choose(np.array(1), [10, 20, 30], out=out)
+        assert out is ret
+        assert_equal(out[()], 20)
+
+        # gh-6272 check overlap on out
+        x = np.arange(5)
+        y = np.choose([0, 0, 0], [x[:3], x[:3], x[:3]], out=x[1:4], mode='wrap')
+        assert_equal(y, np.array([0, 1, 2]))
+
+        # gh_28206 check fail when out not writeable
+        x = np.arange(3)
+        out = np.zeros(3)
+        out.setflags(write=False)
+        assert_raises(ValueError, np.choose, [0, 1, 2], [x, x, x], out=out)
+
+    def test_prod(self):
+        ba = [1, 2, 10, 11, 6, 5, 4]
+        ba2 = [[1, 2, 3, 4], [5, 6, 7, 9], [10, 3, 4, 5]]
+
+        for ctype in [np.int16, np.uint16, np.int32, np.uint32,
+                      np.float32, np.float64, np.complex64, np.complex128]:
+            a = np.array(ba, ctype)
+            a2 = np.array(ba2, ctype)
+            if ctype in ['1', 'b']:
+                assert_raises(ArithmeticError, a.prod)
+                assert_raises(ArithmeticError, a2.prod, axis=1)
+            else:
+                assert_equal(a.prod(axis=0), 26400)
+                assert_array_equal(a2.prod(axis=0),
+                                   np.array([50, 36, 84, 180], ctype))
+                assert_array_equal(a2.prod(axis=-1),
+                                   np.array([24, 1890, 600], ctype))
+
+    @pytest.mark.parametrize('dtype', [None, object])
+    def test_repeat(self, dtype):
+        m = np.array([1, 2, 3, 4, 5, 6], dtype=dtype)
+        m_rect = m.reshape((2, 3))
+
+        A = m.repeat([1, 3, 2, 1, 1, 2])
+        assert_equal(A, [1, 2, 2, 2, 3,
+                         3, 4, 5, 6, 6])
+
+        A = m.repeat(2)
+        assert_equal(A, [1, 1, 2, 2, 3, 3,
+                         4, 4, 5, 5, 6, 6])
+
+        A = m_rect.repeat([2, 1], axis=0)
+        assert_equal(A, [[1, 2, 3],
+                         [1, 2, 3],
+                         [4, 5, 6]])
+
+        A = m_rect.repeat([1, 3, 2], axis=1)
+        assert_equal(A, [[1, 2, 2, 2, 3, 3],
+                         [4, 5, 5, 5, 6, 6]])
+
+        A = m_rect.repeat(2, axis=0)
+        assert_equal(A, [[1, 2, 3],
+                         [1, 2, 3],
+                         [4, 5, 6],
+                         [4, 5, 6]])
+
+        A = m_rect.repeat(2, axis=1)
+        assert_equal(A, [[1, 1, 2, 2, 3, 3],
+                         [4, 4, 5, 5, 6, 6]])
+
+    def test_reshape(self):
+        arr = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
+
+        tgt = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]]
+        assert_equal(arr.reshape(2, 6), tgt)
+
+        tgt = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
+        assert_equal(arr.reshape(3, 4), tgt)
+
+        tgt = [[1, 10, 8, 6], [4, 2, 11, 9], [7, 5, 3, 12]]
+        assert_equal(arr.reshape((3, 4), order='F'), tgt)
+
+        tgt = [[1, 4, 7, 10], [2, 5, 8, 11], [3, 6, 9, 12]]
+        assert_equal(arr.T.reshape((3, 4), order='C'), tgt)
+
+    def test_round(self):
+        def check_round(arr, expected, *round_args):
+            assert_equal(arr.round(*round_args), expected)
+            # With output array
+            out = np.zeros_like(arr)
+            res = arr.round(*round_args, out=out)
+            assert_equal(out, expected)
+            assert out is res
+
+        check_round(np.array([1.2, 1.5]), [1, 2])
+        check_round(np.array(1.5), 2)
+        check_round(np.array([12.2, 15.5]), [10, 20], -1)
+        check_round(np.array([12.15, 15.51]), [12.2, 15.5], 1)
+        # Complex rounding
+        check_round(np.array([4.5 + 1.5j]), [4 + 2j])
+        check_round(np.array([12.5 + 15.5j]), [10 + 20j], -1)
+
+    def test_squeeze(self):
+        a = np.array([[[1], [2], [3]]])
+        assert_equal(a.squeeze(), [1, 2, 3])
+        assert_equal(a.squeeze(axis=(0,)), [[1], [2], [3]])
+        assert_raises(ValueError, a.squeeze, axis=(1,))
+        assert_equal(a.squeeze(axis=(2,)), [[1, 2, 3]])
+
+    def test_transpose(self):
+        a = np.array([[1, 2], [3, 4]])
+        assert_equal(a.transpose(), [[1, 3], [2, 4]])
+        assert_raises(ValueError, lambda: a.transpose(0))
+        assert_raises(ValueError, lambda: a.transpose(0, 0))
+        assert_raises(ValueError, lambda: a.transpose(0, 1, 2))
+
+    def test_sort(self):
+        # test ordering for floats and complex containing nans. It is only
+        # necessary to check the less-than comparison, so sorts that
+        # only follow the insertion sort path are sufficient. We only
+        # test doubles and complex doubles as the logic is the same.
+
+        # check doubles
+        msg = "Test real sort order with nans"
+        a = np.array([np.nan, 1, 0])
+        b = np.sort(a)
+        assert_equal(b, a[::-1], msg)
+        # check complex
+        msg = "Test complex sort order with nans"
+        a = np.zeros(9, dtype=np.complex128)
+        a.real += [np.nan, np.nan, np.nan, 1, 0, 1, 1, 0, 0]
+        a.imag += [np.nan, 1, 0, np.nan, np.nan, 1, 0, 1, 0]
+        b = np.sort(a)
+        assert_equal(b, a[::-1], msg)
+
+        with assert_raises_regex(
+            ValueError,
+            "kind` and `stable` parameters can't be provided at the same time"
+        ):
+            np.sort(a, kind="stable", stable=True)
+
+    # all c scalar sorts use the same code with different types
+    # so it suffices to run a quick check with one type. The number
+    # of sorted items must be greater than ~50 to check the actual
+    # algorithm because quick and merge sort fall over to insertion
+    # sort for small arrays.
+
+    @pytest.mark.parametrize('dtype', [np.uint8, np.uint16, np.uint32, np.uint64,
+                                       np.float16, np.float32, np.float64,
+                                       np.longdouble])
+    def test_sort_unsigned(self, dtype):
+        a = np.arange(101, dtype=dtype)
+        b = a[::-1].copy()
+        for kind in self.sort_kinds:
+            msg = f"scalar sort, kind={kind}"
+            c = a.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+            c = b.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+
+    @pytest.mark.parametrize('dtype',
+                             [np.int8, np.int16, np.int32, np.int64, np.float16,
+                              np.float32, np.float64, np.longdouble])
+    def test_sort_signed(self, dtype):
+        a = np.arange(-50, 51, dtype=dtype)
+        b = a[::-1].copy()
+        for kind in self.sort_kinds:
+            msg = f"scalar sort, kind={kind}"
+            c = a.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+            c = b.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+
+    @pytest.mark.parametrize('dtype', [np.float32, np.float64, np.longdouble])
+    @pytest.mark.parametrize('part', ['real', 'imag'])
+    def test_sort_complex(self, part, dtype):
+        # test complex sorts. These use the same code as the scalars
+        # but the compare function differs.
+        cdtype = {
+            np.single: np.csingle,
+            np.double: np.cdouble,
+            np.longdouble: np.clongdouble,
+        }[dtype]
+        a = np.arange(-50, 51, dtype=dtype)
+        b = a[::-1].copy()
+        ai = (a * (1 + 1j)).astype(cdtype)
+        bi = (b * (1 + 1j)).astype(cdtype)
+        setattr(ai, part, 1)
+        setattr(bi, part, 1)
+        for kind in self.sort_kinds:
+            msg = f"complex sort, {part} part == 1, kind={kind}"
+            c = ai.copy()
+            c.sort(kind=kind)
+            assert_equal(c, ai, msg)
+            c = bi.copy()
+            c.sort(kind=kind)
+            assert_equal(c, ai, msg)
+
+    def test_sort_complex_byte_swapping(self):
+        # test sorting of complex arrays requiring byte-swapping, gh-5441
+        for endianness in '<>':
+            for dt in np.typecodes['Complex']:
+                arr = np.array([1 + 3.j, 2 + 2.j, 3 + 1.j], dtype=endianness + dt)
+                c = arr.copy()
+                c.sort()
+                msg = f'byte-swapped complex sort, dtype={dt}'
+                assert_equal(c, arr, msg)
+
+    @pytest.mark.parametrize('dtype', [np.bytes_, np.str_])
+    def test_sort_string(self, dtype):
+        # np.array will perform the encoding to bytes for us in the bytes test
+        a = np.array(['aaaaaaaa' + chr(i) for i in range(101)], dtype=dtype)
+        b = a[::-1].copy()
+        for kind in self.sort_kinds:
+            msg = f"kind={kind}"
+            c = a.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+            c = b.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+
+    def test_sort_object(self):
+        # test object array sorts.
+        a = np.empty((101,), dtype=object)
+        a[:] = list(range(101))
+        b = a[::-1]
+        for kind in ['q', 'h', 'm']:
+            msg = f"kind={kind}"
+            c = a.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+            c = b.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+
+    @pytest.mark.parametrize("dt", [
+            np.dtype([('f', float), ('i', int)]),
+            np.dtype([('f', float), ('i', object)])])
+    @pytest.mark.parametrize("step", [1, 2])
+    def test_sort_structured(self, dt, step):
+        # test record array sorts.
+        a = np.array([(i, i) for i in range(101 * step)], dtype=dt)
+        b = a[::-1]
+        for kind in ['q', 'h', 'm']:
+            msg = f"kind={kind}"
+            c = a.copy()[::step]
+            indx = c.argsort(kind=kind)
+            c.sort(kind=kind)
+            assert_equal(c, a[::step], msg)
+            assert_equal(a[::step][indx], a[::step], msg)
+            c = b.copy()[::step]
+            indx = c.argsort(kind=kind)
+            c.sort(kind=kind)
+            assert_equal(c, a[step - 1::step], msg)
+            assert_equal(b[::step][indx], a[step - 1::step], msg)
+
+    @pytest.mark.parametrize('dtype', ['datetime64[D]', 'timedelta64[D]'])
+    def test_sort_time(self, dtype):
+        # test datetime64 and timedelta64 sorts.
+        a = np.arange(0, 101, dtype=dtype)
+        b = a[::-1]
+        for kind in ['q', 'h', 'm']:
+            msg = f"kind={kind}"
+            c = a.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+            c = b.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+
+    def test_sort_axis(self):
+        # check axis handling. This should be the same for all type
+        # specific sorts, so we only check it for one type and one kind
+        a = np.array([[3, 2], [1, 0]])
+        b = np.array([[1, 0], [3, 2]])
+        c = np.array([[2, 3], [0, 1]])
+        d = a.copy()
+        d.sort(axis=0)
+        assert_equal(d, b, "test sort with axis=0")
+        d = a.copy()
+        d.sort(axis=1)
+        assert_equal(d, c, "test sort with axis=1")
+        d = a.copy()
+        d.sort()
+        assert_equal(d, c, "test sort with default axis")
+
+    def test_sort_size_0(self):
+        # check axis handling for multidimensional empty arrays
+        a = np.array([])
+        a.shape = (3, 2, 1, 0)
+        for axis in range(-a.ndim, a.ndim):
+            msg = f'test empty array sort with axis={axis}'
+            assert_equal(np.sort(a, axis=axis), a, msg)
+        msg = 'test empty array sort with axis=None'
+        assert_equal(np.sort(a, axis=None), a.ravel(), msg)
+
+    def test_sort_bad_ordering(self):
+        # test generic class with bogus ordering,
+        # should not segfault.
+        class Boom:
+            def __lt__(self, other):
+                return True
+
+        a = np.array([Boom()] * 100, dtype=object)
+        for kind in self.sort_kinds:
+            msg = f"kind={kind}"
+            c = a.copy()
+            c.sort(kind=kind)
+            assert_equal(c, a, msg)
+
+    def test_void_sort(self):
+        # gh-8210 - previously segfaulted
+        for i in range(4):
+            rand = np.random.randint(256, size=4000, dtype=np.uint8)
+            arr = rand.view('V4')
+            arr[::-1].sort()
+
+        dt = np.dtype([('val', 'i4', (1,))])
+        for i in range(4):
+            rand = np.random.randint(256, size=4000, dtype=np.uint8)
+            arr = rand.view(dt)
+            arr[::-1].sort()
+
+    def test_sort_raises(self):
+        # gh-9404
+        arr = np.array([0, datetime.now(), 1], dtype=object)
+        for kind in self.sort_kinds:
+            assert_raises(TypeError, arr.sort, kind=kind)
+        # gh-3879
+
+        class Raiser:
+            def raises_anything(*args, **kwargs):
+                raise TypeError("SOMETHING ERRORED")
+            __eq__ = __ne__ = __lt__ = __gt__ = __ge__ = __le__ = raises_anything
+        arr = np.array([[Raiser(), n] for n in range(10)]).reshape(-1)
+        np.random.shuffle(arr)
+        for kind in self.sort_kinds:
+            assert_raises(TypeError, arr.sort, kind=kind)
+
+    def test_sort_degraded(self):
+        # test degraded dataset would take minutes to run with normal qsort
+        d = np.arange(1000000)
+        do = d.copy()
+        x = d
+        # create a median of 3 killer where each median is the sorted second
+        # last element of the quicksort partition
+        while x.size > 3:
+            mid = x.size // 2
+            x[mid], x[-2] = x[-2], x[mid]
+            x = x[:-2]
+
+        assert_equal(np.sort(d), do)
+        assert_equal(d[np.argsort(d)], do)
+
+    def test_copy(self):
+        def assert_fortran(arr):
+            assert_(arr.flags.fortran)
+            assert_(arr.flags.f_contiguous)
+            assert_(not arr.flags.c_contiguous)
+
+        def assert_c(arr):
+            assert_(not arr.flags.fortran)
+            assert_(not arr.flags.f_contiguous)
+            assert_(arr.flags.c_contiguous)
+
+        a = np.empty((2, 2), order='F')
+        # Test copying a Fortran array
+        assert_c(a.copy())
+        assert_c(a.copy('C'))
+        assert_fortran(a.copy('F'))
+        assert_fortran(a.copy('A'))
+
+        # Now test starting with a C array.
+        a = np.empty((2, 2), order='C')
+        assert_c(a.copy())
+        assert_c(a.copy('C'))
+        assert_fortran(a.copy('F'))
+        assert_c(a.copy('A'))
+
+    @pytest.mark.parametrize("dtype", ['O', np.int32, 'i,O'])
+    def test__deepcopy__(self, dtype):
+        # Force the entry of NULLs into array
+        a = np.empty(4, dtype=dtype)
+        ctypes.memset(a.ctypes.data, 0, a.nbytes)
+
+        # Ensure no error is raised, see gh-21833
+        b = a.__deepcopy__({})
+
+        a[0] = 42
+        with pytest.raises(AssertionError):
+            assert_array_equal(a, b)
+
+    def test__deepcopy__catches_failure(self):
+        class MyObj:
+            def __deepcopy__(self, *args, **kwargs):
+                raise RuntimeError
+
+        arr = np.array([1, MyObj(), 3], dtype='O')
+        with pytest.raises(RuntimeError):
+            arr.__deepcopy__({})
+
+    def test_sort_order(self):
+        # Test sorting an array with fields
+        x1 = np.array([21, 32, 14])
+        x2 = np.array(['my', 'first', 'name'])
+        x3 = np.array([3.1, 4.5, 6.2])
+        r = np.rec.fromarrays([x1, x2, x3], names='id,word,number')
+
+        r.sort(order=['id'])
+        assert_equal(r.id, np.array([14, 21, 32]))
+        assert_equal(r.word, np.array(['name', 'my', 'first']))
+        assert_equal(r.number, np.array([6.2, 3.1, 4.5]))
+
+        r.sort(order=['word'])
+        assert_equal(r.id, np.array([32, 21, 14]))
+        assert_equal(r.word, np.array(['first', 'my', 'name']))
+        assert_equal(r.number, np.array([4.5, 3.1, 6.2]))
+
+        r.sort(order=['number'])
+        assert_equal(r.id, np.array([21, 32, 14]))
+        assert_equal(r.word, np.array(['my', 'first', 'name']))
+        assert_equal(r.number, np.array([3.1, 4.5, 6.2]))
+
+        assert_raises_regex(ValueError, 'duplicate',
+            lambda: r.sort(order=['id', 'id']))
+
+        if sys.byteorder == 'little':
+            strtype = '>i2'
+        else:
+            strtype = '<i2'
+        mydtype = [('name', 'U5'), ('col2', strtype)]
+        r = np.array([('a', 1), ('b', 255), ('c', 3), ('d', 258)],
+                     dtype=mydtype)
+        r.sort(order='col2')
+        assert_equal(r['col2'], [1, 3, 255, 258])
+        assert_equal(r, np.array([('a', 1), ('c', 3), ('b', 255), ('d', 258)],
+                                 dtype=mydtype))
+
+    def test_argsort(self):
+        # all c scalar argsorts use the same code with different types
+        # so it suffices to run a quick check with one type. The number
+        # of sorted items must be greater than ~50 to check the actual
+        # algorithm because quick and merge sort fall over to insertion
+        # sort for small arrays.
+
+        for dtype in [np.int32, np.uint32, np.float32]:
+            a = np.arange(101, dtype=dtype)
+            b = a[::-1].copy()
+            for kind in self.sort_kinds:
+                msg = f"scalar argsort, kind={kind}, dtype={dtype}"
+                assert_equal(a.copy().argsort(kind=kind), a, msg)
+                assert_equal(b.copy().argsort(kind=kind), b, msg)
+
+        # test complex argsorts. These use the same code as the scalars
+        # but the compare function differs.
+        ai = a * 1j + 1
+        bi = b * 1j + 1
+        for kind in self.sort_kinds:
+            msg = f"complex argsort, kind={kind}"
+            assert_equal(ai.copy().argsort(kind=kind), a, msg)
+            assert_equal(bi.copy().argsort(kind=kind), b, msg)
+        ai = a + 1j
+        bi = b + 1j
+        for kind in self.sort_kinds:
+            msg = f"complex argsort, kind={kind}"
+            assert_equal(ai.copy().argsort(kind=kind), a, msg)
+            assert_equal(bi.copy().argsort(kind=kind), b, msg)
+
+        # test argsort of complex arrays requiring byte-swapping, gh-5441
+        for endianness in '<>':
+            for dt in np.typecodes['Complex']:
+                arr = np.array([1 + 3.j, 2 + 2.j, 3 + 1.j], dtype=endianness + dt)
+                msg = f'byte-swapped complex argsort, dtype={dt}'
+                assert_equal(arr.argsort(),
+                             np.arange(len(arr), dtype=np.intp), msg)
+
+        # test string argsorts.
+        s = 'aaaaaaaa'
+        a = np.array([s + chr(i) for i in range(101)])
+        b = a[::-1].copy()
+        r = np.arange(101)
+        rr = r[::-1]
+        for kind in self.sort_kinds:
+            msg = f"string argsort, kind={kind}"
+            assert_equal(a.copy().argsort(kind=kind), r, msg)
+            assert_equal(b.copy().argsort(kind=kind), rr, msg)
+
+        # test unicode argsorts.
+        s = 'aaaaaaaa'
+        a = np.array([s + chr(i) for i in range(101)], dtype=np.str_)
+        b = a[::-1]
+        r = np.arange(101)
+        rr = r[::-1]
+        for kind in self.sort_kinds:
+            msg = f"unicode argsort, kind={kind}"
+            assert_equal(a.copy().argsort(kind=kind), r, msg)
+            assert_equal(b.copy().argsort(kind=kind), rr, msg)
+
+        # test object array argsorts.
+        a = np.empty((101,), dtype=object)
+        a[:] = list(range(101))
+        b = a[::-1]
+        r = np.arange(101)
+        rr = r[::-1]
+        for kind in self.sort_kinds:
+            msg = f"object argsort, kind={kind}"
+            assert_equal(a.copy().argsort(kind=kind), r, msg)
+            assert_equal(b.copy().argsort(kind=kind), rr, msg)
+
+        # test structured array argsorts.
+        dt = np.dtype([('f', float), ('i', int)])
+        a = np.array([(i, i) for i in range(101)], dtype=dt)
+        b = a[::-1]
+        r = np.arange(101)
+        rr = r[::-1]
+        for kind in self.sort_kinds:
+            msg = f"structured array argsort, kind={kind}"
+            assert_equal(a.copy().argsort(kind=kind), r, msg)
+            assert_equal(b.copy().argsort(kind=kind), rr, msg)
+
+        # test datetime64 argsorts.
+        a = np.arange(0, 101, dtype='datetime64[D]')
+        b = a[::-1]
+        r = np.arange(101)
+        rr = r[::-1]
+        for kind in ['q', 'h', 'm']:
+            msg = f"datetime64 argsort, kind={kind}"
+            assert_equal(a.copy().argsort(kind=kind), r, msg)
+            assert_equal(b.copy().argsort(kind=kind), rr, msg)
+
+        # test timedelta64 argsorts.
+        a = np.arange(0, 101, dtype='timedelta64[D]')
+        b = a[::-1]
+        r = np.arange(101)
+        rr = r[::-1]
+        for kind in ['q', 'h', 'm']:
+            msg = f"timedelta64 argsort, kind={kind}"
+            assert_equal(a.copy().argsort(kind=kind), r, msg)
+            assert_equal(b.copy().argsort(kind=kind), rr, msg)
+
+        # check axis handling. This should be the same for all type
+        # specific argsorts, so we only check it for one type and one kind
+        a = np.array([[3, 2], [1, 0]])
+        b = np.array([[1, 1], [0, 0]])
+        c = np.array([[1, 0], [1, 0]])
+        assert_equal(a.copy().argsort(axis=0), b)
+        assert_equal(a.copy().argsort(axis=1), c)
+        assert_equal(a.copy().argsort(), c)
+
+        # check axis handling for multidimensional empty arrays
+        a = np.array([])
+        a.shape = (3, 2, 1, 0)
+        for axis in range(-a.ndim, a.ndim):
+            msg = f'test empty array argsort with axis={axis}'
+            assert_equal(np.argsort(a, axis=axis),
+                         np.zeros_like(a, dtype=np.intp), msg)
+        msg = 'test empty array argsort with axis=None'
+        assert_equal(np.argsort(a, axis=None),
+                     np.zeros_like(a.ravel(), dtype=np.intp), msg)
+
+        # check that stable argsorts are stable
+        r = np.arange(100)
+        # scalars
+        a = np.zeros(100)
+        assert_equal(a.argsort(kind='m'), r)
+        # complex
+        a = np.zeros(100, dtype=complex)
+        assert_equal(a.argsort(kind='m'), r)
+        # string
+        a = np.array(['aaaaaaaaa' for i in range(100)])
+        assert_equal(a.argsort(kind='m'), r)
+        # unicode
+        a = np.array(['aaaaaaaaa' for i in range(100)], dtype=np.str_)
+        assert_equal(a.argsort(kind='m'), r)
+
+        with assert_raises_regex(
+            ValueError,
+            "kind` and `stable` parameters can't be provided at the same time"
+        ):
+            np.argsort(a, kind="stable", stable=True)
+
+    def test_sort_unicode_kind(self):
+        d = np.arange(10)
+        k = b'\xc3\xa4'.decode("UTF8")
+        assert_raises(ValueError, d.sort, kind=k)
+        assert_raises(ValueError, d.argsort, kind=k)
+
+    @pytest.mark.parametrize('a', [
+        np.array([0, 1, np.nan], dtype=np.float16),
+        np.array([0, 1, np.nan], dtype=np.float32),
+        np.array([0, 1, np.nan]),
+    ])
+    def test_searchsorted_floats(self, a):
+        # test for floats arrays containing nans. Explicitly test
+        # half, single, and double precision floats to verify that
+        # the NaN-handling is correct.
+        msg = f"Test real ({a.dtype}) searchsorted with nans, side='l'"
+        b = a.searchsorted(a, side='left')
+        assert_equal(b, np.arange(3), msg)
+        msg = f"Test real ({a.dtype}) searchsorted with nans, side='r'"
+        b = a.searchsorted(a, side='right')
+        assert_equal(b, np.arange(1, 4), msg)
+        # check keyword arguments
+        a.searchsorted(v=1)
+        x = np.array([0, 1, np.nan], dtype='float32')
+        y = np.searchsorted(x, x[-1])
+        assert_equal(y, 2)
+
+    def test_searchsorted_complex(self):
+        # test for complex arrays containing nans.
+        # The search sorted routines use the compare functions for the
+        # array type, so this checks if that is consistent with the sort
+        # order.
+        # check double complex
+        a = np.zeros(9, dtype=np.complex128)
+        a.real += [0, 0, 1, 1, 0, 1, np.nan, np.nan, np.nan]
+        a.imag += [0, 1, 0, 1, np.nan, np.nan, 0, 1, np.nan]
+        msg = "Test complex searchsorted with nans, side='l'"
+        b = a.searchsorted(a, side='left')
+        assert_equal(b, np.arange(9), msg)
+        msg = "Test complex searchsorted with nans, side='r'"
+        b = a.searchsorted(a, side='right')
+        assert_equal(b, np.arange(1, 10), msg)
+        msg = "Test searchsorted with little endian, side='l'"
+        a = np.array([0, 128], dtype='<i4')
+        b = a.searchsorted(np.array(128, dtype='<i4'))
+        assert_equal(b, 1, msg)
+        msg = "Test searchsorted with big endian, side='l'"
+        a = np.array([0, 128], dtype='>i4')
+        b = a.searchsorted(np.array(128, dtype='>i4'))
+        assert_equal(b, 1, msg)
+
+    def test_searchsorted_n_elements(self):
+        # Check 0 elements
+        a = np.ones(0)
+        b = a.searchsorted([0, 1, 2], 'left')
+        assert_equal(b, [0, 0, 0])
+        b = a.searchsorted([0, 1, 2], 'right')
+        assert_equal(b, [0, 0, 0])
+        a = np.ones(1)
+        # Check 1 element
+        b = a.searchsorted([0, 1, 2], 'left')
+        assert_equal(b, [0, 0, 1])
+        b = a.searchsorted([0, 1, 2], 'right')
+        assert_equal(b, [0, 1, 1])
+        # Check all elements equal
+        a = np.ones(2)
+        b = a.searchsorted([0, 1, 2], 'left')
+        assert_equal(b, [0, 0, 2])
+        b = a.searchsorted([0, 1, 2], 'right')
+        assert_equal(b, [0, 2, 2])
+
+    def test_searchsorted_unaligned_array(self):
+        # Test searching unaligned array
+        a = np.arange(10)
+        aligned = np.empty(a.itemsize * a.size + 1, 'uint8')
+        unaligned = aligned[1:].view(a.dtype)
+        unaligned[:] = a
+        # Test searching unaligned array
+        b = unaligned.searchsorted(a, 'left')
+        assert_equal(b, a)
+        b = unaligned.searchsorted(a, 'right')
+        assert_equal(b, a + 1)
+        # Test searching for unaligned keys
+        b = a.searchsorted(unaligned, 'left')
+        assert_equal(b, a)
+        b = a.searchsorted(unaligned, 'right')
+        assert_equal(b, a + 1)
+
+    def test_searchsorted_resetting(self):
+        # Test smart resetting of binsearch indices
+        a = np.arange(5)
+        b = a.searchsorted([6, 5, 4], 'left')
+        assert_equal(b, [5, 5, 4])
+        b = a.searchsorted([6, 5, 4], 'right')
+        assert_equal(b, [5, 5, 5])
+
+    def test_searchsorted_type_specific(self):
+        # Test all type specific binary search functions
+        types = ''.join((np.typecodes['AllInteger'], np.typecodes['AllFloat'],
+                         np.typecodes['Datetime'], '?O'))
+        for dt in types:
+            if dt == 'M':
+                dt = 'M8[D]'
+            if dt == '?':
+                a = np.arange(2, dtype=dt)
+                out = np.arange(2)
+            else:
+                a = np.arange(0, 5, dtype=dt)
+                out = np.arange(5)
+            b = a.searchsorted(a, 'left')
+            assert_equal(b, out)
+            b = a.searchsorted(a, 'right')
+            assert_equal(b, out + 1)
+            # Test empty array, use a fresh array to get warnings in
+            # valgrind if access happens.
+            e = np.ndarray(shape=0, buffer=b'', dtype=dt)
+            b = e.searchsorted(a, 'left')
+            assert_array_equal(b, np.zeros(len(a), dtype=np.intp))
+            b = a.searchsorted(e, 'left')
+            assert_array_equal(b, np.zeros(0, dtype=np.intp))
+
+    def test_searchsorted_unicode(self):
+        # Test searchsorted on unicode strings.
+
+        # 1.6.1 contained a string length miscalculation in
+        # arraytypes.c.src:UNICODE_compare() which manifested as
+        # incorrect/inconsistent results from searchsorted.
+        a = np.array(['P:\\20x_dapi_cy3\\20x_dapi_cy3_20100185_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100186_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100187_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100189_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100190_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100191_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100192_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100193_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100194_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100195_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100196_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100197_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100198_1',
+                      'P:\\20x_dapi_cy3\\20x_dapi_cy3_20100199_1'],
+                     dtype=np.str_)
+        ind = np.arange(len(a))
+        assert_equal([a.searchsorted(v, 'left') for v in a], ind)
+        assert_equal([a.searchsorted(v, 'right') for v in a], ind + 1)
+        assert_equal([a.searchsorted(a[i], 'left') for i in ind], ind)
+        assert_equal([a.searchsorted(a[i], 'right') for i in ind], ind + 1)
+
+    def test_searchsorted_with_invalid_sorter(self):
+        a = np.array([5, 2, 1, 3, 4])
+        s = np.argsort(a)
+        assert_raises(TypeError, np.searchsorted, a, 0,
+                      sorter=np.array((1, (2, 3)), dtype=object))
+        assert_raises(TypeError, np.searchsorted, a, 0, sorter=[1.1])
+        assert_raises(ValueError, np.searchsorted, a, 0, sorter=[1, 2, 3, 4])
+        assert_raises(ValueError, np.searchsorted, a, 0, sorter=[1, 2, 3, 4, 5, 6])
+
+        # bounds check
+        assert_raises(ValueError, np.searchsorted, a, 4, sorter=[0, 1, 2, 3, 5])
+        assert_raises(ValueError, np.searchsorted, a, 0, sorter=[-1, 0, 1, 2, 3])
+        assert_raises(ValueError, np.searchsorted, a, 0, sorter=[4, 0, -1, 2, 3])
+
+    def test_searchsorted_with_sorter(self):
+        a = np.random.rand(300)
+        s = a.argsort()
+        b = np.sort(a)
+        k = np.linspace(0, 1, 20)
+        assert_equal(b.searchsorted(k), a.searchsorted(k, sorter=s))
+
+        a = np.array([0, 1, 2, 3, 5] * 20)
+        s = a.argsort()
+        k = [0, 1, 2, 3, 5]
+        expected = [0, 20, 40, 60, 80]
+        assert_equal(a.searchsorted(k, side='left', sorter=s), expected)
+        expected = [20, 40, 60, 80, 100]
+        assert_equal(a.searchsorted(k, side='right', sorter=s), expected)
+
+        # Test searching unaligned array
+        keys = np.arange(10)
+        a = keys.copy()
+        np.random.shuffle(s)
+        s = a.argsort()
+        aligned = np.empty(a.itemsize * a.size + 1, 'uint8')
+        unaligned = aligned[1:].view(a.dtype)
+        # Test searching unaligned array
+        unaligned[:] = a
+        b = unaligned.searchsorted(keys, 'left', s)
+        assert_equal(b, keys)
+        b = unaligned.searchsorted(keys, 'right', s)
+        assert_equal(b, keys + 1)
+        # Test searching for unaligned keys
+        unaligned[:] = keys
+        b = a.searchsorted(unaligned, 'left', s)
+        assert_equal(b, keys)
+        b = a.searchsorted(unaligned, 'right', s)
+        assert_equal(b, keys + 1)
+
+        # Test all type specific indirect binary search functions
+        types = ''.join((np.typecodes['AllInteger'], np.typecodes['AllFloat'],
+                         np.typecodes['Datetime'], '?O'))
+        for dt in types:
+            if dt == 'M':
+                dt = 'M8[D]'
+            if dt == '?':
+                a = np.array([1, 0], dtype=dt)
+                # We want the sorter array to be of a type that is different
+                # from np.intp in all platforms, to check for #4698
+                s = np.array([1, 0], dtype=np.int16)
+                out = np.array([1, 0])
+            else:
+                a = np.array([3, 4, 1, 2, 0], dtype=dt)
+                # We want the sorter array to be of a type that is different
+                # from np.intp in all platforms, to check for #4698
+                s = np.array([4, 2, 3, 0, 1], dtype=np.int16)
+                out = np.array([3, 4, 1, 2, 0], dtype=np.intp)
+            b = a.searchsorted(a, 'left', s)
+            assert_equal(b, out)
+            b = a.searchsorted(a, 'right', s)
+            assert_equal(b, out + 1)
+            # Test empty array, use a fresh array to get warnings in
+            # valgrind if access happens.
+            e = np.ndarray(shape=0, buffer=b'', dtype=dt)
+            b = e.searchsorted(a, 'left', s[:0])
+            assert_array_equal(b, np.zeros(len(a), dtype=np.intp))
+            b = a.searchsorted(e, 'left', s)
+            assert_array_equal(b, np.zeros(0, dtype=np.intp))
+
+        # Test non-contiguous sorter array
+        a = np.array([3, 4, 1, 2, 0])
+        srt = np.empty((10,), dtype=np.intp)
+        srt[1::2] = -1
+        srt[::2] = [4, 2, 3, 0, 1]
+        s = srt[::2]
+        out = np.array([3, 4, 1, 2, 0], dtype=np.intp)
+        b = a.searchsorted(a, 'left', s)
+        assert_equal(b, out)
+        b = a.searchsorted(a, 'right', s)
+        assert_equal(b, out + 1)
+
+    def test_searchsorted_return_type(self):
+        # Functions returning indices should always return base ndarrays
+        class A(np.ndarray):
+            pass
+        a = np.arange(5).view(A)
+        b = np.arange(1, 3).view(A)
+        s = np.arange(5).view(A)
+        assert_(not isinstance(a.searchsorted(b, 'left'), A))
+        assert_(not isinstance(a.searchsorted(b, 'right'), A))
+        assert_(not isinstance(a.searchsorted(b, 'left', s), A))
+        assert_(not isinstance(a.searchsorted(b, 'right', s), A))
+
+    @pytest.mark.parametrize("dtype", np.typecodes["All"])
+    def test_argpartition_out_of_range(self, dtype):
+        # Test out of range values in kth raise an error, gh-5469
+        d = np.arange(10).astype(dtype=dtype)
+        assert_raises(ValueError, d.argpartition, 10)
+        assert_raises(ValueError, d.argpartition, -11)
+
+    @pytest.mark.parametrize("dtype", np.typecodes["All"])
+    def test_partition_out_of_range(self, dtype):
+        # Test out of range values in kth raise an error, gh-5469
+        d = np.arange(10).astype(dtype=dtype)
+        assert_raises(ValueError, d.partition, 10)
+        assert_raises(ValueError, d.partition, -11)
+
+    def test_argpartition_integer(self):
+        # Test non-integer values in kth raise an error/
+        d = np.arange(10)
+        assert_raises(TypeError, d.argpartition, 9.)
+        # Test also for generic type argpartition, which uses sorting
+        # and used to not bound check kth
+        d_obj = np.arange(10, dtype=object)
+        assert_raises(TypeError, d_obj.argpartition, 9.)
+
+    def test_partition_integer(self):
+        # Test out of range values in kth raise an error, gh-5469
+        d = np.arange(10)
+        assert_raises(TypeError, d.partition, 9.)
+        # Test also for generic type partition, which uses sorting
+        # and used to not bound check kth
+        d_obj = np.arange(10, dtype=object)
+        assert_raises(TypeError, d_obj.partition, 9.)
+
+    @pytest.mark.parametrize("kth_dtype", np.typecodes["AllInteger"])
+    def test_partition_empty_array(self, kth_dtype):
+        # check axis handling for multidimensional empty arrays
+        kth = np.array(0, dtype=kth_dtype)[()]
+        a = np.array([])
+        a.shape = (3, 2, 1, 0)
+        for axis in range(-a.ndim, a.ndim):
+            msg = f'test empty array partition with axis={axis}'
+            assert_equal(np.partition(a, kth, axis=axis), a, msg)
+        msg = 'test empty array partition with axis=None'
+        assert_equal(np.partition(a, kth, axis=None), a.ravel(), msg)
+
+    @pytest.mark.parametrize("kth_dtype", np.typecodes["AllInteger"])
+    def test_argpartition_empty_array(self, kth_dtype):
+        # check axis handling for multidimensional empty arrays
+        kth = np.array(0, dtype=kth_dtype)[()]
+        a = np.array([])
+        a.shape = (3, 2, 1, 0)
+        for axis in range(-a.ndim, a.ndim):
+            msg = f'test empty array argpartition with axis={axis}'
+            assert_equal(np.partition(a, kth, axis=axis),
+                         np.zeros_like(a, dtype=np.intp), msg)
+        msg = 'test empty array argpartition with axis=None'
+        assert_equal(np.partition(a, kth, axis=None),
+                     np.zeros_like(a.ravel(), dtype=np.intp), msg)
+
+    def test_partition(self):
+        d = np.arange(10)
+        assert_raises(TypeError, np.partition, d, 2, kind=1)
+        assert_raises(ValueError, np.partition, d, 2, kind="nonsense")
+        assert_raises(ValueError, np.argpartition, d, 2, kind="nonsense")
+        assert_raises(ValueError, d.partition, 2, axis=0, kind="nonsense")
+        assert_raises(ValueError, d.argpartition, 2, axis=0, kind="nonsense")
+        for k in ("introselect",):
+            d = np.array([])
+            assert_array_equal(np.partition(d, 0, kind=k), d)
+            assert_array_equal(np.argpartition(d, 0, kind=k), d)
+            d = np.ones(1)
+            assert_array_equal(np.partition(d, 0, kind=k)[0], d)
+            assert_array_equal(d[np.argpartition(d, 0, kind=k)],
+                               np.partition(d, 0, kind=k))
+
+            # kth not modified
+            kth = np.array([30, 15, 5])
+            okth = kth.copy()
+            np.partition(np.arange(40), kth)
+            assert_array_equal(kth, okth)
+
+            for r in ([2, 1], [1, 2], [1, 1]):
+                d = np.array(r)
+                tgt = np.sort(d)
+                assert_array_equal(np.partition(d, 0, kind=k)[0], tgt[0])
+                assert_array_equal(np.partition(d, 1, kind=k)[1], tgt[1])
+                self.assert_partitioned(np.partition(d, 0, kind=k), [0])
+                self.assert_partitioned(d[np.argpartition(d, 0, kind=k)], [0])
+                self.assert_partitioned(np.partition(d, 1, kind=k), [1])
+                self.assert_partitioned(d[np.argpartition(d, 1, kind=k)], [1])
+                for i in range(d.size):
+                    d[i:].partition(0, kind=k)
+                assert_array_equal(d, tgt)
+
+            for r in ([3, 2, 1], [1, 2, 3], [2, 1, 3], [2, 3, 1],
+                      [1, 1, 1], [1, 2, 2], [2, 2, 1], [1, 2, 1]):
+                d = np.array(r)
+                tgt = np.sort(d)
+                assert_array_equal(np.partition(d, 0, kind=k)[0], tgt[0])
+                assert_array_equal(np.partition(d, 1, kind=k)[1], tgt[1])
+                assert_array_equal(np.partition(d, 2, kind=k)[2], tgt[2])
+                self.assert_partitioned(np.partition(d, 0, kind=k), [0])
+                self.assert_partitioned(d[np.argpartition(d, 0, kind=k)], [0])
+                self.assert_partitioned(np.partition(d, 1, kind=k), [1])
+                self.assert_partitioned(d[np.argpartition(d, 1, kind=k)], [1])
+                self.assert_partitioned(np.partition(d, 2, kind=k), [2])
+                self.assert_partitioned(d[np.argpartition(d, 2, kind=k)], [2])
+                for i in range(d.size):
+                    d[i:].partition(0, kind=k)
+                assert_array_equal(d, tgt)
+
+            d = np.ones(50)
+            assert_array_equal(np.partition(d, 0, kind=k), d)
+            assert_array_equal(d[np.argpartition(d, 0, kind=k)],
+                               np.partition(d, 0, kind=k))
+
+            # sorted
+            d = np.arange(49)
+            assert_equal(np.partition(d, 5, kind=k)[5], 5)
+            assert_equal(np.partition(d, 15, kind=k)[15], 15)
+            self.assert_partitioned(np.partition(d, 5, kind=k), [5])
+            self.assert_partitioned(d[np.argpartition(d, 5, kind=k)], [5])
+            self.assert_partitioned(np.partition(d, 15, kind=k), [15])
+            self.assert_partitioned(d[np.argpartition(d, 15, kind=k)], [15])
+
+            # rsorted
+            d = np.arange(47)[::-1]
+            assert_equal(np.partition(d, 6, kind=k)[6], 6)
+            assert_equal(np.partition(d, 16, kind=k)[16], 16)
+            self.assert_partitioned(np.partition(d, 6, kind=k), [6])
+            self.assert_partitioned(d[np.argpartition(d, 6, kind=k)], [6])
+            self.assert_partitioned(np.partition(d, 16, kind=k), [16])
+            self.assert_partitioned(d[np.argpartition(d, 16, kind=k)], [16])
+
+            assert_array_equal(np.partition(d, -6, kind=k),
+                               np.partition(d, 41, kind=k))
+            assert_array_equal(np.partition(d, -16, kind=k),
+                               np.partition(d, 31, kind=k))
+            self.assert_partitioned(np.partition(d, 41, kind=k), [41])
+            self.assert_partitioned(d[np.argpartition(d, -6, kind=k)], [41])
+
+            # median of 3 killer, O(n^2) on pure median 3 pivot quickselect
+            # exercises the median of median of 5 code used to keep O(n)
+            d = np.arange(1000000)
+            x = np.roll(d, d.size // 2)
+            mid = x.size // 2 + 1
+            assert_equal(np.partition(x, mid)[mid], mid)
+            d = np.arange(1000001)
+            x = np.roll(d, d.size // 2 + 1)
+            mid = x.size // 2 + 1
+            assert_equal(np.partition(x, mid)[mid], mid)
+
+            # max
+            d = np.ones(10)
+            d[1] = 4
+            assert_equal(np.partition(d, (2, -1))[-1], 4)
+            assert_equal(np.partition(d, (2, -1))[2], 1)
+            assert_equal(d[np.argpartition(d, (2, -1))][-1], 4)
+            assert_equal(d[np.argpartition(d, (2, -1))][2], 1)
+            d[1] = np.nan
+            assert_(np.isnan(d[np.argpartition(d, (2, -1))][-1]))
+            assert_(np.isnan(np.partition(d, (2, -1))[-1]))
+
+            # equal elements
+            d = np.arange(47) % 7
+            tgt = np.sort(np.arange(47) % 7)
+            np.random.shuffle(d)
+            for i in range(d.size):
+                assert_equal(np.partition(d, i, kind=k)[i], tgt[i])
+            self.assert_partitioned(np.partition(d, 6, kind=k), [6])
+            self.assert_partitioned(d[np.argpartition(d, 6, kind=k)], [6])
+            self.assert_partitioned(np.partition(d, 16, kind=k), [16])
+            self.assert_partitioned(d[np.argpartition(d, 16, kind=k)], [16])
+            for i in range(d.size):
+                d[i:].partition(0, kind=k)
+            assert_array_equal(d, tgt)
+
+            d = np.array([0, 1, 2, 3, 4, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+                          7, 7, 7, 7, 7, 9])
+            kth = [0, 3, 19, 20]
+            assert_equal(np.partition(d, kth, kind=k)[kth], (0, 3, 7, 7))
+            assert_equal(d[np.argpartition(d, kth, kind=k)][kth], (0, 3, 7, 7))
+
+            d = np.array([2, 1])
+            d.partition(0, kind=k)
+            assert_raises(ValueError, d.partition, 2)
+            assert_raises(AxisError, d.partition, 3, axis=1)
+            assert_raises(ValueError, np.partition, d, 2)
+            assert_raises(AxisError, np.partition, d, 2, axis=1)
+            assert_raises(ValueError, d.argpartition, 2)
+            assert_raises(AxisError, d.argpartition, 3, axis=1)
+            assert_raises(ValueError, np.argpartition, d, 2)
+            assert_raises(AxisError, np.argpartition, d, 2, axis=1)
+            d = np.arange(10).reshape((2, 5))
+            d.partition(1, axis=0, kind=k)
+            d.partition(4, axis=1, kind=k)
+            np.partition(d, 1, axis=0, kind=k)
+            np.partition(d, 4, axis=1, kind=k)
+            np.partition(d, 1, axis=None, kind=k)
+            np.partition(d, 9, axis=None, kind=k)
+            d.argpartition(1, axis=0, kind=k)
+            d.argpartition(4, axis=1, kind=k)
+            np.argpartition(d, 1, axis=0, kind=k)
+            np.argpartition(d, 4, axis=1, kind=k)
+            np.argpartition(d, 1, axis=None, kind=k)
+            np.argpartition(d, 9, axis=None, kind=k)
+            assert_raises(ValueError, d.partition, 2, axis=0)
+            assert_raises(ValueError, d.partition, 11, axis=1)
+            assert_raises(TypeError, d.partition, 2, axis=None)
+            assert_raises(ValueError, np.partition, d, 9, axis=1)
+            assert_raises(ValueError, np.partition, d, 11, axis=None)
+            assert_raises(ValueError, d.argpartition, 2, axis=0)
+            assert_raises(ValueError, d.argpartition, 11, axis=1)
+            assert_raises(ValueError, np.argpartition, d, 9, axis=1)
+            assert_raises(ValueError, np.argpartition, d, 11, axis=None)
+
+            td = [(dt, s) for dt in [np.int32, np.float32, np.complex64]
+                  for s in (9, 16)]
+            for dt, s in td:
+                aae = assert_array_equal
+                at = assert_
+
+                d = np.arange(s, dtype=dt)
+                np.random.shuffle(d)
+                d1 = np.tile(np.arange(s, dtype=dt), (4, 1))
+                map(np.random.shuffle, d1)
+                d0 = np.transpose(d1)
+                for i in range(d.size):
+                    p = np.partition(d, i, kind=k)
+                    assert_equal(p[i], i)
+                    # all before are smaller
+                    assert_array_less(p[:i], p[i])
+                    # all after are larger
+                    assert_array_less(p[i], p[i + 1:])
+                    self.assert_partitioned(p, [i])
+                    self.assert_partitioned(
+                            d[np.argpartition(d, i, kind=k)], [i])
+
+                    p = np.partition(d1, i, axis=1, kind=k)
+                    parg = d1[np.arange(d1.shape[0])[:, None],
+                            np.argpartition(d1, i, axis=1, kind=k)]
+                    aae(p[:, i], np.array([i] * d1.shape[0], dtype=dt))
+                    # array_less does not seem to work right
+                    at((p[:, :i].T <= p[:, i]).all(),
+                       msg="%d: %r <= %r" % (i, p[:, i], p[:, :i].T))
+                    at((p[:, i + 1:].T > p[:, i]).all(),
+                       msg="%d: %r < %r" % (i, p[:, i], p[:, i + 1:].T))
+                    for row in range(p.shape[0]):
+                        self.assert_partitioned(p[row], [i])
+                        self.assert_partitioned(parg[row], [i])
+
+                    p = np.partition(d0, i, axis=0, kind=k)
+                    parg = d0[np.argpartition(d0, i, axis=0, kind=k),
+                            np.arange(d0.shape[1])[None, :]]
+                    aae(p[i, :], np.array([i] * d1.shape[0], dtype=dt))
+                    # array_less does not seem to work right
+                    at((p[:i, :] <= p[i, :]).all(),
+                       msg="%d: %r <= %r" % (i, p[i, :], p[:i, :]))
+                    at((p[i + 1:, :] > p[i, :]).all(),
+                       msg="%d: %r < %r" % (i, p[i, :], p[:, i + 1:]))
+                    for col in range(p.shape[1]):
+                        self.assert_partitioned(p[:, col], [i])
+                        self.assert_partitioned(parg[:, col], [i])
+
+                    # check inplace
+                    dc = d.copy()
+                    dc.partition(i, kind=k)
+                    assert_equal(dc, np.partition(d, i, kind=k))
+                    dc = d0.copy()
+                    dc.partition(i, axis=0, kind=k)
+                    assert_equal(dc, np.partition(d0, i, axis=0, kind=k))
+                    dc = d1.copy()
+                    dc.partition(i, axis=1, kind=k)
+                    assert_equal(dc, np.partition(d1, i, axis=1, kind=k))
+
+    def assert_partitioned(self, d, kth):
+        prev = 0
+        for k in np.sort(kth):
+            assert_array_compare(operator.__le__, d[prev:k], d[k],
+                    err_msg='kth %d' % k)
+            assert_((d[k:] >= d[k]).all(),
+                    msg="kth %d, %r not greater equal %r" % (k, d[k:], d[k]))
+            prev = k + 1
+
+    def test_partition_iterative(self):
+        d = np.arange(17)
+        kth = (0, 1, 2, 429, 231)
+        assert_raises(ValueError, d.partition, kth)
+        assert_raises(ValueError, d.argpartition, kth)
+        d = np.arange(10).reshape((2, 5))
+        assert_raises(ValueError, d.partition, kth, axis=0)
+        assert_raises(ValueError, d.partition, kth, axis=1)
+        assert_raises(ValueError, np.partition, d, kth, axis=1)
+        assert_raises(ValueError, np.partition, d, kth, axis=None)
+
+        d = np.array([3, 4, 2, 1])
+        p = np.partition(d, (0, 3))
+        self.assert_partitioned(p, (0, 3))
+        self.assert_partitioned(d[np.argpartition(d, (0, 3))], (0, 3))
+
+        assert_array_equal(p, np.partition(d, (-3, -1)))
+        assert_array_equal(p, d[np.argpartition(d, (-3, -1))])
+
+        d = np.arange(17)
+        np.random.shuffle(d)
+        d.partition(range(d.size))
+        assert_array_equal(np.arange(17), d)
+        np.random.shuffle(d)
+        assert_array_equal(np.arange(17), d[d.argpartition(range(d.size))])
+
+        # test unsorted kth
+        d = np.arange(17)
+        np.random.shuffle(d)
+        keys = np.array([1, 3, 8, -2])
+        np.random.shuffle(d)
+        p = np.partition(d, keys)
+        self.assert_partitioned(p, keys)
+        p = d[np.argpartition(d, keys)]
+        self.assert_partitioned(p, keys)
+        np.random.shuffle(keys)
+        assert_array_equal(np.partition(d, keys), p)
+        assert_array_equal(d[np.argpartition(d, keys)], p)
+
+        # equal kth
+        d = np.arange(20)[::-1]
+        self.assert_partitioned(np.partition(d, [5] * 4), [5])
+        self.assert_partitioned(np.partition(d, [5] * 4 + [6, 13]),
+                                [5] * 4 + [6, 13])
+        self.assert_partitioned(d[np.argpartition(d, [5] * 4)], [5])
+        self.assert_partitioned(d[np.argpartition(d, [5] * 4 + [6, 13])],
+                                [5] * 4 + [6, 13])
+
+        d = np.arange(12)
+        np.random.shuffle(d)
+        d1 = np.tile(np.arange(12), (4, 1))
+        map(np.random.shuffle, d1)
+        d0 = np.transpose(d1)
+
+        kth = (1, 6, 7, -1)
+        p = np.partition(d1, kth, axis=1)
+        pa = d1[np.arange(d1.shape[0])[:, None],
+                d1.argpartition(kth, axis=1)]
+        assert_array_equal(p, pa)
+        for i in range(d1.shape[0]):
+            self.assert_partitioned(p[i, :], kth)
+        p = np.partition(d0, kth, axis=0)
+        pa = d0[np.argpartition(d0, kth, axis=0),
+                np.arange(d0.shape[1])[None, :]]
+        assert_array_equal(p, pa)
+        for i in range(d0.shape[1]):
+            self.assert_partitioned(p[:, i], kth)
+
+    def test_partition_cdtype(self):
+        d = np.array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),
+                   ('Lancelot', 1.9, 38)],
+                  dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])
+
+        tgt = np.sort(d, order=['age', 'height'])
+        assert_array_equal(np.partition(d, range(d.size),
+                                        order=['age', 'height']),
+                           tgt)
+        assert_array_equal(d[np.argpartition(d, range(d.size),
+                                             order=['age', 'height'])],
+                           tgt)
+        for k in range(d.size):
+            assert_equal(np.partition(d, k, order=['age', 'height'])[k],
+                        tgt[k])
+            assert_equal(d[np.argpartition(d, k, order=['age', 'height'])][k],
+                         tgt[k])
+
+        d = np.array(['Galahad', 'Arthur', 'zebra', 'Lancelot'])
+        tgt = np.sort(d)
+        assert_array_equal(np.partition(d, range(d.size)), tgt)
+        for k in range(d.size):
+            assert_equal(np.partition(d, k)[k], tgt[k])
+            assert_equal(d[np.argpartition(d, k)][k], tgt[k])
+
+    def test_partition_unicode_kind(self):
+        d = np.arange(10)
+        k = b'\xc3\xa4'.decode("UTF8")
+        assert_raises(ValueError, d.partition, 2, kind=k)
+        assert_raises(ValueError, d.argpartition, 2, kind=k)
+
+    def test_partition_fuzz(self):
+        # a few rounds of random data testing
+        for j in range(10, 30):
+            for i in range(1, j - 2):
+                d = np.arange(j)
+                np.random.shuffle(d)
+                d = d % np.random.randint(2, 30)
+                idx = np.random.randint(d.size)
+                kth = [0, idx, i, i + 1]
+                tgt = np.sort(d)[kth]
+                assert_array_equal(np.partition(d, kth)[kth], tgt,
+                                   err_msg=f"data: {d!r}\n kth: {kth!r}")
+
+    @pytest.mark.parametrize("kth_dtype", np.typecodes["AllInteger"])
+    def test_argpartition_gh5524(self, kth_dtype):
+        #  A test for functionality of argpartition on lists.
+        kth = np.array(1, dtype=kth_dtype)[()]
+        d = [6, 7, 3, 2, 9, 0]
+        p = np.argpartition(d, kth)
+        self.assert_partitioned(np.array(d)[p], [1])
+
+    def test_flatten(self):
+        x0 = np.array([[1, 2, 3], [4, 5, 6]], np.int32)
+        x1 = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]], np.int32)
+        y0 = np.array([1, 2, 3, 4, 5, 6], np.int32)
+        y0f = np.array([1, 4, 2, 5, 3, 6], np.int32)
+        y1 = np.array([1, 2, 3, 4, 5, 6, 7, 8], np.int32)
+        y1f = np.array([1, 5, 3, 7, 2, 6, 4, 8], np.int32)
+        assert_equal(x0.flatten(), y0)
+        assert_equal(x0.flatten('F'), y0f)
+        assert_equal(x0.flatten('F'), x0.T.flatten())
+        assert_equal(x1.flatten(), y1)
+        assert_equal(x1.flatten('F'), y1f)
+        assert_equal(x1.flatten('F'), x1.T.flatten())
+
+    @pytest.mark.parametrize('func', (np.dot, np.matmul))
+    def test_arr_mult(self, func):
+        a = np.array([[1, 0], [0, 1]])
+        b = np.array([[0, 1], [1, 0]])
+        c = np.array([[9, 1], [1, -9]])
+        d = np.arange(24).reshape(4, 6)
+        ddt = np.array(
+            [[  55,  145,  235,  325],
+             [ 145,  451,  757, 1063],
+             [ 235,  757, 1279, 1801],
+             [ 325, 1063, 1801, 2539]]
+        )
+        dtd = np.array(
+            [[504, 540, 576, 612, 648, 684],
+             [540, 580, 620, 660, 700, 740],
+             [576, 620, 664, 708, 752, 796],
+             [612, 660, 708, 756, 804, 852],
+             [648, 700, 752, 804, 856, 908],
+             [684, 740, 796, 852, 908, 964]]
+        )
+
+        # gemm vs syrk optimizations
+        for et in [np.float32, np.float64, np.complex64, np.complex128]:
+            eaf = a.astype(et)
+            assert_equal(func(eaf, eaf), eaf)
+            assert_equal(func(eaf.T, eaf), eaf)
+            assert_equal(func(eaf, eaf.T), eaf)
+            assert_equal(func(eaf.T, eaf.T), eaf)
+            assert_equal(func(eaf.T.copy(), eaf), eaf)
+            assert_equal(func(eaf, eaf.T.copy()), eaf)
+            assert_equal(func(eaf.T.copy(), eaf.T.copy()), eaf)
+
+        # syrk validations
+        for et in [np.float32, np.float64, np.complex64, np.complex128]:
+            eaf = a.astype(et)
+            ebf = b.astype(et)
+            assert_equal(func(ebf, ebf), eaf)
+            assert_equal(func(ebf.T, ebf), eaf)
+            assert_equal(func(ebf, ebf.T), eaf)
+            assert_equal(func(ebf.T, ebf.T), eaf)
+
+        # syrk - different shape, stride, and view validations
+        for et in [np.float32, np.float64, np.complex64, np.complex128]:
+            edf = d.astype(et)
+            assert_equal(
+                func(edf[::-1, :], edf.T),
+                func(edf[::-1, :].copy(), edf.T.copy())
+            )
+            assert_equal(
+                func(edf[:, ::-1], edf.T),
+                func(edf[:, ::-1].copy(), edf.T.copy())
+            )
+            assert_equal(
+                func(edf, edf[::-1, :].T),
+                func(edf, edf[::-1, :].T.copy())
+            )
+            assert_equal(
+                func(edf, edf[:, ::-1].T),
+                func(edf, edf[:, ::-1].T.copy())
+            )
+            assert_equal(
+                func(edf[:edf.shape[0] // 2, :], edf[::2, :].T),
+                func(edf[:edf.shape[0] // 2, :].copy(), edf[::2, :].T.copy())
+            )
+            assert_equal(
+                func(edf[::2, :], edf[:edf.shape[0] // 2, :].T),
+                func(edf[::2, :].copy(), edf[:edf.shape[0] // 2, :].T.copy())
+            )
+
+        # syrk - different shape
+        for et in [np.float32, np.float64, np.complex64, np.complex128]:
+            edf = d.astype(et)
+            eddtf = ddt.astype(et)
+            edtdf = dtd.astype(et)
+            assert_equal(func(edf, edf.T), eddtf)
+            assert_equal(func(edf.T, edf), edtdf)
+
+    @pytest.mark.parametrize('func', (np.dot, np.matmul))
+    @pytest.mark.parametrize('dtype', 'ifdFD')
+    def test_no_dgemv(self, func, dtype):
+        # check vector arg for contiguous before gemv
+        # gh-12156
+        a = np.arange(8.0, dtype=dtype).reshape(2, 4)
+        b = np.broadcast_to(1., (4, 1))
+        ret1 = func(a, b)
+        ret2 = func(a, b.copy())
+        assert_equal(ret1, ret2)
+
+        ret1 = func(b.T, a.T)
+        ret2 = func(b.T.copy(), a.T)
+        assert_equal(ret1, ret2)
+
+        # check for unaligned data
+        dt = np.dtype(dtype)
+        a = np.zeros(8 * dt.itemsize // 2 + 1, dtype='int16')[1:].view(dtype)
+        a = a.reshape(2, 4)
+        b = a[0]
+        # make sure it is not aligned
+        assert_(a.__array_interface__['data'][0] % dt.itemsize != 0)
+        ret1 = func(a, b)
+        ret2 = func(a.copy(), b.copy())
+        assert_equal(ret1, ret2)
+
+        ret1 = func(b.T, a.T)
+        ret2 = func(b.T.copy(), a.T.copy())
+        assert_equal(ret1, ret2)
+
+    def test_dot(self):
+        a = np.array([[1, 0], [0, 1]])
+        b = np.array([[0, 1], [1, 0]])
+        c = np.array([[9, 1], [1, -9]])
+        # function versus methods
+        assert_equal(np.dot(a, b), a.dot(b))
+        assert_equal(np.dot(np.dot(a, b), c), a.dot(b).dot(c))
+
+        # test passing in an output array
+        c = np.zeros_like(a)
+        a.dot(b, c)
+        assert_equal(c, np.dot(a, b))
+
+        # test keyword args
+        c = np.zeros_like(a)
+        a.dot(b=b, out=c)
+        assert_equal(c, np.dot(a, b))
+
+    @pytest.mark.parametrize("dtype", [np.half, np.double, np.longdouble])
+    @pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support")
+    def test_dot_errstate(self, dtype):
+        # Some dtypes use BLAS for 'dot' operation and
+        # not all BLAS support floating-point errors.
+        if not BLAS_SUPPORTS_FPE and dtype == np.double:
+            pytest.skip("BLAS does not support FPE")
+
+        a = np.array([1, 1], dtype=dtype)
+        b = np.array([-np.inf, np.inf], dtype=dtype)
+
+        with np.errstate(invalid='raise'):
+            # there are two paths, depending on the number of dimensions - test
+            # them both
+            with pytest.raises(FloatingPointError,
+                    match="invalid value encountered in dot"):
+                np.dot(a, b)
+
+            # test that fp exceptions are properly cleared
+            np.dot(a, a)
+
+            with pytest.raises(FloatingPointError,
+                    match="invalid value encountered in dot"):
+                np.dot(a[np.newaxis, np.newaxis, ...],
+                       b[np.newaxis, ..., np.newaxis])
+
+            np.dot(a[np.newaxis, np.newaxis, ...],
+                   a[np.newaxis, ..., np.newaxis])
+
+    def test_dot_type_mismatch(self):
+        c = 1.
+        A = np.array((1, 1), dtype='i,i')
+
+        assert_raises(TypeError, np.dot, c, A)
+        assert_raises(TypeError, np.dot, A, c)
+
+    def test_dot_out_mem_overlap(self):
+        np.random.seed(1)
+
+        # Test BLAS and non-BLAS code paths, including all dtypes
+        # that dot() supports
+        dtypes = [np.dtype(code) for code in np.typecodes['All']
+                  if code not in 'USVM']
+        for dtype in dtypes:
+            a = np.random.rand(3, 3).astype(dtype)
+
+            # Valid dot() output arrays must be aligned
+            b = _aligned_zeros((3, 3), dtype=dtype)
+            b[...] = np.random.rand(3, 3)
+
+            y = np.dot(a, b)
+            x = np.dot(a, b, out=b)
+            assert_equal(x, y, err_msg=repr(dtype))
+
+            # Check invalid output array
+            assert_raises(ValueError, np.dot, a, b, out=b[::2])
+            assert_raises(ValueError, np.dot, a, b, out=b.T)
+
+    def test_dot_matmul_out(self):
+        # gh-9641
+        class Sub(np.ndarray):
+            pass
+        a = np.ones((2, 2)).view(Sub)
+        b = np.ones((2, 2)).view(Sub)
+        out = np.ones((2, 2))
+
+        # make sure out can be any ndarray (not only subclass of inputs)
+        np.dot(a, b, out=out)
+        np.matmul(a, b, out=out)
+
+    def test_dot_matmul_inner_array_casting_fails(self):
+
+        class A:
+            def __array__(self, *args, **kwargs):
+                raise NotImplementedError
+
+        # Don't override the error from calling __array__()
+        assert_raises(NotImplementedError, np.dot, A(), A())
+        assert_raises(NotImplementedError, np.matmul, A(), A())
+        assert_raises(NotImplementedError, np.inner, A(), A())
+
+    def test_matmul_out(self):
+        # overlapping memory
+        a = np.arange(18).reshape(2, 3, 3)
+        b = np.matmul(a, a)
+        c = np.matmul(a, a, out=a)
+        assert_(c is a)
+        assert_equal(c, b)
+        a = np.arange(18).reshape(2, 3, 3)
+        c = np.matmul(a, a, out=a[::-1, ...])
+        assert_(c.base is a.base)
+        assert_equal(c, b)
+
+    def test_diagonal(self):
+        a = np.arange(12).reshape((3, 4))
+        assert_equal(a.diagonal(), [0, 5, 10])
+        assert_equal(a.diagonal(0), [0, 5, 10])
+        assert_equal(a.diagonal(1), [1, 6, 11])
+        assert_equal(a.diagonal(-1), [4, 9])
+        assert_raises(AxisError, a.diagonal, axis1=0, axis2=5)
+        assert_raises(AxisError, a.diagonal, axis1=5, axis2=0)
+        assert_raises(AxisError, a.diagonal, axis1=5, axis2=5)
+        assert_raises(ValueError, a.diagonal, axis1=1, axis2=1)
+
+        b = np.arange(8).reshape((2, 2, 2))
+        assert_equal(b.diagonal(), [[0, 6], [1, 7]])
+        assert_equal(b.diagonal(0), [[0, 6], [1, 7]])
+        assert_equal(b.diagonal(1), [[2], [3]])
+        assert_equal(b.diagonal(-1), [[4], [5]])
+        assert_raises(ValueError, b.diagonal, axis1=0, axis2=0)
+        assert_equal(b.diagonal(0, 1, 2), [[0, 3], [4, 7]])
+        assert_equal(b.diagonal(0, 0, 1), [[0, 6], [1, 7]])
+        assert_equal(b.diagonal(offset=1, axis1=0, axis2=2), [[1], [3]])
+        # Order of axis argument doesn't matter:
+        assert_equal(b.diagonal(0, 2, 1), [[0, 3], [4, 7]])
+
+    def test_diagonal_view_notwriteable(self):
+        a = np.eye(3).diagonal()
+        assert_(not a.flags.writeable)
+        assert_(not a.flags.owndata)
+
+        a = np.diagonal(np.eye(3))
+        assert_(not a.flags.writeable)
+        assert_(not a.flags.owndata)
+
+        a = np.diag(np.eye(3))
+        assert_(not a.flags.writeable)
+        assert_(not a.flags.owndata)
+
+    def test_diagonal_memleak(self):
+        # Regression test for a bug that crept in at one point
+        a = np.zeros((100, 100))
+        if HAS_REFCOUNT:
+            assert_(sys.getrefcount(a) < 50)
+        for i in range(100):
+            a.diagonal()
+        if HAS_REFCOUNT:
+            assert_(sys.getrefcount(a) < 50)
+
+    def test_size_zero_memleak(self):
+        # Regression test for issue 9615
+        # Exercises a special-case code path for dot products of length
+        # zero in cblasfuncs (making it is specific to floating dtypes).
+        a = np.array([], dtype=np.float64)
+        x = np.array(2.0)
+        for _ in range(100):
+            np.dot(a, a, out=x)
+        if HAS_REFCOUNT:
+            assert_(sys.getrefcount(x) < 50)
+
+    def test_trace(self):
+        a = np.arange(12).reshape((3, 4))
+        assert_equal(a.trace(), 15)
+        assert_equal(a.trace(0), 15)
+        assert_equal(a.trace(1), 18)
+        assert_equal(a.trace(-1), 13)
+
+        b = np.arange(8).reshape((2, 2, 2))
+        assert_equal(b.trace(), [6, 8])
+        assert_equal(b.trace(0), [6, 8])
+        assert_equal(b.trace(1), [2, 3])
+        assert_equal(b.trace(-1), [4, 5])
+        assert_equal(b.trace(0, 0, 1), [6, 8])
+        assert_equal(b.trace(0, 0, 2), [5, 9])
+        assert_equal(b.trace(0, 1, 2), [3, 11])
+        assert_equal(b.trace(offset=1, axis1=0, axis2=2), [1, 3])
+
+        out = np.array(1)
+        ret = a.trace(out=out)
+        assert ret is out
+
+    def test_trace_subclass(self):
+        # The class would need to overwrite trace to ensure single-element
+        # output also has the right subclass.
+        class MyArray(np.ndarray):
+            pass
+
+        b = np.arange(8).reshape((2, 2, 2)).view(MyArray)
+        t = b.trace()
+        assert_(isinstance(t, MyArray))
+
+    def test_put(self):
+        icodes = np.typecodes['AllInteger']
+        fcodes = np.typecodes['AllFloat']
+        for dt in icodes + fcodes + 'O':
+            tgt = np.array([0, 1, 0, 3, 0, 5], dtype=dt)
+
+            # test 1-d
+            a = np.zeros(6, dtype=dt)
+            a.put([1, 3, 5], [1, 3, 5])
+            assert_equal(a, tgt)
+
+            # test 2-d
+            a = np.zeros((2, 3), dtype=dt)
+            a.put([1, 3, 5], [1, 3, 5])
+            assert_equal(a, tgt.reshape(2, 3))
+
+        for dt in '?':
+            tgt = np.array([False, True, False, True, False, True], dtype=dt)
+
+            # test 1-d
+            a = np.zeros(6, dtype=dt)
+            a.put([1, 3, 5], [True] * 3)
+            assert_equal(a, tgt)
+
+            # test 2-d
+            a = np.zeros((2, 3), dtype=dt)
+            a.put([1, 3, 5], [True] * 3)
+            assert_equal(a, tgt.reshape(2, 3))
+
+        # check must be writeable
+        a = np.zeros(6)
+        a.flags.writeable = False
+        assert_raises(ValueError, a.put, [1, 3, 5], [1, 3, 5])
+
+        # when calling np.put, make sure a
+        # TypeError is raised if the object
+        # isn't an ndarray
+        bad_array = [1, 2, 3]
+        assert_raises(TypeError, np.put, bad_array, [0, 2], 5)
+
+        # when calling np.put, make sure an
+        # IndexError is raised if the
+        # array is empty
+        empty_array = np.asarray([])
+        with pytest.raises(IndexError,
+                            match="cannot replace elements of an empty array"):
+            np.put(empty_array, 1, 1, mode="wrap")
+        with pytest.raises(IndexError,
+                            match="cannot replace elements of an empty array"):
+            np.put(empty_array, 1, 1, mode="clip")
+
+    def test_ravel(self):
+        a = np.array([[0, 1], [2, 3]])
+        assert_equal(a.ravel(), [0, 1, 2, 3])
+        assert_(not a.ravel().flags.owndata)
+        assert_equal(a.ravel('F'), [0, 2, 1, 3])
+        assert_equal(a.ravel(order='C'), [0, 1, 2, 3])
+        assert_equal(a.ravel(order='F'), [0, 2, 1, 3])
+        assert_equal(a.ravel(order='A'), [0, 1, 2, 3])
+        assert_(not a.ravel(order='A').flags.owndata)
+        assert_equal(a.ravel(order='K'), [0, 1, 2, 3])
+        assert_(not a.ravel(order='K').flags.owndata)
+        assert_equal(a.ravel(), a.reshape(-1))
+
+        a = np.array([[0, 1], [2, 3]], order='F')
+        assert_equal(a.ravel(), [0, 1, 2, 3])
+        assert_equal(a.ravel(order='A'), [0, 2, 1, 3])
+        assert_equal(a.ravel(order='K'), [0, 2, 1, 3])
+        assert_(not a.ravel(order='A').flags.owndata)
+        assert_(not a.ravel(order='K').flags.owndata)
+        assert_equal(a.ravel(), a.reshape(-1))
+        assert_equal(a.ravel(order='A'), a.reshape(-1, order='A'))
+
+        a = np.array([[0, 1], [2, 3]])[::-1, :]
+        assert_equal(a.ravel(), [2, 3, 0, 1])
+        assert_equal(a.ravel(order='C'), [2, 3, 0, 1])
+        assert_equal(a.ravel(order='F'), [2, 0, 3, 1])
+        assert_equal(a.ravel(order='A'), [2, 3, 0, 1])
+        # 'K' doesn't reverse the axes of negative strides
+        assert_equal(a.ravel(order='K'), [2, 3, 0, 1])
+        assert_(a.ravel(order='K').flags.owndata)
+
+        # Test simple 1-d copy behaviour:
+        a = np.arange(10)[::2]
+        assert_(a.ravel('K').flags.owndata)
+        assert_(a.ravel('C').flags.owndata)
+        assert_(a.ravel('F').flags.owndata)
+
+        # Not contiguous and 1-sized axis with non matching stride
+        a = np.arange(2**3 * 2)[::2]
+        a = a.reshape(2, 1, 2, 2).swapaxes(-1, -2)
+        strides = list(a.strides)
+        strides[1] = 123
+        a.strides = strides
+        assert_(a.ravel(order='K').flags.owndata)
+        assert_equal(a.ravel('K'), np.arange(0, 15, 2))
+
+        # contiguous and 1-sized axis with non matching stride works:
+        a = np.arange(2**3)
+        a = a.reshape(2, 1, 2, 2).swapaxes(-1, -2)
+        strides = list(a.strides)
+        strides[1] = 123
+        a.strides = strides
+        assert_(np.may_share_memory(a.ravel(order='K'), a))
+        assert_equal(a.ravel(order='K'), np.arange(2**3))
+
+        # Test negative strides (not very interesting since non-contiguous):
+        a = np.arange(4)[::-1].reshape(2, 2)
+        assert_(a.ravel(order='C').flags.owndata)
+        assert_(a.ravel(order='K').flags.owndata)
+        assert_equal(a.ravel('C'), [3, 2, 1, 0])
+        assert_equal(a.ravel('K'), [3, 2, 1, 0])
+
+        # 1-element tidy strides test:
+        a = np.array([[1]])
+        a.strides = (123, 432)
+        if np.ones(1).strides == (8,):
+            assert_(np.may_share_memory(a.ravel('K'), a))
+            assert_equal(a.ravel('K').strides, (a.dtype.itemsize,))
+
+        for order in ('C', 'F', 'A', 'K'):
+            # 0-d corner case:
+            a = np.array(0)
+            assert_equal(a.ravel(order), [0])
+            assert_(np.may_share_memory(a.ravel(order), a))
+
+        # Test that certain non-inplace ravels work right (mostly) for 'K':
+        b = np.arange(2**4 * 2)[::2].reshape(2, 2, 2, 2)
+        a = b[..., ::2]
+        assert_equal(a.ravel('K'), [0, 4, 8, 12, 16, 20, 24, 28])
+        assert_equal(a.ravel('C'), [0, 4, 8, 12, 16, 20, 24, 28])
+        assert_equal(a.ravel('A'), [0, 4, 8, 12, 16, 20, 24, 28])
+        assert_equal(a.ravel('F'), [0, 16, 8, 24, 4, 20, 12, 28])
+
+        a = b[::2, ...]
+        assert_equal(a.ravel('K'), [0, 2, 4, 6, 8, 10, 12, 14])
+        assert_equal(a.ravel('C'), [0, 2, 4, 6, 8, 10, 12, 14])
+        assert_equal(a.ravel('A'), [0, 2, 4, 6, 8, 10, 12, 14])
+        assert_equal(a.ravel('F'), [0, 8, 4, 12, 2, 10, 6, 14])
+
+    def test_ravel_subclass(self):
+        class ArraySubclass(np.ndarray):
+            pass
+
+        a = np.arange(10).view(ArraySubclass)
+        assert_(isinstance(a.ravel('C'), ArraySubclass))
+        assert_(isinstance(a.ravel('F'), ArraySubclass))
+        assert_(isinstance(a.ravel('A'), ArraySubclass))
+        assert_(isinstance(a.ravel('K'), ArraySubclass))
+
+        a = np.arange(10)[::2].view(ArraySubclass)
+        assert_(isinstance(a.ravel('C'), ArraySubclass))
+        assert_(isinstance(a.ravel('F'), ArraySubclass))
+        assert_(isinstance(a.ravel('A'), ArraySubclass))
+        assert_(isinstance(a.ravel('K'), ArraySubclass))
+
+    def test_swapaxes(self):
+        a = np.arange(1 * 2 * 3 * 4).reshape(1, 2, 3, 4).copy()
+        idx = np.indices(a.shape)
+        assert_(a.flags['OWNDATA'])
+        b = a.copy()
+        # check exceptions
+        assert_raises(AxisError, a.swapaxes, -5, 0)
+        assert_raises(AxisError, a.swapaxes, 4, 0)
+        assert_raises(AxisError, a.swapaxes, 0, -5)
+        assert_raises(AxisError, a.swapaxes, 0, 4)
+
+        for i in range(-4, 4):
+            for j in range(-4, 4):
+                for k, src in enumerate((a, b)):
+                    c = src.swapaxes(i, j)
+                    # check shape
+                    shape = list(src.shape)
+                    shape[i] = src.shape[j]
+                    shape[j] = src.shape[i]
+                    assert_equal(c.shape, shape, str((i, j, k)))
+                    # check array contents
+                    i0, i1, i2, i3 = [dim - 1 for dim in c.shape]
+                    j0, j1, j2, j3 = [dim - 1 for dim in src.shape]
+                    assert_equal(src[idx[j0], idx[j1], idx[j2], idx[j3]],
+                                 c[idx[i0], idx[i1], idx[i2], idx[i3]],
+                                 str((i, j, k)))
+                    # check a view is always returned, gh-5260
+                    assert_(not c.flags['OWNDATA'], str((i, j, k)))
+                    # check on non-contiguous input array
+                    if k == 1:
+                        b = c
+
+    def test_conjugate(self):
+        a = np.array([1 - 1j, 1 + 1j, 23 + 23.0j])
+        ac = a.conj()
+        assert_equal(a.real, ac.real)
+        assert_equal(a.imag, -ac.imag)
+        assert_equal(ac, a.conjugate())
+        assert_equal(ac, np.conjugate(a))
+
+        a = np.array([1 - 1j, 1 + 1j, 23 + 23.0j], 'F')
+        ac = a.conj()
+        assert_equal(a.real, ac.real)
+        assert_equal(a.imag, -ac.imag)
+        assert_equal(ac, a.conjugate())
+        assert_equal(ac, np.conjugate(a))
+
+        a = np.array([1, 2, 3])
+        ac = a.conj()
+        assert_equal(a, ac)
+        assert_equal(ac, a.conjugate())
+        assert_equal(ac, np.conjugate(a))
+
+        a = np.array([1.0, 2.0, 3.0])
+        ac = a.conj()
+        assert_equal(a, ac)
+        assert_equal(ac, a.conjugate())
+        assert_equal(ac, np.conjugate(a))
+
+        a = np.array([1 - 1j, 1 + 1j, 1, 2.0], object)
+        ac = a.conj()
+        assert_equal(ac, [k.conjugate() for k in a])
+        assert_equal(ac, a.conjugate())
+        assert_equal(ac, np.conjugate(a))
+
+        a = np.array([1 - 1j, 1, 2.0, 'f'], object)
+        assert_raises(TypeError, a.conj)
+        assert_raises(TypeError, a.conjugate)
+
+    def test_conjugate_out(self):
+        # Minimal test for the out argument being passed on correctly
+        # NOTE: The ability to pass `out` is currently undocumented!
+        a = np.array([1 - 1j, 1 + 1j, 23 + 23.0j])
+        out = np.empty_like(a)
+        res = a.conjugate(out)
+        assert res is out
+        assert_array_equal(out, a.conjugate())
+
+    def test_conjugate_scalar(self):
+        for v in 5, 5j:
+            a = np.array(v)
+            assert a.conjugate() == v.conjugate()
+        for a in (np.array('s'), np.array('2016', 'M'),
+                np.array((1, 2), [('a', int), ('b', int)])):
+            with pytest.raises(TypeError):
+                a.conjugate()
+
+    def test__complex__(self):
+        dtypes = ['i1', 'i2', 'i4', 'i8',
+                  'u1', 'u2', 'u4', 'u8',
+                  'f', 'd', 'g', 'F', 'D', 'G',
+                  '?', 'O']
+        for dt in dtypes:
+            a = np.array(7, dtype=dt)
+            b = np.array([7], dtype=dt)
+            c = np.array([[[[[7]]]]], dtype=dt)
+
+            msg = f'dtype: {dt}'
+            ap = complex(a)
+            assert_equal(ap, a, msg)
+
+            with assert_warns(DeprecationWarning):
+                bp = complex(b)
+            assert_equal(bp, b, msg)
+
+            with assert_warns(DeprecationWarning):
+                cp = complex(c)
+            assert_equal(cp, c, msg)
+
+    def test__complex__should_not_work(self):
+        dtypes = ['i1', 'i2', 'i4', 'i8',
+                  'u1', 'u2', 'u4', 'u8',
+                  'f', 'd', 'g', 'F', 'D', 'G',
+                  '?', 'O']
+        for dt in dtypes:
+            a = np.array([1, 2, 3], dtype=dt)
+            assert_raises(TypeError, complex, a)
+
+        dt = np.dtype([('a', 'f8'), ('b', 'i1')])
+        b = np.array((1.0, 3), dtype=dt)
+        assert_raises(TypeError, complex, b)
+
+        c = np.array([(1.0, 3), (2e-3, 7)], dtype=dt)
+        assert_raises(TypeError, complex, c)
+
+        d = np.array('1+1j')
+        assert_raises(TypeError, complex, d)
+
+        e = np.array(['1+1j'], 'U')
+        with assert_warns(DeprecationWarning):
+            assert_raises(TypeError, complex, e)
+
+class TestCequenceMethods:
+    def test_array_contains(self):
+        assert_(4.0 in np.arange(16.).reshape(4, 4))
+        assert_(20.0 not in np.arange(16.).reshape(4, 4))
+
+class TestBinop:
+    def test_inplace(self):
+        # test refcount 1 inplace conversion
+        assert_array_almost_equal(np.array([0.5]) * np.array([1.0, 2.0]),
+                                  [0.5, 1.0])
+
+        d = np.array([0.5, 0.5])[::2]
+        assert_array_almost_equal(d * (d * np.array([1.0, 2.0])),
+                                  [0.25, 0.5])
+
+        a = np.array([0.5])
+        b = np.array([0.5])
+        c = a + b
+        c = a - b
+        c = a * b
+        c = a / b
+        assert_equal(a, b)
+        assert_almost_equal(c, 1.)
+
+        c = a + b * 2. / b * a - a / b
+        assert_equal(a, b)
+        assert_equal(c, 0.5)
+
+        # true divide
+        a = np.array([5])
+        b = np.array([3])
+        c = (a * a) / b
+
+        assert_almost_equal(c, 25 / 3)
+        assert_equal(a, 5)
+        assert_equal(b, 3)
+
+    # ndarray.__rop__ always calls ufunc
+    # ndarray.__iop__ always calls ufunc
+    # ndarray.__op__, __rop__:
+    #   - defer if other has __array_ufunc__ and it is None
+    #           or other is not a subclass and has higher array priority
+    #   - else, call ufunc
+    @pytest.mark.xfail(IS_PYPY, reason="Bug in pypy3.{9, 10}-v7.3.13, #24862")
+    def test_ufunc_binop_interaction(self):
+        # Python method name (without underscores)
+        #   -> (numpy ufunc, has_in_place_version, preferred_dtype)
+        ops = {
+            'add':      (np.add, True, float),
+            'sub':      (np.subtract, True, float),
+            'mul':      (np.multiply, True, float),
+            'truediv':  (np.true_divide, True, float),
+            'floordiv': (np.floor_divide, True, float),
+            'mod':      (np.remainder, True, float),
+            'divmod':   (np.divmod, False, float),
+            'pow':      (np.power, True, int),
+            'lshift':   (np.left_shift, True, int),
+            'rshift':   (np.right_shift, True, int),
+            'and':      (np.bitwise_and, True, int),
+            'xor':      (np.bitwise_xor, True, int),
+            'or':       (np.bitwise_or, True, int),
+            'matmul':   (np.matmul, True, float),
+            # 'ge':       (np.less_equal, False),
+            # 'gt':       (np.less, False),
+            # 'le':       (np.greater_equal, False),
+            # 'lt':       (np.greater, False),
+            # 'eq':       (np.equal, False),
+            # 'ne':       (np.not_equal, False),
+        }
+
+        class Coerced(Exception):
+            pass
+
+        def array_impl(self):
+            raise Coerced
+
+        def op_impl(self, other):
+            return "forward"
+
+        def rop_impl(self, other):
+            return "reverse"
+
+        def iop_impl(self, other):
+            return "in-place"
+
+        def array_ufunc_impl(self, ufunc, method, *args, **kwargs):
+            return ("__array_ufunc__", ufunc, method, args, kwargs)
+
+        # Create an object with the given base, in the given module, with a
+        # bunch of placeholder __op__ methods, and optionally a
+        # __array_ufunc__ and __array_priority__.
+        def make_obj(base, array_priority=False, array_ufunc=False,
+                     alleged_module="__main__"):
+            class_namespace = {"__array__": array_impl}
+            if array_priority is not False:
+                class_namespace["__array_priority__"] = array_priority
+            for op in ops:
+                class_namespace[f"__{op}__"] = op_impl
+                class_namespace[f"__r{op}__"] = rop_impl
+                class_namespace[f"__i{op}__"] = iop_impl
+            if array_ufunc is not False:
+                class_namespace["__array_ufunc__"] = array_ufunc
+            eval_namespace = {"base": base,
+                              "class_namespace": class_namespace,
+                              "__name__": alleged_module,
+                              }
+            MyType = eval("type('MyType', (base,), class_namespace)",
+                          eval_namespace)
+            if issubclass(MyType, np.ndarray):
+                # Use this range to avoid special case weirdnesses around
+                # divide-by-0, pow(x, 2), overflow due to pow(big, big), etc.
+                return np.arange(3, 7).reshape(2, 2).view(MyType)
+            else:
+                return MyType()
+
+        def check(obj, binop_override_expected, ufunc_override_expected,
+                  inplace_override_expected, check_scalar=True):
+            for op, (ufunc, has_inplace, dtype) in ops.items():
+                err_msg = ('op: %s, ufunc: %s, has_inplace: %s, dtype: %s'
+                           % (op, ufunc, has_inplace, dtype))
+                check_objs = [np.arange(3, 7, dtype=dtype).reshape(2, 2)]
+                if check_scalar:
+                    check_objs.append(check_objs[0][0])
+                for arr in check_objs:
+                    arr_method = getattr(arr, f"__{op}__")
+
+                    def first_out_arg(result):
+                        if op == "divmod":
+                            assert_(isinstance(result, tuple))
+                            return result[0]
+                        else:
+                            return result
+
+                    # arr __op__ obj
+                    if binop_override_expected:
+                        assert_equal(arr_method(obj), NotImplemented, err_msg)
+                    elif ufunc_override_expected:
+                        assert_equal(arr_method(obj)[0], "__array_ufunc__",
+                                     err_msg)
+                    elif (isinstance(obj, np.ndarray) and
+                        (type(obj).__array_ufunc__ is
+                         np.ndarray.__array_ufunc__)):
+                        # __array__ gets ignored
+                        res = first_out_arg(arr_method(obj))
+                        assert_(res.__class__ is obj.__class__, err_msg)
+                    else:
+                        assert_raises((TypeError, Coerced),
+                                      arr_method, obj, err_msg=err_msg)
+                    # obj __op__ arr
+                    arr_rmethod = getattr(arr, f"__r{op}__")
+                    if ufunc_override_expected:
+                        res = arr_rmethod(obj)
+                        assert_equal(res[0], "__array_ufunc__",
+                                     err_msg=err_msg)
+                        assert_equal(res[1], ufunc, err_msg=err_msg)
+                    elif (isinstance(obj, np.ndarray) and
+                            (type(obj).__array_ufunc__ is
+                             np.ndarray.__array_ufunc__)):
+                        # __array__ gets ignored
+                        res = first_out_arg(arr_rmethod(obj))
+                        assert_(res.__class__ is obj.__class__, err_msg)
+                    else:
+                        # __array_ufunc__ = "asdf" creates a TypeError
+                        assert_raises((TypeError, Coerced),
+                                      arr_rmethod, obj, err_msg=err_msg)
+
+                    # arr __iop__ obj
+                    # array scalars don't have in-place operators
+                    if has_inplace and isinstance(arr, np.ndarray):
+                        arr_imethod = getattr(arr, f"__i{op}__")
+                        if inplace_override_expected:
+                            assert_equal(arr_method(obj), NotImplemented,
+                                         err_msg=err_msg)
+                        elif ufunc_override_expected:
+                            res = arr_imethod(obj)
+                            assert_equal(res[0], "__array_ufunc__", err_msg)
+                            assert_equal(res[1], ufunc, err_msg)
+                            assert_(type(res[-1]["out"]) is tuple, err_msg)
+                            assert_(res[-1]["out"][0] is arr, err_msg)
+                        elif (isinstance(obj, np.ndarray) and
+                                (type(obj).__array_ufunc__ is
+                                np.ndarray.__array_ufunc__)):
+                            # __array__ gets ignored
+                            assert_(arr_imethod(obj) is arr, err_msg)
+                        else:
+                            assert_raises((TypeError, Coerced),
+                                          arr_imethod, obj,
+                                          err_msg=err_msg)
+
+                    op_fn = getattr(operator, op, None)
+                    if op_fn is None:
+                        op_fn = getattr(operator, op + "_", None)
+                    if op_fn is None:
+                        op_fn = getattr(builtins, op)
+                    assert_equal(op_fn(obj, arr), "forward", err_msg)
+                    if not isinstance(obj, np.ndarray):
+                        if binop_override_expected:
+                            assert_equal(op_fn(arr, obj), "reverse", err_msg)
+                        elif ufunc_override_expected:
+                            assert_equal(op_fn(arr, obj)[0], "__array_ufunc__",
+                                         err_msg)
+                    if ufunc_override_expected:
+                        assert_equal(ufunc(obj, arr)[0], "__array_ufunc__",
+                                     err_msg)
+
+        # No array priority, no array_ufunc -> nothing called
+        check(make_obj(object), False, False, False)
+        # Negative array priority, no array_ufunc -> nothing called
+        # (has to be very negative, because scalar priority is -1000000.0)
+        check(make_obj(object, array_priority=-2**30), False, False, False)
+        # Positive array priority, no array_ufunc -> binops and iops only
+        check(make_obj(object, array_priority=1), True, False, True)
+        # ndarray ignores array_priority for ndarray subclasses
+        check(make_obj(np.ndarray, array_priority=1), False, False, False,
+              check_scalar=False)
+        # Positive array_priority and array_ufunc -> array_ufunc only
+        check(make_obj(object, array_priority=1,
+                       array_ufunc=array_ufunc_impl), False, True, False)
+        check(make_obj(np.ndarray, array_priority=1,
+                       array_ufunc=array_ufunc_impl), False, True, False)
+        # array_ufunc set to None -> defer binops only
+        check(make_obj(object, array_ufunc=None), True, False, False)
+        check(make_obj(np.ndarray, array_ufunc=None), True, False, False,
+              check_scalar=False)
+
+    @pytest.mark.parametrize("priority", [None, "runtime error"])
+    def test_ufunc_binop_bad_array_priority(self, priority):
+        # Mainly checks that this does not crash.  The second array has a lower
+        # priority than -1 ("error value").  If the __radd__ actually exists,
+        # bad things can happen (I think via the scalar paths).
+        # In principle both of these can probably just be errors in the future.
+        class BadPriority:
+            @property
+            def __array_priority__(self):
+                if priority == "runtime error":
+                    raise RuntimeError("RuntimeError in __array_priority__!")
+                return priority
+
+            def __radd__(self, other):
+                return "result"
+
+        class LowPriority(np.ndarray):
+            __array_priority__ = -1000
+
+        # Priority failure uses the same as scalars (smaller -1000).  So the
+        # LowPriority wins with 'result' for each element (inner operation).
+        res = np.arange(3).view(LowPriority) + BadPriority()
+        assert res.shape == (3,)
+        assert res[0] == 'result'
+
+    @pytest.mark.parametrize("scalar", [
+            np.longdouble(1), np.timedelta64(120, 'm')])
+    @pytest.mark.parametrize("op", [operator.add, operator.xor])
+    def test_scalar_binop_guarantees_ufunc(self, scalar, op):
+        # Test that __array_ufunc__ will always cause ufunc use even when
+        # we have to protect some other calls from recursing (see gh-26904).
+        class SomeClass:
+            def __array_ufunc__(self, ufunc, method, *inputs, **kw):
+                return "result"
+
+        assert SomeClass() + scalar == "result"
+        assert scalar + SomeClass() == "result"
+
+    def test_ufunc_override_normalize_signature(self):
+        # gh-5674
+        class SomeClass:
+            def __array_ufunc__(self, ufunc, method, *inputs, **kw):
+                return kw
+
+        a = SomeClass()
+        kw = np.add(a, [1])
+        assert_('sig' not in kw and 'signature' not in kw)
+        kw = np.add(a, [1], sig='ii->i')
+        assert_('sig' not in kw and 'signature' in kw)
+        assert_equal(kw['signature'], 'ii->i')
+        kw = np.add(a, [1], signature='ii->i')
+        assert_('sig' not in kw and 'signature' in kw)
+        assert_equal(kw['signature'], 'ii->i')
+
+    def test_array_ufunc_index(self):
+        # Check that index is set appropriately, also if only an output
+        # is passed on (latter is another regression tests for github bug 4753)
+        # This also checks implicitly that 'out' is always a tuple.
+        class CheckIndex:
+            def __array_ufunc__(self, ufunc, method, *inputs, **kw):
+                for i, a in enumerate(inputs):
+                    if a is self:
+                        return i
+                # calls below mean we must be in an output.
+                for j, a in enumerate(kw['out']):
+                    if a is self:
+                        return (j,)
+
+        a = CheckIndex()
+        dummy = np.arange(2.)
+        # 1 input, 1 output
+        assert_equal(np.sin(a), 0)
+        assert_equal(np.sin(dummy, a), (0,))
+        assert_equal(np.sin(dummy, out=a), (0,))
+        assert_equal(np.sin(dummy, out=(a,)), (0,))
+        assert_equal(np.sin(a, a), 0)
+        assert_equal(np.sin(a, out=a), 0)
+        assert_equal(np.sin(a, out=(a,)), 0)
+        # 1 input, 2 outputs
+        assert_equal(np.modf(dummy, a), (0,))
+        assert_equal(np.modf(dummy, None, a), (1,))
+        assert_equal(np.modf(dummy, dummy, a), (1,))
+        assert_equal(np.modf(dummy, out=(a, None)), (0,))
+        assert_equal(np.modf(dummy, out=(a, dummy)), (0,))
+        assert_equal(np.modf(dummy, out=(None, a)), (1,))
+        assert_equal(np.modf(dummy, out=(dummy, a)), (1,))
+        assert_equal(np.modf(a, out=(dummy, a)), 0)
+        with assert_raises(TypeError):
+            # Out argument must be tuple, since there are multiple outputs
+            np.modf(dummy, out=a)
+
+        assert_raises(ValueError, np.modf, dummy, out=(a,))
+
+        # 2 inputs, 1 output
+        assert_equal(np.add(a, dummy), 0)
+        assert_equal(np.add(dummy, a), 1)
+        assert_equal(np.add(dummy, dummy, a), (0,))
+        assert_equal(np.add(dummy, a, a), 1)
+        assert_equal(np.add(dummy, dummy, out=a), (0,))
+        assert_equal(np.add(dummy, dummy, out=(a,)), (0,))
+        assert_equal(np.add(a, dummy, out=a), 0)
+
+    def test_out_override(self):
+        # regression test for github bug 4753
+        class OutClass(np.ndarray):
+            def __array_ufunc__(self, ufunc, method, *inputs, **kw):
+                if 'out' in kw:
+                    tmp_kw = kw.copy()
+                    tmp_kw.pop('out')
+                    func = getattr(ufunc, method)
+                    kw['out'][0][...] = func(*inputs, **tmp_kw)
+
+        A = np.array([0]).view(OutClass)
+        B = np.array([5])
+        C = np.array([6])
+        np.multiply(C, B, A)
+        assert_equal(A[0], 30)
+        assert_(isinstance(A, OutClass))
+        A[0] = 0
+        np.multiply(C, B, out=A)
+        assert_equal(A[0], 30)
+        assert_(isinstance(A, OutClass))
+
+    def test_pow_array_object_dtype(self):
+        # test pow on arrays of object dtype
+        class SomeClass:
+            def __init__(self, num=None):
+                self.num = num
+
+            # want to ensure a fast pow path is not taken
+            def __mul__(self, other):
+                raise AssertionError('__mul__ should not be called')
+
+            def __truediv__(self, other):
+                raise AssertionError('__truediv__ should not be called')
+
+            def __pow__(self, exp):
+                return SomeClass(num=self.num ** exp)
+
+            def __eq__(self, other):
+                if isinstance(other, SomeClass):
+                    return self.num == other.num
+
+            __rpow__ = __pow__
+
+        def pow_for(exp, arr):
+            return np.array([x ** exp for x in arr])
+
+        obj_arr = np.array([SomeClass(1), SomeClass(2), SomeClass(3)])
+
+        assert_equal(obj_arr ** 0.5, pow_for(0.5, obj_arr))
+        assert_equal(obj_arr ** 0, pow_for(0, obj_arr))
+        assert_equal(obj_arr ** 1, pow_for(1, obj_arr))
+        assert_equal(obj_arr ** -1, pow_for(-1, obj_arr))
+        assert_equal(obj_arr ** 2, pow_for(2, obj_arr))
+
+    def test_pow_calls_square_structured_dtype(self):
+        # gh-29388
+        dt = np.dtype([('a', 'i4'), ('b', 'i4')])
+        a = np.array([(1, 2), (3, 4)], dtype=dt)
+        with pytest.raises(TypeError, match="ufunc 'square' not supported"):
+            a ** 2
+
+    def test_pos_array_ufunc_override(self):
+        class A(np.ndarray):
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+                return getattr(ufunc, method)(*[i.view(np.ndarray) for
+                                                i in inputs], **kwargs)
+        tst = np.array('foo').view(A)
+        with assert_raises(TypeError):
+            +tst
+
+
+class TestTemporaryElide:
+    # elision is only triggered on relatively large arrays
+
+    def test_extension_incref_elide(self):
+        # test extension (e.g. cython) calling PyNumber_* slots without
+        # increasing the reference counts
+        #
+        # def incref_elide(a):
+        #    d = input.copy() # refcount 1
+        #    return d, d + d # PyNumber_Add without increasing refcount
+        from numpy._core._multiarray_tests import incref_elide
+        d = np.ones(100000)
+        orig, res = incref_elide(d)
+        d + d
+        # the return original should not be changed to an inplace operation
+        assert_array_equal(orig, d)
+        assert_array_equal(res, d + d)
+
+    def test_extension_incref_elide_stack(self):
+        # scanning if the refcount == 1 object is on the python stack to check
+        # that we are called directly from python is flawed as object may still
+        # be above the stack pointer and we have no access to the top of it
+        #
+        # def incref_elide_l(d):
+        #    return l[4] + l[4] # PyNumber_Add without increasing refcount
+        from numpy._core._multiarray_tests import incref_elide_l
+        # padding with 1 makes sure the object on the stack is not overwritten
+        l = [1, 1, 1, 1, np.ones(100000)]
+        res = incref_elide_l(l)
+        # the return original should not be changed to an inplace operation
+        assert_array_equal(l[4], np.ones(100000))
+        assert_array_equal(res, l[4] + l[4])
+
+    def test_temporary_with_cast(self):
+        # check that we don't elide into a temporary which would need casting
+        d = np.ones(200000, dtype=np.int64)
+        r = ((d + d) + np.array(2**222, dtype='O'))
+        assert_equal(r.dtype, np.dtype('O'))
+
+        r = ((d + d) / 2)
+        assert_equal(r.dtype, np.dtype('f8'))
+
+        r = np.true_divide((d + d), 2)
+        assert_equal(r.dtype, np.dtype('f8'))
+
+        r = ((d + d) / 2.)
+        assert_equal(r.dtype, np.dtype('f8'))
+
+        r = ((d + d) // 2)
+        assert_equal(r.dtype, np.dtype(np.int64))
+
+        # commutative elision into the astype result
+        f = np.ones(100000, dtype=np.float32)
+        assert_equal(((f + f) + f.astype(np.float64)).dtype, np.dtype('f8'))
+
+        # no elision into lower type
+        d = f.astype(np.float64)
+        assert_equal(((f + f) + d).dtype, d.dtype)
+        l = np.ones(100000, dtype=np.longdouble)
+        assert_equal(((d + d) + l).dtype, l.dtype)
+
+        # test unary abs with different output dtype
+        for dt in (np.complex64, np.complex128, np.clongdouble):
+            c = np.ones(100000, dtype=dt)
+            r = abs(c * 2.0)
+            assert_equal(r.dtype, np.dtype('f%d' % (c.itemsize // 2)))
+
+    def test_elide_broadcast(self):
+        # test no elision on broadcast to higher dimension
+        # only triggers elision code path in debug mode as triggering it in
+        # normal mode needs 256kb large matching dimension, so a lot of memory
+        d = np.ones((2000, 1), dtype=int)
+        b = np.ones((2000), dtype=bool)
+        r = (1 - d) + b
+        assert_equal(r, 1)
+        assert_equal(r.shape, (2000, 2000))
+
+    def test_elide_scalar(self):
+        # check inplace op does not create ndarray from scalars
+        a = np.bool()
+        assert_(type(~(a & a)) is np.bool)
+
+    def test_elide_scalar_readonly(self):
+        # The imaginary part of a real array is readonly. This needs to go
+        # through fast_scalar_power which is only called for powers of
+        # +1, -1, 0, 0.5, and 2, so use 2. Also need valid refcount for
+        # elision which can be gotten for the imaginary part of a real
+        # array. Should not error.
+        a = np.empty(100000, dtype=np.float64)
+        a.imag ** 2
+
+    def test_elide_readonly(self):
+        # don't try to elide readonly temporaries
+        r = np.asarray(np.broadcast_to(np.zeros(1), 100000).flat) * 0.0
+        assert_equal(r, 0)
+
+    def test_elide_updateifcopy(self):
+        a = np.ones(2**20)[::2]
+        b = a.flat.__array__() + 1
+        del b
+        assert_equal(a, 1)
+
+
+class TestCAPI:
+    def test_IsPythonScalar(self):
+        from numpy._core._multiarray_tests import IsPythonScalar
+        assert_(IsPythonScalar(b'foobar'))
+        assert_(IsPythonScalar(1))
+        assert_(IsPythonScalar(2**80))
+        assert_(IsPythonScalar(2.))
+        assert_(IsPythonScalar("a"))
+
+    @pytest.mark.parametrize("converter",
+             [_multiarray_tests.run_scalar_intp_converter,
+              _multiarray_tests.run_scalar_intp_from_sequence])
+    def test_intp_sequence_converters(self, converter):
+        # Test simple values (-1 is special for error return paths)
+        assert converter(10) == (10,)
+        assert converter(-1) == (-1,)
+        # A 0-D array looks a bit like a sequence but must take the integer
+        # path:
+        assert converter(np.array(123)) == (123,)
+        # Test simple sequences (intp_from_sequence only supports length 1):
+        assert converter((10,)) == (10,)
+        assert converter(np.array([11])) == (11,)
+
+    @pytest.mark.parametrize("converter",
+             [_multiarray_tests.run_scalar_intp_converter,
+              _multiarray_tests.run_scalar_intp_from_sequence])
+    @pytest.mark.skipif(IS_PYPY and sys.implementation.version <= (7, 3, 8),
+            reason="PyPy bug in error formatting")
+    def test_intp_sequence_converters_errors(self, converter):
+        with pytest.raises(TypeError,
+                match="expected a sequence of integers or a single integer, "):
+            converter(object())
+        with pytest.raises(TypeError,
+                match="expected a sequence of integers or a single integer, "
+                      "got '32.0'"):
+            converter(32.)
+        with pytest.raises(TypeError,
+                match="'float' object cannot be interpreted as an integer"):
+            converter([32.])
+        with pytest.raises(ValueError,
+                match="Maximum allowed dimension"):
+            # These converters currently convert overflows to a ValueError
+            converter(2**64)
+
+
+class TestSubscripting:
+    def test_test_zero_rank(self):
+        x = np.array([1, 2, 3])
+        assert_(isinstance(x[0], np.int_))
+        assert_(type(x[0, ...]) is np.ndarray)
+
+
+class TestPickling:
+    @pytest.mark.skipif(pickle.HIGHEST_PROTOCOL >= 5,
+                        reason=('this tests the error messages when trying to'
+                                'protocol 5 although it is not available'))
+    def test_correct_protocol5_error_message(self):
+        array = np.arange(10)
+
+    def test_record_array_with_object_dtype(self):
+        my_object = object()
+
+        arr_with_object = np.array(
+                [(my_object, 1, 2.0)],
+                dtype=[('a', object), ('b', int), ('c', float)])
+        arr_without_object = np.array(
+                [('xxx', 1, 2.0)],
+                dtype=[('a', str), ('b', int), ('c', float)])
+
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            depickled_arr_with_object = pickle.loads(
+                    pickle.dumps(arr_with_object, protocol=proto))
+            depickled_arr_without_object = pickle.loads(
+                    pickle.dumps(arr_without_object, protocol=proto))
+
+            assert_equal(arr_with_object.dtype,
+                         depickled_arr_with_object.dtype)
+            assert_equal(arr_without_object.dtype,
+                         depickled_arr_without_object.dtype)
+
+    @pytest.mark.skipif(pickle.HIGHEST_PROTOCOL < 5,
+                        reason="requires pickle protocol 5")
+    def test_f_contiguous_array(self):
+        f_contiguous_array = np.array([[1, 2, 3], [4, 5, 6]], order='F')
+        buffers = []
+
+        # When using pickle protocol 5, Fortran-contiguous arrays can be
+        # serialized using out-of-band buffers
+        bytes_string = pickle.dumps(f_contiguous_array, protocol=5,
+                                    buffer_callback=buffers.append)
+
+        assert len(buffers) > 0
+
+        depickled_f_contiguous_array = pickle.loads(bytes_string,
+                                                    buffers=buffers)
+
+        assert_equal(f_contiguous_array, depickled_f_contiguous_array)
+
+    @pytest.mark.skipif(pickle.HIGHEST_PROTOCOL < 5, reason="requires pickle protocol 5")
+    @pytest.mark.parametrize('transposed_contiguous_array',
+        [np.random.default_rng(42).random((2, 3, 4)).transpose((1, 0, 2)),
+         np.random.default_rng(42).random((2, 3, 4, 5)).transpose((1, 3, 0, 2))] +
+        [np.random.default_rng(42).random(np.arange(2, 7)).transpose(np.random.permutation(5)) for _ in range(3)])
+    def test_transposed_contiguous_array(self, transposed_contiguous_array):
+        buffers = []
+        # When using pickle protocol 5, arrays which can be transposed to c_contiguous
+        # can be serialized using out-of-band buffers
+        bytes_string = pickle.dumps(transposed_contiguous_array, protocol=5,
+                                    buffer_callback=buffers.append)
+
+        assert len(buffers) > 0
+
+        depickled_transposed_contiguous_array = pickle.loads(bytes_string,
+                                                    buffers=buffers)
+
+        assert_equal(transposed_contiguous_array, depickled_transposed_contiguous_array)
+
+    @pytest.mark.skipif(pickle.HIGHEST_PROTOCOL < 5, reason="requires pickle protocol 5")
+    def test_load_legacy_pkl_protocol5(self):
+        # legacy byte strs are dumped in 2.2.1
+        c_contiguous_dumped = b'\x80\x05\x95\x90\x00\x00\x00\x00\x00\x00\x00\x8c\x13numpy._core.numeric\x94\x8c\x0b_frombuffer\x94\x93\x94(\x96\x18\x00\x00\x00\x00\x00\x00\x00\x00\x01\x02\x03\x04\x05\x06\x07\x08\t\n\x0b\x0c\r\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x94\x8c\x05numpy\x94\x8c\x05dtype\x94\x93\x94\x8c\x02u1\x94\x89\x88\x87\x94R\x94(K\x03\x8c\x01|\x94NNNJ\xff\xff\xff\xffJ\xff\xff\xff\xffK\x00t\x94bK\x03K\x04K\x02\x87\x94\x8c\x01C\x94t\x94R\x94.'  # noqa: E501
+        f_contiguous_dumped = b'\x80\x05\x95\x90\x00\x00\x00\x00\x00\x00\x00\x8c\x13numpy._core.numeric\x94\x8c\x0b_frombuffer\x94\x93\x94(\x96\x18\x00\x00\x00\x00\x00\x00\x00\x00\x01\x02\x03\x04\x05\x06\x07\x08\t\n\x0b\x0c\r\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x94\x8c\x05numpy\x94\x8c\x05dtype\x94\x93\x94\x8c\x02u1\x94\x89\x88\x87\x94R\x94(K\x03\x8c\x01|\x94NNNJ\xff\xff\xff\xffJ\xff\xff\xff\xffK\x00t\x94bK\x03K\x04K\x02\x87\x94\x8c\x01F\x94t\x94R\x94.'   # noqa: E501
+        transposed_contiguous_dumped = b'\x80\x05\x95\xa5\x00\x00\x00\x00\x00\x00\x00\x8c\x16numpy._core.multiarray\x94\x8c\x0c_reconstruct\x94\x93\x94\x8c\x05numpy\x94\x8c\x07ndarray\x94\x93\x94K\x00\x85\x94C\x01b\x94\x87\x94R\x94(K\x01K\x04K\x03K\x02\x87\x94h\x03\x8c\x05dtype\x94\x93\x94\x8c\x02u1\x94\x89\x88\x87\x94R\x94(K\x03\x8c\x01|\x94NNNJ\xff\xff\xff\xffJ\xff\xff\xff\xffK\x00t\x94b\x89C\x18\x00\x01\x08\t\x10\x11\x02\x03\n\x0b\x12\x13\x04\x05\x0c\r\x14\x15\x06\x07\x0e\x0f\x16\x17\x94t\x94b.'   # noqa: E501
+        no_contiguous_dumped = b'\x80\x05\x95\x91\x00\x00\x00\x00\x00\x00\x00\x8c\x16numpy._core.multiarray\x94\x8c\x0c_reconstruct\x94\x93\x94\x8c\x05numpy\x94\x8c\x07ndarray\x94\x93\x94K\x00\x85\x94C\x01b\x94\x87\x94R\x94(K\x01K\x03K\x02\x86\x94h\x03\x8c\x05dtype\x94\x93\x94\x8c\x02u1\x94\x89\x88\x87\x94R\x94(K\x03\x8c\x01|\x94NNNJ\xff\xff\xff\xffJ\xff\xff\xff\xffK\x00t\x94b\x89C\x06\x00\x01\x04\x05\x08\t\x94t\x94b.'  # noqa: E501
+        x = np.arange(24, dtype='uint8').reshape(3, 4, 2)
+        assert_equal(x, pickle.loads(c_contiguous_dumped))
+        x = np.arange(24, dtype='uint8').reshape(3, 4, 2, order='F')
+        assert_equal(x, pickle.loads(f_contiguous_dumped))
+        x = np.arange(24, dtype='uint8').reshape(3, 4, 2).transpose((1, 0, 2))
+        assert_equal(x, pickle.loads(transposed_contiguous_dumped))
+        x = np.arange(12, dtype='uint8').reshape(3, 4)[:, :2]
+        assert_equal(x, pickle.loads(no_contiguous_dumped))
+
+    def test_non_contiguous_array(self):
+        non_contiguous_array = np.arange(12).reshape(3, 4)[:, :2]
+        assert not non_contiguous_array.flags.c_contiguous
+        assert not non_contiguous_array.flags.f_contiguous
+
+        # make sure non-contiguous arrays can be pickled-depickled
+        # using any protocol
+        buffers = []
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            depickled_non_contiguous_array = pickle.loads(
+                    pickle.dumps(non_contiguous_array, protocol=proto,
+                                 buffer_callback=buffers.append if proto >= 5 else None))
+
+            assert_equal(len(buffers), 0)
+            assert_equal(non_contiguous_array, depickled_non_contiguous_array)
+
+    def test_roundtrip(self):
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            carray = np.array([[2, 9], [7, 0], [3, 8]])
+            DATA = [
+                carray,
+                np.transpose(carray),
+                np.array([('xxx', 1, 2.0)], dtype=[('a', (str, 3)), ('b', int),
+                                                   ('c', float)])
+            ]
+
+            refs = [weakref.ref(a) for a in DATA]
+            for a in DATA:
+                assert_equal(
+                        a, pickle.loads(pickle.dumps(a, protocol=proto)),
+                        err_msg=f"{a!r}")
+            del a, DATA, carray
+            break_cycles()
+            # check for reference leaks (gh-12793)
+            for ref in refs:
+                assert ref() is None
+
+    def _loads(self, obj):
+        return pickle.loads(obj, encoding='latin1')
+
+    # version 0 pickles, using protocol=2 to pickle
+    # version 0 doesn't have a version field
+    def test_version0_int8(self):
+        s = b"\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x04\x85cnumpy\ndtype\nq\x04U\x02i1K\x00K\x01\x87Rq\x05(U\x01|NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89U\x04\x01\x02\x03\x04tb."
+        a = np.array([1, 2, 3, 4], dtype=np.int8)
+        p = self._loads(s)
+        assert_equal(a, p)
+
+    def test_version0_float32(self):
+        s = b"\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x04\x85cnumpy\ndtype\nq\x04U\x02f4K\x00K\x01\x87Rq\x05(U\x01<NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89U\x10\x00\x00\x80?\x00\x00\x00@\x00\x00@@\x00\x00\x80@tb."
+        a = np.array([1.0, 2.0, 3.0, 4.0], dtype=np.float32)
+        p = self._loads(s)
+        assert_equal(a, p)
+
+    def test_version0_object(self):
+        s = b"\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x02\x85cnumpy\ndtype\nq\x04U\x02O8K\x00K\x01\x87Rq\x05(U\x01|NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89]q\x06(}q\x07U\x01aK\x01s}q\x08U\x01bK\x02setb."
+        a = np.array([{'a': 1}, {'b': 2}])
+        p = self._loads(s)
+        assert_equal(a, p)
+
+    # version 1 pickles, using protocol=2 to pickle
+    def test_version1_int8(self):
+        s = b"\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x01K\x04\x85cnumpy\ndtype\nq\x04U\x02i1K\x00K\x01\x87Rq\x05(K\x01U\x01|NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89U\x04\x01\x02\x03\x04tb."
+        a = np.array([1, 2, 3, 4], dtype=np.int8)
+        p = self._loads(s)
+        assert_equal(a, p)
+
+    def test_version1_float32(self):
+        s = b"\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x01K\x04\x85cnumpy\ndtype\nq\x04U\x02f4K\x00K\x01\x87Rq\x05(K\x01U\x01<NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89U\x10\x00\x00\x80?\x00\x00\x00@\x00\x00@@\x00\x00\x80@tb."
+        a = np.array([1.0, 2.0, 3.0, 4.0], dtype=np.float32)
+        p = self._loads(s)
+        assert_equal(a, p)
+
+    def test_version1_object(self):
+        s = b"\x80\x02cnumpy.core._internal\n_reconstruct\nq\x01cnumpy\nndarray\nq\x02K\x00\x85U\x01b\x87Rq\x03(K\x01K\x02\x85cnumpy\ndtype\nq\x04U\x02O8K\x00K\x01\x87Rq\x05(K\x01U\x01|NNJ\xff\xff\xff\xffJ\xff\xff\xff\xfftb\x89]q\x06(}q\x07U\x01aK\x01s}q\x08U\x01bK\x02setb."
+        a = np.array([{'a': 1}, {'b': 2}])
+        p = self._loads(s)
+        assert_equal(a, p)
+
+    def test_subarray_int_shape(self):
+        s = b"cnumpy.core.multiarray\n_reconstruct\np0\n(cnumpy\nndarray\np1\n(I0\ntp2\nS'b'\np3\ntp4\nRp5\n(I1\n(I1\ntp6\ncnumpy\ndtype\np7\n(S'V6'\np8\nI0\nI1\ntp9\nRp10\n(I3\nS'|'\np11\nN(S'a'\np12\ng3\ntp13\n(dp14\ng12\n(g7\n(S'V4'\np15\nI0\nI1\ntp16\nRp17\n(I3\nS'|'\np18\n(g7\n(S'i1'\np19\nI0\nI1\ntp20\nRp21\n(I3\nS'|'\np22\nNNNI-1\nI-1\nI0\ntp23\nb(I2\nI2\ntp24\ntp25\nNNI4\nI1\nI0\ntp26\nbI0\ntp27\nsg3\n(g7\n(S'V2'\np28\nI0\nI1\ntp29\nRp30\n(I3\nS'|'\np31\n(g21\nI2\ntp32\nNNI2\nI1\nI0\ntp33\nbI4\ntp34\nsI6\nI1\nI0\ntp35\nbI00\nS'\\x01\\x01\\x01\\x01\\x01\\x02'\np36\ntp37\nb."
+        a = np.array([(1, (1, 2))], dtype=[('a', 'i1', (2, 2)), ('b', 'i1', 2)])
+        p = self._loads(s)
+        assert_equal(a, p)
+
+    def test_datetime64_byteorder(self):
+        original = np.array([['2015-02-24T00:00:00.000000000']], dtype='datetime64[ns]')
+
+        original_byte_reversed = original.copy(order='K')
+        original_byte_reversed.dtype = original_byte_reversed.dtype.newbyteorder('S')
+        original_byte_reversed.byteswap(inplace=True)
+
+        new = pickle.loads(pickle.dumps(original_byte_reversed))
+
+        assert_equal(original.dtype, new.dtype)
+
+
+class TestFancyIndexing:
+    def test_list(self):
+        x = np.ones((1, 1))
+        x[:, [0]] = 2.0
+        assert_array_equal(x, np.array([[2.0]]))
+
+        x = np.ones((1, 1, 1))
+        x[:, :, [0]] = 2.0
+        assert_array_equal(x, np.array([[[2.0]]]))
+
+    def test_tuple(self):
+        x = np.ones((1, 1))
+        x[:, (0,)] = 2.0
+        assert_array_equal(x, np.array([[2.0]]))
+        x = np.ones((1, 1, 1))
+        x[:, :, (0,)] = 2.0
+        assert_array_equal(x, np.array([[[2.0]]]))
+
+    def test_mask(self):
+        x = np.array([1, 2, 3, 4])
+        m = np.array([0, 1, 0, 0], bool)
+        assert_array_equal(x[m], np.array([2]))
+
+    def test_mask2(self):
+        x = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])
+        m = np.array([0, 1], bool)
+        m2 = np.array([[0, 1, 0, 0], [1, 0, 0, 0]], bool)
+        m3 = np.array([[0, 1, 0, 0], [0, 0, 0, 0]], bool)
+        assert_array_equal(x[m], np.array([[5, 6, 7, 8]]))
+        assert_array_equal(x[m2], np.array([2, 5]))
+        assert_array_equal(x[m3], np.array([2]))
+
+    def test_assign_mask(self):
+        x = np.array([1, 2, 3, 4])
+        m = np.array([0, 1, 0, 0], bool)
+        x[m] = 5
+        assert_array_equal(x, np.array([1, 5, 3, 4]))
+
+    def test_assign_mask2(self):
+        xorig = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])
+        m = np.array([0, 1], bool)
+        m2 = np.array([[0, 1, 0, 0], [1, 0, 0, 0]], bool)
+        m3 = np.array([[0, 1, 0, 0], [0, 0, 0, 0]], bool)
+        x = xorig.copy()
+        x[m] = 10
+        assert_array_equal(x, np.array([[1, 2, 3, 4], [10, 10, 10, 10]]))
+        x = xorig.copy()
+        x[m2] = 10
+        assert_array_equal(x, np.array([[1, 10, 3, 4], [10, 6, 7, 8]]))
+        x = xorig.copy()
+        x[m3] = 10
+        assert_array_equal(x, np.array([[1, 10, 3, 4], [5, 6, 7, 8]]))
+
+
+class TestStringCompare:
+    def test_string(self):
+        g1 = np.array(["This", "is", "example"])
+        g2 = np.array(["This", "was", "example"])
+        assert_array_equal(g1 == g2, [g1[i] == g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 != g2, [g1[i] != g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 <= g2, [g1[i] <= g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 >= g2, [g1[i] >= g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 < g2, [g1[i] < g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 > g2, [g1[i] > g2[i] for i in [0, 1, 2]])
+
+    def test_mixed(self):
+        g1 = np.array(["spam", "spa", "spammer", "and eggs"])
+        g2 = "spam"
+        assert_array_equal(g1 == g2, [x == g2 for x in g1])
+        assert_array_equal(g1 != g2, [x != g2 for x in g1])
+        assert_array_equal(g1 < g2, [x < g2 for x in g1])
+        assert_array_equal(g1 > g2, [x > g2 for x in g1])
+        assert_array_equal(g1 <= g2, [x <= g2 for x in g1])
+        assert_array_equal(g1 >= g2, [x >= g2 for x in g1])
+
+    def test_unicode(self):
+        g1 = np.array(["This", "is", "example"])
+        g2 = np.array(["This", "was", "example"])
+        assert_array_equal(g1 == g2, [g1[i] == g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 != g2, [g1[i] != g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 <= g2, [g1[i] <= g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 >= g2, [g1[i] >= g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 < g2,  [g1[i] < g2[i] for i in [0, 1, 2]])
+        assert_array_equal(g1 > g2,  [g1[i] > g2[i] for i in [0, 1, 2]])
+
+class TestArgmaxArgminCommon:
+
+    sizes = [(), (3,), (3, 2), (2, 3),
+             (3, 3), (2, 3, 4), (4, 3, 2),
+             (1, 2, 3, 4), (2, 3, 4, 1),
+             (3, 4, 1, 2), (4, 1, 2, 3),
+             (64,), (128,), (256,)]
+
+    @pytest.mark.parametrize("size, axis", itertools.chain(*[[(size, axis)
+        for axis in list(range(-len(size), len(size))) + [None]]
+        for size in sizes]))
+    @pytest.mark.parametrize('method', [np.argmax, np.argmin])
+    def test_np_argmin_argmax_keepdims(self, size, axis, method):
+
+        arr = np.random.normal(size=size)
+
+        # contiguous arrays
+        if axis is None:
+            new_shape = [1 for _ in range(len(size))]
+        else:
+            new_shape = list(size)
+            new_shape[axis] = 1
+        new_shape = tuple(new_shape)
+
+        _res_orig = method(arr, axis=axis)
+        res_orig = _res_orig.reshape(new_shape)
+        res = method(arr, axis=axis, keepdims=True)
+        assert_equal(res, res_orig)
+        assert_(res.shape == new_shape)
+        outarray = np.empty(res.shape, dtype=res.dtype)
+        res1 = method(arr, axis=axis, out=outarray,
+                            keepdims=True)
+        assert_(res1 is outarray)
+        assert_equal(res, outarray)
+
+        if len(size) > 0:
+            wrong_shape = list(new_shape)
+            if axis is not None:
+                wrong_shape[axis] = 2
+            else:
+                wrong_shape[0] = 2
+            wrong_outarray = np.empty(wrong_shape, dtype=res.dtype)
+            with pytest.raises(ValueError):
+                method(arr.T, axis=axis,
+                        out=wrong_outarray, keepdims=True)
+
+        # non-contiguous arrays
+        if axis is None:
+            new_shape = [1 for _ in range(len(size))]
+        else:
+            new_shape = list(size)[::-1]
+            new_shape[axis] = 1
+        new_shape = tuple(new_shape)
+
+        _res_orig = method(arr.T, axis=axis)
+        res_orig = _res_orig.reshape(new_shape)
+        res = method(arr.T, axis=axis, keepdims=True)
+        assert_equal(res, res_orig)
+        assert_(res.shape == new_shape)
+        outarray = np.empty(new_shape[::-1], dtype=res.dtype)
+        outarray = outarray.T
+        res1 = method(arr.T, axis=axis, out=outarray,
+                            keepdims=True)
+        assert_(res1 is outarray)
+        assert_equal(res, outarray)
+
+        if len(size) > 0:
+            # one dimension lesser for non-zero sized
+            # array should raise an error
+            with pytest.raises(ValueError):
+                method(arr[0], axis=axis,
+                        out=outarray, keepdims=True)
+
+        if len(size) > 0:
+            wrong_shape = list(new_shape)
+            if axis is not None:
+                wrong_shape[axis] = 2
+            else:
+                wrong_shape[0] = 2
+            wrong_outarray = np.empty(wrong_shape, dtype=res.dtype)
+            with pytest.raises(ValueError):
+                method(arr.T, axis=axis,
+                        out=wrong_outarray, keepdims=True)
+
+    @pytest.mark.parametrize('method', ['max', 'min'])
+    def test_all(self, method):
+        a = np.random.normal(0, 1, (4, 5, 6, 7, 8))
+        arg_method = getattr(a, 'arg' + method)
+        val_method = getattr(a, method)
+        for i in range(a.ndim):
+            a_maxmin = val_method(i)
+            aarg_maxmin = arg_method(i)
+            axes = list(range(a.ndim))
+            axes.remove(i)
+            assert_(np.all(a_maxmin == aarg_maxmin.choose(
+                                        *a.transpose(i, *axes))))
+
+    @pytest.mark.parametrize('method', ['argmax', 'argmin'])
+    def test_output_shape(self, method):
+        # see also gh-616
+        a = np.ones((10, 5))
+        arg_method = getattr(a, method)
+        # Check some simple shape mismatches
+        out = np.ones(11, dtype=np.int_)
+        assert_raises(ValueError, arg_method, -1, out)
+
+        out = np.ones((2, 5), dtype=np.int_)
+        assert_raises(ValueError, arg_method, -1, out)
+
+        # these could be relaxed possibly (used to allow even the previous)
+        out = np.ones((1, 10), dtype=np.int_)
+        assert_raises(ValueError, arg_method, -1, out)
+
+        out = np.ones(10, dtype=np.int_)
+        arg_method(-1, out=out)
+        assert_equal(out, arg_method(-1))
+
+    @pytest.mark.parametrize('ndim', [0, 1])
+    @pytest.mark.parametrize('method', ['argmax', 'argmin'])
+    def test_ret_is_out(self, ndim, method):
+        a = np.ones((4,) + (256,) * ndim)
+        arg_method = getattr(a, method)
+        out = np.empty((256,) * ndim, dtype=np.intp)
+        ret = arg_method(axis=0, out=out)
+        assert ret is out
+
+    @pytest.mark.parametrize('np_array, method, idx, val',
+        [(np.zeros, 'argmax', 5942, "as"),
+         (np.ones, 'argmin', 6001, "0")])
+    def test_unicode(self, np_array, method, idx, val):
+        d = np_array(6031, dtype='<U9')
+        arg_method = getattr(d, method)
+        d[idx] = val
+        assert_equal(arg_method(), idx)
+
+    @pytest.mark.parametrize('arr_method, np_method',
+        [('argmax', np.argmax),
+         ('argmin', np.argmin)])
+    def test_np_vs_ndarray(self, arr_method, np_method):
+        # make sure both ndarray.argmax/argmin and
+        # numpy.argmax/argmin support out/axis args
+        a = np.random.normal(size=(2, 3))
+        arg_method = getattr(a, arr_method)
+
+        # check positional args
+        out1 = np.zeros(2, dtype=int)
+        out2 = np.zeros(2, dtype=int)
+        assert_equal(arg_method(1, out1), np_method(a, 1, out2))
+        assert_equal(out1, out2)
+
+        # check keyword args
+        out1 = np.zeros(3, dtype=int)
+        out2 = np.zeros(3, dtype=int)
+        assert_equal(arg_method(out=out1, axis=0),
+                     np_method(a, out=out2, axis=0))
+        assert_equal(out1, out2)
+
+    @pytest.mark.leaks_references(reason="replaces None with NULL.")
+    @pytest.mark.parametrize('method, vals',
+        [('argmax', (10, 30)),
+         ('argmin', (30, 10))])
+    def test_object_with_NULLs(self, method, vals):
+        # See gh-6032
+        a = np.empty(4, dtype='O')
+        arg_method = getattr(a, method)
+        ctypes.memset(a.ctypes.data, 0, a.nbytes)
+        assert_equal(arg_method(), 0)
+        a[3] = vals[0]
+        assert_equal(arg_method(), 3)
+        a[1] = vals[1]
+        assert_equal(arg_method(), 1)
+
+class TestArgmax:
+    usg_data = [
+        ([1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 0),
+        ([3, 3, 3, 3,  2,  2,  2,  2], 0),
+        ([0, 1, 2, 3,  4,  5,  6,  7], 7),
+        ([7, 6, 5, 4,  3,  2,  1,  0], 0)
+    ]
+    sg_data = usg_data + [
+        ([1, 2, 3, 4, -4, -3, -2, -1], 3),
+        ([1, 2, 3, 4, -1, -2, -3, -4], 3)
+    ]
+    darr = [(np.array(d[0], dtype=t), d[1]) for d, t in (
+        itertools.product(usg_data, (
+            np.uint8, np.uint16, np.uint32, np.uint64
+        ))
+    )]
+    darr = darr + [(np.array(d[0], dtype=t), d[1]) for d, t in (
+        itertools.product(sg_data, (
+            np.int8, np.int16, np.int32, np.int64, np.float32, np.float64
+        ))
+    )]
+    darr = darr + [(np.array(d[0], dtype=t), d[1]) for d, t in (
+        itertools.product((
+            ([0, 1, 2, 3, np.nan], 4),
+            ([0, 1, 2, np.nan, 3], 3),
+            ([np.nan, 0, 1, 2, 3], 0),
+            ([np.nan, 0, np.nan, 2, 3], 0),
+            # To hit the tail of SIMD multi-level(x4, x1) inner loops
+            # on variant SIMD widths
+            ([1] * (2 * 5 - 1) + [np.nan], 2 * 5 - 1),
+            ([1] * (4 * 5 - 1) + [np.nan], 4 * 5 - 1),
+            ([1] * (8 * 5 - 1) + [np.nan], 8 * 5 - 1),
+            ([1] * (16 * 5 - 1) + [np.nan], 16 * 5 - 1),
+            ([1] * (32 * 5 - 1) + [np.nan], 32 * 5 - 1)
+        ), (
+            np.float32, np.float64
+        ))
+    )]
+    nan_arr = darr + [
+        ([0, 1, 2, 3, complex(0, np.nan)], 4),
+        ([0, 1, 2, 3, complex(np.nan, 0)], 4),
+        ([0, 1, 2, complex(np.nan, 0), 3], 3),
+        ([0, 1, 2, complex(0, np.nan), 3], 3),
+        ([complex(0, np.nan), 0, 1, 2, 3], 0),
+        ([complex(np.nan, np.nan), 0, 1, 2, 3], 0),
+        ([complex(np.nan, 0), complex(np.nan, 2), complex(np.nan, 1)], 0),
+        ([complex(np.nan, np.nan), complex(np.nan, 2), complex(np.nan, 1)], 0),
+        ([complex(np.nan, 0), complex(np.nan, 2), complex(np.nan, np.nan)], 0),
+
+        ([complex(0, 0), complex(0, 2), complex(0, 1)], 1),
+        ([complex(1, 0), complex(0, 2), complex(0, 1)], 0),
+        ([complex(1, 0), complex(0, 2), complex(1, 1)], 2),
+
+        ([np.datetime64('1923-04-14T12:43:12'),
+          np.datetime64('1994-06-21T14:43:15'),
+          np.datetime64('2001-10-15T04:10:32'),
+          np.datetime64('1995-11-25T16:02:16'),
+          np.datetime64('2005-01-04T03:14:12'),
+          np.datetime64('2041-12-03T14:05:03')], 5),
+        ([np.datetime64('1935-09-14T04:40:11'),
+          np.datetime64('1949-10-12T12:32:11'),
+          np.datetime64('2010-01-03T05:14:12'),
+          np.datetime64('2015-11-20T12:20:59'),
+          np.datetime64('1932-09-23T10:10:13'),
+          np.datetime64('2014-10-10T03:50:30')], 3),
+        # Assorted tests with NaTs
+        ([np.datetime64('NaT'),
+          np.datetime64('NaT'),
+          np.datetime64('2010-01-03T05:14:12'),
+          np.datetime64('NaT'),
+          np.datetime64('2015-09-23T10:10:13'),
+          np.datetime64('1932-10-10T03:50:30')], 0),
+        ([np.datetime64('2059-03-14T12:43:12'),
+          np.datetime64('1996-09-21T14:43:15'),
+          np.datetime64('NaT'),
+          np.datetime64('2022-12-25T16:02:16'),
+          np.datetime64('1963-10-04T03:14:12'),
+          np.datetime64('2013-05-08T18:15:23')], 2),
+        ([np.timedelta64(2, 's'),
+          np.timedelta64(1, 's'),
+          np.timedelta64('NaT', 's'),
+          np.timedelta64(3, 's')], 2),
+        ([np.timedelta64('NaT', 's')] * 3, 0),
+
+        ([timedelta(days=5, seconds=14), timedelta(days=2, seconds=35),
+          timedelta(days=-1, seconds=23)], 0),
+        ([timedelta(days=1, seconds=43), timedelta(days=10, seconds=5),
+          timedelta(days=5, seconds=14)], 1),
+        ([timedelta(days=10, seconds=24), timedelta(days=10, seconds=5),
+          timedelta(days=10, seconds=43)], 2),
+
+        ([False, False, False, False, True], 4),
+        ([False, False, False, True, False], 3),
+        ([True, False, False, False, False], 0),
+        ([True, False, True, False, False], 0),
+    ]
+
+    @pytest.mark.parametrize('data', nan_arr)
+    def test_combinations(self, data):
+        arr, pos = data
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning,
+                        "invalid value encountered in reduce")
+            val = np.max(arr)
+
+        assert_equal(np.argmax(arr), pos, err_msg=f"{arr!r}")
+        assert_equal(arr[np.argmax(arr)], val, err_msg=f"{arr!r}")
+
+        # add padding to test SIMD loops
+        rarr = np.repeat(arr, 129)
+        rpos = pos * 129
+        assert_equal(np.argmax(rarr), rpos, err_msg=f"{rarr!r}")
+        assert_equal(rarr[np.argmax(rarr)], val, err_msg=f"{rarr!r}")
+
+        padd = np.repeat(np.min(arr), 513)
+        rarr = np.concatenate((arr, padd))
+        rpos = pos
+        assert_equal(np.argmax(rarr), rpos, err_msg=f"{rarr!r}")
+        assert_equal(rarr[np.argmax(rarr)], val, err_msg=f"{rarr!r}")
+
+    def test_maximum_signed_integers(self):
+
+        a = np.array([1, 2**7 - 1, -2**7], dtype=np.int8)
+        assert_equal(np.argmax(a), 1)
+        a = a.repeat(129)
+        assert_equal(np.argmax(a), 129)
+
+        a = np.array([1, 2**15 - 1, -2**15], dtype=np.int16)
+        assert_equal(np.argmax(a), 1)
+        a = a.repeat(129)
+        assert_equal(np.argmax(a), 129)
+
+        a = np.array([1, 2**31 - 1, -2**31], dtype=np.int32)
+        assert_equal(np.argmax(a), 1)
+        a = a.repeat(129)
+        assert_equal(np.argmax(a), 129)
+
+        a = np.array([1, 2**63 - 1, -2**63], dtype=np.int64)
+        assert_equal(np.argmax(a), 1)
+        a = a.repeat(129)
+        assert_equal(np.argmax(a), 129)
+
+class TestArgmin:
+    usg_data = [
+        ([1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 8),
+        ([3, 3, 3, 3,  2,  2,  2,  2], 4),
+        ([0, 1, 2, 3,  4,  5,  6,  7], 0),
+        ([7, 6, 5, 4,  3,  2,  1,  0], 7)
+    ]
+    sg_data = usg_data + [
+        ([1, 2, 3, 4, -4, -3, -2, -1], 4),
+        ([1, 2, 3, 4, -1, -2, -3, -4], 7)
+    ]
+    darr = [(np.array(d[0], dtype=t), d[1]) for d, t in (
+        itertools.product(usg_data, (
+            np.uint8, np.uint16, np.uint32, np.uint64
+        ))
+    )]
+    darr = darr + [(np.array(d[0], dtype=t), d[1]) for d, t in (
+        itertools.product(sg_data, (
+            np.int8, np.int16, np.int32, np.int64, np.float32, np.float64
+        ))
+    )]
+    darr = darr + [(np.array(d[0], dtype=t), d[1]) for d, t in (
+        itertools.product((
+            ([0, 1, 2, 3, np.nan], 4),
+            ([0, 1, 2, np.nan, 3], 3),
+            ([np.nan, 0, 1, 2, 3], 0),
+            ([np.nan, 0, np.nan, 2, 3], 0),
+            # To hit the tail of SIMD multi-level(x4, x1) inner loops
+            # on variant SIMD widths
+            ([1] * (2 * 5 - 1) + [np.nan], 2 * 5 - 1),
+            ([1] * (4 * 5 - 1) + [np.nan], 4 * 5 - 1),
+            ([1] * (8 * 5 - 1) + [np.nan], 8 * 5 - 1),
+            ([1] * (16 * 5 - 1) + [np.nan], 16 * 5 - 1),
+            ([1] * (32 * 5 - 1) + [np.nan], 32 * 5 - 1)
+        ), (
+            np.float32, np.float64
+        ))
+    )]
+    nan_arr = darr + [
+        ([0, 1, 2, 3, complex(0, np.nan)], 4),
+        ([0, 1, 2, 3, complex(np.nan, 0)], 4),
+        ([0, 1, 2, complex(np.nan, 0), 3], 3),
+        ([0, 1, 2, complex(0, np.nan), 3], 3),
+        ([complex(0, np.nan), 0, 1, 2, 3], 0),
+        ([complex(np.nan, np.nan), 0, 1, 2, 3], 0),
+        ([complex(np.nan, 0), complex(np.nan, 2), complex(np.nan, 1)], 0),
+        ([complex(np.nan, np.nan), complex(np.nan, 2), complex(np.nan, 1)], 0),
+        ([complex(np.nan, 0), complex(np.nan, 2), complex(np.nan, np.nan)], 0),
+
+        ([complex(0, 0), complex(0, 2), complex(0, 1)], 0),
+        ([complex(1, 0), complex(0, 2), complex(0, 1)], 2),
+        ([complex(1, 0), complex(0, 2), complex(1, 1)], 1),
+
+        ([np.datetime64('1923-04-14T12:43:12'),
+          np.datetime64('1994-06-21T14:43:15'),
+          np.datetime64('2001-10-15T04:10:32'),
+          np.datetime64('1995-11-25T16:02:16'),
+          np.datetime64('2005-01-04T03:14:12'),
+          np.datetime64('2041-12-03T14:05:03')], 0),
+        ([np.datetime64('1935-09-14T04:40:11'),
+          np.datetime64('1949-10-12T12:32:11'),
+          np.datetime64('2010-01-03T05:14:12'),
+          np.datetime64('2014-11-20T12:20:59'),
+          np.datetime64('2015-09-23T10:10:13'),
+          np.datetime64('1932-10-10T03:50:30')], 5),
+        # Assorted tests with NaTs
+        ([np.datetime64('NaT'),
+          np.datetime64('NaT'),
+          np.datetime64('2010-01-03T05:14:12'),
+          np.datetime64('NaT'),
+          np.datetime64('2015-09-23T10:10:13'),
+          np.datetime64('1932-10-10T03:50:30')], 0),
+        ([np.datetime64('2059-03-14T12:43:12'),
+          np.datetime64('1996-09-21T14:43:15'),
+          np.datetime64('NaT'),
+          np.datetime64('2022-12-25T16:02:16'),
+          np.datetime64('1963-10-04T03:14:12'),
+          np.datetime64('2013-05-08T18:15:23')], 2),
+        ([np.timedelta64(2, 's'),
+          np.timedelta64(1, 's'),
+          np.timedelta64('NaT', 's'),
+          np.timedelta64(3, 's')], 2),
+        ([np.timedelta64('NaT', 's')] * 3, 0),
+
+        ([timedelta(days=5, seconds=14), timedelta(days=2, seconds=35),
+          timedelta(days=-1, seconds=23)], 2),
+        ([timedelta(days=1, seconds=43), timedelta(days=10, seconds=5),
+          timedelta(days=5, seconds=14)], 0),
+        ([timedelta(days=10, seconds=24), timedelta(days=10, seconds=5),
+          timedelta(days=10, seconds=43)], 1),
+
+        ([True, True, True, True, False], 4),
+        ([True, True, True, False, True], 3),
+        ([False, True, True, True, True], 0),
+        ([False, True, False, True, True], 0),
+    ]
+
+    @pytest.mark.parametrize('data', nan_arr)
+    def test_combinations(self, data):
+        arr, pos = data
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning,
+                       "invalid value encountered in reduce")
+            min_val = np.min(arr)
+
+        assert_equal(np.argmin(arr), pos, err_msg=f"{arr!r}")
+        assert_equal(arr[np.argmin(arr)], min_val, err_msg=f"{arr!r}")
+
+        # add padding to test SIMD loops
+        rarr = np.repeat(arr, 129)
+        rpos = pos * 129
+        assert_equal(np.argmin(rarr), rpos, err_msg=f"{rarr!r}")
+        assert_equal(rarr[np.argmin(rarr)], min_val, err_msg=f"{rarr!r}")
+
+        padd = np.repeat(np.max(arr), 513)
+        rarr = np.concatenate((arr, padd))
+        rpos = pos
+        assert_equal(np.argmin(rarr), rpos, err_msg=f"{rarr!r}")
+        assert_equal(rarr[np.argmin(rarr)], min_val, err_msg=f"{rarr!r}")
+
+    def test_minimum_signed_integers(self):
+
+        a = np.array([1, -2**7, -2**7 + 1, 2**7 - 1], dtype=np.int8)
+        assert_equal(np.argmin(a), 1)
+        a = a.repeat(129)
+        assert_equal(np.argmin(a), 129)
+
+        a = np.array([1, -2**15, -2**15 + 1, 2**15 - 1], dtype=np.int16)
+        assert_equal(np.argmin(a), 1)
+        a = a.repeat(129)
+        assert_equal(np.argmin(a), 129)
+
+        a = np.array([1, -2**31, -2**31 + 1, 2**31 - 1], dtype=np.int32)
+        assert_equal(np.argmin(a), 1)
+        a = a.repeat(129)
+        assert_equal(np.argmin(a), 129)
+
+        a = np.array([1, -2**63, -2**63 + 1, 2**63 - 1], dtype=np.int64)
+        assert_equal(np.argmin(a), 1)
+        a = a.repeat(129)
+        assert_equal(np.argmin(a), 129)
+
+class TestMinMax:
+
+    def test_scalar(self):
+        assert_raises(AxisError, np.amax, 1, 1)
+        assert_raises(AxisError, np.amin, 1, 1)
+
+        assert_equal(np.amax(1, axis=0), 1)
+        assert_equal(np.amin(1, axis=0), 1)
+        assert_equal(np.amax(1, axis=None), 1)
+        assert_equal(np.amin(1, axis=None), 1)
+
+    def test_axis(self):
+        assert_raises(AxisError, np.amax, [1, 2, 3], 1000)
+        assert_equal(np.amax([[1, 2, 3]], axis=1), 3)
+
+    def test_datetime(self):
+        # Do not ignore NaT
+        for dtype in ('m8[s]', 'm8[Y]'):
+            a = np.arange(10).astype(dtype)
+            assert_equal(np.amin(a), a[0])
+            assert_equal(np.amax(a), a[9])
+            a[3] = 'NaT'
+            assert_equal(np.amin(a), a[3])
+            assert_equal(np.amax(a), a[3])
+
+
+class TestNewaxis:
+    def test_basic(self):
+        sk = np.array([0, -0.1, 0.1])
+        res = 250 * sk[:, np.newaxis]
+        assert_almost_equal(res.ravel(), 250 * sk)
+
+
+class TestClip:
+    def _check_range(self, x, cmin, cmax):
+        assert_(np.all(x >= cmin))
+        assert_(np.all(x <= cmax))
+
+    def _clip_type(self, type_group, array_max,
+                   clip_min, clip_max, inplace=False,
+                   expected_min=None, expected_max=None):
+        if expected_min is None:
+            expected_min = clip_min
+        if expected_max is None:
+            expected_max = clip_max
+
+        for T in np._core.sctypes[type_group]:
+            if sys.byteorder == 'little':
+                byte_orders = ['=', '>']
+            else:
+                byte_orders = ['<', '=']
+
+            for byteorder in byte_orders:
+                dtype = np.dtype(T).newbyteorder(byteorder)
+
+                x = (np.random.random(1000) * array_max).astype(dtype)
+                if inplace:
+                    # The tests that call us pass clip_min and clip_max that
+                    # might not fit in the destination dtype. They were written
+                    # assuming the previous unsafe casting, which now must be
+                    # passed explicitly to avoid a warning.
+                    x.clip(clip_min, clip_max, x, casting='unsafe')
+                else:
+                    x = x.clip(clip_min, clip_max)
+                    byteorder = '='
+
+                if x.dtype.byteorder == '|':
+                    byteorder = '|'
+                assert_equal(x.dtype.byteorder, byteorder)
+                self._check_range(x, expected_min, expected_max)
+        return x
+
+    def test_basic(self):
+        for inplace in [False, True]:
+            self._clip_type(
+                'float', 1024, -12.8, 100.2, inplace=inplace)
+            self._clip_type(
+                'float', 1024, 0, 0, inplace=inplace)
+
+            self._clip_type(
+                'int', 1024, -120, 100, inplace=inplace)
+            self._clip_type(
+                'int', 1024, 0, 0, inplace=inplace)
+
+            self._clip_type(
+                'uint', 1024, 0, 0, inplace=inplace)
+            self._clip_type(
+                'uint', 1024, 10, 100, inplace=inplace)
+
+    @pytest.mark.parametrize("inplace", [False, True])
+    def test_int_out_of_range(self, inplace):
+        # Simple check for out-of-bound integers, also testing the in-place
+        # path.
+        x = (np.random.random(1000) * 255).astype("uint8")
+        out = np.empty_like(x)
+        res = x.clip(-1, 300, out=out if inplace else None)
+        assert res is out or not inplace
+        assert (res == x).all()
+
+        res = x.clip(-1, 50, out=out if inplace else None)
+        assert res is out or not inplace
+        assert (res <= 50).all()
+        assert (res[x <= 50] == x[x <= 50]).all()
+
+        res = x.clip(100, 1000, out=out if inplace else None)
+        assert res is out or not inplace
+        assert (res >= 100).all()
+        assert (res[x >= 100] == x[x >= 100]).all()
+
+    def test_record_array(self):
+        rec = np.array([(-5, 2.0, 3.0), (5.0, 4.0, 3.0)],
+                       dtype=[('x', '<f8'), ('y', '<f8'), ('z', '<f8')])
+        y = rec['x'].clip(-0.3, 0.5)
+        self._check_range(y, -0.3, 0.5)
+
+    def test_max_or_min(self):
+        val = np.array([0, 1, 2, 3, 4, 5, 6, 7])
+        x = val.clip(3)
+        assert_(np.all(x >= 3))
+        x = val.clip(min=3)
+        assert_(np.all(x >= 3))
+        x = val.clip(max=4)
+        assert_(np.all(x <= 4))
+
+    def test_nan(self):
+        input_arr = np.array([-2., np.nan, 0.5, 3., 0.25, np.nan])
+        result = input_arr.clip(-1, 1)
+        expected = np.array([-1., np.nan, 0.5, 1., 0.25, np.nan])
+        assert_array_equal(result, expected)
+
+
+class TestCompress:
+    def test_axis(self):
+        tgt = [[5, 6, 7, 8, 9]]
+        arr = np.arange(10).reshape(2, 5)
+        out = np.compress([0, 1], arr, axis=0)
+        assert_equal(out, tgt)
+
+        tgt = [[1, 3], [6, 8]]
+        out = np.compress([0, 1, 0, 1, 0], arr, axis=1)
+        assert_equal(out, tgt)
+
+    def test_truncate(self):
+        tgt = [[1], [6]]
+        arr = np.arange(10).reshape(2, 5)
+        out = np.compress([0, 1], arr, axis=1)
+        assert_equal(out, tgt)
+
+    def test_flatten(self):
+        arr = np.arange(10).reshape(2, 5)
+        out = np.compress([0, 1], arr)
+        assert_equal(out, 1)
+
+
+class TestPutmask:
+    def tst_basic(self, x, T, mask, val):
+        np.putmask(x, mask, val)
+        assert_equal(x[mask], np.array(val, T))
+
+    def test_ip_types(self):
+        unchecked_types = [bytes, str, np.void]
+
+        x = np.random.random(1000) * 100
+        mask = x < 40
+
+        for val in [-100, 0, 15]:
+            for types in np._core.sctypes.values():
+                for T in types:
+                    if T not in unchecked_types:
+                        if val < 0 and np.dtype(T).kind == "u":
+                            val = np.iinfo(T).max - 99
+                        self.tst_basic(x.copy().astype(T), T, mask, val)
+
+            # Also test string of a length which uses an untypical length
+            dt = np.dtype("S3")
+            self.tst_basic(x.astype(dt), dt.type, mask, dt.type(val)[:3])
+
+    def test_mask_size(self):
+        assert_raises(ValueError, np.putmask, np.array([1, 2, 3]), [True], 5)
+
+    @pytest.mark.parametrize('dtype', ('>i4', '<i4'))
+    def test_byteorder(self, dtype):
+        x = np.array([1, 2, 3], dtype)
+        np.putmask(x, [True, False, True], -1)
+        assert_array_equal(x, [-1, 2, -1])
+
+    def test_record_array(self):
+        # Note mixed byteorder.
+        rec = np.array([(-5, 2.0, 3.0), (5.0, 4.0, 3.0)],
+                      dtype=[('x', '<f8'), ('y', '>f8'), ('z', '<f8')])
+        np.putmask(rec['x'], [True, False], 10)
+        assert_array_equal(rec['x'], [10, 5])
+        assert_array_equal(rec['y'], [2, 4])
+        assert_array_equal(rec['z'], [3, 3])
+        np.putmask(rec['y'], [True, False], 11)
+        assert_array_equal(rec['x'], [10, 5])
+        assert_array_equal(rec['y'], [11, 4])
+        assert_array_equal(rec['z'], [3, 3])
+
+    def test_overlaps(self):
+        # gh-6272 check overlap
+        x = np.array([True, False, True, False])
+        np.putmask(x[1:4], [True, True, True], x[:3])
+        assert_equal(x, np.array([True, True, False, True]))
+
+        x = np.array([True, False, True, False])
+        np.putmask(x[1:4], x[:3], [True, False, True])
+        assert_equal(x, np.array([True, True, True, True]))
+
+    def test_writeable(self):
+        a = np.arange(5)
+        a.flags.writeable = False
+
+        with pytest.raises(ValueError):
+            np.putmask(a, a >= 2, 3)
+
+    def test_kwargs(self):
+        x = np.array([0, 0])
+        np.putmask(x, [0, 1], [-1, -2])
+        assert_array_equal(x, [0, -2])
+
+        x = np.array([0, 0])
+        np.putmask(x, mask=[0, 1], values=[-1, -2])
+        assert_array_equal(x, [0, -2])
+
+        x = np.array([0, 0])
+        np.putmask(x, values=[-1, -2],  mask=[0, 1])
+        assert_array_equal(x, [0, -2])
+
+        with pytest.raises(TypeError):
+            np.putmask(a=x, values=[-1, -2],  mask=[0, 1])
+
+
+class TestTake:
+    def tst_basic(self, x):
+        ind = list(range(x.shape[0]))
+        assert_array_equal(x.take(ind, axis=0), x)
+
+    def test_ip_types(self):
+        unchecked_types = [bytes, str, np.void]
+
+        x = np.random.random(24) * 100
+        x.shape = 2, 3, 4
+        for types in np._core.sctypes.values():
+            for T in types:
+                if T not in unchecked_types:
+                    self.tst_basic(x.copy().astype(T))
+
+            # Also test string of a length which uses an untypical length
+            self.tst_basic(x.astype("S3"))
+
+    def test_raise(self):
+        x = np.random.random(24) * 100
+        x.shape = 2, 3, 4
+        assert_raises(IndexError, x.take, [0, 1, 2], axis=0)
+        assert_raises(IndexError, x.take, [-3], axis=0)
+        assert_array_equal(x.take([-1], axis=0)[0], x[1])
+
+    def test_clip(self):
+        x = np.random.random(24) * 100
+        x.shape = 2, 3, 4
+        assert_array_equal(x.take([-1], axis=0, mode='clip')[0], x[0])
+        assert_array_equal(x.take([2], axis=0, mode='clip')[0], x[1])
+
+    def test_wrap(self):
+        x = np.random.random(24) * 100
+        x.shape = 2, 3, 4
+        assert_array_equal(x.take([-1], axis=0, mode='wrap')[0], x[1])
+        assert_array_equal(x.take([2], axis=0, mode='wrap')[0], x[0])
+        assert_array_equal(x.take([3], axis=0, mode='wrap')[0], x[1])
+
+    @pytest.mark.parametrize('dtype', ('>i4', '<i4'))
+    def test_byteorder(self, dtype):
+        x = np.array([1, 2, 3], dtype)
+        assert_array_equal(x.take([0, 2, 1]), [1, 3, 2])
+
+    def test_record_array(self):
+        # Note mixed byteorder.
+        rec = np.array([(-5, 2.0, 3.0), (5.0, 4.0, 3.0)],
+                      dtype=[('x', '<f8'), ('y', '>f8'), ('z', '<f8')])
+        rec1 = rec.take([1])
+        assert_(rec1['x'] == 5.0 and rec1['y'] == 4.0)
+
+    def test_out_overlap(self):
+        # gh-6272 check overlap on out
+        x = np.arange(5)
+        y = np.take(x, [1, 2, 3], out=x[2:5], mode='wrap')
+        assert_equal(y, np.array([1, 2, 3]))
+
+    @pytest.mark.parametrize('shape', [(1, 2), (1,), ()])
+    def test_ret_is_out(self, shape):
+        # 0d arrays should not be an exception to this rule
+        x = np.arange(5)
+        inds = np.zeros(shape, dtype=np.intp)
+        out = np.zeros(shape, dtype=x.dtype)
+        ret = np.take(x, inds, out=out)
+        assert ret is out
+
+
+class TestLexsort:
+    @pytest.mark.parametrize('dtype', [
+        np.uint8, np.uint16, np.uint32, np.uint64,
+        np.int8, np.int16, np.int32, np.int64,
+        np.float16, np.float32, np.float64
+    ])
+    def test_basic(self, dtype):
+        a = np.array([1, 2, 1, 3, 1, 5], dtype=dtype)
+        b = np.array([0, 4, 5, 6, 2, 3], dtype=dtype)
+        idx = np.lexsort((b, a))
+        expected_idx = np.array([0, 4, 2, 1, 3, 5])
+        assert_array_equal(idx, expected_idx)
+        assert_array_equal(a[idx], np.sort(a))
+
+    def test_mixed(self):
+        a = np.array([1, 2, 1, 3, 1, 5])
+        b = np.array([0, 4, 5, 6, 2, 3], dtype='datetime64[D]')
+
+        idx = np.lexsort((b, a))
+        expected_idx = np.array([0, 4, 2, 1, 3, 5])
+        assert_array_equal(idx, expected_idx)
+
+    def test_datetime(self):
+        a = np.array([0, 0, 0], dtype='datetime64[D]')
+        b = np.array([2, 1, 0], dtype='datetime64[D]')
+        idx = np.lexsort((b, a))
+        expected_idx = np.array([2, 1, 0])
+        assert_array_equal(idx, expected_idx)
+
+        a = np.array([0, 0, 0], dtype='timedelta64[D]')
+        b = np.array([2, 1, 0], dtype='timedelta64[D]')
+        idx = np.lexsort((b, a))
+        expected_idx = np.array([2, 1, 0])
+        assert_array_equal(idx, expected_idx)
+
+    def test_object(self):  # gh-6312
+        a = np.random.choice(10, 1000)
+        b = np.random.choice(['abc', 'xy', 'wz', 'efghi', 'qwst', 'x'], 1000)
+
+        for u in a, b:
+            left = np.lexsort((u.astype('O'),))
+            right = np.argsort(u, kind='mergesort')
+            assert_array_equal(left, right)
+
+        for u, v in (a, b), (b, a):
+            idx = np.lexsort((u, v))
+            assert_array_equal(idx, np.lexsort((u.astype('O'), v)))
+            assert_array_equal(idx, np.lexsort((u, v.astype('O'))))
+            u, v = np.array(u, dtype='object'), np.array(v, dtype='object')
+            assert_array_equal(idx, np.lexsort((u, v)))
+
+    def test_strings(self):  # gh-27984
+        for dtype in "TU":
+            surnames = np.array(['Hertz',    'Galilei', 'Hertz'], dtype=dtype)
+            first_names = np.array(['Heinrich', 'Galileo', 'Gustav'], dtype=dtype)
+            assert_array_equal(np.lexsort((first_names, surnames)), [1, 2, 0])
+
+    def test_invalid_axis(self):  # gh-7528
+        x = np.linspace(0., 1., 42 * 3).reshape(42, 3)
+        assert_raises(AxisError, np.lexsort, x, axis=2)
+
+class TestIO:
+    """Test tofile, fromfile, tobytes, and fromstring"""
+
+    @pytest.fixture()
+    def x(self):
+        shape = (2, 4, 3)
+        rand = np.random.random
+        x = rand(shape) + rand(shape).astype(complex) * 1j
+        x[0, :, 1] = [np.nan, np.inf, -np.inf, np.nan]
+        return x
+
+    @pytest.fixture(params=["string", "path_obj"])
+    def tmp_filename(self, tmp_path, request):
+        # This fixture covers two cases:
+        # one where the filename is a string and
+        # another where it is a pathlib object
+        filename = tmp_path / "file"
+        if request.param == "string":
+            filename = str(filename)
+        yield filename
+
+    def test_nofile(self):
+        # this should probably be supported as a file
+        # but for now test for proper errors
+        b = io.BytesIO()
+        assert_raises(OSError, np.fromfile, b, np.uint8, 80)
+        d = np.ones(7)
+        assert_raises(OSError, lambda x: x.tofile(b), d)
+
+    def test_bool_fromstring(self):
+        v = np.array([True, False, True, False], dtype=np.bool)
+        y = np.fromstring('1 0 -2.3 0.0', sep=' ', dtype=np.bool)
+        assert_array_equal(v, y)
+
+    def test_uint64_fromstring(self):
+        d = np.fromstring("9923372036854775807 104783749223640",
+                          dtype=np.uint64, sep=' ')
+        e = np.array([9923372036854775807, 104783749223640], dtype=np.uint64)
+        assert_array_equal(d, e)
+
+    def test_int64_fromstring(self):
+        d = np.fromstring("-25041670086757 104783749223640",
+                          dtype=np.int64, sep=' ')
+        e = np.array([-25041670086757, 104783749223640], dtype=np.int64)
+        assert_array_equal(d, e)
+
+    def test_fromstring_count0(self):
+        d = np.fromstring("1,2", sep=",", dtype=np.int64, count=0)
+        assert d.shape == (0,)
+
+    def test_empty_files_text(self, tmp_filename):
+        with open(tmp_filename, 'w') as f:
+            pass
+        y = np.fromfile(tmp_filename)
+        assert_(y.size == 0, "Array not empty")
+
+    def test_empty_files_binary(self, tmp_filename):
+        with open(tmp_filename, 'wb') as f:
+            pass
+        y = np.fromfile(tmp_filename, sep=" ")
+        assert_(y.size == 0, "Array not empty")
+
+    def test_roundtrip_file(self, x, tmp_filename):
+        with open(tmp_filename, 'wb') as f:
+            x.tofile(f)
+        # NB. doesn't work with flush+seek, due to use of C stdio
+        with open(tmp_filename, 'rb') as f:
+            y = np.fromfile(f, dtype=x.dtype)
+        assert_array_equal(y, x.flat)
+
+    def test_roundtrip(self, x, tmp_filename):
+        x.tofile(tmp_filename)
+        y = np.fromfile(tmp_filename, dtype=x.dtype)
+        assert_array_equal(y, x.flat)
+
+    def test_roundtrip_dump_pathlib(self, x, tmp_filename):
+        p = pathlib.Path(tmp_filename)
+        x.dump(p)
+        y = np.load(p, allow_pickle=True)
+        assert_array_equal(y, x)
+
+    def test_roundtrip_binary_str(self, x):
+        s = x.tobytes()
+        y = np.frombuffer(s, dtype=x.dtype)
+        assert_array_equal(y, x.flat)
+
+        s = x.tobytes('F')
+        y = np.frombuffer(s, dtype=x.dtype)
+        assert_array_equal(y, x.flatten('F'))
+
+    def test_roundtrip_str(self, x):
+        x = x.real.ravel()
+        s = "@".join(map(str, x))
+        y = np.fromstring(s, sep="@")
+        nan_mask = ~np.isfinite(x)
+        assert_array_equal(x[nan_mask], y[nan_mask])
+        assert_array_equal(x[~nan_mask], y[~nan_mask])
+
+    def test_roundtrip_repr(self, x):
+        x = x.real.ravel()
+        s = "@".join(repr(x)[11:-1] for x in x)
+        y = np.fromstring(s, sep="@")
+        assert_array_equal(x, y)
+
+    def test_unseekable_fromfile(self, x, tmp_filename):
+        # gh-6246
+        x.tofile(tmp_filename)
+
+        def fail(*args, **kwargs):
+            raise OSError('Can not tell or seek')
+
+        with open(tmp_filename, 'rb', buffering=0) as f:
+            f.seek = fail
+            f.tell = fail
+            assert_raises(OSError, np.fromfile, f, dtype=x.dtype)
+
+    def test_io_open_unbuffered_fromfile(self, x, tmp_filename):
+        # gh-6632
+        x.tofile(tmp_filename)
+        with open(tmp_filename, 'rb', buffering=0) as f:
+            y = np.fromfile(f, dtype=x.dtype)
+            assert_array_equal(y, x.flat)
+
+    def test_largish_file(self, tmp_filename):
+        # check the fallocate path on files > 16MB
+        d = np.zeros(4 * 1024 ** 2)
+        d.tofile(tmp_filename)
+        assert_equal(os.path.getsize(tmp_filename), d.nbytes)
+        assert_array_equal(d, np.fromfile(tmp_filename))
+        # check offset
+        with open(tmp_filename, "r+b") as f:
+            f.seek(d.nbytes)
+            d.tofile(f)
+            assert_equal(os.path.getsize(tmp_filename), d.nbytes * 2)
+        # check append mode (gh-8329)
+        open(tmp_filename, "w").close()  # delete file contents
+        with open(tmp_filename, "ab") as f:
+            d.tofile(f)
+        assert_array_equal(d, np.fromfile(tmp_filename))
+        with open(tmp_filename, "ab") as f:
+            d.tofile(f)
+        assert_equal(os.path.getsize(tmp_filename), d.nbytes * 2)
+
+    def test_io_open_buffered_fromfile(self, x, tmp_filename):
+        # gh-6632
+        x.tofile(tmp_filename)
+        with open(tmp_filename, 'rb', buffering=-1) as f:
+            y = np.fromfile(f, dtype=x.dtype)
+        assert_array_equal(y, x.flat)
+
+    def test_file_position_after_fromfile(self, tmp_filename):
+        # gh-4118
+        sizes = [io.DEFAULT_BUFFER_SIZE // 8,
+                 io.DEFAULT_BUFFER_SIZE,
+                 io.DEFAULT_BUFFER_SIZE * 8]
+
+        for size in sizes:
+            with open(tmp_filename, 'wb') as f:
+                f.seek(size - 1)
+                f.write(b'\0')
+
+            for mode in ['rb', 'r+b']:
+                err_msg = "%d %s" % (size, mode)
+
+                with open(tmp_filename, mode) as f:
+                    f.read(2)
+                    np.fromfile(f, dtype=np.float64, count=1)
+                    pos = f.tell()
+                assert_equal(pos, 10, err_msg=err_msg)
+
+    def test_file_position_after_tofile(self, tmp_filename):
+        # gh-4118
+        sizes = [io.DEFAULT_BUFFER_SIZE // 8,
+                 io.DEFAULT_BUFFER_SIZE,
+                 io.DEFAULT_BUFFER_SIZE * 8]
+
+        for size in sizes:
+            err_msg = "%d" % (size,)
+
+            with open(tmp_filename, 'wb') as f:
+                f.seek(size - 1)
+                f.write(b'\0')
+                f.seek(10)
+                f.write(b'12')
+                np.array([0], dtype=np.float64).tofile(f)
+                pos = f.tell()
+            assert_equal(pos, 10 + 2 + 8, err_msg=err_msg)
+
+            with open(tmp_filename, 'r+b') as f:
+                f.read(2)
+                f.seek(0, 1)  # seek between read&write required by ANSI C
+                np.array([0], dtype=np.float64).tofile(f)
+                pos = f.tell()
+            assert_equal(pos, 10, err_msg=err_msg)
+
+    def test_load_object_array_fromfile(self, tmp_filename):
+        # gh-12300
+        with open(tmp_filename, 'w') as f:
+            # Ensure we have a file with consistent contents
+            pass
+
+        with open(tmp_filename, 'rb') as f:
+            assert_raises_regex(ValueError, "Cannot read into object array",
+                                np.fromfile, f, dtype=object)
+
+        assert_raises_regex(ValueError, "Cannot read into object array",
+                            np.fromfile, tmp_filename, dtype=object)
+
+    def test_fromfile_offset(self, x, tmp_filename):
+        with open(tmp_filename, 'wb') as f:
+            x.tofile(f)
+
+        with open(tmp_filename, 'rb') as f:
+            y = np.fromfile(f, dtype=x.dtype, offset=0)
+            assert_array_equal(y, x.flat)
+
+        with open(tmp_filename, 'rb') as f:
+            count_items = len(x.flat) // 8
+            offset_items = len(x.flat) // 4
+            offset_bytes = x.dtype.itemsize * offset_items
+            y = np.fromfile(
+                f, dtype=x.dtype, count=count_items, offset=offset_bytes
+            )
+            assert_array_equal(
+                y, x.flat[offset_items:offset_items + count_items]
+            )
+
+            # subsequent seeks should stack
+            offset_bytes = x.dtype.itemsize
+            z = np.fromfile(f, dtype=x.dtype, offset=offset_bytes)
+            assert_array_equal(z, x.flat[offset_items + count_items + 1:])
+
+        with open(tmp_filename, 'wb') as f:
+            x.tofile(f, sep=",")
+
+        with open(tmp_filename, 'rb') as f:
+            assert_raises_regex(
+                    TypeError,
+                    "'offset' argument only permitted for binary files",
+                    np.fromfile, tmp_filename, dtype=x.dtype,
+                    sep=",", offset=1)
+
+    @pytest.mark.skipif(IS_PYPY, reason="bug in PyPy's PyNumber_AsSsize_t")
+    def test_fromfile_bad_dup(self, x, tmp_filename):
+        def dup_str(fd):
+            return 'abc'
+
+        def dup_bigint(fd):
+            return 2**68
+
+        old_dup = os.dup
+        try:
+            with open(tmp_filename, 'wb') as f:
+                x.tofile(f)
+                for dup, exc in ((dup_str, TypeError), (dup_bigint, OSError)):
+                    os.dup = dup
+                    assert_raises(exc, np.fromfile, f)
+        finally:
+            os.dup = old_dup
+
+    def _check_from(self, s, value, filename, **kw):
+        if 'sep' not in kw:
+            y = np.frombuffer(s, **kw)
+        else:
+            y = np.fromstring(s, **kw)
+        assert_array_equal(y, value)
+
+        with open(filename, 'wb') as f:
+            f.write(s)
+        y = np.fromfile(filename, **kw)
+        assert_array_equal(y, value)
+
+    @pytest.fixture(params=["period", "comma"])
+    def decimal_sep_localization(self, request):
+        """
+        Including this fixture in a test will automatically
+        execute it with both types of decimal separator.
+
+        So::
+
+            def test_decimal(decimal_sep_localization):
+                pass
+
+        is equivalent to the following two tests::
+
+            def test_decimal_period_separator():
+                pass
+
+            def test_decimal_comma_separator():
+                with CommaDecimalPointLocale():
+                    pass
+        """
+        if request.param == "period":
+            yield
+        elif request.param == "comma":
+            with CommaDecimalPointLocale():
+                yield
+        else:
+            assert False, request.param
+
+    def test_nan(self, tmp_filename, decimal_sep_localization):
+        self._check_from(
+            b"nan +nan -nan NaN nan(foo) +NaN(BAR) -NAN(q_u_u_x_)",
+            [np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan],
+            tmp_filename,
+            sep=' ')
+
+    def test_inf(self, tmp_filename, decimal_sep_localization):
+        self._check_from(
+            b"inf +inf -inf infinity -Infinity iNfInItY -inF",
+            [np.inf, np.inf, -np.inf, np.inf, -np.inf, np.inf, -np.inf],
+            tmp_filename,
+            sep=' ')
+
+    def test_numbers(self, tmp_filename, decimal_sep_localization):
+        self._check_from(
+            b"1.234 -1.234 .3 .3e55 -123133.1231e+133",
+            [1.234, -1.234, .3, .3e55, -123133.1231e+133],
+            tmp_filename,
+            sep=' ')
+
+    def test_binary(self, tmp_filename):
+        self._check_from(
+            b'\x00\x00\x80?\x00\x00\x00@\x00\x00@@\x00\x00\x80@',
+            np.array([1, 2, 3, 4]),
+            tmp_filename,
+            dtype='<f4')
+
+    def test_string(self, tmp_filename):
+        self._check_from(b'1,2,3,4', [1., 2., 3., 4.], tmp_filename, sep=',')
+
+    def test_counted_string(self, tmp_filename, decimal_sep_localization):
+        self._check_from(
+            b'1,2,3,4', [1., 2., 3., 4.], tmp_filename, count=4, sep=',')
+        self._check_from(
+            b'1,2,3,4', [1., 2., 3.], tmp_filename, count=3, sep=',')
+        self._check_from(
+            b'1,2,3,4', [1., 2., 3., 4.], tmp_filename, count=-1, sep=',')
+
+    def test_string_with_ws(self, tmp_filename):
+        self._check_from(
+            b'1 2  3     4   ', [1, 2, 3, 4], tmp_filename, dtype=int, sep=' ')
+
+    def test_counted_string_with_ws(self, tmp_filename):
+        self._check_from(
+            b'1 2  3     4   ', [1, 2, 3], tmp_filename, count=3, dtype=int,
+            sep=' ')
+
+    def test_ascii(self, tmp_filename, decimal_sep_localization):
+        self._check_from(
+            b'1 , 2 , 3 , 4', [1., 2., 3., 4.], tmp_filename, sep=',')
+        self._check_from(
+            b'1,2,3,4', [1., 2., 3., 4.], tmp_filename, dtype=float, sep=',')
+
+    def test_malformed(self, tmp_filename, decimal_sep_localization):
+        with assert_raises(ValueError):
+            self._check_from(
+                b'1.234 1,234', [1.234, 1.], tmp_filename, sep=' ')
+
+    def test_long_sep(self, tmp_filename):
+        self._check_from(
+            b'1_x_3_x_4_x_5', [1, 3, 4, 5], tmp_filename, sep='_x_')
+
+    def test_dtype(self, tmp_filename):
+        v = np.array([1, 2, 3, 4], dtype=np.int_)
+        self._check_from(b'1,2,3,4', v, tmp_filename, sep=',', dtype=np.int_)
+
+    def test_dtype_bool(self, tmp_filename):
+        # can't use _check_from because fromstring can't handle True/False
+        v = np.array([True, False, True, False], dtype=np.bool)
+        s = b'1,0,-2.3,0'
+        with open(tmp_filename, 'wb') as f:
+            f.write(s)
+        y = np.fromfile(tmp_filename, sep=',', dtype=np.bool)
+        assert_(y.dtype == '?')
+        assert_array_equal(y, v)
+
+    def test_tofile_sep(self, tmp_filename, decimal_sep_localization):
+        x = np.array([1.51, 2, 3.51, 4], dtype=float)
+        with open(tmp_filename, 'w') as f:
+            x.tofile(f, sep=',')
+        with open(tmp_filename, 'r') as f:
+            s = f.read()
+        #assert_equal(s, '1.51,2.0,3.51,4.0')
+        y = np.array([float(p) for p in s.split(',')])
+        assert_array_equal(x, y)
+
+    def test_tofile_format(self, tmp_filename, decimal_sep_localization):
+        x = np.array([1.51, 2, 3.51, 4], dtype=float)
+        with open(tmp_filename, 'w') as f:
+            x.tofile(f, sep=',', format='%.2f')
+        with open(tmp_filename, 'r') as f:
+            s = f.read()
+        assert_equal(s, '1.51,2.00,3.51,4.00')
+
+    def test_tofile_cleanup(self, tmp_filename):
+        x = np.zeros((10), dtype=object)
+        with open(tmp_filename, 'wb') as f:
+            assert_raises(OSError, lambda: x.tofile(f, sep=''))
+        # Dup-ed file handle should be closed or remove will fail on Windows OS
+        os.remove(tmp_filename)
+
+        # Also make sure that we close the Python handle
+        assert_raises(OSError, lambda: x.tofile(tmp_filename))
+        os.remove(tmp_filename)
+
+    def test_fromfile_subarray_binary(self, tmp_filename):
+        # Test subarray dtypes which are absorbed into the shape
+        x = np.arange(24, dtype="i4").reshape(2, 3, 4)
+        x.tofile(tmp_filename)
+        res = np.fromfile(tmp_filename, dtype="(3,4)i4")
+        assert_array_equal(x, res)
+
+        x_str = x.tobytes()
+        with pytest.raises(ValueError):
+            # binary fromstring raises
+            np.fromstring(x_str, dtype="(3,4)i4")
+
+    def test_parsing_subarray_unsupported(self, tmp_filename):
+        # We currently do not support parsing subarray dtypes
+        data = "12,42,13," * 50
+        with pytest.raises(ValueError):
+            expected = np.fromstring(data, dtype="(3,)i", sep=",")
+
+        with open(tmp_filename, "w") as f:
+            f.write(data)
+
+        with pytest.raises(ValueError):
+            np.fromfile(tmp_filename, dtype="(3,)i", sep=",")
+
+    def test_read_shorter_than_count_subarray(self, tmp_filename):
+        # Test that requesting more values does not cause any problems
+        # in conjunction with subarray dimensions being absorbed into the
+        # array dimension.
+        expected = np.arange(511 * 10, dtype="i").reshape(-1, 10)
+
+        binary = expected.tobytes()
+        with pytest.raises(ValueError):
+            np.fromstring(binary, dtype="(10,)i", count=10000)
+
+        expected.tofile(tmp_filename)
+        res = np.fromfile(tmp_filename, dtype="(10,)i", count=10000)
+        assert_array_equal(res, expected)
+
+
+class TestFromBuffer:
+    @pytest.mark.parametrize('byteorder', ['<', '>'])
+    @pytest.mark.parametrize('dtype', [float, int, complex])
+    def test_basic(self, byteorder, dtype):
+        dt = np.dtype(dtype).newbyteorder(byteorder)
+        x = (np.random.random((4, 7)) * 5).astype(dt)
+        buf = x.tobytes()
+        assert_array_equal(np.frombuffer(buf, dtype=dt), x.flat)
+
+    @pytest.mark.parametrize("obj", [np.arange(10), b"12345678"])
+    def test_array_base(self, obj):
+        # Objects (including NumPy arrays), which do not use the
+        # `release_buffer` slot should be directly used as a base object.
+        # See also gh-21612
+        new = np.frombuffer(obj)
+        assert new.base is obj
+
+    def test_empty(self):
+        assert_array_equal(np.frombuffer(b''), np.array([]))
+
+    @pytest.mark.skipif(IS_PYPY,
+            reason="PyPy's memoryview currently does not track exports. See: "
+                   "https://foss.heptapod.net/pypy/pypy/-/issues/3724")
+    def test_mmap_close(self):
+        # The old buffer protocol was not safe for some things that the new
+        # one is.  But `frombuffer` always used the old one for a long time.
+        # Checks that it is safe with the new one (using memoryviews)
+        with tempfile.TemporaryFile(mode='wb') as tmp:
+            tmp.write(b"asdf")
+            tmp.flush()
+            mm = mmap.mmap(tmp.fileno(), 0)
+            arr = np.frombuffer(mm, dtype=np.uint8)
+            with pytest.raises(BufferError):
+                mm.close()  # cannot close while array uses the buffer
+            del arr
+            mm.close()
+
+class TestFlat:
+    def setup_method(self):
+        a0 = np.arange(20.0)
+        a = a0.reshape(4, 5)
+        a0.shape = (4, 5)
+        a.flags.writeable = False
+        self.a = a
+        self.b = a[::2, ::2]
+        self.a0 = a0
+        self.b0 = a0[::2, ::2]
+
+    def test_contiguous(self):
+        testpassed = False
+        try:
+            self.a.flat[12] = 100.0
+        except ValueError:
+            testpassed = True
+        assert_(testpassed)
+        assert_(self.a.flat[12] == 12.0)
+
+    def test_discontiguous(self):
+        testpassed = False
+        try:
+            self.b.flat[4] = 100.0
+        except ValueError:
+            testpassed = True
+        assert_(testpassed)
+        assert_(self.b.flat[4] == 12.0)
+
+    def test___array__(self):
+        c = self.a.flat.__array__()
+        d = self.b.flat.__array__()
+        e = self.a0.flat.__array__()
+        f = self.b0.flat.__array__()
+
+        assert_(c.flags.writeable is False)
+        assert_(d.flags.writeable is False)
+        assert_(e.flags.writeable is True)
+        assert_(f.flags.writeable is False)
+        assert_(c.flags.writebackifcopy is False)
+        assert_(d.flags.writebackifcopy is False)
+        assert_(e.flags.writebackifcopy is False)
+        assert_(f.flags.writebackifcopy is False)
+
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test_refcount(self):
+        # includes regression test for reference count error gh-13165
+        inds = [np.intp(0), np.array([True] * self.a.size), np.array([0]), None]
+        indtype = np.dtype(np.intp)
+        rc_indtype = sys.getrefcount(indtype)
+        for ind in inds:
+            rc_ind = sys.getrefcount(ind)
+            for _ in range(100):
+                try:
+                    self.a.flat[ind]
+                except IndexError:
+                    pass
+            assert_(abs(sys.getrefcount(ind) - rc_ind) < 50)
+            assert_(abs(sys.getrefcount(indtype) - rc_indtype) < 50)
+
+    def test_index_getset(self):
+        it = np.arange(10).reshape(2, 1, 5).flat
+        with pytest.raises(AttributeError):
+            it.index = 10
+
+        for _ in it:
+            pass
+        # Check the value of `.index` is updated correctly (see also gh-19153)
+        # If the type was incorrect, this would show up on big-endian machines
+        assert it.index == it.base.size
+
+    def test_maxdims(self):
+        # The flat iterator and thus attribute is currently unfortunately
+        # limited to only 32 dimensions (after bumping it to 64 for 2.0)
+        a = np.ones((1,) * 64)
+
+        with pytest.raises(RuntimeError,
+                match=".*32 dimensions but the array has 64"):
+            a.flat
+
+
+class TestResize:
+
+    @_no_tracing
+    def test_basic(self):
+        x = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+        if IS_PYPY:
+            x.resize((5, 5), refcheck=False)
+        else:
+            x.resize((5, 5))
+        assert_array_equal(x.flat[:9],
+                np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]).flat)
+        assert_array_equal(x[9:].flat, 0)
+
+    def test_check_reference(self):
+        x = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+        y = x
+        assert_raises(ValueError, x.resize, (5, 1))
+
+    @_no_tracing
+    def test_int_shape(self):
+        x = np.eye(3)
+        if IS_PYPY:
+            x.resize(3, refcheck=False)
+        else:
+            x.resize(3)
+        assert_array_equal(x, np.eye(3)[0, :])
+
+    def test_none_shape(self):
+        x = np.eye(3)
+        x.resize(None)
+        assert_array_equal(x, np.eye(3))
+        x.resize()
+        assert_array_equal(x, np.eye(3))
+
+    def test_0d_shape(self):
+        # to it multiple times to test it does not break alloc cache gh-9216
+        for i in range(10):
+            x = np.empty((1,))
+            x.resize(())
+            assert_equal(x.shape, ())
+            assert_equal(x.size, 1)
+            x = np.empty(())
+            x.resize((1,))
+            assert_equal(x.shape, (1,))
+            assert_equal(x.size, 1)
+
+    def test_invalid_arguments(self):
+        assert_raises(TypeError, np.eye(3).resize, 'hi')
+        assert_raises(ValueError, np.eye(3).resize, -1)
+        assert_raises(TypeError, np.eye(3).resize, order=1)
+        assert_raises(TypeError, np.eye(3).resize, refcheck='hi')
+
+    @_no_tracing
+    def test_freeform_shape(self):
+        x = np.eye(3)
+        if IS_PYPY:
+            x.resize(3, 2, 1, refcheck=False)
+        else:
+            x.resize(3, 2, 1)
+        assert_(x.shape == (3, 2, 1))
+
+    @_no_tracing
+    def test_zeros_appended(self):
+        x = np.eye(3)
+        if IS_PYPY:
+            x.resize(2, 3, 3, refcheck=False)
+        else:
+            x.resize(2, 3, 3)
+        assert_array_equal(x[0], np.eye(3))
+        assert_array_equal(x[1], np.zeros((3, 3)))
+
+    @_no_tracing
+    def test_obj_obj(self):
+        # check memory is initialized on resize, gh-4857
+        a = np.ones(10, dtype=[('k', object, 2)])
+        if IS_PYPY:
+            a.resize(15, refcheck=False)
+        else:
+            a.resize(15,)
+        assert_equal(a.shape, (15,))
+        assert_array_equal(a['k'][-5:], 0)
+        assert_array_equal(a['k'][:-5], 1)
+
+    def test_empty_view(self):
+        # check that sizes containing a zero don't trigger a reallocate for
+        # already empty arrays
+        x = np.zeros((10, 0), int)
+        x_view = x[...]
+        x_view.resize((0, 10))
+        x_view.resize((0, 100))
+
+    def test_check_weakref(self):
+        x = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+        xref = weakref.ref(x)
+        assert_raises(ValueError, x.resize, (5, 1))
+
+
+class TestRecord:
+    def test_field_rename(self):
+        dt = np.dtype([('f', float), ('i', int)])
+        dt.names = ['p', 'q']
+        assert_equal(dt.names, ['p', 'q'])
+
+    def test_multiple_field_name_occurrence(self):
+        def test_dtype_init():
+            np.dtype([("A", "f8"), ("B", "f8"), ("A", "f8")])
+
+        # Error raised when multiple fields have the same name
+        assert_raises(ValueError, test_dtype_init)
+
+    def test_bytes_fields(self):
+        # Bytes are not allowed in field names and not recognized in titles
+        # on Py3
+        assert_raises(TypeError, np.dtype, [(b'a', int)])
+        assert_raises(TypeError, np.dtype, [(('b', b'a'), int)])
+
+        dt = np.dtype([((b'a', 'b'), int)])
+        assert_raises(TypeError, dt.__getitem__, b'a')
+
+        x = np.array([(1,), (2,), (3,)], dtype=dt)
+        assert_raises(IndexError, x.__getitem__, b'a')
+
+        y = x[0]
+        assert_raises(IndexError, y.__getitem__, b'a')
+
+    def test_multiple_field_name_unicode(self):
+        def test_dtype_unicode():
+            np.dtype([("\u20B9", "f8"), ("B", "f8"), ("\u20B9", "f8")])
+
+        # Error raised when multiple fields have the same name(unicode included)
+        assert_raises(ValueError, test_dtype_unicode)
+
+    def test_fromarrays_unicode(self):
+        # A single name string provided to fromarrays() is allowed to be unicode
+        x = np._core.records.fromarrays(
+            [[0], [1]], names='a,b', formats='i4,i4')
+        assert_equal(x['a'][0], 0)
+        assert_equal(x['b'][0], 1)
+
+    def test_unicode_order(self):
+        # Test that we can sort with order as a unicode field name
+        name = 'b'
+        x = np.array([1, 3, 2], dtype=[(name, int)])
+        x.sort(order=name)
+        assert_equal(x['b'], np.array([1, 2, 3]))
+
+    def test_field_names(self):
+        # Test unicode and 8-bit / byte strings can be used
+        a = np.zeros((1,), dtype=[('f1', 'i4'),
+                                  ('f2', 'i4'),
+                                  ('f3', [('sf1', 'i4')])])
+        # byte string indexing fails gracefully
+        assert_raises(IndexError, a.__setitem__, b'f1', 1)
+        assert_raises(IndexError, a.__getitem__, b'f1')
+        assert_raises(IndexError, a['f1'].__setitem__, b'sf1', 1)
+        assert_raises(IndexError, a['f1'].__getitem__, b'sf1')
+        b = a.copy()
+        fn1 = 'f1'
+        b[fn1] = 1
+        assert_equal(b[fn1], 1)
+        fnn = 'not at all'
+        assert_raises(ValueError, b.__setitem__, fnn, 1)
+        assert_raises(ValueError, b.__getitem__, fnn)
+        b[0][fn1] = 2
+        assert_equal(b[fn1], 2)
+        # Subfield
+        assert_raises(ValueError, b[0].__setitem__, fnn, 1)
+        assert_raises(ValueError, b[0].__getitem__, fnn)
+        # Subfield
+        fn3 = 'f3'
+        sfn1 = 'sf1'
+        b[fn3][sfn1] = 1
+        assert_equal(b[fn3][sfn1], 1)
+        assert_raises(ValueError, b[fn3].__setitem__, fnn, 1)
+        assert_raises(ValueError, b[fn3].__getitem__, fnn)
+        # multiple subfields
+        fn2 = 'f2'
+        b[fn2] = 3
+
+        assert_equal(b[['f1', 'f2']][0].tolist(), (2, 3))
+        assert_equal(b[['f2', 'f1']][0].tolist(), (3, 2))
+        assert_equal(b[['f1', 'f3']][0].tolist(), (2, (1,)))
+
+        # non-ascii unicode field indexing is well behaved
+        assert_raises(ValueError, a.__setitem__, '\u03e0', 1)
+        assert_raises(ValueError, a.__getitem__, '\u03e0')
+
+    def test_record_hash(self):
+        a = np.array([(1, 2), (1, 2)], dtype='i1,i2')
+        a.flags.writeable = False
+        b = np.array([(1, 2), (3, 4)], dtype=[('num1', 'i1'), ('num2', 'i2')])
+        b.flags.writeable = False
+        c = np.array([(1, 2), (3, 4)], dtype='i1,i2')
+        c.flags.writeable = False
+        assert_(hash(a[0]) == hash(a[1]))
+        assert_(hash(a[0]) == hash(b[0]))
+        assert_(hash(a[0]) != hash(b[1]))
+        assert_(hash(c[0]) == hash(a[0]) and c[0] == a[0])
+
+    def test_record_no_hash(self):
+        a = np.array([(1, 2), (1, 2)], dtype='i1,i2')
+        assert_raises(TypeError, hash, a[0])
+
+    def test_empty_structure_creation(self):
+        # make sure these do not raise errors (gh-5631)
+        np.array([()], dtype={'names': [], 'formats': [],
+                           'offsets': [], 'itemsize': 12})
+        np.array([(), (), (), (), ()], dtype={'names': [], 'formats': [],
+                                           'offsets': [], 'itemsize': 12})
+
+    def test_multifield_indexing_view(self):
+        a = np.ones(3, dtype=[('a', 'i4'), ('b', 'f4'), ('c', 'u4')])
+        v = a[['a', 'c']]
+        assert_(v.base is a)
+        assert_(v.dtype == np.dtype({'names': ['a', 'c'],
+                                     'formats': ['i4', 'u4'],
+                                     'offsets': [0, 8]}))
+        v[:] = (4, 5)
+        assert_equal(a[0].item(), (4, 1, 5))
+
+class TestView:
+    def test_basic(self):
+        x = np.array([(1, 2, 3, 4), (5, 6, 7, 8)],
+                     dtype=[('r', np.int8), ('g', np.int8),
+                            ('b', np.int8), ('a', np.int8)])
+        # We must be specific about the endianness here:
+        y = x.view(dtype='<i4')
+        # ... and again without the keyword.
+        z = x.view('<i4')
+        assert_array_equal(y, z)
+        assert_array_equal(y, [67305985, 134678021])
+
+
+def _mean(a, **args):
+    return a.mean(**args)
+
+
+def _var(a, **args):
+    return a.var(**args)
+
+
+def _std(a, **args):
+    return a.std(**args)
+
+
+class TestStats:
+
+    funcs = [_mean, _var, _std]
+
+    def setup_method(self):
+        np.random.seed(range(3))
+        self.rmat = np.random.random((4, 5))
+        self.cmat = self.rmat + 1j * self.rmat
+        self.omat = np.array([Decimal(str(r)) for r in self.rmat.flat])
+        self.omat = self.omat.reshape(4, 5)
+
+    def test_python_type(self):
+        for x in (np.float16(1.), 1, 1., 1 + 0j):
+            assert_equal(np.mean([x]), 1.)
+            assert_equal(np.std([x]), 0.)
+            assert_equal(np.var([x]), 0.)
+
+    def test_keepdims(self):
+        mat = np.eye(3)
+        for f in self.funcs:
+            for axis in [0, 1]:
+                res = f(mat, axis=axis, keepdims=True)
+                assert_(res.ndim == mat.ndim)
+                assert_(res.shape[axis] == 1)
+            for axis in [None]:
+                res = f(mat, axis=axis, keepdims=True)
+                assert_(res.shape == (1, 1))
+
+    def test_out(self):
+        mat = np.eye(3)
+        for f in self.funcs:
+            out = np.zeros(3)
+            tgt = f(mat, axis=1)
+            res = f(mat, axis=1, out=out)
+            assert_almost_equal(res, out)
+            assert_almost_equal(res, tgt)
+        out = np.empty(2)
+        assert_raises(ValueError, f, mat, axis=1, out=out)
+        out = np.empty((2, 2))
+        assert_raises(ValueError, f, mat, axis=1, out=out)
+
+    def test_dtype_from_input(self):
+
+        icodes = np.typecodes['AllInteger']
+        fcodes = np.typecodes['AllFloat']
+
+        # object type
+        for f in self.funcs:
+            mat = np.array([[Decimal(1)] * 3] * 3)
+            tgt = mat.dtype.type
+            res = f(mat, axis=1).dtype.type
+            assert_(res is tgt)
+            # scalar case
+            res = type(f(mat, axis=None))
+            assert_(res is Decimal)
+
+        # integer types
+        for f in self.funcs:
+            for c in icodes:
+                mat = np.eye(3, dtype=c)
+                tgt = np.float64
+                res = f(mat, axis=1).dtype.type
+                assert_(res is tgt)
+                # scalar case
+                res = f(mat, axis=None).dtype.type
+                assert_(res is tgt)
+
+        # mean for float types
+        for f in [_mean]:
+            for c in fcodes:
+                mat = np.eye(3, dtype=c)
+                tgt = mat.dtype.type
+                res = f(mat, axis=1).dtype.type
+                assert_(res is tgt)
+                # scalar case
+                res = f(mat, axis=None).dtype.type
+                assert_(res is tgt)
+
+        # var, std for float types
+        for f in [_var, _std]:
+            for c in fcodes:
+                mat = np.eye(3, dtype=c)
+                # deal with complex types
+                tgt = mat.real.dtype.type
+                res = f(mat, axis=1).dtype.type
+                assert_(res is tgt)
+                # scalar case
+                res = f(mat, axis=None).dtype.type
+                assert_(res is tgt)
+
+    def test_dtype_from_dtype(self):
+        mat = np.eye(3)
+
+        # stats for integer types
+        # FIXME:
+        # this needs definition as there are lots places along the line
+        # where type casting may take place.
+
+        # for f in self.funcs:
+        #    for c in np.typecodes['AllInteger']:
+        #        tgt = np.dtype(c).type
+        #        res = f(mat, axis=1, dtype=c).dtype.type
+        #        assert_(res is tgt)
+        #        # scalar case
+        #        res = f(mat, axis=None, dtype=c).dtype.type
+        #        assert_(res is tgt)
+
+        # stats for float types
+        for f in self.funcs:
+            for c in np.typecodes['AllFloat']:
+                tgt = np.dtype(c).type
+                res = f(mat, axis=1, dtype=c).dtype.type
+                assert_(res is tgt)
+                # scalar case
+                res = f(mat, axis=None, dtype=c).dtype.type
+                assert_(res is tgt)
+
+    def test_ddof(self):
+        for f in [_var]:
+            for ddof in range(3):
+                dim = self.rmat.shape[1]
+                tgt = f(self.rmat, axis=1) * dim
+                res = f(self.rmat, axis=1, ddof=ddof) * (dim - ddof)
+        for f in [_std]:
+            for ddof in range(3):
+                dim = self.rmat.shape[1]
+                tgt = f(self.rmat, axis=1) * np.sqrt(dim)
+                res = f(self.rmat, axis=1, ddof=ddof) * np.sqrt(dim - ddof)
+                assert_almost_equal(res, tgt)
+                assert_almost_equal(res, tgt)
+
+    def test_ddof_too_big(self):
+        dim = self.rmat.shape[1]
+        for f in [_var, _std]:
+            for ddof in range(dim, dim + 2):
+                with warnings.catch_warnings(record=True) as w:
+                    warnings.simplefilter('always')
+                    res = f(self.rmat, axis=1, ddof=ddof)
+                    assert_(not (res < 0).any())
+                    assert_(len(w) > 0)
+                    assert_(issubclass(w[0].category, RuntimeWarning))
+
+    def test_empty(self):
+        A = np.zeros((0, 3))
+        for f in self.funcs:
+            for axis in [0, None]:
+                with warnings.catch_warnings(record=True) as w:
+                    warnings.simplefilter('always')
+                    assert_(np.isnan(f(A, axis=axis)).all())
+                    assert_(len(w) > 0)
+                    assert_(issubclass(w[0].category, RuntimeWarning))
+            for axis in [1]:
+                with warnings.catch_warnings(record=True) as w:
+                    warnings.simplefilter('always')
+                    assert_equal(f(A, axis=axis), np.zeros([]))
+
+    def test_mean_values(self):
+        for mat in [self.rmat, self.cmat, self.omat]:
+            for axis in [0, 1]:
+                tgt = mat.sum(axis=axis)
+                res = _mean(mat, axis=axis) * mat.shape[axis]
+                assert_almost_equal(res, tgt)
+            for axis in [None]:
+                tgt = mat.sum(axis=axis)
+                res = _mean(mat, axis=axis) * np.prod(mat.shape)
+                assert_almost_equal(res, tgt)
+
+    def test_mean_float16(self):
+        # This fail if the sum inside mean is done in float16 instead
+        # of float32.
+        assert_(_mean(np.ones(100000, dtype='float16')) == 1)
+
+    def test_mean_axis_error(self):
+        # Ensure that AxisError is raised instead of IndexError when axis is
+        # out of bounds, see gh-15817.
+        with assert_raises(np.exceptions.AxisError):
+            np.arange(10).mean(axis=2)
+
+    def test_mean_where(self):
+        a = np.arange(16).reshape((4, 4))
+        wh_full = np.array([[False, True, False, True],
+                            [True, False, True, False],
+                            [True, True, False, False],
+                            [False, False, True, True]])
+        wh_partial = np.array([[False],
+                               [True],
+                               [True],
+                               [False]])
+        _cases = [(1, True, [1.5, 5.5, 9.5, 13.5]),
+                  (0, wh_full, [6., 5., 10., 9.]),
+                  (1, wh_full, [2., 5., 8.5, 14.5]),
+                  (0, wh_partial, [6., 7., 8., 9.])]
+        for _ax, _wh, _res in _cases:
+            assert_allclose(a.mean(axis=_ax, where=_wh),
+                            np.array(_res))
+            assert_allclose(np.mean(a, axis=_ax, where=_wh),
+                            np.array(_res))
+
+        a3d = np.arange(16).reshape((2, 2, 4))
+        _wh_partial = np.array([False, True, True, False])
+        _res = [[1.5, 5.5], [9.5, 13.5]]
+        assert_allclose(a3d.mean(axis=2, where=_wh_partial),
+                        np.array(_res))
+        assert_allclose(np.mean(a3d, axis=2, where=_wh_partial),
+                        np.array(_res))
+
+        with pytest.warns(RuntimeWarning) as w:
+            assert_allclose(a.mean(axis=1, where=wh_partial),
+                            np.array([np.nan, 5.5, 9.5, np.nan]))
+        with pytest.warns(RuntimeWarning) as w:
+            assert_equal(a.mean(where=False), np.nan)
+        with pytest.warns(RuntimeWarning) as w:
+            assert_equal(np.mean(a, where=False), np.nan)
+
+    def test_var_values(self):
+        for mat in [self.rmat, self.cmat, self.omat]:
+            for axis in [0, 1, None]:
+                msqr = _mean(mat * mat.conj(), axis=axis)
+                mean = _mean(mat, axis=axis)
+                tgt = msqr - mean * mean.conjugate()
+                res = _var(mat, axis=axis)
+                assert_almost_equal(res, tgt)
+
+    @pytest.mark.parametrize(('complex_dtype', 'ndec'), (
+        ('complex64', 6),
+        ('complex128', 7),
+        ('clongdouble', 7),
+    ))
+    def test_var_complex_values(self, complex_dtype, ndec):
+        # Test fast-paths for every builtin complex type
+        for axis in [0, 1, None]:
+            mat = self.cmat.copy().astype(complex_dtype)
+            msqr = _mean(mat * mat.conj(), axis=axis)
+            mean = _mean(mat, axis=axis)
+            tgt = msqr - mean * mean.conjugate()
+            res = _var(mat, axis=axis)
+            assert_almost_equal(res, tgt, decimal=ndec)
+
+    def test_var_dimensions(self):
+        # _var paths for complex number introduce additions on views that
+        # increase dimensions. Ensure this generalizes to higher dims
+        mat = np.stack([self.cmat] * 3)
+        for axis in [0, 1, 2, -1, None]:
+            msqr = _mean(mat * mat.conj(), axis=axis)
+            mean = _mean(mat, axis=axis)
+            tgt = msqr - mean * mean.conjugate()
+            res = _var(mat, axis=axis)
+            assert_almost_equal(res, tgt)
+
+    def test_var_complex_byteorder(self):
+        # Test that var fast-path does not cause failures for complex arrays
+        # with non-native byteorder
+        cmat = self.cmat.copy().astype('complex128')
+        cmat_swapped = cmat.astype(cmat.dtype.newbyteorder())
+        assert_almost_equal(cmat.var(), cmat_swapped.var())
+
+    def test_var_axis_error(self):
+        # Ensure that AxisError is raised instead of IndexError when axis is
+        # out of bounds, see gh-15817.
+        with assert_raises(np.exceptions.AxisError):
+            np.arange(10).var(axis=2)
+
+    def test_var_where(self):
+        a = np.arange(25).reshape((5, 5))
+        wh_full = np.array([[False, True, False, True, True],
+                            [True, False, True, True, False],
+                            [True, True, False, False, True],
+                            [False, True, True, False, True],
+                            [True, False, True, True, False]])
+        wh_partial = np.array([[False],
+                               [True],
+                               [True],
+                               [False],
+                               [True]])
+        _cases = [(0, True, [50., 50., 50., 50., 50.]),
+                  (1, True, [2., 2., 2., 2., 2.])]
+        for _ax, _wh, _res in _cases:
+            assert_allclose(a.var(axis=_ax, where=_wh),
+                            np.array(_res))
+            assert_allclose(np.var(a, axis=_ax, where=_wh),
+                            np.array(_res))
+
+        a3d = np.arange(16).reshape((2, 2, 4))
+        _wh_partial = np.array([False, True, True, False])
+        _res = [[0.25, 0.25], [0.25, 0.25]]
+        assert_allclose(a3d.var(axis=2, where=_wh_partial),
+                        np.array(_res))
+        assert_allclose(np.var(a3d, axis=2, where=_wh_partial),
+                        np.array(_res))
+
+        assert_allclose(np.var(a, axis=1, where=wh_full),
+                        np.var(a[wh_full].reshape((5, 3)), axis=1))
+        assert_allclose(np.var(a, axis=0, where=wh_partial),
+                        np.var(a[wh_partial[:, 0]], axis=0))
+        with pytest.warns(RuntimeWarning) as w:
+            assert_equal(a.var(where=False), np.nan)
+        with pytest.warns(RuntimeWarning) as w:
+            assert_equal(np.var(a, where=False), np.nan)
+
+    def test_std_values(self):
+        for mat in [self.rmat, self.cmat, self.omat]:
+            for axis in [0, 1, None]:
+                tgt = np.sqrt(_var(mat, axis=axis))
+                res = _std(mat, axis=axis)
+                assert_almost_equal(res, tgt)
+
+    def test_std_where(self):
+        a = np.arange(25).reshape((5, 5))[::-1]
+        whf = np.array([[False, True, False, True, True],
+                        [True, False, True, False, True],
+                        [True, True, False, True, False],
+                        [True, False, True, True, False],
+                        [False, True, False, True, True]])
+        whp = np.array([[False],
+                        [False],
+                        [True],
+                        [True],
+                        [False]])
+        _cases = [
+            (0, True, 7.07106781 * np.ones(5)),
+            (1, True, 1.41421356 * np.ones(5)),
+            (0, whf,
+             np.array([4.0824829, 8.16496581, 5., 7.39509973, 8.49836586])),
+            (0, whp, 2.5 * np.ones(5))
+        ]
+        for _ax, _wh, _res in _cases:
+            assert_allclose(a.std(axis=_ax, where=_wh), _res)
+            assert_allclose(np.std(a, axis=_ax, where=_wh), _res)
+
+        a3d = np.arange(16).reshape((2, 2, 4))
+        _wh_partial = np.array([False, True, True, False])
+        _res = [[0.5, 0.5], [0.5, 0.5]]
+        assert_allclose(a3d.std(axis=2, where=_wh_partial),
+                        np.array(_res))
+        assert_allclose(np.std(a3d, axis=2, where=_wh_partial),
+                        np.array(_res))
+
+        assert_allclose(a.std(axis=1, where=whf),
+                        np.std(a[whf].reshape((5, 3)), axis=1))
+        assert_allclose(np.std(a, axis=1, where=whf),
+                        (a[whf].reshape((5, 3))).std(axis=1))
+        assert_allclose(a.std(axis=0, where=whp),
+                        np.std(a[whp[:, 0]], axis=0))
+        assert_allclose(np.std(a, axis=0, where=whp),
+                        (a[whp[:, 0]]).std(axis=0))
+        with pytest.warns(RuntimeWarning) as w:
+            assert_equal(a.std(where=False), np.nan)
+        with pytest.warns(RuntimeWarning) as w:
+            assert_equal(np.std(a, where=False), np.nan)
+
+    def test_subclass(self):
+        class TestArray(np.ndarray):
+            def __new__(cls, data, info):
+                result = np.array(data)
+                result = result.view(cls)
+                result.info = info
+                return result
+
+            def __array_finalize__(self, obj):
+                self.info = getattr(obj, "info", '')
+
+        dat = TestArray([[1, 2, 3, 4], [5, 6, 7, 8]], 'jubba')
+        res = dat.mean(1)
+        assert_(res.info == dat.info)
+        res = dat.std(1)
+        assert_(res.info == dat.info)
+        res = dat.var(1)
+        assert_(res.info == dat.info)
+
+
+class TestVdot:
+    def test_basic(self):
+        dt_numeric = np.typecodes['AllFloat'] + np.typecodes['AllInteger']
+        dt_complex = np.typecodes['Complex']
+
+        # test real
+        a = np.eye(3)
+        for dt in dt_numeric + 'O':
+            b = a.astype(dt)
+            res = np.vdot(b, b)
+            assert_(np.isscalar(res))
+            assert_equal(np.vdot(b, b), 3)
+
+        # test complex
+        a = np.eye(3) * 1j
+        for dt in dt_complex + 'O':
+            b = a.astype(dt)
+            res = np.vdot(b, b)
+            assert_(np.isscalar(res))
+            assert_equal(np.vdot(b, b), 3)
+
+        # test boolean
+        b = np.eye(3, dtype=bool)
+        res = np.vdot(b, b)
+        assert_(np.isscalar(res))
+        assert_equal(np.vdot(b, b), True)
+
+    def test_vdot_array_order(self):
+        a = np.array([[1, 2], [3, 4]], order='C')
+        b = np.array([[1, 2], [3, 4]], order='F')
+        res = np.vdot(a, a)
+
+        # integer arrays are exact
+        assert_equal(np.vdot(a, b), res)
+        assert_equal(np.vdot(b, a), res)
+        assert_equal(np.vdot(b, b), res)
+
+    def test_vdot_uncontiguous(self):
+        for size in [2, 1000]:
+            # Different sizes match different branches in vdot.
+            a = np.zeros((size, 2, 2))
+            b = np.zeros((size, 2, 2))
+            a[:, 0, 0] = np.arange(size)
+            b[:, 0, 0] = np.arange(size) + 1
+            # Make a and b uncontiguous:
+            a = a[..., 0]
+            b = b[..., 0]
+
+            assert_equal(np.vdot(a, b),
+                         np.vdot(a.flatten(), b.flatten()))
+            assert_equal(np.vdot(a, b.copy()),
+                         np.vdot(a.flatten(), b.flatten()))
+            assert_equal(np.vdot(a.copy(), b),
+                         np.vdot(a.flatten(), b.flatten()))
+            assert_equal(np.vdot(a.copy('F'), b),
+                         np.vdot(a.flatten(), b.flatten()))
+            assert_equal(np.vdot(a, b.copy('F')),
+                         np.vdot(a.flatten(), b.flatten()))
+
+
+class TestDot:
+    def setup_method(self):
+        np.random.seed(128)
+        self.A = np.random.rand(4, 2)
+        self.b1 = np.random.rand(2, 1)
+        self.b2 = np.random.rand(2)
+        self.b3 = np.random.rand(1, 2)
+        self.b4 = np.random.rand(4)
+        self.N = 7
+
+    def test_dotmatmat(self):
+        A = self.A
+        res = np.dot(A.transpose(), A)
+        tgt = np.array([[1.45046013, 0.86323640],
+                        [0.86323640, 0.84934569]])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotmatvec(self):
+        A, b1 = self.A, self.b1
+        res = np.dot(A, b1)
+        tgt = np.array([[0.32114320], [0.04889721],
+                        [0.15696029], [0.33612621]])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotmatvec2(self):
+        A, b2 = self.A, self.b2
+        res = np.dot(A, b2)
+        tgt = np.array([0.29677940, 0.04518649, 0.14468333, 0.31039293])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotvecmat(self):
+        A, b4 = self.A, self.b4
+        res = np.dot(b4, A)
+        tgt = np.array([1.23495091, 1.12222648])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotvecmat2(self):
+        b3, A = self.b3, self.A
+        res = np.dot(b3, A.transpose())
+        tgt = np.array([[0.58793804, 0.08957460, 0.30605758, 0.62716383]])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotvecmat3(self):
+        A, b4 = self.A, self.b4
+        res = np.dot(A.transpose(), b4)
+        tgt = np.array([1.23495091, 1.12222648])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotvecvecouter(self):
+        b1, b3 = self.b1, self.b3
+        res = np.dot(b1, b3)
+        tgt = np.array([[0.20128610, 0.08400440], [0.07190947, 0.03001058]])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotvecvecinner(self):
+        b1, b3 = self.b1, self.b3
+        res = np.dot(b3, b1)
+        tgt = np.array([[0.23129668]])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotcolumnvect1(self):
+        b1 = np.ones((3, 1))
+        b2 = [5.3]
+        res = np.dot(b1, b2)
+        tgt = np.array([5.3, 5.3, 5.3])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotcolumnvect2(self):
+        b1 = np.ones((3, 1)).transpose()
+        b2 = [6.2]
+        res = np.dot(b2, b1)
+        tgt = np.array([6.2, 6.2, 6.2])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotvecscalar(self):
+        np.random.seed(100)
+        b1 = np.random.rand(1, 1)
+        b2 = np.random.rand(1, 4)
+        res = np.dot(b1, b2)
+        tgt = np.array([[0.15126730, 0.23068496, 0.45905553, 0.00256425]])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_dotvecscalar2(self):
+        np.random.seed(100)
+        b1 = np.random.rand(4, 1)
+        b2 = np.random.rand(1, 1)
+        res = np.dot(b1, b2)
+        tgt = np.array([[0.00256425], [0.00131359], [0.00200324], [0.00398638]])
+        assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_all(self):
+        dims = [(), (1,), (1, 1)]
+        dout = [(), (1,), (1, 1), (1,), (), (1,), (1, 1), (1,), (1, 1)]
+        for dim, (dim1, dim2) in zip(dout, itertools.product(dims, dims)):
+            b1 = np.zeros(dim1)
+            b2 = np.zeros(dim2)
+            res = np.dot(b1, b2)
+            tgt = np.zeros(dim)
+            assert_(res.shape == tgt.shape)
+            assert_almost_equal(res, tgt, decimal=self.N)
+
+    def test_vecobject(self):
+        class Vec:
+            def __init__(self, sequence=None):
+                if sequence is None:
+                    sequence = []
+                self.array = np.array(sequence)
+
+            def __add__(self, other):
+                out = Vec()
+                out.array = self.array + other.array
+                return out
+
+            def __sub__(self, other):
+                out = Vec()
+                out.array = self.array - other.array
+                return out
+
+            def __mul__(self, other):  # with scalar
+                out = Vec(self.array.copy())
+                out.array *= other
+                return out
+
+            def __rmul__(self, other):
+                return self * other
+
+        U_non_cont = np.transpose([[1., 1.], [1., 2.]])
+        U_cont = np.ascontiguousarray(U_non_cont)
+        x = np.array([Vec([1., 0.]), Vec([0., 1.])])
+        zeros = np.array([Vec([0., 0.]), Vec([0., 0.])])
+        zeros_test = np.dot(U_cont, x) - np.dot(U_non_cont, x)
+        assert_equal(zeros[0].array, zeros_test[0].array)
+        assert_equal(zeros[1].array, zeros_test[1].array)
+
+    def test_dot_2args(self):
+
+        a = np.array([[1, 2], [3, 4]], dtype=float)
+        b = np.array([[1, 0], [1, 1]], dtype=float)
+        c = np.array([[3, 2], [7, 4]], dtype=float)
+
+        d = dot(a, b)
+        assert_allclose(c, d)
+
+    def test_dot_3args(self):
+
+        np.random.seed(22)
+        f = np.random.random_sample((1024, 16))
+        v = np.random.random_sample((16, 32))
+
+        r = np.empty((1024, 32))
+        if HAS_REFCOUNT:
+            orig_refcount = sys.getrefcount(r)
+        for i in range(12):
+            dot(f, v, r)
+        if HAS_REFCOUNT:
+            assert_equal(sys.getrefcount(r), orig_refcount)
+        r2 = dot(f, v, out=None)
+        assert_array_equal(r2, r)
+        assert_(r is dot(f, v, out=r))
+
+        v = v[:, 0].copy()  # v.shape == (16,)
+        r = r[:, 0].copy()  # r.shape == (1024,)
+        r2 = dot(f, v)
+        assert_(r is dot(f, v, r))
+        assert_array_equal(r2, r)
+
+    def test_dot_3args_errors(self):
+
+        np.random.seed(22)
+        f = np.random.random_sample((1024, 16))
+        v = np.random.random_sample((16, 32))
+
+        r = np.empty((1024, 31))
+        assert_raises(ValueError, dot, f, v, r)
+
+        r = np.empty((1024,))
+        assert_raises(ValueError, dot, f, v, r)
+
+        r = np.empty((32,))
+        assert_raises(ValueError, dot, f, v, r)
+
+        r = np.empty((32, 1024))
+        assert_raises(ValueError, dot, f, v, r)
+        assert_raises(ValueError, dot, f, v, r.T)
+
+        r = np.empty((1024, 64))
+        assert_raises(ValueError, dot, f, v, r[:, ::2])
+        assert_raises(ValueError, dot, f, v, r[:, :32])
+
+        r = np.empty((1024, 32), dtype=np.float32)
+        assert_raises(ValueError, dot, f, v, r)
+
+        r = np.empty((1024, 32), dtype=int)
+        assert_raises(ValueError, dot, f, v, r)
+
+    def test_dot_out_result(self):
+        x = np.ones((), dtype=np.float16)
+        y = np.ones((5,), dtype=np.float16)
+        z = np.zeros((5,), dtype=np.float16)
+        res = x.dot(y, out=z)
+        assert np.array_equal(res, y)
+        assert np.array_equal(z, y)
+
+    def test_dot_out_aliasing(self):
+        x = np.ones((), dtype=np.float16)
+        y = np.ones((5,), dtype=np.float16)
+        z = np.zeros((5,), dtype=np.float16)
+        res = x.dot(y, out=z)
+        z[0] = 2
+        assert np.array_equal(res, z)
+
+    def test_dot_array_order(self):
+        a = np.array([[1, 2], [3, 4]], order='C')
+        b = np.array([[1, 2], [3, 4]], order='F')
+        res = np.dot(a, a)
+
+        # integer arrays are exact
+        assert_equal(np.dot(a, b), res)
+        assert_equal(np.dot(b, a), res)
+        assert_equal(np.dot(b, b), res)
+
+    def test_accelerate_framework_sgemv_fix(self):
+
+        def aligned_array(shape, align, dtype, order='C'):
+            d = dtype(0)
+            N = np.prod(shape)
+            tmp = np.zeros(N * d.nbytes + align, dtype=np.uint8)
+            address = tmp.__array_interface__["data"][0]
+            for offset in range(align):
+                if (address + offset) % align == 0:
+                    break
+            tmp = tmp[offset:offset + N * d.nbytes].view(dtype=dtype)
+            return tmp.reshape(shape, order=order)
+
+        def as_aligned(arr, align, dtype, order='C'):
+            aligned = aligned_array(arr.shape, align, dtype, order)
+            aligned[:] = arr[:]
+            return aligned
+
+        def assert_dot_close(A, X, desired):
+            assert_allclose(np.dot(A, X), desired, rtol=1e-5, atol=1e-7)
+
+        m = aligned_array(100, 15, np.float32)
+        s = aligned_array((100, 100), 15, np.float32)
+        np.dot(s, m)  # this will always segfault if the bug is present
+
+        testdata = itertools.product((15, 32), (10000,), (200, 89), ('C', 'F'))
+        for align, m, n, a_order in testdata:
+            # Calculation in double precision
+            A_d = np.random.rand(m, n)
+            X_d = np.random.rand(n)
+            desired = np.dot(A_d, X_d)
+            # Calculation with aligned single precision
+            A_f = as_aligned(A_d, align, np.float32, order=a_order)
+            X_f = as_aligned(X_d, align, np.float32)
+            assert_dot_close(A_f, X_f, desired)
+            # Strided A rows
+            A_d_2 = A_d[::2]
+            desired = np.dot(A_d_2, X_d)
+            A_f_2 = A_f[::2]
+            assert_dot_close(A_f_2, X_f, desired)
+            # Strided A columns, strided X vector
+            A_d_22 = A_d_2[:, ::2]
+            X_d_2 = X_d[::2]
+            desired = np.dot(A_d_22, X_d_2)
+            A_f_22 = A_f_2[:, ::2]
+            X_f_2 = X_f[::2]
+            assert_dot_close(A_f_22, X_f_2, desired)
+            # Check the strides are as expected
+            if a_order == 'F':
+                assert_equal(A_f_22.strides, (8, 8 * m))
+            else:
+                assert_equal(A_f_22.strides, (8 * n, 8))
+            assert_equal(X_f_2.strides, (8,))
+            # Strides in A rows + cols only
+            X_f_2c = as_aligned(X_f_2, align, np.float32)
+            assert_dot_close(A_f_22, X_f_2c, desired)
+            # Strides just in A cols
+            A_d_12 = A_d[:, ::2]
+            desired = np.dot(A_d_12, X_d_2)
+            A_f_12 = A_f[:, ::2]
+            assert_dot_close(A_f_12, X_f_2c, desired)
+            # Strides in A cols and X
+            assert_dot_close(A_f_12, X_f_2, desired)
+
+    @pytest.mark.slow
+    @pytest.mark.parametrize("dtype", [np.float64, np.complex128])
+    @requires_memory(free_bytes=18e9)  # complex case needs 18GiB+
+    def test_huge_vectordot(self, dtype):
+        # Large vector multiplications are chunked with 32bit BLAS
+        # Test that the chunking does the right thing, see also gh-22262
+        data = np.ones(2**30 + 100, dtype=dtype)
+        res = np.dot(data, data)
+        assert res == 2**30 + 100
+
+    def test_dtype_discovery_fails(self):
+        # See gh-14247, error checking was missing for failed dtype discovery
+        class BadObject:
+            def __array__(self, dtype=None, copy=None):
+                raise TypeError("just this tiny mint leaf")
+
+        with pytest.raises(TypeError):
+            np.dot(BadObject(), BadObject())
+
+        with pytest.raises(TypeError):
+            np.dot(3.0, BadObject())
+
+
+class MatmulCommon:
+    """Common tests for '@' operator and numpy.matmul.
+
+    """
+    # Should work with these types. Will want to add
+    # "O" at some point
+    types = "?bhilqBHILQefdgFDGO"
+
+    def test_exceptions(self):
+        dims = [
+            ((1,), (2,)),            # mismatched vector vector
+            ((2, 1,), (2,)),         # mismatched matrix vector
+            ((2,), (1, 2)),          # mismatched vector matrix
+            ((1, 2), (3, 1)),        # mismatched matrix matrix
+            ((1,), ()),              # vector scalar
+            ((), (1)),               # scalar vector
+            ((1, 1), ()),            # matrix scalar
+            ((), (1, 1)),            # scalar matrix
+            ((2, 2, 1), (3, 1, 2)),  # cannot broadcast
+            ]
+
+        for dt, (dm1, dm2) in itertools.product(self.types, dims):
+            a = np.ones(dm1, dtype=dt)
+            b = np.ones(dm2, dtype=dt)
+            assert_raises(ValueError, self.matmul, a, b)
+
+    def test_shapes(self):
+        dims = [
+            ((1, 1), (2, 1, 1)),     # broadcast first argument
+            ((2, 1, 1), (1, 1)),     # broadcast second argument
+            ((2, 1, 1), (2, 1, 1)),  # matrix stack sizes match
+            ]
+
+        for dt, (dm1, dm2) in itertools.product(self.types, dims):
+            a = np.ones(dm1, dtype=dt)
+            b = np.ones(dm2, dtype=dt)
+            res = self.matmul(a, b)
+            assert_(res.shape == (2, 1, 1))
+
+        # vector vector returns scalars.
+        for dt in self.types:
+            a = np.ones((2,), dtype=dt)
+            b = np.ones((2,), dtype=dt)
+            c = self.matmul(a, b)
+            assert_(np.array(c).shape == ())
+
+    def test_result_types(self):
+        mat = np.ones((1, 1))
+        vec = np.ones((1,))
+        for dt in self.types:
+            m = mat.astype(dt)
+            v = vec.astype(dt)
+            for arg in [(m, v), (v, m), (m, m)]:
+                res = self.matmul(*arg)
+                assert_(res.dtype == dt)
+
+            # vector vector returns scalars
+            if dt != "O":
+                res = self.matmul(v, v)
+                assert_(type(res) is np.dtype(dt).type)
+
+    def test_scalar_output(self):
+        vec1 = np.array([2])
+        vec2 = np.array([3, 4]).reshape(1, -1)
+        tgt = np.array([6, 8])
+        for dt in self.types[1:]:
+            v1 = vec1.astype(dt)
+            v2 = vec2.astype(dt)
+            res = self.matmul(v1, v2)
+            assert_equal(res, tgt)
+            res = self.matmul(v2.T, v1)
+            assert_equal(res, tgt)
+
+        # boolean type
+        vec = np.array([True, True], dtype='?').reshape(1, -1)
+        res = self.matmul(vec[:, 0], vec)
+        assert_equal(res, True)
+
+    def test_vector_vector_values(self):
+        vec1 = np.array([1, 2])
+        vec2 = np.array([3, 4]).reshape(-1, 1)
+        tgt1 = np.array([11])
+        tgt2 = np.array([[3, 6], [4, 8]])
+        for dt in self.types[1:]:
+            v1 = vec1.astype(dt)
+            v2 = vec2.astype(dt)
+            res = self.matmul(v1, v2)
+            assert_equal(res, tgt1)
+            # no broadcast, we must make v1 into a 2d ndarray
+            res = self.matmul(v2, v1.reshape(1, -1))
+            assert_equal(res, tgt2)
+
+        # boolean type
+        vec = np.array([True, True], dtype='?')
+        res = self.matmul(vec, vec)
+        assert_equal(res, True)
+
+    def test_vector_matrix_values(self):
+        vec = np.array([1, 2])
+        mat1 = np.array([[1, 2], [3, 4]])
+        mat2 = np.stack([mat1] * 2, axis=0)
+        tgt1 = np.array([7, 10])
+        tgt2 = np.stack([tgt1] * 2, axis=0)
+        for dt in self.types[1:]:
+            v = vec.astype(dt)
+            m1 = mat1.astype(dt)
+            m2 = mat2.astype(dt)
+            res = self.matmul(v, m1)
+            assert_equal(res, tgt1)
+            res = self.matmul(v, m2)
+            assert_equal(res, tgt2)
+
+        # boolean type
+        vec = np.array([True, False])
+        mat1 = np.array([[True, False], [False, True]])
+        mat2 = np.stack([mat1] * 2, axis=0)
+        tgt1 = np.array([True, False])
+        tgt2 = np.stack([tgt1] * 2, axis=0)
+
+        res = self.matmul(vec, mat1)
+        assert_equal(res, tgt1)
+        res = self.matmul(vec, mat2)
+        assert_equal(res, tgt2)
+
+    def test_matrix_vector_values(self):
+        vec = np.array([1, 2])
+        mat1 = np.array([[1, 2], [3, 4]])
+        mat2 = np.stack([mat1] * 2, axis=0)
+        tgt1 = np.array([5, 11])
+        tgt2 = np.stack([tgt1] * 2, axis=0)
+        for dt in self.types[1:]:
+            v = vec.astype(dt)
+            m1 = mat1.astype(dt)
+            m2 = mat2.astype(dt)
+            res = self.matmul(m1, v)
+            assert_equal(res, tgt1)
+            res = self.matmul(m2, v)
+            assert_equal(res, tgt2)
+
+        # boolean type
+        vec = np.array([True, False])
+        mat1 = np.array([[True, False], [False, True]])
+        mat2 = np.stack([mat1] * 2, axis=0)
+        tgt1 = np.array([True, False])
+        tgt2 = np.stack([tgt1] * 2, axis=0)
+
+        res = self.matmul(vec, mat1)
+        assert_equal(res, tgt1)
+        res = self.matmul(vec, mat2)
+        assert_equal(res, tgt2)
+
+    def test_matrix_matrix_values(self):
+        mat1 = np.array([[1, 2], [3, 4]])
+        mat2 = np.array([[1, 0], [1, 1]])
+        mat12 = np.stack([mat1, mat2], axis=0)
+        mat21 = np.stack([mat2, mat1], axis=0)
+        tgt11 = np.array([[7, 10], [15, 22]])
+        tgt12 = np.array([[3, 2], [7, 4]])
+        tgt21 = np.array([[1, 2], [4, 6]])
+        tgt12_21 = np.stack([tgt12, tgt21], axis=0)
+        tgt11_12 = np.stack((tgt11, tgt12), axis=0)
+        tgt11_21 = np.stack((tgt11, tgt21), axis=0)
+        for dt in self.types[1:]:
+            m1 = mat1.astype(dt)
+            m2 = mat2.astype(dt)
+            m12 = mat12.astype(dt)
+            m21 = mat21.astype(dt)
+
+            # matrix @ matrix
+            res = self.matmul(m1, m2)
+            assert_equal(res, tgt12)
+            res = self.matmul(m2, m1)
+            assert_equal(res, tgt21)
+
+            # stacked @ matrix
+            res = self.matmul(m12, m1)
+            assert_equal(res, tgt11_21)
+
+            # matrix @ stacked
+            res = self.matmul(m1, m12)
+            assert_equal(res, tgt11_12)
+
+            # stacked @ stacked
+            res = self.matmul(m12, m21)
+            assert_equal(res, tgt12_21)
+
+        # boolean type
+        m1 = np.array([[1, 1], [0, 0]], dtype=np.bool)
+        m2 = np.array([[1, 0], [1, 1]], dtype=np.bool)
+        m12 = np.stack([m1, m2], axis=0)
+        m21 = np.stack([m2, m1], axis=0)
+        tgt11 = m1
+        tgt12 = m1
+        tgt21 = np.array([[1, 1], [1, 1]], dtype=np.bool)
+        tgt12_21 = np.stack([tgt12, tgt21], axis=0)
+        tgt11_12 = np.stack((tgt11, tgt12), axis=0)
+        tgt11_21 = np.stack((tgt11, tgt21), axis=0)
+
+        # matrix @ matrix
+        res = self.matmul(m1, m2)
+        assert_equal(res, tgt12)
+        res = self.matmul(m2, m1)
+        assert_equal(res, tgt21)
+
+        # stacked @ matrix
+        res = self.matmul(m12, m1)
+        assert_equal(res, tgt11_21)
+
+        # matrix @ stacked
+        res = self.matmul(m1, m12)
+        assert_equal(res, tgt11_12)
+
+        # stacked @ stacked
+        res = self.matmul(m12, m21)
+        assert_equal(res, tgt12_21)
+
+
+class TestMatmul(MatmulCommon):
+    matmul = np.matmul
+
+    def test_out_arg(self):
+        a = np.ones((5, 2), dtype=float)
+        b = np.array([[1, 3], [5, 7]], dtype=float)
+        tgt = np.dot(a, b)
+
+        # test as positional argument
+        msg = "out positional argument"
+        out = np.zeros((5, 2), dtype=float)
+        self.matmul(a, b, out)
+        assert_array_equal(out, tgt, err_msg=msg)
+
+        # test as keyword argument
+        msg = "out keyword argument"
+        out = np.zeros((5, 2), dtype=float)
+        self.matmul(a, b, out=out)
+        assert_array_equal(out, tgt, err_msg=msg)
+
+        # test out with not allowed type cast (safe casting)
+        msg = "Cannot cast ufunc .* output"
+        out = np.zeros((5, 2), dtype=np.int32)
+        assert_raises_regex(TypeError, msg, self.matmul, a, b, out=out)
+
+        # test out with type upcast to complex
+        out = np.zeros((5, 2), dtype=np.complex128)
+        c = self.matmul(a, b, out=out)
+        assert_(c is out)
+        with suppress_warnings() as sup:
+            sup.filter(ComplexWarning, '')
+            c = c.astype(tgt.dtype)
+        assert_array_equal(c, tgt)
+
+    def test_empty_out(self):
+        # Check that the output cannot be broadcast, so that it cannot be
+        # size zero when the outer dimensions (iterator size) has size zero.
+        arr = np.ones((0, 1, 1))
+        out = np.ones((1, 1, 1))
+        assert self.matmul(arr, arr).shape == (0, 1, 1)
+
+        with pytest.raises(ValueError, match=r"non-broadcastable"):
+            self.matmul(arr, arr, out=out)
+
+    def test_out_contiguous(self):
+        a = np.ones((5, 2), dtype=float)
+        b = np.array([[1, 3], [5, 7]], dtype=float)
+        v = np.array([1, 3], dtype=float)
+        tgt = np.dot(a, b)
+        tgt_mv = np.dot(a, v)
+
+        # test out non-contiguous
+        out = np.ones((5, 2, 2), dtype=float)
+        c = self.matmul(a, b, out=out[..., 0])
+        assert c.base is out
+        assert_array_equal(c, tgt)
+        c = self.matmul(a, v, out=out[:, 0, 0])
+        assert_array_equal(c, tgt_mv)
+        c = self.matmul(v, a.T, out=out[:, 0, 0])
+        assert_array_equal(c, tgt_mv)
+
+        # test out contiguous in only last dim
+        out = np.ones((10, 2), dtype=float)
+        c = self.matmul(a, b, out=out[::2, :])
+        assert_array_equal(c, tgt)
+
+        # test transposes of out, args
+        out = np.ones((5, 2), dtype=float)
+        c = self.matmul(b.T, a.T, out=out.T)
+        assert_array_equal(out, tgt)
+
+    m1 = np.arange(15.).reshape(5, 3)
+    m2 = np.arange(21.).reshape(3, 7)
+    m3 = np.arange(30.).reshape(5, 6)[:, ::2]  # non-contiguous
+    vc = np.arange(10.)
+    vr = np.arange(6.)
+    m0 = np.zeros((3, 0))
+
+    @pytest.mark.parametrize('args', (
+            # matrix-matrix
+            (m1, m2), (m2.T, m1.T), (m2.T.copy(), m1.T), (m2.T, m1.T.copy()),
+            # matrix-matrix-transpose, contiguous and non
+            (m1, m1.T), (m1.T, m1), (m1, m3.T), (m3, m1.T),
+            (m3, m3.T), (m3.T, m3),
+            # matrix-matrix non-contiguous
+            (m3, m2), (m2.T, m3.T), (m2.T.copy(), m3.T),
+            # vector-matrix, matrix-vector, contiguous
+            (m1, vr[:3]), (vc[:5], m1), (m1.T, vc[:5]), (vr[:3], m1.T),
+            # vector-matrix, matrix-vector, vector non-contiguous
+            (m1, vr[::2]), (vc[::2], m1), (m1.T, vc[::2]), (vr[::2], m1.T),
+            # vector-matrix, matrix-vector, matrix non-contiguous
+            (m3, vr[:3]), (vc[:5], m3), (m3.T, vc[:5]), (vr[:3], m3.T),
+            # vector-matrix, matrix-vector, both non-contiguous
+            (m3, vr[::2]), (vc[::2], m3), (m3.T, vc[::2]), (vr[::2], m3.T),
+            # size == 0
+            (m0, m0.T), (m0.T, m0), (m1, m0), (m0.T, m1.T),
+        ))
+    def test_dot_equivalent(self, args):
+        r1 = np.matmul(*args)
+        r2 = np.dot(*args)
+        assert_equal(r1, r2)
+
+        r3 = np.matmul(args[0].copy(), args[1].copy())
+        assert_equal(r1, r3)
+
+        # matrix matrix, issue 29164
+        if [len(args[0].shape), len(args[1].shape)] == [2, 2]:
+            out_f = np.zeros((r2.shape[0] * 2, r2.shape[1] * 2), order='F')
+            r4 = np.matmul(*args, out=out_f[::2, ::2])
+            assert_equal(r2, r4)
+
+    def test_matmul_object(self):
+        import fractions
+
+        f = np.vectorize(fractions.Fraction)
+
+        def random_ints():
+            return np.random.randint(1, 1000, size=(10, 3, 3))
+        M1 = f(random_ints(), random_ints())
+        M2 = f(random_ints(), random_ints())
+
+        M3 = self.matmul(M1, M2)
+
+        [N1, N2, N3] = [a.astype(float) for a in [M1, M2, M3]]
+
+        assert_allclose(N3, self.matmul(N1, N2))
+
+    def test_matmul_object_type_scalar(self):
+        from fractions import Fraction as F
+        v = np.array([F(2, 3), F(5, 7)])
+        res = self.matmul(v, v)
+        assert_(type(res) is F)
+
+    def test_matmul_empty(self):
+        a = np.empty((3, 0), dtype=object)
+        b = np.empty((0, 3), dtype=object)
+        c = np.zeros((3, 3))
+        assert_array_equal(np.matmul(a, b), c)
+
+    def test_matmul_exception_multiply(self):
+        # test that matmul fails if `__mul__` is missing
+        class add_not_multiply:
+            def __add__(self, other):
+                return self
+        a = np.full((3, 3), add_not_multiply())
+        with assert_raises(TypeError):
+            b = np.matmul(a, a)
+
+    def test_matmul_exception_add(self):
+        # test that matmul fails if `__add__` is missing
+        class multiply_not_add:
+            def __mul__(self, other):
+                return self
+        a = np.full((3, 3), multiply_not_add())
+        with assert_raises(TypeError):
+            b = np.matmul(a, a)
+
+    def test_matmul_bool(self):
+        # gh-14439
+        a = np.array([[1, 0], [1, 1]], dtype=bool)
+        assert np.max(a.view(np.uint8)) == 1
+        b = np.matmul(a, a)
+        # matmul with boolean output should always be 0, 1
+        assert np.max(b.view(np.uint8)) == 1
+
+        rg = np.random.default_rng(np.random.PCG64(43))
+        d = rg.integers(2, size=4 * 5, dtype=np.int8)
+        d = d.reshape(4, 5) > 0
+        out1 = np.matmul(d, d.reshape(5, 4))
+        out2 = np.dot(d, d.reshape(5, 4))
+        assert_equal(out1, out2)
+
+        c = np.matmul(np.zeros((2, 0), dtype=bool), np.zeros(0, dtype=bool))
+        assert not np.any(c)
+
+
+class TestMatmulOperator(MatmulCommon):
+    import operator
+    matmul = operator.matmul
+
+    def test_array_priority_override(self):
+
+        class A:
+            __array_priority__ = 1000
+
+            def __matmul__(self, other):
+                return "A"
+
+            def __rmatmul__(self, other):
+                return "A"
+
+        a = A()
+        b = np.ones(2)
+        assert_equal(self.matmul(a, b), "A")
+        assert_equal(self.matmul(b, a), "A")
+
+    def test_matmul_raises(self):
+        assert_raises(TypeError, self.matmul, np.int8(5), np.int8(5))
+        assert_raises(TypeError, self.matmul, np.void(b'abc'), np.void(b'abc'))
+        assert_raises(TypeError, self.matmul, np.arange(10), np.void(b'abc'))
+
+
+class TestMatmulInplace:
+    DTYPES = {}
+    for i in MatmulCommon.types:
+        for j in MatmulCommon.types:
+            if np.can_cast(j, i):
+                DTYPES[f"{i}-{j}"] = (np.dtype(i), np.dtype(j))
+
+    @pytest.mark.parametrize("dtype1,dtype2", DTYPES.values(), ids=DTYPES)
+    def test_basic(self, dtype1: np.dtype, dtype2: np.dtype) -> None:
+        a = np.arange(10).reshape(5, 2).astype(dtype1)
+        a_id = id(a)
+        b = np.ones((2, 2), dtype=dtype2)
+
+        ref = a @ b
+        a @= b
+
+        assert id(a) == a_id
+        assert a.dtype == dtype1
+        assert a.shape == (5, 2)
+        if dtype1.kind in "fc":
+            np.testing.assert_allclose(a, ref)
+        else:
+            np.testing.assert_array_equal(a, ref)
+
+    SHAPES = {
+        "2d_large": ((10**5, 10), (10, 10)),
+        "3d_large": ((10**4, 10, 10), (1, 10, 10)),
+        "1d": ((3,), (3,)),
+        "2d_1d": ((3, 3), (3,)),
+        "1d_2d": ((3,), (3, 3)),
+        "2d_broadcast": ((3, 3), (3, 1)),
+        "2d_broadcast_reverse": ((1, 3), (3, 3)),
+        "3d_broadcast1": ((3, 3, 3), (1, 3, 1)),
+        "3d_broadcast2": ((3, 3, 3), (1, 3, 3)),
+        "3d_broadcast3": ((3, 3, 3), (3, 3, 1)),
+        "3d_broadcast_reverse1": ((1, 3, 3), (3, 3, 3)),
+        "3d_broadcast_reverse2": ((3, 1, 3), (3, 3, 3)),
+        "3d_broadcast_reverse3": ((1, 1, 3), (3, 3, 3)),
+    }
+
+    @pytest.mark.parametrize("a_shape,b_shape", SHAPES.values(), ids=SHAPES)
+    def test_shapes(self, a_shape: tuple[int, ...], b_shape: tuple[int, ...]):
+        a_size = np.prod(a_shape)
+        a = np.arange(a_size).reshape(a_shape).astype(np.float64)
+        a_id = id(a)
+
+        b_size = np.prod(b_shape)
+        b = np.arange(b_size).reshape(b_shape)
+
+        ref = a @ b
+        if ref.shape != a_shape:
+            with pytest.raises(ValueError):
+                a @= b
+            return
+        else:
+            a @= b
+
+        assert id(a) == a_id
+        assert a.dtype.type == np.float64
+        assert a.shape == a_shape
+        np.testing.assert_allclose(a, ref)
+
+
+def test_matmul_axes():
+    a = np.arange(3 * 4 * 5).reshape(3, 4, 5)
+    c = np.matmul(a, a, axes=[(-2, -1), (-1, -2), (1, 2)])
+    assert c.shape == (3, 4, 4)
+    d = np.matmul(a, a, axes=[(-2, -1), (-1, -2), (0, 1)])
+    assert d.shape == (4, 4, 3)
+    e = np.swapaxes(d, 0, 2)
+    assert_array_equal(e, c)
+    f = np.matmul(a, np.arange(3), axes=[(1, 0), (0), (0)])
+    assert f.shape == (4, 5)
+
+
+class TestInner:
+
+    def test_inner_type_mismatch(self):
+        c = 1.
+        A = np.array((1, 1), dtype='i,i')
+
+        assert_raises(TypeError, np.inner, c, A)
+        assert_raises(TypeError, np.inner, A, c)
+
+    def test_inner_scalar_and_vector(self):
+        for dt in np.typecodes['AllInteger'] + np.typecodes['AllFloat'] + '?':
+            sca = np.array(3, dtype=dt)[()]
+            vec = np.array([1, 2], dtype=dt)
+            desired = np.array([3, 6], dtype=dt)
+            assert_equal(np.inner(vec, sca), desired)
+            assert_equal(np.inner(sca, vec), desired)
+
+    def test_vecself(self):
+        # Ticket 844.
+        # Inner product of a vector with itself segfaults or give
+        # meaningless result
+        a = np.zeros(shape=(1, 80), dtype=np.float64)
+        p = np.inner(a, a)
+        assert_almost_equal(p, 0, decimal=14)
+
+    def test_inner_product_with_various_contiguities(self):
+        # github issue 6532
+        for dt in np.typecodes['AllInteger'] + np.typecodes['AllFloat'] + '?':
+            # check an inner product involving a matrix transpose
+            A = np.array([[1, 2], [3, 4]], dtype=dt)
+            B = np.array([[1, 3], [2, 4]], dtype=dt)
+            C = np.array([1, 1], dtype=dt)
+            desired = np.array([4, 6], dtype=dt)
+            assert_equal(np.inner(A.T, C), desired)
+            assert_equal(np.inner(C, A.T), desired)
+            assert_equal(np.inner(B, C), desired)
+            assert_equal(np.inner(C, B), desired)
+            # check a matrix product
+            desired = np.array([[7, 10], [15, 22]], dtype=dt)
+            assert_equal(np.inner(A, B), desired)
+            # check the syrk vs. gemm paths
+            desired = np.array([[5, 11], [11, 25]], dtype=dt)
+            assert_equal(np.inner(A, A), desired)
+            assert_equal(np.inner(A, A.copy()), desired)
+            # check an inner product involving an aliased and reversed view
+            a = np.arange(5).astype(dt)
+            b = a[::-1]
+            desired = np.array(10, dtype=dt).item()
+            assert_equal(np.inner(b, a), desired)
+
+    def test_3d_tensor(self):
+        for dt in np.typecodes['AllInteger'] + np.typecodes['AllFloat'] + '?':
+            a = np.arange(24).reshape(2, 3, 4).astype(dt)
+            b = np.arange(24, 48).reshape(2, 3, 4).astype(dt)
+            desired = np.array(
+                [[[[ 158,  182,  206],
+                   [ 230,  254,  278]],
+
+                  [[ 566,  654,  742],
+                   [ 830,  918, 1006]],
+
+                  [[ 974, 1126, 1278],
+                   [1430, 1582, 1734]]],
+
+                 [[[1382, 1598, 1814],
+                   [2030, 2246, 2462]],
+
+                  [[1790, 2070, 2350],
+                   [2630, 2910, 3190]],
+
+                  [[2198, 2542, 2886],
+                   [3230, 3574, 3918]]]]
+            ).astype(dt)
+            assert_equal(np.inner(a, b), desired)
+            assert_equal(np.inner(b, a).transpose(2, 3, 0, 1), desired)
+
+
+class TestChoose:
+    def setup_method(self):
+        self.x = 2 * np.ones((3,), dtype=int)
+        self.y = 3 * np.ones((3,), dtype=int)
+        self.x2 = 2 * np.ones((2, 3), dtype=int)
+        self.y2 = 3 * np.ones((2, 3), dtype=int)
+        self.ind = [0, 0, 1]
+
+    def test_basic(self):
+        A = np.choose(self.ind, (self.x, self.y))
+        assert_equal(A, [2, 2, 3])
+
+    def test_broadcast1(self):
+        A = np.choose(self.ind, (self.x2, self.y2))
+        assert_equal(A, [[2, 2, 3], [2, 2, 3]])
+
+    def test_broadcast2(self):
+        A = np.choose(self.ind, (self.x, self.y2))
+        assert_equal(A, [[2, 2, 3], [2, 2, 3]])
+
+    @pytest.mark.parametrize("ops",
+        [(1000, np.array([1], dtype=np.uint8)),
+         (-1, np.array([1], dtype=np.uint8)),
+         (1., np.float32(3)),
+         (1., np.array([3], dtype=np.float32))],)
+    def test_output_dtype(self, ops):
+        expected_dt = np.result_type(*ops)
+        assert np.choose([0], ops).dtype == expected_dt
+
+    def test_dimension_and_args_limit(self):
+        # Maxdims for the legacy iterator is 32, but the maximum number
+        # of arguments is actually larger (a itself also counts here)
+        a = np.ones((1,) * 32, dtype=np.intp)
+        res = a.choose([0, a] + [2] * 61)
+        with pytest.raises(ValueError,
+                match="Need at least 0 and at most 64 array objects"):
+            a.choose([0, a] + [2] * 62)
+
+        assert_array_equal(res, a)
+        # Choose is unfortunately limited to 32 dims as of NumPy 2.0
+        a = np.ones((1,) * 60, dtype=np.intp)
+        with pytest.raises(RuntimeError,
+                match=".*32 dimensions but the array has 60"):
+            a.choose([a, a])
+
+
+class TestRepeat:
+    def setup_method(self):
+        self.m = np.array([1, 2, 3, 4, 5, 6])
+        self.m_rect = self.m.reshape((2, 3))
+
+    def test_basic(self):
+        A = np.repeat(self.m, [1, 3, 2, 1, 1, 2])
+        assert_equal(A, [1, 2, 2, 2, 3,
+                         3, 4, 5, 6, 6])
+
+    def test_broadcast1(self):
+        A = np.repeat(self.m, 2)
+        assert_equal(A, [1, 1, 2, 2, 3, 3,
+                         4, 4, 5, 5, 6, 6])
+
+    def test_axis_spec(self):
+        A = np.repeat(self.m_rect, [2, 1], axis=0)
+        assert_equal(A, [[1, 2, 3],
+                         [1, 2, 3],
+                         [4, 5, 6]])
+
+        A = np.repeat(self.m_rect, [1, 3, 2], axis=1)
+        assert_equal(A, [[1, 2, 2, 2, 3, 3],
+                         [4, 5, 5, 5, 6, 6]])
+
+    def test_broadcast2(self):
+        A = np.repeat(self.m_rect, 2, axis=0)
+        assert_equal(A, [[1, 2, 3],
+                         [1, 2, 3],
+                         [4, 5, 6],
+                         [4, 5, 6]])
+
+        A = np.repeat(self.m_rect, 2, axis=1)
+        assert_equal(A, [[1, 1, 2, 2, 3, 3],
+                         [4, 4, 5, 5, 6, 6]])
+
+
+# TODO: test for multidimensional
+NEIGH_MODE = {'zero': 0, 'one': 1, 'constant': 2, 'circular': 3, 'mirror': 4}
+
+
+@pytest.mark.parametrize('dt', [float, Decimal], ids=['float', 'object'])
+class TestNeighborhoodIter:
+    # Simple, 2d tests
+    def test_simple2d(self, dt):
+        # Test zero and one padding for simple data type
+        x = np.array([[0, 1], [2, 3]], dtype=dt)
+        r = [np.array([[0, 0, 0], [0, 0, 1]], dtype=dt),
+             np.array([[0, 0, 0], [0, 1, 0]], dtype=dt),
+             np.array([[0, 0, 1], [0, 2, 3]], dtype=dt),
+             np.array([[0, 1, 0], [2, 3, 0]], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-1, 0, -1, 1], x[0], NEIGH_MODE['zero'])
+        assert_array_equal(l, r)
+
+        r = [np.array([[1, 1, 1], [1, 0, 1]], dtype=dt),
+             np.array([[1, 1, 1], [0, 1, 1]], dtype=dt),
+             np.array([[1, 0, 1], [1, 2, 3]], dtype=dt),
+             np.array([[0, 1, 1], [2, 3, 1]], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-1, 0, -1, 1], x[0], NEIGH_MODE['one'])
+        assert_array_equal(l, r)
+
+        r = [np.array([[4, 4, 4], [4, 0, 1]], dtype=dt),
+             np.array([[4, 4, 4], [0, 1, 4]], dtype=dt),
+             np.array([[4, 0, 1], [4, 2, 3]], dtype=dt),
+             np.array([[0, 1, 4], [2, 3, 4]], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-1, 0, -1, 1], 4, NEIGH_MODE['constant'])
+        assert_array_equal(l, r)
+
+        # Test with start in the middle
+        r = [np.array([[4, 0, 1], [4, 2, 3]], dtype=dt),
+             np.array([[0, 1, 4], [2, 3, 4]], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-1, 0, -1, 1], 4, NEIGH_MODE['constant'], 2)
+        assert_array_equal(l, r)
+
+    def test_mirror2d(self, dt):
+        x = np.array([[0, 1], [2, 3]], dtype=dt)
+        r = [np.array([[0, 0, 1], [0, 0, 1]], dtype=dt),
+             np.array([[0, 1, 1], [0, 1, 1]], dtype=dt),
+             np.array([[0, 0, 1], [2, 2, 3]], dtype=dt),
+             np.array([[0, 1, 1], [2, 3, 3]], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-1, 0, -1, 1], x[0], NEIGH_MODE['mirror'])
+        assert_array_equal(l, r)
+
+    # Simple, 1d tests
+    def test_simple(self, dt):
+        # Test padding with constant values
+        x = np.linspace(1, 5, 5).astype(dt)
+        r = [[0, 1, 2], [1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, 0]]
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-1, 1], x[0], NEIGH_MODE['zero'])
+        assert_array_equal(l, r)
+
+        r = [[1, 1, 2], [1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, 1]]
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-1, 1], x[0], NEIGH_MODE['one'])
+        assert_array_equal(l, r)
+
+        r = [[x[4], 1, 2], [1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, x[4]]]
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-1, 1], x[4], NEIGH_MODE['constant'])
+        assert_array_equal(l, r)
+
+    # Test mirror modes
+    def test_mirror(self, dt):
+        x = np.linspace(1, 5, 5).astype(dt)
+        r = np.array([[2, 1, 1, 2, 3], [1, 1, 2, 3, 4], [1, 2, 3, 4, 5],
+                [2, 3, 4, 5, 5], [3, 4, 5, 5, 4]], dtype=dt)
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-2, 2], x[1], NEIGH_MODE['mirror'])
+        assert_([i.dtype == dt for i in l])
+        assert_array_equal(l, r)
+
+    # Circular mode
+    def test_circular(self, dt):
+        x = np.linspace(1, 5, 5).astype(dt)
+        r = np.array([[4, 5, 1, 2, 3], [5, 1, 2, 3, 4], [1, 2, 3, 4, 5],
+                [2, 3, 4, 5, 1], [3, 4, 5, 1, 2]], dtype=dt)
+        l = _multiarray_tests.test_neighborhood_iterator(
+                x, [-2, 2], x[0], NEIGH_MODE['circular'])
+        assert_array_equal(l, r)
+
+
+# Test stacking neighborhood iterators
+class TestStackedNeighborhoodIter:
+    # Simple, 1d test: stacking 2 constant-padded neigh iterators
+    def test_simple_const(self):
+        dt = np.float64
+        # Test zero and one padding for simple data type
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([0], dtype=dt),
+             np.array([0], dtype=dt),
+             np.array([1], dtype=dt),
+             np.array([2], dtype=dt),
+             np.array([3], dtype=dt),
+             np.array([0], dtype=dt),
+             np.array([0], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-2, 4], NEIGH_MODE['zero'], [0, 0], NEIGH_MODE['zero'])
+        assert_array_equal(l, r)
+
+        r = [np.array([1, 0, 1], dtype=dt),
+             np.array([0, 1, 2], dtype=dt),
+             np.array([1, 2, 3], dtype=dt),
+             np.array([2, 3, 0], dtype=dt),
+             np.array([3, 0, 1], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-1, 3], NEIGH_MODE['zero'], [-1, 1], NEIGH_MODE['one'])
+        assert_array_equal(l, r)
+
+    # 2nd simple, 1d test: stacking 2 neigh iterators, mixing const padding and
+    # mirror padding
+    def test_simple_mirror(self):
+        dt = np.float64
+        # Stacking zero on top of mirror
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([0, 1, 1], dtype=dt),
+             np.array([1, 1, 2], dtype=dt),
+             np.array([1, 2, 3], dtype=dt),
+             np.array([2, 3, 3], dtype=dt),
+             np.array([3, 3, 0], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-1, 3], NEIGH_MODE['mirror'], [-1, 1], NEIGH_MODE['zero'])
+        assert_array_equal(l, r)
+
+        # Stacking mirror on top of zero
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([1, 0, 0], dtype=dt),
+             np.array([0, 0, 1], dtype=dt),
+             np.array([0, 1, 2], dtype=dt),
+             np.array([1, 2, 3], dtype=dt),
+             np.array([2, 3, 0], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-1, 3], NEIGH_MODE['zero'], [-2, 0], NEIGH_MODE['mirror'])
+        assert_array_equal(l, r)
+
+        # Stacking mirror on top of zero: 2nd
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([0, 1, 2], dtype=dt),
+             np.array([1, 2, 3], dtype=dt),
+             np.array([2, 3, 0], dtype=dt),
+             np.array([3, 0, 0], dtype=dt),
+             np.array([0, 0, 3], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-1, 3], NEIGH_MODE['zero'], [0, 2], NEIGH_MODE['mirror'])
+        assert_array_equal(l, r)
+
+        # Stacking mirror on top of zero: 3rd
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([1, 0, 0, 1, 2], dtype=dt),
+             np.array([0, 0, 1, 2, 3], dtype=dt),
+             np.array([0, 1, 2, 3, 0], dtype=dt),
+             np.array([1, 2, 3, 0, 0], dtype=dt),
+             np.array([2, 3, 0, 0, 3], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-1, 3], NEIGH_MODE['zero'], [-2, 2], NEIGH_MODE['mirror'])
+        assert_array_equal(l, r)
+
+    # 3rd simple, 1d test: stacking 2 neigh iterators, mixing const padding and
+    # circular padding
+    def test_simple_circular(self):
+        dt = np.float64
+        # Stacking zero on top of mirror
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([0, 3, 1], dtype=dt),
+             np.array([3, 1, 2], dtype=dt),
+             np.array([1, 2, 3], dtype=dt),
+             np.array([2, 3, 1], dtype=dt),
+             np.array([3, 1, 0], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-1, 3], NEIGH_MODE['circular'], [-1, 1], NEIGH_MODE['zero'])
+        assert_array_equal(l, r)
+
+        # Stacking mirror on top of zero
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([3, 0, 0], dtype=dt),
+             np.array([0, 0, 1], dtype=dt),
+             np.array([0, 1, 2], dtype=dt),
+             np.array([1, 2, 3], dtype=dt),
+             np.array([2, 3, 0], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-1, 3], NEIGH_MODE['zero'], [-2, 0], NEIGH_MODE['circular'])
+        assert_array_equal(l, r)
+
+        # Stacking mirror on top of zero: 2nd
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([0, 1, 2], dtype=dt),
+             np.array([1, 2, 3], dtype=dt),
+             np.array([2, 3, 0], dtype=dt),
+             np.array([3, 0, 0], dtype=dt),
+             np.array([0, 0, 1], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-1, 3], NEIGH_MODE['zero'], [0, 2], NEIGH_MODE['circular'])
+        assert_array_equal(l, r)
+
+        # Stacking mirror on top of zero: 3rd
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([3, 0, 0, 1, 2], dtype=dt),
+             np.array([0, 0, 1, 2, 3], dtype=dt),
+             np.array([0, 1, 2, 3, 0], dtype=dt),
+             np.array([1, 2, 3, 0, 0], dtype=dt),
+             np.array([2, 3, 0, 0, 1], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [-1, 3], NEIGH_MODE['zero'], [-2, 2], NEIGH_MODE['circular'])
+        assert_array_equal(l, r)
+
+    # 4th simple, 1d test: stacking 2 neigh iterators, but with lower iterator
+    # being strictly within the array
+    def test_simple_strict_within(self):
+        dt = np.float64
+        # Stacking zero on top of zero, first neighborhood strictly inside the
+        # array
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([1, 2, 3, 0], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [1, 1], NEIGH_MODE['zero'], [-1, 2], NEIGH_MODE['zero'])
+        assert_array_equal(l, r)
+
+        # Stacking mirror on top of zero, first neighborhood strictly inside the
+        # array
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([1, 2, 3, 3], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [1, 1], NEIGH_MODE['zero'], [-1, 2], NEIGH_MODE['mirror'])
+        assert_array_equal(l, r)
+
+        # Stacking mirror on top of zero, first neighborhood strictly inside the
+        # array
+        x = np.array([1, 2, 3], dtype=dt)
+        r = [np.array([1, 2, 3, 1], dtype=dt)]
+        l = _multiarray_tests.test_neighborhood_iterator_oob(
+                x, [1, 1], NEIGH_MODE['zero'], [-1, 2], NEIGH_MODE['circular'])
+        assert_array_equal(l, r)
+
+class TestWarnings:
+
+    def test_complex_warning(self):
+        x = np.array([1, 2])
+        y = np.array([1 - 2j, 1 + 2j])
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", ComplexWarning)
+            assert_raises(ComplexWarning, x.__setitem__, slice(None), y)
+            assert_equal(x, [1, 2])
+
+
+class TestMinScalarType:
+
+    def test_usigned_shortshort(self):
+        dt = np.min_scalar_type(2**8 - 1)
+        wanted = np.dtype('uint8')
+        assert_equal(wanted, dt)
+
+    def test_usigned_short(self):
+        dt = np.min_scalar_type(2**16 - 1)
+        wanted = np.dtype('uint16')
+        assert_equal(wanted, dt)
+
+    def test_usigned_int(self):
+        dt = np.min_scalar_type(2**32 - 1)
+        wanted = np.dtype('uint32')
+        assert_equal(wanted, dt)
+
+    def test_usigned_longlong(self):
+        dt = np.min_scalar_type(2**63 - 1)
+        wanted = np.dtype('uint64')
+        assert_equal(wanted, dt)
+
+    def test_object(self):
+        dt = np.min_scalar_type(2**64)
+        wanted = np.dtype('O')
+        assert_equal(wanted, dt)
+
+
+from numpy._core._internal import _dtype_from_pep3118
+
+
+class TestPEP3118Dtype:
+    def _check(self, spec, wanted):
+        dt = np.dtype(wanted)
+        actual = _dtype_from_pep3118(spec)
+        assert_equal(actual, dt,
+                     err_msg=f"spec {spec!r} != dtype {wanted!r}")
+
+    def test_native_padding(self):
+        align = np.dtype('i').alignment
+        for j in range(8):
+            if j == 0:
+                s = 'bi'
+            else:
+                s = 'b%dxi' % j
+            self._check('@' + s, {'f0': ('i1', 0),
+                                'f1': ('i', align * (1 + j // align))})
+            self._check('=' + s, {'f0': ('i1', 0),
+                                'f1': ('i', 1 + j)})
+
+    def test_native_padding_2(self):
+        # Native padding should work also for structs and sub-arrays
+        self._check('x3T{xi}', {'f0': (({'f0': ('i', 4)}, (3,)), 4)})
+        self._check('^x3T{xi}', {'f0': (({'f0': ('i', 1)}, (3,)), 1)})
+
+    def test_trailing_padding(self):
+        # Trailing padding should be included, *and*, the item size
+        # should match the alignment if in aligned mode
+        align = np.dtype('i').alignment
+        size = np.dtype('i').itemsize
+
+        def aligned(n):
+            return align * (1 + (n - 1) // align)
+
+        base = {"formats": ['i'], "names": ['f0']}
+
+        self._check('ix',    dict(itemsize=aligned(size + 1), **base))
+        self._check('ixx',   dict(itemsize=aligned(size + 2), **base))
+        self._check('ixxx',  dict(itemsize=aligned(size + 3), **base))
+        self._check('ixxxx', dict(itemsize=aligned(size + 4), **base))
+        self._check('i7x',   dict(itemsize=aligned(size + 7), **base))
+
+        self._check('^ix',    dict(itemsize=size + 1, **base))
+        self._check('^ixx',   dict(itemsize=size + 2, **base))
+        self._check('^ixxx',  dict(itemsize=size + 3, **base))
+        self._check('^ixxxx', dict(itemsize=size + 4, **base))
+        self._check('^i7x',   dict(itemsize=size + 7, **base))
+
+    def test_native_padding_3(self):
+        dt = np.dtype(
+                [('a', 'b'), ('b', 'i'),
+                    ('sub', np.dtype('b,i')), ('c', 'i')],
+                align=True)
+        self._check("T{b:a:xxxi:b:T{b:f0:=i:f1:}:sub:xxxi:c:}", dt)
+
+        dt = np.dtype(
+                [('a', 'b'), ('b', 'i'), ('c', 'b'), ('d', 'b'),
+                    ('e', 'b'), ('sub', np.dtype('b,i', align=True))])
+        self._check("T{b:a:=i:b:b:c:b:d:b:e:T{b:f0:xxxi:f1:}:sub:}", dt)
+
+    def test_padding_with_array_inside_struct(self):
+        dt = np.dtype(
+                [('a', 'b'), ('b', 'i'), ('c', 'b', (3,)),
+                    ('d', 'i')],
+                align=True)
+        self._check("T{b:a:xxxi:b:3b:c:xi:d:}", dt)
+
+    def test_byteorder_inside_struct(self):
+        # The byte order after @T{=i} should be '=', not '@'.
+        # Check this by noting the absence of native alignment.
+        self._check('@T{^i}xi', {'f0': ({'f0': ('i', 0)}, 0),
+                                 'f1': ('i', 5)})
+
+    def test_intra_padding(self):
+        # Natively aligned sub-arrays may require some internal padding
+        align = np.dtype('i').alignment
+        size = np.dtype('i').itemsize
+
+        def aligned(n):
+            return (align * (1 + (n - 1) // align))
+
+        self._check('(3)T{ix}', ({
+            "names": ['f0'],
+            "formats": ['i'],
+            "offsets": [0],
+            "itemsize": aligned(size + 1)
+        }, (3,)))
+
+    def test_char_vs_string(self):
+        dt = np.dtype('c')
+        self._check('c', dt)
+
+        dt = np.dtype([('f0', 'S1', (4,)), ('f1', 'S4')])
+        self._check('4c4s', dt)
+
+    def test_field_order(self):
+        # gh-9053 - previously, we relied on dictionary key order
+        self._check("(0)I:a:f:b:", [('a', 'I', (0,)), ('b', 'f')])
+        self._check("(0)I:b:f:a:", [('b', 'I', (0,)), ('a', 'f')])
+
+    def test_unnamed_fields(self):
+        self._check('ii',     [('f0', 'i'), ('f1', 'i')])
+        self._check('ii:f0:', [('f1', 'i'), ('f0', 'i')])
+
+        self._check('i', 'i')
+        self._check('i:f0:', [('f0', 'i')])
+
+
+class TestNewBufferProtocol:
+    """ Test PEP3118 buffers """
+
+    def _check_roundtrip(self, obj):
+        obj = np.asarray(obj)
+        x = memoryview(obj)
+        y = np.asarray(x)
+        y2 = np.array(x)
+        assert_(not y.flags.owndata)
+        assert_(y2.flags.owndata)
+
+        assert_equal(y.dtype, obj.dtype)
+        assert_equal(y.shape, obj.shape)
+        assert_array_equal(obj, y)
+
+        assert_equal(y2.dtype, obj.dtype)
+        assert_equal(y2.shape, obj.shape)
+        assert_array_equal(obj, y2)
+
+    def test_roundtrip(self):
+        x = np.array([1, 2, 3, 4, 5], dtype='i4')
+        self._check_roundtrip(x)
+
+        x = np.array([[1, 2], [3, 4]], dtype=np.float64)
+        self._check_roundtrip(x)
+
+        x = np.zeros((3, 3, 3), dtype=np.float32)[:, 0, :]
+        self._check_roundtrip(x)
+
+        dt = [('a', 'b'),
+              ('b', 'h'),
+              ('c', 'i'),
+              ('d', 'l'),
+              ('dx', 'q'),
+              ('e', 'B'),
+              ('f', 'H'),
+              ('g', 'I'),
+              ('h', 'L'),
+              ('hx', 'Q'),
+              ('i', np.single),
+              ('j', np.double),
+              ('k', np.longdouble),
+              ('ix', np.csingle),
+              ('jx', np.cdouble),
+              ('kx', np.clongdouble),
+              ('l', 'S4'),
+              ('m', 'U4'),
+              ('n', 'V3'),
+              ('o', '?'),
+              ('p', np.half),
+              ]
+        x = np.array(
+                [(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+                    b'aaaa', 'bbbb', b'xxx', True, 1.0)],
+                dtype=dt)
+        self._check_roundtrip(x)
+
+        x = np.array(([[1, 2], [3, 4]],), dtype=[('a', (int, (2, 2)))])
+        self._check_roundtrip(x)
+
+        x = np.array([1, 2, 3], dtype='>i2')
+        self._check_roundtrip(x)
+
+        x = np.array([1, 2, 3], dtype='<i2')
+        self._check_roundtrip(x)
+
+        x = np.array([1, 2, 3], dtype='>i4')
+        self._check_roundtrip(x)
+
+        x = np.array([1, 2, 3], dtype='<i4')
+        self._check_roundtrip(x)
+
+        # check long long can be represented as non-native
+        x = np.array([1, 2, 3], dtype='>q')
+        self._check_roundtrip(x)
+
+        # Native-only data types can be passed through the buffer interface
+        # only in native byte order
+        if sys.byteorder == 'little':
+            x = np.array([1, 2, 3], dtype='>g')
+            assert_raises(ValueError, self._check_roundtrip, x)
+            x = np.array([1, 2, 3], dtype='<g')
+            self._check_roundtrip(x)
+        else:
+            x = np.array([1, 2, 3], dtype='>g')
+            self._check_roundtrip(x)
+            x = np.array([1, 2, 3], dtype='<g')
+            assert_raises(ValueError, self._check_roundtrip, x)
+
+    def test_roundtrip_half(self):
+        half_list = [
+            1.0,
+            -2.0,
+            6.5504 * 10**4,  # (max half precision)
+            2**-14,  # ~= 6.10352 * 10**-5 (minimum positive normal)
+            2**-24,  # ~= 5.96046 * 10**-8 (minimum strictly positive subnormal)
+            0.0,
+            -0.0,
+            float('+inf'),
+            float('-inf'),
+            0.333251953125,  # ~= 1/3
+        ]
+
+        x = np.array(half_list, dtype='>e')
+        self._check_roundtrip(x)
+        x = np.array(half_list, dtype='<e')
+        self._check_roundtrip(x)
+
+    def test_roundtrip_single_types(self):
+        for typ in np._core.sctypeDict.values():
+            dtype = np.dtype(typ)
+
+            if dtype.char in 'Mm':
+                # datetimes cannot be used in buffers
+                continue
+            if dtype.char == 'V':
+                # skip void
+                continue
+
+            x = np.zeros(4, dtype=dtype)
+            self._check_roundtrip(x)
+
+            if dtype.char not in 'qQgG':
+                dt = dtype.newbyteorder('<')
+                x = np.zeros(4, dtype=dt)
+                self._check_roundtrip(x)
+
+                dt = dtype.newbyteorder('>')
+                x = np.zeros(4, dtype=dt)
+                self._check_roundtrip(x)
+
+    def test_roundtrip_scalar(self):
+        # Issue #4015.
+        self._check_roundtrip(0)
+
+    def test_invalid_buffer_format(self):
+        # datetime64 cannot be used fully in a buffer yet
+        # Should be fixed in the next Numpy major release
+        dt = np.dtype([('a', 'uint16'), ('b', 'M8[s]')])
+        a = np.empty(3, dt)
+        assert_raises((ValueError, BufferError), memoryview, a)
+        assert_raises((ValueError, BufferError), memoryview, np.array((3), 'M8[D]'))
+
+    def test_export_simple_1d(self):
+        x = np.array([1, 2, 3, 4, 5], dtype='i')
+        y = memoryview(x)
+        assert_equal(y.format, 'i')
+        assert_equal(y.shape, (5,))
+        assert_equal(y.ndim, 1)
+        assert_equal(y.strides, (4,))
+        assert_equal(y.suboffsets, ())
+        assert_equal(y.itemsize, 4)
+
+    def test_export_simple_nd(self):
+        x = np.array([[1, 2], [3, 4]], dtype=np.float64)
+        y = memoryview(x)
+        assert_equal(y.format, 'd')
+        assert_equal(y.shape, (2, 2))
+        assert_equal(y.ndim, 2)
+        assert_equal(y.strides, (16, 8))
+        assert_equal(y.suboffsets, ())
+        assert_equal(y.itemsize, 8)
+
+    def test_export_discontiguous(self):
+        x = np.zeros((3, 3, 3), dtype=np.float32)[:, 0, :]
+        y = memoryview(x)
+        assert_equal(y.format, 'f')
+        assert_equal(y.shape, (3, 3))
+        assert_equal(y.ndim, 2)
+        assert_equal(y.strides, (36, 4))
+        assert_equal(y.suboffsets, ())
+        assert_equal(y.itemsize, 4)
+
+    def test_export_record(self):
+        dt = [('a', 'b'),
+              ('b', 'h'),
+              ('c', 'i'),
+              ('d', 'l'),
+              ('dx', 'q'),
+              ('e', 'B'),
+              ('f', 'H'),
+              ('g', 'I'),
+              ('h', 'L'),
+              ('hx', 'Q'),
+              ('i', np.single),
+              ('j', np.double),
+              ('k', np.longdouble),
+              ('ix', np.csingle),
+              ('jx', np.cdouble),
+              ('kx', np.clongdouble),
+              ('l', 'S4'),
+              ('m', 'U4'),
+              ('n', 'V3'),
+              ('o', '?'),
+              ('p', np.half),
+              ]
+        x = np.array(
+                [(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+                    b'aaaa', 'bbbb', b'   ', True, 1.0)],
+                dtype=dt)
+        y = memoryview(x)
+        assert_equal(y.shape, (1,))
+        assert_equal(y.ndim, 1)
+        assert_equal(y.suboffsets, ())
+
+        sz = sum(np.dtype(b).itemsize for a, b in dt)
+        if np.dtype('l').itemsize == 4:
+            assert_equal(y.format, 'T{b:a:=h:b:i:c:l:d:q:dx:B:e:@H:f:=I:g:L:h:Q:hx:f:i:d:j:^g:k:=Zf:ix:Zd:jx:^Zg:kx:4s:l:=4w:m:3x:n:?:o:@e:p:}')
+        else:
+            assert_equal(y.format, 'T{b:a:=h:b:i:c:q:d:q:dx:B:e:@H:f:=I:g:Q:h:Q:hx:f:i:d:j:^g:k:=Zf:ix:Zd:jx:^Zg:kx:4s:l:=4w:m:3x:n:?:o:@e:p:}')
+        assert_equal(y.strides, (sz,))
+        assert_equal(y.itemsize, sz)
+
+    def test_export_subarray(self):
+        x = np.array(([[1, 2], [3, 4]],), dtype=[('a', ('i', (2, 2)))])
+        y = memoryview(x)
+        assert_equal(y.format, 'T{(2,2)i:a:}')
+        assert_equal(y.shape, ())
+        assert_equal(y.ndim, 0)
+        assert_equal(y.strides, ())
+        assert_equal(y.suboffsets, ())
+        assert_equal(y.itemsize, 16)
+
+    def test_export_endian(self):
+        x = np.array([1, 2, 3], dtype='>i')
+        y = memoryview(x)
+        if sys.byteorder == 'little':
+            assert_equal(y.format, '>i')
+        else:
+            assert_equal(y.format, 'i')
+
+        x = np.array([1, 2, 3], dtype='<i')
+        y = memoryview(x)
+        if sys.byteorder == 'little':
+            assert_equal(y.format, 'i')
+        else:
+            assert_equal(y.format, '<i')
+
+    def test_export_flags(self):
+        # Check SIMPLE flag, see also gh-3613 (exception should be BufferError)
+        assert_raises(ValueError,
+                      _multiarray_tests.get_buffer_info,
+                       np.arange(5)[::2], ('SIMPLE',))
+
+    @pytest.mark.parametrize(["obj", "error"], [
+            pytest.param(np.array([1, 2], dtype=rational), ValueError, id="array"),
+            pytest.param(rational(1, 2), TypeError, id="scalar")])
+    def test_export_and_pickle_user_dtype(self, obj, error):
+        # User dtypes should export successfully when FORMAT was not requested.
+        with pytest.raises(error):
+            _multiarray_tests.get_buffer_info(obj, ("STRIDED_RO", "FORMAT"))
+
+        _multiarray_tests.get_buffer_info(obj, ("STRIDED_RO",))
+
+        # This is currently also necessary to implement pickling:
+        pickle_obj = pickle.dumps(obj)
+        res = pickle.loads(pickle_obj)
+        assert_array_equal(res, obj)
+
+    def test_repr_user_dtype(self):
+        dt = np.dtype(rational)
+        assert_equal(repr(dt), 'dtype(rational)')
+
+    def test_padding(self):
+        for j in range(8):
+            x = np.array([(1,), (2,)], dtype={'f0': (int, j)})
+            self._check_roundtrip(x)
+
+    def test_reference_leak(self):
+        if HAS_REFCOUNT:
+            count_1 = sys.getrefcount(np._core._internal)
+        a = np.zeros(4)
+        b = memoryview(a)
+        c = np.asarray(b)
+        if HAS_REFCOUNT:
+            count_2 = sys.getrefcount(np._core._internal)
+            assert_equal(count_1, count_2)
+
+    def test_padded_struct_array(self):
+        dt1 = np.dtype(
+                [('a', 'b'), ('b', 'i'), ('sub', np.dtype('b,i')), ('c', 'i')],
+                align=True)
+        x1 = np.arange(dt1.itemsize, dtype=np.int8).view(dt1)
+        self._check_roundtrip(x1)
+
+        dt2 = np.dtype(
+                [('a', 'b'), ('b', 'i'), ('c', 'b', (3,)), ('d', 'i')],
+                align=True)
+        x2 = np.arange(dt2.itemsize, dtype=np.int8).view(dt2)
+        self._check_roundtrip(x2)
+
+        dt3 = np.dtype(
+                [('a', 'b'), ('b', 'i'), ('c', 'b'), ('d', 'b'),
+                    ('e', 'b'), ('sub', np.dtype('b,i', align=True))])
+        x3 = np.arange(dt3.itemsize, dtype=np.int8).view(dt3)
+        self._check_roundtrip(x3)
+
+    @pytest.mark.valgrind_error(reason="leaks buffer info cache temporarily.")
+    def test_relaxed_strides(self, c=np.ones((1, 10, 10), dtype='i8')):  # noqa: B008
+        # Note: c defined as parameter so that it is persistent and leak
+        # checks will notice gh-16934 (buffer info cache leak).
+        c.strides = (-1, 80, 8)  # strides need to be fixed at export
+
+        assert_(memoryview(c).strides == (800, 80, 8))
+
+        # Writing C-contiguous data to a BytesIO buffer should work
+        fd = io.BytesIO()
+        fd.write(c.data)
+
+        fortran = c.T
+        assert_(memoryview(fortran).strides == (8, 80, 800))
+
+        arr = np.ones((1, 10))
+        if arr.flags.f_contiguous:
+            shape, strides = _multiarray_tests.get_buffer_info(
+                    arr, ['F_CONTIGUOUS'])
+            assert_(strides[0] == 8)
+            arr = np.ones((10, 1), order='F')
+            shape, strides = _multiarray_tests.get_buffer_info(
+                    arr, ['C_CONTIGUOUS'])
+            assert_(strides[-1] == 8)
+
+    def test_out_of_order_fields(self):
+        dt = np.dtype({
+            "formats": ['<i4', '<i4'],
+            "names": ['one', 'two'],
+            "offsets": [4, 0],
+            "itemsize": 8
+        })
+
+        # overlapping fields cannot be represented by PEP3118
+        arr = np.empty(1, dt)
+        with assert_raises(ValueError):
+            memoryview(arr)
+
+    def test_max_dims(self):
+        a = np.ones((1,) * 32)
+        self._check_roundtrip(a)
+
+    def test_error_pointer_type(self):
+        # gh-6741
+        m = memoryview(ctypes.pointer(ctypes.c_uint8()))
+        assert_('&' in m.format)
+
+        assert_raises_regex(
+            ValueError, "format string",
+            np.array, m)
+
+    def test_error_message_unsupported(self):
+        # wchar has no corresponding numpy type - if this changes in future, we
+        # need a better way to construct an invalid memoryview format.
+        t = ctypes.c_wchar * 4
+        with assert_raises(ValueError) as cm:
+            np.array(t())
+
+        exc = cm.exception
+        with assert_raises_regex(
+            NotImplementedError,
+            r"Unrepresentable .* 'u' \(UCS-2 strings\)"
+        ):
+            raise exc.__cause__
+
+    def test_ctypes_integer_via_memoryview(self):
+        # gh-11150, due to bpo-10746
+        for c_integer in {ctypes.c_int, ctypes.c_long, ctypes.c_longlong}:
+            value = c_integer(42)
+            with warnings.catch_warnings(record=True):
+                warnings.filterwarnings('always', r'.*\bctypes\b', RuntimeWarning)
+                np.asarray(value)
+
+    def test_ctypes_struct_via_memoryview(self):
+        # gh-10528
+        class foo(ctypes.Structure):
+            _fields_ = [('a', ctypes.c_uint8), ('b', ctypes.c_uint32)]
+        f = foo(a=1, b=2)
+
+        with warnings.catch_warnings(record=True):
+            warnings.filterwarnings('always', r'.*\bctypes\b', RuntimeWarning)
+            arr = np.asarray(f)
+
+        assert_equal(arr['a'], 1)
+        assert_equal(arr['b'], 2)
+        f.a = 3
+        assert_equal(arr['a'], 3)
+
+    @pytest.mark.parametrize("obj", [np.ones(3), np.ones(1, dtype="i,i")[()]])
+    def test_error_if_stored_buffer_info_is_corrupted(self, obj):
+        """
+        If a user extends a NumPy array before 1.20 and then runs it
+        on NumPy 1.20+. A C-subclassed array might in theory modify
+        the new buffer-info field. This checks that an error is raised
+        if this happens (for buffer export), an error is written on delete.
+        This is a sanity check to help users transition to safe code, it
+        may be deleted at any point.
+        """
+        # corrupt buffer info:
+        _multiarray_tests.corrupt_or_fix_bufferinfo(obj)
+        name = type(obj)
+        with pytest.raises(RuntimeError,
+                    match=f".*{name} appears to be C subclassed"):
+            memoryview(obj)
+        # Fix buffer info again before we delete (or we lose the memory)
+        _multiarray_tests.corrupt_or_fix_bufferinfo(obj)
+
+    def test_no_suboffsets(self):
+        try:
+            import _testbuffer
+        except ImportError:
+            raise pytest.skip("_testbuffer is not available")
+
+        for shape in [(2, 3), (2, 3, 4)]:
+            data = list(range(np.prod(shape)))
+            buffer = _testbuffer.ndarray(data, shape, format='i',
+                                         flags=_testbuffer.ND_PIL)
+            msg = "NumPy currently does not support.*suboffsets"
+            with pytest.raises(BufferError, match=msg):
+                np.asarray(buffer)
+            with pytest.raises(BufferError, match=msg):
+                np.asarray([buffer])
+
+            # Also check (unrelated and more limited but similar) frombuffer:
+            with pytest.raises(BufferError):
+                np.frombuffer(buffer)
+
+
+class TestArrayCreationCopyArgument:
+
+    class RaiseOnBool:
+
+        def __bool__(self):
+            raise ValueError
+
+    true_vals = [True, np._CopyMode.ALWAYS, np.True_]
+    if_needed_vals = [None, np._CopyMode.IF_NEEDED]
+    false_vals = [False, np._CopyMode.NEVER, np.False_]
+
+    def test_scalars(self):
+        # Test both numpy and python scalars
+        for dtype in np.typecodes["All"]:
+            arr = np.zeros((), dtype=dtype)
+            scalar = arr[()]
+            pyscalar = arr.item(0)
+
+            # Test never-copy raises error:
+            assert_raises(ValueError, np.array, pyscalar,
+                            copy=self.RaiseOnBool())
+            assert_raises(ValueError, _multiarray_tests.npy_ensurenocopy,
+                            [1])
+            for copy in self.false_vals:
+                assert_raises(ValueError, np.array, scalar, copy=copy)
+                assert_raises(ValueError, np.array, pyscalar, copy=copy)
+                # Casting with a dtype (to unsigned integers) can be special:
+                with pytest.raises(ValueError):
+                    np.array(pyscalar, dtype=np.int64, copy=copy)
+
+    def test_compatible_cast(self):
+
+        # Some types are compatible even though they are different, no
+        # copy is necessary for them. This is mostly true for some integers
+        def int_types(byteswap=False):
+            int_types = (np.typecodes["Integer"] +
+                         np.typecodes["UnsignedInteger"])
+            for int_type in int_types:
+                yield np.dtype(int_type)
+                if byteswap:
+                    yield np.dtype(int_type).newbyteorder()
+
+        for int1 in int_types():
+            for int2 in int_types(True):
+                arr = np.arange(10, dtype=int1)
+
+                for copy in self.true_vals:
+                    res = np.array(arr, copy=copy, dtype=int2)
+                    assert res is not arr and res.flags.owndata
+                    assert_array_equal(res, arr)
+
+                if int1 == int2:
+                    # Casting is not necessary, base check is sufficient here
+                    for copy in self.if_needed_vals:
+                        res = np.array(arr, copy=copy, dtype=int2)
+                        assert res is arr or res.base is arr
+
+                    for copy in self.false_vals:
+                        res = np.array(arr, copy=copy, dtype=int2)
+                        assert res is arr or res.base is arr
+
+                else:
+                    # Casting is necessary, assert copy works:
+                    for copy in self.if_needed_vals:
+                        res = np.array(arr, copy=copy, dtype=int2)
+                        assert res is not arr and res.flags.owndata
+                        assert_array_equal(res, arr)
+
+                    assert_raises(ValueError, np.array,
+                                  arr, copy=False,
+                                  dtype=int2)
+
+    def test_buffer_interface(self):
+
+        # Buffer interface gives direct memory access (no copy)
+        arr = np.arange(10)
+        view = memoryview(arr)
+
+        # Checking bases is a bit tricky since numpy creates another
+        # memoryview, so use may_share_memory.
+        for copy in self.true_vals:
+            res = np.array(view, copy=copy)
+            assert not np.may_share_memory(arr, res)
+        for copy in self.false_vals:
+            res = np.array(view, copy=copy)
+            assert np.may_share_memory(arr, res)
+        res = np.array(view, copy=np._CopyMode.NEVER)
+        assert np.may_share_memory(arr, res)
+
+    def test_array_interfaces(self):
+        base_arr = np.arange(10)
+
+        # Array interface gives direct memory access (much like a memoryview)
+        class ArrayLike:
+            __array_interface__ = base_arr.__array_interface__
+
+        arr = ArrayLike()
+
+        for copy, val in [(True, None), (np._CopyMode.ALWAYS, None),
+                          (False, arr), (np._CopyMode.IF_NEEDED, arr),
+                          (np._CopyMode.NEVER, arr)]:
+            res = np.array(arr, copy=copy)
+            assert res.base is val
+
+    def test___array__(self):
+        base_arr = np.arange(10)
+
+        class ArrayLike:
+            def __array__(self, dtype=None, copy=None):
+                return base_arr
+
+        arr = ArrayLike()
+
+        for copy in self.true_vals:
+            res = np.array(arr, copy=copy)
+            assert_array_equal(res, base_arr)
+            # An additional copy is no longer forced by NumPy in this case.
+            # NumPy trusts the ArrayLike made a copy:
+            assert res is base_arr
+
+        for copy in self.if_needed_vals + self.false_vals:
+            res = np.array(arr, copy=copy)
+            assert_array_equal(res, base_arr)
+            assert res is base_arr  # numpy trusts the ArrayLike
+
+    def test___array__copy_arg(self):
+        a = np.ones((10, 10), dtype=int)
+
+        assert np.shares_memory(a, a.__array__())
+        assert not np.shares_memory(a, a.__array__(float))
+        assert not np.shares_memory(a, a.__array__(float, copy=None))
+        assert not np.shares_memory(a, a.__array__(copy=True))
+        assert np.shares_memory(a, a.__array__(copy=None))
+        assert np.shares_memory(a, a.__array__(copy=False))
+        assert np.shares_memory(a, a.__array__(int, copy=False))
+        with pytest.raises(ValueError):
+            np.shares_memory(a, a.__array__(float, copy=False))
+
+        base_arr = np.arange(10)
+
+        class ArrayLikeNoCopy:
+            def __array__(self, dtype=None):
+                return base_arr
+
+        a = ArrayLikeNoCopy()
+
+        # explicitly passing copy=None shouldn't raise a warning
+        arr = np.array(a, copy=None)
+        assert_array_equal(arr, base_arr)
+        assert arr is base_arr
+
+        # As of NumPy 2.1, explicitly passing copy=True does trigger passing
+        # it to __array__ (deprecation warning is triggered).
+        with pytest.warns(DeprecationWarning,
+                          match="__array__.*must implement.*'copy'"):
+            arr = np.array(a, copy=True)
+        assert_array_equal(arr, base_arr)
+        assert arr is not base_arr
+
+        # And passing copy=False gives a deprecation warning, but also raises
+        # an error:
+        with pytest.warns(DeprecationWarning, match="__array__.*'copy'"):
+            with pytest.raises(ValueError,
+                    match=r"Unable to avoid copy(.|\n)*numpy_2_0_migration_guide.html"):
+                np.array(a, copy=False)
+
+    def test___array__copy_once(self):
+        size = 100
+        base_arr = np.zeros((size, size))
+        copy_arr = np.zeros((size, size))
+
+        class ArrayRandom:
+            def __init__(self):
+                self.true_passed = False
+
+            def __array__(self, dtype=None, copy=None):
+                if copy:
+                    self.true_passed = True
+                    return copy_arr
+                else:
+                    return base_arr
+
+        arr_random = ArrayRandom()
+        first_copy = np.array(arr_random, copy=True)
+        assert arr_random.true_passed
+        assert first_copy is copy_arr
+
+        arr_random = ArrayRandom()
+        no_copy = np.array(arr_random, copy=False)
+        assert not arr_random.true_passed
+        assert no_copy is base_arr
+
+        arr_random = ArrayRandom()
+        _ = np.array([arr_random], copy=True)
+        assert not arr_random.true_passed
+
+        arr_random = ArrayRandom()
+        second_copy = np.array(arr_random, copy=True, order="F")
+        assert arr_random.true_passed
+        assert second_copy is not copy_arr
+
+        arr_random = ArrayRandom()
+        arr = np.ones((size, size))
+        arr[...] = arr_random
+        assert not arr_random.true_passed
+        assert not np.shares_memory(arr, base_arr)
+
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test__array__reference_leak(self):
+        class NotAnArray:
+            def __array__(self, dtype=None, copy=None):
+                raise NotImplementedError
+
+        x = NotAnArray()
+
+        refcount = sys.getrefcount(x)
+
+        try:
+            np.array(x)
+        except NotImplementedError:
+            pass
+
+        gc.collect()
+
+        assert refcount == sys.getrefcount(x)
+
+    @pytest.mark.parametrize(
+            "arr", [np.ones(()), np.arange(81).reshape((9, 9))])
+    @pytest.mark.parametrize("order1", ["C", "F", None])
+    @pytest.mark.parametrize("order2", ["C", "F", "A", "K"])
+    def test_order_mismatch(self, arr, order1, order2):
+        # The order is the main (python side) reason that can cause
+        # a never-copy to fail.
+        # Prepare C-order, F-order and non-contiguous arrays:
+        arr = arr.copy(order1)
+        if order1 == "C":
+            assert arr.flags.c_contiguous
+        elif order1 == "F":
+            assert arr.flags.f_contiguous
+        elif arr.ndim != 0:
+            # Make array non-contiguous
+            arr = arr[::2, ::2]
+            assert not arr.flags.forc
+
+        # Whether a copy is necessary depends on the order of arr:
+        if order2 == "C":
+            no_copy_necessary = arr.flags.c_contiguous
+        elif order2 == "F":
+            no_copy_necessary = arr.flags.f_contiguous
+        else:
+            # Keeporder and Anyorder are OK with non-contiguous output.
+            # This is not consistent with the `astype` behaviour which
+            # enforces contiguity for "A". It is probably historic from when
+            # "K" did not exist.
+            no_copy_necessary = True
+
+        # Test it for both the array and a memoryview
+        for view in [arr, memoryview(arr)]:
+            for copy in self.true_vals:
+                res = np.array(view, copy=copy, order=order2)
+                assert res is not arr and res.flags.owndata
+                assert_array_equal(arr, res)
+
+            if no_copy_necessary:
+                for copy in self.if_needed_vals + self.false_vals:
+                    res = np.array(view, copy=copy, order=order2)
+                    # res.base.obj refers to the memoryview
+                    if not IS_PYPY:
+                        assert res is arr or res.base.obj is arr
+            else:
+                for copy in self.if_needed_vals:
+                    res = np.array(arr, copy=copy, order=order2)
+                    assert_array_equal(arr, res)
+                for copy in self.false_vals:
+                    assert_raises(ValueError, np.array,
+                                  view, copy=copy, order=order2)
+
+    def test_striding_not_ok(self):
+        arr = np.array([[1, 2, 4], [3, 4, 5]])
+        assert_raises(ValueError, np.array,
+                      arr.T, copy=np._CopyMode.NEVER,
+                      order='C')
+        assert_raises(ValueError, np.array,
+                      arr.T, copy=np._CopyMode.NEVER,
+                      order='C', dtype=np.int64)
+        assert_raises(ValueError, np.array,
+                      arr, copy=np._CopyMode.NEVER,
+                      order='F')
+        assert_raises(ValueError, np.array,
+                      arr, copy=np._CopyMode.NEVER,
+                      order='F', dtype=np.int64)
+
+
+class TestArrayAttributeDeletion:
+
+    def test_multiarray_writable_attributes_deletion(self):
+        # ticket #2046, should not seqfault, raise AttributeError
+        a = np.ones(2)
+        attr = ['shape', 'strides', 'data', 'dtype', 'real', 'imag', 'flat']
+        with suppress_warnings() as sup:
+            sup.filter(DeprecationWarning, "Assigning the 'data' attribute")
+            for s in attr:
+                assert_raises(AttributeError, delattr, a, s)
+
+    def test_multiarray_not_writable_attributes_deletion(self):
+        a = np.ones(2)
+        attr = ["ndim", "flags", "itemsize", "size", "nbytes", "base",
+                "ctypes", "T", "__array_interface__", "__array_struct__",
+                "__array_priority__", "__array_finalize__"]
+        for s in attr:
+            assert_raises(AttributeError, delattr, a, s)
+
+    def test_multiarray_flags_writable_attribute_deletion(self):
+        a = np.ones(2).flags
+        attr = ['writebackifcopy', 'updateifcopy', 'aligned', 'writeable']
+        for s in attr:
+            assert_raises(AttributeError, delattr, a, s)
+
+    def test_multiarray_flags_not_writable_attribute_deletion(self):
+        a = np.ones(2).flags
+        attr = ["contiguous", "c_contiguous", "f_contiguous", "fortran",
+                "owndata", "fnc", "forc", "behaved", "carray", "farray",
+                "num"]
+        for s in attr:
+            assert_raises(AttributeError, delattr, a, s)
+
+
+class TestArrayInterface:
+    class Foo:
+        def __init__(self, value):
+            self.value = value
+            self.iface = {'typestr': 'f8'}
+
+        def __float__(self):
+            return float(self.value)
+
+        @property
+        def __array_interface__(self):
+            return self.iface
+
+    f = Foo(0.5)
+
+    @pytest.mark.parametrize('val, iface, expected', [
+        (f, {}, 0.5),
+        ([f], {}, [0.5]),
+        ([f, f], {}, [0.5, 0.5]),
+        (f, {'shape': ()}, 0.5),
+        (f, {'shape': None}, TypeError),
+        (f, {'shape': (1, 1)}, [[0.5]]),
+        (f, {'shape': (2,)}, ValueError),
+        (f, {'strides': ()}, 0.5),
+        (f, {'strides': (2,)}, ValueError),
+        (f, {'strides': 16}, TypeError),
+        ])
+    def test_scalar_interface(self, val, iface, expected):
+        # Test scalar coercion within the array interface
+        self.f.iface = {'typestr': 'f8'}
+        self.f.iface.update(iface)
+        if HAS_REFCOUNT:
+            pre_cnt = sys.getrefcount(np.dtype('f8'))
+        if isinstance(expected, type):
+            assert_raises(expected, np.array, val)
+        else:
+            result = np.array(val)
+            assert_equal(np.array(val), expected)
+            assert result.dtype == 'f8'
+            del result
+        if HAS_REFCOUNT:
+            post_cnt = sys.getrefcount(np.dtype('f8'))
+            assert_equal(pre_cnt, post_cnt)
+
+def test_interface_no_shape():
+    class ArrayLike:
+        array = np.array(1)
+        __array_interface__ = array.__array_interface__
+    assert_equal(np.array(ArrayLike()), 1)
+
+
+def test_interface_no_shape_error():
+    class ArrayLike:
+        __array_interface__ = {"data": None, "typestr": "f8"}
+
+    with pytest.raises(ValueError, match="Missing __array_interface__ shape"):
+        np.array(ArrayLike())
+
+
+def test_array_interface_itemsize():
+    # See gh-6361
+    my_dtype = np.dtype({'names': ['A', 'B'], 'formats': ['f4', 'f4'],
+                         'offsets': [0, 8], 'itemsize': 16})
+    a = np.ones(10, dtype=my_dtype)
+    descr_t = np.dtype(a.__array_interface__['descr'])
+    typestr_t = np.dtype(a.__array_interface__['typestr'])
+    assert_equal(descr_t.itemsize, typestr_t.itemsize)
+
+
+def test_array_interface_empty_shape():
+    # See gh-7994
+    arr = np.array([1, 2, 3])
+    interface1 = dict(arr.__array_interface__)
+    interface1['shape'] = ()
+
+    class DummyArray1:
+        __array_interface__ = interface1
+
+    # NOTE: Because Py2 str/Py3 bytes supports the buffer interface, setting
+    # the interface data to bytes would invoke the bug this tests for, that
+    # __array_interface__ with shape=() is not allowed if the data is an object
+    # exposing the buffer interface
+    interface2 = dict(interface1)
+    interface2['data'] = arr[0].tobytes()
+
+    class DummyArray2:
+        __array_interface__ = interface2
+
+    arr1 = np.asarray(DummyArray1())
+    arr2 = np.asarray(DummyArray2())
+    arr3 = arr[:1].reshape(())
+    assert_equal(arr1, arr2)
+    assert_equal(arr1, arr3)
+
+def test_array_interface_offset():
+    arr = np.array([1, 2, 3], dtype='int32')
+    interface = dict(arr.__array_interface__)
+    interface['data'] = memoryview(arr)
+    interface['shape'] = (2,)
+    interface['offset'] = 4
+
+    class DummyArray:
+        __array_interface__ = interface
+
+    arr1 = np.asarray(DummyArray())
+    assert_equal(arr1, arr[1:])
+
+def test_array_interface_unicode_typestr():
+    arr = np.array([1, 2, 3], dtype='int32')
+    interface = dict(arr.__array_interface__)
+    interface['typestr'] = '\N{check mark}'
+
+    class DummyArray:
+        __array_interface__ = interface
+
+    # should not be UnicodeEncodeError
+    with pytest.raises(TypeError):
+        np.asarray(DummyArray())
+
+def test_flat_element_deletion():
+    it = np.ones(3).flat
+    try:
+        del it[1]
+        del it[1:2]
+    except TypeError:
+        pass
+    except Exception:
+        raise AssertionError
+
+
+def test_scalar_element_deletion():
+    a = np.zeros(2, dtype=[('x', 'int'), ('y', 'int')])
+    assert_raises(ValueError, a[0].__delitem__, 'x')
+
+
+class TestAsCArray:
+    def test_1darray(self):
+        array = np.arange(24, dtype=np.double)
+        from_c = _multiarray_tests.test_as_c_array(array, 3)
+        assert_equal(array[3], from_c)
+
+    def test_2darray(self):
+        array = np.arange(24, dtype=np.double).reshape(3, 8)
+        from_c = _multiarray_tests.test_as_c_array(array, 2, 4)
+        assert_equal(array[2, 4], from_c)
+
+    def test_3darray(self):
+        array = np.arange(24, dtype=np.double).reshape(2, 3, 4)
+        from_c = _multiarray_tests.test_as_c_array(array, 1, 2, 3)
+        assert_equal(array[1, 2, 3], from_c)
+
+
+class TestConversion:
+    def test_array_scalar_relational_operation(self):
+        # All integer
+        for dt1 in np.typecodes['AllInteger']:
+            assert_(1 > np.array(0, dtype=dt1), f"type {dt1} failed")
+            assert_(not 1 < np.array(0, dtype=dt1), f"type {dt1} failed")
+
+            for dt2 in np.typecodes['AllInteger']:
+                assert_(np.array(1, dtype=dt1) > np.array(0, dtype=dt2),
+                        f"type {dt1} and {dt2} failed")
+                assert_(not np.array(1, dtype=dt1) < np.array(0, dtype=dt2),
+                        f"type {dt1} and {dt2} failed")
+
+        # Unsigned integers
+        for dt1 in 'BHILQP':
+            assert_(-1 < np.array(1, dtype=dt1), f"type {dt1} failed")
+            assert_(not -1 > np.array(1, dtype=dt1), f"type {dt1} failed")
+            assert_(-1 != np.array(1, dtype=dt1), f"type {dt1} failed")
+
+            # Unsigned vs signed
+            for dt2 in 'bhilqp':
+                assert_(np.array(1, dtype=dt1) > np.array(-1, dtype=dt2),
+                        f"type {dt1} and {dt2} failed")
+                assert_(not np.array(1, dtype=dt1) < np.array(-1, dtype=dt2),
+                        f"type {dt1} and {dt2} failed")
+                assert_(np.array(1, dtype=dt1) != np.array(-1, dtype=dt2),
+                        f"type {dt1} and {dt2} failed")
+
+        # Signed integers and floats
+        for dt1 in 'bhlqp' + np.typecodes['Float']:
+            assert_(1 > np.array(-1, dtype=dt1), f"type {dt1} failed")
+            assert_(not 1 < np.array(-1, dtype=dt1), f"type {dt1} failed")
+            assert_(-1 == np.array(-1, dtype=dt1), f"type {dt1} failed")
+
+            for dt2 in 'bhlqp' + np.typecodes['Float']:
+                assert_(np.array(1, dtype=dt1) > np.array(-1, dtype=dt2),
+                        f"type {dt1} and {dt2} failed")
+                assert_(not np.array(1, dtype=dt1) < np.array(-1, dtype=dt2),
+                        f"type {dt1} and {dt2} failed")
+                assert_(np.array(-1, dtype=dt1) == np.array(-1, dtype=dt2),
+                        f"type {dt1} and {dt2} failed")
+
+    def test_to_bool_scalar(self):
+        assert_equal(bool(np.array([False])), False)
+        assert_equal(bool(np.array([True])), True)
+        assert_equal(bool(np.array([[42]])), True)
+
+    def test_to_bool_scalar_not_convertible(self):
+
+        class NotConvertible:
+            def __bool__(self):
+                raise NotImplementedError
+
+        assert_raises(NotImplementedError, bool, np.array(NotConvertible()))
+        assert_raises(NotImplementedError, bool, np.array([NotConvertible()]))
+        if IS_PYSTON:
+            pytest.skip("Pyston disables recursion checking")
+        if IS_WASM:
+            pytest.skip("Pyodide/WASM has limited stack size")
+
+        self_containing = np.array([None])
+        self_containing[0] = self_containing
+
+        Error = RecursionError
+
+        assert_raises(Error, bool, self_containing)  # previously stack overflow
+        self_containing[0] = None  # resolve circular reference
+
+    def test_to_bool_scalar_size_errors(self):
+        with pytest.raises(ValueError, match=".*one element is ambiguous"):
+            bool(np.array([1, 2]))
+
+        with pytest.raises(ValueError, match=".*empty array is ambiguous"):
+            bool(np.empty((3, 0)))
+
+        with pytest.raises(ValueError, match=".*empty array is ambiguous"):
+            bool(np.empty((0,)))
+
+    def test_to_int_scalar(self):
+        # gh-9972 means that these aren't always the same
+        int_funcs = (int, lambda x: x.__int__())
+        for int_func in int_funcs:
+            assert_equal(int_func(np.array(0)), 0)
+            with assert_warns(DeprecationWarning):
+                assert_equal(int_func(np.array([1])), 1)
+            with assert_warns(DeprecationWarning):
+                assert_equal(int_func(np.array([[42]])), 42)
+            assert_raises(TypeError, int_func, np.array([1, 2]))
+
+            # gh-9972
+            assert_equal(4, int_func(np.array('4')))
+            assert_equal(5, int_func(np.bytes_(b'5')))
+            assert_equal(6, int_func(np.str_('6')))
+
+            class NotConvertible:
+                def __int__(self):
+                    raise NotImplementedError
+            assert_raises(NotImplementedError,
+                int_func, np.array(NotConvertible()))
+            with assert_warns(DeprecationWarning):
+                assert_raises(NotImplementedError,
+                    int_func, np.array([NotConvertible()]))
+
+
+class TestWhere:
+    def test_basic(self):
+        dts = [bool, np.int16, np.int32, np.int64, np.double, np.complex128,
+               np.longdouble, np.clongdouble]
+        for dt in dts:
+            c = np.ones(53, dtype=bool)
+            assert_equal(np.where( c, dt(0), dt(1)), dt(0))
+            assert_equal(np.where(~c, dt(0), dt(1)), dt(1))
+            assert_equal(np.where(True, dt(0), dt(1)), dt(0))
+            assert_equal(np.where(False, dt(0), dt(1)), dt(1))
+            d = np.ones_like(c).astype(dt)
+            e = np.zeros_like(d)
+            r = d.astype(dt)
+            c[7] = False
+            r[7] = e[7]
+            assert_equal(np.where(c, e, e), e)
+            assert_equal(np.where(c, d, e), r)
+            assert_equal(np.where(c, d, e[0]), r)
+            assert_equal(np.where(c, d[0], e), r)
+            assert_equal(np.where(c[::2], d[::2], e[::2]), r[::2])
+            assert_equal(np.where(c[1::2], d[1::2], e[1::2]), r[1::2])
+            assert_equal(np.where(c[::3], d[::3], e[::3]), r[::3])
+            assert_equal(np.where(c[1::3], d[1::3], e[1::3]), r[1::3])
+            assert_equal(np.where(c[::-2], d[::-2], e[::-2]), r[::-2])
+            assert_equal(np.where(c[::-3], d[::-3], e[::-3]), r[::-3])
+            assert_equal(np.where(c[1::-3], d[1::-3], e[1::-3]), r[1::-3])
+
+    @pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support")
+    def test_exotic(self):
+        # object
+        assert_array_equal(np.where(True, None, None), np.array(None))
+        # zero sized
+        m = np.array([], dtype=bool).reshape(0, 3)
+        b = np.array([], dtype=np.float64).reshape(0, 3)
+        assert_array_equal(np.where(m, 0, b), np.array([]).reshape(0, 3))
+
+        # object cast
+        d = np.array([-1.34, -0.16, -0.54, -0.31, -0.08, -0.95, 0.000, 0.313,
+                      0.547, -0.18, 0.876, 0.236, 1.969, 0.310, 0.699, 1.013,
+                      1.267, 0.229, -1.39, 0.487])
+        nan = float('NaN')
+        e = np.array(['5z', '0l', nan, 'Wz', nan, nan, 'Xq', 'cs', nan, nan,
+                     'QN', nan, nan, 'Fd', nan, nan, 'kp', nan, '36', 'i1'],
+                     dtype=object)
+        m = np.array([0, 0, 1, 0, 1, 1, 0, 0, 1, 1,
+                      0, 1, 1, 0, 1, 1, 0, 1, 0, 0], dtype=bool)
+
+        r = e[:]
+        r[np.where(m)] = d[np.where(m)]
+        assert_array_equal(np.where(m, d, e), r)
+
+        r = e[:]
+        r[np.where(~m)] = d[np.where(~m)]
+        assert_array_equal(np.where(m, e, d), r)
+
+        assert_array_equal(np.where(m, e, e), e)
+
+        # minimal dtype result with NaN scalar (e.g required by pandas)
+        d = np.array([1., 2.], dtype=np.float32)
+        e = float('NaN')
+        assert_equal(np.where(True, d, e).dtype, np.float32)
+        e = float('Infinity')
+        assert_equal(np.where(True, d, e).dtype, np.float32)
+        e = float('-Infinity')
+        assert_equal(np.where(True, d, e).dtype, np.float32)
+        # With NEP 50 adopted, the float will overflow here:
+        e = 1e150
+        with pytest.warns(RuntimeWarning, match="overflow"):
+            res = np.where(True, d, e)
+        assert res.dtype == np.float32
+
+    def test_ndim(self):
+        c = [True, False]
+        a = np.zeros((2, 25))
+        b = np.ones((2, 25))
+        r = np.where(np.array(c)[:, np.newaxis], a, b)
+        assert_array_equal(r[0], a[0])
+        assert_array_equal(r[1], b[0])
+
+        a = a.T
+        b = b.T
+        r = np.where(c, a, b)
+        assert_array_equal(r[:, 0], a[:, 0])
+        assert_array_equal(r[:, 1], b[:, 0])
+
+    def test_dtype_mix(self):
+        c = np.array([False, True, False, False, False, False, True, False,
+                     False, False, True, False])
+        a = np.uint32(1)
+        b = np.array([5., 0., 3., 2., -1., -4., 0., -10., 10., 1., 0., 3.],
+                      dtype=np.float64)
+        r = np.array([5., 1., 3., 2., -1., -4., 1., -10., 10., 1., 1., 3.],
+                     dtype=np.float64)
+        assert_equal(np.where(c, a, b), r)
+
+        a = a.astype(np.float32)
+        b = b.astype(np.int64)
+        assert_equal(np.where(c, a, b), r)
+
+        # non bool mask
+        c = c.astype(int)
+        c[c != 0] = 34242324
+        assert_equal(np.where(c, a, b), r)
+        # invert
+        tmpmask = c != 0
+        c[c == 0] = 41247212
+        c[tmpmask] = 0
+        assert_equal(np.where(c, b, a), r)
+
+    def test_foreign(self):
+        c = np.array([False, True, False, False, False, False, True, False,
+                     False, False, True, False])
+        r = np.array([5., 1., 3., 2., -1., -4., 1., -10., 10., 1., 1., 3.],
+                     dtype=np.float64)
+        a = np.ones(1, dtype='>i4')
+        b = np.array([5., 0., 3., 2., -1., -4., 0., -10., 10., 1., 0., 3.],
+                     dtype=np.float64)
+        assert_equal(np.where(c, a, b), r)
+
+        b = b.astype('>f8')
+        assert_equal(np.where(c, a, b), r)
+
+        a = a.astype('<i4')
+        assert_equal(np.where(c, a, b), r)
+
+        c = c.astype('>i4')
+        assert_equal(np.where(c, a, b), r)
+
+    def test_error(self):
+        c = [True, True]
+        a = np.ones((4, 5))
+        b = np.ones((5, 5))
+        assert_raises(ValueError, np.where, c, a, a)
+        assert_raises(ValueError, np.where, c[0], a, b)
+
+    def test_string(self):
+        # gh-4778 check strings are properly filled with nulls
+        a = np.array("abc")
+        b = np.array("x" * 753)
+        assert_equal(np.where(True, a, b), "abc")
+        assert_equal(np.where(False, b, a), "abc")
+
+        # check native datatype sized strings
+        a = np.array("abcd")
+        b = np.array("x" * 8)
+        assert_equal(np.where(True, a, b), "abcd")
+        assert_equal(np.where(False, b, a), "abcd")
+
+    def test_empty_result(self):
+        # pass empty where result through an assignment which reads the data of
+        # empty arrays, error detectable with valgrind, see gh-8922
+        x = np.zeros((1, 1))
+        ibad = np.vstack(np.where(x == 99.))
+        assert_array_equal(ibad,
+                           np.atleast_2d(np.array([[], []], dtype=np.intp)))
+
+    def test_largedim(self):
+        # invalid read regression gh-9304
+        shape = [10, 2, 3, 4, 5, 6]
+        np.random.seed(2)
+        array = np.random.rand(*shape)
+
+        for i in range(10):
+            benchmark = array.nonzero()
+            result = array.nonzero()
+            assert_array_equal(benchmark, result)
+
+    def test_kwargs(self):
+        a = np.zeros(1)
+        with assert_raises(TypeError):
+            np.where(a, x=a, y=a)
+
+
+if not IS_PYPY:
+    # sys.getsizeof() is not valid on PyPy
+    class TestSizeOf:
+
+        def test_empty_array(self):
+            x = np.array([])
+            assert_(sys.getsizeof(x) > 0)
+
+        def check_array(self, dtype):
+            elem_size = dtype(0).itemsize
+
+            for length in [10, 50, 100, 500]:
+                x = np.arange(length, dtype=dtype)
+                assert_(sys.getsizeof(x) > length * elem_size)
+
+        def test_array_int32(self):
+            self.check_array(np.int32)
+
+        def test_array_int64(self):
+            self.check_array(np.int64)
+
+        def test_array_float32(self):
+            self.check_array(np.float32)
+
+        def test_array_float64(self):
+            self.check_array(np.float64)
+
+        def test_view(self):
+            d = np.ones(100)
+            assert_(sys.getsizeof(d[...]) < sys.getsizeof(d))
+
+        def test_reshape(self):
+            d = np.ones(100)
+            assert_(sys.getsizeof(d) < sys.getsizeof(d.reshape(100, 1, 1).copy()))
+
+        @_no_tracing
+        def test_resize(self):
+            d = np.ones(100)
+            old = sys.getsizeof(d)
+            d.resize(50)
+            assert_(old > sys.getsizeof(d))
+            d.resize(150)
+            assert_(old < sys.getsizeof(d))
+
+        @pytest.mark.parametrize("dtype", ["u4,f4", "u4,O"])
+        def test_resize_structured(self, dtype):
+            a = np.array([(0, 0.0) for i in range(5)], dtype=dtype)
+            a.resize(1000)
+            assert_array_equal(a, np.zeros(1000, dtype=dtype))
+
+        def test_error(self):
+            d = np.ones(100)
+            assert_raises(TypeError, d.__sizeof__, "a")
+
+
+class TestHashing:
+
+    def test_arrays_not_hashable(self):
+        x = np.ones(3)
+        assert_raises(TypeError, hash, x)
+
+    def test_collections_hashable(self):
+        x = np.array([])
+        assert_(not isinstance(x, collections.abc.Hashable))
+
+
+class TestArrayPriority:
+    # This will go away when __array_priority__ is settled, meanwhile
+    # it serves to check unintended changes.
+    op = operator
+    binary_ops = [
+        op.pow, op.add, op.sub, op.mul, op.floordiv, op.truediv, op.mod,
+        op.and_, op.or_, op.xor, op.lshift, op.rshift, op.mod, op.gt,
+        op.ge, op.lt, op.le, op.ne, op.eq
+        ]
+
+    class Foo(np.ndarray):
+        __array_priority__ = 100.
+
+        def __new__(cls, *args, **kwargs):
+            return np.array(*args, **kwargs).view(cls)
+
+    class Bar(np.ndarray):
+        __array_priority__ = 101.
+
+        def __new__(cls, *args, **kwargs):
+            return np.array(*args, **kwargs).view(cls)
+
+    class Other:
+        __array_priority__ = 1000.
+
+        def _all(self, other):
+            return self.__class__()
+
+        __add__ = __radd__ = _all
+        __sub__ = __rsub__ = _all
+        __mul__ = __rmul__ = _all
+        __pow__ = __rpow__ = _all
+        __mod__ = __rmod__ = _all
+        __truediv__ = __rtruediv__ = _all
+        __floordiv__ = __rfloordiv__ = _all
+        __and__ = __rand__ = _all
+        __xor__ = __rxor__ = _all
+        __or__ = __ror__ = _all
+        __lshift__ = __rlshift__ = _all
+        __rshift__ = __rrshift__ = _all
+        __eq__ = _all
+        __ne__ = _all
+        __gt__ = _all
+        __ge__ = _all
+        __lt__ = _all
+        __le__ = _all
+
+    def test_ndarray_subclass(self):
+        a = np.array([1, 2])
+        b = self.Bar([1, 2])
+        for f in self.binary_ops:
+            msg = repr(f)
+            assert_(isinstance(f(a, b), self.Bar), msg)
+            assert_(isinstance(f(b, a), self.Bar), msg)
+
+    def test_ndarray_other(self):
+        a = np.array([1, 2])
+        b = self.Other()
+        for f in self.binary_ops:
+            msg = repr(f)
+            assert_(isinstance(f(a, b), self.Other), msg)
+            assert_(isinstance(f(b, a), self.Other), msg)
+
+    def test_subclass_subclass(self):
+        a = self.Foo([1, 2])
+        b = self.Bar([1, 2])
+        for f in self.binary_ops:
+            msg = repr(f)
+            assert_(isinstance(f(a, b), self.Bar), msg)
+            assert_(isinstance(f(b, a), self.Bar), msg)
+
+    def test_subclass_other(self):
+        a = self.Foo([1, 2])
+        b = self.Other()
+        for f in self.binary_ops:
+            msg = repr(f)
+            assert_(isinstance(f(a, b), self.Other), msg)
+            assert_(isinstance(f(b, a), self.Other), msg)
+
+
+class TestBytestringArrayNonzero:
+
+    def test_empty_bstring_array_is_falsey(self):
+        assert_(not np.array([''], dtype=str))
+
+    def test_whitespace_bstring_array_is_truthy(self):
+        a = np.array(['spam'], dtype=str)
+        a[0] = '  \0\0'
+        assert_(a)
+
+    def test_all_null_bstring_array_is_falsey(self):
+        a = np.array(['spam'], dtype=str)
+        a[0] = '\0\0\0\0'
+        assert_(not a)
+
+    def test_null_inside_bstring_array_is_truthy(self):
+        a = np.array(['spam'], dtype=str)
+        a[0] = ' \0 \0'
+        assert_(a)
+
+
+class TestUnicodeEncoding:
+    """
+    Tests for encoding related bugs, such as UCS2 vs UCS4, round-tripping
+    issues, etc
+    """
+    def test_round_trip(self):
+        """ Tests that GETITEM, SETITEM, and PyArray_Scalar roundtrip """
+        # gh-15363
+        arr = np.zeros(shape=(), dtype="U1")
+        for i in range(1, sys.maxunicode + 1):
+            expected = chr(i)
+            arr[()] = expected
+            assert arr[()] == expected
+            assert arr.item() == expected
+
+    def test_assign_scalar(self):
+        # gh-3258
+        l = np.array(['aa', 'bb'])
+        l[:] = np.str_('cc')
+        assert_equal(l, ['cc', 'cc'])
+
+    def test_fill_scalar(self):
+        # gh-7227
+        l = np.array(['aa', 'bb'])
+        l.fill(np.str_('cc'))
+        assert_equal(l, ['cc', 'cc'])
+
+
+class TestUnicodeArrayNonzero:
+
+    def test_empty_ustring_array_is_falsey(self):
+        assert_(not np.array([''], dtype=np.str_))
+
+    def test_whitespace_ustring_array_is_truthy(self):
+        a = np.array(['eggs'], dtype=np.str_)
+        a[0] = '  \0\0'
+        assert_(a)
+
+    def test_all_null_ustring_array_is_falsey(self):
+        a = np.array(['eggs'], dtype=np.str_)
+        a[0] = '\0\0\0\0'
+        assert_(not a)
+
+    def test_null_inside_ustring_array_is_truthy(self):
+        a = np.array(['eggs'], dtype=np.str_)
+        a[0] = ' \0 \0'
+        assert_(a)
+
+
+class TestFormat:
+
+    def test_0d(self):
+        a = np.array(np.pi)
+        assert_equal(f'{a:0.3g}', '3.14')
+        assert_equal(f'{a[()]:0.3g}', '3.14')
+
+    def test_1d_no_format(self):
+        a = np.array([np.pi])
+        assert_equal(f'{a}', str(a))
+
+    def test_1d_format(self):
+        # until gh-5543, ensure that the behaviour matches what it used to be
+        a = np.array([np.pi])
+        assert_raises(TypeError, '{:30}'.format, a)
+
+
+from numpy.testing import IS_PYPY
+
+
+class TestCTypes:
+
+    def test_ctypes_is_available(self):
+        test_arr = np.array([[1, 2, 3], [4, 5, 6]])
+
+        assert_equal(ctypes, test_arr.ctypes._ctypes)
+        assert_equal(tuple(test_arr.ctypes.shape), (2, 3))
+
+    def test_ctypes_is_not_available(self):
+        from numpy._core import _internal
+        _internal.ctypes = None
+        try:
+            test_arr = np.array([[1, 2, 3], [4, 5, 6]])
+
+            assert_(isinstance(test_arr.ctypes._ctypes,
+                               _internal._missing_ctypes))
+            assert_equal(tuple(test_arr.ctypes.shape), (2, 3))
+        finally:
+            _internal.ctypes = ctypes
+
+    def _make_readonly(x):
+        x.flags.writeable = False
+        return x
+
+    @pytest.mark.parametrize('arr', [
+        np.array([1, 2, 3]),
+        np.array([['one', 'two'], ['three', 'four']]),
+        np.array((1, 2), dtype='i4,i4'),
+        np.zeros((2,), dtype=np.dtype({
+                "formats": ['<i4', '<i4'],
+                "names": ['a', 'b'],
+                "offsets": [0, 2],
+                "itemsize": 6
+            })
+        ),
+        np.array([None], dtype=object),
+        np.array([]),
+        np.empty((0, 0)),
+        _make_readonly(np.array([1, 2, 3])),
+    ], ids=[
+        '1d',
+        '2d',
+        'structured',
+        'overlapping',
+        'object',
+        'empty',
+        'empty-2d',
+        'readonly'
+    ])
+    def test_ctypes_data_as_holds_reference(self, arr):
+        # gh-9647
+        # create a copy to ensure that pytest does not mess with the refcounts
+        arr = arr.copy()
+
+        arr_ref = weakref.ref(arr)
+
+        ctypes_ptr = arr.ctypes.data_as(ctypes.c_void_p)
+
+        # `ctypes_ptr` should hold onto `arr`
+        del arr
+        break_cycles()
+        assert_(arr_ref() is not None, "ctypes pointer did not hold onto a reference")
+
+        # but when the `ctypes_ptr` object dies, so should `arr`
+        del ctypes_ptr
+        if IS_PYPY:
+            # Pypy does not recycle arr objects immediately. Trigger gc to
+            # release arr. Cpython uses refcounts. An explicit call to gc
+            # should not be needed here.
+            break_cycles()
+        assert_(arr_ref() is None, "unknowable whether ctypes pointer holds a reference")
+
+    def test_ctypes_as_parameter_holds_reference(self):
+        arr = np.array([None]).copy()
+
+        arr_ref = weakref.ref(arr)
+
+        ctypes_ptr = arr.ctypes._as_parameter_
+
+        # `ctypes_ptr` should hold onto `arr`
+        del arr
+        break_cycles()
+        assert_(arr_ref() is not None, "ctypes pointer did not hold onto a reference")
+
+        # but when the `ctypes_ptr` object dies, so should `arr`
+        del ctypes_ptr
+        if IS_PYPY:
+            break_cycles()
+        assert_(arr_ref() is None, "unknowable whether ctypes pointer holds a reference")
+
+
+class TestWritebackIfCopy:
+    # all these tests use the WRITEBACKIFCOPY mechanism
+    def test_argmax_with_out(self):
+        mat = np.eye(5)
+        out = np.empty(5, dtype='i2')
+        res = np.argmax(mat, 0, out=out)
+        assert_equal(res, range(5))
+
+    def test_argmin_with_out(self):
+        mat = -np.eye(5)
+        out = np.empty(5, dtype='i2')
+        res = np.argmin(mat, 0, out=out)
+        assert_equal(res, range(5))
+
+    def test_insert_noncontiguous(self):
+        a = np.arange(6).reshape(2, 3).T  # force non-c-contiguous
+        # uses arr_insert
+        np.place(a, a > 2, [44, 55])
+        assert_equal(a, np.array([[0, 44], [1, 55], [2, 44]]))
+        # hit one of the failing paths
+        assert_raises(ValueError, np.place, a, a > 20, [])
+
+    def test_put_noncontiguous(self):
+        a = np.arange(6).reshape(2, 3).T  # force non-c-contiguous
+        np.put(a, [0, 2], [44, 55])
+        assert_equal(a, np.array([[44, 3], [55, 4], [2, 5]]))
+
+    def test_putmask_noncontiguous(self):
+        a = np.arange(6).reshape(2, 3).T  # force non-c-contiguous
+        # uses arr_putmask
+        np.putmask(a, a > 2, a**2)
+        assert_equal(a, np.array([[0, 9], [1, 16], [2, 25]]))
+
+    def test_take_mode_raise(self):
+        a = np.arange(6, dtype='int')
+        out = np.empty(2, dtype='int')
+        np.take(a, [0, 2], out=out, mode='raise')
+        assert_equal(out, np.array([0, 2]))
+
+    def test_choose_mod_raise(self):
+        a = np.array([[1, 0, 1], [0, 1, 0], [1, 0, 1]])
+        out = np.empty((3, 3), dtype='int')
+        choices = [-10, 10]
+        np.choose(a, choices, out=out, mode='raise')
+        assert_equal(out, np.array([[ 10, -10,  10],
+                                    [-10,  10, -10],
+                                    [ 10, -10,  10]]))
+
+    def test_flatiter__array__(self):
+        a = np.arange(9).reshape(3, 3)
+        b = a.T.flat
+        c = b.__array__()
+        # triggers the WRITEBACKIFCOPY resolution, assuming refcount semantics
+        del c
+
+    def test_dot_out(self):
+        # if HAVE_CBLAS, will use WRITEBACKIFCOPY
+        a = np.arange(9, dtype=float).reshape(3, 3)
+        b = np.dot(a, a, out=a)
+        assert_equal(b, np.array([[15, 18, 21], [42, 54, 66], [69, 90, 111]]))
+
+    def test_view_assign(self):
+        from numpy._core._multiarray_tests import (
+            npy_create_writebackifcopy,
+            npy_resolve,
+        )
+
+        arr = np.arange(9).reshape(3, 3).T
+        arr_wb = npy_create_writebackifcopy(arr)
+        assert_(arr_wb.flags.writebackifcopy)
+        assert_(arr_wb.base is arr)
+        arr_wb[...] = -100
+        npy_resolve(arr_wb)
+        # arr changes after resolve, even though we assigned to arr_wb
+        assert_equal(arr, -100)
+        # after resolve, the two arrays no longer reference each other
+        assert_(arr_wb.ctypes.data != 0)
+        assert_equal(arr_wb.base, None)
+        # assigning to arr_wb does not get transferred to arr
+        arr_wb[...] = 100
+        assert_equal(arr, -100)
+
+    @pytest.mark.leaks_references(
+            reason="increments self in dealloc; ignore since deprecated path.")
+    def test_dealloc_warning(self):
+        with suppress_warnings() as sup:
+            sup.record(RuntimeWarning)
+            arr = np.arange(9).reshape(3, 3)
+            v = arr.T
+            _multiarray_tests.npy_abuse_writebackifcopy(v)
+            assert len(sup.log) == 1
+
+    def test_view_discard_refcount(self):
+        from numpy._core._multiarray_tests import (
+            npy_create_writebackifcopy,
+            npy_discard,
+        )
+
+        arr = np.arange(9).reshape(3, 3).T
+        orig = arr.copy()
+        if HAS_REFCOUNT:
+            arr_cnt = sys.getrefcount(arr)
+        arr_wb = npy_create_writebackifcopy(arr)
+        assert_(arr_wb.flags.writebackifcopy)
+        assert_(arr_wb.base is arr)
+        arr_wb[...] = -100
+        npy_discard(arr_wb)
+        # arr remains unchanged after discard
+        assert_equal(arr, orig)
+        # after discard, the two arrays no longer reference each other
+        assert_(arr_wb.ctypes.data != 0)
+        assert_equal(arr_wb.base, None)
+        if HAS_REFCOUNT:
+            assert_equal(arr_cnt, sys.getrefcount(arr))
+        # assigning to arr_wb does not get transferred to arr
+        arr_wb[...] = 100
+        assert_equal(arr, orig)
+
+
+class TestArange:
+    def test_infinite(self):
+        assert_raises_regex(
+            ValueError, "size exceeded",
+            np.arange, 0, np.inf
+        )
+
+    def test_nan_step(self):
+        assert_raises_regex(
+            ValueError, "cannot compute length",
+            np.arange, 0, 1, np.nan
+        )
+
+    def test_zero_step(self):
+        assert_raises(ZeroDivisionError, np.arange, 0, 10, 0)
+        assert_raises(ZeroDivisionError, np.arange, 0.0, 10.0, 0.0)
+
+        # empty range
+        assert_raises(ZeroDivisionError, np.arange, 0, 0, 0)
+        assert_raises(ZeroDivisionError, np.arange, 0.0, 0.0, 0.0)
+
+    def test_require_range(self):
+        assert_raises(TypeError, np.arange)
+        assert_raises(TypeError, np.arange, step=3)
+        assert_raises(TypeError, np.arange, dtype='int64')
+        assert_raises(TypeError, np.arange, start=4)
+
+    def test_start_stop_kwarg(self):
+        keyword_stop = np.arange(stop=3)
+        keyword_zerotostop = np.arange(0, stop=3)
+        keyword_start_stop = np.arange(start=3, stop=9)
+
+        assert len(keyword_stop) == 3
+        assert len(keyword_zerotostop) == 3
+        assert len(keyword_start_stop) == 6
+        assert_array_equal(keyword_stop, keyword_zerotostop)
+
+    def test_arange_booleans(self):
+        # Arange makes some sense for booleans and works up to length 2.
+        # But it is weird since `arange(2, 4, dtype=bool)` works.
+        # Arguably, much or all of this could be deprecated/removed.
+        res = np.arange(False, dtype=bool)
+        assert_array_equal(res, np.array([], dtype="bool"))
+
+        res = np.arange(True, dtype="bool")
+        assert_array_equal(res, [False])
+
+        res = np.arange(2, dtype="bool")
+        assert_array_equal(res, [False, True])
+
+        # This case is especially weird, but drops out without special case:
+        res = np.arange(6, 8, dtype="bool")
+        assert_array_equal(res, [True, True])
+
+        with pytest.raises(TypeError):
+            np.arange(3, dtype="bool")
+
+    @pytest.mark.parametrize("dtype", ["S3", "U", "5i"])
+    def test_rejects_bad_dtypes(self, dtype):
+        dtype = np.dtype(dtype)
+        DType_name = re.escape(str(type(dtype)))
+        with pytest.raises(TypeError,
+                match=rf"arange\(\) not supported for inputs .* {DType_name}"):
+            np.arange(2, dtype=dtype)
+
+    def test_rejects_strings(self):
+        # Explicitly test error for strings which may call "b" - "a":
+        DType_name = re.escape(str(type(np.array("a").dtype)))
+        with pytest.raises(TypeError,
+                match=rf"arange\(\) not supported for inputs .* {DType_name}"):
+            np.arange("a", "b")
+
+    def test_byteswapped(self):
+        res_be = np.arange(1, 1000, dtype=">i4")
+        res_le = np.arange(1, 1000, dtype="<i4")
+        assert res_be.dtype == ">i4"
+        assert res_le.dtype == "<i4"
+        assert_array_equal(res_le, res_be)
+
+    @pytest.mark.parametrize("which", [0, 1, 2])
+    def test_error_paths_and_promotion(self, which):
+        args = [0, 1, 2]  # start, stop, and step
+        args[which] = np.float64(2.)  # should ensure float64 output
+
+        assert np.arange(*args).dtype == np.float64
+
+        # Cover stranger error path, test only to achieve code coverage!
+        args[which] = [None, []]
+        with pytest.raises(ValueError):
+            # Fails discovering start dtype
+            np.arange(*args)
+
+    def test_dtype_attribute_ignored(self):
+        # Until 2.3 this would raise a DeprecationWarning
+        class dt:
+            dtype = "f8"
+
+        class vdt(np.void):
+            dtype = "f,f"
+
+        assert_raises(ValueError, np.dtype, dt)
+        assert_raises(ValueError, np.dtype, dt())
+        assert_raises(ValueError, np.dtype, vdt)
+        assert_raises(ValueError, np.dtype, vdt(1))
+
+
+class TestDTypeCoercionForbidden:
+    forbidden_types = [
+        # The builtin scalar super types:
+        np.generic, np.flexible, np.number,
+        np.inexact, np.floating, np.complexfloating,
+        np.integer, np.unsignedinteger, np.signedinteger,
+        # character is a deprecated S1 special case:
+        np.character,
+    ]
+
+    def test_dtype_coercion(self):
+        for scalar_type in self.forbidden_types:
+            assert_raises(TypeError, np.dtype, args=(scalar_type,))
+
+    def test_array_construction(self):
+        for scalar_type in self.forbidden_types:
+            assert_raises(TypeError, np.array, args=([], scalar_type,))
+
+    def test_not_deprecated(self):
+        # All specific types work
+        for group in np._core.sctypes.values():
+            for scalar_type in group:
+                np.dtype(scalar_type)
+
+        for scalar_type in [type, dict, list, tuple]:
+            # Typical python types are coerced to object currently:
+            np.dtype(scalar_type)
+
+
+class TestDateTimeCreationTuple:
+    @pytest.mark.parametrize("cls", [np.datetime64, np.timedelta64])
+    def test_dt_tuple(self, cls):
+        # two valid uses - (unit, num) and (unit, num, den, None)
+        cls(1, ('ms', 2))
+        cls(1, ('ms', 2, 1, None))
+
+        # trying to use the event argument, removed in 1.7.0
+        # it used to be a uint8
+        assert_raises(TypeError, cls, args=(1, ('ms', 2, 'event')))
+        assert_raises(TypeError, cls, args=(1, ('ms', 2, 63)))
+        assert_raises(TypeError, cls, args=(1, ('ms', 2, 1, 'event')))
+        assert_raises(TypeError, cls, args=(1, ('ms', 2, 1, 63)))
+
+
+class TestArrayFinalize:
+    """ Tests __array_finalize__ """
+
+    def test_receives_base(self):
+        # gh-11237
+        class SavesBase(np.ndarray):
+            def __array_finalize__(self, obj):
+                self.saved_base = self.base
+
+        a = np.array(1).view(SavesBase)
+        assert_(a.saved_base is a.base)
+
+    def test_bad_finalize1(self):
+        class BadAttributeArray(np.ndarray):
+            @property
+            def __array_finalize__(self):
+                raise RuntimeError("boohoo!")
+
+        with pytest.raises(TypeError, match="not callable"):
+            np.arange(10).view(BadAttributeArray)
+
+    def test_bad_finalize2(self):
+        class BadAttributeArray(np.ndarray):
+            def __array_finalize__(self):
+                raise RuntimeError("boohoo!")
+
+        with pytest.raises(TypeError, match="takes 1 positional"):
+            np.arange(10).view(BadAttributeArray)
+
+    def test_bad_finalize3(self):
+        class BadAttributeArray(np.ndarray):
+            def __array_finalize__(self, obj):
+                raise RuntimeError("boohoo!")
+
+        with pytest.raises(RuntimeError, match="boohoo!"):
+            np.arange(10).view(BadAttributeArray)
+
+    def test_lifetime_on_error(self):
+        # gh-11237
+        class RaisesInFinalize(np.ndarray):
+            def __array_finalize__(self, obj):
+                # crash, but keep this object alive
+                raise Exception(self)
+
+        # a plain object can't be weakref'd
+        class Dummy:
+            pass
+
+        # get a weak reference to an object within an array
+        obj_arr = np.array(Dummy())
+        obj_ref = weakref.ref(obj_arr[()])
+
+        # get an array that crashed in __array_finalize__
+        with assert_raises(Exception) as e:
+            obj_arr.view(RaisesInFinalize)
+
+        obj_subarray = e.exception.args[0]
+        del e
+        assert_(isinstance(obj_subarray, RaisesInFinalize))
+
+        # reference should still be held by obj_arr
+        break_cycles()
+        assert_(obj_ref() is not None, "object should not already be dead")
+
+        del obj_arr
+        break_cycles()
+        assert_(obj_ref() is not None, "obj_arr should not hold the last reference")
+
+        del obj_subarray
+        break_cycles()
+        assert_(obj_ref() is None, "no references should remain")
+
+    def test_can_use_super(self):
+        class SuperFinalize(np.ndarray):
+            def __array_finalize__(self, obj):
+                self.saved_result = super().__array_finalize__(obj)
+
+        a = np.array(1).view(SuperFinalize)
+        assert_(a.saved_result is None)
+
+
+def test_orderconverter_with_nonASCII_unicode_ordering():
+    # gh-7475
+    a = np.arange(5)
+    assert_raises(ValueError, a.flatten, order='\xe2')
+
+
+def test_equal_override():
+    # gh-9153: ndarray.__eq__ uses special logic for structured arrays, which
+    # did not respect overrides with __array_priority__ or __array_ufunc__.
+    # The PR fixed this for __array_priority__ and __array_ufunc__ = None.
+    class MyAlwaysEqual:
+        def __eq__(self, other):
+            return "eq"
+
+        def __ne__(self, other):
+            return "ne"
+
+    class MyAlwaysEqualOld(MyAlwaysEqual):
+        __array_priority__ = 10000
+
+    class MyAlwaysEqualNew(MyAlwaysEqual):
+        __array_ufunc__ = None
+
+    array = np.array([(0, 1), (2, 3)], dtype='i4,i4')
+    for my_always_equal_cls in MyAlwaysEqualOld, MyAlwaysEqualNew:
+        my_always_equal = my_always_equal_cls()
+        assert_equal(my_always_equal == array, 'eq')
+        assert_equal(array == my_always_equal, 'eq')
+        assert_equal(my_always_equal != array, 'ne')
+        assert_equal(array != my_always_equal, 'ne')
+
+
+@pytest.mark.parametrize("op", [operator.eq, operator.ne])
+@pytest.mark.parametrize(["dt1", "dt2"], [
+        ([("f", "i")], [("f", "i")]),  # structured comparison (successful)
+        ("M8", "d"),  # impossible comparison: result is all True or False
+        ("d", "d"),  # valid comparison
+        ])
+def test_equal_subclass_no_override(op, dt1, dt2):
+    # Test how the three different possible code-paths deal with subclasses
+
+    class MyArr(np.ndarray):
+        called_wrap = 0
+
+        def __array_wrap__(self, new, context=None, return_scalar=False):
+            type(self).called_wrap += 1
+            return super().__array_wrap__(new, context, return_scalar)
+
+    numpy_arr = np.zeros(5, dtype=dt1)
+    my_arr = np.zeros(5, dtype=dt2).view(MyArr)
+
+    assert type(op(numpy_arr, my_arr)) is MyArr
+    assert type(op(my_arr, numpy_arr)) is MyArr
+    # We expect 2 calls (more if there were more fields):
+    assert MyArr.called_wrap == 2
+
+
+@pytest.mark.parametrize(["dt1", "dt2"], [
+        ("M8[ns]", "d"),
+        ("M8[s]", "l"),
+        ("m8[ns]", "d"),
+        # Missing: ("m8[ns]", "l") as timedelta currently promotes ints
+        ("M8[s]", "m8[s]"),
+        ("S5", "U5"),
+        # Structured/void dtypes have explicit paths not tested here.
+])
+def test_no_loop_gives_all_true_or_false(dt1, dt2):
+    # Make sure they broadcast to test result shape, use random values, since
+    # the actual value should be ignored
+    arr1 = np.random.randint(5, size=100).astype(dt1)
+    arr2 = np.random.randint(5, size=99)[:, np.newaxis].astype(dt2)
+
+    res = arr1 == arr2
+    assert res.shape == (99, 100)
+    assert res.dtype == bool
+    assert not res.any()
+
+    res = arr1 != arr2
+    assert res.shape == (99, 100)
+    assert res.dtype == bool
+    assert res.all()
+
+    # incompatible shapes raise though
+    arr2 = np.random.randint(5, size=99).astype(dt2)
+    with pytest.raises(ValueError):
+        arr1 == arr2
+
+    with pytest.raises(ValueError):
+        arr1 != arr2
+
+    # Basic test with another operation:
+    with pytest.raises(np._core._exceptions._UFuncNoLoopError):
+        arr1 > arr2
+
+
+@pytest.mark.parametrize("op", [
+        operator.eq, operator.ne, operator.le, operator.lt, operator.ge,
+        operator.gt])
+def test_comparisons_forwards_error(op):
+    class NotArray:
+        def __array__(self, dtype=None, copy=None):
+            raise TypeError("run you fools")
+
+    with pytest.raises(TypeError, match="run you fools"):
+        op(np.arange(2), NotArray())
+
+    with pytest.raises(TypeError, match="run you fools"):
+        op(NotArray(), np.arange(2))
+
+
+def test_richcompare_scalar_boolean_singleton_return():
+    # These are currently guaranteed to be the boolean numpy singletons
+    assert (np.array(0) == "a") is np.bool_(False)
+    assert (np.array(0) != "a") is np.bool_(True)
+    assert (np.int16(0) == "a") is np.bool_(False)
+    assert (np.int16(0) != "a") is np.bool_(True)
+
+
+@pytest.mark.parametrize("op", [
+        operator.eq, operator.ne, operator.le, operator.lt, operator.ge,
+        operator.gt])
+def test_ragged_comparison_fails(op):
+    # This needs to convert the internal array to True/False, which fails:
+    a = np.array([1, np.array([1, 2, 3])], dtype=object)
+    b = np.array([1, np.array([1, 2, 3])], dtype=object)
+
+    with pytest.raises(ValueError, match="The truth value.*ambiguous"):
+        op(a, b)
+
+
+@pytest.mark.parametrize(
+    ["fun", "npfun"],
+    [
+        (_multiarray_tests.npy_cabs, np.absolute),
+        (_multiarray_tests.npy_carg, np.angle)
+    ]
+)
+@pytest.mark.parametrize("x", [1, np.inf, -np.inf, np.nan])
+@pytest.mark.parametrize("y", [1, np.inf, -np.inf, np.nan])
+@pytest.mark.parametrize("test_dtype", np.complexfloating.__subclasses__())
+def test_npymath_complex(fun, npfun, x, y, test_dtype):
+    # Smoketest npymath functions
+    z = test_dtype(complex(x, y))
+    with np.errstate(invalid='ignore'):
+        # Fallback implementations may emit a warning for +-inf (see gh-24876):
+        #     RuntimeWarning: invalid value encountered in absolute
+        got = fun(z)
+        expected = npfun(z)
+        assert_allclose(got, expected)
+
+
+def test_npymath_real():
+    # Smoketest npymath functions
+    from numpy._core._multiarray_tests import (
+        npy_cosh,
+        npy_log10,
+        npy_sinh,
+        npy_tan,
+        npy_tanh,
+    )
+
+    funcs = {npy_log10: np.log10,
+             npy_cosh: np.cosh,
+             npy_sinh: np.sinh,
+             npy_tan: np.tan,
+             npy_tanh: np.tanh}
+    vals = (1, np.inf, -np.inf, np.nan)
+    types = (np.float32, np.float64, np.longdouble)
+
+    with np.errstate(all='ignore'):
+        for fun, npfun in funcs.items():
+            for x, t in itertools.product(vals, types):
+                z = t(x)
+                got = fun(z)
+                expected = npfun(z)
+                assert_allclose(got, expected)
+
+def test_uintalignment_and_alignment():
+    # alignment code needs to satisfy these requirements:
+    #  1. numpy structs match C struct layout
+    #  2. ufuncs/casting is safe wrt to aligned access
+    #  3. copy code is safe wrt to "uint alidned" access
+    #
+    # Complex types are the main problem, whose alignment may not be the same
+    # as their "uint alignment".
+    #
+    # This test might only fail on certain platforms, where uint64 alignment is
+    # not equal to complex64 alignment. The second 2 tests will only fail
+    # for DEBUG=1.
+
+    d1 = np.dtype('u1,c8', align=True)
+    d2 = np.dtype('u4,c8', align=True)
+    d3 = np.dtype({'names': ['a', 'b'], 'formats': ['u1', d1]}, align=True)
+
+    assert_equal(np.zeros(1, dtype=d1)['f1'].flags['ALIGNED'], True)
+    assert_equal(np.zeros(1, dtype=d2)['f1'].flags['ALIGNED'], True)
+    assert_equal(np.zeros(1, dtype='u1,c8')['f1'].flags['ALIGNED'], False)
+
+    # check that C struct matches numpy struct size
+    s = _multiarray_tests.get_struct_alignments()
+    for d, (alignment, size) in zip([d1, d2, d3], s):
+        assert_equal(d.alignment, alignment)
+        assert_equal(d.itemsize, size)
+
+    # check that ufuncs don't complain in debug mode
+    # (this is probably OK if the aligned flag is true above)
+    src = np.zeros((2, 2), dtype=d1)['f1']  # 4-byte aligned, often
+    np.exp(src)  # assert fails?
+
+    # check that copy code doesn't complain in debug mode
+    dst = np.zeros((2, 2), dtype='c8')
+    dst[:, 1] = src[:, 1]  # assert in lowlevel_strided_loops fails?
+
+class TestAlignment:
+    # adapted from scipy._lib.tests.test__util.test__aligned_zeros
+    # Checks that unusual memory alignments don't trip up numpy.
+
+    def check(self, shape, dtype, order, align):
+        err_msg = repr((shape, dtype, order, align))
+        x = _aligned_zeros(shape, dtype, order, align=align)
+        if align is None:
+            align = np.dtype(dtype).alignment
+        assert_equal(x.__array_interface__['data'][0] % align, 0)
+        if hasattr(shape, '__len__'):
+            assert_equal(x.shape, shape, err_msg)
+        else:
+            assert_equal(x.shape, (shape,), err_msg)
+        assert_equal(x.dtype, dtype)
+        if order == "C":
+            assert_(x.flags.c_contiguous, err_msg)
+        elif order == "F":
+            if x.size > 0:
+                assert_(x.flags.f_contiguous, err_msg)
+        elif order is None:
+            assert_(x.flags.c_contiguous, err_msg)
+        else:
+            raise ValueError
+
+    def test_various_alignments(self):
+        for align in [1, 2, 3, 4, 8, 12, 16, 32, 64, None]:
+            for n in [0, 1, 3, 11]:
+                for order in ["C", "F", None]:
+                    for dtype in list(np.typecodes["All"]) + ['i4,i4,i4']:
+                        if dtype == 'O':
+                            # object dtype can't be misaligned
+                            continue
+                        for shape in [n, (1, 2, 3, n)]:
+                            self.check(shape, np.dtype(dtype), order, align)
+
+    def test_strided_loop_alignments(self):
+        # particularly test that complex64 and float128 use right alignment
+        # code-paths, since these are particularly problematic. It is useful to
+        # turn on USE_DEBUG for this test, so lowlevel-loop asserts are run.
+        for align in [1, 2, 4, 8, 12, 16, None]:
+            xf64 = _aligned_zeros(3, np.float64)
+
+            xc64 = _aligned_zeros(3, np.complex64, align=align)
+            xf128 = _aligned_zeros(3, np.longdouble, align=align)
+
+            # test casting, both to and from misaligned
+            with suppress_warnings() as sup:
+                sup.filter(ComplexWarning, "Casting complex values")
+                xc64.astype('f8')
+            xf64.astype(np.complex64)
+            test = xc64 + xf64
+
+            xf128.astype('f8')
+            xf64.astype(np.longdouble)
+            test = xf128 + xf64
+
+            test = xf128 + xc64
+
+            # test copy, both to and from misaligned
+            # contig copy
+            xf64[:] = xf64.copy()
+            xc64[:] = xc64.copy()
+            xf128[:] = xf128.copy()
+            # strided copy
+            xf64[::2] = xf64[::2].copy()
+            xc64[::2] = xc64[::2].copy()
+            xf128[::2] = xf128[::2].copy()
+
+def test_getfield():
+    a = np.arange(32, dtype='uint16')
+    if sys.byteorder == 'little':
+        i = 0
+        j = 1
+    else:
+        i = 1
+        j = 0
+    b = a.getfield('int8', i)
+    assert_equal(b, a)
+    b = a.getfield('int8', j)
+    assert_equal(b, 0)
+    pytest.raises(ValueError, a.getfield, 'uint8', -1)
+    pytest.raises(ValueError, a.getfield, 'uint8', 16)
+    pytest.raises(ValueError, a.getfield, 'uint64', 0)
+
+
+class TestViewDtype:
+    """
+    Verify that making a view of a non-contiguous array works as expected.
+    """
+    def test_smaller_dtype_multiple(self):
+        # x is non-contiguous
+        x = np.arange(10, dtype='<i4')[::2]
+        with pytest.raises(ValueError,
+                           match='the last axis must be contiguous'):
+            x.view('<i2')
+        expected = [[0, 0], [2, 0], [4, 0], [6, 0], [8, 0]]
+        assert_array_equal(x[:, np.newaxis].view('<i2'), expected)
+
+    def test_smaller_dtype_not_multiple(self):
+        # x is non-contiguous
+        x = np.arange(5, dtype='<i4')[::2]
+
+        with pytest.raises(ValueError,
+                           match='the last axis must be contiguous'):
+            x.view('S3')
+        with pytest.raises(ValueError,
+                           match='When changing to a smaller dtype'):
+            x[:, np.newaxis].view('S3')
+
+        # Make sure the problem is because of the dtype size
+        expected = [[b''], [b'\x02'], [b'\x04']]
+        assert_array_equal(x[:, np.newaxis].view('S4'), expected)
+
+    def test_larger_dtype_multiple(self):
+        # x is non-contiguous in the first dimension, contiguous in the last
+        x = np.arange(20, dtype='<i2').reshape(10, 2)[::2, :]
+        expected = np.array([[65536], [327684], [589832],
+                             [851980], [1114128]], dtype='<i4')
+        assert_array_equal(x.view('<i4'), expected)
+
+    def test_larger_dtype_not_multiple(self):
+        # x is non-contiguous in the first dimension, contiguous in the last
+        x = np.arange(20, dtype='<i2').reshape(10, 2)[::2, :]
+        with pytest.raises(ValueError,
+                           match='When changing to a larger dtype'):
+            x.view('S3')
+        # Make sure the problem is because of the dtype size
+        expected = [[b'\x00\x00\x01'], [b'\x04\x00\x05'], [b'\x08\x00\t'],
+                    [b'\x0c\x00\r'], [b'\x10\x00\x11']]
+        assert_array_equal(x.view('S4'), expected)
+
+    def test_f_contiguous(self):
+        # x is F-contiguous
+        x = np.arange(4 * 3, dtype='<i4').reshape(4, 3).T
+        with pytest.raises(ValueError,
+                           match='the last axis must be contiguous'):
+            x.view('<i2')
+
+    def test_non_c_contiguous(self):
+        # x is contiguous in axis=-1, but not C-contiguous in other axes
+        x = np.arange(2 * 3 * 4, dtype='i1').\
+                    reshape(2, 3, 4).transpose(1, 0, 2)
+        expected = [[[256, 770], [3340, 3854]],
+                    [[1284, 1798], [4368, 4882]],
+                    [[2312, 2826], [5396, 5910]]]
+        assert_array_equal(x.view('<i2'), expected)
+
+
+@pytest.mark.xfail(check_support_sve(), reason="gh-22982")
+# Test various array sizes that hit different code paths in quicksort-avx512
+@pytest.mark.parametrize("N", np.arange(1, 512))
+@pytest.mark.parametrize("dtype", ['e', 'f', 'd'])
+def test_sort_float(N, dtype):
+    # Regular data with nan sprinkled
+    np.random.seed(42)
+    arr = -0.5 + np.random.sample(N).astype(dtype)
+    arr[np.random.choice(arr.shape[0], 3)] = np.nan
+    assert_equal(np.sort(arr, kind='quick'), np.sort(arr, kind='heap'))
+
+    # (2) with +INF
+    infarr = np.inf * np.ones(N, dtype=dtype)
+    infarr[np.random.choice(infarr.shape[0], 5)] = -1.0
+    assert_equal(np.sort(infarr, kind='quick'), np.sort(infarr, kind='heap'))
+
+    # (3) with -INF
+    neginfarr = -np.inf * np.ones(N, dtype=dtype)
+    neginfarr[np.random.choice(neginfarr.shape[0], 5)] = 1.0
+    assert_equal(np.sort(neginfarr, kind='quick'),
+                 np.sort(neginfarr, kind='heap'))
+
+    # (4) with +/-INF
+    infarr = np.inf * np.ones(N, dtype=dtype)
+    infarr[np.random.choice(infarr.shape[0], (int)(N / 2))] = -np.inf
+    assert_equal(np.sort(infarr, kind='quick'), np.sort(infarr, kind='heap'))
+
+def test_sort_float16():
+    arr = np.arange(65536, dtype=np.int16)
+    temp = np.frombuffer(arr.tobytes(), dtype=np.float16)
+    data = np.copy(temp)
+    np.random.shuffle(data)
+    data_backup = data
+    assert_equal(np.sort(data, kind='quick'),
+            np.sort(data_backup, kind='heap'))
+
+
+@pytest.mark.parametrize("N", np.arange(1, 512))
+@pytest.mark.parametrize("dtype", ['h', 'H', 'i', 'I', 'l', 'L'])
+def test_sort_int(N, dtype):
+    # Random data with MAX and MIN sprinkled
+    minv = np.iinfo(dtype).min
+    maxv = np.iinfo(dtype).max
+    arr = np.random.randint(low=minv, high=maxv - 1, size=N, dtype=dtype)
+    arr[np.random.choice(arr.shape[0], 10)] = minv
+    arr[np.random.choice(arr.shape[0], 10)] = maxv
+    assert_equal(np.sort(arr, kind='quick'), np.sort(arr, kind='heap'))
+
+
+def test_sort_uint():
+    # Random data with NPY_MAX_UINT32 sprinkled
+    rng = np.random.default_rng(42)
+    N = 2047
+    maxv = np.iinfo(np.uint32).max
+    arr = rng.integers(low=0, high=maxv, size=N).astype('uint32')
+    arr[np.random.choice(arr.shape[0], 10)] = maxv
+    assert_equal(np.sort(arr, kind='quick'), np.sort(arr, kind='heap'))
+
+def test_private_get_ndarray_c_version():
+    assert isinstance(_get_ndarray_c_version(), int)
+
+
+@pytest.mark.parametrize("N", np.arange(1, 512))
+@pytest.mark.parametrize("dtype", [np.float32, np.float64])
+def test_argsort_float(N, dtype):
+    rnd = np.random.RandomState(116112)
+    # (1) Regular data with a few nan: doesn't use vectorized sort
+    arr = -0.5 + rnd.random(N).astype(dtype)
+    arr[rnd.choice(arr.shape[0], 3)] = np.nan
+    assert_arg_sorted(arr, np.argsort(arr, kind='quick'))
+
+    # (2) Random data with inf at the end of array
+    # See: https://github.com/intel/x86-simd-sort/pull/39
+    arr = -0.5 + rnd.rand(N).astype(dtype)
+    arr[N - 1] = np.inf
+    assert_arg_sorted(arr, np.argsort(arr, kind='quick'))
+
+
+@pytest.mark.parametrize("N", np.arange(2, 512))
+@pytest.mark.parametrize("dtype", [np.int32, np.uint32, np.int64, np.uint64])
+def test_argsort_int(N, dtype):
+    rnd = np.random.RandomState(1100710816)
+    # (1) random data with min and max values
+    minv = np.iinfo(dtype).min
+    maxv = np.iinfo(dtype).max
+    arr = rnd.randint(low=minv, high=maxv, size=N, dtype=dtype)
+    i, j = rnd.choice(N, 2, replace=False)
+    arr[i] = minv
+    arr[j] = maxv
+    assert_arg_sorted(arr, np.argsort(arr, kind='quick'))
+
+    # (2) random data with max value at the end of array
+    # See: https://github.com/intel/x86-simd-sort/pull/39
+    arr = rnd.randint(low=minv, high=maxv, size=N, dtype=dtype)
+    arr[N - 1] = maxv
+    assert_arg_sorted(arr, np.argsort(arr, kind='quick'))
+
+# Test large arrays that leverage openMP implementations from x86-simd-sort:
+@pytest.mark.parametrize("dtype", [np.float16, np.float32, np.float64])
+def test_sort_largearrays(dtype):
+    N = 1000000
+    rnd = np.random.RandomState(1100710816)
+    arr = -0.5 + rnd.random(N).astype(dtype)
+    assert_equal(np.sort(arr, kind='quick'), np.sort(arr, kind='heap'))
+
+# Test large arrays that leverage openMP implementations from x86-simd-sort:
+@pytest.mark.parametrize("dtype", [np.float32, np.float64])
+def test_argsort_largearrays(dtype):
+    N = 1000000
+    rnd = np.random.RandomState(1100710816)
+    arr = -0.5 + rnd.random(N).astype(dtype)
+    assert_arg_sorted(arr, np.argsort(arr, kind='quick'))
+
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+def test_gh_22683():
+    b = 777.68760986
+    a = np.array([b] * 10000, dtype=object)
+    refc_start = sys.getrefcount(b)
+    np.choose(np.zeros(10000, dtype=int), [a], out=a)
+    np.choose(np.zeros(10000, dtype=int), [a], out=a)
+    refc_end = sys.getrefcount(b)
+    assert refc_end - refc_start < 10
+
+
+def test_gh_24459():
+    a = np.zeros((50, 3), dtype=np.float64)
+    with pytest.raises(TypeError):
+        np.choose(a, [3, -1])
+
+
+def test_gh_28206():
+    a = np.arange(3)
+    b = np.ones((3, 3), dtype=np.int64)
+    out = np.array([np.nan, np.nan, np.nan])
+
+    with warnings.catch_warnings():
+        warnings.simplefilter("error", RuntimeWarning)
+        np.choose(a, b, out=out)
+
+
+@pytest.mark.parametrize("N", np.arange(2, 512))
+@pytest.mark.parametrize("dtype", [np.int16, np.uint16,
+                        np.int32, np.uint32, np.int64, np.uint64])
+def test_partition_int(N, dtype):
+    rnd = np.random.RandomState(1100710816)
+    # (1) random data with min and max values
+    minv = np.iinfo(dtype).min
+    maxv = np.iinfo(dtype).max
+    arr = rnd.randint(low=minv, high=maxv, size=N, dtype=dtype)
+    i, j = rnd.choice(N, 2, replace=False)
+    arr[i] = minv
+    arr[j] = maxv
+    k = rnd.choice(N, 1)[0]
+    assert_arr_partitioned(np.sort(arr)[k], k,
+            np.partition(arr, k, kind='introselect'))
+    assert_arr_partitioned(np.sort(arr)[k], k,
+            arr[np.argpartition(arr, k, kind='introselect')])
+
+    # (2) random data with max value at the end of array
+    arr = rnd.randint(low=minv, high=maxv, size=N, dtype=dtype)
+    arr[N - 1] = maxv
+    assert_arr_partitioned(np.sort(arr)[k], k,
+            np.partition(arr, k, kind='introselect'))
+    assert_arr_partitioned(np.sort(arr)[k], k,
+            arr[np.argpartition(arr, k, kind='introselect')])
+
+
+@pytest.mark.parametrize("N", np.arange(2, 512))
+@pytest.mark.parametrize("dtype", [np.float16, np.float32, np.float64])
+def test_partition_fp(N, dtype):
+    rnd = np.random.RandomState(1100710816)
+    arr = -0.5 + rnd.random(N).astype(dtype)
+    k = rnd.choice(N, 1)[0]
+    assert_arr_partitioned(np.sort(arr)[k], k,
+            np.partition(arr, k, kind='introselect'))
+    assert_arr_partitioned(np.sort(arr)[k], k,
+            arr[np.argpartition(arr, k, kind='introselect')])
+
+    # Check that `np.inf < np.nan`
+    # This follows np.sort
+    arr[0] = np.nan
+    arr[1] = np.inf
+    o1 = np.partition(arr, -2, kind='introselect')
+    o2 = arr[np.argpartition(arr, -2, kind='introselect')]
+    for out in [o1, o2]:
+        assert_(np.isnan(out[-1]))
+        assert_equal(out[-2], np.inf)
+
+def test_cannot_assign_data():
+    a = np.arange(10)
+    b = np.linspace(0, 1, 10)
+    with pytest.raises(AttributeError):
+        a.data = b.data
+
+def test_insufficient_width():
+    """
+    If a 'width' parameter is passed into ``binary_repr`` that is insufficient
+    to represent the number in base 2 (positive) or 2's complement (negative)
+    form, the function used to silently ignore the parameter and return a
+    representation using the minimal number of bits needed for the form in
+    question. Such behavior is now considered unsafe from a user perspective
+    and will raise an error.
+    """
+    with pytest.raises(ValueError):
+        np.binary_repr(10, width=2)
+    with pytest.raises(ValueError):
+        np.binary_repr(-5, width=2)
+
+def test_npy_char_raises():
+    from numpy._core._multiarray_tests import npy_char_deprecation
+    with pytest.raises(ValueError):
+        npy_char_deprecation()
+
+
+class TestDevice:
+    """
+    Test arr.device attribute and arr.to_device() method.
+    """
+    @pytest.mark.parametrize("func, arg", [
+        (np.arange, 5),
+        (np.empty_like, []),
+        (np.zeros, 5),
+        (np.empty, (5, 5)),
+        (np.asarray, []),
+        (np.asanyarray, []),
+    ])
+    def test_device(self, func, arg):
+        arr = func(arg)
+        assert arr.device == "cpu"
+        arr = func(arg, device=None)
+        assert arr.device == "cpu"
+        arr = func(arg, device="cpu")
+        assert arr.device == "cpu"
+
+        with assert_raises_regex(
+            ValueError,
+            r"Device not understood. Only \"cpu\" is allowed, "
+            r"but received: nonsense"
+        ):
+            func(arg, device="nonsense")
+
+        with assert_raises_regex(
+            AttributeError,
+            r"attribute 'device' of '(numpy.|)ndarray' objects is "
+            r"not writable"
+        ):
+            arr.device = "other"
+
+    def test_to_device(self):
+        arr = np.arange(5)
+
+        assert arr.to_device("cpu") is arr
+        with assert_raises_regex(
+            ValueError,
+            r"The stream argument in to_device\(\) is not supported"
+        ):
+            arr.to_device("cpu", stream=1)
+
+def test_array_interface_excess_dimensions_raises():
+    """Regression test for gh-27949: ensure too many dims raises ValueError instead of segfault."""
+
+    # Dummy object to hold a custom __array_interface__
+    class DummyArray:
+        def __init__(self, interface):
+            # Attach the array interface dict to mimic an array
+            self.__array_interface__ = interface
+
+    # Create a base array (scalar) and copy its interface
+    base = np.array(42)  # base can be any scalar or array
+    interface = dict(base.__array_interface__)
+
+    # Modify the shape to exceed NumPy's dimension limit (NPY_MAXDIMS, typically 64)
+    interface['shape'] = tuple([1] * 136)  # match the original bug report
+
+    dummy = DummyArray(interface)
+    # Now, using np.asanyarray on this dummy should trigger a ValueError (not segfault)
+    with pytest.raises(ValueError, match="dimensions must be within"):
+        np.asanyarray(dummy)
+
+@pytest.mark.parametrize("dtype", [np.float32, np.float64, np.uint32, np.complex128])
+def test_array_dunder_array_preserves_dtype_on_none(dtype):
+    """
+    Regression test for: https://github.com/numpy/numpy/issues/27407
+    Ensure that __array__(None) returns an array of the same dtype.
+    """
+    a = np.array([1], dtype=dtype)
+    b = a.__array__(None)
+    assert_array_equal(a, b, strict=True)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_multithreading.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_multithreading.py
new file mode 100644
index 0000000..09f9075
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_multithreading.py
@@ -0,0 +1,292 @@
+import concurrent.futures
+import string
+import threading
+
+import pytest
+
+import numpy as np
+from numpy._core import _rational_tests
+from numpy.testing import IS_64BIT, IS_WASM
+from numpy.testing._private.utils import run_threaded
+
+if IS_WASM:
+    pytest.skip(allow_module_level=True, reason="no threading support in wasm")
+
+
+def test_parallel_randomstate_creation():
+    # if the coercion cache is enabled and not thread-safe, creating
+    # RandomState instances simultaneously leads to a data race
+    def func(seed):
+        np.random.RandomState(seed)
+
+    run_threaded(func, 500, pass_count=True)
+
+
+def test_parallel_ufunc_execution():
+    # if the loop data cache or dispatch cache are not thread-safe
+    # computing ufuncs simultaneously in multiple threads leads
+    # to a data race that causes crashes or spurious exceptions
+    def func():
+        arr = np.random.random((25,))
+        np.isnan(arr)
+
+    run_threaded(func, 500)
+
+    # see gh-26690
+    NUM_THREADS = 50
+
+    a = np.ones(1000)
+
+    def f(b):
+        b.wait()
+        return a.sum()
+
+    run_threaded(f, NUM_THREADS, pass_barrier=True)
+
+
+def test_temp_elision_thread_safety():
+    amid = np.ones(50000)
+    bmid = np.ones(50000)
+    alarge = np.ones(1000000)
+    blarge = np.ones(1000000)
+
+    def func(count):
+        if count % 4 == 0:
+            (amid * 2) + bmid
+        elif count % 4 == 1:
+            (amid + bmid) - 2
+        elif count % 4 == 2:
+            (alarge * 2) + blarge
+        else:
+            (alarge + blarge) - 2
+
+    run_threaded(func, 100, pass_count=True)
+
+
+def test_eigvalsh_thread_safety():
+    # if lapack isn't thread safe this will randomly segfault or error
+    # see gh-24512
+    rng = np.random.RandomState(873699172)
+    matrices = (
+        rng.random((5, 10, 10, 3, 3)),
+        rng.random((5, 10, 10, 3, 3)),
+    )
+
+    run_threaded(lambda i: np.linalg.eigvalsh(matrices[i]), 2,
+                 pass_count=True)
+
+
+def test_printoptions_thread_safety():
+    # until NumPy 2.1 the printoptions state was stored in globals
+    # this verifies that they are now stored in a context variable
+    b = threading.Barrier(2)
+
+    def legacy_113():
+        np.set_printoptions(legacy='1.13', precision=12)
+        b.wait()
+        po = np.get_printoptions()
+        assert po['legacy'] == '1.13'
+        assert po['precision'] == 12
+        orig_linewidth = po['linewidth']
+        with np.printoptions(linewidth=34, legacy='1.21'):
+            po = np.get_printoptions()
+            assert po['legacy'] == '1.21'
+            assert po['precision'] == 12
+            assert po['linewidth'] == 34
+        po = np.get_printoptions()
+        assert po['linewidth'] == orig_linewidth
+        assert po['legacy'] == '1.13'
+        assert po['precision'] == 12
+
+    def legacy_125():
+        np.set_printoptions(legacy='1.25', precision=7)
+        b.wait()
+        po = np.get_printoptions()
+        assert po['legacy'] == '1.25'
+        assert po['precision'] == 7
+        orig_linewidth = po['linewidth']
+        with np.printoptions(linewidth=6, legacy='1.13'):
+            po = np.get_printoptions()
+            assert po['legacy'] == '1.13'
+            assert po['precision'] == 7
+            assert po['linewidth'] == 6
+        po = np.get_printoptions()
+        assert po['linewidth'] == orig_linewidth
+        assert po['legacy'] == '1.25'
+        assert po['precision'] == 7
+
+    task1 = threading.Thread(target=legacy_113)
+    task2 = threading.Thread(target=legacy_125)
+
+    task1.start()
+    task2.start()
+
+
+def test_parallel_reduction():
+    # gh-28041
+    NUM_THREADS = 50
+
+    x = np.arange(1000)
+
+    def closure(b):
+        b.wait()
+        np.sum(x)
+
+    run_threaded(closure, NUM_THREADS, pass_barrier=True)
+
+
+def test_parallel_flat_iterator():
+    # gh-28042
+    x = np.arange(20).reshape(5, 4).T
+
+    def closure(b):
+        b.wait()
+        for _ in range(100):
+            list(x.flat)
+
+    run_threaded(closure, outer_iterations=100, pass_barrier=True)
+
+    # gh-28143
+    def prepare_args():
+        return [np.arange(10)]
+
+    def closure(x, b):
+        b.wait()
+        for _ in range(100):
+            y = np.arange(10)
+            y.flat[x] = x
+
+    run_threaded(closure, pass_barrier=True, prepare_args=prepare_args)
+
+
+def test_multithreaded_repeat():
+    x0 = np.arange(10)
+
+    def closure(b):
+        b.wait()
+        for _ in range(100):
+            x = np.repeat(x0, 2, axis=0)[::2]
+
+    run_threaded(closure, max_workers=10, pass_barrier=True)
+
+
+def test_structured_advanced_indexing():
+    # Test that copyswap(n) used by integer array indexing is threadsafe
+    # for structured datatypes, see gh-15387. This test can behave randomly.
+
+    # Create a deeply nested dtype to make a failure more likely:
+    dt = np.dtype([("", "f8")])
+    dt = np.dtype([("", dt)] * 2)
+    dt = np.dtype([("", dt)] * 2)
+    # The array should be large enough to likely run into threading issues
+    arr = np.random.uniform(size=(6000, 8)).view(dt)[:, 0]
+
+    rng = np.random.default_rng()
+
+    def func(arr):
+        indx = rng.integers(0, len(arr), size=6000, dtype=np.intp)
+        arr[indx]
+
+    tpe = concurrent.futures.ThreadPoolExecutor(max_workers=8)
+    futures = [tpe.submit(func, arr) for _ in range(10)]
+    for f in futures:
+        f.result()
+
+    assert arr.dtype is dt
+
+
+def test_structured_threadsafety2():
+    # Nonzero (and some other functions) should be threadsafe for
+    # structured datatypes, see gh-15387. This test can behave randomly.
+    from concurrent.futures import ThreadPoolExecutor
+
+    # Create a deeply nested dtype to make a failure more likely:
+    dt = np.dtype([("", "f8")])
+    dt = np.dtype([("", dt)])
+    dt = np.dtype([("", dt)] * 2)
+    # The array should be large enough to likely run into threading issues
+    arr = np.random.uniform(size=(5000, 4)).view(dt)[:, 0]
+
+    def func(arr):
+        arr.nonzero()
+
+    tpe = ThreadPoolExecutor(max_workers=8)
+    futures = [tpe.submit(func, arr) for _ in range(10)]
+    for f in futures:
+        f.result()
+
+    assert arr.dtype is dt
+
+
+def test_stringdtype_multithreaded_access_and_mutation(
+        dtype, random_string_list):
+    # this test uses an RNG and may crash or cause deadlocks if there is a
+    # threading bug
+    rng = np.random.default_rng(0x4D3D3D3)
+
+    chars = list(string.ascii_letters + string.digits)
+    chars = np.array(chars, dtype="U1")
+    ret = rng.choice(chars, size=100 * 10, replace=True)
+    random_string_list = ret.view("U100")
+
+    def func(arr):
+        rnd = rng.random()
+        # either write to random locations in the array, compute a ufunc, or
+        # re-initialize the array
+        if rnd < 0.25:
+            num = np.random.randint(0, arr.size)
+            arr[num] = arr[num] + "hello"
+        elif rnd < 0.5:
+            if rnd < 0.375:
+                np.add(arr, arr)
+            else:
+                np.add(arr, arr, out=arr)
+        elif rnd < 0.75:
+            if rnd < 0.875:
+                np.multiply(arr, np.int64(2))
+            else:
+                np.multiply(arr, np.int64(2), out=arr)
+        else:
+            arr[:] = random_string_list
+
+    with concurrent.futures.ThreadPoolExecutor(max_workers=8) as tpe:
+        arr = np.array(random_string_list, dtype=dtype)
+        futures = [tpe.submit(func, arr) for _ in range(500)]
+
+        for f in futures:
+            f.result()
+
+
+@pytest.mark.skipif(
+    not IS_64BIT,
+    reason="Sometimes causes failures or crashes due to OOM on 32 bit runners"
+)
+def test_legacy_usertype_cast_init_thread_safety():
+    def closure(b):
+        b.wait()
+        np.full((10, 10), 1, _rational_tests.rational)
+
+    run_threaded(closure, 250, pass_barrier=True)
+
+@pytest.mark.parametrize("dtype", [bool, int, float])
+def test_nonzero(dtype):
+    # See: gh-28361
+    #
+    # np.nonzero uses np.count_nonzero to determine the size of the output array
+    # In a second pass the indices of the non-zero elements are determined, but they can have changed
+    #
+    # This test triggers a data race which is suppressed in the TSAN CI. The test is to ensure
+    # np.nonzero does not generate a segmentation fault
+    x = np.random.randint(4, size=100).astype(dtype)
+
+    def func(index):
+        for _ in range(10):
+            if index == 0:
+                x[::2] = np.random.randint(2)
+            else:
+                try:
+                    _ = np.nonzero(x)
+                except RuntimeError as ex:
+                    assert 'number of non-zero array elements changed during function execution' in str(ex)
+
+    run_threaded(func, max_workers=10, pass_count=True, outer_iterations=5)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_nditer.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_nditer.py
new file mode 100644
index 0000000..ec28e48
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_nditer.py
@@ -0,0 +1,3498 @@
+import subprocess
+import sys
+import textwrap
+
+import numpy._core._multiarray_tests as _multiarray_tests
+import pytest
+
+import numpy as np
+import numpy._core.umath as ncu
+from numpy import all, arange, array, nditer
+from numpy.testing import (
+    HAS_REFCOUNT,
+    IS_WASM,
+    assert_,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    suppress_warnings,
+)
+from numpy.testing._private.utils import requires_memory
+
+
+def iter_multi_index(i):
+    ret = []
+    while not i.finished:
+        ret.append(i.multi_index)
+        i.iternext()
+    return ret
+
+def iter_indices(i):
+    ret = []
+    while not i.finished:
+        ret.append(i.index)
+        i.iternext()
+    return ret
+
+def iter_iterindices(i):
+    ret = []
+    while not i.finished:
+        ret.append(i.iterindex)
+        i.iternext()
+    return ret
+
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+def test_iter_refcount():
+    # Make sure the iterator doesn't leak
+
+    # Basic
+    a = arange(6)
+    dt = np.dtype('f4').newbyteorder()
+    rc_a = sys.getrefcount(a)
+    rc_dt = sys.getrefcount(dt)
+    with nditer(a, [],
+                [['readwrite', 'updateifcopy']],
+                casting='unsafe',
+                op_dtypes=[dt]) as it:
+        assert_(not it.iterationneedsapi)
+        assert_(sys.getrefcount(a) > rc_a)
+        assert_(sys.getrefcount(dt) > rc_dt)
+    # del 'it'
+    it = None
+    assert_equal(sys.getrefcount(a), rc_a)
+    assert_equal(sys.getrefcount(dt), rc_dt)
+
+    # With a copy
+    a = arange(6, dtype='f4')
+    dt = np.dtype('f4')
+    rc_a = sys.getrefcount(a)
+    rc_dt = sys.getrefcount(dt)
+    it = nditer(a, [],
+                [['readwrite']],
+                op_dtypes=[dt])
+    rc2_a = sys.getrefcount(a)
+    rc2_dt = sys.getrefcount(dt)
+    it2 = it.copy()
+    assert_(sys.getrefcount(a) > rc2_a)
+    if sys.version_info < (3, 13):
+        # np.dtype('f4') is immortal after Python 3.13
+        assert_(sys.getrefcount(dt) > rc2_dt)
+    it = None
+    assert_equal(sys.getrefcount(a), rc2_a)
+    assert_equal(sys.getrefcount(dt), rc2_dt)
+    it2 = None
+    assert_equal(sys.getrefcount(a), rc_a)
+    assert_equal(sys.getrefcount(dt), rc_dt)
+
+def test_iter_best_order():
+    # The iterator should always find the iteration order
+    # with increasing memory addresses
+
+    # Test the ordering for 1-D to 5-D shapes
+    for shape in [(5,), (3, 4), (2, 3, 4), (2, 3, 4, 3), (2, 3, 2, 2, 3)]:
+        a = arange(np.prod(shape))
+        # Test each combination of positive and negative strides
+        for dirs in range(2**len(shape)):
+            dirs_index = [slice(None)] * len(shape)
+            for bit in range(len(shape)):
+                if ((2**bit) & dirs):
+                    dirs_index[bit] = slice(None, None, -1)
+            dirs_index = tuple(dirs_index)
+
+            aview = a.reshape(shape)[dirs_index]
+            # C-order
+            i = nditer(aview, [], [['readonly']])
+            assert_equal(list(i), a)
+            # Fortran-order
+            i = nditer(aview.T, [], [['readonly']])
+            assert_equal(list(i), a)
+            # Other order
+            if len(shape) > 2:
+                i = nditer(aview.swapaxes(0, 1), [], [['readonly']])
+                assert_equal(list(i), a)
+
+def test_iter_c_order():
+    # Test forcing C order
+
+    # Test the ordering for 1-D to 5-D shapes
+    for shape in [(5,), (3, 4), (2, 3, 4), (2, 3, 4, 3), (2, 3, 2, 2, 3)]:
+        a = arange(np.prod(shape))
+        # Test each combination of positive and negative strides
+        for dirs in range(2**len(shape)):
+            dirs_index = [slice(None)] * len(shape)
+            for bit in range(len(shape)):
+                if ((2**bit) & dirs):
+                    dirs_index[bit] = slice(None, None, -1)
+            dirs_index = tuple(dirs_index)
+
+            aview = a.reshape(shape)[dirs_index]
+            # C-order
+            i = nditer(aview, order='C')
+            assert_equal(list(i), aview.ravel(order='C'))
+            # Fortran-order
+            i = nditer(aview.T, order='C')
+            assert_equal(list(i), aview.T.ravel(order='C'))
+            # Other order
+            if len(shape) > 2:
+                i = nditer(aview.swapaxes(0, 1), order='C')
+                assert_equal(list(i),
+                                    aview.swapaxes(0, 1).ravel(order='C'))
+
+def test_iter_f_order():
+    # Test forcing F order
+
+    # Test the ordering for 1-D to 5-D shapes
+    for shape in [(5,), (3, 4), (2, 3, 4), (2, 3, 4, 3), (2, 3, 2, 2, 3)]:
+        a = arange(np.prod(shape))
+        # Test each combination of positive and negative strides
+        for dirs in range(2**len(shape)):
+            dirs_index = [slice(None)] * len(shape)
+            for bit in range(len(shape)):
+                if ((2**bit) & dirs):
+                    dirs_index[bit] = slice(None, None, -1)
+            dirs_index = tuple(dirs_index)
+
+            aview = a.reshape(shape)[dirs_index]
+            # C-order
+            i = nditer(aview, order='F')
+            assert_equal(list(i), aview.ravel(order='F'))
+            # Fortran-order
+            i = nditer(aview.T, order='F')
+            assert_equal(list(i), aview.T.ravel(order='F'))
+            # Other order
+            if len(shape) > 2:
+                i = nditer(aview.swapaxes(0, 1), order='F')
+                assert_equal(list(i),
+                                    aview.swapaxes(0, 1).ravel(order='F'))
+
+def test_iter_c_or_f_order():
+    # Test forcing any contiguous (C or F) order
+
+    # Test the ordering for 1-D to 5-D shapes
+    for shape in [(5,), (3, 4), (2, 3, 4), (2, 3, 4, 3), (2, 3, 2, 2, 3)]:
+        a = arange(np.prod(shape))
+        # Test each combination of positive and negative strides
+        for dirs in range(2**len(shape)):
+            dirs_index = [slice(None)] * len(shape)
+            for bit in range(len(shape)):
+                if ((2**bit) & dirs):
+                    dirs_index[bit] = slice(None, None, -1)
+            dirs_index = tuple(dirs_index)
+
+            aview = a.reshape(shape)[dirs_index]
+            # C-order
+            i = nditer(aview, order='A')
+            assert_equal(list(i), aview.ravel(order='A'))
+            # Fortran-order
+            i = nditer(aview.T, order='A')
+            assert_equal(list(i), aview.T.ravel(order='A'))
+            # Other order
+            if len(shape) > 2:
+                i = nditer(aview.swapaxes(0, 1), order='A')
+                assert_equal(list(i),
+                                    aview.swapaxes(0, 1).ravel(order='A'))
+
+def test_nditer_multi_index_set():
+    # Test the multi_index set
+    a = np.arange(6).reshape(2, 3)
+    it = np.nditer(a, flags=['multi_index'])
+
+    # Removes the iteration on two first elements of a[0]
+    it.multi_index = (0, 2,)
+
+    assert_equal(list(it), [2, 3, 4, 5])
+
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+def test_nditer_multi_index_set_refcount():
+    # Test if the reference count on index variable is decreased
+
+    index = 0
+    i = np.nditer(np.array([111, 222, 333, 444]), flags=['multi_index'])
+
+    start_count = sys.getrefcount(index)
+    i.multi_index = (index,)
+    end_count = sys.getrefcount(index)
+
+    assert_equal(start_count, end_count)
+
+def test_iter_best_order_multi_index_1d():
+    # The multi-indices should be correct with any reordering
+
+    a = arange(4)
+    # 1D order
+    i = nditer(a, ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(0,), (1,), (2,), (3,)])
+    # 1D reversed order
+    i = nditer(a[::-1], ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(3,), (2,), (1,), (0,)])
+
+def test_iter_best_order_multi_index_2d():
+    # The multi-indices should be correct with any reordering
+
+    a = arange(6)
+    # 2D C-order
+    i = nditer(a.reshape(2, 3), ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2)])
+    # 2D Fortran-order
+    i = nditer(a.reshape(2, 3).copy(order='F'), ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(0, 0), (1, 0), (0, 1), (1, 1), (0, 2), (1, 2)])
+    # 2D reversed C-order
+    i = nditer(a.reshape(2, 3)[::-1], ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(1, 0), (1, 1), (1, 2), (0, 0), (0, 1), (0, 2)])
+    i = nditer(a.reshape(2, 3)[:, ::-1], ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(0, 2), (0, 1), (0, 0), (1, 2), (1, 1), (1, 0)])
+    i = nditer(a.reshape(2, 3)[::-1, ::-1], ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(1, 2), (1, 1), (1, 0), (0, 2), (0, 1), (0, 0)])
+    # 2D reversed Fortran-order
+    i = nditer(a.reshape(2, 3).copy(order='F')[::-1], ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(1, 0), (0, 0), (1, 1), (0, 1), (1, 2), (0, 2)])
+    i = nditer(a.reshape(2, 3).copy(order='F')[:, ::-1],
+                                                   ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(0, 2), (1, 2), (0, 1), (1, 1), (0, 0), (1, 0)])
+    i = nditer(a.reshape(2, 3).copy(order='F')[::-1, ::-1],
+                                                   ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i), [(1, 2), (0, 2), (1, 1), (0, 1), (1, 0), (0, 0)])
+
+def test_iter_best_order_multi_index_3d():
+    # The multi-indices should be correct with any reordering
+
+    a = arange(12)
+    # 3D C-order
+    i = nditer(a.reshape(2, 3, 2), ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i),
+                            [(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (0, 2, 0), (0, 2, 1),
+                             (1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1), (1, 2, 0), (1, 2, 1)])
+    # 3D Fortran-order
+    i = nditer(a.reshape(2, 3, 2).copy(order='F'), ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i),
+                            [(0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0), (0, 2, 0), (1, 2, 0),
+                             (0, 0, 1), (1, 0, 1), (0, 1, 1), (1, 1, 1), (0, 2, 1), (1, 2, 1)])
+    # 3D reversed C-order
+    i = nditer(a.reshape(2, 3, 2)[::-1], ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i),
+                            [(1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1), (1, 2, 0), (1, 2, 1),
+                             (0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (0, 2, 0), (0, 2, 1)])
+    i = nditer(a.reshape(2, 3, 2)[:, ::-1], ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i),
+                            [(0, 2, 0), (0, 2, 1), (0, 1, 0), (0, 1, 1), (0, 0, 0), (0, 0, 1),
+                             (1, 2, 0), (1, 2, 1), (1, 1, 0), (1, 1, 1), (1, 0, 0), (1, 0, 1)])
+    i = nditer(a.reshape(2, 3, 2)[:, :, ::-1], ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i),
+                            [(0, 0, 1), (0, 0, 0), (0, 1, 1), (0, 1, 0), (0, 2, 1), (0, 2, 0),
+                             (1, 0, 1), (1, 0, 0), (1, 1, 1), (1, 1, 0), (1, 2, 1), (1, 2, 0)])
+    # 3D reversed Fortran-order
+    i = nditer(a.reshape(2, 3, 2).copy(order='F')[::-1],
+                                                    ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i),
+                            [(1, 0, 0), (0, 0, 0), (1, 1, 0), (0, 1, 0), (1, 2, 0), (0, 2, 0),
+                             (1, 0, 1), (0, 0, 1), (1, 1, 1), (0, 1, 1), (1, 2, 1), (0, 2, 1)])
+    i = nditer(a.reshape(2, 3, 2).copy(order='F')[:, ::-1],
+                                                    ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i),
+                            [(0, 2, 0), (1, 2, 0), (0, 1, 0), (1, 1, 0), (0, 0, 0), (1, 0, 0),
+                             (0, 2, 1), (1, 2, 1), (0, 1, 1), (1, 1, 1), (0, 0, 1), (1, 0, 1)])
+    i = nditer(a.reshape(2, 3, 2).copy(order='F')[:, :, ::-1],
+                                                    ['multi_index'], [['readonly']])
+    assert_equal(iter_multi_index(i),
+                            [(0, 0, 1), (1, 0, 1), (0, 1, 1), (1, 1, 1), (0, 2, 1), (1, 2, 1),
+                             (0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0), (0, 2, 0), (1, 2, 0)])
+
+def test_iter_best_order_c_index_1d():
+    # The C index should be correct with any reordering
+
+    a = arange(4)
+    # 1D order
+    i = nditer(a, ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [0, 1, 2, 3])
+    # 1D reversed order
+    i = nditer(a[::-1], ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [3, 2, 1, 0])
+
+def test_iter_best_order_c_index_2d():
+    # The C index should be correct with any reordering
+
+    a = arange(6)
+    # 2D C-order
+    i = nditer(a.reshape(2, 3), ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [0, 1, 2, 3, 4, 5])
+    # 2D Fortran-order
+    i = nditer(a.reshape(2, 3).copy(order='F'),
+                                    ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [0, 3, 1, 4, 2, 5])
+    # 2D reversed C-order
+    i = nditer(a.reshape(2, 3)[::-1], ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [3, 4, 5, 0, 1, 2])
+    i = nditer(a.reshape(2, 3)[:, ::-1], ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [2, 1, 0, 5, 4, 3])
+    i = nditer(a.reshape(2, 3)[::-1, ::-1], ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [5, 4, 3, 2, 1, 0])
+    # 2D reversed Fortran-order
+    i = nditer(a.reshape(2, 3).copy(order='F')[::-1],
+                                    ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [3, 0, 4, 1, 5, 2])
+    i = nditer(a.reshape(2, 3).copy(order='F')[:, ::-1],
+                                    ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [2, 5, 1, 4, 0, 3])
+    i = nditer(a.reshape(2, 3).copy(order='F')[::-1, ::-1],
+                                    ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i), [5, 2, 4, 1, 3, 0])
+
+def test_iter_best_order_c_index_3d():
+    # The C index should be correct with any reordering
+
+    a = arange(12)
+    # 3D C-order
+    i = nditer(a.reshape(2, 3, 2), ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
+    # 3D Fortran-order
+    i = nditer(a.reshape(2, 3, 2).copy(order='F'),
+                                    ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [0, 6, 2, 8, 4, 10, 1, 7, 3, 9, 5, 11])
+    # 3D reversed C-order
+    i = nditer(a.reshape(2, 3, 2)[::-1], ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5])
+    i = nditer(a.reshape(2, 3, 2)[:, ::-1], ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [4, 5, 2, 3, 0, 1, 10, 11, 8, 9, 6, 7])
+    i = nditer(a.reshape(2, 3, 2)[:, :, ::-1], ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10])
+    # 3D reversed Fortran-order
+    i = nditer(a.reshape(2, 3, 2).copy(order='F')[::-1],
+                                    ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [6, 0, 8, 2, 10, 4, 7, 1, 9, 3, 11, 5])
+    i = nditer(a.reshape(2, 3, 2).copy(order='F')[:, ::-1],
+                                    ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [4, 10, 2, 8, 0, 6, 5, 11, 3, 9, 1, 7])
+    i = nditer(a.reshape(2, 3, 2).copy(order='F')[:, :, ::-1],
+                                    ['c_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [1, 7, 3, 9, 5, 11, 0, 6, 2, 8, 4, 10])
+
+def test_iter_best_order_f_index_1d():
+    # The Fortran index should be correct with any reordering
+
+    a = arange(4)
+    # 1D order
+    i = nditer(a, ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [0, 1, 2, 3])
+    # 1D reversed order
+    i = nditer(a[::-1], ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [3, 2, 1, 0])
+
+def test_iter_best_order_f_index_2d():
+    # The Fortran index should be correct with any reordering
+
+    a = arange(6)
+    # 2D C-order
+    i = nditer(a.reshape(2, 3), ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [0, 2, 4, 1, 3, 5])
+    # 2D Fortran-order
+    i = nditer(a.reshape(2, 3).copy(order='F'),
+                                    ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [0, 1, 2, 3, 4, 5])
+    # 2D reversed C-order
+    i = nditer(a.reshape(2, 3)[::-1], ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [1, 3, 5, 0, 2, 4])
+    i = nditer(a.reshape(2, 3)[:, ::-1], ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [4, 2, 0, 5, 3, 1])
+    i = nditer(a.reshape(2, 3)[::-1, ::-1], ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [5, 3, 1, 4, 2, 0])
+    # 2D reversed Fortran-order
+    i = nditer(a.reshape(2, 3).copy(order='F')[::-1],
+                                    ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [1, 0, 3, 2, 5, 4])
+    i = nditer(a.reshape(2, 3).copy(order='F')[:, ::-1],
+                                    ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [4, 5, 2, 3, 0, 1])
+    i = nditer(a.reshape(2, 3).copy(order='F')[::-1, ::-1],
+                                    ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i), [5, 4, 3, 2, 1, 0])
+
+def test_iter_best_order_f_index_3d():
+    # The Fortran index should be correct with any reordering
+
+    a = arange(12)
+    # 3D C-order
+    i = nditer(a.reshape(2, 3, 2), ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [0, 6, 2, 8, 4, 10, 1, 7, 3, 9, 5, 11])
+    # 3D Fortran-order
+    i = nditer(a.reshape(2, 3, 2).copy(order='F'),
+                                    ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
+    # 3D reversed C-order
+    i = nditer(a.reshape(2, 3, 2)[::-1], ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [1, 7, 3, 9, 5, 11, 0, 6, 2, 8, 4, 10])
+    i = nditer(a.reshape(2, 3, 2)[:, ::-1], ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [4, 10, 2, 8, 0, 6, 5, 11, 3, 9, 1, 7])
+    i = nditer(a.reshape(2, 3, 2)[:, :, ::-1], ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [6, 0, 8, 2, 10, 4, 7, 1, 9, 3, 11, 5])
+    # 3D reversed Fortran-order
+    i = nditer(a.reshape(2, 3, 2).copy(order='F')[::-1],
+                                    ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10])
+    i = nditer(a.reshape(2, 3, 2).copy(order='F')[:, ::-1],
+                                    ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [4, 5, 2, 3, 0, 1, 10, 11, 8, 9, 6, 7])
+    i = nditer(a.reshape(2, 3, 2).copy(order='F')[:, :, ::-1],
+                                    ['f_index'], [['readonly']])
+    assert_equal(iter_indices(i),
+                            [6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5])
+
+def test_iter_no_inner_full_coalesce():
+    # Check no_inner iterators which coalesce into a single inner loop
+
+    for shape in [(5,), (3, 4), (2, 3, 4), (2, 3, 4, 3), (2, 3, 2, 2, 3)]:
+        size = np.prod(shape)
+        a = arange(size)
+        # Test each combination of forward and backwards indexing
+        for dirs in range(2**len(shape)):
+            dirs_index = [slice(None)] * len(shape)
+            for bit in range(len(shape)):
+                if ((2**bit) & dirs):
+                    dirs_index[bit] = slice(None, None, -1)
+            dirs_index = tuple(dirs_index)
+
+            aview = a.reshape(shape)[dirs_index]
+            # C-order
+            i = nditer(aview, ['external_loop'], [['readonly']])
+            assert_equal(i.ndim, 1)
+            assert_equal(i[0].shape, (size,))
+            # Fortran-order
+            i = nditer(aview.T, ['external_loop'], [['readonly']])
+            assert_equal(i.ndim, 1)
+            assert_equal(i[0].shape, (size,))
+            # Other order
+            if len(shape) > 2:
+                i = nditer(aview.swapaxes(0, 1),
+                                    ['external_loop'], [['readonly']])
+                assert_equal(i.ndim, 1)
+                assert_equal(i[0].shape, (size,))
+
+def test_iter_no_inner_dim_coalescing():
+    # Check no_inner iterators whose dimensions may not coalesce completely
+
+    # Skipping the last element in a dimension prevents coalescing
+    # with the next-bigger dimension
+    a = arange(24).reshape(2, 3, 4)[:, :, :-1]
+    i = nditer(a, ['external_loop'], [['readonly']])
+    assert_equal(i.ndim, 2)
+    assert_equal(i[0].shape, (3,))
+    a = arange(24).reshape(2, 3, 4)[:, :-1, :]
+    i = nditer(a, ['external_loop'], [['readonly']])
+    assert_equal(i.ndim, 2)
+    assert_equal(i[0].shape, (8,))
+    a = arange(24).reshape(2, 3, 4)[:-1, :, :]
+    i = nditer(a, ['external_loop'], [['readonly']])
+    assert_equal(i.ndim, 1)
+    assert_equal(i[0].shape, (12,))
+
+    # Even with lots of 1-sized dimensions, should still coalesce
+    a = arange(24).reshape(1, 1, 2, 1, 1, 3, 1, 1, 4, 1, 1)
+    i = nditer(a, ['external_loop'], [['readonly']])
+    assert_equal(i.ndim, 1)
+    assert_equal(i[0].shape, (24,))
+
+def test_iter_dim_coalescing():
+    # Check that the correct number of dimensions are coalesced
+
+    # Tracking a multi-index disables coalescing
+    a = arange(24).reshape(2, 3, 4)
+    i = nditer(a, ['multi_index'], [['readonly']])
+    assert_equal(i.ndim, 3)
+
+    # A tracked index can allow coalescing if it's compatible with the array
+    a3d = arange(24).reshape(2, 3, 4)
+    i = nditer(a3d, ['c_index'], [['readonly']])
+    assert_equal(i.ndim, 1)
+    i = nditer(a3d.swapaxes(0, 1), ['c_index'], [['readonly']])
+    assert_equal(i.ndim, 3)
+    i = nditer(a3d.T, ['c_index'], [['readonly']])
+    assert_equal(i.ndim, 3)
+    i = nditer(a3d.T, ['f_index'], [['readonly']])
+    assert_equal(i.ndim, 1)
+    i = nditer(a3d.T.swapaxes(0, 1), ['f_index'], [['readonly']])
+    assert_equal(i.ndim, 3)
+
+    # When C or F order is forced, coalescing may still occur
+    a3d = arange(24).reshape(2, 3, 4)
+    i = nditer(a3d, order='C')
+    assert_equal(i.ndim, 1)
+    i = nditer(a3d.T, order='C')
+    assert_equal(i.ndim, 3)
+    i = nditer(a3d, order='F')
+    assert_equal(i.ndim, 3)
+    i = nditer(a3d.T, order='F')
+    assert_equal(i.ndim, 1)
+    i = nditer(a3d, order='A')
+    assert_equal(i.ndim, 1)
+    i = nditer(a3d.T, order='A')
+    assert_equal(i.ndim, 1)
+
+def test_iter_broadcasting():
+    # Standard NumPy broadcasting rules
+
+    # 1D with scalar
+    i = nditer([arange(6), np.int32(2)], ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 6)
+    assert_equal(i.shape, (6,))
+
+    # 2D with scalar
+    i = nditer([arange(6).reshape(2, 3), np.int32(2)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 6)
+    assert_equal(i.shape, (2, 3))
+    # 2D with 1D
+    i = nditer([arange(6).reshape(2, 3), arange(3)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 6)
+    assert_equal(i.shape, (2, 3))
+    i = nditer([arange(2).reshape(2, 1), arange(3)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 6)
+    assert_equal(i.shape, (2, 3))
+    # 2D with 2D
+    i = nditer([arange(2).reshape(2, 1), arange(3).reshape(1, 3)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 6)
+    assert_equal(i.shape, (2, 3))
+
+    # 3D with scalar
+    i = nditer([np.int32(2), arange(24).reshape(4, 2, 3)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 24)
+    assert_equal(i.shape, (4, 2, 3))
+    # 3D with 1D
+    i = nditer([arange(3), arange(24).reshape(4, 2, 3)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 24)
+    assert_equal(i.shape, (4, 2, 3))
+    i = nditer([arange(3), arange(8).reshape(4, 2, 1)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 24)
+    assert_equal(i.shape, (4, 2, 3))
+    # 3D with 2D
+    i = nditer([arange(6).reshape(2, 3), arange(24).reshape(4, 2, 3)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 24)
+    assert_equal(i.shape, (4, 2, 3))
+    i = nditer([arange(2).reshape(2, 1), arange(24).reshape(4, 2, 3)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 24)
+    assert_equal(i.shape, (4, 2, 3))
+    i = nditer([arange(3).reshape(1, 3), arange(8).reshape(4, 2, 1)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 24)
+    assert_equal(i.shape, (4, 2, 3))
+    # 3D with 3D
+    i = nditer([arange(2).reshape(1, 2, 1), arange(3).reshape(1, 1, 3),
+                        arange(4).reshape(4, 1, 1)],
+                        ['multi_index'], [['readonly']] * 3)
+    assert_equal(i.itersize, 24)
+    assert_equal(i.shape, (4, 2, 3))
+    i = nditer([arange(6).reshape(1, 2, 3), arange(4).reshape(4, 1, 1)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 24)
+    assert_equal(i.shape, (4, 2, 3))
+    i = nditer([arange(24).reshape(4, 2, 3), arange(12).reshape(4, 1, 3)],
+                        ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.itersize, 24)
+    assert_equal(i.shape, (4, 2, 3))
+
+def test_iter_itershape():
+    # Check that allocated outputs work with a specified shape
+    a = np.arange(6, dtype='i2').reshape(2, 3)
+    i = nditer([a, None], [], [['readonly'], ['writeonly', 'allocate']],
+                            op_axes=[[0, 1, None], None],
+                            itershape=(-1, -1, 4))
+    assert_equal(i.operands[1].shape, (2, 3, 4))
+    assert_equal(i.operands[1].strides, (24, 8, 2))
+
+    i = nditer([a.T, None], [], [['readonly'], ['writeonly', 'allocate']],
+                            op_axes=[[0, 1, None], None],
+                            itershape=(-1, -1, 4))
+    assert_equal(i.operands[1].shape, (3, 2, 4))
+    assert_equal(i.operands[1].strides, (8, 24, 2))
+
+    i = nditer([a.T, None], [], [['readonly'], ['writeonly', 'allocate']],
+                            order='F',
+                            op_axes=[[0, 1, None], None],
+                            itershape=(-1, -1, 4))
+    assert_equal(i.operands[1].shape, (3, 2, 4))
+    assert_equal(i.operands[1].strides, (2, 6, 12))
+
+    # If we specify 1 in the itershape, it shouldn't allow broadcasting
+    # of that dimension to a bigger value
+    assert_raises(ValueError, nditer, [a, None], [],
+                            [['readonly'], ['writeonly', 'allocate']],
+                            op_axes=[[0, 1, None], None],
+                            itershape=(-1, 1, 4))
+    # Test bug that for no op_axes but itershape, they are NULLed correctly
+    i = np.nditer([np.ones(2), None, None], itershape=(2,))
+
+def test_iter_broadcasting_errors():
+    # Check that errors are thrown for bad broadcasting shapes
+
+    # 1D with 1D
+    assert_raises(ValueError, nditer, [arange(2), arange(3)],
+                    [], [['readonly']] * 2)
+    # 2D with 1D
+    assert_raises(ValueError, nditer,
+                    [arange(6).reshape(2, 3), arange(2)],
+                    [], [['readonly']] * 2)
+    # 2D with 2D
+    assert_raises(ValueError, nditer,
+                    [arange(6).reshape(2, 3), arange(9).reshape(3, 3)],
+                    [], [['readonly']] * 2)
+    assert_raises(ValueError, nditer,
+                    [arange(6).reshape(2, 3), arange(4).reshape(2, 2)],
+                    [], [['readonly']] * 2)
+    # 3D with 3D
+    assert_raises(ValueError, nditer,
+                    [arange(36).reshape(3, 3, 4), arange(24).reshape(2, 3, 4)],
+                    [], [['readonly']] * 2)
+    assert_raises(ValueError, nditer,
+                    [arange(8).reshape(2, 4, 1), arange(24).reshape(2, 3, 4)],
+                    [], [['readonly']] * 2)
+
+    # Verify that the error message mentions the right shapes
+    try:
+        nditer([arange(2).reshape(1, 2, 1),
+                arange(3).reshape(1, 3),
+                arange(6).reshape(2, 3)],
+               [],
+               [['readonly'], ['readonly'], ['writeonly', 'no_broadcast']])
+        raise AssertionError('Should have raised a broadcast error')
+    except ValueError as e:
+        msg = str(e)
+        # The message should contain the shape of the 3rd operand
+        assert_(msg.find('(2,3)') >= 0,
+                f'Message "{msg}" doesn\'t contain operand shape (2,3)')
+        # The message should contain the broadcast shape
+        assert_(msg.find('(1,2,3)') >= 0,
+                f'Message "{msg}" doesn\'t contain broadcast shape (1,2,3)')
+
+    try:
+        nditer([arange(6).reshape(2, 3), arange(2)],
+               [],
+               [['readonly'], ['readonly']],
+               op_axes=[[0, 1], [0, np.newaxis]],
+               itershape=(4, 3))
+        raise AssertionError('Should have raised a broadcast error')
+    except ValueError as e:
+        msg = str(e)
+        # The message should contain "shape->remappedshape" for each operand
+        assert_(msg.find('(2,3)->(2,3)') >= 0,
+            f'Message "{msg}" doesn\'t contain operand shape (2,3)->(2,3)')
+        assert_(msg.find('(2,)->(2,newaxis)') >= 0,
+                ('Message "%s" doesn\'t contain remapped operand shape'
+                '(2,)->(2,newaxis)') % msg)
+        # The message should contain the itershape parameter
+        assert_(msg.find('(4,3)') >= 0,
+                f'Message "{msg}" doesn\'t contain itershape parameter (4,3)')
+
+    try:
+        nditer([np.zeros((2, 1, 1)), np.zeros((2,))],
+               [],
+               [['writeonly', 'no_broadcast'], ['readonly']])
+        raise AssertionError('Should have raised a broadcast error')
+    except ValueError as e:
+        msg = str(e)
+        # The message should contain the shape of the bad operand
+        assert_(msg.find('(2,1,1)') >= 0,
+            f'Message "{msg}" doesn\'t contain operand shape (2,1,1)')
+        # The message should contain the broadcast shape
+        assert_(msg.find('(2,1,2)') >= 0,
+                f'Message "{msg}" doesn\'t contain the broadcast shape (2,1,2)')
+
+def test_iter_flags_errors():
+    # Check that bad combinations of flags produce errors
+
+    a = arange(6)
+
+    # Not enough operands
+    assert_raises(ValueError, nditer, [], [], [])
+    # Bad global flag
+    assert_raises(ValueError, nditer, [a], ['bad flag'], [['readonly']])
+    # Bad op flag
+    assert_raises(ValueError, nditer, [a], [], [['readonly', 'bad flag']])
+    # Bad order parameter
+    assert_raises(ValueError, nditer, [a], [], [['readonly']], order='G')
+    # Bad casting parameter
+    assert_raises(ValueError, nditer, [a], [], [['readonly']], casting='noon')
+    # op_flags must match ops
+    assert_raises(ValueError, nditer, [a] * 3, [], [['readonly']] * 2)
+    # Cannot track both a C and an F index
+    assert_raises(ValueError, nditer, a,
+                ['c_index', 'f_index'], [['readonly']])
+    # Inner iteration and multi-indices/indices are incompatible
+    assert_raises(ValueError, nditer, a,
+                ['external_loop', 'multi_index'], [['readonly']])
+    assert_raises(ValueError, nditer, a,
+                ['external_loop', 'c_index'], [['readonly']])
+    assert_raises(ValueError, nditer, a,
+                ['external_loop', 'f_index'], [['readonly']])
+    # Must specify exactly one of readwrite/readonly/writeonly per operand
+    assert_raises(ValueError, nditer, a, [], [[]])
+    assert_raises(ValueError, nditer, a, [], [['readonly', 'writeonly']])
+    assert_raises(ValueError, nditer, a, [], [['readonly', 'readwrite']])
+    assert_raises(ValueError, nditer, a, [], [['writeonly', 'readwrite']])
+    assert_raises(ValueError, nditer, a,
+                [], [['readonly', 'writeonly', 'readwrite']])
+    # Python scalars are always readonly
+    assert_raises(TypeError, nditer, 1.5, [], [['writeonly']])
+    assert_raises(TypeError, nditer, 1.5, [], [['readwrite']])
+    # Array scalars are always readonly
+    assert_raises(TypeError, nditer, np.int32(1), [], [['writeonly']])
+    assert_raises(TypeError, nditer, np.int32(1), [], [['readwrite']])
+    # Check readonly array
+    a.flags.writeable = False
+    assert_raises(ValueError, nditer, a, [], [['writeonly']])
+    assert_raises(ValueError, nditer, a, [], [['readwrite']])
+    a.flags.writeable = True
+    # Multi-indices available only with the multi_index flag
+    i = nditer(arange(6), [], [['readonly']])
+    assert_raises(ValueError, lambda i: i.multi_index, i)
+    # Index available only with an index flag
+    assert_raises(ValueError, lambda i: i.index, i)
+    # GotoCoords and GotoIndex incompatible with buffering or no_inner
+
+    def assign_multi_index(i):
+        i.multi_index = (0,)
+
+    def assign_index(i):
+        i.index = 0
+
+    def assign_iterindex(i):
+        i.iterindex = 0
+
+    def assign_iterrange(i):
+        i.iterrange = (0, 1)
+    i = nditer(arange(6), ['external_loop'])
+    assert_raises(ValueError, assign_multi_index, i)
+    assert_raises(ValueError, assign_index, i)
+    assert_raises(ValueError, assign_iterindex, i)
+    assert_raises(ValueError, assign_iterrange, i)
+    i = nditer(arange(6), ['buffered'])
+    assert_raises(ValueError, assign_multi_index, i)
+    assert_raises(ValueError, assign_index, i)
+    assert_raises(ValueError, assign_iterrange, i)
+    # Can't iterate if size is zero
+    assert_raises(ValueError, nditer, np.array([]))
+
+def test_iter_slice():
+    a, b, c = np.arange(3), np.arange(3), np.arange(3.)
+    i = nditer([a, b, c], [], ['readwrite'])
+    with i:
+        i[0:2] = (3, 3)
+        assert_equal(a, [3, 1, 2])
+        assert_equal(b, [3, 1, 2])
+        assert_equal(c, [0, 1, 2])
+        i[1] = 12
+        assert_equal(i[0:2], [3, 12])
+
+def test_iter_assign_mapping():
+    a = np.arange(24, dtype='f8').reshape(2, 3, 4).T
+    it = np.nditer(a, [], [['readwrite', 'updateifcopy']],
+                       casting='same_kind', op_dtypes=[np.dtype('f4')])
+    with it:
+        it.operands[0][...] = 3
+        it.operands[0][...] = 14
+    assert_equal(a, 14)
+    it = np.nditer(a, [], [['readwrite', 'updateifcopy']],
+                       casting='same_kind', op_dtypes=[np.dtype('f4')])
+    with it:
+        x = it.operands[0][-1:1]
+        x[...] = 14
+        it.operands[0][...] = -1234
+    assert_equal(a, -1234)
+    # check for no warnings on dealloc
+    x = None
+    it = None
+
+def test_iter_nbo_align_contig():
+    # Check that byte order, alignment, and contig changes work
+
+    # Byte order change by requesting a specific dtype
+    a = np.arange(6, dtype='f4')
+    au = a.byteswap()
+    au = au.view(au.dtype.newbyteorder())
+    assert_(a.dtype.byteorder != au.dtype.byteorder)
+    i = nditer(au, [], [['readwrite', 'updateifcopy']],
+                        casting='equiv',
+                        op_dtypes=[np.dtype('f4')])
+    with i:
+        # context manager triggers WRITEBACKIFCOPY on i at exit
+        assert_equal(i.dtypes[0].byteorder, a.dtype.byteorder)
+        assert_equal(i.operands[0].dtype.byteorder, a.dtype.byteorder)
+        assert_equal(i.operands[0], a)
+        i.operands[0][:] = 2
+    assert_equal(au, [2] * 6)
+    del i  # should not raise a warning
+    # Byte order change by requesting NBO
+    a = np.arange(6, dtype='f4')
+    au = a.byteswap()
+    au = au.view(au.dtype.newbyteorder())
+    assert_(a.dtype.byteorder != au.dtype.byteorder)
+    with nditer(au, [], [['readwrite', 'updateifcopy', 'nbo']],
+                        casting='equiv') as i:
+        # context manager triggers UPDATEIFCOPY on i at exit
+        assert_equal(i.dtypes[0].byteorder, a.dtype.byteorder)
+        assert_equal(i.operands[0].dtype.byteorder, a.dtype.byteorder)
+        assert_equal(i.operands[0], a)
+        i.operands[0][:] = 12345
+        i.operands[0][:] = 2
+    assert_equal(au, [2] * 6)
+
+    # Unaligned input
+    a = np.zeros((6 * 4 + 1,), dtype='i1')[1:]
+    a.dtype = 'f4'
+    a[:] = np.arange(6, dtype='f4')
+    assert_(not a.flags.aligned)
+    # Without 'aligned', shouldn't copy
+    i = nditer(a, [], [['readonly']])
+    assert_(not i.operands[0].flags.aligned)
+    assert_equal(i.operands[0], a)
+    # With 'aligned', should make a copy
+    with nditer(a, [], [['readwrite', 'updateifcopy', 'aligned']]) as i:
+        assert_(i.operands[0].flags.aligned)
+        # context manager triggers UPDATEIFCOPY on i at exit
+        assert_equal(i.operands[0], a)
+        i.operands[0][:] = 3
+    assert_equal(a, [3] * 6)
+
+    # Discontiguous input
+    a = arange(12)
+    # If it is contiguous, shouldn't copy
+    i = nditer(a[:6], [], [['readonly']])
+    assert_(i.operands[0].flags.contiguous)
+    assert_equal(i.operands[0], a[:6])
+    # If it isn't contiguous, should buffer
+    i = nditer(a[::2], ['buffered', 'external_loop'],
+                        [['readonly', 'contig']],
+                        buffersize=10)
+    assert_(i[0].flags.contiguous)
+    assert_equal(i[0], a[::2])
+
+def test_iter_array_cast():
+    # Check that arrays are cast as requested
+
+    # No cast 'f4' -> 'f4'
+    a = np.arange(6, dtype='f4').reshape(2, 3)
+    i = nditer(a, [], [['readwrite']], op_dtypes=[np.dtype('f4')])
+    with i:
+        assert_equal(i.operands[0], a)
+        assert_equal(i.operands[0].dtype, np.dtype('f4'))
+
+    # Byte-order cast '<f4' -> '>f4'
+    a = np.arange(6, dtype='<f4').reshape(2, 3)
+    with nditer(a, [], [['readwrite', 'updateifcopy']],
+            casting='equiv',
+            op_dtypes=[np.dtype('>f4')]) as i:
+        assert_equal(i.operands[0], a)
+        assert_equal(i.operands[0].dtype, np.dtype('>f4'))
+
+    # Safe case 'f4' -> 'f8'
+    a = np.arange(24, dtype='f4').reshape(2, 3, 4).swapaxes(1, 2)
+    i = nditer(a, [], [['readonly', 'copy']],
+            casting='safe',
+            op_dtypes=[np.dtype('f8')])
+    assert_equal(i.operands[0], a)
+    assert_equal(i.operands[0].dtype, np.dtype('f8'))
+    # The memory layout of the temporary should match a (a is (48,4,16))
+    # except negative strides get flipped to positive strides.
+    assert_equal(i.operands[0].strides, (96, 8, 32))
+    a = a[::-1, :, ::-1]
+    i = nditer(a, [], [['readonly', 'copy']],
+            casting='safe',
+            op_dtypes=[np.dtype('f8')])
+    assert_equal(i.operands[0], a)
+    assert_equal(i.operands[0].dtype, np.dtype('f8'))
+    assert_equal(i.operands[0].strides, (96, 8, 32))
+
+    # Same-kind cast 'f8' -> 'f4' -> 'f8'
+    a = np.arange(24, dtype='f8').reshape(2, 3, 4).T
+    with nditer(a, [],
+            [['readwrite', 'updateifcopy']],
+            casting='same_kind',
+            op_dtypes=[np.dtype('f4')]) as i:
+        assert_equal(i.operands[0], a)
+        assert_equal(i.operands[0].dtype, np.dtype('f4'))
+        assert_equal(i.operands[0].strides, (4, 16, 48))
+        # Check that WRITEBACKIFCOPY is activated at exit
+        i.operands[0][2, 1, 1] = -12.5
+        assert_(a[2, 1, 1] != -12.5)
+    assert_equal(a[2, 1, 1], -12.5)
+
+    a = np.arange(6, dtype='i4')[::-2]
+    with nditer(a, [],
+            [['writeonly', 'updateifcopy']],
+            casting='unsafe',
+            op_dtypes=[np.dtype('f4')]) as i:
+        assert_equal(i.operands[0].dtype, np.dtype('f4'))
+        # Even though the stride was negative in 'a', it
+        # becomes positive in the temporary
+        assert_equal(i.operands[0].strides, (4,))
+        i.operands[0][:] = [1, 2, 3]
+    assert_equal(a, [1, 2, 3])
+
+def test_iter_array_cast_errors():
+    # Check that invalid casts are caught
+
+    # Need to enable copying for casts to occur
+    assert_raises(TypeError, nditer, arange(2, dtype='f4'), [],
+                [['readonly']], op_dtypes=[np.dtype('f8')])
+    # Also need to allow casting for casts to occur
+    assert_raises(TypeError, nditer, arange(2, dtype='f4'), [],
+                [['readonly', 'copy']], casting='no',
+                op_dtypes=[np.dtype('f8')])
+    assert_raises(TypeError, nditer, arange(2, dtype='f4'), [],
+                [['readonly', 'copy']], casting='equiv',
+                op_dtypes=[np.dtype('f8')])
+    assert_raises(TypeError, nditer, arange(2, dtype='f8'), [],
+                [['writeonly', 'updateifcopy']],
+                casting='no',
+                op_dtypes=[np.dtype('f4')])
+    assert_raises(TypeError, nditer, arange(2, dtype='f8'), [],
+                [['writeonly', 'updateifcopy']],
+                casting='equiv',
+                op_dtypes=[np.dtype('f4')])
+    # '<f4' -> '>f4' should not work with casting='no'
+    assert_raises(TypeError, nditer, arange(2, dtype='<f4'), [],
+                [['readonly', 'copy']], casting='no',
+                op_dtypes=[np.dtype('>f4')])
+    # 'f4' -> 'f8' is a safe cast, but 'f8' -> 'f4' isn't
+    assert_raises(TypeError, nditer, arange(2, dtype='f4'), [],
+                [['readwrite', 'updateifcopy']],
+                casting='safe',
+                op_dtypes=[np.dtype('f8')])
+    assert_raises(TypeError, nditer, arange(2, dtype='f8'), [],
+                [['readwrite', 'updateifcopy']],
+                casting='safe',
+                op_dtypes=[np.dtype('f4')])
+    # 'f4' -> 'i4' is neither a safe nor a same-kind cast
+    assert_raises(TypeError, nditer, arange(2, dtype='f4'), [],
+                [['readonly', 'copy']],
+                casting='same_kind',
+                op_dtypes=[np.dtype('i4')])
+    assert_raises(TypeError, nditer, arange(2, dtype='i4'), [],
+                [['writeonly', 'updateifcopy']],
+                casting='same_kind',
+                op_dtypes=[np.dtype('f4')])
+
+def test_iter_scalar_cast():
+    # Check that scalars are cast as requested
+
+    # No cast 'f4' -> 'f4'
+    i = nditer(np.float32(2.5), [], [['readonly']],
+                    op_dtypes=[np.dtype('f4')])
+    assert_equal(i.dtypes[0], np.dtype('f4'))
+    assert_equal(i.value.dtype, np.dtype('f4'))
+    assert_equal(i.value, 2.5)
+    # Safe cast 'f4' -> 'f8'
+    i = nditer(np.float32(2.5), [],
+                    [['readonly', 'copy']],
+                    casting='safe',
+                    op_dtypes=[np.dtype('f8')])
+    assert_equal(i.dtypes[0], np.dtype('f8'))
+    assert_equal(i.value.dtype, np.dtype('f8'))
+    assert_equal(i.value, 2.5)
+    # Same-kind cast 'f8' -> 'f4'
+    i = nditer(np.float64(2.5), [],
+                    [['readonly', 'copy']],
+                    casting='same_kind',
+                    op_dtypes=[np.dtype('f4')])
+    assert_equal(i.dtypes[0], np.dtype('f4'))
+    assert_equal(i.value.dtype, np.dtype('f4'))
+    assert_equal(i.value, 2.5)
+    # Unsafe cast 'f8' -> 'i4'
+    i = nditer(np.float64(3.0), [],
+                    [['readonly', 'copy']],
+                    casting='unsafe',
+                    op_dtypes=[np.dtype('i4')])
+    assert_equal(i.dtypes[0], np.dtype('i4'))
+    assert_equal(i.value.dtype, np.dtype('i4'))
+    assert_equal(i.value, 3)
+    # Readonly scalars may be cast even without setting COPY or BUFFERED
+    i = nditer(3, [], [['readonly']], op_dtypes=[np.dtype('f8')])
+    assert_equal(i[0].dtype, np.dtype('f8'))
+    assert_equal(i[0], 3.)
+
+def test_iter_scalar_cast_errors():
+    # Check that invalid casts are caught
+
+    # Need to allow copying/buffering for write casts of scalars to occur
+    assert_raises(TypeError, nditer, np.float32(2), [],
+                [['readwrite']], op_dtypes=[np.dtype('f8')])
+    assert_raises(TypeError, nditer, 2.5, [],
+                [['readwrite']], op_dtypes=[np.dtype('f4')])
+    # 'f8' -> 'f4' isn't a safe cast if the value would overflow
+    assert_raises(TypeError, nditer, np.float64(1e60), [],
+                [['readonly']],
+                casting='safe',
+                op_dtypes=[np.dtype('f4')])
+    # 'f4' -> 'i4' is neither a safe nor a same-kind cast
+    assert_raises(TypeError, nditer, np.float32(2), [],
+                [['readonly']],
+                casting='same_kind',
+                op_dtypes=[np.dtype('i4')])
+
+def test_iter_object_arrays_basic():
+    # Check that object arrays work
+
+    obj = {'a': 3, 'b': 'd'}
+    a = np.array([[1, 2, 3], None, obj, None], dtype='O')
+    if HAS_REFCOUNT:
+        rc = sys.getrefcount(obj)
+
+    # Need to allow references for object arrays
+    assert_raises(TypeError, nditer, a)
+    if HAS_REFCOUNT:
+        assert_equal(sys.getrefcount(obj), rc)
+
+    i = nditer(a, ['refs_ok'], ['readonly'])
+    vals = [x_[()] for x_ in i]
+    assert_equal(np.array(vals, dtype='O'), a)
+    vals, i, x = [None] * 3
+    if HAS_REFCOUNT:
+        assert_equal(sys.getrefcount(obj), rc)
+
+    i = nditer(a.reshape(2, 2).T, ['refs_ok', 'buffered'],
+                        ['readonly'], order='C')
+    assert_(i.iterationneedsapi)
+    vals = [x_[()] for x_ in i]
+    assert_equal(np.array(vals, dtype='O'), a.reshape(2, 2).ravel(order='F'))
+    vals, i, x = [None] * 3
+    if HAS_REFCOUNT:
+        assert_equal(sys.getrefcount(obj), rc)
+
+    i = nditer(a.reshape(2, 2).T, ['refs_ok', 'buffered'],
+                        ['readwrite'], order='C')
+    with i:
+        for x in i:
+            x[...] = None
+        vals, i, x = [None] * 3
+    if HAS_REFCOUNT:
+        assert_(sys.getrefcount(obj) == rc - 1)
+    assert_equal(a, np.array([None] * 4, dtype='O'))
+
+def test_iter_object_arrays_conversions():
+    # Conversions to/from objects
+    a = np.arange(6, dtype='O')
+    i = nditer(a, ['refs_ok', 'buffered'], ['readwrite'],
+                    casting='unsafe', op_dtypes='i4')
+    with i:
+        for x in i:
+            x[...] += 1
+    assert_equal(a, np.arange(6) + 1)
+
+    a = np.arange(6, dtype='i4')
+    i = nditer(a, ['refs_ok', 'buffered'], ['readwrite'],
+                    casting='unsafe', op_dtypes='O')
+    with i:
+        for x in i:
+            x[...] += 1
+    assert_equal(a, np.arange(6) + 1)
+
+    # Non-contiguous object array
+    a = np.zeros((6,), dtype=[('p', 'i1'), ('a', 'O')])
+    a = a['a']
+    a[:] = np.arange(6)
+    i = nditer(a, ['refs_ok', 'buffered'], ['readwrite'],
+                    casting='unsafe', op_dtypes='i4')
+    with i:
+        for x in i:
+            x[...] += 1
+    assert_equal(a, np.arange(6) + 1)
+
+    # Non-contiguous value array
+    a = np.zeros((6,), dtype=[('p', 'i1'), ('a', 'i4')])
+    a = a['a']
+    a[:] = np.arange(6) + 98172488
+    i = nditer(a, ['refs_ok', 'buffered'], ['readwrite'],
+                    casting='unsafe', op_dtypes='O')
+    with i:
+        ob = i[0][()]
+        if HAS_REFCOUNT:
+            rc = sys.getrefcount(ob)
+        for x in i:
+            x[...] += 1
+        if HAS_REFCOUNT:
+            newrc = sys.getrefcount(ob)
+            assert_(newrc == rc - 1)
+    assert_equal(a, np.arange(6) + 98172489)
+
+def test_iter_common_dtype():
+    # Check that the iterator finds a common data type correctly
+    # (some checks are somewhat duplicate after adopting NEP 50)
+
+    i = nditer([array([3], dtype='f4'), array([0], dtype='f8')],
+                    ['common_dtype'],
+                    [['readonly', 'copy']] * 2,
+                    casting='safe')
+    assert_equal(i.dtypes[0], np.dtype('f8'))
+    assert_equal(i.dtypes[1], np.dtype('f8'))
+    i = nditer([array([3], dtype='i4'), array([0], dtype='f4')],
+                    ['common_dtype'],
+                    [['readonly', 'copy']] * 2,
+                    casting='safe')
+    assert_equal(i.dtypes[0], np.dtype('f8'))
+    assert_equal(i.dtypes[1], np.dtype('f8'))
+    i = nditer([array([3], dtype='f4'), array(0, dtype='f8')],
+                    ['common_dtype'],
+                    [['readonly', 'copy']] * 2,
+                    casting='same_kind')
+    assert_equal(i.dtypes[0], np.dtype('f8'))
+    assert_equal(i.dtypes[1], np.dtype('f8'))
+    i = nditer([array([3], dtype='u4'), array(0, dtype='i4')],
+                    ['common_dtype'],
+                    [['readonly', 'copy']] * 2,
+                    casting='safe')
+    assert_equal(i.dtypes[0], np.dtype('i8'))
+    assert_equal(i.dtypes[1], np.dtype('i8'))
+    i = nditer([array([3], dtype='u4'), array(-12, dtype='i4')],
+                    ['common_dtype'],
+                    [['readonly', 'copy']] * 2,
+                    casting='safe')
+    assert_equal(i.dtypes[0], np.dtype('i8'))
+    assert_equal(i.dtypes[1], np.dtype('i8'))
+    i = nditer([array([3], dtype='u4'), array(-12, dtype='i4'),
+                 array([2j], dtype='c8'), array([9], dtype='f8')],
+                    ['common_dtype'],
+                    [['readonly', 'copy']] * 4,
+                    casting='safe')
+    assert_equal(i.dtypes[0], np.dtype('c16'))
+    assert_equal(i.dtypes[1], np.dtype('c16'))
+    assert_equal(i.dtypes[2], np.dtype('c16'))
+    assert_equal(i.dtypes[3], np.dtype('c16'))
+    assert_equal(i.value, (3, -12, 2j, 9))
+
+    # When allocating outputs, other outputs aren't factored in
+    i = nditer([array([3], dtype='i4'), None, array([2j], dtype='c16')], [],
+                    [['readonly', 'copy'],
+                     ['writeonly', 'allocate'],
+                     ['writeonly']],
+                    casting='safe')
+    assert_equal(i.dtypes[0], np.dtype('i4'))
+    assert_equal(i.dtypes[1], np.dtype('i4'))
+    assert_equal(i.dtypes[2], np.dtype('c16'))
+    # But, if common data types are requested, they are
+    i = nditer([array([3], dtype='i4'), None, array([2j], dtype='c16')],
+                    ['common_dtype'],
+                    [['readonly', 'copy'],
+                     ['writeonly', 'allocate'],
+                     ['writeonly']],
+                    casting='safe')
+    assert_equal(i.dtypes[0], np.dtype('c16'))
+    assert_equal(i.dtypes[1], np.dtype('c16'))
+    assert_equal(i.dtypes[2], np.dtype('c16'))
+
+def test_iter_copy_if_overlap():
+    # Ensure the iterator makes copies on read/write overlap, if requested
+
+    # Copy not needed, 1 op
+    for flag in ['readonly', 'writeonly', 'readwrite']:
+        a = arange(10)
+        i = nditer([a], ['copy_if_overlap'], [[flag]])
+        with i:
+            assert_(i.operands[0] is a)
+
+    # Copy needed, 2 ops, read-write overlap
+    x = arange(10)
+    a = x[1:]
+    b = x[:-1]
+    with nditer([a, b], ['copy_if_overlap'], [['readonly'], ['readwrite']]) as i:
+        assert_(not np.shares_memory(*i.operands))
+
+    # Copy not needed with elementwise, 2 ops, exactly same arrays
+    x = arange(10)
+    a = x
+    b = x
+    i = nditer([a, b], ['copy_if_overlap'], [['readonly', 'overlap_assume_elementwise'],
+                                             ['readwrite', 'overlap_assume_elementwise']])
+    with i:
+        assert_(i.operands[0] is a and i.operands[1] is b)
+    with nditer([a, b], ['copy_if_overlap'], [['readonly'], ['readwrite']]) as i:
+        assert_(i.operands[0] is a and not np.shares_memory(i.operands[1], b))
+
+    # Copy not needed, 2 ops, no overlap
+    x = arange(10)
+    a = x[::2]
+    b = x[1::2]
+    i = nditer([a, b], ['copy_if_overlap'], [['readonly'], ['writeonly']])
+    assert_(i.operands[0] is a and i.operands[1] is b)
+
+    # Copy needed, 2 ops, read-write overlap
+    x = arange(4, dtype=np.int8)
+    a = x[3:]
+    b = x.view(np.int32)[:1]
+    with nditer([a, b], ['copy_if_overlap'], [['readonly'], ['writeonly']]) as i:
+        assert_(not np.shares_memory(*i.operands))
+
+    # Copy needed, 3 ops, read-write overlap
+    for flag in ['writeonly', 'readwrite']:
+        x = np.ones([10, 10])
+        a = x
+        b = x.T
+        c = x
+        with nditer([a, b, c], ['copy_if_overlap'],
+                   [['readonly'], ['readonly'], [flag]]) as i:
+            a2, b2, c2 = i.operands
+            assert_(not np.shares_memory(a2, c2))
+            assert_(not np.shares_memory(b2, c2))
+
+    # Copy not needed, 3 ops, read-only overlap
+    x = np.ones([10, 10])
+    a = x
+    b = x.T
+    c = x
+    i = nditer([a, b, c], ['copy_if_overlap'],
+               [['readonly'], ['readonly'], ['readonly']])
+    a2, b2, c2 = i.operands
+    assert_(a is a2)
+    assert_(b is b2)
+    assert_(c is c2)
+
+    # Copy not needed, 3 ops, read-only overlap
+    x = np.ones([10, 10])
+    a = x
+    b = np.ones([10, 10])
+    c = x.T
+    i = nditer([a, b, c], ['copy_if_overlap'],
+               [['readonly'], ['writeonly'], ['readonly']])
+    a2, b2, c2 = i.operands
+    assert_(a is a2)
+    assert_(b is b2)
+    assert_(c is c2)
+
+    # Copy not needed, 3 ops, write-only overlap
+    x = np.arange(7)
+    a = x[:3]
+    b = x[3:6]
+    c = x[4:7]
+    i = nditer([a, b, c], ['copy_if_overlap'],
+               [['readonly'], ['writeonly'], ['writeonly']])
+    a2, b2, c2 = i.operands
+    assert_(a is a2)
+    assert_(b is b2)
+    assert_(c is c2)
+
+def test_iter_op_axes():
+    # Check that custom axes work
+
+    # Reverse the axes
+    a = arange(6).reshape(2, 3)
+    i = nditer([a, a.T], [], [['readonly']] * 2, op_axes=[[0, 1], [1, 0]])
+    assert_(all([x == y for (x, y) in i]))
+    a = arange(24).reshape(2, 3, 4)
+    i = nditer([a.T, a], [], [['readonly']] * 2, op_axes=[[2, 1, 0], None])
+    assert_(all([x == y for (x, y) in i]))
+
+    # Broadcast 1D to any dimension
+    a = arange(1, 31).reshape(2, 3, 5)
+    b = arange(1, 3)
+    i = nditer([a, b], [], [['readonly']] * 2, op_axes=[None, [0, -1, -1]])
+    assert_equal([x * y for (x, y) in i], (a * b.reshape(2, 1, 1)).ravel())
+    b = arange(1, 4)
+    i = nditer([a, b], [], [['readonly']] * 2, op_axes=[None, [-1, 0, -1]])
+    assert_equal([x * y for (x, y) in i], (a * b.reshape(1, 3, 1)).ravel())
+    b = arange(1, 6)
+    i = nditer([a, b], [], [['readonly']] * 2,
+                            op_axes=[None, [np.newaxis, np.newaxis, 0]])
+    assert_equal([x * y for (x, y) in i], (a * b.reshape(1, 1, 5)).ravel())
+
+    # Inner product-style broadcasting
+    a = arange(24).reshape(2, 3, 4)
+    b = arange(40).reshape(5, 2, 4)
+    i = nditer([a, b], ['multi_index'], [['readonly']] * 2,
+                            op_axes=[[0, 1, -1, -1], [-1, -1, 0, 1]])
+    assert_equal(i.shape, (2, 3, 5, 2))
+
+    # Matrix product-style broadcasting
+    a = arange(12).reshape(3, 4)
+    b = arange(20).reshape(4, 5)
+    i = nditer([a, b], ['multi_index'], [['readonly']] * 2,
+                            op_axes=[[0, -1], [-1, 1]])
+    assert_equal(i.shape, (3, 5))
+
+def test_iter_op_axes_errors():
+    # Check that custom axes throws errors for bad inputs
+
+    # Wrong number of items in op_axes
+    a = arange(6).reshape(2, 3)
+    assert_raises(ValueError, nditer, [a, a], [], [['readonly']] * 2,
+                                    op_axes=[[0], [1], [0]])
+    # Out of bounds items in op_axes
+    assert_raises(ValueError, nditer, [a, a], [], [['readonly']] * 2,
+                                    op_axes=[[2, 1], [0, 1]])
+    assert_raises(ValueError, nditer, [a, a], [], [['readonly']] * 2,
+                                    op_axes=[[0, 1], [2, -1]])
+    # Duplicate items in op_axes
+    assert_raises(ValueError, nditer, [a, a], [], [['readonly']] * 2,
+                                    op_axes=[[0, 0], [0, 1]])
+    assert_raises(ValueError, nditer, [a, a], [], [['readonly']] * 2,
+                                    op_axes=[[0, 1], [1, 1]])
+
+    # Different sized arrays in op_axes
+    assert_raises(ValueError, nditer, [a, a], [], [['readonly']] * 2,
+                                    op_axes=[[0, 1], [0, 1, 0]])
+
+    # Non-broadcastable dimensions in the result
+    assert_raises(ValueError, nditer, [a, a], [], [['readonly']] * 2,
+                                    op_axes=[[0, 1], [1, 0]])
+
+def test_iter_copy():
+    # Check that copying the iterator works correctly
+    a = arange(24).reshape(2, 3, 4)
+
+    # Simple iterator
+    i = nditer(a)
+    j = i.copy()
+    assert_equal([x[()] for x in i], [x[()] for x in j])
+
+    i.iterindex = 3
+    j = i.copy()
+    assert_equal([x[()] for x in i], [x[()] for x in j])
+
+    # Buffered iterator
+    i = nditer(a, ['buffered', 'ranged'], order='F', buffersize=3)
+    j = i.copy()
+    assert_equal([x[()] for x in i], [x[()] for x in j])
+
+    i.iterindex = 3
+    j = i.copy()
+    assert_equal([x[()] for x in i], [x[()] for x in j])
+
+    i.iterrange = (3, 9)
+    j = i.copy()
+    assert_equal([x[()] for x in i], [x[()] for x in j])
+
+    i.iterrange = (2, 18)
+    next(i)
+    next(i)
+    j = i.copy()
+    assert_equal([x[()] for x in i], [x[()] for x in j])
+
+    # Casting iterator
+    with nditer(a, ['buffered'], order='F', casting='unsafe',
+                op_dtypes='f8', buffersize=5) as i:
+        j = i.copy()
+    assert_equal([x[()] for x in j], a.ravel(order='F'))
+
+    a = arange(24, dtype='<i4').reshape(2, 3, 4)
+    with nditer(a, ['buffered'], order='F', casting='unsafe',
+                op_dtypes='>f8', buffersize=5) as i:
+        j = i.copy()
+    assert_equal([x[()] for x in j], a.ravel(order='F'))
+
+
+@pytest.mark.parametrize("dtype", np.typecodes["All"])
+@pytest.mark.parametrize("loop_dtype", np.typecodes["All"])
+@pytest.mark.filterwarnings("ignore::numpy.exceptions.ComplexWarning")
+def test_iter_copy_casts(dtype, loop_dtype):
+    # Ensure the dtype is never flexible:
+    if loop_dtype.lower() == "m":
+        loop_dtype = loop_dtype + "[ms]"
+    elif np.dtype(loop_dtype).itemsize == 0:
+        loop_dtype = loop_dtype + "50"
+
+    # Make things a bit more interesting by requiring a byte-swap as well:
+    arr = np.ones(1000, dtype=np.dtype(dtype).newbyteorder())
+    try:
+        expected = arr.astype(loop_dtype)
+    except Exception:
+        # Some casts are not possible, do not worry about them
+        return
+
+    it = np.nditer((arr,), ["buffered", "external_loop", "refs_ok"],
+                   op_dtypes=[loop_dtype], casting="unsafe")
+
+    if np.issubdtype(np.dtype(loop_dtype), np.number):
+        # Casting to strings may be strange, but for simple dtypes do not rely
+        # on the cast being correct:
+        assert_array_equal(expected, np.ones(1000, dtype=loop_dtype))
+
+    it_copy = it.copy()
+    res = next(it)
+    del it
+    res_copy = next(it_copy)
+    del it_copy
+
+    assert_array_equal(res, expected)
+    assert_array_equal(res_copy, expected)
+
+
+def test_iter_copy_casts_structured():
+    # Test a complicated structured dtype for casting, as it requires
+    # both multiple steps and a more complex casting setup.
+    # Includes a structured -> unstructured (any to object), and many other
+    # casts, which cause this to require all steps in the casting machinery
+    # one level down as well as the iterator copy (which uses NpyAuxData clone)
+    in_dtype = np.dtype([("a", np.dtype("i,")),
+                         ("b", np.dtype(">i,<i,>d,S17,>d,3f,O,i1"))])
+    out_dtype = np.dtype([("a", np.dtype("O")),
+                          ("b", np.dtype(">i,>i,S17,>d,>U3,3d,i1,O"))])
+    arr = np.ones(1000, dtype=in_dtype)
+
+    it = np.nditer((arr,), ["buffered", "external_loop", "refs_ok"],
+                   op_dtypes=[out_dtype], casting="unsafe")
+    it_copy = it.copy()
+
+    res1 = next(it)
+    del it
+    res2 = next(it_copy)
+    del it_copy
+
+    expected = arr["a"].astype(out_dtype["a"])
+    assert_array_equal(res1["a"], expected)
+    assert_array_equal(res2["a"], expected)
+
+    for field in in_dtype["b"].names:
+        # Note that the .base avoids the subarray field
+        expected = arr["b"][field].astype(out_dtype["b"][field].base)
+        assert_array_equal(res1["b"][field], expected)
+        assert_array_equal(res2["b"][field], expected)
+
+
+def test_iter_copy_casts_structured2():
+    # Similar to the above, this is a fairly arcane test to cover internals
+    in_dtype = np.dtype([("a", np.dtype("O,O")),
+                         ("b", np.dtype("5O,3O,(1,)O,(1,)i,(1,)O"))])
+    out_dtype = np.dtype([("a", np.dtype("O")),
+                          ("b", np.dtype("O,3i,4O,4O,4i"))])
+
+    arr = np.ones(1, dtype=in_dtype)
+    it = np.nditer((arr,), ["buffered", "external_loop", "refs_ok"],
+                   op_dtypes=[out_dtype], casting="unsafe")
+    it_copy = it.copy()
+
+    res1 = next(it)
+    del it
+    res2 = next(it_copy)
+    del it_copy
+
+    # Array of two structured scalars:
+    for res in res1, res2:
+        # Cast to tuple by getitem, which may be weird and changeable?:
+        assert isinstance(res["a"][0], tuple)
+        assert res["a"][0] == (1, 1)
+
+    for res in res1, res2:
+        assert_array_equal(res["b"]["f0"][0], np.ones(5, dtype=object))
+        assert_array_equal(res["b"]["f1"], np.ones((1, 3), dtype="i"))
+        assert res["b"]["f2"].shape == (1, 4)
+        assert_array_equal(res["b"]["f2"][0], np.ones(4, dtype=object))
+        assert_array_equal(res["b"]["f3"][0], np.ones(4, dtype=object))
+        assert_array_equal(res["b"]["f3"][0], np.ones(4, dtype="i"))
+
+
+def test_iter_allocate_output_simple():
+    # Check that the iterator will properly allocate outputs
+
+    # Simple case
+    a = arange(6)
+    i = nditer([a, None], [], [['readonly'], ['writeonly', 'allocate']],
+                        op_dtypes=[None, np.dtype('f4')])
+    assert_equal(i.operands[1].shape, a.shape)
+    assert_equal(i.operands[1].dtype, np.dtype('f4'))
+
+def test_iter_allocate_output_buffered_readwrite():
+    # Allocated output with buffering + delay_bufalloc
+
+    a = arange(6)
+    i = nditer([a, None], ['buffered', 'delay_bufalloc'],
+                        [['readonly'], ['allocate', 'readwrite']])
+    with i:
+        i.operands[1][:] = 1
+        i.reset()
+        for x in i:
+            x[1][...] += x[0][...]
+        assert_equal(i.operands[1], a + 1)
+
+def test_iter_allocate_output_itorder():
+    # The allocated output should match the iteration order
+
+    # C-order input, best iteration order
+    a = arange(6, dtype='i4').reshape(2, 3)
+    i = nditer([a, None], [], [['readonly'], ['writeonly', 'allocate']],
+                        op_dtypes=[None, np.dtype('f4')])
+    assert_equal(i.operands[1].shape, a.shape)
+    assert_equal(i.operands[1].strides, a.strides)
+    assert_equal(i.operands[1].dtype, np.dtype('f4'))
+    # F-order input, best iteration order
+    a = arange(24, dtype='i4').reshape(2, 3, 4).T
+    i = nditer([a, None], [], [['readonly'], ['writeonly', 'allocate']],
+                        op_dtypes=[None, np.dtype('f4')])
+    assert_equal(i.operands[1].shape, a.shape)
+    assert_equal(i.operands[1].strides, a.strides)
+    assert_equal(i.operands[1].dtype, np.dtype('f4'))
+    # Non-contiguous input, C iteration order
+    a = arange(24, dtype='i4').reshape(2, 3, 4).swapaxes(0, 1)
+    i = nditer([a, None], [],
+                        [['readonly'], ['writeonly', 'allocate']],
+                        order='C',
+                        op_dtypes=[None, np.dtype('f4')])
+    assert_equal(i.operands[1].shape, a.shape)
+    assert_equal(i.operands[1].strides, (32, 16, 4))
+    assert_equal(i.operands[1].dtype, np.dtype('f4'))
+
+def test_iter_allocate_output_opaxes():
+    # Specifying op_axes should work
+
+    a = arange(24, dtype='i4').reshape(2, 3, 4)
+    i = nditer([None, a], [], [['writeonly', 'allocate'], ['readonly']],
+                        op_dtypes=[np.dtype('u4'), None],
+                        op_axes=[[1, 2, 0], None])
+    assert_equal(i.operands[0].shape, (4, 2, 3))
+    assert_equal(i.operands[0].strides, (4, 48, 16))
+    assert_equal(i.operands[0].dtype, np.dtype('u4'))
+
+def test_iter_allocate_output_types_promotion():
+    # Check type promotion of automatic outputs (this was more interesting
+    # before NEP 50...)
+
+    i = nditer([array([3], dtype='f4'), array([0], dtype='f8'), None], [],
+                    [['readonly']] * 2 + [['writeonly', 'allocate']])
+    assert_equal(i.dtypes[2], np.dtype('f8'))
+    i = nditer([array([3], dtype='i4'), array([0], dtype='f4'), None], [],
+                    [['readonly']] * 2 + [['writeonly', 'allocate']])
+    assert_equal(i.dtypes[2], np.dtype('f8'))
+    i = nditer([array([3], dtype='f4'), array(0, dtype='f8'), None], [],
+                    [['readonly']] * 2 + [['writeonly', 'allocate']])
+    assert_equal(i.dtypes[2], np.dtype('f8'))
+    i = nditer([array([3], dtype='u4'), array(0, dtype='i4'), None], [],
+                    [['readonly']] * 2 + [['writeonly', 'allocate']])
+    assert_equal(i.dtypes[2], np.dtype('i8'))
+    i = nditer([array([3], dtype='u4'), array(-12, dtype='i4'), None], [],
+                    [['readonly']] * 2 + [['writeonly', 'allocate']])
+    assert_equal(i.dtypes[2], np.dtype('i8'))
+
+def test_iter_allocate_output_types_byte_order():
+    # Verify the rules for byte order changes
+
+    # When there's just one input, the output type exactly matches
+    a = array([3], dtype='u4')
+    a = a.view(a.dtype.newbyteorder())
+    i = nditer([a, None], [],
+                    [['readonly'], ['writeonly', 'allocate']])
+    assert_equal(i.dtypes[0], i.dtypes[1])
+    # With two or more inputs, the output type is in native byte order
+    i = nditer([a, a, None], [],
+                    [['readonly'], ['readonly'], ['writeonly', 'allocate']])
+    assert_(i.dtypes[0] != i.dtypes[2])
+    assert_equal(i.dtypes[0].newbyteorder('='), i.dtypes[2])
+
+def test_iter_allocate_output_types_scalar():
+    # If the inputs are all scalars, the output should be a scalar
+
+    i = nditer([None, 1, 2.3, np.float32(12), np.complex128(3)], [],
+                [['writeonly', 'allocate']] + [['readonly']] * 4)
+    assert_equal(i.operands[0].dtype, np.dtype('complex128'))
+    assert_equal(i.operands[0].ndim, 0)
+
+def test_iter_allocate_output_subtype():
+    # Make sure that the subtype with priority wins
+    class MyNDArray(np.ndarray):
+        __array_priority__ = 15
+
+    # subclass vs ndarray
+    a = np.array([[1, 2], [3, 4]]).view(MyNDArray)
+    b = np.arange(4).reshape(2, 2).T
+    i = nditer([a, b, None], [],
+               [['readonly'], ['readonly'], ['writeonly', 'allocate']])
+    assert_equal(type(a), type(i.operands[2]))
+    assert_(type(b) is not type(i.operands[2]))
+    assert_equal(i.operands[2].shape, (2, 2))
+
+    # If subtypes are disabled, we should get back an ndarray.
+    i = nditer([a, b, None], [],
+               [['readonly'], ['readonly'],
+                ['writeonly', 'allocate', 'no_subtype']])
+    assert_equal(type(b), type(i.operands[2]))
+    assert_(type(a) is not type(i.operands[2]))
+    assert_equal(i.operands[2].shape, (2, 2))
+
+def test_iter_allocate_output_errors():
+    # Check that the iterator will throw errors for bad output allocations
+
+    # Need an input if no output data type is specified
+    a = arange(6)
+    assert_raises(TypeError, nditer, [a, None], [],
+                        [['writeonly'], ['writeonly', 'allocate']])
+    # Allocated output should be flagged for writing
+    assert_raises(ValueError, nditer, [a, None], [],
+                        [['readonly'], ['allocate', 'readonly']])
+    # Allocated output can't have buffering without delayed bufalloc
+    assert_raises(ValueError, nditer, [a, None], ['buffered'],
+                                            ['allocate', 'readwrite'])
+    # Must specify dtype if there are no inputs (cannot promote existing ones;
+    # maybe this should use the 'f4' here, but it does not historically.)
+    assert_raises(TypeError, nditer, [None, None], [],
+                        [['writeonly', 'allocate'],
+                         ['writeonly', 'allocate']],
+                        op_dtypes=[None, np.dtype('f4')])
+    # If using op_axes, must specify all the axes
+    a = arange(24, dtype='i4').reshape(2, 3, 4)
+    assert_raises(ValueError, nditer, [a, None], [],
+                        [['readonly'], ['writeonly', 'allocate']],
+                        op_dtypes=[None, np.dtype('f4')],
+                        op_axes=[None, [0, np.newaxis, 1]])
+    # If using op_axes, the axes must be within bounds
+    assert_raises(ValueError, nditer, [a, None], [],
+                        [['readonly'], ['writeonly', 'allocate']],
+                        op_dtypes=[None, np.dtype('f4')],
+                        op_axes=[None, [0, 3, 1]])
+    # If using op_axes, there can't be duplicates
+    assert_raises(ValueError, nditer, [a, None], [],
+                        [['readonly'], ['writeonly', 'allocate']],
+                        op_dtypes=[None, np.dtype('f4')],
+                        op_axes=[None, [0, 2, 1, 0]])
+    # Not all axes may be specified if a reduction. If there is a hole
+    # in op_axes, this is an error.
+    a = arange(24, dtype='i4').reshape(2, 3, 4)
+    assert_raises(ValueError, nditer, [a, None], ["reduce_ok"],
+                        [['readonly'], ['readwrite', 'allocate']],
+                        op_dtypes=[None, np.dtype('f4')],
+                        op_axes=[None, [0, np.newaxis, 2]])
+
+def test_all_allocated():
+    # When no output and no shape is given, `()` is used as shape.
+    i = np.nditer([None], op_dtypes=["int64"])
+    assert i.operands[0].shape == ()
+    assert i.dtypes == (np.dtype("int64"),)
+
+    i = np.nditer([None], op_dtypes=["int64"], itershape=(2, 3, 4))
+    assert i.operands[0].shape == (2, 3, 4)
+
+def test_iter_remove_axis():
+    a = arange(24).reshape(2, 3, 4)
+
+    i = nditer(a, ['multi_index'])
+    i.remove_axis(1)
+    assert_equal(list(i), a[:, 0, :].ravel())
+
+    a = a[::-1, :, :]
+    i = nditer(a, ['multi_index'])
+    i.remove_axis(0)
+    assert_equal(list(i), a[0, :, :].ravel())
+
+def test_iter_remove_multi_index_inner_loop():
+    # Check that removing multi-index support works
+
+    a = arange(24).reshape(2, 3, 4)
+
+    i = nditer(a, ['multi_index'])
+    assert_equal(i.ndim, 3)
+    assert_equal(i.shape, (2, 3, 4))
+    assert_equal(i.itviews[0].shape, (2, 3, 4))
+
+    # Removing the multi-index tracking causes all dimensions to coalesce
+    before = list(i)
+    i.remove_multi_index()
+    after = list(i)
+
+    assert_equal(before, after)
+    assert_equal(i.ndim, 1)
+    assert_raises(ValueError, lambda i: i.shape, i)
+    assert_equal(i.itviews[0].shape, (24,))
+
+    # Removing the inner loop means there's just one iteration
+    i.reset()
+    assert_equal(i.itersize, 24)
+    assert_equal(i[0].shape, ())
+    i.enable_external_loop()
+    assert_equal(i.itersize, 24)
+    assert_equal(i[0].shape, (24,))
+    assert_equal(i.value, arange(24))
+
+def test_iter_iterindex():
+    # Make sure iterindex works
+
+    buffersize = 5
+    a = arange(24).reshape(4, 3, 2)
+    for flags in ([], ['buffered']):
+        i = nditer(a, flags, buffersize=buffersize)
+        assert_equal(iter_iterindices(i), list(range(24)))
+        i.iterindex = 2
+        assert_equal(iter_iterindices(i), list(range(2, 24)))
+
+        i = nditer(a, flags, order='F', buffersize=buffersize)
+        assert_equal(iter_iterindices(i), list(range(24)))
+        i.iterindex = 5
+        assert_equal(iter_iterindices(i), list(range(5, 24)))
+
+        i = nditer(a[::-1], flags, order='F', buffersize=buffersize)
+        assert_equal(iter_iterindices(i), list(range(24)))
+        i.iterindex = 9
+        assert_equal(iter_iterindices(i), list(range(9, 24)))
+
+        i = nditer(a[::-1, ::-1], flags, order='C', buffersize=buffersize)
+        assert_equal(iter_iterindices(i), list(range(24)))
+        i.iterindex = 13
+        assert_equal(iter_iterindices(i), list(range(13, 24)))
+
+        i = nditer(a[::1, ::-1], flags, buffersize=buffersize)
+        assert_equal(iter_iterindices(i), list(range(24)))
+        i.iterindex = 23
+        assert_equal(iter_iterindices(i), list(range(23, 24)))
+        i.reset()
+        i.iterindex = 2
+        assert_equal(iter_iterindices(i), list(range(2, 24)))
+
+def test_iter_iterrange():
+    # Make sure getting and resetting the iterrange works
+
+    buffersize = 5
+    a = arange(24, dtype='i4').reshape(4, 3, 2)
+    a_fort = a.ravel(order='F')
+
+    i = nditer(a, ['ranged'], ['readonly'], order='F',
+                buffersize=buffersize)
+    assert_equal(i.iterrange, (0, 24))
+    assert_equal([x[()] for x in i], a_fort)
+    for r in [(0, 24), (1, 2), (3, 24), (5, 5), (0, 20), (23, 24)]:
+        i.iterrange = r
+        assert_equal(i.iterrange, r)
+        assert_equal([x[()] for x in i], a_fort[r[0]:r[1]])
+
+    i = nditer(a, ['ranged', 'buffered'], ['readonly'], order='F',
+                op_dtypes='f8', buffersize=buffersize)
+    assert_equal(i.iterrange, (0, 24))
+    assert_equal([x[()] for x in i], a_fort)
+    for r in [(0, 24), (1, 2), (3, 24), (5, 5), (0, 20), (23, 24)]:
+        i.iterrange = r
+        assert_equal(i.iterrange, r)
+        assert_equal([x[()] for x in i], a_fort[r[0]:r[1]])
+
+    def get_array(i):
+        val = np.array([], dtype='f8')
+        for x in i:
+            val = np.concatenate((val, x))
+        return val
+
+    i = nditer(a, ['ranged', 'buffered', 'external_loop'],
+                ['readonly'], order='F',
+                op_dtypes='f8', buffersize=buffersize)
+    assert_equal(i.iterrange, (0, 24))
+    assert_equal(get_array(i), a_fort)
+    for r in [(0, 24), (1, 2), (3, 24), (5, 5), (0, 20), (23, 24)]:
+        i.iterrange = r
+        assert_equal(i.iterrange, r)
+        assert_equal(get_array(i), a_fort[r[0]:r[1]])
+
+def test_iter_buffering():
+    # Test buffering with several buffer sizes and types
+    arrays = []
+    # F-order swapped array
+    _tmp = np.arange(24, dtype='c16').reshape(2, 3, 4).T
+    _tmp = _tmp.view(_tmp.dtype.newbyteorder()).byteswap()
+    arrays.append(_tmp)
+    # Contiguous 1-dimensional array
+    arrays.append(np.arange(10, dtype='f4'))
+    # Unaligned array
+    a = np.zeros((4 * 16 + 1,), dtype='i1')[1:]
+    a.dtype = 'i4'
+    a[:] = np.arange(16, dtype='i4')
+    arrays.append(a)
+    # 4-D F-order array
+    arrays.append(np.arange(120, dtype='i4').reshape(5, 3, 2, 4).T)
+    for a in arrays:
+        for buffersize in (1, 2, 3, 5, 8, 11, 16, 1024):
+            vals = []
+            i = nditer(a, ['buffered', 'external_loop'],
+                           [['readonly', 'nbo', 'aligned']],
+                           order='C',
+                           casting='equiv',
+                           buffersize=buffersize)
+            while not i.finished:
+                assert_(i[0].size <= buffersize)
+                vals.append(i[0].copy())
+                i.iternext()
+            assert_equal(np.concatenate(vals), a.ravel(order='C'))
+
+def test_iter_write_buffering():
+    # Test that buffering of writes is working
+
+    # F-order swapped array
+    a = np.arange(24).reshape(2, 3, 4).T
+    a = a.view(a.dtype.newbyteorder()).byteswap()
+    i = nditer(a, ['buffered'],
+                   [['readwrite', 'nbo', 'aligned']],
+                   casting='equiv',
+                   order='C',
+                   buffersize=16)
+    x = 0
+    with i:
+        while not i.finished:
+            i[0] = x
+            x += 1
+            i.iternext()
+    assert_equal(a.ravel(order='C'), np.arange(24))
+
+def test_iter_buffering_delayed_alloc():
+    # Test that delaying buffer allocation works
+
+    a = np.arange(6)
+    b = np.arange(1, dtype='f4')
+    i = nditer([a, b], ['buffered', 'delay_bufalloc', 'multi_index', 'reduce_ok'],
+                    ['readwrite'],
+                    casting='unsafe',
+                    op_dtypes='f4')
+    assert_(i.has_delayed_bufalloc)
+    assert_raises(ValueError, lambda i: i.multi_index, i)
+    assert_raises(ValueError, lambda i: i[0], i)
+    assert_raises(ValueError, lambda i: i[0:2], i)
+
+    def assign_iter(i):
+        i[0] = 0
+    assert_raises(ValueError, assign_iter, i)
+
+    i.reset()
+    assert_(not i.has_delayed_bufalloc)
+    assert_equal(i.multi_index, (0,))
+    with i:
+        assert_equal(i[0], 0)
+        i[1] = 1
+        assert_equal(i[0:2], [0, 1])
+        assert_equal([[x[0][()], x[1][()]] for x in i], list(zip(range(6), [1] * 6)))
+
+def test_iter_buffered_cast_simple():
+    # Test that buffering can handle a simple cast
+
+    a = np.arange(10, dtype='f4')
+    i = nditer(a, ['buffered', 'external_loop'],
+                   [['readwrite', 'nbo', 'aligned']],
+                   casting='same_kind',
+                   op_dtypes=[np.dtype('f8')],
+                   buffersize=3)
+    with i:
+        for v in i:
+            v[...] *= 2
+
+    assert_equal(a, 2 * np.arange(10, dtype='f4'))
+
+def test_iter_buffered_cast_byteswapped():
+    # Test that buffering can handle a cast which requires swap->cast->swap
+
+    a = np.arange(10, dtype='f4')
+    a = a.view(a.dtype.newbyteorder()).byteswap()
+    i = nditer(a, ['buffered', 'external_loop'],
+                   [['readwrite', 'nbo', 'aligned']],
+                   casting='same_kind',
+                   op_dtypes=[np.dtype('f8').newbyteorder()],
+                   buffersize=3)
+    with i:
+        for v in i:
+            v[...] *= 2
+
+    assert_equal(a, 2 * np.arange(10, dtype='f4'))
+
+    with suppress_warnings() as sup:
+        sup.filter(np.exceptions.ComplexWarning)
+
+        a = np.arange(10, dtype='f8')
+        a = a.view(a.dtype.newbyteorder()).byteswap()
+        i = nditer(a, ['buffered', 'external_loop'],
+                       [['readwrite', 'nbo', 'aligned']],
+                       casting='unsafe',
+                       op_dtypes=[np.dtype('c8').newbyteorder()],
+                       buffersize=3)
+        with i:
+            for v in i:
+                v[...] *= 2
+
+        assert_equal(a, 2 * np.arange(10, dtype='f8'))
+
+def test_iter_buffered_cast_byteswapped_complex():
+    # Test that buffering can handle a cast which requires swap->cast->copy
+
+    a = np.arange(10, dtype='c8')
+    a = a.view(a.dtype.newbyteorder()).byteswap()
+    a += 2j
+    i = nditer(a, ['buffered', 'external_loop'],
+                   [['readwrite', 'nbo', 'aligned']],
+                   casting='same_kind',
+                   op_dtypes=[np.dtype('c16')],
+                   buffersize=3)
+    with i:
+        for v in i:
+            v[...] *= 2
+    assert_equal(a, 2 * np.arange(10, dtype='c8') + 4j)
+
+    a = np.arange(10, dtype='c8')
+    a += 2j
+    i = nditer(a, ['buffered', 'external_loop'],
+                   [['readwrite', 'nbo', 'aligned']],
+                   casting='same_kind',
+                   op_dtypes=[np.dtype('c16').newbyteorder()],
+                   buffersize=3)
+    with i:
+        for v in i:
+            v[...] *= 2
+    assert_equal(a, 2 * np.arange(10, dtype='c8') + 4j)
+
+    a = np.arange(10, dtype=np.clongdouble)
+    a = a.view(a.dtype.newbyteorder()).byteswap()
+    a += 2j
+    i = nditer(a, ['buffered', 'external_loop'],
+                   [['readwrite', 'nbo', 'aligned']],
+                   casting='same_kind',
+                   op_dtypes=[np.dtype('c16')],
+                   buffersize=3)
+    with i:
+        for v in i:
+            v[...] *= 2
+    assert_equal(a, 2 * np.arange(10, dtype=np.clongdouble) + 4j)
+
+    a = np.arange(10, dtype=np.longdouble)
+    a = a.view(a.dtype.newbyteorder()).byteswap()
+    i = nditer(a, ['buffered', 'external_loop'],
+                   [['readwrite', 'nbo', 'aligned']],
+                   casting='same_kind',
+                   op_dtypes=[np.dtype('f4')],
+                   buffersize=7)
+    with i:
+        for v in i:
+            v[...] *= 2
+    assert_equal(a, 2 * np.arange(10, dtype=np.longdouble))
+
+def test_iter_buffered_cast_structured_type():
+    # Tests buffering of structured types
+
+    # simple -> struct type (duplicates the value)
+    sdt = [('a', 'f4'), ('b', 'i8'), ('c', 'c8', (2, 3)), ('d', 'O')]
+    a = np.arange(3, dtype='f4') + 0.5
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt)
+    vals = [np.array(x) for x in i]
+    assert_equal(vals[0]['a'], 0.5)
+    assert_equal(vals[0]['b'], 0)
+    assert_equal(vals[0]['c'], [[(0.5)] * 3] * 2)
+    assert_equal(vals[0]['d'], 0.5)
+    assert_equal(vals[1]['a'], 1.5)
+    assert_equal(vals[1]['b'], 1)
+    assert_equal(vals[1]['c'], [[(1.5)] * 3] * 2)
+    assert_equal(vals[1]['d'], 1.5)
+    assert_equal(vals[0].dtype, np.dtype(sdt))
+
+    # object -> struct type
+    sdt = [('a', 'f4'), ('b', 'i8'), ('c', 'c8', (2, 3)), ('d', 'O')]
+    a = np.zeros((3,), dtype='O')
+    a[0] = (0.5, 0.5, [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]], 0.5)
+    a[1] = (1.5, 1.5, [[1.5, 1.5, 1.5], [1.5, 1.5, 1.5]], 1.5)
+    a[2] = (2.5, 2.5, [[2.5, 2.5, 2.5], [2.5, 2.5, 2.5]], 2.5)
+    if HAS_REFCOUNT:
+        rc = sys.getrefcount(a[0])
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt)
+    vals = [x.copy() for x in i]
+    assert_equal(vals[0]['a'], 0.5)
+    assert_equal(vals[0]['b'], 0)
+    assert_equal(vals[0]['c'], [[(0.5)] * 3] * 2)
+    assert_equal(vals[0]['d'], 0.5)
+    assert_equal(vals[1]['a'], 1.5)
+    assert_equal(vals[1]['b'], 1)
+    assert_equal(vals[1]['c'], [[(1.5)] * 3] * 2)
+    assert_equal(vals[1]['d'], 1.5)
+    assert_equal(vals[0].dtype, np.dtype(sdt))
+    vals, i, x = [None] * 3
+    if HAS_REFCOUNT:
+        assert_equal(sys.getrefcount(a[0]), rc)
+
+    # single-field struct type -> simple
+    sdt = [('a', 'f4')]
+    a = np.array([(5.5,), (8,)], dtype=sdt)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes='i4')
+    assert_equal([x_[()] for x_ in i], [5, 8])
+
+    # make sure multi-field struct type -> simple doesn't work
+    sdt = [('a', 'f4'), ('b', 'i8'), ('d', 'O')]
+    a = np.array([(5.5, 7, 'test'), (8, 10, 11)], dtype=sdt)
+    assert_raises(TypeError, lambda: (
+        nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+               casting='unsafe',
+               op_dtypes='i4')))
+
+    # struct type -> struct type (field-wise copy)
+    sdt1 = [('a', 'f4'), ('b', 'i8'), ('d', 'O')]
+    sdt2 = [('d', 'u2'), ('a', 'O'), ('b', 'f8')]
+    a = np.array([(1, 2, 3), (4, 5, 6)], dtype=sdt1)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    assert_equal([np.array(x_) for x_ in i],
+                 [np.array((1, 2, 3), dtype=sdt2),
+                  np.array((4, 5, 6), dtype=sdt2)])
+
+
+def test_iter_buffered_cast_structured_type_failure_with_cleanup():
+    # make sure struct type -> struct type with different
+    # number of fields fails
+    sdt1 = [('a', 'f4'), ('b', 'i8'), ('d', 'O')]
+    sdt2 = [('b', 'O'), ('a', 'f8')]
+    a = np.array([(1, 2, 3), (4, 5, 6)], dtype=sdt1)
+
+    for intent in ["readwrite", "readonly", "writeonly"]:
+        # This test was initially designed to test an error at a different
+        # place, but will now raise earlier to to the cast not being possible:
+        # `assert np.can_cast(a.dtype, sdt2, casting="unsafe")` fails.
+        # Without a faulty DType, there is probably no reliable
+        # way to get the initial tested behaviour.
+        simple_arr = np.array([1, 2], dtype="i,i")  # requires clean up
+        with pytest.raises(TypeError):
+            nditer((simple_arr, a), ['buffered', 'refs_ok'], [intent, intent],
+                   casting='unsafe', op_dtypes=["f,f", sdt2])
+
+
+def test_buffered_cast_error_paths():
+    with pytest.raises(ValueError):
+        # The input is cast into an `S3` buffer
+        np.nditer((np.array("a", dtype="S1"),), op_dtypes=["i"],
+                  casting="unsafe", flags=["buffered"])
+
+    # The `M8[ns]` is cast into the `S3` output
+    it = np.nditer((np.array(1, dtype="i"),), op_dtypes=["S1"],
+                   op_flags=["writeonly"], casting="unsafe", flags=["buffered"])
+    with pytest.raises(ValueError):
+        with it:
+            buf = next(it)
+            buf[...] = "a"  # cannot be converted to int.
+
+@pytest.mark.skipif(IS_WASM, reason="Cannot start subprocess")
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="PyPy seems to not hit this.")
+def test_buffered_cast_error_paths_unraisable():
+    # The following gives an unraisable error. Pytest sometimes captures that
+    # (depending python and/or pytest version). So with Python>=3.8 this can
+    # probably be cleaned out in the future to check for
+    # pytest.PytestUnraisableExceptionWarning:
+    code = textwrap.dedent("""
+        import numpy as np
+
+        it = np.nditer((np.array(1, dtype="i"),), op_dtypes=["S1"],
+                       op_flags=["writeonly"], casting="unsafe", flags=["buffered"])
+        buf = next(it)
+        buf[...] = "a"
+        del buf, it  # Flushing only happens during deallocate right now.
+        """)
+    res = subprocess.check_output([sys.executable, "-c", code],
+                                  stderr=subprocess.STDOUT, text=True)
+    assert "ValueError" in res
+
+
+def test_iter_buffered_cast_subarray():
+    # Tests buffering of subarrays
+
+    # one element -> many (copies it to all)
+    sdt1 = [('a', 'f4')]
+    sdt2 = [('a', 'f8', (3, 2, 2))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'] = np.arange(6)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    for x, count in zip(i, list(range(6))):
+        assert_(np.all(x['a'] == count))
+
+    # one element -> many -> back (copies it to all)
+    sdt1 = [('a', 'O', (1, 1))]
+    sdt2 = [('a', 'O', (3, 2, 2))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'][:, 0, 0] = np.arange(6)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readwrite'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    with i:
+        assert_equal(i[0].dtype, np.dtype(sdt2))
+        count = 0
+        for x in i:
+            assert_(np.all(x['a'] == count))
+            x['a'][0] += 2
+            count += 1
+    assert_equal(a['a'], np.arange(6).reshape(6, 1, 1) + 2)
+
+    # many -> one element -> back (copies just element 0)
+    sdt1 = [('a', 'O', (3, 2, 2))]
+    sdt2 = [('a', 'O', (1,))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'][:, 0, 0, 0] = np.arange(6)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readwrite'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    with i:
+        assert_equal(i[0].dtype, np.dtype(sdt2))
+        count = 0
+        for x in i:
+            assert_equal(x['a'], count)
+            x['a'] += 2
+            count += 1
+    assert_equal(a['a'], np.arange(6).reshape(6, 1, 1, 1) * np.ones((1, 3, 2, 2)) + 2)
+
+    # many -> one element -> back (copies just element 0)
+    sdt1 = [('a', 'f8', (3, 2, 2))]
+    sdt2 = [('a', 'O', (1,))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'][:, 0, 0, 0] = np.arange(6)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    count = 0
+    for x in i:
+        assert_equal(x['a'], count)
+        count += 1
+
+    # many -> one element (copies just element 0)
+    sdt1 = [('a', 'O', (3, 2, 2))]
+    sdt2 = [('a', 'f4', (1,))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'][:, 0, 0, 0] = np.arange(6)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    count = 0
+    for x in i:
+        assert_equal(x['a'], count)
+        count += 1
+
+    # many -> matching shape (straightforward copy)
+    sdt1 = [('a', 'O', (3, 2, 2))]
+    sdt2 = [('a', 'f4', (3, 2, 2))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'] = np.arange(6 * 3 * 2 * 2).reshape(6, 3, 2, 2)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    count = 0
+    for x in i:
+        assert_equal(x['a'], a[count]['a'])
+        count += 1
+
+    # vector -> smaller vector (truncates)
+    sdt1 = [('a', 'f8', (6,))]
+    sdt2 = [('a', 'f4', (2,))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'] = np.arange(6 * 6).reshape(6, 6)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    count = 0
+    for x in i:
+        assert_equal(x['a'], a[count]['a'][:2])
+        count += 1
+
+    # vector -> bigger vector (pads with zeros)
+    sdt1 = [('a', 'f8', (2,))]
+    sdt2 = [('a', 'f4', (6,))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'] = np.arange(6 * 2).reshape(6, 2)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    count = 0
+    for x in i:
+        assert_equal(x['a'][:2], a[count]['a'])
+        assert_equal(x['a'][2:], [0, 0, 0, 0])
+        count += 1
+
+    # vector -> matrix (broadcasts)
+    sdt1 = [('a', 'f8', (2,))]
+    sdt2 = [('a', 'f4', (2, 2))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'] = np.arange(6 * 2).reshape(6, 2)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    count = 0
+    for x in i:
+        assert_equal(x['a'][0], a[count]['a'])
+        assert_equal(x['a'][1], a[count]['a'])
+        count += 1
+
+    # vector -> matrix (broadcasts and zero-pads)
+    sdt1 = [('a', 'f8', (2, 1))]
+    sdt2 = [('a', 'f4', (3, 2))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'] = np.arange(6 * 2).reshape(6, 2, 1)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    count = 0
+    for x in i:
+        assert_equal(x['a'][:2, 0], a[count]['a'][:, 0])
+        assert_equal(x['a'][:2, 1], a[count]['a'][:, 0])
+        assert_equal(x['a'][2, :], [0, 0])
+        count += 1
+
+    # matrix -> matrix (truncates and zero-pads)
+    sdt1 = [('a', 'f8', (2, 3))]
+    sdt2 = [('a', 'f4', (3, 2))]
+    a = np.zeros((6,), dtype=sdt1)
+    a['a'] = np.arange(6 * 2 * 3).reshape(6, 2, 3)
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe',
+                    op_dtypes=sdt2)
+    assert_equal(i[0].dtype, np.dtype(sdt2))
+    count = 0
+    for x in i:
+        assert_equal(x['a'][:2, 0], a[count]['a'][:, 0])
+        assert_equal(x['a'][:2, 1], a[count]['a'][:, 1])
+        assert_equal(x['a'][2, :], [0, 0])
+        count += 1
+
+def test_iter_buffering_badwriteback():
+    # Writing back from a buffer cannot combine elements
+
+    # a needs write buffering, but had a broadcast dimension
+    a = np.arange(6).reshape(2, 3, 1)
+    b = np.arange(12).reshape(2, 3, 2)
+    assert_raises(ValueError, nditer, [a, b],
+                  ['buffered', 'external_loop'],
+                  [['readwrite'], ['writeonly']],
+                  order='C')
+
+    # But if a is readonly, it's fine
+    nditer([a, b], ['buffered', 'external_loop'],
+           [['readonly'], ['writeonly']],
+           order='C')
+
+    # If a has just one element, it's fine too (constant 0 stride, a reduction)
+    a = np.arange(1).reshape(1, 1, 1)
+    nditer([a, b], ['buffered', 'external_loop', 'reduce_ok'],
+           [['readwrite'], ['writeonly']],
+           order='C')
+
+    # check that it fails on other dimensions too
+    a = np.arange(6).reshape(1, 3, 2)
+    assert_raises(ValueError, nditer, [a, b],
+                  ['buffered', 'external_loop'],
+                  [['readwrite'], ['writeonly']],
+                  order='C')
+    a = np.arange(4).reshape(2, 1, 2)
+    assert_raises(ValueError, nditer, [a, b],
+                  ['buffered', 'external_loop'],
+                  [['readwrite'], ['writeonly']],
+                  order='C')
+
+def test_iter_buffering_string():
+    # Safe casting disallows shrinking strings
+    a = np.array(['abc', 'a', 'abcd'], dtype=np.bytes_)
+    assert_equal(a.dtype, np.dtype('S4'))
+    assert_raises(TypeError, nditer, a, ['buffered'], ['readonly'],
+                  op_dtypes='S2')
+    i = nditer(a, ['buffered'], ['readonly'], op_dtypes='S6')
+    assert_equal(i[0], b'abc')
+    assert_equal(i[0].dtype, np.dtype('S6'))
+
+    a = np.array(['abc', 'a', 'abcd'], dtype=np.str_)
+    assert_equal(a.dtype, np.dtype('U4'))
+    assert_raises(TypeError, nditer, a, ['buffered'], ['readonly'],
+                    op_dtypes='U2')
+    i = nditer(a, ['buffered'], ['readonly'], op_dtypes='U6')
+    assert_equal(i[0], 'abc')
+    assert_equal(i[0].dtype, np.dtype('U6'))
+
+def test_iter_buffering_growinner():
+    # Test that the inner loop grows when no buffering is needed
+    a = np.arange(30)
+    i = nditer(a, ['buffered', 'growinner', 'external_loop'],
+                           buffersize=5)
+    # Should end up with just one inner loop here
+    assert_equal(i[0].size, a.size)
+
+
+@pytest.mark.parametrize("read_or_readwrite", ["readonly", "readwrite"])
+def test_iter_contig_flag_reduce_error(read_or_readwrite):
+    # Test that a non-contiguous operand is rejected without buffering.
+    # NOTE: This is true even for a reduction, where we return a 0-stride
+    #       below!
+    with pytest.raises(TypeError, match="Iterator operand required buffering"):
+        it = np.nditer(
+            (np.zeros(()),), flags=["external_loop", "reduce_ok"],
+            op_flags=[(read_or_readwrite, "contig"),], itershape=(10,))
+
+
+@pytest.mark.parametrize("arr", [
+        lambda: np.zeros(()),
+        lambda: np.zeros((20, 1))[::20],
+        lambda: np.zeros((1, 20))[:, ::20]
+    ])
+def test_iter_contig_flag_single_operand_strides(arr):
+    """
+    Tests the strides with the contig flag for both broadcast and non-broadcast
+    operands in 3 cases where the logic is needed:
+    1. When everything has a zero stride, the broadcast op needs to repeated
+    2. When the reduce axis is the last axis (first to iterate).
+    3. When the reduce axis is the first axis (last to iterate).
+
+    NOTE: The semantics of the cast flag are not clearly defined when
+          it comes to reduction.  It is unclear that there are any users.
+    """
+    first_op = np.ones((10, 10))
+    broadcast_op = arr()
+    red_op = arr()
+    # Add a first operand to ensure no axis-reordering and the result shape.
+    iterator = np.nditer(
+        (first_op, broadcast_op, red_op),
+        flags=["external_loop", "reduce_ok", "buffered", "delay_bufalloc"],
+        op_flags=[("readonly", "contig")] * 2 + [("readwrite", "contig")])
+
+    with iterator:
+        iterator.reset()
+        for f, b, r in iterator:
+            # The first operand is contigouos, we should have a view
+            assert np.shares_memory(f, first_op)
+            # Although broadcast, the second op always has a contiguous stride
+            assert b.strides[0] == 8
+            assert not np.shares_memory(b, broadcast_op)
+            # The reduction has a contiguous stride or a 0 stride
+            if red_op.ndim == 0 or red_op.shape[-1] == 1:
+                assert r.strides[0] == 0
+            else:
+                # The stride is 8, although it was not originally:
+                assert r.strides[0] == 8
+            # If the reduce stride is 0, buffering makes no difference, but we
+            # do it anyway right now:
+            assert not np.shares_memory(r, red_op)
+
+
+@pytest.mark.xfail(reason="The contig flag was always buggy.")
+def test_iter_contig_flag_incorrect():
+    # This case does the wrong thing...
+    iterator = np.nditer(
+        (np.ones((10, 10)).T, np.ones((1, 10))),
+        flags=["external_loop", "reduce_ok", "buffered", "delay_bufalloc"],
+        op_flags=[("readonly", "contig")] * 2)
+
+    with iterator:
+        iterator.reset()
+        for a, b in iterator:
+            # Remove a and b from locals (pytest may want to format them)
+            a, b = a.strides, b.strides
+            assert a == 8
+            assert b == 8  # should be 8 but is 0 due to axis reorder
+
+
+@pytest.mark.slow
+def test_iter_buffered_reduce_reuse():
+    # large enough array for all views, including negative strides.
+    a = np.arange(2 * 3**5)[3**5:3**5 + 1]
+    flags = ['buffered', 'delay_bufalloc', 'multi_index', 'reduce_ok', 'refs_ok']
+    op_flags = [('readonly',), ('readwrite', 'allocate')]
+    op_axes_list = [[(0, 1, 2), (0, 1, -1)], [(0, 1, 2), (0, -1, -1)]]
+    # wrong dtype to force buffering
+    op_dtypes = [float, a.dtype]
+
+    def get_params():
+        for xs in range(-3**2, 3**2 + 1):
+            for ys in range(xs, 3**2 + 1):
+                for op_axes in op_axes_list:
+                    # last stride is reduced and because of that not
+                    # important for this test, as it is the inner stride.
+                    strides = (xs * a.itemsize, ys * a.itemsize, a.itemsize)
+                    arr = np.lib.stride_tricks.as_strided(a, (3, 3, 3), strides)
+
+                    for skip in [0, 1]:
+                        yield arr, op_axes, skip
+
+    for arr, op_axes, skip in get_params():
+        nditer2 = np.nditer([arr.copy(), None],
+                            op_axes=op_axes, flags=flags, op_flags=op_flags,
+                            op_dtypes=op_dtypes)
+        with nditer2:
+            nditer2.operands[-1][...] = 0
+            nditer2.reset()
+            nditer2.iterindex = skip
+
+            for (a2_in, b2_in) in nditer2:
+                b2_in += a2_in.astype(np.int_)
+
+            comp_res = nditer2.operands[-1]
+
+        for bufsize in range(3**3):
+            nditer1 = np.nditer([arr, None],
+                                op_axes=op_axes, flags=flags, op_flags=op_flags,
+                                buffersize=bufsize, op_dtypes=op_dtypes)
+            with nditer1:
+                nditer1.operands[-1][...] = 0
+                nditer1.reset()
+                nditer1.iterindex = skip
+
+                for (a1_in, b1_in) in nditer1:
+                    b1_in += a1_in.astype(np.int_)
+
+                res = nditer1.operands[-1]
+            assert_array_equal(res, comp_res)
+
+
+def test_iter_buffered_reduce_reuse_core():
+    # NumPy re-uses buffers for broadcast operands (as of writing when reading).
+    # Test this even if the offset is manually set at some point during
+    # the iteration.  (not a particularly tricky path)
+    arr = np.empty((1, 6, 4, 1)).reshape(1, 6, 4, 1)[:, ::3, ::2, :]
+    arr[...] = np.arange(arr.size).reshape(arr.shape)
+    # First and last dimension are broadcast dimensions.
+    arr = np.broadcast_to(arr, (100, 2, 2, 2))
+
+    flags = ['buffered', 'reduce_ok', 'refs_ok', 'multi_index']
+    op_flags = [('readonly',)]
+
+    buffersize = 100  # small enough to not fit the whole array
+    it = np.nditer(arr, flags=flags, op_flags=op_flags, buffersize=100)
+
+    # Iterate a bit (this will cause buffering internally)
+    expected = [next(it) for i in range(11)]
+    # Now, manually advance to inside the core (the +1)
+    it.iterindex = 10 * (2 * 2 * 2) + 1
+    result = [next(it) for i in range(10)]
+
+    assert expected[1:] == result
+
+
+def test_iter_no_broadcast():
+    # Test that the no_broadcast flag works
+    a = np.arange(24).reshape(2, 3, 4)
+    b = np.arange(6).reshape(2, 3, 1)
+    c = np.arange(12).reshape(3, 4)
+
+    nditer([a, b, c], [],
+           [['readonly', 'no_broadcast'],
+            ['readonly'], ['readonly']])
+    assert_raises(ValueError, nditer, [a, b, c], [],
+                  [['readonly'], ['readonly', 'no_broadcast'], ['readonly']])
+    assert_raises(ValueError, nditer, [a, b, c], [],
+                  [['readonly'], ['readonly'], ['readonly', 'no_broadcast']])
+
+
+class TestIterNested:
+
+    def test_basic(self):
+        # Test nested iteration basic usage
+        a = arange(12).reshape(2, 3, 2)
+
+        i, j = np.nested_iters(a, [[0], [1, 2]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 1, 2, 3, 4, 5], [6, 7, 8, 9, 10, 11]])
+
+        i, j = np.nested_iters(a, [[0, 1], [2]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11]])
+
+        i, j = np.nested_iters(a, [[0, 2], [1]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 2, 4], [1, 3, 5], [6, 8, 10], [7, 9, 11]])
+
+    def test_reorder(self):
+        # Test nested iteration basic usage
+        a = arange(12).reshape(2, 3, 2)
+
+        # In 'K' order (default), it gets reordered
+        i, j = np.nested_iters(a, [[0], [2, 1]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 1, 2, 3, 4, 5], [6, 7, 8, 9, 10, 11]])
+
+        i, j = np.nested_iters(a, [[1, 0], [2]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11]])
+
+        i, j = np.nested_iters(a, [[2, 0], [1]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 2, 4], [1, 3, 5], [6, 8, 10], [7, 9, 11]])
+
+        # In 'C' order, it doesn't
+        i, j = np.nested_iters(a, [[0], [2, 1]], order='C')
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 2, 4, 1, 3, 5], [6, 8, 10, 7, 9, 11]])
+
+        i, j = np.nested_iters(a, [[1, 0], [2]], order='C')
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 1], [6, 7], [2, 3], [8, 9], [4, 5], [10, 11]])
+
+        i, j = np.nested_iters(a, [[2, 0], [1]], order='C')
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 2, 4], [6, 8, 10], [1, 3, 5], [7, 9, 11]])
+
+    def test_flip_axes(self):
+        # Test nested iteration with negative axes
+        a = arange(12).reshape(2, 3, 2)[::-1, ::-1, ::-1]
+
+        # In 'K' order (default), the axes all get flipped
+        i, j = np.nested_iters(a, [[0], [1, 2]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 1, 2, 3, 4, 5], [6, 7, 8, 9, 10, 11]])
+
+        i, j = np.nested_iters(a, [[0, 1], [2]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11]])
+
+        i, j = np.nested_iters(a, [[0, 2], [1]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 2, 4], [1, 3, 5], [6, 8, 10], [7, 9, 11]])
+
+        # In 'C' order, flipping axes is disabled
+        i, j = np.nested_iters(a, [[0], [1, 2]], order='C')
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[11, 10, 9, 8, 7, 6], [5, 4, 3, 2, 1, 0]])
+
+        i, j = np.nested_iters(a, [[0, 1], [2]], order='C')
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[11, 10], [9, 8], [7, 6], [5, 4], [3, 2], [1, 0]])
+
+        i, j = np.nested_iters(a, [[0, 2], [1]], order='C')
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[11, 9, 7], [10, 8, 6], [5, 3, 1], [4, 2, 0]])
+
+    def test_broadcast(self):
+        # Test nested iteration with broadcasting
+        a = arange(2).reshape(2, 1)
+        b = arange(3).reshape(1, 3)
+
+        i, j = np.nested_iters([a, b], [[0], [1]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[[0, 0], [0, 1], [0, 2]], [[1, 0], [1, 1], [1, 2]]])
+
+        i, j = np.nested_iters([a, b], [[1], [0]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[[0, 0], [1, 0]], [[0, 1], [1, 1]], [[0, 2], [1, 2]]])
+
+    def test_dtype_copy(self):
+        # Test nested iteration with a copy to change dtype
+
+        # copy
+        a = arange(6, dtype='i4').reshape(2, 3)
+        i, j = np.nested_iters(a, [[0], [1]],
+                            op_flags=['readonly', 'copy'],
+                            op_dtypes='f8')
+        assert_equal(j[0].dtype, np.dtype('f8'))
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 1, 2], [3, 4, 5]])
+        vals = None
+
+        # writebackifcopy - using context manager
+        a = arange(6, dtype='f4').reshape(2, 3)
+        i, j = np.nested_iters(a, [[0], [1]],
+                            op_flags=['readwrite', 'updateifcopy'],
+                            casting='same_kind',
+                            op_dtypes='f8')
+        with i, j:
+            assert_equal(j[0].dtype, np.dtype('f8'))
+            for x in i:
+                for y in j:
+                    y[...] += 1
+            assert_equal(a, [[0, 1, 2], [3, 4, 5]])
+        assert_equal(a, [[1, 2, 3], [4, 5, 6]])
+
+        # writebackifcopy - using close()
+        a = arange(6, dtype='f4').reshape(2, 3)
+        i, j = np.nested_iters(a, [[0], [1]],
+                            op_flags=['readwrite', 'updateifcopy'],
+                            casting='same_kind',
+                            op_dtypes='f8')
+        assert_equal(j[0].dtype, np.dtype('f8'))
+        for x in i:
+            for y in j:
+                y[...] += 1
+        assert_equal(a, [[0, 1, 2], [3, 4, 5]])
+        i.close()
+        j.close()
+        assert_equal(a, [[1, 2, 3], [4, 5, 6]])
+
+    def test_dtype_buffered(self):
+        # Test nested iteration with buffering to change dtype
+
+        a = arange(6, dtype='f4').reshape(2, 3)
+        i, j = np.nested_iters(a, [[0], [1]],
+                            flags=['buffered'],
+                            op_flags=['readwrite'],
+                            casting='same_kind',
+                            op_dtypes='f8')
+        assert_equal(j[0].dtype, np.dtype('f8'))
+        for x in i:
+            for y in j:
+                y[...] += 1
+        assert_equal(a, [[1, 2, 3], [4, 5, 6]])
+
+    def test_0d(self):
+        a = np.arange(12).reshape(2, 3, 2)
+        i, j = np.nested_iters(a, [[], [1, 0, 2]])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]])
+
+        i, j = np.nested_iters(a, [[1, 0, 2], []])
+        vals = [list(j) for _ in i]
+        assert_equal(vals, [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]])
+
+        i, j, k = np.nested_iters(a, [[2, 0], [], [1]])
+        vals = []
+        for x in i:
+            for y in j:
+                vals.append(list(k))
+        assert_equal(vals, [[0, 2, 4], [1, 3, 5], [6, 8, 10], [7, 9, 11]])
+
+    def test_iter_nested_iters_dtype_buffered(self):
+        # Test nested iteration with buffering to change dtype
+
+        a = arange(6, dtype='f4').reshape(2, 3)
+        i, j = np.nested_iters(a, [[0], [1]],
+                            flags=['buffered'],
+                            op_flags=['readwrite'],
+                            casting='same_kind',
+                            op_dtypes='f8')
+        with i, j:
+            assert_equal(j[0].dtype, np.dtype('f8'))
+            for x in i:
+                for y in j:
+                    y[...] += 1
+        assert_equal(a, [[1, 2, 3], [4, 5, 6]])
+
+def test_iter_reduction_error():
+
+    a = np.arange(6)
+    assert_raises(ValueError, nditer, [a, None], [],
+                    [['readonly'], ['readwrite', 'allocate']],
+                    op_axes=[[0], [-1]])
+
+    a = np.arange(6).reshape(2, 3)
+    assert_raises(ValueError, nditer, [a, None], ['external_loop'],
+                    [['readonly'], ['readwrite', 'allocate']],
+                    op_axes=[[0, 1], [-1, -1]])
+
+def test_iter_reduction():
+    # Test doing reductions with the iterator
+
+    a = np.arange(6)
+    i = nditer([a, None], ['reduce_ok'],
+                    [['readonly'], ['readwrite', 'allocate']],
+                    op_axes=[[0], [-1]])
+    # Need to initialize the output operand to the addition unit
+    with i:
+        i.operands[1][...] = 0
+        # Do the reduction
+        for x, y in i:
+            y[...] += x
+        # Since no axes were specified, should have allocated a scalar
+        assert_equal(i.operands[1].ndim, 0)
+        assert_equal(i.operands[1], np.sum(a))
+
+    a = np.arange(6).reshape(2, 3)
+    i = nditer([a, None], ['reduce_ok', 'external_loop'],
+                    [['readonly'], ['readwrite', 'allocate']],
+                    op_axes=[[0, 1], [-1, -1]])
+    # Need to initialize the output operand to the addition unit
+    with i:
+        i.operands[1][...] = 0
+        # Reduction shape/strides for the output
+        assert_equal(i[1].shape, (6,))
+        assert_equal(i[1].strides, (0,))
+        # Do the reduction
+        for x, y in i:
+            # Use a for loop instead of ``y[...] += x``
+            # (equivalent to ``y[...] = y[...].copy() + x``),
+            # because y has zero strides we use for the reduction
+            for j in range(len(y)):
+                y[j] += x[j]
+        # Since no axes were specified, should have allocated a scalar
+        assert_equal(i.operands[1].ndim, 0)
+        assert_equal(i.operands[1], np.sum(a))
+
+    # This is a tricky reduction case for the buffering double loop
+    # to handle
+    a = np.ones((2, 3, 5))
+    it1 = nditer([a, None], ['reduce_ok', 'external_loop'],
+                    [['readonly'], ['readwrite', 'allocate']],
+                    op_axes=[None, [0, -1, 1]])
+    it2 = nditer([a, None], ['reduce_ok', 'external_loop',
+                            'buffered', 'delay_bufalloc'],
+                    [['readonly'], ['readwrite', 'allocate']],
+                    op_axes=[None, [0, -1, 1]], buffersize=10)
+    with it1, it2:
+        it1.operands[1].fill(0)
+        it2.operands[1].fill(0)
+        it2.reset()
+        for x in it1:
+            x[1][...] += x[0]
+        for x in it2:
+            x[1][...] += x[0]
+        assert_equal(it1.operands[1], it2.operands[1])
+        assert_equal(it2.operands[1].sum(), a.size)
+
+def test_iter_buffering_reduction():
+    # Test doing buffered reductions with the iterator
+
+    a = np.arange(6)
+    b = np.array(0., dtype='f8').byteswap()
+    b = b.view(b.dtype.newbyteorder())
+    i = nditer([a, b], ['reduce_ok', 'buffered'],
+                    [['readonly'], ['readwrite', 'nbo']],
+                    op_axes=[[0], [-1]])
+    with i:
+        assert_equal(i[1].dtype, np.dtype('f8'))
+        assert_(i[1].dtype != b.dtype)
+        # Do the reduction
+        for x, y in i:
+            y[...] += x
+    # Since no axes were specified, should have allocated a scalar
+    assert_equal(b, np.sum(a))
+
+    a = np.arange(6).reshape(2, 3)
+    b = np.array([0, 0], dtype='f8').byteswap()
+    b = b.view(b.dtype.newbyteorder())
+    i = nditer([a, b], ['reduce_ok', 'external_loop', 'buffered'],
+                    [['readonly'], ['readwrite', 'nbo']],
+                    op_axes=[[0, 1], [0, -1]])
+    # Reduction shape/strides for the output
+    with i:
+        assert_equal(i[1].shape, (3,))
+        assert_equal(i[1].strides, (0,))
+        # Do the reduction
+        for x, y in i:
+            # Use a for loop instead of ``y[...] += x``
+            # (equivalent to ``y[...] = y[...].copy() + x``),
+            # because y has zero strides we use for the reduction
+            for j in range(len(y)):
+                y[j] += x[j]
+    assert_equal(b, np.sum(a, axis=1))
+
+    # Iterator inner double loop was wrong on this one
+    p = np.arange(2) + 1
+    it = np.nditer([p, None],
+            ['delay_bufalloc', 'reduce_ok', 'buffered', 'external_loop'],
+            [['readonly'], ['readwrite', 'allocate']],
+            op_axes=[[-1, 0], [-1, -1]],
+            itershape=(2, 2))
+    with it:
+        it.operands[1].fill(0)
+        it.reset()
+        assert_equal(it[0], [1, 2, 1, 2])
+
+    # Iterator inner loop should take argument contiguity into account
+    x = np.ones((7, 13, 8), np.int8)[4:6, 1:11:6, 1:5].transpose(1, 2, 0)
+    x[...] = np.arange(x.size).reshape(x.shape)
+    y_base = np.arange(4 * 4, dtype=np.int8).reshape(4, 4)
+    y_base_copy = y_base.copy()
+    y = y_base[::2, :, None]
+
+    it = np.nditer([y, x],
+                   ['buffered', 'external_loop', 'reduce_ok'],
+                   [['readwrite'], ['readonly']])
+    with it:
+        for a, b in it:
+            a.fill(2)
+
+    assert_equal(y_base[1::2], y_base_copy[1::2])
+    assert_equal(y_base[::2], 2)
+
+def test_iter_buffering_reduction_reuse_reduce_loops():
+    # There was a bug triggering reuse of the reduce loop inappropriately,
+    # which caused processing to happen in unnecessarily small chunks
+    # and overran the buffer.
+
+    a = np.zeros((2, 7))
+    b = np.zeros((1, 7))
+    it = np.nditer([a, b], flags=['reduce_ok', 'external_loop', 'buffered'],
+                    op_flags=[['readonly'], ['readwrite']],
+                    buffersize=5)
+
+    with it:
+        bufsizes = [x.shape[0] for x, y in it]
+    assert_equal(bufsizes, [5, 2, 5, 2])
+    assert_equal(sum(bufsizes), a.size)
+
+def test_iter_writemasked_badinput():
+    a = np.zeros((2, 3))
+    b = np.zeros((3,))
+    m = np.array([[True, True, False], [False, True, False]])
+    m2 = np.array([True, True, False])
+    m3 = np.array([0, 1, 1], dtype='u1')
+    mbad1 = np.array([0, 1, 1], dtype='i1')
+    mbad2 = np.array([0, 1, 1], dtype='f4')
+
+    # Need an 'arraymask' if any operand is 'writemasked'
+    assert_raises(ValueError, nditer, [a, m], [],
+                    [['readwrite', 'writemasked'], ['readonly']])
+
+    # A 'writemasked' operand must not be readonly
+    assert_raises(ValueError, nditer, [a, m], [],
+                    [['readonly', 'writemasked'], ['readonly', 'arraymask']])
+
+    # 'writemasked' and 'arraymask' may not be used together
+    assert_raises(ValueError, nditer, [a, m], [],
+                    [['readonly'], ['readwrite', 'arraymask', 'writemasked']])
+
+    # 'arraymask' may only be specified once
+    assert_raises(ValueError, nditer, [a, m, m2], [],
+                    [['readwrite', 'writemasked'],
+                     ['readonly', 'arraymask'],
+                     ['readonly', 'arraymask']])
+
+    # An 'arraymask' with nothing 'writemasked' also doesn't make sense
+    assert_raises(ValueError, nditer, [a, m], [],
+                    [['readwrite'], ['readonly', 'arraymask']])
+
+    # A writemasked reduction requires a similarly smaller mask
+    assert_raises(ValueError, nditer, [a, b, m], ['reduce_ok'],
+                    [['readonly'],
+                     ['readwrite', 'writemasked'],
+                     ['readonly', 'arraymask']])
+    # But this should work with a smaller/equal mask to the reduction operand
+    np.nditer([a, b, m2], ['reduce_ok'],
+                    [['readonly'],
+                     ['readwrite', 'writemasked'],
+                     ['readonly', 'arraymask']])
+    # The arraymask itself cannot be a reduction
+    assert_raises(ValueError, nditer, [a, b, m2], ['reduce_ok'],
+                    [['readonly'],
+                     ['readwrite', 'writemasked'],
+                     ['readwrite', 'arraymask']])
+
+    # A uint8 mask is ok too
+    np.nditer([a, m3], ['buffered'],
+                    [['readwrite', 'writemasked'],
+                     ['readonly', 'arraymask']],
+                    op_dtypes=['f4', None],
+                    casting='same_kind')
+    # An int8 mask isn't ok
+    assert_raises(TypeError, np.nditer, [a, mbad1], ['buffered'],
+                    [['readwrite', 'writemasked'],
+                     ['readonly', 'arraymask']],
+                    op_dtypes=['f4', None],
+                    casting='same_kind')
+    # A float32 mask isn't ok
+    assert_raises(TypeError, np.nditer, [a, mbad2], ['buffered'],
+                    [['readwrite', 'writemasked'],
+                     ['readonly', 'arraymask']],
+                    op_dtypes=['f4', None],
+                    casting='same_kind')
+
+
+def _is_buffered(iterator):
+    try:
+        iterator.itviews
+    except ValueError:
+        return True
+    return False
+
+@pytest.mark.parametrize("a",
+        [np.zeros((3,), dtype='f8'),
+         np.zeros((9876, 3 * 5), dtype='f8')[::2, :],
+         np.zeros((4, 312, 124, 3), dtype='f8')[::2, :, ::2, :],
+         # Also test with the last dimension strided (so it does not fit if
+         # there is repeated access)
+         np.zeros((9,), dtype='f8')[::3],
+         np.zeros((9876, 3 * 10), dtype='f8')[::2, ::5],
+         np.zeros((4, 312, 124, 3), dtype='f8')[::2, :, ::2, ::-1]])
+def test_iter_writemasked(a):
+    # Note, the slicing above is to ensure that nditer cannot combine multiple
+    # axes into one.  The repetition is just to make things a bit more
+    # interesting.
+    shape = a.shape
+    reps = shape[-1] // 3
+    msk = np.empty(shape, dtype=bool)
+    msk[...] = [True, True, False] * reps
+
+    # When buffering is unused, 'writemasked' effectively does nothing.
+    # It's up to the user of the iterator to obey the requested semantics.
+    it = np.nditer([a, msk], [],
+                [['readwrite', 'writemasked'],
+                 ['readonly', 'arraymask']])
+    with it:
+        for x, m in it:
+            x[...] = 1
+    # Because we violated the semantics, all the values became 1
+    assert_equal(a, np.broadcast_to([1, 1, 1] * reps, shape))
+
+    # Even if buffering is enabled, we still may be accessing the array
+    # directly.
+    it = np.nditer([a, msk], ['buffered'],
+                [['readwrite', 'writemasked'],
+                 ['readonly', 'arraymask']])
+    # @seberg: I honestly don't currently understand why a "buffered" iterator
+    # would end up not using a buffer for the small array here at least when
+    # "writemasked" is used, that seems confusing...  Check by testing for
+    # actual memory overlap!
+    is_buffered = True
+    with it:
+        for x, m in it:
+            x[...] = 2.5
+            if np.may_share_memory(x, a):
+                is_buffered = False
+
+    if not is_buffered:
+        # Because we violated the semantics, all the values became 2.5
+        assert_equal(a, np.broadcast_to([2.5, 2.5, 2.5] * reps, shape))
+    else:
+        # For large sizes, the iterator may be buffered:
+        assert_equal(a, np.broadcast_to([2.5, 2.5, 1] * reps, shape))
+        a[...] = 2.5
+
+    # If buffering will definitely happening, for instance because of
+    # a cast, only the items selected by the mask will be copied back from
+    # the buffer.
+    it = np.nditer([a, msk], ['buffered'],
+                [['readwrite', 'writemasked'],
+                 ['readonly', 'arraymask']],
+                op_dtypes=['i8', None],
+                casting='unsafe')
+    with it:
+        for x, m in it:
+            x[...] = 3
+    # Even though we violated the semantics, only the selected values
+    # were copied back
+    assert_equal(a, np.broadcast_to([3, 3, 2.5] * reps, shape))
+
+
+@pytest.mark.parametrize(["mask", "mask_axes"], [
+        # Allocated operand (only broadcasts with -1)
+        (None, [-1, 0]),
+        # Reduction along the first dimension (with and without op_axes)
+        (np.zeros((1, 4), dtype="bool"), [0, 1]),
+        (np.zeros((1, 4), dtype="bool"), None),
+        # Test 0-D and -1 op_axes
+        (np.zeros(4, dtype="bool"), [-1, 0]),
+        (np.zeros((), dtype="bool"), [-1, -1]),
+        (np.zeros((), dtype="bool"), None)])
+def test_iter_writemasked_broadcast_error(mask, mask_axes):
+    # This assumes that a readwrite mask makes sense. This is likely not the
+    # case and should simply be deprecated.
+    arr = np.zeros((3, 4))
+    itflags = ["reduce_ok"]
+    mask_flags = ["arraymask", "readwrite", "allocate"]
+    a_flags = ["writeonly", "writemasked"]
+    if mask_axes is None:
+        op_axes = None
+    else:
+        op_axes = [mask_axes, [0, 1]]
+
+    with assert_raises(ValueError):
+        np.nditer((mask, arr), flags=itflags, op_flags=[mask_flags, a_flags],
+                  op_axes=op_axes)
+
+
+def test_iter_writemasked_decref():
+    # force casting (to make it interesting) by using a structured dtype.
+    arr = np.arange(10000).astype(">i,O")
+    original = arr.copy()
+    mask = np.random.randint(0, 2, size=10000).astype(bool)
+
+    it = np.nditer([arr, mask], ['buffered', "refs_ok"],
+                   [['readwrite', 'writemasked'],
+                    ['readonly', 'arraymask']],
+                   op_dtypes=["<i,O", "?"])
+    singleton = object()
+    if HAS_REFCOUNT:
+        count = sys.getrefcount(singleton)
+    for buf, mask_buf in it:
+        buf[...] = (3, singleton)
+
+    del buf, mask_buf, it   # delete everything to ensure correct cleanup
+
+    if HAS_REFCOUNT:
+        # The buffer would have included additional items, they must be
+        # cleared correctly:
+        assert sys.getrefcount(singleton) - count == np.count_nonzero(mask)
+
+    assert_array_equal(arr[~mask], original[~mask])
+    assert (arr[mask] == np.array((3, singleton), arr.dtype)).all()
+    del arr
+
+    if HAS_REFCOUNT:
+        assert sys.getrefcount(singleton) == count
+
+
+def test_iter_non_writable_attribute_deletion():
+    it = np.nditer(np.ones(2))
+    attr = ["value", "shape", "operands", "itviews", "has_delayed_bufalloc",
+            "iterationneedsapi", "has_multi_index", "has_index", "dtypes",
+            "ndim", "nop", "itersize", "finished"]
+
+    for s in attr:
+        assert_raises(AttributeError, delattr, it, s)
+
+
+def test_iter_writable_attribute_deletion():
+    it = np.nditer(np.ones(2))
+    attr = ["multi_index", "index", "iterrange", "iterindex"]
+    for s in attr:
+        assert_raises(AttributeError, delattr, it, s)
+
+
+def test_iter_element_deletion():
+    it = np.nditer(np.ones(3))
+    try:
+        del it[1]
+        del it[1:2]
+    except TypeError:
+        pass
+    except Exception:
+        raise AssertionError
+
+def test_iter_allocated_array_dtypes():
+    # If the dtype of an allocated output has a shape, the shape gets
+    # tacked onto the end of the result.
+    it = np.nditer(([1, 3, 20], None), op_dtypes=[None, ('i4', (2,))])
+    for a, b in it:
+        b[0] = a - 1
+        b[1] = a + 1
+    assert_equal(it.operands[1], [[0, 2], [2, 4], [19, 21]])
+
+    # Check the same (less sensitive) thing when `op_axes` with -1 is given.
+    it = np.nditer(([[1, 3, 20]], None), op_dtypes=[None, ('i4', (2,))],
+                   flags=["reduce_ok"], op_axes=[None, (-1, 0)])
+    for a, b in it:
+        b[0] = a - 1
+        b[1] = a + 1
+    assert_equal(it.operands[1], [[0, 2], [2, 4], [19, 21]])
+
+    # Make sure this works for scalars too
+    it = np.nditer((10, 2, None), op_dtypes=[None, None, ('i4', (2, 2))])
+    for a, b, c in it:
+        c[0, 0] = a - b
+        c[0, 1] = a + b
+        c[1, 0] = a * b
+        c[1, 1] = a / b
+    assert_equal(it.operands[2], [[8, 12], [20, 5]])
+
+
+def test_0d_iter():
+    # Basic test for iteration of 0-d arrays:
+    i = nditer([2, 3], ['multi_index'], [['readonly']] * 2)
+    assert_equal(i.ndim, 0)
+    assert_equal(next(i), (2, 3))
+    assert_equal(i.multi_index, ())
+    assert_equal(i.iterindex, 0)
+    assert_raises(StopIteration, next, i)
+    # test reset:
+    i.reset()
+    assert_equal(next(i), (2, 3))
+    assert_raises(StopIteration, next, i)
+
+    # test forcing to 0-d
+    i = nditer(np.arange(5), ['multi_index'], [['readonly']], op_axes=[()])
+    assert_equal(i.ndim, 0)
+    assert_equal(len(i), 1)
+
+    i = nditer(np.arange(5), ['multi_index'], [['readonly']],
+               op_axes=[()], itershape=())
+    assert_equal(i.ndim, 0)
+    assert_equal(len(i), 1)
+
+    # passing an itershape alone is not enough, the op_axes are also needed
+    with assert_raises(ValueError):
+        nditer(np.arange(5), ['multi_index'], [['readonly']], itershape=())
+
+    # Test a more complex buffered casting case (same as another test above)
+    sdt = [('a', 'f4'), ('b', 'i8'), ('c', 'c8', (2, 3)), ('d', 'O')]
+    a = np.array(0.5, dtype='f4')
+    i = nditer(a, ['buffered', 'refs_ok'], ['readonly'],
+                    casting='unsafe', op_dtypes=sdt)
+    vals = next(i)
+    assert_equal(vals['a'], 0.5)
+    assert_equal(vals['b'], 0)
+    assert_equal(vals['c'], [[(0.5)] * 3] * 2)
+    assert_equal(vals['d'], 0.5)
+
+def test_object_iter_cleanup():
+    # see gh-18450
+    # object arrays can raise a python exception in ufunc inner loops using
+    # nditer, which should cause iteration to stop & cleanup. There were bugs
+    # in the nditer cleanup when decref'ing object arrays.
+    # This test would trigger valgrind "uninitialized read" before the bugfix.
+    assert_raises(TypeError, lambda: np.zeros((17000, 2), dtype='f4') * None)
+
+    # this more explicit code also triggers the invalid access
+    arr = np.arange(ncu.BUFSIZE * 10).reshape(10, -1).astype(str)
+    oarr = arr.astype(object)
+    oarr[:, -1] = None
+    assert_raises(TypeError, lambda: np.add(oarr[:, ::-1], arr[:, ::-1]))
+
+    # followup: this tests for a bug introduced in the first pass of gh-18450,
+    # caused by an incorrect fallthrough of the TypeError
+    class T:
+        def __bool__(self):
+            raise TypeError("Ambiguous")
+    assert_raises(TypeError, np.logical_or.reduce,
+                             np.array([T(), T()], dtype='O'))
+
+def test_object_iter_cleanup_reduce():
+    # Similar as above, but a complex reduction case that was previously
+    # missed (see gh-18810).
+    # The following array is special in that it cannot be flattened:
+    arr = np.array([[None, 1], [-1, -1], [None, 2], [-1, -1]])[::2]
+    with pytest.raises(TypeError):
+        np.sum(arr)
+
+@pytest.mark.parametrize("arr", [
+        np.ones((8000, 4, 2), dtype=object)[:, ::2, :],
+        np.ones((8000, 4, 2), dtype=object, order="F")[:, ::2, :],
+        np.ones((8000, 4, 2), dtype=object)[:, ::2, :].copy("F")])
+def test_object_iter_cleanup_large_reduce(arr):
+    # More complicated calls are possible for large arrays:
+    out = np.ones(8000, dtype=np.intp)
+    # force casting with `dtype=object`
+    res = np.sum(arr, axis=(1, 2), dtype=object, out=out)
+    assert_array_equal(res, np.full(8000, 4, dtype=object))
+
+def test_iter_too_large():
+    # The total size of the iterator must not exceed the maximum intp due
+    # to broadcasting. Dividing by 1024 will keep it small enough to
+    # give a legal array.
+    size = np.iinfo(np.intp).max // 1024
+    arr = np.lib.stride_tricks.as_strided(np.zeros(1), (size,), (0,))
+    assert_raises(ValueError, nditer, (arr, arr[:, None]))
+    # test the same for multiindex. That may get more interesting when
+    # removing 0 dimensional axis is allowed (since an iterator can grow then)
+    assert_raises(ValueError, nditer,
+                  (arr, arr[:, None]), flags=['multi_index'])
+
+
+def test_iter_too_large_with_multiindex():
+    # When a multi index is being tracked, the error is delayed this
+    # checks the delayed error messages and getting below that by
+    # removing an axis.
+    base_size = 2**10
+    num = 1
+    while base_size**num < np.iinfo(np.intp).max:
+        num += 1
+
+    shape_template = [1, 1] * num
+    arrays = []
+    for i in range(num):
+        shape = shape_template[:]
+        shape[i * 2] = 2**10
+        arrays.append(np.empty(shape))
+    arrays = tuple(arrays)
+
+    # arrays are now too large to be broadcast. The different modes test
+    # different nditer functionality with or without GIL.
+    for mode in range(6):
+        with assert_raises(ValueError):
+            _multiarray_tests.test_nditer_too_large(arrays, -1, mode)
+    # but if we do nothing with the nditer, it can be constructed:
+    _multiarray_tests.test_nditer_too_large(arrays, -1, 7)
+
+    # When an axis is removed, things should work again (half the time):
+    for i in range(num):
+        for mode in range(6):
+            # an axis with size 1024 is removed:
+            _multiarray_tests.test_nditer_too_large(arrays, i * 2, mode)
+            # an axis with size 1 is removed:
+            with assert_raises(ValueError):
+                _multiarray_tests.test_nditer_too_large(arrays, i * 2 + 1, mode)
+
+def test_writebacks():
+    a = np.arange(6, dtype='f4')
+    au = a.byteswap()
+    au = au.view(au.dtype.newbyteorder())
+    assert_(a.dtype.byteorder != au.dtype.byteorder)
+    it = nditer(au, [], [['readwrite', 'updateifcopy']],
+                        casting='equiv', op_dtypes=[np.dtype('f4')])
+    with it:
+        it.operands[0][:] = 100
+    assert_equal(au, 100)
+    # do it again, this time raise an error,
+    it = nditer(au, [], [['readwrite', 'updateifcopy']],
+                        casting='equiv', op_dtypes=[np.dtype('f4')])
+    try:
+        with it:
+            assert_equal(au.flags.writeable, False)
+            it.operands[0][:] = 0
+            raise ValueError('exit context manager on exception')
+    except Exception:
+        pass
+    assert_equal(au, 0)
+    assert_equal(au.flags.writeable, True)
+    # cannot reuse i outside context manager
+    assert_raises(ValueError, getattr, it, 'operands')
+
+    it = nditer(au, [], [['readwrite', 'updateifcopy']],
+                        casting='equiv', op_dtypes=[np.dtype('f4')])
+    with it:
+        x = it.operands[0]
+        x[:] = 6
+        assert_(x.flags.writebackifcopy)
+    assert_equal(au, 6)
+    assert_(not x.flags.writebackifcopy)
+    x[:] = 123  # x.data still valid
+    assert_equal(au, 6)  # but not connected to au
+
+    it = nditer(au, [],
+                 [['readwrite', 'updateifcopy']],
+                 casting='equiv', op_dtypes=[np.dtype('f4')])
+    # reentering works
+    with it:
+        with it:
+            for x in it:
+                x[...] = 123
+
+    it = nditer(au, [],
+                 [['readwrite', 'updateifcopy']],
+                 casting='equiv', op_dtypes=[np.dtype('f4')])
+    # make sure exiting the inner context manager closes the iterator
+    with it:
+        with it:
+            for x in it:
+                x[...] = 123
+        assert_raises(ValueError, getattr, it, 'operands')
+    # do not crash if original data array is decrefed
+    it = nditer(au, [],
+                 [['readwrite', 'updateifcopy']],
+                 casting='equiv', op_dtypes=[np.dtype('f4')])
+    del au
+    with it:
+        for x in it:
+            x[...] = 123
+    # make sure we cannot reenter the closed iterator
+    enter = it.__enter__
+    assert_raises(RuntimeError, enter)
+
+def test_close_equivalent():
+    ''' using a context amanger and using nditer.close are equivalent
+    '''
+    def add_close(x, y, out=None):
+        addop = np.add
+        it = np.nditer([x, y, out], [],
+                    [['readonly'], ['readonly'], ['writeonly', 'allocate']])
+        for (a, b, c) in it:
+            addop(a, b, out=c)
+        ret = it.operands[2]
+        it.close()
+        return ret
+
+    def add_context(x, y, out=None):
+        addop = np.add
+        it = np.nditer([x, y, out], [],
+                    [['readonly'], ['readonly'], ['writeonly', 'allocate']])
+        with it:
+            for (a, b, c) in it:
+                addop(a, b, out=c)
+            return it.operands[2]
+    z = add_close(range(5), range(5))
+    assert_equal(z, range(0, 10, 2))
+    z = add_context(range(5), range(5))
+    assert_equal(z, range(0, 10, 2))
+
+def test_close_raises():
+    it = np.nditer(np.arange(3))
+    assert_equal(next(it), 0)
+    it.close()
+    assert_raises(StopIteration, next, it)
+    assert_raises(ValueError, getattr, it, 'operands')
+
+def test_close_parameters():
+    it = np.nditer(np.arange(3))
+    assert_raises(TypeError, it.close, 1)
+
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+def test_warn_noclose():
+    a = np.arange(6, dtype='f4')
+    au = a.byteswap()
+    au = au.view(au.dtype.newbyteorder())
+    with suppress_warnings() as sup:
+        sup.record(RuntimeWarning)
+        it = np.nditer(au, [], [['readwrite', 'updateifcopy']],
+                        casting='equiv', op_dtypes=[np.dtype('f4')])
+        del it
+        assert len(sup.log) == 1
+
+
+@pytest.mark.parametrize(["in_dtype", "buf_dtype"],
+        [("i", "O"), ("O", "i"),  # most simple cases
+         ("i,O", "O,O"),  # structured partially only copying O
+         ("O,i", "i,O"),  # structured casting to and from O
+         ])
+@pytest.mark.parametrize("steps", [1, 2, 3])
+def test_partial_iteration_cleanup(in_dtype, buf_dtype, steps):
+    """
+    Checks for reference counting leaks during cleanup.  Using explicit
+    reference counts lead to occasional false positives (at least in parallel
+    test setups).  This test now should still test leaks correctly when
+    run e.g. with pytest-valgrind or pytest-leaks
+    """
+    value = 2**30 + 1  # just a random value that Python won't intern
+    arr = np.full(int(ncu.BUFSIZE * 2.5), value).astype(in_dtype)
+
+    it = np.nditer(arr, op_dtypes=[np.dtype(buf_dtype)],
+            flags=["buffered", "external_loop", "refs_ok"], casting="unsafe")
+    for step in range(steps):
+        # The iteration finishes in 3 steps, the first two are partial
+        next(it)
+
+    del it  # not necessary, but we test the cleanup
+
+    # Repeat the test with `iternext`
+    it = np.nditer(arr, op_dtypes=[np.dtype(buf_dtype)],
+                   flags=["buffered", "external_loop", "refs_ok"], casting="unsafe")
+    for step in range(steps):
+        it.iternext()
+
+    del it  # not necessary, but we test the cleanup
+
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+@pytest.mark.parametrize(["in_dtype", "buf_dtype"],
+         [("O", "i"),  # most simple cases
+          ("O,i", "i,O"),  # structured casting to and from O
+          ])
+def test_partial_iteration_error(in_dtype, buf_dtype):
+    value = 123  # relies on python cache (leak-check will still find it)
+    arr = np.full(int(ncu.BUFSIZE * 2.5), value).astype(in_dtype)
+    if in_dtype == "O":
+        arr[int(ncu.BUFSIZE * 1.5)] = None
+    else:
+        arr[int(ncu.BUFSIZE * 1.5)]["f0"] = None
+
+    count = sys.getrefcount(value)
+
+    it = np.nditer(arr, op_dtypes=[np.dtype(buf_dtype)],
+            flags=["buffered", "external_loop", "refs_ok"], casting="unsafe")
+    with pytest.raises(TypeError):
+        # pytest.raises seems to have issues with the error originating
+        # in the for loop, so manually unravel:
+        next(it)
+        next(it)  # raises TypeError
+
+    # Repeat the test with `iternext` after resetting, the buffers should
+    # already be cleared from any references, so resetting is sufficient.
+    it.reset()
+    with pytest.raises(TypeError):
+        it.iternext()
+        it.iternext()
+
+    assert count == sys.getrefcount(value)
+
+
+def test_arbitrary_number_of_ops():
+    # 2*16 + 1 is still just a few kiB, so should be fast and easy to deal with
+    # but larger than any small custom integer.
+    ops = [np.arange(10) for a in range(2**16 + 1)]
+
+    it = np.nditer(ops)
+    for i, vals in enumerate(it):
+        assert all(v == i for v in vals)
+
+
+def test_arbitrary_number_of_ops_nested():
+    # 2*16 + 1 is still just a few kiB, so should be fast and easy to deal with
+    # but larger than any small custom integer.
+    ops = [np.arange(10) for a in range(2**16 + 1)]
+
+    it = np.nested_iters(ops, [[0], []])
+    for i, vals in enumerate(it):
+        assert all(v == i for v in vals)
+
+
+@pytest.mark.slow
+@requires_memory(9 * np.iinfo(np.intc).max)
+def test_arbitrary_number_of_ops_error():
+    # A different error may happen for more than integer operands, but that
+    # is too large to test nicely.
+    a = np.ones(1)
+    args = [a] * (np.iinfo(np.intc).max + 1)
+    with pytest.raises(ValueError, match="Too many operands to nditer"):
+        np.nditer(args)
+
+    with pytest.raises(ValueError, match="Too many operands to nditer"):
+        np.nested_iters(args, [[0], []])
+
+
+def test_debug_print(capfd):
+    """
+    Matches the expected output of a debug print with the actual output.
+    Note that the iterator dump should not be considered stable API,
+    this test is mainly to ensure the print does not crash.
+
+    Currently uses a subprocess to avoid dealing with the C level `printf`s.
+    """
+    # the expected output with all addresses and sizes stripped (they vary
+    # and/or are platform dependent).
+    expected = """
+    ------ BEGIN ITERATOR DUMP ------
+    | Iterator Address:
+    | ItFlags: BUFFER REDUCE
+    | NDim: 2
+    | NOp: 2
+    | IterSize: 50
+    | IterStart: 0
+    | IterEnd: 50
+    | IterIndex: 0
+    | Iterator SizeOf:
+    | BufferData SizeOf:
+    | AxisData SizeOf:
+    |
+    | Perm: 0 1
+    | DTypes:
+    | DTypes: dtype('float64') dtype('int32')
+    | InitDataPtrs:
+    | BaseOffsets: 0 0
+    | Ptrs:
+    | User/buffer ptrs:
+    | Operands:
+    | Operand DTypes: dtype('int64') dtype('float64')
+    | OpItFlags:
+    |   Flags[0]: READ CAST
+    |   Flags[1]: READ WRITE CAST REDUCE
+    |
+    | BufferData:
+    |   BufferSize: 50
+    |   Size: 5
+    |   BufIterEnd: 5
+    |   BUFFER CoreSize: 5
+    |   REDUCE Pos: 0
+    |   REDUCE OuterSize: 10
+    |   REDUCE OuterDim: 1
+    |   Strides: 8 4
+    |   REDUCE Outer Strides: 40 0
+    |   REDUCE Outer Ptrs:
+    |   ReadTransferFn:
+    |   ReadTransferData:
+    |   WriteTransferFn:
+    |   WriteTransferData:
+    |   Buffers:
+    |
+    | AxisData[0]:
+    |   Shape: 5
+    |   Index: 0
+    |   Strides: 16 8
+    | AxisData[1]:
+    |   Shape: 10
+    |   Index: 0
+    |   Strides: 80 0
+    ------- END ITERATOR DUMP -------
+    """.strip().splitlines()
+
+    arr1 = np.arange(100, dtype=np.int64).reshape(10, 10)[:, ::2]
+    arr2 = np.arange(5.)
+    it = np.nditer((arr1, arr2), op_dtypes=["d", "i4"], casting="unsafe",
+                   flags=["reduce_ok", "buffered"],
+                   op_flags=[["readonly"], ["readwrite"]])
+    it.debug_print()
+    res = capfd.readouterr().out
+    res = res.strip().splitlines()
+
+    assert len(res) == len(expected)
+    for res_line, expected_line in zip(res, expected):
+        # The actual output may have additional pointers listed that are
+        # stripped from the example output:
+        assert res_line.startswith(expected_line.strip())
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_nep50_promotions.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_nep50_promotions.py
new file mode 100644
index 0000000..8d9d9e6
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_nep50_promotions.py
@@ -0,0 +1,287 @@
+"""
+This file adds basic tests to test the NEP 50 style promotion compatibility
+mode.  Most of these test are likely to be simply deleted again once NEP 50
+is adopted in the main test suite.  A few may be moved elsewhere.
+"""
+
+import operator
+
+import hypothesis
+import pytest
+from hypothesis import strategies
+
+import numpy as np
+from numpy.testing import IS_WASM, assert_array_equal
+
+
+@pytest.mark.skipif(IS_WASM, reason="wasm doesn't have support for fp errors")
+def test_nep50_examples():
+    res = np.uint8(1) + 2
+    assert res.dtype == np.uint8
+
+    res = np.array([1], np.uint8) + np.int64(1)
+    assert res.dtype == np.int64
+
+    res = np.array([1], np.uint8) + np.array(1, dtype=np.int64)
+    assert res.dtype == np.int64
+
+    with pytest.warns(RuntimeWarning, match="overflow"):
+        res = np.uint8(100) + 200
+    assert res.dtype == np.uint8
+
+    with pytest.warns(RuntimeWarning, match="overflow"):
+        res = np.float32(1) + 3e100
+
+    assert np.isinf(res)
+    assert res.dtype == np.float32
+
+    res = np.array([0.1], np.float32) == np.float64(0.1)
+    assert res[0] == False
+
+    res = np.array([0.1], np.float32) + np.float64(0.1)
+    assert res.dtype == np.float64
+
+    res = np.array([1.], np.float32) + np.int64(3)
+    assert res.dtype == np.float64
+
+
+@pytest.mark.parametrize("dtype", np.typecodes["AllInteger"])
+def test_nep50_weak_integers(dtype):
+    # Avoids warning (different code path for scalars)
+    scalar_type = np.dtype(dtype).type
+
+    maxint = int(np.iinfo(dtype).max)
+
+    with np.errstate(over="warn"):
+        with pytest.warns(RuntimeWarning):
+            res = scalar_type(100) + maxint
+    assert res.dtype == dtype
+
+    # Array operations are not expected to warn, but should give the same
+    # result dtype.
+    res = np.array(100, dtype=dtype) + maxint
+    assert res.dtype == dtype
+
+
+@pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
+def test_nep50_weak_integers_with_inexact(dtype):
+    # Avoids warning (different code path for scalars)
+    scalar_type = np.dtype(dtype).type
+
+    too_big_int = int(np.finfo(dtype).max) * 2
+
+    if dtype in "dDG":
+        # These dtypes currently convert to Python float internally, which
+        # raises an OverflowError, while the other dtypes overflow to inf.
+        # NOTE: It may make sense to normalize the behavior!
+        with pytest.raises(OverflowError):
+            scalar_type(1) + too_big_int
+
+        with pytest.raises(OverflowError):
+            np.array(1, dtype=dtype) + too_big_int
+    else:
+        # NumPy uses (or used) `int -> string -> longdouble` for the
+        # conversion.  But Python may refuse `str(int)` for huge ints.
+        # In that case, RuntimeWarning would be correct, but conversion
+        # fails earlier (seems to happen on 32bit linux, possibly only debug).
+        if dtype in "gG":
+            try:
+                str(too_big_int)
+            except ValueError:
+                pytest.skip("`huge_int -> string -> longdouble` failed")
+
+        # Otherwise, we overflow to infinity:
+        with pytest.warns(RuntimeWarning):
+            res = scalar_type(1) + too_big_int
+        assert res.dtype == dtype
+        assert res == np.inf
+
+        with pytest.warns(RuntimeWarning):
+            # We force the dtype here, since windows may otherwise pick the
+            # double instead of the longdouble loop.  That leads to slightly
+            # different results (conversion of the int fails as above).
+            res = np.add(np.array(1, dtype=dtype), too_big_int, dtype=dtype)
+        assert res.dtype == dtype
+        assert res == np.inf
+
+
+@pytest.mark.parametrize("op", [operator.add, operator.pow])
+def test_weak_promotion_scalar_path(op):
+    # Some additional paths exercising the weak scalars.
+
+    # Integer path:
+    res = op(np.uint8(3), 5)
+    assert res == op(3, 5)
+    assert res.dtype == np.uint8 or res.dtype == bool  # noqa: PLR1714
+
+    with pytest.raises(OverflowError):
+        op(np.uint8(3), 1000)
+
+    # Float path:
+    res = op(np.float32(3), 5.)
+    assert res == op(3., 5.)
+    assert res.dtype == np.float32 or res.dtype == bool  # noqa: PLR1714
+
+
+def test_nep50_complex_promotion():
+    with pytest.warns(RuntimeWarning, match=".*overflow"):
+        res = np.complex64(3) + complex(2**300)
+
+    assert type(res) == np.complex64
+
+
+def test_nep50_integer_conversion_errors():
+    # Implementation for error paths is mostly missing (as of writing)
+    with pytest.raises(OverflowError, match=".*uint8"):
+        np.array([1], np.uint8) + 300
+
+    with pytest.raises(OverflowError, match=".*uint8"):
+        np.uint8(1) + 300
+
+    # Error message depends on platform (maybe unsigned int or unsigned long)
+    with pytest.raises(OverflowError,
+            match="Python integer -1 out of bounds for uint8"):
+        np.uint8(1) + -1
+
+
+def test_nep50_with_axisconcatenator():
+    # Concatenate/r_ does not promote, so this has to error:
+    with pytest.raises(OverflowError):
+        np.r_[np.arange(5, dtype=np.int8), 255]
+
+
+@pytest.mark.parametrize("ufunc", [np.add, np.power])
+def test_nep50_huge_integers(ufunc):
+    # Very large integers are complicated, because they go to uint64 or
+    # object dtype.  This tests covers a few possible paths.
+    with pytest.raises(OverflowError):
+        ufunc(np.int64(0), 2**63)  # 2**63 too large for int64
+
+    with pytest.raises(OverflowError):
+        ufunc(np.uint64(0), 2**64)  # 2**64 cannot be represented by uint64
+
+    # However, 2**63 can be represented by the uint64 (and that is used):
+    res = ufunc(np.uint64(1), 2**63)
+
+    assert res.dtype == np.uint64
+    assert res == ufunc(1, 2**63, dtype=object)
+
+    # The following paths fail to warn correctly about the change:
+    with pytest.raises(OverflowError):
+        ufunc(np.int64(1), 2**63)  # np.array(2**63) would go to uint
+
+    with pytest.raises(OverflowError):
+        ufunc(np.int64(1), 2**100)  # np.array(2**100) would go to object
+
+    # This would go to object and thus a Python float, not a NumPy one:
+    res = ufunc(1.0, 2**100)
+    assert isinstance(res, np.float64)
+
+
+def test_nep50_in_concat_and_choose():
+    res = np.concatenate([np.float32(1), 1.], axis=None)
+    assert res.dtype == "float32"
+
+    res = np.choose(1, [np.float32(1), 1.])
+    assert res.dtype == "float32"
+
+
+@pytest.mark.parametrize("expected,dtypes,optional_dtypes", [
+        (np.float32, [np.float32],
+            [np.float16, 0.0, np.uint16, np.int16, np.int8, 0]),
+        (np.complex64, [np.float32, 0j],
+            [np.float16, 0.0, np.uint16, np.int16, np.int8, 0]),
+        (np.float32, [np.int16, np.uint16, np.float16],
+            [np.int8, np.uint8, np.float32, 0., 0]),
+        (np.int32, [np.int16, np.uint16],
+            [np.int8, np.uint8, 0, np.bool]),
+        ])
+@hypothesis.given(data=strategies.data())
+def test_expected_promotion(expected, dtypes, optional_dtypes, data):
+    # Sample randomly while ensuring "dtypes" is always present:
+    optional = data.draw(strategies.lists(
+            strategies.sampled_from(dtypes + optional_dtypes)))
+    all_dtypes = dtypes + optional
+    dtypes_sample = data.draw(strategies.permutations(all_dtypes))
+
+    res = np.result_type(*dtypes_sample)
+    assert res == expected
+
+
+@pytest.mark.parametrize("sctype",
+        [np.int8, np.int16, np.int32, np.int64,
+         np.uint8, np.uint16, np.uint32, np.uint64])
+@pytest.mark.parametrize("other_val",
+        [-2 * 100, -1, 0, 9, 10, 11, 2**63, 2 * 100])
+@pytest.mark.parametrize("comp",
+        [operator.eq, operator.ne, operator.le, operator.lt,
+         operator.ge, operator.gt])
+def test_integer_comparison(sctype, other_val, comp):
+    # Test that comparisons with integers (especially out-of-bound) ones
+    # works correctly.
+    val_obj = 10
+    val = sctype(val_obj)
+    # Check that the scalar behaves the same as the python int:
+    assert comp(10, other_val) == comp(val, other_val)
+    assert comp(val, other_val) == comp(10, other_val)
+    # Except for the result type:
+    assert type(comp(val, other_val)) is np.bool
+
+    # Check that the integer array and object array behave the same:
+    val_obj = np.array([10, 10], dtype=object)
+    val = val_obj.astype(sctype)
+    assert_array_equal(comp(val_obj, other_val), comp(val, other_val))
+    assert_array_equal(comp(other_val, val_obj), comp(other_val, val))
+
+
+@pytest.mark.parametrize("arr", [
+    np.ones((100, 100), dtype=np.uint8)[::2],  # not trivially iterable
+    np.ones(20000, dtype=">u4"),  # cast and >buffersize
+    np.ones(100, dtype=">u4"),  # fast path compatible with cast
+])
+def test_integer_comparison_with_cast(arr):
+    # Similar to above, but mainly test a few cases that cover the slow path
+    # the test is limited to unsigned ints and -1 for simplicity.
+    res = arr >= -1
+    assert_array_equal(res, np.ones_like(arr, dtype=bool))
+    res = arr < -1
+    assert_array_equal(res, np.zeros_like(arr, dtype=bool))
+
+
+@pytest.mark.parametrize("comp",
+        [np.equal, np.not_equal, np.less_equal, np.less,
+         np.greater_equal, np.greater])
+def test_integer_integer_comparison(comp):
+    # Test that the NumPy comparison ufuncs work with large Python integers
+    assert comp(2**200, -2**200) == comp(2**200, -2**200, dtype=object)
+
+
+def create_with_scalar(sctype, value):
+    return sctype(value)
+
+
+def create_with_array(sctype, value):
+    return np.array([value], dtype=sctype)
+
+
+@pytest.mark.parametrize("sctype",
+        [np.int8, np.int16, np.int32, np.int64,
+         np.uint8, np.uint16, np.uint32, np.uint64])
+@pytest.mark.parametrize("create", [create_with_scalar, create_with_array])
+def test_oob_creation(sctype, create):
+    iinfo = np.iinfo(sctype)
+
+    with pytest.raises(OverflowError):
+        create(sctype, iinfo.min - 1)
+
+    with pytest.raises(OverflowError):
+        create(sctype, iinfo.max + 1)
+
+    with pytest.raises(OverflowError):
+        create(sctype, str(iinfo.min - 1))
+
+    with pytest.raises(OverflowError):
+        create(sctype, str(iinfo.max + 1))
+
+    assert create(sctype, iinfo.min) == iinfo.min
+    assert create(sctype, iinfo.max) == iinfo.max
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_numeric.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_numeric.py
new file mode 100644
index 0000000..5b58b34
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_numeric.py
@@ -0,0 +1,4247 @@
+import itertools
+import math
+import platform
+import sys
+import warnings
+from decimal import Decimal
+
+import pytest
+from hypothesis import given
+from hypothesis import strategies as st
+from hypothesis.extra import numpy as hynp
+from numpy._core._rational_tests import rational
+
+import numpy as np
+from numpy import ma
+from numpy._core import sctypes
+from numpy._core.numerictypes import obj2sctype
+from numpy.exceptions import AxisError
+from numpy.random import rand, randint, randn
+from numpy.testing import (
+    HAS_REFCOUNT,
+    IS_WASM,
+    assert_,
+    assert_almost_equal,
+    assert_array_almost_equal,
+    assert_array_equal,
+    assert_array_max_ulp,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+)
+
+
+class TestResize:
+    def test_copies(self):
+        A = np.array([[1, 2], [3, 4]])
+        Ar1 = np.array([[1, 2, 3, 4], [1, 2, 3, 4]])
+        assert_equal(np.resize(A, (2, 4)), Ar1)
+
+        Ar2 = np.array([[1, 2], [3, 4], [1, 2], [3, 4]])
+        assert_equal(np.resize(A, (4, 2)), Ar2)
+
+        Ar3 = np.array([[1, 2, 3], [4, 1, 2], [3, 4, 1], [2, 3, 4]])
+        assert_equal(np.resize(A, (4, 3)), Ar3)
+
+    def test_repeats(self):
+        A = np.array([1, 2, 3])
+        Ar1 = np.array([[1, 2, 3, 1], [2, 3, 1, 2]])
+        assert_equal(np.resize(A, (2, 4)), Ar1)
+
+        Ar2 = np.array([[1, 2], [3, 1], [2, 3], [1, 2]])
+        assert_equal(np.resize(A, (4, 2)), Ar2)
+
+        Ar3 = np.array([[1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3]])
+        assert_equal(np.resize(A, (4, 3)), Ar3)
+
+    def test_zeroresize(self):
+        A = np.array([[1, 2], [3, 4]])
+        Ar = np.resize(A, (0,))
+        assert_array_equal(Ar, np.array([]))
+        assert_equal(A.dtype, Ar.dtype)
+
+        Ar = np.resize(A, (0, 2))
+        assert_equal(Ar.shape, (0, 2))
+
+        Ar = np.resize(A, (2, 0))
+        assert_equal(Ar.shape, (2, 0))
+
+    def test_reshape_from_zero(self):
+        # See also gh-6740
+        A = np.zeros(0, dtype=[('a', np.float32)])
+        Ar = np.resize(A, (2, 1))
+        assert_array_equal(Ar, np.zeros((2, 1), Ar.dtype))
+        assert_equal(A.dtype, Ar.dtype)
+
+    def test_negative_resize(self):
+        A = np.arange(0, 10, dtype=np.float32)
+        new_shape = (-10, -1)
+        with pytest.raises(ValueError, match=r"negative"):
+            np.resize(A, new_shape=new_shape)
+
+    def test_unsigned_resize(self):
+        # ensure unsigned integer sizes don't lead to underflows
+        for dt_pair in [(np.int32, np.uint32), (np.int64, np.uint64)]:
+            arr = np.array([[23, 95], [66, 37]])
+            assert_array_equal(np.resize(arr, dt_pair[0](1)),
+                               np.resize(arr, dt_pair[1](1)))
+
+    def test_subclass(self):
+        class MyArray(np.ndarray):
+            __array_priority__ = 1.
+
+        my_arr = np.array([1]).view(MyArray)
+        assert type(np.resize(my_arr, 5)) is MyArray
+        assert type(np.resize(my_arr, 0)) is MyArray
+
+        my_arr = np.array([]).view(MyArray)
+        assert type(np.resize(my_arr, 5)) is MyArray
+
+
+class TestNonarrayArgs:
+    # check that non-array arguments to functions wrap them in arrays
+    def test_choose(self):
+        choices = [[0, 1, 2],
+                   [3, 4, 5],
+                   [5, 6, 7]]
+        tgt = [5, 1, 5]
+        a = [2, 0, 1]
+
+        out = np.choose(a, choices)
+        assert_equal(out, tgt)
+
+    def test_clip(self):
+        arr = [-1, 5, 2, 3, 10, -4, -9]
+        out = np.clip(arr, 2, 7)
+        tgt = [2, 5, 2, 3, 7, 2, 2]
+        assert_equal(out, tgt)
+
+    def test_compress(self):
+        arr = [[0, 1, 2, 3, 4],
+               [5, 6, 7, 8, 9]]
+        tgt = [[5, 6, 7, 8, 9]]
+        out = np.compress([0, 1], arr, axis=0)
+        assert_equal(out, tgt)
+
+    def test_count_nonzero(self):
+        arr = [[0, 1, 7, 0, 0],
+               [3, 0, 0, 2, 19]]
+        tgt = np.array([2, 3])
+        out = np.count_nonzero(arr, axis=1)
+        assert_equal(out, tgt)
+
+    def test_diagonal(self):
+        a = [[0, 1, 2, 3],
+             [4, 5, 6, 7],
+             [8, 9, 10, 11]]
+        out = np.diagonal(a)
+        tgt = [0, 5, 10]
+
+        assert_equal(out, tgt)
+
+    def test_mean(self):
+        A = [[1, 2, 3], [4, 5, 6]]
+        assert_(np.mean(A) == 3.5)
+        assert_(np.all(np.mean(A, 0) == np.array([2.5, 3.5, 4.5])))
+        assert_(np.all(np.mean(A, 1) == np.array([2., 5.])))
+
+        with warnings.catch_warnings(record=True) as w:
+            warnings.filterwarnings('always', '', RuntimeWarning)
+            assert_(np.isnan(np.mean([])))
+            assert_(w[0].category is RuntimeWarning)
+
+    def test_ptp(self):
+        a = [3, 4, 5, 10, -3, -5, 6.0]
+        assert_equal(np.ptp(a, axis=0), 15.0)
+
+    def test_prod(self):
+        arr = [[1, 2, 3, 4],
+               [5, 6, 7, 9],
+               [10, 3, 4, 5]]
+        tgt = [24, 1890, 600]
+
+        assert_equal(np.prod(arr, axis=-1), tgt)
+
+    def test_ravel(self):
+        a = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
+        tgt = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
+        assert_equal(np.ravel(a), tgt)
+
+    def test_repeat(self):
+        a = [1, 2, 3]
+        tgt = [1, 1, 2, 2, 3, 3]
+
+        out = np.repeat(a, 2)
+        assert_equal(out, tgt)
+
+    def test_reshape(self):
+        arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
+        tgt = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]]
+        assert_equal(np.reshape(arr, (2, 6)), tgt)
+
+    def test_reshape_shape_arg(self):
+        arr = np.arange(12)
+        shape = (3, 4)
+        expected = arr.reshape(shape)
+
+        with pytest.raises(
+            TypeError,
+            match="You cannot specify 'newshape' and 'shape' "
+                  "arguments at the same time."
+        ):
+            np.reshape(arr, shape=shape, newshape=shape)
+        with pytest.raises(
+            TypeError,
+            match=r"reshape\(\) missing 1 required positional "
+                  "argument: 'shape'"
+        ):
+            np.reshape(arr)
+
+        assert_equal(np.reshape(arr, shape), expected)
+        assert_equal(np.reshape(arr, shape, order="C"), expected)
+        assert_equal(np.reshape(arr, shape, "C"), expected)
+        assert_equal(np.reshape(arr, shape=shape), expected)
+        assert_equal(np.reshape(arr, shape=shape, order="C"), expected)
+        with pytest.warns(DeprecationWarning):
+            actual = np.reshape(arr, newshape=shape)
+            assert_equal(actual, expected)
+
+    def test_reshape_copy_arg(self):
+        arr = np.arange(24).reshape(2, 3, 4)
+        arr_f_ord = np.array(arr, order="F")
+        shape = (12, 2)
+
+        assert np.shares_memory(np.reshape(arr, shape), arr)
+        assert np.shares_memory(np.reshape(arr, shape, order="C"), arr)
+        assert np.shares_memory(
+            np.reshape(arr_f_ord, shape, order="F"), arr_f_ord)
+        assert np.shares_memory(np.reshape(arr, shape, copy=None), arr)
+        assert np.shares_memory(np.reshape(arr, shape, copy=False), arr)
+        assert np.shares_memory(arr.reshape(shape, copy=False), arr)
+        assert not np.shares_memory(np.reshape(arr, shape, copy=True), arr)
+        assert not np.shares_memory(
+            np.reshape(arr, shape, order="C", copy=True), arr)
+        assert not np.shares_memory(
+            np.reshape(arr, shape, order="F", copy=True), arr)
+        assert not np.shares_memory(
+            np.reshape(arr, shape, order="F", copy=None), arr)
+
+        err_msg = "Unable to avoid creating a copy while reshaping."
+        with pytest.raises(ValueError, match=err_msg):
+            np.reshape(arr, shape, order="F", copy=False)
+        with pytest.raises(ValueError, match=err_msg):
+            np.reshape(arr_f_ord, shape, order="C", copy=False)
+
+    def test_round(self):
+        arr = [1.56, 72.54, 6.35, 3.25]
+        tgt = [1.6, 72.5, 6.4, 3.2]
+        assert_equal(np.around(arr, decimals=1), tgt)
+        s = np.float64(1.)
+        assert_(isinstance(s.round(), np.float64))
+        assert_equal(s.round(), 1.)
+
+    @pytest.mark.parametrize('dtype', [
+        np.int8, np.int16, np.int32, np.int64,
+        np.uint8, np.uint16, np.uint32, np.uint64,
+        np.float16, np.float32, np.float64,
+    ])
+    def test_dunder_round(self, dtype):
+        s = dtype(1)
+        assert_(isinstance(round(s), int))
+        assert_(isinstance(round(s, None), int))
+        assert_(isinstance(round(s, ndigits=None), int))
+        assert_equal(round(s), 1)
+        assert_equal(round(s, None), 1)
+        assert_equal(round(s, ndigits=None), 1)
+
+    @pytest.mark.parametrize('val, ndigits', [
+        pytest.param(2**31 - 1, -1,
+            marks=pytest.mark.skip(reason="Out of range of int32")
+        ),
+        (2**31 - 1, 1 - math.ceil(math.log10(2**31 - 1))),
+        (2**31 - 1, -math.ceil(math.log10(2**31 - 1)))
+    ])
+    def test_dunder_round_edgecases(self, val, ndigits):
+        assert_equal(round(val, ndigits), round(np.int32(val), ndigits))
+
+    def test_dunder_round_accuracy(self):
+        f = np.float64(5.1 * 10**73)
+        assert_(isinstance(round(f, -73), np.float64))
+        assert_array_max_ulp(round(f, -73), 5.0 * 10**73)
+        assert_(isinstance(round(f, ndigits=-73), np.float64))
+        assert_array_max_ulp(round(f, ndigits=-73), 5.0 * 10**73)
+
+        i = np.int64(501)
+        assert_(isinstance(round(i, -2), np.int64))
+        assert_array_max_ulp(round(i, -2), 500)
+        assert_(isinstance(round(i, ndigits=-2), np.int64))
+        assert_array_max_ulp(round(i, ndigits=-2), 500)
+
+    @pytest.mark.xfail(raises=AssertionError, reason="gh-15896")
+    def test_round_py_consistency(self):
+        f = 5.1 * 10**73
+        assert_equal(round(np.float64(f), -73), round(f, -73))
+
+    def test_searchsorted(self):
+        arr = [-8, -5, -1, 3, 6, 10]
+        out = np.searchsorted(arr, 0)
+        assert_equal(out, 3)
+
+    def test_size(self):
+        A = [[1, 2, 3], [4, 5, 6]]
+        assert_(np.size(A) == 6)
+        assert_(np.size(A, 0) == 2)
+        assert_(np.size(A, 1) == 3)
+
+    def test_squeeze(self):
+        A = [[[1, 1, 1], [2, 2, 2], [3, 3, 3]]]
+        assert_equal(np.squeeze(A).shape, (3, 3))
+        assert_equal(np.squeeze(np.zeros((1, 3, 1))).shape, (3,))
+        assert_equal(np.squeeze(np.zeros((1, 3, 1)), axis=0).shape, (3, 1))
+        assert_equal(np.squeeze(np.zeros((1, 3, 1)), axis=-1).shape, (1, 3))
+        assert_equal(np.squeeze(np.zeros((1, 3, 1)), axis=2).shape, (1, 3))
+        assert_equal(np.squeeze([np.zeros((3, 1))]).shape, (3,))
+        assert_equal(np.squeeze([np.zeros((3, 1))], axis=0).shape, (3, 1))
+        assert_equal(np.squeeze([np.zeros((3, 1))], axis=2).shape, (1, 3))
+        assert_equal(np.squeeze([np.zeros((3, 1))], axis=-1).shape, (1, 3))
+
+    def test_std(self):
+        A = [[1, 2, 3], [4, 5, 6]]
+        assert_almost_equal(np.std(A), 1.707825127659933)
+        assert_almost_equal(np.std(A, 0), np.array([1.5, 1.5, 1.5]))
+        assert_almost_equal(np.std(A, 1), np.array([0.81649658, 0.81649658]))
+
+        with warnings.catch_warnings(record=True) as w:
+            warnings.filterwarnings('always', '', RuntimeWarning)
+            assert_(np.isnan(np.std([])))
+            assert_(w[0].category is RuntimeWarning)
+
+    def test_swapaxes(self):
+        tgt = [[[0, 4], [2, 6]], [[1, 5], [3, 7]]]
+        a = [[[0, 1], [2, 3]], [[4, 5], [6, 7]]]
+        out = np.swapaxes(a, 0, 2)
+        assert_equal(out, tgt)
+
+    def test_sum(self):
+        m = [[1, 2, 3],
+             [4, 5, 6],
+             [7, 8, 9]]
+        tgt = [[6], [15], [24]]
+        out = np.sum(m, axis=1, keepdims=True)
+
+        assert_equal(tgt, out)
+
+    def test_take(self):
+        tgt = [2, 3, 5]
+        indices = [1, 2, 4]
+        a = [1, 2, 3, 4, 5]
+
+        out = np.take(a, indices)
+        assert_equal(out, tgt)
+
+        pairs = [
+            (np.int32, np.int32), (np.int32, np.int64),
+            (np.int64, np.int32), (np.int64, np.int64)
+        ]
+        for array_type, indices_type in pairs:
+            x = np.array([1, 2, 3, 4, 5], dtype=array_type)
+            ind = np.array([0, 2, 2, 3], dtype=indices_type)
+            tgt = np.array([1, 3, 3, 4], dtype=array_type)
+            out = np.take(x, ind)
+            assert_equal(out, tgt)
+            assert_equal(out.dtype, tgt.dtype)
+
+    def test_trace(self):
+        c = [[1, 2], [3, 4], [5, 6]]
+        assert_equal(np.trace(c), 5)
+
+    def test_transpose(self):
+        arr = [[1, 2], [3, 4], [5, 6]]
+        tgt = [[1, 3, 5], [2, 4, 6]]
+        assert_equal(np.transpose(arr, (1, 0)), tgt)
+        assert_equal(np.transpose(arr, (-1, -2)), tgt)
+        assert_equal(np.matrix_transpose(arr), tgt)
+
+    def test_var(self):
+        A = [[1, 2, 3], [4, 5, 6]]
+        assert_almost_equal(np.var(A), 2.9166666666666665)
+        assert_almost_equal(np.var(A, 0), np.array([2.25, 2.25, 2.25]))
+        assert_almost_equal(np.var(A, 1), np.array([0.66666667, 0.66666667]))
+
+        with warnings.catch_warnings(record=True) as w:
+            warnings.filterwarnings('always', '', RuntimeWarning)
+            assert_(np.isnan(np.var([])))
+            assert_(w[0].category is RuntimeWarning)
+
+        B = np.array([None, 0])
+        B[0] = 1j
+        assert_almost_equal(np.var(B), 0.25)
+
+    def test_std_with_mean_keyword(self):
+        # Setting the seed to make the test reproducible
+        rng = np.random.RandomState(1234)
+        A = rng.randn(10, 20, 5) + 0.5
+
+        mean_out = np.zeros((10, 1, 5))
+        std_out = np.zeros((10, 1, 5))
+
+        mean = np.mean(A,
+                       out=mean_out,
+                       axis=1,
+                       keepdims=True)
+
+        # The returned  object should be the object specified during calling
+        assert mean_out is mean
+
+        std = np.std(A,
+                     out=std_out,
+                     axis=1,
+                     keepdims=True,
+                     mean=mean)
+
+        # The returned  object should be the object specified during calling
+        assert std_out is std
+
+        # Shape of returned mean and std should be same
+        assert std.shape == mean.shape
+        assert std.shape == (10, 1, 5)
+
+        # Output should be the same as from the individual algorithms
+        std_old = np.std(A, axis=1, keepdims=True)
+
+        assert std_old.shape == mean.shape
+        assert_almost_equal(std, std_old)
+
+    def test_var_with_mean_keyword(self):
+        # Setting the seed to make the test reproducible
+        rng = np.random.RandomState(1234)
+        A = rng.randn(10, 20, 5) + 0.5
+
+        mean_out = np.zeros((10, 1, 5))
+        var_out = np.zeros((10, 1, 5))
+
+        mean = np.mean(A,
+                       out=mean_out,
+                       axis=1,
+                       keepdims=True)
+
+        # The returned  object should be the object specified during calling
+        assert mean_out is mean
+
+        var = np.var(A,
+                     out=var_out,
+                     axis=1,
+                     keepdims=True,
+                     mean=mean)
+
+        # The returned  object should be the object specified during calling
+        assert var_out is var
+
+        # Shape of returned mean and var should be same
+        assert var.shape == mean.shape
+        assert var.shape == (10, 1, 5)
+
+        # Output should be the same as from the individual algorithms
+        var_old = np.var(A, axis=1, keepdims=True)
+
+        assert var_old.shape == mean.shape
+        assert_almost_equal(var, var_old)
+
+    def test_std_with_mean_keyword_keepdims_false(self):
+        rng = np.random.RandomState(1234)
+        A = rng.randn(10, 20, 5) + 0.5
+
+        mean = np.mean(A,
+                       axis=1,
+                       keepdims=True)
+
+        std = np.std(A,
+                     axis=1,
+                     keepdims=False,
+                     mean=mean)
+
+        # Shape of returned mean and std should be same
+        assert std.shape == (10, 5)
+
+        # Output should be the same as from the individual algorithms
+        std_old = np.std(A, axis=1, keepdims=False)
+        mean_old = np.mean(A, axis=1, keepdims=False)
+
+        assert std_old.shape == mean_old.shape
+        assert_equal(std, std_old)
+
+    def test_var_with_mean_keyword_keepdims_false(self):
+        rng = np.random.RandomState(1234)
+        A = rng.randn(10, 20, 5) + 0.5
+
+        mean = np.mean(A,
+                       axis=1,
+                       keepdims=True)
+
+        var = np.var(A,
+                     axis=1,
+                     keepdims=False,
+                     mean=mean)
+
+        # Shape of returned mean and var should be same
+        assert var.shape == (10, 5)
+
+        # Output should be the same as from the individual algorithms
+        var_old = np.var(A, axis=1, keepdims=False)
+        mean_old = np.mean(A, axis=1, keepdims=False)
+
+        assert var_old.shape == mean_old.shape
+        assert_equal(var, var_old)
+
+    def test_std_with_mean_keyword_where_nontrivial(self):
+        rng = np.random.RandomState(1234)
+        A = rng.randn(10, 20, 5) + 0.5
+
+        where = A > 0.5
+
+        mean = np.mean(A,
+                       axis=1,
+                       keepdims=True,
+                       where=where)
+
+        std = np.std(A,
+                     axis=1,
+                     keepdims=False,
+                     mean=mean,
+                     where=where)
+
+        # Shape of returned mean and std should be same
+        assert std.shape == (10, 5)
+
+        # Output should be the same as from the individual algorithms
+        std_old = np.std(A, axis=1, where=where)
+        mean_old = np.mean(A, axis=1, where=where)
+
+        assert std_old.shape == mean_old.shape
+        assert_equal(std, std_old)
+
+    def test_var_with_mean_keyword_where_nontrivial(self):
+        rng = np.random.RandomState(1234)
+        A = rng.randn(10, 20, 5) + 0.5
+
+        where = A > 0.5
+
+        mean = np.mean(A,
+                       axis=1,
+                       keepdims=True,
+                       where=where)
+
+        var = np.var(A,
+                     axis=1,
+                     keepdims=False,
+                     mean=mean,
+                     where=where)
+
+        # Shape of returned mean and var should be same
+        assert var.shape == (10, 5)
+
+        # Output should be the same as from the individual algorithms
+        var_old = np.var(A, axis=1, where=where)
+        mean_old = np.mean(A, axis=1, where=where)
+
+        assert var_old.shape == mean_old.shape
+        assert_equal(var, var_old)
+
+    def test_std_with_mean_keyword_multiple_axis(self):
+        # Setting the seed to make the test reproducible
+        rng = np.random.RandomState(1234)
+        A = rng.randn(10, 20, 5) + 0.5
+
+        axis = (0, 2)
+
+        mean = np.mean(A,
+                       out=None,
+                       axis=axis,
+                       keepdims=True)
+
+        std = np.std(A,
+                     out=None,
+                     axis=axis,
+                     keepdims=False,
+                     mean=mean)
+
+        # Shape of returned mean and std should be same
+        assert std.shape == (20,)
+
+        # Output should be the same as from the individual algorithms
+        std_old = np.std(A, axis=axis, keepdims=False)
+
+        assert_almost_equal(std, std_old)
+
+    def test_std_with_mean_keyword_axis_None(self):
+        # Setting the seed to make the test reproducible
+        rng = np.random.RandomState(1234)
+        A = rng.randn(10, 20, 5) + 0.5
+
+        axis = None
+
+        mean = np.mean(A,
+                       out=None,
+                       axis=axis,
+                       keepdims=True)
+
+        std = np.std(A,
+                     out=None,
+                     axis=axis,
+                     keepdims=False,
+                     mean=mean)
+
+        # Shape of returned mean and std should be same
+        assert std.shape == ()
+
+        # Output should be the same as from the individual algorithms
+        std_old = np.std(A, axis=axis, keepdims=False)
+
+        assert_almost_equal(std, std_old)
+
+    def test_std_with_mean_keyword_keepdims_true_masked(self):
+
+        A = ma.array([[2., 3., 4., 5.],
+                      [1., 2., 3., 4.]],
+                     mask=[[True, False, True, False],
+                           [True, False, True, False]])
+
+        B = ma.array([[100., 3., 104., 5.],
+                      [101., 2., 103., 4.]],
+                      mask=[[True, False, True, False],
+                            [True, False, True, False]])
+
+        mean_out = ma.array([[0., 0., 0., 0.]],
+                            mask=[[False, False, False, False]])
+        std_out = ma.array([[0., 0., 0., 0.]],
+                           mask=[[False, False, False, False]])
+
+        axis = 0
+
+        mean = np.mean(A, out=mean_out,
+                       axis=axis, keepdims=True)
+
+        std = np.std(A, out=std_out,
+                     axis=axis, keepdims=True,
+                     mean=mean)
+
+        # Shape of returned mean and std should be same
+        assert std.shape == mean.shape
+        assert std.shape == (1, 4)
+
+        # Output should be the same as from the individual algorithms
+        std_old = np.std(A, axis=axis, keepdims=True)
+        mean_old = np.mean(A, axis=axis, keepdims=True)
+
+        assert std_old.shape == mean_old.shape
+        assert_almost_equal(std, std_old)
+        assert_almost_equal(mean, mean_old)
+
+        assert mean_out is mean
+        assert std_out is std
+
+        # masked elements should be ignored
+        mean_b = np.mean(B, axis=axis, keepdims=True)
+        std_b = np.std(B, axis=axis, keepdims=True, mean=mean_b)
+        assert_almost_equal(std, std_b)
+        assert_almost_equal(mean, mean_b)
+
+    def test_var_with_mean_keyword_keepdims_true_masked(self):
+
+        A = ma.array([[2., 3., 4., 5.],
+                      [1., 2., 3., 4.]],
+                     mask=[[True, False, True, False],
+                           [True, False, True, False]])
+
+        B = ma.array([[100., 3., 104., 5.],
+                      [101., 2., 103., 4.]],
+                      mask=[[True, False, True, False],
+                            [True, False, True, False]])
+
+        mean_out = ma.array([[0., 0., 0., 0.]],
+                            mask=[[False, False, False, False]])
+        var_out = ma.array([[0., 0., 0., 0.]],
+                           mask=[[False, False, False, False]])
+
+        axis = 0
+
+        mean = np.mean(A, out=mean_out,
+                       axis=axis, keepdims=True)
+
+        var = np.var(A, out=var_out,
+                     axis=axis, keepdims=True,
+                     mean=mean)
+
+        # Shape of returned mean and var should be same
+        assert var.shape == mean.shape
+        assert var.shape == (1, 4)
+
+        # Output should be the same as from the individual algorithms
+        var_old = np.var(A, axis=axis, keepdims=True)
+        mean_old = np.mean(A, axis=axis, keepdims=True)
+
+        assert var_old.shape == mean_old.shape
+        assert_almost_equal(var, var_old)
+        assert_almost_equal(mean, mean_old)
+
+        assert mean_out is mean
+        assert var_out is var
+
+        # masked elements should be ignored
+        mean_b = np.mean(B, axis=axis, keepdims=True)
+        var_b = np.var(B, axis=axis, keepdims=True, mean=mean_b)
+        assert_almost_equal(var, var_b)
+        assert_almost_equal(mean, mean_b)
+
+
+class TestIsscalar:
+    def test_isscalar(self):
+        assert_(np.isscalar(3.1))
+        assert_(np.isscalar(np.int16(12345)))
+        assert_(np.isscalar(False))
+        assert_(np.isscalar('numpy'))
+        assert_(not np.isscalar([3.1]))
+        assert_(not np.isscalar(None))
+
+        # PEP 3141
+        from fractions import Fraction
+        assert_(np.isscalar(Fraction(5, 17)))
+        from numbers import Number
+        assert_(np.isscalar(Number()))
+
+
+class TestBoolScalar:
+    def test_logical(self):
+        f = np.False_
+        t = np.True_
+        s = "xyz"
+        assert_((t and s) is s)
+        assert_((f and s) is f)
+
+    def test_bitwise_or(self):
+        f = np.False_
+        t = np.True_
+        assert_((t | t) is t)
+        assert_((f | t) is t)
+        assert_((t | f) is t)
+        assert_((f | f) is f)
+
+    def test_bitwise_and(self):
+        f = np.False_
+        t = np.True_
+        assert_((t & t) is t)
+        assert_((f & t) is f)
+        assert_((t & f) is f)
+        assert_((f & f) is f)
+
+    def test_bitwise_xor(self):
+        f = np.False_
+        t = np.True_
+        assert_((t ^ t) is f)
+        assert_((f ^ t) is t)
+        assert_((t ^ f) is t)
+        assert_((f ^ f) is f)
+
+
+class TestBoolArray:
+    def setup_method(self):
+        # offset for simd tests
+        self.t = np.array([True] * 41, dtype=bool)[1::]
+        self.f = np.array([False] * 41, dtype=bool)[1::]
+        self.o = np.array([False] * 42, dtype=bool)[2::]
+        self.nm = self.f.copy()
+        self.im = self.t.copy()
+        self.nm[3] = True
+        self.nm[-2] = True
+        self.im[3] = False
+        self.im[-2] = False
+
+    def test_all_any(self):
+        assert_(self.t.all())
+        assert_(self.t.any())
+        assert_(not self.f.all())
+        assert_(not self.f.any())
+        assert_(self.nm.any())
+        assert_(self.im.any())
+        assert_(not self.nm.all())
+        assert_(not self.im.all())
+        # check bad element in all positions
+        for i in range(256 - 7):
+            d = np.array([False] * 256, dtype=bool)[7::]
+            d[i] = True
+            assert_(np.any(d))
+            e = np.array([True] * 256, dtype=bool)[7::]
+            e[i] = False
+            assert_(not np.all(e))
+            assert_array_equal(e, ~d)
+        # big array test for blocked libc loops
+        for i in list(range(9, 6000, 507)) + [7764, 90021, -10]:
+            d = np.array([False] * 100043, dtype=bool)
+            d[i] = True
+            assert_(np.any(d), msg=f"{i!r}")
+            e = np.array([True] * 100043, dtype=bool)
+            e[i] = False
+            assert_(not np.all(e), msg=f"{i!r}")
+
+    def test_logical_not_abs(self):
+        assert_array_equal(~self.t, self.f)
+        assert_array_equal(np.abs(~self.t), self.f)
+        assert_array_equal(np.abs(~self.f), self.t)
+        assert_array_equal(np.abs(self.f), self.f)
+        assert_array_equal(~np.abs(self.f), self.t)
+        assert_array_equal(~np.abs(self.t), self.f)
+        assert_array_equal(np.abs(~self.nm), self.im)
+        np.logical_not(self.t, out=self.o)
+        assert_array_equal(self.o, self.f)
+        np.abs(self.t, out=self.o)
+        assert_array_equal(self.o, self.t)
+
+    def test_logical_and_or_xor(self):
+        assert_array_equal(self.t | self.t, self.t)
+        assert_array_equal(self.f | self.f, self.f)
+        assert_array_equal(self.t | self.f, self.t)
+        assert_array_equal(self.f | self.t, self.t)
+        np.logical_or(self.t, self.t, out=self.o)
+        assert_array_equal(self.o, self.t)
+        assert_array_equal(self.t & self.t, self.t)
+        assert_array_equal(self.f & self.f, self.f)
+        assert_array_equal(self.t & self.f, self.f)
+        assert_array_equal(self.f & self.t, self.f)
+        np.logical_and(self.t, self.t, out=self.o)
+        assert_array_equal(self.o, self.t)
+        assert_array_equal(self.t ^ self.t, self.f)
+        assert_array_equal(self.f ^ self.f, self.f)
+        assert_array_equal(self.t ^ self.f, self.t)
+        assert_array_equal(self.f ^ self.t, self.t)
+        np.logical_xor(self.t, self.t, out=self.o)
+        assert_array_equal(self.o, self.f)
+
+        assert_array_equal(self.nm & self.t, self.nm)
+        assert_array_equal(self.im & self.f, False)
+        assert_array_equal(self.nm & True, self.nm)
+        assert_array_equal(self.im & False, self.f)
+        assert_array_equal(self.nm | self.t, self.t)
+        assert_array_equal(self.im | self.f, self.im)
+        assert_array_equal(self.nm | True, self.t)
+        assert_array_equal(self.im | False, self.im)
+        assert_array_equal(self.nm ^ self.t, self.im)
+        assert_array_equal(self.im ^ self.f, self.im)
+        assert_array_equal(self.nm ^ True, self.im)
+        assert_array_equal(self.im ^ False, self.im)
+
+
+class TestBoolCmp:
+    def setup_method(self):
+        self.f = np.ones(256, dtype=np.float32)
+        self.ef = np.ones(self.f.size, dtype=bool)
+        self.d = np.ones(128, dtype=np.float64)
+        self.ed = np.ones(self.d.size, dtype=bool)
+        # generate values for all permutation of 256bit simd vectors
+        s = 0
+        for i in range(32):
+            self.f[s:s + 8] = [i & 2**x for x in range(8)]
+            self.ef[s:s + 8] = [(i & 2**x) != 0 for x in range(8)]
+            s += 8
+        s = 0
+        for i in range(16):
+            self.d[s:s + 4] = [i & 2**x for x in range(4)]
+            self.ed[s:s + 4] = [(i & 2**x) != 0 for x in range(4)]
+            s += 4
+
+        self.nf = self.f.copy()
+        self.nd = self.d.copy()
+        self.nf[self.ef] = np.nan
+        self.nd[self.ed] = np.nan
+
+        self.inff = self.f.copy()
+        self.infd = self.d.copy()
+        self.inff[::3][self.ef[::3]] = np.inf
+        self.infd[::3][self.ed[::3]] = np.inf
+        self.inff[1::3][self.ef[1::3]] = -np.inf
+        self.infd[1::3][self.ed[1::3]] = -np.inf
+        self.inff[2::3][self.ef[2::3]] = np.nan
+        self.infd[2::3][self.ed[2::3]] = np.nan
+        self.efnonan = self.ef.copy()
+        self.efnonan[2::3] = False
+        self.ednonan = self.ed.copy()
+        self.ednonan[2::3] = False
+
+        self.signf = self.f.copy()
+        self.signd = self.d.copy()
+        self.signf[self.ef] *= -1.
+        self.signd[self.ed] *= -1.
+        self.signf[1::6][self.ef[1::6]] = -np.inf
+        self.signd[1::6][self.ed[1::6]] = -np.inf
+        # On RISC-V, many operations that produce NaNs, such as converting
+        # a -NaN from f64 to f32, return a canonical NaN.  The canonical
+        # NaNs are always positive.  See section 11.3 NaN Generation and
+        # Propagation of the RISC-V Unprivileged ISA for more details.
+        # We disable the float32 sign test on riscv64 for -np.nan as the sign
+        # of the NaN will be lost when it's converted to a float32.
+        if platform.machine() != 'riscv64':
+            self.signf[3::6][self.ef[3::6]] = -np.nan
+        self.signd[3::6][self.ed[3::6]] = -np.nan
+        self.signf[4::6][self.ef[4::6]] = -0.
+        self.signd[4::6][self.ed[4::6]] = -0.
+
+    def test_float(self):
+        # offset for alignment test
+        for i in range(4):
+            assert_array_equal(self.f[i:] > 0, self.ef[i:])
+            assert_array_equal(self.f[i:] - 1 >= 0, self.ef[i:])
+            assert_array_equal(self.f[i:] == 0, ~self.ef[i:])
+            assert_array_equal(-self.f[i:] < 0, self.ef[i:])
+            assert_array_equal(-self.f[i:] + 1 <= 0, self.ef[i:])
+            r = self.f[i:] != 0
+            assert_array_equal(r, self.ef[i:])
+            r2 = self.f[i:] != np.zeros_like(self.f[i:])
+            r3 = 0 != self.f[i:]
+            assert_array_equal(r, r2)
+            assert_array_equal(r, r3)
+            # check bool == 0x1
+            assert_array_equal(r.view(np.int8), r.astype(np.int8))
+            assert_array_equal(r2.view(np.int8), r2.astype(np.int8))
+            assert_array_equal(r3.view(np.int8), r3.astype(np.int8))
+
+            # isnan on amd64 takes the same code path
+            assert_array_equal(np.isnan(self.nf[i:]), self.ef[i:])
+            assert_array_equal(np.isfinite(self.nf[i:]), ~self.ef[i:])
+            assert_array_equal(np.isfinite(self.inff[i:]), ~self.ef[i:])
+            assert_array_equal(np.isinf(self.inff[i:]), self.efnonan[i:])
+            assert_array_equal(np.signbit(self.signf[i:]), self.ef[i:])
+
+    def test_double(self):
+        # offset for alignment test
+        for i in range(2):
+            assert_array_equal(self.d[i:] > 0, self.ed[i:])
+            assert_array_equal(self.d[i:] - 1 >= 0, self.ed[i:])
+            assert_array_equal(self.d[i:] == 0, ~self.ed[i:])
+            assert_array_equal(-self.d[i:] < 0, self.ed[i:])
+            assert_array_equal(-self.d[i:] + 1 <= 0, self.ed[i:])
+            r = self.d[i:] != 0
+            assert_array_equal(r, self.ed[i:])
+            r2 = self.d[i:] != np.zeros_like(self.d[i:])
+            r3 = 0 != self.d[i:]
+            assert_array_equal(r, r2)
+            assert_array_equal(r, r3)
+            # check bool == 0x1
+            assert_array_equal(r.view(np.int8), r.astype(np.int8))
+            assert_array_equal(r2.view(np.int8), r2.astype(np.int8))
+            assert_array_equal(r3.view(np.int8), r3.astype(np.int8))
+
+            # isnan on amd64 takes the same code path
+            assert_array_equal(np.isnan(self.nd[i:]), self.ed[i:])
+            assert_array_equal(np.isfinite(self.nd[i:]), ~self.ed[i:])
+            assert_array_equal(np.isfinite(self.infd[i:]), ~self.ed[i:])
+            assert_array_equal(np.isinf(self.infd[i:]), self.ednonan[i:])
+            assert_array_equal(np.signbit(self.signd[i:]), self.ed[i:])
+
+
+class TestSeterr:
+    def test_default(self):
+        err = np.geterr()
+        assert_equal(err,
+                     {'divide': 'warn',
+                          'invalid': 'warn',
+                          'over': 'warn',
+                          'under': 'ignore'}
+                     )
+
+    def test_set(self):
+        with np.errstate():
+            err = np.seterr()
+            old = np.seterr(divide='print')
+            assert_(err == old)
+            new = np.seterr()
+            assert_(new['divide'] == 'print')
+            np.seterr(over='raise')
+            assert_(np.geterr()['over'] == 'raise')
+            assert_(new['divide'] == 'print')
+            np.seterr(**old)
+            assert_(np.geterr() == old)
+
+    @pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support")
+    @pytest.mark.skipif(platform.machine() == "armv5tel", reason="See gh-413.")
+    def test_divide_err(self):
+        with np.errstate(divide='raise'):
+            with assert_raises(FloatingPointError):
+                np.array([1.]) / np.array([0.])
+
+            np.seterr(divide='ignore')
+            np.array([1.]) / np.array([0.])
+
+
+class TestFloatExceptions:
+    def assert_raises_fpe(self, fpeerr, flop, x, y):
+        ftype = type(x)
+        try:
+            flop(x, y)
+            assert_(False,
+                    f"Type {ftype} did not raise fpe error '{fpeerr}'.")
+        except FloatingPointError as exc:
+            assert_(str(exc).find(fpeerr) >= 0,
+                    f"Type {ftype} raised wrong fpe error '{exc}'.")
+
+    def assert_op_raises_fpe(self, fpeerr, flop, sc1, sc2):
+        # Check that fpe exception is raised.
+        #
+        # Given a floating operation `flop` and two scalar values, check that
+        # the operation raises the floating point exception specified by
+        # `fpeerr`. Tests all variants with 0-d array scalars as well.
+
+        self.assert_raises_fpe(fpeerr, flop, sc1, sc2)
+        self.assert_raises_fpe(fpeerr, flop, sc1[()], sc2)
+        self.assert_raises_fpe(fpeerr, flop, sc1, sc2[()])
+        self.assert_raises_fpe(fpeerr, flop, sc1[()], sc2[()])
+
+    # Test for all real and complex float types
+    @pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support")
+    @pytest.mark.parametrize("typecode", np.typecodes["AllFloat"])
+    def test_floating_exceptions(self, typecode):
+        if 'bsd' in sys.platform and typecode in 'gG':
+            pytest.skip(reason="Fallback impl for (c)longdouble may not raise "
+                               "FPE errors as expected on BSD OSes, "
+                               "see gh-24876, gh-23379")
+
+        # Test basic arithmetic function errors
+        with np.errstate(all='raise'):
+            ftype = obj2sctype(typecode)
+            if np.dtype(ftype).kind == 'f':
+                # Get some extreme values for the type
+                fi = np.finfo(ftype)
+                ft_tiny = fi._machar.tiny
+                ft_max = fi.max
+                ft_eps = fi.eps
+                underflow = 'underflow'
+                divbyzero = 'divide by zero'
+            else:
+                # 'c', complex, corresponding real dtype
+                rtype = type(ftype(0).real)
+                fi = np.finfo(rtype)
+                ft_tiny = ftype(fi._machar.tiny)
+                ft_max = ftype(fi.max)
+                ft_eps = ftype(fi.eps)
+                # The complex types raise different exceptions
+                underflow = ''
+                divbyzero = ''
+            overflow = 'overflow'
+            invalid = 'invalid'
+
+            # The value of tiny for double double is NaN, so we need to
+            # pass the assert
+            if not np.isnan(ft_tiny):
+                self.assert_raises_fpe(underflow,
+                                    lambda a, b: a / b, ft_tiny, ft_max)
+                self.assert_raises_fpe(underflow,
+                                    lambda a, b: a * b, ft_tiny, ft_tiny)
+            self.assert_raises_fpe(overflow,
+                                   lambda a, b: a * b, ft_max, ftype(2))
+            self.assert_raises_fpe(overflow,
+                                   lambda a, b: a / b, ft_max, ftype(0.5))
+            self.assert_raises_fpe(overflow,
+                                   lambda a, b: a + b, ft_max, ft_max * ft_eps)
+            self.assert_raises_fpe(overflow,
+                                   lambda a, b: a - b, -ft_max, ft_max * ft_eps)
+            self.assert_raises_fpe(overflow,
+                                   np.power, ftype(2), ftype(2**fi.nexp))
+            self.assert_raises_fpe(divbyzero,
+                                   lambda a, b: a / b, ftype(1), ftype(0))
+            self.assert_raises_fpe(
+                invalid, lambda a, b: a / b, ftype(np.inf), ftype(np.inf)
+            )
+            self.assert_raises_fpe(invalid,
+                                   lambda a, b: a / b, ftype(0), ftype(0))
+            self.assert_raises_fpe(
+                invalid, lambda a, b: a - b, ftype(np.inf), ftype(np.inf)
+            )
+            self.assert_raises_fpe(
+                invalid, lambda a, b: a + b, ftype(np.inf), ftype(-np.inf)
+            )
+            self.assert_raises_fpe(invalid,
+                                   lambda a, b: a * b, ftype(0), ftype(np.inf))
+
+    @pytest.mark.skipif(IS_WASM, reason="no wasm fp exception support")
+    def test_warnings(self):
+        # test warning code path
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter("always")
+            with np.errstate(all="warn"):
+                np.divide(1, 0.)
+                assert_equal(len(w), 1)
+                assert_("divide by zero" in str(w[0].message))
+                np.array(1e300) * np.array(1e300)
+                assert_equal(len(w), 2)
+                assert_("overflow" in str(w[-1].message))
+                np.array(np.inf) - np.array(np.inf)
+                assert_equal(len(w), 3)
+                assert_("invalid value" in str(w[-1].message))
+                np.array(1e-300) * np.array(1e-300)
+                assert_equal(len(w), 4)
+                assert_("underflow" in str(w[-1].message))
+
+
+class TestTypes:
+    def check_promotion_cases(self, promote_func):
+        # tests that the scalars get coerced correctly.
+        b = np.bool(0)
+        i8, i16, i32, i64 = np.int8(0), np.int16(0), np.int32(0), np.int64(0)
+        u8, u16, u32, u64 = np.uint8(0), np.uint16(0), np.uint32(0), np.uint64(0)
+        f32, f64, fld = np.float32(0), np.float64(0), np.longdouble(0)
+        c64, c128, cld = np.complex64(0), np.complex128(0), np.clongdouble(0)
+
+        # coercion within the same kind
+        assert_equal(promote_func(i8, i16), np.dtype(np.int16))
+        assert_equal(promote_func(i32, i8), np.dtype(np.int32))
+        assert_equal(promote_func(i16, i64), np.dtype(np.int64))
+        assert_equal(promote_func(u8, u32), np.dtype(np.uint32))
+        assert_equal(promote_func(f32, f64), np.dtype(np.float64))
+        assert_equal(promote_func(fld, f32), np.dtype(np.longdouble))
+        assert_equal(promote_func(f64, fld), np.dtype(np.longdouble))
+        assert_equal(promote_func(c128, c64), np.dtype(np.complex128))
+        assert_equal(promote_func(cld, c128), np.dtype(np.clongdouble))
+        assert_equal(promote_func(c64, fld), np.dtype(np.clongdouble))
+
+        # coercion between kinds
+        assert_equal(promote_func(b, i32), np.dtype(np.int32))
+        assert_equal(promote_func(b, u8), np.dtype(np.uint8))
+        assert_equal(promote_func(i8, u8), np.dtype(np.int16))
+        assert_equal(promote_func(u8, i32), np.dtype(np.int32))
+        assert_equal(promote_func(i64, u32), np.dtype(np.int64))
+        assert_equal(promote_func(u64, i32), np.dtype(np.float64))
+        assert_equal(promote_func(i32, f32), np.dtype(np.float64))
+        assert_equal(promote_func(i64, f32), np.dtype(np.float64))
+        assert_equal(promote_func(f32, i16), np.dtype(np.float32))
+        assert_equal(promote_func(f32, u32), np.dtype(np.float64))
+        assert_equal(promote_func(f32, c64), np.dtype(np.complex64))
+        assert_equal(promote_func(c128, f32), np.dtype(np.complex128))
+        assert_equal(promote_func(cld, f64), np.dtype(np.clongdouble))
+
+        # coercion between scalars and 1-D arrays
+        assert_equal(promote_func(np.array([b]), i8), np.dtype(np.int8))
+        assert_equal(promote_func(np.array([b]), u8), np.dtype(np.uint8))
+        assert_equal(promote_func(np.array([b]), i32), np.dtype(np.int32))
+        assert_equal(promote_func(np.array([b]), u32), np.dtype(np.uint32))
+        assert_equal(promote_func(np.array([i8]), i64), np.dtype(np.int64))
+        # unsigned and signed unfortunately tend to promote to float64:
+        assert_equal(promote_func(u64, np.array([i32])), np.dtype(np.float64))
+        assert_equal(promote_func(i64, np.array([u32])), np.dtype(np.int64))
+        assert_equal(promote_func(np.array([u16]), i32), np.dtype(np.int32))
+        assert_equal(promote_func(np.int32(-1), np.array([u64])),
+                     np.dtype(np.float64))
+        assert_equal(promote_func(f64, np.array([f32])), np.dtype(np.float64))
+        assert_equal(promote_func(fld, np.array([f32])),
+                     np.dtype(np.longdouble))
+        assert_equal(promote_func(np.array([f64]), fld),
+                     np.dtype(np.longdouble))
+        assert_equal(promote_func(fld, np.array([c64])),
+                     np.dtype(np.clongdouble))
+        assert_equal(promote_func(c64, np.array([f64])),
+                     np.dtype(np.complex128))
+        assert_equal(promote_func(np.complex64(3j), np.array([f64])),
+                     np.dtype(np.complex128))
+        assert_equal(promote_func(np.array([f32]), c128),
+                     np.dtype(np.complex128))
+
+        # coercion between scalars and 1-D arrays, where
+        # the scalar has greater kind than the array
+        assert_equal(promote_func(np.array([b]), f64), np.dtype(np.float64))
+        assert_equal(promote_func(np.array([b]), i64), np.dtype(np.int64))
+        assert_equal(promote_func(np.array([b]), u64), np.dtype(np.uint64))
+        assert_equal(promote_func(np.array([i8]), f64), np.dtype(np.float64))
+        assert_equal(promote_func(np.array([u16]), f64), np.dtype(np.float64))
+
+    def test_coercion(self):
+        def res_type(a, b):
+            return np.add(a, b).dtype
+
+        self.check_promotion_cases(res_type)
+
+        # Use-case: float/complex scalar * bool/int8 array
+        #           shouldn't narrow the float/complex type
+        for a in [np.array([True, False]), np.array([-3, 12], dtype=np.int8)]:
+            b = 1.234 * a
+            assert_equal(b.dtype, np.dtype('f8'), f"array type {a.dtype}")
+            b = np.longdouble(1.234) * a
+            assert_equal(b.dtype, np.dtype(np.longdouble),
+                         f"array type {a.dtype}")
+            b = np.float64(1.234) * a
+            assert_equal(b.dtype, np.dtype('f8'), f"array type {a.dtype}")
+            b = np.float32(1.234) * a
+            assert_equal(b.dtype, np.dtype('f4'), f"array type {a.dtype}")
+            b = np.float16(1.234) * a
+            assert_equal(b.dtype, np.dtype('f2'), f"array type {a.dtype}")
+
+            b = 1.234j * a
+            assert_equal(b.dtype, np.dtype('c16'), f"array type {a.dtype}")
+            b = np.clongdouble(1.234j) * a
+            assert_equal(b.dtype, np.dtype(np.clongdouble),
+                         f"array type {a.dtype}")
+            b = np.complex128(1.234j) * a
+            assert_equal(b.dtype, np.dtype('c16'), f"array type {a.dtype}")
+            b = np.complex64(1.234j) * a
+            assert_equal(b.dtype, np.dtype('c8'), f"array type {a.dtype}")
+
+        # The following use-case is problematic, and to resolve its
+        # tricky side-effects requires more changes.
+        #
+        # Use-case: (1-t)*a, where 't' is a boolean array and 'a' is
+        #            a float32, shouldn't promote to float64
+        #
+        # a = np.array([1.0, 1.5], dtype=np.float32)
+        # t = np.array([True, False])
+        # b = t*a
+        # assert_equal(b, [1.0, 0.0])
+        # assert_equal(b.dtype, np.dtype('f4'))
+        # b = (1-t)*a
+        # assert_equal(b, [0.0, 1.5])
+        # assert_equal(b.dtype, np.dtype('f4'))
+        #
+        # Probably ~t (bitwise negation) is more proper to use here,
+        # but this is arguably less intuitive to understand at a glance, and
+        # would fail if 't' is actually an integer array instead of boolean:
+        #
+        # b = (~t)*a
+        # assert_equal(b, [0.0, 1.5])
+        # assert_equal(b.dtype, np.dtype('f4'))
+
+    def test_result_type(self):
+        self.check_promotion_cases(np.result_type)
+        assert_(np.result_type(None) == np.dtype(None))
+
+    def test_promote_types_endian(self):
+        # promote_types should always return native-endian types
+        assert_equal(np.promote_types('<i8', '<i8'), np.dtype('i8'))
+        assert_equal(np.promote_types('>i8', '>i8'), np.dtype('i8'))
+
+        assert_equal(np.promote_types('>i8', '>U16'), np.dtype('U21'))
+        assert_equal(np.promote_types('<i8', '<U16'), np.dtype('U21'))
+        assert_equal(np.promote_types('>U16', '>i8'), np.dtype('U21'))
+        assert_equal(np.promote_types('<U16', '<i8'), np.dtype('U21'))
+
+        assert_equal(np.promote_types('<S5', '<U8'), np.dtype('U8'))
+        assert_equal(np.promote_types('>S5', '>U8'), np.dtype('U8'))
+        assert_equal(np.promote_types('<U8', '<S5'), np.dtype('U8'))
+        assert_equal(np.promote_types('>U8', '>S5'), np.dtype('U8'))
+        assert_equal(np.promote_types('<U5', '<U8'), np.dtype('U8'))
+        assert_equal(np.promote_types('>U8', '>U5'), np.dtype('U8'))
+
+        assert_equal(np.promote_types('<M8', '<M8'), np.dtype('M8'))
+        assert_equal(np.promote_types('>M8', '>M8'), np.dtype('M8'))
+        assert_equal(np.promote_types('<m8', '<m8'), np.dtype('m8'))
+        assert_equal(np.promote_types('>m8', '>m8'), np.dtype('m8'))
+
+    def test_can_cast_and_promote_usertypes(self):
+        # The rational type defines safe casting for signed integers,
+        # boolean. Rational itself *does* cast safely to double.
+        # (rational does not actually cast to all signed integers, e.g.
+        # int64 can be both long and longlong and it registers only the first)
+        valid_types = ["int8", "int16", "int32", "int64", "bool"]
+        invalid_types = "BHILQP" + "FDG" + "mM" + "f" + "V"
+
+        rational_dt = np.dtype(rational)
+        for numpy_dtype in valid_types:
+            numpy_dtype = np.dtype(numpy_dtype)
+            assert np.can_cast(numpy_dtype, rational_dt)
+            assert np.promote_types(numpy_dtype, rational_dt) is rational_dt
+
+        for numpy_dtype in invalid_types:
+            numpy_dtype = np.dtype(numpy_dtype)
+            assert not np.can_cast(numpy_dtype, rational_dt)
+            with pytest.raises(TypeError):
+                np.promote_types(numpy_dtype, rational_dt)
+
+        double_dt = np.dtype("double")
+        assert np.can_cast(rational_dt, double_dt)
+        assert np.promote_types(double_dt, rational_dt) is double_dt
+
+    @pytest.mark.parametrize("swap", ["", "swap"])
+    @pytest.mark.parametrize("string_dtype", ["U", "S"])
+    def test_promote_types_strings(self, swap, string_dtype):
+        if swap == "swap":
+            promote_types = lambda a, b: np.promote_types(b, a)
+        else:
+            promote_types = np.promote_types
+
+        S = string_dtype
+
+        # Promote numeric with unsized string:
+        assert_equal(promote_types('bool', S), np.dtype(S + '5'))
+        assert_equal(promote_types('b', S), np.dtype(S + '4'))
+        assert_equal(promote_types('u1', S), np.dtype(S + '3'))
+        assert_equal(promote_types('u2', S), np.dtype(S + '5'))
+        assert_equal(promote_types('u4', S), np.dtype(S + '10'))
+        assert_equal(promote_types('u8', S), np.dtype(S + '20'))
+        assert_equal(promote_types('i1', S), np.dtype(S + '4'))
+        assert_equal(promote_types('i2', S), np.dtype(S + '6'))
+        assert_equal(promote_types('i4', S), np.dtype(S + '11'))
+        assert_equal(promote_types('i8', S), np.dtype(S + '21'))
+        # Promote numeric with sized string:
+        assert_equal(promote_types('bool', S + '1'), np.dtype(S + '5'))
+        assert_equal(promote_types('bool', S + '30'), np.dtype(S + '30'))
+        assert_equal(promote_types('b', S + '1'), np.dtype(S + '4'))
+        assert_equal(promote_types('b', S + '30'), np.dtype(S + '30'))
+        assert_equal(promote_types('u1', S + '1'), np.dtype(S + '3'))
+        assert_equal(promote_types('u1', S + '30'), np.dtype(S + '30'))
+        assert_equal(promote_types('u2', S + '1'), np.dtype(S + '5'))
+        assert_equal(promote_types('u2', S + '30'), np.dtype(S + '30'))
+        assert_equal(promote_types('u4', S + '1'), np.dtype(S + '10'))
+        assert_equal(promote_types('u4', S + '30'), np.dtype(S + '30'))
+        assert_equal(promote_types('u8', S + '1'), np.dtype(S + '20'))
+        assert_equal(promote_types('u8', S + '30'), np.dtype(S + '30'))
+        # Promote with object:
+        assert_equal(promote_types('O', S + '30'), np.dtype('O'))
+
+    @pytest.mark.parametrize(["dtype1", "dtype2"],
+            [[np.dtype("V6"), np.dtype("V10")],  # mismatch shape
+             # Mismatching names:
+             [np.dtype([("name1", "i8")]), np.dtype([("name2", "i8")])],
+            ])
+    def test_invalid_void_promotion(self, dtype1, dtype2):
+        with pytest.raises(TypeError):
+            np.promote_types(dtype1, dtype2)
+
+    @pytest.mark.parametrize(["dtype1", "dtype2"],
+            [[np.dtype("V10"), np.dtype("V10")],
+             [np.dtype([("name1", "i8")]),
+              np.dtype([("name1", np.dtype("i8").newbyteorder())])],
+             [np.dtype("i8,i8"), np.dtype("i8,>i8")],
+             [np.dtype("i8,i8"), np.dtype("i4,i4")],
+            ])
+    def test_valid_void_promotion(self, dtype1, dtype2):
+        assert np.promote_types(dtype1, dtype2) == dtype1
+
+    @pytest.mark.parametrize("dtype",
+            list(np.typecodes["All"]) +
+            ["i,i", "10i", "S3", "S100", "U3", "U100", rational])
+    def test_promote_identical_types_metadata(self, dtype):
+        # The same type passed in twice to promote types always
+        # preserves metadata
+        metadata = {1: 1}
+        dtype = np.dtype(dtype, metadata=metadata)
+
+        res = np.promote_types(dtype, dtype)
+        assert res.metadata == dtype.metadata
+
+        # byte-swapping preserves and makes the dtype native:
+        dtype = dtype.newbyteorder()
+        if dtype.isnative:
+            # The type does not have byte swapping
+            return
+
+        res = np.promote_types(dtype, dtype)
+
+        # Metadata is (currently) generally lost on byte-swapping (except for
+        # unicode.
+        if dtype.char != "U":
+            assert res.metadata is None
+        else:
+            assert res.metadata == metadata
+        assert res.isnative
+
+    @pytest.mark.slow
+    @pytest.mark.filterwarnings('ignore:Promotion of numbers:FutureWarning')
+    @pytest.mark.parametrize(["dtype1", "dtype2"],
+            itertools.product(
+                list(np.typecodes["All"]) +
+                ["i,i", "S3", "S100", "U3", "U100", rational],
+                repeat=2))
+    def test_promote_types_metadata(self, dtype1, dtype2):
+        """Metadata handling in promotion does not appear formalized
+        right now in NumPy. This test should thus be considered to
+        document behaviour, rather than test the correct definition of it.
+
+        This test is very ugly, it was useful for rewriting part of the
+        promotion, but probably should eventually be replaced/deleted
+        (i.e. when metadata handling in promotion is better defined).
+        """
+        metadata1 = {1: 1}
+        metadata2 = {2: 2}
+        dtype1 = np.dtype(dtype1, metadata=metadata1)
+        dtype2 = np.dtype(dtype2, metadata=metadata2)
+
+        try:
+            res = np.promote_types(dtype1, dtype2)
+        except TypeError:
+            # Promotion failed, this test only checks metadata
+            return
+
+        if res.char not in "USV" or res.names is not None or res.shape != ():
+            # All except string dtypes (and unstructured void) lose metadata
+            # on promotion (unless both dtypes are identical).
+            # At some point structured ones did not, but were restrictive.
+            assert res.metadata is None
+        elif res == dtype1:
+            # If one result is the result, it is usually returned unchanged:
+            assert res is dtype1
+        elif res == dtype2:
+            # dtype1 may have been cast to the same type/kind as dtype2.
+            # If the resulting dtype is identical we currently pick the cast
+            # version of dtype1, which lost the metadata:
+            if np.promote_types(dtype1, dtype2.kind) == dtype2:
+                res.metadata is None
+            else:
+                res.metadata == metadata2
+        else:
+            assert res.metadata is None
+
+        # Try again for byteswapped version
+        dtype1 = dtype1.newbyteorder()
+        assert dtype1.metadata == metadata1
+        res_bs = np.promote_types(dtype1, dtype2)
+        assert res_bs == res
+        assert res_bs.metadata == res.metadata
+
+    def test_can_cast(self):
+        assert_(np.can_cast(np.int32, np.int64))
+        assert_(np.can_cast(np.float64, complex))
+        assert_(not np.can_cast(complex, float))
+
+        assert_(np.can_cast('i8', 'f8'))
+        assert_(not np.can_cast('i8', 'f4'))
+        assert_(np.can_cast('i4', 'S11'))
+
+        assert_(np.can_cast('i8', 'i8', 'no'))
+        assert_(not np.can_cast('<i8', '>i8', 'no'))
+
+        assert_(np.can_cast('<i8', '>i8', 'equiv'))
+        assert_(not np.can_cast('<i4', '>i8', 'equiv'))
+
+        assert_(np.can_cast('<i4', '>i8', 'safe'))
+        assert_(not np.can_cast('<i8', '>i4', 'safe'))
+
+        assert_(np.can_cast('<i8', '>i4', 'same_kind'))
+        assert_(not np.can_cast('<i8', '>u4', 'same_kind'))
+
+        assert_(np.can_cast('<i8', '>u4', 'unsafe'))
+
+        assert_(np.can_cast('bool', 'S5'))
+        assert_(not np.can_cast('bool', 'S4'))
+
+        assert_(np.can_cast('b', 'S4'))
+        assert_(not np.can_cast('b', 'S3'))
+
+        assert_(np.can_cast('u1', 'S3'))
+        assert_(not np.can_cast('u1', 'S2'))
+        assert_(np.can_cast('u2', 'S5'))
+        assert_(not np.can_cast('u2', 'S4'))
+        assert_(np.can_cast('u4', 'S10'))
+        assert_(not np.can_cast('u4', 'S9'))
+        assert_(np.can_cast('u8', 'S20'))
+        assert_(not np.can_cast('u8', 'S19'))
+
+        assert_(np.can_cast('i1', 'S4'))
+        assert_(not np.can_cast('i1', 'S3'))
+        assert_(np.can_cast('i2', 'S6'))
+        assert_(not np.can_cast('i2', 'S5'))
+        assert_(np.can_cast('i4', 'S11'))
+        assert_(not np.can_cast('i4', 'S10'))
+        assert_(np.can_cast('i8', 'S21'))
+        assert_(not np.can_cast('i8', 'S20'))
+
+        assert_(np.can_cast('bool', 'S5'))
+        assert_(not np.can_cast('bool', 'S4'))
+
+        assert_(np.can_cast('b', 'U4'))
+        assert_(not np.can_cast('b', 'U3'))
+
+        assert_(np.can_cast('u1', 'U3'))
+        assert_(not np.can_cast('u1', 'U2'))
+        assert_(np.can_cast('u2', 'U5'))
+        assert_(not np.can_cast('u2', 'U4'))
+        assert_(np.can_cast('u4', 'U10'))
+        assert_(not np.can_cast('u4', 'U9'))
+        assert_(np.can_cast('u8', 'U20'))
+        assert_(not np.can_cast('u8', 'U19'))
+
+        assert_(np.can_cast('i1', 'U4'))
+        assert_(not np.can_cast('i1', 'U3'))
+        assert_(np.can_cast('i2', 'U6'))
+        assert_(not np.can_cast('i2', 'U5'))
+        assert_(np.can_cast('i4', 'U11'))
+        assert_(not np.can_cast('i4', 'U10'))
+        assert_(np.can_cast('i8', 'U21'))
+        assert_(not np.can_cast('i8', 'U20'))
+
+        assert_raises(TypeError, np.can_cast, 'i4', None)
+        assert_raises(TypeError, np.can_cast, None, 'i4')
+
+        # Also test keyword arguments
+        assert_(np.can_cast(from_=np.int32, to=np.int64))
+
+    def test_can_cast_simple_to_structured(self):
+        # Non-structured can only be cast to structured in 'unsafe' mode.
+        assert_(not np.can_cast('i4', 'i4,i4'))
+        assert_(not np.can_cast('i4', 'i4,i2'))
+        assert_(np.can_cast('i4', 'i4,i4', casting='unsafe'))
+        assert_(np.can_cast('i4', 'i4,i2', casting='unsafe'))
+        # Even if there is just a single field which is OK.
+        assert_(not np.can_cast('i2', [('f1', 'i4')]))
+        assert_(not np.can_cast('i2', [('f1', 'i4')], casting='same_kind'))
+        assert_(np.can_cast('i2', [('f1', 'i4')], casting='unsafe'))
+        # It should be the same for recursive structured or subarrays.
+        assert_(not np.can_cast('i2', [('f1', 'i4,i4')]))
+        assert_(np.can_cast('i2', [('f1', 'i4,i4')], casting='unsafe'))
+        assert_(not np.can_cast('i2', [('f1', '(2,3)i4')]))
+        assert_(np.can_cast('i2', [('f1', '(2,3)i4')], casting='unsafe'))
+
+    def test_can_cast_structured_to_simple(self):
+        # Need unsafe casting for structured to simple.
+        assert_(not np.can_cast([('f1', 'i4')], 'i4'))
+        assert_(np.can_cast([('f1', 'i4')], 'i4', casting='unsafe'))
+        assert_(np.can_cast([('f1', 'i4')], 'i2', casting='unsafe'))
+        # Since it is unclear what is being cast, multiple fields to
+        # single should not work even for unsafe casting.
+        assert_(not np.can_cast('i4,i4', 'i4', casting='unsafe'))
+        # But a single field inside a single field is OK.
+        assert_(not np.can_cast([('f1', [('x', 'i4')])], 'i4'))
+        assert_(np.can_cast([('f1', [('x', 'i4')])], 'i4', casting='unsafe'))
+        # And a subarray is fine too - it will just take the first element
+        # (arguably not very consistently; might also take the first field).
+        assert_(not np.can_cast([('f0', '(3,)i4')], 'i4'))
+        assert_(np.can_cast([('f0', '(3,)i4')], 'i4', casting='unsafe'))
+        # But a structured subarray with multiple fields should fail.
+        assert_(not np.can_cast([('f0', ('i4,i4'), (2,))], 'i4',
+                                casting='unsafe'))
+
+    def test_can_cast_values(self):
+        # With NumPy 2 and NEP 50, can_cast errors on Python scalars.  We could
+        # define this as (usually safe) at some point, and already do so
+        # in `copyto` and ufuncs (but there an error is raised if the integer
+        # is out of bounds and a warning for out-of-bound floats).
+        # Raises even for unsafe, previously checked within range (for floats
+        # that was approximately whether it would overflow to inf).
+        with pytest.raises(TypeError):
+            np.can_cast(4, "int8", casting="unsafe")
+
+        with pytest.raises(TypeError):
+            np.can_cast(4.0, "float64", casting="unsafe")
+
+        with pytest.raises(TypeError):
+            np.can_cast(4j, "complex128", casting="unsafe")
+
+    @pytest.mark.parametrize("dtype",
+            list("?bhilqBHILQefdgFDG") + [rational])
+    def test_can_cast_scalars(self, dtype):
+        # Basic test to ensure that scalars are supported in can-cast
+        # (does not check behavior exhaustively).
+        dtype = np.dtype(dtype)
+        scalar = dtype.type(0)
+
+        assert np.can_cast(scalar, "int64") == np.can_cast(dtype, "int64")
+        assert np.can_cast(scalar, "float32", casting="unsafe")
+
+
+# Custom exception class to test exception propagation in fromiter
+class NIterError(Exception):
+    pass
+
+
+class TestFromiter:
+    def makegen(self):
+        return (x**2 for x in range(24))
+
+    def test_types(self):
+        ai32 = np.fromiter(self.makegen(), np.int32)
+        ai64 = np.fromiter(self.makegen(), np.int64)
+        af = np.fromiter(self.makegen(), float)
+        assert_(ai32.dtype == np.dtype(np.int32))
+        assert_(ai64.dtype == np.dtype(np.int64))
+        assert_(af.dtype == np.dtype(float))
+
+    def test_lengths(self):
+        expected = np.array(list(self.makegen()))
+        a = np.fromiter(self.makegen(), int)
+        a20 = np.fromiter(self.makegen(), int, 20)
+        assert_(len(a) == len(expected))
+        assert_(len(a20) == 20)
+        assert_raises(ValueError, np.fromiter,
+                          self.makegen(), int, len(expected) + 10)
+
+    def test_values(self):
+        expected = np.array(list(self.makegen()))
+        a = np.fromiter(self.makegen(), int)
+        a20 = np.fromiter(self.makegen(), int, 20)
+        assert_(np.all(a == expected, axis=0))
+        assert_(np.all(a20 == expected[:20], axis=0))
+
+    def load_data(self, n, eindex):
+        # Utility method for the issue 2592 tests.
+        # Raise an exception at the desired index in the iterator.
+        for e in range(n):
+            if e == eindex:
+                raise NIterError(f'error at index {eindex}')
+            yield e
+
+    @pytest.mark.parametrize("dtype", [int, object])
+    @pytest.mark.parametrize(["count", "error_index"], [(10, 5), (10, 9)])
+    def test_2592(self, count, error_index, dtype):
+        # Test iteration exceptions are correctly raised. The data/generator
+        # has `count` elements but errors at `error_index`
+        iterable = self.load_data(count, error_index)
+        with pytest.raises(NIterError):
+            np.fromiter(iterable, dtype=dtype, count=count)
+
+    @pytest.mark.parametrize("dtype", ["S", "S0", "V0", "U0"])
+    def test_empty_not_structured(self, dtype):
+        # Note, "S0" could be allowed at some point, so long "S" (without
+        # any length) is rejected.
+        with pytest.raises(ValueError, match="Must specify length"):
+            np.fromiter([], dtype=dtype)
+
+    @pytest.mark.parametrize(["dtype", "data"],
+            [("d", [1, 2, 3, 4, 5, 6, 7, 8, 9]),
+             ("O", [1, 2, 3, 4, 5, 6, 7, 8, 9]),
+             ("i,O", [(1, 2), (5, 4), (2, 3), (9, 8), (6, 7)]),
+             # subarray dtypes (important because their dimensions end up
+             # in the result arrays dimension:
+             ("2i", [(1, 2), (5, 4), (2, 3), (9, 8), (6, 7)]),
+             (np.dtype(("O", (2, 3))),
+              [((1, 2, 3), (3, 4, 5)), ((3, 2, 1), (5, 4, 3))])])
+    @pytest.mark.parametrize("length_hint", [0, 1])
+    def test_growth_and_complicated_dtypes(self, dtype, data, length_hint):
+        dtype = np.dtype(dtype)
+
+        data = data * 100  # make sure we realloc a bit
+
+        class MyIter:
+            # Class/example from gh-15789
+            def __length_hint__(self):
+                # only required to be an estimate, this is legal
+                return length_hint  # 0 or 1
+
+            def __iter__(self):
+                return iter(data)
+
+        res = np.fromiter(MyIter(), dtype=dtype)
+        expected = np.array(data, dtype=dtype)
+
+        assert_array_equal(res, expected)
+
+    def test_empty_result(self):
+        class MyIter:
+            def __length_hint__(self):
+                return 10
+
+            def __iter__(self):
+                return iter([])  # actual iterator is empty.
+
+        res = np.fromiter(MyIter(), dtype="d")
+        assert res.shape == (0,)
+        assert res.dtype == "d"
+
+    def test_too_few_items(self):
+        msg = "iterator too short: Expected 10 but iterator had only 3 items."
+        with pytest.raises(ValueError, match=msg):
+            np.fromiter([1, 2, 3], count=10, dtype=int)
+
+    def test_failed_itemsetting(self):
+        with pytest.raises(TypeError):
+            np.fromiter([1, None, 3], dtype=int)
+
+        # The following manages to hit somewhat trickier code paths:
+        iterable = ((2, 3, 4) for i in range(5))
+        with pytest.raises(ValueError):
+            np.fromiter(iterable, dtype=np.dtype((int, 2)))
+
+class TestNonzero:
+    def test_nonzero_trivial(self):
+        assert_equal(np.count_nonzero(np.array([])), 0)
+        assert_equal(np.count_nonzero(np.array([], dtype='?')), 0)
+        assert_equal(np.nonzero(np.array([])), ([],))
+
+        assert_equal(np.count_nonzero(np.array([0])), 0)
+        assert_equal(np.count_nonzero(np.array([0], dtype='?')), 0)
+        assert_equal(np.nonzero(np.array([0])), ([],))
+
+        assert_equal(np.count_nonzero(np.array([1])), 1)
+        assert_equal(np.count_nonzero(np.array([1], dtype='?')), 1)
+        assert_equal(np.nonzero(np.array([1])), ([0],))
+
+    def test_nonzero_zerodim(self):
+        err_msg = "Calling nonzero on 0d arrays is not allowed"
+        with assert_raises_regex(ValueError, err_msg):
+            np.nonzero(np.array(0))
+        with assert_raises_regex(ValueError, err_msg):
+            np.array(1).nonzero()
+
+    def test_nonzero_onedim(self):
+        x = np.array([1, 0, 2, -1, 0, 0, 8])
+        assert_equal(np.count_nonzero(x), 4)
+        assert_equal(np.count_nonzero(x), 4)
+        assert_equal(np.nonzero(x), ([0, 2, 3, 6],))
+
+        # x = np.array([(1, 2), (0, 0), (1, 1), (-1, 3), (0, 7)],
+        #              dtype=[('a', 'i4'), ('b', 'i2')])
+        x = np.array([(1, 2, -5, -3), (0, 0, 2, 7), (1, 1, 0, 1), (-1, 3, 1, 0), (0, 7, 0, 4)],
+                     dtype=[('a', 'i4'), ('b', 'i2'), ('c', 'i1'), ('d', 'i8')])
+        assert_equal(np.count_nonzero(x['a']), 3)
+        assert_equal(np.count_nonzero(x['b']), 4)
+        assert_equal(np.count_nonzero(x['c']), 3)
+        assert_equal(np.count_nonzero(x['d']), 4)
+        assert_equal(np.nonzero(x['a']), ([0, 2, 3],))
+        assert_equal(np.nonzero(x['b']), ([0, 2, 3, 4],))
+
+    def test_nonzero_twodim(self):
+        x = np.array([[0, 1, 0], [2, 0, 3]])
+        assert_equal(np.count_nonzero(x.astype('i1')), 3)
+        assert_equal(np.count_nonzero(x.astype('i2')), 3)
+        assert_equal(np.count_nonzero(x.astype('i4')), 3)
+        assert_equal(np.count_nonzero(x.astype('i8')), 3)
+        assert_equal(np.nonzero(x), ([0, 1, 1], [1, 0, 2]))
+
+        x = np.eye(3)
+        assert_equal(np.count_nonzero(x.astype('i1')), 3)
+        assert_equal(np.count_nonzero(x.astype('i2')), 3)
+        assert_equal(np.count_nonzero(x.astype('i4')), 3)
+        assert_equal(np.count_nonzero(x.astype('i8')), 3)
+        assert_equal(np.nonzero(x), ([0, 1, 2], [0, 1, 2]))
+
+        x = np.array([[(0, 1), (0, 0), (1, 11)],
+                   [(1, 1), (1, 0), (0, 0)],
+                   [(0, 0), (1, 5), (0, 1)]], dtype=[('a', 'f4'), ('b', 'u1')])
+        assert_equal(np.count_nonzero(x['a']), 4)
+        assert_equal(np.count_nonzero(x['b']), 5)
+        assert_equal(np.nonzero(x['a']), ([0, 1, 1, 2], [2, 0, 1, 1]))
+        assert_equal(np.nonzero(x['b']), ([0, 0, 1, 2, 2], [0, 2, 0, 1, 2]))
+
+        assert_(not x['a'].T.flags.aligned)
+        assert_equal(np.count_nonzero(x['a'].T), 4)
+        assert_equal(np.count_nonzero(x['b'].T), 5)
+        assert_equal(np.nonzero(x['a'].T), ([0, 1, 1, 2], [1, 1, 2, 0]))
+        assert_equal(np.nonzero(x['b'].T), ([0, 0, 1, 2, 2], [0, 1, 2, 0, 2]))
+
+    def test_sparse(self):
+        # test special sparse condition boolean code path
+        for i in range(20):
+            c = np.zeros(200, dtype=bool)
+            c[i::20] = True
+            assert_equal(np.nonzero(c)[0], np.arange(i, 200 + i, 20))
+
+            c = np.zeros(400, dtype=bool)
+            c[10 + i:20 + i] = True
+            c[20 + i * 2] = True
+            assert_equal(np.nonzero(c)[0],
+                         np.concatenate((np.arange(10 + i, 20 + i), [20 + i * 2])))
+
+    @pytest.mark.parametrize('dtype', [np.float32, np.float64])
+    def test_nonzero_float_dtypes(self, dtype):
+        rng = np.random.default_rng(seed=10)
+        x = ((2**33) * rng.normal(size=100)).astype(dtype)
+        x[rng.choice(50, size=100)] = 0
+        idxs = np.nonzero(x)[0]
+        assert_equal(np.array_equal(np.where(x != 0)[0], idxs), True)
+
+    @pytest.mark.parametrize('dtype', [bool, np.int8, np.int16, np.int32, np.int64,
+                                       np.uint8, np.uint16, np.uint32, np.uint64])
+    def test_nonzero_integer_dtypes(self, dtype):
+        rng = np.random.default_rng(seed=10)
+        x = rng.integers(0, 255, size=100).astype(dtype)
+        x[rng.choice(50, size=100)] = 0
+        idxs = np.nonzero(x)[0]
+        assert_equal(np.array_equal(np.where(x != 0)[0], idxs), True)
+
+    def test_return_type(self):
+        class C(np.ndarray):
+            pass
+
+        for view in (C, np.ndarray):
+            for nd in range(1, 4):
+                shape = tuple(range(2, 2 + nd))
+                x = np.arange(np.prod(shape)).reshape(shape).view(view)
+                for nzx in (np.nonzero(x), x.nonzero()):
+                    for nzx_i in nzx:
+                        assert_(type(nzx_i) is np.ndarray)
+                        assert_(nzx_i.flags.writeable)
+
+    def test_count_nonzero_axis(self):
+        # Basic check of functionality
+        m = np.array([[0, 1, 7, 0, 0], [3, 0, 0, 2, 19]])
+
+        expected = np.array([1, 1, 1, 1, 1])
+        assert_equal(np.count_nonzero(m, axis=0), expected)
+
+        expected = np.array([2, 3])
+        assert_equal(np.count_nonzero(m, axis=1), expected)
+
+        assert_raises(ValueError, np.count_nonzero, m, axis=(1, 1))
+        assert_raises(TypeError, np.count_nonzero, m, axis='foo')
+        assert_raises(AxisError, np.count_nonzero, m, axis=3)
+        assert_raises(TypeError, np.count_nonzero,
+                      m, axis=np.array([[1], [2]]))
+
+    def test_count_nonzero_axis_all_dtypes(self):
+        # More thorough test that the axis argument is respected
+        # for all dtypes and responds correctly when presented with
+        # either integer or tuple arguments for axis
+        msg = "Mismatch for dtype: %s"
+
+        def assert_equal_w_dt(a, b, err_msg):
+            assert_equal(a.dtype, b.dtype, err_msg=err_msg)
+            assert_equal(a, b, err_msg=err_msg)
+
+        for dt in np.typecodes['All']:
+            err_msg = msg % (np.dtype(dt).name,)
+
+            if dt != 'V':
+                if dt != 'M':
+                    m = np.zeros((3, 3), dtype=dt)
+                    n = np.ones(1, dtype=dt)
+
+                    m[0, 0] = n[0]
+                    m[1, 0] = n[0]
+
+                else:  # np.zeros doesn't work for np.datetime64
+                    m = np.array(['1970-01-01'] * 9)
+                    m = m.reshape((3, 3))
+
+                    m[0, 0] = '1970-01-12'
+                    m[1, 0] = '1970-01-12'
+                    m = m.astype(dt)
+
+                expected = np.array([2, 0, 0], dtype=np.intp)
+                assert_equal_w_dt(np.count_nonzero(m, axis=0),
+                                  expected, err_msg=err_msg)
+
+                expected = np.array([1, 1, 0], dtype=np.intp)
+                assert_equal_w_dt(np.count_nonzero(m, axis=1),
+                                  expected, err_msg=err_msg)
+
+                expected = np.array(2)
+                assert_equal(np.count_nonzero(m, axis=(0, 1)),
+                             expected, err_msg=err_msg)
+                assert_equal(np.count_nonzero(m, axis=None),
+                             expected, err_msg=err_msg)
+                assert_equal(np.count_nonzero(m),
+                             expected, err_msg=err_msg)
+
+            if dt == 'V':
+                # There are no 'nonzero' objects for np.void, so the testing
+                # setup is slightly different for this dtype
+                m = np.array([np.void(1)] * 6).reshape((2, 3))
+
+                expected = np.array([0, 0, 0], dtype=np.intp)
+                assert_equal_w_dt(np.count_nonzero(m, axis=0),
+                                  expected, err_msg=err_msg)
+
+                expected = np.array([0, 0], dtype=np.intp)
+                assert_equal_w_dt(np.count_nonzero(m, axis=1),
+                                  expected, err_msg=err_msg)
+
+                expected = np.array(0)
+                assert_equal(np.count_nonzero(m, axis=(0, 1)),
+                             expected, err_msg=err_msg)
+                assert_equal(np.count_nonzero(m, axis=None),
+                             expected, err_msg=err_msg)
+                assert_equal(np.count_nonzero(m),
+                             expected, err_msg=err_msg)
+
+    def test_count_nonzero_axis_consistent(self):
+        # Check that the axis behaviour for valid axes in
+        # non-special cases is consistent (and therefore
+        # correct) by checking it against an integer array
+        # that is then casted to the generic object dtype
+        from itertools import combinations, permutations
+
+        axis = (0, 1, 2, 3)
+        size = (5, 5, 5, 5)
+        msg = "Mismatch for axis: %s"
+
+        rng = np.random.RandomState(1234)
+        m = rng.randint(-100, 100, size=size)
+        n = m.astype(object)
+
+        for length in range(len(axis)):
+            for combo in combinations(axis, length):
+                for perm in permutations(combo):
+                    assert_equal(
+                        np.count_nonzero(m, axis=perm),
+                        np.count_nonzero(n, axis=perm),
+                        err_msg=msg % (perm,))
+
+    def test_countnonzero_axis_empty(self):
+        a = np.array([[0, 0, 1], [1, 0, 1]])
+        assert_equal(np.count_nonzero(a, axis=()), a.astype(bool))
+
+    def test_countnonzero_keepdims(self):
+        a = np.array([[0, 0, 1, 0],
+                      [0, 3, 5, 0],
+                      [7, 9, 2, 0]])
+        assert_equal(np.count_nonzero(a, axis=0, keepdims=True),
+                     [[1, 2, 3, 0]])
+        assert_equal(np.count_nonzero(a, axis=1, keepdims=True),
+                     [[1], [2], [3]])
+        assert_equal(np.count_nonzero(a, keepdims=True),
+                     [[6]])
+
+    def test_array_method(self):
+        # Tests that the array method
+        # call to nonzero works
+        m = np.array([[1, 0, 0], [4, 0, 6]])
+        tgt = [[0, 1, 1], [0, 0, 2]]
+
+        assert_equal(m.nonzero(), tgt)
+
+    def test_nonzero_invalid_object(self):
+        # gh-9295
+        a = np.array([np.array([1, 2]), 3], dtype=object)
+        assert_raises(ValueError, np.nonzero, a)
+
+        class BoolErrors:
+            def __bool__(self):
+                raise ValueError("Not allowed")
+
+        assert_raises(ValueError, np.nonzero, np.array([BoolErrors()]))
+
+    def test_nonzero_sideeffect_safety(self):
+        # gh-13631
+        class FalseThenTrue:
+            _val = False
+
+            def __bool__(self):
+                try:
+                    return self._val
+                finally:
+                    self._val = True
+
+        class TrueThenFalse:
+            _val = True
+
+            def __bool__(self):
+                try:
+                    return self._val
+                finally:
+                    self._val = False
+
+        # result grows on the second pass
+        a = np.array([True, FalseThenTrue()])
+        assert_raises(RuntimeError, np.nonzero, a)
+
+        a = np.array([[True], [FalseThenTrue()]])
+        assert_raises(RuntimeError, np.nonzero, a)
+
+        # result shrinks on the second pass
+        a = np.array([False, TrueThenFalse()])
+        assert_raises(RuntimeError, np.nonzero, a)
+
+        a = np.array([[False], [TrueThenFalse()]])
+        assert_raises(RuntimeError, np.nonzero, a)
+
+    def test_nonzero_sideffects_structured_void(self):
+        # Checks that structured void does not mutate alignment flag of
+        # original array.
+        arr = np.zeros(5, dtype="i1,i8,i8")  # `ones` may short-circuit
+        assert arr.flags.aligned  # structs are considered "aligned"
+        assert not arr["f2"].flags.aligned
+        # make sure that nonzero/count_nonzero do not flip the flag:
+        np.nonzero(arr)
+        assert arr.flags.aligned
+        np.count_nonzero(arr)
+        assert arr.flags.aligned
+
+    def test_nonzero_exception_safe(self):
+        # gh-13930
+
+        class ThrowsAfter:
+            def __init__(self, iters):
+                self.iters_left = iters
+
+            def __bool__(self):
+                if self.iters_left == 0:
+                    raise ValueError("called `iters` times")
+
+                self.iters_left -= 1
+                return True
+
+        """
+        Test that a ValueError is raised instead of a SystemError
+
+        If the __bool__ function is called after the error state is set,
+        Python (cpython) will raise a SystemError.
+        """
+
+        # assert that an exception in first pass is handled correctly
+        a = np.array([ThrowsAfter(5)] * 10)
+        assert_raises(ValueError, np.nonzero, a)
+
+        # raise exception in second pass for 1-dimensional loop
+        a = np.array([ThrowsAfter(15)] * 10)
+        assert_raises(ValueError, np.nonzero, a)
+
+        # raise exception in second pass for n-dimensional loop
+        a = np.array([[ThrowsAfter(15)]] * 10)
+        assert_raises(ValueError, np.nonzero, a)
+
+    def test_nonzero_byteorder(self):
+        values = [0., -0., 1, float('nan'), 0, 1,
+                  np.float16(0), np.float16(12.3)]
+        expected_values = [0, 0, 1, 1, 0, 1, 0, 1]
+
+        for value, expected in zip(values, expected_values):
+            A = np.array([value])
+            A_byteswapped = (A.view(A.dtype.newbyteorder()).byteswap()).copy()
+
+            assert np.count_nonzero(A) == expected
+            assert np.count_nonzero(A_byteswapped) == expected
+
+    def test_count_nonzero_non_aligned_array(self):
+        # gh-27523
+        b = np.zeros(64 + 1, dtype=np.int8)[1:]
+        b = b.view(int)
+        b[:] = np.arange(b.size)
+        b[::2] = 0
+        assert b.flags.aligned is False
+        assert np.count_nonzero(b) == b.size / 2
+
+        b = np.zeros(64 + 1, dtype=np.float16)[1:]
+        b = b.view(float)
+        b[:] = np.arange(b.size)
+        b[::2] = 0
+        assert b.flags.aligned is False
+        assert np.count_nonzero(b) == b.size / 2
+
+
+class TestIndex:
+    def test_boolean(self):
+        a = rand(3, 5, 8)
+        V = rand(5, 8)
+        g1 = randint(0, 5, size=15)
+        g2 = randint(0, 8, size=15)
+        V[g1, g2] = -V[g1, g2]
+        assert_((np.array([a[0][V > 0], a[1][V > 0], a[2][V > 0]]) == a[:, V > 0]).all())
+
+    def test_boolean_edgecase(self):
+        a = np.array([], dtype='int32')
+        b = np.array([], dtype='bool')
+        c = a[b]
+        assert_equal(c, [])
+        assert_equal(c.dtype, np.dtype('int32'))
+
+
+class TestBinaryRepr:
+    def test_zero(self):
+        assert_equal(np.binary_repr(0), '0')
+
+    def test_positive(self):
+        assert_equal(np.binary_repr(10), '1010')
+        assert_equal(np.binary_repr(12522),
+                     '11000011101010')
+        assert_equal(np.binary_repr(10736848),
+                     '101000111101010011010000')
+
+    def test_negative(self):
+        assert_equal(np.binary_repr(-1), '-1')
+        assert_equal(np.binary_repr(-10), '-1010')
+        assert_equal(np.binary_repr(-12522),
+                     '-11000011101010')
+        assert_equal(np.binary_repr(-10736848),
+                     '-101000111101010011010000')
+
+    def test_sufficient_width(self):
+        assert_equal(np.binary_repr(0, width=5), '00000')
+        assert_equal(np.binary_repr(10, width=7), '0001010')
+        assert_equal(np.binary_repr(-5, width=7), '1111011')
+
+    def test_neg_width_boundaries(self):
+        # see gh-8670
+
+        # Ensure that the example in the issue does not
+        # break before proceeding to a more thorough test.
+        assert_equal(np.binary_repr(-128, width=8), '10000000')
+
+        for width in range(1, 11):
+            num = -2**(width - 1)
+            exp = '1' + (width - 1) * '0'
+            assert_equal(np.binary_repr(num, width=width), exp)
+
+    def test_large_neg_int64(self):
+        # See gh-14289.
+        assert_equal(np.binary_repr(np.int64(-2**62), width=64),
+                     '11' + '0' * 62)
+
+
+class TestBaseRepr:
+    def test_base3(self):
+        assert_equal(np.base_repr(3**5, 3), '100000')
+
+    def test_positive(self):
+        assert_equal(np.base_repr(12, 10), '12')
+        assert_equal(np.base_repr(12, 10, 4), '000012')
+        assert_equal(np.base_repr(12, 4), '30')
+        assert_equal(np.base_repr(3731624803700888, 36), '10QR0ROFCEW')
+
+    def test_negative(self):
+        assert_equal(np.base_repr(-12, 10), '-12')
+        assert_equal(np.base_repr(-12, 10, 4), '-000012')
+        assert_equal(np.base_repr(-12, 4), '-30')
+
+    def test_base_range(self):
+        with assert_raises(ValueError):
+            np.base_repr(1, 1)
+        with assert_raises(ValueError):
+            np.base_repr(1, 37)
+
+    def test_minimal_signed_int(self):
+        assert_equal(np.base_repr(np.int8(-128)), '-10000000')
+
+
+def _test_array_equal_parametrizations():
+    """
+    we pre-create arrays as we sometime want to pass the same instance
+    and sometime not. Passing the same instances may not mean the array are
+    equal, especially when containing None
+    """
+    # those are 0-d arrays, it used to be a special case
+    # where (e0 == e0).all() would raise
+    e0 = np.array(0, dtype="int")
+    e1 = np.array(1, dtype="float")
+    # x,y, nan_equal, expected_result
+    yield (e0, e0.copy(), None, True)
+    yield (e0, e0.copy(), False, True)
+    yield (e0, e0.copy(), True, True)
+
+    #
+    yield (e1, e1.copy(), None, True)
+    yield (e1, e1.copy(), False, True)
+    yield (e1, e1.copy(), True, True)
+
+    # Non-nanable - those cannot hold nans
+    a12 = np.array([1, 2])
+    a12b = a12.copy()
+    a123 = np.array([1, 2, 3])
+    a13 = np.array([1, 3])
+    a34 = np.array([3, 4])
+
+    aS1 = np.array(["a"], dtype="S1")
+    aS1b = aS1.copy()
+    aS1u4 = np.array([("a", 1)], dtype="S1,u4")
+    aS1u4b = aS1u4.copy()
+
+    yield (a12, a12b, None, True)
+    yield (a12, a12, None, True)
+    yield (a12, a123, None, False)
+    yield (a12, a34, None, False)
+    yield (a12, a13, None, False)
+    yield (aS1, aS1b, None, True)
+    yield (aS1, aS1, None, True)
+
+    # Non-float dtype - equal_nan should have no effect,
+    yield (a123, a123, None, True)
+    yield (a123, a123, False, True)
+    yield (a123, a123, True, True)
+    yield (a123, a123.copy(), None, True)
+    yield (a123, a123.copy(), False, True)
+    yield (a123, a123.copy(), True, True)
+    yield (a123.astype("float"), a123.astype("float"), None, True)
+    yield (a123.astype("float"), a123.astype("float"), False, True)
+    yield (a123.astype("float"), a123.astype("float"), True, True)
+
+    # these can hold None
+    b1 = np.array([1, 2, np.nan])
+    b2 = np.array([1, np.nan, 2])
+    b3 = np.array([1, 2, np.inf])
+    b4 = np.array(np.nan)
+
+    # instances are the same
+    yield (b1, b1, None, False)
+    yield (b1, b1, False, False)
+    yield (b1, b1, True, True)
+
+    # equal but not same instance
+    yield (b1, b1.copy(), None, False)
+    yield (b1, b1.copy(), False, False)
+    yield (b1, b1.copy(), True, True)
+
+    # same once stripped of Nan
+    yield (b1, b2, None, False)
+    yield (b1, b2, False, False)
+    yield (b1, b2, True, False)
+
+    # nan's not conflated with inf's
+    yield (b1, b3, None, False)
+    yield (b1, b3, False, False)
+    yield (b1, b3, True, False)
+
+    # all Nan
+    yield (b4, b4, None, False)
+    yield (b4, b4, False, False)
+    yield (b4, b4, True, True)
+    yield (b4, b4.copy(), None, False)
+    yield (b4, b4.copy(), False, False)
+    yield (b4, b4.copy(), True, True)
+
+    t1 = b1.astype("timedelta64")
+    t2 = b2.astype("timedelta64")
+
+    # Timedeltas are particular
+    yield (t1, t1, None, False)
+    yield (t1, t1, False, False)
+    yield (t1, t1, True, True)
+
+    yield (t1, t1.copy(), None, False)
+    yield (t1, t1.copy(), False, False)
+    yield (t1, t1.copy(), True, True)
+
+    yield (t1, t2, None, False)
+    yield (t1, t2, False, False)
+    yield (t1, t2, True, False)
+
+    # Multi-dimensional array
+    md1 = np.array([[0, 1], [np.nan, 1]])
+
+    yield (md1, md1, None, False)
+    yield (md1, md1, False, False)
+    yield (md1, md1, True, True)
+    yield (md1, md1.copy(), None, False)
+    yield (md1, md1.copy(), False, False)
+    yield (md1, md1.copy(), True, True)
+    # both complexes are nan+nan.j but the same instance
+    cplx1, cplx2 = [np.array([np.nan + np.nan * 1j])] * 2
+
+    # only real or img are nan.
+    cplx3, cplx4 = np.complex64(1, np.nan), np.complex64(np.nan, 1)
+
+    # Complex values
+    yield (cplx1, cplx2, None, False)
+    yield (cplx1, cplx2, False, False)
+    yield (cplx1, cplx2, True, True)
+
+    # Complex values, 1+nan, nan+1j
+    yield (cplx3, cplx4, None, False)
+    yield (cplx3, cplx4, False, False)
+    yield (cplx3, cplx4, True, True)
+
+
+class TestArrayComparisons:
+    @pytest.mark.parametrize(
+        "bx,by,equal_nan,expected", _test_array_equal_parametrizations()
+    )
+    def test_array_equal_equal_nan(self, bx, by, equal_nan, expected):
+        """
+        This test array_equal for a few combinations:
+
+        - are the two inputs the same object or not (same object may not
+          be equal if contains NaNs)
+        - Whether we should consider or not, NaNs, being equal.
+
+        """
+        if equal_nan is None:
+            res = np.array_equal(bx, by)
+        else:
+            res = np.array_equal(bx, by, equal_nan=equal_nan)
+        assert_(res is expected)
+        assert_(type(res) is bool)
+
+    def test_array_equal_different_scalar_types(self):
+        # https://github.com/numpy/numpy/issues/27271
+        a = np.array("foo")
+        b = np.array(1)
+        assert not np.array_equal(a, b)
+        assert not np.array_equiv(a, b)
+
+    def test_none_compares_elementwise(self):
+        a = np.array([None, 1, None], dtype=object)
+        assert_equal(a == None, [True, False, True])  # noqa: E711
+        assert_equal(a != None, [False, True, False])  # noqa: E711
+
+        a = np.ones(3)
+        assert_equal(a == None, [False, False, False])  # noqa: E711
+        assert_equal(a != None, [True, True, True])  # noqa: E711
+
+    def test_array_equiv(self):
+        res = np.array_equiv(np.array([1, 2]), np.array([1, 2]))
+        assert_(res)
+        assert_(type(res) is bool)
+        res = np.array_equiv(np.array([1, 2]), np.array([1, 2, 3]))
+        assert_(not res)
+        assert_(type(res) is bool)
+        res = np.array_equiv(np.array([1, 2]), np.array([3, 4]))
+        assert_(not res)
+        assert_(type(res) is bool)
+        res = np.array_equiv(np.array([1, 2]), np.array([1, 3]))
+        assert_(not res)
+        assert_(type(res) is bool)
+
+        res = np.array_equiv(np.array([1, 1]), np.array([1]))
+        assert_(res)
+        assert_(type(res) is bool)
+        res = np.array_equiv(np.array([1, 1]), np.array([[1], [1]]))
+        assert_(res)
+        assert_(type(res) is bool)
+        res = np.array_equiv(np.array([1, 2]), np.array([2]))
+        assert_(not res)
+        assert_(type(res) is bool)
+        res = np.array_equiv(np.array([1, 2]), np.array([[1], [2]]))
+        assert_(not res)
+        assert_(type(res) is bool)
+        res = np.array_equiv(np.array([1, 2]), np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
+        assert_(not res)
+        assert_(type(res) is bool)
+
+    @pytest.mark.parametrize("dtype", ["V0", "V3", "V10"])
+    def test_compare_unstructured_voids(self, dtype):
+        zeros = np.zeros(3, dtype=dtype)
+
+        assert_array_equal(zeros, zeros)
+        assert not (zeros != zeros).any()
+
+        if dtype == "V0":
+            # Can't test != of actually different data
+            return
+
+        nonzeros = np.array([b"1", b"2", b"3"], dtype=dtype)
+
+        assert not (zeros == nonzeros).any()
+        assert (zeros != nonzeros).all()
+
+
+def assert_array_strict_equal(x, y):
+    assert_array_equal(x, y)
+    # Check flags, 32 bit arches typically don't provide 16 byte alignment
+    if ((x.dtype.alignment <= 8 or
+            np.intp().dtype.itemsize != 4) and
+            sys.platform != 'win32'):
+        assert_(x.flags == y.flags)
+    else:
+        assert_(x.flags.owndata == y.flags.owndata)
+        assert_(x.flags.writeable == y.flags.writeable)
+        assert_(x.flags.c_contiguous == y.flags.c_contiguous)
+        assert_(x.flags.f_contiguous == y.flags.f_contiguous)
+        assert_(x.flags.writebackifcopy == y.flags.writebackifcopy)
+    # check endianness
+    assert_(x.dtype.isnative == y.dtype.isnative)
+
+
+class TestClip:
+    def setup_method(self):
+        self.nr = 5
+        self.nc = 3
+
+    def fastclip(self, a, m, M, out=None, **kwargs):
+        return a.clip(m, M, out=out, **kwargs)
+
+    def clip(self, a, m, M, out=None):
+        # use a.choose to verify fastclip result
+        selector = np.less(a, m) + 2 * np.greater(a, M)
+        return selector.choose((a, m, M), out=out)
+
+    # Handy functions
+    def _generate_data(self, n, m):
+        return randn(n, m)
+
+    def _generate_data_complex(self, n, m):
+        return randn(n, m) + 1.j * rand(n, m)
+
+    def _generate_flt_data(self, n, m):
+        return (randn(n, m)).astype(np.float32)
+
+    def _neg_byteorder(self, a):
+        a = np.asarray(a)
+        if sys.byteorder == 'little':
+            a = a.astype(a.dtype.newbyteorder('>'))
+        else:
+            a = a.astype(a.dtype.newbyteorder('<'))
+        return a
+
+    def _generate_non_native_data(self, n, m):
+        data = randn(n, m)
+        data = self._neg_byteorder(data)
+        assert_(not data.dtype.isnative)
+        return data
+
+    def _generate_int_data(self, n, m):
+        return (10 * rand(n, m)).astype(np.int64)
+
+    def _generate_int32_data(self, n, m):
+        return (10 * rand(n, m)).astype(np.int32)
+
+    # Now the real test cases
+
+    @pytest.mark.parametrize("dtype", '?bhilqpBHILQPefdgFDGO')
+    def test_ones_pathological(self, dtype):
+        # for preservation of behavior described in
+        # gh-12519; amin > amax behavior may still change
+        # in the future
+        arr = np.ones(10, dtype=dtype)
+        expected = np.zeros(10, dtype=dtype)
+        actual = np.clip(arr, 1, 0)
+        if dtype == 'O':
+            assert actual.tolist() == expected.tolist()
+        else:
+            assert_equal(actual, expected)
+
+    def test_simple_double(self):
+        # Test native double input with scalar min/max.
+        a = self._generate_data(self.nr, self.nc)
+        m = 0.1
+        M = 0.6
+        ac = self.fastclip(a, m, M)
+        act = self.clip(a, m, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_simple_int(self):
+        # Test native int input with scalar min/max.
+        a = self._generate_int_data(self.nr, self.nc)
+        a = a.astype(int)
+        m = -2
+        M = 4
+        ac = self.fastclip(a, m, M)
+        act = self.clip(a, m, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_array_double(self):
+        # Test native double input with array min/max.
+        a = self._generate_data(self.nr, self.nc)
+        m = np.zeros(a.shape)
+        M = m + 0.5
+        ac = self.fastclip(a, m, M)
+        act = self.clip(a, m, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_simple_nonnative(self):
+        # Test non native double input with scalar min/max.
+        # Test native double input with non native double scalar min/max.
+        a = self._generate_non_native_data(self.nr, self.nc)
+        m = -0.5
+        M = 0.6
+        ac = self.fastclip(a, m, M)
+        act = self.clip(a, m, M)
+        assert_array_equal(ac, act)
+
+        # Test native double input with non native double scalar min/max.
+        a = self._generate_data(self.nr, self.nc)
+        m = -0.5
+        M = self._neg_byteorder(0.6)
+        assert_(not M.dtype.isnative)
+        ac = self.fastclip(a, m, M)
+        act = self.clip(a, m, M)
+        assert_array_equal(ac, act)
+
+    def test_simple_complex(self):
+        # Test native complex input with native double scalar min/max.
+        # Test native input with complex double scalar min/max.
+        a = 3 * self._generate_data_complex(self.nr, self.nc)
+        m = -0.5
+        M = 1.
+        ac = self.fastclip(a, m, M)
+        act = self.clip(a, m, M)
+        assert_array_strict_equal(ac, act)
+
+        # Test native input with complex double scalar min/max.
+        a = 3 * self._generate_data(self.nr, self.nc)
+        m = -0.5 + 1.j
+        M = 1. + 2.j
+        ac = self.fastclip(a, m, M)
+        act = self.clip(a, m, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_clip_complex(self):
+        # Address Issue gh-5354 for clipping complex arrays
+        # Test native complex input without explicit min/max
+        # ie, either min=None or max=None
+        a = np.ones(10, dtype=complex)
+        m = a.min()
+        M = a.max()
+        am = self.fastclip(a, m, None)
+        aM = self.fastclip(a, None, M)
+        assert_array_strict_equal(am, a)
+        assert_array_strict_equal(aM, a)
+
+    def test_clip_non_contig(self):
+        # Test clip for non contiguous native input and native scalar min/max.
+        a = self._generate_data(self.nr * 2, self.nc * 3)
+        a = a[::2, ::3]
+        assert_(not a.flags['F_CONTIGUOUS'])
+        assert_(not a.flags['C_CONTIGUOUS'])
+        ac = self.fastclip(a, -1.6, 1.7)
+        act = self.clip(a, -1.6, 1.7)
+        assert_array_strict_equal(ac, act)
+
+    def test_simple_out(self):
+        # Test native double input with scalar min/max.
+        a = self._generate_data(self.nr, self.nc)
+        m = -0.5
+        M = 0.6
+        ac = np.zeros(a.shape)
+        act = np.zeros(a.shape)
+        self.fastclip(a, m, M, ac)
+        self.clip(a, m, M, act)
+        assert_array_strict_equal(ac, act)
+
+    @pytest.mark.parametrize("casting", [None, "unsafe"])
+    def test_simple_int32_inout(self, casting):
+        # Test native int32 input with double min/max and int32 out.
+        a = self._generate_int32_data(self.nr, self.nc)
+        m = np.float64(0)
+        M = np.float64(2)
+        ac = np.zeros(a.shape, dtype=np.int32)
+        act = ac.copy()
+        if casting is None:
+            with pytest.raises(TypeError):
+                self.fastclip(a, m, M, ac, casting=casting)
+        else:
+            # explicitly passing "unsafe" will silence warning
+            self.fastclip(a, m, M, ac, casting=casting)
+            self.clip(a, m, M, act)
+            assert_array_strict_equal(ac, act)
+
+    def test_simple_int64_out(self):
+        # Test native int32 input with int32 scalar min/max and int64 out.
+        a = self._generate_int32_data(self.nr, self.nc)
+        m = np.int32(-1)
+        M = np.int32(1)
+        ac = np.zeros(a.shape, dtype=np.int64)
+        act = ac.copy()
+        self.fastclip(a, m, M, ac)
+        self.clip(a, m, M, act)
+        assert_array_strict_equal(ac, act)
+
+    def test_simple_int64_inout(self):
+        # Test native int32 input with double array min/max and int32 out.
+        a = self._generate_int32_data(self.nr, self.nc)
+        m = np.zeros(a.shape, np.float64)
+        M = np.float64(1)
+        ac = np.zeros(a.shape, dtype=np.int32)
+        act = ac.copy()
+        self.fastclip(a, m, M, out=ac, casting="unsafe")
+        self.clip(a, m, M, act)
+        assert_array_strict_equal(ac, act)
+
+    def test_simple_int32_out(self):
+        # Test native double input with scalar min/max and int out.
+        a = self._generate_data(self.nr, self.nc)
+        m = -1.0
+        M = 2.0
+        ac = np.zeros(a.shape, dtype=np.int32)
+        act = ac.copy()
+        self.fastclip(a, m, M, out=ac, casting="unsafe")
+        self.clip(a, m, M, act)
+        assert_array_strict_equal(ac, act)
+
+    def test_simple_inplace_01(self):
+        # Test native double input with array min/max in-place.
+        a = self._generate_data(self.nr, self.nc)
+        ac = a.copy()
+        m = np.zeros(a.shape)
+        M = 1.0
+        self.fastclip(a, m, M, a)
+        self.clip(a, m, M, ac)
+        assert_array_strict_equal(a, ac)
+
+    def test_simple_inplace_02(self):
+        # Test native double input with scalar min/max in-place.
+        a = self._generate_data(self.nr, self.nc)
+        ac = a.copy()
+        m = -0.5
+        M = 0.6
+        self.fastclip(a, m, M, a)
+        self.clip(ac, m, M, ac)
+        assert_array_strict_equal(a, ac)
+
+    def test_noncontig_inplace(self):
+        # Test non contiguous double input with double scalar min/max in-place.
+        a = self._generate_data(self.nr * 2, self.nc * 3)
+        a = a[::2, ::3]
+        assert_(not a.flags['F_CONTIGUOUS'])
+        assert_(not a.flags['C_CONTIGUOUS'])
+        ac = a.copy()
+        m = -0.5
+        M = 0.6
+        self.fastclip(a, m, M, a)
+        self.clip(ac, m, M, ac)
+        assert_array_equal(a, ac)
+
+    def test_type_cast_01(self):
+        # Test native double input with scalar min/max.
+        a = self._generate_data(self.nr, self.nc)
+        m = -0.5
+        M = 0.6
+        ac = self.fastclip(a, m, M)
+        act = self.clip(a, m, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_02(self):
+        # Test native int32 input with int32 scalar min/max.
+        a = self._generate_int_data(self.nr, self.nc)
+        a = a.astype(np.int32)
+        m = -2
+        M = 4
+        ac = self.fastclip(a, m, M)
+        act = self.clip(a, m, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_03(self):
+        # Test native int32 input with float64 scalar min/max.
+        a = self._generate_int32_data(self.nr, self.nc)
+        m = -2
+        M = 4
+        ac = self.fastclip(a, np.float64(m), np.float64(M))
+        act = self.clip(a, np.float64(m), np.float64(M))
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_04(self):
+        # Test native int32 input with float32 scalar min/max.
+        a = self._generate_int32_data(self.nr, self.nc)
+        m = np.float32(-2)
+        M = np.float32(4)
+        act = self.fastclip(a, m, M)
+        ac = self.clip(a, m, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_05(self):
+        # Test native int32 with double arrays min/max.
+        a = self._generate_int_data(self.nr, self.nc)
+        m = -0.5
+        M = 1.
+        ac = self.fastclip(a, m * np.zeros(a.shape), M)
+        act = self.clip(a, m * np.zeros(a.shape), M)
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_06(self):
+        # Test native with NON native scalar min/max.
+        a = self._generate_data(self.nr, self.nc)
+        m = 0.5
+        m_s = self._neg_byteorder(m)
+        M = 1.
+        act = self.clip(a, m_s, M)
+        ac = self.fastclip(a, m_s, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_07(self):
+        # Test NON native with native array min/max.
+        a = self._generate_data(self.nr, self.nc)
+        m = -0.5 * np.ones(a.shape)
+        M = 1.
+        a_s = self._neg_byteorder(a)
+        assert_(not a_s.dtype.isnative)
+        act = a_s.clip(m, M)
+        ac = self.fastclip(a_s, m, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_08(self):
+        # Test NON native with native scalar min/max.
+        a = self._generate_data(self.nr, self.nc)
+        m = -0.5
+        M = 1.
+        a_s = self._neg_byteorder(a)
+        assert_(not a_s.dtype.isnative)
+        ac = self.fastclip(a_s, m, M)
+        act = a_s.clip(m, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_09(self):
+        # Test native with NON native array min/max.
+        a = self._generate_data(self.nr, self.nc)
+        m = -0.5 * np.ones(a.shape)
+        M = 1.
+        m_s = self._neg_byteorder(m)
+        assert_(not m_s.dtype.isnative)
+        ac = self.fastclip(a, m_s, M)
+        act = self.clip(a, m_s, M)
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_10(self):
+        # Test native int32 with float min/max and float out for output argument.
+        a = self._generate_int_data(self.nr, self.nc)
+        b = np.zeros(a.shape, dtype=np.float32)
+        m = np.float32(-0.5)
+        M = np.float32(1)
+        act = self.clip(a, m, M, out=b)
+        ac = self.fastclip(a, m, M, out=b)
+        assert_array_strict_equal(ac, act)
+
+    def test_type_cast_11(self):
+        # Test non native with native scalar, min/max, out non native
+        a = self._generate_non_native_data(self.nr, self.nc)
+        b = a.copy()
+        b = b.astype(b.dtype.newbyteorder('>'))
+        bt = b.copy()
+        m = -0.5
+        M = 1.
+        self.fastclip(a, m, M, out=b)
+        self.clip(a, m, M, out=bt)
+        assert_array_strict_equal(b, bt)
+
+    def test_type_cast_12(self):
+        # Test native int32 input and min/max and float out
+        a = self._generate_int_data(self.nr, self.nc)
+        b = np.zeros(a.shape, dtype=np.float32)
+        m = np.int32(0)
+        M = np.int32(1)
+        act = self.clip(a, m, M, out=b)
+        ac = self.fastclip(a, m, M, out=b)
+        assert_array_strict_equal(ac, act)
+
+    def test_clip_with_out_simple(self):
+        # Test native double input with scalar min/max
+        a = self._generate_data(self.nr, self.nc)
+        m = -0.5
+        M = 0.6
+        ac = np.zeros(a.shape)
+        act = np.zeros(a.shape)
+        self.fastclip(a, m, M, ac)
+        self.clip(a, m, M, act)
+        assert_array_strict_equal(ac, act)
+
+    def test_clip_with_out_simple2(self):
+        # Test native int32 input with double min/max and int32 out
+        a = self._generate_int32_data(self.nr, self.nc)
+        m = np.float64(0)
+        M = np.float64(2)
+        ac = np.zeros(a.shape, dtype=np.int32)
+        act = ac.copy()
+        self.fastclip(a, m, M, out=ac, casting="unsafe")
+        self.clip(a, m, M, act)
+        assert_array_strict_equal(ac, act)
+
+    def test_clip_with_out_simple_int32(self):
+        # Test native int32 input with int32 scalar min/max and int64 out
+        a = self._generate_int32_data(self.nr, self.nc)
+        m = np.int32(-1)
+        M = np.int32(1)
+        ac = np.zeros(a.shape, dtype=np.int64)
+        act = ac.copy()
+        self.fastclip(a, m, M, ac)
+        self.clip(a, m, M, act)
+        assert_array_strict_equal(ac, act)
+
+    def test_clip_with_out_array_int32(self):
+        # Test native int32 input with double array min/max and int32 out
+        a = self._generate_int32_data(self.nr, self.nc)
+        m = np.zeros(a.shape, np.float64)
+        M = np.float64(1)
+        ac = np.zeros(a.shape, dtype=np.int32)
+        act = ac.copy()
+        self.fastclip(a, m, M, out=ac, casting="unsafe")
+        self.clip(a, m, M, act)
+        assert_array_strict_equal(ac, act)
+
+    def test_clip_with_out_array_outint32(self):
+        # Test native double input with scalar min/max and int out
+        a = self._generate_data(self.nr, self.nc)
+        m = -1.0
+        M = 2.0
+        ac = np.zeros(a.shape, dtype=np.int32)
+        act = ac.copy()
+        self.fastclip(a, m, M, out=ac, casting="unsafe")
+        self.clip(a, m, M, act)
+        assert_array_strict_equal(ac, act)
+
+    def test_clip_with_out_transposed(self):
+        # Test that the out argument works when transposed
+        a = np.arange(16).reshape(4, 4)
+        out = np.empty_like(a).T
+        a.clip(4, 10, out=out)
+        expected = self.clip(a, 4, 10)
+        assert_array_equal(out, expected)
+
+    def test_clip_with_out_memory_overlap(self):
+        # Test that the out argument works when it has memory overlap
+        a = np.arange(16).reshape(4, 4)
+        ac = a.copy()
+        a[:-1].clip(4, 10, out=a[1:])
+        expected = self.clip(ac[:-1], 4, 10)
+        assert_array_equal(a[1:], expected)
+
+    def test_clip_inplace_array(self):
+        # Test native double input with array min/max
+        a = self._generate_data(self.nr, self.nc)
+        ac = a.copy()
+        m = np.zeros(a.shape)
+        M = 1.0
+        self.fastclip(a, m, M, a)
+        self.clip(a, m, M, ac)
+        assert_array_strict_equal(a, ac)
+
+    def test_clip_inplace_simple(self):
+        # Test native double input with scalar min/max
+        a = self._generate_data(self.nr, self.nc)
+        ac = a.copy()
+        m = -0.5
+        M = 0.6
+        self.fastclip(a, m, M, a)
+        self.clip(a, m, M, ac)
+        assert_array_strict_equal(a, ac)
+
+    def test_clip_func_takes_out(self):
+        # Ensure that the clip() function takes an out=argument.
+        a = self._generate_data(self.nr, self.nc)
+        ac = a.copy()
+        m = -0.5
+        M = 0.6
+        a2 = np.clip(a, m, M, out=a)
+        self.clip(a, m, M, ac)
+        assert_array_strict_equal(a2, ac)
+        assert_(a2 is a)
+
+    def test_clip_nan(self):
+        d = np.arange(7.)
+        assert_equal(d.clip(min=np.nan), np.nan)
+        assert_equal(d.clip(max=np.nan), np.nan)
+        assert_equal(d.clip(min=np.nan, max=np.nan), np.nan)
+        assert_equal(d.clip(min=-2, max=np.nan), np.nan)
+        assert_equal(d.clip(min=np.nan, max=10), np.nan)
+
+    def test_object_clip(self):
+        a = np.arange(10, dtype=object)
+        actual = np.clip(a, 1, 5)
+        expected = np.array([1, 1, 2, 3, 4, 5, 5, 5, 5, 5])
+        assert actual.tolist() == expected.tolist()
+
+    def test_clip_all_none(self):
+        arr = np.arange(10, dtype=object)
+        assert_equal(np.clip(arr, None, None), arr)
+        assert_equal(np.clip(arr), arr)
+
+    def test_clip_invalid_casting(self):
+        a = np.arange(10, dtype=object)
+        with assert_raises_regex(ValueError,
+                                 'casting must be one of'):
+            self.fastclip(a, 1, 8, casting="garbage")
+
+    @pytest.mark.parametrize("amin, amax", [
+        # two scalars
+        (1, 0),
+        # mix scalar and array
+        (1, np.zeros(10)),
+        # two arrays
+        (np.ones(10), np.zeros(10)),
+        ])
+    def test_clip_value_min_max_flip(self, amin, amax):
+        a = np.arange(10, dtype=np.int64)
+        # requirement from ufunc_docstrings.py
+        expected = np.minimum(np.maximum(a, amin), amax)
+        actual = np.clip(a, amin, amax)
+        assert_equal(actual, expected)
+
+    @pytest.mark.parametrize("arr, amin, amax, exp", [
+        # for a bug in npy_ObjectClip, based on a
+        # case produced by hypothesis
+        (np.zeros(10, dtype=object),
+         0,
+         -2**64 + 1,
+         np.full(10, -2**64 + 1, dtype=object)),
+        # for bugs in NPY_TIMEDELTA_MAX, based on a case
+        # produced by hypothesis
+        (np.zeros(10, dtype='m8') - 1,
+         0,
+         0,
+         np.zeros(10, dtype='m8')),
+    ])
+    def test_clip_problem_cases(self, arr, amin, amax, exp):
+        actual = np.clip(arr, amin, amax)
+        assert_equal(actual, exp)
+
+    @pytest.mark.parametrize("arr, amin, amax", [
+        # problematic scalar nan case from hypothesis
+        (np.zeros(10, dtype=np.int64),
+         np.array(np.nan),
+         np.zeros(10, dtype=np.int32)),
+    ])
+    def test_clip_scalar_nan_propagation(self, arr, amin, amax):
+        # enforcement of scalar nan propagation for comparisons
+        # called through clip()
+        expected = np.minimum(np.maximum(arr, amin), amax)
+        actual = np.clip(arr, amin, amax)
+        assert_equal(actual, expected)
+
+    @pytest.mark.xfail(reason="propagation doesn't match spec")
+    @pytest.mark.parametrize("arr, amin, amax", [
+        (np.array([1] * 10, dtype='m8'),
+         np.timedelta64('NaT'),
+         np.zeros(10, dtype=np.int32)),
+    ])
+    @pytest.mark.filterwarnings("ignore::DeprecationWarning")
+    def test_NaT_propagation(self, arr, amin, amax):
+        # NOTE: the expected function spec doesn't
+        # propagate NaT, but clip() now does
+        expected = np.minimum(np.maximum(arr, amin), amax)
+        actual = np.clip(arr, amin, amax)
+        assert_equal(actual, expected)
+
+    @given(
+        data=st.data(),
+        arr=hynp.arrays(
+            dtype=hynp.integer_dtypes() | hynp.floating_dtypes(),
+            shape=hynp.array_shapes()
+        )
+    )
+    def test_clip_property(self, data, arr):
+        """A property-based test using Hypothesis.
+
+        This aims for maximum generality: it could in principle generate *any*
+        valid inputs to np.clip, and in practice generates much more varied
+        inputs than human testers come up with.
+
+        Because many of the inputs have tricky dependencies - compatible dtypes
+        and mutually-broadcastable shapes - we use `st.data()` strategy draw
+        values *inside* the test function, from strategies we construct based
+        on previous values.  An alternative would be to define a custom strategy
+        with `@st.composite`, but until we have duplicated code inline is fine.
+
+        That accounts for most of the function; the actual test is just three
+        lines to calculate and compare actual vs expected results!
+        """
+        numeric_dtypes = hynp.integer_dtypes() | hynp.floating_dtypes()
+        # Generate shapes for the bounds which can be broadcast with each other
+        # and with the base shape.  Below, we might decide to use scalar bounds,
+        # but it's clearer to generate these shapes unconditionally in advance.
+        in_shapes, result_shape = data.draw(
+            hynp.mutually_broadcastable_shapes(
+                num_shapes=2, base_shape=arr.shape
+            )
+        )
+        # Scalar `nan` is deprecated due to the differing behaviour it shows.
+        s = numeric_dtypes.flatmap(
+            lambda x: hynp.from_dtype(x, allow_nan=False))
+        amin = data.draw(s | hynp.arrays(dtype=numeric_dtypes,
+            shape=in_shapes[0], elements={"allow_nan": False}))
+        amax = data.draw(s | hynp.arrays(dtype=numeric_dtypes,
+            shape=in_shapes[1], elements={"allow_nan": False}))
+
+        # Then calculate our result and expected result and check that they're
+        # equal!  See gh-12519 and gh-19457 for discussion deciding on this
+        # property and the result_type argument.
+        result = np.clip(arr, amin, amax)
+        t = np.result_type(arr, amin, amax)
+        expected = np.minimum(amax, np.maximum(arr, amin, dtype=t), dtype=t)
+        assert result.dtype == t
+        assert_array_equal(result, expected)
+
+    def test_clip_min_max_args(self):
+        arr = np.arange(5)
+
+        assert_array_equal(np.clip(arr), arr)
+        assert_array_equal(np.clip(arr, min=2, max=3), np.clip(arr, 2, 3))
+        assert_array_equal(np.clip(arr, min=None, max=2),
+                           np.clip(arr, None, 2))
+
+        with assert_raises_regex(TypeError, "missing 1 required positional "
+                                 "argument: 'a_max'"):
+            np.clip(arr, 2)
+        with assert_raises_regex(TypeError, "missing 1 required positional "
+                                 "argument: 'a_min'"):
+            np.clip(arr, a_max=2)
+        msg = ("Passing `min` or `max` keyword argument when `a_min` and "
+               "`a_max` are provided is forbidden.")
+        with assert_raises_regex(ValueError, msg):
+            np.clip(arr, 2, 3, max=3)
+        with assert_raises_regex(ValueError, msg):
+            np.clip(arr, 2, 3, min=2)
+
+    @pytest.mark.parametrize("dtype,min,max", [
+        ("int32", -2**32 - 1, 2**32),
+        ("int32", -2**320, None),
+        ("int32", None, 2**300),
+        ("int32", -1000, 2**32),
+        ("int32", -2**32 - 1, 1000),
+        ("uint8", -1, 129),
+    ])
+    def test_out_of_bound_pyints(self, dtype, min, max):
+        a = np.arange(10000).astype(dtype)
+        # Check min only
+        c = np.clip(a, min=min, max=max)
+        assert not np.may_share_memory(a, c)
+        assert c.dtype == a.dtype
+        if min is not None:
+            assert (c >= min).all()
+        if max is not None:
+            assert (c <= max).all()
+
+class TestAllclose:
+    rtol = 1e-5
+    atol = 1e-8
+
+    def setup_method(self):
+        self.olderr = np.seterr(invalid='ignore')
+
+    def teardown_method(self):
+        np.seterr(**self.olderr)
+
+    def tst_allclose(self, x, y):
+        assert_(np.allclose(x, y), f"{x} and {y} not close")
+
+    def tst_not_allclose(self, x, y):
+        assert_(not np.allclose(x, y), f"{x} and {y} shouldn't be close")
+
+    def test_ip_allclose(self):
+        # Parametric test factory.
+        arr = np.array([100, 1000])
+        aran = np.arange(125).reshape((5, 5, 5))
+
+        atol = self.atol
+        rtol = self.rtol
+
+        data = [([1, 0], [1, 0]),
+                ([atol], [0]),
+                ([1], [1 + rtol + atol]),
+                (arr, arr + arr * rtol),
+                (arr, arr + arr * rtol + atol * 2),
+                (aran, aran + aran * rtol),
+                (np.inf, np.inf),
+                (np.inf, [np.inf])]
+
+        for (x, y) in data:
+            self.tst_allclose(x, y)
+
+    def test_ip_not_allclose(self):
+        # Parametric test factory.
+        aran = np.arange(125).reshape((5, 5, 5))
+
+        atol = self.atol
+        rtol = self.rtol
+
+        data = [([np.inf, 0], [1, np.inf]),
+                ([np.inf, 0], [1, 0]),
+                ([np.inf, np.inf], [1, np.inf]),
+                ([np.inf, np.inf], [1, 0]),
+                ([-np.inf, 0], [np.inf, 0]),
+                ([np.nan, 0], [np.nan, 0]),
+                ([atol * 2], [0]),
+                ([1], [1 + rtol + atol * 2]),
+                (aran, aran + aran * atol + atol * 2),
+                (np.array([np.inf, 1]), np.array([0, np.inf]))]
+
+        for (x, y) in data:
+            self.tst_not_allclose(x, y)
+
+    def test_no_parameter_modification(self):
+        x = np.array([np.inf, 1])
+        y = np.array([0, np.inf])
+        np.allclose(x, y)
+        assert_array_equal(x, np.array([np.inf, 1]))
+        assert_array_equal(y, np.array([0, np.inf]))
+
+    def test_min_int(self):
+        # Could make problems because of abs(min_int) == min_int
+        min_int = np.iinfo(np.int_).min
+        a = np.array([min_int], dtype=np.int_)
+        assert_(np.allclose(a, a))
+
+    def test_equalnan(self):
+        x = np.array([1.0, np.nan])
+        assert_(np.allclose(x, x, equal_nan=True))
+
+    def test_return_class_is_ndarray(self):
+        # Issue gh-6475
+        # Check that allclose does not preserve subtypes
+        class Foo(np.ndarray):
+            def __new__(cls, *args, **kwargs):
+                return np.array(*args, **kwargs).view(cls)
+
+        a = Foo([1])
+        assert_(type(np.allclose(a, a)) is bool)
+
+
+class TestIsclose:
+    rtol = 1e-5
+    atol = 1e-8
+
+    def _setup(self):
+        atol = self.atol
+        rtol = self.rtol
+        arr = np.array([100, 1000])
+        aran = np.arange(125).reshape((5, 5, 5))
+
+        self.all_close_tests = [
+                ([1, 0], [1, 0]),
+                ([atol], [0]),
+                ([1], [1 + rtol + atol]),
+                (arr, arr + arr * rtol),
+                (arr, arr + arr * rtol + atol),
+                (aran, aran + aran * rtol),
+                (np.inf, np.inf),
+                (np.inf, [np.inf]),
+                ([np.inf, -np.inf], [np.inf, -np.inf]),
+                ]
+        self.none_close_tests = [
+                ([np.inf, 0], [1, np.inf]),
+                ([np.inf, -np.inf], [1, 0]),
+                ([np.inf, np.inf], [1, -np.inf]),
+                ([np.inf, np.inf], [1, 0]),
+                ([np.nan, 0], [np.nan, -np.inf]),
+                ([atol * 2], [0]),
+                ([1], [1 + rtol + atol * 2]),
+                (aran, aran + rtol * 1.1 * aran + atol * 1.1),
+                (np.array([np.inf, 1]), np.array([0, np.inf])),
+                ]
+        self.some_close_tests = [
+                ([np.inf, 0], [np.inf, atol * 2]),
+                ([atol, 1, 1e6 * (1 + 2 * rtol) + atol], [0, np.nan, 1e6]),
+                (np.arange(3), [0, 1, 2.1]),
+                (np.nan, [np.nan, np.nan, np.nan]),
+                ([0], [atol, np.inf, -np.inf, np.nan]),
+                (0, [atol, np.inf, -np.inf, np.nan]),
+                ]
+        self.some_close_results = [
+                [True, False],
+                [True, False, False],
+                [True, True, False],
+                [False, False, False],
+                [True, False, False, False],
+                [True, False, False, False],
+                ]
+
+    def test_ip_isclose(self):
+        self._setup()
+        tests = self.some_close_tests
+        results = self.some_close_results
+        for (x, y), result in zip(tests, results):
+            assert_array_equal(np.isclose(x, y), result)
+
+        x = np.array([2.1, 2.1, 2.1, 2.1, 5, np.nan])
+        y = np.array([2, 2, 2, 2, np.nan, 5])
+        atol = [0.11, 0.09, 1e-8, 1e-8, 1, 1]
+        rtol = [1e-8, 1e-8, 0.06, 0.04, 1, 1]
+        expected = np.array([True, False, True, False, False, False])
+        assert_array_equal(np.isclose(x, y, rtol=rtol, atol=atol), expected)
+
+        message = "operands could not be broadcast together..."
+        atol = np.array([1e-8, 1e-8])
+        with assert_raises(ValueError, msg=message):
+            np.isclose(x, y, atol=atol)
+
+        rtol = np.array([1e-5, 1e-5])
+        with assert_raises(ValueError, msg=message):
+            np.isclose(x, y, rtol=rtol)
+
+    def test_nep50_isclose(self):
+        below_one = float(1. - np.finfo('f8').eps)
+        f32 = np.array(below_one, 'f4')  # This is just 1 at float32 precision
+        assert f32 > np.array(below_one)
+        # NEP 50 broadcasting of python scalars
+        assert f32 == below_one
+        # Test that it works for isclose arguments too (and that those fail if
+        # one uses a numpy float64).
+        assert np.isclose(f32, below_one, atol=0, rtol=0)
+        assert np.isclose(f32, np.float32(0), atol=below_one)
+        assert np.isclose(f32, 2, atol=0, rtol=below_one / 2)
+        assert not np.isclose(f32, np.float64(below_one), atol=0, rtol=0)
+        assert not np.isclose(f32, np.float32(0), atol=np.float64(below_one))
+        assert not np.isclose(f32, 2, atol=0, rtol=np.float64(below_one / 2))
+
+    def tst_all_isclose(self, x, y):
+        assert_(np.all(np.isclose(x, y)), f"{x} and {y} not close")
+
+    def tst_none_isclose(self, x, y):
+        msg = "%s and %s shouldn't be close"
+        assert_(not np.any(np.isclose(x, y)), msg % (x, y))
+
+    def tst_isclose_allclose(self, x, y):
+        msg = "isclose.all() and allclose aren't same for %s and %s"
+        msg2 = "isclose and allclose aren't same for %s and %s"
+        if np.isscalar(x) and np.isscalar(y):
+            assert_(np.isclose(x, y) == np.allclose(x, y), msg=msg2 % (x, y))
+        else:
+            assert_array_equal(np.isclose(x, y).all(), np.allclose(x, y), msg % (x, y))
+
+    def test_ip_all_isclose(self):
+        self._setup()
+        for (x, y) in self.all_close_tests:
+            self.tst_all_isclose(x, y)
+
+        x = np.array([2.3, 3.6, 4.4, np.nan])
+        y = np.array([2, 3, 4, np.nan])
+        atol = [0.31, 0, 0, 1]
+        rtol = [0, 0.21, 0.11, 1]
+        assert np.allclose(x, y, atol=atol, rtol=rtol, equal_nan=True)
+        assert not np.allclose(x, y, atol=0.1, rtol=0.1, equal_nan=True)
+
+        # Show that gh-14330 is resolved
+        assert np.allclose([1, 2, float('nan')], [1, 2, float('nan')],
+                           atol=[1, 1, 1], equal_nan=True)
+
+    def test_ip_none_isclose(self):
+        self._setup()
+        for (x, y) in self.none_close_tests:
+            self.tst_none_isclose(x, y)
+
+    def test_ip_isclose_allclose(self):
+        self._setup()
+        tests = (self.all_close_tests + self.none_close_tests +
+                 self.some_close_tests)
+        for (x, y) in tests:
+            self.tst_isclose_allclose(x, y)
+
+    def test_equal_nan(self):
+        assert_array_equal(np.isclose(np.nan, np.nan, equal_nan=True), [True])
+        arr = np.array([1.0, np.nan])
+        assert_array_equal(np.isclose(arr, arr, equal_nan=True), [True, True])
+
+    def test_masked_arrays(self):
+        # Make sure to test the output type when arguments are interchanged.
+
+        x = np.ma.masked_where([True, True, False], np.arange(3))
+        assert_(type(x) is type(np.isclose(2, x)))
+        assert_(type(x) is type(np.isclose(x, 2)))
+
+        x = np.ma.masked_where([True, True, False], [np.nan, np.inf, np.nan])
+        assert_(type(x) is type(np.isclose(np.inf, x)))
+        assert_(type(x) is type(np.isclose(x, np.inf)))
+
+        x = np.ma.masked_where([True, True, False], [np.nan, np.nan, np.nan])
+        y = np.isclose(np.nan, x, equal_nan=True)
+        assert_(type(x) is type(y))
+        # Ensure that the mask isn't modified...
+        assert_array_equal([True, True, False], y.mask)
+        y = np.isclose(x, np.nan, equal_nan=True)
+        assert_(type(x) is type(y))
+        # Ensure that the mask isn't modified...
+        assert_array_equal([True, True, False], y.mask)
+
+        x = np.ma.masked_where([True, True, False], [np.nan, np.nan, np.nan])
+        y = np.isclose(x, x, equal_nan=True)
+        assert_(type(x) is type(y))
+        # Ensure that the mask isn't modified...
+        assert_array_equal([True, True, False], y.mask)
+
+    def test_scalar_return(self):
+        assert_(np.isscalar(np.isclose(1, 1)))
+
+    def test_no_parameter_modification(self):
+        x = np.array([np.inf, 1])
+        y = np.array([0, np.inf])
+        np.isclose(x, y)
+        assert_array_equal(x, np.array([np.inf, 1]))
+        assert_array_equal(y, np.array([0, np.inf]))
+
+    def test_non_finite_scalar(self):
+        # GH7014, when two scalars are compared the output should also be a
+        # scalar
+        assert_(np.isclose(np.inf, -np.inf) is np.False_)
+        assert_(np.isclose(0, np.inf) is np.False_)
+        assert_(type(np.isclose(0, np.inf)) is np.bool)
+
+    def test_timedelta(self):
+        # Allclose currently works for timedelta64 as long as `atol` is
+        # an integer or also a timedelta64
+        a = np.array([[1, 2, 3, "NaT"]], dtype="m8[ns]")
+        assert np.isclose(a, a, atol=0, equal_nan=True).all()
+        assert np.isclose(a, a, atol=np.timedelta64(1, "ns"), equal_nan=True).all()
+        assert np.allclose(a, a, atol=0, equal_nan=True)
+        assert np.allclose(a, a, atol=np.timedelta64(1, "ns"), equal_nan=True)
+
+    def test_tol_warnings(self):
+        a = np.array([1, 2, 3])
+        b = np.array([np.inf, np.nan, 1])
+
+        for i in b:
+            for j in b:
+                # Making sure that i and j are not both numbers, because that won't create a warning
+                if (i == 1) and (j == 1):
+                    continue
+
+                with warnings.catch_warnings(record=True) as w:
+
+                    warnings.simplefilter("always")
+                    c = np.isclose(a, a, atol=i, rtol=j)
+                    assert len(w) == 1
+                    assert issubclass(w[-1].category, RuntimeWarning)
+                    assert f"One of rtol or atol is not valid, atol: {i}, rtol: {j}" in str(w[-1].message)
+
+
+class TestStdVar:
+    def setup_method(self):
+        self.A = np.array([1, -1, 1, -1])
+        self.real_var = 1
+
+    def test_basic(self):
+        assert_almost_equal(np.var(self.A), self.real_var)
+        assert_almost_equal(np.std(self.A)**2, self.real_var)
+
+    def test_scalars(self):
+        assert_equal(np.var(1), 0)
+        assert_equal(np.std(1), 0)
+
+    def test_ddof1(self):
+        assert_almost_equal(np.var(self.A, ddof=1),
+                            self.real_var * len(self.A) / (len(self.A) - 1))
+        assert_almost_equal(np.std(self.A, ddof=1)**2,
+                            self.real_var * len(self.A) / (len(self.A) - 1))
+
+    def test_ddof2(self):
+        assert_almost_equal(np.var(self.A, ddof=2),
+                            self.real_var * len(self.A) / (len(self.A) - 2))
+        assert_almost_equal(np.std(self.A, ddof=2)**2,
+                            self.real_var * len(self.A) / (len(self.A) - 2))
+
+    def test_correction(self):
+        assert_almost_equal(
+            np.var(self.A, correction=1), np.var(self.A, ddof=1)
+        )
+        assert_almost_equal(
+            np.std(self.A, correction=1), np.std(self.A, ddof=1)
+        )
+
+        err_msg = "ddof and correction can't be provided simultaneously."
+
+        with assert_raises_regex(ValueError, err_msg):
+            np.var(self.A, ddof=1, correction=0)
+
+        with assert_raises_regex(ValueError, err_msg):
+            np.std(self.A, ddof=1, correction=1)
+
+    def test_out_scalar(self):
+        d = np.arange(10)
+        out = np.array(0.)
+        r = np.std(d, out=out)
+        assert_(r is out)
+        assert_array_equal(r, out)
+        r = np.var(d, out=out)
+        assert_(r is out)
+        assert_array_equal(r, out)
+        r = np.mean(d, out=out)
+        assert_(r is out)
+        assert_array_equal(r, out)
+
+
+class TestStdVarComplex:
+    def test_basic(self):
+        A = np.array([1, 1.j, -1, -1.j])
+        real_var = 1
+        assert_almost_equal(np.var(A), real_var)
+        assert_almost_equal(np.std(A)**2, real_var)
+
+    def test_scalars(self):
+        assert_equal(np.var(1j), 0)
+        assert_equal(np.std(1j), 0)
+
+
+class TestCreationFuncs:
+    # Test ones, zeros, empty and full.
+
+    def setup_method(self):
+        dtypes = {np.dtype(tp) for tp in itertools.chain(*sctypes.values())}
+        # void, bytes, str
+        variable_sized = {tp for tp in dtypes if tp.str.endswith('0')}
+        keyfunc = lambda dtype: dtype.str
+        self.dtypes = sorted(dtypes - variable_sized |
+                             {np.dtype(tp.str.replace("0", str(i)))
+                              for tp in variable_sized for i in range(1, 10)},
+                             key=keyfunc)
+        self.dtypes += [type(dt) for dt in sorted(dtypes, key=keyfunc)]
+        self.orders = {'C': 'c_contiguous', 'F': 'f_contiguous'}
+        self.ndims = 10
+
+    def check_function(self, func, fill_value=None):
+        par = ((0, 1, 2),
+               range(self.ndims),
+               self.orders,
+               self.dtypes)
+        fill_kwarg = {}
+        if fill_value is not None:
+            fill_kwarg = {'fill_value': fill_value}
+
+        for size, ndims, order, dtype in itertools.product(*par):
+            shape = ndims * [size]
+
+            is_void = dtype is np.dtypes.VoidDType or (
+                isinstance(dtype, np.dtype) and dtype.str.startswith('|V'))
+
+            # do not fill void type
+            if fill_kwarg and is_void:
+                continue
+
+            arr = func(shape, order=order, dtype=dtype,
+                       **fill_kwarg)
+
+            if isinstance(dtype, np.dtype):
+                assert_equal(arr.dtype, dtype)
+            elif isinstance(dtype, type(np.dtype)):
+                if dtype in (np.dtypes.StrDType, np.dtypes.BytesDType):
+                    dtype_str = np.dtype(dtype.type).str.replace('0', '1')
+                    assert_equal(arr.dtype, np.dtype(dtype_str))
+                else:
+                    assert_equal(arr.dtype, np.dtype(dtype.type))
+            assert_(getattr(arr.flags, self.orders[order]))
+
+            if fill_value is not None:
+                if arr.dtype.str.startswith('|S'):
+                    val = str(fill_value)
+                else:
+                    val = fill_value
+                assert_equal(arr, dtype.type(val))
+
+    def test_zeros(self):
+        self.check_function(np.zeros)
+
+    def test_ones(self):
+        self.check_function(np.ones)
+
+    def test_empty(self):
+        self.check_function(np.empty)
+
+    def test_full(self):
+        self.check_function(np.full, 0)
+        self.check_function(np.full, 1)
+
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test_for_reference_leak(self):
+        # Make sure we have an object for reference
+        dim = 1
+        beg = sys.getrefcount(dim)
+        np.zeros([dim] * 10)
+        assert_(sys.getrefcount(dim) == beg)
+        np.ones([dim] * 10)
+        assert_(sys.getrefcount(dim) == beg)
+        np.empty([dim] * 10)
+        assert_(sys.getrefcount(dim) == beg)
+        np.full([dim] * 10, 0)
+        assert_(sys.getrefcount(dim) == beg)
+
+
+class TestLikeFuncs:
+    '''Test ones_like, zeros_like, empty_like and full_like'''
+
+    def setup_method(self):
+        self.data = [
+                # Array scalars
+                (np.array(3.), None),
+                (np.array(3), 'f8'),
+                # 1D arrays
+                (np.arange(6, dtype='f4'), None),
+                (np.arange(6), 'c16'),
+                # 2D C-layout arrays
+                (np.arange(6).reshape(2, 3), None),
+                (np.arange(6).reshape(3, 2), 'i1'),
+                # 2D F-layout arrays
+                (np.arange(6).reshape((2, 3), order='F'), None),
+                (np.arange(6).reshape((3, 2), order='F'), 'i1'),
+                # 3D C-layout arrays
+                (np.arange(24).reshape(2, 3, 4), None),
+                (np.arange(24).reshape(4, 3, 2), 'f4'),
+                # 3D F-layout arrays
+                (np.arange(24).reshape((2, 3, 4), order='F'), None),
+                (np.arange(24).reshape((4, 3, 2), order='F'), 'f4'),
+                # 3D non-C/F-layout arrays
+                (np.arange(24).reshape(2, 3, 4).swapaxes(0, 1), None),
+                (np.arange(24).reshape(4, 3, 2).swapaxes(0, 1), '?'),
+                     ]
+        self.shapes = [(), (5,), (5, 6,), (5, 6, 7,)]
+
+    def compare_array_value(self, dz, value, fill_value):
+        if value is not None:
+            if fill_value:
+                # Conversion is close to what np.full_like uses
+                # but we  may want to convert directly in the future
+                # which may result in errors (where this does not).
+                z = np.array(value).astype(dz.dtype)
+                assert_(np.all(dz == z))
+            else:
+                assert_(np.all(dz == value))
+
+    def check_like_function(self, like_function, value, fill_value=False):
+        if fill_value:
+            fill_kwarg = {'fill_value': value}
+        else:
+            fill_kwarg = {}
+        for d, dtype in self.data:
+            # default (K) order, dtype
+            dz = like_function(d, dtype=dtype, **fill_kwarg)
+            assert_equal(dz.shape, d.shape)
+            assert_equal(np.array(dz.strides) * d.dtype.itemsize,
+                         np.array(d.strides) * dz.dtype.itemsize)
+            assert_equal(d.flags.c_contiguous, dz.flags.c_contiguous)
+            assert_equal(d.flags.f_contiguous, dz.flags.f_contiguous)
+            if dtype is None:
+                assert_equal(dz.dtype, d.dtype)
+            else:
+                assert_equal(dz.dtype, np.dtype(dtype))
+            self.compare_array_value(dz, value, fill_value)
+
+            # C order, default dtype
+            dz = like_function(d, order='C', dtype=dtype, **fill_kwarg)
+            assert_equal(dz.shape, d.shape)
+            assert_(dz.flags.c_contiguous)
+            if dtype is None:
+                assert_equal(dz.dtype, d.dtype)
+            else:
+                assert_equal(dz.dtype, np.dtype(dtype))
+            self.compare_array_value(dz, value, fill_value)
+
+            # F order, default dtype
+            dz = like_function(d, order='F', dtype=dtype, **fill_kwarg)
+            assert_equal(dz.shape, d.shape)
+            assert_(dz.flags.f_contiguous)
+            if dtype is None:
+                assert_equal(dz.dtype, d.dtype)
+            else:
+                assert_equal(dz.dtype, np.dtype(dtype))
+            self.compare_array_value(dz, value, fill_value)
+
+            # A order
+            dz = like_function(d, order='A', dtype=dtype, **fill_kwarg)
+            assert_equal(dz.shape, d.shape)
+            if d.flags.f_contiguous:
+                assert_(dz.flags.f_contiguous)
+            else:
+                assert_(dz.flags.c_contiguous)
+            if dtype is None:
+                assert_equal(dz.dtype, d.dtype)
+            else:
+                assert_equal(dz.dtype, np.dtype(dtype))
+            self.compare_array_value(dz, value, fill_value)
+
+            # Test the 'shape' parameter
+            for s in self.shapes:
+                for o in 'CFA':
+                    sz = like_function(d, dtype=dtype, shape=s, order=o,
+                                       **fill_kwarg)
+                    assert_equal(sz.shape, s)
+                    if dtype is None:
+                        assert_equal(sz.dtype, d.dtype)
+                    else:
+                        assert_equal(sz.dtype, np.dtype(dtype))
+                    if o == 'C' or (o == 'A' and d.flags.c_contiguous):
+                        assert_(sz.flags.c_contiguous)
+                    elif o == 'F' or (o == 'A' and d.flags.f_contiguous):
+                        assert_(sz.flags.f_contiguous)
+                    self.compare_array_value(sz, value, fill_value)
+
+                if (d.ndim != len(s)):
+                    assert_equal(np.argsort(like_function(d, dtype=dtype,
+                                                          shape=s, order='K',
+                                                          **fill_kwarg).strides),
+                                 np.argsort(np.empty(s, dtype=dtype,
+                                                     order='C').strides))
+                else:
+                    assert_equal(np.argsort(like_function(d, dtype=dtype,
+                                                          shape=s, order='K',
+                                                          **fill_kwarg).strides),
+                                 np.argsort(d.strides))
+
+        # Test the 'subok' parameter
+        class MyNDArray(np.ndarray):
+            pass
+
+        a = np.array([[1, 2], [3, 4]]).view(MyNDArray)
+
+        b = like_function(a, **fill_kwarg)
+        assert_(type(b) is MyNDArray)
+
+        b = like_function(a, subok=False, **fill_kwarg)
+        assert_(type(b) is not MyNDArray)
+
+        # Test invalid dtype
+        with assert_raises(TypeError):
+            a = np.array(b"abc")
+            like_function(a, dtype="S-1", **fill_kwarg)
+
+    def test_ones_like(self):
+        self.check_like_function(np.ones_like, 1)
+
+    def test_zeros_like(self):
+        self.check_like_function(np.zeros_like, 0)
+
+    def test_empty_like(self):
+        self.check_like_function(np.empty_like, None)
+
+    def test_filled_like(self):
+        self.check_like_function(np.full_like, 0, True)
+        self.check_like_function(np.full_like, 1, True)
+        # Large integers may overflow, but using int64 is OK (casts)
+        # see also gh-27075
+        with pytest.raises(OverflowError):
+            np.full_like(np.ones(3, dtype=np.int8), 1000)
+        self.check_like_function(np.full_like, np.int64(1000), True)
+        self.check_like_function(np.full_like, 123.456, True)
+        # Inf to integer casts cause invalid-value errors: ignore them.
+        with np.errstate(invalid="ignore"):
+            self.check_like_function(np.full_like, np.inf, True)
+
+    @pytest.mark.parametrize('likefunc', [np.empty_like, np.full_like,
+                                          np.zeros_like, np.ones_like])
+    @pytest.mark.parametrize('dtype', [str, bytes])
+    def test_dtype_str_bytes(self, likefunc, dtype):
+        # Regression test for gh-19860
+        a = np.arange(16).reshape(2, 8)
+        b = a[:, ::2]  # Ensure b is not contiguous.
+        kwargs = {'fill_value': ''} if likefunc == np.full_like else {}
+        result = likefunc(b, dtype=dtype, **kwargs)
+        if dtype == str:
+            assert result.strides == (16, 4)
+        else:
+            # dtype is bytes
+            assert result.strides == (4, 1)
+
+
+class TestCorrelate:
+    def _setup(self, dt):
+        self.x = np.array([1, 2, 3, 4, 5], dtype=dt)
+        self.xs = np.arange(1, 20)[::3]
+        self.y = np.array([-1, -2, -3], dtype=dt)
+        self.z1 = np.array([-3., -8., -14., -20., -26., -14., -5.], dtype=dt)
+        self.z1_4 = np.array([-2., -5., -8., -11., -14., -5.], dtype=dt)
+        self.z1r = np.array([-15., -22., -22., -16., -10., -4., -1.], dtype=dt)
+        self.z2 = np.array([-5., -14., -26., -20., -14., -8., -3.], dtype=dt)
+        self.z2r = np.array([-1., -4., -10., -16., -22., -22., -15.], dtype=dt)
+        self.zs = np.array([-3., -14., -30., -48., -66., -84.,
+                           -102., -54., -19.], dtype=dt)
+
+    def test_float(self):
+        self._setup(float)
+        z = np.correlate(self.x, self.y, 'full')
+        assert_array_almost_equal(z, self.z1)
+        z = np.correlate(self.x, self.y[:-1], 'full')
+        assert_array_almost_equal(z, self.z1_4)
+        z = np.correlate(self.y, self.x, 'full')
+        assert_array_almost_equal(z, self.z2)
+        z = np.correlate(self.x[::-1], self.y, 'full')
+        assert_array_almost_equal(z, self.z1r)
+        z = np.correlate(self.y, self.x[::-1], 'full')
+        assert_array_almost_equal(z, self.z2r)
+        z = np.correlate(self.xs, self.y, 'full')
+        assert_array_almost_equal(z, self.zs)
+
+    def test_object(self):
+        self._setup(Decimal)
+        z = np.correlate(self.x, self.y, 'full')
+        assert_array_almost_equal(z, self.z1)
+        z = np.correlate(self.y, self.x, 'full')
+        assert_array_almost_equal(z, self.z2)
+
+    def test_no_overwrite(self):
+        d = np.ones(100)
+        k = np.ones(3)
+        np.correlate(d, k)
+        assert_array_equal(d, np.ones(100))
+        assert_array_equal(k, np.ones(3))
+
+    def test_complex(self):
+        x = np.array([1, 2, 3, 4 + 1j], dtype=complex)
+        y = np.array([-1, -2j, 3 + 1j], dtype=complex)
+        r_z = np.array([3 - 1j, 6, 8 + 1j, 11 + 5j, -5 + 8j, -4 - 1j], dtype=complex)
+        r_z = r_z[::-1].conjugate()
+        z = np.correlate(y, x, mode='full')
+        assert_array_almost_equal(z, r_z)
+
+    def test_zero_size(self):
+        with pytest.raises(ValueError):
+            np.correlate(np.array([]), np.ones(1000), mode='full')
+        with pytest.raises(ValueError):
+            np.correlate(np.ones(1000), np.array([]), mode='full')
+
+    def test_mode(self):
+        d = np.ones(100)
+        k = np.ones(3)
+        default_mode = np.correlate(d, k, mode='valid')
+        with assert_raises(ValueError):
+            np.correlate(d, k, mode='v')
+        # integer mode
+        with assert_raises(ValueError):
+            np.correlate(d, k, mode=-1)
+        # assert_array_equal(np.correlate(d, k, mode=), default_mode)
+        # illegal arguments
+        with assert_raises(TypeError):
+            np.correlate(d, k, mode=None)
+
+
+class TestConvolve:
+    def test_object(self):
+        d = [1.] * 100
+        k = [1.] * 3
+        assert_array_almost_equal(np.convolve(d, k)[2:-2], np.full(98, 3))
+
+    def test_no_overwrite(self):
+        d = np.ones(100)
+        k = np.ones(3)
+        np.convolve(d, k)
+        assert_array_equal(d, np.ones(100))
+        assert_array_equal(k, np.ones(3))
+
+    def test_mode(self):
+        d = np.ones(100)
+        k = np.ones(3)
+        default_mode = np.convolve(d, k, mode='full')
+        with assert_raises(ValueError):
+            np.convolve(d, k, mode='f')
+        # integer mode
+        with assert_raises(ValueError):
+            np.convolve(d, k, mode=-1)
+        assert_array_equal(np.convolve(d, k, mode=2), default_mode)
+        # illegal arguments
+        with assert_raises(TypeError):
+            np.convolve(d, k, mode=None)
+
+
+class TestArgwhere:
+
+    @pytest.mark.parametrize('nd', [0, 1, 2])
+    def test_nd(self, nd):
+        # get an nd array with multiple elements in every dimension
+        x = np.empty((2,) * nd, bool)
+
+        # none
+        x[...] = False
+        assert_equal(np.argwhere(x).shape, (0, nd))
+
+        # only one
+        x[...] = False
+        x.flat[0] = True
+        assert_equal(np.argwhere(x).shape, (1, nd))
+
+        # all but one
+        x[...] = True
+        x.flat[0] = False
+        assert_equal(np.argwhere(x).shape, (x.size - 1, nd))
+
+        # all
+        x[...] = True
+        assert_equal(np.argwhere(x).shape, (x.size, nd))
+
+    def test_2D(self):
+        x = np.arange(6).reshape((2, 3))
+        assert_array_equal(np.argwhere(x > 1),
+                           [[0, 2],
+                            [1, 0],
+                            [1, 1],
+                            [1, 2]])
+
+    def test_list(self):
+        assert_equal(np.argwhere([4, 0, 2, 1, 3]), [[0], [2], [3], [4]])
+
+
+class TestRoll:
+    def test_roll1d(self):
+        x = np.arange(10)
+        xr = np.roll(x, 2)
+        assert_equal(xr, np.array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]))
+
+    def test_roll2d(self):
+        x2 = np.reshape(np.arange(10), (2, 5))
+        x2r = np.roll(x2, 1)
+        assert_equal(x2r, np.array([[9, 0, 1, 2, 3], [4, 5, 6, 7, 8]]))
+
+        x2r = np.roll(x2, 1, axis=0)
+        assert_equal(x2r, np.array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]))
+
+        x2r = np.roll(x2, 1, axis=1)
+        assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]))
+
+        # Roll multiple axes at once.
+        x2r = np.roll(x2, 1, axis=(0, 1))
+        assert_equal(x2r, np.array([[9, 5, 6, 7, 8], [4, 0, 1, 2, 3]]))
+
+        x2r = np.roll(x2, (1, 0), axis=(0, 1))
+        assert_equal(x2r, np.array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]))
+
+        x2r = np.roll(x2, (-1, 0), axis=(0, 1))
+        assert_equal(x2r, np.array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]))
+
+        x2r = np.roll(x2, (0, 1), axis=(0, 1))
+        assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]))
+
+        x2r = np.roll(x2, (0, -1), axis=(0, 1))
+        assert_equal(x2r, np.array([[1, 2, 3, 4, 0], [6, 7, 8, 9, 5]]))
+
+        x2r = np.roll(x2, (1, 1), axis=(0, 1))
+        assert_equal(x2r, np.array([[9, 5, 6, 7, 8], [4, 0, 1, 2, 3]]))
+
+        x2r = np.roll(x2, (-1, -1), axis=(0, 1))
+        assert_equal(x2r, np.array([[6, 7, 8, 9, 5], [1, 2, 3, 4, 0]]))
+
+        # Roll the same axis multiple times.
+        x2r = np.roll(x2, 1, axis=(0, 0))
+        assert_equal(x2r, np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]))
+
+        x2r = np.roll(x2, 1, axis=(1, 1))
+        assert_equal(x2r, np.array([[3, 4, 0, 1, 2], [8, 9, 5, 6, 7]]))
+
+        # Roll more than one turn in either direction.
+        x2r = np.roll(x2, 6, axis=1)
+        assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]))
+
+        x2r = np.roll(x2, -4, axis=1)
+        assert_equal(x2r, np.array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]))
+
+    def test_roll_empty(self):
+        x = np.array([])
+        assert_equal(np.roll(x, 1), np.array([]))
+
+    def test_roll_unsigned_shift(self):
+        x = np.arange(4)
+        shift = np.uint16(2)
+        assert_equal(np.roll(x, shift), np.roll(x, 2))
+
+        shift = np.uint64(2**63 + 2)
+        assert_equal(np.roll(x, shift), np.roll(x, 2))
+
+    def test_roll_big_int(self):
+        x = np.arange(4)
+        assert_equal(np.roll(x, 2**100), x)
+
+
+class TestRollaxis:
+
+    # expected shape indexed by (axis, start) for array of
+    # shape (1, 2, 3, 4)
+    tgtshape = {(0, 0): (1, 2, 3, 4), (0, 1): (1, 2, 3, 4),
+                (0, 2): (2, 1, 3, 4), (0, 3): (2, 3, 1, 4),
+                (0, 4): (2, 3, 4, 1),
+                (1, 0): (2, 1, 3, 4), (1, 1): (1, 2, 3, 4),
+                (1, 2): (1, 2, 3, 4), (1, 3): (1, 3, 2, 4),
+                (1, 4): (1, 3, 4, 2),
+                (2, 0): (3, 1, 2, 4), (2, 1): (1, 3, 2, 4),
+                (2, 2): (1, 2, 3, 4), (2, 3): (1, 2, 3, 4),
+                (2, 4): (1, 2, 4, 3),
+                (3, 0): (4, 1, 2, 3), (3, 1): (1, 4, 2, 3),
+                (3, 2): (1, 2, 4, 3), (3, 3): (1, 2, 3, 4),
+                (3, 4): (1, 2, 3, 4)}
+
+    def test_exceptions(self):
+        a = np.arange(1 * 2 * 3 * 4).reshape(1, 2, 3, 4)
+        assert_raises(AxisError, np.rollaxis, a, -5, 0)
+        assert_raises(AxisError, np.rollaxis, a, 0, -5)
+        assert_raises(AxisError, np.rollaxis, a, 4, 0)
+        assert_raises(AxisError, np.rollaxis, a, 0, 5)
+
+    def test_results(self):
+        a = np.arange(1 * 2 * 3 * 4).reshape(1, 2, 3, 4).copy()
+        aind = np.indices(a.shape)
+        assert_(a.flags['OWNDATA'])
+        for (i, j) in self.tgtshape:
+            # positive axis, positive start
+            res = np.rollaxis(a, axis=i, start=j)
+            i0, i1, i2, i3 = aind[np.array(res.shape) - 1]
+            assert_(np.all(res[i0, i1, i2, i3] == a))
+            assert_(res.shape == self.tgtshape[(i, j)], str((i, j)))
+            assert_(not res.flags['OWNDATA'])
+
+            # negative axis, positive start
+            ip = i + 1
+            res = np.rollaxis(a, axis=-ip, start=j)
+            i0, i1, i2, i3 = aind[np.array(res.shape) - 1]
+            assert_(np.all(res[i0, i1, i2, i3] == a))
+            assert_(res.shape == self.tgtshape[(4 - ip, j)])
+            assert_(not res.flags['OWNDATA'])
+
+            # positive axis, negative start
+            jp = j + 1 if j < 4 else j
+            res = np.rollaxis(a, axis=i, start=-jp)
+            i0, i1, i2, i3 = aind[np.array(res.shape) - 1]
+            assert_(np.all(res[i0, i1, i2, i3] == a))
+            assert_(res.shape == self.tgtshape[(i, 4 - jp)])
+            assert_(not res.flags['OWNDATA'])
+
+            # negative axis, negative start
+            ip = i + 1
+            jp = j + 1 if j < 4 else j
+            res = np.rollaxis(a, axis=-ip, start=-jp)
+            i0, i1, i2, i3 = aind[np.array(res.shape) - 1]
+            assert_(np.all(res[i0, i1, i2, i3] == a))
+            assert_(res.shape == self.tgtshape[(4 - ip, 4 - jp)])
+            assert_(not res.flags['OWNDATA'])
+
+
+class TestMoveaxis:
+    def test_move_to_end(self):
+        x = np.random.randn(5, 6, 7)
+        for source, expected in [(0, (6, 7, 5)),
+                                 (1, (5, 7, 6)),
+                                 (2, (5, 6, 7)),
+                                 (-1, (5, 6, 7))]:
+            actual = np.moveaxis(x, source, -1).shape
+            assert_(actual, expected)
+
+    def test_move_new_position(self):
+        x = np.random.randn(1, 2, 3, 4)
+        for source, destination, expected in [
+                (0, 1, (2, 1, 3, 4)),
+                (1, 2, (1, 3, 2, 4)),
+                (1, -1, (1, 3, 4, 2)),
+                ]:
+            actual = np.moveaxis(x, source, destination).shape
+            assert_(actual, expected)
+
+    def test_preserve_order(self):
+        x = np.zeros((1, 2, 3, 4))
+        for source, destination in [
+                (0, 0),
+                (3, -1),
+                (-1, 3),
+                ([0, -1], [0, -1]),
+                ([2, 0], [2, 0]),
+                (range(4), range(4)),
+                ]:
+            actual = np.moveaxis(x, source, destination).shape
+            assert_(actual, (1, 2, 3, 4))
+
+    def test_move_multiples(self):
+        x = np.zeros((0, 1, 2, 3))
+        for source, destination, expected in [
+                ([0, 1], [2, 3], (2, 3, 0, 1)),
+                ([2, 3], [0, 1], (2, 3, 0, 1)),
+                ([0, 1, 2], [2, 3, 0], (2, 3, 0, 1)),
+                ([3, 0], [1, 0], (0, 3, 1, 2)),
+                ([0, 3], [0, 1], (0, 3, 1, 2)),
+                ]:
+            actual = np.moveaxis(x, source, destination).shape
+            assert_(actual, expected)
+
+    def test_errors(self):
+        x = np.random.randn(1, 2, 3)
+        assert_raises_regex(AxisError, 'source.*out of bounds',
+                            np.moveaxis, x, 3, 0)
+        assert_raises_regex(AxisError, 'source.*out of bounds',
+                            np.moveaxis, x, -4, 0)
+        assert_raises_regex(AxisError, 'destination.*out of bounds',
+                            np.moveaxis, x, 0, 5)
+        assert_raises_regex(ValueError, 'repeated axis in `source`',
+                            np.moveaxis, x, [0, 0], [0, 1])
+        assert_raises_regex(ValueError, 'repeated axis in `destination`',
+                            np.moveaxis, x, [0, 1], [1, 1])
+        assert_raises_regex(ValueError, 'must have the same number',
+                            np.moveaxis, x, 0, [0, 1])
+        assert_raises_regex(ValueError, 'must have the same number',
+                            np.moveaxis, x, [0, 1], [0])
+
+    def test_array_likes(self):
+        x = np.ma.zeros((1, 2, 3))
+        result = np.moveaxis(x, 0, 0)
+        assert_(x.shape, result.shape)
+        assert_(isinstance(result, np.ma.MaskedArray))
+
+        x = [1, 2, 3]
+        result = np.moveaxis(x, 0, 0)
+        assert_(x, list(result))
+        assert_(isinstance(result, np.ndarray))
+
+
+class TestCross:
+    @pytest.mark.filterwarnings(
+        "ignore:.*2-dimensional vectors.*:DeprecationWarning"
+    )
+    def test_2x2(self):
+        u = [1, 2]
+        v = [3, 4]
+        z = -2
+        cp = np.cross(u, v)
+        assert_equal(cp, z)
+        cp = np.cross(v, u)
+        assert_equal(cp, -z)
+
+    @pytest.mark.filterwarnings(
+        "ignore:.*2-dimensional vectors.*:DeprecationWarning"
+    )
+    def test_2x3(self):
+        u = [1, 2]
+        v = [3, 4, 5]
+        z = np.array([10, -5, -2])
+        cp = np.cross(u, v)
+        assert_equal(cp, z)
+        cp = np.cross(v, u)
+        assert_equal(cp, -z)
+
+    def test_3x3(self):
+        u = [1, 2, 3]
+        v = [4, 5, 6]
+        z = np.array([-3, 6, -3])
+        cp = np.cross(u, v)
+        assert_equal(cp, z)
+        cp = np.cross(v, u)
+        assert_equal(cp, -z)
+
+    @pytest.mark.filterwarnings(
+        "ignore:.*2-dimensional vectors.*:DeprecationWarning"
+    )
+    def test_broadcasting(self):
+        # Ticket #2624 (Trac #2032)
+        u = np.tile([1, 2], (11, 1))
+        v = np.tile([3, 4], (11, 1))
+        z = -2
+        assert_equal(np.cross(u, v), z)
+        assert_equal(np.cross(v, u), -z)
+        assert_equal(np.cross(u, u), 0)
+
+        u = np.tile([1, 2], (11, 1)).T
+        v = np.tile([3, 4, 5], (11, 1))
+        z = np.tile([10, -5, -2], (11, 1))
+        assert_equal(np.cross(u, v, axisa=0), z)
+        assert_equal(np.cross(v, u.T), -z)
+        assert_equal(np.cross(v, v), 0)
+
+        u = np.tile([1, 2, 3], (11, 1)).T
+        v = np.tile([3, 4], (11, 1)).T
+        z = np.tile([-12, 9, -2], (11, 1))
+        assert_equal(np.cross(u, v, axisa=0, axisb=0), z)
+        assert_equal(np.cross(v.T, u.T), -z)
+        assert_equal(np.cross(u.T, u.T), 0)
+
+        u = np.tile([1, 2, 3], (5, 1))
+        v = np.tile([4, 5, 6], (5, 1)).T
+        z = np.tile([-3, 6, -3], (5, 1))
+        assert_equal(np.cross(u, v, axisb=0), z)
+        assert_equal(np.cross(v.T, u), -z)
+        assert_equal(np.cross(u, u), 0)
+
+    @pytest.mark.filterwarnings(
+        "ignore:.*2-dimensional vectors.*:DeprecationWarning"
+    )
+    def test_broadcasting_shapes(self):
+        u = np.ones((2, 1, 3))
+        v = np.ones((5, 3))
+        assert_equal(np.cross(u, v).shape, (2, 5, 3))
+        u = np.ones((10, 3, 5))
+        v = np.ones((2, 5))
+        assert_equal(np.cross(u, v, axisa=1, axisb=0).shape, (10, 5, 3))
+        assert_raises(AxisError, np.cross, u, v, axisa=1, axisb=2)
+        assert_raises(AxisError, np.cross, u, v, axisa=3, axisb=0)
+        u = np.ones((10, 3, 5, 7))
+        v = np.ones((5, 7, 2))
+        assert_equal(np.cross(u, v, axisa=1, axisc=2).shape, (10, 5, 3, 7))
+        assert_raises(AxisError, np.cross, u, v, axisa=-5, axisb=2)
+        assert_raises(AxisError, np.cross, u, v, axisa=1, axisb=-4)
+        # gh-5885
+        u = np.ones((3, 4, 2))
+        for axisc in range(-2, 2):
+            assert_equal(np.cross(u, u, axisc=axisc).shape, (3, 4))
+
+    def test_uint8_int32_mixed_dtypes(self):
+        # regression test for gh-19138
+        u = np.array([[195, 8, 9]], np.uint8)
+        v = np.array([250, 166, 68], np.int32)
+        z = np.array([[950, 11010, -30370]], dtype=np.int32)
+        assert_equal(np.cross(v, u), z)
+        assert_equal(np.cross(u, v), -z)
+
+    @pytest.mark.parametrize("a, b", [(0, [1, 2]), ([1, 2], 3)])
+    def test_zero_dimension(self, a, b):
+        with pytest.raises(ValueError) as exc:
+            np.cross(a, b)
+        assert "At least one array has zero dimension" in str(exc.value)
+
+
+def test_outer_out_param():
+    arr1 = np.ones((5,))
+    arr2 = np.ones((2,))
+    arr3 = np.linspace(-2, 2, 5)
+    out1 = np.ndarray(shape=(5, 5))
+    out2 = np.ndarray(shape=(2, 5))
+    res1 = np.outer(arr1, arr3, out1)
+    assert_equal(res1, out1)
+    assert_equal(np.outer(arr2, arr3, out2), out2)
+
+
+class TestIndices:
+
+    def test_simple(self):
+        [x, y] = np.indices((4, 3))
+        assert_array_equal(x, np.array([[0, 0, 0],
+                                        [1, 1, 1],
+                                        [2, 2, 2],
+                                        [3, 3, 3]]))
+        assert_array_equal(y, np.array([[0, 1, 2],
+                                        [0, 1, 2],
+                                        [0, 1, 2],
+                                        [0, 1, 2]]))
+
+    def test_single_input(self):
+        [x] = np.indices((4,))
+        assert_array_equal(x, np.array([0, 1, 2, 3]))
+
+        [x] = np.indices((4,), sparse=True)
+        assert_array_equal(x, np.array([0, 1, 2, 3]))
+
+    def test_scalar_input(self):
+        assert_array_equal([], np.indices(()))
+        assert_array_equal([], np.indices((), sparse=True))
+        assert_array_equal([[]], np.indices((0,)))
+        assert_array_equal([[]], np.indices((0,), sparse=True))
+
+    def test_sparse(self):
+        [x, y] = np.indices((4, 3), sparse=True)
+        assert_array_equal(x, np.array([[0], [1], [2], [3]]))
+        assert_array_equal(y, np.array([[0, 1, 2]]))
+
+    @pytest.mark.parametrize("dtype", [np.int32, np.int64, np.float32, np.float64])
+    @pytest.mark.parametrize("dims", [(), (0,), (4, 3)])
+    def test_return_type(self, dtype, dims):
+        inds = np.indices(dims, dtype=dtype)
+        assert_(inds.dtype == dtype)
+
+        for arr in np.indices(dims, dtype=dtype, sparse=True):
+            assert_(arr.dtype == dtype)
+
+
+class TestRequire:
+    flag_names = ['C', 'C_CONTIGUOUS', 'CONTIGUOUS',
+                  'F', 'F_CONTIGUOUS', 'FORTRAN',
+                  'A', 'ALIGNED',
+                  'W', 'WRITEABLE',
+                  'O', 'OWNDATA']
+
+    def generate_all_false(self, dtype):
+        arr = np.zeros((2, 2), [('junk', 'i1'), ('a', dtype)])
+        arr.setflags(write=False)
+        a = arr['a']
+        assert_(not a.flags['C'])
+        assert_(not a.flags['F'])
+        assert_(not a.flags['O'])
+        assert_(not a.flags['W'])
+        assert_(not a.flags['A'])
+        return a
+
+    def set_and_check_flag(self, flag, dtype, arr):
+        if dtype is None:
+            dtype = arr.dtype
+        b = np.require(arr, dtype, [flag])
+        assert_(b.flags[flag])
+        assert_(b.dtype == dtype)
+
+        # a further call to np.require ought to return the same array
+        # unless OWNDATA is specified.
+        c = np.require(b, None, [flag])
+        if flag[0] != 'O':
+            assert_(c is b)
+        else:
+            assert_(c.flags[flag])
+
+    def test_require_each(self):
+
+        id = ['f8', 'i4']
+        fd = [None, 'f8', 'c16']
+        for idtype, fdtype, flag in itertools.product(id, fd, self.flag_names):
+            a = self.generate_all_false(idtype)
+            self.set_and_check_flag(flag, fdtype,  a)
+
+    def test_unknown_requirement(self):
+        a = self.generate_all_false('f8')
+        assert_raises(KeyError, np.require, a, None, 'Q')
+
+    def test_non_array_input(self):
+        a = np.require([1, 2, 3, 4], 'i4', ['C', 'A', 'O'])
+        assert_(a.flags['O'])
+        assert_(a.flags['C'])
+        assert_(a.flags['A'])
+        assert_(a.dtype == 'i4')
+        assert_equal(a, [1, 2, 3, 4])
+
+    def test_C_and_F_simul(self):
+        a = self.generate_all_false('f8')
+        assert_raises(ValueError, np.require, a, None, ['C', 'F'])
+
+    def test_ensure_array(self):
+        class ArraySubclass(np.ndarray):
+            pass
+
+        a = ArraySubclass((2, 2))
+        b = np.require(a, None, ['E'])
+        assert_(type(b) is np.ndarray)
+
+    def test_preserve_subtype(self):
+        class ArraySubclass(np.ndarray):
+            pass
+
+        for flag in self.flag_names:
+            a = ArraySubclass((2, 2))
+            self.set_and_check_flag(flag, None, a)
+
+
+class TestBroadcast:
+    def test_broadcast_in_args(self):
+        # gh-5881
+        arrs = [np.empty((6, 7)), np.empty((5, 6, 1)), np.empty((7,)),
+                np.empty((5, 1, 7))]
+        mits = [np.broadcast(*arrs),
+                np.broadcast(np.broadcast(*arrs[:0]), np.broadcast(*arrs[0:])),
+                np.broadcast(np.broadcast(*arrs[:1]), np.broadcast(*arrs[1:])),
+                np.broadcast(np.broadcast(*arrs[:2]), np.broadcast(*arrs[2:])),
+                np.broadcast(arrs[0], np.broadcast(*arrs[1:-1]), arrs[-1])]
+        for mit in mits:
+            assert_equal(mit.shape, (5, 6, 7))
+            assert_equal(mit.ndim, 3)
+            assert_equal(mit.nd, 3)
+            assert_equal(mit.numiter, 4)
+            for a, ia in zip(arrs, mit.iters):
+                assert_(a is ia.base)
+
+    def test_broadcast_single_arg(self):
+        # gh-6899
+        arrs = [np.empty((5, 6, 7))]
+        mit = np.broadcast(*arrs)
+        assert_equal(mit.shape, (5, 6, 7))
+        assert_equal(mit.ndim, 3)
+        assert_equal(mit.nd, 3)
+        assert_equal(mit.numiter, 1)
+        assert_(arrs[0] is mit.iters[0].base)
+
+    def test_number_of_arguments(self):
+        arr = np.empty((5,))
+        for j in range(70):
+            arrs = [arr] * j
+            if j > 64:
+                assert_raises(ValueError, np.broadcast, *arrs)
+            else:
+                mit = np.broadcast(*arrs)
+                assert_equal(mit.numiter, j)
+
+    def test_broadcast_error_kwargs(self):
+        # gh-13455
+        arrs = [np.empty((5, 6, 7))]
+        mit = np.broadcast(*arrs)
+        mit2 = np.broadcast(*arrs, **{})  # noqa: PIE804
+        assert_equal(mit.shape, mit2.shape)
+        assert_equal(mit.ndim, mit2.ndim)
+        assert_equal(mit.nd, mit2.nd)
+        assert_equal(mit.numiter, mit2.numiter)
+        assert_(mit.iters[0].base is mit2.iters[0].base)
+
+        assert_raises(ValueError, np.broadcast, 1, x=1)
+
+    def test_shape_mismatch_error_message(self):
+        with pytest.raises(ValueError, match=r"arg 0 with shape \(1, 3\) and "
+                                             r"arg 2 with shape \(2,\)"):
+            np.broadcast([[1, 2, 3]], [[4], [5]], [6, 7])
+
+
+class TestKeepdims:
+
+    class sub_array(np.ndarray):
+        def sum(self, axis=None, dtype=None, out=None):
+            return np.ndarray.sum(self, axis, dtype, out, keepdims=True)
+
+    def test_raise(self):
+        sub_class = self.sub_array
+        x = np.arange(30).view(sub_class)
+        assert_raises(TypeError, np.sum, x, keepdims=True)
+
+
+class TestTensordot:
+
+    def test_zero_dimension(self):
+        # Test resolution to issue #5663
+        a = np.ndarray((3, 0))
+        b = np.ndarray((0, 4))
+        td = np.tensordot(a, b, (1, 0))
+        assert_array_equal(td, np.dot(a, b))
+        assert_array_equal(td, np.einsum('ij,jk', a, b))
+
+    def test_zero_dimensional(self):
+        # gh-12130
+        arr_0d = np.array(1)
+        ret = np.tensordot(arr_0d, arr_0d, ([], []))  # contracting no axes is well defined
+        assert_array_equal(ret, arr_0d)
+
+
+class TestAsType:
+
+    def test_astype(self):
+        data = [[1, 2], [3, 4]]
+        actual = np.astype(
+            np.array(data, dtype=np.int64), np.uint32
+        )
+        expected = np.array(data, dtype=np.uint32)
+
+        assert_array_equal(actual, expected)
+        assert_equal(actual.dtype, expected.dtype)
+
+        assert np.shares_memory(
+            actual, np.astype(actual, actual.dtype, copy=False)
+        )
+
+        actual = np.astype(np.int64(10), np.float64)
+        expected = np.float64(10)
+        assert_equal(actual, expected)
+        assert_equal(actual.dtype, expected.dtype)
+
+        with pytest.raises(TypeError, match="Input should be a NumPy array"):
+            np.astype(data, np.float64)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_numerictypes.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_numerictypes.py
new file mode 100644
index 0000000..c9a2ac0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_numerictypes.py
@@ -0,0 +1,622 @@
+import itertools
+import sys
+
+import pytest
+
+import numpy as np
+import numpy._core.numerictypes as nt
+from numpy._core.numerictypes import issctype, maximum_sctype, sctype2char, sctypes
+from numpy.testing import (
+    IS_PYPY,
+    assert_,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+)
+
+# This is the structure of the table used for plain objects:
+#
+# +-+-+-+
+# |x|y|z|
+# +-+-+-+
+
+# Structure of a plain array description:
+Pdescr = [
+    ('x', 'i4', (2,)),
+    ('y', 'f8', (2, 2)),
+    ('z', 'u1')]
+
+# A plain list of tuples with values for testing:
+PbufferT = [
+    # x     y                  z
+    ([3, 2], [[6., 4.], [6., 4.]], 8),
+    ([4, 3], [[7., 5.], [7., 5.]], 9),
+    ]
+
+
+# This is the structure of the table used for nested objects (DON'T PANIC!):
+#
+# +-+---------------------------------+-----+----------+-+-+
+# |x|Info                             |color|info      |y|z|
+# | +-----+--+----------------+----+--+     +----+-----+ | |
+# | |value|y2|Info2           |name|z2|     |Name|Value| | |
+# | |     |  +----+-----+--+--+    |  |     |    |     | | |
+# | |     |  |name|value|y3|z3|    |  |     |    |     | | |
+# +-+-----+--+----+-----+--+--+----+--+-----+----+-----+-+-+
+#
+
+# The corresponding nested array description:
+Ndescr = [
+    ('x', 'i4', (2,)),
+    ('Info', [
+        ('value', 'c16'),
+        ('y2', 'f8'),
+        ('Info2', [
+            ('name', 'S2'),
+            ('value', 'c16', (2,)),
+            ('y3', 'f8', (2,)),
+            ('z3', 'u4', (2,))]),
+        ('name', 'S2'),
+        ('z2', 'b1')]),
+    ('color', 'S2'),
+    ('info', [
+        ('Name', 'U8'),
+        ('Value', 'c16')]),
+    ('y', 'f8', (2, 2)),
+    ('z', 'u1')]
+
+NbufferT = [
+    # x     Info                                                color info        y                  z
+    #       value y2 Info2                            name z2         Name Value
+    #                name   value    y3       z3
+    ([3, 2], (6j, 6., (b'nn', [6j, 4j], [6., 4.], [1, 2]), b'NN', True),
+     b'cc', ('NN', 6j), [[6., 4.], [6., 4.]], 8),
+    ([4, 3], (7j, 7., (b'oo', [7j, 5j], [7., 5.], [2, 1]), b'OO', False),
+     b'dd', ('OO', 7j), [[7., 5.], [7., 5.]], 9),
+    ]
+
+
+byteorder = {'little': '<', 'big': '>'}[sys.byteorder]
+
+def normalize_descr(descr):
+    "Normalize a description adding the platform byteorder."
+
+    out = []
+    for item in descr:
+        dtype = item[1]
+        if isinstance(dtype, str):
+            if dtype[0] not in ['|', '<', '>']:
+                onebyte = dtype[1:] == "1"
+                if onebyte or dtype[0] in ['S', 'V', 'b']:
+                    dtype = "|" + dtype
+                else:
+                    dtype = byteorder + dtype
+            if len(item) > 2 and np.prod(item[2]) > 1:
+                nitem = (item[0], dtype, item[2])
+            else:
+                nitem = (item[0], dtype)
+            out.append(nitem)
+        elif isinstance(dtype, list):
+            l = normalize_descr(dtype)
+            out.append((item[0], l))
+        else:
+            raise ValueError(f"Expected a str or list and got {type(item)}")
+    return out
+
+
+############################################################
+#    Creation tests
+############################################################
+
+class CreateZeros:
+    """Check the creation of heterogeneous arrays zero-valued"""
+
+    def test_zeros0D(self):
+        """Check creation of 0-dimensional objects"""
+        h = np.zeros((), dtype=self._descr)
+        assert_(normalize_descr(self._descr) == h.dtype.descr)
+        assert_(h.dtype.fields['x'][0].name[:4] == 'void')
+        assert_(h.dtype.fields['x'][0].char == 'V')
+        assert_(h.dtype.fields['x'][0].type == np.void)
+        # A small check that data is ok
+        assert_equal(h['z'], np.zeros((), dtype='u1'))
+
+    def test_zerosSD(self):
+        """Check creation of single-dimensional objects"""
+        h = np.zeros((2,), dtype=self._descr)
+        assert_(normalize_descr(self._descr) == h.dtype.descr)
+        assert_(h.dtype['y'].name[:4] == 'void')
+        assert_(h.dtype['y'].char == 'V')
+        assert_(h.dtype['y'].type == np.void)
+        # A small check that data is ok
+        assert_equal(h['z'], np.zeros((2,), dtype='u1'))
+
+    def test_zerosMD(self):
+        """Check creation of multi-dimensional objects"""
+        h = np.zeros((2, 3), dtype=self._descr)
+        assert_(normalize_descr(self._descr) == h.dtype.descr)
+        assert_(h.dtype['z'].name == 'uint8')
+        assert_(h.dtype['z'].char == 'B')
+        assert_(h.dtype['z'].type == np.uint8)
+        # A small check that data is ok
+        assert_equal(h['z'], np.zeros((2, 3), dtype='u1'))
+
+
+class TestCreateZerosPlain(CreateZeros):
+    """Check the creation of heterogeneous arrays zero-valued (plain)"""
+    _descr = Pdescr
+
+class TestCreateZerosNested(CreateZeros):
+    """Check the creation of heterogeneous arrays zero-valued (nested)"""
+    _descr = Ndescr
+
+
+class CreateValues:
+    """Check the creation of heterogeneous arrays with values"""
+
+    def test_tuple(self):
+        """Check creation from tuples"""
+        h = np.array(self._buffer, dtype=self._descr)
+        assert_(normalize_descr(self._descr) == h.dtype.descr)
+        if self.multiple_rows:
+            assert_(h.shape == (2,))
+        else:
+            assert_(h.shape == ())
+
+    def test_list_of_tuple(self):
+        """Check creation from list of tuples"""
+        h = np.array([self._buffer], dtype=self._descr)
+        assert_(normalize_descr(self._descr) == h.dtype.descr)
+        if self.multiple_rows:
+            assert_(h.shape == (1, 2))
+        else:
+            assert_(h.shape == (1,))
+
+    def test_list_of_list_of_tuple(self):
+        """Check creation from list of list of tuples"""
+        h = np.array([[self._buffer]], dtype=self._descr)
+        assert_(normalize_descr(self._descr) == h.dtype.descr)
+        if self.multiple_rows:
+            assert_(h.shape == (1, 1, 2))
+        else:
+            assert_(h.shape == (1, 1))
+
+
+class TestCreateValuesPlainSingle(CreateValues):
+    """Check the creation of heterogeneous arrays (plain, single row)"""
+    _descr = Pdescr
+    multiple_rows = 0
+    _buffer = PbufferT[0]
+
+class TestCreateValuesPlainMultiple(CreateValues):
+    """Check the creation of heterogeneous arrays (plain, multiple rows)"""
+    _descr = Pdescr
+    multiple_rows = 1
+    _buffer = PbufferT
+
+class TestCreateValuesNestedSingle(CreateValues):
+    """Check the creation of heterogeneous arrays (nested, single row)"""
+    _descr = Ndescr
+    multiple_rows = 0
+    _buffer = NbufferT[0]
+
+class TestCreateValuesNestedMultiple(CreateValues):
+    """Check the creation of heterogeneous arrays (nested, multiple rows)"""
+    _descr = Ndescr
+    multiple_rows = 1
+    _buffer = NbufferT
+
+
+############################################################
+#    Reading tests
+############################################################
+
+class ReadValuesPlain:
+    """Check the reading of values in heterogeneous arrays (plain)"""
+
+    def test_access_fields(self):
+        h = np.array(self._buffer, dtype=self._descr)
+        if not self.multiple_rows:
+            assert_(h.shape == ())
+            assert_equal(h['x'], np.array(self._buffer[0], dtype='i4'))
+            assert_equal(h['y'], np.array(self._buffer[1], dtype='f8'))
+            assert_equal(h['z'], np.array(self._buffer[2], dtype='u1'))
+        else:
+            assert_(len(h) == 2)
+            assert_equal(h['x'], np.array([self._buffer[0][0],
+                                             self._buffer[1][0]], dtype='i4'))
+            assert_equal(h['y'], np.array([self._buffer[0][1],
+                                             self._buffer[1][1]], dtype='f8'))
+            assert_equal(h['z'], np.array([self._buffer[0][2],
+                                             self._buffer[1][2]], dtype='u1'))
+
+
+class TestReadValuesPlainSingle(ReadValuesPlain):
+    """Check the creation of heterogeneous arrays (plain, single row)"""
+    _descr = Pdescr
+    multiple_rows = 0
+    _buffer = PbufferT[0]
+
+class TestReadValuesPlainMultiple(ReadValuesPlain):
+    """Check the values of heterogeneous arrays (plain, multiple rows)"""
+    _descr = Pdescr
+    multiple_rows = 1
+    _buffer = PbufferT
+
+class ReadValuesNested:
+    """Check the reading of values in heterogeneous arrays (nested)"""
+
+    def test_access_top_fields(self):
+        """Check reading the top fields of a nested array"""
+        h = np.array(self._buffer, dtype=self._descr)
+        if not self.multiple_rows:
+            assert_(h.shape == ())
+            assert_equal(h['x'], np.array(self._buffer[0], dtype='i4'))
+            assert_equal(h['y'], np.array(self._buffer[4], dtype='f8'))
+            assert_equal(h['z'], np.array(self._buffer[5], dtype='u1'))
+        else:
+            assert_(len(h) == 2)
+            assert_equal(h['x'], np.array([self._buffer[0][0],
+                                           self._buffer[1][0]], dtype='i4'))
+            assert_equal(h['y'], np.array([self._buffer[0][4],
+                                           self._buffer[1][4]], dtype='f8'))
+            assert_equal(h['z'], np.array([self._buffer[0][5],
+                                           self._buffer[1][5]], dtype='u1'))
+
+    def test_nested1_acessors(self):
+        """Check reading the nested fields of a nested array (1st level)"""
+        h = np.array(self._buffer, dtype=self._descr)
+        if not self.multiple_rows:
+            assert_equal(h['Info']['value'],
+                         np.array(self._buffer[1][0], dtype='c16'))
+            assert_equal(h['Info']['y2'],
+                         np.array(self._buffer[1][1], dtype='f8'))
+            assert_equal(h['info']['Name'],
+                         np.array(self._buffer[3][0], dtype='U2'))
+            assert_equal(h['info']['Value'],
+                         np.array(self._buffer[3][1], dtype='c16'))
+        else:
+            assert_equal(h['Info']['value'],
+                         np.array([self._buffer[0][1][0],
+                                self._buffer[1][1][0]],
+                                dtype='c16'))
+            assert_equal(h['Info']['y2'],
+                         np.array([self._buffer[0][1][1],
+                                self._buffer[1][1][1]],
+                                dtype='f8'))
+            assert_equal(h['info']['Name'],
+                         np.array([self._buffer[0][3][0],
+                                self._buffer[1][3][0]],
+                               dtype='U2'))
+            assert_equal(h['info']['Value'],
+                         np.array([self._buffer[0][3][1],
+                                self._buffer[1][3][1]],
+                               dtype='c16'))
+
+    def test_nested2_acessors(self):
+        """Check reading the nested fields of a nested array (2nd level)"""
+        h = np.array(self._buffer, dtype=self._descr)
+        if not self.multiple_rows:
+            assert_equal(h['Info']['Info2']['value'],
+                         np.array(self._buffer[1][2][1], dtype='c16'))
+            assert_equal(h['Info']['Info2']['z3'],
+                         np.array(self._buffer[1][2][3], dtype='u4'))
+        else:
+            assert_equal(h['Info']['Info2']['value'],
+                         np.array([self._buffer[0][1][2][1],
+                                self._buffer[1][1][2][1]],
+                               dtype='c16'))
+            assert_equal(h['Info']['Info2']['z3'],
+                         np.array([self._buffer[0][1][2][3],
+                                self._buffer[1][1][2][3]],
+                               dtype='u4'))
+
+    def test_nested1_descriptor(self):
+        """Check access nested descriptors of a nested array (1st level)"""
+        h = np.array(self._buffer, dtype=self._descr)
+        assert_(h.dtype['Info']['value'].name == 'complex128')
+        assert_(h.dtype['Info']['y2'].name == 'float64')
+        assert_(h.dtype['info']['Name'].name == 'str256')
+        assert_(h.dtype['info']['Value'].name == 'complex128')
+
+    def test_nested2_descriptor(self):
+        """Check access nested descriptors of a nested array (2nd level)"""
+        h = np.array(self._buffer, dtype=self._descr)
+        assert_(h.dtype['Info']['Info2']['value'].name == 'void256')
+        assert_(h.dtype['Info']['Info2']['z3'].name == 'void64')
+
+
+class TestReadValuesNestedSingle(ReadValuesNested):
+    """Check the values of heterogeneous arrays (nested, single row)"""
+    _descr = Ndescr
+    multiple_rows = False
+    _buffer = NbufferT[0]
+
+class TestReadValuesNestedMultiple(ReadValuesNested):
+    """Check the values of heterogeneous arrays (nested, multiple rows)"""
+    _descr = Ndescr
+    multiple_rows = True
+    _buffer = NbufferT
+
+class TestEmptyField:
+    def test_assign(self):
+        a = np.arange(10, dtype=np.float32)
+        a.dtype = [("int",   "<0i4"), ("float", "<2f4")]
+        assert_(a['int'].shape == (5, 0))
+        assert_(a['float'].shape == (5, 2))
+
+
+class TestMultipleFields:
+    def setup_method(self):
+        self.ary = np.array([(1, 2, 3, 4), (5, 6, 7, 8)], dtype='i4,f4,i2,c8')
+
+    def _bad_call(self):
+        return self.ary['f0', 'f1']
+
+    def test_no_tuple(self):
+        assert_raises(IndexError, self._bad_call)
+
+    def test_return(self):
+        res = self.ary[['f0', 'f2']].tolist()
+        assert_(res == [(1, 3), (5, 7)])
+
+
+class TestIsSubDType:
+    # scalar types can be promoted into dtypes
+    wrappers = [np.dtype, lambda x: x]
+
+    def test_both_abstract(self):
+        assert_(np.issubdtype(np.floating, np.inexact))
+        assert_(not np.issubdtype(np.inexact, np.floating))
+
+    def test_same(self):
+        for cls in (np.float32, np.int32):
+            for w1, w2 in itertools.product(self.wrappers, repeat=2):
+                assert_(np.issubdtype(w1(cls), w2(cls)))
+
+    def test_subclass(self):
+        # note we cannot promote floating to a dtype, as it would turn into a
+        # concrete type
+        for w in self.wrappers:
+            assert_(np.issubdtype(w(np.float32), np.floating))
+            assert_(np.issubdtype(w(np.float64), np.floating))
+
+    def test_subclass_backwards(self):
+        for w in self.wrappers:
+            assert_(not np.issubdtype(np.floating, w(np.float32)))
+            assert_(not np.issubdtype(np.floating, w(np.float64)))
+
+    def test_sibling_class(self):
+        for w1, w2 in itertools.product(self.wrappers, repeat=2):
+            assert_(not np.issubdtype(w1(np.float32), w2(np.float64)))
+            assert_(not np.issubdtype(w1(np.float64), w2(np.float32)))
+
+    def test_nondtype_nonscalartype(self):
+        # See gh-14619 and gh-9505 which introduced the deprecation to fix
+        # this. These tests are directly taken from gh-9505
+        assert not np.issubdtype(np.float32, 'float64')
+        assert not np.issubdtype(np.float32, 'f8')
+        assert not np.issubdtype(np.int32, str)
+        assert not np.issubdtype(np.int32, 'int64')
+        assert not np.issubdtype(np.str_, 'void')
+        # for the following the correct spellings are
+        # np.integer, np.floating, or np.complexfloating respectively:
+        assert not np.issubdtype(np.int8, int)  # np.int8 is never np.int_
+        assert not np.issubdtype(np.float32, float)
+        assert not np.issubdtype(np.complex64, complex)
+        assert not np.issubdtype(np.float32, "float")
+        assert not np.issubdtype(np.float64, "f")
+
+        # Test the same for the correct first datatype and abstract one
+        # in the case of int, float, complex:
+        assert np.issubdtype(np.float64, 'float64')
+        assert np.issubdtype(np.float64, 'f8')
+        assert np.issubdtype(np.str_, str)
+        assert np.issubdtype(np.int64, 'int64')
+        assert np.issubdtype(np.void, 'void')
+        assert np.issubdtype(np.int8, np.integer)
+        assert np.issubdtype(np.float32, np.floating)
+        assert np.issubdtype(np.complex64, np.complexfloating)
+        assert np.issubdtype(np.float64, "float")
+        assert np.issubdtype(np.float32, "f")
+
+
+class TestIsDType:
+    """
+    Check correctness of `np.isdtype`. The test considers different argument
+    configurations: `np.isdtype(dtype, k1)` and `np.isdtype(dtype, (k1, k2))`
+    with concrete dtypes and dtype groups.
+    """
+    dtype_group_dict = {
+        "signed integer": sctypes["int"],
+        "unsigned integer": sctypes["uint"],
+        "integral": sctypes["int"] + sctypes["uint"],
+        "real floating": sctypes["float"],
+        "complex floating": sctypes["complex"],
+        "numeric": (
+            sctypes["int"] + sctypes["uint"] + sctypes["float"] +
+            sctypes["complex"]
+        )
+    }
+
+    @pytest.mark.parametrize(
+        "dtype,close_dtype",
+        [
+            (np.int64, np.int32), (np.uint64, np.uint32),
+            (np.float64, np.float32), (np.complex128, np.complex64)
+        ]
+    )
+    @pytest.mark.parametrize(
+        "dtype_group",
+        [
+            None, "signed integer", "unsigned integer", "integral",
+            "real floating", "complex floating", "numeric"
+        ]
+    )
+    def test_isdtype(self, dtype, close_dtype, dtype_group):
+        # First check if same dtypes return `true` and different ones
+        # give `false` (even if they're close in the dtype hierarchy!)
+        if dtype_group is None:
+            assert np.isdtype(dtype, dtype)
+            assert not np.isdtype(dtype, close_dtype)
+            assert np.isdtype(dtype, (dtype, close_dtype))
+
+        # Check that dtype and a dtype group that it belongs to
+        # return `true`, and `false` otherwise.
+        elif dtype in self.dtype_group_dict[dtype_group]:
+            assert np.isdtype(dtype, dtype_group)
+            assert np.isdtype(dtype, (close_dtype, dtype_group))
+        else:
+            assert not np.isdtype(dtype, dtype_group)
+
+    def test_isdtype_invalid_args(self):
+        with assert_raises_regex(TypeError, r".*must be a NumPy dtype.*"):
+            np.isdtype("int64", np.int64)
+        with assert_raises_regex(TypeError, r".*kind argument must.*"):
+            np.isdtype(np.int64, 1)
+        with assert_raises_regex(ValueError, r".*not a known kind name.*"):
+            np.isdtype(np.int64, "int64")
+
+    def test_sctypes_complete(self):
+        # issue 26439: int32/intc were masking each other on 32-bit builds
+        assert np.int32 in sctypes['int']
+        assert np.intc in sctypes['int']
+        assert np.int64 in sctypes['int']
+        assert np.uint32 in sctypes['uint']
+        assert np.uintc in sctypes['uint']
+        assert np.uint64 in sctypes['uint']
+
+class TestSctypeDict:
+    def test_longdouble(self):
+        assert_(np._core.sctypeDict['float64'] is not np.longdouble)
+        assert_(np._core.sctypeDict['complex128'] is not np.clongdouble)
+
+    def test_ulong(self):
+        assert np._core.sctypeDict['ulong'] is np.ulong
+        assert np.dtype(np.ulong) is np.dtype("ulong")
+        assert np.dtype(np.ulong).itemsize == np.dtype(np.long).itemsize
+
+
+@pytest.mark.filterwarnings("ignore:.*maximum_sctype.*:DeprecationWarning")
+class TestMaximumSctype:
+
+    # note that parametrizing with sctype['int'] and similar would skip types
+    # with the same size (gh-11923)
+
+    @pytest.mark.parametrize(
+        't', [np.byte, np.short, np.intc, np.long, np.longlong]
+    )
+    def test_int(self, t):
+        assert_equal(maximum_sctype(t), np._core.sctypes['int'][-1])
+
+    @pytest.mark.parametrize(
+        't', [np.ubyte, np.ushort, np.uintc, np.ulong, np.ulonglong]
+    )
+    def test_uint(self, t):
+        assert_equal(maximum_sctype(t), np._core.sctypes['uint'][-1])
+
+    @pytest.mark.parametrize('t', [np.half, np.single, np.double, np.longdouble])
+    def test_float(self, t):
+        assert_equal(maximum_sctype(t), np._core.sctypes['float'][-1])
+
+    @pytest.mark.parametrize('t', [np.csingle, np.cdouble, np.clongdouble])
+    def test_complex(self, t):
+        assert_equal(maximum_sctype(t), np._core.sctypes['complex'][-1])
+
+    @pytest.mark.parametrize('t', [np.bool, np.object_, np.str_, np.bytes_,
+                                   np.void])
+    def test_other(self, t):
+        assert_equal(maximum_sctype(t), t)
+
+
+class Test_sctype2char:
+    # This function is old enough that we're really just documenting the quirks
+    # at this point.
+
+    def test_scalar_type(self):
+        assert_equal(sctype2char(np.double), 'd')
+        assert_equal(sctype2char(np.long), 'l')
+        assert_equal(sctype2char(np.int_), np.array(0).dtype.char)
+        assert_equal(sctype2char(np.str_), 'U')
+        assert_equal(sctype2char(np.bytes_), 'S')
+
+    def test_other_type(self):
+        assert_equal(sctype2char(float), 'd')
+        assert_equal(sctype2char(list), 'O')
+        assert_equal(sctype2char(np.ndarray), 'O')
+
+    def test_third_party_scalar_type(self):
+        from numpy._core._rational_tests import rational
+        assert_raises(KeyError, sctype2char, rational)
+        assert_raises(KeyError, sctype2char, rational(1))
+
+    def test_array_instance(self):
+        assert_equal(sctype2char(np.array([1.0, 2.0])), 'd')
+
+    def test_abstract_type(self):
+        assert_raises(KeyError, sctype2char, np.floating)
+
+    def test_non_type(self):
+        assert_raises(ValueError, sctype2char, 1)
+
+@pytest.mark.parametrize("rep, expected", [
+    (np.int32, True),
+    (list, False),
+    (1.1, False),
+    (str, True),
+    (np.dtype(np.float64), True),
+    (np.dtype((np.int16, (3, 4))), True),
+    (np.dtype([('a', np.int8)]), True),
+    ])
+def test_issctype(rep, expected):
+    # ensure proper identification of scalar
+    # data-types by issctype()
+    actual = issctype(rep)
+    assert type(actual) is bool
+    assert_equal(actual, expected)
+
+
+@pytest.mark.skipif(sys.flags.optimize > 1,
+                    reason="no docstrings present to inspect when PYTHONOPTIMIZE/Py_OptimizeFlag > 1")
+@pytest.mark.xfail(IS_PYPY,
+                   reason="PyPy cannot modify tp_doc after PyType_Ready")
+class TestDocStrings:
+    def test_platform_dependent_aliases(self):
+        if np.int64 is np.int_:
+            assert_('int64' in np.int_.__doc__)
+        elif np.int64 is np.longlong:
+            assert_('int64' in np.longlong.__doc__)
+
+
+class TestScalarTypeNames:
+    # gh-9799
+
+    numeric_types = [
+        np.byte, np.short, np.intc, np.long, np.longlong,
+        np.ubyte, np.ushort, np.uintc, np.ulong, np.ulonglong,
+        np.half, np.single, np.double, np.longdouble,
+        np.csingle, np.cdouble, np.clongdouble,
+    ]
+
+    def test_names_are_unique(self):
+        # none of the above may be aliases for each other
+        assert len(set(self.numeric_types)) == len(self.numeric_types)
+
+        # names must be unique
+        names = [t.__name__ for t in self.numeric_types]
+        assert len(set(names)) == len(names)
+
+    @pytest.mark.parametrize('t', numeric_types)
+    def test_names_reflect_attributes(self, t):
+        """ Test that names correspond to where the type is under ``np.`` """
+        assert getattr(np, t.__name__) is t
+
+    @pytest.mark.parametrize('t', numeric_types)
+    def test_names_are_undersood_by_dtype(self, t):
+        """ Test the dtype constructor maps names back to the type """
+        assert np.dtype(t.__name__).type is t
+
+
+class TestBoolDefinition:
+    def test_bool_definition(self):
+        assert nt.bool is np.bool
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_overrides.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_overrides.py
new file mode 100644
index 0000000..b0d7337
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_overrides.py
@@ -0,0 +1,791 @@
+import inspect
+import os
+import pickle
+import sys
+import tempfile
+from io import StringIO
+from unittest import mock
+
+import pytest
+
+import numpy as np
+from numpy._core.overrides import (
+    _get_implementing_args,
+    array_function_dispatch,
+    verify_matching_signatures,
+)
+from numpy.testing import assert_, assert_equal, assert_raises, assert_raises_regex
+from numpy.testing.overrides import get_overridable_numpy_array_functions
+
+
+def _return_not_implemented(self, *args, **kwargs):
+    return NotImplemented
+
+
+# need to define this at the top level to test pickling
+@array_function_dispatch(lambda array: (array,))
+def dispatched_one_arg(array):
+    """Docstring."""
+    return 'original'
+
+
+@array_function_dispatch(lambda array1, array2: (array1, array2))
+def dispatched_two_arg(array1, array2):
+    """Docstring."""
+    return 'original'
+
+
+class TestGetImplementingArgs:
+
+    def test_ndarray(self):
+        array = np.array(1)
+
+        args = _get_implementing_args([array])
+        assert_equal(list(args), [array])
+
+        args = _get_implementing_args([array, array])
+        assert_equal(list(args), [array])
+
+        args = _get_implementing_args([array, 1])
+        assert_equal(list(args), [array])
+
+        args = _get_implementing_args([1, array])
+        assert_equal(list(args), [array])
+
+    def test_ndarray_subclasses(self):
+
+        class OverrideSub(np.ndarray):
+            __array_function__ = _return_not_implemented
+
+        class NoOverrideSub(np.ndarray):
+            pass
+
+        array = np.array(1).view(np.ndarray)
+        override_sub = np.array(1).view(OverrideSub)
+        no_override_sub = np.array(1).view(NoOverrideSub)
+
+        args = _get_implementing_args([array, override_sub])
+        assert_equal(list(args), [override_sub, array])
+
+        args = _get_implementing_args([array, no_override_sub])
+        assert_equal(list(args), [no_override_sub, array])
+
+        args = _get_implementing_args(
+            [override_sub, no_override_sub])
+        assert_equal(list(args), [override_sub, no_override_sub])
+
+    def test_ndarray_and_duck_array(self):
+
+        class Other:
+            __array_function__ = _return_not_implemented
+
+        array = np.array(1)
+        other = Other()
+
+        args = _get_implementing_args([other, array])
+        assert_equal(list(args), [other, array])
+
+        args = _get_implementing_args([array, other])
+        assert_equal(list(args), [array, other])
+
+    def test_ndarray_subclass_and_duck_array(self):
+
+        class OverrideSub(np.ndarray):
+            __array_function__ = _return_not_implemented
+
+        class Other:
+            __array_function__ = _return_not_implemented
+
+        array = np.array(1)
+        subarray = np.array(1).view(OverrideSub)
+        other = Other()
+
+        assert_equal(_get_implementing_args([array, subarray, other]),
+                     [subarray, array, other])
+        assert_equal(_get_implementing_args([array, other, subarray]),
+                     [subarray, array, other])
+
+    def test_many_duck_arrays(self):
+
+        class A:
+            __array_function__ = _return_not_implemented
+
+        class B(A):
+            __array_function__ = _return_not_implemented
+
+        class C(A):
+            __array_function__ = _return_not_implemented
+
+        class D:
+            __array_function__ = _return_not_implemented
+
+        a = A()
+        b = B()
+        c = C()
+        d = D()
+
+        assert_equal(_get_implementing_args([1]), [])
+        assert_equal(_get_implementing_args([a]), [a])
+        assert_equal(_get_implementing_args([a, 1]), [a])
+        assert_equal(_get_implementing_args([a, a, a]), [a])
+        assert_equal(_get_implementing_args([a, d, a]), [a, d])
+        assert_equal(_get_implementing_args([a, b]), [b, a])
+        assert_equal(_get_implementing_args([b, a]), [b, a])
+        assert_equal(_get_implementing_args([a, b, c]), [b, c, a])
+        assert_equal(_get_implementing_args([a, c, b]), [c, b, a])
+
+    def test_too_many_duck_arrays(self):
+        namespace = {'__array_function__': _return_not_implemented}
+        types = [type('A' + str(i), (object,), namespace) for i in range(65)]
+        relevant_args = [t() for t in types]
+
+        actual = _get_implementing_args(relevant_args[:64])
+        assert_equal(actual, relevant_args[:64])
+
+        with assert_raises_regex(TypeError, 'distinct argument types'):
+            _get_implementing_args(relevant_args)
+
+
+class TestNDArrayArrayFunction:
+
+    def test_method(self):
+
+        class Other:
+            __array_function__ = _return_not_implemented
+
+        class NoOverrideSub(np.ndarray):
+            pass
+
+        class OverrideSub(np.ndarray):
+            __array_function__ = _return_not_implemented
+
+        array = np.array([1])
+        other = Other()
+        no_override_sub = array.view(NoOverrideSub)
+        override_sub = array.view(OverrideSub)
+
+        result = array.__array_function__(func=dispatched_two_arg,
+                                          types=(np.ndarray,),
+                                          args=(array, 1.), kwargs={})
+        assert_equal(result, 'original')
+
+        result = array.__array_function__(func=dispatched_two_arg,
+                                          types=(np.ndarray, Other),
+                                          args=(array, other), kwargs={})
+        assert_(result is NotImplemented)
+
+        result = array.__array_function__(func=dispatched_two_arg,
+                                          types=(np.ndarray, NoOverrideSub),
+                                          args=(array, no_override_sub),
+                                          kwargs={})
+        assert_equal(result, 'original')
+
+        result = array.__array_function__(func=dispatched_two_arg,
+                                          types=(np.ndarray, OverrideSub),
+                                          args=(array, override_sub),
+                                          kwargs={})
+        assert_equal(result, 'original')
+
+        with assert_raises_regex(TypeError, 'no implementation found'):
+            np.concatenate((array, other))
+
+        expected = np.concatenate((array, array))
+        result = np.concatenate((array, no_override_sub))
+        assert_equal(result, expected.view(NoOverrideSub))
+        result = np.concatenate((array, override_sub))
+        assert_equal(result, expected.view(OverrideSub))
+
+    def test_no_wrapper(self):
+        # Regular numpy functions have wrappers, but do not presume
+        # all functions do (array creation ones do not): check that
+        # we just call the function in that case.
+        array = np.array(1)
+        func = lambda x: x * 2
+        result = array.__array_function__(func=func, types=(np.ndarray,),
+                                          args=(array,), kwargs={})
+        assert_equal(result, array * 2)
+
+    def test_wrong_arguments(self):
+        # Check our implementation guards against wrong arguments.
+        a = np.array([1, 2])
+        with pytest.raises(TypeError, match="args must be a tuple"):
+            a.__array_function__(np.reshape, (np.ndarray,), a, (2, 1))
+        with pytest.raises(TypeError, match="kwargs must be a dict"):
+            a.__array_function__(np.reshape, (np.ndarray,), (a,), (2, 1))
+
+
+class TestArrayFunctionDispatch:
+
+    def test_pickle(self):
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            roundtripped = pickle.loads(
+                    pickle.dumps(dispatched_one_arg, protocol=proto))
+            assert_(roundtripped is dispatched_one_arg)
+
+    def test_name_and_docstring(self):
+        assert_equal(dispatched_one_arg.__name__, 'dispatched_one_arg')
+        if sys.flags.optimize < 2:
+            assert_equal(dispatched_one_arg.__doc__, 'Docstring.')
+
+    def test_interface(self):
+
+        class MyArray:
+            def __array_function__(self, func, types, args, kwargs):
+                return (self, func, types, args, kwargs)
+
+        original = MyArray()
+        (obj, func, types, args, kwargs) = dispatched_one_arg(original)
+        assert_(obj is original)
+        assert_(func is dispatched_one_arg)
+        assert_equal(set(types), {MyArray})
+        # assert_equal uses the overloaded np.iscomplexobj() internally
+        assert_(args == (original,))
+        assert_equal(kwargs, {})
+
+    def test_not_implemented(self):
+
+        class MyArray:
+            def __array_function__(self, func, types, args, kwargs):
+                return NotImplemented
+
+        array = MyArray()
+        with assert_raises_regex(TypeError, 'no implementation found'):
+            dispatched_one_arg(array)
+
+    def test_where_dispatch(self):
+
+        class DuckArray:
+            def __array_function__(self, ufunc, method, *inputs, **kwargs):
+                return "overridden"
+
+        array = np.array(1)
+        duck_array = DuckArray()
+
+        result = np.std(array, where=duck_array)
+
+        assert_equal(result, "overridden")
+
+
+class TestVerifyMatchingSignatures:
+
+    def test_verify_matching_signatures(self):
+
+        verify_matching_signatures(lambda x: 0, lambda x: 0)
+        verify_matching_signatures(lambda x=None: 0, lambda x=None: 0)
+        verify_matching_signatures(lambda x=1: 0, lambda x=None: 0)
+
+        with assert_raises(RuntimeError):
+            verify_matching_signatures(lambda a: 0, lambda b: 0)
+        with assert_raises(RuntimeError):
+            verify_matching_signatures(lambda x: 0, lambda x=None: 0)
+        with assert_raises(RuntimeError):
+            verify_matching_signatures(lambda x=None: 0, lambda y=None: 0)
+        with assert_raises(RuntimeError):
+            verify_matching_signatures(lambda x=1: 0, lambda y=1: 0)
+
+    def test_array_function_dispatch(self):
+
+        with assert_raises(RuntimeError):
+            @array_function_dispatch(lambda x: (x,))
+            def f(y):
+                pass
+
+        # should not raise
+        @array_function_dispatch(lambda x: (x,), verify=False)
+        def f(y):
+            pass
+
+
+def _new_duck_type_and_implements():
+    """Create a duck array type and implements functions."""
+    HANDLED_FUNCTIONS = {}
+
+    class MyArray:
+        def __array_function__(self, func, types, args, kwargs):
+            if func not in HANDLED_FUNCTIONS:
+                return NotImplemented
+            if not all(issubclass(t, MyArray) for t in types):
+                return NotImplemented
+            return HANDLED_FUNCTIONS[func](*args, **kwargs)
+
+    def implements(numpy_function):
+        """Register an __array_function__ implementations."""
+        def decorator(func):
+            HANDLED_FUNCTIONS[numpy_function] = func
+            return func
+        return decorator
+
+    return (MyArray, implements)
+
+
+class TestArrayFunctionImplementation:
+
+    def test_one_arg(self):
+        MyArray, implements = _new_duck_type_and_implements()
+
+        @implements(dispatched_one_arg)
+        def _(array):
+            return 'myarray'
+
+        assert_equal(dispatched_one_arg(1), 'original')
+        assert_equal(dispatched_one_arg(MyArray()), 'myarray')
+
+    def test_optional_args(self):
+        MyArray, implements = _new_duck_type_and_implements()
+
+        @array_function_dispatch(lambda array, option=None: (array,))
+        def func_with_option(array, option='default'):
+            return option
+
+        @implements(func_with_option)
+        def my_array_func_with_option(array, new_option='myarray'):
+            return new_option
+
+        # we don't need to implement every option on __array_function__
+        # implementations
+        assert_equal(func_with_option(1), 'default')
+        assert_equal(func_with_option(1, option='extra'), 'extra')
+        assert_equal(func_with_option(MyArray()), 'myarray')
+        with assert_raises(TypeError):
+            func_with_option(MyArray(), option='extra')
+
+        # but new options on implementations can't be used
+        result = my_array_func_with_option(MyArray(), new_option='yes')
+        assert_equal(result, 'yes')
+        with assert_raises(TypeError):
+            func_with_option(MyArray(), new_option='no')
+
+    def test_not_implemented(self):
+        MyArray, implements = _new_duck_type_and_implements()
+
+        @array_function_dispatch(lambda array: (array,), module='my')
+        def func(array):
+            return array
+
+        array = np.array(1)
+        assert_(func(array) is array)
+        assert_equal(func.__module__, 'my')
+
+        with assert_raises_regex(
+                TypeError, "no implementation found for 'my.func'"):
+            func(MyArray())
+
+    @pytest.mark.parametrize("name", ["concatenate", "mean", "asarray"])
+    def test_signature_error_message_simple(self, name):
+        func = getattr(np, name)
+        try:
+            # all of these functions need an argument:
+            func()
+        except TypeError as e:
+            exc = e
+
+        assert exc.args[0].startswith(f"{name}()")
+
+    def test_signature_error_message(self):
+        # The lambda function will be named "<lambda>", but the TypeError
+        # should show the name as "func"
+        def _dispatcher():
+            return ()
+
+        @array_function_dispatch(_dispatcher)
+        def func():
+            pass
+
+        try:
+            func._implementation(bad_arg=3)
+        except TypeError as e:
+            expected_exception = e
+
+        try:
+            func(bad_arg=3)
+            raise AssertionError("must fail")
+        except TypeError as exc:
+            if exc.args[0].startswith("_dispatcher"):
+                # We replace the qualname currently, but it used `__name__`
+                # (relevant functions have the same name and qualname anyway)
+                pytest.skip("Python version is not using __qualname__ for "
+                            "TypeError formatting.")
+
+            assert exc.args == expected_exception.args
+
+    @pytest.mark.parametrize("value", [234, "this func is not replaced"])
+    def test_dispatcher_error(self, value):
+        # If the dispatcher raises an error, we must not attempt to mutate it
+        error = TypeError(value)
+
+        def dispatcher():
+            raise error
+
+        @array_function_dispatch(dispatcher)
+        def func():
+            return 3
+
+        try:
+            func()
+            raise AssertionError("must fail")
+        except TypeError as exc:
+            assert exc is error  # unmodified exception
+
+    def test_properties(self):
+        # Check that str and repr are sensible
+        func = dispatched_two_arg
+        assert str(func) == str(func._implementation)
+        repr_no_id = repr(func).split("at ")[0]
+        repr_no_id_impl = repr(func._implementation).split("at ")[0]
+        assert repr_no_id == repr_no_id_impl
+
+    @pytest.mark.parametrize("func", [
+            lambda x, y: 0,  # no like argument
+            lambda like=None: 0,  # not keyword only
+            lambda *, like=None, a=3: 0,  # not last (not that it matters)
+        ])
+    def test_bad_like_sig(self, func):
+        # We sanity check the signature, and these should fail.
+        with pytest.raises(RuntimeError):
+            array_function_dispatch()(func)
+
+    def test_bad_like_passing(self):
+        # Cover internal sanity check for passing like as first positional arg
+        def func(*, like=None):
+            pass
+
+        func_with_like = array_function_dispatch()(func)
+        with pytest.raises(TypeError):
+            func_with_like()
+        with pytest.raises(TypeError):
+            func_with_like(like=234)
+
+    def test_too_many_args(self):
+        # Mainly a unit-test to increase coverage
+        objs = []
+        for i in range(80):
+            class MyArr:
+                def __array_function__(self, *args, **kwargs):
+                    return NotImplemented
+
+            objs.append(MyArr())
+
+        def _dispatch(*args):
+            return args
+
+        @array_function_dispatch(_dispatch)
+        def func(*args):
+            pass
+
+        with pytest.raises(TypeError, match="maximum number"):
+            func(*objs)
+
+
+class TestNDArrayMethods:
+
+    def test_repr(self):
+        # gh-12162: should still be defined even if __array_function__ doesn't
+        # implement np.array_repr()
+
+        class MyArray(np.ndarray):
+            def __array_function__(*args, **kwargs):
+                return NotImplemented
+
+        array = np.array(1).view(MyArray)
+        assert_equal(repr(array), 'MyArray(1)')
+        assert_equal(str(array), '1')
+
+
+class TestNumPyFunctions:
+
+    def test_set_module(self):
+        assert_equal(np.sum.__module__, 'numpy')
+        assert_equal(np.char.equal.__module__, 'numpy.char')
+        assert_equal(np.fft.fft.__module__, 'numpy.fft')
+        assert_equal(np.linalg.solve.__module__, 'numpy.linalg')
+
+    def test_inspect_sum(self):
+        signature = inspect.signature(np.sum)
+        assert_('axis' in signature.parameters)
+
+    def test_override_sum(self):
+        MyArray, implements = _new_duck_type_and_implements()
+
+        @implements(np.sum)
+        def _(array):
+            return 'yes'
+
+        assert_equal(np.sum(MyArray()), 'yes')
+
+    def test_sum_on_mock_array(self):
+
+        # We need a proxy for mocks because __array_function__ is only looked
+        # up in the class dict
+        class ArrayProxy:
+            def __init__(self, value):
+                self.value = value
+
+            def __array_function__(self, *args, **kwargs):
+                return self.value.__array_function__(*args, **kwargs)
+
+            def __array__(self, *args, **kwargs):
+                return self.value.__array__(*args, **kwargs)
+
+        proxy = ArrayProxy(mock.Mock(spec=ArrayProxy))
+        proxy.value.__array_function__.return_value = 1
+        result = np.sum(proxy)
+        assert_equal(result, 1)
+        proxy.value.__array_function__.assert_called_once_with(
+            np.sum, (ArrayProxy,), (proxy,), {})
+        proxy.value.__array__.assert_not_called()
+
+    def test_sum_forwarding_implementation(self):
+
+        class MyArray(np.ndarray):
+
+            def sum(self, axis, out):
+                return 'summed'
+
+            def __array_function__(self, func, types, args, kwargs):
+                return super().__array_function__(func, types, args, kwargs)
+
+        # note: the internal implementation of np.sum() calls the .sum() method
+        array = np.array(1).view(MyArray)
+        assert_equal(np.sum(array), 'summed')
+
+
+class TestArrayLike:
+    def setup_method(self):
+        class MyArray:
+            def __init__(self, function=None):
+                self.function = function
+
+            def __array_function__(self, func, types, args, kwargs):
+                assert func is getattr(np, func.__name__)
+                try:
+                    my_func = getattr(self, func.__name__)
+                except AttributeError:
+                    return NotImplemented
+                return my_func(*args, **kwargs)
+
+        self.MyArray = MyArray
+
+        class MyNoArrayFunctionArray:
+            def __init__(self, function=None):
+                self.function = function
+
+        self.MyNoArrayFunctionArray = MyNoArrayFunctionArray
+
+        class MySubclass(np.ndarray):
+            def __array_function__(self, func, types, args, kwargs):
+                result = super().__array_function__(func, types, args, kwargs)
+                return result.view(self.__class__)
+
+        self.MySubclass = MySubclass
+
+    def add_method(self, name, arr_class, enable_value_error=False):
+        def _definition(*args, **kwargs):
+            # Check that `like=` isn't propagated downstream
+            assert 'like' not in kwargs
+
+            if enable_value_error and 'value_error' in kwargs:
+                raise ValueError
+
+            return arr_class(getattr(arr_class, name))
+        setattr(arr_class, name, _definition)
+
+    def func_args(*args, **kwargs):
+        return args, kwargs
+
+    def test_array_like_not_implemented(self):
+        self.add_method('array', self.MyArray)
+
+        ref = self.MyArray.array()
+
+        with assert_raises_regex(TypeError, 'no implementation found'):
+            array_like = np.asarray(1, like=ref)
+
+    _array_tests = [
+        ('array', *func_args((1,))),
+        ('asarray', *func_args((1,))),
+        ('asanyarray', *func_args((1,))),
+        ('ascontiguousarray', *func_args((2, 3))),
+        ('asfortranarray', *func_args((2, 3))),
+        ('require', *func_args((np.arange(6).reshape(2, 3),),
+                               requirements=['A', 'F'])),
+        ('empty', *func_args((1,))),
+        ('full', *func_args((1,), 2)),
+        ('ones', *func_args((1,))),
+        ('zeros', *func_args((1,))),
+        ('arange', *func_args(3)),
+        ('frombuffer', *func_args(b'\x00' * 8, dtype=int)),
+        ('fromiter', *func_args(range(3), dtype=int)),
+        ('fromstring', *func_args('1,2', dtype=int, sep=',')),
+        ('loadtxt', *func_args(lambda: StringIO('0 1\n2 3'))),
+        ('genfromtxt', *func_args(lambda: StringIO('1,2.1'),
+                                  dtype=[('int', 'i8'), ('float', 'f8')],
+                                  delimiter=',')),
+    ]
+
+    def test_nep35_functions_as_array_functions(self,):
+        all_array_functions = get_overridable_numpy_array_functions()
+        like_array_functions_subset = {
+            getattr(np, func_name) for func_name, *_ in self.__class__._array_tests
+        }
+        assert like_array_functions_subset.issubset(all_array_functions)
+
+        nep35_python_functions = {
+            np.eye, np.fromfunction, np.full, np.genfromtxt,
+            np.identity, np.loadtxt, np.ones, np.require, np.tri,
+        }
+        assert nep35_python_functions.issubset(all_array_functions)
+
+        nep35_C_functions = {
+            np.arange, np.array, np.asanyarray, np.asarray,
+            np.ascontiguousarray, np.asfortranarray, np.empty,
+            np.frombuffer, np.fromfile, np.fromiter, np.fromstring,
+            np.zeros,
+        }
+        assert nep35_C_functions.issubset(all_array_functions)
+
+    @pytest.mark.parametrize('function, args, kwargs', _array_tests)
+    @pytest.mark.parametrize('numpy_ref', [True, False])
+    def test_array_like(self, function, args, kwargs, numpy_ref):
+        self.add_method('array', self.MyArray)
+        self.add_method(function, self.MyArray)
+        np_func = getattr(np, function)
+        my_func = getattr(self.MyArray, function)
+
+        if numpy_ref is True:
+            ref = np.array(1)
+        else:
+            ref = self.MyArray.array()
+
+        like_args = tuple(a() if callable(a) else a for a in args)
+        array_like = np_func(*like_args, **kwargs, like=ref)
+
+        if numpy_ref is True:
+            assert type(array_like) is np.ndarray
+
+            np_args = tuple(a() if callable(a) else a for a in args)
+            np_arr = np_func(*np_args, **kwargs)
+
+            # Special-case np.empty to ensure values match
+            if function == "empty":
+                np_arr.fill(1)
+                array_like.fill(1)
+
+            assert_equal(array_like, np_arr)
+        else:
+            assert type(array_like) is self.MyArray
+            assert array_like.function is my_func
+
+    @pytest.mark.parametrize('function, args, kwargs', _array_tests)
+    @pytest.mark.parametrize('ref', [1, [1], "MyNoArrayFunctionArray"])
+    def test_no_array_function_like(self, function, args, kwargs, ref):
+        self.add_method('array', self.MyNoArrayFunctionArray)
+        self.add_method(function, self.MyNoArrayFunctionArray)
+        np_func = getattr(np, function)
+
+        # Instantiate ref if it's the MyNoArrayFunctionArray class
+        if ref == "MyNoArrayFunctionArray":
+            ref = self.MyNoArrayFunctionArray.array()
+
+        like_args = tuple(a() if callable(a) else a for a in args)
+
+        with assert_raises_regex(TypeError,
+                'The `like` argument must be an array-like that implements'):
+            np_func(*like_args, **kwargs, like=ref)
+
+    @pytest.mark.parametrize('function, args, kwargs', _array_tests)
+    def test_subclass(self, function, args, kwargs):
+        ref = np.array(1).view(self.MySubclass)
+        np_func = getattr(np, function)
+        like_args = tuple(a() if callable(a) else a for a in args)
+        array_like = np_func(*like_args, **kwargs, like=ref)
+        assert type(array_like) is self.MySubclass
+        if np_func is np.empty:
+            return
+        np_args = tuple(a() if callable(a) else a for a in args)
+        np_arr = np_func(*np_args, **kwargs)
+        assert_equal(array_like.view(np.ndarray), np_arr)
+
+    @pytest.mark.parametrize('numpy_ref', [True, False])
+    def test_array_like_fromfile(self, numpy_ref):
+        self.add_method('array', self.MyArray)
+        self.add_method("fromfile", self.MyArray)
+
+        if numpy_ref is True:
+            ref = np.array(1)
+        else:
+            ref = self.MyArray.array()
+
+        data = np.random.random(5)
+
+        with tempfile.TemporaryDirectory() as tmpdir:
+            fname = os.path.join(tmpdir, "testfile")
+            data.tofile(fname)
+
+            array_like = np.fromfile(fname, like=ref)
+            if numpy_ref is True:
+                assert type(array_like) is np.ndarray
+                np_res = np.fromfile(fname, like=ref)
+                assert_equal(np_res, data)
+                assert_equal(array_like, np_res)
+            else:
+                assert type(array_like) is self.MyArray
+                assert array_like.function is self.MyArray.fromfile
+
+    def test_exception_handling(self):
+        self.add_method('array', self.MyArray, enable_value_error=True)
+
+        ref = self.MyArray.array()
+
+        with assert_raises(TypeError):
+            # Raises the error about `value_error` being invalid first
+            np.array(1, value_error=True, like=ref)
+
+    @pytest.mark.parametrize('function, args, kwargs', _array_tests)
+    def test_like_as_none(self, function, args, kwargs):
+        self.add_method('array', self.MyArray)
+        self.add_method(function, self.MyArray)
+        np_func = getattr(np, function)
+
+        like_args = tuple(a() if callable(a) else a for a in args)
+        # required for loadtxt and genfromtxt to init w/o error.
+        like_args_exp = tuple(a() if callable(a) else a for a in args)
+
+        array_like = np_func(*like_args, **kwargs, like=None)
+        expected = np_func(*like_args_exp, **kwargs)
+        # Special-case np.empty to ensure values match
+        if function == "empty":
+            array_like.fill(1)
+            expected.fill(1)
+        assert_equal(array_like, expected)
+
+
+def test_function_like():
+    # We provide a `__get__` implementation, make sure it works
+    assert type(np.mean) is np._core._multiarray_umath._ArrayFunctionDispatcher
+
+    class MyClass:
+        def __array__(self, dtype=None, copy=None):
+            # valid argument to mean:
+            return np.arange(3)
+
+        func1 = staticmethod(np.mean)
+        func2 = np.mean
+        func3 = classmethod(np.mean)
+
+    m = MyClass()
+    assert m.func1([10]) == 10
+    assert m.func2() == 1  # mean of the arange
+    with pytest.raises(TypeError, match="unsupported operand type"):
+        # Tries to operate on the class
+        m.func3()
+
+    # Manual binding also works (the above may shortcut):
+    bound = np.mean.__get__(m, MyClass)
+    assert bound() == 1
+
+    bound = np.mean.__get__(None, MyClass)  # unbound actually
+    assert bound([10]) == 10
+
+    bound = np.mean.__get__(MyClass)  # classmethod
+    with pytest.raises(TypeError, match="unsupported operand type"):
+        bound()
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_print.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_print.py
new file mode 100644
index 0000000..d99b279
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_print.py
@@ -0,0 +1,200 @@
+import sys
+from io import StringIO
+
+import pytest
+
+import numpy as np
+from numpy._core.tests._locales import CommaDecimalPointLocale
+from numpy.testing import IS_MUSL, assert_, assert_equal
+
+_REF = {np.inf: 'inf', -np.inf: '-inf', np.nan: 'nan'}
+
+
+@pytest.mark.parametrize('tp', [np.float32, np.double, np.longdouble])
+def test_float_types(tp):
+    """ Check formatting.
+
+        This is only for the str function, and only for simple types.
+        The precision of np.float32 and np.longdouble aren't the same as the
+        python float precision.
+
+    """
+    for x in [0, 1, -1, 1e20]:
+        assert_equal(str(tp(x)), str(float(x)),
+                     err_msg=f'Failed str formatting for type {tp}')
+
+    if tp(1e16).itemsize > 4:
+        assert_equal(str(tp(1e16)), str(float('1e16')),
+                     err_msg=f'Failed str formatting for type {tp}')
+    else:
+        ref = '1e+16'
+        assert_equal(str(tp(1e16)), ref,
+                     err_msg=f'Failed str formatting for type {tp}')
+
+
+@pytest.mark.parametrize('tp', [np.float32, np.double, np.longdouble])
+def test_nan_inf_float(tp):
+    """ Check formatting of nan & inf.
+
+        This is only for the str function, and only for simple types.
+        The precision of np.float32 and np.longdouble aren't the same as the
+        python float precision.
+
+    """
+    for x in [np.inf, -np.inf, np.nan]:
+        assert_equal(str(tp(x)), _REF[x],
+                     err_msg=f'Failed str formatting for type {tp}')
+
+
+@pytest.mark.parametrize('tp', [np.complex64, np.cdouble, np.clongdouble])
+def test_complex_types(tp):
+    """Check formatting of complex types.
+
+        This is only for the str function, and only for simple types.
+        The precision of np.float32 and np.longdouble aren't the same as the
+        python float precision.
+
+    """
+    for x in [0, 1, -1, 1e20]:
+        assert_equal(str(tp(x)), str(complex(x)),
+                     err_msg=f'Failed str formatting for type {tp}')
+        assert_equal(str(tp(x * 1j)), str(complex(x * 1j)),
+                     err_msg=f'Failed str formatting for type {tp}')
+        assert_equal(str(tp(x + x * 1j)), str(complex(x + x * 1j)),
+                     err_msg=f'Failed str formatting for type {tp}')
+
+    if tp(1e16).itemsize > 8:
+        assert_equal(str(tp(1e16)), str(complex(1e16)),
+                     err_msg=f'Failed str formatting for type {tp}')
+    else:
+        ref = '(1e+16+0j)'
+        assert_equal(str(tp(1e16)), ref,
+                     err_msg=f'Failed str formatting for type {tp}')
+
+
+@pytest.mark.parametrize('dtype', [np.complex64, np.cdouble, np.clongdouble])
+def test_complex_inf_nan(dtype):
+    """Check inf/nan formatting of complex types."""
+    TESTS = {
+        complex(np.inf, 0): "(inf+0j)",
+        complex(0, np.inf): "infj",
+        complex(-np.inf, 0): "(-inf+0j)",
+        complex(0, -np.inf): "-infj",
+        complex(np.inf, 1): "(inf+1j)",
+        complex(1, np.inf): "(1+infj)",
+        complex(-np.inf, 1): "(-inf+1j)",
+        complex(1, -np.inf): "(1-infj)",
+        complex(np.nan, 0): "(nan+0j)",
+        complex(0, np.nan): "nanj",
+        complex(-np.nan, 0): "(nan+0j)",
+        complex(0, -np.nan): "nanj",
+        complex(np.nan, 1): "(nan+1j)",
+        complex(1, np.nan): "(1+nanj)",
+        complex(-np.nan, 1): "(nan+1j)",
+        complex(1, -np.nan): "(1+nanj)",
+    }
+    for c, s in TESTS.items():
+        assert_equal(str(dtype(c)), s)
+
+
+# print tests
+def _test_redirected_print(x, tp, ref=None):
+    file = StringIO()
+    file_tp = StringIO()
+    stdout = sys.stdout
+    try:
+        sys.stdout = file_tp
+        print(tp(x))
+        sys.stdout = file
+        if ref:
+            print(ref)
+        else:
+            print(x)
+    finally:
+        sys.stdout = stdout
+
+    assert_equal(file.getvalue(), file_tp.getvalue(),
+                 err_msg=f'print failed for type{tp}')
+
+
+@pytest.mark.parametrize('tp', [np.float32, np.double, np.longdouble])
+def test_float_type_print(tp):
+    """Check formatting when using print """
+    for x in [0, 1, -1, 1e20]:
+        _test_redirected_print(float(x), tp)
+
+    for x in [np.inf, -np.inf, np.nan]:
+        _test_redirected_print(float(x), tp, _REF[x])
+
+    if tp(1e16).itemsize > 4:
+        _test_redirected_print(1e16, tp)
+    else:
+        ref = '1e+16'
+        _test_redirected_print(1e16, tp, ref)
+
+
+@pytest.mark.parametrize('tp', [np.complex64, np.cdouble, np.clongdouble])
+def test_complex_type_print(tp):
+    """Check formatting when using print """
+    # We do not create complex with inf/nan directly because the feature is
+    # missing in python < 2.6
+    for x in [0, 1, -1, 1e20]:
+        _test_redirected_print(complex(x), tp)
+
+    if tp(1e16).itemsize > 8:
+        _test_redirected_print(complex(1e16), tp)
+    else:
+        ref = '(1e+16+0j)'
+        _test_redirected_print(complex(1e16), tp, ref)
+
+    _test_redirected_print(complex(np.inf, 1), tp, '(inf+1j)')
+    _test_redirected_print(complex(-np.inf, 1), tp, '(-inf+1j)')
+    _test_redirected_print(complex(-np.nan, 1), tp, '(nan+1j)')
+
+
+def test_scalar_format():
+    """Test the str.format method with NumPy scalar types"""
+    tests = [('{0}', True, np.bool),
+            ('{0}', False, np.bool),
+            ('{0:d}', 130, np.uint8),
+            ('{0:d}', 50000, np.uint16),
+            ('{0:d}', 3000000000, np.uint32),
+            ('{0:d}', 15000000000000000000, np.uint64),
+            ('{0:d}', -120, np.int8),
+            ('{0:d}', -30000, np.int16),
+            ('{0:d}', -2000000000, np.int32),
+            ('{0:d}', -7000000000000000000, np.int64),
+            ('{0:g}', 1.5, np.float16),
+            ('{0:g}', 1.5, np.float32),
+            ('{0:g}', 1.5, np.float64),
+            ('{0:g}', 1.5, np.longdouble),
+            ('{0:g}', 1.5 + 0.5j, np.complex64),
+            ('{0:g}', 1.5 + 0.5j, np.complex128),
+            ('{0:g}', 1.5 + 0.5j, np.clongdouble)]
+
+    for (fmat, val, valtype) in tests:
+        try:
+            assert_equal(fmat.format(val), fmat.format(valtype(val)),
+                    f"failed with val {val}, type {valtype}")
+        except ValueError as e:
+            assert_(False,
+               "format raised exception (fmt='%s', val=%s, type=%s, exc='%s')" %
+                            (fmat, repr(val), repr(valtype), str(e)))
+
+
+#
+# Locale tests: scalar types formatting should be independent of the locale
+#
+
+class TestCommaDecimalPointLocale(CommaDecimalPointLocale):
+
+    def test_locale_single(self):
+        assert_equal(str(np.float32(1.2)), str(1.2))
+
+    def test_locale_double(self):
+        assert_equal(str(np.double(1.2)), str(1.2))
+
+    @pytest.mark.skipif(IS_MUSL,
+                        reason="test flaky on musllinux")
+    def test_locale_longdouble(self):
+        assert_equal(str(np.longdouble('1.2')), str(1.2))
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_protocols.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_protocols.py
new file mode 100644
index 0000000..96bb600
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_protocols.py
@@ -0,0 +1,46 @@
+import warnings
+
+import pytest
+
+import numpy as np
+
+
+@pytest.mark.filterwarnings("error")
+def test_getattr_warning():
+    # issue gh-14735: make sure we clear only getattr errors, and let warnings
+    # through
+    class Wrapper:
+        def __init__(self, array):
+            self.array = array
+
+        def __len__(self):
+            return len(self.array)
+
+        def __getitem__(self, item):
+            return type(self)(self.array[item])
+
+        def __getattr__(self, name):
+            if name.startswith("__array_"):
+                warnings.warn("object got converted", UserWarning, stacklevel=1)
+
+            return getattr(self.array, name)
+
+        def __repr__(self):
+            return f"<Wrapper({self.array})>"
+
+    array = Wrapper(np.arange(10))
+    with pytest.raises(UserWarning, match="object got converted"):
+        np.asarray(array)
+
+
+def test_array_called():
+    class Wrapper:
+        val = '0' * 100
+
+        def __array__(self, dtype=None, copy=None):
+            return np.array([self.val], dtype=dtype, copy=copy)
+
+    wrapped = Wrapper()
+    arr = np.array(wrapped, dtype=str)
+    assert arr.dtype == 'U100'
+    assert arr[0] == Wrapper.val
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_records.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_records.py
new file mode 100644
index 0000000..b4b93ae
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_records.py
@@ -0,0 +1,544 @@
+import collections.abc
+import pickle
+import textwrap
+from io import BytesIO
+from os import path
+from pathlib import Path
+
+import pytest
+
+import numpy as np
+from numpy.testing import (
+    assert_,
+    assert_array_almost_equal,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    temppath,
+)
+
+
+class TestFromrecords:
+    def test_fromrecords(self):
+        r = np.rec.fromrecords([[456, 'dbe', 1.2], [2, 'de', 1.3]],
+                            names='col1,col2,col3')
+        assert_equal(r[0].item(), (456, 'dbe', 1.2))
+        assert_equal(r['col1'].dtype.kind, 'i')
+        assert_equal(r['col2'].dtype.kind, 'U')
+        assert_equal(r['col2'].dtype.itemsize, 12)
+        assert_equal(r['col3'].dtype.kind, 'f')
+
+    def test_fromrecords_0len(self):
+        """ Verify fromrecords works with a 0-length input """
+        dtype = [('a', float), ('b', float)]
+        r = np.rec.fromrecords([], dtype=dtype)
+        assert_equal(r.shape, (0,))
+
+    def test_fromrecords_2d(self):
+        data = [
+            [(1, 2), (3, 4), (5, 6)],
+            [(6, 5), (4, 3), (2, 1)]
+        ]
+        expected_a = [[1, 3, 5], [6, 4, 2]]
+        expected_b = [[2, 4, 6], [5, 3, 1]]
+
+        # try with dtype
+        r1 = np.rec.fromrecords(data, dtype=[('a', int), ('b', int)])
+        assert_equal(r1['a'], expected_a)
+        assert_equal(r1['b'], expected_b)
+
+        # try with names
+        r2 = np.rec.fromrecords(data, names=['a', 'b'])
+        assert_equal(r2['a'], expected_a)
+        assert_equal(r2['b'], expected_b)
+
+        assert_equal(r1, r2)
+
+    def test_method_array(self):
+        r = np.rec.array(
+            b'abcdefg' * 100, formats='i2,S3,i4', shape=3, byteorder='big'
+        )
+        assert_equal(r[1].item(), (25444, b'efg', 1633837924))
+
+    def test_method_array2(self):
+        r = np.rec.array(
+            [
+                (1, 11, 'a'), (2, 22, 'b'), (3, 33, 'c'), (4, 44, 'd'),
+                (5, 55, 'ex'), (6, 66, 'f'), (7, 77, 'g')
+            ],
+            formats='u1,f4,S1'
+        )
+        assert_equal(r[1].item(), (2, 22.0, b'b'))
+
+    def test_recarray_slices(self):
+        r = np.rec.array(
+            [
+                (1, 11, 'a'), (2, 22, 'b'), (3, 33, 'c'), (4, 44, 'd'),
+                (5, 55, 'ex'), (6, 66, 'f'), (7, 77, 'g')
+            ],
+            formats='u1,f4,S1'
+        )
+        assert_equal(r[1::2][1].item(), (4, 44.0, b'd'))
+
+    def test_recarray_fromarrays(self):
+        x1 = np.array([1, 2, 3, 4])
+        x2 = np.array(['a', 'dd', 'xyz', '12'])
+        x3 = np.array([1.1, 2, 3, 4])
+        r = np.rec.fromarrays([x1, x2, x3], names='a,b,c')
+        assert_equal(r[1].item(), (2, 'dd', 2.0))
+        x1[1] = 34
+        assert_equal(r.a, np.array([1, 2, 3, 4]))
+
+    def test_recarray_fromfile(self):
+        data_dir = path.join(path.dirname(__file__), 'data')
+        filename = path.join(data_dir, 'recarray_from_file.fits')
+        fd = open(filename, 'rb')
+        fd.seek(2880 * 2)
+        r1 = np.rec.fromfile(fd, formats='f8,i4,S5', shape=3, byteorder='big')
+        fd.seek(2880 * 2)
+        r2 = np.rec.array(fd, formats='f8,i4,S5', shape=3, byteorder='big')
+        fd.seek(2880 * 2)
+        bytes_array = BytesIO()
+        bytes_array.write(fd.read())
+        bytes_array.seek(0)
+        r3 = np.rec.fromfile(
+            bytes_array, formats='f8,i4,S5', shape=3, byteorder='big'
+        )
+        fd.close()
+        assert_equal(r1, r2)
+        assert_equal(r2, r3)
+
+    def test_recarray_from_obj(self):
+        count = 10
+        a = np.zeros(count, dtype='O')
+        b = np.zeros(count, dtype='f8')
+        c = np.zeros(count, dtype='f8')
+        for i in range(len(a)):
+            a[i] = list(range(1, 10))
+
+        mine = np.rec.fromarrays([a, b, c], names='date,data1,data2')
+        for i in range(len(a)):
+            assert_(mine.date[i] == list(range(1, 10)))
+            assert_(mine.data1[i] == 0.0)
+            assert_(mine.data2[i] == 0.0)
+
+    def test_recarray_repr(self):
+        a = np.array([(1, 0.1), (2, 0.2)],
+                     dtype=[('foo', '<i4'), ('bar', '<f8')])
+        a = np.rec.array(a)
+        assert_equal(
+            repr(a),
+            textwrap.dedent("""\
+            rec.array([(1, 0.1), (2, 0.2)],
+                      dtype=[('foo', '<i4'), ('bar', '<f8')])""")
+        )
+
+        # make sure non-structured dtypes also show up as rec.array
+        a = np.array(np.ones(4, dtype='f8'))
+        assert_(repr(np.rec.array(a)).startswith('rec.array'))
+
+        # check that the 'np.record' part of the dtype isn't shown
+        a = np.rec.array(np.ones(3, dtype='i4,i4'))
+        assert_equal(repr(a).find('numpy.record'), -1)
+        a = np.rec.array(np.ones(3, dtype='i4'))
+        assert_(repr(a).find('dtype=int32') != -1)
+
+    def test_0d_recarray_repr(self):
+        arr_0d = np.rec.array((1, 2.0, '2003'), dtype='<i4,<f8,<M8[Y]')
+        assert_equal(repr(arr_0d), textwrap.dedent("""\
+            rec.array((1, 2., '2003'),
+                      dtype=[('f0', '<i4'), ('f1', '<f8'), ('f2', '<M8[Y]')])"""))
+
+        record = arr_0d[()]
+        assert_equal(repr(record),
+            "np.record((1, 2.0, '2003'), "
+            "dtype=[('f0', '<i4'), ('f1', '<f8'), ('f2', '<M8[Y]')])")
+        # 1.13 converted to python scalars before the repr
+        try:
+            np.set_printoptions(legacy='1.13')
+            assert_equal(repr(record), '(1, 2.0, datetime.date(2003, 1, 1))')
+        finally:
+            np.set_printoptions(legacy=False)
+
+    def test_recarray_from_repr(self):
+        a = np.array([(1, 'ABC'), (2, "DEF")],
+                     dtype=[('foo', int), ('bar', 'S4')])
+        recordarr = np.rec.array(a)
+        recarr = a.view(np.recarray)
+        recordview = a.view(np.dtype((np.record, a.dtype)))
+
+        recordarr_r = eval("np." + repr(recordarr), {'np': np})
+        recarr_r = eval("np." + repr(recarr), {'np': np})
+        # Prints the type `numpy.record` as part of the dtype:
+        recordview_r = eval("np." + repr(recordview), {'np': np, 'numpy': np})
+
+        assert_equal(type(recordarr_r), np.recarray)
+        assert_equal(recordarr_r.dtype.type, np.record)
+        assert_equal(recordarr, recordarr_r)
+
+        assert_equal(type(recarr_r), np.recarray)
+        assert_equal(recarr_r.dtype.type, np.record)
+        assert_equal(recarr, recarr_r)
+
+        assert_equal(type(recordview_r), np.ndarray)
+        assert_equal(recordview.dtype.type, np.record)
+        assert_equal(recordview, recordview_r)
+
+    def test_recarray_views(self):
+        a = np.array([(1, 'ABC'), (2, "DEF")],
+                     dtype=[('foo', int), ('bar', 'S4')])
+        b = np.array([1, 2, 3, 4, 5], dtype=np.int64)
+
+        # check that np.rec.array gives right dtypes
+        assert_equal(np.rec.array(a).dtype.type, np.record)
+        assert_equal(type(np.rec.array(a)), np.recarray)
+        assert_equal(np.rec.array(b).dtype.type, np.int64)
+        assert_equal(type(np.rec.array(b)), np.recarray)
+
+        # check that viewing as recarray does the same
+        assert_equal(a.view(np.recarray).dtype.type, np.record)
+        assert_equal(type(a.view(np.recarray)), np.recarray)
+        assert_equal(b.view(np.recarray).dtype.type, np.int64)
+        assert_equal(type(b.view(np.recarray)), np.recarray)
+
+        # check that view to non-structured dtype preserves type=np.recarray
+        r = np.rec.array(np.ones(4, dtype="f4,i4"))
+        rv = r.view('f8').view('f4,i4')
+        assert_equal(type(rv), np.recarray)
+        assert_equal(rv.dtype.type, np.record)
+
+        # check that getitem also preserves np.recarray and np.record
+        r = np.rec.array(np.ones(4, dtype=[('a', 'i4'), ('b', 'i4'),
+                                           ('c', 'i4,i4')]))
+        assert_equal(r['c'].dtype.type, np.record)
+        assert_equal(type(r['c']), np.recarray)
+
+        # and that it preserves subclasses (gh-6949)
+        class C(np.recarray):
+            pass
+
+        c = r.view(C)
+        assert_equal(type(c['c']), C)
+
+        # check that accessing nested structures keep record type, but
+        # not for subarrays, non-void structures, non-structured voids
+        test_dtype = [('a', 'f4,f4'), ('b', 'V8'), ('c', ('f4', 2)),
+                      ('d', ('i8', 'i4,i4'))]
+        r = np.rec.array([((1, 1), b'11111111', [1, 1], 1),
+                          ((1, 1), b'11111111', [1, 1], 1)], dtype=test_dtype)
+        assert_equal(r.a.dtype.type, np.record)
+        assert_equal(r.b.dtype.type, np.void)
+        assert_equal(r.c.dtype.type, np.float32)
+        assert_equal(r.d.dtype.type, np.int64)
+        # check the same, but for views
+        r = np.rec.array(np.ones(4, dtype='i4,i4'))
+        assert_equal(r.view('f4,f4').dtype.type, np.record)
+        assert_equal(r.view(('i4', 2)).dtype.type, np.int32)
+        assert_equal(r.view('V8').dtype.type, np.void)
+        assert_equal(r.view(('i8', 'i4,i4')).dtype.type, np.int64)
+
+        # check that we can undo the view
+        arrs = [np.ones(4, dtype='f4,i4'), np.ones(4, dtype='f8')]
+        for arr in arrs:
+            rec = np.rec.array(arr)
+            # recommended way to view as an ndarray:
+            arr2 = rec.view(rec.dtype.fields or rec.dtype, np.ndarray)
+            assert_equal(arr2.dtype.type, arr.dtype.type)
+            assert_equal(type(arr2), type(arr))
+
+    def test_recarray_from_names(self):
+        ra = np.rec.array([
+            (1, 'abc', 3.7000002861022949, 0),
+            (2, 'xy', 6.6999998092651367, 1),
+            (0, ' ', 0.40000000596046448, 0)],
+                       names='c1, c2, c3, c4')
+        pa = np.rec.fromrecords([
+            (1, 'abc', 3.7000002861022949, 0),
+            (2, 'xy', 6.6999998092651367, 1),
+            (0, ' ', 0.40000000596046448, 0)],
+                       names='c1, c2, c3, c4')
+        assert_(ra.dtype == pa.dtype)
+        assert_(ra.shape == pa.shape)
+        for k in range(len(ra)):
+            assert_(ra[k].item() == pa[k].item())
+
+    def test_recarray_conflict_fields(self):
+        ra = np.rec.array([(1, 'abc', 2.3), (2, 'xyz', 4.2),
+                        (3, 'wrs', 1.3)],
+                       names='field, shape, mean')
+        ra.mean = [1.1, 2.2, 3.3]
+        assert_array_almost_equal(ra['mean'], [1.1, 2.2, 3.3])
+        assert_(type(ra.mean) is type(ra.var))
+        ra.shape = (1, 3)
+        assert_(ra.shape == (1, 3))
+        ra.shape = ['A', 'B', 'C']
+        assert_array_equal(ra['shape'], [['A', 'B', 'C']])
+        ra.field = 5
+        assert_array_equal(ra['field'], [[5, 5, 5]])
+        assert_(isinstance(ra.field, collections.abc.Callable))
+
+    def test_fromrecords_with_explicit_dtype(self):
+        a = np.rec.fromrecords([(1, 'a'), (2, 'bbb')],
+                                dtype=[('a', int), ('b', object)])
+        assert_equal(a.a, [1, 2])
+        assert_equal(a[0].a, 1)
+        assert_equal(a.b, ['a', 'bbb'])
+        assert_equal(a[-1].b, 'bbb')
+        #
+        ndtype = np.dtype([('a', int), ('b', object)])
+        a = np.rec.fromrecords([(1, 'a'), (2, 'bbb')], dtype=ndtype)
+        assert_equal(a.a, [1, 2])
+        assert_equal(a[0].a, 1)
+        assert_equal(a.b, ['a', 'bbb'])
+        assert_equal(a[-1].b, 'bbb')
+
+    def test_recarray_stringtypes(self):
+        # Issue #3993
+        a = np.array([('abc ', 1), ('abc', 2)],
+                     dtype=[('foo', 'S4'), ('bar', int)])
+        a = a.view(np.recarray)
+        assert_equal(a.foo[0] == a.foo[1], False)
+
+    def test_recarray_returntypes(self):
+        qux_fields = {'C': (np.dtype('S5'), 0), 'D': (np.dtype('S5'), 6)}
+        a = np.rec.array([('abc ', (1, 1), 1, ('abcde', 'fgehi')),
+                          ('abc', (2, 3), 1, ('abcde', 'jklmn'))],
+                         dtype=[('foo', 'S4'),
+                                ('bar', [('A', int), ('B', int)]),
+                                ('baz', int), ('qux', qux_fields)])
+        assert_equal(type(a.foo), np.ndarray)
+        assert_equal(type(a['foo']), np.ndarray)
+        assert_equal(type(a.bar), np.recarray)
+        assert_equal(type(a['bar']), np.recarray)
+        assert_equal(a.bar.dtype.type, np.record)
+        assert_equal(type(a['qux']), np.recarray)
+        assert_equal(a.qux.dtype.type, np.record)
+        assert_equal(dict(a.qux.dtype.fields), qux_fields)
+        assert_equal(type(a.baz), np.ndarray)
+        assert_equal(type(a['baz']), np.ndarray)
+        assert_equal(type(a[0].bar), np.record)
+        assert_equal(type(a[0]['bar']), np.record)
+        assert_equal(a[0].bar.A, 1)
+        assert_equal(a[0].bar['A'], 1)
+        assert_equal(a[0]['bar'].A, 1)
+        assert_equal(a[0]['bar']['A'], 1)
+        assert_equal(a[0].qux.D, b'fgehi')
+        assert_equal(a[0].qux['D'], b'fgehi')
+        assert_equal(a[0]['qux'].D, b'fgehi')
+        assert_equal(a[0]['qux']['D'], b'fgehi')
+
+    def test_zero_width_strings(self):
+        # Test for #6430, based on the test case from #1901
+
+        cols = [['test'] * 3, [''] * 3]
+        rec = np.rec.fromarrays(cols)
+        assert_equal(rec['f0'], ['test', 'test', 'test'])
+        assert_equal(rec['f1'], ['', '', ''])
+
+        dt = np.dtype([('f0', '|S4'), ('f1', '|S')])
+        rec = np.rec.fromarrays(cols, dtype=dt)
+        assert_equal(rec.itemsize, 4)
+        assert_equal(rec['f0'], [b'test', b'test', b'test'])
+        assert_equal(rec['f1'], [b'', b'', b''])
+
+
+class TestPathUsage:
+    # Test that pathlib.Path can be used
+    def test_tofile_fromfile(self):
+        with temppath(suffix='.bin') as path:
+            path = Path(path)
+            np.random.seed(123)
+            a = np.random.rand(10).astype('f8,i4,S5')
+            a[5] = (0.5, 10, 'abcde')
+            with path.open("wb") as fd:
+                a.tofile(fd)
+            x = np._core.records.fromfile(
+                path, formats='f8,i4,S5', shape=10
+            )
+            assert_array_equal(x, a)
+
+
+class TestRecord:
+    def setup_method(self):
+        self.data = np.rec.fromrecords([(1, 2, 3), (4, 5, 6)],
+                            dtype=[("col1", "<i4"),
+                                   ("col2", "<i4"),
+                                   ("col3", "<i4")])
+
+    def test_assignment1(self):
+        a = self.data
+        assert_equal(a.col1[0], 1)
+        a[0].col1 = 0
+        assert_equal(a.col1[0], 0)
+
+    def test_assignment2(self):
+        a = self.data
+        assert_equal(a.col1[0], 1)
+        a.col1[0] = 0
+        assert_equal(a.col1[0], 0)
+
+    def test_invalid_assignment(self):
+        a = self.data
+
+        def assign_invalid_column(x):
+            x[0].col5 = 1
+
+        assert_raises(AttributeError, assign_invalid_column, a)
+
+    def test_nonwriteable_setfield(self):
+        # gh-8171
+        r = np.rec.array([(0,), (1,)], dtype=[('f', 'i4')])
+        r.flags.writeable = False
+        with assert_raises(ValueError):
+            r.f = [2, 3]
+        with assert_raises(ValueError):
+            r.setfield([2, 3], *r.dtype.fields['f'])
+
+    def test_out_of_order_fields(self):
+        # names in the same order, padding added to descr
+        x = self.data[['col1', 'col2']]
+        assert_equal(x.dtype.names, ('col1', 'col2'))
+        assert_equal(x.dtype.descr,
+                     [('col1', '<i4'), ('col2', '<i4'), ('', '|V4')])
+
+        # names change order to match indexing, as of 1.14 - descr can't
+        # represent that
+        y = self.data[['col2', 'col1']]
+        assert_equal(y.dtype.names, ('col2', 'col1'))
+        assert_raises(ValueError, lambda: y.dtype.descr)
+
+    def test_pickle_1(self):
+        # Issue #1529
+        a = np.array([(1, [])], dtype=[('a', np.int32), ('b', np.int32, 0)])
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            assert_equal(a, pickle.loads(pickle.dumps(a, protocol=proto)))
+            assert_equal(a[0], pickle.loads(pickle.dumps(a[0],
+                                                         protocol=proto)))
+
+    def test_pickle_2(self):
+        a = self.data
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            assert_equal(a, pickle.loads(pickle.dumps(a, protocol=proto)))
+            assert_equal(a[0], pickle.loads(pickle.dumps(a[0],
+                                                         protocol=proto)))
+
+    def test_pickle_3(self):
+        # Issue #7140
+        a = self.data
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            pa = pickle.loads(pickle.dumps(a[0], protocol=proto))
+            assert_(pa.flags.c_contiguous)
+            assert_(pa.flags.f_contiguous)
+            assert_(pa.flags.writeable)
+            assert_(pa.flags.aligned)
+
+    def test_pickle_void(self):
+        # issue gh-13593
+        dt = np.dtype([('obj', 'O'), ('int', 'i')])
+        a = np.empty(1, dtype=dt)
+        data = (bytearray(b'eman'),)
+        a['obj'] = data
+        a['int'] = 42
+        ctor, args = a[0].__reduce__()
+        # check the constructor is what we expect before interpreting the arguments
+        assert ctor is np._core.multiarray.scalar
+        dtype, obj = args
+        # make sure we did not pickle the address
+        assert not isinstance(obj, bytes)
+
+        assert_raises(RuntimeError, ctor, dtype, 13)
+
+        # Test roundtrip:
+        dump = pickle.dumps(a[0])
+        unpickled = pickle.loads(dump)
+        assert a[0] == unpickled
+
+        # Also check the similar (impossible) "object scalar" path:
+        with assert_raises(TypeError):
+            ctor(np.dtype("O"), data)
+
+    def test_objview_record(self):
+        # https://github.com/numpy/numpy/issues/2599
+        dt = np.dtype([('foo', 'i8'), ('bar', 'O')])
+        r = np.zeros((1, 3), dtype=dt).view(np.recarray)
+        r.foo = np.array([1, 2, 3])  # TypeError?
+
+        # https://github.com/numpy/numpy/issues/3256
+        ra = np.recarray(
+            (2,), dtype=[('x', object), ('y', float), ('z', int)]
+        )
+        ra[['x', 'y']]  # TypeError?
+
+    def test_record_scalar_setitem(self):
+        # https://github.com/numpy/numpy/issues/3561
+        rec = np.recarray(1, dtype=[('x', float, 5)])
+        rec[0].x = 1
+        assert_equal(rec[0].x, np.ones(5))
+
+    def test_missing_field(self):
+        # https://github.com/numpy/numpy/issues/4806
+        arr = np.zeros((3,), dtype=[('x', int), ('y', int)])
+        assert_raises(KeyError, lambda: arr[['nofield']])
+
+    def test_fromarrays_nested_structured_arrays(self):
+        arrays = [
+            np.arange(10),
+            np.ones(10, dtype=[('a', '<u2'), ('b', '<f4')]),
+        ]
+        arr = np.rec.fromarrays(arrays)  # ValueError?
+
+    @pytest.mark.parametrize('nfields', [0, 1, 2])
+    def test_assign_dtype_attribute(self, nfields):
+        dt = np.dtype([('a', np.uint8), ('b', np.uint8), ('c', np.uint8)][:nfields])
+        data = np.zeros(3, dt).view(np.recarray)
+
+        # the original and resulting dtypes differ on whether they are records
+        assert data.dtype.type == np.record
+        assert dt.type != np.record
+
+        # ensure that the dtype remains a record even when assigned
+        data.dtype = dt
+        assert data.dtype.type == np.record
+
+    @pytest.mark.parametrize('nfields', [0, 1, 2])
+    def test_nested_fields_are_records(self, nfields):
+        """ Test that nested structured types are treated as records too """
+        dt = np.dtype([('a', np.uint8), ('b', np.uint8), ('c', np.uint8)][:nfields])
+        dt_outer = np.dtype([('inner', dt)])
+
+        data = np.zeros(3, dt_outer).view(np.recarray)
+        assert isinstance(data, np.recarray)
+        assert isinstance(data['inner'], np.recarray)
+
+        data0 = data[0]
+        assert isinstance(data0, np.record)
+        assert isinstance(data0['inner'], np.record)
+
+    def test_nested_dtype_padding(self):
+        """ test that trailing padding is preserved """
+        # construct a dtype with padding at the end
+        dt = np.dtype([('a', np.uint8), ('b', np.uint8), ('c', np.uint8)])
+        dt_padded_end = dt[['a', 'b']]
+        assert dt_padded_end.itemsize == dt.itemsize
+
+        dt_outer = np.dtype([('inner', dt_padded_end)])
+
+        data = np.zeros(3, dt_outer).view(np.recarray)
+        assert_equal(data['inner'].dtype, dt_padded_end)
+
+        data0 = data[0]
+        assert_equal(data0['inner'].dtype, dt_padded_end)
+
+
+def test_find_duplicate():
+    l1 = [1, 2, 3, 4, 5, 6]
+    assert_(np.rec.find_duplicate(l1) == [])
+
+    l2 = [1, 2, 1, 4, 5, 6]
+    assert_(np.rec.find_duplicate(l2) == [1])
+
+    l3 = [1, 2, 1, 4, 1, 6, 2, 3]
+    assert_(np.rec.find_duplicate(l3) == [1, 2])
+
+    l3 = [2, 2, 1, 4, 1, 6, 2, 3]
+    assert_(np.rec.find_duplicate(l3) == [2, 1])
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_regression.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_regression.py
new file mode 100644
index 0000000..fbfa931
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_regression.py
@@ -0,0 +1,2670 @@
+import copy
+import gc
+import pickle
+import sys
+import tempfile
+from io import BytesIO
+from itertools import chain
+from os import path
+
+import pytest
+
+import numpy as np
+from numpy._utils import asbytes, asunicode
+from numpy.exceptions import AxisError, ComplexWarning
+from numpy.testing import (
+    HAS_REFCOUNT,
+    IS_64BIT,
+    IS_PYPY,
+    IS_PYSTON,
+    IS_WASM,
+    _assert_valid_refcount,
+    assert_,
+    assert_almost_equal,
+    assert_array_almost_equal,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+    assert_warns,
+    suppress_warnings,
+)
+from numpy.testing._private.utils import _no_tracing, requires_memory
+
+
+class TestRegression:
+    def test_invalid_round(self):
+        # Ticket #3
+        v = 4.7599999999999998
+        assert_array_equal(np.array([v]), np.array(v))
+
+    def test_mem_empty(self):
+        # Ticket #7
+        np.empty((1,), dtype=[('x', np.int64)])
+
+    def test_pickle_transposed(self):
+        # Ticket #16
+        a = np.transpose(np.array([[2, 9], [7, 0], [3, 8]]))
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            with BytesIO() as f:
+                pickle.dump(a, f, protocol=proto)
+                f.seek(0)
+                b = pickle.load(f)
+            assert_array_equal(a, b)
+
+    def test_dtype_names(self):
+        # Ticket #35
+        # Should succeed
+        np.dtype([(('name', 'label'), np.int32, 3)])
+
+    def test_reduce(self):
+        # Ticket #40
+        assert_almost_equal(np.add.reduce([1., .5], dtype=None), 1.5)
+
+    def test_zeros_order(self):
+        # Ticket #43
+        np.zeros([3], int, 'C')
+        np.zeros([3], order='C')
+        np.zeros([3], int, order='C')
+
+    def test_asarray_with_order(self):
+        # Check that nothing is done when order='F' and array C/F-contiguous
+        a = np.ones(2)
+        assert_(a is np.asarray(a, order='F'))
+
+    def test_ravel_with_order(self):
+        # Check that ravel works when order='F' and array C/F-contiguous
+        a = np.ones(2)
+        assert_(not a.ravel('F').flags.owndata)
+
+    def test_sort_bigendian(self):
+        # Ticket #47
+        a = np.linspace(0, 10, 11)
+        c = a.astype(np.dtype('<f8'))
+        c.sort()
+        assert_array_almost_equal(c, a)
+
+    def test_negative_nd_indexing(self):
+        # Ticket #49
+        c = np.arange(125).reshape((5, 5, 5))
+        origidx = np.array([-1, 0, 1])
+        idx = np.array(origidx)
+        c[idx]
+        assert_array_equal(idx, origidx)
+
+    def test_char_dump(self):
+        # Ticket #50
+        ca = np.char.array(np.arange(1000, 1010), itemsize=4)
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            with BytesIO() as f:
+                pickle.dump(ca, f, protocol=proto)
+                f.seek(0)
+                ca = np.load(f, allow_pickle=True)
+
+    def test_noncontiguous_fill(self):
+        # Ticket #58.
+        a = np.zeros((5, 3))
+        b = a[:, :2,]
+
+        def rs():
+            b.shape = (10,)
+
+        assert_raises(AttributeError, rs)
+
+    def test_bool(self):
+        # Ticket #60
+        np.bool(1)  # Should succeed
+
+    def test_indexing1(self):
+        # Ticket #64
+        descr = [('x', [('y', [('z', 'c16', (2,)),]),]),]
+        buffer = ((([6j, 4j],),),)
+        h = np.array(buffer, dtype=descr)
+        h['x']['y']['z']
+
+    def test_indexing2(self):
+        # Ticket #65
+        descr = [('x', 'i4', (2,))]
+        buffer = ([3, 2],)
+        h = np.array(buffer, dtype=descr)
+        h['x']
+
+    def test_round(self):
+        # Ticket #67
+        x = np.array([1 + 2j])
+        assert_almost_equal(x**(-1), [1 / (1 + 2j)])
+
+    def test_scalar_compare(self):
+        # Trac Ticket #72
+        # https://github.com/numpy/numpy/issues/565
+        a = np.array(['test', 'auto'])
+        assert_array_equal(a == 'auto', np.array([False, True]))
+        assert_(a[1] == 'auto')
+        assert_(a[0] != 'auto')
+        b = np.linspace(0, 10, 11)
+        assert_array_equal(b != 'auto', np.ones(11, dtype=bool))
+        assert_(b[0] != 'auto')
+
+    def test_unicode_swapping(self):
+        # Ticket #79
+        ulen = 1
+        ucs_value = '\U0010FFFF'
+        ua = np.array([[[ucs_value * ulen] * 2] * 3] * 4, dtype=f'U{ulen}')
+        ua.view(ua.dtype.newbyteorder())  # Should succeed.
+
+    def test_object_array_fill(self):
+        # Ticket #86
+        x = np.zeros(1, 'O')
+        x.fill([])
+
+    def test_mem_dtype_align(self):
+        # Ticket #93
+        assert_raises(TypeError, np.dtype,
+                              {'names': ['a'], 'formats': ['foo']}, align=1)
+
+    def test_endian_bool_indexing(self):
+        # Ticket #105
+        a = np.arange(10., dtype='>f8')
+        b = np.arange(10., dtype='<f8')
+        xa = np.where((a > 2) & (a < 6))
+        xb = np.where((b > 2) & (b < 6))
+        ya = ((a > 2) & (a < 6))
+        yb = ((b > 2) & (b < 6))
+        assert_array_almost_equal(xa, ya.nonzero())
+        assert_array_almost_equal(xb, yb.nonzero())
+        assert_(np.all(a[ya] > 0.5))
+        assert_(np.all(b[yb] > 0.5))
+
+    def test_endian_where(self):
+        # GitHub issue #369
+        net = np.zeros(3, dtype='>f4')
+        net[1] = 0.00458849
+        net[2] = 0.605202
+        max_net = net.max()
+        test = np.where(net <= 0., max_net, net)
+        correct = np.array([0.60520202, 0.00458849, 0.60520202])
+        assert_array_almost_equal(test, correct)
+
+    def test_endian_recarray(self):
+        # Ticket #2185
+        dt = np.dtype([
+               ('head', '>u4'),
+               ('data', '>u4', 2),
+            ])
+        buf = np.recarray(1, dtype=dt)
+        buf[0]['head'] = 1
+        buf[0]['data'][:] = [1, 1]
+
+        h = buf[0]['head']
+        d = buf[0]['data'][0]
+        buf[0]['head'] = h
+        buf[0]['data'][0] = d
+        assert_(buf[0]['head'] == 1)
+
+    def test_mem_dot(self):
+        # Ticket #106
+        x = np.random.randn(0, 1)
+        y = np.random.randn(10, 1)
+        # Dummy array to detect bad memory access:
+        _z = np.ones(10)
+        _dummy = np.empty((0, 10))
+        z = np.lib.stride_tricks.as_strided(_z, _dummy.shape, _dummy.strides)
+        np.dot(x, np.transpose(y), out=z)
+        assert_equal(_z, np.ones(10))
+        # Do the same for the built-in dot:
+        np._core.multiarray.dot(x, np.transpose(y), out=z)
+        assert_equal(_z, np.ones(10))
+
+    def test_arange_endian(self):
+        # Ticket #111
+        ref = np.arange(10)
+        x = np.arange(10, dtype='<f8')
+        assert_array_equal(ref, x)
+        x = np.arange(10, dtype='>f8')
+        assert_array_equal(ref, x)
+
+    def test_arange_inf_step(self):
+        ref = np.arange(0, 1, 10)
+        x = np.arange(0, 1, np.inf)
+        assert_array_equal(ref, x)
+
+        ref = np.arange(0, 1, -10)
+        x = np.arange(0, 1, -np.inf)
+        assert_array_equal(ref, x)
+
+        ref = np.arange(0, -1, -10)
+        x = np.arange(0, -1, -np.inf)
+        assert_array_equal(ref, x)
+
+        ref = np.arange(0, -1, 10)
+        x = np.arange(0, -1, np.inf)
+        assert_array_equal(ref, x)
+
+    def test_arange_underflow_stop_and_step(self):
+        finfo = np.finfo(np.float64)
+
+        ref = np.arange(0, finfo.eps, 2 * finfo.eps)
+        x = np.arange(0, finfo.eps, finfo.max)
+        assert_array_equal(ref, x)
+
+        ref = np.arange(0, finfo.eps, -2 * finfo.eps)
+        x = np.arange(0, finfo.eps, -finfo.max)
+        assert_array_equal(ref, x)
+
+        ref = np.arange(0, -finfo.eps, -2 * finfo.eps)
+        x = np.arange(0, -finfo.eps, -finfo.max)
+        assert_array_equal(ref, x)
+
+        ref = np.arange(0, -finfo.eps, 2 * finfo.eps)
+        x = np.arange(0, -finfo.eps, finfo.max)
+        assert_array_equal(ref, x)
+
+    def test_argmax(self):
+        # Ticket #119
+        a = np.random.normal(0, 1, (4, 5, 6, 7, 8))
+        for i in range(a.ndim):
+            a.argmax(i)  # Should succeed
+
+    def test_mem_divmod(self):
+        # Ticket #126
+        for i in range(10):
+            divmod(np.array([i])[0], 10)
+
+    def test_hstack_invalid_dims(self):
+        # Ticket #128
+        x = np.arange(9).reshape((3, 3))
+        y = np.array([0, 0, 0])
+        assert_raises(ValueError, np.hstack, (x, y))
+
+    def test_squeeze_type(self):
+        # Ticket #133
+        a = np.array([3])
+        b = np.array(3)
+        assert_(type(a.squeeze()) is np.ndarray)
+        assert_(type(b.squeeze()) is np.ndarray)
+
+    def test_add_identity(self):
+        # Ticket #143
+        assert_equal(0, np.add.identity)
+
+    def test_numpy_float_python_long_addition(self):
+        # Check that numpy float and python longs can be added correctly.
+        a = np.float64(23.) + 2**135
+        assert_equal(a, 23. + 2**135)
+
+    def test_binary_repr_0(self):
+        # Ticket #151
+        assert_equal('0', np.binary_repr(0))
+
+    def test_rec_iterate(self):
+        # Ticket #160
+        descr = np.dtype([('i', int), ('f', float), ('s', '|S3')])
+        x = np.rec.array([(1, 1.1, '1.0'),
+                         (2, 2.2, '2.0')], dtype=descr)
+        x[0].tolist()
+        list(x[0])
+
+    def test_unicode_string_comparison(self):
+        # Ticket #190
+        a = np.array('hello', np.str_)
+        b = np.array('world')
+        a == b
+
+    def test_tobytes_FORTRANORDER_discontiguous(self):
+        # Fix in r2836
+        # Create non-contiguous Fortran ordered array
+        x = np.array(np.random.rand(3, 3), order='F')[:, :2]
+        assert_array_almost_equal(x.ravel(), np.frombuffer(x.tobytes()))
+
+    def test_flat_assignment(self):
+        # Correct behaviour of ticket #194
+        x = np.empty((3, 1))
+        x.flat = np.arange(3)
+        assert_array_almost_equal(x, [[0], [1], [2]])
+        x.flat = np.arange(3, dtype=float)
+        assert_array_almost_equal(x, [[0], [1], [2]])
+
+    def test_broadcast_flat_assignment(self):
+        # Ticket #194
+        x = np.empty((3, 1))
+
+        def bfa():
+            x[:] = np.arange(3)
+
+        def bfb():
+            x[:] = np.arange(3, dtype=float)
+
+        assert_raises(ValueError, bfa)
+        assert_raises(ValueError, bfb)
+
+    @pytest.mark.xfail(IS_WASM, reason="not sure why")
+    @pytest.mark.parametrize("index",
+            [np.ones(10, dtype=bool), np.arange(10)],
+            ids=["boolean-arr-index", "integer-arr-index"])
+    def test_nonarray_assignment(self, index):
+        # See also Issue gh-2870, test for non-array assignment
+        # and equivalent unsafe casted array assignment
+        a = np.arange(10)
+
+        with pytest.raises(ValueError):
+            a[index] = np.nan
+
+        with np.errstate(invalid="warn"):
+            with pytest.warns(RuntimeWarning, match="invalid value"):
+                a[index] = np.array(np.nan)  # Only warns
+
+    def test_unpickle_dtype_with_object(self):
+        # Implemented in r2840
+        dt = np.dtype([('x', int), ('y', np.object_), ('z', 'O')])
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            with BytesIO() as f:
+                pickle.dump(dt, f, protocol=proto)
+                f.seek(0)
+                dt_ = pickle.load(f)
+            assert_equal(dt, dt_)
+
+    def test_mem_array_creation_invalid_specification(self):
+        # Ticket #196
+        dt = np.dtype([('x', int), ('y', np.object_)])
+        # Wrong way
+        assert_raises(ValueError, np.array, [1, 'object'], dt)
+        # Correct way
+        np.array([(1, 'object')], dt)
+
+    def test_recarray_single_element(self):
+        # Ticket #202
+        a = np.array([1, 2, 3], dtype=np.int32)
+        b = a.copy()
+        r = np.rec.array(a, shape=1, formats=['3i4'], names=['d'])
+        assert_array_equal(a, b)
+        assert_equal(a, r[0][0])
+
+    def test_zero_sized_array_indexing(self):
+        # Ticket #205
+        tmp = np.array([])
+
+        def index_tmp():
+            tmp[np.array(10)]
+
+        assert_raises(IndexError, index_tmp)
+
+    def test_chararray_rstrip(self):
+        # Ticket #222
+        x = np.char.chararray((1,), 5)
+        x[0] = b'a   '
+        x = x.rstrip()
+        assert_equal(x[0], b'a')
+
+    def test_object_array_shape(self):
+        # Ticket #239
+        assert_equal(np.array([[1, 2], 3, 4], dtype=object).shape, (3,))
+        assert_equal(np.array([[1, 2], [3, 4]], dtype=object).shape, (2, 2))
+        assert_equal(np.array([(1, 2), (3, 4)], dtype=object).shape, (2, 2))
+        assert_equal(np.array([], dtype=object).shape, (0,))
+        assert_equal(np.array([[], [], []], dtype=object).shape, (3, 0))
+        assert_equal(np.array([[3, 4], [5, 6], None], dtype=object).shape, (3,))
+
+    def test_mem_around(self):
+        # Ticket #243
+        x = np.zeros((1,))
+        y = [0]
+        decimal = 6
+        np.around(abs(x - y), decimal) <= 10.0**(-decimal)
+
+    def test_character_array_strip(self):
+        # Ticket #246
+        x = np.char.array(("x", "x ", "x  "))
+        for c in x:
+            assert_equal(c, "x")
+
+    def test_lexsort(self):
+        # Lexsort memory error
+        v = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
+        assert_equal(np.lexsort(v), 0)
+
+    def test_lexsort_invalid_sequence(self):
+        # Issue gh-4123
+        class BuggySequence:
+            def __len__(self):
+                return 4
+
+            def __getitem__(self, key):
+                raise KeyError
+
+        assert_raises(KeyError, np.lexsort, BuggySequence())
+
+    def test_lexsort_zerolen_custom_strides(self):
+        # Ticket #14228
+        xs = np.array([], dtype='i8')
+        assert np.lexsort((xs,)).shape[0] == 0  # Works
+
+        xs.strides = (16,)
+        assert np.lexsort((xs,)).shape[0] == 0  # Was: MemoryError
+
+    def test_lexsort_zerolen_custom_strides_2d(self):
+        xs = np.array([], dtype='i8')
+
+        xs.shape = (0, 2)
+        xs.strides = (16, 16)
+        assert np.lexsort((xs,), axis=0).shape[0] == 0
+
+        xs.shape = (2, 0)
+        xs.strides = (16, 16)
+        assert np.lexsort((xs,), axis=0).shape[0] == 2
+
+    def test_lexsort_invalid_axis(self):
+        assert_raises(AxisError, np.lexsort, (np.arange(1),), axis=2)
+        assert_raises(AxisError, np.lexsort, (np.array([]),), axis=1)
+        assert_raises(AxisError, np.lexsort, (np.array(1),), axis=10)
+
+    def test_lexsort_zerolen_element(self):
+        dt = np.dtype([])  # a void dtype with no fields
+        xs = np.empty(4, dt)
+
+        assert np.lexsort((xs,)).shape[0] == xs.shape[0]
+
+    def test_pickle_py2_bytes_encoding(self):
+        # Check that arrays and scalars pickled on Py2 are
+        # unpickleable on Py3 using encoding='bytes'
+
+        test_data = [
+            # (original, py2_pickle)
+            (
+                np.str_('\u6f2c'),
+                b"cnumpy.core.multiarray\nscalar\np0\n(cnumpy\ndtype\np1\n(S'U1'\np2\nI0\nI1\ntp3\nRp4\n(I3\nS'<'\np5\nNNNI4\nI4\nI0\ntp6\nbS',o\\x00\\x00'\np7\ntp8\nRp9\n."
+            ),
+
+            (
+                np.array([9e123], dtype=np.float64),
+                b"cnumpy.core.multiarray\n_reconstruct\np0\n(cnumpy\nndarray\np1\n(I0\ntp2\nS'b'\np3\ntp4\nRp5\n(I1\n(I1\ntp6\ncnumpy\ndtype\np7\n(S'f8'\np8\nI0\nI1\ntp9\nRp10\n(I3\nS'<'\np11\nNNNI-1\nI-1\nI0\ntp12\nbI00\nS'O\\x81\\xb7Z\\xaa:\\xabY'\np13\ntp14\nb."
+            ),
+
+            (
+                np.array([(9e123,)], dtype=[('name', float)]),
+                b"cnumpy.core.multiarray\n_reconstruct\np0\n(cnumpy\nndarray\np1\n(I0\ntp2\nS'b'\np3\ntp4\nRp5\n(I1\n(I1\ntp6\ncnumpy\ndtype\np7\n(S'V8'\np8\nI0\nI1\ntp9\nRp10\n(I3\nS'|'\np11\nN(S'name'\np12\ntp13\n(dp14\ng12\n(g7\n(S'f8'\np15\nI0\nI1\ntp16\nRp17\n(I3\nS'<'\np18\nNNNI-1\nI-1\nI0\ntp19\nbI0\ntp20\nsI8\nI1\nI0\ntp21\nbI00\nS'O\\x81\\xb7Z\\xaa:\\xabY'\np22\ntp23\nb."
+            ),
+        ]
+
+        for original, data in test_data:
+            result = pickle.loads(data, encoding='bytes')
+            assert_equal(result, original)
+
+            if isinstance(result, np.ndarray) and result.dtype.names is not None:
+                for name in result.dtype.names:
+                    assert_(isinstance(name, str))
+
+    def test_pickle_dtype(self):
+        # Ticket #251
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            pickle.dumps(float, protocol=proto)
+
+    def test_swap_real(self):
+        # Ticket #265
+        assert_equal(np.arange(4, dtype='>c8').imag.max(), 0.0)
+        assert_equal(np.arange(4, dtype='<c8').imag.max(), 0.0)
+        assert_equal(np.arange(4, dtype='>c8').real.max(), 3.0)
+        assert_equal(np.arange(4, dtype='<c8').real.max(), 3.0)
+
+    def test_object_array_from_list(self):
+        # Ticket #270 (gh-868)
+        assert_(np.array([1, None, 'A']).shape == (3,))
+
+    def test_multiple_assign(self):
+        # Ticket #273
+        a = np.zeros((3, 1), int)
+        a[[1, 2]] = 1
+
+    def test_empty_array_type(self):
+        assert_equal(np.array([]).dtype, np.zeros(0).dtype)
+
+    def test_void_copyswap(self):
+        dt = np.dtype([('one', '<i4'), ('two', '<i4')])
+        x = np.array((1, 2), dtype=dt)
+        x = x.byteswap()
+        assert_(x['one'] > 1 and x['two'] > 2)
+
+    def test_method_args(self):
+        # Make sure methods and functions have same default axis
+        # keyword and arguments
+        funcs1 = ['argmax', 'argmin', 'sum', 'any', 'all', 'cumsum',
+                  'cumprod', 'prod', 'std', 'var', 'mean',
+                  'round', 'min', 'max', 'argsort', 'sort']
+        funcs2 = ['compress', 'take', 'repeat']
+
+        for func in funcs1:
+            arr = np.random.rand(8, 7)
+            arr2 = arr.copy()
+            res1 = getattr(arr, func)()
+            res2 = getattr(np, func)(arr2)
+            if res1 is None:
+                res1 = arr
+
+            if res1.dtype.kind in 'uib':
+                assert_((res1 == res2).all(), func)
+            else:
+                assert_(abs(res1 - res2).max() < 1e-8, func)
+
+        for func in funcs2:
+            arr1 = np.random.rand(8, 7)
+            arr2 = np.random.rand(8, 7)
+            res1 = None
+            if func == 'compress':
+                arr1 = arr1.ravel()
+                res1 = getattr(arr2, func)(arr1)
+            else:
+                arr2 = (15 * arr2).astype(int).ravel()
+            if res1 is None:
+                res1 = getattr(arr1, func)(arr2)
+            res2 = getattr(np, func)(arr1, arr2)
+            assert_(abs(res1 - res2).max() < 1e-8, func)
+
+    def test_mem_lexsort_strings(self):
+        # Ticket #298
+        lst = ['abc', 'cde', 'fgh']
+        np.lexsort((lst,))
+
+    def test_fancy_index(self):
+        # Ticket #302
+        x = np.array([1, 2])[np.array([0])]
+        assert_equal(x.shape, (1,))
+
+    def test_recarray_copy(self):
+        # Ticket #312
+        dt = [('x', np.int16), ('y', np.float64)]
+        ra = np.array([(1, 2.3)], dtype=dt)
+        rb = np.rec.array(ra, dtype=dt)
+        rb['x'] = 2.
+        assert_(ra['x'] != rb['x'])
+
+    def test_rec_fromarray(self):
+        # Ticket #322
+        x1 = np.array([[1, 2], [3, 4], [5, 6]])
+        x2 = np.array(['a', 'dd', 'xyz'])
+        x3 = np.array([1.1, 2, 3])
+        np.rec.fromarrays([x1, x2, x3], formats="(2,)i4,S3,f8")
+
+    def test_object_array_assign(self):
+        x = np.empty((2, 2), object)
+        x.flat[2] = (1, 2, 3)
+        assert_equal(x.flat[2], (1, 2, 3))
+
+    def test_ndmin_float64(self):
+        # Ticket #324
+        x = np.array([1, 2, 3], dtype=np.float64)
+        assert_equal(np.array(x, dtype=np.float32, ndmin=2).ndim, 2)
+        assert_equal(np.array(x, dtype=np.float64, ndmin=2).ndim, 2)
+
+    def test_ndmin_order(self):
+        # Issue #465 and related checks
+        assert_(np.array([1, 2], order='C', ndmin=3).flags.c_contiguous)
+        assert_(np.array([1, 2], order='F', ndmin=3).flags.f_contiguous)
+        assert_(np.array(np.ones((2, 2), order='F'), ndmin=3).flags.f_contiguous)
+        assert_(np.array(np.ones((2, 2), order='C'), ndmin=3).flags.c_contiguous)
+
+    def test_mem_axis_minimization(self):
+        # Ticket #327
+        data = np.arange(5)
+        data = np.add.outer(data, data)
+
+    def test_mem_float_imag(self):
+        # Ticket #330
+        np.float64(1.0).imag
+
+    def test_dtype_tuple(self):
+        # Ticket #334
+        assert_(np.dtype('i4') == np.dtype(('i4', ())))
+
+    def test_dtype_posttuple(self):
+        # Ticket #335
+        np.dtype([('col1', '()i4')])
+
+    def test_numeric_carray_compare(self):
+        # Ticket #341
+        assert_equal(np.array(['X'], 'c'), b'X')
+
+    def test_string_array_size(self):
+        # Ticket #342
+        assert_raises(ValueError,
+                              np.array, [['X'], ['X', 'X', 'X']], '|S1')
+
+    def test_dtype_repr(self):
+        # Ticket #344
+        dt1 = np.dtype(('uint32', 2))
+        dt2 = np.dtype(('uint32', (2,)))
+        assert_equal(dt1.__repr__(), dt2.__repr__())
+
+    def test_reshape_order(self):
+        # Make sure reshape order works.
+        a = np.arange(6).reshape(2, 3, order='F')
+        assert_equal(a, [[0, 2, 4], [1, 3, 5]])
+        a = np.array([[1, 2], [3, 4], [5, 6], [7, 8]])
+        b = a[:, 1]
+        assert_equal(b.reshape(2, 2, order='F'), [[2, 6], [4, 8]])
+
+    def test_reshape_zero_strides(self):
+        # Issue #380, test reshaping of zero strided arrays
+        a = np.ones(1)
+        a = np.lib.stride_tricks.as_strided(a, shape=(5,), strides=(0,))
+        assert_(a.reshape(5, 1).strides[0] == 0)
+
+    def test_reshape_zero_size(self):
+        # GitHub Issue #2700, setting shape failed for 0-sized arrays
+        a = np.ones((0, 2))
+        a.shape = (-1, 2)
+
+    def test_reshape_trailing_ones_strides(self):
+        # GitHub issue gh-2949, bad strides for trailing ones of new shape
+        a = np.zeros(12, dtype=np.int32)[::2]  # not contiguous
+        strides_c = (16, 8, 8, 8)
+        strides_f = (8, 24, 48, 48)
+        assert_equal(a.reshape(3, 2, 1, 1).strides, strides_c)
+        assert_equal(a.reshape(3, 2, 1, 1, order='F').strides, strides_f)
+        assert_equal(np.array(0, dtype=np.int32).reshape(1, 1).strides, (4, 4))
+
+    def test_repeat_discont(self):
+        # Ticket #352
+        a = np.arange(12).reshape(4, 3)[:, 2]
+        assert_equal(a.repeat(3), [2, 2, 2, 5, 5, 5, 8, 8, 8, 11, 11, 11])
+
+    def test_array_index(self):
+        # Make sure optimization is not called in this case.
+        a = np.array([1, 2, 3])
+        a2 = np.array([[1, 2, 3]])
+        assert_equal(a[np.where(a == 3)], a2[np.where(a2 == 3)])
+
+    def test_object_argmax(self):
+        a = np.array([1, 2, 3], dtype=object)
+        assert_(a.argmax() == 2)
+
+    def test_recarray_fields(self):
+        # Ticket #372
+        dt0 = np.dtype([('f0', 'i4'), ('f1', 'i4')])
+        dt1 = np.dtype([('f0', 'i8'), ('f1', 'i8')])
+        for a in [np.array([(1, 2), (3, 4)], "i4,i4"),
+                  np.rec.array([(1, 2), (3, 4)], "i4,i4"),
+                  np.rec.array([(1, 2), (3, 4)]),
+                  np.rec.fromarrays([(1, 2), (3, 4)], "i4,i4"),
+                  np.rec.fromarrays([(1, 2), (3, 4)])]:
+            assert_(a.dtype in [dt0, dt1])
+
+    def test_random_shuffle(self):
+        # Ticket #374
+        a = np.arange(5).reshape((5, 1))
+        b = a.copy()
+        np.random.shuffle(b)
+        assert_equal(np.sort(b, axis=0), a)
+
+    def test_refcount_vdot(self):
+        # Changeset #3443
+        _assert_valid_refcount(np.vdot)
+
+    def test_startswith(self):
+        ca = np.char.array(['Hi', 'There'])
+        assert_equal(ca.startswith('H'), [True, False])
+
+    def test_noncommutative_reduce_accumulate(self):
+        # Ticket #413
+        tosubtract = np.arange(5)
+        todivide = np.array([2.0, 0.5, 0.25])
+        assert_equal(np.subtract.reduce(tosubtract), -10)
+        assert_equal(np.divide.reduce(todivide), 16.0)
+        assert_array_equal(np.subtract.accumulate(tosubtract),
+            np.array([0, -1, -3, -6, -10]))
+        assert_array_equal(np.divide.accumulate(todivide),
+            np.array([2., 4., 16.]))
+
+    def test_convolve_empty(self):
+        # Convolve should raise an error for empty input array.
+        assert_raises(ValueError, np.convolve, [], [1])
+        assert_raises(ValueError, np.convolve, [1], [])
+
+    def test_multidim_byteswap(self):
+        # Ticket #449
+        r = np.array([(1, (0, 1, 2))], dtype="i2,3i2")
+        assert_array_equal(r.byteswap(),
+                           np.array([(256, (0, 256, 512))], r.dtype))
+
+    def test_string_NULL(self):
+        # Changeset 3557
+        assert_equal(np.array("a\x00\x0b\x0c\x00").item(),
+                     'a\x00\x0b\x0c')
+
+    def test_junk_in_string_fields_of_recarray(self):
+        # Ticket #483
+        r = np.array([[b'abc']], dtype=[('var1', '|S20')])
+        assert_(asbytes(r['var1'][0][0]) == b'abc')
+
+    def test_take_output(self):
+        # Ensure that 'take' honours output parameter.
+        x = np.arange(12).reshape((3, 4))
+        a = np.take(x, [0, 2], axis=1)
+        b = np.zeros_like(a)
+        np.take(x, [0, 2], axis=1, out=b)
+        assert_array_equal(a, b)
+
+    def test_take_object_fail(self):
+        # Issue gh-3001
+        d = 123.
+        a = np.array([d, 1], dtype=object)
+        if HAS_REFCOUNT:
+            ref_d = sys.getrefcount(d)
+        try:
+            a.take([0, 100])
+        except IndexError:
+            pass
+        if HAS_REFCOUNT:
+            assert_(ref_d == sys.getrefcount(d))
+
+    def test_array_str_64bit(self):
+        # Ticket #501
+        s = np.array([1, np.nan], dtype=np.float64)
+        with np.errstate(all='raise'):
+            np.array_str(s)  # Should succeed
+
+    def test_frompyfunc_endian(self):
+        # Ticket #503
+        from math import radians
+        uradians = np.frompyfunc(radians, 1, 1)
+        big_endian = np.array([83.4, 83.5], dtype='>f8')
+        little_endian = np.array([83.4, 83.5], dtype='<f8')
+        assert_almost_equal(uradians(big_endian).astype(float),
+                            uradians(little_endian).astype(float))
+
+    def test_mem_string_arr(self):
+        # Ticket #514
+        s = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"
+        t = []
+        np.hstack((t, s))
+
+    def test_arr_transpose(self):
+        # Ticket #516
+        x = np.random.rand(*(2,) * 16)
+        x.transpose(list(range(16)))  # Should succeed
+
+    def test_string_mergesort(self):
+        # Ticket #540
+        x = np.array(['a'] * 32)
+        assert_array_equal(x.argsort(kind='m'), np.arange(32))
+
+    def test_argmax_byteorder(self):
+        # Ticket #546
+        a = np.arange(3, dtype='>f')
+        assert_(a[a.argmax()] == a.max())
+
+    def test_rand_seed(self):
+        # Ticket #555
+        for l in np.arange(4):
+            np.random.seed(l)
+
+    def test_mem_deallocation_leak(self):
+        # Ticket #562
+        a = np.zeros(5, dtype=float)
+        b = np.array(a, dtype=float)
+        del a, b
+
+    def test_mem_on_invalid_dtype(self):
+        "Ticket #583"
+        assert_raises(ValueError, np.fromiter, [['12', ''], ['13', '']], str)
+
+    def test_dot_negative_stride(self):
+        # Ticket #588
+        x = np.array([[1, 5, 25, 125., 625]])
+        y = np.array([[20.], [160.], [640.], [1280.], [1024.]])
+        z = y[::-1].copy()
+        y2 = y[::-1]
+        assert_equal(np.dot(x, z), np.dot(x, y2))
+
+    def test_object_casting(self):
+        # This used to trigger the object-type version of
+        # the bitwise_or operation, because float64 -> object
+        # casting succeeds
+        def rs():
+            x = np.ones([484, 286])
+            y = np.zeros([484, 286])
+            x |= y
+
+        assert_raises(TypeError, rs)
+
+    def test_unicode_scalar(self):
+        # Ticket #600
+        x = np.array(["DROND", "DROND1"], dtype="U6")
+        el = x[1]
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            new = pickle.loads(pickle.dumps(el, protocol=proto))
+            assert_equal(new, el)
+
+    def test_arange_non_native_dtype(self):
+        # Ticket #616
+        for T in ('>f4', '<f4'):
+            dt = np.dtype(T)
+            assert_equal(np.arange(0, dtype=dt).dtype, dt)
+            assert_equal(np.arange(0.5, dtype=dt).dtype, dt)
+            assert_equal(np.arange(5, dtype=dt).dtype, dt)
+
+    def test_bool_flat_indexing_invalid_nr_elements(self):
+        s = np.ones(10, dtype=float)
+        x = np.array((15,), dtype=float)
+
+        def ia(x, s, v):
+            x[(s > 0)] = v
+
+        assert_raises(IndexError, ia, x, s, np.zeros(9, dtype=float))
+        assert_raises(IndexError, ia, x, s, np.zeros(11, dtype=float))
+
+        # Old special case (different code path):
+        assert_raises(ValueError, ia, x.flat, s, np.zeros(9, dtype=float))
+        assert_raises(ValueError, ia, x.flat, s, np.zeros(11, dtype=float))
+
+    def test_mem_scalar_indexing(self):
+        # Ticket #603
+        x = np.array([0], dtype=float)
+        index = np.array(0, dtype=np.int32)
+        x[index]
+
+    def test_binary_repr_0_width(self):
+        assert_equal(np.binary_repr(0, width=3), '000')
+
+    def test_fromstring(self):
+        assert_equal(np.fromstring("12:09:09", dtype=int, sep=":"),
+                     [12, 9, 9])
+
+    def test_searchsorted_variable_length(self):
+        x = np.array(['a', 'aa', 'b'])
+        y = np.array(['d', 'e'])
+        assert_equal(x.searchsorted(y), [3, 3])
+
+    def test_string_argsort_with_zeros(self):
+        # Check argsort for strings containing zeros.
+        x = np.frombuffer(b"\x00\x02\x00\x01", dtype="|S2")
+        assert_array_equal(x.argsort(kind='m'), np.array([1, 0]))
+        assert_array_equal(x.argsort(kind='q'), np.array([1, 0]))
+
+    def test_string_sort_with_zeros(self):
+        # Check sort for strings containing zeros.
+        x = np.frombuffer(b"\x00\x02\x00\x01", dtype="|S2")
+        y = np.frombuffer(b"\x00\x01\x00\x02", dtype="|S2")
+        assert_array_equal(np.sort(x, kind="q"), y)
+
+    def test_copy_detection_zero_dim(self):
+        # Ticket #658
+        np.indices((0, 3, 4)).T.reshape(-1, 3)
+
+    def test_flat_byteorder(self):
+        # Ticket #657
+        x = np.arange(10)
+        assert_array_equal(x.astype('>i4'), x.astype('<i4').flat[:])
+        assert_array_equal(x.astype('>i4').flat[:], x.astype('<i4'))
+
+    def test_sign_bit(self):
+        x = np.array([0, -0.0, 0])
+        assert_equal(str(np.abs(x)), '[0. 0. 0.]')
+
+    def test_flat_index_byteswap(self):
+        for dt in (np.dtype('<i4'), np.dtype('>i4')):
+            x = np.array([-1, 0, 1], dtype=dt)
+            assert_equal(x.flat[0].dtype, x[0].dtype)
+
+    def test_copy_detection_corner_case(self):
+        # Ticket #658
+        np.indices((0, 3, 4)).T.reshape(-1, 3)
+
+    def test_object_array_refcounting(self):
+        # Ticket #633
+        if not hasattr(sys, 'getrefcount'):
+            return
+
+        # NB. this is probably CPython-specific
+
+        cnt = sys.getrefcount
+
+        a = object()
+        b = object()
+        c = object()
+
+        cnt0_a = cnt(a)
+        cnt0_b = cnt(b)
+        cnt0_c = cnt(c)
+
+        # -- 0d -> 1-d broadcast slice assignment
+
+        arr = np.zeros(5, dtype=np.object_)
+
+        arr[:] = a
+        assert_equal(cnt(a), cnt0_a + 5)
+
+        arr[:] = b
+        assert_equal(cnt(a), cnt0_a)
+        assert_equal(cnt(b), cnt0_b + 5)
+
+        arr[:2] = c
+        assert_equal(cnt(b), cnt0_b + 3)
+        assert_equal(cnt(c), cnt0_c + 2)
+
+        del arr
+
+        # -- 1-d -> 2-d broadcast slice assignment
+
+        arr = np.zeros((5, 2), dtype=np.object_)
+        arr0 = np.zeros(2, dtype=np.object_)
+
+        arr0[0] = a
+        assert_(cnt(a) == cnt0_a + 1)
+        arr0[1] = b
+        assert_(cnt(b) == cnt0_b + 1)
+
+        arr[:, :] = arr0
+        assert_(cnt(a) == cnt0_a + 6)
+        assert_(cnt(b) == cnt0_b + 6)
+
+        arr[:, 0] = None
+        assert_(cnt(a) == cnt0_a + 1)
+
+        del arr, arr0
+
+        # -- 2-d copying + flattening
+
+        arr = np.zeros((5, 2), dtype=np.object_)
+
+        arr[:, 0] = a
+        arr[:, 1] = b
+        assert_(cnt(a) == cnt0_a + 5)
+        assert_(cnt(b) == cnt0_b + 5)
+
+        arr2 = arr.copy()
+        assert_(cnt(a) == cnt0_a + 10)
+        assert_(cnt(b) == cnt0_b + 10)
+
+        arr2 = arr[:, 0].copy()
+        assert_(cnt(a) == cnt0_a + 10)
+        assert_(cnt(b) == cnt0_b + 5)
+
+        arr2 = arr.flatten()
+        assert_(cnt(a) == cnt0_a + 10)
+        assert_(cnt(b) == cnt0_b + 10)
+
+        del arr, arr2
+
+        # -- concatenate, repeat, take, choose
+
+        arr1 = np.zeros((5, 1), dtype=np.object_)
+        arr2 = np.zeros((5, 1), dtype=np.object_)
+
+        arr1[...] = a
+        arr2[...] = b
+        assert_(cnt(a) == cnt0_a + 5)
+        assert_(cnt(b) == cnt0_b + 5)
+
+        tmp = np.concatenate((arr1, arr2))
+        assert_(cnt(a) == cnt0_a + 5 + 5)
+        assert_(cnt(b) == cnt0_b + 5 + 5)
+
+        tmp = arr1.repeat(3, axis=0)
+        assert_(cnt(a) == cnt0_a + 5 + 3 * 5)
+
+        tmp = arr1.take([1, 2, 3], axis=0)
+        assert_(cnt(a) == cnt0_a + 5 + 3)
+
+        x = np.array([[0], [1], [0], [1], [1]], int)
+        tmp = x.choose(arr1, arr2)
+        assert_(cnt(a) == cnt0_a + 5 + 2)
+        assert_(cnt(b) == cnt0_b + 5 + 3)
+
+    def test_mem_custom_float_to_array(self):
+        # Ticket 702
+        class MyFloat:
+            def __float__(self):
+                return 1.0
+
+        tmp = np.atleast_1d([MyFloat()])
+        tmp.astype(float)  # Should succeed
+
+    def test_object_array_refcount_self_assign(self):
+        # Ticket #711
+        class VictimObject:
+            deleted = False
+
+            def __del__(self):
+                self.deleted = True
+
+        d = VictimObject()
+        arr = np.zeros(5, dtype=np.object_)
+        arr[:] = d
+        del d
+        arr[:] = arr  # refcount of 'd' might hit zero here
+        assert_(not arr[0].deleted)
+        arr[:] = arr  # trying to induce a segfault by doing it again...
+        assert_(not arr[0].deleted)
+
+    def test_mem_fromiter_invalid_dtype_string(self):
+        x = [1, 2, 3]
+        assert_raises(ValueError,
+                              np.fromiter, list(x), dtype='S')
+
+    def test_reduce_big_object_array(self):
+        # Ticket #713
+        oldsize = np.setbufsize(10 * 16)
+        a = np.array([None] * 161, object)
+        assert_(not np.any(a))
+        np.setbufsize(oldsize)
+
+    def test_mem_0d_array_index(self):
+        # Ticket #714
+        np.zeros(10)[np.array(0)]
+
+    def test_nonnative_endian_fill(self):
+        # Non-native endian arrays were incorrectly filled with scalars
+        # before r5034.
+        if sys.byteorder == 'little':
+            dtype = np.dtype('>i4')
+        else:
+            dtype = np.dtype('<i4')
+        x = np.empty([1], dtype=dtype)
+        x.fill(1)
+        assert_equal(x, np.array([1], dtype=dtype))
+
+    def test_dot_alignment_sse2(self):
+        # Test for ticket #551, changeset r5140
+        x = np.zeros((30, 40))
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            y = pickle.loads(pickle.dumps(x, protocol=proto))
+            # y is now typically not aligned on a 8-byte boundary
+            z = np.ones((1, y.shape[0]))
+            # This shouldn't cause a segmentation fault:
+            np.dot(z, y)
+
+    def test_astype_copy(self):
+        # Ticket #788, changeset r5155
+        # The test data file was generated by scipy.io.savemat.
+        # The dtype is float64, but the isbuiltin attribute is 0.
+        data_dir = path.join(path.dirname(__file__), 'data')
+        filename = path.join(data_dir, "astype_copy.pkl")
+        with open(filename, 'rb') as f:
+            xp = pickle.load(f, encoding='latin1')
+        xpd = xp.astype(np.float64)
+        assert_(xp.__array_interface__['data'][0] !=
+                xpd.__array_interface__['data'][0])
+
+    def test_compress_small_type(self):
+        # Ticket #789, changeset 5217.
+        # compress with out argument segfaulted if cannot cast safely
+        import numpy as np
+        a = np.array([[1, 2], [3, 4]])
+        b = np.zeros((2, 1), dtype=np.single)
+        try:
+            a.compress([True, False], axis=1, out=b)
+            raise AssertionError("compress with an out which cannot be "
+                                 "safely casted should not return "
+                                 "successfully")
+        except TypeError:
+            pass
+
+    def test_attributes(self):
+        # Ticket #791
+        class TestArray(np.ndarray):
+            def __new__(cls, data, info):
+                result = np.array(data)
+                result = result.view(cls)
+                result.info = info
+                return result
+
+            def __array_finalize__(self, obj):
+                self.info = getattr(obj, 'info', '')
+
+        dat = TestArray([[1, 2, 3, 4], [5, 6, 7, 8]], 'jubba')
+        assert_(dat.info == 'jubba')
+        dat.resize((4, 2))
+        assert_(dat.info == 'jubba')
+        dat.sort()
+        assert_(dat.info == 'jubba')
+        dat.fill(2)
+        assert_(dat.info == 'jubba')
+        dat.put([2, 3, 4], [6, 3, 4])
+        assert_(dat.info == 'jubba')
+        dat.setfield(4, np.int32, 0)
+        assert_(dat.info == 'jubba')
+        dat.setflags()
+        assert_(dat.info == 'jubba')
+        assert_(dat.all(1).info == 'jubba')
+        assert_(dat.any(1).info == 'jubba')
+        assert_(dat.argmax(1).info == 'jubba')
+        assert_(dat.argmin(1).info == 'jubba')
+        assert_(dat.argsort(1).info == 'jubba')
+        assert_(dat.astype(TestArray).info == 'jubba')
+        assert_(dat.byteswap().info == 'jubba')
+        assert_(dat.clip(2, 7).info == 'jubba')
+        assert_(dat.compress([0, 1, 1]).info == 'jubba')
+        assert_(dat.conj().info == 'jubba')
+        assert_(dat.conjugate().info == 'jubba')
+        assert_(dat.copy().info == 'jubba')
+        dat2 = TestArray([2, 3, 1, 0], 'jubba')
+        choices = [[0, 1, 2, 3], [10, 11, 12, 13],
+                   [20, 21, 22, 23], [30, 31, 32, 33]]
+        assert_(dat2.choose(choices).info == 'jubba')
+        assert_(dat.cumprod(1).info == 'jubba')
+        assert_(dat.cumsum(1).info == 'jubba')
+        assert_(dat.diagonal().info == 'jubba')
+        assert_(dat.flatten().info == 'jubba')
+        assert_(dat.getfield(np.int32, 0).info == 'jubba')
+        assert_(dat.imag.info == 'jubba')
+        assert_(dat.max(1).info == 'jubba')
+        assert_(dat.mean(1).info == 'jubba')
+        assert_(dat.min(1).info == 'jubba')
+        assert_(dat.prod(1).info == 'jubba')
+        assert_(dat.ravel().info == 'jubba')
+        assert_(dat.real.info == 'jubba')
+        assert_(dat.repeat(2).info == 'jubba')
+        assert_(dat.reshape((2, 4)).info == 'jubba')
+        assert_(dat.round().info == 'jubba')
+        assert_(dat.squeeze().info == 'jubba')
+        assert_(dat.std(1).info == 'jubba')
+        assert_(dat.sum(1).info == 'jubba')
+        assert_(dat.swapaxes(0, 1).info == 'jubba')
+        assert_(dat.take([2, 3, 5]).info == 'jubba')
+        assert_(dat.transpose().info == 'jubba')
+        assert_(dat.T.info == 'jubba')
+        assert_(dat.var(1).info == 'jubba')
+        assert_(dat.view(TestArray).info == 'jubba')
+        # These methods do not preserve subclasses
+        assert_(type(dat.nonzero()[0]) is np.ndarray)
+        assert_(type(dat.nonzero()[1]) is np.ndarray)
+
+    def test_recarray_tolist(self):
+        # Ticket #793, changeset r5215
+        # Comparisons fail for NaN, so we can't use random memory
+        # for the test.
+        buf = np.zeros(40, dtype=np.int8)
+        a = np.recarray(2, formats="i4,f8,f8", names="id,x,y", buf=buf)
+        b = a.tolist()
+        assert_(a[0].tolist() == b[0])
+        assert_(a[1].tolist() == b[1])
+
+    def test_nonscalar_item_method(self):
+        # Make sure that .item() fails graciously when it should
+        a = np.arange(5)
+        assert_raises(ValueError, a.item)
+
+    def test_char_array_creation(self):
+        a = np.array('123', dtype='c')
+        b = np.array([b'1', b'2', b'3'])
+        assert_equal(a, b)
+
+    def test_unaligned_unicode_access(self):
+        # Ticket #825
+        for i in range(1, 9):
+            msg = 'unicode offset: %d chars' % i
+            t = np.dtype([('a', 'S%d' % i), ('b', 'U2')])
+            x = np.array([(b'a', 'b')], dtype=t)
+            assert_equal(str(x), "[(b'a', 'b')]", err_msg=msg)
+
+    def test_sign_for_complex_nan(self):
+        # Ticket 794.
+        with np.errstate(invalid='ignore'):
+            C = np.array([-np.inf, -3 + 4j, 0, 4 - 3j, np.inf, np.nan])
+            have = np.sign(C)
+            want = np.array([-1 + 0j, -0.6 + 0.8j, 0 + 0j, 0.8 - 0.6j, 1 + 0j,
+                             complex(np.nan, np.nan)])
+            assert_equal(have, want)
+
+    def test_for_equal_names(self):
+        # Ticket #674
+        dt = np.dtype([('foo', float), ('bar', float)])
+        a = np.zeros(10, dt)
+        b = list(a.dtype.names)
+        b[0] = "notfoo"
+        a.dtype.names = b
+        assert_(a.dtype.names[0] == "notfoo")
+        assert_(a.dtype.names[1] == "bar")
+
+    def test_for_object_scalar_creation(self):
+        # Ticket #816
+        a = np.object_()
+        b = np.object_(3)
+        b2 = np.object_(3.0)
+        c = np.object_([4, 5])
+        d = np.object_([None, {}, []])
+        assert_(a is None)
+        assert_(type(b) is int)
+        assert_(type(b2) is float)
+        assert_(type(c) is np.ndarray)
+        assert_(c.dtype == object)
+        assert_(d.dtype == object)
+
+    def test_array_resize_method_system_error(self):
+        # Ticket #840 - order should be an invalid keyword.
+        x = np.array([[0, 1], [2, 3]])
+        assert_raises(TypeError, x.resize, (2, 2), order='C')
+
+    def test_for_zero_length_in_choose(self):
+        "Ticket #882"
+        a = np.array(1)
+        assert_raises(ValueError, lambda x: x.choose([]), a)
+
+    def test_array_ndmin_overflow(self):
+        "Ticket #947."
+        assert_raises(ValueError, lambda: np.array([1], ndmin=65))
+
+    def test_void_scalar_with_titles(self):
+        # No ticket
+        data = [('john', 4), ('mary', 5)]
+        dtype1 = [(('source:yy', 'name'), 'O'), (('source:xx', 'id'), int)]
+        arr = np.array(data, dtype=dtype1)
+        assert_(arr[0][0] == 'john')
+        assert_(arr[0][1] == 4)
+
+    def test_void_scalar_constructor(self):
+        # Issue #1550
+
+        # Create test string data, construct void scalar from data and assert
+        # that void scalar contains original data.
+        test_string = np.array("test")
+        test_string_void_scalar = np._core.multiarray.scalar(
+            np.dtype(("V", test_string.dtype.itemsize)), test_string.tobytes())
+
+        assert_(test_string_void_scalar.view(test_string.dtype) == test_string)
+
+        # Create record scalar, construct from data and assert that
+        # reconstructed scalar is correct.
+        test_record = np.ones((), "i,i")
+        test_record_void_scalar = np._core.multiarray.scalar(
+            test_record.dtype, test_record.tobytes())
+
+        assert_(test_record_void_scalar == test_record)
+
+        # Test pickle and unpickle of void and record scalars
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            assert_(pickle.loads(
+                pickle.dumps(test_string, protocol=proto)) == test_string)
+            assert_(pickle.loads(
+                pickle.dumps(test_record, protocol=proto)) == test_record)
+
+    @_no_tracing
+    def test_blasdot_uninitialized_memory(self):
+        # Ticket #950
+        for m in [0, 1, 2]:
+            for n in [0, 1, 2]:
+                for k in range(3):
+                    # Try to ensure that x->data contains non-zero floats
+                    x = np.array([123456789e199], dtype=np.float64)
+                    if IS_PYPY:
+                        x.resize((m, 0), refcheck=False)
+                    else:
+                        x.resize((m, 0))
+                    y = np.array([123456789e199], dtype=np.float64)
+                    if IS_PYPY:
+                        y.resize((0, n), refcheck=False)
+                    else:
+                        y.resize((0, n))
+
+                    # `dot` should just return zero (m, n) matrix
+                    z = np.dot(x, y)
+                    assert_(np.all(z == 0))
+                    assert_(z.shape == (m, n))
+
+    def test_zeros(self):
+        # Regression test for #1061.
+        # Set a size which cannot fit into a 64 bits signed integer
+        sz = 2 ** 64
+        with assert_raises_regex(ValueError,
+                                 'Maximum allowed dimension exceeded'):
+            np.empty(sz)
+
+    def test_huge_arange(self):
+        # Regression test for #1062.
+        # Set a size which cannot fit into a 64 bits signed integer
+        sz = 2 ** 64
+        with assert_raises_regex(ValueError,
+                                 'Maximum allowed size exceeded'):
+            np.arange(sz)
+            assert_(np.size == sz)
+
+    def test_fromiter_bytes(self):
+        # Ticket #1058
+        a = np.fromiter(list(range(10)), dtype='b')
+        b = np.fromiter(list(range(10)), dtype='B')
+        assert_(np.all(a == np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])))
+        assert_(np.all(b == np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])))
+
+    def test_array_from_sequence_scalar_array(self):
+        # Ticket #1078: segfaults when creating an array with a sequence of
+        # 0d arrays.
+        a = np.array((np.ones(2), np.array(2)), dtype=object)
+        assert_equal(a.shape, (2,))
+        assert_equal(a.dtype, np.dtype(object))
+        assert_equal(a[0], np.ones(2))
+        assert_equal(a[1], np.array(2))
+
+        a = np.array(((1,), np.array(1)), dtype=object)
+        assert_equal(a.shape, (2,))
+        assert_equal(a.dtype, np.dtype(object))
+        assert_equal(a[0], (1,))
+        assert_equal(a[1], np.array(1))
+
+    def test_array_from_sequence_scalar_array2(self):
+        # Ticket #1081: weird array with strange input...
+        t = np.array([np.array([]), np.array(0, object)], dtype=object)
+        assert_equal(t.shape, (2,))
+        assert_equal(t.dtype, np.dtype(object))
+
+    def test_array_too_big(self):
+        # Ticket #1080.
+        assert_raises(ValueError, np.zeros, [975] * 7, np.int8)
+        assert_raises(ValueError, np.zeros, [26244] * 5, np.int8)
+
+    def test_dtype_keyerrors_(self):
+        # Ticket #1106.
+        dt = np.dtype([('f1', np.uint)])
+        assert_raises(KeyError, dt.__getitem__, "f2")
+        assert_raises(IndexError, dt.__getitem__, 1)
+        assert_raises(TypeError, dt.__getitem__, 0.0)
+
+    def test_lexsort_buffer_length(self):
+        # Ticket #1217, don't segfault.
+        a = np.ones(100, dtype=np.int8)
+        b = np.ones(100, dtype=np.int32)
+        i = np.lexsort((a[::-1], b))
+        assert_equal(i, np.arange(100, dtype=int))
+
+    def test_object_array_to_fixed_string(self):
+        # Ticket #1235.
+        a = np.array(['abcdefgh', 'ijklmnop'], dtype=np.object_)
+        b = np.array(a, dtype=(np.str_, 8))
+        assert_equal(a, b)
+        c = np.array(a, dtype=(np.str_, 5))
+        assert_equal(c, np.array(['abcde', 'ijklm']))
+        d = np.array(a, dtype=(np.str_, 12))
+        assert_equal(a, d)
+        e = np.empty((2, ), dtype=(np.str_, 8))
+        e[:] = a[:]
+        assert_equal(a, e)
+
+    def test_unicode_to_string_cast(self):
+        # Ticket #1240.
+        a = np.array([['abc', '\u03a3'],
+                      ['asdf', 'erw']],
+                     dtype='U')
+        assert_raises(UnicodeEncodeError, np.array, a, 'S4')
+
+    def test_unicode_to_string_cast_error(self):
+        # gh-15790
+        a = np.array(['\x80'] * 129, dtype='U3')
+        assert_raises(UnicodeEncodeError, np.array, a, 'S')
+        b = a.reshape(3, 43)[:-1, :-1]
+        assert_raises(UnicodeEncodeError, np.array, b, 'S')
+
+    def test_mixed_string_byte_array_creation(self):
+        a = np.array(['1234', b'123'])
+        assert_(a.itemsize == 16)
+        a = np.array([b'123', '1234'])
+        assert_(a.itemsize == 16)
+        a = np.array(['1234', b'123', '12345'])
+        assert_(a.itemsize == 20)
+        a = np.array([b'123', '1234', b'12345'])
+        assert_(a.itemsize == 20)
+        a = np.array([b'123', '1234', b'1234'])
+        assert_(a.itemsize == 16)
+
+    def test_misaligned_objects_segfault(self):
+        # Ticket #1198 and #1267
+        a1 = np.zeros((10,), dtype='O,c')
+        a2 = np.array(['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j'], 'S10')
+        a1['f0'] = a2
+        repr(a1)
+        np.argmax(a1['f0'])
+        a1['f0'][1] = "FOO"
+        a1['f0'] = "FOO"
+        np.array(a1['f0'], dtype='S')
+        np.nonzero(a1['f0'])
+        a1.sort()
+        copy.deepcopy(a1)
+
+    def test_misaligned_scalars_segfault(self):
+        # Ticket #1267
+        s1 = np.array(('a', 'Foo'), dtype='c,O')
+        s2 = np.array(('b', 'Bar'), dtype='c,O')
+        s1['f1'] = s2['f1']
+        s1['f1'] = 'Baz'
+
+    def test_misaligned_dot_product_objects(self):
+        # Ticket #1267
+        # This didn't require a fix, but it's worth testing anyway, because
+        # it may fail if .dot stops enforcing the arrays to be BEHAVED
+        a = np.array([[(1, 'a'), (0, 'a')], [(0, 'a'), (1, 'a')]], dtype='O,c')
+        b = np.array([[(4, 'a'), (1, 'a')], [(2, 'a'), (2, 'a')]], dtype='O,c')
+        np.dot(a['f0'], b['f0'])
+
+    def test_byteswap_complex_scalar(self):
+        # Ticket #1259 and gh-441
+        for dtype in [np.dtype('<' + t) for t in np.typecodes['Complex']]:
+            z = np.array([2.2 - 1.1j], dtype)
+            x = z[0]  # always native-endian
+            y = x.byteswap()
+            if x.dtype.byteorder == z.dtype.byteorder:
+                # little-endian machine
+                assert_equal(x, np.frombuffer(y.tobytes(), dtype=dtype.newbyteorder()))
+            else:
+                # big-endian machine
+                assert_equal(x, np.frombuffer(y.tobytes(), dtype=dtype))
+            # double check real and imaginary parts:
+            assert_equal(x.real, y.real.byteswap())
+            assert_equal(x.imag, y.imag.byteswap())
+
+    def test_structured_arrays_with_objects1(self):
+        # Ticket #1299
+        stra = 'aaaa'
+        strb = 'bbbb'
+        x = np.array([[(0, stra), (1, strb)]], 'i8,O')
+        x[x.nonzero()] = x.ravel()[:1]
+        assert_(x[0, 1] == x[0, 0])
+
+    @pytest.mark.skipif(
+        sys.version_info >= (3, 12),
+        reason="Python 3.12 has immortal refcounts, this test no longer works."
+    )
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test_structured_arrays_with_objects2(self):
+        # Ticket #1299 second test
+        stra = 'aaaa'
+        strb = 'bbbb'
+        numb = sys.getrefcount(strb)
+        numa = sys.getrefcount(stra)
+        x = np.array([[(0, stra), (1, strb)]], 'i8,O')
+        x[x.nonzero()] = x.ravel()[:1]
+        assert_(sys.getrefcount(strb) == numb)
+        assert_(sys.getrefcount(stra) == numa + 2)
+
+    def test_duplicate_title_and_name(self):
+        # Ticket #1254
+        dtspec = [(('a', 'a'), 'i'), ('b', 'i')]
+        assert_raises(ValueError, np.dtype, dtspec)
+
+    def test_signed_integer_division_overflow(self):
+        # Ticket #1317.
+        def test_type(t):
+            min = np.array([np.iinfo(t).min])
+            min //= -1
+
+        with np.errstate(over="ignore"):
+            for t in (np.int8, np.int16, np.int32, np.int64, int):
+                test_type(t)
+
+    def test_buffer_hashlib(self):
+        from hashlib import sha256
+
+        x = np.array([1, 2, 3], dtype=np.dtype('<i4'))
+        assert_equal(
+            sha256(x).hexdigest(),
+            '4636993d3e1da4e9d6b8f87b79e8f7c6d018580d52661950eabc3845c5897a4d'
+        )
+
+    def test_0d_string_scalar(self):
+        # Bug #1436; the following should succeed
+        np.asarray('x', '>c')
+
+    def test_log1p_compiler_shenanigans(self):
+        # Check if log1p is behaving on 32 bit intel systems.
+        assert_(np.isfinite(np.log1p(np.exp2(-53))))
+
+    def test_fromiter_comparison(self):
+        a = np.fromiter(list(range(10)), dtype='b')
+        b = np.fromiter(list(range(10)), dtype='B')
+        assert_(np.all(a == np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])))
+        assert_(np.all(b == np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])))
+
+    def test_fromstring_crash(self):
+        with assert_raises(ValueError):
+            np.fromstring(b'aa, aa, 1.0', sep=',')
+
+    def test_ticket_1539(self):
+        dtypes = [x for x in np._core.sctypeDict.values()
+                  if (issubclass(x, np.number)
+                      and not issubclass(x, np.timedelta64))]
+        a = np.array([], np.bool)  # not x[0] because it is unordered
+        failures = []
+
+        for x in dtypes:
+            b = a.astype(x)
+            for y in dtypes:
+                c = a.astype(y)
+                try:
+                    d = np.dot(b, c)
+                except TypeError:
+                    failures.append((x, y))
+                else:
+                    if d != 0:
+                        failures.append((x, y))
+        if failures:
+            raise AssertionError(f"Failures: {failures!r}")
+
+    def test_ticket_1538(self):
+        x = np.finfo(np.float32)
+        for name in ('eps', 'epsneg', 'max', 'min', 'resolution', 'tiny'):
+            assert_equal(type(getattr(x, name)), np.float32,
+                         err_msg=name)
+
+    def test_ticket_1434(self):
+        # Check that the out= argument in var and std has an effect
+        data = np.array(((1, 2, 3), (4, 5, 6), (7, 8, 9)))
+        out = np.zeros((3,))
+
+        ret = data.var(axis=1, out=out)
+        assert_(ret is out)
+        assert_array_equal(ret, data.var(axis=1))
+
+        ret = data.std(axis=1, out=out)
+        assert_(ret is out)
+        assert_array_equal(ret, data.std(axis=1))
+
+    def test_complex_nan_maximum(self):
+        cnan = complex(0, np.nan)
+        assert_equal(np.maximum(1, cnan), cnan)
+
+    def test_subclass_int_tuple_assignment(self):
+        # ticket #1563
+        class Subclass(np.ndarray):
+            def __new__(cls, i):
+                return np.ones((i,)).view(cls)
+
+        x = Subclass(5)
+        x[(0,)] = 2  # shouldn't raise an exception
+        assert_equal(x[0], 2)
+
+    def test_ufunc_no_unnecessary_views(self):
+        # ticket #1548
+        class Subclass(np.ndarray):
+            pass
+        x = np.array([1, 2, 3]).view(Subclass)
+        y = np.add(x, x, x)
+        assert_equal(id(x), id(y))
+
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test_take_refcount(self):
+        # ticket #939
+        a = np.arange(16, dtype=float)
+        a.shape = (4, 4)
+        lut = np.ones((5 + 3, 4), float)
+        rgba = np.empty(shape=a.shape + (4,), dtype=lut.dtype)
+        c1 = sys.getrefcount(rgba)
+        try:
+            lut.take(a, axis=0, mode='clip', out=rgba)
+        except TypeError:
+            pass
+        c2 = sys.getrefcount(rgba)
+        assert_equal(c1, c2)
+
+    def test_fromfile_tofile_seeks(self):
+        # tofile/fromfile used to get (#1610) the Python file handle out of sync
+        with tempfile.NamedTemporaryFile() as f:
+            f.write(np.arange(255, dtype='u1').tobytes())
+
+            f.seek(20)
+            ret = np.fromfile(f, count=4, dtype='u1')
+            assert_equal(ret, np.array([20, 21, 22, 23], dtype='u1'))
+            assert_equal(f.tell(), 24)
+
+            f.seek(40)
+            np.array([1, 2, 3], dtype='u1').tofile(f)
+            assert_equal(f.tell(), 43)
+
+            f.seek(40)
+            data = f.read(3)
+            assert_equal(data, b"\x01\x02\x03")
+
+            f.seek(80)
+            f.read(4)
+            data = np.fromfile(f, dtype='u1', count=4)
+            assert_equal(data, np.array([84, 85, 86, 87], dtype='u1'))
+
+    def test_complex_scalar_warning(self):
+        for tp in [np.csingle, np.cdouble, np.clongdouble]:
+            x = tp(1 + 2j)
+            assert_warns(ComplexWarning, float, x)
+            with suppress_warnings() as sup:
+                sup.filter(ComplexWarning)
+                assert_equal(float(x), float(x.real))
+
+    def test_complex_scalar_complex_cast(self):
+        for tp in [np.csingle, np.cdouble, np.clongdouble]:
+            x = tp(1 + 2j)
+            assert_equal(complex(x), 1 + 2j)
+
+    def test_complex_boolean_cast(self):
+        # Ticket #2218
+        for tp in [np.csingle, np.cdouble, np.clongdouble]:
+            x = np.array([0, 0 + 0.5j, 0.5 + 0j], dtype=tp)
+            assert_equal(x.astype(bool), np.array([0, 1, 1], dtype=bool))
+            assert_(np.any(x))
+            assert_(np.all(x[1:]))
+
+    def test_uint_int_conversion(self):
+        x = 2**64 - 1
+        assert_equal(int(np.uint64(x)), x)
+
+    def test_duplicate_field_names_assign(self):
+        ra = np.fromiter(((i * 3, i * 2) for i in range(10)), dtype='i8,f8')
+        ra.dtype.names = ('f1', 'f2')
+        repr(ra)  # should not cause a segmentation fault
+        assert_raises(ValueError, setattr, ra.dtype, 'names', ('f1', 'f1'))
+
+    def test_eq_string_and_object_array(self):
+        # From e-mail thread "__eq__ with str and object" (Keith Goodman)
+        a1 = np.array(['a', 'b'], dtype=object)
+        a2 = np.array(['a', 'c'])
+        assert_array_equal(a1 == a2, [True, False])
+        assert_array_equal(a2 == a1, [True, False])
+
+    def test_nonzero_byteswap(self):
+        a = np.array([0x80000000, 0x00000080, 0], dtype=np.uint32)
+        a.dtype = np.float32
+        assert_equal(a.nonzero()[0], [1])
+        a = a.byteswap()
+        a = a.view(a.dtype.newbyteorder())
+        assert_equal(a.nonzero()[0], [1])  # [0] if nonzero() ignores swap
+
+    def test_empty_mul(self):
+        a = np.array([1.])
+        a[1:1] *= 2
+        assert_equal(a, [1.])
+
+    def test_array_side_effect(self):
+        # The second use of itemsize was throwing an exception because in
+        # ctors.c, discover_itemsize was calling PyObject_Length without
+        # checking the return code.  This failed to get the length of the
+        # number 2, and the exception hung around until something checked
+        # PyErr_Occurred() and returned an error.
+        assert_equal(np.dtype('S10').itemsize, 10)
+        np.array([['abc', 2], ['long   ', '0123456789']], dtype=np.bytes_)
+        assert_equal(np.dtype('S10').itemsize, 10)
+
+    def test_any_float(self):
+        # all and any for floats
+        a = np.array([0.1, 0.9])
+        assert_(np.any(a))
+        assert_(np.all(a))
+
+    def test_large_float_sum(self):
+        a = np.arange(10000, dtype='f')
+        assert_equal(a.sum(dtype='d'), a.astype('d').sum())
+
+    def test_ufunc_casting_out(self):
+        a = np.array(1.0, dtype=np.float32)
+        b = np.array(1.0, dtype=np.float64)
+        c = np.array(1.0, dtype=np.float32)
+        np.add(a, b, out=c)
+        assert_equal(c, 2.0)
+
+    def test_array_scalar_contiguous(self):
+        # Array scalars are both C and Fortran contiguous
+        assert_(np.array(1.0).flags.c_contiguous)
+        assert_(np.array(1.0).flags.f_contiguous)
+        assert_(np.array(np.float32(1.0)).flags.c_contiguous)
+        assert_(np.array(np.float32(1.0)).flags.f_contiguous)
+
+    def test_squeeze_contiguous(self):
+        # Similar to GitHub issue #387
+        a = np.zeros((1, 2)).squeeze()
+        b = np.zeros((2, 2, 2), order='F')[:, :, ::2].squeeze()
+        assert_(a.flags.c_contiguous)
+        assert_(a.flags.f_contiguous)
+        assert_(b.flags.f_contiguous)
+
+    def test_squeeze_axis_handling(self):
+        # Issue #10779
+        # Ensure proper handling of objects
+        # that don't support axis specification
+        # when squeezing
+
+        class OldSqueeze(np.ndarray):
+
+            def __new__(cls,
+                        input_array):
+                obj = np.asarray(input_array).view(cls)
+                return obj
+
+            # it is perfectly reasonable that prior
+            # to numpy version 1.7.0 a subclass of ndarray
+            # might have been created that did not expect
+            # squeeze to have an axis argument
+            # NOTE: this example is somewhat artificial;
+            # it is designed to simulate an old API
+            # expectation to guard against regression
+            def squeeze(self):
+                return super().squeeze()
+
+        oldsqueeze = OldSqueeze(np.array([[1], [2], [3]]))
+
+        # if no axis argument is specified the old API
+        # expectation should give the correct result
+        assert_equal(np.squeeze(oldsqueeze),
+                     np.array([1, 2, 3]))
+
+        # likewise, axis=None should work perfectly well
+        # with the old API expectation
+        assert_equal(np.squeeze(oldsqueeze, axis=None),
+                     np.array([1, 2, 3]))
+
+        # however, specification of any particular axis
+        # should raise a TypeError in the context of the
+        # old API specification, even when using a valid
+        # axis specification like 1 for this array
+        with assert_raises(TypeError):
+            # this would silently succeed for array
+            # subclasses / objects that did not support
+            # squeeze axis argument handling before fixing
+            # Issue #10779
+            np.squeeze(oldsqueeze, axis=1)
+
+        # check for the same behavior when using an invalid
+        # axis specification -- in this case axis=0 does not
+        # have size 1, but the priority should be to raise
+        # a TypeError for the axis argument and NOT a
+        # ValueError for squeezing a non-empty dimension
+        with assert_raises(TypeError):
+            np.squeeze(oldsqueeze, axis=0)
+
+        # the new API knows how to handle the axis
+        # argument and will return a ValueError if
+        # attempting to squeeze an axis that is not
+        # of length 1
+        with assert_raises(ValueError):
+            np.squeeze(np.array([[1], [2], [3]]), axis=0)
+
+    def test_reduce_contiguous(self):
+        # GitHub issue #387
+        a = np.add.reduce(np.zeros((2, 1, 2)), (0, 1))
+        b = np.add.reduce(np.zeros((2, 1, 2)), 1)
+        assert_(a.flags.c_contiguous)
+        assert_(a.flags.f_contiguous)
+        assert_(b.flags.c_contiguous)
+
+    @pytest.mark.skipif(IS_PYSTON, reason="Pyston disables recursion checking")
+    @pytest.mark.skipif(IS_WASM, reason="Pyodide/WASM has limited stack size")
+    def test_object_array_self_reference(self):
+        # Object arrays with references to themselves can cause problems
+        a = np.array(0, dtype=object)
+        a[()] = a
+        assert_raises(RecursionError, int, a)
+        assert_raises(RecursionError, float, a)
+        a[()] = None
+
+    @pytest.mark.skipif(IS_PYSTON, reason="Pyston disables recursion checking")
+    @pytest.mark.skipif(IS_WASM, reason="Pyodide/WASM has limited stack size")
+    def test_object_array_circular_reference(self):
+        # Test the same for a circular reference.
+        a = np.array(0, dtype=object)
+        b = np.array(0, dtype=object)
+        a[()] = b
+        b[()] = a
+        assert_raises(RecursionError, int, a)
+        # NumPy has no tp_traverse currently, so circular references
+        # cannot be detected. So resolve it:
+        a[()] = None
+
+        # This was causing a to become like the above
+        a = np.array(0, dtype=object)
+        a[...] += 1
+        assert_equal(a, 1)
+
+    def test_object_array_nested(self):
+        # but is fine with a reference to a different array
+        a = np.array(0, dtype=object)
+        b = np.array(0, dtype=object)
+        a[()] = b
+        assert_equal(int(a), int(0))  # noqa: UP018
+        assert_equal(float(a), float(0))
+
+    def test_object_array_self_copy(self):
+        # An object array being copied into itself DECREF'ed before INCREF'ing
+        # causing segmentation faults (gh-3787)
+        a = np.array(object(), dtype=object)
+        np.copyto(a, a)
+        if HAS_REFCOUNT:
+            assert_(sys.getrefcount(a[()]) == 2)
+        a[()].__class__  # will segfault if object was deleted
+
+    def test_zerosize_accumulate(self):
+        "Ticket #1733"
+        x = np.array([[42, 0]], dtype=np.uint32)
+        assert_equal(np.add.accumulate(x[:-1, 0]), [])
+
+    def test_objectarray_setfield(self):
+        # Setfield should not overwrite Object fields with non-Object data
+        x = np.array([1, 2, 3], dtype=object)
+        assert_raises(TypeError, x.setfield, 4, np.int32, 0)
+
+    def test_setting_rank0_string(self):
+        "Ticket #1736"
+        s1 = b"hello1"
+        s2 = b"hello2"
+        a = np.zeros((), dtype="S10")
+        a[()] = s1
+        assert_equal(a, np.array(s1))
+        a[()] = np.array(s2)
+        assert_equal(a, np.array(s2))
+
+        a = np.zeros((), dtype='f4')
+        a[()] = 3
+        assert_equal(a, np.array(3))
+        a[()] = np.array(4)
+        assert_equal(a, np.array(4))
+
+    def test_string_astype(self):
+        "Ticket #1748"
+        s1 = b'black'
+        s2 = b'white'
+        s3 = b'other'
+        a = np.array([[s1], [s2], [s3]])
+        assert_equal(a.dtype, np.dtype('S5'))
+        b = a.astype(np.dtype('S0'))
+        assert_equal(b.dtype, np.dtype('S5'))
+
+    def test_ticket_1756(self):
+        # Ticket #1756
+        s = b'0123456789abcdef'
+        a = np.array([s] * 5)
+        for i in range(1, 17):
+            a1 = np.array(a, "|S%d" % i)
+            a2 = np.array([s[:i]] * 5)
+            assert_equal(a1, a2)
+
+    def test_fields_strides(self):
+        "gh-2355"
+        r = np.frombuffer(b'abcdefghijklmnop' * 4 * 3, dtype='i4,(2,3)u2')
+        assert_equal(r[0:3:2]['f1'], r['f1'][0:3:2])
+        assert_equal(r[0:3:2]['f1'][0], r[0:3:2][0]['f1'])
+        assert_equal(r[0:3:2]['f1'][0][()], r[0:3:2][0]['f1'][()])
+        assert_equal(r[0:3:2]['f1'][0].strides, r[0:3:2][0]['f1'].strides)
+
+    def test_alignment_update(self):
+        # Check that alignment flag is updated on stride setting
+        a = np.arange(10)
+        assert_(a.flags.aligned)
+        a.strides = 3
+        assert_(not a.flags.aligned)
+
+    def test_ticket_1770(self):
+        "Should not segfault on python 3k"
+        import numpy as np
+        try:
+            a = np.zeros((1,), dtype=[('f1', 'f')])
+            a['f1'] = 1
+            a['f2'] = 1
+        except ValueError:
+            pass
+        except Exception:
+            raise AssertionError
+
+    def test_ticket_1608(self):
+        "x.flat shouldn't modify data"
+        x = np.array([[1, 2], [3, 4]]).T
+        np.array(x.flat)
+        assert_equal(x, [[1, 3], [2, 4]])
+
+    def test_pickle_string_overwrite(self):
+        import re
+
+        data = np.array([1], dtype='b')
+        blob = pickle.dumps(data, protocol=1)
+        data = pickle.loads(blob)
+
+        # Check that loads does not clobber interned strings
+        s = re.sub(r"a(.)", "\x01\\1", "a_")
+        assert_equal(s[0], "\x01")
+        data[0] = 0x6a
+        s = re.sub(r"a(.)", "\x01\\1", "a_")
+        assert_equal(s[0], "\x01")
+
+    def test_pickle_bytes_overwrite(self):
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            data = np.array([1], dtype='b')
+            data = pickle.loads(pickle.dumps(data, protocol=proto))
+            data[0] = 0x7d
+            bytestring = "\x01  ".encode('ascii')
+            assert_equal(bytestring[0:1], '\x01'.encode('ascii'))
+
+    def test_pickle_py2_array_latin1_hack(self):
+        # Check that unpickling hacks in Py3 that support
+        # encoding='latin1' work correctly.
+
+        # Python2 output for pickle.dumps(numpy.array([129], dtype='b'))
+        data = b"cnumpy.core.multiarray\n_reconstruct\np0\n(cnumpy\nndarray\np1\n(I0\ntp2\nS'b'\np3\ntp4\nRp5\n(I1\n(I1\ntp6\ncnumpy\ndtype\np7\n(S'i1'\np8\nI0\nI1\ntp9\nRp10\n(I3\nS'|'\np11\nNNNI-1\nI-1\nI0\ntp12\nbI00\nS'\\x81'\np13\ntp14\nb."
+        # This should work:
+        result = pickle.loads(data, encoding='latin1')
+        assert_array_equal(result, np.array([129]).astype('b'))
+        # Should not segfault:
+        assert_raises(Exception, pickle.loads, data, encoding='koi8-r')
+
+    def test_pickle_py2_scalar_latin1_hack(self):
+        # Check that scalar unpickling hack in Py3 that supports
+        # encoding='latin1' work correctly.
+
+        # Python2 output for pickle.dumps(...)
+        datas = [
+            # (original, python2_pickle, koi8r_validity)
+            (np.str_('\u6bd2'),
+             b"cnumpy.core.multiarray\nscalar\np0\n(cnumpy\ndtype\np1\n(S'U1'\np2\nI0\nI1\ntp3\nRp4\n(I3\nS'<'\np5\nNNNI4\nI4\nI0\ntp6\nbS'\\xd2k\\x00\\x00'\np7\ntp8\nRp9\n.",
+             'invalid'),
+
+            (np.float64(9e123),
+             b"cnumpy.core.multiarray\nscalar\np0\n(cnumpy\ndtype\np1\n(S'f8'\np2\nI0\nI1\ntp3\nRp4\n(I3\nS'<'\np5\nNNNI-1\nI-1\nI0\ntp6\nbS'O\\x81\\xb7Z\\xaa:\\xabY'\np7\ntp8\nRp9\n.",
+             'invalid'),
+
+            # different 8-bit code point in KOI8-R vs latin1
+            (np.bytes_(b'\x9c'),
+             b"cnumpy.core.multiarray\nscalar\np0\n(cnumpy\ndtype\np1\n(S'S1'\np2\nI0\nI1\ntp3\nRp4\n(I3\nS'|'\np5\nNNNI1\nI1\nI0\ntp6\nbS'\\x9c'\np7\ntp8\nRp9\n.",
+             'different'),
+        ]
+        for original, data, koi8r_validity in datas:
+            result = pickle.loads(data, encoding='latin1')
+            assert_equal(result, original)
+
+            # Decoding under non-latin1 encoding (e.g.) KOI8-R can
+            # produce bad results, but should not segfault.
+            if koi8r_validity == 'different':
+                # Unicode code points happen to lie within latin1,
+                # but are different in koi8-r, resulting to silent
+                # bogus results
+                result = pickle.loads(data, encoding='koi8-r')
+                assert_(result != original)
+            elif koi8r_validity == 'invalid':
+                # Unicode code points outside latin1, so results
+                # to an encoding exception
+                assert_raises(
+                    ValueError, pickle.loads, data, encoding='koi8-r'
+                )
+            else:
+                raise ValueError(koi8r_validity)
+
+    def test_structured_type_to_object(self):
+        a_rec = np.array([(0, 1), (3, 2)], dtype='i4,i8')
+        a_obj = np.empty((2,), dtype=object)
+        a_obj[0] = (0, 1)
+        a_obj[1] = (3, 2)
+        # astype records -> object
+        assert_equal(a_rec.astype(object), a_obj)
+        # '=' records -> object
+        b = np.empty_like(a_obj)
+        b[...] = a_rec
+        assert_equal(b, a_obj)
+        # '=' object -> records
+        b = np.empty_like(a_rec)
+        b[...] = a_obj
+        assert_equal(b, a_rec)
+
+    def test_assign_obj_listoflists(self):
+        # Ticket # 1870
+        # The inner list should get assigned to the object elements
+        a = np.zeros(4, dtype=object)
+        b = a.copy()
+        a[0] = [1]
+        a[1] = [2]
+        a[2] = [3]
+        a[3] = [4]
+        b[...] = [[1], [2], [3], [4]]
+        assert_equal(a, b)
+        # The first dimension should get broadcast
+        a = np.zeros((2, 2), dtype=object)
+        a[...] = [[1, 2]]
+        assert_equal(a, [[1, 2], [1, 2]])
+
+    @pytest.mark.slow_pypy
+    def test_memoryleak(self):
+        # Ticket #1917 - ensure that array data doesn't leak
+        for i in range(1000):
+            # 100MB times 1000 would give 100GB of memory usage if it leaks
+            a = np.empty((100000000,), dtype='i1')
+            del a
+
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test_ufunc_reduce_memoryleak(self):
+        a = np.arange(6)
+        acnt = sys.getrefcount(a)
+        np.add.reduce(a)
+        assert_equal(sys.getrefcount(a), acnt)
+
+    def test_search_sorted_invalid_arguments(self):
+        # Ticket #2021, should not segfault.
+        x = np.arange(0, 4, dtype='datetime64[D]')
+        assert_raises(TypeError, x.searchsorted, 1)
+
+    def test_string_truncation(self):
+        # Ticket #1990 - Data can be truncated in creation of an array from a
+        # mixed sequence of numeric values and strings (gh-2583)
+        for val in [True, 1234, 123.4, complex(1, 234)]:
+            for tostr, dtype in [(asunicode, "U"), (asbytes, "S")]:
+                b = np.array([val, tostr('xx')], dtype=dtype)
+                assert_equal(tostr(b[0]), tostr(val))
+                b = np.array([tostr('xx'), val], dtype=dtype)
+                assert_equal(tostr(b[1]), tostr(val))
+
+                # test also with longer strings
+                b = np.array([val, tostr('xxxxxxxxxx')], dtype=dtype)
+                assert_equal(tostr(b[0]), tostr(val))
+                b = np.array([tostr('xxxxxxxxxx'), val], dtype=dtype)
+                assert_equal(tostr(b[1]), tostr(val))
+
+    def test_string_truncation_ucs2(self):
+        # Ticket #2081. Python compiled with two byte unicode
+        # can lead to truncation if itemsize is not properly
+        # adjusted for NumPy's four byte unicode.
+        a = np.array(['abcd'])
+        assert_equal(a.dtype.itemsize, 16)
+
+    def test_unique_stable(self):
+        # Ticket #2063 must always choose stable sort for argsort to
+        # get consistent results
+        v = np.array(([0] * 5 + [1] * 6 + [2] * 6) * 4)
+        res = np.unique(v, return_index=True)
+        tgt = (np.array([0, 1, 2]), np.array([0, 5, 11]))
+        assert_equal(res, tgt)
+
+    def test_unicode_alloc_dealloc_match(self):
+        # Ticket #1578, the mismatch only showed up when running
+        # python-debug for python versions >= 2.7, and then as
+        # a core dump and error message.
+        a = np.array(['abc'], dtype=np.str_)[0]
+        del a
+
+    def test_refcount_error_in_clip(self):
+        # Ticket #1588
+        a = np.zeros((2,), dtype='>i2').clip(min=0)
+        x = a + a
+        # This used to segfault:
+        y = str(x)
+        # Check the final string:
+        assert_(y == "[0 0]")
+
+    def test_searchsorted_wrong_dtype(self):
+        # Ticket #2189, it used to segfault, so we check that it raises the
+        # proper exception.
+        a = np.array([('a', 1)], dtype='S1, int')
+        assert_raises(TypeError, np.searchsorted, a, 1.2)
+        # Ticket #2066, similar problem:
+        dtype = np.rec.format_parser(['i4', 'i4'], [], [])
+        a = np.recarray((2,), dtype)
+        a[...] = [(1, 2), (3, 4)]
+        assert_raises(TypeError, np.searchsorted, a, 1)
+
+    def test_complex64_alignment(self):
+        # Issue gh-2668 (trac 2076), segfault on sparc due to misalignment
+        dtt = np.complex64
+        arr = np.arange(10, dtype=dtt)
+        # 2D array
+        arr2 = np.reshape(arr, (2, 5))
+        # Fortran write followed by (C or F) read caused bus error
+        data_str = arr2.tobytes('F')
+        data_back = np.ndarray(arr2.shape,
+                              arr2.dtype,
+                              buffer=data_str,
+                              order='F')
+        assert_array_equal(arr2, data_back)
+
+    def test_structured_count_nonzero(self):
+        arr = np.array([0, 1]).astype('i4, 2i4')[:1]
+        count = np.count_nonzero(arr)
+        assert_equal(count, 0)
+
+    def test_copymodule_preserves_f_contiguity(self):
+        a = np.empty((2, 2), order='F')
+        b = copy.copy(a)
+        c = copy.deepcopy(a)
+        assert_(b.flags.fortran)
+        assert_(b.flags.f_contiguous)
+        assert_(c.flags.fortran)
+        assert_(c.flags.f_contiguous)
+
+    def test_fortran_order_buffer(self):
+        import numpy as np
+        a = np.array([['Hello', 'Foob']], dtype='U5', order='F')
+        arr = np.ndarray(shape=[1, 2, 5], dtype='U1', buffer=a)
+        arr2 = np.array([[['H', 'e', 'l', 'l', 'o'],
+                          ['F', 'o', 'o', 'b', '']]])
+        assert_array_equal(arr, arr2)
+
+    def test_assign_from_sequence_error(self):
+        # Ticket #4024.
+        arr = np.array([1, 2, 3])
+        assert_raises(ValueError, arr.__setitem__, slice(None), [9, 9])
+        arr.__setitem__(slice(None), [9])
+        assert_equal(arr, [9, 9, 9])
+
+    def test_format_on_flex_array_element(self):
+        # Ticket #4369.
+        dt = np.dtype([('date', '<M8[D]'), ('val', '<f8')])
+        arr = np.array([('2000-01-01', 1)], dt)
+        formatted = f'{arr[0]}'
+        assert_equal(formatted, str(arr[0]))
+
+    def test_deepcopy_on_0d_array(self):
+        # Ticket #3311.
+        arr = np.array(3)
+        arr_cp = copy.deepcopy(arr)
+
+        assert_equal(arr, arr_cp)
+        assert_equal(arr.shape, arr_cp.shape)
+        assert_equal(int(arr), int(arr_cp))
+        assert_(arr is not arr_cp)
+        assert_(isinstance(arr_cp, type(arr)))
+
+    def test_deepcopy_F_order_object_array(self):
+        # Ticket #6456.
+        a = {'a': 1}
+        b = {'b': 2}
+        arr = np.array([[a, b], [a, b]], order='F')
+        arr_cp = copy.deepcopy(arr)
+
+        assert_equal(arr, arr_cp)
+        assert_(arr is not arr_cp)
+        # Ensure that we have actually copied the item.
+        assert_(arr[0, 1] is not arr_cp[1, 1])
+        # Ensure we are allowed to have references to the same object.
+        assert_(arr[0, 1] is arr[1, 1])
+        # Check the references hold for the copied objects.
+        assert_(arr_cp[0, 1] is arr_cp[1, 1])
+
+    def test_deepcopy_empty_object_array(self):
+        # Ticket #8536.
+        # Deepcopy should succeed
+        a = np.array([], dtype=object)
+        b = copy.deepcopy(a)
+        assert_(a.shape == b.shape)
+
+    def test_bool_subscript_crash(self):
+        # gh-4494
+        c = np.rec.array([(1, 2, 3), (4, 5, 6)])
+        masked = c[np.array([True, False])]
+        base = masked.base
+        del masked, c
+        base.dtype
+
+    def test_richcompare_crash(self):
+        # gh-4613
+        import operator as op
+
+        # dummy class where __array__ throws exception
+        class Foo:
+            __array_priority__ = 1002
+
+            def __array__(self, *args, **kwargs):
+                raise Exception
+
+        rhs = Foo()
+        lhs = np.array(1)
+        for f in [op.lt, op.le, op.gt, op.ge]:
+            assert_raises(TypeError, f, lhs, rhs)
+        assert_(not op.eq(lhs, rhs))
+        assert_(op.ne(lhs, rhs))
+
+    def test_richcompare_scalar_and_subclass(self):
+        # gh-4709
+        class Foo(np.ndarray):
+            def __eq__(self, other):
+                return "OK"
+
+        x = np.array([1, 2, 3]).view(Foo)
+        assert_equal(10 == x, "OK")
+        assert_equal(np.int32(10) == x, "OK")
+        assert_equal(np.array([10]) == x, "OK")
+
+    def test_pickle_empty_string(self):
+        # gh-3926
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            test_string = np.bytes_('')
+            assert_equal(pickle.loads(
+                pickle.dumps(test_string, protocol=proto)), test_string)
+
+    def test_frompyfunc_many_args(self):
+        # gh-5672
+
+        def passer(*args):
+            pass
+
+        assert_raises(ValueError, np.frompyfunc, passer, 64, 1)
+
+    def test_repeat_broadcasting(self):
+        # gh-5743
+        a = np.arange(60).reshape(3, 4, 5)
+        for axis in chain(range(-a.ndim, a.ndim), [None]):
+            assert_equal(a.repeat(2, axis=axis), a.repeat([2], axis=axis))
+
+    def test_frompyfunc_nout_0(self):
+        # gh-2014
+
+        def f(x):
+            x[0], x[-1] = x[-1], x[0]
+
+        uf = np.frompyfunc(f, 1, 0)
+        a = np.array([[1, 2, 3], [4, 5], [6, 7, 8, 9]], dtype=object)
+        assert_equal(uf(a), ())
+        expected = np.array([[3, 2, 1], [5, 4], [9, 7, 8, 6]], dtype=object)
+        assert_array_equal(a, expected)
+
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test_leak_in_structured_dtype_comparison(self):
+        # gh-6250
+        recordtype = np.dtype([('a', np.float64),
+                               ('b', np.int32),
+                               ('d', (str, 5))])
+
+        # Simple case
+        a = np.zeros(2, dtype=recordtype)
+        for i in range(100):
+            a == a
+        assert_(sys.getrefcount(a) < 10)
+
+        # The case in the bug report.
+        before = sys.getrefcount(a)
+        u, v = a[0], a[1]
+        u == v
+        del u, v
+        gc.collect()
+        after = sys.getrefcount(a)
+        assert_equal(before, after)
+
+    def test_empty_percentile(self):
+        # gh-6530 / gh-6553
+        assert_array_equal(np.percentile(np.arange(10), []), np.array([]))
+
+    def test_void_compare_segfault(self):
+        # gh-6922. The following should not segfault
+        a = np.ones(3, dtype=[('object', 'O'), ('int', '<i2')])
+        a.sort()
+
+    def test_reshape_size_overflow(self):
+        # gh-7455
+        a = np.ones(20)[::2]
+        if IS_64BIT:
+            # 64 bit. The following are the prime factors of 2**63 + 5,
+            # plus a leading 2, so when multiplied together as int64,
+            # the result overflows to a total size of 10.
+            new_shape = (2, 13, 419, 691, 823, 2977518503)
+        else:
+            # 32 bit. The following are the prime factors of 2**31 + 5,
+            # plus a leading 2, so when multiplied together as int32,
+            # the result overflows to a total size of 10.
+            new_shape = (2, 7, 7, 43826197)
+        assert_raises(ValueError, a.reshape, new_shape)
+
+    @pytest.mark.skipif(IS_PYPY and sys.implementation.version <= (7, 3, 8),
+            reason="PyPy bug in error formatting")
+    def test_invalid_structured_dtypes(self):
+        # gh-2865
+        # mapping python objects to other dtypes
+        assert_raises(ValueError, np.dtype, ('O', [('name', 'i8')]))
+        assert_raises(ValueError, np.dtype, ('i8', [('name', 'O')]))
+        assert_raises(ValueError, np.dtype,
+                      ('i8', [('name', [('name', 'O')])]))
+        assert_raises(ValueError, np.dtype, ([('a', 'i4'), ('b', 'i4')], 'O'))
+        assert_raises(ValueError, np.dtype, ('i8', 'O'))
+        # wrong number/type of tuple elements in dict
+        assert_raises(ValueError, np.dtype,
+                      ('i', {'name': ('i', 0, 'title', 'oops')}))
+        assert_raises(ValueError, np.dtype,
+                      ('i', {'name': ('i', 'wrongtype', 'title')}))
+        # disallowed as of 1.13
+        assert_raises(ValueError, np.dtype,
+                      ([('a', 'O'), ('b', 'O')], [('c', 'O'), ('d', 'O')]))
+        # allowed as a special case due to existing use, see gh-2798
+        a = np.ones(1, dtype=('O', [('name', 'O')]))
+        assert_equal(a[0], 1)
+        # In particular, the above union dtype (and union dtypes in general)
+        # should mainly behave like the main (object) dtype:
+        assert a[0] is a.item()
+        assert type(a[0]) is int
+
+    def test_correct_hash_dict(self):
+        # gh-8887 - __hash__ would be None despite tp_hash being set
+        all_types = set(np._core.sctypeDict.values()) - {np.void}
+        for t in all_types:
+            val = t()
+
+            try:
+                hash(val)
+            except TypeError:
+                assert_(t.__hash__ is None)
+            except ValueError:
+                assert_(t is np.timedelta64)
+                assert_(t.__hash__ is not None)
+            else:
+                assert_(t.__hash__ is not None)
+
+    def test_scalar_copy(self):
+        scalar_types = set(np._core.sctypeDict.values())
+        values = {
+            np.void: b"a",
+            np.bytes_: b"a",
+            np.str_: "a",
+            np.datetime64: "2017-08-25",
+        }
+        for sctype in scalar_types:
+            item = sctype(values.get(sctype, 1))
+            item2 = copy.copy(item)
+            assert_equal(item, item2)
+
+    def test_void_item_memview(self):
+        va = np.zeros(10, 'V4')
+        x = va[:1].item()
+        va[0] = b'\xff\xff\xff\xff'
+        del va
+        assert_equal(x, b'\x00\x00\x00\x00')
+
+    def test_void_getitem(self):
+        # Test fix for gh-11668.
+        assert_(np.array([b'a'], 'V1').astype('O') == b'a')
+        assert_(np.array([b'ab'], 'V2').astype('O') == b'ab')
+        assert_(np.array([b'abc'], 'V3').astype('O') == b'abc')
+        assert_(np.array([b'abcd'], 'V4').astype('O') == b'abcd')
+
+    def test_structarray_title(self):
+        # The following used to segfault on pypy, due to NPY_TITLE_KEY
+        # not working properly and resulting to double-decref of the
+        # structured array field items:
+        # See: https://bitbucket.org/pypy/pypy/issues/2789
+        for j in range(5):
+            structure = np.array([1], dtype=[(('x', 'X'), np.object_)])
+            structure[0]['x'] = np.array([2])
+            gc.collect()
+
+    def test_dtype_scalar_squeeze(self):
+        # gh-11384
+        values = {
+            'S': b"a",
+            'M': "2018-06-20",
+        }
+        for ch in np.typecodes['All']:
+            if ch in 'O':
+                continue
+            sctype = np.dtype(ch).type
+            scvalue = sctype(values.get(ch, 3))
+            for axis in [None, ()]:
+                squeezed = scvalue.squeeze(axis=axis)
+                assert_equal(squeezed, scvalue)
+                assert_equal(type(squeezed), type(scvalue))
+
+    def test_field_access_by_title(self):
+        # gh-11507
+        s = 'Some long field name'
+        if HAS_REFCOUNT:
+            base = sys.getrefcount(s)
+        t = np.dtype([((s, 'f1'), np.float64)])
+        data = np.zeros(10, t)
+        for i in range(10):
+            str(data[['f1']])
+            if HAS_REFCOUNT:
+                assert_(base <= sys.getrefcount(s))
+
+    @pytest.mark.parametrize('val', [
+        # arrays and scalars
+        np.ones((10, 10), dtype='int32'),
+        np.uint64(10),
+        ])
+    @pytest.mark.parametrize('protocol',
+        range(2, pickle.HIGHEST_PROTOCOL + 1)
+        )
+    def test_pickle_module(self, protocol, val):
+        # gh-12837
+        s = pickle.dumps(val, protocol)
+        assert b'_multiarray_umath' not in s
+        if protocol == 5 and len(val.shape) > 0:
+            # unpickling ndarray goes through _frombuffer for protocol 5
+            assert b'numpy._core.numeric' in s
+        else:
+            assert b'numpy._core.multiarray' in s
+
+    def test_object_casting_errors(self):
+        # gh-11993 update to ValueError (see gh-16909), since strings can in
+        # principle be converted to complex, but this string cannot.
+        arr = np.array(['AAAAA', 18465886.0, 18465886.0], dtype=object)
+        assert_raises(ValueError, arr.astype, 'c8')
+
+    def test_eff1d_casting(self):
+        # gh-12711
+        x = np.array([1, 2, 4, 7, 0], dtype=np.int16)
+        res = np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))
+        assert_equal(res, [-99, 1, 2, 3, -7, 88, 99])
+
+        # The use of safe casting means, that 1<<20 is cast unsafely, an
+        # error may be better, but currently there is no mechanism for it.
+        res = np.ediff1d(x, to_begin=(1 << 20), to_end=(1 << 20))
+        assert_equal(res, [0, 1, 2, 3, -7, 0])
+
+    def test_pickle_datetime64_array(self):
+        # gh-12745 (would fail with pickle5 installed)
+        d = np.datetime64('2015-07-04 12:59:59.50', 'ns')
+        arr = np.array([d])
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            dumped = pickle.dumps(arr, protocol=proto)
+            assert_equal(pickle.loads(dumped), arr)
+
+    def test_bad_array_interface(self):
+        class T:
+            __array_interface__ = {}
+
+        with assert_raises(ValueError):
+            np.array([T()])
+
+    def test_2d__array__shape(self):
+        class T:
+            def __array__(self, dtype=None, copy=None):
+                return np.ndarray(shape=(0, 0))
+
+            # Make sure __array__ is used instead of Sequence methods.
+            def __iter__(self):
+                return iter([])
+
+            def __getitem__(self, idx):
+                raise AssertionError("__getitem__ was called")
+
+            def __len__(self):
+                return 0
+
+        t = T()
+        # gh-13659, would raise in broadcasting [x=t for x in result]
+        arr = np.array([t])
+        assert arr.shape == (1, 0, 0)
+
+    @pytest.mark.skipif(sys.maxsize < 2 ** 31 + 1, reason='overflows 32-bit python')
+    def test_to_ctypes(self):
+        # gh-14214
+        arr = np.zeros((2 ** 31 + 1,), 'b')
+        assert arr.size * arr.itemsize > 2 ** 31
+        c_arr = np.ctypeslib.as_ctypes(arr)
+        assert_equal(c_arr._length_, arr.size)
+
+    def test_complex_conversion_error(self):
+        # gh-17068
+        with pytest.raises(TypeError, match=r"Unable to convert dtype.*"):
+            complex(np.array("now", np.datetime64))
+
+    def test__array_interface__descr(self):
+        # gh-17068
+        dt = np.dtype({'names': ['a', 'b'],
+                           'offsets': [0, 0],
+                           'formats': [np.int64, np.int64]})
+        descr = np.array((1, 1), dtype=dt).__array_interface__['descr']
+        assert descr == [('', '|V8')]  # instead of [(b'', '|V8')]
+
+    @pytest.mark.skipif(sys.maxsize < 2 ** 31 + 1, reason='overflows 32-bit python')
+    @requires_memory(free_bytes=9e9)
+    def test_dot_big_stride(self):
+        # gh-17111
+        # blas stride = stride//itemsize > int32 max
+        int32_max = np.iinfo(np.int32).max
+        n = int32_max + 3
+        a = np.empty([n], dtype=np.float32)
+        b = a[::n - 1]
+        b[...] = 1
+        assert b.strides[0] > int32_max * b.dtype.itemsize
+        assert np.dot(b, b) == 2.0
+
+    def test_frompyfunc_name(self):
+        # name conversion was failing for python 3 strings
+        # resulting in the default '?' name. Also test utf-8
+        # encoding using non-ascii name.
+        def cassé(x):
+            return x
+
+        f = np.frompyfunc(cassé, 1, 1)
+        assert str(f) == "<ufunc 'cassé (vectorized)'>"
+
+    @pytest.mark.parametrize("operation", [
+        'add', 'subtract', 'multiply', 'floor_divide',
+        'conjugate', 'fmod', 'square', 'reciprocal',
+        'power', 'absolute', 'negative', 'positive',
+        'greater', 'greater_equal', 'less',
+        'less_equal', 'equal', 'not_equal', 'logical_and',
+        'logical_not', 'logical_or', 'bitwise_and', 'bitwise_or',
+        'bitwise_xor', 'invert', 'left_shift', 'right_shift',
+        'gcd', 'lcm'
+        ]
+    )
+    @pytest.mark.parametrize("order", [
+        ('b->', 'B->'),
+        ('h->', 'H->'),
+        ('i->', 'I->'),
+        ('l->', 'L->'),
+        ('q->', 'Q->'),
+        ]
+    )
+    def test_ufunc_order(self, operation, order):
+        # gh-18075
+        # Ensure signed types before unsigned
+        def get_idx(string, str_lst):
+            for i, s in enumerate(str_lst):
+                if string in s:
+                    return i
+            raise ValueError(f"{string} not in list")
+        types = getattr(np, operation).types
+        assert get_idx(order[0], types) < get_idx(order[1], types), (
+                f"Unexpected types order of ufunc in {operation}"
+                f"for {order}. Possible fix: Use signed before unsigned"
+                "in generate_umath.py")
+
+    def test_nonbool_logical(self):
+        # gh-22845
+        # create two arrays with bit patterns that do not overlap.
+        # needs to be large enough to test both SIMD and scalar paths
+        size = 100
+        a = np.frombuffer(b'\x01' * size, dtype=np.bool)
+        b = np.frombuffer(b'\x80' * size, dtype=np.bool)
+        expected = np.ones(size, dtype=np.bool)
+        assert_array_equal(np.logical_and(a, b), expected)
+
+    @pytest.mark.skipif(IS_PYPY, reason="PyPy issue 2742")
+    def test_gh_23737(self):
+        with pytest.raises(TypeError, match="not an acceptable base type"):
+            class Y(np.flexible):
+                pass
+
+        with pytest.raises(TypeError, match="not an acceptable base type"):
+            class X(np.flexible, np.ma.core.MaskedArray):
+                pass
+
+    def test_load_ufunc_pickle(self):
+        # ufuncs are pickled with a semi-private path in
+        # numpy.core._multiarray_umath and must be loadable without warning
+        # despite np.core being deprecated.
+        test_data = b'\x80\x04\x95(\x00\x00\x00\x00\x00\x00\x00\x8c\x1cnumpy.core._multiarray_umath\x94\x8c\x03add\x94\x93\x94.'
+        result = pickle.loads(test_data, encoding='bytes')
+        assert result is np.add
+
+    def test__array_namespace__(self):
+        arr = np.arange(2)
+
+        xp = arr.__array_namespace__()
+        assert xp is np
+        xp = arr.__array_namespace__(api_version="2021.12")
+        assert xp is np
+        xp = arr.__array_namespace__(api_version="2022.12")
+        assert xp is np
+        xp = arr.__array_namespace__(api_version="2023.12")
+        assert xp is np
+        xp = arr.__array_namespace__(api_version="2024.12")
+        assert xp is np
+        xp = arr.__array_namespace__(api_version=None)
+        assert xp is np
+
+        with pytest.raises(
+            ValueError,
+            match="Version \"2025.12\" of the Array API Standard "
+                  "is not supported."
+        ):
+            arr.__array_namespace__(api_version="2025.12")
+
+        with pytest.raises(
+            ValueError,
+            match="Only None and strings are allowed as the Array API version"
+        ):
+            arr.__array_namespace__(api_version=2024)
+
+    def test_isin_refcnt_bug(self):
+        # gh-25295
+        for _ in range(1000):
+            np.isclose(np.int64(2), np.int64(2), atol=1e-15, rtol=1e-300)
+
+    def test_replace_regression(self):
+        # gh-25513 segfault
+        carr = np.char.chararray((2,), itemsize=25)
+        test_strings = [b'  4.52173913043478315E+00',
+                        b'  4.95652173913043548E+00']
+        carr[:] = test_strings
+        out = carr.replace(b"E", b"D")
+        expected = np.char.chararray((2,), itemsize=25)
+        expected[:] = [s.replace(b"E", b"D") for s in test_strings]
+        assert_array_equal(out, expected)
+
+    def test_logspace_base_does_not_determine_dtype(self):
+        # gh-24957 and cupy/cupy/issues/7946
+        start = np.array([0, 2], dtype=np.float16)
+        stop = np.array([2, 0], dtype=np.float16)
+        out = np.logspace(start, stop, num=5, axis=1, dtype=np.float32)
+        expected = np.array([[1., 3.1621094, 10., 31.625, 100.],
+                             [100., 31.625, 10., 3.1621094, 1.]],
+                            dtype=np.float32)
+        assert_almost_equal(out, expected)
+        # Check test fails if the calculation is done in float64, as happened
+        # before when a python float base incorrectly influenced the dtype.
+        out2 = np.logspace(start, stop, num=5, axis=1, dtype=np.float32,
+                           base=np.array([10.0]))
+        with pytest.raises(AssertionError, match="not almost equal"):
+            assert_almost_equal(out2, expected)
+
+    def test_vectorize_fixed_width_string(self):
+        arr = np.array(["SOme wOrd DŽ ß ᾛ ΣΣ ffi⁵Å Ç Ⅰ"]).astype(np.str_)
+        f = str.casefold
+        res = np.vectorize(f, otypes=[arr.dtype])(arr)
+        assert res.dtype == "U30"
+
+    def test_repeated_square_consistency(self):
+        # gh-26940
+        buf = np.array([-5.171866611150749e-07 + 2.5618634555957426e-07j,
+                        0, 0, 0, 0, 0])
+        # Test buffer with regular and reverse strides
+        for in_vec in [buf[:3], buf[:3][::-1]]:
+            expected_res = np.square(in_vec)
+            # Output vector immediately follows input vector
+            # to reproduce off-by-one in nomemoverlap check.
+            for res in [buf[3:], buf[3:][::-1]]:
+                res = buf[3:]
+                np.square(in_vec, out=res)
+                assert_equal(res, expected_res)
+
+    def test_sort_unique_crash(self):
+        # gh-27037
+        for _ in range(4):
+            vals = np.linspace(0, 1, num=128)
+            data = np.broadcast_to(vals, (128, 128, 128))
+            data = data.transpose(0, 2, 1).copy()
+            np.unique(data)
+
+    def test_sort_overlap(self):
+        # gh-27273
+        size = 100
+        inp = np.linspace(0, size, num=size, dtype=np.intc)
+        out = np.sort(inp)
+        assert_equal(inp, out)
+
+    def test_searchsorted_structured(self):
+        # gh-28190
+        x = np.array([(0, 1.)], dtype=[('time', '<i8'), ('value', '<f8')])
+        y = np.array((0, 0.), dtype=[('time', '<i8'), ('value', '<f8')])
+        x.searchsorted(y)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalar_ctors.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalar_ctors.py
new file mode 100644
index 0000000..be3ef04
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalar_ctors.py
@@ -0,0 +1,207 @@
+"""
+Test the scalar constructors, which also do type-coercion
+"""
+import pytest
+
+import numpy as np
+from numpy.testing import (
+    assert_almost_equal,
+    assert_equal,
+    assert_warns,
+)
+
+
+class TestFromString:
+    def test_floating(self):
+        # Ticket #640, floats from string
+        fsingle = np.single('1.234')
+        fdouble = np.double('1.234')
+        flongdouble = np.longdouble('1.234')
+        assert_almost_equal(fsingle, 1.234)
+        assert_almost_equal(fdouble, 1.234)
+        assert_almost_equal(flongdouble, 1.234)
+
+    def test_floating_overflow(self):
+        """ Strings containing an unrepresentable float overflow """
+        fhalf = np.half('1e10000')
+        assert_equal(fhalf, np.inf)
+        fsingle = np.single('1e10000')
+        assert_equal(fsingle, np.inf)
+        fdouble = np.double('1e10000')
+        assert_equal(fdouble, np.inf)
+        flongdouble = assert_warns(RuntimeWarning, np.longdouble, '1e10000')
+        assert_equal(flongdouble, np.inf)
+
+        fhalf = np.half('-1e10000')
+        assert_equal(fhalf, -np.inf)
+        fsingle = np.single('-1e10000')
+        assert_equal(fsingle, -np.inf)
+        fdouble = np.double('-1e10000')
+        assert_equal(fdouble, -np.inf)
+        flongdouble = assert_warns(RuntimeWarning, np.longdouble, '-1e10000')
+        assert_equal(flongdouble, -np.inf)
+
+
+class TestExtraArgs:
+    def test_superclass(self):
+        # try both positional and keyword arguments
+        s = np.str_(b'\\x61', encoding='unicode-escape')
+        assert s == 'a'
+        s = np.str_(b'\\x61', 'unicode-escape')
+        assert s == 'a'
+
+        # previously this would return '\\xx'
+        with pytest.raises(UnicodeDecodeError):
+            np.str_(b'\\xx', encoding='unicode-escape')
+        with pytest.raises(UnicodeDecodeError):
+            np.str_(b'\\xx', 'unicode-escape')
+
+        # superclass fails, but numpy succeeds
+        assert np.bytes_(-2) == b'-2'
+
+    def test_datetime(self):
+        dt = np.datetime64('2000-01', ('M', 2))
+        assert np.datetime_data(dt) == ('M', 2)
+
+        with pytest.raises(TypeError):
+            np.datetime64('2000', garbage=True)
+
+    def test_bool(self):
+        with pytest.raises(TypeError):
+            np.bool(False, garbage=True)
+
+    def test_void(self):
+        with pytest.raises(TypeError):
+            np.void(b'test', garbage=True)
+
+
+class TestFromInt:
+    def test_intp(self):
+        # Ticket #99
+        assert_equal(1024, np.intp(1024))
+
+    def test_uint64_from_negative(self):
+        with pytest.raises(OverflowError):
+            np.uint64(-2)
+
+
+int_types = [np.byte, np.short, np.intc, np.long, np.longlong]
+uint_types = [np.ubyte, np.ushort, np.uintc, np.ulong, np.ulonglong]
+float_types = [np.half, np.single, np.double, np.longdouble]
+cfloat_types = [np.csingle, np.cdouble, np.clongdouble]
+
+
+class TestArrayFromScalar:
+    """ gh-15467 and gh-19125 """
+
+    def _do_test(self, t1, t2, arg=2):
+        if arg is None:
+            x = t1()
+        elif isinstance(arg, tuple):
+            if t1 is np.clongdouble:
+                pytest.xfail("creating a clongdouble from real and "
+                             "imaginary parts isn't supported")
+            x = t1(*arg)
+        else:
+            x = t1(arg)
+        arr = np.array(x, dtype=t2)
+        # type should be preserved exactly
+        if t2 is None:
+            assert arr.dtype.type is t1
+        else:
+            assert arr.dtype.type is t2
+
+    @pytest.mark.parametrize('t1', int_types + uint_types)
+    @pytest.mark.parametrize('t2', int_types + uint_types + [None])
+    def test_integers(self, t1, t2):
+        return self._do_test(t1, t2)
+
+    @pytest.mark.parametrize('t1', float_types)
+    @pytest.mark.parametrize('t2', float_types + [None])
+    def test_reals(self, t1, t2):
+        return self._do_test(t1, t2)
+
+    @pytest.mark.parametrize('t1', cfloat_types)
+    @pytest.mark.parametrize('t2', cfloat_types + [None])
+    @pytest.mark.parametrize('arg', [2, 1 + 3j, (1, 2), None])
+    def test_complex(self, t1, t2, arg):
+        self._do_test(t1, t2, arg)
+
+    @pytest.mark.parametrize('t', cfloat_types)
+    def test_complex_errors(self, t):
+        with pytest.raises(TypeError):
+            t(1j, 1j)
+        with pytest.raises(TypeError):
+            t(1, None)
+        with pytest.raises(TypeError):
+            t(None, 1)
+
+
+@pytest.mark.parametrize("length",
+        [5, np.int8(5), np.array(5, dtype=np.uint16)])
+def test_void_via_length(length):
+    res = np.void(length)
+    assert type(res) is np.void
+    assert res.item() == b"\0" * 5
+    assert res.dtype == "V5"
+
+@pytest.mark.parametrize("bytes_",
+        [b"spam", np.array(567.)])
+def test_void_from_byteslike(bytes_):
+    res = np.void(bytes_)
+    expected = bytes(bytes_)
+    assert type(res) is np.void
+    assert res.item() == expected
+
+    # Passing dtype can extend it (this is how filling works)
+    res = np.void(bytes_, dtype="V100")
+    assert type(res) is np.void
+    assert res.item()[:len(expected)] == expected
+    assert res.item()[len(expected):] == b"\0" * (res.nbytes - len(expected))
+    # As well as shorten:
+    res = np.void(bytes_, dtype="V4")
+    assert type(res) is np.void
+    assert res.item() == expected[:4]
+
+def test_void_arraylike_trumps_byteslike():
+    # The memoryview is converted as an array-like of shape (18,)
+    # rather than a single bytes-like of that length.
+    m = memoryview(b"just one mintleaf?")
+    res = np.void(m)
+    assert type(res) is np.ndarray
+    assert res.dtype == "V1"
+    assert res.shape == (18,)
+
+def test_void_dtype_arg():
+    # Basic test for the dtype argument (positional and keyword)
+    res = np.void((1, 2), dtype="i,i")
+    assert res.item() == (1, 2)
+    res = np.void((2, 3), "i,i")
+    assert res.item() == (2, 3)
+
+@pytest.mark.parametrize("data",
+        [5, np.int8(5), np.array(5, dtype=np.uint16)])
+def test_void_from_integer_with_dtype(data):
+    # The "length" meaning is ignored, rather data is used:
+    res = np.void(data, dtype="i,i")
+    assert type(res) is np.void
+    assert res.dtype == "i,i"
+    assert res["f0"] == 5 and res["f1"] == 5
+
+def test_void_from_structure():
+    dtype = np.dtype([('s', [('f', 'f8'), ('u', 'U1')]), ('i', 'i2')])
+    data = np.array(((1., 'a'), 2), dtype=dtype)
+    res = np.void(data[()], dtype=dtype)
+    assert type(res) is np.void
+    assert res.dtype == dtype
+    assert res == data[()]
+
+def test_void_bad_dtype():
+    with pytest.raises(TypeError,
+            match="void: descr must be a `void.*int64"):
+        np.void(4, dtype="i8")
+
+    # Subarray dtype (with shape `(4,)` is rejected):
+    with pytest.raises(TypeError,
+            match=r"void: descr must be a `void.*\(4,\)"):
+        np.void(4, dtype="4i")
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalar_methods.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalar_methods.py
new file mode 100644
index 0000000..2d508a0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalar_methods.py
@@ -0,0 +1,246 @@
+"""
+Test the scalar constructors, which also do type-coercion
+"""
+import fractions
+import platform
+import types
+from typing import Any
+
+import pytest
+
+import numpy as np
+from numpy._core import sctypes
+from numpy.testing import assert_equal, assert_raises
+
+
+class TestAsIntegerRatio:
+    # derived in part from the cpython test "test_floatasratio"
+
+    @pytest.mark.parametrize("ftype", [
+        np.half, np.single, np.double, np.longdouble])
+    @pytest.mark.parametrize("f, ratio", [
+        (0.875, (7, 8)),
+        (-0.875, (-7, 8)),
+        (0.0, (0, 1)),
+        (11.5, (23, 2)),
+        ])
+    def test_small(self, ftype, f, ratio):
+        assert_equal(ftype(f).as_integer_ratio(), ratio)
+
+    @pytest.mark.parametrize("ftype", [
+        np.half, np.single, np.double, np.longdouble])
+    def test_simple_fractions(self, ftype):
+        R = fractions.Fraction
+        assert_equal(R(0, 1),
+                     R(*ftype(0.0).as_integer_ratio()))
+        assert_equal(R(5, 2),
+                     R(*ftype(2.5).as_integer_ratio()))
+        assert_equal(R(1, 2),
+                     R(*ftype(0.5).as_integer_ratio()))
+        assert_equal(R(-2100, 1),
+                     R(*ftype(-2100.0).as_integer_ratio()))
+
+    @pytest.mark.parametrize("ftype", [
+        np.half, np.single, np.double, np.longdouble])
+    def test_errors(self, ftype):
+        assert_raises(OverflowError, ftype('inf').as_integer_ratio)
+        assert_raises(OverflowError, ftype('-inf').as_integer_ratio)
+        assert_raises(ValueError, ftype('nan').as_integer_ratio)
+
+    def test_against_known_values(self):
+        R = fractions.Fraction
+        assert_equal(R(1075, 512),
+                     R(*np.half(2.1).as_integer_ratio()))
+        assert_equal(R(-1075, 512),
+                     R(*np.half(-2.1).as_integer_ratio()))
+        assert_equal(R(4404019, 2097152),
+                     R(*np.single(2.1).as_integer_ratio()))
+        assert_equal(R(-4404019, 2097152),
+                     R(*np.single(-2.1).as_integer_ratio()))
+        assert_equal(R(4728779608739021, 2251799813685248),
+                     R(*np.double(2.1).as_integer_ratio()))
+        assert_equal(R(-4728779608739021, 2251799813685248),
+                     R(*np.double(-2.1).as_integer_ratio()))
+        # longdouble is platform dependent
+
+    @pytest.mark.parametrize("ftype, frac_vals, exp_vals", [
+        # dtype test cases generated using hypothesis
+        # first five generated cases per dtype
+        (np.half, [0.0, 0.01154830649280303, 0.31082276347447274,
+                   0.527350517124794, 0.8308562335072596],
+                  [0, 1, 0, -8, 12]),
+        (np.single, [0.0, 0.09248576989263226, 0.8160498218131407,
+                     0.17389442853722373, 0.7956044195067877],
+                    [0, 12, 10, 17, -26]),
+        (np.double, [0.0, 0.031066908499895136, 0.5214135908877832,
+                     0.45780736035689296, 0.5906586745934036],
+                    [0, -801, 51, 194, -653]),
+        pytest.param(
+            np.longdouble,
+            [0.0, 0.20492557202724854, 0.4277180662199366, 0.9888085019891495,
+             0.9620175814461964],
+            [0, -7400, 14266, -7822, -8721],
+            marks=[
+                pytest.mark.skipif(
+                    np.finfo(np.double) == np.finfo(np.longdouble),
+                    reason="long double is same as double"),
+                pytest.mark.skipif(
+                    platform.machine().startswith("ppc"),
+                    reason="IBM double double"),
+            ]
+        )
+    ])
+    def test_roundtrip(self, ftype, frac_vals, exp_vals):
+        for frac, exp in zip(frac_vals, exp_vals):
+            f = np.ldexp(ftype(frac), exp)
+            assert f.dtype == ftype
+            n, d = f.as_integer_ratio()
+
+            try:
+                nf = np.longdouble(n)
+                df = np.longdouble(d)
+                if not np.isfinite(df):
+                    raise OverflowError
+            except (OverflowError, RuntimeWarning):
+                # the values may not fit in any float type
+                pytest.skip("longdouble too small on this platform")
+
+            assert_equal(nf / df, f, f"{n}/{d}")
+
+
+class TestIsInteger:
+    @pytest.mark.parametrize("str_value", ["inf", "nan"])
+    @pytest.mark.parametrize("code", np.typecodes["Float"])
+    def test_special(self, code: str, str_value: str) -> None:
+        cls = np.dtype(code).type
+        value = cls(str_value)
+        assert not value.is_integer()
+
+    @pytest.mark.parametrize(
+        "code", np.typecodes["Float"] + np.typecodes["AllInteger"]
+    )
+    def test_true(self, code: str) -> None:
+        float_array = np.arange(-5, 5).astype(code)
+        for value in float_array:
+            assert value.is_integer()
+
+    @pytest.mark.parametrize("code", np.typecodes["Float"])
+    def test_false(self, code: str) -> None:
+        float_array = np.arange(-5, 5).astype(code)
+        float_array *= 1.1
+        for value in float_array:
+            if value == 0:
+                continue
+            assert not value.is_integer()
+
+
+class TestClassGetItem:
+    @pytest.mark.parametrize("cls", [
+        np.number,
+        np.integer,
+        np.inexact,
+        np.unsignedinteger,
+        np.signedinteger,
+        np.floating,
+    ])
+    def test_abc(self, cls: type[np.number]) -> None:
+        alias = cls[Any]
+        assert isinstance(alias, types.GenericAlias)
+        assert alias.__origin__ is cls
+
+    def test_abc_complexfloating(self) -> None:
+        alias = np.complexfloating[Any, Any]
+        assert isinstance(alias, types.GenericAlias)
+        assert alias.__origin__ is np.complexfloating
+
+    @pytest.mark.parametrize("arg_len", range(4))
+    def test_abc_complexfloating_subscript_tuple(self, arg_len: int) -> None:
+        arg_tup = (Any,) * arg_len
+        if arg_len in (1, 2):
+            assert np.complexfloating[arg_tup]
+        else:
+            match = f"Too {'few' if arg_len == 0 else 'many'} arguments"
+            with pytest.raises(TypeError, match=match):
+                np.complexfloating[arg_tup]
+
+    @pytest.mark.parametrize("cls", [np.generic, np.flexible, np.character])
+    def test_abc_non_numeric(self, cls: type[np.generic]) -> None:
+        with pytest.raises(TypeError):
+            cls[Any]
+
+    @pytest.mark.parametrize("code", np.typecodes["All"])
+    def test_concrete(self, code: str) -> None:
+        cls = np.dtype(code).type
+        with pytest.raises(TypeError):
+            cls[Any]
+
+    @pytest.mark.parametrize("arg_len", range(4))
+    def test_subscript_tuple(self, arg_len: int) -> None:
+        arg_tup = (Any,) * arg_len
+        if arg_len == 1:
+            assert np.number[arg_tup]
+        else:
+            with pytest.raises(TypeError):
+                np.number[arg_tup]
+
+    def test_subscript_scalar(self) -> None:
+        assert np.number[Any]
+
+
+class TestBitCount:
+    # derived in part from the cpython test "test_bit_count"
+
+    @pytest.mark.parametrize("itype", sctypes['int'] + sctypes['uint'])
+    def test_small(self, itype):
+        for a in range(max(np.iinfo(itype).min, 0), 128):
+            msg = f"Smoke test for {itype}({a}).bit_count()"
+            assert itype(a).bit_count() == a.bit_count(), msg
+
+    def test_bit_count(self):
+        for exp in [10, 17, 63]:
+            a = 2**exp
+            assert np.uint64(a).bit_count() == 1
+            assert np.uint64(a - 1).bit_count() == exp
+            assert np.uint64(a ^ 63).bit_count() == 7
+            assert np.uint64((a - 1) ^ 510).bit_count() == exp - 8
+
+
+class TestDevice:
+    """
+    Test scalar.device attribute and scalar.to_device() method.
+    """
+    scalars = [np.bool(True), np.int64(1), np.uint64(1), np.float64(1.0),
+               np.complex128(1 + 1j)]
+
+    @pytest.mark.parametrize("scalar", scalars)
+    def test_device(self, scalar):
+        assert scalar.device == "cpu"
+
+    @pytest.mark.parametrize("scalar", scalars)
+    def test_to_device(self, scalar):
+        assert scalar.to_device("cpu") is scalar
+
+    @pytest.mark.parametrize("scalar", scalars)
+    def test___array_namespace__(self, scalar):
+        assert scalar.__array_namespace__() is np
+
+
+@pytest.mark.parametrize("scalar", [np.bool(True), np.int8(1), np.float64(1)])
+def test_array_wrap(scalar):
+    # Test scalars array wrap as long as it exists.  NumPy itself should
+    # probably not use it, so it may not be necessary to keep it around.
+
+    arr0d = np.array(3, dtype=np.int8)
+    # Third argument not passed, None, or True "decays" to scalar.
+    # (I don't think NumPy would pass `None`, but it seems clear to support)
+    assert type(scalar.__array_wrap__(arr0d)) is np.int8
+    assert type(scalar.__array_wrap__(arr0d, None, None)) is np.int8
+    assert type(scalar.__array_wrap__(arr0d, None, True)) is np.int8
+
+    # Otherwise, result should be the input
+    assert scalar.__array_wrap__(arr0d, None, False) is arr0d
+
+    # An old bug.  A non 0-d array cannot be converted to scalar:
+    arr1d = np.array([3], dtype=np.int8)
+    assert scalar.__array_wrap__(arr1d) is arr1d
+    assert scalar.__array_wrap__(arr1d, None, True) is arr1d
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarbuffer.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarbuffer.py
new file mode 100644
index 0000000..4d6b5bd
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarbuffer.py
@@ -0,0 +1,153 @@
+"""
+Test scalar buffer interface adheres to PEP 3118
+"""
+import pytest
+from numpy._core._multiarray_tests import get_buffer_info
+from numpy._core._rational_tests import rational
+
+import numpy as np
+from numpy.testing import assert_, assert_equal, assert_raises
+
+# PEP3118 format strings for native (standard alignment and byteorder) types
+scalars_and_codes = [
+    (np.bool, '?'),
+    (np.byte, 'b'),
+    (np.short, 'h'),
+    (np.intc, 'i'),
+    (np.long, 'l'),
+    (np.longlong, 'q'),
+    (np.ubyte, 'B'),
+    (np.ushort, 'H'),
+    (np.uintc, 'I'),
+    (np.ulong, 'L'),
+    (np.ulonglong, 'Q'),
+    (np.half, 'e'),
+    (np.single, 'f'),
+    (np.double, 'd'),
+    (np.longdouble, 'g'),
+    (np.csingle, 'Zf'),
+    (np.cdouble, 'Zd'),
+    (np.clongdouble, 'Zg'),
+]
+scalars_only, codes_only = zip(*scalars_and_codes)
+
+
+class TestScalarPEP3118:
+
+    @pytest.mark.parametrize('scalar', scalars_only, ids=codes_only)
+    def test_scalar_match_array(self, scalar):
+        x = scalar()
+        a = np.array([], dtype=np.dtype(scalar))
+        mv_x = memoryview(x)
+        mv_a = memoryview(a)
+        assert_equal(mv_x.format, mv_a.format)
+
+    @pytest.mark.parametrize('scalar', scalars_only, ids=codes_only)
+    def test_scalar_dim(self, scalar):
+        x = scalar()
+        mv_x = memoryview(x)
+        assert_equal(mv_x.itemsize, np.dtype(scalar).itemsize)
+        assert_equal(mv_x.ndim, 0)
+        assert_equal(mv_x.shape, ())
+        assert_equal(mv_x.strides, ())
+        assert_equal(mv_x.suboffsets, ())
+
+    @pytest.mark.parametrize('scalar, code', scalars_and_codes, ids=codes_only)
+    def test_scalar_code_and_properties(self, scalar, code):
+        x = scalar()
+        expected = {'strides': (), 'itemsize': x.dtype.itemsize, 'ndim': 0,
+                        'shape': (), 'format': code, 'readonly': True}
+
+        mv_x = memoryview(x)
+        assert self._as_dict(mv_x) == expected
+
+    @pytest.mark.parametrize('scalar', scalars_only, ids=codes_only)
+    def test_scalar_buffers_readonly(self, scalar):
+        x = scalar()
+        with pytest.raises(BufferError, match="scalar buffer is readonly"):
+            get_buffer_info(x, ["WRITABLE"])
+
+    def test_void_scalar_structured_data(self):
+        dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
+        x = np.array(('ndarray_scalar', (1.2, 3.0)), dtype=dt)[()]
+        assert_(isinstance(x, np.void))
+        mv_x = memoryview(x)
+        expected_size = 16 * np.dtype((np.str_, 1)).itemsize
+        expected_size += 2 * np.dtype(np.float64).itemsize
+        assert_equal(mv_x.itemsize, expected_size)
+        assert_equal(mv_x.ndim, 0)
+        assert_equal(mv_x.shape, ())
+        assert_equal(mv_x.strides, ())
+        assert_equal(mv_x.suboffsets, ())
+
+        # check scalar format string against ndarray format string
+        a = np.array([('Sarah', (8.0, 7.0)), ('John', (6.0, 7.0))], dtype=dt)
+        assert_(isinstance(a, np.ndarray))
+        mv_a = memoryview(a)
+        assert_equal(mv_x.itemsize, mv_a.itemsize)
+        assert_equal(mv_x.format, mv_a.format)
+
+        # Check that we do not allow writeable buffer export (technically
+        # we could allow it sometimes here...)
+        with pytest.raises(BufferError, match="scalar buffer is readonly"):
+            get_buffer_info(x, ["WRITABLE"])
+
+    def _as_dict(self, m):
+        return {'strides': m.strides, 'shape': m.shape, 'itemsize': m.itemsize,
+                    'ndim': m.ndim, 'format': m.format, 'readonly': m.readonly}
+
+    def test_datetime_memoryview(self):
+        # gh-11656
+        # Values verified with v1.13.3, shape is not () as in test_scalar_dim
+
+        dt1 = np.datetime64('2016-01-01')
+        dt2 = np.datetime64('2017-01-01')
+        expected = {'strides': (1,), 'itemsize': 1, 'ndim': 1, 'shape': (8,),
+                        'format': 'B', 'readonly': True}
+        v = memoryview(dt1)
+        assert self._as_dict(v) == expected
+
+        v = memoryview(dt2 - dt1)
+        assert self._as_dict(v) == expected
+
+        dt = np.dtype([('a', 'uint16'), ('b', 'M8[s]')])
+        a = np.empty(1, dt)
+        # Fails to create a PEP 3118 valid buffer
+        assert_raises((ValueError, BufferError), memoryview, a[0])
+
+        # Check that we do not allow writeable buffer export
+        with pytest.raises(BufferError, match="scalar buffer is readonly"):
+            get_buffer_info(dt1, ["WRITABLE"])
+
+    @pytest.mark.parametrize('s', [
+        pytest.param("\x32\x32", id="ascii"),
+        pytest.param("\uFE0F\uFE0F", id="basic multilingual"),
+        pytest.param("\U0001f4bb\U0001f4bb", id="non-BMP"),
+    ])
+    def test_str_ucs4(self, s):
+        s = np.str_(s)  # only our subclass implements the buffer protocol
+
+        # all the same, characters always encode as ucs4
+        expected = {'strides': (), 'itemsize': 8, 'ndim': 0, 'shape': (), 'format': '2w',
+                        'readonly': True}
+
+        v = memoryview(s)
+        assert self._as_dict(v) == expected
+
+        # integers of the paltform-appropriate endianness
+        code_points = np.frombuffer(v, dtype='i4')
+
+        assert_equal(code_points, [ord(c) for c in s])
+
+        # Check that we do not allow writeable buffer export
+        with pytest.raises(BufferError, match="scalar buffer is readonly"):
+            get_buffer_info(s, ["WRITABLE"])
+
+    def test_user_scalar_fails_buffer(self):
+        r = rational(1)
+        with assert_raises(TypeError):
+            memoryview(r)
+
+        # Check that we do not allow writeable buffer export
+        with pytest.raises(BufferError, match="scalar buffer is readonly"):
+            get_buffer_info(r, ["WRITABLE"])
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarinherit.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarinherit.py
new file mode 100644
index 0000000..746a157
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarinherit.py
@@ -0,0 +1,105 @@
+""" Test printing of scalar types.
+
+"""
+import pytest
+
+import numpy as np
+from numpy.testing import assert_, assert_raises
+
+
+class A:
+    pass
+class B(A, np.float64):
+    pass
+
+class C(B):
+    pass
+class D(C, B):
+    pass
+
+class B0(np.float64, A):
+    pass
+class C0(B0):
+    pass
+
+class HasNew:
+    def __new__(cls, *args, **kwargs):
+        return cls, args, kwargs
+
+class B1(np.float64, HasNew):
+    pass
+
+
+class TestInherit:
+    def test_init(self):
+        x = B(1.0)
+        assert_(str(x) == '1.0')
+        y = C(2.0)
+        assert_(str(y) == '2.0')
+        z = D(3.0)
+        assert_(str(z) == '3.0')
+
+    def test_init2(self):
+        x = B0(1.0)
+        assert_(str(x) == '1.0')
+        y = C0(2.0)
+        assert_(str(y) == '2.0')
+
+    def test_gh_15395(self):
+        # HasNew is the second base, so `np.float64` should have priority
+        x = B1(1.0)
+        assert_(str(x) == '1.0')
+
+        # previously caused RecursionError!?
+        with pytest.raises(TypeError):
+            B1(1.0, 2.0)
+
+    def test_int_repr(self):
+        # Test that integer repr works correctly for subclasses (gh-27106)
+        class my_int16(np.int16):
+            pass
+
+        s = repr(my_int16(3))
+        assert s == "my_int16(3)"
+
+class TestCharacter:
+    def test_char_radd(self):
+        # GH issue 9620, reached gentype_add and raise TypeError
+        np_s = np.bytes_('abc')
+        np_u = np.str_('abc')
+        s = b'def'
+        u = 'def'
+        assert_(np_s.__radd__(np_s) is NotImplemented)
+        assert_(np_s.__radd__(np_u) is NotImplemented)
+        assert_(np_s.__radd__(s) is NotImplemented)
+        assert_(np_s.__radd__(u) is NotImplemented)
+        assert_(np_u.__radd__(np_s) is NotImplemented)
+        assert_(np_u.__radd__(np_u) is NotImplemented)
+        assert_(np_u.__radd__(s) is NotImplemented)
+        assert_(np_u.__radd__(u) is NotImplemented)
+        assert_(s + np_s == b'defabc')
+        assert_(u + np_u == 'defabc')
+
+        class MyStr(str, np.generic):
+            # would segfault
+            pass
+
+        with assert_raises(TypeError):
+            # Previously worked, but gave completely wrong result
+            ret = s + MyStr('abc')
+
+        class MyBytes(bytes, np.generic):
+            # would segfault
+            pass
+
+        ret = s + MyBytes(b'abc')
+        assert type(ret) is type(s)
+        assert ret == b"defabc"
+
+    def test_char_repeat(self):
+        np_s = np.bytes_('abc')
+        np_u = np.str_('abc')
+        res_s = b'abc' * 5
+        res_u = 'abc' * 5
+        assert_(np_s * 5 == res_s)
+        assert_(np_u * 5 == res_u)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarmath.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarmath.py
new file mode 100644
index 0000000..fc37897
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarmath.py
@@ -0,0 +1,1176 @@
+import contextlib
+import itertools
+import operator
+import platform
+import sys
+import warnings
+
+import pytest
+from hypothesis import given, settings
+from hypothesis.extra import numpy as hynp
+from hypothesis.strategies import sampled_from
+from numpy._core._rational_tests import rational
+
+import numpy as np
+from numpy._utils import _pep440
+from numpy.exceptions import ComplexWarning
+from numpy.testing import (
+    IS_PYPY,
+    _gen_alignment_data,
+    assert_,
+    assert_almost_equal,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    check_support_sve,
+    suppress_warnings,
+)
+
+types = [np.bool, np.byte, np.ubyte, np.short, np.ushort, np.intc, np.uintc,
+         np.int_, np.uint, np.longlong, np.ulonglong,
+         np.single, np.double, np.longdouble, np.csingle,
+         np.cdouble, np.clongdouble]
+
+floating_types = np.floating.__subclasses__()
+complex_floating_types = np.complexfloating.__subclasses__()
+
+objecty_things = [object(), None, np.array(None, dtype=object)]
+
+binary_operators_for_scalars = [
+    operator.lt, operator.le, operator.eq, operator.ne, operator.ge,
+    operator.gt, operator.add, operator.floordiv, operator.mod,
+    operator.mul, operator.pow, operator.sub, operator.truediv
+]
+binary_operators_for_scalar_ints = binary_operators_for_scalars + [
+    operator.xor, operator.or_, operator.and_
+]
+
+
+# This compares scalarmath against ufuncs.
+
+class TestTypes:
+    def test_types(self):
+        for atype in types:
+            a = atype(1)
+            assert_(a == 1, f"error with {atype!r}: got {a!r}")
+
+    def test_type_add(self):
+        # list of types
+        for k, atype in enumerate(types):
+            a_scalar = atype(3)
+            a_array = np.array([3], dtype=atype)
+            for l, btype in enumerate(types):
+                b_scalar = btype(1)
+                b_array = np.array([1], dtype=btype)
+                c_scalar = a_scalar + b_scalar
+                c_array = a_array + b_array
+                # It was comparing the type numbers, but the new ufunc
+                # function-finding mechanism finds the lowest function
+                # to which both inputs can be cast - which produces 'l'
+                # when you do 'q' + 'b'.  The old function finding mechanism
+                # skipped ahead based on the first argument, but that
+                # does not produce properly symmetric results...
+                assert_equal(c_scalar.dtype, c_array.dtype,
+                           "error with types (%d/'%c' + %d/'%c')" %
+                            (k, np.dtype(atype).char, l, np.dtype(btype).char))
+
+    def test_type_create(self):
+        for atype in types:
+            a = np.array([1, 2, 3], atype)
+            b = atype([1, 2, 3])
+            assert_equal(a, b)
+
+    def test_leak(self):
+        # test leak of scalar objects
+        # a leak would show up in valgrind as still-reachable of ~2.6MB
+        for i in range(200000):
+            np.add(1, 1)
+
+
+def check_ufunc_scalar_equivalence(op, arr1, arr2):
+    scalar1 = arr1[()]
+    scalar2 = arr2[()]
+    assert isinstance(scalar1, np.generic)
+    assert isinstance(scalar2, np.generic)
+
+    if arr1.dtype.kind == "c" or arr2.dtype.kind == "c":
+        comp_ops = {operator.ge, operator.gt, operator.le, operator.lt}
+        if op in comp_ops and (np.isnan(scalar1) or np.isnan(scalar2)):
+            pytest.xfail("complex comp ufuncs use sort-order, scalars do not.")
+    if op == operator.pow and arr2.item() in [-1, 0, 0.5, 1, 2]:
+        # array**scalar special case can have different result dtype
+        # (Other powers may have issues also, but are not hit here.)
+        # TODO: It would be nice to resolve this issue.
+        pytest.skip("array**2 can have incorrect/weird result dtype")
+
+    # ignore fpe's since they may just mismatch for integers anyway.
+    with warnings.catch_warnings(), np.errstate(all="ignore"):
+        # Comparisons DeprecationWarnings replacing errors (2022-03):
+        warnings.simplefilter("error", DeprecationWarning)
+        try:
+            res = op(arr1, arr2)
+        except Exception as e:
+            with pytest.raises(type(e)):
+                op(scalar1, scalar2)
+        else:
+            scalar_res = op(scalar1, scalar2)
+            assert_array_equal(scalar_res, res, strict=True)
+
+
+@pytest.mark.slow
+@settings(max_examples=10000, deadline=2000)
+@given(sampled_from(binary_operators_for_scalars),
+       hynp.arrays(dtype=hynp.scalar_dtypes(), shape=()),
+       hynp.arrays(dtype=hynp.scalar_dtypes(), shape=()))
+def test_array_scalar_ufunc_equivalence(op, arr1, arr2):
+    """
+    This is a thorough test attempting to cover important promotion paths
+    and ensuring that arrays and scalars stay as aligned as possible.
+    However, if it creates troubles, it should maybe just be removed.
+    """
+    check_ufunc_scalar_equivalence(op, arr1, arr2)
+
+
+@pytest.mark.slow
+@given(sampled_from(binary_operators_for_scalars),
+       hynp.scalar_dtypes(), hynp.scalar_dtypes())
+def test_array_scalar_ufunc_dtypes(op, dt1, dt2):
+    # Same as above, but don't worry about sampling weird values so that we
+    # do not have to sample as much
+    arr1 = np.array(2, dtype=dt1)
+    arr2 = np.array(3, dtype=dt2)  # some power do weird things.
+
+    check_ufunc_scalar_equivalence(op, arr1, arr2)
+
+
+@pytest.mark.parametrize("fscalar", [np.float16, np.float32])
+def test_int_float_promotion_truediv(fscalar):
+    # Promotion for mixed int and float32/float16 must not go to float64
+    i = np.int8(1)
+    f = fscalar(1)
+    expected = np.result_type(i, f)
+    assert (i / f).dtype == expected
+    assert (f / i).dtype == expected
+    # But normal int / int true division goes to float64:
+    assert (i / i).dtype == np.dtype("float64")
+    # For int16, result has to be ast least float32 (takes ufunc path):
+    assert (np.int16(1) / f).dtype == np.dtype("float32")
+
+
+class TestBaseMath:
+    @pytest.mark.xfail(check_support_sve(), reason="gh-22982")
+    def test_blocked(self):
+        # test alignments offsets for simd instructions
+        # alignments for vz + 2 * (vs - 1) + 1
+        for dt, sz in [(np.float32, 11), (np.float64, 7), (np.int32, 11)]:
+            for out, inp1, inp2, msg in _gen_alignment_data(dtype=dt,
+                                                            type='binary',
+                                                            max_size=sz):
+                exp1 = np.ones_like(inp1)
+                inp1[...] = np.ones_like(inp1)
+                inp2[...] = np.zeros_like(inp2)
+                assert_almost_equal(np.add(inp1, inp2), exp1, err_msg=msg)
+                assert_almost_equal(np.add(inp1, 2), exp1 + 2, err_msg=msg)
+                assert_almost_equal(np.add(1, inp2), exp1, err_msg=msg)
+
+                np.add(inp1, inp2, out=out)
+                assert_almost_equal(out, exp1, err_msg=msg)
+
+                inp2[...] += np.arange(inp2.size, dtype=dt) + 1
+                assert_almost_equal(np.square(inp2),
+                                    np.multiply(inp2, inp2), err_msg=msg)
+                # skip true divide for ints
+                if dt != np.int32:
+                    assert_almost_equal(np.reciprocal(inp2),
+                                        np.divide(1, inp2), err_msg=msg)
+
+                inp1[...] = np.ones_like(inp1)
+                np.add(inp1, 2, out=out)
+                assert_almost_equal(out, exp1 + 2, err_msg=msg)
+                inp2[...] = np.ones_like(inp2)
+                np.add(2, inp2, out=out)
+                assert_almost_equal(out, exp1 + 2, err_msg=msg)
+
+    def test_lower_align(self):
+        # check data that is not aligned to element size
+        # i.e doubles are aligned to 4 bytes on i386
+        d = np.zeros(23 * 8, dtype=np.int8)[4:-4].view(np.float64)
+        o = np.zeros(23 * 8, dtype=np.int8)[4:-4].view(np.float64)
+        assert_almost_equal(d + d, d * 2)
+        np.add(d, d, out=o)
+        np.add(np.ones_like(d), d, out=o)
+        np.add(d, np.ones_like(d), out=o)
+        np.add(np.ones_like(d), d)
+        np.add(d, np.ones_like(d))
+
+
+class TestPower:
+    def test_small_types(self):
+        for t in [np.int8, np.int16, np.float16]:
+            a = t(3)
+            b = a ** 4
+            assert_(b == 81, f"error with {t!r}: got {b!r}")
+
+    def test_large_types(self):
+        for t in [np.int32, np.int64, np.float32, np.float64, np.longdouble]:
+            a = t(51)
+            b = a ** 4
+            msg = f"error with {t!r}: got {b!r}"
+            if np.issubdtype(t, np.integer):
+                assert_(b == 6765201, msg)
+            else:
+                assert_almost_equal(b, 6765201, err_msg=msg)
+
+    def test_integers_to_negative_integer_power(self):
+        # Note that the combination of uint64 with a signed integer
+        # has common type np.float64. The other combinations should all
+        # raise a ValueError for integer ** negative integer.
+        exp = [np.array(-1, dt)[()] for dt in 'bhilq']
+
+        # 1 ** -1 possible special case
+        base = [np.array(1, dt)[()] for dt in 'bhilqBHILQ']
+        for i1, i2 in itertools.product(base, exp):
+            if i1.dtype != np.uint64:
+                assert_raises(ValueError, operator.pow, i1, i2)
+            else:
+                res = operator.pow(i1, i2)
+                assert_(res.dtype.type is np.float64)
+                assert_almost_equal(res, 1.)
+
+        # -1 ** -1 possible special case
+        base = [np.array(-1, dt)[()] for dt in 'bhilq']
+        for i1, i2 in itertools.product(base, exp):
+            if i1.dtype != np.uint64:
+                assert_raises(ValueError, operator.pow, i1, i2)
+            else:
+                res = operator.pow(i1, i2)
+                assert_(res.dtype.type is np.float64)
+                assert_almost_equal(res, -1.)
+
+        # 2 ** -1 perhaps generic
+        base = [np.array(2, dt)[()] for dt in 'bhilqBHILQ']
+        for i1, i2 in itertools.product(base, exp):
+            if i1.dtype != np.uint64:
+                assert_raises(ValueError, operator.pow, i1, i2)
+            else:
+                res = operator.pow(i1, i2)
+                assert_(res.dtype.type is np.float64)
+                assert_almost_equal(res, .5)
+
+    def test_mixed_types(self):
+        typelist = [np.int8, np.int16, np.float16,
+                    np.float32, np.float64, np.int8,
+                    np.int16, np.int32, np.int64]
+        for t1 in typelist:
+            for t2 in typelist:
+                a = t1(3)
+                b = t2(2)
+                result = a**b
+                msg = f"error with {t1!r} and {t2!r}:got {result!r}, expected {9!r}"
+                if np.issubdtype(np.dtype(result), np.integer):
+                    assert_(result == 9, msg)
+                else:
+                    assert_almost_equal(result, 9, err_msg=msg)
+
+    def test_modular_power(self):
+        # modular power is not implemented, so ensure it errors
+        a = 5
+        b = 4
+        c = 10
+        expected = pow(a, b, c)  # noqa: F841
+        for t in (np.int32, np.float32, np.complex64):
+            # note that 3-operand power only dispatches on the first argument
+            assert_raises(TypeError, operator.pow, t(a), b, c)
+            assert_raises(TypeError, operator.pow, np.array(t(a)), b, c)
+
+
+def floordiv_and_mod(x, y):
+    return (x // y, x % y)
+
+
+def _signs(dt):
+    if dt in np.typecodes['UnsignedInteger']:
+        return (+1,)
+    else:
+        return (+1, -1)
+
+
+class TestModulus:
+
+    def test_modulus_basic(self):
+        dt = np.typecodes['AllInteger'] + np.typecodes['Float']
+        for op in [floordiv_and_mod, divmod]:
+            for dt1, dt2 in itertools.product(dt, dt):
+                for sg1, sg2 in itertools.product(_signs(dt1), _signs(dt2)):
+                    fmt = 'op: %s, dt1: %s, dt2: %s, sg1: %s, sg2: %s'
+                    msg = fmt % (op.__name__, dt1, dt2, sg1, sg2)
+                    a = np.array(sg1 * 71, dtype=dt1)[()]
+                    b = np.array(sg2 * 19, dtype=dt2)[()]
+                    div, rem = op(a, b)
+                    assert_equal(div * b + rem, a, err_msg=msg)
+                    if sg2 == -1:
+                        assert_(b < rem <= 0, msg)
+                    else:
+                        assert_(b > rem >= 0, msg)
+
+    def test_float_modulus_exact(self):
+        # test that float results are exact for small integers. This also
+        # holds for the same integers scaled by powers of two.
+        nlst = list(range(-127, 0))
+        plst = list(range(1, 128))
+        dividend = nlst + [0] + plst
+        divisor = nlst + plst
+        arg = list(itertools.product(dividend, divisor))
+        tgt = [divmod(*t) for t in arg]
+
+        a, b = np.array(arg, dtype=int).T
+        # convert exact integer results from Python to float so that
+        # signed zero can be used, it is checked.
+        tgtdiv, tgtrem = np.array(tgt, dtype=float).T
+        tgtdiv = np.where((tgtdiv == 0.0) & ((b < 0) ^ (a < 0)), -0.0, tgtdiv)
+        tgtrem = np.where((tgtrem == 0.0) & (b < 0), -0.0, tgtrem)
+
+        for op in [floordiv_and_mod, divmod]:
+            for dt in np.typecodes['Float']:
+                msg = f'op: {op.__name__}, dtype: {dt}'
+                fa = a.astype(dt)
+                fb = b.astype(dt)
+                # use list comprehension so a_ and b_ are scalars
+                div, rem = zip(*[op(a_, b_) for a_, b_ in zip(fa, fb)])
+                assert_equal(div, tgtdiv, err_msg=msg)
+                assert_equal(rem, tgtrem, err_msg=msg)
+
+    def test_float_modulus_roundoff(self):
+        # gh-6127
+        dt = np.typecodes['Float']
+        for op in [floordiv_and_mod, divmod]:
+            for dt1, dt2 in itertools.product(dt, dt):
+                for sg1, sg2 in itertools.product((+1, -1), (+1, -1)):
+                    fmt = 'op: %s, dt1: %s, dt2: %s, sg1: %s, sg2: %s'
+                    msg = fmt % (op.__name__, dt1, dt2, sg1, sg2)
+                    a = np.array(sg1 * 78 * 6e-8, dtype=dt1)[()]
+                    b = np.array(sg2 * 6e-8, dtype=dt2)[()]
+                    div, rem = op(a, b)
+                    # Equal assertion should hold when fmod is used
+                    assert_equal(div * b + rem, a, err_msg=msg)
+                    if sg2 == -1:
+                        assert_(b < rem <= 0, msg)
+                    else:
+                        assert_(b > rem >= 0, msg)
+
+    def test_float_modulus_corner_cases(self):
+        # Check remainder magnitude.
+        for dt in np.typecodes['Float']:
+            b = np.array(1.0, dtype=dt)
+            a = np.nextafter(np.array(0.0, dtype=dt), -b)
+            rem = operator.mod(a, b)
+            assert_(rem <= b, f'dt: {dt}')
+            rem = operator.mod(-a, -b)
+            assert_(rem >= -b, f'dt: {dt}')
+
+        # Check nans, inf
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in remainder")
+            sup.filter(RuntimeWarning, "divide by zero encountered in remainder")
+            sup.filter(RuntimeWarning, "divide by zero encountered in floor_divide")
+            sup.filter(RuntimeWarning, "divide by zero encountered in divmod")
+            sup.filter(RuntimeWarning, "invalid value encountered in divmod")
+            for dt in np.typecodes['Float']:
+                fone = np.array(1.0, dtype=dt)
+                fzer = np.array(0.0, dtype=dt)
+                finf = np.array(np.inf, dtype=dt)
+                fnan = np.array(np.nan, dtype=dt)
+                rem = operator.mod(fone, fzer)
+                assert_(np.isnan(rem), f'dt: {dt}')
+                # MSVC 2008 returns NaN here, so disable the check.
+                #rem = operator.mod(fone, finf)
+                #assert_(rem == fone, 'dt: %s' % dt)
+                rem = operator.mod(fone, fnan)
+                assert_(np.isnan(rem), f'dt: {dt}')
+                rem = operator.mod(finf, fone)
+                assert_(np.isnan(rem), f'dt: {dt}')
+                for op in [floordiv_and_mod, divmod]:
+                    div, mod = op(fone, fzer)
+                    assert_(np.isinf(div)) and assert_(np.isnan(mod))
+
+    def test_inplace_floordiv_handling(self):
+        # issue gh-12927
+        # this only applies to in-place floordiv //=, because the output type
+        # promotes to float which does not fit
+        a = np.array([1, 2], np.int64)
+        b = np.array([1, 2], np.uint64)
+        with pytest.raises(TypeError,
+                match=r"Cannot cast ufunc 'floor_divide' output from"):
+            a //= b
+
+class TestComparison:
+    def test_comparision_different_types(self):
+        x = np.array(1)
+        y = np.array('s')
+        eq = x == y
+        neq = x != y
+        assert eq is np.bool_(False)
+        assert neq is np.bool_(True)
+
+
+class TestComplexDivision:
+    def test_zero_division(self):
+        with np.errstate(all="ignore"):
+            for t in [np.complex64, np.complex128]:
+                a = t(0.0)
+                b = t(1.0)
+                assert_(np.isinf(b / a))
+                b = t(complex(np.inf, np.inf))
+                assert_(np.isinf(b / a))
+                b = t(complex(np.inf, np.nan))
+                assert_(np.isinf(b / a))
+                b = t(complex(np.nan, np.inf))
+                assert_(np.isinf(b / a))
+                b = t(complex(np.nan, np.nan))
+                assert_(np.isnan(b / a))
+                b = t(0.)
+                assert_(np.isnan(b / a))
+
+    def test_signed_zeros(self):
+        with np.errstate(all="ignore"):
+            for t in [np.complex64, np.complex128]:
+                # tupled (numerator, denominator, expected)
+                # for testing as expected == numerator/denominator
+                data = (
+                    (( 0.0, -1.0), ( 0.0, 1.0), (-1.0, -0.0)),
+                    (( 0.0, -1.0), ( 0.0, -1.0), ( 1.0, -0.0)),
+                    (( 0.0, -1.0), (-0.0, -1.0), ( 1.0, 0.0)),
+                    (( 0.0, -1.0), (-0.0, 1.0), (-1.0, 0.0)),
+                    (( 0.0, 1.0), ( 0.0, -1.0), (-1.0, 0.0)),
+                    (( 0.0, -1.0), ( 0.0, -1.0), ( 1.0, -0.0)),
+                    ((-0.0, -1.0), ( 0.0, -1.0), ( 1.0, -0.0)),
+                    ((-0.0, 1.0), ( 0.0, -1.0), (-1.0, -0.0))
+                )
+                for cases in data:
+                    n = cases[0]
+                    d = cases[1]
+                    ex = cases[2]
+                    result = t(complex(n[0], n[1])) / t(complex(d[0], d[1]))
+                    # check real and imag parts separately to avoid comparison
+                    # in array context, which does not account for signed zeros
+                    assert_equal(result.real, ex[0])
+                    assert_equal(result.imag, ex[1])
+
+    def test_branches(self):
+        with np.errstate(all="ignore"):
+            for t in [np.complex64, np.complex128]:
+                # tupled (numerator, denominator, expected)
+                # for testing as expected == numerator/denominator
+                data = []
+
+                # trigger branch: real(fabs(denom)) > imag(fabs(denom))
+                # followed by else condition as neither are == 0
+                data.append((( 2.0, 1.0), ( 2.0, 1.0), (1.0, 0.0)))
+
+                # trigger branch: real(fabs(denom)) > imag(fabs(denom))
+                # followed by if condition as both are == 0
+                # is performed in test_zero_division(), so this is skipped
+
+                # trigger else if branch: real(fabs(denom)) < imag(fabs(denom))
+                data.append(((1.0, 2.0), (1.0, 2.0), (1.0, 0.0)))
+
+                for cases in data:
+                    n = cases[0]
+                    d = cases[1]
+                    ex = cases[2]
+                    result = t(complex(n[0], n[1])) / t(complex(d[0], d[1]))
+                    # check real and imag parts separately to avoid comparison
+                    # in array context, which does not account for signed zeros
+                    assert_equal(result.real, ex[0])
+                    assert_equal(result.imag, ex[1])
+
+
+class TestConversion:
+    def test_int_from_long(self):
+        l = [1e6, 1e12, 1e18, -1e6, -1e12, -1e18]
+        li = [10**6, 10**12, 10**18, -10**6, -10**12, -10**18]
+        for T in [None, np.float64, np.int64]:
+            a = np.array(l, dtype=T)
+            assert_equal([int(_m) for _m in a], li)
+
+        a = np.array(l[:3], dtype=np.uint64)
+        assert_equal([int(_m) for _m in a], li[:3])
+
+    def test_iinfo_long_values(self):
+        for code in 'bBhH':
+            with pytest.raises(OverflowError):
+                np.array(np.iinfo(code).max + 1, dtype=code)
+
+        for code in np.typecodes['AllInteger']:
+            res = np.array(np.iinfo(code).max, dtype=code)
+            tgt = np.iinfo(code).max
+            assert_(res == tgt)
+
+        for code in np.typecodes['AllInteger']:
+            res = np.dtype(code).type(np.iinfo(code).max)
+            tgt = np.iinfo(code).max
+            assert_(res == tgt)
+
+    def test_int_raise_behaviour(self):
+        def overflow_error_func(dtype):
+            dtype(np.iinfo(dtype).max + 1)
+
+        for code in [np.int_, np.uint, np.longlong, np.ulonglong]:
+            assert_raises(OverflowError, overflow_error_func, code)
+
+    def test_int_from_infinite_longdouble(self):
+        # gh-627
+        x = np.longdouble(np.inf)
+        assert_raises(OverflowError, int, x)
+        with suppress_warnings() as sup:
+            sup.record(ComplexWarning)
+            x = np.clongdouble(np.inf)
+            assert_raises(OverflowError, int, x)
+            assert_equal(len(sup.log), 1)
+
+    @pytest.mark.skipif(not IS_PYPY, reason="Test is PyPy only (gh-9972)")
+    def test_int_from_infinite_longdouble___int__(self):
+        x = np.longdouble(np.inf)
+        assert_raises(OverflowError, x.__int__)
+        with suppress_warnings() as sup:
+            sup.record(ComplexWarning)
+            x = np.clongdouble(np.inf)
+            assert_raises(OverflowError, x.__int__)
+            assert_equal(len(sup.log), 1)
+
+    @pytest.mark.skipif(np.finfo(np.double) == np.finfo(np.longdouble),
+                        reason="long double is same as double")
+    @pytest.mark.skipif(platform.machine().startswith("ppc"),
+                        reason="IBM double double")
+    def test_int_from_huge_longdouble(self):
+        # Produce a longdouble that would overflow a double,
+        # use exponent that avoids bug in Darwin pow function.
+        exp = np.finfo(np.double).maxexp - 1
+        huge_ld = 2 * 1234 * np.longdouble(2) ** exp
+        huge_i = 2 * 1234 * 2 ** exp
+        assert_(huge_ld != np.inf)
+        assert_equal(int(huge_ld), huge_i)
+
+    def test_int_from_longdouble(self):
+        x = np.longdouble(1.5)
+        assert_equal(int(x), 1)
+        x = np.longdouble(-10.5)
+        assert_equal(int(x), -10)
+
+    def test_numpy_scalar_relational_operators(self):
+        # All integer
+        for dt1 in np.typecodes['AllInteger']:
+            assert_(1 > np.array(0, dtype=dt1)[()], f"type {dt1} failed")
+            assert_(not 1 < np.array(0, dtype=dt1)[()], f"type {dt1} failed")
+
+            for dt2 in np.typecodes['AllInteger']:
+                assert_(np.array(1, dtype=dt1)[()] > np.array(0, dtype=dt2)[()],
+                        f"type {dt1} and {dt2} failed")
+                assert_(not np.array(1, dtype=dt1)[()] < np.array(0, dtype=dt2)[()],
+                        f"type {dt1} and {dt2} failed")
+
+        # Unsigned integers
+        for dt1 in 'BHILQP':
+            assert_(-1 < np.array(1, dtype=dt1)[()], f"type {dt1} failed")
+            assert_(not -1 > np.array(1, dtype=dt1)[()], f"type {dt1} failed")
+            assert_(-1 != np.array(1, dtype=dt1)[()], f"type {dt1} failed")
+
+            # unsigned vs signed
+            for dt2 in 'bhilqp':
+                assert_(np.array(1, dtype=dt1)[()] > np.array(-1, dtype=dt2)[()],
+                        f"type {dt1} and {dt2} failed")
+                assert_(not np.array(1, dtype=dt1)[()] < np.array(-1, dtype=dt2)[()],
+                        f"type {dt1} and {dt2} failed")
+                assert_(np.array(1, dtype=dt1)[()] != np.array(-1, dtype=dt2)[()],
+                        f"type {dt1} and {dt2} failed")
+
+        # Signed integers and floats
+        for dt1 in 'bhlqp' + np.typecodes['Float']:
+            assert_(1 > np.array(-1, dtype=dt1)[()], f"type {dt1} failed")
+            assert_(not 1 < np.array(-1, dtype=dt1)[()], f"type {dt1} failed")
+            assert_(-1 == np.array(-1, dtype=dt1)[()], f"type {dt1} failed")
+
+            for dt2 in 'bhlqp' + np.typecodes['Float']:
+                assert_(np.array(1, dtype=dt1)[()] > np.array(-1, dtype=dt2)[()],
+                        f"type {dt1} and {dt2} failed")
+                assert_(not np.array(1, dtype=dt1)[()] < np.array(-1, dtype=dt2)[()],
+                        f"type {dt1} and {dt2} failed")
+                assert_(np.array(-1, dtype=dt1)[()] == np.array(-1, dtype=dt2)[()],
+                        f"type {dt1} and {dt2} failed")
+
+    def test_scalar_comparison_to_none(self):
+        # Scalars should just return False and not give a warnings.
+        # The comparisons are flagged by pep8, ignore that.
+        with warnings.catch_warnings(record=True) as w:
+            warnings.filterwarnings('always', '', FutureWarning)
+            assert_(not np.float32(1) == None)  # noqa: E711
+            assert_(not np.str_('test') == None)  # noqa: E711
+            # This is dubious (see below):
+            assert_(not np.datetime64('NaT') == None)  # noqa: E711
+
+            assert_(np.float32(1) != None)  # noqa: E711
+            assert_(np.str_('test') != None)  # noqa: E711
+            # This is dubious (see below):
+            assert_(np.datetime64('NaT') != None)  # noqa: E711
+        assert_(len(w) == 0)
+
+        # For documentation purposes, this is why the datetime is dubious.
+        # At the time of deprecation this was no behaviour change, but
+        # it has to be considered when the deprecations are done.
+        assert_(np.equal(np.datetime64('NaT'), None))
+
+
+#class TestRepr:
+#    def test_repr(self):
+#        for t in types:
+#            val = t(1197346475.0137341)
+#            val_repr = repr(val)
+#            val2 = eval(val_repr)
+#            assert_equal( val, val2 )
+
+
+class TestRepr:
+    def _test_type_repr(self, t):
+        finfo = np.finfo(t)
+        last_fraction_bit_idx = finfo.nexp + finfo.nmant
+        last_exponent_bit_idx = finfo.nexp
+        storage_bytes = np.dtype(t).itemsize * 8
+        # could add some more types to the list below
+        for which in ['small denorm', 'small norm']:
+            # Values from https://en.wikipedia.org/wiki/IEEE_754
+            constr = np.array([0x00] * storage_bytes, dtype=np.uint8)
+            if which == 'small denorm':
+                byte = last_fraction_bit_idx // 8
+                bytebit = 7 - (last_fraction_bit_idx % 8)
+                constr[byte] = 1 << bytebit
+            elif which == 'small norm':
+                byte = last_exponent_bit_idx // 8
+                bytebit = 7 - (last_exponent_bit_idx % 8)
+                constr[byte] = 1 << bytebit
+            else:
+                raise ValueError('hmm')
+            val = constr.view(t)[0]
+            val_repr = repr(val)
+            val2 = t(eval(val_repr))
+            if not (val2 == 0 and val < 1e-100):
+                assert_equal(val, val2)
+
+    def test_float_repr(self):
+        # long double test cannot work, because eval goes through a python
+        # float
+        for t in [np.float32, np.float64]:
+            self._test_type_repr(t)
+
+
+if not IS_PYPY:
+    # sys.getsizeof() is not valid on PyPy
+    class TestSizeOf:
+
+        def test_equal_nbytes(self):
+            for type in types:
+                x = type(0)
+                assert_(sys.getsizeof(x) > x.nbytes)
+
+        def test_error(self):
+            d = np.float32()
+            assert_raises(TypeError, d.__sizeof__, "a")
+
+
+class TestMultiply:
+    def test_seq_repeat(self):
+        # Test that basic sequences get repeated when multiplied with
+        # numpy integers. And errors are raised when multiplied with others.
+        # Some of this behaviour may be controversial and could be open for
+        # change.
+        accepted_types = set(np.typecodes["AllInteger"])
+        deprecated_types = {'?'}
+        forbidden_types = (
+            set(np.typecodes["All"]) - accepted_types - deprecated_types)
+        forbidden_types -= {'V'}  # can't default-construct void scalars
+
+        for seq_type in (list, tuple):
+            seq = seq_type([1, 2, 3])
+            for numpy_type in accepted_types:
+                i = np.dtype(numpy_type).type(2)
+                assert_equal(seq * i, seq * int(i))
+                assert_equal(i * seq, int(i) * seq)
+
+            for numpy_type in deprecated_types:
+                i = np.dtype(numpy_type).type()
+                with assert_raises(TypeError):
+                    operator.mul(seq, i)
+
+            for numpy_type in forbidden_types:
+                i = np.dtype(numpy_type).type()
+                assert_raises(TypeError, operator.mul, seq, i)
+                assert_raises(TypeError, operator.mul, i, seq)
+
+    def test_no_seq_repeat_basic_array_like(self):
+        # Test that an array-like which does not know how to be multiplied
+        # does not attempt sequence repeat (raise TypeError).
+        # See also gh-7428.
+        class ArrayLike:
+            def __init__(self, arr):
+                self.arr = arr
+
+            def __array__(self, dtype=None, copy=None):
+                return self.arr
+
+        # Test for simple ArrayLike above and memoryviews (original report)
+        for arr_like in (ArrayLike(np.ones(3)), memoryview(np.ones(3))):
+            assert_array_equal(arr_like * np.float32(3.), np.full(3, 3.))
+            assert_array_equal(np.float32(3.) * arr_like, np.full(3, 3.))
+            assert_array_equal(arr_like * np.int_(3), np.full(3, 3))
+            assert_array_equal(np.int_(3) * arr_like, np.full(3, 3))
+
+
+class TestNegative:
+    def test_exceptions(self):
+        a = np.ones((), dtype=np.bool)[()]
+        assert_raises(TypeError, operator.neg, a)
+
+    def test_result(self):
+        types = np.typecodes['AllInteger'] + np.typecodes['AllFloat']
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning)
+            for dt in types:
+                a = np.ones((), dtype=dt)[()]
+                if dt in np.typecodes['UnsignedInteger']:
+                    st = np.dtype(dt).type
+                    max = st(np.iinfo(dt).max)
+                    assert_equal(operator.neg(a), max)
+                else:
+                    assert_equal(operator.neg(a) + a, 0)
+
+class TestSubtract:
+    def test_exceptions(self):
+        a = np.ones((), dtype=np.bool)[()]
+        assert_raises(TypeError, operator.sub, a, a)
+
+    def test_result(self):
+        types = np.typecodes['AllInteger'] + np.typecodes['AllFloat']
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning)
+            for dt in types:
+                a = np.ones((), dtype=dt)[()]
+                assert_equal(operator.sub(a, a), 0)
+
+
+class TestAbs:
+    def _test_abs_func(self, absfunc, test_dtype):
+        x = test_dtype(-1.5)
+        assert_equal(absfunc(x), 1.5)
+        x = test_dtype(0.0)
+        res = absfunc(x)
+        # assert_equal() checks zero signedness
+        assert_equal(res, 0.0)
+        x = test_dtype(-0.0)
+        res = absfunc(x)
+        assert_equal(res, 0.0)
+
+        x = test_dtype(np.finfo(test_dtype).max)
+        assert_equal(absfunc(x), x.real)
+
+        with suppress_warnings() as sup:
+            sup.filter(UserWarning)
+            x = test_dtype(np.finfo(test_dtype).tiny)
+            assert_equal(absfunc(x), x.real)
+
+        x = test_dtype(np.finfo(test_dtype).min)
+        assert_equal(absfunc(x), -x.real)
+
+    @pytest.mark.parametrize("dtype", floating_types + complex_floating_types)
+    def test_builtin_abs(self, dtype):
+        if (
+                sys.platform == "cygwin" and dtype == np.clongdouble and
+                (
+                    _pep440.parse(platform.release().split("-")[0])
+                    < _pep440.Version("3.3.0")
+                )
+        ):
+            pytest.xfail(
+                reason="absl is computed in double precision on cygwin < 3.3"
+            )
+        self._test_abs_func(abs, dtype)
+
+    @pytest.mark.parametrize("dtype", floating_types + complex_floating_types)
+    def test_numpy_abs(self, dtype):
+        if (
+                sys.platform == "cygwin" and dtype == np.clongdouble and
+                (
+                    _pep440.parse(platform.release().split("-")[0])
+                    < _pep440.Version("3.3.0")
+                )
+        ):
+            pytest.xfail(
+                reason="absl is computed in double precision on cygwin < 3.3"
+            )
+        self._test_abs_func(np.abs, dtype)
+
+class TestBitShifts:
+
+    @pytest.mark.parametrize('type_code', np.typecodes['AllInteger'])
+    @pytest.mark.parametrize('op',
+        [operator.rshift, operator.lshift], ids=['>>', '<<'])
+    def test_shift_all_bits(self, type_code, op):
+        """Shifts where the shift amount is the width of the type or wider """
+        # gh-2449
+        dt = np.dtype(type_code)
+        nbits = dt.itemsize * 8
+        for val in [5, -5]:
+            for shift in [nbits, nbits + 4]:
+                val_scl = np.array(val).astype(dt)[()]
+                shift_scl = dt.type(shift)
+                res_scl = op(val_scl, shift_scl)
+                if val_scl < 0 and op is operator.rshift:
+                    # sign bit is preserved
+                    assert_equal(res_scl, -1)
+                else:
+                    assert_equal(res_scl, 0)
+
+                # Result on scalars should be the same as on arrays
+                val_arr = np.array([val_scl] * 32, dtype=dt)
+                shift_arr = np.array([shift] * 32, dtype=dt)
+                res_arr = op(val_arr, shift_arr)
+                assert_equal(res_arr, res_scl)
+
+
+class TestHash:
+    @pytest.mark.parametrize("type_code", np.typecodes['AllInteger'])
+    def test_integer_hashes(self, type_code):
+        scalar = np.dtype(type_code).type
+        for i in range(128):
+            assert hash(i) == hash(scalar(i))
+
+    @pytest.mark.parametrize("type_code", np.typecodes['AllFloat'])
+    def test_float_and_complex_hashes(self, type_code):
+        scalar = np.dtype(type_code).type
+        for val in [np.pi, np.inf, 3, 6.]:
+            numpy_val = scalar(val)
+            # Cast back to Python, in case the NumPy scalar has less precision
+            if numpy_val.dtype.kind == 'c':
+                val = complex(numpy_val)
+            else:
+                val = float(numpy_val)
+            assert val == numpy_val
+            assert hash(val) == hash(numpy_val)
+
+        if hash(float(np.nan)) != hash(float(np.nan)):
+            # If Python distinguishes different NaNs we do so too (gh-18833)
+            assert hash(scalar(np.nan)) != hash(scalar(np.nan))
+
+    @pytest.mark.parametrize("type_code", np.typecodes['Complex'])
+    def test_complex_hashes(self, type_code):
+        # Test some complex valued hashes specifically:
+        scalar = np.dtype(type_code).type
+        for val in [np.pi + 1j, np.inf - 3j, 3j, 6. + 1j]:
+            numpy_val = scalar(val)
+            assert hash(complex(numpy_val)) == hash(numpy_val)
+
+
+@contextlib.contextmanager
+def recursionlimit(n):
+    o = sys.getrecursionlimit()
+    try:
+        sys.setrecursionlimit(n)
+        yield
+    finally:
+        sys.setrecursionlimit(o)
+
+
+@given(sampled_from(objecty_things),
+       sampled_from(binary_operators_for_scalar_ints),
+       sampled_from(types + [rational]))
+def test_operator_object_left(o, op, type_):
+    try:
+        with recursionlimit(200):
+            op(o, type_(1))
+    except TypeError:
+        pass
+
+
+@given(sampled_from(objecty_things),
+       sampled_from(binary_operators_for_scalar_ints),
+       sampled_from(types + [rational]))
+def test_operator_object_right(o, op, type_):
+    try:
+        with recursionlimit(200):
+            op(type_(1), o)
+    except TypeError:
+        pass
+
+
+@given(sampled_from(binary_operators_for_scalars),
+       sampled_from(types),
+       sampled_from(types))
+def test_operator_scalars(op, type1, type2):
+    try:
+        op(type1(1), type2(1))
+    except TypeError:
+        pass
+
+
+@pytest.mark.parametrize("op", binary_operators_for_scalars)
+@pytest.mark.parametrize("sctype", [np.longdouble, np.clongdouble])
+def test_longdouble_operators_with_obj(sctype, op):
+    # This is/used to be tricky, because NumPy generally falls back to
+    # using the ufunc via `np.asarray()`, this effectively might do:
+    # longdouble + None
+    #   -> asarray(longdouble) + np.array(None, dtype=object)
+    #   -> asarray(longdouble).astype(object) + np.array(None, dtype=object)
+    # And after getting the scalars in the inner loop:
+    #   -> longdouble + None
+    #
+    # That would recurse infinitely.  Other scalars return the python object
+    # on cast, so this type of things works OK.
+    #
+    # As of NumPy 2.1, this has been consolidated into the np.generic binops
+    # and now checks `.item()`.  That also allows the below path to work now.
+    try:
+        op(sctype(3), None)
+    except TypeError:
+        pass
+    try:
+        op(None, sctype(3))
+    except TypeError:
+        pass
+
+
+@pytest.mark.parametrize("op", [operator.add, operator.pow, operator.sub])
+@pytest.mark.parametrize("sctype", [np.longdouble, np.clongdouble])
+def test_longdouble_with_arrlike(sctype, op):
+    # As of NumPy 2.1, longdouble behaves like other types and can coerce
+    # e.g. lists.  (Not necessarily better, but consistent.)
+    assert_array_equal(op(sctype(3), [1, 2]), op(3, np.array([1, 2])))
+    assert_array_equal(op([1, 2], sctype(3)), op(np.array([1, 2]), 3))
+
+
+@pytest.mark.parametrize("op", binary_operators_for_scalars)
+@pytest.mark.parametrize("sctype", [np.longdouble, np.clongdouble])
+@np.errstate(all="ignore")
+def test_longdouble_operators_with_large_int(sctype, op):
+    # (See `test_longdouble_operators_with_obj` for why longdouble is special)
+    # NEP 50 means that the result is clearly a (c)longdouble here:
+    if sctype == np.clongdouble and op in [operator.mod, operator.floordiv]:
+        # The above operators are not support for complex though...
+        with pytest.raises(TypeError):
+            op(sctype(3), 2**64)
+        with pytest.raises(TypeError):
+            op(sctype(3), 2**64)
+    else:
+        assert op(sctype(3), -2**64) == op(sctype(3), sctype(-2**64))
+        assert op(2**64, sctype(3)) == op(sctype(2**64), sctype(3))
+
+
+@pytest.mark.parametrize("dtype", np.typecodes["AllInteger"])
+@pytest.mark.parametrize("operation", [
+        lambda min, max: max + max,
+        lambda min, max: min - max,
+        lambda min, max: max * max], ids=["+", "-", "*"])
+def test_scalar_integer_operation_overflow(dtype, operation):
+    st = np.dtype(dtype).type
+    min = st(np.iinfo(dtype).min)
+    max = st(np.iinfo(dtype).max)
+
+    with pytest.warns(RuntimeWarning, match="overflow encountered"):
+        operation(min, max)
+
+
+@pytest.mark.parametrize("dtype", np.typecodes["Integer"])
+@pytest.mark.parametrize("operation", [
+        lambda min, neg_1: -min,
+        lambda min, neg_1: abs(min),
+        lambda min, neg_1: min * neg_1,
+        pytest.param(lambda min, neg_1: min // neg_1,
+            marks=pytest.mark.skip(reason="broken on some platforms"))],
+        ids=["neg", "abs", "*", "//"])
+def test_scalar_signed_integer_overflow(dtype, operation):
+    # The minimum signed integer can "overflow" for some additional operations
+    st = np.dtype(dtype).type
+    min = st(np.iinfo(dtype).min)
+    neg_1 = st(-1)
+
+    with pytest.warns(RuntimeWarning, match="overflow encountered"):
+        operation(min, neg_1)
+
+
+@pytest.mark.parametrize("dtype", np.typecodes["UnsignedInteger"])
+def test_scalar_unsigned_integer_overflow(dtype):
+    val = np.dtype(dtype).type(8)
+    with pytest.warns(RuntimeWarning, match="overflow encountered"):
+        -val
+
+    zero = np.dtype(dtype).type(0)
+    -zero  # does not warn
+
+@pytest.mark.parametrize("dtype", np.typecodes["AllInteger"])
+@pytest.mark.parametrize("operation", [
+        lambda val, zero: val // zero,
+        lambda val, zero: val % zero, ], ids=["//", "%"])
+def test_scalar_integer_operation_divbyzero(dtype, operation):
+    st = np.dtype(dtype).type
+    val = st(100)
+    zero = st(0)
+
+    with pytest.warns(RuntimeWarning, match="divide by zero"):
+        operation(val, zero)
+
+
+ops_with_names = [
+    ("__lt__", "__gt__", operator.lt, True),
+    ("__le__", "__ge__", operator.le, True),
+    ("__eq__", "__eq__", operator.eq, True),
+    # Note __op__ and __rop__ may be identical here:
+    ("__ne__", "__ne__", operator.ne, True),
+    ("__gt__", "__lt__", operator.gt, True),
+    ("__ge__", "__le__", operator.ge, True),
+    ("__floordiv__", "__rfloordiv__", operator.floordiv, False),
+    ("__truediv__", "__rtruediv__", operator.truediv, False),
+    ("__add__", "__radd__", operator.add, False),
+    ("__mod__", "__rmod__", operator.mod, False),
+    ("__mul__", "__rmul__", operator.mul, False),
+    ("__pow__", "__rpow__", operator.pow, False),
+    ("__sub__", "__rsub__", operator.sub, False),
+]
+
+
+@pytest.mark.parametrize(["__op__", "__rop__", "op", "cmp"], ops_with_names)
+@pytest.mark.parametrize("sctype", [np.float32, np.float64, np.longdouble])
+def test_subclass_deferral(sctype, __op__, __rop__, op, cmp):
+    """
+    This test covers scalar subclass deferral.  Note that this is exceedingly
+    complicated, especially since it tends to fall back to the array paths and
+    these additionally add the "array priority" mechanism.
+
+    The behaviour was modified subtly in 1.22 (to make it closer to how Python
+    scalars work).  Due to its complexity and the fact that subclassing NumPy
+    scalars is probably a bad idea to begin with.  There is probably room
+    for adjustments here.
+    """
+    class myf_simple1(sctype):
+        pass
+
+    class myf_simple2(sctype):
+        pass
+
+    def op_func(self, other):
+        return __op__
+
+    def rop_func(self, other):
+        return __rop__
+
+    myf_op = type("myf_op", (sctype,), {__op__: op_func, __rop__: rop_func})
+
+    # inheritance has to override, or this is correctly lost:
+    res = op(myf_simple1(1), myf_simple2(2))
+    assert type(res) == sctype or type(res) == np.bool
+    assert op(myf_simple1(1), myf_simple2(2)) == op(1, 2)  # inherited
+
+    # Two independent subclasses do not really define an order.  This could
+    # be attempted, but we do not since Python's `int` does neither:
+    assert op(myf_op(1), myf_simple1(2)) == __op__
+    assert op(myf_simple1(1), myf_op(2)) == op(1, 2)  # inherited
+
+
+def test_longdouble_complex():
+    # Simple test to check longdouble and complex combinations, since these
+    # need to go through promotion, which longdouble needs to be careful about.
+    x = np.longdouble(1)
+    assert x + 1j == 1 + 1j
+    assert 1j + x == 1 + 1j
+
+
+@pytest.mark.parametrize(["__op__", "__rop__", "op", "cmp"], ops_with_names)
+@pytest.mark.parametrize("subtype", [float, int, complex, np.float16])
+def test_pyscalar_subclasses(subtype, __op__, __rop__, op, cmp):
+    # This tests that python scalar subclasses behave like a float64 (if they
+    # don't override it).
+    # In an earlier version of NEP 50, they behaved like the Python buildins.
+    def op_func(self, other):
+        return __op__
+
+    def rop_func(self, other):
+        return __rop__
+
+    # Check that deferring is indicated using `__array_ufunc__`:
+    myt = type("myt", (subtype,),
+               {__op__: op_func, __rop__: rop_func, "__array_ufunc__": None})
+
+    # Just like normally, we should never presume we can modify the float.
+    assert op(myt(1), np.float64(2)) == __op__
+    assert op(np.float64(1), myt(2)) == __rop__
+
+    if op in {operator.mod, operator.floordiv} and subtype == complex:
+        return  # module is not support for complex.  Do not test.
+
+    if __rop__ == __op__:
+        return
+
+    # When no deferring is indicated, subclasses are handled normally.
+    myt = type("myt", (subtype,), {__rop__: rop_func})
+    behaves_like = lambda x: np.array(subtype(x))[()]
+
+    # Check for float32, as a float subclass float64 may behave differently
+    res = op(myt(1), np.float16(2))
+    expected = op(behaves_like(1), np.float16(2))
+    assert res == expected
+    assert type(res) == type(expected)
+    res = op(np.float32(2), myt(1))
+    expected = op(np.float32(2), behaves_like(1))
+    assert res == expected
+    assert type(res) == type(expected)
+
+    # Same check for longdouble (compare via dtype to accept float64 when
+    # longdouble has the identical size), which is currently not perfectly
+    # consistent.
+    res = op(myt(1), np.longdouble(2))
+    expected = op(behaves_like(1), np.longdouble(2))
+    assert res == expected
+    assert np.dtype(type(res)) == np.dtype(type(expected))
+    res = op(np.float32(2), myt(1))
+    expected = op(np.float32(2), behaves_like(1))
+    assert res == expected
+    assert np.dtype(type(res)) == np.dtype(type(expected))
+
+
+def test_truediv_int():
+    # This should work, as the result is float:
+    assert np.uint8(3) / 123454 == np.float64(3) / 123454
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize("op",
+    # TODO: Power is a bit special, but here mostly bools seem to behave oddly
+    [op for op in binary_operators_for_scalars if op is not operator.pow])
+@pytest.mark.parametrize("sctype", types)
+@pytest.mark.parametrize("other_type", [float, int, complex])
+@pytest.mark.parametrize("rop", [True, False])
+def test_scalar_matches_array_op_with_pyscalar(op, sctype, other_type, rop):
+    # Check that the ufunc path matches by coercing to an array explicitly
+    val1 = sctype(2)
+    val2 = other_type(2)
+
+    if rop:
+        _op = op
+        op = lambda x, y: _op(y, x)
+
+    try:
+        res = op(val1, val2)
+    except TypeError:
+        try:
+            expected = op(np.asarray(val1), val2)
+            raise AssertionError("ufunc didn't raise.")
+        except TypeError:
+            return
+    else:
+        expected = op(np.asarray(val1), val2)
+
+    # Note that we only check dtype equivalency, as ufuncs may pick the lower
+    # dtype if they are equivalent.
+    assert res == expected
+    if isinstance(val1, float) and other_type is complex and rop:
+        # Python complex accepts float subclasses, so we don't get a chance
+        # and the result may be a Python complex (thus, the `np.array()``)
+        assert np.array(res).dtype == expected.dtype
+    else:
+        assert res.dtype == expected.dtype
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarprint.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarprint.py
new file mode 100644
index 0000000..38ed778
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_scalarprint.py
@@ -0,0 +1,403 @@
+""" Test printing of scalar types.
+
+"""
+import platform
+
+import pytest
+
+import numpy as np
+from numpy.testing import IS_MUSL, assert_, assert_equal, assert_raises
+
+
+class TestRealScalars:
+    def test_str(self):
+        svals = [0.0, -0.0, 1, -1, np.inf, -np.inf, np.nan]
+        styps = [np.float16, np.float32, np.float64, np.longdouble]
+        wanted = [
+             ['0.0',  '0.0',  '0.0',  '0.0' ],  # noqa: E202
+             ['-0.0', '-0.0', '-0.0', '-0.0'],
+             ['1.0',  '1.0',  '1.0',  '1.0' ],  # noqa: E202
+             ['-1.0', '-1.0', '-1.0', '-1.0'],
+             ['inf',  'inf',  'inf',  'inf' ],  # noqa: E202
+             ['-inf', '-inf', '-inf', '-inf'],
+             ['nan',  'nan',  'nan',  'nan' ]]  # noqa: E202
+
+        for wants, val in zip(wanted, svals):
+            for want, styp in zip(wants, styps):
+                msg = f'for str({np.dtype(styp).name}({val!r}))'
+                assert_equal(str(styp(val)), want, err_msg=msg)
+
+    def test_scalar_cutoffs(self):
+        # test that both the str and repr of np.float64 behaves
+        # like python floats in python3.
+        def check(v):
+            assert_equal(str(np.float64(v)), str(v))
+            assert_equal(str(np.float64(v)), repr(v))
+            assert_equal(repr(np.float64(v)), f"np.float64({v!r})")
+            assert_equal(repr(np.float64(v)), f"np.float64({v})")
+
+        # check we use the same number of significant digits
+        check(1.12345678901234567890)
+        check(0.0112345678901234567890)
+
+        # check switch from scientific output to positional and back
+        check(1e-5)
+        check(1e-4)
+        check(1e15)
+        check(1e16)
+
+    test_cases_gh_28679 = [
+        (np.half, -0.000099, "-9.9e-05"),
+        (np.half, 0.0001, "0.0001"),
+        (np.half, 999, "999.0"),
+        (np.half, -1000, "-1e+03"),
+        (np.single, 0.000099, "9.9e-05"),
+        (np.single, -0.000100001, "-0.000100001"),
+        (np.single, 999999, "999999.0"),
+        (np.single, -1000000, "-1e+06")
+    ]
+
+    @pytest.mark.parametrize("dtype, input_val, expected_str", test_cases_gh_28679)
+    def test_gh_28679(self, dtype, input_val, expected_str):
+        # test cutoff to exponent notation for half and single
+        assert_equal(str(dtype(input_val)), expected_str)
+
+    test_cases_legacy_2_2 = [
+        (np.half(65504), "65500.0"),
+        (np.single(1.e15), "1000000000000000.0"),
+        (np.single(1.e16), "1e+16"),
+    ]
+
+    @pytest.mark.parametrize("input_val, expected_str", test_cases_legacy_2_2)
+    def test_legacy_2_2_mode(self, input_val, expected_str):
+        # test legacy cutoff to exponent notation for half and single
+        with np.printoptions(legacy='2.2'):
+            assert_equal(str(input_val), expected_str)
+
+    def test_dragon4(self):
+        # these tests are adapted from Ryan Juckett's dragon4 implementation,
+        # see dragon4.c for details.
+
+        fpos32 = lambda x, **k: np.format_float_positional(np.float32(x), **k)
+        fsci32 = lambda x, **k: np.format_float_scientific(np.float32(x), **k)
+        fpos64 = lambda x, **k: np.format_float_positional(np.float64(x), **k)
+        fsci64 = lambda x, **k: np.format_float_scientific(np.float64(x), **k)
+
+        preckwd = lambda prec: {'unique': False, 'precision': prec}
+
+        assert_equal(fpos32('1.0'), "1.")
+        assert_equal(fsci32('1.0'), "1.e+00")
+        assert_equal(fpos32('10.234'), "10.234")
+        assert_equal(fpos32('-10.234'), "-10.234")
+        assert_equal(fsci32('10.234'), "1.0234e+01")
+        assert_equal(fsci32('-10.234'), "-1.0234e+01")
+        assert_equal(fpos32('1000.0'), "1000.")
+        assert_equal(fpos32('1.0', precision=0), "1.")
+        assert_equal(fsci32('1.0', precision=0), "1.e+00")
+        assert_equal(fpos32('10.234', precision=0), "10.")
+        assert_equal(fpos32('-10.234', precision=0), "-10.")
+        assert_equal(fsci32('10.234', precision=0), "1.e+01")
+        assert_equal(fsci32('-10.234', precision=0), "-1.e+01")
+        assert_equal(fpos32('10.234', precision=2), "10.23")
+        assert_equal(fsci32('-10.234', precision=2), "-1.02e+01")
+        assert_equal(fsci64('9.9999999999999995e-08', **preckwd(16)),
+                            '9.9999999999999995e-08')
+        assert_equal(fsci64('9.8813129168249309e-324', **preckwd(16)),
+                            '9.8813129168249309e-324')
+        assert_equal(fsci64('9.9999999999999694e-311', **preckwd(16)),
+                            '9.9999999999999694e-311')
+
+        # test rounding
+        # 3.1415927410 is closest float32 to np.pi
+        assert_equal(fpos32('3.14159265358979323846', **preckwd(10)),
+                            "3.1415927410")
+        assert_equal(fsci32('3.14159265358979323846', **preckwd(10)),
+                            "3.1415927410e+00")
+        assert_equal(fpos64('3.14159265358979323846', **preckwd(10)),
+                            "3.1415926536")
+        assert_equal(fsci64('3.14159265358979323846', **preckwd(10)),
+                            "3.1415926536e+00")
+        # 299792448 is closest float32 to 299792458
+        assert_equal(fpos32('299792458.0', **preckwd(5)), "299792448.00000")
+        assert_equal(fsci32('299792458.0', **preckwd(5)), "2.99792e+08")
+        assert_equal(fpos64('299792458.0', **preckwd(5)), "299792458.00000")
+        assert_equal(fsci64('299792458.0', **preckwd(5)), "2.99792e+08")
+
+        assert_equal(fpos32('3.14159265358979323846', **preckwd(25)),
+                            "3.1415927410125732421875000")
+        assert_equal(fpos64('3.14159265358979323846', **preckwd(50)),
+                         "3.14159265358979311599796346854418516159057617187500")
+        assert_equal(fpos64('3.14159265358979323846'), "3.141592653589793")
+
+        # smallest numbers
+        assert_equal(fpos32(0.5**(126 + 23), unique=False, precision=149),
+                    "0.00000000000000000000000000000000000000000000140129846432"
+                    "4817070923729583289916131280261941876515771757068283889791"
+                    "08268586060148663818836212158203125")
+
+        assert_equal(fpos64(5e-324, unique=False, precision=1074),
+                    "0.00000000000000000000000000000000000000000000000000000000"
+                    "0000000000000000000000000000000000000000000000000000000000"
+                    "0000000000000000000000000000000000000000000000000000000000"
+                    "0000000000000000000000000000000000000000000000000000000000"
+                    "0000000000000000000000000000000000000000000000000000000000"
+                    "0000000000000000000000000000000000049406564584124654417656"
+                    "8792868221372365059802614324764425585682500675507270208751"
+                    "8652998363616359923797965646954457177309266567103559397963"
+                    "9877479601078187812630071319031140452784581716784898210368"
+                    "8718636056998730723050006387409153564984387312473397273169"
+                    "6151400317153853980741262385655911710266585566867681870395"
+                    "6031062493194527159149245532930545654440112748012970999954"
+                    "1931989409080416563324524757147869014726780159355238611550"
+                    "1348035264934720193790268107107491703332226844753335720832"
+                    "4319360923828934583680601060115061698097530783422773183292"
+                    "4790498252473077637592724787465608477820373446969953364701"
+                    "7972677717585125660551199131504891101451037862738167250955"
+                    "8373897335989936648099411642057026370902792427675445652290"
+                    "87538682506419718265533447265625")
+
+        # largest numbers
+        f32x = np.finfo(np.float32).max
+        assert_equal(fpos32(f32x, **preckwd(0)),
+                    "340282346638528859811704183484516925440.")
+        assert_equal(fpos64(np.finfo(np.float64).max, **preckwd(0)),
+                    "1797693134862315708145274237317043567980705675258449965989"
+                    "1747680315726078002853876058955863276687817154045895351438"
+                    "2464234321326889464182768467546703537516986049910576551282"
+                    "0762454900903893289440758685084551339423045832369032229481"
+                    "6580855933212334827479782620414472316873817718091929988125"
+                    "0404026184124858368.")
+        # Warning: In unique mode only the integer digits necessary for
+        # uniqueness are computed, the rest are 0.
+        assert_equal(fpos32(f32x),
+                    "340282350000000000000000000000000000000.")
+
+        # Further tests of zero-padding vs rounding in different combinations
+        # of unique, fractional, precision, min_digits
+        # precision can only reduce digits, not add them.
+        # min_digits can only extend digits, not reduce them.
+        assert_equal(fpos32(f32x, unique=True, fractional=True, precision=0),
+                    "340282350000000000000000000000000000000.")
+        assert_equal(fpos32(f32x, unique=True, fractional=True, precision=4),
+                    "340282350000000000000000000000000000000.")
+        assert_equal(fpos32(f32x, unique=True, fractional=True, min_digits=0),
+                    "340282346638528859811704183484516925440.")
+        assert_equal(fpos32(f32x, unique=True, fractional=True, min_digits=4),
+                    "340282346638528859811704183484516925440.0000")
+        assert_equal(fpos32(f32x, unique=True, fractional=True,
+                                    min_digits=4, precision=4),
+                    "340282346638528859811704183484516925440.0000")
+        assert_raises(ValueError, fpos32, f32x, unique=True, fractional=False,
+                                          precision=0)
+        assert_equal(fpos32(f32x, unique=True, fractional=False, precision=4),
+                    "340300000000000000000000000000000000000.")
+        assert_equal(fpos32(f32x, unique=True, fractional=False, precision=20),
+                    "340282350000000000000000000000000000000.")
+        assert_equal(fpos32(f32x, unique=True, fractional=False, min_digits=4),
+                    "340282350000000000000000000000000000000.")
+        assert_equal(fpos32(f32x, unique=True, fractional=False,
+                                  min_digits=20),
+                    "340282346638528859810000000000000000000.")
+        assert_equal(fpos32(f32x, unique=True, fractional=False,
+                                  min_digits=15),
+                    "340282346638529000000000000000000000000.")
+        assert_equal(fpos32(f32x, unique=False, fractional=False, precision=4),
+                    "340300000000000000000000000000000000000.")
+        # test that unique rounding is preserved when precision is supplied
+        # but no extra digits need to be printed (gh-18609)
+        a = np.float64.fromhex('-1p-97')
+        assert_equal(fsci64(a, unique=True), '-6.310887241768095e-30')
+        assert_equal(fsci64(a, unique=False, precision=15),
+                     '-6.310887241768094e-30')
+        assert_equal(fsci64(a, unique=True, precision=15),
+                     '-6.310887241768095e-30')
+        assert_equal(fsci64(a, unique=True, min_digits=15),
+                     '-6.310887241768095e-30')
+        assert_equal(fsci64(a, unique=True, precision=15, min_digits=15),
+                     '-6.310887241768095e-30')
+        # adds/remove digits in unique mode with unbiased rnding
+        assert_equal(fsci64(a, unique=True, precision=14),
+                     '-6.31088724176809e-30')
+        assert_equal(fsci64(a, unique=True, min_digits=16),
+                     '-6.3108872417680944e-30')
+        assert_equal(fsci64(a, unique=True, precision=16),
+                     '-6.310887241768095e-30')
+        assert_equal(fsci64(a, unique=True, min_digits=14),
+                     '-6.310887241768095e-30')
+        # test min_digits in unique mode with different rounding cases
+        assert_equal(fsci64('1e120', min_digits=3), '1.000e+120')
+        assert_equal(fsci64('1e100', min_digits=3), '1.000e+100')
+
+        # test trailing zeros
+        assert_equal(fpos32('1.0', unique=False, precision=3), "1.000")
+        assert_equal(fpos64('1.0', unique=False, precision=3), "1.000")
+        assert_equal(fsci32('1.0', unique=False, precision=3), "1.000e+00")
+        assert_equal(fsci64('1.0', unique=False, precision=3), "1.000e+00")
+        assert_equal(fpos32('1.5', unique=False, precision=3), "1.500")
+        assert_equal(fpos64('1.5', unique=False, precision=3), "1.500")
+        assert_equal(fsci32('1.5', unique=False, precision=3), "1.500e+00")
+        assert_equal(fsci64('1.5', unique=False, precision=3), "1.500e+00")
+        # gh-10713
+        assert_equal(fpos64('324', unique=False, precision=5,
+                                   fractional=False), "324.00")
+
+    available_float_dtypes = [np.float16, np.float32, np.float64, np.float128]\
+        if hasattr(np, 'float128') else [np.float16, np.float32, np.float64]
+
+    @pytest.mark.parametrize("tp", available_float_dtypes)
+    def test_dragon4_positional_interface(self, tp):
+        # test is flaky for musllinux on np.float128
+        if IS_MUSL and tp == np.float128:
+            pytest.skip("Skipping flaky test of float128 on musllinux")
+
+        fpos = np.format_float_positional
+
+        # test padding
+        assert_equal(fpos(tp('1.0'), pad_left=4, pad_right=4), "   1.    ")
+        assert_equal(fpos(tp('-1.0'), pad_left=4, pad_right=4), "  -1.    ")
+        assert_equal(fpos(tp('-10.2'),
+                        pad_left=4, pad_right=4), " -10.2   ")
+
+        # test fixed (non-unique) mode
+        assert_equal(fpos(tp('1.0'), unique=False, precision=4), "1.0000")
+
+    @pytest.mark.parametrize("tp", available_float_dtypes)
+    def test_dragon4_positional_interface_trim(self, tp):
+        # test is flaky for musllinux on np.float128
+        if IS_MUSL and tp == np.float128:
+            pytest.skip("Skipping flaky test of float128 on musllinux")
+
+        fpos = np.format_float_positional
+        # test trimming
+        # trim of 'k' or '.' only affects non-unique mode, since unique
+        # mode will not output trailing 0s.
+        assert_equal(fpos(tp('1.'), unique=False, precision=4, trim='k'),
+                        "1.0000")
+
+        assert_equal(fpos(tp('1.'), unique=False, precision=4, trim='.'),
+                        "1.")
+        assert_equal(fpos(tp('1.2'), unique=False, precision=4, trim='.'),
+                        "1.2" if tp != np.float16 else "1.2002")
+
+        assert_equal(fpos(tp('1.'), unique=False, precision=4, trim='0'),
+                        "1.0")
+        assert_equal(fpos(tp('1.2'), unique=False, precision=4, trim='0'),
+                        "1.2" if tp != np.float16 else "1.2002")
+        assert_equal(fpos(tp('1.'), trim='0'), "1.0")
+
+        assert_equal(fpos(tp('1.'), unique=False, precision=4, trim='-'),
+                        "1")
+        assert_equal(fpos(tp('1.2'), unique=False, precision=4, trim='-'),
+                        "1.2" if tp != np.float16 else "1.2002")
+        assert_equal(fpos(tp('1.'), trim='-'), "1")
+        assert_equal(fpos(tp('1.001'), precision=1, trim='-'), "1")
+
+    @pytest.mark.parametrize("tp", available_float_dtypes)
+    @pytest.mark.parametrize("pad_val", [10**5, np.iinfo("int32").max])
+    def test_dragon4_positional_interface_overflow(self, tp, pad_val):
+        # test is flaky for musllinux on np.float128
+        if IS_MUSL and tp == np.float128:
+            pytest.skip("Skipping flaky test of float128 on musllinux")
+
+        fpos = np.format_float_positional
+
+        # gh-28068
+        with pytest.raises(RuntimeError,
+                           match="Float formatting result too large"):
+            fpos(tp('1.047'), unique=False, precision=pad_val)
+
+        with pytest.raises(RuntimeError,
+                           match="Float formatting result too large"):
+            fpos(tp('1.047'), precision=2, pad_left=pad_val)
+
+        with pytest.raises(RuntimeError,
+                           match="Float formatting result too large"):
+            fpos(tp('1.047'), precision=2, pad_right=pad_val)
+
+    @pytest.mark.parametrize("tp", available_float_dtypes)
+    def test_dragon4_scientific_interface(self, tp):
+        # test is flaky for musllinux on np.float128
+        if IS_MUSL and tp == np.float128:
+            pytest.skip("Skipping flaky test of float128 on musllinux")
+
+        fsci = np.format_float_scientific
+
+        # test exp_digits
+        assert_equal(fsci(tp('1.23e1'), exp_digits=5), "1.23e+00001")
+
+        # test fixed (non-unique) mode
+        assert_equal(fsci(tp('1.0'), unique=False, precision=4),
+                        "1.0000e+00")
+
+    @pytest.mark.skipif(not platform.machine().startswith("ppc64"),
+                        reason="only applies to ppc float128 values")
+    def test_ppc64_ibm_double_double128(self):
+        # check that the precision decreases once we get into the subnormal
+        # range. Unlike float64, this starts around 1e-292 instead of 1e-308,
+        # which happens when the first double is normal and the second is
+        # subnormal.
+        x = np.float128('2.123123123123123123123123123123123e-286')
+        got = [str(x / np.float128('2e' + str(i))) for i in range(40)]
+        expected = [
+            "1.06156156156156156156156156156157e-286",
+            "1.06156156156156156156156156156158e-287",
+            "1.06156156156156156156156156156159e-288",
+            "1.0615615615615615615615615615616e-289",
+            "1.06156156156156156156156156156157e-290",
+            "1.06156156156156156156156156156156e-291",
+            "1.0615615615615615615615615615616e-292",
+            "1.0615615615615615615615615615615e-293",
+            "1.061561561561561561561561561562e-294",
+            "1.06156156156156156156156156155e-295",
+            "1.0615615615615615615615615616e-296",
+            "1.06156156156156156156156156e-297",
+            "1.06156156156156156156156157e-298",
+            "1.0615615615615615615615616e-299",
+            "1.06156156156156156156156e-300",
+            "1.06156156156156156156155e-301",
+            "1.0615615615615615615616e-302",
+            "1.061561561561561561562e-303",
+            "1.06156156156156156156e-304",
+            "1.0615615615615615618e-305",
+            "1.06156156156156156e-306",
+            "1.06156156156156157e-307",
+            "1.0615615615615616e-308",
+            "1.06156156156156e-309",
+            "1.06156156156157e-310",
+            "1.0615615615616e-311",
+            "1.06156156156e-312",
+            "1.06156156154e-313",
+            "1.0615615616e-314",
+            "1.06156156e-315",
+            "1.06156155e-316",
+            "1.061562e-317",
+            "1.06156e-318",
+            "1.06155e-319",
+            "1.0617e-320",
+            "1.06e-321",
+            "1.04e-322",
+            "1e-323",
+            "0.0",
+            "0.0"]
+        assert_equal(got, expected)
+
+        # Note: we follow glibc behavior, but it (or gcc) might not be right.
+        # In particular we can get two values that print the same but are not
+        # equal:
+        a = np.float128('2') / np.float128('3')
+        b = np.float128(str(a))
+        assert_equal(str(a), str(b))
+        assert_(a != b)
+
+    def float32_roundtrip(self):
+        # gh-9360
+        x = np.float32(1024 - 2**-14)
+        y = np.float32(1024 - 2**-13)
+        assert_(repr(x) != repr(y))
+        assert_equal(np.float32(repr(x)), x)
+        assert_equal(np.float32(repr(y)), y)
+
+    def float64_vs_python(self):
+        # gh-2643, gh-6136, gh-6908
+        assert_equal(repr(np.float64(0.1)), repr(0.1))
+        assert_(repr(np.float64(0.20000000000000004)) != repr(0.2))
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_shape_base.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_shape_base.py
new file mode 100644
index 0000000..8de2427
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_shape_base.py
@@ -0,0 +1,891 @@
+import sys
+
+import pytest
+
+import numpy as np
+from numpy._core import (
+    arange,
+    array,
+    atleast_1d,
+    atleast_2d,
+    atleast_3d,
+    block,
+    concatenate,
+    hstack,
+    newaxis,
+    stack,
+    vstack,
+)
+from numpy._core.shape_base import (
+    _block_concatenate,
+    _block_dispatcher,
+    _block_setup,
+    _block_slicing,
+)
+from numpy.exceptions import AxisError
+from numpy.testing import (
+    IS_PYPY,
+    assert_,
+    assert_array_equal,
+    assert_equal,
+    assert_raises,
+    assert_raises_regex,
+)
+from numpy.testing._private.utils import requires_memory
+
+
+class TestAtleast1d:
+    def test_0D_array(self):
+        a = array(1)
+        b = array(2)
+        res = [atleast_1d(a), atleast_1d(b)]
+        desired = [array([1]), array([2])]
+        assert_array_equal(res, desired)
+
+    def test_1D_array(self):
+        a = array([1, 2])
+        b = array([2, 3])
+        res = [atleast_1d(a), atleast_1d(b)]
+        desired = [array([1, 2]), array([2, 3])]
+        assert_array_equal(res, desired)
+
+    def test_2D_array(self):
+        a = array([[1, 2], [1, 2]])
+        b = array([[2, 3], [2, 3]])
+        res = [atleast_1d(a), atleast_1d(b)]
+        desired = [a, b]
+        assert_array_equal(res, desired)
+
+    def test_3D_array(self):
+        a = array([[1, 2], [1, 2]])
+        b = array([[2, 3], [2, 3]])
+        a = array([a, a])
+        b = array([b, b])
+        res = [atleast_1d(a), atleast_1d(b)]
+        desired = [a, b]
+        assert_array_equal(res, desired)
+
+    def test_r1array(self):
+        """ Test to make sure equivalent Travis O's r1array function
+        """
+        assert_(atleast_1d(3).shape == (1,))
+        assert_(atleast_1d(3j).shape == (1,))
+        assert_(atleast_1d(3.0).shape == (1,))
+        assert_(atleast_1d([[2, 3], [4, 5]]).shape == (2, 2))
+
+
+class TestAtleast2d:
+    def test_0D_array(self):
+        a = array(1)
+        b = array(2)
+        res = [atleast_2d(a), atleast_2d(b)]
+        desired = [array([[1]]), array([[2]])]
+        assert_array_equal(res, desired)
+
+    def test_1D_array(self):
+        a = array([1, 2])
+        b = array([2, 3])
+        res = [atleast_2d(a), atleast_2d(b)]
+        desired = [array([[1, 2]]), array([[2, 3]])]
+        assert_array_equal(res, desired)
+
+    def test_2D_array(self):
+        a = array([[1, 2], [1, 2]])
+        b = array([[2, 3], [2, 3]])
+        res = [atleast_2d(a), atleast_2d(b)]
+        desired = [a, b]
+        assert_array_equal(res, desired)
+
+    def test_3D_array(self):
+        a = array([[1, 2], [1, 2]])
+        b = array([[2, 3], [2, 3]])
+        a = array([a, a])
+        b = array([b, b])
+        res = [atleast_2d(a), atleast_2d(b)]
+        desired = [a, b]
+        assert_array_equal(res, desired)
+
+    def test_r2array(self):
+        """ Test to make sure equivalent Travis O's r2array function
+        """
+        assert_(atleast_2d(3).shape == (1, 1))
+        assert_(atleast_2d([3j, 1]).shape == (1, 2))
+        assert_(atleast_2d([[[3, 1], [4, 5]], [[3, 5], [1, 2]]]).shape == (2, 2, 2))
+
+
+class TestAtleast3d:
+    def test_0D_array(self):
+        a = array(1)
+        b = array(2)
+        res = [atleast_3d(a), atleast_3d(b)]
+        desired = [array([[[1]]]), array([[[2]]])]
+        assert_array_equal(res, desired)
+
+    def test_1D_array(self):
+        a = array([1, 2])
+        b = array([2, 3])
+        res = [atleast_3d(a), atleast_3d(b)]
+        desired = [array([[[1], [2]]]), array([[[2], [3]]])]
+        assert_array_equal(res, desired)
+
+    def test_2D_array(self):
+        a = array([[1, 2], [1, 2]])
+        b = array([[2, 3], [2, 3]])
+        res = [atleast_3d(a), atleast_3d(b)]
+        desired = [a[:, :, newaxis], b[:, :, newaxis]]
+        assert_array_equal(res, desired)
+
+    def test_3D_array(self):
+        a = array([[1, 2], [1, 2]])
+        b = array([[2, 3], [2, 3]])
+        a = array([a, a])
+        b = array([b, b])
+        res = [atleast_3d(a), atleast_3d(b)]
+        desired = [a, b]
+        assert_array_equal(res, desired)
+
+
+class TestHstack:
+    def test_non_iterable(self):
+        assert_raises(TypeError, hstack, 1)
+
+    def test_empty_input(self):
+        assert_raises(ValueError, hstack, ())
+
+    def test_0D_array(self):
+        a = array(1)
+        b = array(2)
+        res = hstack([a, b])
+        desired = array([1, 2])
+        assert_array_equal(res, desired)
+
+    def test_1D_array(self):
+        a = array([1])
+        b = array([2])
+        res = hstack([a, b])
+        desired = array([1, 2])
+        assert_array_equal(res, desired)
+
+    def test_2D_array(self):
+        a = array([[1], [2]])
+        b = array([[1], [2]])
+        res = hstack([a, b])
+        desired = array([[1, 1], [2, 2]])
+        assert_array_equal(res, desired)
+
+    def test_generator(self):
+        with pytest.raises(TypeError, match="arrays to stack must be"):
+            hstack(np.arange(3) for _ in range(2))
+        with pytest.raises(TypeError, match="arrays to stack must be"):
+            hstack(x for x in np.ones((3, 2)))
+
+    def test_casting_and_dtype(self):
+        a = np.array([1, 2, 3])
+        b = np.array([2.5, 3.5, 4.5])
+        res = np.hstack((a, b), casting="unsafe", dtype=np.int64)
+        expected_res = np.array([1, 2, 3, 2, 3, 4])
+        assert_array_equal(res, expected_res)
+
+    def test_casting_and_dtype_type_error(self):
+        a = np.array([1, 2, 3])
+        b = np.array([2.5, 3.5, 4.5])
+        with pytest.raises(TypeError):
+            hstack((a, b), casting="safe", dtype=np.int64)
+
+
+class TestVstack:
+    def test_non_iterable(self):
+        assert_raises(TypeError, vstack, 1)
+
+    def test_empty_input(self):
+        assert_raises(ValueError, vstack, ())
+
+    def test_0D_array(self):
+        a = array(1)
+        b = array(2)
+        res = vstack([a, b])
+        desired = array([[1], [2]])
+        assert_array_equal(res, desired)
+
+    def test_1D_array(self):
+        a = array([1])
+        b = array([2])
+        res = vstack([a, b])
+        desired = array([[1], [2]])
+        assert_array_equal(res, desired)
+
+    def test_2D_array(self):
+        a = array([[1], [2]])
+        b = array([[1], [2]])
+        res = vstack([a, b])
+        desired = array([[1], [2], [1], [2]])
+        assert_array_equal(res, desired)
+
+    def test_2D_array2(self):
+        a = array([1, 2])
+        b = array([1, 2])
+        res = vstack([a, b])
+        desired = array([[1, 2], [1, 2]])
+        assert_array_equal(res, desired)
+
+    def test_generator(self):
+        with pytest.raises(TypeError, match="arrays to stack must be"):
+            vstack(np.arange(3) for _ in range(2))
+
+    def test_casting_and_dtype(self):
+        a = np.array([1, 2, 3])
+        b = np.array([2.5, 3.5, 4.5])
+        res = np.vstack((a, b), casting="unsafe", dtype=np.int64)
+        expected_res = np.array([[1, 2, 3], [2, 3, 4]])
+        assert_array_equal(res, expected_res)
+
+    def test_casting_and_dtype_type_error(self):
+        a = np.array([1, 2, 3])
+        b = np.array([2.5, 3.5, 4.5])
+        with pytest.raises(TypeError):
+            vstack((a, b), casting="safe", dtype=np.int64)
+
+
+class TestConcatenate:
+    def test_returns_copy(self):
+        a = np.eye(3)
+        b = np.concatenate([a])
+        b[0, 0] = 2
+        assert b[0, 0] != a[0, 0]
+
+    def test_exceptions(self):
+        # test axis must be in bounds
+        for ndim in [1, 2, 3]:
+            a = np.ones((1,) * ndim)
+            np.concatenate((a, a), axis=0)  # OK
+            assert_raises(AxisError, np.concatenate, (a, a), axis=ndim)
+            assert_raises(AxisError, np.concatenate, (a, a), axis=-(ndim + 1))
+
+        # Scalars cannot be concatenated
+        assert_raises(ValueError, concatenate, (0,))
+        assert_raises(ValueError, concatenate, (np.array(0),))
+
+        # dimensionality must match
+        assert_raises_regex(
+            ValueError,
+            r"all the input arrays must have same number of dimensions, but "
+            r"the array at index 0 has 1 dimension\(s\) and the array at "
+            r"index 1 has 2 dimension\(s\)",
+            np.concatenate, (np.zeros(1), np.zeros((1, 1))))
+
+        # test shapes must match except for concatenation axis
+        a = np.ones((1, 2, 3))
+        b = np.ones((2, 2, 3))
+        axis = list(range(3))
+        for i in range(3):
+            np.concatenate((a, b), axis=axis[0])  # OK
+            assert_raises_regex(
+                ValueError,
+                "all the input array dimensions except for the concatenation axis "
+                f"must match exactly, but along dimension {i}, the array at "
+                "index 0 has size 1 and the array at index 1 has size 2",
+                np.concatenate, (a, b), axis=axis[1])
+            assert_raises(ValueError, np.concatenate, (a, b), axis=axis[2])
+            a = np.moveaxis(a, -1, 0)
+            b = np.moveaxis(b, -1, 0)
+            axis.append(axis.pop(0))
+
+        # No arrays to concatenate raises ValueError
+        assert_raises(ValueError, concatenate, ())
+
+    @pytest.mark.slow
+    @pytest.mark.skipif(sys.maxsize < 2**32, reason="only problematic on 64bit platforms")
+    @requires_memory(2 * np.iinfo(np.intc).max)
+    def test_huge_list_error(self):
+        a = np.array([1])
+        max_int = np.iinfo(np.intc).max
+        arrs = (a,) * (max_int + 1)
+        msg = fr"concatenate\(\) only supports up to {max_int} arrays but got {max_int + 1}."
+        with pytest.raises(ValueError, match=msg):
+            np.concatenate(arrs)
+
+    def test_concatenate_axis_None(self):
+        a = np.arange(4, dtype=np.float64).reshape((2, 2))
+        b = list(range(3))
+        c = ['x']
+        r = np.concatenate((a, a), axis=None)
+        assert_equal(r.dtype, a.dtype)
+        assert_equal(r.ndim, 1)
+        r = np.concatenate((a, b), axis=None)
+        assert_equal(r.size, a.size + len(b))
+        assert_equal(r.dtype, a.dtype)
+        r = np.concatenate((a, b, c), axis=None, dtype="U")
+        d = array(['0.0', '1.0', '2.0', '3.0',
+                   '0', '1', '2', 'x'])
+        assert_array_equal(r, d)
+
+        out = np.zeros(a.size + len(b))
+        r = np.concatenate((a, b), axis=None)
+        rout = np.concatenate((a, b), axis=None, out=out)
+        assert_(out is rout)
+        assert_equal(r, rout)
+
+    def test_large_concatenate_axis_None(self):
+        # When no axis is given, concatenate uses flattened versions.
+        # This also had a bug with many arrays (see gh-5979).
+        x = np.arange(1, 100)
+        r = np.concatenate(x, None)
+        assert_array_equal(x, r)
+
+        # Once upon a time, this was the same as `axis=None` now it fails
+        # (with an unspecified error, as multiple things are wrong here)
+        with pytest.raises(ValueError):
+            np.concatenate(x, 100)
+
+    def test_concatenate(self):
+        # Test concatenate function
+        # One sequence returns unmodified (but as array)
+        r4 = list(range(4))
+        assert_array_equal(concatenate((r4,)), r4)
+        # Any sequence
+        assert_array_equal(concatenate((tuple(r4),)), r4)
+        assert_array_equal(concatenate((array(r4),)), r4)
+        # 1D default concatenation
+        r3 = list(range(3))
+        assert_array_equal(concatenate((r4, r3)), r4 + r3)
+        # Mixed sequence types
+        assert_array_equal(concatenate((tuple(r4), r3)), r4 + r3)
+        assert_array_equal(concatenate((array(r4), r3)), r4 + r3)
+        # Explicit axis specification
+        assert_array_equal(concatenate((r4, r3), 0), r4 + r3)
+        # Including negative
+        assert_array_equal(concatenate((r4, r3), -1), r4 + r3)
+        # 2D
+        a23 = array([[10, 11, 12], [13, 14, 15]])
+        a13 = array([[0, 1, 2]])
+        res = array([[10, 11, 12], [13, 14, 15], [0, 1, 2]])
+        assert_array_equal(concatenate((a23, a13)), res)
+        assert_array_equal(concatenate((a23, a13), 0), res)
+        assert_array_equal(concatenate((a23.T, a13.T), 1), res.T)
+        assert_array_equal(concatenate((a23.T, a13.T), -1), res.T)
+        # Arrays much match shape
+        assert_raises(ValueError, concatenate, (a23.T, a13.T), 0)
+        # 3D
+        res = arange(2 * 3 * 7).reshape((2, 3, 7))
+        a0 = res[..., :4]
+        a1 = res[..., 4:6]
+        a2 = res[..., 6:]
+        assert_array_equal(concatenate((a0, a1, a2), 2), res)
+        assert_array_equal(concatenate((a0, a1, a2), -1), res)
+        assert_array_equal(concatenate((a0.T, a1.T, a2.T), 0), res.T)
+
+        out = res.copy()
+        rout = concatenate((a0, a1, a2), 2, out=out)
+        assert_(out is rout)
+        assert_equal(res, rout)
+
+    @pytest.mark.skipif(IS_PYPY, reason="PYPY handles sq_concat, nb_add differently than cpython")
+    def test_operator_concat(self):
+        import operator
+        a = array([1, 2])
+        b = array([3, 4])
+        n = [1, 2]
+        res = array([1, 2, 3, 4])
+        assert_raises(TypeError, operator.concat, a, b)
+        assert_raises(TypeError, operator.concat, a, n)
+        assert_raises(TypeError, operator.concat, n, a)
+        assert_raises(TypeError, operator.concat, a, 1)
+        assert_raises(TypeError, operator.concat, 1, a)
+
+    def test_bad_out_shape(self):
+        a = array([1, 2])
+        b = array([3, 4])
+
+        assert_raises(ValueError, concatenate, (a, b), out=np.empty(5))
+        assert_raises(ValueError, concatenate, (a, b), out=np.empty((4, 1)))
+        assert_raises(ValueError, concatenate, (a, b), out=np.empty((1, 4)))
+        concatenate((a, b), out=np.empty(4))
+
+    @pytest.mark.parametrize("axis", [None, 0])
+    @pytest.mark.parametrize("out_dtype", ["c8", "f4", "f8", ">f8", "i8", "S4"])
+    @pytest.mark.parametrize("casting",
+            ['no', 'equiv', 'safe', 'same_kind', 'unsafe'])
+    def test_out_and_dtype(self, axis, out_dtype, casting):
+        # Compare usage of `out=out` with `dtype=out.dtype`
+        out = np.empty(4, dtype=out_dtype)
+        to_concat = (array([1.1, 2.2]), array([3.3, 4.4]))
+
+        if not np.can_cast(to_concat[0], out_dtype, casting=casting):
+            with assert_raises(TypeError):
+                concatenate(to_concat, out=out, axis=axis, casting=casting)
+            with assert_raises(TypeError):
+                concatenate(to_concat, dtype=out.dtype,
+                            axis=axis, casting=casting)
+        else:
+            res_out = concatenate(to_concat, out=out,
+                                  axis=axis, casting=casting)
+            res_dtype = concatenate(to_concat, dtype=out.dtype,
+                                    axis=axis, casting=casting)
+            assert res_out is out
+            assert_array_equal(out, res_dtype)
+            assert res_dtype.dtype == out_dtype
+
+        with assert_raises(TypeError):
+            concatenate(to_concat, out=out, dtype=out_dtype, axis=axis)
+
+    @pytest.mark.parametrize("axis", [None, 0])
+    @pytest.mark.parametrize("string_dt", ["S", "U", "S0", "U0"])
+    @pytest.mark.parametrize("arrs",
+            [([0.],), ([0.], [1]), ([0], ["string"], [1.])])
+    def test_dtype_with_promotion(self, arrs, string_dt, axis):
+        # Note that U0 and S0 should be deprecated eventually and changed to
+        # actually give the empty string result (together with `np.array`)
+        res = np.concatenate(arrs, axis=axis, dtype=string_dt, casting="unsafe")
+        # The actual dtype should be identical to a cast (of a double array):
+        assert res.dtype == np.array(1.).astype(string_dt).dtype
+
+    @pytest.mark.parametrize("axis", [None, 0])
+    def test_string_dtype_does_not_inspect(self, axis):
+        with pytest.raises(TypeError):
+            np.concatenate(([None], [1]), dtype="S", axis=axis)
+        with pytest.raises(TypeError):
+            np.concatenate(([None], [1]), dtype="U", axis=axis)
+
+    @pytest.mark.parametrize("axis", [None, 0])
+    def test_subarray_error(self, axis):
+        with pytest.raises(TypeError, match=".*subarray dtype"):
+            np.concatenate(([1], [1]), dtype="(2,)i", axis=axis)
+
+
+def test_stack():
+    # non-iterable input
+    assert_raises(TypeError, stack, 1)
+
+    # 0d input
+    for input_ in [(1, 2, 3),
+                   [np.int32(1), np.int32(2), np.int32(3)],
+                   [np.array(1), np.array(2), np.array(3)]]:
+        assert_array_equal(stack(input_), [1, 2, 3])
+    # 1d input examples
+    a = np.array([1, 2, 3])
+    b = np.array([4, 5, 6])
+    r1 = array([[1, 2, 3], [4, 5, 6]])
+    assert_array_equal(np.stack((a, b)), r1)
+    assert_array_equal(np.stack((a, b), axis=1), r1.T)
+    # all input types
+    assert_array_equal(np.stack([a, b]), r1)
+    assert_array_equal(np.stack(array([a, b])), r1)
+    # all shapes for 1d input
+    arrays = [np.random.randn(3) for _ in range(10)]
+    axes = [0, 1, -1, -2]
+    expected_shapes = [(10, 3), (3, 10), (3, 10), (10, 3)]
+    for axis, expected_shape in zip(axes, expected_shapes):
+        assert_equal(np.stack(arrays, axis).shape, expected_shape)
+    assert_raises_regex(AxisError, 'out of bounds', stack, arrays, axis=2)
+    assert_raises_regex(AxisError, 'out of bounds', stack, arrays, axis=-3)
+    # all shapes for 2d input
+    arrays = [np.random.randn(3, 4) for _ in range(10)]
+    axes = [0, 1, 2, -1, -2, -3]
+    expected_shapes = [(10, 3, 4), (3, 10, 4), (3, 4, 10),
+                       (3, 4, 10), (3, 10, 4), (10, 3, 4)]
+    for axis, expected_shape in zip(axes, expected_shapes):
+        assert_equal(np.stack(arrays, axis).shape, expected_shape)
+    # empty arrays
+    assert_(stack([[], [], []]).shape == (3, 0))
+    assert_(stack([[], [], []], axis=1).shape == (0, 3))
+    # out
+    out = np.zeros_like(r1)
+    np.stack((a, b), out=out)
+    assert_array_equal(out, r1)
+    # edge cases
+    assert_raises_regex(ValueError, 'need at least one array', stack, [])
+    assert_raises_regex(ValueError, 'must have the same shape',
+                        stack, [1, np.arange(3)])
+    assert_raises_regex(ValueError, 'must have the same shape',
+                        stack, [np.arange(3), 1])
+    assert_raises_regex(ValueError, 'must have the same shape',
+                        stack, [np.arange(3), 1], axis=1)
+    assert_raises_regex(ValueError, 'must have the same shape',
+                        stack, [np.zeros((3, 3)), np.zeros(3)], axis=1)
+    assert_raises_regex(ValueError, 'must have the same shape',
+                        stack, [np.arange(2), np.arange(3)])
+
+    # do not accept generators
+    with pytest.raises(TypeError, match="arrays to stack must be"):
+        stack(x for x in range(3))
+
+    # casting and dtype test
+    a = np.array([1, 2, 3])
+    b = np.array([2.5, 3.5, 4.5])
+    res = np.stack((a, b), axis=1, casting="unsafe", dtype=np.int64)
+    expected_res = np.array([[1, 2], [2, 3], [3, 4]])
+    assert_array_equal(res, expected_res)
+    # casting and dtype with TypeError
+    with assert_raises(TypeError):
+        stack((a, b), dtype=np.int64, axis=1, casting="safe")
+
+
+def test_unstack():
+    a = np.arange(24).reshape((2, 3, 4))
+
+    for stacks in [np.unstack(a),
+                   np.unstack(a, axis=0),
+                   np.unstack(a, axis=-3)]:
+        assert isinstance(stacks, tuple)
+        assert len(stacks) == 2
+        assert_array_equal(stacks[0], a[0])
+        assert_array_equal(stacks[1], a[1])
+
+    for stacks in [np.unstack(a, axis=1),
+                   np.unstack(a, axis=-2)]:
+        assert isinstance(stacks, tuple)
+        assert len(stacks) == 3
+        assert_array_equal(stacks[0], a[:, 0])
+        assert_array_equal(stacks[1], a[:, 1])
+        assert_array_equal(stacks[2], a[:, 2])
+
+    for stacks in [np.unstack(a, axis=2),
+                   np.unstack(a, axis=-1)]:
+        assert isinstance(stacks, tuple)
+        assert len(stacks) == 4
+        assert_array_equal(stacks[0], a[:, :, 0])
+        assert_array_equal(stacks[1], a[:, :, 1])
+        assert_array_equal(stacks[2], a[:, :, 2])
+        assert_array_equal(stacks[3], a[:, :, 3])
+
+    assert_raises(ValueError, np.unstack, a, axis=3)
+    assert_raises(ValueError, np.unstack, a, axis=-4)
+    assert_raises(ValueError, np.unstack, np.array(0), axis=0)
+
+
+@pytest.mark.parametrize("axis", [0])
+@pytest.mark.parametrize("out_dtype", ["c8", "f4", "f8", ">f8", "i8"])
+@pytest.mark.parametrize("casting",
+                         ['no', 'equiv', 'safe', 'same_kind', 'unsafe'])
+def test_stack_out_and_dtype(axis, out_dtype, casting):
+    to_concat = (array([1, 2]), array([3, 4]))
+    res = array([[1, 2], [3, 4]])
+    out = np.zeros_like(res)
+
+    if not np.can_cast(to_concat[0], out_dtype, casting=casting):
+        with assert_raises(TypeError):
+            stack(to_concat, dtype=out_dtype,
+                  axis=axis, casting=casting)
+    else:
+        res_out = stack(to_concat, out=out,
+                        axis=axis, casting=casting)
+        res_dtype = stack(to_concat, dtype=out_dtype,
+                          axis=axis, casting=casting)
+        assert res_out is out
+        assert_array_equal(out, res_dtype)
+        assert res_dtype.dtype == out_dtype
+
+    with assert_raises(TypeError):
+        stack(to_concat, out=out, dtype=out_dtype, axis=axis)
+
+
+class TestBlock:
+    @pytest.fixture(params=['block', 'force_concatenate', 'force_slicing'])
+    def block(self, request):
+        # blocking small arrays and large arrays go through different paths.
+        # the algorithm is triggered depending on the number of element
+        # copies required.
+        # We define a test fixture that forces most tests to go through
+        # both code paths.
+        # Ultimately, this should be removed if a single algorithm is found
+        # to be faster for both small and large arrays.
+        def _block_force_concatenate(arrays):
+            arrays, list_ndim, result_ndim, _ = _block_setup(arrays)
+            return _block_concatenate(arrays, list_ndim, result_ndim)
+
+        def _block_force_slicing(arrays):
+            arrays, list_ndim, result_ndim, _ = _block_setup(arrays)
+            return _block_slicing(arrays, list_ndim, result_ndim)
+
+        if request.param == 'force_concatenate':
+            return _block_force_concatenate
+        elif request.param == 'force_slicing':
+            return _block_force_slicing
+        elif request.param == 'block':
+            return block
+        else:
+            raise ValueError('Unknown blocking request. There is a typo in the tests.')
+
+    def test_returns_copy(self, block):
+        a = np.eye(3)
+        b = block(a)
+        b[0, 0] = 2
+        assert b[0, 0] != a[0, 0]
+
+    def test_block_total_size_estimate(self, block):
+        _, _, _, total_size = _block_setup([1])
+        assert total_size == 1
+
+        _, _, _, total_size = _block_setup([[1]])
+        assert total_size == 1
+
+        _, _, _, total_size = _block_setup([[1, 1]])
+        assert total_size == 2
+
+        _, _, _, total_size = _block_setup([[1], [1]])
+        assert total_size == 2
+
+        _, _, _, total_size = _block_setup([[1, 2], [3, 4]])
+        assert total_size == 4
+
+    def test_block_simple_row_wise(self, block):
+        a_2d = np.ones((2, 2))
+        b_2d = 2 * a_2d
+        desired = np.array([[1, 1, 2, 2],
+                            [1, 1, 2, 2]])
+        result = block([a_2d, b_2d])
+        assert_equal(desired, result)
+
+    def test_block_simple_column_wise(self, block):
+        a_2d = np.ones((2, 2))
+        b_2d = 2 * a_2d
+        expected = np.array([[1, 1],
+                             [1, 1],
+                             [2, 2],
+                             [2, 2]])
+        result = block([[a_2d], [b_2d]])
+        assert_equal(expected, result)
+
+    def test_block_with_1d_arrays_row_wise(self, block):
+        # # # 1-D vectors are treated as row arrays
+        a = np.array([1, 2, 3])
+        b = np.array([2, 3, 4])
+        expected = np.array([1, 2, 3, 2, 3, 4])
+        result = block([a, b])
+        assert_equal(expected, result)
+
+    def test_block_with_1d_arrays_multiple_rows(self, block):
+        a = np.array([1, 2, 3])
+        b = np.array([2, 3, 4])
+        expected = np.array([[1, 2, 3, 2, 3, 4],
+                             [1, 2, 3, 2, 3, 4]])
+        result = block([[a, b], [a, b]])
+        assert_equal(expected, result)
+
+    def test_block_with_1d_arrays_column_wise(self, block):
+        # # # 1-D vectors are treated as row arrays
+        a_1d = np.array([1, 2, 3])
+        b_1d = np.array([2, 3, 4])
+        expected = np.array([[1, 2, 3],
+                             [2, 3, 4]])
+        result = block([[a_1d], [b_1d]])
+        assert_equal(expected, result)
+
+    def test_block_mixed_1d_and_2d(self, block):
+        a_2d = np.ones((2, 2))
+        b_1d = np.array([2, 2])
+        result = block([[a_2d], [b_1d]])
+        expected = np.array([[1, 1],
+                             [1, 1],
+                             [2, 2]])
+        assert_equal(expected, result)
+
+    def test_block_complicated(self, block):
+        # a bit more complicated
+        one_2d = np.array([[1, 1, 1]])
+        two_2d = np.array([[2, 2, 2]])
+        three_2d = np.array([[3, 3, 3, 3, 3, 3]])
+        four_1d = np.array([4, 4, 4, 4, 4, 4])
+        five_0d = np.array(5)
+        six_1d = np.array([6, 6, 6, 6, 6])
+        zero_2d = np.zeros((2, 6))
+
+        expected = np.array([[1, 1, 1, 2, 2, 2],
+                             [3, 3, 3, 3, 3, 3],
+                             [4, 4, 4, 4, 4, 4],
+                             [5, 6, 6, 6, 6, 6],
+                             [0, 0, 0, 0, 0, 0],
+                             [0, 0, 0, 0, 0, 0]])
+
+        result = block([[one_2d, two_2d],
+                        [three_2d],
+                        [four_1d],
+                        [five_0d, six_1d],
+                        [zero_2d]])
+        assert_equal(result, expected)
+
+    def test_nested(self, block):
+        one = np.array([1, 1, 1])
+        two = np.array([[2, 2, 2], [2, 2, 2], [2, 2, 2]])
+        three = np.array([3, 3, 3])
+        four = np.array([4, 4, 4])
+        five = np.array(5)
+        six = np.array([6, 6, 6, 6, 6])
+        zero = np.zeros((2, 6))
+
+        result = block([
+            [
+                block([
+                   [one],
+                   [three],
+                   [four]
+                ]),
+                two
+            ],
+            [five, six],
+            [zero]
+        ])
+        expected = np.array([[1, 1, 1, 2, 2, 2],
+                             [3, 3, 3, 2, 2, 2],
+                             [4, 4, 4, 2, 2, 2],
+                             [5, 6, 6, 6, 6, 6],
+                             [0, 0, 0, 0, 0, 0],
+                             [0, 0, 0, 0, 0, 0]])
+
+        assert_equal(result, expected)
+
+    def test_3d(self, block):
+        a000 = np.ones((2, 2, 2), int) * 1
+
+        a100 = np.ones((3, 2, 2), int) * 2
+        a010 = np.ones((2, 3, 2), int) * 3
+        a001 = np.ones((2, 2, 3), int) * 4
+
+        a011 = np.ones((2, 3, 3), int) * 5
+        a101 = np.ones((3, 2, 3), int) * 6
+        a110 = np.ones((3, 3, 2), int) * 7
+
+        a111 = np.ones((3, 3, 3), int) * 8
+
+        result = block([
+            [
+                [a000, a001],
+                [a010, a011],
+            ],
+            [
+                [a100, a101],
+                [a110, a111],
+            ]
+        ])
+        expected = array([[[1, 1, 4, 4, 4],
+                           [1, 1, 4, 4, 4],
+                           [3, 3, 5, 5, 5],
+                           [3, 3, 5, 5, 5],
+                           [3, 3, 5, 5, 5]],
+
+                          [[1, 1, 4, 4, 4],
+                           [1, 1, 4, 4, 4],
+                           [3, 3, 5, 5, 5],
+                           [3, 3, 5, 5, 5],
+                           [3, 3, 5, 5, 5]],
+
+                          [[2, 2, 6, 6, 6],
+                           [2, 2, 6, 6, 6],
+                           [7, 7, 8, 8, 8],
+                           [7, 7, 8, 8, 8],
+                           [7, 7, 8, 8, 8]],
+
+                          [[2, 2, 6, 6, 6],
+                           [2, 2, 6, 6, 6],
+                           [7, 7, 8, 8, 8],
+                           [7, 7, 8, 8, 8],
+                           [7, 7, 8, 8, 8]],
+
+                          [[2, 2, 6, 6, 6],
+                           [2, 2, 6, 6, 6],
+                           [7, 7, 8, 8, 8],
+                           [7, 7, 8, 8, 8],
+                           [7, 7, 8, 8, 8]]])
+
+        assert_array_equal(result, expected)
+
+    def test_block_with_mismatched_shape(self, block):
+        a = np.array([0, 0])
+        b = np.eye(2)
+        assert_raises(ValueError, block, [a, b])
+        assert_raises(ValueError, block, [b, a])
+
+        to_block = [[np.ones((2, 3)), np.ones((2, 2))],
+                    [np.ones((2, 2)), np.ones((2, 2))]]
+        assert_raises(ValueError, block, to_block)
+
+    def test_no_lists(self, block):
+        assert_equal(block(1),         np.array(1))
+        assert_equal(block(np.eye(3)), np.eye(3))
+
+    def test_invalid_nesting(self, block):
+        msg = 'depths are mismatched'
+        assert_raises_regex(ValueError, msg, block, [1, [2]])
+        assert_raises_regex(ValueError, msg, block, [1, []])
+        assert_raises_regex(ValueError, msg, block, [[1], 2])
+        assert_raises_regex(ValueError, msg, block, [[], 2])
+        assert_raises_regex(ValueError, msg, block, [
+            [[1], [2]],
+            [[3, 4]],
+            [5]  # missing brackets
+        ])
+
+    def test_empty_lists(self, block):
+        assert_raises_regex(ValueError, 'empty', block, [])
+        assert_raises_regex(ValueError, 'empty', block, [[]])
+        assert_raises_regex(ValueError, 'empty', block, [[1], []])
+
+    def test_tuple(self, block):
+        assert_raises_regex(TypeError, 'tuple', block, ([1, 2], [3, 4]))
+        assert_raises_regex(TypeError, 'tuple', block, [(1, 2), (3, 4)])
+
+    def test_different_ndims(self, block):
+        a = 1.
+        b = 2 * np.ones((1, 2))
+        c = 3 * np.ones((1, 1, 3))
+
+        result = block([a, b, c])
+        expected = np.array([[[1., 2., 2., 3., 3., 3.]]])
+
+        assert_equal(result, expected)
+
+    def test_different_ndims_depths(self, block):
+        a = 1.
+        b = 2 * np.ones((1, 2))
+        c = 3 * np.ones((1, 2, 3))
+
+        result = block([[a, b], [c]])
+        expected = np.array([[[1., 2., 2.],
+                              [3., 3., 3.],
+                              [3., 3., 3.]]])
+
+        assert_equal(result, expected)
+
+    def test_block_memory_order(self, block):
+        # 3D
+        arr_c = np.zeros((3,) * 3, order='C')
+        arr_f = np.zeros((3,) * 3, order='F')
+
+        b_c = [[[arr_c, arr_c],
+                [arr_c, arr_c]],
+               [[arr_c, arr_c],
+                [arr_c, arr_c]]]
+
+        b_f = [[[arr_f, arr_f],
+                [arr_f, arr_f]],
+               [[arr_f, arr_f],
+                [arr_f, arr_f]]]
+
+        assert block(b_c).flags['C_CONTIGUOUS']
+        assert block(b_f).flags['F_CONTIGUOUS']
+
+        arr_c = np.zeros((3, 3), order='C')
+        arr_f = np.zeros((3, 3), order='F')
+        # 2D
+        b_c = [[arr_c, arr_c],
+               [arr_c, arr_c]]
+
+        b_f = [[arr_f, arr_f],
+               [arr_f, arr_f]]
+
+        assert block(b_c).flags['C_CONTIGUOUS']
+        assert block(b_f).flags['F_CONTIGUOUS']
+
+
+def test_block_dispatcher():
+    class ArrayLike:
+        pass
+    a = ArrayLike()
+    b = ArrayLike()
+    c = ArrayLike()
+    assert_equal(list(_block_dispatcher(a)), [a])
+    assert_equal(list(_block_dispatcher([a])), [a])
+    assert_equal(list(_block_dispatcher([a, b])), [a, b])
+    assert_equal(list(_block_dispatcher([[a], [b, [c]]])), [a, b, c])
+    # don't recurse into non-lists
+    assert_equal(list(_block_dispatcher((a, b))), [(a, b)])
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_simd.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_simd.py
new file mode 100644
index 0000000..697d89b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_simd.py
@@ -0,0 +1,1341 @@
+# NOTE: Please avoid the use of numpy.testing since NPYV intrinsics
+# may be involved in their functionality.
+import itertools
+import math
+import operator
+import re
+
+import pytest
+from numpy._core._multiarray_umath import __cpu_baseline__
+
+from numpy._core._simd import clear_floatstatus, get_floatstatus, targets
+
+
+def check_floatstatus(divbyzero=False, overflow=False,
+                      underflow=False, invalid=False,
+                      all=False):
+    #define NPY_FPE_DIVIDEBYZERO  1
+    #define NPY_FPE_OVERFLOW      2
+    #define NPY_FPE_UNDERFLOW     4
+    #define NPY_FPE_INVALID       8
+    err = get_floatstatus()
+    ret = (all or divbyzero) and (err & 1) != 0
+    ret |= (all or overflow) and (err & 2) != 0
+    ret |= (all or underflow) and (err & 4) != 0
+    ret |= (all or invalid) and (err & 8) != 0
+    return ret
+
+class _Test_Utility:
+    # submodule of the desired SIMD extension, e.g. targets["AVX512F"]
+    npyv = None
+    # the current data type suffix e.g. 's8'
+    sfx = None
+    # target name can be 'baseline' or one or more of CPU features
+    target_name = None
+
+    def __getattr__(self, attr):
+        """
+        To call NPV intrinsics without the attribute 'npyv' and
+        auto suffixing intrinsics according to class attribute 'sfx'
+        """
+        return getattr(self.npyv, attr + "_" + self.sfx)
+
+    def _x2(self, intrin_name):
+        return getattr(self.npyv, f"{intrin_name}_{self.sfx}x2")
+
+    def _data(self, start=None, count=None, reverse=False):
+        """
+        Create list of consecutive numbers according to number of vector's lanes.
+        """
+        if start is None:
+            start = 1
+        if count is None:
+            count = self.nlanes
+        rng = range(start, start + count)
+        if reverse:
+            rng = reversed(rng)
+        if self._is_fp():
+            return [x / 1.0 for x in rng]
+        return list(rng)
+
+    def _is_unsigned(self):
+        return self.sfx[0] == 'u'
+
+    def _is_signed(self):
+        return self.sfx[0] == 's'
+
+    def _is_fp(self):
+        return self.sfx[0] == 'f'
+
+    def _scalar_size(self):
+        return int(self.sfx[1:])
+
+    def _int_clip(self, seq):
+        if self._is_fp():
+            return seq
+        max_int = self._int_max()
+        min_int = self._int_min()
+        return [min(max(v, min_int), max_int) for v in seq]
+
+    def _int_max(self):
+        if self._is_fp():
+            return None
+        max_u = self._to_unsigned(self.setall(-1))[0]
+        if self._is_signed():
+            return max_u // 2
+        return max_u
+
+    def _int_min(self):
+        if self._is_fp():
+            return None
+        if self._is_unsigned():
+            return 0
+        return -(self._int_max() + 1)
+
+    def _true_mask(self):
+        max_unsig = getattr(self.npyv, "setall_u" + self.sfx[1:])(-1)
+        return max_unsig[0]
+
+    def _to_unsigned(self, vector):
+        if isinstance(vector, (list, tuple)):
+            return getattr(self.npyv, "load_u" + self.sfx[1:])(vector)
+        else:
+            sfx = vector.__name__.replace("npyv_", "")
+            if sfx[0] == "b":
+                cvt_intrin = "cvt_u{0}_b{0}"
+            else:
+                cvt_intrin = "reinterpret_u{0}_{1}"
+            return getattr(self.npyv, cvt_intrin.format(sfx[1:], sfx))(vector)
+
+    def _pinfinity(self):
+        return float("inf")
+
+    def _ninfinity(self):
+        return -float("inf")
+
+    def _nan(self):
+        return float("nan")
+
+    def _cpu_features(self):
+        target = self.target_name
+        if target == "baseline":
+            target = __cpu_baseline__
+        else:
+            target = target.split('__')  # multi-target separator
+        return ' '.join(target)
+
+class _SIMD_BOOL(_Test_Utility):
+    """
+    To test all boolean vector types at once
+    """
+    def _nlanes(self):
+        return getattr(self.npyv, "nlanes_u" + self.sfx[1:])
+
+    def _data(self, start=None, count=None, reverse=False):
+        true_mask = self._true_mask()
+        rng = range(self._nlanes())
+        if reverse:
+            rng = reversed(rng)
+        return [true_mask if x % 2 else 0 for x in rng]
+
+    def _load_b(self, data):
+        len_str = self.sfx[1:]
+        load = getattr(self.npyv, "load_u" + len_str)
+        cvt = getattr(self.npyv, f"cvt_b{len_str}_u{len_str}")
+        return cvt(load(data))
+
+    def test_operators_logical(self):
+        """
+        Logical operations for boolean types.
+        Test intrinsics:
+            npyv_xor_##SFX, npyv_and_##SFX, npyv_or_##SFX, npyv_not_##SFX,
+            npyv_andc_b8, npvy_orc_b8, nvpy_xnor_b8
+        """
+        data_a = self._data()
+        data_b = self._data(reverse=True)
+        vdata_a = self._load_b(data_a)
+        vdata_b = self._load_b(data_b)
+
+        data_and = [a & b for a, b in zip(data_a, data_b)]
+        vand = getattr(self, "and")(vdata_a, vdata_b)
+        assert vand == data_and
+
+        data_or = [a | b for a, b in zip(data_a, data_b)]
+        vor = getattr(self, "or")(vdata_a, vdata_b)
+        assert vor == data_or
+
+        data_xor = [a ^ b for a, b in zip(data_a, data_b)]
+        vxor = self.xor(vdata_a, vdata_b)
+        assert vxor == data_xor
+
+        vnot = getattr(self, "not")(vdata_a)
+        assert vnot == data_b
+
+        # among the boolean types, andc, orc and xnor only support b8
+        if self.sfx not in ("b8"):
+            return
+
+        data_andc = [(a & ~b) & 0xFF for a, b in zip(data_a, data_b)]
+        vandc = self.andc(vdata_a, vdata_b)
+        assert data_andc == vandc
+
+        data_orc = [(a | ~b) & 0xFF for a, b in zip(data_a, data_b)]
+        vorc = self.orc(vdata_a, vdata_b)
+        assert data_orc == vorc
+
+        data_xnor = [~(a ^ b) & 0xFF for a, b in zip(data_a, data_b)]
+        vxnor = self.xnor(vdata_a, vdata_b)
+        assert data_xnor == vxnor
+
+    def test_tobits(self):
+        data2bits = lambda data: sum(int(x != 0) << i for i, x in enumerate(data, 0))
+        for data in (self._data(), self._data(reverse=True)):
+            vdata = self._load_b(data)
+            data_bits = data2bits(data)
+            tobits = self.tobits(vdata)
+            bin_tobits = bin(tobits)
+            assert bin_tobits == bin(data_bits)
+
+    def test_pack(self):
+        """
+        Pack multiple vectors into one
+        Test intrinsics:
+            npyv_pack_b8_b16
+            npyv_pack_b8_b32
+            npyv_pack_b8_b64
+        """
+        if self.sfx not in ("b16", "b32", "b64"):
+            return
+        # create the vectors
+        data = self._data()
+        rdata = self._data(reverse=True)
+        vdata = self._load_b(data)
+        vrdata = self._load_b(rdata)
+        pack_simd = getattr(self.npyv, f"pack_b8_{self.sfx}")
+        # for scalar execution, concatenate the elements of the multiple lists
+        # into a single list (spack) and then iterate over the elements of
+        # the created list applying a mask to capture the first byte of them.
+        if self.sfx == "b16":
+            spack = [(i & 0xFF) for i in (list(rdata) + list(data))]
+            vpack = pack_simd(vrdata, vdata)
+        elif self.sfx == "b32":
+            spack = [(i & 0xFF) for i in (2 * list(rdata) + 2 * list(data))]
+            vpack = pack_simd(vrdata, vrdata, vdata, vdata)
+        elif self.sfx == "b64":
+            spack = [(i & 0xFF) for i in (4 * list(rdata) + 4 * list(data))]
+            vpack = pack_simd(vrdata, vrdata, vrdata, vrdata,
+                               vdata,  vdata,  vdata,  vdata)
+        assert vpack == spack
+
+    @pytest.mark.parametrize("intrin", ["any", "all"])
+    @pytest.mark.parametrize("data", (
+        [-1, 0],
+        [0, -1],
+        [-1],
+        [0]
+    ))
+    def test_operators_crosstest(self, intrin, data):
+        """
+        Test intrinsics:
+            npyv_any_##SFX
+            npyv_all_##SFX
+        """
+        data_a = self._load_b(data * self._nlanes())
+        func = eval(intrin)
+        intrin = getattr(self, intrin)
+        desired = func(data_a)
+        simd = intrin(data_a)
+        assert not not simd == desired
+
+class _SIMD_INT(_Test_Utility):
+    """
+    To test all integer vector types at once
+    """
+    def test_operators_shift(self):
+        if self.sfx in ("u8", "s8"):
+            return
+
+        data_a = self._data(self._int_max() - self.nlanes)
+        data_b = self._data(self._int_min(), reverse=True)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+
+        for count in range(self._scalar_size()):
+            # load to cast
+            data_shl_a = self.load([a << count for a in data_a])
+            # left shift
+            shl = self.shl(vdata_a, count)
+            assert shl == data_shl_a
+            # load to cast
+            data_shr_a = self.load([a >> count for a in data_a])
+            # right shift
+            shr = self.shr(vdata_a, count)
+            assert shr == data_shr_a
+
+        # shift by zero or max or out-range immediate constant is not applicable and illogical
+        for count in range(1, self._scalar_size()):
+            # load to cast
+            data_shl_a = self.load([a << count for a in data_a])
+            # left shift by an immediate constant
+            shli = self.shli(vdata_a, count)
+            assert shli == data_shl_a
+            # load to cast
+            data_shr_a = self.load([a >> count for a in data_a])
+            # right shift by an immediate constant
+            shri = self.shri(vdata_a, count)
+            assert shri == data_shr_a
+
+    def test_arithmetic_subadd_saturated(self):
+        if self.sfx in ("u32", "s32", "u64", "s64"):
+            return
+
+        data_a = self._data(self._int_max() - self.nlanes)
+        data_b = self._data(self._int_min(), reverse=True)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+
+        data_adds = self._int_clip([a + b for a, b in zip(data_a, data_b)])
+        adds = self.adds(vdata_a, vdata_b)
+        assert adds == data_adds
+
+        data_subs = self._int_clip([a - b for a, b in zip(data_a, data_b)])
+        subs = self.subs(vdata_a, vdata_b)
+        assert subs == data_subs
+
+    def test_math_max_min(self):
+        data_a = self._data()
+        data_b = self._data(self.nlanes)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+
+        data_max = [max(a, b) for a, b in zip(data_a, data_b)]
+        simd_max = self.max(vdata_a, vdata_b)
+        assert simd_max == data_max
+
+        data_min = [min(a, b) for a, b in zip(data_a, data_b)]
+        simd_min = self.min(vdata_a, vdata_b)
+        assert simd_min == data_min
+
+    @pytest.mark.parametrize("start", [-100, -10000, 0, 100, 10000])
+    def test_reduce_max_min(self, start):
+        """
+        Test intrinsics:
+            npyv_reduce_max_##sfx
+            npyv_reduce_min_##sfx
+        """
+        vdata_a = self.load(self._data(start))
+        assert self.reduce_max(vdata_a) == max(vdata_a)
+        assert self.reduce_min(vdata_a) == min(vdata_a)
+
+
+class _SIMD_FP32(_Test_Utility):
+    """
+    To only test single precision
+    """
+    def test_conversions(self):
+        """
+        Round to nearest even integer, assume CPU control register is set to rounding.
+        Test intrinsics:
+            npyv_round_s32_##SFX
+        """
+        features = self._cpu_features()
+        if not self.npyv.simd_f64 and re.match(r".*(NEON|ASIMD)", features):
+            # very costly to emulate nearest even on Armv7
+            # instead we round halves to up. e.g. 0.5 -> 1, -0.5 -> -1
+            _round = lambda v: int(v + (0.5 if v >= 0 else -0.5))
+        else:
+            _round = round
+        vdata_a = self.load(self._data())
+        vdata_a = self.sub(vdata_a, self.setall(0.5))
+        data_round = [_round(x) for x in vdata_a]
+        vround = self.round_s32(vdata_a)
+        assert vround == data_round
+
+class _SIMD_FP64(_Test_Utility):
+    """
+    To only test double precision
+    """
+    def test_conversions(self):
+        """
+        Round to nearest even integer, assume CPU control register is set to rounding.
+        Test intrinsics:
+            npyv_round_s32_##SFX
+        """
+        vdata_a = self.load(self._data())
+        vdata_a = self.sub(vdata_a, self.setall(0.5))
+        vdata_b = self.mul(vdata_a, self.setall(-1.5))
+        data_round = [round(x) for x in list(vdata_a) + list(vdata_b)]
+        vround = self.round_s32(vdata_a, vdata_b)
+        assert vround == data_round
+
+class _SIMD_FP(_Test_Utility):
+    """
+    To test all float vector types at once
+    """
+    def test_arithmetic_fused(self):
+        vdata_a, vdata_b, vdata_c = [self.load(self._data())] * 3
+        vdata_cx2 = self.add(vdata_c, vdata_c)
+        # multiply and add, a*b + c
+        data_fma = self.load([a * b + c for a, b, c in zip(vdata_a, vdata_b, vdata_c)])
+        fma = self.muladd(vdata_a, vdata_b, vdata_c)
+        assert fma == data_fma
+        # multiply and subtract, a*b - c
+        fms = self.mulsub(vdata_a, vdata_b, vdata_c)
+        data_fms = self.sub(data_fma, vdata_cx2)
+        assert fms == data_fms
+        # negate multiply and add, -(a*b) + c
+        nfma = self.nmuladd(vdata_a, vdata_b, vdata_c)
+        data_nfma = self.sub(vdata_cx2, data_fma)
+        assert nfma == data_nfma
+        # negate multiply and subtract, -(a*b) - c
+        nfms = self.nmulsub(vdata_a, vdata_b, vdata_c)
+        data_nfms = self.mul(data_fma, self.setall(-1))
+        assert nfms == data_nfms
+        # multiply, add for odd elements and subtract even elements.
+        # (a * b) -+ c
+        fmas = list(self.muladdsub(vdata_a, vdata_b, vdata_c))
+        assert fmas[0::2] == list(data_fms)[0::2]
+        assert fmas[1::2] == list(data_fma)[1::2]
+
+    def test_abs(self):
+        pinf, ninf, nan = self._pinfinity(), self._ninfinity(), self._nan()
+        data = self._data()
+        vdata = self.load(self._data())
+
+        abs_cases = ((-0, 0), (ninf, pinf), (pinf, pinf), (nan, nan))
+        for case, desired in abs_cases:
+            data_abs = [desired] * self.nlanes
+            vabs = self.abs(self.setall(case))
+            assert vabs == pytest.approx(data_abs, nan_ok=True)
+
+        vabs = self.abs(self.mul(vdata, self.setall(-1)))
+        assert vabs == data
+
+    def test_sqrt(self):
+        pinf, ninf, nan = self._pinfinity(), self._ninfinity(), self._nan()
+        data = self._data()
+        vdata = self.load(self._data())
+
+        sqrt_cases = ((-0.0, -0.0), (0.0, 0.0), (-1.0, nan), (ninf, nan), (pinf, pinf))
+        for case, desired in sqrt_cases:
+            data_sqrt = [desired] * self.nlanes
+            sqrt = self.sqrt(self.setall(case))
+            assert sqrt == pytest.approx(data_sqrt, nan_ok=True)
+
+        data_sqrt = self.load([math.sqrt(x) for x in data])  # load to truncate precision
+        sqrt = self.sqrt(vdata)
+        assert sqrt == data_sqrt
+
+    def test_square(self):
+        pinf, ninf, nan = self._pinfinity(), self._ninfinity(), self._nan()
+        data = self._data()
+        vdata = self.load(self._data())
+        # square
+        square_cases = ((nan, nan), (pinf, pinf), (ninf, pinf))
+        for case, desired in square_cases:
+            data_square = [desired] * self.nlanes
+            square = self.square(self.setall(case))
+            assert square == pytest.approx(data_square, nan_ok=True)
+
+        data_square = [x * x for x in data]
+        square = self.square(vdata)
+        assert square == data_square
+
+    @pytest.mark.parametrize("intrin, func", [("ceil", math.ceil),
+    ("trunc", math.trunc), ("floor", math.floor), ("rint", round)])
+    def test_rounding(self, intrin, func):
+        """
+        Test intrinsics:
+            npyv_rint_##SFX
+            npyv_ceil_##SFX
+            npyv_trunc_##SFX
+            npyv_floor##SFX
+        """
+        intrin_name = intrin
+        intrin = getattr(self, intrin)
+        pinf, ninf, nan = self._pinfinity(), self._ninfinity(), self._nan()
+        # special cases
+        round_cases = ((nan, nan), (pinf, pinf), (ninf, ninf))
+        for case, desired in round_cases:
+            data_round = [desired] * self.nlanes
+            _round = intrin(self.setall(case))
+            assert _round == pytest.approx(data_round, nan_ok=True)
+
+        for x in range(0, 2**20, 256**2):
+            for w in (-1.05, -1.10, -1.15, 1.05, 1.10, 1.15):
+                data = self.load([(x + a) * w for a in range(self.nlanes)])
+                data_round = [func(x) for x in data]
+                _round = intrin(data)
+                assert _round == data_round
+
+        # test large numbers
+        for i in (
+            1.1529215045988576e+18, 4.6116860183954304e+18,
+            5.902958103546122e+20, 2.3611832414184488e+21
+        ):
+            x = self.setall(i)
+            y = intrin(x)
+            data_round = [func(n) for n in x]
+            assert y == data_round
+
+        # signed zero
+        if intrin_name == "floor":
+            data_szero = (-0.0,)
+        else:
+            data_szero = (-0.0, -0.25, -0.30, -0.45, -0.5)
+
+        for w in data_szero:
+            _round = self._to_unsigned(intrin(self.setall(w)))
+            data_round = self._to_unsigned(self.setall(-0.0))
+            assert _round == data_round
+
+    @pytest.mark.parametrize("intrin", [
+        "max", "maxp", "maxn", "min", "minp", "minn"
+    ])
+    def test_max_min(self, intrin):
+        """
+        Test intrinsics:
+            npyv_max_##sfx
+            npyv_maxp_##sfx
+            npyv_maxn_##sfx
+            npyv_min_##sfx
+            npyv_minp_##sfx
+            npyv_minn_##sfx
+            npyv_reduce_max_##sfx
+            npyv_reduce_maxp_##sfx
+            npyv_reduce_maxn_##sfx
+            npyv_reduce_min_##sfx
+            npyv_reduce_minp_##sfx
+            npyv_reduce_minn_##sfx
+        """
+        pinf, ninf, nan = self._pinfinity(), self._ninfinity(), self._nan()
+        chk_nan = {"xp": 1, "np": 1, "nn": 2, "xn": 2}.get(intrin[-2:], 0)
+        func = eval(intrin[:3])
+        reduce_intrin = getattr(self, "reduce_" + intrin)
+        intrin = getattr(self, intrin)
+        hf_nlanes = self.nlanes // 2
+
+        cases = (
+            ([0.0, -0.0], [-0.0, 0.0]),
+            ([10, -10],  [10, -10]),
+            ([pinf, 10], [10, ninf]),
+            ([10, pinf], [ninf, 10]),
+            ([10, -10], [10, -10]),
+            ([-10, 10], [-10, 10])
+        )
+        for op1, op2 in cases:
+            vdata_a = self.load(op1 * hf_nlanes)
+            vdata_b = self.load(op2 * hf_nlanes)
+            data = func(vdata_a, vdata_b)
+            simd = intrin(vdata_a, vdata_b)
+            assert simd == data
+            data = func(vdata_a)
+            simd = reduce_intrin(vdata_a)
+            assert simd == data
+
+        if not chk_nan:
+            return
+        if chk_nan == 1:
+            test_nan = lambda a, b: (
+                b if math.isnan(a) else a if math.isnan(b) else b
+            )
+        else:
+            test_nan = lambda a, b: (
+                nan if math.isnan(a) or math.isnan(b) else b
+            )
+        cases = (
+            (nan, 10),
+            (10, nan),
+            (nan, pinf),
+            (pinf, nan),
+            (nan, nan)
+        )
+        for op1, op2 in cases:
+            vdata_ab = self.load([op1, op2] * hf_nlanes)
+            data = test_nan(op1, op2)
+            simd = reduce_intrin(vdata_ab)
+            assert simd == pytest.approx(data, nan_ok=True)
+            vdata_a = self.setall(op1)
+            vdata_b = self.setall(op2)
+            data = [data] * self.nlanes
+            simd = intrin(vdata_a, vdata_b)
+            assert simd == pytest.approx(data, nan_ok=True)
+
+    def test_reciprocal(self):
+        pinf, ninf, nan = self._pinfinity(), self._ninfinity(), self._nan()
+        data = self._data()
+        vdata = self.load(self._data())
+
+        recip_cases = ((nan, nan), (pinf, 0.0), (ninf, -0.0), (0.0, pinf), (-0.0, ninf))
+        for case, desired in recip_cases:
+            data_recip = [desired] * self.nlanes
+            recip = self.recip(self.setall(case))
+            assert recip == pytest.approx(data_recip, nan_ok=True)
+
+        data_recip = self.load([1 / x for x in data])  # load to truncate precision
+        recip = self.recip(vdata)
+        assert recip == data_recip
+
+    def test_special_cases(self):
+        """
+        Compare Not NaN. Test intrinsics:
+            npyv_notnan_##SFX
+        """
+        nnan = self.notnan(self.setall(self._nan()))
+        assert nnan == [0] * self.nlanes
+
+    @pytest.mark.parametrize("intrin_name", [
+        "rint", "trunc", "ceil", "floor"
+    ])
+    def test_unary_invalid_fpexception(self, intrin_name):
+        intrin = getattr(self, intrin_name)
+        for d in [float("nan"), float("inf"), -float("inf")]:
+            v = self.setall(d)
+            clear_floatstatus()
+            intrin(v)
+            assert check_floatstatus(invalid=True) is False
+
+    @pytest.mark.parametrize('py_comp,np_comp', [
+        (operator.lt, "cmplt"),
+        (operator.le, "cmple"),
+        (operator.gt, "cmpgt"),
+        (operator.ge, "cmpge"),
+        (operator.eq, "cmpeq"),
+        (operator.ne, "cmpneq")
+    ])
+    def test_comparison_with_nan(self, py_comp, np_comp):
+        pinf, ninf, nan = self._pinfinity(), self._ninfinity(), self._nan()
+        mask_true = self._true_mask()
+
+        def to_bool(vector):
+            return [lane == mask_true for lane in vector]
+
+        intrin = getattr(self, np_comp)
+        cmp_cases = ((0, nan), (nan, 0), (nan, nan), (pinf, nan),
+                     (ninf, nan), (-0.0, +0.0))
+        for case_operand1, case_operand2 in cmp_cases:
+            data_a = [case_operand1] * self.nlanes
+            data_b = [case_operand2] * self.nlanes
+            vdata_a = self.setall(case_operand1)
+            vdata_b = self.setall(case_operand2)
+            vcmp = to_bool(intrin(vdata_a, vdata_b))
+            data_cmp = [py_comp(a, b) for a, b in zip(data_a, data_b)]
+            assert vcmp == data_cmp
+
+    @pytest.mark.parametrize("intrin", ["any", "all"])
+    @pytest.mark.parametrize("data", (
+        [float("nan"), 0],
+        [0, float("nan")],
+        [float("nan"), 1],
+        [1, float("nan")],
+        [float("nan"), float("nan")],
+        [0.0, -0.0],
+        [-0.0, 0.0],
+        [1.0, -0.0]
+    ))
+    def test_operators_crosstest(self, intrin, data):
+        """
+        Test intrinsics:
+            npyv_any_##SFX
+            npyv_all_##SFX
+        """
+        data_a = self.load(data * self.nlanes)
+        func = eval(intrin)
+        intrin = getattr(self, intrin)
+        desired = func(data_a)
+        simd = intrin(data_a)
+        assert not not simd == desired
+
+class _SIMD_ALL(_Test_Utility):
+    """
+    To test all vector types at once
+    """
+    def test_memory_load(self):
+        data = self._data()
+        # unaligned load
+        load_data = self.load(data)
+        assert load_data == data
+        # aligned load
+        loada_data = self.loada(data)
+        assert loada_data == data
+        # stream load
+        loads_data = self.loads(data)
+        assert loads_data == data
+        # load lower part
+        loadl = self.loadl(data)
+        loadl_half = list(loadl)[:self.nlanes // 2]
+        data_half = data[:self.nlanes // 2]
+        assert loadl_half == data_half
+        assert loadl != data  # detect overflow
+
+    def test_memory_store(self):
+        data = self._data()
+        vdata = self.load(data)
+        # unaligned store
+        store = [0] * self.nlanes
+        self.store(store, vdata)
+        assert store == data
+        # aligned store
+        store_a = [0] * self.nlanes
+        self.storea(store_a, vdata)
+        assert store_a == data
+        # stream store
+        store_s = [0] * self.nlanes
+        self.stores(store_s, vdata)
+        assert store_s == data
+        # store lower part
+        store_l = [0] * self.nlanes
+        self.storel(store_l, vdata)
+        assert store_l[:self.nlanes // 2] == data[:self.nlanes // 2]
+        assert store_l != vdata  # detect overflow
+        # store higher part
+        store_h = [0] * self.nlanes
+        self.storeh(store_h, vdata)
+        assert store_h[:self.nlanes // 2] == data[self.nlanes // 2:]
+        assert store_h != vdata  # detect overflow
+
+    @pytest.mark.parametrize("intrin, elsizes, scale, fill", [
+        ("self.load_tillz, self.load_till", (32, 64), 1, [0xffff]),
+        ("self.load2_tillz, self.load2_till", (32, 64), 2, [0xffff, 0x7fff]),
+    ])
+    def test_memory_partial_load(self, intrin, elsizes, scale, fill):
+        if self._scalar_size() not in elsizes:
+            return
+        npyv_load_tillz, npyv_load_till = eval(intrin)
+        data = self._data()
+        lanes = list(range(1, self.nlanes + 1))
+        lanes += [self.nlanes**2, self.nlanes**4]  # test out of range
+        for n in lanes:
+            load_till = npyv_load_till(data, n, *fill)
+            load_tillz = npyv_load_tillz(data, n)
+            n *= scale
+            data_till = data[:n] + fill * ((self.nlanes - n) // scale)
+            assert load_till == data_till
+            data_tillz = data[:n] + [0] * (self.nlanes - n)
+            assert load_tillz == data_tillz
+
+    @pytest.mark.parametrize("intrin, elsizes, scale", [
+        ("self.store_till", (32, 64), 1),
+        ("self.store2_till", (32, 64), 2),
+    ])
+    def test_memory_partial_store(self, intrin, elsizes, scale):
+        if self._scalar_size() not in elsizes:
+            return
+        npyv_store_till = eval(intrin)
+        data = self._data()
+        data_rev = self._data(reverse=True)
+        vdata = self.load(data)
+        lanes = list(range(1, self.nlanes + 1))
+        lanes += [self.nlanes**2, self.nlanes**4]
+        for n in lanes:
+            data_till = data_rev.copy()
+            data_till[:n * scale] = data[:n * scale]
+            store_till = self._data(reverse=True)
+            npyv_store_till(store_till, n, vdata)
+            assert store_till == data_till
+
+    @pytest.mark.parametrize("intrin, elsizes, scale", [
+        ("self.loadn", (32, 64), 1),
+        ("self.loadn2", (32, 64), 2),
+    ])
+    def test_memory_noncont_load(self, intrin, elsizes, scale):
+        if self._scalar_size() not in elsizes:
+            return
+        npyv_loadn = eval(intrin)
+        for stride in range(-64, 64):
+            if stride < 0:
+                data = self._data(stride, -stride * self.nlanes)
+                data_stride = list(itertools.chain(
+                    *zip(*[data[-i::stride] for i in range(scale, 0, -1)])
+                ))
+            elif stride == 0:
+                data = self._data()
+                data_stride = data[0:scale] * (self.nlanes // scale)
+            else:
+                data = self._data(count=stride * self.nlanes)
+                data_stride = list(itertools.chain(
+                    *zip(*[data[i::stride] for i in range(scale)]))
+                )
+            data_stride = self.load(data_stride)  # cast unsigned
+            loadn = npyv_loadn(data, stride)
+            assert loadn == data_stride
+
+    @pytest.mark.parametrize("intrin, elsizes, scale, fill", [
+        ("self.loadn_tillz, self.loadn_till", (32, 64), 1, [0xffff]),
+        ("self.loadn2_tillz, self.loadn2_till", (32, 64), 2, [0xffff, 0x7fff]),
+    ])
+    def test_memory_noncont_partial_load(self, intrin, elsizes, scale, fill):
+        if self._scalar_size() not in elsizes:
+            return
+        npyv_loadn_tillz, npyv_loadn_till = eval(intrin)
+        lanes = list(range(1, self.nlanes + 1))
+        lanes += [self.nlanes**2, self.nlanes**4]
+        for stride in range(-64, 64):
+            if stride < 0:
+                data = self._data(stride, -stride * self.nlanes)
+                data_stride = list(itertools.chain(
+                    *zip(*[data[-i::stride] for i in range(scale, 0, -1)])
+                ))
+            elif stride == 0:
+                data = self._data()
+                data_stride = data[0:scale] * (self.nlanes // scale)
+            else:
+                data = self._data(count=stride * self.nlanes)
+                data_stride = list(itertools.chain(
+                    *zip(*[data[i::stride] for i in range(scale)])
+                ))
+            data_stride = list(self.load(data_stride))  # cast unsigned
+            for n in lanes:
+                nscale = n * scale
+                llanes = self.nlanes - nscale
+                data_stride_till = (
+                    data_stride[:nscale] + fill * (llanes // scale)
+                )
+                loadn_till = npyv_loadn_till(data, stride, n, *fill)
+                assert loadn_till == data_stride_till
+                data_stride_tillz = data_stride[:nscale] + [0] * llanes
+                loadn_tillz = npyv_loadn_tillz(data, stride, n)
+                assert loadn_tillz == data_stride_tillz
+
+    @pytest.mark.parametrize("intrin, elsizes, scale", [
+        ("self.storen", (32, 64), 1),
+        ("self.storen2", (32, 64), 2),
+    ])
+    def test_memory_noncont_store(self, intrin, elsizes, scale):
+        if self._scalar_size() not in elsizes:
+            return
+        npyv_storen = eval(intrin)
+        data = self._data()
+        vdata = self.load(data)
+        hlanes = self.nlanes // scale
+        for stride in range(1, 64):
+            data_storen = [0xff] * stride * self.nlanes
+            for s in range(0, hlanes * stride, stride):
+                i = (s // stride) * scale
+                data_storen[s:s + scale] = data[i:i + scale]
+            storen = [0xff] * stride * self.nlanes
+            storen += [0x7f] * 64
+            npyv_storen(storen, stride, vdata)
+            assert storen[:-64] == data_storen
+            assert storen[-64:] == [0x7f] * 64  # detect overflow
+
+        for stride in range(-64, 0):
+            data_storen = [0xff] * -stride * self.nlanes
+            for s in range(0, hlanes * stride, stride):
+                i = (s // stride) * scale
+                data_storen[s - scale:s or None] = data[i:i + scale]
+            storen = [0x7f] * 64
+            storen += [0xff] * -stride * self.nlanes
+            npyv_storen(storen, stride, vdata)
+            assert storen[64:] == data_storen
+            assert storen[:64] == [0x7f] * 64  # detect overflow
+        # stride 0
+        data_storen = [0x7f] * self.nlanes
+        storen = data_storen.copy()
+        data_storen[0:scale] = data[-scale:]
+        npyv_storen(storen, 0, vdata)
+        assert storen == data_storen
+
+    @pytest.mark.parametrize("intrin, elsizes, scale", [
+        ("self.storen_till", (32, 64), 1),
+        ("self.storen2_till", (32, 64), 2),
+    ])
+    def test_memory_noncont_partial_store(self, intrin, elsizes, scale):
+        if self._scalar_size() not in elsizes:
+            return
+        npyv_storen_till = eval(intrin)
+        data = self._data()
+        vdata = self.load(data)
+        lanes = list(range(1, self.nlanes + 1))
+        lanes += [self.nlanes**2, self.nlanes**4]
+        hlanes = self.nlanes // scale
+        for stride in range(1, 64):
+            for n in lanes:
+                data_till = [0xff] * stride * self.nlanes
+                tdata = data[:n * scale] + [0xff] * (self.nlanes - n * scale)
+                for s in range(0, hlanes * stride, stride)[:n]:
+                    i = (s // stride) * scale
+                    data_till[s:s + scale] = tdata[i:i + scale]
+                storen_till = [0xff] * stride * self.nlanes
+                storen_till += [0x7f] * 64
+                npyv_storen_till(storen_till, stride, n, vdata)
+                assert storen_till[:-64] == data_till
+                assert storen_till[-64:] == [0x7f] * 64  # detect overflow
+
+        for stride in range(-64, 0):
+            for n in lanes:
+                data_till = [0xff] * -stride * self.nlanes
+                tdata = data[:n * scale] + [0xff] * (self.nlanes - n * scale)
+                for s in range(0, hlanes * stride, stride)[:n]:
+                    i = (s // stride) * scale
+                    data_till[s - scale:s or None] = tdata[i:i + scale]
+                storen_till = [0x7f] * 64
+                storen_till += [0xff] * -stride * self.nlanes
+                npyv_storen_till(storen_till, stride, n, vdata)
+                assert storen_till[64:] == data_till
+                assert storen_till[:64] == [0x7f] * 64  # detect overflow
+
+        # stride 0
+        for n in lanes:
+            data_till = [0x7f] * self.nlanes
+            storen_till = data_till.copy()
+            data_till[0:scale] = data[:n * scale][-scale:]
+            npyv_storen_till(storen_till, 0, n, vdata)
+            assert storen_till == data_till
+
+    @pytest.mark.parametrize("intrin, table_size, elsize", [
+        ("self.lut32", 32, 32),
+        ("self.lut16", 16, 64)
+    ])
+    def test_lut(self, intrin, table_size, elsize):
+        """
+        Test lookup table intrinsics:
+            npyv_lut32_##sfx
+            npyv_lut16_##sfx
+        """
+        if elsize != self._scalar_size():
+            return
+        intrin = eval(intrin)
+        idx_itrin = getattr(self.npyv, f"setall_u{elsize}")
+        table = range(table_size)
+        for i in table:
+            broadi = self.setall(i)
+            idx = idx_itrin(i)
+            lut = intrin(table, idx)
+            assert lut == broadi
+
+    def test_misc(self):
+        broadcast_zero = self.zero()
+        assert broadcast_zero == [0] * self.nlanes
+        for i in range(1, 10):
+            broadcasti = self.setall(i)
+            assert broadcasti == [i] * self.nlanes
+
+        data_a, data_b = self._data(), self._data(reverse=True)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+
+        # py level of npyv_set_* don't support ignoring the extra specified lanes or
+        # fill non-specified lanes with zero.
+        vset = self.set(*data_a)
+        assert vset == data_a
+        # py level of npyv_setf_* don't support ignoring the extra specified lanes or
+        # fill non-specified lanes with the specified scalar.
+        vsetf = self.setf(10, *data_a)
+        assert vsetf == data_a
+
+        # We're testing the sanity of _simd's type-vector,
+        # reinterpret* intrinsics itself are tested via compiler
+        # during the build of _simd module
+        sfxes = ["u8", "s8", "u16", "s16", "u32", "s32", "u64", "s64"]
+        if self.npyv.simd_f64:
+            sfxes.append("f64")
+        if self.npyv.simd_f32:
+            sfxes.append("f32")
+        for sfx in sfxes:
+            vec_name = getattr(self, "reinterpret_" + sfx)(vdata_a).__name__
+            assert vec_name == "npyv_" + sfx
+
+        # select & mask operations
+        select_a = self.select(self.cmpeq(self.zero(), self.zero()), vdata_a, vdata_b)
+        assert select_a == data_a
+        select_b = self.select(self.cmpneq(self.zero(), self.zero()), vdata_a, vdata_b)
+        assert select_b == data_b
+
+        # test extract elements
+        assert self.extract0(vdata_b) == vdata_b[0]
+
+        # cleanup intrinsic is only used with AVX for
+        # zeroing registers to avoid the AVX-SSE transition penalty,
+        # so nothing to test here
+        self.npyv.cleanup()
+
+    def test_reorder(self):
+        data_a, data_b = self._data(), self._data(reverse=True)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+        # lower half part
+        data_a_lo = data_a[:self.nlanes // 2]
+        data_b_lo = data_b[:self.nlanes // 2]
+        # higher half part
+        data_a_hi = data_a[self.nlanes // 2:]
+        data_b_hi = data_b[self.nlanes // 2:]
+        # combine two lower parts
+        combinel = self.combinel(vdata_a, vdata_b)
+        assert combinel == data_a_lo + data_b_lo
+        # combine two higher parts
+        combineh = self.combineh(vdata_a, vdata_b)
+        assert combineh == data_a_hi + data_b_hi
+        # combine x2
+        combine = self.combine(vdata_a, vdata_b)
+        assert combine == (data_a_lo + data_b_lo, data_a_hi + data_b_hi)
+
+        # zip(interleave)
+        data_zipl = self.load([
+            v for p in zip(data_a_lo, data_b_lo) for v in p
+        ])
+        data_ziph = self.load([
+            v for p in zip(data_a_hi, data_b_hi) for v in p
+        ])
+        vzip = self.zip(vdata_a, vdata_b)
+        assert vzip == (data_zipl, data_ziph)
+        vzip = [0] * self.nlanes * 2
+        self._x2("store")(vzip, (vdata_a, vdata_b))
+        assert vzip == list(data_zipl) + list(data_ziph)
+
+        # unzip(deinterleave)
+        unzip = self.unzip(data_zipl, data_ziph)
+        assert unzip == (data_a, data_b)
+        unzip = self._x2("load")(list(data_zipl) + list(data_ziph))
+        assert unzip == (data_a, data_b)
+
+    def test_reorder_rev64(self):
+        # Reverse elements of each 64-bit lane
+        ssize = self._scalar_size()
+        if ssize == 64:
+            return
+        data_rev64 = [
+            y for x in range(0, self.nlanes, 64 // ssize)
+              for y in reversed(range(x, x + 64 // ssize))
+        ]
+        rev64 = self.rev64(self.load(range(self.nlanes)))
+        assert rev64 == data_rev64
+
+    def test_reorder_permi128(self):
+        """
+        Test permuting elements for each 128-bit lane.
+        npyv_permi128_##sfx
+        """
+        ssize = self._scalar_size()
+        if ssize < 32:
+            return
+        data = self.load(self._data())
+        permn = 128 // ssize
+        permd = permn - 1
+        nlane128 = self.nlanes // permn
+        shfl = [0, 1] if ssize == 64 else [0, 2, 4, 6]
+        for i in range(permn):
+            indices = [(i >> shf) & permd for shf in shfl]
+            vperm = self.permi128(data, *indices)
+            data_vperm = [
+                data[j + (e & -permn)]
+                for e, j in enumerate(indices * nlane128)
+            ]
+            assert vperm == data_vperm
+
+    @pytest.mark.parametrize('func, intrin', [
+        (operator.lt, "cmplt"),
+        (operator.le, "cmple"),
+        (operator.gt, "cmpgt"),
+        (operator.ge, "cmpge"),
+        (operator.eq, "cmpeq")
+    ])
+    def test_operators_comparison(self, func, intrin):
+        if self._is_fp():
+            data_a = self._data()
+        else:
+            data_a = self._data(self._int_max() - self.nlanes)
+        data_b = self._data(self._int_min(), reverse=True)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+        intrin = getattr(self, intrin)
+
+        mask_true = self._true_mask()
+
+        def to_bool(vector):
+            return [lane == mask_true for lane in vector]
+
+        data_cmp = [func(a, b) for a, b in zip(data_a, data_b)]
+        cmp = to_bool(intrin(vdata_a, vdata_b))
+        assert cmp == data_cmp
+
+    def test_operators_logical(self):
+        if self._is_fp():
+            data_a = self._data()
+        else:
+            data_a = self._data(self._int_max() - self.nlanes)
+        data_b = self._data(self._int_min(), reverse=True)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+
+        if self._is_fp():
+            data_cast_a = self._to_unsigned(vdata_a)
+            data_cast_b = self._to_unsigned(vdata_b)
+            cast, cast_data = self._to_unsigned, self._to_unsigned
+        else:
+            data_cast_a, data_cast_b = data_a, data_b
+            cast, cast_data = lambda a: a, self.load
+
+        data_xor = cast_data([a ^ b for a, b in zip(data_cast_a, data_cast_b)])
+        vxor = cast(self.xor(vdata_a, vdata_b))
+        assert vxor == data_xor
+
+        data_or = cast_data([a | b for a, b in zip(data_cast_a, data_cast_b)])
+        vor = cast(getattr(self, "or")(vdata_a, vdata_b))
+        assert vor == data_or
+
+        data_and = cast_data([a & b for a, b in zip(data_cast_a, data_cast_b)])
+        vand = cast(getattr(self, "and")(vdata_a, vdata_b))
+        assert vand == data_and
+
+        data_not = cast_data([~a for a in data_cast_a])
+        vnot = cast(getattr(self, "not")(vdata_a))
+        assert vnot == data_not
+
+        if self.sfx not in ("u8"):
+            return
+        data_andc = [a & ~b for a, b in zip(data_cast_a, data_cast_b)]
+        vandc = cast(self.andc(vdata_a, vdata_b))
+        assert vandc == data_andc
+
+    @pytest.mark.parametrize("intrin", ["any", "all"])
+    @pytest.mark.parametrize("data", (
+        [1, 2, 3, 4],
+        [-1, -2, -3, -4],
+        [0, 1, 2, 3, 4],
+        [0x7f, 0x7fff, 0x7fffffff, 0x7fffffffffffffff],
+        [0, -1, -2, -3, 4],
+        [0],
+        [1],
+        [-1]
+    ))
+    def test_operators_crosstest(self, intrin, data):
+        """
+        Test intrinsics:
+            npyv_any_##SFX
+            npyv_all_##SFX
+        """
+        data_a = self.load(data * self.nlanes)
+        func = eval(intrin)
+        intrin = getattr(self, intrin)
+        desired = func(data_a)
+        simd = intrin(data_a)
+        assert not not simd == desired
+
+    def test_conversion_boolean(self):
+        bsfx = "b" + self.sfx[1:]
+        to_boolean = getattr(self.npyv, f"cvt_{bsfx}_{self.sfx}")
+        from_boolean = getattr(self.npyv, f"cvt_{self.sfx}_{bsfx}")
+
+        false_vb = to_boolean(self.setall(0))
+        true_vb = self.cmpeq(self.setall(0), self.setall(0))
+        assert false_vb != true_vb
+
+        false_vsfx = from_boolean(false_vb)
+        true_vsfx = from_boolean(true_vb)
+        assert false_vsfx != true_vsfx
+
+    def test_conversion_expand(self):
+        """
+        Test expand intrinsics:
+            npyv_expand_u16_u8
+            npyv_expand_u32_u16
+        """
+        if self.sfx not in ("u8", "u16"):
+            return
+        totype = self.sfx[0] + str(int(self.sfx[1:]) * 2)
+        expand = getattr(self.npyv, f"expand_{totype}_{self.sfx}")
+        # close enough from the edge to detect any deviation
+        data = self._data(self._int_max() - self.nlanes)
+        vdata = self.load(data)
+        edata = expand(vdata)
+        # lower half part
+        data_lo = data[:self.nlanes // 2]
+        # higher half part
+        data_hi = data[self.nlanes // 2:]
+        assert edata == (data_lo, data_hi)
+
+    def test_arithmetic_subadd(self):
+        if self._is_fp():
+            data_a = self._data()
+        else:
+            data_a = self._data(self._int_max() - self.nlanes)
+        data_b = self._data(self._int_min(), reverse=True)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+
+        # non-saturated
+        data_add = self.load([a + b for a, b in zip(data_a, data_b)])  # load to cast
+        add = self.add(vdata_a, vdata_b)
+        assert add == data_add
+        data_sub = self.load([a - b for a, b in zip(data_a, data_b)])
+        sub = self.sub(vdata_a, vdata_b)
+        assert sub == data_sub
+
+    def test_arithmetic_mul(self):
+        if self.sfx in ("u64", "s64"):
+            return
+
+        if self._is_fp():
+            data_a = self._data()
+        else:
+            data_a = self._data(self._int_max() - self.nlanes)
+        data_b = self._data(self._int_min(), reverse=True)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+
+        data_mul = self.load([a * b for a, b in zip(data_a, data_b)])
+        mul = self.mul(vdata_a, vdata_b)
+        assert mul == data_mul
+
+    def test_arithmetic_div(self):
+        if not self._is_fp():
+            return
+
+        data_a, data_b = self._data(), self._data(reverse=True)
+        vdata_a, vdata_b = self.load(data_a), self.load(data_b)
+
+        # load to truncate f64 to precision of f32
+        data_div = self.load([a / b for a, b in zip(data_a, data_b)])
+        div = self.div(vdata_a, vdata_b)
+        assert div == data_div
+
+    def test_arithmetic_intdiv(self):
+        """
+        Test integer division intrinsics:
+            npyv_divisor_##sfx
+            npyv_divc_##sfx
+        """
+        if self._is_fp():
+            return
+
+        int_min = self._int_min()
+
+        def trunc_div(a, d):
+            """
+            Divide towards zero works with large integers > 2^53,
+            and wrap around overflow similar to what C does.
+            """
+            if d == -1 and a == int_min:
+                return a
+            sign_a, sign_d = a < 0, d < 0
+            if a == 0 or sign_a == sign_d:
+                return a // d
+            return (a + sign_d - sign_a) // d + 1
+
+        data = [1, -int_min]  # to test overflow
+        data += range(0, 2**8, 2**5)
+        data += range(0, 2**8, 2**5 - 1)
+        bsize = self._scalar_size()
+        if bsize > 8:
+            data += range(2**8, 2**16, 2**13)
+            data += range(2**8, 2**16, 2**13 - 1)
+        if bsize > 16:
+            data += range(2**16, 2**32, 2**29)
+            data += range(2**16, 2**32, 2**29 - 1)
+        if bsize > 32:
+            data += range(2**32, 2**64, 2**61)
+            data += range(2**32, 2**64, 2**61 - 1)
+        # negate
+        data += [-x for x in data]
+        for dividend, divisor in itertools.product(data, data):
+            divisor = self.setall(divisor)[0]  # cast
+            if divisor == 0:
+                continue
+            dividend = self.load(self._data(dividend))
+            data_divc = [trunc_div(a, divisor) for a in dividend]
+            divisor_parms = self.divisor(divisor)
+            divc = self.divc(dividend, divisor_parms)
+            assert divc == data_divc
+
+    def test_arithmetic_reduce_sum(self):
+        """
+        Test reduce sum intrinsics:
+            npyv_sum_##sfx
+        """
+        if self.sfx not in ("u32", "u64", "f32", "f64"):
+            return
+        # reduce sum
+        data = self._data()
+        vdata = self.load(data)
+
+        data_sum = sum(data)
+        vsum = self.sum(vdata)
+        assert vsum == data_sum
+
+    def test_arithmetic_reduce_sumup(self):
+        """
+        Test extend reduce sum intrinsics:
+            npyv_sumup_##sfx
+        """
+        if self.sfx not in ("u8", "u16"):
+            return
+        rdata = (0, self.nlanes, self._int_min(), self._int_max() - self.nlanes)
+        for r in rdata:
+            data = self._data(r)
+            vdata = self.load(data)
+            data_sum = sum(data)
+            vsum = self.sumup(vdata)
+            assert vsum == data_sum
+
+    def test_mask_conditional(self):
+        """
+        Conditional addition and subtraction for all supported data types.
+        Test intrinsics:
+            npyv_ifadd_##SFX, npyv_ifsub_##SFX
+        """
+        vdata_a = self.load(self._data())
+        vdata_b = self.load(self._data(reverse=True))
+        true_mask = self.cmpeq(self.zero(), self.zero())
+        false_mask = self.cmpneq(self.zero(), self.zero())
+
+        data_sub = self.sub(vdata_b, vdata_a)
+        ifsub = self.ifsub(true_mask, vdata_b, vdata_a, vdata_b)
+        assert ifsub == data_sub
+        ifsub = self.ifsub(false_mask, vdata_a, vdata_b, vdata_b)
+        assert ifsub == vdata_b
+
+        data_add = self.add(vdata_b, vdata_a)
+        ifadd = self.ifadd(true_mask, vdata_b, vdata_a, vdata_b)
+        assert ifadd == data_add
+        ifadd = self.ifadd(false_mask, vdata_a, vdata_b, vdata_b)
+        assert ifadd == vdata_b
+
+        if not self._is_fp():
+            return
+        data_div = self.div(vdata_b, vdata_a)
+        ifdiv = self.ifdiv(true_mask, vdata_b, vdata_a, vdata_b)
+        assert ifdiv == data_div
+        ifdivz = self.ifdivz(true_mask, vdata_b, vdata_a)
+        assert ifdivz == data_div
+        ifdiv = self.ifdiv(false_mask, vdata_a, vdata_b, vdata_b)
+        assert ifdiv == vdata_b
+        ifdivz = self.ifdivz(false_mask, vdata_a, vdata_b)
+        assert ifdivz == self.zero()
+
+
+bool_sfx = ("b8", "b16", "b32", "b64")
+int_sfx = ("u8", "s8", "u16", "s16", "u32", "s32", "u64", "s64")
+fp_sfx = ("f32", "f64")
+all_sfx = int_sfx + fp_sfx
+tests_registry = {
+    bool_sfx: _SIMD_BOOL,
+    int_sfx:  _SIMD_INT,
+    fp_sfx:   _SIMD_FP,
+    ("f32",): _SIMD_FP32,
+    ("f64",): _SIMD_FP64,
+    all_sfx:  _SIMD_ALL
+}
+for target_name, npyv in targets.items():
+    simd_width = npyv.simd if npyv else ''
+    pretty_name = target_name.split('__')  # multi-target separator
+    if len(pretty_name) > 1:
+        # multi-target
+        pretty_name = f"({' '.join(pretty_name)})"
+    else:
+        pretty_name = pretty_name[0]
+
+    skip = ""
+    skip_sfx = {}
+    if not npyv:
+        skip = f"target '{pretty_name}' isn't supported by current machine"
+    elif not npyv.simd:
+        skip = f"target '{pretty_name}' isn't supported by NPYV"
+    else:
+        if not npyv.simd_f32:
+            skip_sfx["f32"] = f"target '{pretty_name}' "\
+                               "doesn't support single-precision"
+        if not npyv.simd_f64:
+            skip_sfx["f64"] = f"target '{pretty_name}' doesn't"\
+                               "support double-precision"
+
+    for sfxes, cls in tests_registry.items():
+        for sfx in sfxes:
+            skip_m = skip_sfx.get(sfx, skip)
+            inhr = (cls,)
+            attr = {"npyv": targets[target_name], "sfx": sfx, "target_name": target_name}
+            tcls = type(f"Test{cls.__name__}_{simd_width}_{target_name}_{sfx}", inhr, attr)
+            if skip_m:
+                pytest.mark.skip(reason=skip_m)(tcls)
+            globals()[tcls.__name__] = tcls
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_simd_module.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_simd_module.py
new file mode 100644
index 0000000..dca83fd
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_simd_module.py
@@ -0,0 +1,103 @@
+import pytest
+
+from numpy._core._simd import targets
+
+"""
+This testing unit only for checking the sanity of common functionality,
+therefore all we need is just to take one submodule that represents any
+of enabled SIMD extensions to run the test on it and the second submodule
+required to run only one check related to the possibility of mixing
+the data types among each submodule.
+"""
+npyvs = [npyv_mod for npyv_mod in targets.values() if npyv_mod and npyv_mod.simd]
+npyv, npyv2 = (npyvs + [None, None])[:2]
+
+unsigned_sfx = ["u8", "u16", "u32", "u64"]
+signed_sfx = ["s8", "s16", "s32", "s64"]
+fp_sfx = []
+if npyv and npyv.simd_f32:
+    fp_sfx.append("f32")
+if npyv and npyv.simd_f64:
+    fp_sfx.append("f64")
+
+int_sfx = unsigned_sfx + signed_sfx
+all_sfx = unsigned_sfx + int_sfx
+
+@pytest.mark.skipif(not npyv, reason="could not find any SIMD extension with NPYV support")
+class Test_SIMD_MODULE:
+
+    @pytest.mark.parametrize('sfx', all_sfx)
+    def test_num_lanes(self, sfx):
+        nlanes = getattr(npyv, "nlanes_" + sfx)
+        vector = getattr(npyv, "setall_" + sfx)(1)
+        assert len(vector) == nlanes
+
+    @pytest.mark.parametrize('sfx', all_sfx)
+    def test_type_name(self, sfx):
+        vector = getattr(npyv, "setall_" + sfx)(1)
+        assert vector.__name__ == "npyv_" + sfx
+
+    def test_raises(self):
+        a, b = [npyv.setall_u32(1)] * 2
+        for sfx in all_sfx:
+            vcb = lambda intrin: getattr(npyv, f"{intrin}_{sfx}")
+            pytest.raises(TypeError, vcb("add"), a)
+            pytest.raises(TypeError, vcb("add"), a, b, a)
+            pytest.raises(TypeError, vcb("setall"))
+            pytest.raises(TypeError, vcb("setall"), [1])
+            pytest.raises(TypeError, vcb("load"), 1)
+            pytest.raises(ValueError, vcb("load"), [1])
+            pytest.raises(ValueError, vcb("store"), [1], getattr(npyv, f"reinterpret_{sfx}_u32")(a))
+
+    @pytest.mark.skipif(not npyv2, reason=(
+        "could not find a second SIMD extension with NPYV support"
+    ))
+    def test_nomix(self):
+        # mix among submodules isn't allowed
+        a = npyv.setall_u32(1)
+        a2 = npyv2.setall_u32(1)
+        pytest.raises(TypeError, npyv.add_u32, a2, a2)
+        pytest.raises(TypeError, npyv2.add_u32, a, a)
+
+    @pytest.mark.parametrize('sfx', unsigned_sfx)
+    def test_unsigned_overflow(self, sfx):
+        nlanes = getattr(npyv, "nlanes_" + sfx)
+        maxu = (1 << int(sfx[1:])) - 1
+        maxu_72 = (1 << 72) - 1
+        lane = getattr(npyv, "setall_" + sfx)(maxu_72)[0]
+        assert lane == maxu
+        lanes = getattr(npyv, "load_" + sfx)([maxu_72] * nlanes)
+        assert lanes == [maxu] * nlanes
+        lane = getattr(npyv, "setall_" + sfx)(-1)[0]
+        assert lane == maxu
+        lanes = getattr(npyv, "load_" + sfx)([-1] * nlanes)
+        assert lanes == [maxu] * nlanes
+
+    @pytest.mark.parametrize('sfx', signed_sfx)
+    def test_signed_overflow(self, sfx):
+        nlanes = getattr(npyv, "nlanes_" + sfx)
+        maxs_72 = (1 << 71) - 1
+        lane = getattr(npyv, "setall_" + sfx)(maxs_72)[0]
+        assert lane == -1
+        lanes = getattr(npyv, "load_" + sfx)([maxs_72] * nlanes)
+        assert lanes == [-1] * nlanes
+        mins_72 = -1 << 71
+        lane = getattr(npyv, "setall_" + sfx)(mins_72)[0]
+        assert lane == 0
+        lanes = getattr(npyv, "load_" + sfx)([mins_72] * nlanes)
+        assert lanes == [0] * nlanes
+
+    def test_truncate_f32(self):
+        if not npyv.simd_f32:
+            pytest.skip("F32 isn't support by the SIMD extension")
+        f32 = npyv.setall_f32(0.1)[0]
+        assert f32 != 0.1
+        assert round(f32, 1) == 0.1
+
+    def test_compare(self):
+        data_range = range(npyv.nlanes_u32)
+        vdata = npyv.load_u32(data_range)
+        assert vdata == list(data_range)
+        assert vdata == tuple(data_range)
+        for i in data_range:
+            assert vdata[i] == data_range[i]
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_stringdtype.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_stringdtype.py
new file mode 100644
index 0000000..e39d746
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_stringdtype.py
@@ -0,0 +1,1807 @@
+import copy
+import itertools
+import os
+import pickle
+import sys
+import tempfile
+
+import pytest
+
+import numpy as np
+from numpy._core.tests._natype import get_stringdtype_dtype as get_dtype
+from numpy._core.tests._natype import pd_NA
+from numpy.dtypes import StringDType
+from numpy.testing import IS_PYPY, assert_array_equal
+
+
+@pytest.fixture
+def string_list():
+    return ["abc", "def", "ghi" * 10, "A¢☃€ 😊" * 100, "Abc" * 1000, "DEF"]
+
+
+# second copy for cast tests to do a cartesian product over dtypes
+@pytest.fixture(params=[True, False])
+def coerce2(request):
+    return request.param
+
+
+@pytest.fixture(
+    params=["unset", None, pd_NA, np.nan, float("nan"), "__nan__"],
+    ids=["unset", "None", "pandas.NA", "np.nan", "float('nan')", "string nan"],
+)
+def na_object2(request):
+    return request.param
+
+
+@pytest.fixture()
+def dtype2(na_object2, coerce2):
+    # explicit is check for pd_NA because != with pd_NA returns pd_NA
+    if na_object2 is pd_NA or na_object2 != "unset":
+        return StringDType(na_object=na_object2, coerce=coerce2)
+    else:
+        return StringDType(coerce=coerce2)
+
+
+def test_dtype_creation():
+    hashes = set()
+    dt = StringDType()
+    assert not hasattr(dt, "na_object") and dt.coerce is True
+    hashes.add(hash(dt))
+
+    dt = StringDType(na_object=None)
+    assert dt.na_object is None and dt.coerce is True
+    hashes.add(hash(dt))
+
+    dt = StringDType(coerce=False)
+    assert not hasattr(dt, "na_object") and dt.coerce is False
+    hashes.add(hash(dt))
+
+    dt = StringDType(na_object=None, coerce=False)
+    assert dt.na_object is None and dt.coerce is False
+    hashes.add(hash(dt))
+
+    assert len(hashes) == 4
+
+    dt = np.dtype("T")
+    assert dt == StringDType()
+    assert dt.kind == "T"
+    assert dt.char == "T"
+
+    hashes.add(hash(dt))
+    assert len(hashes) == 4
+
+
+def test_dtype_equality(dtype):
+    assert dtype == dtype
+    for ch in "SU":
+        assert dtype != np.dtype(ch)
+        assert dtype != np.dtype(f"{ch}8")
+
+
+def test_dtype_repr(dtype):
+    if not hasattr(dtype, "na_object") and dtype.coerce:
+        assert repr(dtype) == "StringDType()"
+    elif dtype.coerce:
+        assert repr(dtype) == f"StringDType(na_object={dtype.na_object!r})"
+    elif not hasattr(dtype, "na_object"):
+        assert repr(dtype) == "StringDType(coerce=False)"
+    else:
+        assert (
+            repr(dtype)
+            == f"StringDType(na_object={dtype.na_object!r}, coerce=False)"
+        )
+
+
+def test_create_with_na(dtype):
+    if not hasattr(dtype, "na_object"):
+        pytest.skip("does not have an na object")
+    na_val = dtype.na_object
+    string_list = ["hello", na_val, "world"]
+    arr = np.array(string_list, dtype=dtype)
+    assert str(arr) == "[" + " ".join([repr(s) for s in string_list]) + "]"
+    assert arr[1] is dtype.na_object
+
+
+@pytest.mark.parametrize("i", list(range(5)))
+def test_set_replace_na(i):
+    # Test strings of various lengths can be set to NaN and then replaced.
+    s_empty = ""
+    s_short = "0123456789"
+    s_medium = "abcdefghijklmnopqrstuvwxyz"
+    s_long = "-=+" * 100
+    strings = [s_medium, s_empty, s_short, s_medium, s_long]
+    a = np.array(strings, StringDType(na_object=np.nan))
+    for s in [a[i], s_medium + s_short, s_short, s_empty, s_long]:
+        a[i] = np.nan
+        assert np.isnan(a[i])
+        a[i] = s
+        assert a[i] == s
+        assert_array_equal(a, strings[:i] + [s] + strings[i + 1:])
+
+
+def test_null_roundtripping():
+    data = ["hello\0world", "ABC\0DEF\0\0"]
+    arr = np.array(data, dtype="T")
+    assert data[0] == arr[0]
+    assert data[1] == arr[1]
+
+
+def test_string_too_large_error():
+    arr = np.array(["a", "b", "c"], dtype=StringDType())
+    with pytest.raises(OverflowError):
+        arr * (sys.maxsize + 1)
+
+
+@pytest.mark.parametrize(
+    "data",
+    [
+        ["abc", "def", "ghi"],
+        ["🤣", "📵", "😰"],
+        ["🚜", "🙃", "😾"],
+        ["😹", "🚠", "🚌"],
+    ],
+)
+def test_array_creation_utf8(dtype, data):
+    arr = np.array(data, dtype=dtype)
+    assert str(arr) == "[" + " ".join(["'" + str(d) + "'" for d in data]) + "]"
+    assert arr.dtype == dtype
+
+
+@pytest.mark.parametrize(
+    "data",
+    [
+        [1, 2, 3],
+        [b"abc", b"def", b"ghi"],
+        [object, object, object],
+    ],
+)
+def test_scalars_string_conversion(data, dtype):
+    try:
+        str_vals = [str(d.decode('utf-8')) for d in data]
+    except AttributeError:
+        str_vals = [str(d) for d in data]
+    if dtype.coerce:
+        assert_array_equal(
+            np.array(data, dtype=dtype),
+            np.array(str_vals, dtype=dtype),
+        )
+    else:
+        with pytest.raises(ValueError):
+            np.array(data, dtype=dtype)
+
+
+@pytest.mark.parametrize(
+    ("strings"),
+    [
+        ["this", "is", "an", "array"],
+        ["€", "", "😊"],
+        ["A¢☃€ 😊", " A☃€¢😊", "☃€😊 A¢", "😊☃A¢ €"],
+    ],
+)
+def test_self_casts(dtype, dtype2, strings):
+    if hasattr(dtype, "na_object"):
+        strings = strings + [dtype.na_object]
+    elif hasattr(dtype2, "na_object"):
+        strings = strings + [""]
+    arr = np.array(strings, dtype=dtype)
+    newarr = arr.astype(dtype2)
+
+    if hasattr(dtype, "na_object") and not hasattr(dtype2, "na_object"):
+        assert newarr[-1] == str(dtype.na_object)
+        with pytest.raises(TypeError):
+            arr.astype(dtype2, casting="safe")
+    elif hasattr(dtype, "na_object") and hasattr(dtype2, "na_object"):
+        assert newarr[-1] is dtype2.na_object
+        arr.astype(dtype2, casting="safe")
+    elif hasattr(dtype2, "na_object"):
+        assert newarr[-1] == ""
+        arr.astype(dtype2, casting="safe")
+    else:
+        arr.astype(dtype2, casting="safe")
+
+    if hasattr(dtype, "na_object") and hasattr(dtype2, "na_object"):
+        na1 = dtype.na_object
+        na2 = dtype2.na_object
+        if (na1 is not na2 and
+             # check for pd_NA first because bool(pd_NA) is an error
+             ((na1 is pd_NA or na2 is pd_NA) or
+              # the second check is a NaN check, spelled this way
+              # to avoid errors from math.isnan and np.isnan
+              (na1 != na2 and not (na1 != na1 and na2 != na2)))):
+            with pytest.raises(TypeError):
+                arr[:-1] == newarr[:-1]
+            return
+    assert_array_equal(arr[:-1], newarr[:-1])
+
+
+@pytest.mark.parametrize(
+    ("strings"),
+    [
+        ["this", "is", "an", "array"],
+        ["€", "", "😊"],
+        ["A¢☃€ 😊", " A☃€¢😊", "☃€😊 A¢", "😊☃A¢ €"],
+    ],
+)
+class TestStringLikeCasts:
+    def test_unicode_casts(self, dtype, strings):
+        arr = np.array(strings, dtype=np.str_).astype(dtype)
+        expected = np.array(strings, dtype=dtype)
+        assert_array_equal(arr, expected)
+
+        arr_as_U8 = expected.astype("U8")
+        assert_array_equal(arr_as_U8, np.array(strings, dtype="U8"))
+        assert_array_equal(arr_as_U8.astype(dtype), arr)
+        arr_as_U3 = expected.astype("U3")
+        assert_array_equal(arr_as_U3, np.array(strings, dtype="U3"))
+        assert_array_equal(
+            arr_as_U3.astype(dtype),
+            np.array([s[:3] for s in strings], dtype=dtype),
+        )
+
+    def test_void_casts(self, dtype, strings):
+        sarr = np.array(strings, dtype=dtype)
+        utf8_bytes = [s.encode("utf-8") for s in strings]
+        void_dtype = f"V{max(len(s) for s in utf8_bytes)}"
+        varr = np.array(utf8_bytes, dtype=void_dtype)
+        assert_array_equal(varr, sarr.astype(void_dtype))
+        assert_array_equal(varr.astype(dtype), sarr)
+
+    def test_bytes_casts(self, dtype, strings):
+        sarr = np.array(strings, dtype=dtype)
+        try:
+            utf8_bytes = [s.encode("ascii") for s in strings]
+            bytes_dtype = f"S{max(len(s) for s in utf8_bytes)}"
+            barr = np.array(utf8_bytes, dtype=bytes_dtype)
+            assert_array_equal(barr, sarr.astype(bytes_dtype))
+            assert_array_equal(barr.astype(dtype), sarr)
+            if dtype.coerce:
+                barr = np.array(utf8_bytes, dtype=dtype)
+                assert_array_equal(barr, sarr)
+                barr = np.array(utf8_bytes, dtype="O")
+                assert_array_equal(barr.astype(dtype), sarr)
+            else:
+                with pytest.raises(ValueError):
+                    np.array(utf8_bytes, dtype=dtype)
+        except UnicodeEncodeError:
+            with pytest.raises(UnicodeEncodeError):
+                sarr.astype("S20")
+
+
+def test_additional_unicode_cast(random_string_list, dtype):
+    arr = np.array(random_string_list, dtype=dtype)
+    # test that this short-circuits correctly
+    assert_array_equal(arr, arr.astype(arr.dtype))
+    # tests the casts via the comparison promoter
+    assert_array_equal(arr, arr.astype(random_string_list.dtype))
+
+
+def test_insert_scalar(dtype, string_list):
+    """Test that inserting a scalar works."""
+    arr = np.array(string_list, dtype=dtype)
+    scalar_instance = "what"
+    arr[1] = scalar_instance
+    assert_array_equal(
+        arr,
+        np.array(string_list[:1] + ["what"] + string_list[2:], dtype=dtype),
+    )
+
+
+comparison_operators = [
+    np.equal,
+    np.not_equal,
+    np.greater,
+    np.greater_equal,
+    np.less,
+    np.less_equal,
+]
+
+
+@pytest.mark.parametrize("op", comparison_operators)
+@pytest.mark.parametrize("o_dtype", [np.str_, object, StringDType()])
+def test_comparisons(string_list, dtype, op, o_dtype):
+    sarr = np.array(string_list, dtype=dtype)
+    oarr = np.array(string_list, dtype=o_dtype)
+
+    # test that comparison operators work
+    res = op(sarr, sarr)
+    ores = op(oarr, oarr)
+    # test that promotion works as well
+    orres = op(sarr, oarr)
+    olres = op(oarr, sarr)
+
+    assert_array_equal(res, ores)
+    assert_array_equal(res, orres)
+    assert_array_equal(res, olres)
+
+    # test we get the correct answer for unequal length strings
+    sarr2 = np.array([s + "2" for s in string_list], dtype=dtype)
+    oarr2 = np.array([s + "2" for s in string_list], dtype=o_dtype)
+
+    res = op(sarr, sarr2)
+    ores = op(oarr, oarr2)
+    olres = op(oarr, sarr2)
+    orres = op(sarr, oarr2)
+
+    assert_array_equal(res, ores)
+    assert_array_equal(res, olres)
+    assert_array_equal(res, orres)
+
+    res = op(sarr2, sarr)
+    ores = op(oarr2, oarr)
+    olres = op(oarr2, sarr)
+    orres = op(sarr2, oarr)
+
+    assert_array_equal(res, ores)
+    assert_array_equal(res, olres)
+    assert_array_equal(res, orres)
+
+
+def test_isnan(dtype, string_list):
+    if not hasattr(dtype, "na_object"):
+        pytest.skip("no na support")
+    sarr = np.array(string_list + [dtype.na_object], dtype=dtype)
+    is_nan = isinstance(dtype.na_object, float) and np.isnan(dtype.na_object)
+    bool_errors = 0
+    try:
+        bool(dtype.na_object)
+    except TypeError:
+        bool_errors = 1
+    if is_nan or bool_errors:
+        # isnan is only true when na_object is a NaN
+        assert_array_equal(
+            np.isnan(sarr),
+            np.array([0] * len(string_list) + [1], dtype=np.bool),
+        )
+    else:
+        assert not np.any(np.isnan(sarr))
+
+
+def test_pickle(dtype, string_list):
+    arr = np.array(string_list, dtype=dtype)
+
+    with tempfile.NamedTemporaryFile("wb", delete=False) as f:
+        pickle.dump([arr, dtype], f)
+
+    with open(f.name, "rb") as f:
+        res = pickle.load(f)
+
+    assert_array_equal(res[0], arr)
+    assert res[1] == dtype
+
+    os.remove(f.name)
+
+
+def test_stdlib_copy(dtype, string_list):
+    arr = np.array(string_list, dtype=dtype)
+
+    assert_array_equal(copy.copy(arr), arr)
+    assert_array_equal(copy.deepcopy(arr), arr)
+
+
+@pytest.mark.parametrize(
+    "strings",
+    [
+        ["left", "right", "leftovers", "righty", "up", "down"],
+        [
+            "left" * 10,
+            "right" * 10,
+            "leftovers" * 10,
+            "righty" * 10,
+            "up" * 10,
+        ],
+        ["🤣🤣", "🤣", "📵", "😰"],
+        ["🚜", "🙃", "😾"],
+        ["😹", "🚠", "🚌"],
+        ["A¢☃€ 😊", " A☃€¢😊", "☃€😊 A¢", "😊☃A¢ €"],
+    ],
+)
+def test_sort(dtype, strings):
+    """Test that sorting matches python's internal sorting."""
+
+    def test_sort(strings, arr_sorted):
+        arr = np.array(strings, dtype=dtype)
+        na_object = getattr(arr.dtype, "na_object", "")
+        if na_object is None and None in strings:
+            with pytest.raises(
+                ValueError,
+                match="Cannot compare null that is not a nan-like value",
+            ):
+                np.argsort(arr)
+            argsorted = None
+        elif na_object is pd_NA or na_object != '':
+            argsorted = None
+        else:
+            argsorted = np.argsort(arr)
+        np.random.default_rng().shuffle(arr)
+        if na_object is None and None in strings:
+            with pytest.raises(
+                ValueError,
+                match="Cannot compare null that is not a nan-like value",
+            ):
+                arr.sort()
+        else:
+            arr.sort()
+            assert np.array_equal(arr, arr_sorted, equal_nan=True)
+        if argsorted is not None:
+            assert np.array_equal(argsorted, np.argsort(strings))
+
+    # make a copy so we don't mutate the lists in the fixture
+    strings = strings.copy()
+    arr_sorted = np.array(sorted(strings), dtype=dtype)
+    test_sort(strings, arr_sorted)
+
+    if not hasattr(dtype, "na_object"):
+        return
+
+    # make sure NAs get sorted to the end of the array and string NAs get
+    # sorted like normal strings
+    strings.insert(0, dtype.na_object)
+    strings.insert(2, dtype.na_object)
+    # can't use append because doing that with NA converts
+    # the result to object dtype
+    if not isinstance(dtype.na_object, str):
+        arr_sorted = np.array(
+            arr_sorted.tolist() + [dtype.na_object, dtype.na_object],
+            dtype=dtype,
+        )
+    else:
+        arr_sorted = np.array(sorted(strings), dtype=dtype)
+
+    test_sort(strings, arr_sorted)
+
+
+@pytest.mark.parametrize(
+    "strings",
+    [
+        ["A¢☃€ 😊", " A☃€¢😊", "☃€😊 A¢", "😊☃A¢ €"],
+        ["A¢☃€ 😊", "", " ", " "],
+        ["", "a", "😸", "ááðfáíóåéë"],
+    ],
+)
+def test_nonzero(strings, na_object):
+    dtype = get_dtype(na_object)
+    arr = np.array(strings, dtype=dtype)
+    is_nonzero = np.array(
+        [i for i, item in enumerate(strings) if len(item) != 0])
+    assert_array_equal(arr.nonzero()[0], is_nonzero)
+
+    if na_object is not pd_NA and na_object == 'unset':
+        return
+
+    strings_with_na = np.array(strings + [na_object], dtype=dtype)
+    is_nan = np.isnan(np.array([dtype.na_object], dtype=dtype))[0]
+
+    if is_nan:
+        assert strings_with_na.nonzero()[0][-1] == 4
+    else:
+        assert strings_with_na.nonzero()[0][-1] == 3
+
+    # check that the casting to bool and nonzero give consistent results
+    assert_array_equal(strings_with_na[strings_with_na.nonzero()],
+                       strings_with_na[strings_with_na.astype(bool)])
+
+
+def test_where(string_list, na_object):
+    dtype = get_dtype(na_object)
+    a = np.array(string_list, dtype=dtype)
+    b = a[::-1]
+    res = np.where([True, False, True, False, True, False], a, b)
+    assert_array_equal(res, [a[0], b[1], a[2], b[3], a[4], b[5]])
+
+
+def test_fancy_indexing(string_list):
+    sarr = np.array(string_list, dtype="T")
+    assert_array_equal(sarr, sarr[np.arange(sarr.shape[0])])
+
+    inds = [
+        [True, True],
+        [0, 1],
+        ...,
+        np.array([0, 1], dtype='uint8'),
+    ]
+
+    lops = [
+        ['a' * 25, 'b' * 25],
+        ['', ''],
+        ['hello', 'world'],
+        ['hello', 'world' * 25],
+    ]
+
+    # see gh-27003 and gh-27053
+    for ind in inds:
+        for lop in lops:
+            a = np.array(lop, dtype="T")
+            assert_array_equal(a[ind], a)
+            rop = ['d' * 25, 'e' * 25]
+            for b in [rop, np.array(rop, dtype="T")]:
+                a[ind] = b
+                assert_array_equal(a, b)
+                assert a[0] == 'd' * 25
+
+    # see gh-29279
+    data = [
+        ["AAAAAAAAAAAAAAAAA"],
+        ["BBBBBBBBBBBBBBBBBBBBBBBBBBBBB"],
+        ["CCCCCCCCCCCCCCCCC"],
+        ["DDDDDDDDDDDDDDDDD"],
+    ]
+    sarr = np.array(data, dtype=np.dtypes.StringDType())
+    uarr = np.array(data, dtype="U30")
+    for ind in [[0], [1], [2], [3], [[0, 0]], [[1, 1, 3]], [[1, 1]]]:
+        assert_array_equal(sarr[ind], uarr[ind])
+
+
+def test_creation_functions():
+    assert_array_equal(np.zeros(3, dtype="T"), ["", "", ""])
+    assert_array_equal(np.empty(3, dtype="T"), ["", "", ""])
+
+    assert np.zeros(3, dtype="T")[0] == ""
+    assert np.empty(3, dtype="T")[0] == ""
+
+
+def test_concatenate(string_list):
+    sarr = np.array(string_list, dtype="T")
+    sarr_cat = np.array(string_list + string_list, dtype="T")
+
+    assert_array_equal(np.concatenate([sarr], axis=0), sarr)
+
+
+def test_resize_method(string_list):
+    sarr = np.array(string_list, dtype="T")
+    if IS_PYPY:
+        sarr.resize(len(string_list) + 3, refcheck=False)
+    else:
+        sarr.resize(len(string_list) + 3)
+    assert_array_equal(sarr, np.array(string_list + [''] * 3,  dtype="T"))
+
+
+def test_create_with_copy_none(string_list):
+    arr = np.array(string_list, dtype=StringDType())
+    # create another stringdtype array with an arena that has a different
+    # in-memory layout than the first array
+    arr_rev = np.array(string_list[::-1], dtype=StringDType())
+
+    # this should create a copy and the resulting array
+    # shouldn't share an allocator or arena with arr_rev, despite
+    # explicitly passing arr_rev.dtype
+    arr_copy = np.array(arr, copy=None, dtype=arr_rev.dtype)
+    np.testing.assert_array_equal(arr, arr_copy)
+    assert arr_copy.base is None
+
+    with pytest.raises(ValueError, match="Unable to avoid copy"):
+        np.array(arr, copy=False, dtype=arr_rev.dtype)
+
+    # because we're using arr's dtype instance, the view is safe
+    arr_view = np.array(arr, copy=None, dtype=arr.dtype)
+    np.testing.assert_array_equal(arr, arr)
+    np.testing.assert_array_equal(arr_view[::-1], arr_rev)
+    assert arr_view is arr
+
+
+def test_astype_copy_false():
+    orig_dt = StringDType()
+    arr = np.array(["hello", "world"], dtype=StringDType())
+    assert not arr.astype(StringDType(coerce=False), copy=False).dtype.coerce
+
+    assert arr.astype(orig_dt, copy=False).dtype is orig_dt
+
+@pytest.mark.parametrize(
+    "strings",
+    [
+        ["left", "right", "leftovers", "righty", "up", "down"],
+        ["🤣🤣", "🤣", "📵", "😰"],
+        ["🚜", "🙃", "😾"],
+        ["😹", "🚠", "🚌"],
+        ["A¢☃€ 😊", " A☃€¢😊", "☃€😊 A¢", "😊☃A¢ €"],
+    ],
+)
+def test_argmax(strings):
+    """Test that argmax/argmin matches what python calculates."""
+    arr = np.array(strings, dtype="T")
+    assert np.argmax(arr) == strings.index(max(strings))
+    assert np.argmin(arr) == strings.index(min(strings))
+
+
+@pytest.mark.parametrize(
+    "arrfunc,expected",
+    [
+        [np.sort, None],
+        [np.nonzero, (np.array([], dtype=np.int_),)],
+        [np.argmax, 0],
+        [np.argmin, 0],
+    ],
+)
+def test_arrfuncs_zeros(arrfunc, expected):
+    arr = np.zeros(10, dtype="T")
+    result = arrfunc(arr)
+    if expected is None:
+        expected = arr
+    assert_array_equal(result, expected, strict=True)
+
+
+@pytest.mark.parametrize(
+    ("strings", "cast_answer", "any_answer", "all_answer"),
+    [
+        [["hello", "world"], [True, True], True, True],
+        [["", ""], [False, False], False, False],
+        [["hello", ""], [True, False], True, False],
+        [["", "world"], [False, True], True, False],
+    ],
+)
+def test_cast_to_bool(strings, cast_answer, any_answer, all_answer):
+    sarr = np.array(strings, dtype="T")
+    assert_array_equal(sarr.astype("bool"), cast_answer)
+
+    assert np.any(sarr) == any_answer
+    assert np.all(sarr) == all_answer
+
+
+@pytest.mark.parametrize(
+    ("strings", "cast_answer"),
+    [
+        [[True, True], ["True", "True"]],
+        [[False, False], ["False", "False"]],
+        [[True, False], ["True", "False"]],
+        [[False, True], ["False", "True"]],
+    ],
+)
+def test_cast_from_bool(strings, cast_answer):
+    barr = np.array(strings, dtype=bool)
+    assert_array_equal(barr.astype("T"), np.array(cast_answer, dtype="T"))
+
+
+@pytest.mark.parametrize("bitsize", [8, 16, 32, 64])
+@pytest.mark.parametrize("signed", [True, False])
+def test_sized_integer_casts(bitsize, signed):
+    idtype = f"int{bitsize}"
+    if signed:
+        inp = [-(2**p - 1) for p in reversed(range(bitsize - 1))]
+        inp += [2**p - 1 for p in range(1, bitsize - 1)]
+    else:
+        idtype = "u" + idtype
+        inp = [2**p - 1 for p in range(bitsize)]
+    ainp = np.array(inp, dtype=idtype)
+    assert_array_equal(ainp, ainp.astype("T").astype(idtype))
+
+    # safe casting works
+    ainp.astype("T", casting="safe")
+
+    with pytest.raises(TypeError):
+        ainp.astype("T").astype(idtype, casting="safe")
+
+    oob = [str(2**bitsize), str(-(2**bitsize))]
+    with pytest.raises(OverflowError):
+        np.array(oob, dtype="T").astype(idtype)
+
+    with pytest.raises(ValueError):
+        np.array(["1", np.nan, "3"],
+                 dtype=StringDType(na_object=np.nan)).astype(idtype)
+
+
+@pytest.mark.parametrize("typename", ["byte", "short", "int", "longlong"])
+@pytest.mark.parametrize("signed", ["", "u"])
+def test_unsized_integer_casts(typename, signed):
+    idtype = f"{signed}{typename}"
+
+    inp = [1, 2, 3, 4]
+    ainp = np.array(inp, dtype=idtype)
+    assert_array_equal(ainp, ainp.astype("T").astype(idtype))
+
+
+@pytest.mark.parametrize(
+    "typename",
+    [
+        pytest.param(
+            "longdouble",
+            marks=pytest.mark.xfail(
+                np.dtypes.LongDoubleDType() != np.dtypes.Float64DType(),
+                reason="numpy lacks an ld2a implementation",
+                strict=True,
+            ),
+        ),
+        "float64",
+        "float32",
+        "float16",
+    ],
+)
+def test_float_casts(typename):
+    inp = [1.1, 2.8, -3.2, 2.7e4]
+    ainp = np.array(inp, dtype=typename)
+    assert_array_equal(ainp, ainp.astype("T").astype(typename))
+
+    inp = [0.1]
+    sres = np.array(inp, dtype=typename).astype("T")
+    res = sres.astype(typename)
+    assert_array_equal(np.array(inp, dtype=typename), res)
+    assert sres[0] == "0.1"
+
+    if typename == "longdouble":
+        # let's not worry about platform-dependent rounding of longdouble
+        return
+
+    fi = np.finfo(typename)
+
+    inp = [1e-324, fi.smallest_subnormal, -1e-324, -fi.smallest_subnormal]
+    eres = [0, fi.smallest_subnormal, -0, -fi.smallest_subnormal]
+    res = np.array(inp, dtype=typename).astype("T").astype(typename)
+    assert_array_equal(eres, res)
+
+    inp = [2e308, fi.max, -2e308, fi.min]
+    eres = [np.inf, fi.max, -np.inf, fi.min]
+    res = np.array(inp, dtype=typename).astype("T").astype(typename)
+    assert_array_equal(eres, res)
+
+
+def test_float_nan_cast_na_object():
+    # gh-28157
+    dt = np.dtypes.StringDType(na_object=np.nan)
+    arr1 = np.full((1,), fill_value=np.nan, dtype=dt)
+    arr2 = np.full_like(arr1, fill_value=np.nan)
+
+    assert arr1.item() is np.nan
+    assert arr2.item() is np.nan
+
+    inp = [1.2, 2.3, np.nan]
+    arr = np.array(inp).astype(dt)
+    assert arr[2] is np.nan
+    assert arr[0] == '1.2'
+
+
+@pytest.mark.parametrize(
+    "typename",
+    [
+        "csingle",
+        "cdouble",
+        pytest.param(
+            "clongdouble",
+            marks=pytest.mark.xfail(
+                np.dtypes.CLongDoubleDType() != np.dtypes.Complex128DType(),
+                reason="numpy lacks an ld2a implementation",
+                strict=True,
+            ),
+        ),
+    ],
+)
+def test_cfloat_casts(typename):
+    inp = [1.1 + 1.1j, 2.8 + 2.8j, -3.2 - 3.2j, 2.7e4 + 2.7e4j]
+    ainp = np.array(inp, dtype=typename)
+    assert_array_equal(ainp, ainp.astype("T").astype(typename))
+
+    inp = [0.1 + 0.1j]
+    sres = np.array(inp, dtype=typename).astype("T")
+    res = sres.astype(typename)
+    assert_array_equal(np.array(inp, dtype=typename), res)
+    assert sres[0] == "(0.1+0.1j)"
+
+
+def test_take(string_list):
+    sarr = np.array(string_list, dtype="T")
+    res = sarr.take(np.arange(len(string_list)))
+    assert_array_equal(sarr, res)
+
+    # make sure it also works for out
+    out = np.empty(len(string_list), dtype="T")
+    out[0] = "hello"
+    res = sarr.take(np.arange(len(string_list)), out=out)
+    assert res is out
+    assert_array_equal(sarr, res)
+
+
+@pytest.mark.parametrize("use_out", [True, False])
+@pytest.mark.parametrize(
+    "ufunc_name,func",
+    [
+        ("min", min),
+        ("max", max),
+    ],
+)
+def test_ufuncs_minmax(string_list, ufunc_name, func, use_out):
+    """Test that the min/max ufuncs match Python builtin min/max behavior."""
+    arr = np.array(string_list, dtype="T")
+    uarr = np.array(string_list, dtype=str)
+    res = np.array(func(string_list), dtype="T")
+    assert_array_equal(getattr(arr, ufunc_name)(), res)
+
+    ufunc = getattr(np, ufunc_name + "imum")
+
+    if use_out:
+        res = ufunc(arr, arr, out=arr)
+    else:
+        res = ufunc(arr, arr)
+
+    assert_array_equal(uarr, res)
+    assert_array_equal(getattr(arr, ufunc_name)(), func(string_list))
+
+
+def test_max_regression():
+    arr = np.array(['y', 'y', 'z'], dtype="T")
+    assert arr.max() == 'z'
+
+
+@pytest.mark.parametrize("use_out", [True, False])
+@pytest.mark.parametrize(
+    "other_strings",
+    [
+        ["abc", "def" * 500, "ghi" * 16, "🤣" * 100, "📵", "😰"],
+        ["🚜", "🙃", "😾", "😹", "🚠", "🚌"],
+        ["🥦", "¨", "⨯", "∰ ", "⨌ ", "⎶ "],
+    ],
+)
+def test_ufunc_add(dtype, string_list, other_strings, use_out):
+    arr1 = np.array(string_list, dtype=dtype)
+    arr2 = np.array(other_strings, dtype=dtype)
+    result = np.array([a + b for a, b in zip(arr1, arr2)], dtype=dtype)
+
+    if use_out:
+        res = np.add(arr1, arr2, out=arr1)
+    else:
+        res = np.add(arr1, arr2)
+
+    assert_array_equal(res, result)
+
+    if not hasattr(dtype, "na_object"):
+        return
+
+    is_nan = isinstance(dtype.na_object, float) and np.isnan(dtype.na_object)
+    is_str = isinstance(dtype.na_object, str)
+    bool_errors = 0
+    try:
+        bool(dtype.na_object)
+    except TypeError:
+        bool_errors = 1
+
+    arr1 = np.array([dtype.na_object] + string_list, dtype=dtype)
+    arr2 = np.array(other_strings + [dtype.na_object], dtype=dtype)
+
+    if is_nan or bool_errors or is_str:
+        res = np.add(arr1, arr2)
+        assert_array_equal(res[1:-1], arr1[1:-1] + arr2[1:-1])
+        if not is_str:
+            assert res[0] is dtype.na_object and res[-1] is dtype.na_object
+        else:
+            assert res[0] == dtype.na_object + arr2[0]
+            assert res[-1] == arr1[-1] + dtype.na_object
+    else:
+        with pytest.raises(ValueError):
+            np.add(arr1, arr2)
+
+
+def test_ufunc_add_reduce(dtype):
+    values = ["a", "this is a long string", "c"]
+    arr = np.array(values, dtype=dtype)
+    out = np.empty((), dtype=dtype)
+
+    expected = np.array("".join(values), dtype=dtype)
+    assert_array_equal(np.add.reduce(arr), expected)
+
+    np.add.reduce(arr, out=out)
+    assert_array_equal(out, expected)
+
+
+def test_add_promoter(string_list):
+    arr = np.array(string_list, dtype=StringDType())
+    lresult = np.array(["hello" + s for s in string_list], dtype=StringDType())
+    rresult = np.array([s + "hello" for s in string_list], dtype=StringDType())
+
+    for op in ["hello", np.str_("hello"), np.array(["hello"])]:
+        assert_array_equal(op + arr, lresult)
+        assert_array_equal(arr + op, rresult)
+
+    # The promoter should be able to handle things if users pass `dtype=`
+    res = np.add("hello", string_list, dtype=StringDType)
+    assert res.dtype == StringDType()
+
+    # The promoter should not kick in if users override the input,
+    # which means arr is cast, this fails because of the unknown length.
+    with pytest.raises(TypeError, match="cannot cast dtype"):
+        np.add(arr, "add", signature=("U", "U", None), casting="unsafe")
+
+    # But it must simply reject the following:
+    with pytest.raises(TypeError, match=".*did not contain a loop"):
+        np.add(arr, "add", signature=(None, "U", None))
+
+    with pytest.raises(TypeError, match=".*did not contain a loop"):
+        np.add("a", "b", signature=("U", "U", StringDType))
+
+
+def test_add_no_legacy_promote_with_signature():
+    # Possibly misplaced, but useful to test with string DType.  We check that
+    # if there is clearly no loop found, a stray `dtype=` doesn't break things
+    # Regression test for the bad error in gh-26735
+    # (If legacy promotion is gone, this can be deleted...)
+    with pytest.raises(TypeError, match=".*did not contain a loop"):
+        np.add("3", 6, dtype=StringDType)
+
+
+def test_add_promoter_reduce():
+    # Exact TypeError could change, but ensure StringDtype doesn't match
+    with pytest.raises(TypeError, match="the resolved dtypes are not"):
+        np.add.reduce(np.array(["a", "b"], dtype="U"))
+
+    # On the other hand, using `dtype=T` in the *ufunc* should work.
+    np.add.reduce(np.array(["a", "b"], dtype="U"), dtype=np.dtypes.StringDType)
+
+
+def test_multiply_reduce():
+    # At the time of writing (NumPy 2.0) this is very limited (and rather
+    # ridiculous anyway).  But it works and actually makes some sense...
+    # (NumPy does not allow non-scalar initial values)
+    repeats = np.array([2, 3, 4])
+    val = "school-🚌"
+    res = np.multiply.reduce(repeats, initial=val, dtype=np.dtypes.StringDType)
+    assert res == val * np.prod(repeats)
+
+
+def test_multiply_two_string_raises():
+    arr = np.array(["hello", "world"], dtype="T")
+    with pytest.raises(np._core._exceptions._UFuncNoLoopError):
+        np.multiply(arr, arr)
+
+
+@pytest.mark.parametrize("use_out", [True, False])
+@pytest.mark.parametrize("other", [2, [2, 1, 3, 4, 1, 3]])
+@pytest.mark.parametrize(
+    "other_dtype",
+    [
+        None,
+        "int8",
+        "int16",
+        "int32",
+        "int64",
+        "uint8",
+        "uint16",
+        "uint32",
+        "uint64",
+        "short",
+        "int",
+        "intp",
+        "long",
+        "longlong",
+        "ushort",
+        "uint",
+        "uintp",
+        "ulong",
+        "ulonglong",
+    ],
+)
+def test_ufunc_multiply(dtype, string_list, other, other_dtype, use_out):
+    """Test the two-argument ufuncs match python builtin behavior."""
+    arr = np.array(string_list, dtype=dtype)
+    if other_dtype is not None:
+        other_dtype = np.dtype(other_dtype)
+    try:
+        len(other)
+        result = [s * o for s, o in zip(string_list, other)]
+        other = np.array(other)
+        if other_dtype is not None:
+            other = other.astype(other_dtype)
+    except TypeError:
+        if other_dtype is not None:
+            other = other_dtype.type(other)
+        result = [s * other for s in string_list]
+
+    if use_out:
+        arr_cache = arr.copy()
+        lres = np.multiply(arr, other, out=arr)
+        assert_array_equal(lres, result)
+        arr[:] = arr_cache
+        assert lres is arr
+        arr *= other
+        assert_array_equal(arr, result)
+        arr[:] = arr_cache
+        rres = np.multiply(other, arr, out=arr)
+        assert rres is arr
+        assert_array_equal(rres, result)
+    else:
+        lres = arr * other
+        assert_array_equal(lres, result)
+        rres = other * arr
+        assert_array_equal(rres, result)
+
+    if not hasattr(dtype, "na_object"):
+        return
+
+    is_nan = np.isnan(np.array([dtype.na_object], dtype=dtype))[0]
+    is_str = isinstance(dtype.na_object, str)
+    bool_errors = 0
+    try:
+        bool(dtype.na_object)
+    except TypeError:
+        bool_errors = 1
+
+    arr = np.array(string_list + [dtype.na_object], dtype=dtype)
+
+    try:
+        len(other)
+        other = np.append(other, 3)
+        if other_dtype is not None:
+            other = other.astype(other_dtype)
+    except TypeError:
+        pass
+
+    if is_nan or bool_errors or is_str:
+        for res in [arr * other, other * arr]:
+            assert_array_equal(res[:-1], result)
+            if not is_str:
+                assert res[-1] is dtype.na_object
+            else:
+                try:
+                    assert res[-1] == dtype.na_object * other[-1]
+                except (IndexError, TypeError):
+                    assert res[-1] == dtype.na_object * other
+    else:
+        with pytest.raises(TypeError):
+            arr * other
+        with pytest.raises(TypeError):
+            other * arr
+
+
+def test_findlike_promoters():
+    r = "Wally"
+    l = "Where's Wally?"
+    s = np.int32(3)
+    e = np.int8(13)
+    for dtypes in [("T", "U"), ("U", "T")]:
+        for function, answer in [
+            (np.strings.index, 8),
+            (np.strings.endswith, True),
+        ]:
+            assert answer == function(
+                np.array(l, dtype=dtypes[0]), np.array(r, dtype=dtypes[1]), s, e
+            )
+
+
+def test_strip_promoter():
+    arg = ["Hello!!!!", "Hello??!!"]
+    strip_char = "!"
+    answer = ["Hello", "Hello??"]
+    for dtypes in [("T", "U"), ("U", "T")]:
+        result = np.strings.strip(
+            np.array(arg, dtype=dtypes[0]),
+            np.array(strip_char, dtype=dtypes[1])
+        )
+        assert_array_equal(result, answer)
+        assert result.dtype.char == "T"
+
+
+def test_replace_promoter():
+    arg = ["Hello, planet!", "planet, Hello!"]
+    old = "planet"
+    new = "world"
+    answer = ["Hello, world!", "world, Hello!"]
+    for dtypes in itertools.product("TU", repeat=3):
+        if dtypes == ("U", "U", "U"):
+            continue
+        answer_arr = np.strings.replace(
+            np.array(arg, dtype=dtypes[0]),
+            np.array(old, dtype=dtypes[1]),
+            np.array(new, dtype=dtypes[2]),
+        )
+        assert_array_equal(answer_arr, answer)
+        assert answer_arr.dtype.char == "T"
+
+
+def test_center_promoter():
+    arg = ["Hello", "planet!"]
+    fillchar = "/"
+    for dtypes in [("T", "U"), ("U", "T")]:
+        answer = np.strings.center(
+            np.array(arg, dtype=dtypes[0]), 9, np.array(fillchar, dtype=dtypes[1])
+        )
+        assert_array_equal(answer, ["//Hello//", "/planet!/"])
+        assert answer.dtype.char == "T"
+
+
+DATETIME_INPUT = [
+    np.datetime64("1923-04-14T12:43:12"),
+    np.datetime64("1994-06-21T14:43:15"),
+    np.datetime64("2001-10-15T04:10:32"),
+    np.datetime64("NaT"),
+    np.datetime64("1995-11-25T16:02:16"),
+    np.datetime64("2005-01-04T03:14:12"),
+    np.datetime64("2041-12-03T14:05:03"),
+]
+
+
+TIMEDELTA_INPUT = [
+    np.timedelta64(12358, "s"),
+    np.timedelta64(23, "s"),
+    np.timedelta64(74, "s"),
+    np.timedelta64("NaT"),
+    np.timedelta64(23, "s"),
+    np.timedelta64(73, "s"),
+    np.timedelta64(7, "s"),
+]
+
+
+@pytest.mark.parametrize(
+    "input_data, input_dtype",
+    [
+        (DATETIME_INPUT, "M8[s]"),
+        (TIMEDELTA_INPUT, "m8[s]")
+    ]
+)
+def test_datetime_timedelta_cast(dtype, input_data, input_dtype):
+
+    a = np.array(input_data, dtype=input_dtype)
+
+    has_na = hasattr(dtype, "na_object")
+    is_str = isinstance(getattr(dtype, "na_object", None), str)
+
+    if not has_na or is_str:
+        a = np.delete(a, 3)
+
+    sa = a.astype(dtype)
+    ra = sa.astype(a.dtype)
+
+    if has_na and not is_str:
+        assert sa[3] is dtype.na_object
+        assert np.isnat(ra[3])
+
+    assert_array_equal(a, ra)
+
+    if has_na and not is_str:
+        # don't worry about comparing how NaT is converted
+        sa = np.delete(sa, 3)
+        a = np.delete(a, 3)
+
+    if input_dtype.startswith("M"):
+        assert_array_equal(sa, a.astype("U"))
+    else:
+        # The timedelta to unicode cast produces strings
+        # that aren't round-trippable and we don't want to
+        # reproduce that behavior in stringdtype
+        assert_array_equal(sa, a.astype("int64").astype("U"))
+
+
+def test_nat_casts():
+    s = 'nat'
+    all_nats = itertools.product(*zip(s.upper(), s.lower()))
+    all_nats = list(map(''.join, all_nats))
+    NaT_dt = np.datetime64('NaT')
+    NaT_td = np.timedelta64('NaT')
+    for na_object in [np._NoValue, None, np.nan, 'nat', '']:
+        # numpy treats empty string and all case combinations of 'nat' as NaT
+        dtype = StringDType(na_object=na_object)
+        arr = np.array([''] + all_nats, dtype=dtype)
+        dt_array = arr.astype('M8[s]')
+        td_array = arr.astype('m8[s]')
+        assert_array_equal(dt_array, NaT_dt)
+        assert_array_equal(td_array, NaT_td)
+
+        if na_object is np._NoValue:
+            output_object = 'NaT'
+        else:
+            output_object = na_object
+
+        for arr in [dt_array, td_array]:
+            assert_array_equal(
+                arr.astype(dtype),
+                np.array([output_object] * arr.size, dtype=dtype))
+
+
+def test_nat_conversion():
+    for nat in [np.datetime64("NaT", "s"), np.timedelta64("NaT", "s")]:
+        with pytest.raises(ValueError, match="string coercion is disabled"):
+            np.array(["a", nat], dtype=StringDType(coerce=False))
+
+
+def test_growing_strings(dtype):
+    # growing a string leads to a heap allocation, this tests to make sure
+    # we do that bookkeeping correctly for all possible starting cases
+    data = [
+        "hello",  # a short string
+        "abcdefghijklmnopqestuvwxyz",  # a medium heap-allocated string
+        "hello" * 200,  # a long heap-allocated string
+    ]
+
+    arr = np.array(data, dtype=dtype)
+    uarr = np.array(data, dtype=str)
+
+    for _ in range(5):
+        arr = arr + arr
+        uarr = uarr + uarr
+
+    assert_array_equal(arr, uarr)
+
+
+def test_assign_medium_strings():
+    # see gh-29261
+    N = 9
+    src = np.array(
+        (
+            ['0' * 256] * 3 + ['0' * 255] + ['0' * 256] + ['0' * 255] +
+            ['0' * 256] * 2 + ['0' * 255]
+        ), dtype='T')
+    dst = np.array(
+        (
+            ['0' * 255] + ['0' * 256] * 2 + ['0' * 255] + ['0' * 256] +
+            ['0' * 255] + [''] * 5
+        ), dtype='T')
+
+    dst[1:N + 1] = src
+    assert_array_equal(dst[1:N + 1], src)
+
+
+UFUNC_TEST_DATA = [
+    "hello" * 10,
+    "Ae¢☃€ 😊" * 20,
+    "entry\nwith\nnewlines",
+    "entry\twith\ttabs",
+]
+
+
+@pytest.fixture
+def string_array(dtype):
+    return np.array(UFUNC_TEST_DATA, dtype=dtype)
+
+
+@pytest.fixture
+def unicode_array():
+    return np.array(UFUNC_TEST_DATA, dtype=np.str_)
+
+
+NAN_PRESERVING_FUNCTIONS = [
+    "capitalize",
+    "expandtabs",
+    "lower",
+    "lstrip",
+    "rstrip",
+    "splitlines",
+    "strip",
+    "swapcase",
+    "title",
+    "upper",
+]
+
+BOOL_OUTPUT_FUNCTIONS = [
+    "isalnum",
+    "isalpha",
+    "isdigit",
+    "islower",
+    "isspace",
+    "istitle",
+    "isupper",
+    "isnumeric",
+    "isdecimal",
+]
+
+UNARY_FUNCTIONS = [
+    "str_len",
+    "capitalize",
+    "expandtabs",
+    "isalnum",
+    "isalpha",
+    "isdigit",
+    "islower",
+    "isspace",
+    "istitle",
+    "isupper",
+    "lower",
+    "lstrip",
+    "rstrip",
+    "splitlines",
+    "strip",
+    "swapcase",
+    "title",
+    "upper",
+    "isnumeric",
+    "isdecimal",
+    "isalnum",
+    "islower",
+    "istitle",
+    "isupper",
+]
+
+UNIMPLEMENTED_VEC_STRING_FUNCTIONS = [
+    "capitalize",
+    "expandtabs",
+    "lower",
+    "splitlines",
+    "swapcase",
+    "title",
+    "upper",
+]
+
+ONLY_IN_NP_CHAR = [
+    "join",
+    "split",
+    "rsplit",
+    "splitlines"
+]
+
+
+@pytest.mark.parametrize("function_name", UNARY_FUNCTIONS)
+def test_unary(string_array, unicode_array, function_name):
+    if function_name in ONLY_IN_NP_CHAR:
+        func = getattr(np.char, function_name)
+    else:
+        func = getattr(np.strings, function_name)
+    dtype = string_array.dtype
+    sres = func(string_array)
+    ures = func(unicode_array)
+    if sres.dtype == StringDType():
+        ures = ures.astype(StringDType())
+    assert_array_equal(sres, ures)
+
+    if not hasattr(dtype, "na_object"):
+        return
+
+    is_nan = np.isnan(np.array([dtype.na_object], dtype=dtype))[0]
+    is_str = isinstance(dtype.na_object, str)
+    na_arr = np.insert(string_array, 0, dtype.na_object)
+
+    if function_name in UNIMPLEMENTED_VEC_STRING_FUNCTIONS:
+        if not is_str:
+            # to avoid these errors we'd need to add NA support to _vec_string
+            with pytest.raises((ValueError, TypeError)):
+                func(na_arr)
+        elif function_name == "splitlines":
+            assert func(na_arr)[0] == func(dtype.na_object)[()]
+        else:
+            assert func(na_arr)[0] == func(dtype.na_object)
+        return
+    if function_name == "str_len" and not is_str:
+        # str_len always errors for any non-string null, even NA ones because
+        # it has an integer result
+        with pytest.raises(ValueError):
+            func(na_arr)
+        return
+    if function_name in BOOL_OUTPUT_FUNCTIONS:
+        if is_nan:
+            assert func(na_arr)[0] is np.False_
+        elif is_str:
+            assert func(na_arr)[0] == func(dtype.na_object)
+        else:
+            with pytest.raises(ValueError):
+                func(na_arr)
+        return
+    if not (is_nan or is_str):
+        with pytest.raises(ValueError):
+            func(na_arr)
+        return
+    res = func(na_arr)
+    if is_nan and function_name in NAN_PRESERVING_FUNCTIONS:
+        assert res[0] is dtype.na_object
+    elif is_str:
+        assert res[0] == func(dtype.na_object)
+
+
+unicode_bug_fail = pytest.mark.xfail(
+    reason="unicode output width is buggy", strict=True
+)
+
+# None means that the argument is a string array
+BINARY_FUNCTIONS = [
+    ("add", (None, None)),
+    ("multiply", (None, 2)),
+    ("mod", ("format: %s", None)),
+    ("center", (None, 25)),
+    ("count", (None, "A")),
+    ("encode", (None, "UTF-8")),
+    ("endswith", (None, "lo")),
+    ("find", (None, "A")),
+    ("index", (None, "e")),
+    ("join", ("-", None)),
+    ("ljust", (None, 12)),
+    ("lstrip", (None, "A")),
+    ("partition", (None, "A")),
+    ("replace", (None, "A", "B")),
+    ("rfind", (None, "A")),
+    ("rindex", (None, "e")),
+    ("rjust", (None, 12)),
+    ("rsplit", (None, "A")),
+    ("rstrip", (None, "A")),
+    ("rpartition", (None, "A")),
+    ("split", (None, "A")),
+    ("strip", (None, "A")),
+    ("startswith", (None, "A")),
+    ("zfill", (None, 12)),
+]
+
+PASSES_THROUGH_NAN_NULLS = [
+    "add",
+    "center",
+    "ljust",
+    "multiply",
+    "replace",
+    "rjust",
+    "strip",
+    "lstrip",
+    "rstrip",
+    "replace"
+    "zfill",
+]
+
+NULLS_ARE_FALSEY = [
+    "startswith",
+    "endswith",
+]
+
+NULLS_ALWAYS_ERROR = [
+    "count",
+    "find",
+    "rfind",
+]
+
+SUPPORTS_NULLS = (
+    PASSES_THROUGH_NAN_NULLS +
+    NULLS_ARE_FALSEY +
+    NULLS_ALWAYS_ERROR
+)
+
+
+def call_func(func, args, array, sanitize=True):
+    if args == (None, None):
+        return func(array, array)
+    if args[0] is None:
+        if sanitize:
+            san_args = tuple(
+                np.array(arg, dtype=array.dtype) if isinstance(arg, str) else
+                arg for arg in args[1:]
+            )
+        else:
+            san_args = args[1:]
+        return func(array, *san_args)
+    if args[1] is None:
+        return func(args[0], array)
+    # shouldn't ever happen
+    assert 0
+
+
+@pytest.mark.parametrize("function_name, args", BINARY_FUNCTIONS)
+def test_binary(string_array, unicode_array, function_name, args):
+    if function_name in ONLY_IN_NP_CHAR:
+        func = getattr(np.char, function_name)
+    else:
+        func = getattr(np.strings, function_name)
+    sres = call_func(func, args, string_array)
+    ures = call_func(func, args, unicode_array, sanitize=False)
+    if not isinstance(sres, tuple) and sres.dtype == StringDType():
+        ures = ures.astype(StringDType())
+    assert_array_equal(sres, ures)
+
+    dtype = string_array.dtype
+    if function_name not in SUPPORTS_NULLS or not hasattr(dtype, "na_object"):
+        return
+
+    na_arr = np.insert(string_array, 0, dtype.na_object)
+    is_nan = np.isnan(np.array([dtype.na_object], dtype=dtype))[0]
+    is_str = isinstance(dtype.na_object, str)
+    should_error = not (is_nan or is_str)
+
+    if (
+        (function_name in NULLS_ALWAYS_ERROR and not is_str)
+        or (function_name in PASSES_THROUGH_NAN_NULLS and should_error)
+        or (function_name in NULLS_ARE_FALSEY and should_error)
+    ):
+        with pytest.raises((ValueError, TypeError)):
+            call_func(func, args, na_arr)
+        return
+
+    res = call_func(func, args, na_arr)
+
+    if is_str:
+        assert res[0] == call_func(func, args, na_arr[:1])
+    elif function_name in NULLS_ARE_FALSEY:
+        assert res[0] is np.False_
+    elif function_name in PASSES_THROUGH_NAN_NULLS:
+        assert res[0] is dtype.na_object
+    else:
+        # shouldn't ever get here
+        assert 0
+
+
+@pytest.mark.parametrize("function, expected", [
+    (np.strings.find, [[2, -1], [1, -1]]),
+    (np.strings.startswith, [[False, False], [True, False]])])
+@pytest.mark.parametrize("start, stop", [
+    (1, 4),
+    (np.int8(1), np.int8(4)),
+    (np.array([1, 1], dtype='u2'), np.array([4, 4], dtype='u2'))])
+def test_non_default_start_stop(function, start, stop, expected):
+    a = np.array([["--🐍--", "--🦜--"],
+                  ["-🐍---", "-🦜---"]], "T")
+    indx = function(a, "🐍", start, stop)
+    assert_array_equal(indx, expected)
+
+
+@pytest.mark.parametrize("count", [2, np.int8(2), np.array([2, 2], 'u2')])
+def test_replace_non_default_repeat(count):
+    a = np.array(["🐍--", "🦜-🦜-"], "T")
+    result = np.strings.replace(a, "🦜-", "🦜†", count)
+    assert_array_equal(result, np.array(["🐍--", "🦜†🦜†"], "T"))
+
+
+def test_strip_ljust_rjust_consistency(string_array, unicode_array):
+    rjs = np.char.rjust(string_array, 1000)
+    rju = np.char.rjust(unicode_array, 1000)
+
+    ljs = np.char.ljust(string_array, 1000)
+    lju = np.char.ljust(unicode_array, 1000)
+
+    assert_array_equal(
+        np.char.lstrip(rjs),
+        np.char.lstrip(rju).astype(StringDType()),
+    )
+
+    assert_array_equal(
+        np.char.rstrip(ljs),
+        np.char.rstrip(lju).astype(StringDType()),
+    )
+
+    assert_array_equal(
+        np.char.strip(ljs),
+        np.char.strip(lju).astype(StringDType()),
+    )
+
+    assert_array_equal(
+        np.char.strip(rjs),
+        np.char.strip(rju).astype(StringDType()),
+    )
+
+
+def test_unset_na_coercion():
+    # a dtype instance with an unset na object is compatible
+    # with a dtype that has one set
+
+    # this test uses the "add" and "equal" ufunc but all ufuncs that
+    # accept more than one string argument and produce a string should
+    # behave this way
+    # TODO: generalize to more ufuncs
+    inp = ["hello", "world"]
+    arr = np.array(inp, dtype=StringDType(na_object=None))
+    for op_dtype in [None, StringDType(), StringDType(coerce=False),
+                     StringDType(na_object=None)]:
+        if op_dtype is None:
+            op = "2"
+        else:
+            op = np.array("2", dtype=op_dtype)
+        res = arr + op
+        assert_array_equal(res, ["hello2", "world2"])
+
+    # dtype instances with distinct explicitly set NA objects are incompatible
+    for op_dtype in [StringDType(na_object=pd_NA), StringDType(na_object="")]:
+        op = np.array("2", dtype=op_dtype)
+        with pytest.raises(TypeError):
+            arr + op
+
+    # comparisons only consider the na_object
+    for op_dtype in [None, StringDType(), StringDType(coerce=True),
+                     StringDType(na_object=None)]:
+        if op_dtype is None:
+            op = inp
+        else:
+            op = np.array(inp, dtype=op_dtype)
+        assert_array_equal(arr, op)
+
+    for op_dtype in [StringDType(na_object=pd_NA),
+                     StringDType(na_object=np.nan)]:
+        op = np.array(inp, dtype=op_dtype)
+        with pytest.raises(TypeError):
+            arr == op
+
+
+def test_repeat(string_array):
+    res = string_array.repeat(1000)
+    # Create an empty array with expanded dimension, and fill it.  Then,
+    # reshape it to the expected result.
+    expected = np.empty_like(string_array, shape=string_array.shape + (1000,))
+    expected[...] = string_array[:, np.newaxis]
+    expected = expected.reshape(-1)
+
+    assert_array_equal(res, expected, strict=True)
+
+
+@pytest.mark.parametrize("tile", [1, 6, (2, 5)])
+def test_accumulation(string_array, tile):
+    """Accumulation is odd for StringDType but tests dtypes with references.
+    """
+    # Fill with mostly empty strings to not create absurdly big strings
+    arr = np.zeros_like(string_array, shape=(100,))
+    arr[:len(string_array)] = string_array
+    arr[-len(string_array):] = string_array
+
+    # Bloat size a bit (get above thresholds and test >1 ndim).
+    arr = np.tile(string_array, tile)
+
+    res = np.add.accumulate(arr, axis=0)
+    res_obj = np.add.accumulate(arr.astype(object), axis=0)
+    assert_array_equal(res, res_obj.astype(arr.dtype), strict=True)
+
+    if arr.ndim > 1:
+        res = np.add.accumulate(arr, axis=-1)
+        res_obj = np.add.accumulate(arr.astype(object), axis=-1)
+
+        assert_array_equal(res, res_obj.astype(arr.dtype), strict=True)
+
+
+class TestImplementation:
+    """Check that strings are stored in the arena when possible.
+
+    This tests implementation details, so should be adjusted if
+    the implementation changes.
+    """
+
+    @classmethod
+    def setup_class(self):
+        self.MISSING = 0x80
+        self.INITIALIZED = 0x40
+        self.OUTSIDE_ARENA = 0x20
+        self.LONG = 0x10
+        self.dtype = StringDType(na_object=np.nan)
+        self.sizeofstr = self.dtype.itemsize
+        sp = self.dtype.itemsize // 2  # pointer size = sizeof(size_t)
+        # Below, size is not strictly correct, since it really uses
+        # 7 (or 3) bytes, but good enough for the tests here.
+        self.view_dtype = np.dtype([
+            ('offset', f'u{sp}'),
+            ('size', f'u{sp // 2}'),
+            ('xsiz', f'V{sp // 2 - 1}'),
+            ('size_and_flags', 'u1'),
+        ] if sys.byteorder == 'little' else [
+            ('size_and_flags', 'u1'),
+            ('xsiz', f'V{sp // 2 - 1}'),
+            ('size', f'u{sp // 2}'),
+            ('offset', f'u{sp}'),
+        ])
+        self.s_empty = ""
+        self.s_short = "01234"
+        self.s_medium = "abcdefghijklmnopqrstuvwxyz"
+        self.s_long = "-=+" * 100
+        self.a = np.array(
+            [self.s_empty, self.s_short, self.s_medium, self.s_long],
+            self.dtype)
+
+    def get_view(self, a):
+        # Cannot view a StringDType as anything else directly, since
+        # it has references. So, we use a stride trick hack.
+        from numpy.lib._stride_tricks_impl import DummyArray
+        interface = dict(a.__array_interface__)
+        interface['descr'] = self.view_dtype.descr
+        interface['typestr'] = self.view_dtype.str
+        return np.asarray(DummyArray(interface, base=a))
+
+    def get_flags(self, a):
+        return self.get_view(a)['size_and_flags'] & 0xf0
+
+    def is_short(self, a):
+        return self.get_flags(a) == self.INITIALIZED | self.OUTSIDE_ARENA
+
+    def is_on_heap(self, a):
+        return self.get_flags(a) == (self.INITIALIZED
+                                     | self.OUTSIDE_ARENA
+                                     | self.LONG)
+
+    def is_missing(self, a):
+        return self.get_flags(a) & self.MISSING == self.MISSING
+
+    def in_arena(self, a):
+        return (self.get_flags(a) & (self.INITIALIZED | self.OUTSIDE_ARENA)
+                == self.INITIALIZED)
+
+    def test_setup(self):
+        is_short = self.is_short(self.a)
+        length = np.strings.str_len(self.a)
+        assert_array_equal(is_short, (length > 0) & (length <= 15))
+        assert_array_equal(self.in_arena(self.a), [False, False, True, True])
+        assert_array_equal(self.is_on_heap(self.a), False)
+        assert_array_equal(self.is_missing(self.a), False)
+        view = self.get_view(self.a)
+        sizes = np.where(is_short, view['size_and_flags'] & 0xf,
+                         view['size'])
+        assert_array_equal(sizes, np.strings.str_len(self.a))
+        assert_array_equal(view['xsiz'][2:],
+                           np.void(b'\x00' * (self.sizeofstr // 4 - 1)))
+        # Check that the medium string uses only 1 byte for its length
+        # in the arena, while the long string takes 8 (or 4).
+        offsets = view['offset']
+        assert offsets[2] == 1
+        assert offsets[3] == 1 + len(self.s_medium) + self.sizeofstr // 2
+
+    def test_empty(self):
+        e = np.empty((3,), self.dtype)
+        assert_array_equal(self.get_flags(e), 0)
+        assert_array_equal(e, "")
+
+    def test_zeros(self):
+        z = np.zeros((2,), self.dtype)
+        assert_array_equal(self.get_flags(z), 0)
+        assert_array_equal(z, "")
+
+    def test_copy(self):
+        for c in [self.a.copy(), copy.copy(self.a), copy.deepcopy(self.a)]:
+            assert_array_equal(self.get_flags(c), self.get_flags(self.a))
+            assert_array_equal(c, self.a)
+            offsets = self.get_view(c)['offset']
+            assert offsets[2] == 1
+            assert offsets[3] == 1 + len(self.s_medium) + self.sizeofstr // 2
+
+    def test_arena_use_with_setting(self):
+        c = np.zeros_like(self.a)
+        assert_array_equal(self.get_flags(c), 0)
+        c[:] = self.a
+        assert_array_equal(self.get_flags(c), self.get_flags(self.a))
+        assert_array_equal(c, self.a)
+
+    def test_arena_reuse_with_setting(self):
+        c = self.a.copy()
+        c[:] = self.a
+        assert_array_equal(self.get_flags(c), self.get_flags(self.a))
+        assert_array_equal(c, self.a)
+
+    def test_arena_reuse_after_missing(self):
+        c = self.a.copy()
+        c[:] = np.nan
+        assert np.all(self.is_missing(c))
+        # Replacing with the original strings, the arena should be reused.
+        c[:] = self.a
+        assert_array_equal(self.get_flags(c), self.get_flags(self.a))
+        assert_array_equal(c, self.a)
+
+    def test_arena_reuse_after_empty(self):
+        c = self.a.copy()
+        c[:] = ""
+        assert_array_equal(c, "")
+        # Replacing with the original strings, the arena should be reused.
+        c[:] = self.a
+        assert_array_equal(self.get_flags(c), self.get_flags(self.a))
+        assert_array_equal(c, self.a)
+
+    def test_arena_reuse_for_shorter(self):
+        c = self.a.copy()
+        # A string slightly shorter than the shortest in the arena
+        # should be used for all strings in the arena.
+        c[:] = self.s_medium[:-1]
+        assert_array_equal(c, self.s_medium[:-1])
+        # first empty string in original was never initialized, so
+        # filling it in now leaves it initialized inside the arena.
+        # second string started as a short string so it can never live
+        # in the arena.
+        in_arena = np.array([True, False, True, True])
+        assert_array_equal(self.in_arena(c), in_arena)
+        # But when a short string is replaced, it will go on the heap.
+        assert_array_equal(self.is_short(c), False)
+        assert_array_equal(self.is_on_heap(c), ~in_arena)
+        # We can put the originals back, and they'll still fit,
+        # and short strings are back as short strings
+        c[:] = self.a
+        assert_array_equal(c, self.a)
+        assert_array_equal(self.in_arena(c), in_arena)
+        assert_array_equal(self.is_short(c), self.is_short(self.a))
+        assert_array_equal(self.is_on_heap(c), False)
+
+    def test_arena_reuse_if_possible(self):
+        c = self.a.copy()
+        # A slightly longer string will not fit in the arena for
+        # the medium string, but will fit for the longer one.
+        c[:] = self.s_medium + "±"
+        assert_array_equal(c, self.s_medium + "±")
+        in_arena_exp = np.strings.str_len(self.a) >= len(self.s_medium) + 1
+        # first entry started uninitialized and empty, so filling it leaves
+        # it in the arena
+        in_arena_exp[0] = True
+        assert not np.all(in_arena_exp == self.in_arena(self.a))
+        assert_array_equal(self.in_arena(c), in_arena_exp)
+        assert_array_equal(self.is_short(c), False)
+        assert_array_equal(self.is_on_heap(c), ~in_arena_exp)
+        # And once outside arena, it stays outside, since offset is lost.
+        # But short strings are used again.
+        c[:] = self.a
+        is_short_exp = self.is_short(self.a)
+        assert_array_equal(c, self.a)
+        assert_array_equal(self.in_arena(c), in_arena_exp)
+        assert_array_equal(self.is_short(c), is_short_exp)
+        assert_array_equal(self.is_on_heap(c), ~in_arena_exp & ~is_short_exp)
+
+    def test_arena_no_reuse_after_short(self):
+        c = self.a.copy()
+        # If we replace a string with a short string, it cannot
+        # go into the arena after because the offset is lost.
+        c[:] = self.s_short
+        assert_array_equal(c, self.s_short)
+        assert_array_equal(self.in_arena(c), False)
+        c[:] = self.a
+        assert_array_equal(c, self.a)
+        assert_array_equal(self.in_arena(c), False)
+        assert_array_equal(self.is_on_heap(c), self.in_arena(self.a))
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_strings.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_strings.py
new file mode 100644
index 0000000..e29151a
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_strings.py
@@ -0,0 +1,1454 @@
+import operator
+import sys
+
+import pytest
+
+import numpy as np
+from numpy.testing import IS_PYPY, assert_array_equal, assert_raises
+from numpy.testing._private.utils import requires_memory
+
+COMPARISONS = [
+    (operator.eq, np.equal, "=="),
+    (operator.ne, np.not_equal, "!="),
+    (operator.lt, np.less, "<"),
+    (operator.le, np.less_equal, "<="),
+    (operator.gt, np.greater, ">"),
+    (operator.ge, np.greater_equal, ">="),
+]
+
+MAX = np.iinfo(np.int64).max
+
+IS_PYPY_LT_7_3_16 = IS_PYPY and sys.implementation.version < (7, 3, 16)
+
+@pytest.mark.parametrize(["op", "ufunc", "sym"], COMPARISONS)
+def test_mixed_string_comparison_ufuncs_fail(op, ufunc, sym):
+    arr_string = np.array(["a", "b"], dtype="S")
+    arr_unicode = np.array(["a", "c"], dtype="U")
+
+    with pytest.raises(TypeError, match="did not contain a loop"):
+        ufunc(arr_string, arr_unicode)
+
+    with pytest.raises(TypeError, match="did not contain a loop"):
+        ufunc(arr_unicode, arr_string)
+
+@pytest.mark.parametrize(["op", "ufunc", "sym"], COMPARISONS)
+def test_mixed_string_comparisons_ufuncs_with_cast(op, ufunc, sym):
+    arr_string = np.array(["a", "b"], dtype="S")
+    arr_unicode = np.array(["a", "c"], dtype="U")
+
+    # While there is no loop, manual casting is acceptable:
+    res1 = ufunc(arr_string, arr_unicode, signature="UU->?", casting="unsafe")
+    res2 = ufunc(arr_string, arr_unicode, signature="SS->?", casting="unsafe")
+
+    expected = op(arr_string.astype("U"), arr_unicode)
+    assert_array_equal(res1, expected)
+    assert_array_equal(res2, expected)
+
+
+@pytest.mark.parametrize(["op", "ufunc", "sym"], COMPARISONS)
+@pytest.mark.parametrize("dtypes", [
+        ("S2", "S2"), ("S2", "S10"),
+        ("<U1", "<U1"), ("<U1", ">U1"), (">U1", ">U1"),
+        ("<U1", "<U10"), ("<U1", ">U10")])
+@pytest.mark.parametrize("aligned", [True, False])
+def test_string_comparisons(op, ufunc, sym, dtypes, aligned):
+    # ensure native byte-order for the first view to stay within unicode range
+    native_dt = np.dtype(dtypes[0]).newbyteorder("=")
+    arr = np.arange(2**15).view(native_dt).astype(dtypes[0])
+    if not aligned:
+        # Make `arr` unaligned:
+        new = np.zeros(arr.nbytes + 1, dtype=np.uint8)[1:].view(dtypes[0])
+        new[...] = arr
+        arr = new
+
+    arr2 = arr.astype(dtypes[1], copy=True)
+    np.random.shuffle(arr2)
+    arr[0] = arr2[0]  # make sure one matches
+
+    expected = [op(d1, d2) for d1, d2 in zip(arr.tolist(), arr2.tolist())]
+    assert_array_equal(op(arr, arr2), expected)
+    assert_array_equal(ufunc(arr, arr2), expected)
+    assert_array_equal(
+        np.char.compare_chararrays(arr, arr2, sym, False), expected
+    )
+
+    expected = [op(d2, d1) for d1, d2 in zip(arr.tolist(), arr2.tolist())]
+    assert_array_equal(op(arr2, arr), expected)
+    assert_array_equal(ufunc(arr2, arr), expected)
+    assert_array_equal(
+        np.char.compare_chararrays(arr2, arr, sym, False), expected
+    )
+
+
+@pytest.mark.parametrize(["op", "ufunc", "sym"], COMPARISONS)
+@pytest.mark.parametrize("dtypes", [
+        ("S2", "S2"), ("S2", "S10"), ("<U1", "<U1"), ("<U1", ">U10")])
+def test_string_comparisons_empty(op, ufunc, sym, dtypes):
+    arr = np.empty((1, 0, 1, 5), dtype=dtypes[0])
+    arr2 = np.empty((100, 1, 0, 1), dtype=dtypes[1])
+
+    expected = np.empty(np.broadcast_shapes(arr.shape, arr2.shape), dtype=bool)
+    assert_array_equal(op(arr, arr2), expected)
+    assert_array_equal(ufunc(arr, arr2), expected)
+    assert_array_equal(
+        np.char.compare_chararrays(arr, arr2, sym, False), expected
+    )
+
+
+@pytest.mark.parametrize("str_dt", ["S", "U"])
+@pytest.mark.parametrize("float_dt", np.typecodes["AllFloat"])
+def test_float_to_string_cast(str_dt, float_dt):
+    float_dt = np.dtype(float_dt)
+    fi = np.finfo(float_dt)
+    arr = np.array([np.nan, np.inf, -np.inf, fi.max, fi.min], dtype=float_dt)
+    expected = ["nan", "inf", "-inf", str(fi.max), str(fi.min)]
+    if float_dt.kind == "c":
+        expected = [f"({r}+0j)" for r in expected]
+
+    res = arr.astype(str_dt)
+    assert_array_equal(res, np.array(expected, dtype=str_dt))
+
+
+@pytest.mark.parametrize("str_dt", "US")
+@pytest.mark.parametrize("size", [-1, np.iinfo(np.intc).max])
+def test_string_size_dtype_errors(str_dt, size):
+    if size > 0:
+        size = size // np.dtype(f"{str_dt}1").itemsize + 1
+
+    with pytest.raises(ValueError):
+        np.dtype((str_dt, size))
+    with pytest.raises(TypeError):
+        np.dtype(f"{str_dt}{size}")
+
+
+@pytest.mark.parametrize("str_dt", "US")
+def test_string_size_dtype_large_repr(str_dt):
+    size = np.iinfo(np.intc).max // np.dtype(f"{str_dt}1").itemsize
+    size_str = str(size)
+
+    dtype = np.dtype((str_dt, size))
+    assert size_str in dtype.str
+    assert size_str in str(dtype)
+    assert size_str in repr(dtype)
+
+
+@pytest.mark.slow
+@requires_memory(2 * np.iinfo(np.intc).max)
+@pytest.mark.parametrize("str_dt", "US")
+def test_large_string_coercion_error(str_dt):
+    very_large = np.iinfo(np.intc).max // np.dtype(f"{str_dt}1").itemsize
+    try:
+        large_string = "A" * (very_large + 1)
+    except Exception:
+        # We may not be able to create this Python string on 32bit.
+        pytest.skip("python failed to create huge string")
+
+    class MyStr:
+        def __str__(self):
+            return large_string
+
+    try:
+        # TypeError from NumPy, or OverflowError from 32bit Python.
+        with pytest.raises((TypeError, OverflowError)):
+            np.array([large_string], dtype=str_dt)
+
+        # Same as above, but input has to be converted to a string.
+        with pytest.raises((TypeError, OverflowError)):
+            np.array([MyStr()], dtype=str_dt)
+    except MemoryError:
+        # Catch memory errors, because `requires_memory` would do so.
+        raise AssertionError("Ops should raise before any large allocation.")
+
+@pytest.mark.slow
+@requires_memory(2 * np.iinfo(np.intc).max)
+@pytest.mark.parametrize("str_dt", "US")
+def test_large_string_addition_error(str_dt):
+    very_large = np.iinfo(np.intc).max // np.dtype(f"{str_dt}1").itemsize
+
+    a = np.array(["A" * very_large], dtype=str_dt)
+    b = np.array("B", dtype=str_dt)
+    try:
+        with pytest.raises(TypeError):
+            np.add(a, b)
+        with pytest.raises(TypeError):
+            np.add(a, a)
+    except MemoryError:
+        # Catch memory errors, because `requires_memory` would do so.
+        raise AssertionError("Ops should raise before any large allocation.")
+
+
+def test_large_string_cast():
+    very_large = np.iinfo(np.intc).max // 4
+    # Could be nice to test very large path, but it makes too many huge
+    # allocations right now (need non-legacy cast loops for this).
+    # a = np.array([], dtype=np.dtype(("S", very_large)))
+    # assert a.astype("U").dtype.itemsize == very_large * 4
+
+    a = np.array([], dtype=np.dtype(("S", very_large + 1)))
+    # It is not perfect but OK if this raises a MemoryError during setup
+    # (this happens due clunky code and/or buffer setup.)
+    with pytest.raises((TypeError, MemoryError)):
+        a.astype("U")
+
+
+@pytest.mark.parametrize("dt", ["S", "U", "T"])
+class TestMethods:
+
+    @pytest.mark.parametrize("in1,in2,out", [
+        ("", "", ""),
+        ("abc", "abc", "abcabc"),
+        ("12345", "12345", "1234512345"),
+        ("MixedCase", "MixedCase", "MixedCaseMixedCase"),
+        ("12345 \0 ", "12345 \0 ", "12345 \0 12345 \0 "),
+        ("UPPER", "UPPER", "UPPERUPPER"),
+        (["abc", "def"], ["hello", "world"], ["abchello", "defworld"]),
+    ])
+    def test_add(self, in1, in2, out, dt):
+        in1 = np.array(in1, dtype=dt)
+        in2 = np.array(in2, dtype=dt)
+        out = np.array(out, dtype=dt)
+        assert_array_equal(np.strings.add(in1, in2), out)
+
+    @pytest.mark.parametrize("in1,in2,out", [
+        ("abc", 3, "abcabcabc"),
+        ("abc", 0, ""),
+        ("abc", -1, ""),
+        (["abc", "def"], [1, 4], ["abc", "defdefdefdef"]),
+    ])
+    def test_multiply(self, in1, in2, out, dt):
+        in1 = np.array(in1, dtype=dt)
+        out = np.array(out, dtype=dt)
+        assert_array_equal(np.strings.multiply(in1, in2), out)
+
+    def test_multiply_raises(self, dt):
+        with pytest.raises(TypeError, match="unsupported type"):
+            np.strings.multiply(np.array("abc", dtype=dt), 3.14)
+
+        with pytest.raises(OverflowError):
+            np.strings.multiply(np.array("abc", dtype=dt), sys.maxsize)
+
+    def test_inplace_multiply(self, dt):
+        arr = np.array(['foo ', 'bar'], dtype=dt)
+        arr *= 2
+        if dt != "T":
+            assert_array_equal(arr, np.array(['foo ', 'barb'], dtype=dt))
+        else:
+            assert_array_equal(arr, ['foo foo ', 'barbar'])
+
+        with pytest.raises(OverflowError):
+            arr *= sys.maxsize
+
+    @pytest.mark.parametrize("i_dt", [np.int8, np.int16, np.int32,
+                                      np.int64, np.int_])
+    def test_multiply_integer_dtypes(self, i_dt, dt):
+        a = np.array("abc", dtype=dt)
+        i = np.array(3, dtype=i_dt)
+        res = np.array("abcabcabc", dtype=dt)
+        assert_array_equal(np.strings.multiply(a, i), res)
+
+    @pytest.mark.parametrize("in_,out", [
+        ("", False),
+        ("a", True),
+        ("A", True),
+        ("\n", False),
+        ("abc", True),
+        ("aBc123", False),
+        ("abc\n", False),
+        (["abc", "aBc123"], [True, False]),
+    ])
+    def test_isalpha(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.isalpha(in_), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ('', False),
+        ('a', True),
+        ('A', True),
+        ('\n', False),
+        ('123abc456', True),
+        ('a1b3c', True),
+        ('aBc000 ', False),
+        ('abc\n', False),
+    ])
+    def test_isalnum(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.isalnum(in_), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ("", False),
+        ("a", False),
+        ("0", True),
+        ("012345", True),
+        ("012345a", False),
+        (["a", "012345"], [False, True]),
+    ])
+    def test_isdigit(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.isdigit(in_), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ("", False),
+        ("a", False),
+        ("1", False),
+        (" ", True),
+        ("\t", True),
+        ("\r", True),
+        ("\n", True),
+        (" \t\r \n", True),
+        (" \t\r\na", False),
+        (["\t1", " \t\r \n"], [False, True])
+    ])
+    def test_isspace(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.isspace(in_), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ('', False),
+        ('a', True),
+        ('A', False),
+        ('\n', False),
+        ('abc', True),
+        ('aBc', False),
+        ('abc\n', True),
+    ])
+    def test_islower(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.islower(in_), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ('', False),
+        ('a', False),
+        ('A', True),
+        ('\n', False),
+        ('ABC', True),
+        ('AbC', False),
+        ('ABC\n', True),
+    ])
+    def test_isupper(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.isupper(in_), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ('', False),
+        ('a', False),
+        ('A', True),
+        ('\n', False),
+        ('A Titlecased Line', True),
+        ('A\nTitlecased Line', True),
+        ('A Titlecased, Line', True),
+        ('Not a capitalized String', False),
+        ('Not\ta Titlecase String', False),
+        ('Not--a Titlecase String', False),
+        ('NOT', False),
+    ])
+    def test_istitle(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.istitle(in_), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ("", 0),
+        ("abc", 3),
+        ("12345", 5),
+        ("MixedCase", 9),
+        ("12345 \x00 ", 8),
+        ("UPPER", 5),
+        (["abc", "12345 \x00 "], [3, 8]),
+    ])
+    def test_str_len(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.str_len(in_), out)
+
+    @pytest.mark.parametrize("a,sub,start,end,out", [
+        ("abcdefghiabc", "abc", 0, None, 0),
+        ("abcdefghiabc", "abc", 1, None, 9),
+        ("abcdefghiabc", "def", 4, None, -1),
+        ("abc", "", 0, None, 0),
+        ("abc", "", 3, None, 3),
+        ("abc", "", 4, None, -1),
+        ("rrarrrrrrrrra", "a", 0, None, 2),
+        ("rrarrrrrrrrra", "a", 4, None, 12),
+        ("rrarrrrrrrrra", "a", 4, 6, -1),
+        ("", "", 0, None, 0),
+        ("", "", 1, 1, -1),
+        ("", "", MAX, 0, -1),
+        ("", "xx", 0, None, -1),
+        ("", "xx", 1, 1, -1),
+        ("", "xx", MAX, 0, -1),
+        pytest.param(99 * "a" + "b", "b", 0, None, 99,
+                     id="99*a+b-b-0-None-99"),
+        pytest.param(98 * "a" + "ba", "ba", 0, None, 98,
+                     id="98*a+ba-ba-0-None-98"),
+        pytest.param(100 * "a", "b", 0, None, -1,
+                     id="100*a-b-0-None--1"),
+        pytest.param(30000 * "a" + 100 * "b", 100 * "b", 0, None, 30000,
+                     id="30000*a+100*b-100*b-0-None-30000"),
+        pytest.param(30000 * "a", 100 * "b", 0, None, -1,
+                     id="30000*a-100*b-0-None--1"),
+        pytest.param(15000 * "a" + 15000 * "b", 15000 * "b", 0, None, 15000,
+                     id="15000*a+15000*b-15000*b-0-None-15000"),
+        pytest.param(15000 * "a" + 15000 * "b", 15000 * "c", 0, None, -1,
+                     id="15000*a+15000*b-15000*c-0-None--1"),
+        (["abcdefghiabc", "rrarrrrrrrrra"], ["def", "arr"], [0, 3],
+         None, [3, -1]),
+        ("Ae¢☃€ 😊" * 2, "😊", 0, None, 6),
+        ("Ae¢☃€ 😊" * 2, "😊", 7, None, 13),
+        pytest.param("A" * (2 ** 17), r"[\w]+\Z", 0, None, -1,
+                     id=r"A*2**17-[\w]+\Z-0-None--1"),
+    ])
+    def test_find(self, a, sub, start, end, out, dt):
+        if "😊" in a and dt == "S":
+            pytest.skip("Bytes dtype does not support non-ascii input")
+        a = np.array(a, dtype=dt)
+        sub = np.array(sub, dtype=dt)
+        assert_array_equal(np.strings.find(a, sub, start, end), out)
+
+    @pytest.mark.parametrize("a,sub,start,end,out", [
+        ("abcdefghiabc", "abc", 0, None, 9),
+        ("abcdefghiabc", "", 0, None, 12),
+        ("abcdefghiabc", "abcd", 0, None, 0),
+        ("abcdefghiabc", "abcz", 0, None, -1),
+        ("abc", "", 0, None, 3),
+        ("abc", "", 3, None, 3),
+        ("abc", "", 4, None, -1),
+        ("rrarrrrrrrrra", "a", 0, None, 12),
+        ("rrarrrrrrrrra", "a", 4, None, 12),
+        ("rrarrrrrrrrra", "a", 4, 6, -1),
+        (["abcdefghiabc", "rrarrrrrrrrra"], ["abc", "a"], [0, 0],
+         None, [9, 12]),
+        ("Ae¢☃€ 😊" * 2, "😊", 0, None, 13),
+        ("Ae¢☃€ 😊" * 2, "😊", 0, 7, 6),
+    ])
+    def test_rfind(self, a, sub, start, end, out, dt):
+        if "😊" in a and dt == "S":
+            pytest.skip("Bytes dtype does not support non-ascii input")
+        a = np.array(a, dtype=dt)
+        sub = np.array(sub, dtype=dt)
+        assert_array_equal(np.strings.rfind(a, sub, start, end), out)
+
+    @pytest.mark.parametrize("a,sub,start,end,out", [
+        ("aaa", "a", 0, None, 3),
+        ("aaa", "b", 0, None, 0),
+        ("aaa", "a", 1, None, 2),
+        ("aaa", "a", 10, None, 0),
+        ("aaa", "a", -1, None, 1),
+        ("aaa", "a", -10, None, 3),
+        ("aaa", "a", 0, 1, 1),
+        ("aaa", "a", 0, 10, 3),
+        ("aaa", "a", 0, -1, 2),
+        ("aaa", "a", 0, -10, 0),
+        ("aaa", "", 1, None, 3),
+        ("aaa", "", 3, None, 1),
+        ("aaa", "", 10, None, 0),
+        ("aaa", "", -1, None, 2),
+        ("aaa", "", -10, None, 4),
+        ("aaa", "aaaa", 0, None, 0),
+        pytest.param(98 * "a" + "ba", "ba", 0, None, 1,
+                     id="98*a+ba-ba-0-None-1"),
+        pytest.param(30000 * "a" + 100 * "b", 100 * "b", 0, None, 1,
+                     id="30000*a+100*b-100*b-0-None-1"),
+        pytest.param(30000 * "a", 100 * "b", 0, None, 0,
+                     id="30000*a-100*b-0-None-0"),
+        pytest.param(30000 * "a" + 100 * "ab", "ab", 0, None, 100,
+                     id="30000*a+100*ab-ab-0-None-100"),
+        pytest.param(15000 * "a" + 15000 * "b", 15000 * "b", 0, None, 1,
+                     id="15000*a+15000*b-15000*b-0-None-1"),
+        pytest.param(15000 * "a" + 15000 * "b", 15000 * "c", 0, None, 0,
+                     id="15000*a+15000*b-15000*c-0-None-0"),
+        ("", "", 0, None, 1),
+        ("", "", 1, 1, 0),
+        ("", "", MAX, 0, 0),
+        ("", "xx", 0, None, 0),
+        ("", "xx", 1, 1, 0),
+        ("", "xx", MAX, 0, 0),
+        (["aaa", ""], ["a", ""], [0, 0], None, [3, 1]),
+        ("Ae¢☃€ 😊" * 100, "😊", 0, None, 100),
+    ])
+    def test_count(self, a, sub, start, end, out, dt):
+        if "😊" in a and dt == "S":
+            pytest.skip("Bytes dtype does not support non-ascii input")
+        a = np.array(a, dtype=dt)
+        sub = np.array(sub, dtype=dt)
+        assert_array_equal(np.strings.count(a, sub, start, end), out)
+
+    @pytest.mark.parametrize("a,prefix,start,end,out", [
+        ("hello", "he", 0, None, True),
+        ("hello", "hello", 0, None, True),
+        ("hello", "hello world", 0, None, False),
+        ("hello", "", 0, None, True),
+        ("hello", "ello", 0, None, False),
+        ("hello", "ello", 1, None, True),
+        ("hello", "o", 4, None, True),
+        ("hello", "o", 5, None, False),
+        ("hello", "", 5, None, True),
+        ("hello", "lo", 6, None, False),
+        ("helloworld", "lowo", 3, None, True),
+        ("helloworld", "lowo", 3, 7, True),
+        ("helloworld", "lowo", 3, 6, False),
+        ("", "", 0, 1, True),
+        ("", "", 0, 0, True),
+        ("", "", 1, 0, False),
+        ("hello", "he", 0, -1, True),
+        ("hello", "he", -53, -1, True),
+        ("hello", "hello", 0, -1, False),
+        ("hello", "hello world", -1, -10, False),
+        ("hello", "ello", -5, None, False),
+        ("hello", "ello", -4, None, True),
+        ("hello", "o", -2, None, False),
+        ("hello", "o", -1, None, True),
+        ("hello", "", -3, -3, True),
+        ("hello", "lo", -9, None, False),
+        (["hello", ""], ["he", ""], [0, 0], None, [True, True]),
+    ])
+    def test_startswith(self, a, prefix, start, end, out, dt):
+        a = np.array(a, dtype=dt)
+        prefix = np.array(prefix, dtype=dt)
+        assert_array_equal(np.strings.startswith(a, prefix, start, end), out)
+
+    @pytest.mark.parametrize("a,suffix,start,end,out", [
+        ("hello", "lo", 0, None, True),
+        ("hello", "he", 0, None, False),
+        ("hello", "", 0, None, True),
+        ("hello", "hello world", 0, None, False),
+        ("helloworld", "worl", 0, None, False),
+        ("helloworld", "worl", 3, 9, True),
+        ("helloworld", "world", 3, 12, True),
+        ("helloworld", "lowo", 1, 7, True),
+        ("helloworld", "lowo", 2, 7, True),
+        ("helloworld", "lowo", 3, 7, True),
+        ("helloworld", "lowo", 4, 7, False),
+        ("helloworld", "lowo", 3, 8, False),
+        ("ab", "ab", 0, 1, False),
+        ("ab", "ab", 0, 0, False),
+        ("", "", 0, 1, True),
+        ("", "", 0, 0, True),
+        ("", "", 1, 0, False),
+        ("hello", "lo", -2, None, True),
+        ("hello", "he", -2, None, False),
+        ("hello", "", -3, -3, True),
+        ("hello", "hello world", -10, -2, False),
+        ("helloworld", "worl", -6, None, False),
+        ("helloworld", "worl", -5, -1, True),
+        ("helloworld", "worl", -5, 9, True),
+        ("helloworld", "world", -7, 12, True),
+        ("helloworld", "lowo", -99, -3, True),
+        ("helloworld", "lowo", -8, -3, True),
+        ("helloworld", "lowo", -7, -3, True),
+        ("helloworld", "lowo", 3, -4, False),
+        ("helloworld", "lowo", -8, -2, False),
+        (["hello", "helloworld"], ["lo", "worl"], [0, -6], None,
+         [True, False]),
+    ])
+    def test_endswith(self, a, suffix, start, end, out, dt):
+        a = np.array(a, dtype=dt)
+        suffix = np.array(suffix, dtype=dt)
+        assert_array_equal(np.strings.endswith(a, suffix, start, end), out)
+
+    @pytest.mark.parametrize("a,chars,out", [
+        ("", None, ""),
+        ("   hello   ", None, "hello   "),
+        ("hello", None, "hello"),
+        (" \t\n\r\f\vabc \t\n\r\f\v", None, "abc \t\n\r\f\v"),
+        (["   hello   ", "hello"], None, ["hello   ", "hello"]),
+        ("", "", ""),
+        ("", "xyz", ""),
+        ("hello", "", "hello"),
+        ("xyzzyhelloxyzzy", "xyz", "helloxyzzy"),
+        ("hello", "xyz", "hello"),
+        ("xyxz", "xyxz", ""),
+        ("xyxzx", "x", "yxzx"),
+        (["xyzzyhelloxyzzy", "hello"], ["xyz", "xyz"],
+         ["helloxyzzy", "hello"]),
+        (["ba", "ac", "baa", "bba"], "b", ["a", "ac", "aa", "a"]),
+    ])
+    def test_lstrip(self, a, chars, out, dt):
+        a = np.array(a, dtype=dt)
+        out = np.array(out, dtype=dt)
+        if chars is not None:
+            chars = np.array(chars, dtype=dt)
+            assert_array_equal(np.strings.lstrip(a, chars), out)
+        else:
+            assert_array_equal(np.strings.lstrip(a), out)
+
+    @pytest.mark.parametrize("a,chars,out", [
+        ("", None, ""),
+        ("   hello   ", None, "   hello"),
+        ("hello", None, "hello"),
+        (" \t\n\r\f\vabc \t\n\r\f\v", None, " \t\n\r\f\vabc"),
+        (["   hello   ", "hello"], None, ["   hello", "hello"]),
+        ("", "", ""),
+        ("", "xyz", ""),
+        ("hello", "", "hello"),
+        (["hello    ", "abcdefghijklmnop"], None,
+         ["hello", "abcdefghijklmnop"]),
+        ("xyzzyhelloxyzzy", "xyz", "xyzzyhello"),
+        ("hello", "xyz", "hello"),
+        ("xyxz", "xyxz", ""),
+        ("    ", None, ""),
+        ("xyxzx", "x", "xyxz"),
+        (["xyzzyhelloxyzzy", "hello"], ["xyz", "xyz"],
+         ["xyzzyhello", "hello"]),
+        (["ab", "ac", "aab", "abb"], "b", ["a", "ac", "aa", "a"]),
+    ])
+    def test_rstrip(self, a, chars, out, dt):
+        a = np.array(a, dtype=dt)
+        out = np.array(out, dtype=dt)
+        if chars is not None:
+            chars = np.array(chars, dtype=dt)
+            assert_array_equal(np.strings.rstrip(a, chars), out)
+        else:
+            assert_array_equal(np.strings.rstrip(a), out)
+
+    @pytest.mark.parametrize("a,chars,out", [
+        ("", None, ""),
+        ("   hello   ", None, "hello"),
+        ("hello", None, "hello"),
+        (" \t\n\r\f\vabc \t\n\r\f\v", None, "abc"),
+        (["   hello   ", "hello"], None, ["hello", "hello"]),
+        ("", "", ""),
+        ("", "xyz", ""),
+        ("hello", "", "hello"),
+        ("xyzzyhelloxyzzy", "xyz", "hello"),
+        ("hello", "xyz", "hello"),
+        ("xyxz", "xyxz", ""),
+        ("xyxzx", "x", "yxz"),
+        (["xyzzyhelloxyzzy", "hello"], ["xyz", "xyz"],
+         ["hello", "hello"]),
+        (["bab", "ac", "baab", "bbabb"], "b", ["a", "ac", "aa", "a"]),
+    ])
+    def test_strip(self, a, chars, out, dt):
+        a = np.array(a, dtype=dt)
+        if chars is not None:
+            chars = np.array(chars, dtype=dt)
+        out = np.array(out, dtype=dt)
+        assert_array_equal(np.strings.strip(a, chars), out)
+
+    @pytest.mark.parametrize("buf,old,new,count,res", [
+        ("", "", "", -1, ""),
+        ("", "", "A", -1, "A"),
+        ("", "A", "", -1, ""),
+        ("", "A", "A", -1, ""),
+        ("", "", "", 100, ""),
+        ("", "", "A", 100, "A"),
+        ("A", "", "", -1, "A"),
+        ("A", "", "*", -1, "*A*"),
+        ("A", "", "*1", -1, "*1A*1"),
+        ("A", "", "*-#", -1, "*-#A*-#"),
+        ("AA", "", "*-", -1, "*-A*-A*-"),
+        ("AA", "", "*-", -1, "*-A*-A*-"),
+        ("AA", "", "*-", 4, "*-A*-A*-"),
+        ("AA", "", "*-", 3, "*-A*-A*-"),
+        ("AA", "", "*-", 2, "*-A*-A"),
+        ("AA", "", "*-", 1, "*-AA"),
+        ("AA", "", "*-", 0, "AA"),
+        ("A", "A", "", -1, ""),
+        ("AAA", "A", "", -1, ""),
+        ("AAA", "A", "", -1, ""),
+        ("AAA", "A", "", 4, ""),
+        ("AAA", "A", "", 3, ""),
+        ("AAA", "A", "", 2, "A"),
+        ("AAA", "A", "", 1, "AA"),
+        ("AAA", "A", "", 0, "AAA"),
+        ("AAAAAAAAAA", "A", "", -1, ""),
+        ("ABACADA", "A", "", -1, "BCD"),
+        ("ABACADA", "A", "", -1, "BCD"),
+        ("ABACADA", "A", "", 5, "BCD"),
+        ("ABACADA", "A", "", 4, "BCD"),
+        ("ABACADA", "A", "", 3, "BCDA"),
+        ("ABACADA", "A", "", 2, "BCADA"),
+        ("ABACADA", "A", "", 1, "BACADA"),
+        ("ABACADA", "A", "", 0, "ABACADA"),
+        ("ABCAD", "A", "", -1, "BCD"),
+        ("ABCADAA", "A", "", -1, "BCD"),
+        ("BCD", "A", "", -1, "BCD"),
+        ("*************", "A", "", -1, "*************"),
+        ("^" + "A" * 1000 + "^", "A", "", 999, "^A^"),
+        ("the", "the", "", -1, ""),
+        ("theater", "the", "", -1, "ater"),
+        ("thethe", "the", "", -1, ""),
+        ("thethethethe", "the", "", -1, ""),
+        ("theatheatheathea", "the", "", -1, "aaaa"),
+        ("that", "the", "", -1, "that"),
+        ("thaet", "the", "", -1, "thaet"),
+        ("here and there", "the", "", -1, "here and re"),
+        ("here and there and there", "the", "", -1, "here and re and re"),
+        ("here and there and there", "the", "", 3, "here and re and re"),
+        ("here and there and there", "the", "", 2, "here and re and re"),
+        ("here and there and there", "the", "", 1, "here and re and there"),
+        ("here and there and there", "the", "", 0, "here and there and there"),
+        ("here and there and there", "the", "", -1, "here and re and re"),
+        ("abc", "the", "", -1, "abc"),
+        ("abcdefg", "the", "", -1, "abcdefg"),
+        ("bbobob", "bob", "", -1, "bob"),
+        ("bbobobXbbobob", "bob", "", -1, "bobXbob"),
+        ("aaaaaaabob", "bob", "", -1, "aaaaaaa"),
+        ("aaaaaaa", "bob", "", -1, "aaaaaaa"),
+        ("Who goes there?", "o", "o", -1, "Who goes there?"),
+        ("Who goes there?", "o", "O", -1, "WhO gOes there?"),
+        ("Who goes there?", "o", "O", -1, "WhO gOes there?"),
+        ("Who goes there?", "o", "O", 3, "WhO gOes there?"),
+        ("Who goes there?", "o", "O", 2, "WhO gOes there?"),
+        ("Who goes there?", "o", "O", 1, "WhO goes there?"),
+        ("Who goes there?", "o", "O", 0, "Who goes there?"),
+        ("Who goes there?", "a", "q", -1, "Who goes there?"),
+        ("Who goes there?", "W", "w", -1, "who goes there?"),
+        ("WWho goes there?WW", "W", "w", -1, "wwho goes there?ww"),
+        ("Who goes there?", "?", "!", -1, "Who goes there!"),
+        ("Who goes there??", "?", "!", -1, "Who goes there!!"),
+        ("Who goes there?", ".", "!", -1, "Who goes there?"),
+        ("This is a tissue", "is", "**", -1, "Th** ** a t**sue"),
+        ("This is a tissue", "is", "**", -1, "Th** ** a t**sue"),
+        ("This is a tissue", "is", "**", 4, "Th** ** a t**sue"),
+        ("This is a tissue", "is", "**", 3, "Th** ** a t**sue"),
+        ("This is a tissue", "is", "**", 2, "Th** ** a tissue"),
+        ("This is a tissue", "is", "**", 1, "Th** is a tissue"),
+        ("This is a tissue", "is", "**", 0, "This is a tissue"),
+        ("bobob", "bob", "cob", -1, "cobob"),
+        ("bobobXbobobob", "bob", "cob", -1, "cobobXcobocob"),
+        ("bobob", "bot", "bot", -1, "bobob"),
+        ("Reykjavik", "k", "KK", -1, "ReyKKjaviKK"),
+        ("Reykjavik", "k", "KK", -1, "ReyKKjaviKK"),
+        ("Reykjavik", "k", "KK", 2, "ReyKKjaviKK"),
+        ("Reykjavik", "k", "KK", 1, "ReyKKjavik"),
+        ("Reykjavik", "k", "KK", 0, "Reykjavik"),
+        ("A.B.C.", ".", "----", -1, "A----B----C----"),
+        ("Reykjavik", "q", "KK", -1, "Reykjavik"),
+        ("spam, spam, eggs and spam", "spam", "ham", -1,
+            "ham, ham, eggs and ham"),
+        ("spam, spam, eggs and spam", "spam", "ham", -1,
+            "ham, ham, eggs and ham"),
+        ("spam, spam, eggs and spam", "spam", "ham", 4,
+            "ham, ham, eggs and ham"),
+        ("spam, spam, eggs and spam", "spam", "ham", 3,
+            "ham, ham, eggs and ham"),
+        ("spam, spam, eggs and spam", "spam", "ham", 2,
+            "ham, ham, eggs and spam"),
+        ("spam, spam, eggs and spam", "spam", "ham", 1,
+            "ham, spam, eggs and spam"),
+        ("spam, spam, eggs and spam", "spam", "ham", 0,
+            "spam, spam, eggs and spam"),
+        ("bobobob", "bobob", "bob", -1, "bobob"),
+        ("bobobobXbobobob", "bobob", "bob", -1, "bobobXbobob"),
+        ("BOBOBOB", "bob", "bobby", -1, "BOBOBOB"),
+        ("one!two!three!", "!", "@", 1, "one@two!three!"),
+        ("one!two!three!", "!", "", -1, "onetwothree"),
+        ("one!two!three!", "!", "@", 2, "one@two@three!"),
+        ("one!two!three!", "!", "@", 3, "one@two@three@"),
+        ("one!two!three!", "!", "@", 4, "one@two@three@"),
+        ("one!two!three!", "!", "@", 0, "one!two!three!"),
+        ("one!two!three!", "!", "@", -1, "one@two@three@"),
+        ("one!two!three!", "x", "@", -1, "one!two!three!"),
+        ("one!two!three!", "x", "@", 2, "one!two!three!"),
+        ("abc", "", "-", -1, "-a-b-c-"),
+        ("abc", "", "-", 3, "-a-b-c"),
+        ("abc", "", "-", 0, "abc"),
+        ("abc", "ab", "--", 0, "abc"),
+        ("abc", "xy", "--", -1, "abc"),
+        (["abbc", "abbd"], "b", "z", [1, 2], ["azbc", "azzd"]),
+    ])
+    def test_replace(self, buf, old, new, count, res, dt):
+        if "😊" in buf and dt == "S":
+            pytest.skip("Bytes dtype does not support non-ascii input")
+        buf = np.array(buf, dtype=dt)
+        old = np.array(old, dtype=dt)
+        new = np.array(new, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.replace(buf, old, new, count), res)
+
+    @pytest.mark.parametrize("buf,sub,start,end,res", [
+        ("abcdefghiabc", "", 0, None, 0),
+        ("abcdefghiabc", "def", 0, None, 3),
+        ("abcdefghiabc", "abc", 0, None, 0),
+        ("abcdefghiabc", "abc", 1, None, 9),
+    ])
+    def test_index(self, buf, sub, start, end, res, dt):
+        buf = np.array(buf, dtype=dt)
+        sub = np.array(sub, dtype=dt)
+        assert_array_equal(np.strings.index(buf, sub, start, end), res)
+
+    @pytest.mark.parametrize("buf,sub,start,end", [
+        ("abcdefghiabc", "hib", 0, None),
+        ("abcdefghiab", "abc", 1, None),
+        ("abcdefghi", "ghi", 8, None),
+        ("abcdefghi", "ghi", -1, None),
+        ("rrarrrrrrrrra", "a", 4, 6),
+    ])
+    def test_index_raises(self, buf, sub, start, end, dt):
+        buf = np.array(buf, dtype=dt)
+        sub = np.array(sub, dtype=dt)
+        with pytest.raises(ValueError, match="substring not found"):
+            np.strings.index(buf, sub, start, end)
+
+    @pytest.mark.parametrize("buf,sub,start,end,res", [
+        ("abcdefghiabc", "", 0, None, 12),
+        ("abcdefghiabc", "def", 0, None, 3),
+        ("abcdefghiabc", "abc", 0, None, 9),
+        ("abcdefghiabc", "abc", 0, -1, 0),
+    ])
+    def test_rindex(self, buf, sub, start, end, res, dt):
+        buf = np.array(buf, dtype=dt)
+        sub = np.array(sub, dtype=dt)
+        assert_array_equal(np.strings.rindex(buf, sub, start, end), res)
+
+    @pytest.mark.parametrize("buf,sub,start,end", [
+        ("abcdefghiabc", "hib", 0, None),
+        ("defghiabc", "def", 1, None),
+        ("defghiabc", "abc", 0, -1),
+        ("abcdefghi", "ghi", 0, 8),
+        ("abcdefghi", "ghi", 0, -1),
+        ("rrarrrrrrrrra", "a", 4, 6),
+    ])
+    def test_rindex_raises(self, buf, sub, start, end, dt):
+        buf = np.array(buf, dtype=dt)
+        sub = np.array(sub, dtype=dt)
+        with pytest.raises(ValueError, match="substring not found"):
+            np.strings.rindex(buf, sub, start, end)
+
+    @pytest.mark.parametrize("buf,tabsize,res", [
+        ("abc\rab\tdef\ng\thi", 8, "abc\rab      def\ng       hi"),
+        ("abc\rab\tdef\ng\thi", 4, "abc\rab  def\ng   hi"),
+        ("abc\r\nab\tdef\ng\thi", 8, "abc\r\nab      def\ng       hi"),
+        ("abc\r\nab\tdef\ng\thi", 4, "abc\r\nab  def\ng   hi"),
+        ("abc\r\nab\r\ndef\ng\r\nhi", 4, "abc\r\nab\r\ndef\ng\r\nhi"),
+        (" \ta\n\tb", 1, "  a\n b"),
+    ])
+    def test_expandtabs(self, buf, tabsize, res, dt):
+        buf = np.array(buf, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.expandtabs(buf, tabsize), res)
+
+    def test_expandtabs_raises_overflow(self, dt):
+        with pytest.raises(OverflowError, match="new string is too long"):
+            np.strings.expandtabs(np.array("\ta\n\tb", dtype=dt), sys.maxsize)
+            np.strings.expandtabs(np.array("\ta\n\tb", dtype=dt), 2**61)
+
+    FILL_ERROR = "The fill character must be exactly one character long"
+
+    def test_center_raises_multiple_character_fill(self, dt):
+        buf = np.array("abc", dtype=dt)
+        fill = np.array("**", dtype=dt)
+        with pytest.raises(TypeError, match=self.FILL_ERROR):
+            np.strings.center(buf, 10, fill)
+
+    def test_ljust_raises_multiple_character_fill(self, dt):
+        buf = np.array("abc", dtype=dt)
+        fill = np.array("**", dtype=dt)
+        with pytest.raises(TypeError, match=self.FILL_ERROR):
+            np.strings.ljust(buf, 10, fill)
+
+    def test_rjust_raises_multiple_character_fill(self, dt):
+        buf = np.array("abc", dtype=dt)
+        fill = np.array("**", dtype=dt)
+        with pytest.raises(TypeError, match=self.FILL_ERROR):
+            np.strings.rjust(buf, 10, fill)
+
+    @pytest.mark.parametrize("buf,width,fillchar,res", [
+        ('abc', 10, ' ', '   abc    '),
+        ('abc', 6, ' ', ' abc  '),
+        ('abc', 3, ' ', 'abc'),
+        ('abc', 2, ' ', 'abc'),
+        ('abc', -2, ' ', 'abc'),
+        ('abc', 10, '*', '***abc****'),
+    ])
+    def test_center(self, buf, width, fillchar, res, dt):
+        buf = np.array(buf, dtype=dt)
+        fillchar = np.array(fillchar, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.center(buf, width, fillchar), res)
+
+    @pytest.mark.parametrize("buf,width,fillchar,res", [
+        ('abc', 10, ' ', 'abc       '),
+        ('abc', 6, ' ', 'abc   '),
+        ('abc', 3, ' ', 'abc'),
+        ('abc', 2, ' ', 'abc'),
+        ('abc', -2, ' ', 'abc'),
+        ('abc', 10, '*', 'abc*******'),
+    ])
+    def test_ljust(self, buf, width, fillchar, res, dt):
+        buf = np.array(buf, dtype=dt)
+        fillchar = np.array(fillchar, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.ljust(buf, width, fillchar), res)
+
+    @pytest.mark.parametrize("buf,width,fillchar,res", [
+        ('abc', 10, ' ', '       abc'),
+        ('abc', 6, ' ', '   abc'),
+        ('abc', 3, ' ', 'abc'),
+        ('abc', 2, ' ', 'abc'),
+        ('abc', -2, ' ', 'abc'),
+        ('abc', 10, '*', '*******abc'),
+    ])
+    def test_rjust(self, buf, width, fillchar, res, dt):
+        buf = np.array(buf, dtype=dt)
+        fillchar = np.array(fillchar, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.rjust(buf, width, fillchar), res)
+
+    @pytest.mark.parametrize("buf,width,res", [
+        ('123', 2, '123'),
+        ('123', 3, '123'),
+        ('0123', 4, '0123'),
+        ('+123', 3, '+123'),
+        ('+123', 4, '+123'),
+        ('+123', 5, '+0123'),
+        ('+0123', 5, '+0123'),
+        ('-123', 3, '-123'),
+        ('-123', 4, '-123'),
+        ('-0123', 5, '-0123'),
+        ('000', 3, '000'),
+        ('34', 1, '34'),
+        ('34', -1, '34'),
+        ('0034', 4, '0034'),
+    ])
+    def test_zfill(self, buf, width, res, dt):
+        buf = np.array(buf, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.zfill(buf, width), res)
+
+    @pytest.mark.parametrize("buf,sep,res1,res2,res3", [
+        ("this is the partition method", "ti", "this is the par",
+            "ti", "tion method"),
+        ("http://www.python.org", "://", "http", "://", "www.python.org"),
+        ("http://www.python.org", "?", "http://www.python.org", "", ""),
+        ("http://www.python.org", "http://", "", "http://", "www.python.org"),
+        ("http://www.python.org", "org", "http://www.python.", "org", ""),
+        ("http://www.python.org", ["://", "?", "http://", "org"],
+            ["http", "http://www.python.org", "", "http://www.python."],
+            ["://", "", "http://", "org"],
+            ["www.python.org", "", "www.python.org", ""]),
+        ("mississippi", "ss", "mi", "ss", "issippi"),
+        ("mississippi", "i", "m", "i", "ssissippi"),
+        ("mississippi", "w", "mississippi", "", ""),
+    ])
+    def test_partition(self, buf, sep, res1, res2, res3, dt):
+        buf = np.array(buf, dtype=dt)
+        sep = np.array(sep, dtype=dt)
+        res1 = np.array(res1, dtype=dt)
+        res2 = np.array(res2, dtype=dt)
+        res3 = np.array(res3, dtype=dt)
+        act1, act2, act3 = np.strings.partition(buf, sep)
+        assert_array_equal(act1, res1)
+        assert_array_equal(act2, res2)
+        assert_array_equal(act3, res3)
+        assert_array_equal(act1 + act2 + act3, buf)
+
+    @pytest.mark.parametrize("buf,sep,res1,res2,res3", [
+        ("this is the partition method", "ti", "this is the parti",
+            "ti", "on method"),
+        ("http://www.python.org", "://", "http", "://", "www.python.org"),
+        ("http://www.python.org", "?", "", "", "http://www.python.org"),
+        ("http://www.python.org", "http://", "", "http://", "www.python.org"),
+        ("http://www.python.org", "org", "http://www.python.", "org", ""),
+        ("http://www.python.org", ["://", "?", "http://", "org"],
+            ["http", "", "", "http://www.python."],
+            ["://", "", "http://", "org"],
+            ["www.python.org", "http://www.python.org", "www.python.org", ""]),
+        ("mississippi", "ss", "missi", "ss", "ippi"),
+        ("mississippi", "i", "mississipp", "i", ""),
+        ("mississippi", "w", "", "", "mississippi"),
+    ])
+    def test_rpartition(self, buf, sep, res1, res2, res3, dt):
+        buf = np.array(buf, dtype=dt)
+        sep = np.array(sep, dtype=dt)
+        res1 = np.array(res1, dtype=dt)
+        res2 = np.array(res2, dtype=dt)
+        res3 = np.array(res3, dtype=dt)
+        act1, act2, act3 = np.strings.rpartition(buf, sep)
+        assert_array_equal(act1, res1)
+        assert_array_equal(act2, res2)
+        assert_array_equal(act3, res3)
+        assert_array_equal(act1 + act2 + act3, buf)
+
+    @pytest.mark.parametrize("args", [
+        (None,),
+        (0,),
+        (1,),
+        (3,),
+        (5,),
+        (6,),  # test index past the end
+        (-1,),
+        (-3,),
+        ([3, 4],),
+        ([2, 4],),
+        ([-3, 5],),
+        ([0, -5],),
+        (1, 4),
+        (-3, 5),
+        (None, -1),
+        (0, [4, 2]),
+        ([1, 2], [-1, -2]),
+        (1, 5, 2),
+        (None, None, -1),
+        ([0, 6], [-1, 0], [2, -1]),
+    ])
+    def test_slice(self, args, dt):
+        buf = np.array(["hello", "world"], dtype=dt)
+        act = np.strings.slice(buf, *args)
+        bcast_args = tuple(np.broadcast_to(arg, buf.shape) for arg in args)
+        res = np.array([s[slice(*arg)]
+                        for s, arg in zip(buf, zip(*bcast_args))],
+                       dtype=dt)
+        assert_array_equal(act, res)
+
+    def test_slice_unsupported(self, dt):
+        with pytest.raises(TypeError, match="did not contain a loop"):
+            np.strings.slice(np.array([1, 2, 3]), 4)
+
+        with pytest.raises(TypeError, match=r"Cannot cast ufunc '_slice' input .* from .* to dtype\('int(64|32)'\)"):
+            np.strings.slice(np.array(['foo', 'bar'], dtype=dt), np.array(['foo', 'bar'], dtype=dt))
+
+    @pytest.mark.parametrize("int_dt", [np.int8, np.int16, np.int32, np.int64,
+                                        np.uint8, np.uint16, np.uint32, np.uint64])
+    def test_slice_int_type_promotion(self, int_dt, dt):
+        buf = np.array(["hello", "world"], dtype=dt)
+
+        assert_array_equal(np.strings.slice(buf, int_dt(4)), np.array(["hell", "worl"], dtype=dt))
+        assert_array_equal(np.strings.slice(buf, np.array([4, 4], dtype=int_dt)), np.array(["hell", "worl"], dtype=dt))
+
+        assert_array_equal(np.strings.slice(buf, int_dt(2), int_dt(4)), np.array(["ll", "rl"], dtype=dt))
+        assert_array_equal(np.strings.slice(buf, np.array([2, 2], dtype=int_dt), np.array([4, 4], dtype=int_dt)), np.array(["ll", "rl"], dtype=dt))
+
+        assert_array_equal(np.strings.slice(buf, int_dt(0), int_dt(4), int_dt(2)), np.array(["hl", "wr"], dtype=dt))
+        assert_array_equal(np.strings.slice(buf, np.array([0, 0], dtype=int_dt), np.array([4, 4], dtype=int_dt), np.array([2, 2], dtype=int_dt)), np.array(["hl", "wr"], dtype=dt))
+
+@pytest.mark.parametrize("dt", ["U", "T"])
+class TestMethodsWithUnicode:
+    @pytest.mark.parametrize("in_,out", [
+        ("", False),
+        ("a", False),
+        ("0", True),
+        ("\u2460", False),  # CIRCLED DIGIT 1
+        ("\xbc", False),  # VULGAR FRACTION ONE QUARTER
+        ("\u0660", True),  # ARABIC_INDIC DIGIT ZERO
+        ("012345", True),
+        ("012345a", False),
+        (["0", "a"], [True, False]),
+    ])
+    def test_isdecimal_unicode(self, in_, out, dt):
+        buf = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.isdecimal(buf), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ("", False),
+        ("a", False),
+        ("0", True),
+        ("\u2460", True),  # CIRCLED DIGIT 1
+        ("\xbc", True),  # VULGAR FRACTION ONE QUARTER
+        ("\u0660", True),  # ARABIC_INDIC DIGIT ZERO
+        ("012345", True),
+        ("012345a", False),
+        (["0", "a"], [True, False]),
+    ])
+    def test_isnumeric_unicode(self, in_, out, dt):
+        buf = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.isnumeric(buf), out)
+
+    @pytest.mark.parametrize("buf,old,new,count,res", [
+        ("...\u043c......<", "<", "&lt;", -1, "...\u043c......&lt;"),
+        ("Ae¢☃€ 😊" * 2, "A", "B", -1, "Be¢☃€ 😊Be¢☃€ 😊"),
+        ("Ae¢☃€ 😊" * 2, "😊", "B", -1, "Ae¢☃€ BAe¢☃€ B"),
+    ])
+    def test_replace_unicode(self, buf, old, new, count, res, dt):
+        buf = np.array(buf, dtype=dt)
+        old = np.array(old, dtype=dt)
+        new = np.array(new, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.replace(buf, old, new, count), res)
+
+    @pytest.mark.parametrize("in_", [
+        '\U00010401',
+        '\U00010427',
+        '\U00010429',
+        '\U0001044E',
+        '\U0001D7F6',
+        '\U00011066',
+        '\U000104A0',
+        pytest.param('\U0001F107', marks=pytest.mark.xfail(
+            sys.platform == 'win32' and IS_PYPY_LT_7_3_16,
+            reason="PYPY bug in Py_UNICODE_ISALNUM",
+            strict=True)),
+    ])
+    def test_isalnum_unicode(self, in_, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.isalnum(in_), True)
+
+    @pytest.mark.parametrize("in_,out", [
+        ('\u1FFc', False),
+        ('\u2167', False),
+        ('\U00010401', False),
+        ('\U00010427', False),
+        ('\U0001F40D', False),
+        ('\U0001F46F', False),
+        ('\u2177', True),
+        pytest.param('\U00010429', True, marks=pytest.mark.xfail(
+            sys.platform == 'win32' and IS_PYPY_LT_7_3_16,
+            reason="PYPY bug in Py_UNICODE_ISLOWER",
+            strict=True)),
+        ('\U0001044E', True),
+    ])
+    def test_islower_unicode(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.islower(in_), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ('\u1FFc', False),
+        ('\u2167', True),
+        ('\U00010401', True),
+        ('\U00010427', True),
+        ('\U0001F40D', False),
+        ('\U0001F46F', False),
+        ('\u2177', False),
+        pytest.param('\U00010429', False, marks=pytest.mark.xfail(
+            sys.platform == 'win32' and IS_PYPY_LT_7_3_16,
+            reason="PYPY bug in Py_UNICODE_ISUPPER",
+            strict=True)),
+        ('\U0001044E', False),
+    ])
+    def test_isupper_unicode(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.isupper(in_), out)
+
+    @pytest.mark.parametrize("in_,out", [
+        ('\u1FFc', True),
+        ('Greek \u1FFcitlecases ...', True),
+        pytest.param('\U00010401\U00010429', True, marks=pytest.mark.xfail(
+            sys.platform == 'win32' and IS_PYPY_LT_7_3_16,
+            reason="PYPY bug in Py_UNICODE_ISISTITLE",
+            strict=True)),
+        ('\U00010427\U0001044E', True),
+        pytest.param('\U00010429', False, marks=pytest.mark.xfail(
+            sys.platform == 'win32' and IS_PYPY_LT_7_3_16,
+            reason="PYPY bug in Py_UNICODE_ISISTITLE",
+            strict=True)),
+        ('\U0001044E', False),
+        ('\U0001F40D', False),
+        ('\U0001F46F', False),
+    ])
+    def test_istitle_unicode(self, in_, out, dt):
+        in_ = np.array(in_, dtype=dt)
+        assert_array_equal(np.strings.istitle(in_), out)
+
+    @pytest.mark.parametrize("buf,sub,start,end,res", [
+        ("Ae¢☃€ 😊" * 2, "😊", 0, None, 6),
+        ("Ae¢☃€ 😊" * 2, "😊", 7, None, 13),
+    ])
+    def test_index_unicode(self, buf, sub, start, end, res, dt):
+        buf = np.array(buf, dtype=dt)
+        sub = np.array(sub, dtype=dt)
+        assert_array_equal(np.strings.index(buf, sub, start, end), res)
+
+    def test_index_raises_unicode(self, dt):
+        with pytest.raises(ValueError, match="substring not found"):
+            np.strings.index("Ae¢☃€ 😊", "😀")
+
+    @pytest.mark.parametrize("buf,res", [
+        ("Ae¢☃€ \t 😊", "Ae¢☃€    😊"),
+        ("\t\U0001044E", "        \U0001044E"),
+    ])
+    def test_expandtabs(self, buf, res, dt):
+        buf = np.array(buf, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.expandtabs(buf), res)
+
+    @pytest.mark.parametrize("buf,width,fillchar,res", [
+        ('x', 2, '\U0001044E', 'x\U0001044E'),
+        ('x', 3, '\U0001044E', '\U0001044Ex\U0001044E'),
+        ('x', 4, '\U0001044E', '\U0001044Ex\U0001044E\U0001044E'),
+    ])
+    def test_center(self, buf, width, fillchar, res, dt):
+        buf = np.array(buf, dtype=dt)
+        fillchar = np.array(fillchar, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.center(buf, width, fillchar), res)
+
+    @pytest.mark.parametrize("buf,width,fillchar,res", [
+        ('x', 2, '\U0001044E', 'x\U0001044E'),
+        ('x', 3, '\U0001044E', 'x\U0001044E\U0001044E'),
+        ('x', 4, '\U0001044E', 'x\U0001044E\U0001044E\U0001044E'),
+    ])
+    def test_ljust(self, buf, width, fillchar, res, dt):
+        buf = np.array(buf, dtype=dt)
+        fillchar = np.array(fillchar, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.ljust(buf, width, fillchar), res)
+
+    @pytest.mark.parametrize("buf,width,fillchar,res", [
+        ('x', 2, '\U0001044E', '\U0001044Ex'),
+        ('x', 3, '\U0001044E', '\U0001044E\U0001044Ex'),
+        ('x', 4, '\U0001044E', '\U0001044E\U0001044E\U0001044Ex'),
+    ])
+    def test_rjust(self, buf, width, fillchar, res, dt):
+        buf = np.array(buf, dtype=dt)
+        fillchar = np.array(fillchar, dtype=dt)
+        res = np.array(res, dtype=dt)
+        assert_array_equal(np.strings.rjust(buf, width, fillchar), res)
+
+    @pytest.mark.parametrize("buf,sep,res1,res2,res3", [
+        ("āāāāĀĀĀĀ", "Ă", "āāāāĀĀĀĀ", "", ""),
+        ("āāāāĂĀĀĀĀ", "Ă", "āāāā", "Ă", "ĀĀĀĀ"),
+        ("āāāāĂĂĀĀĀĀ", "ĂĂ", "āāāā", "ĂĂ", "ĀĀĀĀ"),
+        ("𐌁𐌁𐌁𐌁𐌀𐌀𐌀𐌀", "𐌂", "𐌁𐌁𐌁𐌁𐌀𐌀𐌀𐌀", "", ""),
+        ("𐌁𐌁𐌁𐌁𐌂𐌀𐌀𐌀𐌀", "𐌂", "𐌁𐌁𐌁𐌁", "𐌂", "𐌀𐌀𐌀𐌀"),
+        ("𐌁𐌁𐌁𐌁𐌂𐌂𐌀𐌀𐌀𐌀", "𐌂𐌂", "𐌁𐌁𐌁𐌁", "𐌂𐌂", "𐌀𐌀𐌀𐌀"),
+        ("𐌁𐌁𐌁𐌁𐌂𐌂𐌂𐌂𐌀𐌀𐌀𐌀", "𐌂𐌂𐌂𐌂", "𐌁𐌁𐌁𐌁", "𐌂𐌂𐌂𐌂", "𐌀𐌀𐌀𐌀"),
+    ])
+    def test_partition(self, buf, sep, res1, res2, res3, dt):
+        buf = np.array(buf, dtype=dt)
+        sep = np.array(sep, dtype=dt)
+        res1 = np.array(res1, dtype=dt)
+        res2 = np.array(res2, dtype=dt)
+        res3 = np.array(res3, dtype=dt)
+        act1, act2, act3 = np.strings.partition(buf, sep)
+        assert_array_equal(act1, res1)
+        assert_array_equal(act2, res2)
+        assert_array_equal(act3, res3)
+        assert_array_equal(act1 + act2 + act3, buf)
+
+    @pytest.mark.parametrize("buf,sep,res1,res2,res3", [
+        ("āāāāĀĀĀĀ", "Ă", "", "", "āāāāĀĀĀĀ"),
+        ("āāāāĂĀĀĀĀ", "Ă", "āāāā", "Ă", "ĀĀĀĀ"),
+        ("āāāāĂĂĀĀĀĀ", "ĂĂ", "āāāā", "ĂĂ", "ĀĀĀĀ"),
+        ("𐌁𐌁𐌁𐌁𐌀𐌀𐌀𐌀", "𐌂", "", "", "𐌁𐌁𐌁𐌁𐌀𐌀𐌀𐌀"),
+        ("𐌁𐌁𐌁𐌁𐌂𐌀𐌀𐌀𐌀", "𐌂", "𐌁𐌁𐌁𐌁", "𐌂", "𐌀𐌀𐌀𐌀"),
+        ("𐌁𐌁𐌁𐌁𐌂𐌂𐌀𐌀𐌀𐌀", "𐌂𐌂", "𐌁𐌁𐌁𐌁", "𐌂𐌂", "𐌀𐌀𐌀𐌀"),
+    ])
+    def test_rpartition(self, buf, sep, res1, res2, res3, dt):
+        buf = np.array(buf, dtype=dt)
+        sep = np.array(sep, dtype=dt)
+        res1 = np.array(res1, dtype=dt)
+        res2 = np.array(res2, dtype=dt)
+        res3 = np.array(res3, dtype=dt)
+        act1, act2, act3 = np.strings.rpartition(buf, sep)
+        assert_array_equal(act1, res1)
+        assert_array_equal(act2, res2)
+        assert_array_equal(act3, res3)
+        assert_array_equal(act1 + act2 + act3, buf)
+
+    @pytest.mark.parametrize("method", ["strip", "lstrip", "rstrip"])
+    @pytest.mark.parametrize(
+        "source,strip",
+        [
+            ("λμ", "μ"),
+            ("λμ", "λ"),
+            ("λ" * 5 + "μ" * 2, "μ"),
+            ("λ" * 5 + "μ" * 2, "λ"),
+            ("λ" * 5 + "A" + "μ" * 2, "μλ"),
+            ("λμ" * 5, "μ"),
+            ("λμ" * 5, "λ"),
+    ])
+    def test_strip_functions_unicode(self, source, strip, method, dt):
+        src_array = np.array([source], dtype=dt)
+
+        npy_func = getattr(np.strings, method)
+        py_func = getattr(str, method)
+
+        expected = np.array([py_func(source, strip)], dtype=dt)
+        actual = npy_func(src_array, strip)
+
+        assert_array_equal(actual, expected)
+
+    @pytest.mark.parametrize("args", [
+        (None,),
+        (0,),
+        (1,),
+        (5,),
+        (15,),
+        (22,),
+        (-1,),
+        (-3,),
+        ([3, 4],),
+        ([-5, 5],),
+        ([0, -8],),
+        (1, 12),
+        (-12, 15),
+        (None, -1),
+        (0, [17, 6]),
+        ([1, 2], [-1, -2]),
+        (1, 11, 2),
+        (None, None, -1),
+        ([0, 10], [-1, 0], [2, -1]),
+    ])
+    def test_slice(self, args, dt):
+        buf = np.array(["Приве́т नमस्ते שָׁלוֹם", "😀😃😄😁😆😅🤣😂🙂🙃"],
+                       dtype=dt)
+        act = np.strings.slice(buf, *args)
+        bcast_args = tuple(np.broadcast_to(arg, buf.shape) for arg in args)
+        res = np.array([s[slice(*arg)]
+                        for s, arg in zip(buf, zip(*bcast_args))],
+                       dtype=dt)
+        assert_array_equal(act, res)
+
+
+class TestMixedTypeMethods:
+    def test_center(self):
+        buf = np.array("😊", dtype="U")
+        fill = np.array("*", dtype="S")
+        res = np.array("*😊*", dtype="U")
+        assert_array_equal(np.strings.center(buf, 3, fill), res)
+
+        buf = np.array("s", dtype="S")
+        fill = np.array("*", dtype="U")
+        res = np.array("*s*", dtype="S")
+        assert_array_equal(np.strings.center(buf, 3, fill), res)
+
+        with pytest.raises(ValueError, match="'ascii' codec can't encode"):
+            buf = np.array("s", dtype="S")
+            fill = np.array("😊", dtype="U")
+            np.strings.center(buf, 3, fill)
+
+    def test_ljust(self):
+        buf = np.array("😊", dtype="U")
+        fill = np.array("*", dtype="S")
+        res = np.array("😊**", dtype="U")
+        assert_array_equal(np.strings.ljust(buf, 3, fill), res)
+
+        buf = np.array("s", dtype="S")
+        fill = np.array("*", dtype="U")
+        res = np.array("s**", dtype="S")
+        assert_array_equal(np.strings.ljust(buf, 3, fill), res)
+
+        with pytest.raises(ValueError, match="'ascii' codec can't encode"):
+            buf = np.array("s", dtype="S")
+            fill = np.array("😊", dtype="U")
+            np.strings.ljust(buf, 3, fill)
+
+    def test_rjust(self):
+        buf = np.array("😊", dtype="U")
+        fill = np.array("*", dtype="S")
+        res = np.array("**😊", dtype="U")
+        assert_array_equal(np.strings.rjust(buf, 3, fill), res)
+
+        buf = np.array("s", dtype="S")
+        fill = np.array("*", dtype="U")
+        res = np.array("**s", dtype="S")
+        assert_array_equal(np.strings.rjust(buf, 3, fill), res)
+
+        with pytest.raises(ValueError, match="'ascii' codec can't encode"):
+            buf = np.array("s", dtype="S")
+            fill = np.array("😊", dtype="U")
+            np.strings.rjust(buf, 3, fill)
+
+
+class TestUnicodeOnlyMethodsRaiseWithBytes:
+    def test_isdecimal_raises(self):
+        in_ = np.array(b"1")
+        with assert_raises(TypeError):
+            np.strings.isdecimal(in_)
+
+    def test_isnumeric_bytes(self):
+        in_ = np.array(b"1")
+        with assert_raises(TypeError):
+            np.strings.isnumeric(in_)
+
+
+def check_itemsize(n_elem, dt):
+    if dt == "T":
+        return np.dtype(dt).itemsize
+    if dt == "S":
+        return n_elem
+    if dt == "U":
+        return n_elem * 4
+
+@pytest.mark.parametrize("dt", ["S", "U", "T"])
+class TestReplaceOnArrays:
+
+    def test_replace_count_and_size(self, dt):
+        a = np.array(["0123456789" * i for i in range(4)], dtype=dt)
+        r1 = np.strings.replace(a, "5", "ABCDE")
+        assert r1.dtype.itemsize == check_itemsize(3 * 10 + 3 * 4, dt)
+        r1_res = np.array(["01234ABCDE6789" * i for i in range(4)], dtype=dt)
+        assert_array_equal(r1, r1_res)
+        r2 = np.strings.replace(a, "5", "ABCDE", 1)
+        assert r2.dtype.itemsize == check_itemsize(3 * 10 + 4, dt)
+        r3 = np.strings.replace(a, "5", "ABCDE", 0)
+        assert r3.dtype.itemsize == a.dtype.itemsize
+        assert_array_equal(r3, a)
+        # Negative values mean to replace all.
+        r4 = np.strings.replace(a, "5", "ABCDE", -1)
+        assert r4.dtype.itemsize == check_itemsize(3 * 10 + 3 * 4, dt)
+        assert_array_equal(r4, r1)
+        # We can do count on an element-by-element basis.
+        r5 = np.strings.replace(a, "5", "ABCDE", [-1, -1, -1, 1])
+        assert r5.dtype.itemsize == check_itemsize(3 * 10 + 4, dt)
+        assert_array_equal(r5, np.array(
+            ["01234ABCDE6789" * i for i in range(3)]
+            + ["01234ABCDE6789" + "0123456789" * 2], dtype=dt))
+
+    def test_replace_broadcasting(self, dt):
+        a = np.array("0,0,0", dtype=dt)
+        r1 = np.strings.replace(a, "0", "1", np.arange(3))
+        assert r1.dtype == a.dtype
+        assert_array_equal(r1, np.array(["0,0,0", "1,0,0", "1,1,0"], dtype=dt))
+        r2 = np.strings.replace(a, "0", [["1"], ["2"]], np.arange(1, 4))
+        assert_array_equal(r2, np.array([["1,0,0", "1,1,0", "1,1,1"],
+                                         ["2,0,0", "2,2,0", "2,2,2"]],
+                                        dtype=dt))
+        r3 = np.strings.replace(a, ["0", "0,0", "0,0,0"], "X")
+        assert_array_equal(r3, np.array(["X,X,X", "X,0", "X"], dtype=dt))
+
+
+class TestOverride:
+    @classmethod
+    def setup_class(cls):
+        class Override:
+
+            def __array_function__(self, *args, **kwargs):
+                return "function"
+
+            def __array_ufunc__(self, *args, **kwargs):
+                return "ufunc"
+
+        cls.override = Override()
+
+    @pytest.mark.parametrize("func, kwargs", [
+        (np.strings.center, dict(width=10)),
+        (np.strings.capitalize, {}),
+        (np.strings.decode, {}),
+        (np.strings.encode, {}),
+        (np.strings.expandtabs, {}),
+        (np.strings.ljust, dict(width=10)),
+        (np.strings.lower, {}),
+        (np.strings.mod, dict(values=2)),
+        (np.strings.multiply, dict(i=2)),
+        (np.strings.partition, dict(sep="foo")),
+        (np.strings.rjust, dict(width=10)),
+        (np.strings.rpartition, dict(sep="foo")),
+        (np.strings.swapcase, {}),
+        (np.strings.title, {}),
+        (np.strings.translate, dict(table=None)),
+        (np.strings.upper, {}),
+        (np.strings.zfill, dict(width=10)),
+    ])
+    def test_override_function(self, func, kwargs):
+        assert func(self.override, **kwargs) == "function"
+
+    @pytest.mark.parametrize("func, args, kwargs", [
+        (np.strings.add, (None, ), {}),
+        (np.strings.lstrip, (), {}),
+        (np.strings.rstrip, (), {}),
+        (np.strings.strip, (), {}),
+        (np.strings.equal, (None, ), {}),
+        (np.strings.not_equal, (None, ), {}),
+        (np.strings.greater_equal, (None, ), {}),
+        (np.strings.less_equal, (None, ), {}),
+        (np.strings.greater, (None, ), {}),
+        (np.strings.less, (None, ), {}),
+        (np.strings.count, ("foo", ), {}),
+        (np.strings.endswith, ("foo", ), {}),
+        (np.strings.find, ("foo", ), {}),
+        (np.strings.index, ("foo", ), {}),
+        (np.strings.isalnum, (), {}),
+        (np.strings.isalpha, (), {}),
+        (np.strings.isdecimal, (), {}),
+        (np.strings.isdigit, (), {}),
+        (np.strings.islower, (), {}),
+        (np.strings.isnumeric, (), {}),
+        (np.strings.isspace, (), {}),
+        (np.strings.istitle, (), {}),
+        (np.strings.isupper, (), {}),
+        (np.strings.rfind, ("foo", ), {}),
+        (np.strings.rindex, ("foo", ), {}),
+        (np.strings.startswith, ("foo", ), {}),
+        (np.strings.str_len, (), {}),
+    ])
+    def test_override_ufunc(self, func, args, kwargs):
+        assert func(self.override, *args, **kwargs) == "ufunc"
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_ufunc.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_ufunc.py
new file mode 100644
index 0000000..af22dce
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_ufunc.py
@@ -0,0 +1,3313 @@
+import ctypes as ct
+import itertools
+import pickle
+import sys
+import warnings
+
+import numpy._core._operand_flag_tests as opflag_tests
+import numpy._core._rational_tests as _rational_tests
+import numpy._core._umath_tests as umt
+import pytest
+from pytest import param
+
+import numpy as np
+import numpy._core.umath as ncu
+import numpy.linalg._umath_linalg as uml
+from numpy.exceptions import AxisError
+from numpy.testing import (
+    HAS_REFCOUNT,
+    IS_PYPY,
+    IS_WASM,
+    assert_,
+    assert_allclose,
+    assert_almost_equal,
+    assert_array_almost_equal,
+    assert_array_equal,
+    assert_equal,
+    assert_no_warnings,
+    assert_raises,
+    suppress_warnings,
+)
+from numpy.testing._private.utils import requires_memory
+
+UNARY_UFUNCS = [obj for obj in np._core.umath.__dict__.values()
+                    if isinstance(obj, np.ufunc)]
+UNARY_OBJECT_UFUNCS = [uf for uf in UNARY_UFUNCS if "O->O" in uf.types]
+
+# Remove functions that do not support `floats`
+UNARY_OBJECT_UFUNCS.remove(np.bitwise_count)
+
+
+class TestUfuncKwargs:
+    def test_kwarg_exact(self):
+        assert_raises(TypeError, np.add, 1, 2, castingx='safe')
+        assert_raises(TypeError, np.add, 1, 2, dtypex=int)
+        assert_raises(TypeError, np.add, 1, 2, extobjx=[4096])
+        assert_raises(TypeError, np.add, 1, 2, outx=None)
+        assert_raises(TypeError, np.add, 1, 2, sigx='ii->i')
+        assert_raises(TypeError, np.add, 1, 2, signaturex='ii->i')
+        assert_raises(TypeError, np.add, 1, 2, subokx=False)
+        assert_raises(TypeError, np.add, 1, 2, wherex=[True])
+
+    def test_sig_signature(self):
+        assert_raises(TypeError, np.add, 1, 2, sig='ii->i',
+                      signature='ii->i')
+
+    def test_sig_dtype(self):
+        assert_raises(TypeError, np.add, 1, 2, sig='ii->i',
+                      dtype=int)
+        assert_raises(TypeError, np.add, 1, 2, signature='ii->i',
+                      dtype=int)
+
+    def test_extobj_removed(self):
+        assert_raises(TypeError, np.add, 1, 2, extobj=[4096])
+
+
+class TestUfuncGenericLoops:
+    """Test generic loops.
+
+    The loops to be tested are:
+
+        PyUFunc_ff_f_As_dd_d
+        PyUFunc_ff_f
+        PyUFunc_dd_d
+        PyUFunc_gg_g
+        PyUFunc_FF_F_As_DD_D
+        PyUFunc_DD_D
+        PyUFunc_FF_F
+        PyUFunc_GG_G
+        PyUFunc_OO_O
+        PyUFunc_OO_O_method
+        PyUFunc_f_f_As_d_d
+        PyUFunc_d_d
+        PyUFunc_f_f
+        PyUFunc_g_g
+        PyUFunc_F_F_As_D_D
+        PyUFunc_F_F
+        PyUFunc_D_D
+        PyUFunc_G_G
+        PyUFunc_O_O
+        PyUFunc_O_O_method
+        PyUFunc_On_Om
+
+    Where:
+
+        f -- float
+        d -- double
+        g -- long double
+        F -- complex float
+        D -- complex double
+        G -- complex long double
+        O -- python object
+
+    It is difficult to assure that each of these loops is entered from the
+    Python level as the special cased loops are a moving target and the
+    corresponding types are architecture dependent. We probably need to
+    define C level testing ufuncs to get at them. For the time being, I've
+    just looked at the signatures registered in the build directory to find
+    relevant functions.
+
+    """
+    np_dtypes = [
+        (np.single, np.single), (np.single, np.double),
+        (np.csingle, np.csingle), (np.csingle, np.cdouble),
+        (np.double, np.double), (np.longdouble, np.longdouble),
+        (np.cdouble, np.cdouble), (np.clongdouble, np.clongdouble)]
+
+    @pytest.mark.parametrize('input_dtype,output_dtype', np_dtypes)
+    def test_unary_PyUFunc(self, input_dtype, output_dtype, f=np.exp, x=0, y=1):
+        xs = np.full(10, input_dtype(x), dtype=output_dtype)
+        ys = f(xs)[::2]
+        assert_allclose(ys, y)
+        assert_equal(ys.dtype, output_dtype)
+
+    def f2(x, y):
+        return x**y
+
+    @pytest.mark.parametrize('input_dtype,output_dtype', np_dtypes)
+    def test_binary_PyUFunc(self, input_dtype, output_dtype, f=f2, x=0, y=1):
+        xs = np.full(10, input_dtype(x), dtype=output_dtype)
+        ys = f(xs, xs)[::2]
+        assert_allclose(ys, y)
+        assert_equal(ys.dtype, output_dtype)
+
+    # class to use in testing object method loops
+    class foo:
+        def conjugate(self):
+            return np.bool(1)
+
+        def logical_xor(self, obj):
+            return np.bool(1)
+
+    def test_unary_PyUFunc_O_O(self):
+        x = np.ones(10, dtype=object)
+        assert_(np.all(np.abs(x) == 1))
+
+    def test_unary_PyUFunc_O_O_method_simple(self, foo=foo):
+        x = np.full(10, foo(), dtype=object)
+        assert_(np.all(np.conjugate(x) == True))
+
+    def test_binary_PyUFunc_OO_O(self):
+        x = np.ones(10, dtype=object)
+        assert_(np.all(np.add(x, x) == 2))
+
+    def test_binary_PyUFunc_OO_O_method(self, foo=foo):
+        x = np.full(10, foo(), dtype=object)
+        assert_(np.all(np.logical_xor(x, x)))
+
+    def test_binary_PyUFunc_On_Om_method(self, foo=foo):
+        x = np.full((10, 2, 3), foo(), dtype=object)
+        assert_(np.all(np.logical_xor(x, x)))
+
+    def test_python_complex_conjugate(self):
+        # The conjugate ufunc should fall back to calling the method:
+        arr = np.array([1 + 2j, 3 - 4j], dtype="O")
+        assert isinstance(arr[0], complex)
+        res = np.conjugate(arr)
+        assert res.dtype == np.dtype("O")
+        assert_array_equal(res, np.array([1 - 2j, 3 + 4j], dtype="O"))
+
+    @pytest.mark.parametrize("ufunc", UNARY_OBJECT_UFUNCS)
+    def test_unary_PyUFunc_O_O_method_full(self, ufunc):
+        """Compare the result of the object loop with non-object one"""
+        val = np.float64(np.pi / 4)
+
+        class MyFloat(np.float64):
+            def __getattr__(self, attr):
+                try:
+                    return super().__getattr__(attr)
+                except AttributeError:
+                    return lambda: getattr(np._core.umath, attr)(val)
+
+        # Use 0-D arrays, to ensure the same element call
+        num_arr = np.array(val, dtype=np.float64)
+        obj_arr = np.array(MyFloat(val), dtype="O")
+
+        with np.errstate(all="raise"):
+            try:
+                res_num = ufunc(num_arr)
+            except Exception as exc:
+                with assert_raises(type(exc)):
+                    ufunc(obj_arr)
+            else:
+                res_obj = ufunc(obj_arr)
+                assert_array_almost_equal(res_num.astype("O"), res_obj)
+
+
+def _pickleable_module_global():
+    pass
+
+
+class TestUfunc:
+    def test_pickle(self):
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            assert_(pickle.loads(pickle.dumps(np.sin,
+                                              protocol=proto)) is np.sin)
+
+            # Check that ufunc not defined in the top level numpy namespace
+            # such as numpy._core._rational_tests.test_add can also be pickled
+            res = pickle.loads(pickle.dumps(_rational_tests.test_add,
+                                            protocol=proto))
+            assert_(res is _rational_tests.test_add)
+
+    def test_pickle_withstring(self):
+        astring = (b"cnumpy.core\n_ufunc_reconstruct\np0\n"
+                   b"(S'numpy._core.umath'\np1\nS'cos'\np2\ntp3\nRp4\n.")
+        assert_(pickle.loads(astring) is np.cos)
+
+    @pytest.mark.skipif(IS_PYPY, reason="'is' check does not work on PyPy")
+    def test_pickle_name_is_qualname(self):
+        # This tests that a simplification of our ufunc pickle code will
+        # lead to allowing qualnames as names.  Future ufuncs should
+        # possible add a specific qualname, or a hook into pickling instead
+        # (dask+numba may benefit).
+        _pickleable_module_global.ufunc = umt._pickleable_module_global_ufunc
+
+        obj = pickle.loads(pickle.dumps(_pickleable_module_global.ufunc))
+        assert obj is umt._pickleable_module_global_ufunc
+
+    def test_reduceat_shifting_sum(self):
+        L = 6
+        x = np.arange(L)
+        idx = np.array(list(zip(np.arange(L - 2), np.arange(L - 2) + 2))).ravel()
+        assert_array_equal(np.add.reduceat(x, idx)[::2], [1, 3, 5, 7])
+
+    def test_all_ufunc(self):
+        """Try to check presence and results of all ufuncs.
+
+        The list of ufuncs comes from generate_umath.py and is as follows:
+
+        =====  ====  =============  ===============  ========================
+        done   args   function        types                notes
+        =====  ====  =============  ===============  ========================
+        n      1     conjugate      nums + O
+        n      1     absolute       nums + O         complex -> real
+        n      1     negative       nums + O
+        n      1     sign           nums + O         -> int
+        n      1     invert         bool + ints + O  flts raise an error
+        n      1     degrees        real + M         cmplx raise an error
+        n      1     radians        real + M         cmplx raise an error
+        n      1     arccos         flts + M
+        n      1     arccosh        flts + M
+        n      1     arcsin         flts + M
+        n      1     arcsinh        flts + M
+        n      1     arctan         flts + M
+        n      1     arctanh        flts + M
+        n      1     cos            flts + M
+        n      1     sin            flts + M
+        n      1     tan            flts + M
+        n      1     cosh           flts + M
+        n      1     sinh           flts + M
+        n      1     tanh           flts + M
+        n      1     exp            flts + M
+        n      1     expm1          flts + M
+        n      1     log            flts + M
+        n      1     log10          flts + M
+        n      1     log1p          flts + M
+        n      1     sqrt           flts + M         real x < 0 raises error
+        n      1     ceil           real + M
+        n      1     trunc          real + M
+        n      1     floor          real + M
+        n      1     fabs           real + M
+        n      1     rint           flts + M
+        n      1     isnan          flts             -> bool
+        n      1     isinf          flts             -> bool
+        n      1     isfinite       flts             -> bool
+        n      1     signbit        real             -> bool
+        n      1     modf           real             -> (frac, int)
+        n      1     logical_not    bool + nums + M  -> bool
+        n      2     left_shift     ints + O         flts raise an error
+        n      2     right_shift    ints + O         flts raise an error
+        n      2     add            bool + nums + O  boolean + is ||
+        n      2     subtract       bool + nums + O  boolean - is ^
+        n      2     multiply       bool + nums + O  boolean * is &
+        n      2     divide         nums + O
+        n      2     floor_divide   nums + O
+        n      2     true_divide    nums + O         bBhH -> f, iIlLqQ -> d
+        n      2     fmod           nums + M
+        n      2     power          nums + O
+        n      2     greater        bool + nums + O  -> bool
+        n      2     greater_equal  bool + nums + O  -> bool
+        n      2     less           bool + nums + O  -> bool
+        n      2     less_equal     bool + nums + O  -> bool
+        n      2     equal          bool + nums + O  -> bool
+        n      2     not_equal      bool + nums + O  -> bool
+        n      2     logical_and    bool + nums + M  -> bool
+        n      2     logical_or     bool + nums + M  -> bool
+        n      2     logical_xor    bool + nums + M  -> bool
+        n      2     maximum        bool + nums + O
+        n      2     minimum        bool + nums + O
+        n      2     bitwise_and    bool + ints + O  flts raise an error
+        n      2     bitwise_or     bool + ints + O  flts raise an error
+        n      2     bitwise_xor    bool + ints + O  flts raise an error
+        n      2     arctan2        real + M
+        n      2     remainder      ints + real + O
+        n      2     hypot          real + M
+        =====  ====  =============  ===============  ========================
+
+        Types other than those listed will be accepted, but they are cast to
+        the smallest compatible type for which the function is defined. The
+        casting rules are:
+
+        bool -> int8 -> float32
+        ints -> double
+
+        """
+        pass
+
+    # from include/numpy/ufuncobject.h
+    size_inferred = 2
+    can_ignore = 4
+
+    def test_signature0(self):
+        # the arguments to test_signature are: nin, nout, core_signature
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            2, 1, "(i),(i)->()")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (1,  1,  0))
+        assert_equal(ixs, (0, 0))
+        assert_equal(flags, (self.size_inferred,))
+        assert_equal(sizes, (-1,))
+
+    def test_signature1(self):
+        # empty core signature; treat as plain ufunc (with trivial core)
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            2, 1, "(),()->()")
+        assert_equal(enabled, 0)
+        assert_equal(num_dims, (0,  0,  0))
+        assert_equal(ixs, ())
+        assert_equal(flags, ())
+        assert_equal(sizes, ())
+
+    def test_signature2(self):
+        # more complicated names for variables
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            2, 1, "(i1,i2),(J_1)->(_kAB)")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (2, 1, 1))
+        assert_equal(ixs, (0, 1, 2, 3))
+        assert_equal(flags, (self.size_inferred,) * 4)
+        assert_equal(sizes, (-1, -1, -1, -1))
+
+    def test_signature3(self):
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            2, 1, "(i1, i12),   (J_1)->(i12, i2)")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (2, 1, 2))
+        assert_equal(ixs, (0, 1, 2, 1, 3))
+        assert_equal(flags, (self.size_inferred,) * 4)
+        assert_equal(sizes, (-1, -1, -1, -1))
+
+    def test_signature4(self):
+        # matrix_multiply signature from _umath_tests
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            2, 1, "(n,k),(k,m)->(n,m)")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (2, 2, 2))
+        assert_equal(ixs, (0, 1, 1, 2, 0, 2))
+        assert_equal(flags, (self.size_inferred,) * 3)
+        assert_equal(sizes, (-1, -1, -1))
+
+    def test_signature5(self):
+        # matmul signature from _umath_tests
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            2, 1, "(n?,k),(k,m?)->(n?,m?)")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (2, 2, 2))
+        assert_equal(ixs, (0, 1, 1, 2, 0, 2))
+        assert_equal(flags, (self.size_inferred | self.can_ignore,
+                             self.size_inferred,
+                             self.size_inferred | self.can_ignore))
+        assert_equal(sizes, (-1, -1, -1))
+
+    def test_signature6(self):
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            1, 1, "(3)->()")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (1, 0))
+        assert_equal(ixs, (0,))
+        assert_equal(flags, (0,))
+        assert_equal(sizes, (3,))
+
+    def test_signature7(self):
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            3, 1, "(3),(03,3),(n)->(9)")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (1, 2, 1, 1))
+        assert_equal(ixs, (0, 0, 0, 1, 2))
+        assert_equal(flags, (0, self.size_inferred, 0))
+        assert_equal(sizes, (3, -1, 9))
+
+    def test_signature8(self):
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            3, 1, "(3?),(3?,3?),(n)->(9)")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (1, 2, 1, 1))
+        assert_equal(ixs, (0, 0, 0, 1, 2))
+        assert_equal(flags, (self.can_ignore, self.size_inferred, 0))
+        assert_equal(sizes, (3, -1, 9))
+
+    def test_signature9(self):
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            1, 1, "(  3)  -> ( )")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (1, 0))
+        assert_equal(ixs, (0,))
+        assert_equal(flags, (0,))
+        assert_equal(sizes, (3,))
+
+    def test_signature10(self):
+        enabled, num_dims, ixs, flags, sizes = umt.test_signature(
+            3, 1, "( 3? ) , (3? ,  3?) ,(n )-> ( 9)")
+        assert_equal(enabled, 1)
+        assert_equal(num_dims, (1, 2, 1, 1))
+        assert_equal(ixs, (0, 0, 0, 1, 2))
+        assert_equal(flags, (self.can_ignore, self.size_inferred, 0))
+        assert_equal(sizes, (3, -1, 9))
+
+    def test_signature_failure_extra_parenthesis(self):
+        with assert_raises(ValueError):
+            umt.test_signature(2, 1, "((i)),(i)->()")
+
+    def test_signature_failure_mismatching_parenthesis(self):
+        with assert_raises(ValueError):
+            umt.test_signature(2, 1, "(i),)i(->()")
+
+    def test_signature_failure_signature_missing_input_arg(self):
+        with assert_raises(ValueError):
+            umt.test_signature(2, 1, "(i),->()")
+
+    def test_signature_failure_signature_missing_output_arg(self):
+        with assert_raises(ValueError):
+            umt.test_signature(2, 2, "(i),(i)->()")
+
+    def test_get_signature(self):
+        assert_equal(np.vecdot.signature, "(n),(n)->()")
+
+    def test_forced_sig(self):
+        a = 0.5 * np.arange(3, dtype='f8')
+        assert_equal(np.add(a, 0.5), [0.5, 1, 1.5])
+        with assert_raises(TypeError):
+            np.add(a, 0.5, sig='i', casting='unsafe')
+        assert_equal(np.add(a, 0.5, sig='ii->i', casting='unsafe'), [0, 0, 1])
+        with assert_raises(TypeError):
+            np.add(a, 0.5, sig=('i4',), casting='unsafe')
+        assert_equal(np.add(a, 0.5, sig=('i4', 'i4', 'i4'),
+                                            casting='unsafe'), [0, 0, 1])
+
+        b = np.zeros((3,), dtype='f8')
+        np.add(a, 0.5, out=b)
+        assert_equal(b, [0.5, 1, 1.5])
+        b[:] = 0
+        with assert_raises(TypeError):
+            np.add(a, 0.5, sig='i', out=b, casting='unsafe')
+        assert_equal(b, [0, 0, 0])
+        np.add(a, 0.5, sig='ii->i', out=b, casting='unsafe')
+        assert_equal(b, [0, 0, 1])
+        b[:] = 0
+        with assert_raises(TypeError):
+            np.add(a, 0.5, sig=('i4',), out=b, casting='unsafe')
+        assert_equal(b, [0, 0, 0])
+        np.add(a, 0.5, sig=('i4', 'i4', 'i4'), out=b, casting='unsafe')
+        assert_equal(b, [0, 0, 1])
+
+    def test_signature_all_None(self):
+        # signature all None, is an acceptable alternative (since 1.21)
+        # to not providing a signature.
+        res1 = np.add([3], [4], sig=(None, None, None))
+        res2 = np.add([3], [4])
+        assert_array_equal(res1, res2)
+        res1 = np.maximum([3], [4], sig=(None, None, None))
+        res2 = np.maximum([3], [4])
+        assert_array_equal(res1, res2)
+
+        with pytest.raises(TypeError):
+            # special case, that would be deprecated anyway, so errors:
+            np.add(3, 4, signature=(None,))
+
+    def test_signature_dtype_type(self):
+        # Since that will be the normal behaviour (past NumPy 1.21)
+        # we do support the types already:
+        float_dtype = type(np.dtype(np.float64))
+        np.add(3, 4, signature=(float_dtype, float_dtype, None))
+
+    @pytest.mark.parametrize("get_kwarg", [
+            param(lambda dt: {"dtype": dt}, id="dtype"),
+            param(lambda dt: {"signature": (dt, None, None)}, id="signature")])
+    def test_signature_dtype_instances_allowed(self, get_kwarg):
+        # We allow certain dtype instances when there is a clear singleton
+        # and the given one is equivalent; mainly for backcompat.
+        int64 = np.dtype("int64")
+        int64_2 = pickle.loads(pickle.dumps(int64))
+        # Relies on pickling behavior, if assert fails just remove test...
+        assert int64 is not int64_2
+
+        assert np.add(1, 2, **get_kwarg(int64_2)).dtype == int64
+        td = np.timedelta64(2, "s")
+        assert np.add(td, td, **get_kwarg("m8")).dtype == "m8[s]"
+
+        msg = "The `dtype` and `signature` arguments to ufuncs"
+
+        with pytest.raises(TypeError, match=msg):
+            np.add(3, 5, **get_kwarg(np.dtype("int64").newbyteorder()))
+        with pytest.raises(TypeError, match=msg):
+            np.add(3, 5, **get_kwarg(np.dtype("m8[ns]")))
+        with pytest.raises(TypeError, match=msg):
+            np.add(3, 5, **get_kwarg("m8[ns]"))
+
+    @pytest.mark.parametrize("casting", ["unsafe", "same_kind", "safe"])
+    def test_partial_signature_mismatch(self, casting):
+        # If the second argument matches already, no need to specify it:
+        res = np.ldexp(np.float32(1.), np.int_(2), dtype="d")
+        assert res.dtype == "d"
+        res = np.ldexp(np.float32(1.), np.int_(2), signature=(None, None, "d"))
+        assert res.dtype == "d"
+
+        # ldexp only has a loop for long input as second argument, overriding
+        # the output cannot help with that (no matter the casting)
+        with pytest.raises(TypeError):
+            np.ldexp(1., np.uint64(3), dtype="d")
+        with pytest.raises(TypeError):
+            np.ldexp(1., np.uint64(3), signature=(None, None, "d"))
+
+    def test_partial_signature_mismatch_with_cache(self):
+        with pytest.raises(TypeError):
+            np.add(np.float16(1), np.uint64(2), sig=("e", "d", None))
+        # Ensure e,d->None is in the dispatching cache (double loop)
+        np.add(np.float16(1), np.float64(2))
+        # The error must still be raised:
+        with pytest.raises(TypeError):
+            np.add(np.float16(1), np.uint64(2), sig=("e", "d", None))
+
+    def test_use_output_signature_for_all_arguments(self):
+        # Test that providing only `dtype=` or `signature=(None, None, dtype)`
+        # is sufficient if falling back to a homogeneous signature works.
+        # In this case, the `intp, intp -> intp` loop is chosen.
+        res = np.power(1.5, 2.8, dtype=np.intp, casting="unsafe")
+        assert res == 1  # the cast happens first.
+        res = np.power(1.5, 2.8, signature=(None, None, np.intp),
+                       casting="unsafe")
+        assert res == 1
+        with pytest.raises(TypeError):
+            # the unsafe casting would normally cause errors though:
+            np.power(1.5, 2.8, dtype=np.intp)
+
+    def test_signature_errors(self):
+        with pytest.raises(TypeError,
+                    match="the signature object to ufunc must be a string or"):
+            np.add(3, 4, signature=123.)  # neither a string nor a tuple
+
+        with pytest.raises(ValueError):
+            # bad symbols that do not translate to dtypes
+            np.add(3, 4, signature="%^->#")
+
+        with pytest.raises(ValueError):
+            np.add(3, 4, signature=b"ii-i")  # incomplete and byte string
+
+        with pytest.raises(ValueError):
+            np.add(3, 4, signature="ii>i")  # incomplete string
+
+        with pytest.raises(ValueError):
+            np.add(3, 4, signature=(None, "f8"))  # bad length
+
+        with pytest.raises(UnicodeDecodeError):
+            np.add(3, 4, signature=b"\xff\xff->i")
+
+    def test_forced_dtype_times(self):
+        # Signatures only set the type numbers (not the actual loop dtypes)
+        # so using `M` in a signature/dtype should generally work:
+        a = np.array(['2010-01-02', '1999-03-14', '1833-03'], dtype='>M8[D]')
+        np.maximum(a, a, dtype="M")
+        np.maximum.reduce(a, dtype="M")
+
+        arr = np.arange(10, dtype="m8[s]")
+        np.add(arr, arr, dtype="m")
+        np.maximum(arr, arr, dtype="m")
+
+    @pytest.mark.parametrize("ufunc", [np.add, np.sqrt])
+    def test_cast_safety(self, ufunc):
+        """Basic test for the safest casts, because ufuncs inner loops can
+        indicate a cast-safety as well (which is normally always "no").
+        """
+        def call_ufunc(arr, **kwargs):
+            return ufunc(*(arr,) * ufunc.nin, **kwargs)
+
+        arr = np.array([1., 2., 3.], dtype=np.float32)
+        arr_bs = arr.astype(arr.dtype.newbyteorder())
+        expected = call_ufunc(arr)
+        # Normally, a "no" cast:
+        res = call_ufunc(arr, casting="no")
+        assert_array_equal(expected, res)
+        # Byte-swapping is not allowed with "no" though:
+        with pytest.raises(TypeError):
+            call_ufunc(arr_bs, casting="no")
+
+        # But is allowed with "equiv":
+        res = call_ufunc(arr_bs, casting="equiv")
+        assert_array_equal(expected, res)
+
+        # Casting to float64 is safe, but not equiv:
+        with pytest.raises(TypeError):
+            call_ufunc(arr_bs, dtype=np.float64, casting="equiv")
+
+        # but it is safe cast:
+        res = call_ufunc(arr_bs, dtype=np.float64, casting="safe")
+        expected = call_ufunc(arr.astype(np.float64))  # upcast
+        assert_array_equal(expected, res)
+
+    @pytest.mark.parametrize("ufunc", [np.add, np.equal])
+    def test_cast_safety_scalar(self, ufunc):
+        # We test add and equal, because equal has special scalar handling
+        # Note that the "equiv" casting behavior should maybe be considered
+        # a current implementation detail.
+        with pytest.raises(TypeError):
+            # this picks an integer loop, which is not safe
+            ufunc(3., 4., dtype=int, casting="safe")
+
+        with pytest.raises(TypeError):
+            # We accept python float as float64 but not float32 for equiv.
+            ufunc(3., 4., dtype="float32", casting="equiv")
+
+        # Special case for object and equal (note that equiv implies safe)
+        ufunc(3, 4, dtype=object, casting="equiv")
+        # Picks a double loop for both, first is equiv, second safe:
+        ufunc(np.array([3.]), 3., casting="equiv")
+        ufunc(np.array([3.]), 3, casting="safe")
+        ufunc(np.array([3]), 3, casting="equiv")
+
+    def test_cast_safety_scalar_special(self):
+        # We allow this (and it succeeds) via object, although the equiv
+        # part may not be important.
+        np.equal(np.array([3]), 2**300, casting="equiv")
+
+    def test_true_divide(self):
+        a = np.array(10)
+        b = np.array(20)
+        tgt = np.array(0.5)
+
+        for tc in 'bhilqBHILQefdgFDG':
+            dt = np.dtype(tc)
+            aa = a.astype(dt)
+            bb = b.astype(dt)
+
+            # Check result value and dtype.
+            for x, y in itertools.product([aa, -aa], [bb, -bb]):
+
+                # Check with no output type specified
+                if tc in 'FDG':
+                    tgt = complex(x) / complex(y)
+                else:
+                    tgt = float(x) / float(y)
+
+                res = np.true_divide(x, y)
+                rtol = max(np.finfo(res).resolution, 1e-15)
+                assert_allclose(res, tgt, rtol=rtol)
+
+                if tc in 'bhilqBHILQ':
+                    assert_(res.dtype.name == 'float64')
+                else:
+                    assert_(res.dtype.name == dt.name)
+
+                # Check with output type specified.  This also checks for the
+                # incorrect casts in issue gh-3484 because the unary '-' does
+                # not change types, even for unsigned types, Hence casts in the
+                # ufunc from signed to unsigned and vice versa will lead to
+                # errors in the values.
+                for tcout in 'bhilqBHILQ':
+                    dtout = np.dtype(tcout)
+                    assert_raises(TypeError, np.true_divide, x, y, dtype=dtout)
+
+                for tcout in 'efdg':
+                    dtout = np.dtype(tcout)
+                    if tc in 'FDG':
+                        # Casting complex to float is not allowed
+                        assert_raises(TypeError, np.true_divide, x, y, dtype=dtout)
+                    else:
+                        tgt = float(x) / float(y)
+                        rtol = max(np.finfo(dtout).resolution, 1e-15)
+                        # The value of tiny for double double is NaN
+                        with suppress_warnings() as sup:
+                            sup.filter(UserWarning)
+                            if not np.isnan(np.finfo(dtout).tiny):
+                                atol = max(np.finfo(dtout).tiny, 3e-308)
+                            else:
+                                atol = 3e-308
+                        # Some test values result in invalid for float16
+                        # and the cast to it may overflow to inf.
+                        with np.errstate(invalid='ignore', over='ignore'):
+                            res = np.true_divide(x, y, dtype=dtout)
+                        if not np.isfinite(res) and tcout == 'e':
+                            continue
+                        assert_allclose(res, tgt, rtol=rtol, atol=atol)
+                        assert_(res.dtype.name == dtout.name)
+
+                for tcout in 'FDG':
+                    dtout = np.dtype(tcout)
+                    tgt = complex(x) / complex(y)
+                    rtol = max(np.finfo(dtout).resolution, 1e-15)
+                    # The value of tiny for double double is NaN
+                    with suppress_warnings() as sup:
+                        sup.filter(UserWarning)
+                        if not np.isnan(np.finfo(dtout).tiny):
+                            atol = max(np.finfo(dtout).tiny, 3e-308)
+                        else:
+                            atol = 3e-308
+                    res = np.true_divide(x, y, dtype=dtout)
+                    if not np.isfinite(res):
+                        continue
+                    assert_allclose(res, tgt, rtol=rtol, atol=atol)
+                    assert_(res.dtype.name == dtout.name)
+
+        # Check booleans
+        a = np.ones((), dtype=np.bool)
+        res = np.true_divide(a, a)
+        assert_(res == 1.0)
+        assert_(res.dtype.name == 'float64')
+        res = np.true_divide(~a, a)
+        assert_(res == 0.0)
+        assert_(res.dtype.name == 'float64')
+
+    def test_sum_stability(self):
+        a = np.ones(500, dtype=np.float32)
+        assert_almost_equal((a / 10.).sum() - a.size / 10., 0, 4)
+
+        a = np.ones(500, dtype=np.float64)
+        assert_almost_equal((a / 10.).sum() - a.size / 10., 0, 13)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_sum(self):
+        for dt in (int, np.float16, np.float32, np.float64, np.longdouble):
+            for v in (0, 1, 2, 7, 8, 9, 15, 16, 19, 127,
+                      128, 1024, 1235):
+                # warning if sum overflows, which it does in float16
+                with warnings.catch_warnings(record=True) as w:
+                    warnings.simplefilter("always", RuntimeWarning)
+
+                    tgt = dt(v * (v + 1) / 2)
+                    overflow = not np.isfinite(tgt)
+                    assert_equal(len(w), 1 * overflow)
+
+                    d = np.arange(1, v + 1, dtype=dt)
+
+                    assert_almost_equal(np.sum(d), tgt)
+                    assert_equal(len(w), 2 * overflow)
+
+                    assert_almost_equal(np.sum(d[::-1]), tgt)
+                    assert_equal(len(w), 3 * overflow)
+
+            d = np.ones(500, dtype=dt)
+            assert_almost_equal(np.sum(d[::2]), 250.)
+            assert_almost_equal(np.sum(d[1::2]), 250.)
+            assert_almost_equal(np.sum(d[::3]), 167.)
+            assert_almost_equal(np.sum(d[1::3]), 167.)
+            assert_almost_equal(np.sum(d[::-2]), 250.)
+            assert_almost_equal(np.sum(d[-1::-2]), 250.)
+            assert_almost_equal(np.sum(d[::-3]), 167.)
+            assert_almost_equal(np.sum(d[-1::-3]), 167.)
+            # sum with first reduction entry != 0
+            d = np.ones((1,), dtype=dt)
+            d += d
+            assert_almost_equal(d, 2.)
+
+    def test_sum_complex(self):
+        for dt in (np.complex64, np.complex128, np.clongdouble):
+            for v in (0, 1, 2, 7, 8, 9, 15, 16, 19, 127,
+                      128, 1024, 1235):
+                tgt = dt(v * (v + 1) / 2) - dt((v * (v + 1) / 2) * 1j)
+                d = np.empty(v, dtype=dt)
+                d.real = np.arange(1, v + 1)
+                d.imag = -np.arange(1, v + 1)
+                assert_almost_equal(np.sum(d), tgt)
+                assert_almost_equal(np.sum(d[::-1]), tgt)
+
+            d = np.ones(500, dtype=dt) + 1j
+            assert_almost_equal(np.sum(d[::2]), 250. + 250j)
+            assert_almost_equal(np.sum(d[1::2]), 250. + 250j)
+            assert_almost_equal(np.sum(d[::3]), 167. + 167j)
+            assert_almost_equal(np.sum(d[1::3]), 167. + 167j)
+            assert_almost_equal(np.sum(d[::-2]), 250. + 250j)
+            assert_almost_equal(np.sum(d[-1::-2]), 250. + 250j)
+            assert_almost_equal(np.sum(d[::-3]), 167. + 167j)
+            assert_almost_equal(np.sum(d[-1::-3]), 167. + 167j)
+            # sum with first reduction entry != 0
+            d = np.ones((1,), dtype=dt) + 1j
+            d += d
+            assert_almost_equal(d, 2. + 2j)
+
+    def test_sum_initial(self):
+        # Integer, single axis
+        assert_equal(np.sum([3], initial=2), 5)
+
+        # Floating point
+        assert_almost_equal(np.sum([0.2], initial=0.1), 0.3)
+
+        # Multiple non-adjacent axes
+        assert_equal(np.sum(np.ones((2, 3, 5), dtype=np.int64), axis=(0, 2), initial=2),
+                     [12, 12, 12])
+
+    def test_sum_where(self):
+        # More extensive tests done in test_reduction_with_where.
+        assert_equal(np.sum([[1., 2.], [3., 4.]], where=[True, False]), 4.)
+        assert_equal(np.sum([[1., 2.], [3., 4.]], axis=0, initial=5.,
+                            where=[True, False]), [9., 5.])
+
+    def test_vecdot(self):
+        arr1 = np.arange(6).reshape((2, 3))
+        arr2 = np.arange(3).reshape((1, 3))
+
+        actual = np.vecdot(arr1, arr2)
+        expected = np.array([5, 14])
+
+        assert_array_equal(actual, expected)
+
+        actual2 = np.vecdot(arr1.T, arr2.T, axis=-2)
+        assert_array_equal(actual2, expected)
+
+        actual3 = np.vecdot(arr1.astype("object"), arr2)
+        assert_array_equal(actual3, expected.astype("object"))
+
+    def test_matvec(self):
+        arr1 = np.arange(6).reshape((2, 3))
+        arr2 = np.arange(3).reshape((1, 3))
+
+        actual = np.matvec(arr1, arr2)
+        expected = np.array([[5, 14]])
+
+        assert_array_equal(actual, expected)
+
+        actual2 = np.matvec(arr1.T, arr2.T, axes=[(-1, -2), -2, -1])
+        assert_array_equal(actual2, expected)
+
+        actual3 = np.matvec(arr1.astype("object"), arr2)
+        assert_array_equal(actual3, expected.astype("object"))
+
+    @pytest.mark.parametrize("vec", [
+        np.array([[1., 2., 3.], [4., 5., 6.]]),
+        np.array([[1., 2j, 3.], [4., 5., 6j]]),
+        np.array([[1., 2., 3.], [4., 5., 6.]], dtype=object),
+        np.array([[1., 2j, 3.], [4., 5., 6j]], dtype=object)])
+    @pytest.mark.parametrize("matrix", [
+        None,
+        np.array([[1. + 1j, 0.5, -0.5j],
+                  [0.25, 2j, 0.],
+                  [4., 0., -1j]])])
+    def test_vecmatvec_identity(self, matrix, vec):
+        """Check that (x†A)x equals x†(Ax)."""
+        mat = matrix if matrix is not None else np.eye(3)
+        matvec = np.matvec(mat, vec)  # Ax
+        vecmat = np.vecmat(vec, mat)  # x†A
+        if matrix is None:
+            assert_array_equal(matvec, vec)
+            assert_array_equal(vecmat.conj(), vec)
+        assert_array_equal(matvec, (mat @ vec[..., np.newaxis]).squeeze(-1))
+        assert_array_equal(vecmat, (vec[..., np.newaxis].mT.conj()
+                                    @ mat).squeeze(-2))
+        expected = np.einsum('...i,ij,...j', vec.conj(), mat, vec)
+        vec_matvec = (vec.conj() * matvec).sum(-1)
+        vecmat_vec = (vecmat * vec).sum(-1)
+        assert_array_equal(vec_matvec, expected)
+        assert_array_equal(vecmat_vec, expected)
+
+    @pytest.mark.parametrize("ufunc, shape1, shape2, conj", [
+        (np.vecdot, (3,), (3,), True),
+        (np.vecmat, (3,), (3, 1), True),
+        (np.matvec, (1, 3), (3,), False),
+        (np.matmul, (1, 3), (3, 1), False),
+    ])
+    def test_vecdot_matvec_vecmat_complex(self, ufunc, shape1, shape2, conj):
+        arr1 = np.array([1, 2j, 3])
+        arr2 = np.array([1, 2, 3])
+
+        actual1 = ufunc(arr1.reshape(shape1), arr2.reshape(shape2))
+        expected1 = np.array(((arr1.conj() if conj else arr1) * arr2).sum(),
+                             ndmin=min(len(shape1), len(shape2)))
+        assert_array_equal(actual1, expected1)
+        # This would fail for conj=True, since matmul omits the conjugate.
+        if not conj:
+            assert_array_equal(arr1.reshape(shape1) @ arr2.reshape(shape2),
+                               expected1)
+
+        actual2 = ufunc(arr2.reshape(shape1), arr1.reshape(shape2))
+        expected2 = np.array(((arr2.conj() if conj else arr2) * arr1).sum(),
+                             ndmin=min(len(shape1), len(shape2)))
+        assert_array_equal(actual2, expected2)
+
+        actual3 = ufunc(arr1.reshape(shape1).astype("object"),
+                        arr2.reshape(shape2).astype("object"))
+        expected3 = expected1.astype(object)
+        assert_array_equal(actual3, expected3)
+
+    def test_vecdot_subclass(self):
+        class MySubclass(np.ndarray):
+            pass
+
+        arr1 = np.arange(6).reshape((2, 3)).view(MySubclass)
+        arr2 = np.arange(3).reshape((1, 3)).view(MySubclass)
+        result = np.vecdot(arr1, arr2)
+        assert isinstance(result, MySubclass)
+
+    def test_vecdot_object_no_conjugate(self):
+        arr = np.array(["1", "2"], dtype=object)
+        with pytest.raises(AttributeError, match="conjugate"):
+            np.vecdot(arr, arr)
+
+    def test_vecdot_object_breaks_outer_loop_on_error(self):
+        arr1 = np.ones((3, 3)).astype(object)
+        arr2 = arr1.copy()
+        arr2[1, 1] = None
+        out = np.zeros(3).astype(object)
+        with pytest.raises(TypeError, match=r"\*: 'float' and 'NoneType'"):
+            np.vecdot(arr1, arr2, out=out)
+        assert out[0] == 3
+        assert out[1] == out[2] == 0
+
+    def test_broadcast(self):
+        msg = "broadcast"
+        a = np.arange(4).reshape((2, 1, 2))
+        b = np.arange(4).reshape((1, 2, 2))
+        assert_array_equal(np.vecdot(a, b), np.sum(a * b, axis=-1), err_msg=msg)
+        msg = "extend & broadcast loop dimensions"
+        b = np.arange(4).reshape((2, 2))
+        assert_array_equal(np.vecdot(a, b), np.sum(a * b, axis=-1), err_msg=msg)
+        # Broadcast in core dimensions should fail
+        a = np.arange(8).reshape((4, 2))
+        b = np.arange(4).reshape((4, 1))
+        assert_raises(ValueError, np.vecdot, a, b)
+        # Extend core dimensions should fail
+        a = np.arange(8).reshape((4, 2))
+        b = np.array(7)
+        assert_raises(ValueError, np.vecdot, a, b)
+        # Broadcast should fail
+        a = np.arange(2).reshape((2, 1, 1))
+        b = np.arange(3).reshape((3, 1, 1))
+        assert_raises(ValueError, np.vecdot, a, b)
+
+        # Writing to a broadcasted array with overlap should warn, gh-2705
+        a = np.arange(2)
+        b = np.arange(4).reshape((2, 2))
+        u, v = np.broadcast_arrays(a, b)
+        assert_equal(u.strides[0], 0)
+        x = u + v
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter("always")
+            u += v
+            assert_equal(len(w), 1)
+            assert_(x[0, 0] != u[0, 0])
+
+        # Output reduction should not be allowed.
+        # See gh-15139
+        a = np.arange(6).reshape(3, 2)
+        b = np.ones(2)
+        out = np.empty(())
+        assert_raises(ValueError, np.vecdot, a, b, out)
+        out2 = np.empty(3)
+        c = np.vecdot(a, b, out2)
+        assert_(c is out2)
+
+    def test_out_broadcasts(self):
+        # For ufuncs and gufuncs (not for reductions), we currently allow
+        # the output to cause broadcasting of the input arrays.
+        # both along dimensions with shape 1 and dimensions which do not
+        # exist at all in the inputs.
+        arr = np.arange(3).reshape(1, 3)
+        out = np.empty((5, 4, 3))
+        np.add(arr, arr, out=out)
+        assert (out == np.arange(3) * 2).all()
+
+        # The same holds for gufuncs (gh-16484)
+        np.vecdot(arr, arr, out=out)
+        # the result would be just a scalar `5`, but is broadcast fully:
+        assert (out == 5).all()
+
+    @pytest.mark.parametrize(["arr", "out"], [
+                ([2], np.empty(())),
+                ([1, 2], np.empty(1)),
+                (np.ones((4, 3)), np.empty((4, 1)))],
+            ids=["(1,)->()", "(2,)->(1,)", "(4, 3)->(4, 1)"])
+    def test_out_broadcast_errors(self, arr, out):
+        # Output is (currently) allowed to broadcast inputs, but it cannot be
+        # smaller than the actual result.
+        with pytest.raises(ValueError, match="non-broadcastable"):
+            np.positive(arr, out=out)
+
+        with pytest.raises(ValueError, match="non-broadcastable"):
+            np.add(np.ones(()), arr, out=out)
+
+    def test_type_cast(self):
+        msg = "type cast"
+        a = np.arange(6, dtype='short').reshape((2, 3))
+        assert_array_equal(np.vecdot(a, a), np.sum(a * a, axis=-1),
+                           err_msg=msg)
+        msg = "type cast on one argument"
+        a = np.arange(6).reshape((2, 3))
+        b = a + 0.1
+        assert_array_almost_equal(np.vecdot(a, b), np.sum(a * b, axis=-1),
+                                  err_msg=msg)
+
+    def test_endian(self):
+        msg = "big endian"
+        a = np.arange(6, dtype='>i4').reshape((2, 3))
+        assert_array_equal(np.vecdot(a, a), np.sum(a * a, axis=-1),
+                           err_msg=msg)
+        msg = "little endian"
+        a = np.arange(6, dtype='<i4').reshape((2, 3))
+        assert_array_equal(np.vecdot(a, a), np.sum(a * a, axis=-1),
+                           err_msg=msg)
+
+        # Output should always be native-endian
+        Ba = np.arange(1, dtype='>f8')
+        La = np.arange(1, dtype='<f8')
+        assert_equal((Ba + Ba).dtype, np.dtype('f8'))
+        assert_equal((Ba + La).dtype, np.dtype('f8'))
+        assert_equal((La + Ba).dtype, np.dtype('f8'))
+        assert_equal((La + La).dtype, np.dtype('f8'))
+
+        assert_equal(np.absolute(La).dtype, np.dtype('f8'))
+        assert_equal(np.absolute(Ba).dtype, np.dtype('f8'))
+        assert_equal(np.negative(La).dtype, np.dtype('f8'))
+        assert_equal(np.negative(Ba).dtype, np.dtype('f8'))
+
+    def test_incontiguous_array(self):
+        msg = "incontiguous memory layout of array"
+        x = np.arange(64).reshape((2, 2, 2, 2, 2, 2))
+        a = x[:, 0, :, 0, :, 0]
+        b = x[:, 1, :, 1, :, 1]
+        a[0, 0, 0] = -1
+        msg2 = "make sure it references to the original array"
+        assert_equal(x[0, 0, 0, 0, 0, 0], -1, err_msg=msg2)
+        assert_array_equal(np.vecdot(a, b), np.sum(a * b, axis=-1), err_msg=msg)
+        x = np.arange(24).reshape(2, 3, 4)
+        a = x.T
+        b = x.T
+        a[0, 0, 0] = -1
+        assert_equal(x[0, 0, 0], -1, err_msg=msg2)
+        assert_array_equal(np.vecdot(a, b), np.sum(a * b, axis=-1), err_msg=msg)
+
+    def test_output_argument(self):
+        msg = "output argument"
+        a = np.arange(12).reshape((2, 3, 2))
+        b = np.arange(4).reshape((2, 1, 2)) + 1
+        c = np.zeros((2, 3), dtype='int')
+        np.vecdot(a, b, c)
+        assert_array_equal(c, np.sum(a * b, axis=-1), err_msg=msg)
+        c[:] = -1
+        np.vecdot(a, b, out=c)
+        assert_array_equal(c, np.sum(a * b, axis=-1), err_msg=msg)
+
+        msg = "output argument with type cast"
+        c = np.zeros((2, 3), dtype='int16')
+        np.vecdot(a, b, c)
+        assert_array_equal(c, np.sum(a * b, axis=-1), err_msg=msg)
+        c[:] = -1
+        np.vecdot(a, b, out=c)
+        assert_array_equal(c, np.sum(a * b, axis=-1), err_msg=msg)
+
+        msg = "output argument with incontiguous layout"
+        c = np.zeros((2, 3, 4), dtype='int16')
+        np.vecdot(a, b, c[..., 0])
+        assert_array_equal(c[..., 0], np.sum(a * b, axis=-1), err_msg=msg)
+        c[:] = -1
+        np.vecdot(a, b, out=c[..., 0])
+        assert_array_equal(c[..., 0], np.sum(a * b, axis=-1), err_msg=msg)
+
+    @pytest.mark.parametrize("arg", ["array", "scalar", "subclass"])
+    def test_output_ellipsis(self, arg):
+        class subclass(np.ndarray):
+            def __array_wrap__(self, obj, context=None, return_value=None):
+                return super().__array_wrap__(obj, context, return_value)
+
+        if arg == "scalar":
+            one = 1
+            expected_type = np.ndarray
+        elif arg == "array":
+            one = np.array(1)
+            expected_type = np.ndarray
+        elif arg == "subclass":
+            one = np.array(1).view(subclass)
+            expected_type = subclass
+
+        assert type(np.add(one, 2, out=...)) is expected_type
+        assert type(np.add.reduce(one, out=...)) is expected_type
+        res1, res2 = np.divmod(one, 2, out=...)
+        assert type(res1) is type(res2) is expected_type
+
+    def test_output_ellipsis_errors(self):
+        with pytest.raises(TypeError,
+                match=r"out=\.\.\. is only allowed as a keyword argument."):
+            np.add(1, 2, ...)
+
+        with pytest.raises(TypeError,
+                match=r"out=\.\.\. is only allowed as a keyword argument."):
+            np.add.reduce(1, (), None, ...)
+
+        with pytest.raises(TypeError,
+                match=r"must use `\.\.\.` as `out=\.\.\.` and not per-operand/in a tuple"):
+            np.negative(1, out=(...,))
+
+        with pytest.raises(TypeError,
+                match=r"must use `\.\.\.` as `out=\.\.\.` and not per-operand/in a tuple"):
+            # We only allow out=... not individual args for now
+            np.divmod(1, 2, out=(np.empty(()), ...))
+
+        with pytest.raises(TypeError,
+                match=r"must use `\.\.\.` as `out=\.\.\.` and not per-operand/in a tuple"):
+            np.add.reduce(1, out=(...,))
+
+    def test_axes_argument(self):
+        # vecdot signature: '(n),(n)->()'
+        a = np.arange(27.).reshape((3, 3, 3))
+        b = np.arange(10., 19.).reshape((3, 1, 3))
+        # basic tests on inputs (outputs tested below with matrix_multiply).
+        c = np.vecdot(a, b)
+        assert_array_equal(c, (a * b).sum(-1))
+        # default
+        c = np.vecdot(a, b, axes=[(-1,), (-1,), ()])
+        assert_array_equal(c, (a * b).sum(-1))
+        # integers ok for single axis.
+        c = np.vecdot(a, b, axes=[-1, -1, ()])
+        assert_array_equal(c, (a * b).sum(-1))
+        # mix fine
+        c = np.vecdot(a, b, axes=[(-1,), -1, ()])
+        assert_array_equal(c, (a * b).sum(-1))
+        # can omit last axis.
+        c = np.vecdot(a, b, axes=[-1, -1])
+        assert_array_equal(c, (a * b).sum(-1))
+        # can pass in other types of integer (with __index__ protocol)
+        c = np.vecdot(a, b, axes=[np.int8(-1), np.array(-1, dtype=np.int32)])
+        assert_array_equal(c, (a * b).sum(-1))
+        # swap some axes
+        c = np.vecdot(a, b, axes=[0, 0])
+        assert_array_equal(c, (a * b).sum(0))
+        c = np.vecdot(a, b, axes=[0, 2])
+        assert_array_equal(c, (a.transpose(1, 2, 0) * b).sum(-1))
+        # Check errors for improperly constructed axes arguments.
+        # should have list.
+        assert_raises(TypeError, np.vecdot, a, b, axes=-1)
+        # needs enough elements
+        assert_raises(ValueError, np.vecdot, a, b, axes=[-1])
+        # should pass in indices.
+        assert_raises(TypeError, np.vecdot, a, b, axes=[-1.0, -1.0])
+        assert_raises(TypeError, np.vecdot, a, b, axes=[(-1.0,), -1])
+        assert_raises(TypeError, np.vecdot, a, b, axes=[None, 1])
+        # cannot pass an index unless there is only one dimension
+        # (output is wrong in this case)
+        assert_raises(AxisError, np.vecdot, a, b, axes=[-1, -1, -1])
+        # or pass in generally the wrong number of axes
+        assert_raises(AxisError, np.vecdot, a, b, axes=[-1, -1, (-1,)])
+        assert_raises(AxisError, np.vecdot, a, b, axes=[-1, (-2, -1), ()])
+        # axes need to have same length.
+        assert_raises(ValueError, np.vecdot, a, b, axes=[0, 1])
+
+        # matrix_multiply signature: '(m,n),(n,p)->(m,p)'
+        mm = umt.matrix_multiply
+        a = np.arange(12).reshape((2, 3, 2))
+        b = np.arange(8).reshape((2, 2, 2, 1)) + 1
+        # Sanity check.
+        c = mm(a, b)
+        assert_array_equal(c, np.matmul(a, b))
+        # Default axes.
+        c = mm(a, b, axes=[(-2, -1), (-2, -1), (-2, -1)])
+        assert_array_equal(c, np.matmul(a, b))
+        # Default with explicit axes.
+        c = mm(a, b, axes=[(1, 2), (2, 3), (2, 3)])
+        assert_array_equal(c, np.matmul(a, b))
+        # swap some axes.
+        c = mm(a, b, axes=[(0, -1), (1, 2), (-2, -1)])
+        assert_array_equal(c, np.matmul(a.transpose(1, 0, 2),
+                                        b.transpose(0, 3, 1, 2)))
+        # Default with output array.
+        c = np.empty((2, 2, 3, 1))
+        d = mm(a, b, out=c, axes=[(1, 2), (2, 3), (2, 3)])
+        assert_(c is d)
+        assert_array_equal(c, np.matmul(a, b))
+        # Transposed output array
+        c = np.empty((1, 2, 2, 3))
+        d = mm(a, b, out=c, axes=[(-2, -1), (-2, -1), (3, 0)])
+        assert_(c is d)
+        assert_array_equal(c, np.matmul(a, b).transpose(3, 0, 1, 2))
+        # Check errors for improperly constructed axes arguments.
+        # wrong argument
+        assert_raises(TypeError, mm, a, b, axis=1)
+        # axes should be list
+        assert_raises(TypeError, mm, a, b, axes=1)
+        assert_raises(TypeError, mm, a, b, axes=((-2, -1), (-2, -1), (-2, -1)))
+        # list needs to have right length
+        assert_raises(ValueError, mm, a, b, axes=[])
+        assert_raises(ValueError, mm, a, b, axes=[(-2, -1)])
+        # list should not contain None, or lists
+        assert_raises(TypeError, mm, a, b, axes=[None, None, None])
+        assert_raises(TypeError,
+                      mm, a, b, axes=[[-2, -1], [-2, -1], [-2, -1]])
+        assert_raises(TypeError,
+                      mm, a, b, axes=[(-2, -1), (-2, -1), [-2, -1]])
+        assert_raises(TypeError, mm, a, b, axes=[(-2, -1), (-2, -1), None])
+        # single integers are AxisErrors if more are required
+        assert_raises(AxisError, mm, a, b, axes=[-1, -1, -1])
+        assert_raises(AxisError, mm, a, b, axes=[(-2, -1), (-2, -1), -1])
+        # tuples should not have duplicated values
+        assert_raises(ValueError, mm, a, b, axes=[(-2, -1), (-2, -1), (-2, -2)])
+        # arrays should have enough axes.
+        z = np.zeros((2, 2))
+        assert_raises(ValueError, mm, z, z[0])
+        assert_raises(ValueError, mm, z, z, out=z[:, 0])
+        assert_raises(ValueError, mm, z[1], z, axes=[0, 1])
+        assert_raises(ValueError, mm, z, z, out=z[0], axes=[0, 1])
+        # Regular ufuncs should not accept axes.
+        assert_raises(TypeError, np.add, 1., 1., axes=[0])
+        # should be able to deal with bad unrelated kwargs.
+        assert_raises(TypeError, mm, z, z, axes=[0, 1], parrot=True)
+
+    def test_axis_argument(self):
+        # vecdot signature: '(n),(n)->()'
+        a = np.arange(27.).reshape((3, 3, 3))
+        b = np.arange(10., 19.).reshape((3, 1, 3))
+        c = np.vecdot(a, b)
+        assert_array_equal(c, (a * b).sum(-1))
+        c = np.vecdot(a, b, axis=-1)
+        assert_array_equal(c, (a * b).sum(-1))
+        out = np.zeros_like(c)
+        d = np.vecdot(a, b, axis=-1, out=out)
+        assert_(d is out)
+        assert_array_equal(d, c)
+        c = np.vecdot(a, b, axis=0)
+        assert_array_equal(c, (a * b).sum(0))
+        # Sanity checks on innerwt and cumsum.
+        a = np.arange(6).reshape((2, 3))
+        b = np.arange(10, 16).reshape((2, 3))
+        w = np.arange(20, 26).reshape((2, 3))
+        assert_array_equal(umt.innerwt(a, b, w, axis=0),
+                           np.sum(a * b * w, axis=0))
+        assert_array_equal(umt.cumsum(a, axis=0), np.cumsum(a, axis=0))
+        assert_array_equal(umt.cumsum(a, axis=-1), np.cumsum(a, axis=-1))
+        out = np.empty_like(a)
+        b = umt.cumsum(a, out=out, axis=0)
+        assert_(out is b)
+        assert_array_equal(b, np.cumsum(a, axis=0))
+        b = umt.cumsum(a, out=out, axis=1)
+        assert_(out is b)
+        assert_array_equal(b, np.cumsum(a, axis=-1))
+        # Check errors.
+        # Cannot pass in both axis and axes.
+        assert_raises(TypeError, np.vecdot, a, b, axis=0, axes=[0, 0])
+        # Not an integer.
+        assert_raises(TypeError, np.vecdot, a, b, axis=[0])
+        # more than 1 core dimensions.
+        mm = umt.matrix_multiply
+        assert_raises(TypeError, mm, a, b, axis=1)
+        # Output wrong size in axis.
+        out = np.empty((1, 2, 3), dtype=a.dtype)
+        assert_raises(ValueError, umt.cumsum, a, out=out, axis=0)
+        # Regular ufuncs should not accept axis.
+        assert_raises(TypeError, np.add, 1., 1., axis=0)
+
+    def test_keepdims_argument(self):
+        # vecdot signature: '(n),(n)->()'
+        a = np.arange(27.).reshape((3, 3, 3))
+        b = np.arange(10., 19.).reshape((3, 1, 3))
+        c = np.vecdot(a, b)
+        assert_array_equal(c, (a * b).sum(-1))
+        c = np.vecdot(a, b, keepdims=False)
+        assert_array_equal(c, (a * b).sum(-1))
+        c = np.vecdot(a, b, keepdims=True)
+        assert_array_equal(c, (a * b).sum(-1, keepdims=True))
+        out = np.zeros_like(c)
+        d = np.vecdot(a, b, keepdims=True, out=out)
+        assert_(d is out)
+        assert_array_equal(d, c)
+        # Now combined with axis and axes.
+        c = np.vecdot(a, b, axis=-1, keepdims=False)
+        assert_array_equal(c, (a * b).sum(-1, keepdims=False))
+        c = np.vecdot(a, b, axis=-1, keepdims=True)
+        assert_array_equal(c, (a * b).sum(-1, keepdims=True))
+        c = np.vecdot(a, b, axis=0, keepdims=False)
+        assert_array_equal(c, (a * b).sum(0, keepdims=False))
+        c = np.vecdot(a, b, axis=0, keepdims=True)
+        assert_array_equal(c, (a * b).sum(0, keepdims=True))
+        c = np.vecdot(a, b, axes=[(-1,), (-1,), ()], keepdims=False)
+        assert_array_equal(c, (a * b).sum(-1))
+        c = np.vecdot(a, b, axes=[(-1,), (-1,), (-1,)], keepdims=True)
+        assert_array_equal(c, (a * b).sum(-1, keepdims=True))
+        c = np.vecdot(a, b, axes=[0, 0], keepdims=False)
+        assert_array_equal(c, (a * b).sum(0))
+        c = np.vecdot(a, b, axes=[0, 0, 0], keepdims=True)
+        assert_array_equal(c, (a * b).sum(0, keepdims=True))
+        c = np.vecdot(a, b, axes=[0, 2], keepdims=False)
+        assert_array_equal(c, (a.transpose(1, 2, 0) * b).sum(-1))
+        c = np.vecdot(a, b, axes=[0, 2], keepdims=True)
+        assert_array_equal(c, (a.transpose(1, 2, 0) * b).sum(-1,
+                                                             keepdims=True))
+        c = np.vecdot(a, b, axes=[0, 2, 2], keepdims=True)
+        assert_array_equal(c, (a.transpose(1, 2, 0) * b).sum(-1,
+                                                             keepdims=True))
+        c = np.vecdot(a, b, axes=[0, 2, 0], keepdims=True)
+        assert_array_equal(c, (a * b.transpose(2, 0, 1)).sum(0, keepdims=True))
+        # Hardly useful, but should work.
+        c = np.vecdot(a, b, axes=[0, 2, 1], keepdims=True)
+        assert_array_equal(c, (a.transpose(1, 0, 2) * b.transpose(0, 2, 1))
+                           .sum(1, keepdims=True))
+        # Check with two core dimensions.
+        a = np.eye(3) * np.arange(4.)[:, np.newaxis, np.newaxis]
+        expected = uml.det(a)
+        c = uml.det(a, keepdims=False)
+        assert_array_equal(c, expected)
+        c = uml.det(a, keepdims=True)
+        assert_array_equal(c, expected[:, np.newaxis, np.newaxis])
+        a = np.eye(3) * np.arange(4.)[:, np.newaxis, np.newaxis]
+        expected_s, expected_l = uml.slogdet(a)
+        cs, cl = uml.slogdet(a, keepdims=False)
+        assert_array_equal(cs, expected_s)
+        assert_array_equal(cl, expected_l)
+        cs, cl = uml.slogdet(a, keepdims=True)
+        assert_array_equal(cs, expected_s[:, np.newaxis, np.newaxis])
+        assert_array_equal(cl, expected_l[:, np.newaxis, np.newaxis])
+        # Sanity check on innerwt.
+        a = np.arange(6).reshape((2, 3))
+        b = np.arange(10, 16).reshape((2, 3))
+        w = np.arange(20, 26).reshape((2, 3))
+        assert_array_equal(umt.innerwt(a, b, w, keepdims=True),
+                           np.sum(a * b * w, axis=-1, keepdims=True))
+        assert_array_equal(umt.innerwt(a, b, w, axis=0, keepdims=True),
+                           np.sum(a * b * w, axis=0, keepdims=True))
+        # Check errors.
+        # Not a boolean
+        assert_raises(TypeError, np.vecdot, a, b, keepdims='true')
+        # More than 1 core dimension, and core output dimensions.
+        mm = umt.matrix_multiply
+        assert_raises(TypeError, mm, a, b, keepdims=True)
+        assert_raises(TypeError, mm, a, b, keepdims=False)
+        # Regular ufuncs should not accept keepdims.
+        assert_raises(TypeError, np.add, 1., 1., keepdims=False)
+
+    def test_innerwt(self):
+        a = np.arange(6).reshape((2, 3))
+        b = np.arange(10, 16).reshape((2, 3))
+        w = np.arange(20, 26).reshape((2, 3))
+        assert_array_equal(umt.innerwt(a, b, w), np.sum(a * b * w, axis=-1))
+        a = np.arange(100, 124).reshape((2, 3, 4))
+        b = np.arange(200, 224).reshape((2, 3, 4))
+        w = np.arange(300, 324).reshape((2, 3, 4))
+        assert_array_equal(umt.innerwt(a, b, w), np.sum(a * b * w, axis=-1))
+
+    def test_innerwt_empty(self):
+        """Test generalized ufunc with zero-sized operands"""
+        a = np.array([], dtype='f8')
+        b = np.array([], dtype='f8')
+        w = np.array([], dtype='f8')
+        assert_array_equal(umt.innerwt(a, b, w), np.sum(a * b * w, axis=-1))
+
+    def test_cross1d(self):
+        """Test with fixed-sized signature."""
+        a = np.eye(3)
+        assert_array_equal(umt.cross1d(a, a), np.zeros((3, 3)))
+        out = np.zeros((3, 3))
+        result = umt.cross1d(a[0], a, out)
+        assert_(result is out)
+        assert_array_equal(result, np.vstack((np.zeros(3), a[2], -a[1])))
+        assert_raises(ValueError, umt.cross1d, np.eye(4), np.eye(4))
+        assert_raises(ValueError, umt.cross1d, a, np.arange(4.))
+        # Wrong output core dimension.
+        assert_raises(ValueError, umt.cross1d, a, np.arange(3.), np.zeros((3, 4)))
+        # Wrong output broadcast dimension (see gh-15139).
+        assert_raises(ValueError, umt.cross1d, a, np.arange(3.), np.zeros(3))
+
+    def test_can_ignore_signature(self):
+        # Comparing the effects of ? in signature:
+        # matrix_multiply: (m,n),(n,p)->(m,p)    # all must be there.
+        # matmul:        (m?,n),(n,p?)->(m?,p?)  # allow missing m, p.
+        mat = np.arange(12).reshape((2, 3, 2))
+        single_vec = np.arange(2)
+        col_vec = single_vec[:, np.newaxis]
+        col_vec_array = np.arange(8).reshape((2, 2, 2, 1)) + 1
+        # matrix @ single column vector with proper dimension
+        mm_col_vec = umt.matrix_multiply(mat, col_vec)
+        # matmul does the same thing
+        matmul_col_vec = umt.matmul(mat, col_vec)
+        assert_array_equal(matmul_col_vec, mm_col_vec)
+        # matrix @ vector without dimension making it a column vector.
+        # matrix multiply fails -> missing core dim.
+        assert_raises(ValueError, umt.matrix_multiply, mat, single_vec)
+        # matmul mimicker passes, and returns a vector.
+        matmul_col = umt.matmul(mat, single_vec)
+        assert_array_equal(matmul_col, mm_col_vec.squeeze())
+        # Now with a column array: same as for column vector,
+        # broadcasting sensibly.
+        mm_col_vec = umt.matrix_multiply(mat, col_vec_array)
+        matmul_col_vec = umt.matmul(mat, col_vec_array)
+        assert_array_equal(matmul_col_vec, mm_col_vec)
+        # As above, but for row vector
+        single_vec = np.arange(3)
+        row_vec = single_vec[np.newaxis, :]
+        row_vec_array = np.arange(24).reshape((4, 2, 1, 1, 3)) + 1
+        # row vector @ matrix
+        mm_row_vec = umt.matrix_multiply(row_vec, mat)
+        matmul_row_vec = umt.matmul(row_vec, mat)
+        assert_array_equal(matmul_row_vec, mm_row_vec)
+        # single row vector @ matrix
+        assert_raises(ValueError, umt.matrix_multiply, single_vec, mat)
+        matmul_row = umt.matmul(single_vec, mat)
+        assert_array_equal(matmul_row, mm_row_vec.squeeze())
+        # row vector array @ matrix
+        mm_row_vec = umt.matrix_multiply(row_vec_array, mat)
+        matmul_row_vec = umt.matmul(row_vec_array, mat)
+        assert_array_equal(matmul_row_vec, mm_row_vec)
+        # Now for vector combinations
+        # row vector @ column vector
+        col_vec = row_vec.T
+        col_vec_array = row_vec_array.swapaxes(-2, -1)
+        mm_row_col_vec = umt.matrix_multiply(row_vec, col_vec)
+        matmul_row_col_vec = umt.matmul(row_vec, col_vec)
+        assert_array_equal(matmul_row_col_vec, mm_row_col_vec)
+        # single row vector @ single col vector
+        assert_raises(ValueError, umt.matrix_multiply, single_vec, single_vec)
+        matmul_row_col = umt.matmul(single_vec, single_vec)
+        assert_array_equal(matmul_row_col, mm_row_col_vec.squeeze())
+        # row vector array @ matrix
+        mm_row_col_array = umt.matrix_multiply(row_vec_array, col_vec_array)
+        matmul_row_col_array = umt.matmul(row_vec_array, col_vec_array)
+        assert_array_equal(matmul_row_col_array, mm_row_col_array)
+        # Finally, check that things are *not* squeezed if one gives an
+        # output.
+        out = np.zeros_like(mm_row_col_array)
+        out = umt.matrix_multiply(row_vec_array, col_vec_array, out=out)
+        assert_array_equal(out, mm_row_col_array)
+        out[:] = 0
+        out = umt.matmul(row_vec_array, col_vec_array, out=out)
+        assert_array_equal(out, mm_row_col_array)
+        # And check one cannot put missing dimensions back.
+        out = np.zeros_like(mm_row_col_vec)
+        assert_raises(ValueError, umt.matrix_multiply, single_vec, single_vec,
+                      out)
+        # But fine for matmul, since it is just a broadcast.
+        out = umt.matmul(single_vec, single_vec, out)
+        assert_array_equal(out, mm_row_col_vec.squeeze())
+
+    def test_matrix_multiply(self):
+        self.compare_matrix_multiply_results(np.int64)
+        self.compare_matrix_multiply_results(np.double)
+
+    def test_matrix_multiply_umath_empty(self):
+        res = umt.matrix_multiply(np.ones((0, 10)), np.ones((10, 0)))
+        assert_array_equal(res, np.zeros((0, 0)))
+        res = umt.matrix_multiply(np.ones((10, 0)), np.ones((0, 10)))
+        assert_array_equal(res, np.zeros((10, 10)))
+
+    def compare_matrix_multiply_results(self, tp):
+        d1 = np.array(np.random.rand(2, 3, 4), dtype=tp)
+        d2 = np.array(np.random.rand(2, 3, 4), dtype=tp)
+        msg = f"matrix multiply on type {d1.dtype.name}"
+
+        def permute_n(n):
+            if n == 1:
+                return ([0],)
+            ret = ()
+            base = permute_n(n - 1)
+            for perm in base:
+                for i in range(n):
+                    new = perm + [n - 1]
+                    new[n - 1] = new[i]
+                    new[i] = n - 1
+                    ret += (new,)
+            return ret
+
+        def slice_n(n):
+            if n == 0:
+                return ((),)
+            ret = ()
+            base = slice_n(n - 1)
+            for sl in base:
+                ret += (sl + (slice(None),),)
+                ret += (sl + (slice(0, 1),),)
+            return ret
+
+        def broadcastable(s1, s2):
+            return s1 == s2 or 1 in {s1, s2}
+
+        permute_3 = permute_n(3)
+        slice_3 = slice_n(3) + ((slice(None, None, -1),) * 3,)
+
+        ref = True
+        for p1 in permute_3:
+            for p2 in permute_3:
+                for s1 in slice_3:
+                    for s2 in slice_3:
+                        a1 = d1.transpose(p1)[s1]
+                        a2 = d2.transpose(p2)[s2]
+                        ref = ref and a1.base is not None
+                        ref = ref and a2.base is not None
+                        if (a1.shape[-1] == a2.shape[-2] and
+                                broadcastable(a1.shape[0], a2.shape[0])):
+                            assert_array_almost_equal(
+                                umt.matrix_multiply(a1, a2),
+                                np.sum(a2[..., np.newaxis].swapaxes(-3, -1) *
+                                       a1[..., np.newaxis, :], axis=-1),
+                                err_msg=msg + f' {str(a1.shape)} {str(a2.shape)}')
+
+        assert_equal(ref, True, err_msg="reference check")
+
+    def test_euclidean_pdist(self):
+        a = np.arange(12, dtype=float).reshape(4, 3)
+        out = np.empty((a.shape[0] * (a.shape[0] - 1) // 2,), dtype=a.dtype)
+        umt.euclidean_pdist(a, out)
+        b = np.sqrt(np.sum((a[:, None] - a)**2, axis=-1))
+        b = b[~np.tri(a.shape[0], dtype=bool)]
+        assert_almost_equal(out, b)
+        # An output array is required to determine p with signature (n,d)->(p)
+        assert_raises(ValueError, umt.euclidean_pdist, a)
+
+    def test_cumsum(self):
+        a = np.arange(10)
+        result = umt.cumsum(a)
+        assert_array_equal(result, a.cumsum())
+
+    def test_object_logical(self):
+        a = np.array([3, None, True, False, "test", ""], dtype=object)
+        assert_equal(np.logical_or(a, None),
+                        np.array([x or None for x in a], dtype=object))
+        assert_equal(np.logical_or(a, True),
+                        np.array([x or True for x in a], dtype=object))
+        assert_equal(np.logical_or(a, 12),
+                        np.array([x or 12 for x in a], dtype=object))
+        assert_equal(np.logical_or(a, "blah"),
+                        np.array([x or "blah" for x in a], dtype=object))
+
+        assert_equal(np.logical_and(a, None),
+                        np.array([x and None for x in a], dtype=object))
+        assert_equal(np.logical_and(a, True),
+                        np.array([x and True for x in a], dtype=object))
+        assert_equal(np.logical_and(a, 12),
+                        np.array([x and 12 for x in a], dtype=object))
+        assert_equal(np.logical_and(a, "blah"),
+                        np.array([x and "blah" for x in a], dtype=object))
+
+        assert_equal(np.logical_not(a),
+                        np.array([not x for x in a], dtype=object))
+
+        assert_equal(np.logical_or.reduce(a), 3)
+        assert_equal(np.logical_and.reduce(a), None)
+
+    def test_object_comparison(self):
+        class HasComparisons:
+            def __eq__(self, other):
+                return '=='
+
+        arr0d = np.array(HasComparisons())
+        assert_equal(arr0d == arr0d, True)
+        assert_equal(np.equal(arr0d, arr0d), True)  # normal behavior is a cast
+
+        arr1d = np.array([HasComparisons()])
+        assert_equal(arr1d == arr1d, np.array([True]))
+        assert_equal(np.equal(arr1d, arr1d), np.array([True]))  # normal behavior is a cast
+        assert_equal(np.equal(arr1d, arr1d, dtype=object), np.array(['==']))
+
+    def test_object_array_reduction(self):
+        # Reductions on object arrays
+        a = np.array(['a', 'b', 'c'], dtype=object)
+        assert_equal(np.sum(a), 'abc')
+        assert_equal(np.max(a), 'c')
+        assert_equal(np.min(a), 'a')
+        a = np.array([True, False, True], dtype=object)
+        assert_equal(np.sum(a), 2)
+        assert_equal(np.prod(a), 0)
+        assert_equal(np.any(a), True)
+        assert_equal(np.all(a), False)
+        assert_equal(np.max(a), True)
+        assert_equal(np.min(a), False)
+        assert_equal(np.array([[1]], dtype=object).sum(), 1)
+        assert_equal(np.array([[[1, 2]]], dtype=object).sum((0, 1)), [1, 2])
+        assert_equal(np.array([1], dtype=object).sum(initial=1), 2)
+        assert_equal(np.array([[1], [2, 3]], dtype=object)
+                     .sum(initial=[0], where=[False, True]), [0, 2, 3])
+
+    def test_object_array_accumulate_inplace(self):
+        # Checks that in-place accumulates work, see also gh-7402
+        arr = np.ones(4, dtype=object)
+        arr[:] = [[1] for i in range(4)]
+        # Twice reproduced also for tuples:
+        np.add.accumulate(arr, out=arr)
+        np.add.accumulate(arr, out=arr)
+        assert_array_equal(arr,
+                           np.array([[1] * i for i in [1, 3, 6, 10]], dtype=object),
+                          )
+
+        # And the same if the axis argument is used
+        arr = np.ones((2, 4), dtype=object)
+        arr[0, :] = [[2] for i in range(4)]
+        np.add.accumulate(arr, out=arr, axis=-1)
+        np.add.accumulate(arr, out=arr, axis=-1)
+        assert_array_equal(arr[0, :],
+                           np.array([[2] * i for i in [1, 3, 6, 10]], dtype=object),
+                          )
+
+    def test_object_array_accumulate_failure(self):
+        # Typical accumulation on object works as expected:
+        res = np.add.accumulate(np.array([1, 0, 2], dtype=object))
+        assert_array_equal(res, np.array([1, 1, 3], dtype=object))
+        # But errors are propagated from the inner-loop if they occur:
+        with pytest.raises(TypeError):
+            np.add.accumulate([1, None, 2])
+
+    def test_object_array_reduceat_inplace(self):
+        # Checks that in-place reduceats work, see also gh-7465
+        arr = np.empty(4, dtype=object)
+        arr[:] = [[1] for i in range(4)]
+        out = np.empty(4, dtype=object)
+        out[:] = [[1] for i in range(4)]
+        np.add.reduceat(arr, np.arange(4), out=arr)
+        np.add.reduceat(arr, np.arange(4), out=arr)
+        assert_array_equal(arr, out)
+
+        # And the same if the axis argument is used
+        arr = np.ones((2, 4), dtype=object)
+        arr[0, :] = [[2] for i in range(4)]
+        out = np.ones((2, 4), dtype=object)
+        out[0, :] = [[2] for i in range(4)]
+        np.add.reduceat(arr, np.arange(4), out=arr, axis=-1)
+        np.add.reduceat(arr, np.arange(4), out=arr, axis=-1)
+        assert_array_equal(arr, out)
+
+    def test_object_array_reduceat_failure(self):
+        # Reduceat works as expected when no invalid operation occurs (None is
+        # not involved in an operation here)
+        res = np.add.reduceat(np.array([1, None, 2], dtype=object), [1, 2])
+        assert_array_equal(res, np.array([None, 2], dtype=object))
+        # But errors when None would be involved in an operation:
+        with pytest.raises(TypeError):
+            np.add.reduceat([1, None, 2], [0, 2])
+
+    def test_zerosize_reduction(self):
+        # Test with default dtype and object dtype
+        for a in [[], np.array([], dtype=object)]:
+            assert_equal(np.sum(a), 0)
+            assert_equal(np.prod(a), 1)
+            assert_equal(np.any(a), False)
+            assert_equal(np.all(a), True)
+            assert_raises(ValueError, np.max, a)
+            assert_raises(ValueError, np.min, a)
+
+    def test_axis_out_of_bounds(self):
+        a = np.array([False, False])
+        assert_raises(AxisError, a.all, axis=1)
+        a = np.array([False, False])
+        assert_raises(AxisError, a.all, axis=-2)
+
+        a = np.array([False, False])
+        assert_raises(AxisError, a.any, axis=1)
+        a = np.array([False, False])
+        assert_raises(AxisError, a.any, axis=-2)
+
+    def test_scalar_reduction(self):
+        # The functions 'sum', 'prod', etc allow specifying axis=0
+        # even for scalars
+        assert_equal(np.sum(3, axis=0), 3)
+        assert_equal(np.prod(3.5, axis=0), 3.5)
+        assert_equal(np.any(True, axis=0), True)
+        assert_equal(np.all(False, axis=0), False)
+        assert_equal(np.max(3, axis=0), 3)
+        assert_equal(np.min(2.5, axis=0), 2.5)
+
+        # Check scalar behaviour for ufuncs without an identity
+        assert_equal(np.power.reduce(3), 3)
+
+        # Make sure that scalars are coming out from this operation
+        assert_(type(np.prod(np.float32(2.5), axis=0)) is np.float32)
+        assert_(type(np.sum(np.float32(2.5), axis=0)) is np.float32)
+        assert_(type(np.max(np.float32(2.5), axis=0)) is np.float32)
+        assert_(type(np.min(np.float32(2.5), axis=0)) is np.float32)
+
+        # check if scalars/0-d arrays get cast
+        assert_(type(np.any(0, axis=0)) is np.bool)
+
+        # assert that 0-d arrays get wrapped
+        class MyArray(np.ndarray):
+            pass
+        a = np.array(1).view(MyArray)
+        assert_(type(np.any(a)) is MyArray)
+
+    def test_casting_out_param(self):
+        # Test that it's possible to do casts on output
+        a = np.ones((200, 100), np.int64)
+        b = np.ones((200, 100), np.int64)
+        c = np.ones((200, 100), np.float64)
+        np.add(a, b, out=c)
+        assert_equal(c, 2)
+
+        a = np.zeros(65536)
+        b = np.zeros(65536, dtype=np.float32)
+        np.subtract(a, 0, out=b)
+        assert_equal(b, 0)
+
+    def test_where_param(self):
+        # Test that the where= ufunc parameter works with regular arrays
+        a = np.arange(7)
+        b = np.ones(7)
+        c = np.zeros(7)
+        np.add(a, b, out=c, where=(a % 2 == 1))
+        assert_equal(c, [0, 2, 0, 4, 0, 6, 0])
+
+        a = np.arange(4).reshape(2, 2) + 2
+        np.power(a, [2, 3], out=a, where=[[0, 1], [1, 0]])
+        assert_equal(a, [[2, 27], [16, 5]])
+        # Broadcasting the where= parameter
+        np.subtract(a, 2, out=a, where=[True, False])
+        assert_equal(a, [[0, 27], [14, 5]])
+
+    def test_where_param_buffer_output(self):
+        # This test is temporarily skipped because it requires
+        # adding masking features to the nditer to work properly
+
+        # With casting on output
+        a = np.ones(10, np.int64)
+        b = np.ones(10, np.int64)
+        c = 1.5 * np.ones(10, np.float64)
+        np.add(a, b, out=c, where=[1, 0, 0, 1, 0, 0, 1, 1, 1, 0])
+        assert_equal(c, [2, 1.5, 1.5, 2, 1.5, 1.5, 2, 2, 2, 1.5])
+
+    def test_where_param_alloc(self):
+        # With casting and allocated output
+        a = np.array([1], dtype=np.int64)
+        m = np.array([True], dtype=bool)
+        assert_equal(np.sqrt(a, where=m), [1])
+
+        # No casting and allocated output
+        a = np.array([1], dtype=np.float64)
+        m = np.array([True], dtype=bool)
+        assert_equal(np.sqrt(a, where=m), [1])
+
+    def test_where_with_broadcasting(self):
+        # See gh-17198
+        a = np.random.random((5000, 4))
+        b = np.random.random((5000, 1))
+
+        where = a > 0.3
+        out = np.full_like(a, 0)
+        np.less(a, b, where=where, out=out)
+        b_where = np.broadcast_to(b, a.shape)[where]
+        assert_array_equal((a[where] < b_where), out[where].astype(bool))
+        assert not out[~where].any()  # outside mask, out remains all 0
+
+    @staticmethod
+    def identityless_reduce_arrs():
+        yield np.empty((2, 3, 4), order='C')
+        yield np.empty((2, 3, 4), order='F')
+        # Mixed order (reduce order differs outer)
+        yield np.empty((2, 4, 3), order='C').swapaxes(1, 2)
+        # Reversed order
+        yield np.empty((2, 3, 4), order='C')[::-1, ::-1, ::-1]
+        # Not contiguous
+        yield np.empty((3, 5, 4), order='C').swapaxes(1, 2)[1:, 1:, 1:]
+        # Not contiguous and not aligned
+        a = np.empty((3 * 4 * 5 * 8 + 1,), dtype='i1')
+        a = a[1:].view(dtype='f8')
+        a.shape = (3, 4, 5)
+        a = a[1:, 1:, 1:]
+        yield a
+
+    @pytest.mark.parametrize("a", identityless_reduce_arrs())
+    @pytest.mark.parametrize("pos", [(1, 0, 0), (0, 1, 0), (0, 0, 1)])
+    def test_identityless_reduction(self, a, pos):
+        # np.minimum.reduce is an identityless reduction
+        a[...] = 1
+        a[pos] = 0
+
+        for axis in [None, (0, 1), (0, 2), (1, 2), 0, 1, 2, ()]:
+            if axis is None:
+                axes = np.array([], dtype=np.intp)
+            else:
+                axes = np.delete(np.arange(a.ndim), axis)
+
+            expected_pos = tuple(np.array(pos)[axes])
+            expected = np.ones(np.array(a.shape)[axes])
+            expected[expected_pos] = 0
+
+            res = np.minimum.reduce(a, axis=axis)
+            assert_equal(res, expected, strict=True)
+
+            res = np.full_like(res, np.nan)
+            np.minimum.reduce(a, axis=axis, out=res)
+            assert_equal(res, expected, strict=True)
+
+    @requires_memory(6 * 1024**3)
+    @pytest.mark.skipif(sys.maxsize < 2**32,
+            reason="test array too large for 32bit platform")
+    def test_identityless_reduction_huge_array(self):
+        # Regression test for gh-20921 (copying identity incorrectly failed)
+        arr = np.zeros((2, 2**31), 'uint8')
+        arr[:, 0] = [1, 3]
+        arr[:, -1] = [4, 1]
+        res = np.maximum.reduce(arr, axis=0)
+        del arr
+        assert res[0] == 3
+        assert res[-1] == 4
+
+    def test_reduce_identity_depends_on_loop(self):
+        """
+        The type of the result should always depend on the selected loop, not
+        necessarily the output (only relevant for object arrays).
+        """
+        # For an object loop, the default value 0 with type int is used:
+        assert type(np.add.reduce([], dtype=object)) is int
+        out = np.array(None, dtype=object)
+        # When the loop is float64 but `out` is object this does not happen,
+        # the result is float64 cast to object (which gives Python `float`).
+        np.add.reduce([], out=out, dtype=np.float64)
+        assert type(out[()]) is float
+
+    def test_initial_reduction(self):
+        # np.minimum.reduce is an identityless reduction
+
+        # For cases like np.maximum(np.abs(...), initial=0)
+        # More generally, a supremum over non-negative numbers.
+        assert_equal(np.maximum.reduce([], initial=0), 0)
+
+        # For cases like reduction of an empty array over the reals.
+        assert_equal(np.minimum.reduce([], initial=np.inf), np.inf)
+        assert_equal(np.maximum.reduce([], initial=-np.inf), -np.inf)
+
+        # Random tests
+        assert_equal(np.minimum.reduce([5], initial=4), 4)
+        assert_equal(np.maximum.reduce([4], initial=5), 5)
+        assert_equal(np.maximum.reduce([5], initial=4), 5)
+        assert_equal(np.minimum.reduce([4], initial=5), 4)
+
+        # Check initial=None raises ValueError for both types of ufunc reductions
+        assert_raises(ValueError, np.minimum.reduce, [], initial=None)
+        assert_raises(ValueError, np.add.reduce, [], initial=None)
+        # Also in the somewhat special object case:
+        with pytest.raises(ValueError):
+            np.add.reduce([], initial=None, dtype=object)
+
+        # Check that np._NoValue gives default behavior.
+        assert_equal(np.add.reduce([], initial=np._NoValue), 0)
+
+        # Check that initial kwarg behaves as intended for dtype=object
+        a = np.array([10], dtype=object)
+        res = np.add.reduce(a, initial=5)
+        assert_equal(res, 15)
+
+    def test_empty_reduction_and_identity(self):
+        arr = np.zeros((0, 5))
+        # OK, since the reduction itself is *not* empty, the result is
+        assert np.true_divide.reduce(arr, axis=1).shape == (0,)
+        # Not OK, the reduction itself is empty and we have no identity
+        with pytest.raises(ValueError):
+            np.true_divide.reduce(arr, axis=0)
+
+        # Test that an empty reduction fails also if the result is empty
+        arr = np.zeros((0, 0, 5))
+        with pytest.raises(ValueError):
+            np.true_divide.reduce(arr, axis=1)
+
+        # Division reduction makes sense with `initial=1` (empty or not):
+        res = np.true_divide.reduce(arr, axis=1, initial=1)
+        assert_array_equal(res, np.ones((0, 5)))
+
+    @pytest.mark.parametrize('axis', (0, 1, None))
+    @pytest.mark.parametrize('where', (np.array([False, True, True]),
+                                       np.array([[True], [False], [True]]),
+                                       np.array([[True, False, False],
+                                                 [False, True, False],
+                                                 [False, True, True]])))
+    def test_reduction_with_where(self, axis, where):
+        a = np.arange(9.).reshape(3, 3)
+        a_copy = a.copy()
+        a_check = np.zeros_like(a)
+        np.positive(a, out=a_check, where=where)
+
+        res = np.add.reduce(a, axis=axis, where=where)
+        check = a_check.sum(axis)
+        assert_equal(res, check)
+        # Check we do not overwrite elements of a internally.
+        assert_array_equal(a, a_copy)
+
+    @pytest.mark.parametrize(('axis', 'where'),
+                             ((0, np.array([True, False, True])),
+                              (1, [True, True, False]),
+                              (None, True)))
+    @pytest.mark.parametrize('initial', (-np.inf, 5.))
+    def test_reduction_with_where_and_initial(self, axis, where, initial):
+        a = np.arange(9.).reshape(3, 3)
+        a_copy = a.copy()
+        a_check = np.full(a.shape, -np.inf)
+        np.positive(a, out=a_check, where=where)
+
+        res = np.maximum.reduce(a, axis=axis, where=where, initial=initial)
+        check = a_check.max(axis, initial=initial)
+        assert_equal(res, check)
+
+    def test_reduction_where_initial_needed(self):
+        a = np.arange(9.).reshape(3, 3)
+        m = [False, True, False]
+        assert_raises(ValueError, np.maximum.reduce, a, where=m)
+
+    def test_identityless_reduction_nonreorderable(self):
+        a = np.array([[8.0, 2.0, 2.0], [1.0, 0.5, 0.25]])
+
+        res = np.divide.reduce(a, axis=0)
+        assert_equal(res, [8.0, 4.0, 8.0])
+
+        res = np.divide.reduce(a, axis=1)
+        assert_equal(res, [2.0, 8.0])
+
+        res = np.divide.reduce(a, axis=())
+        assert_equal(res, a)
+
+        assert_raises(ValueError, np.divide.reduce, a, axis=(0, 1))
+
+    def test_reduce_zero_axis(self):
+        # If we have a n x m array and do a reduction with axis=1, then we are
+        # doing n reductions, and each reduction takes an m-element array. For
+        # a reduction operation without an identity, then:
+        #   n > 0, m > 0: fine
+        #   n = 0, m > 0: fine, doing 0 reductions of m-element arrays
+        #   n > 0, m = 0: can't reduce a 0-element array, ValueError
+        #   n = 0, m = 0: can't reduce a 0-element array, ValueError (for
+        #     consistency with the above case)
+        # This test doesn't actually look at return values, it just checks to
+        # make sure that error we get an error in exactly those cases where we
+        # expect one, and assumes the calculations themselves are done
+        # correctly.
+
+        def ok(f, *args, **kwargs):
+            f(*args, **kwargs)
+
+        def err(f, *args, **kwargs):
+            assert_raises(ValueError, f, *args, **kwargs)
+
+        def t(expect, func, n, m):
+            expect(func, np.zeros((n, m)), axis=1)
+            expect(func, np.zeros((m, n)), axis=0)
+            expect(func, np.zeros((n // 2, n // 2, m)), axis=2)
+            expect(func, np.zeros((n // 2, m, n // 2)), axis=1)
+            expect(func, np.zeros((n, m // 2, m // 2)), axis=(1, 2))
+            expect(func, np.zeros((m // 2, n, m // 2)), axis=(0, 2))
+            expect(func, np.zeros((m // 3, m // 3, m // 3,
+                                  n // 2, n // 2)),
+                                 axis=(0, 1, 2))
+            # Check what happens if the inner (resp. outer) dimensions are a
+            # mix of zero and non-zero:
+            expect(func, np.zeros((10, m, n)), axis=(0, 1))
+            expect(func, np.zeros((10, n, m)), axis=(0, 2))
+            expect(func, np.zeros((m, 10, n)), axis=0)
+            expect(func, np.zeros((10, m, n)), axis=1)
+            expect(func, np.zeros((10, n, m)), axis=2)
+
+        # np.maximum is just an arbitrary ufunc with no reduction identity
+        assert_equal(np.maximum.identity, None)
+        t(ok, np.maximum.reduce, 30, 30)
+        t(ok, np.maximum.reduce, 0, 30)
+        t(err, np.maximum.reduce, 30, 0)
+        t(err, np.maximum.reduce, 0, 0)
+        err(np.maximum.reduce, [])
+        np.maximum.reduce(np.zeros((0, 0)), axis=())
+
+        # all of the combinations are fine for a reduction that has an
+        # identity
+        t(ok, np.add.reduce, 30, 30)
+        t(ok, np.add.reduce, 0, 30)
+        t(ok, np.add.reduce, 30, 0)
+        t(ok, np.add.reduce, 0, 0)
+        np.add.reduce([])
+        np.add.reduce(np.zeros((0, 0)), axis=())
+
+        # OTOH, accumulate always makes sense for any combination of n and m,
+        # because it maps an m-element array to an m-element array. These
+        # tests are simpler because accumulate doesn't accept multiple axes.
+        for uf in (np.maximum, np.add):
+            uf.accumulate(np.zeros((30, 0)), axis=0)
+            uf.accumulate(np.zeros((0, 30)), axis=0)
+            uf.accumulate(np.zeros((30, 30)), axis=0)
+            uf.accumulate(np.zeros((0, 0)), axis=0)
+
+    def test_safe_casting(self):
+        # In old versions of numpy, in-place operations used the 'unsafe'
+        # casting rules. In versions >= 1.10, 'same_kind' is the
+        # default and an exception is raised instead of a warning.
+        # when 'same_kind' is not satisfied.
+        a = np.array([1, 2, 3], dtype=int)
+        # Non-in-place addition is fine
+        assert_array_equal(assert_no_warnings(np.add, a, 1.1),
+                           [2.1, 3.1, 4.1])
+        assert_raises(TypeError, np.add, a, 1.1, out=a)
+
+        def add_inplace(a, b):
+            a += b
+
+        assert_raises(TypeError, add_inplace, a, 1.1)
+        # Make sure that explicitly overriding the exception is allowed:
+        assert_no_warnings(np.add, a, 1.1, out=a, casting="unsafe")
+        assert_array_equal(a, [2, 3, 4])
+
+    def test_ufunc_custom_out(self):
+        # Test ufunc with built in input types and custom output type
+
+        a = np.array([0, 1, 2], dtype='i8')
+        b = np.array([0, 1, 2], dtype='i8')
+        c = np.empty(3, dtype=_rational_tests.rational)
+
+        # Output must be specified so numpy knows what
+        # ufunc signature to look for
+        result = _rational_tests.test_add(a, b, c)
+        target = np.array([0, 2, 4], dtype=_rational_tests.rational)
+        assert_equal(result, target)
+
+        # The new resolution means that we can (usually) find custom loops
+        # as long as they match exactly:
+        result = _rational_tests.test_add(a, b)
+        assert_equal(result, target)
+
+        # This works even more generally, so long the default common-dtype
+        # promoter works out:
+        result = _rational_tests.test_add(a, b.astype(np.uint16), out=c)
+        assert_equal(result, target)
+
+        # This scalar path used to go into legacy promotion, but doesn't now:
+        result = _rational_tests.test_add(a, np.uint16(2))
+        target = np.array([2, 3, 4], dtype=_rational_tests.rational)
+        assert_equal(result, target)
+
+    def test_operand_flags(self):
+        a = np.arange(16, dtype=int).reshape(4, 4)
+        b = np.arange(9, dtype=int).reshape(3, 3)
+        opflag_tests.inplace_add(a[:-1, :-1], b)
+        assert_equal(a, np.array([[0, 2, 4, 3], [7, 9, 11, 7],
+            [14, 16, 18, 11], [12, 13, 14, 15]]))
+
+        a = np.array(0)
+        opflag_tests.inplace_add(a, 3)
+        assert_equal(a, 3)
+        opflag_tests.inplace_add(a, [3, 4])
+        assert_equal(a, 10)
+
+    def test_struct_ufunc(self):
+        import numpy._core._struct_ufunc_tests as struct_ufunc
+
+        a = np.array([(1, 2, 3)], dtype='u8,u8,u8')
+        b = np.array([(1, 2, 3)], dtype='u8,u8,u8')
+
+        result = struct_ufunc.add_triplet(a, b)
+        assert_equal(result, np.array([(2, 4, 6)], dtype='u8,u8,u8'))
+        assert_raises(RuntimeError, struct_ufunc.register_fail)
+
+    def test_custom_ufunc(self):
+        a = np.array(
+            [_rational_tests.rational(1, 2),
+             _rational_tests.rational(1, 3),
+             _rational_tests.rational(1, 4)],
+            dtype=_rational_tests.rational)
+        b = np.array(
+            [_rational_tests.rational(1, 2),
+             _rational_tests.rational(1, 3),
+             _rational_tests.rational(1, 4)],
+            dtype=_rational_tests.rational)
+
+        result = _rational_tests.test_add_rationals(a, b)
+        expected = np.array(
+            [_rational_tests.rational(1),
+             _rational_tests.rational(2, 3),
+             _rational_tests.rational(1, 2)],
+            dtype=_rational_tests.rational)
+        assert_equal(result, expected)
+
+    def test_custom_ufunc_forced_sig(self):
+        # gh-9351 - looking for a non-first userloop would previously hang
+        with assert_raises(TypeError):
+            np.multiply(_rational_tests.rational(1), 1,
+                        signature=(_rational_tests.rational, int, None))
+
+    def test_custom_array_like(self):
+
+        class MyThing:
+            __array_priority__ = 1000
+
+            rmul_count = 0
+            getitem_count = 0
+
+            def __init__(self, shape):
+                self.shape = shape
+
+            def __len__(self):
+                return self.shape[0]
+
+            def __getitem__(self, i):
+                MyThing.getitem_count += 1
+                if not isinstance(i, tuple):
+                    i = (i,)
+                if len(i) > self.ndim:
+                    raise IndexError("boo")
+
+                return MyThing(self.shape[len(i):])
+
+            def __rmul__(self, other):
+                MyThing.rmul_count += 1
+                return self
+
+        np.float64(5) * MyThing((3, 3))
+        assert_(MyThing.rmul_count == 1, MyThing.rmul_count)
+        assert_(MyThing.getitem_count <= 2, MyThing.getitem_count)
+
+    def test_array_wrap_array_priority(self):
+        class ArrayPriorityBase(np.ndarray):
+            @classmethod
+            def __array_wrap__(cls, array, context=None, return_scalar=False):
+                return cls
+
+        class ArrayPriorityMinus0(ArrayPriorityBase):
+            __array_priority__ = 0
+
+        class ArrayPriorityMinus1000(ArrayPriorityBase):
+            __array_priority__ = -1000
+
+        class ArrayPriorityMinus1000b(ArrayPriorityBase):
+            __array_priority__ = -1000
+
+        class ArrayPriorityMinus2000(ArrayPriorityBase):
+            __array_priority__ = -2000
+
+        x = np.ones(2).view(ArrayPriorityMinus1000)
+        xb = np.ones(2).view(ArrayPriorityMinus1000b)
+        y = np.ones(2).view(ArrayPriorityMinus2000)
+
+        assert np.add(x, y) is ArrayPriorityMinus1000
+        assert np.add(y, x) is ArrayPriorityMinus1000
+        assert np.add(x, xb) is ArrayPriorityMinus1000
+        assert np.add(xb, x) is ArrayPriorityMinus1000b
+        y_minus0 = np.zeros(2).view(ArrayPriorityMinus0)
+        assert np.add(np.zeros(2), y_minus0) is ArrayPriorityMinus0
+        assert type(np.add(xb, x, np.zeros(2))) is np.ndarray
+
+    @pytest.mark.parametrize("a", (
+                             np.arange(10, dtype=int),
+                             np.arange(10, dtype=_rational_tests.rational),
+                             ))
+    def test_ufunc_at_basic(self, a):
+
+        aa = a.copy()
+        np.add.at(aa, [2, 5, 2], 1)
+        assert_equal(aa, [0, 1, 4, 3, 4, 6, 6, 7, 8, 9])
+
+        with pytest.raises(ValueError):
+            # missing second operand
+            np.add.at(aa, [2, 5, 3])
+
+        aa = a.copy()
+        np.negative.at(aa, [2, 5, 3])
+        assert_equal(aa, [0, 1, -2, -3, 4, -5, 6, 7, 8, 9])
+
+        aa = a.copy()
+        b = np.array([100, 100, 100])
+        np.add.at(aa, [2, 5, 2], b)
+        assert_equal(aa, [0, 1, 202, 3, 4, 105, 6, 7, 8, 9])
+
+        with pytest.raises(ValueError):
+            # extraneous second operand
+            np.negative.at(a, [2, 5, 3], [1, 2, 3])
+
+        with pytest.raises(ValueError):
+            # second operand cannot be converted to an array
+            np.add.at(a, [2, 5, 3], [[1, 2], 1])
+
+    # ufuncs with indexed loops for performance in ufunc.at
+    indexed_ufuncs = [np.add, np.subtract, np.multiply, np.floor_divide,
+                      np.maximum, np.minimum, np.fmax, np.fmin]
+
+    @pytest.mark.parametrize(
+                "typecode", np.typecodes['AllInteger'] + np.typecodes['Float'])
+    @pytest.mark.parametrize("ufunc", indexed_ufuncs)
+    def test_ufunc_at_inner_loops(self, typecode, ufunc):
+        if ufunc is np.divide and typecode in np.typecodes['AllInteger']:
+            # Avoid divide-by-zero and inf for integer divide
+            a = np.ones(100, dtype=typecode)
+            indx = np.random.randint(100, size=30, dtype=np.intp)
+            vals = np.arange(1, 31, dtype=typecode)
+        else:
+            a = np.ones(1000, dtype=typecode)
+            indx = np.random.randint(1000, size=3000, dtype=np.intp)
+            vals = np.arange(3000, dtype=typecode)
+        atag = a.copy()
+        # Do the calculation twice and compare the answers
+        with warnings.catch_warnings(record=True) as w_at:
+            warnings.simplefilter('always')
+            ufunc.at(a, indx, vals)
+        with warnings.catch_warnings(record=True) as w_loop:
+            warnings.simplefilter('always')
+            for i, v in zip(indx, vals):
+                # Make sure all the work happens inside the ufunc
+                # in order to duplicate error/warning handling
+                ufunc(atag[i], v, out=atag[i:i + 1], casting="unsafe")
+        assert_equal(atag, a)
+        # If w_loop warned, make sure w_at warned as well
+        if len(w_loop) > 0:
+            #
+            assert len(w_at) > 0
+            assert w_at[0].category == w_loop[0].category
+            assert str(w_at[0].message)[:10] == str(w_loop[0].message)[:10]
+
+    @pytest.mark.parametrize("typecode", np.typecodes['Complex'])
+    @pytest.mark.parametrize("ufunc", [np.add, np.subtract, np.multiply])
+    def test_ufunc_at_inner_loops_complex(self, typecode, ufunc):
+        a = np.ones(10, dtype=typecode)
+        indx = np.concatenate([np.ones(6, dtype=np.intp),
+                               np.full(18, 4, dtype=np.intp)])
+        value = a.dtype.type(1j)
+        ufunc.at(a, indx, value)
+        expected = np.ones_like(a)
+        if ufunc is np.multiply:
+            expected[1] = expected[4] = -1
+        else:
+            expected[1] += 6 * (value if ufunc is np.add else -value)
+            expected[4] += 18 * (value if ufunc is np.add else -value)
+
+        assert_array_equal(a, expected)
+
+    def test_ufunc_at_ellipsis(self):
+        # Make sure the indexed loop check does not choke on iters
+        # with subspaces
+        arr = np.zeros(5)
+        np.add.at(arr, slice(None), np.ones(5))
+        assert_array_equal(arr, np.ones(5))
+
+    def test_ufunc_at_negative(self):
+        arr = np.ones(5, dtype=np.int32)
+        indx = np.arange(5)
+        umt.indexed_negative.at(arr, indx)
+        # If it is [-1, -1, -1, -100, 0] then the regular strided loop was used
+        assert np.all(arr == [-1, -1, -1, -200, -1])
+
+    def test_ufunc_at_large(self):
+        # issue gh-23457
+        indices = np.zeros(8195, dtype=np.int16)
+        b = np.zeros(8195, dtype=float)
+        b[0] = 10
+        b[1] = 5
+        b[8192:] = 100
+        a = np.zeros(1, dtype=float)
+        np.add.at(a, indices, b)
+        assert a[0] == b.sum()
+
+    def test_cast_index_fastpath(self):
+        arr = np.zeros(10)
+        values = np.ones(100000)
+        # index must be cast, which may be buffered in chunks:
+        index = np.zeros(len(values), dtype=np.uint8)
+        np.add.at(arr, index, values)
+        assert arr[0] == len(values)
+
+    @pytest.mark.parametrize("value", [
+        np.ones(1), np.ones(()), np.float64(1.), 1.])
+    def test_ufunc_at_scalar_value_fastpath(self, value):
+        arr = np.zeros(1000)
+        # index must be cast, which may be buffered in chunks:
+        index = np.repeat(np.arange(1000), 2)
+        np.add.at(arr, index, value)
+        assert_array_equal(arr, np.full_like(arr, 2 * value))
+
+    def test_ufunc_at_multiD(self):
+        a = np.arange(9).reshape(3, 3)
+        b = np.array([[100, 100, 100], [200, 200, 200], [300, 300, 300]])
+        np.add.at(a, (slice(None), [1, 2, 1]), b)
+        assert_equal(a, [[0, 201, 102], [3, 404, 205], [6, 607, 308]])
+
+        a = np.arange(27).reshape(3, 3, 3)
+        b = np.array([100, 200, 300])
+        np.add.at(a, (slice(None), slice(None), [1, 2, 1]), b)
+        assert_equal(a,
+            [[[0, 401, 202],
+              [3, 404, 205],
+              [6, 407, 208]],
+
+             [[9, 410, 211],
+              [12, 413, 214],
+              [15, 416, 217]],
+
+             [[18, 419, 220],
+              [21, 422, 223],
+              [24, 425, 226]]])
+
+        a = np.arange(9).reshape(3, 3)
+        b = np.array([[100, 100, 100], [200, 200, 200], [300, 300, 300]])
+        np.add.at(a, ([1, 2, 1], slice(None)), b)
+        assert_equal(a, [[0, 1, 2], [403, 404, 405], [206, 207, 208]])
+
+        a = np.arange(27).reshape(3, 3, 3)
+        b = np.array([100, 200, 300])
+        np.add.at(a, (slice(None), [1, 2, 1], slice(None)), b)
+        assert_equal(a,
+            [[[0,  1,  2],
+              [203, 404, 605],
+              [106, 207, 308]],
+
+             [[9,  10, 11],
+              [212, 413, 614],
+              [115, 216, 317]],
+
+             [[18, 19, 20],
+              [221, 422, 623],
+              [124, 225, 326]]])
+
+        a = np.arange(9).reshape(3, 3)
+        b = np.array([100, 200, 300])
+        np.add.at(a, (0, [1, 2, 1]), b)
+        assert_equal(a, [[0, 401, 202], [3, 4, 5], [6, 7, 8]])
+
+        a = np.arange(27).reshape(3, 3, 3)
+        b = np.array([100, 200, 300])
+        np.add.at(a, ([1, 2, 1], 0, slice(None)), b)
+        assert_equal(a,
+            [[[0,  1,  2],
+              [3,  4,  5],
+              [6,  7,  8]],
+
+             [[209, 410, 611],
+              [12,  13, 14],
+              [15,  16, 17]],
+
+             [[118, 219, 320],
+              [21,  22, 23],
+              [24,  25, 26]]])
+
+        a = np.arange(27).reshape(3, 3, 3)
+        b = np.array([100, 200, 300])
+        np.add.at(a, (slice(None), slice(None), slice(None)), b)
+        assert_equal(a,
+            [[[100, 201, 302],
+              [103, 204, 305],
+              [106, 207, 308]],
+
+             [[109, 210, 311],
+              [112, 213, 314],
+              [115, 216, 317]],
+
+             [[118, 219, 320],
+              [121, 222, 323],
+              [124, 225, 326]]])
+
+    def test_ufunc_at_0D(self):
+        a = np.array(0)
+        np.add.at(a, (), 1)
+        assert_equal(a, 1)
+
+        assert_raises(IndexError, np.add.at, a, 0, 1)
+        assert_raises(IndexError, np.add.at, a, [], 1)
+
+    def test_ufunc_at_dtypes(self):
+        # Test mixed dtypes
+        a = np.arange(10)
+        np.power.at(a, [1, 2, 3, 2], 3.5)
+        assert_equal(a, np.array([0, 1, 4414, 46, 4, 5, 6, 7, 8, 9]))
+
+    def test_ufunc_at_boolean(self):
+        # Test boolean indexing and boolean ufuncs
+        a = np.arange(10)
+        index = a % 2 == 0
+        np.equal.at(a, index, [0, 2, 4, 6, 8])
+        assert_equal(a, [1, 1, 1, 3, 1, 5, 1, 7, 1, 9])
+
+        # Test unary operator
+        a = np.arange(10, dtype='u4')
+        np.invert.at(a, [2, 5, 2])
+        assert_equal(a, [0, 1, 2, 3, 4, 5 ^ 0xffffffff, 6, 7, 8, 9])
+
+    def test_ufunc_at_advanced(self):
+        # Test empty subspace
+        orig = np.arange(4)
+        a = orig[:, None][:, 0:0]
+        np.add.at(a, [0, 1], 3)
+        assert_array_equal(orig, np.arange(4))
+
+        # Test with swapped byte order
+        index = np.array([1, 2, 1], np.dtype('i').newbyteorder())
+        values = np.array([1, 2, 3, 4], np.dtype('f').newbyteorder())
+        np.add.at(values, index, 3)
+        assert_array_equal(values, [1, 8, 6, 4])
+
+        # Test exception thrown
+        values = np.array(['a', 1], dtype=object)
+        assert_raises(TypeError, np.add.at, values, [0, 1], 1)
+        assert_array_equal(values, np.array(['a', 1], dtype=object))
+
+        # Test multiple output ufuncs raise error, gh-5665
+        assert_raises(ValueError, np.modf.at, np.arange(10), [1])
+
+        # Test maximum
+        a = np.array([1, 2, 3])
+        np.maximum.at(a, [0], 0)
+        assert_equal(a, np.array([1, 2, 3]))
+
+    @pytest.mark.parametrize("dtype",
+            np.typecodes['AllInteger'] + np.typecodes['Float'])
+    @pytest.mark.parametrize("ufunc",
+            [np.add, np.subtract, np.divide, np.minimum, np.maximum])
+    def test_at_negative_indexes(self, dtype, ufunc):
+        a = np.arange(0, 10).astype(dtype)
+        indxs = np.array([-1, 1, -1, 2]).astype(np.intp)
+        vals = np.array([1, 5, 2, 10], dtype=a.dtype)
+
+        expected = a.copy()
+        for i, v in zip(indxs, vals):
+            expected[i] = ufunc(expected[i], v)
+
+        ufunc.at(a, indxs, vals)
+        assert_array_equal(a, expected)
+        assert np.all(indxs == [-1, 1, -1, 2])
+
+    def test_at_not_none_signature(self):
+        # Test ufuncs with non-trivial signature raise a TypeError
+        a = np.ones((2, 2, 2))
+        b = np.ones((1, 2, 2))
+        assert_raises(TypeError, np.matmul.at, a, [0], b)
+
+        a = np.array([[[1, 2], [3, 4]]])
+        assert_raises(TypeError, np.linalg._umath_linalg.det.at, a, [0])
+
+    def test_at_no_loop_for_op(self):
+        # str dtype does not have a ufunc loop for np.add
+        arr = np.ones(10, dtype=str)
+        with pytest.raises(np._core._exceptions._UFuncNoLoopError):
+            np.add.at(arr, [0, 1], [0, 1])
+
+    def test_at_output_casting(self):
+        arr = np.array([-1])
+        np.equal.at(arr, [0], [0])
+        assert arr[0] == 0
+
+    def test_at_broadcast_failure(self):
+        arr = np.arange(5)
+        with pytest.raises(ValueError):
+            np.add.at(arr, [0, 1], [1, 2, 3])
+
+    def test_reduce_arguments(self):
+        f = np.add.reduce
+        d = np.ones((5, 2), dtype=int)
+        o = np.ones((2,), dtype=d.dtype)
+        r = o * 5
+        assert_equal(f(d), r)
+        # a, axis=0, dtype=None, out=None, keepdims=False
+        assert_equal(f(d, axis=0), r)
+        assert_equal(f(d, 0), r)
+        assert_equal(f(d, 0, dtype=None), r)
+        assert_equal(f(d, 0, dtype='i'), r)
+        assert_equal(f(d, 0, 'i'), r)
+        assert_equal(f(d, 0, None), r)
+        assert_equal(f(d, 0, None, out=None), r)
+        assert_equal(f(d, 0, None, out=o), r)
+        assert_equal(f(d, 0, None, o), r)
+        assert_equal(f(d, 0, None, None), r)
+        assert_equal(f(d, 0, None, None, keepdims=False), r)
+        assert_equal(f(d, 0, None, None, True), r.reshape((1,) + r.shape))
+        assert_equal(f(d, 0, None, None, False, 0), r)
+        assert_equal(f(d, 0, None, None, False, initial=0), r)
+        assert_equal(f(d, 0, None, None, False, 0, True), r)
+        assert_equal(f(d, 0, None, None, False, 0, where=True), r)
+        # multiple keywords
+        assert_equal(f(d, axis=0, dtype=None, out=None, keepdims=False), r)
+        assert_equal(f(d, 0, dtype=None, out=None, keepdims=False), r)
+        assert_equal(f(d, 0, None, out=None, keepdims=False), r)
+        assert_equal(f(d, 0, None, out=None, keepdims=False, initial=0,
+                       where=True), r)
+
+        # too little
+        assert_raises(TypeError, f)
+        # too much
+        assert_raises(TypeError, f, d, 0, None, None, False, 0, True, 1)
+        # invalid axis
+        assert_raises(TypeError, f, d, "invalid")
+        assert_raises(TypeError, f, d, axis="invalid")
+        assert_raises(TypeError, f, d, axis="invalid", dtype=None,
+                      keepdims=True)
+        # invalid dtype
+        assert_raises(TypeError, f, d, 0, "invalid")
+        assert_raises(TypeError, f, d, dtype="invalid")
+        assert_raises(TypeError, f, d, dtype="invalid", out=None)
+        # invalid out
+        assert_raises(TypeError, f, d, 0, None, "invalid")
+        assert_raises(TypeError, f, d, out="invalid")
+        assert_raises(TypeError, f, d, out="invalid", dtype=None)
+        # keepdims boolean, no invalid value
+        # assert_raises(TypeError, f, d, 0, None, None, "invalid")
+        # assert_raises(TypeError, f, d, keepdims="invalid", axis=0, dtype=None)
+        # invalid mix
+        assert_raises(TypeError, f, d, 0, keepdims="invalid", dtype="invalid",
+                     out=None)
+
+        # invalid keyword
+        assert_raises(TypeError, f, d, axis=0, dtype=None, invalid=0)
+        assert_raises(TypeError, f, d, invalid=0)
+        assert_raises(TypeError, f, d, 0, keepdims=True, invalid="invalid",
+                      out=None)
+        assert_raises(TypeError, f, d, axis=0, dtype=None, keepdims=True,
+                      out=None, invalid=0)
+        assert_raises(TypeError, f, d, axis=0, dtype=None,
+                      out=None, invalid=0)
+
+    def test_structured_equal(self):
+        # https://github.com/numpy/numpy/issues/4855
+
+        class MyA(np.ndarray):
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+                return getattr(ufunc, method)(*(input.view(np.ndarray)
+                                              for input in inputs), **kwargs)
+        a = np.arange(12.).reshape(4, 3)
+        ra = a.view(dtype=('f8,f8,f8')).squeeze()
+        mra = ra.view(MyA)
+
+        target = np.array([True, False, False, False], dtype=bool)
+        assert_equal(np.all(target == (mra == ra[0])), True)
+
+    def test_scalar_equal(self):
+        # Scalar comparisons should always work, without deprecation warnings.
+        # even when the ufunc fails.
+        a = np.array(0.)
+        b = np.array('a')
+        assert_(a != b)
+        assert_(b != a)
+        assert_(not (a == b))
+        assert_(not (b == a))
+
+    def test_NotImplemented_not_returned(self):
+        # See gh-5964 and gh-2091. Some of these functions are not operator
+        # related and were fixed for other reasons in the past.
+        binary_funcs = [
+            np.power, np.add, np.subtract, np.multiply, np.divide,
+            np.true_divide, np.floor_divide, np.bitwise_and, np.bitwise_or,
+            np.bitwise_xor, np.left_shift, np.right_shift, np.fmax,
+            np.fmin, np.fmod, np.hypot, np.logaddexp, np.logaddexp2,
+            np.maximum, np.minimum, np.mod,
+            np.greater, np.greater_equal, np.less, np.less_equal,
+            np.equal, np.not_equal]
+
+        a = np.array('1')
+        b = 1
+        c = np.array([1., 2.])
+        for f in binary_funcs:
+            assert_raises(TypeError, f, a, b)
+            assert_raises(TypeError, f, c, a)
+
+    @pytest.mark.parametrize("ufunc",
+             [np.logical_and, np.logical_or])  # logical_xor object loop is bad
+    @pytest.mark.parametrize("signature",
+             [(None, None, object), (object, None, None),
+              (None, object, None)])
+    def test_logical_ufuncs_object_signatures(self, ufunc, signature):
+        a = np.array([True, None, False], dtype=object)
+        res = ufunc(a, a, signature=signature)
+        assert res.dtype == object
+
+    @pytest.mark.parametrize("ufunc",
+            [np.logical_and, np.logical_or, np.logical_xor])
+    @pytest.mark.parametrize("signature",
+                 [(bool, None, object), (object, None, bool),
+                  (None, object, bool)])
+    def test_logical_ufuncs_mixed_object_signatures(self, ufunc, signature):
+        # Most mixed signatures fail (except those with bool out, e.g. `OO->?`)
+        a = np.array([True, None, False])
+        with pytest.raises(TypeError):
+            ufunc(a, a, signature=signature)
+
+    @pytest.mark.parametrize("ufunc",
+            [np.logical_and, np.logical_or, np.logical_xor])
+    def test_logical_ufuncs_support_anything(self, ufunc):
+        # The logical ufuncs support even input that can't be promoted:
+        a = np.array(b'1', dtype="V3")
+        c = np.array([1., 2.])
+        assert_array_equal(ufunc(a, c), ufunc([True, True], True))
+        assert ufunc.reduce(a) == True
+        # check that the output has no effect:
+        out = np.zeros(2, dtype=np.int32)
+        expected = ufunc([True, True], True).astype(out.dtype)
+        assert_array_equal(ufunc(a, c, out=out), expected)
+        out = np.zeros((), dtype=np.int32)
+        assert ufunc.reduce(a, out=out) == True
+        # Last check, test reduction when out and a match (the complexity here
+        # is that the "i,i->?" may seem right, but should not match.
+        a = np.array([3], dtype="i")
+        out = np.zeros((), dtype=a.dtype)
+        assert ufunc.reduce(a, out=out) == 1
+
+    @pytest.mark.parametrize("ufunc",
+            [np.logical_and, np.logical_or, np.logical_xor])
+    @pytest.mark.parametrize("dtype", ["S", "U"])
+    @pytest.mark.parametrize("values", [["1", "hi", "0"], ["", ""]])
+    def test_logical_ufuncs_supports_string(self, ufunc, dtype, values):
+        # note that values are either all true or all false
+        arr = np.array(values, dtype=dtype)
+        obj_arr = np.array(values, dtype=object)
+        res = ufunc(arr, arr)
+        expected = ufunc(obj_arr, obj_arr, dtype=bool)
+
+        assert_array_equal(res, expected)
+
+        res = ufunc.reduce(arr)
+        expected = ufunc.reduce(obj_arr, dtype=bool)
+        assert_array_equal(res, expected)
+
+    @pytest.mark.parametrize("ufunc",
+             [np.logical_and, np.logical_or, np.logical_xor])
+    def test_logical_ufuncs_out_cast_check(self, ufunc):
+        a = np.array('1')
+        c = np.array([1., 2.])
+        out = a.copy()
+        with pytest.raises(TypeError):
+            # It would be safe, but not equiv casting:
+            ufunc(a, c, out=out, casting="equiv")
+
+    def test_reducelike_byteorder_resolution(self):
+        # See gh-20699, byte-order changes need some extra care in the type
+        # resolution to make the following succeed:
+        arr_be = np.arange(10, dtype=">i8")
+        arr_le = np.arange(10, dtype="<i8")
+
+        assert np.add.reduce(arr_be) == np.add.reduce(arr_le)
+        assert_array_equal(np.add.accumulate(arr_be), np.add.accumulate(arr_le))
+        assert_array_equal(
+            np.add.reduceat(arr_be, [1]), np.add.reduceat(arr_le, [1]))
+
+    def test_reducelike_out_promotes(self):
+        # Check that the out argument to reductions is considered for
+        # promotion.  See also gh-20455.
+        # Note that these paths could prefer `initial=` in the future and
+        # do not up-cast to the default integer for add and prod
+        arr = np.ones(1000, dtype=np.uint8)
+        out = np.zeros((), dtype=np.uint16)
+        assert np.add.reduce(arr, out=out) == 1000
+        arr[:10] = 2
+        assert np.multiply.reduce(arr, out=out) == 2**10
+
+        # For legacy dtypes, the signature currently has to be forced if `out=`
+        # is passed.  The two paths below should differ, without `dtype=` the
+        # expected result should be: `np.prod(arr.astype("f8")).astype("f4")`!
+        arr = np.full(5, 2**25 - 1, dtype=np.int64)
+
+        # float32 and int64 promote to float64:
+        res = np.zeros((), dtype=np.float32)
+        # If `dtype=` is passed, the calculation is forced to float32:
+        single_res = np.zeros((), dtype=np.float32)
+        np.multiply.reduce(arr, out=single_res, dtype=np.float32)
+        assert single_res != res
+
+    def test_reducelike_output_needs_identical_cast(self):
+        # Checks the case where a simple byte-swap works, mainly tests that
+        # this is not rejected directly.
+        # (interesting because we require descriptor identity in reducelikes).
+        arr = np.ones(20, dtype="f8")
+        out = np.empty((), dtype=arr.dtype.newbyteorder())
+        expected = np.add.reduce(arr)
+        np.add.reduce(arr, out=out)
+        assert_array_equal(expected, out)
+        # Check reduceat:
+        out = np.empty(2, dtype=arr.dtype.newbyteorder())
+        expected = np.add.reduceat(arr, [0, 1])
+        np.add.reduceat(arr, [0, 1], out=out)
+        assert_array_equal(expected, out)
+        # And accumulate:
+        out = np.empty(arr.shape, dtype=arr.dtype.newbyteorder())
+        expected = np.add.accumulate(arr)
+        np.add.accumulate(arr, out=out)
+        assert_array_equal(expected, out)
+
+    def test_reduce_noncontig_output(self):
+        # Check that reduction deals with non-contiguous output arrays
+        # appropriately.
+        #
+        # gh-8036
+
+        x = np.arange(7 * 13 * 8, dtype=np.int16).reshape(7, 13, 8)
+        x = x[4:6, 1:11:6, 1:5].transpose(1, 2, 0)
+        y_base = np.arange(4 * 4, dtype=np.int16).reshape(4, 4)
+        y = y_base[::2, :]
+
+        y_base_copy = y_base.copy()
+
+        r0 = np.add.reduce(x, out=y.copy(), axis=2)
+        r1 = np.add.reduce(x, out=y, axis=2)
+
+        # The results should match, and y_base shouldn't get clobbered
+        assert_equal(r0, r1)
+        assert_equal(y_base[1, :], y_base_copy[1, :])
+        assert_equal(y_base[3, :], y_base_copy[3, :])
+
+    @pytest.mark.parametrize("with_cast", [True, False])
+    def test_reduceat_and_accumulate_out_shape_mismatch(self, with_cast):
+        # Should raise an error mentioning "shape" or "size"
+        arr = np.arange(5)
+        out = np.arange(3)  # definitely wrong shape
+        if with_cast:
+            # If a cast is necessary on the output, we can be sure to use
+            # the generic NpyIter (non-fast) path.
+            out = out.astype(np.float64)
+
+        with pytest.raises(ValueError, match="(shape|size)"):
+            np.add.reduceat(arr, [0, 3], out=out)
+
+        with pytest.raises(ValueError, match="(shape|size)"):
+            np.add.accumulate(arr, out=out)
+
+    @pytest.mark.parametrize('out_shape',
+                             [(), (1,), (3,), (1, 1), (1, 3), (4, 3)])
+    @pytest.mark.parametrize('keepdims', [True, False])
+    @pytest.mark.parametrize('f_reduce', [np.add.reduce, np.minimum.reduce])
+    def test_reduce_wrong_dimension_output(self, f_reduce, keepdims, out_shape):
+        # Test that we're not incorrectly broadcasting dimensions.
+        # See gh-15144 (failed for np.add.reduce previously).
+        a = np.arange(12.).reshape(4, 3)
+        out = np.empty(out_shape, a.dtype)
+
+        correct_out = f_reduce(a, axis=0, keepdims=keepdims)
+        if out_shape != correct_out.shape:
+            with assert_raises(ValueError):
+                f_reduce(a, axis=0, out=out, keepdims=keepdims)
+        else:
+            check = f_reduce(a, axis=0, out=out, keepdims=keepdims)
+            assert_(check is out)
+            assert_array_equal(check, correct_out)
+
+    def test_reduce_output_does_not_broadcast_input(self):
+        # Test that the output shape cannot broadcast an input dimension
+        # (it never can add dimensions, but it might expand an existing one)
+        a = np.ones((1, 10))
+        out_correct = (np.empty((1, 1)))
+        out_incorrect = np.empty((3, 1))
+        np.add.reduce(a, axis=-1, out=out_correct, keepdims=True)
+        np.add.reduce(a, axis=-1, out=out_correct[:, 0], keepdims=False)
+        with assert_raises(ValueError):
+            np.add.reduce(a, axis=-1, out=out_incorrect, keepdims=True)
+        with assert_raises(ValueError):
+            np.add.reduce(a, axis=-1, out=out_incorrect[:, 0], keepdims=False)
+
+    def test_reduce_output_subclass_ok(self):
+        class MyArr(np.ndarray):
+            pass
+
+        out = np.empty(())
+        np.add.reduce(np.ones(5), out=out)  # no subclass, all fine
+        out = out.view(MyArr)
+        assert np.add.reduce(np.ones(5), out=out) is out
+        assert type(np.add.reduce(out)) is MyArr
+
+    def test_no_doc_string(self):
+        # gh-9337
+        assert_('\n' not in umt.inner1d_no_doc.__doc__)
+
+    def test_invalid_args(self):
+        # gh-7961
+        exc = pytest.raises(TypeError, np.sqrt, None)
+        # minimally check the exception text
+        assert exc.match('loop of ufunc does not support')
+
+    @pytest.mark.parametrize('nat', [np.datetime64('nat'), np.timedelta64('nat')])
+    def test_nat_is_not_finite(self, nat):
+        try:
+            assert not np.isfinite(nat)
+        except TypeError:
+            pass  # ok, just not implemented
+
+    @pytest.mark.parametrize('nat', [np.datetime64('nat'), np.timedelta64('nat')])
+    def test_nat_is_nan(self, nat):
+        try:
+            assert np.isnan(nat)
+        except TypeError:
+            pass  # ok, just not implemented
+
+    @pytest.mark.parametrize('nat', [np.datetime64('nat'), np.timedelta64('nat')])
+    def test_nat_is_not_inf(self, nat):
+        try:
+            assert not np.isinf(nat)
+        except TypeError:
+            pass  # ok, just not implemented
+
+
+class TestGUFuncProcessCoreDims:
+
+    def test_conv1d_full_without_out(self):
+        x = np.arange(5.0)
+        y = np.arange(13.0)
+        w = umt.conv1d_full(x, y)
+        assert_equal(w, np.convolve(x, y, mode='full'))
+
+    def test_conv1d_full_with_out(self):
+        x = np.arange(5.0)
+        y = np.arange(13.0)
+        out = np.zeros(len(x) + len(y) - 1)
+        umt.conv1d_full(x, y, out=out)
+        assert_equal(out, np.convolve(x, y, mode='full'))
+
+    def test_conv1d_full_basic_broadcast(self):
+        # x.shape is (3, 6)
+        x = np.array([[1, 3, 0, -10, 2, 2],
+                      [0, -1, 2, 2, 10, 4],
+                      [8, 9, 10, 2, 23, 3]])
+        # y.shape is (2, 1, 7)
+        y = np.array([[[3, 4, 5, 20, 30, 40, 29]],
+                      [[5, 6, 7, 10, 11, 12, -5]]])
+        # result should have shape (2, 3, 12)
+        result = umt.conv1d_full(x, y)
+        assert result.shape == (2, 3, 12)
+        for i in range(2):
+            for j in range(3):
+                assert_equal(result[i, j], np.convolve(x[j], y[i, 0]))
+
+    def test_bad_out_shape(self):
+        x = np.ones((1, 2))
+        y = np.ones((2, 3))
+        out = np.zeros((2, 3))  # Not the correct shape.
+        with pytest.raises(ValueError, match=r'does not equal m \+ n - 1'):
+            umt.conv1d_full(x, y, out=out)
+
+    def test_bad_input_both_inputs_length_zero(self):
+        with pytest.raises(ValueError,
+                           match='both inputs have core dimension 0'):
+            umt.conv1d_full([], [])
+
+
+@pytest.mark.parametrize('ufunc', [getattr(np, x) for x in dir(np)
+                                   if isinstance(getattr(np, x), np.ufunc)])
+def test_ufunc_types(ufunc):
+    '''
+    Check all ufuncs that the correct type is returned. Avoid
+    object and boolean types since many operations are not defined for
+    for them.
+
+    Choose the shape so even dot and matmul will succeed
+    '''
+    for typ in ufunc.types:
+        # types is a list of strings like ii->i
+        if 'O' in typ or '?' in typ:
+            continue
+        inp, out = typ.split('->')
+        args = [np.ones((3, 3), t) for t in inp]
+        with warnings.catch_warnings(record=True):
+            warnings.filterwarnings("always")
+            res = ufunc(*args)
+        if isinstance(res, tuple):
+            outs = tuple(out)
+            assert len(res) == len(outs)
+            for r, t in zip(res, outs):
+                assert r.dtype == np.dtype(t)
+        else:
+            assert res.dtype == np.dtype(out)
+
+@pytest.mark.parametrize('ufunc', [getattr(np, x) for x in dir(np)
+                                if isinstance(getattr(np, x), np.ufunc)])
+def test_ufunc_noncontiguous(ufunc):
+    '''
+    Check that contiguous and non-contiguous calls to ufuncs
+    have the same results for values in range(9)
+    '''
+    for typ in ufunc.types:
+        # types is a list of strings like ii->i
+        if any(set('O?mM') & set(typ)):
+            # bool, object, datetime are too irregular for this simple test
+            continue
+        inp, out = typ.split('->')
+        args_c = [np.empty((6, 6), t) for t in inp]
+        # non contiguous (2, 3 step on the two dimensions)
+        args_n = [np.empty((12, 18), t)[::2, ::3] for t in inp]
+        # alignment != itemsize is possible.  So create an array with such
+        # an odd step manually.
+        args_o = []
+        for t in inp:
+            orig_dt = np.dtype(t)
+            off_dt = f"S{orig_dt.alignment}"  # offset by alignment
+            dtype = np.dtype([("_", off_dt), ("t", orig_dt)], align=False)
+            args_o.append(np.empty((6, 6), dtype=dtype)["t"])
+        for a in args_c + args_n + args_o:
+            a.flat = range(1, 37)
+
+        with warnings.catch_warnings(record=True):
+            warnings.filterwarnings("always")
+            res_c = ufunc(*args_c)
+            res_n = ufunc(*args_n)
+            res_o = ufunc(*args_o)
+        if len(out) == 1:
+            res_c = (res_c,)
+            res_n = (res_n,)
+            res_o = (res_o,)
+        for c_ar, n_ar, o_ar in zip(res_c, res_n, res_o):
+            dt = c_ar.dtype
+            if np.issubdtype(dt, np.floating):
+                # for floating point results allow a small fuss in comparisons
+                # since different algorithms (libm vs. intrinsics) can be used
+                # for different input strides
+                res_eps = np.finfo(dt).eps
+                tol = 3 * res_eps
+                assert_allclose(res_c, res_n, atol=tol, rtol=tol)
+                assert_allclose(res_c, res_o, atol=tol, rtol=tol)
+            else:
+                assert_equal(c_ar, n_ar)
+                assert_equal(c_ar, o_ar)
+
+
+@pytest.mark.parametrize('ufunc', [np.sign, np.equal])
+def test_ufunc_warn_with_nan(ufunc):
+    # issue gh-15127
+    # test that calling certain ufuncs with a non-standard `nan` value does not
+    # emit a warning
+    # `b` holds a 64 bit signaling nan: the most significant bit of the
+    # significand is zero.
+    b = np.array([0x7ff0000000000001], 'i8').view('f8')
+    assert np.isnan(b)
+    if ufunc.nin == 1:
+        ufunc(b)
+    elif ufunc.nin == 2:
+        ufunc(b, b.copy())
+    else:
+        raise ValueError('ufunc with more than 2 inputs')
+
+
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+def test_ufunc_out_casterrors():
+    # Tests that casting errors are correctly reported and buffers are
+    # cleared.
+    # The following array can be added to itself as an object array, but
+    # the result cannot be cast to an integer output:
+    value = 123  # relies on python cache (leak-check will still find it)
+    arr = np.array([value] * int(ncu.BUFSIZE * 1.5) +
+                   ["string"] +
+                   [value] * int(1.5 * ncu.BUFSIZE), dtype=object)
+    out = np.ones(len(arr), dtype=np.intp)
+
+    count = sys.getrefcount(value)
+    with pytest.raises(ValueError):
+        # Output casting failure:
+        np.add(arr, arr, out=out, casting="unsafe")
+
+    assert count == sys.getrefcount(value)
+    # output is unchanged after the error, this shows that the iteration
+    # was aborted (this is not necessarily defined behaviour)
+    assert out[-1] == 1
+
+    with pytest.raises(ValueError):
+        # Input casting failure:
+        np.add(arr, arr, out=out, dtype=np.intp, casting="unsafe")
+
+    assert count == sys.getrefcount(value)
+    # output is unchanged after the error, this shows that the iteration
+    # was aborted (this is not necessarily defined behaviour)
+    assert out[-1] == 1
+
+
+@pytest.mark.parametrize("bad_offset", [0, int(ncu.BUFSIZE * 1.5)])
+def test_ufunc_input_casterrors(bad_offset):
+    value = 123
+    arr = np.array([value] * bad_offset +
+                   ["string"] +
+                   [value] * int(1.5 * ncu.BUFSIZE), dtype=object)
+    with pytest.raises(ValueError):
+        # Force cast inputs, but the buffered cast of `arr` to intp fails:
+        np.add(arr, arr, dtype=np.intp, casting="unsafe")
+
+
+@pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+@pytest.mark.parametrize("bad_offset", [0, int(ncu.BUFSIZE * 1.5)])
+def test_ufunc_input_floatingpoint_error(bad_offset):
+    value = 123
+    arr = np.array([value] * bad_offset +
+                   [np.nan] +
+                   [value] * int(1.5 * ncu.BUFSIZE))
+    with np.errstate(invalid="raise"), pytest.raises(FloatingPointError):
+        # Force cast inputs, but the buffered cast of `arr` to intp fails:
+        np.add(arr, arr, dtype=np.intp, casting="unsafe")
+
+
+def test_trivial_loop_invalid_cast():
+    # This tests the fast-path "invalid cast", see gh-19904.
+    with pytest.raises(TypeError,
+            match="cast ufunc 'add' input 0"):
+        # the void dtype definitely cannot cast to double:
+        np.add(np.array(1, "i,i"), 3, signature="dd->d")
+
+
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+@pytest.mark.parametrize("offset",
+        [0, ncu.BUFSIZE // 2, int(1.5 * ncu.BUFSIZE)])
+def test_reduce_casterrors(offset):
+    # Test reporting of casting errors in reductions, we test various
+    # offsets to where the casting error will occur, since these may occur
+    # at different places during the reduction procedure. For example
+    # the first item may be special.
+    value = 123  # relies on python cache (leak-check will still find it)
+    arr = np.array([value] * offset +
+                   ["string"] +
+                   [value] * int(1.5 * ncu.BUFSIZE), dtype=object)
+    out = np.array(-1, dtype=np.intp)
+
+    count = sys.getrefcount(value)
+    with pytest.raises(ValueError, match="invalid literal"):
+        # This is an unsafe cast, but we currently always allow that.
+        # Note that the double loop is picked, but the cast fails.
+        # `initial=None` disables the use of an identity here to test failures
+        # while copying the first values path (not used when identity exists).
+        np.add.reduce(arr, dtype=np.intp, out=out, initial=None)
+    assert count == sys.getrefcount(value)
+    # If an error occurred during casting, the operation is done at most until
+    # the error occurs (the result of which would be `value * offset`) and -1
+    # if the error happened immediately.
+    # This does not define behaviour, the output is invalid and thus undefined
+    assert out[()] < value * offset
+
+
+@pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+def test_reduction_no_reference_leak():
+    # Test that the generic reduction does not leak references.
+    # gh-29358
+    arr = np.array([1, 2, 3], dtype=np.int32)
+    count = sys.getrefcount(arr)
+
+    np.add.reduce(arr, dtype=np.int32, initial=0)
+    assert count == sys.getrefcount(arr)
+
+    np.add.accumulate(arr, dtype=np.int32)
+    assert count == sys.getrefcount(arr)
+
+    np.add.reduceat(arr, [0, 1], dtype=np.int32)
+    assert count == sys.getrefcount(arr)
+
+    # with `out=` the reference count is not changed
+    out = np.empty((), dtype=np.int32)
+    out_count = sys.getrefcount(out)
+
+    np.add.reduce(arr, dtype=np.int32, out=out, initial=0)
+    assert count == sys.getrefcount(arr)
+    assert out_count == sys.getrefcount(out)
+
+    out = np.empty(arr.shape, dtype=np.int32)
+    out_count = sys.getrefcount(out)
+
+    np.add.accumulate(arr, dtype=np.int32, out=out)
+    assert count == sys.getrefcount(arr)
+    assert out_count == sys.getrefcount(out)
+
+    out = np.empty((2,), dtype=np.int32)
+    out_count = sys.getrefcount(out)
+
+    np.add.reduceat(arr, [0, 1], dtype=np.int32, out=out)
+    assert count == sys.getrefcount(arr)
+    assert out_count == sys.getrefcount(out)
+
+
+def test_object_reduce_cleanup_on_failure():
+    # Test cleanup, including of the initial value (manually provided or not)
+    with pytest.raises(TypeError):
+        np.add.reduce([1, 2, None], initial=4)
+
+    with pytest.raises(TypeError):
+        np.add.reduce([1, 2, None])
+
+
+@pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+@pytest.mark.parametrize("method",
+        [np.add.accumulate, np.add.reduce,
+         pytest.param(lambda x: np.add.reduceat(x, [0]), id="reduceat"),
+         pytest.param(lambda x: np.log.at(x, [2]), id="at")])
+def test_ufunc_methods_floaterrors(method):
+    # adding inf and -inf (or log(-inf) creates an invalid float and warns
+    arr = np.array([np.inf, 0, -np.inf])
+    with np.errstate(all="warn"):
+        with pytest.warns(RuntimeWarning, match="invalid value"):
+            method(arr)
+
+    arr = np.array([np.inf, 0, -np.inf])
+    with np.errstate(all="raise"):
+        with pytest.raises(FloatingPointError):
+            method(arr)
+
+
+def _check_neg_zero(value):
+    if value != 0.0:
+        return False
+    if not np.signbit(value.real):
+        return False
+    if value.dtype.kind == "c":
+        return np.signbit(value.imag)
+    return True
+
+@pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
+def test_addition_negative_zero(dtype):
+    dtype = np.dtype(dtype)
+    if dtype.kind == "c":
+        neg_zero = dtype.type(complex(-0.0, -0.0))
+    else:
+        neg_zero = dtype.type(-0.0)
+
+    arr = np.array(neg_zero)
+    arr2 = np.array(neg_zero)
+
+    assert _check_neg_zero(arr + arr2)
+    # In-place ops may end up on a different path (reduce path) see gh-21211
+    arr += arr2
+    assert _check_neg_zero(arr)
+
+
+@pytest.mark.parametrize("dtype", np.typecodes["AllFloat"])
+@pytest.mark.parametrize("use_initial", [True, False])
+def test_addition_reduce_negative_zero(dtype, use_initial):
+    dtype = np.dtype(dtype)
+    if dtype.kind == "c":
+        neg_zero = dtype.type(complex(-0.0, -0.0))
+    else:
+        neg_zero = dtype.type(-0.0)
+
+    kwargs = {}
+    if use_initial:
+        kwargs["initial"] = neg_zero
+    else:
+        pytest.xfail("-0. propagation in sum currently requires initial")
+
+    # Test various length, in case SIMD paths or chunking play a role.
+    # 150 extends beyond the pairwise blocksize; probably not important.
+    for i in range(150):
+        arr = np.array([neg_zero] * i, dtype=dtype)
+        res = np.sum(arr, **kwargs)
+        if i > 0 or use_initial:
+            assert _check_neg_zero(res)
+        else:
+            # `sum([])` should probably be 0.0 and not -0.0 like `sum([-0.0])`
+            assert not np.signbit(res.real)
+            assert not np.signbit(res.imag)
+
+
+@pytest.mark.parametrize(["dt1", "dt2"],
+        [("S", "U"), ("U", "S"), ("S", "d"), ("S", "V"), ("U", "l")])
+def test_addition_string_types(dt1, dt2):
+    arr1 = np.array([1234234], dtype=dt1)
+    arr2 = np.array([b"423"], dtype=dt2)
+    with pytest.raises(np._core._exceptions.UFuncTypeError) as exc:
+        np.add(arr1, arr2)
+
+
+@pytest.mark.parametrize("order1,order2",
+                         [(">", ">"), ("<", "<"), (">", "<"), ("<", ">")])
+def test_addition_unicode_inverse_byte_order(order1, order2):
+    element = 'abcd'
+    arr1 = np.array([element], dtype=f"{order1}U4")
+    arr2 = np.array([element], dtype=f"{order2}U4")
+    result = arr1 + arr2
+    assert result == 2 * element
+
+
+@pytest.mark.parametrize("dtype", [np.int8, np.int16, np.int32, np.int64])
+def test_find_non_long_args(dtype):
+    element = 'abcd'
+    start = dtype(0)
+    end = dtype(len(element))
+    arr = np.array([element])
+    result = np._core.umath.find(arr, "a", start, end)
+    assert result.dtype == np.dtype("intp")
+    assert result == 0
+
+
+def test_find_access_past_buffer():
+    # This checks that no read past the string buffer occurs in
+    # string_fastsearch.h. The buffer class makes sure this is checked.
+    # To see it in action, you can remove the checks in the buffer and
+    # this test will produce an 'Invalid read' if run under valgrind.
+    arr = np.array([b'abcd', b'ebcd'])
+    result = np._core.umath.find(arr, b'cde', 0, np.iinfo(np.int64).max)
+    assert np.all(result == -1)
+
+
+class TestLowlevelAPIAccess:
+    def test_resolve_dtypes_basic(self):
+        # Basic test for dtype resolution:
+        i4 = np.dtype("i4")
+        f4 = np.dtype("f4")
+        f8 = np.dtype("f8")
+
+        r = np.add.resolve_dtypes((i4, f4, None))
+        assert r == (f8, f8, f8)
+
+        # Signature uses the same logic to parse as ufunc (less strict)
+        # the following is "same-kind" casting so works:
+        r = np.add.resolve_dtypes((
+                i4, i4, None), signature=(None, None, "f4"))
+        assert r == (f4, f4, f4)
+
+        # Check NEP 50 "weak" promotion also:
+        r = np.add.resolve_dtypes((f4, int, None))
+        assert r == (f4, f4, f4)
+
+        with pytest.raises(TypeError):
+            np.add.resolve_dtypes((i4, f4, None), casting="no")
+
+    def test_resolve_dtypes_comparison(self):
+        i4 = np.dtype("i4")
+        i8 = np.dtype("i8")
+        b = np.dtype("?")
+        r = np.equal.resolve_dtypes((i4, i8, None))
+        assert r == (i8, i8, b)
+
+    def test_weird_dtypes(self):
+        S0 = np.dtype("S0")
+        # S0 is often converted by NumPy to S1, but not here:
+        r = np.equal.resolve_dtypes((S0, S0, None))
+        assert r == (S0, S0, np.dtype(bool))
+
+        # Subarray dtypes are weird and may not work fully, we preserve them
+        # leading to a TypeError (currently no equal loop for void/structured)
+        dts = np.dtype("10i")
+        with pytest.raises(TypeError):
+            np.equal.resolve_dtypes((dts, dts, None))
+
+    def test_resolve_dtypes_reduction(self):
+        i2 = np.dtype("i2")
+        default_int_ = np.dtype(np.int_)
+        # Check special addition resolution:
+        res = np.add.resolve_dtypes((None, i2, None), reduction=True)
+        assert res == (default_int_, default_int_, default_int_)
+
+    def test_resolve_dtypes_reduction_no_output(self):
+        i4 = np.dtype("i4")
+        with pytest.raises(TypeError):
+            # May be allowable at some point?
+            np.add.resolve_dtypes((i4, i4, i4), reduction=True)
+
+    @pytest.mark.parametrize("dtypes", [
+            (np.dtype("i"), np.dtype("i")),
+            (None, np.dtype("i"), np.dtype("f")),
+            (np.dtype("i"), None, np.dtype("f")),
+            ("i4", "i4", None)])
+    def test_resolve_dtypes_errors(self, dtypes):
+        with pytest.raises(TypeError):
+            np.add.resolve_dtypes(dtypes)
+
+    def test_resolve_dtypes_reduction_errors(self):
+        i2 = np.dtype("i2")
+
+        with pytest.raises(TypeError):
+            np.add.resolve_dtypes((None, i2, i2))
+
+        with pytest.raises(TypeError):
+            np.add.signature((None, None, "i4"))
+
+    @pytest.mark.skipif(not hasattr(ct, "pythonapi"),
+            reason="`ctypes.pythonapi` required for capsule unpacking.")
+    def test_loop_access(self):
+        # This is a basic test for the full strided loop access
+        data_t = ct.c_char_p * 2
+        dim_t = ct.c_ssize_t * 1
+        strides_t = ct.c_ssize_t * 2
+        strided_loop_t = ct.CFUNCTYPE(
+                ct.c_int, ct.c_void_p, data_t, dim_t, strides_t, ct.c_void_p)
+
+        class call_info_t(ct.Structure):
+            _fields_ = [
+                ("strided_loop", strided_loop_t),
+                ("context", ct.c_void_p),
+                ("auxdata", ct.c_void_p),
+                ("requires_pyapi", ct.c_byte),
+                ("no_floatingpoint_errors", ct.c_byte),
+            ]
+
+        i4 = np.dtype("i4")
+        dt, call_info_obj = np.negative._resolve_dtypes_and_context((i4, i4))
+        assert dt == (i4, i4)  # can be used without casting
+
+        # Fill in the rest of the information:
+        np.negative._get_strided_loop(call_info_obj)
+
+        ct.pythonapi.PyCapsule_GetPointer.restype = ct.c_void_p
+        call_info = ct.pythonapi.PyCapsule_GetPointer(
+                ct.py_object(call_info_obj),
+                ct.c_char_p(b"numpy_1.24_ufunc_call_info"))
+
+        call_info = ct.cast(call_info, ct.POINTER(call_info_t)).contents
+
+        arr = np.arange(10, dtype=i4)
+        call_info.strided_loop(
+                call_info.context,
+                data_t(arr.ctypes.data, arr.ctypes.data),
+                arr.ctypes.shape,  # is a C-array with 10 here
+                strides_t(arr.ctypes.strides[0], arr.ctypes.strides[0]),
+                call_info.auxdata)
+
+        # We just directly called the negative inner-loop in-place:
+        assert_array_equal(arr, -np.arange(10, dtype=i4))
+
+    @pytest.mark.parametrize("strides", [1, (1, 2, 3), (1, "2")])
+    def test__get_strided_loop_errors_bad_strides(self, strides):
+        i4 = np.dtype("i4")
+        dt, call_info = np.negative._resolve_dtypes_and_context((i4, i4))
+
+        with pytest.raises(TypeError, match="fixed_strides.*tuple.*or None"):
+            np.negative._get_strided_loop(call_info, fixed_strides=strides)
+
+    def test__get_strided_loop_errors_bad_call_info(self):
+        i4 = np.dtype("i4")
+        dt, call_info = np.negative._resolve_dtypes_and_context((i4, i4))
+
+        with pytest.raises(ValueError, match="PyCapsule"):
+            np.negative._get_strided_loop("not the capsule!")
+
+        with pytest.raises(TypeError, match=".*incompatible context"):
+            np.add._get_strided_loop(call_info)
+
+        np.negative._get_strided_loop(call_info)
+        with pytest.raises(TypeError):
+            # cannot call it a second time:
+            np.negative._get_strided_loop(call_info)
+
+    def test_long_arrays(self):
+        t = np.zeros((1029, 917), dtype=np.single)
+        t[0][0] = 1
+        t[28][414] = 1
+        tc = np.cos(t)
+        assert_equal(tc[0][0], tc[28][414])
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_umath.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_umath.py
new file mode 100644
index 0000000..13e139d
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_umath.py
@@ -0,0 +1,4916 @@
+import fnmatch
+import itertools
+import operator
+import platform
+import sys
+import warnings
+from collections import namedtuple
+from fractions import Fraction
+from functools import reduce
+
+import pytest
+
+import numpy as np
+import numpy._core.umath as ncu
+from numpy._core import _umath_tests as ncu_tests
+from numpy._core import sctypes
+from numpy.testing import (
+    HAS_REFCOUNT,
+    IS_MUSL,
+    IS_PYPY,
+    IS_WASM,
+    _gen_alignment_data,
+    assert_,
+    assert_allclose,
+    assert_almost_equal,
+    assert_array_almost_equal,
+    assert_array_almost_equal_nulp,
+    assert_array_equal,
+    assert_array_max_ulp,
+    assert_equal,
+    assert_no_warnings,
+    assert_raises,
+    assert_raises_regex,
+    suppress_warnings,
+)
+from numpy.testing._private.utils import _glibc_older_than
+
+UFUNCS = [obj for obj in np._core.umath.__dict__.values()
+         if isinstance(obj, np.ufunc)]
+
+UFUNCS_UNARY = [
+    uf for uf in UFUNCS if uf.nin == 1
+]
+UFUNCS_UNARY_FP = [
+    uf for uf in UFUNCS_UNARY if 'f->f' in uf.types
+]
+
+UFUNCS_BINARY = [
+    uf for uf in UFUNCS if uf.nin == 2
+]
+UFUNCS_BINARY_ACC = [
+    uf for uf in UFUNCS_BINARY if hasattr(uf, "accumulate") and uf.nout == 1
+]
+
+def interesting_binop_operands(val1, val2, dtype):
+    """
+    Helper to create "interesting" operands to cover common code paths:
+    * scalar inputs
+    * only first "values" is an array (e.g. scalar division fast-paths)
+    * Longer array (SIMD) placing the value of interest at different positions
+    * Oddly strided arrays which may not be SIMD compatible
+
+    It does not attempt to cover unaligned access or mixed dtypes.
+    These are normally handled by the casting/buffering machinery.
+
+    This is not a fixture (currently), since I believe a fixture normally
+    only yields once?
+    """
+    fill_value = 1  # could be a parameter, but maybe not an optional one?
+
+    arr1 = np.full(10003, dtype=dtype, fill_value=fill_value)
+    arr2 = np.full(10003, dtype=dtype, fill_value=fill_value)
+
+    arr1[0] = val1
+    arr2[0] = val2
+
+    extractor = lambda res: res
+    yield arr1[0], arr2[0], extractor, "scalars"
+
+    extractor = lambda res: res
+    yield arr1[0, ...], arr2[0, ...], extractor, "scalar-arrays"
+
+    # reset array values to fill_value:
+    arr1[0] = fill_value
+    arr2[0] = fill_value
+
+    for pos in [0, 1, 2, 3, 4, 5, -1, -2, -3, -4]:
+        arr1[pos] = val1
+        arr2[pos] = val2
+
+        extractor = lambda res: res[pos]
+        yield arr1, arr2, extractor, f"off-{pos}"
+        yield arr1, arr2[pos], extractor, f"off-{pos}-with-scalar"
+
+        arr1[pos] = fill_value
+        arr2[pos] = fill_value
+
+    for stride in [-1, 113]:
+        op1 = arr1[::stride]
+        op2 = arr2[::stride]
+        op1[10] = val1
+        op2[10] = val2
+
+        extractor = lambda res: res[10]
+        yield op1, op2, extractor, f"stride-{stride}"
+
+        op1[10] = fill_value
+        op2[10] = fill_value
+
+
+def on_powerpc():
+    """ True if we are running on a Power PC platform."""
+    return platform.processor() == 'powerpc' or \
+           platform.machine().startswith('ppc')
+
+
+def bad_arcsinh():
+    """The blocklisted trig functions are not accurate on aarch64/PPC for
+    complex256. Rather than dig through the actual problem skip the
+    test. This should be fixed when we can move past glibc2.17
+    which is the version in manylinux2014
+    """
+    if platform.machine() == 'aarch64':
+        x = 1.78e-10
+    elif on_powerpc():
+        x = 2.16e-10
+    else:
+        return False
+    v1 = np.arcsinh(np.float128(x))
+    v2 = np.arcsinh(np.complex256(x)).real
+    # The eps for float128 is 1-e33, so this is way bigger
+    return abs((v1 / v2) - 1.0) > 1e-23
+
+
+class _FilterInvalids:
+    def setup_method(self):
+        self.olderr = np.seterr(invalid='ignore')
+
+    def teardown_method(self):
+        np.seterr(**self.olderr)
+
+
+class TestConstants:
+    def test_pi(self):
+        assert_allclose(ncu.pi, 3.141592653589793, 1e-15)
+
+    def test_e(self):
+        assert_allclose(ncu.e, 2.718281828459045, 1e-15)
+
+    def test_euler_gamma(self):
+        assert_allclose(ncu.euler_gamma, 0.5772156649015329, 1e-15)
+
+
+class TestOut:
+    def test_out_subok(self):
+        for subok in (True, False):
+            a = np.array(0.5)
+            o = np.empty(())
+
+            r = np.add(a, 2, o, subok=subok)
+            assert_(r is o)
+            r = np.add(a, 2, out=o, subok=subok)
+            assert_(r is o)
+            r = np.add(a, 2, out=(o,), subok=subok)
+            assert_(r is o)
+
+            d = np.array(5.7)
+            o1 = np.empty(())
+            o2 = np.empty((), dtype=np.int32)
+
+            r1, r2 = np.frexp(d, o1, None, subok=subok)
+            assert_(r1 is o1)
+            r1, r2 = np.frexp(d, None, o2, subok=subok)
+            assert_(r2 is o2)
+            r1, r2 = np.frexp(d, o1, o2, subok=subok)
+            assert_(r1 is o1)
+            assert_(r2 is o2)
+
+            r1, r2 = np.frexp(d, out=(o1, None), subok=subok)
+            assert_(r1 is o1)
+            r1, r2 = np.frexp(d, out=(None, o2), subok=subok)
+            assert_(r2 is o2)
+            r1, r2 = np.frexp(d, out=(o1, o2), subok=subok)
+            assert_(r1 is o1)
+            assert_(r2 is o2)
+
+            with assert_raises(TypeError):
+                # Out argument must be tuple, since there are multiple outputs.
+                r1, r2 = np.frexp(d, out=o1, subok=subok)
+
+            assert_raises(TypeError, np.add, a, 2, o, o, subok=subok)
+            assert_raises(TypeError, np.add, a, 2, o, out=o, subok=subok)
+            assert_raises(TypeError, np.add, a, 2, None, out=o, subok=subok)
+            assert_raises(ValueError, np.add, a, 2, out=(o, o), subok=subok)
+            assert_raises(ValueError, np.add, a, 2, out=(), subok=subok)
+            assert_raises(TypeError, np.add, a, 2, [], subok=subok)
+            assert_raises(TypeError, np.add, a, 2, out=[], subok=subok)
+            assert_raises(TypeError, np.add, a, 2, out=([],), subok=subok)
+            o.flags.writeable = False
+            assert_raises(ValueError, np.add, a, 2, o, subok=subok)
+            assert_raises(ValueError, np.add, a, 2, out=o, subok=subok)
+            assert_raises(ValueError, np.add, a, 2, out=(o,), subok=subok)
+
+    def test_out_wrap_subok(self):
+        class ArrayWrap(np.ndarray):
+            __array_priority__ = 10
+
+            def __new__(cls, arr):
+                return np.asarray(arr).view(cls).copy()
+
+            def __array_wrap__(self, arr, context=None, return_scalar=False):
+                return arr.view(type(self))
+
+        for subok in (True, False):
+            a = ArrayWrap([0.5])
+
+            r = np.add(a, 2, subok=subok)
+            if subok:
+                assert_(isinstance(r, ArrayWrap))
+            else:
+                assert_(type(r) == np.ndarray)
+
+            r = np.add(a, 2, None, subok=subok)
+            if subok:
+                assert_(isinstance(r, ArrayWrap))
+            else:
+                assert_(type(r) == np.ndarray)
+
+            r = np.add(a, 2, out=None, subok=subok)
+            if subok:
+                assert_(isinstance(r, ArrayWrap))
+            else:
+                assert_(type(r) == np.ndarray)
+
+            r = np.add(a, 2, out=(None,), subok=subok)
+            if subok:
+                assert_(isinstance(r, ArrayWrap))
+            else:
+                assert_(type(r) == np.ndarray)
+
+            d = ArrayWrap([5.7])
+            o1 = np.empty((1,))
+            o2 = np.empty((1,), dtype=np.int32)
+
+            r1, r2 = np.frexp(d, o1, subok=subok)
+            if subok:
+                assert_(isinstance(r2, ArrayWrap))
+            else:
+                assert_(type(r2) == np.ndarray)
+
+            r1, r2 = np.frexp(d, o1, None, subok=subok)
+            if subok:
+                assert_(isinstance(r2, ArrayWrap))
+            else:
+                assert_(type(r2) == np.ndarray)
+
+            r1, r2 = np.frexp(d, None, o2, subok=subok)
+            if subok:
+                assert_(isinstance(r1, ArrayWrap))
+            else:
+                assert_(type(r1) == np.ndarray)
+
+            r1, r2 = np.frexp(d, out=(o1, None), subok=subok)
+            if subok:
+                assert_(isinstance(r2, ArrayWrap))
+            else:
+                assert_(type(r2) == np.ndarray)
+
+            r1, r2 = np.frexp(d, out=(None, o2), subok=subok)
+            if subok:
+                assert_(isinstance(r1, ArrayWrap))
+            else:
+                assert_(type(r1) == np.ndarray)
+
+            with assert_raises(TypeError):
+                # Out argument must be tuple, since there are multiple outputs.
+                r1, r2 = np.frexp(d, out=o1, subok=subok)
+
+    @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
+    def test_out_wrap_no_leak(self):
+        # Regression test for gh-26545
+        class ArrSubclass(np.ndarray):
+            pass
+
+        arr = np.arange(10).view(ArrSubclass)
+        orig_refcount = sys.getrefcount(arr)
+        arr *= 1
+        assert sys.getrefcount(arr) == orig_refcount
+
+
+class TestComparisons:
+    import operator
+
+    @pytest.mark.parametrize('dtype', sctypes['uint'] + sctypes['int'] +
+                             sctypes['float'] + [np.bool])
+    @pytest.mark.parametrize('py_comp,np_comp', [
+        (operator.lt, np.less),
+        (operator.le, np.less_equal),
+        (operator.gt, np.greater),
+        (operator.ge, np.greater_equal),
+        (operator.eq, np.equal),
+        (operator.ne, np.not_equal)
+    ])
+    def test_comparison_functions(self, dtype, py_comp, np_comp):
+        # Initialize input arrays
+        if dtype == np.bool:
+            a = np.random.choice(a=[False, True], size=1000)
+            b = np.random.choice(a=[False, True], size=1000)
+            scalar = True
+        else:
+            a = np.random.randint(low=1, high=10, size=1000).astype(dtype)
+            b = np.random.randint(low=1, high=10, size=1000).astype(dtype)
+            scalar = 5
+        np_scalar = np.dtype(dtype).type(scalar)
+        a_lst = a.tolist()
+        b_lst = b.tolist()
+
+        # (Binary) Comparison (x1=array, x2=array)
+        comp_b = np_comp(a, b).view(np.uint8)
+        comp_b_list = [int(py_comp(x, y)) for x, y in zip(a_lst, b_lst)]
+
+        # (Scalar1) Comparison (x1=scalar, x2=array)
+        comp_s1 = np_comp(np_scalar, b).view(np.uint8)
+        comp_s1_list = [int(py_comp(scalar, x)) for x in b_lst]
+
+        # (Scalar2) Comparison (x1=array, x2=scalar)
+        comp_s2 = np_comp(a, np_scalar).view(np.uint8)
+        comp_s2_list = [int(py_comp(x, scalar)) for x in a_lst]
+
+        # Sequence: Binary, Scalar1 and Scalar2
+        assert_(comp_b.tolist() == comp_b_list,
+            f"Failed comparison ({py_comp.__name__})")
+        assert_(comp_s1.tolist() == comp_s1_list,
+            f"Failed comparison ({py_comp.__name__})")
+        assert_(comp_s2.tolist() == comp_s2_list,
+            f"Failed comparison ({py_comp.__name__})")
+
+    def test_ignore_object_identity_in_equal(self):
+        # Check comparing identical objects whose comparison
+        # is not a simple boolean, e.g., arrays that are compared elementwise.
+        a = np.array([np.array([1, 2, 3]), None], dtype=object)
+        assert_raises(ValueError, np.equal, a, a)
+
+        # Check error raised when comparing identical non-comparable objects.
+        class FunkyType:
+            def __eq__(self, other):
+                raise TypeError("I won't compare")
+
+        a = np.array([FunkyType()])
+        assert_raises(TypeError, np.equal, a, a)
+
+        # Check identity doesn't override comparison mismatch.
+        a = np.array([np.nan], dtype=object)
+        assert_equal(np.equal(a, a), [False])
+
+    def test_ignore_object_identity_in_not_equal(self):
+        # Check comparing identical objects whose comparison
+        # is not a simple boolean, e.g., arrays that are compared elementwise.
+        a = np.array([np.array([1, 2, 3]), None], dtype=object)
+        assert_raises(ValueError, np.not_equal, a, a)
+
+        # Check error raised when comparing identical non-comparable objects.
+        class FunkyType:
+            def __ne__(self, other):
+                raise TypeError("I won't compare")
+
+        a = np.array([FunkyType()])
+        assert_raises(TypeError, np.not_equal, a, a)
+
+        # Check identity doesn't override comparison mismatch.
+        a = np.array([np.nan], dtype=object)
+        assert_equal(np.not_equal(a, a), [True])
+
+    def test_error_in_equal_reduce(self):
+        # gh-20929
+        # make sure np.equal.reduce raises a TypeError if an array is passed
+        # without specifying the dtype
+        a = np.array([0, 0])
+        assert_equal(np.equal.reduce(a, dtype=bool), True)
+        assert_raises(TypeError, np.equal.reduce, a)
+
+    def test_object_dtype(self):
+        assert np.equal(1, [1], dtype=object).dtype == object
+        assert np.equal(1, [1], signature=(None, None, "O")).dtype == object
+
+    def test_object_nonbool_dtype_error(self):
+        # bool output dtype is fine of course:
+        assert np.equal(1, [1], dtype=bool).dtype == bool
+
+        # but the following are examples do not have a loop:
+        with pytest.raises(TypeError, match="No loop matching"):
+            np.equal(1, 1, dtype=np.int64)
+
+        with pytest.raises(TypeError, match="No loop matching"):
+            np.equal(1, 1, sig=(None, None, "l"))
+
+    @pytest.mark.parametrize("dtypes", ["qQ", "Qq"])
+    @pytest.mark.parametrize('py_comp, np_comp', [
+        (operator.lt, np.less),
+        (operator.le, np.less_equal),
+        (operator.gt, np.greater),
+        (operator.ge, np.greater_equal),
+        (operator.eq, np.equal),
+        (operator.ne, np.not_equal)
+    ])
+    @pytest.mark.parametrize("vals", [(2**60, 2**60 + 1), (2**60 + 1, 2**60)])
+    def test_large_integer_direct_comparison(
+            self, dtypes, py_comp, np_comp, vals):
+        # Note that float(2**60) + 1 == float(2**60).
+        a1 = np.array([2**60], dtype=dtypes[0])
+        a2 = np.array([2**60 + 1], dtype=dtypes[1])
+        expected = py_comp(2**60, 2**60 + 1)
+
+        assert py_comp(a1, a2) == expected
+        assert np_comp(a1, a2) == expected
+        # Also check the scalars:
+        s1 = a1[0]
+        s2 = a2[0]
+        assert isinstance(s1, np.integer)
+        assert isinstance(s2, np.integer)
+        # The Python operator here is mainly interesting:
+        assert py_comp(s1, s2) == expected
+        assert np_comp(s1, s2) == expected
+
+    @pytest.mark.parametrize("dtype", np.typecodes['UnsignedInteger'])
+    @pytest.mark.parametrize('py_comp_func, np_comp_func', [
+        (operator.lt, np.less),
+        (operator.le, np.less_equal),
+        (operator.gt, np.greater),
+        (operator.ge, np.greater_equal),
+        (operator.eq, np.equal),
+        (operator.ne, np.not_equal)
+    ])
+    @pytest.mark.parametrize("flip", [True, False])
+    def test_unsigned_signed_direct_comparison(
+            self, dtype, py_comp_func, np_comp_func, flip):
+        if flip:
+            py_comp = lambda x, y: py_comp_func(y, x)
+            np_comp = lambda x, y: np_comp_func(y, x)
+        else:
+            py_comp = py_comp_func
+            np_comp = np_comp_func
+
+        arr = np.array([np.iinfo(dtype).max], dtype=dtype)
+        expected = py_comp(int(arr[0]), -1)
+
+        assert py_comp(arr, -1) == expected
+        assert np_comp(arr, -1) == expected
+
+        scalar = arr[0]
+        assert isinstance(scalar, np.integer)
+        # The Python operator here is mainly interesting:
+        assert py_comp(scalar, -1) == expected
+        assert np_comp(scalar, -1) == expected
+
+
+class TestAdd:
+    def test_reduce_alignment(self):
+        # gh-9876
+        # make sure arrays with weird strides work with the optimizations in
+        # pairwise_sum_@TYPE@. On x86, the 'b' field will count as aligned at a
+        # 4 byte offset, even though its itemsize is 8.
+        a = np.zeros(2, dtype=[('a', np.int32), ('b', np.float64)])
+        a['a'] = -1
+        assert_equal(a['b'].sum(), 0)
+
+
+class TestDivision:
+    def test_division_int(self):
+        # int division should follow Python
+        x = np.array([5, 10, 90, 100, -5, -10, -90, -100, -120])
+        if 5 / 10 == 0.5:
+            assert_equal(x / 100, [0.05, 0.1, 0.9, 1,
+                                   -0.05, -0.1, -0.9, -1, -1.2])
+        else:
+            assert_equal(x / 100, [0, 0, 0, 1, -1, -1, -1, -1, -2])
+        assert_equal(x // 100, [0, 0, 0, 1, -1, -1, -1, -1, -2])
+        assert_equal(x % 100, [5, 10, 90, 0, 95, 90, 10, 0, 80])
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.parametrize("dtype,ex_val", itertools.product(
+        sctypes['int'] + sctypes['uint'], (
+            (
+                # dividend
+                "np.array(range(fo.max-lsize, fo.max)).astype(dtype),"
+                # divisors
+                "np.arange(lsize).astype(dtype),"
+                # scalar divisors
+                "range(15)"
+            ),
+            (
+                # dividend
+                "np.arange(fo.min, fo.min+lsize).astype(dtype),"
+                # divisors
+                "np.arange(lsize//-2, lsize//2).astype(dtype),"
+                # scalar divisors
+                "range(fo.min, fo.min + 15)"
+            ), (
+                # dividend
+                "np.array(range(fo.max-lsize, fo.max)).astype(dtype),"
+                # divisors
+                "np.arange(lsize).astype(dtype),"
+                # scalar divisors
+                "[1,3,9,13,neg, fo.min+1, fo.min//2, fo.max//3, fo.max//4]"
+            )
+        )
+    ))
+    def test_division_int_boundary(self, dtype, ex_val):
+        fo = np.iinfo(dtype)
+        neg = -1 if fo.min < 0 else 1
+        # Large enough to test SIMD loops and remainder elements
+        lsize = 512 + 7
+        a, b, divisors = eval(ex_val)
+        a_lst, b_lst = a.tolist(), b.tolist()
+
+        c_div = lambda n, d: (
+            0 if d == 0 else (
+                fo.min if (n and n == fo.min and d == -1) else n // d
+            )
+        )
+        with np.errstate(divide='ignore'):
+            ac = a.copy()
+            ac //= b
+            div_ab = a // b
+        div_lst = [c_div(x, y) for x, y in zip(a_lst, b_lst)]
+
+        msg = "Integer arrays floor division check (//)"
+        assert all(div_ab == div_lst), msg
+        msg_eq = "Integer arrays floor division check (//=)"
+        assert all(ac == div_lst), msg_eq
+
+        for divisor in divisors:
+            ac = a.copy()
+            with np.errstate(divide='ignore', over='ignore'):
+                div_a = a // divisor
+                ac //= divisor
+            div_lst = [c_div(i, divisor) for i in a_lst]
+
+            assert all(div_a == div_lst), msg
+            assert all(ac == div_lst), msg_eq
+
+        with np.errstate(divide='raise', over='raise'):
+            if 0 in b:
+                # Verify overflow case
+                with pytest.raises(FloatingPointError,
+                        match="divide by zero encountered in floor_divide"):
+                    a // b
+            else:
+                a // b
+            if fo.min and fo.min in a:
+                with pytest.raises(FloatingPointError,
+                        match='overflow encountered in floor_divide'):
+                    a // -1
+            elif fo.min:
+                a // -1
+            with pytest.raises(FloatingPointError,
+                    match="divide by zero encountered in floor_divide"):
+                a // 0
+            with pytest.raises(FloatingPointError,
+                    match="divide by zero encountered in floor_divide"):
+                ac = a.copy()
+                ac //= 0
+
+            np.array([], dtype=dtype) // 0
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.parametrize("dtype,ex_val", itertools.product(
+        sctypes['int'] + sctypes['uint'], (
+            "np.array([fo.max, 1, 2, 1, 1, 2, 3], dtype=dtype)",
+            "np.array([fo.min, 1, -2, 1, 1, 2, -3]).astype(dtype)",
+            "np.arange(fo.min, fo.min+(100*10), 10, dtype=dtype)",
+            "np.array(range(fo.max-(100*7), fo.max, 7)).astype(dtype)",
+        )
+    ))
+    def test_division_int_reduce(self, dtype, ex_val):
+        fo = np.iinfo(dtype)
+        a = eval(ex_val)
+        lst = a.tolist()
+        c_div = lambda n, d: (
+            0 if d == 0 or (n and n == fo.min and d == -1) else n // d
+        )
+
+        with np.errstate(divide='ignore'):
+            div_a = np.floor_divide.reduce(a)
+        div_lst = reduce(c_div, lst)
+        msg = "Reduce floor integer division check"
+        assert div_a == div_lst, msg
+
+        with np.errstate(divide='raise', over='raise'):
+            with pytest.raises(FloatingPointError,
+                    match="divide by zero encountered in reduce"):
+                np.floor_divide.reduce(np.arange(-100, 100).astype(dtype))
+            if fo.min:
+                with pytest.raises(FloatingPointError,
+                        match='overflow encountered in reduce'):
+                    np.floor_divide.reduce(
+                        np.array([fo.min, 1, -1], dtype=dtype)
+                    )
+
+    @pytest.mark.parametrize(
+            "dividend,divisor,quotient",
+            [(np.timedelta64(2, 'Y'), np.timedelta64(2, 'M'), 12),
+             (np.timedelta64(2, 'Y'), np.timedelta64(-2, 'M'), -12),
+             (np.timedelta64(-2, 'Y'), np.timedelta64(2, 'M'), -12),
+             (np.timedelta64(-2, 'Y'), np.timedelta64(-2, 'M'), 12),
+             (np.timedelta64(2, 'M'), np.timedelta64(-2, 'Y'), -1),
+             (np.timedelta64(2, 'Y'), np.timedelta64(0, 'M'), 0),
+             (np.timedelta64(2, 'Y'), 2, np.timedelta64(1, 'Y')),
+             (np.timedelta64(2, 'Y'), -2, np.timedelta64(-1, 'Y')),
+             (np.timedelta64(-2, 'Y'), 2, np.timedelta64(-1, 'Y')),
+             (np.timedelta64(-2, 'Y'), -2, np.timedelta64(1, 'Y')),
+             (np.timedelta64(-2, 'Y'), -2, np.timedelta64(1, 'Y')),
+             (np.timedelta64(-2, 'Y'), -3, np.timedelta64(0, 'Y')),
+             (np.timedelta64(-2, 'Y'), 0, np.timedelta64('Nat', 'Y')),
+            ])
+    def test_division_int_timedelta(self, dividend, divisor, quotient):
+        # If either divisor is 0 or quotient is Nat, check for division by 0
+        if divisor and (isinstance(quotient, int) or not np.isnat(quotient)):
+            msg = "Timedelta floor division check"
+            assert dividend // divisor == quotient, msg
+
+            # Test for arrays as well
+            msg = "Timedelta arrays floor division check"
+            dividend_array = np.array([dividend] * 5)
+            quotient_array = np.array([quotient] * 5)
+            assert all(dividend_array // divisor == quotient_array), msg
+        else:
+            if IS_WASM:
+                pytest.skip("fp errors don't work in wasm")
+            with np.errstate(divide='raise', invalid='raise'):
+                with pytest.raises(FloatingPointError):
+                    dividend // divisor
+
+    def test_division_complex(self):
+        # check that implementation is correct
+        msg = "Complex division implementation check"
+        x = np.array([1. + 1. * 1j, 1. + .5 * 1j, 1. + 2. * 1j], dtype=np.complex128)
+        assert_almost_equal(x**2 / x, x, err_msg=msg)
+        # check overflow, underflow
+        msg = "Complex division overflow/underflow check"
+        x = np.array([1.e+110, 1.e-110], dtype=np.complex128)
+        y = x**2 / x
+        assert_almost_equal(y / x, [1, 1], err_msg=msg)
+
+    def test_zero_division_complex(self):
+        with np.errstate(invalid="ignore", divide="ignore"):
+            x = np.array([0.0], dtype=np.complex128)
+            y = 1.0 / x
+            assert_(np.isinf(y)[0])
+            y = complex(np.inf, np.nan) / x
+            assert_(np.isinf(y)[0])
+            y = complex(np.nan, np.inf) / x
+            assert_(np.isinf(y)[0])
+            y = complex(np.inf, np.inf) / x
+            assert_(np.isinf(y)[0])
+            y = 0.0 / x
+            assert_(np.isnan(y)[0])
+
+    def test_floor_division_complex(self):
+        # check that floor division, divmod and remainder raises type errors
+        x = np.array([.9 + 1j, -.1 + 1j, .9 + .5 * 1j, .9 + 2. * 1j], dtype=np.complex128)
+        with pytest.raises(TypeError):
+            x // 7
+        with pytest.raises(TypeError):
+            np.divmod(x, 7)
+        with pytest.raises(TypeError):
+            np.remainder(x, 7)
+
+    def test_floor_division_signed_zero(self):
+        # Check that the sign bit is correctly set when dividing positive and
+        # negative zero by one.
+        x = np.zeros(10)
+        assert_equal(np.signbit(x // 1), 0)
+        assert_equal(np.signbit((-x) // 1), 1)
+
+    @pytest.mark.skipif(hasattr(np.__config__, "blas_ssl2_info"),
+            reason="gh-22982")
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.parametrize('dtype', np.typecodes['Float'])
+    def test_floor_division_errors(self, dtype):
+        fnan = np.array(np.nan, dtype=dtype)
+        fone = np.array(1.0, dtype=dtype)
+        fzer = np.array(0.0, dtype=dtype)
+        finf = np.array(np.inf, dtype=dtype)
+        # divide by zero error check
+        with np.errstate(divide='raise', invalid='ignore'):
+            assert_raises(FloatingPointError, np.floor_divide, fone, fzer)
+        with np.errstate(divide='ignore', invalid='raise'):
+            np.floor_divide(fone, fzer)
+
+        # The following already contain a NaN and should not warn
+        with np.errstate(all='raise'):
+            np.floor_divide(fnan, fone)
+            np.floor_divide(fone, fnan)
+            np.floor_divide(fnan, fzer)
+            np.floor_divide(fzer, fnan)
+
+    @pytest.mark.parametrize('dtype', np.typecodes['Float'])
+    def test_floor_division_corner_cases(self, dtype):
+        # test corner cases like 1.0//0.0 for errors and return vals
+        x = np.zeros(10, dtype=dtype)
+        y = np.ones(10, dtype=dtype)
+        fnan = np.array(np.nan, dtype=dtype)
+        fone = np.array(1.0, dtype=dtype)
+        fzer = np.array(0.0, dtype=dtype)
+        finf = np.array(np.inf, dtype=dtype)
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in floor_divide")
+            div = np.floor_divide(fnan, fone)
+            assert np.isnan(div), f"div: {div}"
+            div = np.floor_divide(fone, fnan)
+            assert np.isnan(div), f"div: {div}"
+            div = np.floor_divide(fnan, fzer)
+            assert np.isnan(div), f"div: {div}"
+        # verify 1.0//0.0 computations return inf
+        with np.errstate(divide='ignore'):
+            z = np.floor_divide(y, x)
+            assert_(np.isinf(z).all())
+
+def floor_divide_and_remainder(x, y):
+    return (np.floor_divide(x, y), np.remainder(x, y))
+
+
+def _signs(dt):
+    if dt in np.typecodes['UnsignedInteger']:
+        return (+1,)
+    else:
+        return (+1, -1)
+
+
+class TestRemainder:
+
+    def test_remainder_basic(self):
+        dt = np.typecodes['AllInteger'] + np.typecodes['Float']
+        for op in [floor_divide_and_remainder, np.divmod]:
+            for dt1, dt2 in itertools.product(dt, dt):
+                for sg1, sg2 in itertools.product(_signs(dt1), _signs(dt2)):
+                    fmt = 'op: %s, dt1: %s, dt2: %s, sg1: %s, sg2: %s'
+                    msg = fmt % (op.__name__, dt1, dt2, sg1, sg2)
+                    a = np.array(sg1 * 71, dtype=dt1)
+                    b = np.array(sg2 * 19, dtype=dt2)
+                    div, rem = op(a, b)
+                    assert_equal(div * b + rem, a, err_msg=msg)
+                    if sg2 == -1:
+                        assert_(b < rem <= 0, msg)
+                    else:
+                        assert_(b > rem >= 0, msg)
+
+    def test_float_remainder_exact(self):
+        # test that float results are exact for small integers. This also
+        # holds for the same integers scaled by powers of two.
+        nlst = list(range(-127, 0))
+        plst = list(range(1, 128))
+        dividend = nlst + [0] + plst
+        divisor = nlst + plst
+        arg = list(itertools.product(dividend, divisor))
+        tgt = [divmod(*t) for t in arg]
+
+        a, b = np.array(arg, dtype=int).T
+        # convert exact integer results from Python to float so that
+        # signed zero can be used, it is checked.
+        tgtdiv, tgtrem = np.array(tgt, dtype=float).T
+        tgtdiv = np.where((tgtdiv == 0.0) & ((b < 0) ^ (a < 0)), -0.0, tgtdiv)
+        tgtrem = np.where((tgtrem == 0.0) & (b < 0), -0.0, tgtrem)
+
+        for op in [floor_divide_and_remainder, np.divmod]:
+            for dt in np.typecodes['Float']:
+                msg = f'op: {op.__name__}, dtype: {dt}'
+                fa = a.astype(dt)
+                fb = b.astype(dt)
+                div, rem = op(fa, fb)
+                assert_equal(div, tgtdiv, err_msg=msg)
+                assert_equal(rem, tgtrem, err_msg=msg)
+
+    def test_float_remainder_roundoff(self):
+        # gh-6127
+        dt = np.typecodes['Float']
+        for op in [floor_divide_and_remainder, np.divmod]:
+            for dt1, dt2 in itertools.product(dt, dt):
+                for sg1, sg2 in itertools.product((+1, -1), (+1, -1)):
+                    fmt = 'op: %s, dt1: %s, dt2: %s, sg1: %s, sg2: %s'
+                    msg = fmt % (op.__name__, dt1, dt2, sg1, sg2)
+                    a = np.array(sg1 * 78 * 6e-8, dtype=dt1)
+                    b = np.array(sg2 * 6e-8, dtype=dt2)
+                    div, rem = op(a, b)
+                    # Equal assertion should hold when fmod is used
+                    assert_equal(div * b + rem, a, err_msg=msg)
+                    if sg2 == -1:
+                        assert_(b < rem <= 0, msg)
+                    else:
+                        assert_(b > rem >= 0, msg)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.xfail(sys.platform.startswith("darwin"),
+            reason="MacOS seems to not give the correct 'invalid' warning for "
+                   "`fmod`.  Hopefully, others always do.")
+    @pytest.mark.parametrize('dtype', np.typecodes['Float'])
+    def test_float_divmod_errors(self, dtype):
+        # Check valid errors raised for divmod and remainder
+        fzero = np.array(0.0, dtype=dtype)
+        fone = np.array(1.0, dtype=dtype)
+        finf = np.array(np.inf, dtype=dtype)
+        fnan = np.array(np.nan, dtype=dtype)
+        # since divmod is combination of both remainder and divide
+        # ops it will set both dividebyzero and invalid flags
+        with np.errstate(divide='raise', invalid='ignore'):
+            assert_raises(FloatingPointError, np.divmod, fone, fzero)
+        with np.errstate(divide='ignore', invalid='raise'):
+            assert_raises(FloatingPointError, np.divmod, fone, fzero)
+        with np.errstate(invalid='raise'):
+            assert_raises(FloatingPointError, np.divmod, fzero, fzero)
+        with np.errstate(invalid='raise'):
+            assert_raises(FloatingPointError, np.divmod, finf, finf)
+        with np.errstate(divide='ignore', invalid='raise'):
+            assert_raises(FloatingPointError, np.divmod, finf, fzero)
+        with np.errstate(divide='raise', invalid='ignore'):
+            # inf / 0 does not set any flags, only the modulo creates a NaN
+            np.divmod(finf, fzero)
+
+    @pytest.mark.skipif(hasattr(np.__config__, "blas_ssl2_info"),
+            reason="gh-22982")
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.xfail(sys.platform.startswith("darwin"),
+           reason="MacOS seems to not give the correct 'invalid' warning for "
+                  "`fmod`.  Hopefully, others always do.")
+    @pytest.mark.parametrize('dtype', np.typecodes['Float'])
+    @pytest.mark.parametrize('fn', [np.fmod, np.remainder])
+    def test_float_remainder_errors(self, dtype, fn):
+        fzero = np.array(0.0, dtype=dtype)
+        fone = np.array(1.0, dtype=dtype)
+        finf = np.array(np.inf, dtype=dtype)
+        fnan = np.array(np.nan, dtype=dtype)
+
+        # The following already contain a NaN and should not warn.
+        with np.errstate(all='raise'):
+            with pytest.raises(FloatingPointError,
+                    match="invalid value"):
+                fn(fone, fzero)
+            fn(fnan, fzero)
+            fn(fzero, fnan)
+            fn(fone, fnan)
+            fn(fnan, fone)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_float_remainder_overflow(self):
+        a = np.finfo(np.float64).tiny
+        with np.errstate(over='ignore', invalid='ignore'):
+            div, mod = np.divmod(4, a)
+            np.isinf(div)
+            assert_(mod == 0)
+        with np.errstate(over='raise', invalid='ignore'):
+            assert_raises(FloatingPointError, np.divmod, 4, a)
+        with np.errstate(invalid='raise', over='ignore'):
+            assert_raises(FloatingPointError, np.divmod, 4, a)
+
+    def test_float_divmod_corner_cases(self):
+        # check nan cases
+        for dt in np.typecodes['Float']:
+            fnan = np.array(np.nan, dtype=dt)
+            fone = np.array(1.0, dtype=dt)
+            fzer = np.array(0.0, dtype=dt)
+            finf = np.array(np.inf, dtype=dt)
+            with suppress_warnings() as sup:
+                sup.filter(RuntimeWarning, "invalid value encountered in divmod")
+                sup.filter(RuntimeWarning, "divide by zero encountered in divmod")
+                div, rem = np.divmod(fone, fzer)
+                assert np.isinf(div), f'dt: {dt}, div: {rem}'
+                assert np.isnan(rem), f'dt: {dt}, rem: {rem}'
+                div, rem = np.divmod(fzer, fzer)
+                assert np.isnan(rem), f'dt: {dt}, rem: {rem}'
+                assert_(np.isnan(div)), f'dt: {dt}, rem: {rem}'
+                div, rem = np.divmod(finf, finf)
+                assert np.isnan(div), f'dt: {dt}, rem: {rem}'
+                assert np.isnan(rem), f'dt: {dt}, rem: {rem}'
+                div, rem = np.divmod(finf, fzer)
+                assert np.isinf(div), f'dt: {dt}, rem: {rem}'
+                assert np.isnan(rem), f'dt: {dt}, rem: {rem}'
+                div, rem = np.divmod(fnan, fone)
+                assert np.isnan(rem), f"dt: {dt}, rem: {rem}"
+                assert np.isnan(div), f"dt: {dt}, rem: {rem}"
+                div, rem = np.divmod(fone, fnan)
+                assert np.isnan(rem), f"dt: {dt}, rem: {rem}"
+                assert np.isnan(div), f"dt: {dt}, rem: {rem}"
+                div, rem = np.divmod(fnan, fzer)
+                assert np.isnan(rem), f"dt: {dt}, rem: {rem}"
+                assert np.isnan(div), f"dt: {dt}, rem: {rem}"
+
+    def test_float_remainder_corner_cases(self):
+        # Check remainder magnitude.
+        for dt in np.typecodes['Float']:
+            fone = np.array(1.0, dtype=dt)
+            fzer = np.array(0.0, dtype=dt)
+            fnan = np.array(np.nan, dtype=dt)
+            b = np.array(1.0, dtype=dt)
+            a = np.nextafter(np.array(0.0, dtype=dt), -b)
+            rem = np.remainder(a, b)
+            assert_(rem <= b, f'dt: {dt}')
+            rem = np.remainder(-a, -b)
+            assert_(rem >= -b, f'dt: {dt}')
+
+        # Check nans, inf
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, "invalid value encountered in remainder")
+            sup.filter(RuntimeWarning, "invalid value encountered in fmod")
+            for dt in np.typecodes['Float']:
+                fone = np.array(1.0, dtype=dt)
+                fzer = np.array(0.0, dtype=dt)
+                finf = np.array(np.inf, dtype=dt)
+                fnan = np.array(np.nan, dtype=dt)
+                rem = np.remainder(fone, fzer)
+                assert_(np.isnan(rem), f'dt: {dt}, rem: {rem}')
+                # MSVC 2008 returns NaN here, so disable the check.
+                #rem = np.remainder(fone, finf)
+                #assert_(rem == fone, 'dt: %s, rem: %s' % (dt, rem))
+                rem = np.remainder(finf, fone)
+                fmod = np.fmod(finf, fone)
+                assert_(np.isnan(fmod), f'dt: {dt}, fmod: {fmod}')
+                assert_(np.isnan(rem), f'dt: {dt}, rem: {rem}')
+                rem = np.remainder(finf, finf)
+                fmod = np.fmod(finf, fone)
+                assert_(np.isnan(rem), f'dt: {dt}, rem: {rem}')
+                assert_(np.isnan(fmod), f'dt: {dt}, fmod: {fmod}')
+                rem = np.remainder(finf, fzer)
+                fmod = np.fmod(finf, fzer)
+                assert_(np.isnan(rem), f'dt: {dt}, rem: {rem}')
+                assert_(np.isnan(fmod), f'dt: {dt}, fmod: {fmod}')
+                rem = np.remainder(fone, fnan)
+                fmod = np.fmod(fone, fnan)
+                assert_(np.isnan(rem), f'dt: {dt}, rem: {rem}')
+                assert_(np.isnan(fmod), f'dt: {dt}, fmod: {fmod}')
+                rem = np.remainder(fnan, fzer)
+                fmod = np.fmod(fnan, fzer)
+                assert_(np.isnan(rem), f'dt: {dt}, rem: {rem}')
+                assert_(np.isnan(fmod), f'dt: {dt}, fmod: {rem}')
+                rem = np.remainder(fnan, fone)
+                fmod = np.fmod(fnan, fone)
+                assert_(np.isnan(rem), f'dt: {dt}, rem: {rem}')
+                assert_(np.isnan(fmod), f'dt: {dt}, fmod: {rem}')
+
+
+class TestDivisionIntegerOverflowsAndDivideByZero:
+    result_type = namedtuple('result_type',
+            ['nocast', 'casted'])
+    helper_lambdas = {
+        'zero': lambda dtype: 0,
+        'min': lambda dtype: np.iinfo(dtype).min,
+        'neg_min': lambda dtype: -np.iinfo(dtype).min,
+        'min-zero': lambda dtype: (np.iinfo(dtype).min, 0),
+        'neg_min-zero': lambda dtype: (-np.iinfo(dtype).min, 0),
+    }
+    overflow_results = {
+        np.remainder: result_type(
+            helper_lambdas['zero'], helper_lambdas['zero']),
+        np.fmod: result_type(
+            helper_lambdas['zero'], helper_lambdas['zero']),
+        operator.mod: result_type(
+            helper_lambdas['zero'], helper_lambdas['zero']),
+        operator.floordiv: result_type(
+            helper_lambdas['min'], helper_lambdas['neg_min']),
+        np.floor_divide: result_type(
+            helper_lambdas['min'], helper_lambdas['neg_min']),
+        np.divmod: result_type(
+            helper_lambdas['min-zero'], helper_lambdas['neg_min-zero'])
+    }
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.parametrize("dtype", np.typecodes["Integer"])
+    def test_signed_division_overflow(self, dtype):
+        to_check = interesting_binop_operands(np.iinfo(dtype).min, -1, dtype)
+        for op1, op2, extractor, operand_identifier in to_check:
+            with pytest.warns(RuntimeWarning, match="overflow encountered"):
+                res = op1 // op2
+
+            assert res.dtype == op1.dtype
+            assert extractor(res) == np.iinfo(op1.dtype).min
+
+            # Remainder is well defined though, and does not warn:
+            res = op1 % op2
+            assert res.dtype == op1.dtype
+            assert extractor(res) == 0
+            # Check fmod as well:
+            res = np.fmod(op1, op2)
+            assert extractor(res) == 0
+
+            # Divmod warns for the division part:
+            with pytest.warns(RuntimeWarning, match="overflow encountered"):
+                res1, res2 = np.divmod(op1, op2)
+
+            assert res1.dtype == res2.dtype == op1.dtype
+            assert extractor(res1) == np.iinfo(op1.dtype).min
+            assert extractor(res2) == 0
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.parametrize("dtype", np.typecodes["AllInteger"])
+    def test_divide_by_zero(self, dtype):
+        # Note that the return value cannot be well defined here, but NumPy
+        # currently uses 0 consistently.  This could be changed.
+        to_check = interesting_binop_operands(1, 0, dtype)
+        for op1, op2, extractor, operand_identifier in to_check:
+            with pytest.warns(RuntimeWarning, match="divide by zero"):
+                res = op1 // op2
+
+            assert res.dtype == op1.dtype
+            assert extractor(res) == 0
+
+            with pytest.warns(RuntimeWarning, match="divide by zero"):
+                res1, res2 = np.divmod(op1, op2)
+
+            assert res1.dtype == res2.dtype == op1.dtype
+            assert extractor(res1) == 0
+            assert extractor(res2) == 0
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.parametrize("dividend_dtype", sctypes['int'])
+    @pytest.mark.parametrize("divisor_dtype", sctypes['int'])
+    @pytest.mark.parametrize("operation",
+            [np.remainder, np.fmod, np.divmod, np.floor_divide,
+             operator.mod, operator.floordiv])
+    @np.errstate(divide='warn', over='warn')
+    def test_overflows(self, dividend_dtype, divisor_dtype, operation):
+        # SIMD tries to perform the operation on as many elements as possible
+        # that is a multiple of the register's size. We resort to the
+        # default implementation for the leftover elements.
+        # We try to cover all paths here.
+        arrays = [np.array([np.iinfo(dividend_dtype).min] * i,
+                           dtype=dividend_dtype) for i in range(1, 129)]
+        divisor = np.array([-1], dtype=divisor_dtype)
+        # If dividend is a larger type than the divisor (`else` case),
+        # then, result will be a larger type than dividend and will not
+        # result in an overflow for `divmod` and `floor_divide`.
+        if np.dtype(dividend_dtype).itemsize >= np.dtype(
+                divisor_dtype).itemsize and operation in (
+                        np.divmod, np.floor_divide, operator.floordiv):
+            with pytest.warns(
+                    RuntimeWarning,
+                    match="overflow encountered in"):
+                result = operation(
+                            dividend_dtype(np.iinfo(dividend_dtype).min),
+                            divisor_dtype(-1)
+                        )
+                assert result == self.overflow_results[operation].nocast(
+                        dividend_dtype)
+
+            # Arrays
+            for a in arrays:
+                # In case of divmod, we need to flatten the result
+                # column first as we get a column vector of quotient and
+                # remainder and a normal flatten of the expected result.
+                with pytest.warns(
+                        RuntimeWarning,
+                        match="overflow encountered in"):
+                    result = np.array(operation(a, divisor)).flatten('f')
+                    expected_array = np.array(
+                            [self.overflow_results[operation].nocast(
+                                dividend_dtype)] * len(a)).flatten()
+                    assert_array_equal(result, expected_array)
+        else:
+            # Scalars
+            result = operation(
+                        dividend_dtype(np.iinfo(dividend_dtype).min),
+                        divisor_dtype(-1)
+                    )
+            assert result == self.overflow_results[operation].casted(
+                    dividend_dtype)
+
+            # Arrays
+            for a in arrays:
+                # See above comment on flatten
+                result = np.array(operation(a, divisor)).flatten('f')
+                expected_array = np.array(
+                        [self.overflow_results[operation].casted(
+                            dividend_dtype)] * len(a)).flatten()
+                assert_array_equal(result, expected_array)
+
+
+class TestCbrt:
+    def test_cbrt_scalar(self):
+        assert_almost_equal((np.cbrt(np.float32(-2.5)**3)), -2.5)
+
+    def test_cbrt(self):
+        x = np.array([1., 2., -3., np.inf, -np.inf])
+        assert_almost_equal(np.cbrt(x**3), x)
+
+        assert_(np.isnan(np.cbrt(np.nan)))
+        assert_equal(np.cbrt(np.inf), np.inf)
+        assert_equal(np.cbrt(-np.inf), -np.inf)
+
+
+class TestPower:
+    def test_power_float(self):
+        x = np.array([1., 2., 3.])
+        assert_equal(x**0, [1., 1., 1.])
+        assert_equal(x**1, x)
+        assert_equal(x**2, [1., 4., 9.])
+        y = x.copy()
+        y **= 2
+        assert_equal(y, [1., 4., 9.])
+        assert_almost_equal(x**(-1), [1., 0.5, 1. / 3])
+        assert_almost_equal(x**(0.5), [1., ncu.sqrt(2), ncu.sqrt(3)])
+
+        for out, inp, msg in _gen_alignment_data(dtype=np.float32,
+                                                 type='unary',
+                                                 max_size=11):
+            exp = [ncu.sqrt(i) for i in inp]
+            assert_almost_equal(inp**(0.5), exp, err_msg=msg)
+            np.sqrt(inp, out=out)
+            assert_equal(out, exp, err_msg=msg)
+
+        for out, inp, msg in _gen_alignment_data(dtype=np.float64,
+                                                 type='unary',
+                                                 max_size=7):
+            exp = [ncu.sqrt(i) for i in inp]
+            assert_almost_equal(inp**(0.5), exp, err_msg=msg)
+            np.sqrt(inp, out=out)
+            assert_equal(out, exp, err_msg=msg)
+
+    def test_power_complex(self):
+        x = np.array([1 + 2j, 2 + 3j, 3 + 4j])
+        assert_equal(x**0, [1., 1., 1.])
+        assert_equal(x**1, x)
+        assert_almost_equal(x**2, [-3 + 4j, -5 + 12j, -7 + 24j])
+        assert_almost_equal(x**3, [(1 + 2j)**3, (2 + 3j)**3, (3 + 4j)**3])
+        assert_almost_equal(x**4, [(1 + 2j)**4, (2 + 3j)**4, (3 + 4j)**4])
+        assert_almost_equal(x**(-1), [1 / (1 + 2j), 1 / (2 + 3j), 1 / (3 + 4j)])
+        assert_almost_equal(x**(-2), [1 / (1 + 2j)**2, 1 / (2 + 3j)**2, 1 / (3 + 4j)**2])
+        assert_almost_equal(x**(-3), [(-11 + 2j) / 125, (-46 - 9j) / 2197,
+                                      (-117 - 44j) / 15625])
+        assert_almost_equal(x**(0.5), [ncu.sqrt(1 + 2j), ncu.sqrt(2 + 3j),
+                                       ncu.sqrt(3 + 4j)])
+        norm = 1. / ((x**14)[0])
+        assert_almost_equal(x**14 * norm,
+                [i * norm for i in [-76443 + 16124j, 23161315 + 58317492j,
+                                    5583548873 + 2465133864j]])
+
+        # Ticket #836
+        def assert_complex_equal(x, y):
+            assert_array_equal(x.real, y.real)
+            assert_array_equal(x.imag, y.imag)
+
+        for z in [complex(0, np.inf), complex(1, np.inf)]:
+            z = np.array([z], dtype=np.complex128)
+            with np.errstate(invalid="ignore"):
+                assert_complex_equal(z**1, z)
+                assert_complex_equal(z**2, z * z)
+                assert_complex_equal(z**3, z * z * z)
+
+    def test_power_zero(self):
+        # ticket #1271
+        zero = np.array([0j])
+        one = np.array([1 + 0j])
+        cnan = np.array([complex(np.nan, np.nan)])
+        # FIXME cinf not tested.
+        #cinf = np.array([complex(np.inf, 0)])
+
+        def assert_complex_equal(x, y):
+            x, y = np.asarray(x), np.asarray(y)
+            assert_array_equal(x.real, y.real)
+            assert_array_equal(x.imag, y.imag)
+
+        # positive powers
+        for p in [0.33, 0.5, 1, 1.5, 2, 3, 4, 5, 6.6]:
+            assert_complex_equal(np.power(zero, p), zero)
+
+        # zero power
+        assert_complex_equal(np.power(zero, 0), one)
+        with np.errstate(invalid="ignore"):
+            assert_complex_equal(np.power(zero, 0 + 1j), cnan)
+
+            # negative power
+            for p in [0.33, 0.5, 1, 1.5, 2, 3, 4, 5, 6.6]:
+                assert_complex_equal(np.power(zero, -p), cnan)
+            assert_complex_equal(np.power(zero, -1 + 0.2j), cnan)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_zero_power_nonzero(self):
+        # Testing 0^{Non-zero} issue 18378
+        zero = np.array([0.0 + 0.0j])
+        cnan = np.array([complex(np.nan, np.nan)])
+
+        def assert_complex_equal(x, y):
+            assert_array_equal(x.real, y.real)
+            assert_array_equal(x.imag, y.imag)
+
+        # Complex powers with positive real part will not generate a warning
+        assert_complex_equal(np.power(zero, 1 + 4j), zero)
+        assert_complex_equal(np.power(zero, 2 - 3j), zero)
+        # Testing zero values when real part is greater than zero
+        assert_complex_equal(np.power(zero, 1 + 1j), zero)
+        assert_complex_equal(np.power(zero, 1 + 0j), zero)
+        assert_complex_equal(np.power(zero, 1 - 1j), zero)
+        # Complex powers will negative real part or 0 (provided imaginary
+        # part is not zero) will generate a NAN and hence a RUNTIME warning
+        with pytest.warns(expected_warning=RuntimeWarning) as r:
+            assert_complex_equal(np.power(zero, -1 + 1j), cnan)
+            assert_complex_equal(np.power(zero, -2 - 3j), cnan)
+            assert_complex_equal(np.power(zero, -7 + 0j), cnan)
+            assert_complex_equal(np.power(zero, 0 + 1j), cnan)
+            assert_complex_equal(np.power(zero, 0 - 1j), cnan)
+        assert len(r) == 5
+
+    def test_fast_power(self):
+        x = np.array([1, 2, 3], np.int16)
+        res = x**2.0
+        assert_((x**2.00001).dtype is res.dtype)
+        assert_array_equal(res, [1, 4, 9])
+        # check the inplace operation on the casted copy doesn't mess with x
+        assert_(not np.may_share_memory(res, x))
+        assert_array_equal(x, [1, 2, 3])
+
+        # Check that the fast path ignores 1-element not 0-d arrays
+        res = x ** np.array([[[2]]])
+        assert_equal(res.shape, (1, 1, 3))
+
+    def test_integer_power(self):
+        a = np.array([15, 15], 'i8')
+        b = np.power(a, a)
+        assert_equal(b, [437893890380859375, 437893890380859375])
+
+    def test_integer_power_with_integer_zero_exponent(self):
+        dtypes = np.typecodes['Integer']
+        for dt in dtypes:
+            arr = np.arange(-10, 10, dtype=dt)
+            assert_equal(np.power(arr, 0), np.ones_like(arr))
+
+        dtypes = np.typecodes['UnsignedInteger']
+        for dt in dtypes:
+            arr = np.arange(10, dtype=dt)
+            assert_equal(np.power(arr, 0), np.ones_like(arr))
+
+    def test_integer_power_of_1(self):
+        dtypes = np.typecodes['AllInteger']
+        for dt in dtypes:
+            arr = np.arange(10, dtype=dt)
+            assert_equal(np.power(1, arr), np.ones_like(arr))
+
+    def test_integer_power_of_zero(self):
+        dtypes = np.typecodes['AllInteger']
+        for dt in dtypes:
+            arr = np.arange(1, 10, dtype=dt)
+            assert_equal(np.power(0, arr), np.zeros_like(arr))
+
+    def test_integer_to_negative_power(self):
+        dtypes = np.typecodes['Integer']
+        for dt in dtypes:
+            a = np.array([0, 1, 2, 3], dtype=dt)
+            b = np.array([0, 1, 2, -3], dtype=dt)
+            one = np.array(1, dtype=dt)
+            minusone = np.array(-1, dtype=dt)
+            assert_raises(ValueError, np.power, a, b)
+            assert_raises(ValueError, np.power, a, minusone)
+            assert_raises(ValueError, np.power, one, b)
+            assert_raises(ValueError, np.power, one, minusone)
+
+    def test_float_to_inf_power(self):
+        for dt in [np.float32, np.float64]:
+            a = np.array([1, 1, 2, 2, -2, -2, np.inf, -np.inf], dt)
+            b = np.array([np.inf, -np.inf, np.inf, -np.inf,
+                                np.inf, -np.inf, np.inf, -np.inf], dt)
+            r = np.array([1, 1, np.inf, 0, np.inf, 0, np.inf, 0], dt)
+            assert_equal(np.power(a, b), r)
+
+    def test_power_fast_paths(self):
+        # gh-26055
+        for dt in [np.float32, np.float64]:
+            a = np.array([0, 1.1, 2, 12e12, -10., np.inf, -np.inf], dt)
+            expected = np.array([0.0, 1.21, 4., 1.44e+26, 100, np.inf, np.inf])
+            result = np.power(a, 2.)
+            assert_array_max_ulp(result, expected.astype(dt), maxulp=1)
+
+            a = np.array([0, 1.1, 2, 12e12], dt)
+            expected = np.sqrt(a).astype(dt)
+            result = np.power(a, 0.5)
+            assert_array_max_ulp(result, expected, maxulp=1)
+
+
+class TestFloat_power:
+    def test_type_conversion(self):
+        arg_type = '?bhilBHILefdgFDG'
+        res_type = 'ddddddddddddgDDG'
+        for dtin, dtout in zip(arg_type, res_type):
+            msg = f"dtin: {dtin}, dtout: {dtout}"
+            arg = np.ones(1, dtype=dtin)
+            res = np.float_power(arg, arg)
+            assert_(res.dtype.name == np.dtype(dtout).name, msg)
+
+
+class TestLog2:
+    @pytest.mark.parametrize('dt', ['f', 'd', 'g'])
+    def test_log2_values(self, dt):
+        x = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]
+        y = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+        xf = np.array(x, dtype=dt)
+        yf = np.array(y, dtype=dt)
+        assert_almost_equal(np.log2(xf), yf)
+
+    @pytest.mark.parametrize("i", range(1, 65))
+    def test_log2_ints(self, i):
+        # a good log2 implementation should provide this,
+        # might fail on OS with bad libm
+        v = np.log2(2.**i)
+        assert_equal(v, float(i), err_msg='at exponent %d' % i)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_log2_special(self):
+        assert_equal(np.log2(1.), 0.)
+        assert_equal(np.log2(np.inf), np.inf)
+        assert_(np.isnan(np.log2(np.nan)))
+
+        with warnings.catch_warnings(record=True) as w:
+            warnings.filterwarnings('always', '', RuntimeWarning)
+            assert_(np.isnan(np.log2(-1.)))
+            assert_(np.isnan(np.log2(-np.inf)))
+            assert_equal(np.log2(0.), -np.inf)
+            assert_(w[0].category is RuntimeWarning)
+            assert_(w[1].category is RuntimeWarning)
+            assert_(w[2].category is RuntimeWarning)
+
+
+class TestExp2:
+    def test_exp2_values(self):
+        x = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]
+        y = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+        for dt in ['f', 'd', 'g']:
+            xf = np.array(x, dtype=dt)
+            yf = np.array(y, dtype=dt)
+            assert_almost_equal(np.exp2(yf), xf)
+
+
+class TestLogAddExp2(_FilterInvalids):
+    # Need test for intermediate precisions
+    def test_logaddexp2_values(self):
+        x = [1, 2, 3, 4, 5]
+        y = [5, 4, 3, 2, 1]
+        z = [6, 6, 6, 6, 6]
+        for dt, dec_ in zip(['f', 'd', 'g'], [6, 15, 15]):
+            xf = np.log2(np.array(x, dtype=dt))
+            yf = np.log2(np.array(y, dtype=dt))
+            zf = np.log2(np.array(z, dtype=dt))
+            assert_almost_equal(np.logaddexp2(xf, yf), zf, decimal=dec_)
+
+    def test_logaddexp2_range(self):
+        x = [1000000, -1000000, 1000200, -1000200]
+        y = [1000200, -1000200, 1000000, -1000000]
+        z = [1000200, -1000000, 1000200, -1000000]
+        for dt in ['f', 'd', 'g']:
+            logxf = np.array(x, dtype=dt)
+            logyf = np.array(y, dtype=dt)
+            logzf = np.array(z, dtype=dt)
+            assert_almost_equal(np.logaddexp2(logxf, logyf), logzf)
+
+    def test_inf(self):
+        inf = np.inf
+        x = [inf, -inf,  inf, -inf, inf, 1,  -inf,  1]    # noqa: E221
+        y = [inf,  inf, -inf, -inf, 1,   inf, 1,   -inf]  # noqa: E221
+        z = [inf,  inf,  inf, -inf, inf, inf, 1,    1]
+        with np.errstate(invalid='raise'):
+            for dt in ['f', 'd', 'g']:
+                logxf = np.array(x, dtype=dt)
+                logyf = np.array(y, dtype=dt)
+                logzf = np.array(z, dtype=dt)
+                assert_equal(np.logaddexp2(logxf, logyf), logzf)
+
+    def test_nan(self):
+        assert_(np.isnan(np.logaddexp2(np.nan, np.inf)))
+        assert_(np.isnan(np.logaddexp2(np.inf, np.nan)))
+        assert_(np.isnan(np.logaddexp2(np.nan, 0)))
+        assert_(np.isnan(np.logaddexp2(0, np.nan)))
+        assert_(np.isnan(np.logaddexp2(np.nan, np.nan)))
+
+    def test_reduce(self):
+        assert_equal(np.logaddexp2.identity, -np.inf)
+        assert_equal(np.logaddexp2.reduce([]), -np.inf)
+        assert_equal(np.logaddexp2.reduce([-np.inf]), -np.inf)
+        assert_equal(np.logaddexp2.reduce([-np.inf, 0]), 0)
+
+
+class TestLog:
+    def test_log_values(self):
+        x = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]
+        y = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+        for dt in ['f', 'd', 'g']:
+            log2_ = 0.69314718055994530943
+            xf = np.array(x, dtype=dt)
+            yf = np.array(y, dtype=dt) * log2_
+            assert_almost_equal(np.log(xf), yf)
+
+        # test aliasing(issue #17761)
+        x = np.array([2, 0.937500, 3, 0.947500, 1.054697])
+        xf = np.log(x)
+        assert_almost_equal(np.log(x, out=x), xf)
+
+    def test_log_values_maxofdtype(self):
+        # test log() of max for dtype does not raise
+        dtypes = [np.float32, np.float64]
+        # This is failing at least on linux aarch64 (see gh-25460), and on most
+        # other non x86-64 platforms checking `longdouble` isn't too useful as
+        # it's an alias for float64.
+        if platform.machine() == 'x86_64':
+            dtypes += [np.longdouble]
+
+        for dt in dtypes:
+            with np.errstate(all='raise'):
+                x = np.finfo(dt).max
+                np.log(x)
+
+    def test_log_strides(self):
+        np.random.seed(42)
+        strides = np.array([-4, -3, -2, -1, 1, 2, 3, 4])
+        sizes = np.arange(2, 100)
+        for ii in sizes:
+            x_f64 = np.float64(np.random.uniform(low=0.01, high=100.0, size=ii))
+            x_special = x_f64.copy()
+            x_special[3:-1:4] = 1.0
+            y_true = np.log(x_f64)
+            y_special = np.log(x_special)
+            for jj in strides:
+                assert_array_almost_equal_nulp(np.log(x_f64[::jj]), y_true[::jj], nulp=2)
+                assert_array_almost_equal_nulp(np.log(x_special[::jj]), y_special[::jj], nulp=2)
+
+    # Reference values were computed with mpmath, with mp.dps = 200.
+    @pytest.mark.parametrize(
+        'z, wref',
+        [(1 + 1e-12j, 5e-25 + 1e-12j),
+         (1.000000000000001 + 3e-08j,
+          1.5602230246251546e-15 + 2.999999999999996e-08j),
+         (0.9999995000000417 + 0.0009999998333333417j,
+          7.831475869017683e-18 + 0.001j),
+         (0.9999999999999996 + 2.999999999999999e-08j,
+          5.9107901499372034e-18 + 3e-08j),
+         (0.99995000042 - 0.009999833j,
+          -7.015159763822903e-15 - 0.009999999665816696j)],
+    )
+    def test_log_precision_float64(self, z, wref):
+        w = np.log(z)
+        assert_allclose(w, wref, rtol=1e-15)
+
+    # Reference values were computed with mpmath, with mp.dps = 200.
+    @pytest.mark.parametrize(
+        'z, wref',
+        [(np.complex64(1.0 + 3e-6j), np.complex64(4.5e-12 + 3e-06j)),
+         (np.complex64(1.0 - 2e-5j), np.complex64(1.9999999e-10 - 2e-5j)),
+         (np.complex64(0.9999999 + 1e-06j),
+          np.complex64(-1.192088e-07 + 1.0000001e-06j))],
+    )
+    def test_log_precision_float32(self, z, wref):
+        w = np.log(z)
+        assert_allclose(w, wref, rtol=1e-6)
+
+
+class TestExp:
+    def test_exp_values(self):
+        x = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]
+        y = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+        for dt in ['f', 'd', 'g']:
+            log2_ = 0.69314718055994530943
+            xf = np.array(x, dtype=dt)
+            yf = np.array(y, dtype=dt) * log2_
+            assert_almost_equal(np.exp(yf), xf)
+
+    def test_exp_strides(self):
+        np.random.seed(42)
+        strides = np.array([-4, -3, -2, -1, 1, 2, 3, 4])
+        sizes = np.arange(2, 100)
+        for ii in sizes:
+            x_f64 = np.float64(np.random.uniform(low=0.01, high=709.1, size=ii))
+            y_true = np.exp(x_f64)
+            for jj in strides:
+                assert_array_almost_equal_nulp(np.exp(x_f64[::jj]), y_true[::jj], nulp=2)
+
+class TestSpecialFloats:
+    def test_exp_values(self):
+        with np.errstate(under='raise', over='raise'):
+            x = [np.nan,  np.nan, np.inf, 0.]
+            y = [np.nan, -np.nan, np.inf, -np.inf]
+            for dt in ['e', 'f', 'd', 'g']:
+                xf = np.array(x, dtype=dt)
+                yf = np.array(y, dtype=dt)
+                assert_equal(np.exp(yf), xf)
+
+    # See: https://github.com/numpy/numpy/issues/19192
+    @pytest.mark.xfail(
+        _glibc_older_than("2.17"),
+        reason="Older glibc versions may not raise appropriate FP exceptions"
+    )
+    def test_exp_exceptions(self):
+        with np.errstate(over='raise'):
+            assert_raises(FloatingPointError, np.exp, np.float16(11.0899))
+            assert_raises(FloatingPointError, np.exp, np.float32(100.))
+            assert_raises(FloatingPointError, np.exp, np.float32(1E19))
+            assert_raises(FloatingPointError, np.exp, np.float64(800.))
+            assert_raises(FloatingPointError, np.exp, np.float64(1E19))
+
+        with np.errstate(under='raise'):
+            assert_raises(FloatingPointError, np.exp, np.float16(-17.5))
+            assert_raises(FloatingPointError, np.exp, np.float32(-1000.))
+            assert_raises(FloatingPointError, np.exp, np.float32(-1E19))
+            assert_raises(FloatingPointError, np.exp, np.float64(-1000.))
+            assert_raises(FloatingPointError, np.exp, np.float64(-1E19))
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_log_values(self):
+        with np.errstate(all='ignore'):
+            x = [np.nan, np.nan, np.inf, np.nan, -np.inf, np.nan]
+            y = [np.nan, -np.nan, np.inf, -np.inf, 0.0, -1.0]
+            y1p = [np.nan, -np.nan, np.inf, -np.inf, -1.0, -2.0]
+            for dt in ['e', 'f', 'd', 'g']:
+                xf = np.array(x, dtype=dt)
+                yf = np.array(y, dtype=dt)
+                yf1p = np.array(y1p, dtype=dt)
+                assert_equal(np.log(yf), xf)
+                assert_equal(np.log2(yf), xf)
+                assert_equal(np.log10(yf), xf)
+                assert_equal(np.log1p(yf1p), xf)
+
+        with np.errstate(divide='raise'):
+            for dt in ['e', 'f', 'd']:
+                assert_raises(FloatingPointError, np.log,
+                              np.array(0.0, dtype=dt))
+                assert_raises(FloatingPointError, np.log2,
+                              np.array(0.0, dtype=dt))
+                assert_raises(FloatingPointError, np.log10,
+                              np.array(0.0, dtype=dt))
+                assert_raises(FloatingPointError, np.log1p,
+                              np.array(-1.0, dtype=dt))
+
+        with np.errstate(invalid='raise'):
+            for dt in ['e', 'f', 'd']:
+                assert_raises(FloatingPointError, np.log,
+                              np.array(-np.inf, dtype=dt))
+                assert_raises(FloatingPointError, np.log,
+                              np.array(-1.0, dtype=dt))
+                assert_raises(FloatingPointError, np.log2,
+                              np.array(-np.inf, dtype=dt))
+                assert_raises(FloatingPointError, np.log2,
+                              np.array(-1.0, dtype=dt))
+                assert_raises(FloatingPointError, np.log10,
+                              np.array(-np.inf, dtype=dt))
+                assert_raises(FloatingPointError, np.log10,
+                              np.array(-1.0, dtype=dt))
+                assert_raises(FloatingPointError, np.log1p,
+                              np.array(-np.inf, dtype=dt))
+                assert_raises(FloatingPointError, np.log1p,
+                              np.array(-2.0, dtype=dt))
+
+        # See https://github.com/numpy/numpy/issues/18005
+        with assert_no_warnings():
+            a = np.array(1e9, dtype='float32')
+            np.log(a)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.parametrize('dtype', ['e', 'f', 'd', 'g'])
+    def test_sincos_values(self, dtype):
+        with np.errstate(all='ignore'):
+            x = [np.nan, np.nan, np.nan, np.nan]
+            y = [np.nan, -np.nan, np.inf, -np.inf]
+            xf = np.array(x, dtype=dtype)
+            yf = np.array(y, dtype=dtype)
+            assert_equal(np.sin(yf), xf)
+            assert_equal(np.cos(yf), xf)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.xfail(
+        sys.platform.startswith("darwin"),
+        reason="underflow is triggered for scalar 'sin'"
+    )
+    def test_sincos_underflow(self):
+        with np.errstate(under='raise'):
+            underflow_trigger = np.array(
+                float.fromhex("0x1.f37f47a03f82ap-511"),
+                dtype=np.float64
+            )
+            np.sin(underflow_trigger)
+            np.cos(underflow_trigger)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.parametrize('callable', [np.sin, np.cos])
+    @pytest.mark.parametrize('dtype', ['e', 'f', 'd'])
+    @pytest.mark.parametrize('value', [np.inf, -np.inf])
+    def test_sincos_errors(self, callable, dtype, value):
+        with np.errstate(invalid='raise'):
+            assert_raises(FloatingPointError, callable,
+                np.array([value], dtype=dtype))
+
+    @pytest.mark.parametrize('callable', [np.sin, np.cos])
+    @pytest.mark.parametrize('dtype', ['f', 'd'])
+    @pytest.mark.parametrize('stride', [-1, 1, 2, 4, 5])
+    def test_sincos_overlaps(self, callable, dtype, stride):
+        N = 100
+        M = N // abs(stride)
+        rng = np.random.default_rng(42)
+        x = rng.standard_normal(N, dtype)
+        y = callable(x[::stride])
+        callable(x[::stride], out=x[:M])
+        assert_equal(x[:M], y)
+
+    @pytest.mark.parametrize('dt', ['e', 'f', 'd', 'g'])
+    def test_sqrt_values(self, dt):
+        with np.errstate(all='ignore'):
+            x = [np.nan, np.nan, np.inf, np.nan, 0.]
+            y = [np.nan, -np.nan, np.inf, -np.inf, 0.]
+            xf = np.array(x, dtype=dt)
+            yf = np.array(y, dtype=dt)
+            assert_equal(np.sqrt(yf), xf)
+
+        # with np.errstate(invalid='raise'):
+        #     assert_raises(
+        #         FloatingPointError, np.sqrt, np.array(-100., dtype=dt)
+        #     )
+
+    def test_abs_values(self):
+        x = [np.nan,  np.nan, np.inf, np.inf, 0., 0., 1.0, 1.0]
+        y = [np.nan, -np.nan, np.inf, -np.inf, 0., -0., -1.0, 1.0]
+        for dt in ['e', 'f', 'd', 'g']:
+            xf = np.array(x, dtype=dt)
+            yf = np.array(y, dtype=dt)
+            assert_equal(np.abs(yf), xf)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_square_values(self):
+        x = [np.nan,  np.nan, np.inf, np.inf]
+        y = [np.nan, -np.nan, np.inf, -np.inf]
+        with np.errstate(all='ignore'):
+            for dt in ['e', 'f', 'd', 'g']:
+                xf = np.array(x, dtype=dt)
+                yf = np.array(y, dtype=dt)
+                assert_equal(np.square(yf), xf)
+
+        with np.errstate(over='raise'):
+            assert_raises(FloatingPointError, np.square,
+                          np.array(1E3, dtype='e'))
+            assert_raises(FloatingPointError, np.square,
+                          np.array(1E32, dtype='f'))
+            assert_raises(FloatingPointError, np.square,
+                          np.array(1E200, dtype='d'))
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_reciprocal_values(self):
+        with np.errstate(all='ignore'):
+            x = [np.nan,  np.nan, 0.0, -0.0, np.inf, -np.inf]
+            y = [np.nan, -np.nan, np.inf, -np.inf, 0., -0.]
+            for dt in ['e', 'f', 'd', 'g']:
+                xf = np.array(x, dtype=dt)
+                yf = np.array(y, dtype=dt)
+                assert_equal(np.reciprocal(yf), xf)
+
+        with np.errstate(divide='raise'):
+            for dt in ['e', 'f', 'd', 'g']:
+                assert_raises(FloatingPointError, np.reciprocal,
+                              np.array(-0.0, dtype=dt))
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_tan(self):
+        with np.errstate(all='ignore'):
+            in_ = [np.nan, -np.nan, 0.0, -0.0, np.inf, -np.inf]
+            out = [np.nan, np.nan, 0.0, -0.0, np.nan, np.nan]
+            for dt in ['e', 'f', 'd']:
+                in_arr = np.array(in_, dtype=dt)
+                out_arr = np.array(out, dtype=dt)
+                assert_equal(np.tan(in_arr), out_arr)
+
+        with np.errstate(invalid='raise'):
+            for dt in ['e', 'f', 'd']:
+                assert_raises(FloatingPointError, np.tan,
+                              np.array(np.inf, dtype=dt))
+                assert_raises(FloatingPointError, np.tan,
+                              np.array(-np.inf, dtype=dt))
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_arcsincos(self):
+        with np.errstate(all='ignore'):
+            in_ = [np.nan, -np.nan, np.inf, -np.inf]
+            out = [np.nan, np.nan, np.nan, np.nan]
+            for dt in ['e', 'f', 'd']:
+                in_arr = np.array(in_, dtype=dt)
+                out_arr = np.array(out, dtype=dt)
+                assert_equal(np.arcsin(in_arr), out_arr)
+                assert_equal(np.arccos(in_arr), out_arr)
+
+        for callable in [np.arcsin, np.arccos]:
+            for value in [np.inf, -np.inf, 2.0, -2.0]:
+                for dt in ['e', 'f', 'd']:
+                    with np.errstate(invalid='raise'):
+                        assert_raises(FloatingPointError, callable,
+                                      np.array(value, dtype=dt))
+
+    def test_arctan(self):
+        with np.errstate(all='ignore'):
+            in_ = [np.nan, -np.nan]
+            out = [np.nan, np.nan]
+            for dt in ['e', 'f', 'd']:
+                in_arr = np.array(in_, dtype=dt)
+                out_arr = np.array(out, dtype=dt)
+                assert_equal(np.arctan(in_arr), out_arr)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_sinh(self):
+        in_ = [np.nan, -np.nan, np.inf, -np.inf]
+        out = [np.nan, np.nan, np.inf, -np.inf]
+        for dt in ['e', 'f', 'd']:
+            in_arr = np.array(in_, dtype=dt)
+            out_arr = np.array(out, dtype=dt)
+            assert_equal(np.sinh(in_arr), out_arr)
+
+        with np.errstate(over='raise'):
+            assert_raises(FloatingPointError, np.sinh,
+                          np.array(12.0, dtype='e'))
+            assert_raises(FloatingPointError, np.sinh,
+                          np.array(120.0, dtype='f'))
+            assert_raises(FloatingPointError, np.sinh,
+                          np.array(1200.0, dtype='d'))
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    @pytest.mark.skipif('bsd' in sys.platform,
+            reason="fallback implementation may not raise, see gh-2487")
+    def test_cosh(self):
+        in_ = [np.nan, -np.nan, np.inf, -np.inf]
+        out = [np.nan, np.nan, np.inf, np.inf]
+        for dt in ['e', 'f', 'd']:
+            in_arr = np.array(in_, dtype=dt)
+            out_arr = np.array(out, dtype=dt)
+            assert_equal(np.cosh(in_arr), out_arr)
+
+        with np.errstate(over='raise'):
+            assert_raises(FloatingPointError, np.cosh,
+                          np.array(12.0, dtype='e'))
+            assert_raises(FloatingPointError, np.cosh,
+                          np.array(120.0, dtype='f'))
+            assert_raises(FloatingPointError, np.cosh,
+                          np.array(1200.0, dtype='d'))
+
+    def test_tanh(self):
+        in_ = [np.nan, -np.nan, np.inf, -np.inf]
+        out = [np.nan, np.nan, 1.0, -1.0]
+        for dt in ['e', 'f', 'd']:
+            in_arr = np.array(in_, dtype=dt)
+            out_arr = np.array(out, dtype=dt)
+            assert_array_max_ulp(np.tanh(in_arr), out_arr, 3)
+
+    def test_arcsinh(self):
+        in_ = [np.nan, -np.nan, np.inf, -np.inf]
+        out = [np.nan, np.nan, np.inf, -np.inf]
+        for dt in ['e', 'f', 'd']:
+            in_arr = np.array(in_, dtype=dt)
+            out_arr = np.array(out, dtype=dt)
+            assert_equal(np.arcsinh(in_arr), out_arr)
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_arccosh(self):
+        with np.errstate(all='ignore'):
+            in_ = [np.nan, -np.nan, np.inf, -np.inf, 1.0, 0.0]
+            out = [np.nan, np.nan, np.inf, np.nan, 0.0, np.nan]
+            for dt in ['e', 'f', 'd']:
+                in_arr = np.array(in_, dtype=dt)
+                out_arr = np.array(out, dtype=dt)
+                assert_equal(np.arccosh(in_arr), out_arr)
+
+        for value in [0.0, -np.inf]:
+            with np.errstate(invalid='raise'):
+                for dt in ['e', 'f', 'd']:
+                    assert_raises(FloatingPointError, np.arccosh,
+                                  np.array(value, dtype=dt))
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_arctanh(self):
+        with np.errstate(all='ignore'):
+            in_ = [np.nan, -np.nan, np.inf, -np.inf, 1.0, -1.0, 2.0]
+            out = [np.nan, np.nan, np.nan, np.nan, np.inf, -np.inf, np.nan]
+            for dt in ['e', 'f', 'd']:
+                in_arr = np.array(in_, dtype=dt)
+                out_arr = np.array(out, dtype=dt)
+                assert_equal(np.arctanh(in_arr), out_arr)
+
+        for value in [1.01, np.inf, -np.inf, 1.0, -1.0]:
+            with np.errstate(invalid='raise', divide='raise'):
+                for dt in ['e', 'f', 'd']:
+                    assert_raises(FloatingPointError, np.arctanh,
+                                  np.array(value, dtype=dt))
+
+        # Make sure glibc < 2.18 atanh is not used, issue 25087
+        assert np.signbit(np.arctanh(-1j).real)
+
+    # See: https://github.com/numpy/numpy/issues/20448
+    @pytest.mark.xfail(
+        _glibc_older_than("2.17"),
+        reason="Older glibc versions may not raise appropriate FP exceptions"
+    )
+    def test_exp2(self):
+        with np.errstate(all='ignore'):
+            in_ = [np.nan, -np.nan, np.inf, -np.inf]
+            out = [np.nan, np.nan, np.inf, 0.0]
+            for dt in ['e', 'f', 'd']:
+                in_arr = np.array(in_, dtype=dt)
+                out_arr = np.array(out, dtype=dt)
+                assert_equal(np.exp2(in_arr), out_arr)
+
+        for value in [2000.0, -2000.0]:
+            with np.errstate(over='raise', under='raise'):
+                for dt in ['e', 'f', 'd']:
+                    assert_raises(FloatingPointError, np.exp2,
+                                  np.array(value, dtype=dt))
+
+    @pytest.mark.skipif(IS_WASM, reason="fp errors don't work in wasm")
+    def test_expm1(self):
+        with np.errstate(all='ignore'):
+            in_ = [np.nan, -np.nan, np.inf, -np.inf]
+            out = [np.nan, np.nan, np.inf, -1.0]
+            for dt in ['e', 'f', 'd']:
+                in_arr = np.array(in_, dtype=dt)
+                out_arr = np.array(out, dtype=dt)
+                assert_equal(np.expm1(in_arr), out_arr)
+
+        for value in [200.0, 2000.0]:
+            with np.errstate(over='raise'):
+                for dt in ['e', 'f']:
+                    assert_raises(FloatingPointError, np.expm1,
+                                  np.array(value, dtype=dt))
+
+    # test to ensure no spurious FP exceptions are raised due to SIMD
+    INF_INVALID_ERR = [
+        np.cos, np.sin, np.tan, np.arccos, np.arcsin, np.spacing, np.arctanh
+    ]
+    NEG_INVALID_ERR = [
+        np.log, np.log2, np.log10, np.log1p, np.sqrt, np.arccosh,
+        np.arctanh
+    ]
+    ONE_INVALID_ERR = [
+        np.arctanh,
+    ]
+    LTONE_INVALID_ERR = [
+        np.arccosh,
+    ]
+    BYZERO_ERR = [
+        np.log, np.log2, np.log10, np.reciprocal, np.arccosh
+    ]
+
+    @pytest.mark.parametrize("ufunc", UFUNCS_UNARY_FP)
+    @pytest.mark.parametrize("dtype", ('e', 'f', 'd'))
+    @pytest.mark.parametrize("data, escape", (
+        ([0.03], LTONE_INVALID_ERR),
+        ([0.03] * 32, LTONE_INVALID_ERR),
+        # neg
+        ([-1.0], NEG_INVALID_ERR),
+        ([-1.0] * 32, NEG_INVALID_ERR),
+        # flat
+        ([1.0], ONE_INVALID_ERR),
+        ([1.0] * 32, ONE_INVALID_ERR),
+        # zero
+        ([0.0], BYZERO_ERR),
+        ([0.0] * 32, BYZERO_ERR),
+        ([-0.0], BYZERO_ERR),
+        ([-0.0] * 32, BYZERO_ERR),
+        # nan
+        ([0.5, 0.5, 0.5, np.nan], LTONE_INVALID_ERR),
+        ([0.5, 0.5, 0.5, np.nan] * 32, LTONE_INVALID_ERR),
+        ([np.nan, 1.0, 1.0, 1.0], ONE_INVALID_ERR),
+        ([np.nan, 1.0, 1.0, 1.0] * 32, ONE_INVALID_ERR),
+        ([np.nan], []),
+        ([np.nan] * 32, []),
+        # inf
+        ([0.5, 0.5, 0.5, np.inf], INF_INVALID_ERR + LTONE_INVALID_ERR),
+        ([0.5, 0.5, 0.5, np.inf] * 32, INF_INVALID_ERR + LTONE_INVALID_ERR),
+        ([np.inf, 1.0, 1.0, 1.0], INF_INVALID_ERR),
+        ([np.inf, 1.0, 1.0, 1.0] * 32, INF_INVALID_ERR),
+        ([np.inf], INF_INVALID_ERR),
+        ([np.inf] * 32, INF_INVALID_ERR),
+        # ninf
+        ([0.5, 0.5, 0.5, -np.inf],
+         NEG_INVALID_ERR + INF_INVALID_ERR + LTONE_INVALID_ERR),
+        ([0.5, 0.5, 0.5, -np.inf] * 32,
+         NEG_INVALID_ERR + INF_INVALID_ERR + LTONE_INVALID_ERR),
+        ([-np.inf, 1.0, 1.0, 1.0], NEG_INVALID_ERR + INF_INVALID_ERR),
+        ([-np.inf, 1.0, 1.0, 1.0] * 32, NEG_INVALID_ERR + INF_INVALID_ERR),
+        ([-np.inf], NEG_INVALID_ERR + INF_INVALID_ERR),
+        ([-np.inf] * 32, NEG_INVALID_ERR + INF_INVALID_ERR),
+    ))
+    def test_unary_spurious_fpexception(self, ufunc, dtype, data, escape):
+        if escape and ufunc in escape:
+            return
+        # FIXME: NAN raises FP invalid exception:
+        #  - ceil/float16 on MSVC:32-bit
+        #  - spacing/float16 on almost all platforms
+        #  - spacing all floats on MSVC vs2022
+        if ufunc == np.spacing:
+            return
+        if ufunc == np.ceil and dtype == 'e':
+            return
+        array = np.array(data, dtype=dtype)
+        with assert_no_warnings():
+            ufunc(array)
+
+    @pytest.mark.parametrize("dtype", ('e', 'f', 'd'))
+    def test_divide_spurious_fpexception(self, dtype):
+        dt = np.dtype(dtype)
+        dt_info = np.finfo(dt)
+        subnorm = dt_info.smallest_subnormal
+        # Verify a bug fix caused due to filling the remaining lanes of the
+        # partially loaded dividend SIMD vector with ones, which leads to
+        # raising an overflow warning when the divisor is denormal.
+        # see https://github.com/numpy/numpy/issues/25097
+        with assert_no_warnings():
+            np.zeros(128 + 1, dtype=dt) / subnorm
+
+class TestFPClass:
+    @pytest.mark.parametrize("stride", [-5, -4, -3, -2, -1, 1,
+                                2, 4, 5, 6, 7, 8, 9, 10])
+    def test_fpclass(self, stride):
+        arr_f64 = np.array([np.nan, -np.nan, np.inf, -np.inf, -1.0, 1.0, -0.0, 0.0, 2.2251e-308, -2.2251e-308], dtype='d')
+        arr_f32 = np.array([np.nan, -np.nan, np.inf, -np.inf, -1.0, 1.0, -0.0, 0.0, 1.4013e-045, -1.4013e-045], dtype='f')
+        nan     = np.array([True, True, False, False, False, False, False, False, False, False])  # noqa: E221
+        inf     = np.array([False, False, True, True, False, False, False, False, False, False])  # noqa: E221
+        sign    = np.array([False, True, False, True, True, False, True, False, False, True])     # noqa: E221
+        finite  = np.array([False, False, False, False, True, True, True, True, True, True])      # noqa: E221
+        assert_equal(np.isnan(arr_f32[::stride]), nan[::stride])
+        assert_equal(np.isnan(arr_f64[::stride]), nan[::stride])
+        assert_equal(np.isinf(arr_f32[::stride]), inf[::stride])
+        assert_equal(np.isinf(arr_f64[::stride]), inf[::stride])
+        if platform.machine() == 'riscv64':
+            # On RISC-V, many operations that produce NaNs, such as converting
+            # a -NaN from f64 to f32, return a canonical NaN.  The canonical
+            # NaNs are always positive.  See section 11.3 NaN Generation and
+            # Propagation of the RISC-V Unprivileged ISA for more details.
+            # We disable the sign test on riscv64 for -np.nan as we
+            # cannot assume that its sign will be honoured in these tests.
+            arr_f64_rv = np.copy(arr_f64)
+            arr_f32_rv = np.copy(arr_f32)
+            arr_f64_rv[1] = -1.0
+            arr_f32_rv[1] = -1.0
+            assert_equal(np.signbit(arr_f32_rv[::stride]), sign[::stride])
+            assert_equal(np.signbit(arr_f64_rv[::stride]), sign[::stride])
+        else:
+            assert_equal(np.signbit(arr_f32[::stride]), sign[::stride])
+            assert_equal(np.signbit(arr_f64[::stride]), sign[::stride])
+        assert_equal(np.isfinite(arr_f32[::stride]), finite[::stride])
+        assert_equal(np.isfinite(arr_f64[::stride]), finite[::stride])
+
+    @pytest.mark.parametrize("dtype", ['d', 'f'])
+    def test_fp_noncontiguous(self, dtype):
+        data = np.array([np.nan, -np.nan, np.inf, -np.inf, -1.0,
+                            1.0, -0.0, 0.0, 2.2251e-308,
+                            -2.2251e-308], dtype=dtype)
+        nan = np.array([True, True, False, False, False, False,
+                            False, False, False, False])
+        inf = np.array([False, False, True, True, False, False,
+                            False, False, False, False])
+        sign = np.array([False, True, False, True, True, False,
+                            True, False, False, True])
+        finite = np.array([False, False, False, False, True, True,
+                            True, True, True, True])
+        out = np.ndarray(data.shape, dtype='bool')
+        ncontig_in = data[1::3]
+        ncontig_out = out[1::3]
+        contig_in = np.array(ncontig_in)
+
+        if platform.machine() == 'riscv64':
+            # Disable the -np.nan signbit tests on riscv64.  See comments in
+            # test_fpclass for more details.
+            data_rv = np.copy(data)
+            data_rv[1] = -1.0
+            ncontig_sign_in = data_rv[1::3]
+            contig_sign_in = np.array(ncontig_sign_in)
+        else:
+            ncontig_sign_in = ncontig_in
+            contig_sign_in = contig_in
+
+        assert_equal(ncontig_in.flags.c_contiguous, False)
+        assert_equal(ncontig_out.flags.c_contiguous, False)
+        assert_equal(contig_in.flags.c_contiguous, True)
+        assert_equal(ncontig_sign_in.flags.c_contiguous, False)
+        assert_equal(contig_sign_in.flags.c_contiguous, True)
+        # ncontig in, ncontig out
+        assert_equal(np.isnan(ncontig_in, out=ncontig_out), nan[1::3])
+        assert_equal(np.isinf(ncontig_in, out=ncontig_out), inf[1::3])
+        assert_equal(np.signbit(ncontig_sign_in, out=ncontig_out), sign[1::3])
+        assert_equal(np.isfinite(ncontig_in, out=ncontig_out), finite[1::3])
+        # contig in, ncontig out
+        assert_equal(np.isnan(contig_in, out=ncontig_out), nan[1::3])
+        assert_equal(np.isinf(contig_in, out=ncontig_out), inf[1::3])
+        assert_equal(np.signbit(contig_sign_in, out=ncontig_out), sign[1::3])
+        assert_equal(np.isfinite(contig_in, out=ncontig_out), finite[1::3])
+        # ncontig in, contig out
+        assert_equal(np.isnan(ncontig_in), nan[1::3])
+        assert_equal(np.isinf(ncontig_in), inf[1::3])
+        assert_equal(np.signbit(ncontig_sign_in), sign[1::3])
+        assert_equal(np.isfinite(ncontig_in), finite[1::3])
+        # contig in, contig out, nd stride
+        data_split = np.array(np.array_split(data, 2))
+        nan_split = np.array(np.array_split(nan, 2))
+        inf_split = np.array(np.array_split(inf, 2))
+        sign_split = np.array(np.array_split(sign, 2))
+        finite_split = np.array(np.array_split(finite, 2))
+        assert_equal(np.isnan(data_split), nan_split)
+        assert_equal(np.isinf(data_split), inf_split)
+        if platform.machine() == 'riscv64':
+            data_split_rv = np.array(np.array_split(data_rv, 2))
+            assert_equal(np.signbit(data_split_rv), sign_split)
+        else:
+            assert_equal(np.signbit(data_split), sign_split)
+        assert_equal(np.isfinite(data_split), finite_split)
+
+class TestLDExp:
+    @pytest.mark.parametrize("stride", [-4, -2, -1, 1, 2, 4])
+    @pytest.mark.parametrize("dtype", ['f', 'd'])
+    def test_ldexp(self, dtype, stride):
+        mant = np.array([0.125, 0.25, 0.5, 1., 1., 2., 4., 8.], dtype=dtype)
+        exp = np.array([3, 2, 1, 0, 0, -1, -2, -3], dtype='i')
+        out = np.zeros(8, dtype=dtype)
+        assert_equal(np.ldexp(mant[::stride], exp[::stride], out=out[::stride]), np.ones(8, dtype=dtype)[::stride])
+        assert_equal(out[::stride], np.ones(8, dtype=dtype)[::stride])
+
+class TestFRExp:
+    @pytest.mark.parametrize("stride", [-4, -2, -1, 1, 2, 4])
+    @pytest.mark.parametrize("dtype", ['f', 'd'])
+    @pytest.mark.skipif(not sys.platform.startswith('linux'),
+                        reason="np.frexp gives different answers for NAN/INF on windows and linux")
+    @pytest.mark.xfail(IS_MUSL, reason="gh23049")
+    def test_frexp(self, dtype, stride):
+        arr = np.array([np.nan, np.nan, np.inf, -np.inf, 0.0, -0.0, 1.0, -1.0], dtype=dtype)
+        mant_true = np.array([np.nan, np.nan, np.inf, -np.inf, 0.0, -0.0, 0.5, -0.5], dtype=dtype)
+        exp_true = np.array([0, 0, 0, 0, 0, 0, 1, 1], dtype='i')
+        out_mant = np.ones(8, dtype=dtype)
+        out_exp = 2 * np.ones(8, dtype='i')
+        mant, exp = np.frexp(arr[::stride], out=(out_mant[::stride], out_exp[::stride]))
+        assert_equal(mant_true[::stride], mant)
+        assert_equal(exp_true[::stride], exp)
+        assert_equal(out_mant[::stride], mant_true[::stride])
+        assert_equal(out_exp[::stride], exp_true[::stride])
+
+
+# func : [maxulperror, low, high]
+avx_ufuncs = {'sqrt'        : [1,  0.,   100.],   # noqa: E203
+              'absolute'    : [0, -100., 100.],   # noqa: E203
+              'reciprocal'  : [1,  1.,   100.],   # noqa: E203
+              'square'      : [1, -100., 100.],   # noqa: E203
+              'rint'        : [0, -100., 100.],   # noqa: E203
+              'floor'       : [0, -100., 100.],   # noqa: E203
+              'ceil'        : [0, -100., 100.],   # noqa: E203
+              'trunc'       : [0, -100., 100.]}   # noqa: E203
+
+class TestAVXUfuncs:
+    def test_avx_based_ufunc(self):
+        strides = np.array([-4, -3, -2, -1, 1, 2, 3, 4])
+        np.random.seed(42)
+        for func, prop in avx_ufuncs.items():
+            maxulperr = prop[0]
+            minval = prop[1]
+            maxval = prop[2]
+            # various array sizes to ensure masking in AVX is tested
+            for size in range(1, 32):
+                myfunc = getattr(np, func)
+                x_f32 = np.random.uniform(low=minval, high=maxval,
+                                          size=size).astype(np.float32)
+                x_f64 = x_f32.astype(np.float64)
+                x_f128 = x_f32.astype(np.longdouble)
+                y_true128 = myfunc(x_f128)
+                if maxulperr == 0:
+                    assert_equal(myfunc(x_f32), y_true128.astype(np.float32))
+                    assert_equal(myfunc(x_f64), y_true128.astype(np.float64))
+                else:
+                    assert_array_max_ulp(myfunc(x_f32),
+                                         y_true128.astype(np.float32),
+                                         maxulp=maxulperr)
+                    assert_array_max_ulp(myfunc(x_f64),
+                                         y_true128.astype(np.float64),
+                                         maxulp=maxulperr)
+                # various strides to test gather instruction
+                if size > 1:
+                    y_true32 = myfunc(x_f32)
+                    y_true64 = myfunc(x_f64)
+                    for jj in strides:
+                        assert_equal(myfunc(x_f64[::jj]), y_true64[::jj])
+                        assert_equal(myfunc(x_f32[::jj]), y_true32[::jj])
+
+class TestAVXFloat32Transcendental:
+    def test_exp_float32(self):
+        np.random.seed(42)
+        x_f32 = np.float32(np.random.uniform(low=0.0, high=88.1, size=1000000))
+        x_f64 = np.float64(x_f32)
+        assert_array_max_ulp(np.exp(x_f32), np.float32(np.exp(x_f64)), maxulp=3)
+
+    def test_log_float32(self):
+        np.random.seed(42)
+        x_f32 = np.float32(np.random.uniform(low=0.0, high=1000, size=1000000))
+        x_f64 = np.float64(x_f32)
+        assert_array_max_ulp(np.log(x_f32), np.float32(np.log(x_f64)), maxulp=4)
+
+    def test_sincos_float32(self):
+        np.random.seed(42)
+        N = 1000000
+        M = np.int_(N / 20)
+        index = np.random.randint(low=0, high=N, size=M)
+        x_f32 = np.float32(np.random.uniform(low=-100., high=100., size=N))
+        if not _glibc_older_than("2.17"):
+            # test coverage for elements > 117435.992f for which glibc is used
+            # this is known to be problematic on old glibc, so skip it there
+            x_f32[index] = np.float32(10E+10 * np.random.rand(M))
+        x_f64 = np.float64(x_f32)
+        assert_array_max_ulp(np.sin(x_f32), np.float32(np.sin(x_f64)), maxulp=2)
+        assert_array_max_ulp(np.cos(x_f32), np.float32(np.cos(x_f64)), maxulp=2)
+        # test aliasing(issue #17761)
+        tx_f32 = x_f32.copy()
+        assert_array_max_ulp(np.sin(x_f32, out=x_f32), np.float32(np.sin(x_f64)), maxulp=2)
+        assert_array_max_ulp(np.cos(tx_f32, out=tx_f32), np.float32(np.cos(x_f64)), maxulp=2)
+
+    def test_strided_float32(self):
+        np.random.seed(42)
+        strides = np.array([-4, -3, -2, -1, 1, 2, 3, 4])
+        sizes = np.arange(2, 100)
+        for ii in sizes:
+            x_f32 = np.float32(np.random.uniform(low=0.01, high=88.1, size=ii))
+            x_f32_large = x_f32.copy()
+            x_f32_large[3:-1:4] = 120000.0
+            exp_true = np.exp(x_f32)
+            log_true = np.log(x_f32)
+            sin_true = np.sin(x_f32_large)
+            cos_true = np.cos(x_f32_large)
+            for jj in strides:
+                assert_array_almost_equal_nulp(np.exp(x_f32[::jj]), exp_true[::jj], nulp=2)
+                assert_array_almost_equal_nulp(np.log(x_f32[::jj]), log_true[::jj], nulp=2)
+                assert_array_almost_equal_nulp(np.sin(x_f32_large[::jj]), sin_true[::jj], nulp=2)
+                assert_array_almost_equal_nulp(np.cos(x_f32_large[::jj]), cos_true[::jj], nulp=2)
+
+class TestLogAddExp(_FilterInvalids):
+    def test_logaddexp_values(self):
+        x = [1, 2, 3, 4, 5]
+        y = [5, 4, 3, 2, 1]
+        z = [6, 6, 6, 6, 6]
+        for dt, dec_ in zip(['f', 'd', 'g'], [6, 15, 15]):
+            xf = np.log(np.array(x, dtype=dt))
+            yf = np.log(np.array(y, dtype=dt))
+            zf = np.log(np.array(z, dtype=dt))
+            assert_almost_equal(np.logaddexp(xf, yf), zf, decimal=dec_)
+
+    def test_logaddexp_range(self):
+        x = [1000000, -1000000, 1000200, -1000200]
+        y = [1000200, -1000200, 1000000, -1000000]
+        z = [1000200, -1000000, 1000200, -1000000]
+        for dt in ['f', 'd', 'g']:
+            logxf = np.array(x, dtype=dt)
+            logyf = np.array(y, dtype=dt)
+            logzf = np.array(z, dtype=dt)
+            assert_almost_equal(np.logaddexp(logxf, logyf), logzf)
+
+    def test_inf(self):
+        inf = np.inf
+        x = [inf, -inf,  inf, -inf, inf, 1,  -inf,  1]    # noqa: E221
+        y = [inf,  inf, -inf, -inf, 1,   inf, 1,   -inf]  # noqa: E221
+        z = [inf,  inf,  inf, -inf, inf, inf, 1,    1]
+        with np.errstate(invalid='raise'):
+            for dt in ['f', 'd', 'g']:
+                logxf = np.array(x, dtype=dt)
+                logyf = np.array(y, dtype=dt)
+                logzf = np.array(z, dtype=dt)
+                assert_equal(np.logaddexp(logxf, logyf), logzf)
+
+    def test_nan(self):
+        assert_(np.isnan(np.logaddexp(np.nan, np.inf)))
+        assert_(np.isnan(np.logaddexp(np.inf, np.nan)))
+        assert_(np.isnan(np.logaddexp(np.nan, 0)))
+        assert_(np.isnan(np.logaddexp(0, np.nan)))
+        assert_(np.isnan(np.logaddexp(np.nan, np.nan)))
+
+    def test_reduce(self):
+        assert_equal(np.logaddexp.identity, -np.inf)
+        assert_equal(np.logaddexp.reduce([]), -np.inf)
+
+
+class TestLog1p:
+    def test_log1p(self):
+        assert_almost_equal(ncu.log1p(0.2), ncu.log(1.2))
+        assert_almost_equal(ncu.log1p(1e-6), ncu.log(1 + 1e-6))
+
+    def test_special(self):
+        with np.errstate(invalid="ignore", divide="ignore"):
+            assert_equal(ncu.log1p(np.nan), np.nan)
+            assert_equal(ncu.log1p(np.inf), np.inf)
+            assert_equal(ncu.log1p(-1.), -np.inf)
+            assert_equal(ncu.log1p(-2.), np.nan)
+            assert_equal(ncu.log1p(-np.inf), np.nan)
+
+
+class TestExpm1:
+    def test_expm1(self):
+        assert_almost_equal(ncu.expm1(0.2), ncu.exp(0.2) - 1)
+        assert_almost_equal(ncu.expm1(1e-6), ncu.exp(1e-6) - 1)
+
+    def test_special(self):
+        assert_equal(ncu.expm1(np.inf), np.inf)
+        assert_equal(ncu.expm1(0.), 0.)
+        assert_equal(ncu.expm1(-0.), -0.)
+        assert_equal(ncu.expm1(np.inf), np.inf)
+        assert_equal(ncu.expm1(-np.inf), -1.)
+
+    def test_complex(self):
+        x = np.asarray(1e-12)
+        assert_allclose(x, ncu.expm1(x))
+        x = x.astype(np.complex128)
+        assert_allclose(x, ncu.expm1(x))
+
+
+class TestHypot:
+    def test_simple(self):
+        assert_almost_equal(ncu.hypot(1, 1), ncu.sqrt(2))
+        assert_almost_equal(ncu.hypot(0, 0), 0)
+
+    def test_reduce(self):
+        assert_almost_equal(ncu.hypot.reduce([3.0, 4.0]), 5.0)
+        assert_almost_equal(ncu.hypot.reduce([3.0, 4.0, 0]), 5.0)
+        assert_almost_equal(ncu.hypot.reduce([9.0, 12.0, 20.0]), 25.0)
+        assert_equal(ncu.hypot.reduce([]), 0.0)
+
+
+def assert_hypot_isnan(x, y):
+    with np.errstate(invalid='ignore'):
+        assert_(np.isnan(ncu.hypot(x, y)),
+                f"hypot({x}, {y}) is {ncu.hypot(x, y)}, not nan")
+
+
+def assert_hypot_isinf(x, y):
+    with np.errstate(invalid='ignore'):
+        assert_(np.isinf(ncu.hypot(x, y)),
+                f"hypot({x}, {y}) is {ncu.hypot(x, y)}, not inf")
+
+
+class TestHypotSpecialValues:
+    def test_nan_outputs(self):
+        assert_hypot_isnan(np.nan, np.nan)
+        assert_hypot_isnan(np.nan, 1)
+
+    def test_nan_outputs2(self):
+        assert_hypot_isinf(np.nan, np.inf)
+        assert_hypot_isinf(np.inf, np.nan)
+        assert_hypot_isinf(np.inf, 0)
+        assert_hypot_isinf(0, np.inf)
+        assert_hypot_isinf(np.inf, np.inf)
+        assert_hypot_isinf(np.inf, 23.0)
+
+    def test_no_fpe(self):
+        assert_no_warnings(ncu.hypot, np.inf, 0)
+
+
+def assert_arctan2_isnan(x, y):
+    assert_(np.isnan(ncu.arctan2(x, y)), f"arctan({x}, {y}) is {ncu.arctan2(x, y)}, not nan")
+
+
+def assert_arctan2_ispinf(x, y):
+    assert_((np.isinf(ncu.arctan2(x, y)) and ncu.arctan2(x, y) > 0), f"arctan({x}, {y}) is {ncu.arctan2(x, y)}, not +inf")
+
+
+def assert_arctan2_isninf(x, y):
+    assert_((np.isinf(ncu.arctan2(x, y)) and ncu.arctan2(x, y) < 0), f"arctan({x}, {y}) is {ncu.arctan2(x, y)}, not -inf")
+
+
+def assert_arctan2_ispzero(x, y):
+    assert_((ncu.arctan2(x, y) == 0 and not np.signbit(ncu.arctan2(x, y))), f"arctan({x}, {y}) is {ncu.arctan2(x, y)}, not +0")
+
+
+def assert_arctan2_isnzero(x, y):
+    assert_((ncu.arctan2(x, y) == 0 and np.signbit(ncu.arctan2(x, y))), f"arctan({x}, {y}) is {ncu.arctan2(x, y)}, not -0")
+
+
+class TestArctan2SpecialValues:
+    def test_one_one(self):
+        # atan2(1, 1) returns pi/4.
+        assert_almost_equal(ncu.arctan2(1, 1), 0.25 * np.pi)
+        assert_almost_equal(ncu.arctan2(-1, 1), -0.25 * np.pi)
+        assert_almost_equal(ncu.arctan2(1, -1), 0.75 * np.pi)
+
+    def test_zero_nzero(self):
+        # atan2(+-0, -0) returns +-pi.
+        assert_almost_equal(ncu.arctan2(ncu.PZERO, ncu.NZERO), np.pi)
+        assert_almost_equal(ncu.arctan2(ncu.NZERO, ncu.NZERO), -np.pi)
+
+    def test_zero_pzero(self):
+        # atan2(+-0, +0) returns +-0.
+        assert_arctan2_ispzero(ncu.PZERO, ncu.PZERO)
+        assert_arctan2_isnzero(ncu.NZERO, ncu.PZERO)
+
+    def test_zero_negative(self):
+        # atan2(+-0, x) returns +-pi for x < 0.
+        assert_almost_equal(ncu.arctan2(ncu.PZERO, -1), np.pi)
+        assert_almost_equal(ncu.arctan2(ncu.NZERO, -1), -np.pi)
+
+    def test_zero_positive(self):
+        # atan2(+-0, x) returns +-0 for x > 0.
+        assert_arctan2_ispzero(ncu.PZERO, 1)
+        assert_arctan2_isnzero(ncu.NZERO, 1)
+
+    def test_positive_zero(self):
+        # atan2(y, +-0) returns +pi/2 for y > 0.
+        assert_almost_equal(ncu.arctan2(1, ncu.PZERO), 0.5 * np.pi)
+        assert_almost_equal(ncu.arctan2(1, ncu.NZERO), 0.5 * np.pi)
+
+    def test_negative_zero(self):
+        # atan2(y, +-0) returns -pi/2 for y < 0.
+        assert_almost_equal(ncu.arctan2(-1, ncu.PZERO), -0.5 * np.pi)
+        assert_almost_equal(ncu.arctan2(-1, ncu.NZERO), -0.5 * np.pi)
+
+    def test_any_ninf(self):
+        # atan2(+-y, -infinity) returns +-pi for finite y > 0.
+        assert_almost_equal(ncu.arctan2(1, -np.inf),  np.pi)
+        assert_almost_equal(ncu.arctan2(-1, -np.inf), -np.pi)
+
+    def test_any_pinf(self):
+        # atan2(+-y, +infinity) returns +-0 for finite y > 0.
+        assert_arctan2_ispzero(1, np.inf)
+        assert_arctan2_isnzero(-1, np.inf)
+
+    def test_inf_any(self):
+        # atan2(+-infinity, x) returns +-pi/2 for finite x.
+        assert_almost_equal(ncu.arctan2( np.inf, 1),  0.5 * np.pi)
+        assert_almost_equal(ncu.arctan2(-np.inf, 1), -0.5 * np.pi)
+
+    def test_inf_ninf(self):
+        # atan2(+-infinity, -infinity) returns +-3*pi/4.
+        assert_almost_equal(ncu.arctan2( np.inf, -np.inf),  0.75 * np.pi)
+        assert_almost_equal(ncu.arctan2(-np.inf, -np.inf), -0.75 * np.pi)
+
+    def test_inf_pinf(self):
+        # atan2(+-infinity, +infinity) returns +-pi/4.
+        assert_almost_equal(ncu.arctan2( np.inf, np.inf),  0.25 * np.pi)
+        assert_almost_equal(ncu.arctan2(-np.inf, np.inf), -0.25 * np.pi)
+
+    def test_nan_any(self):
+        # atan2(nan, x) returns nan for any x, including inf
+        assert_arctan2_isnan(np.nan, np.inf)
+        assert_arctan2_isnan(np.inf, np.nan)
+        assert_arctan2_isnan(np.nan, np.nan)
+
+
+class TestLdexp:
+    def _check_ldexp(self, tp):
+        assert_almost_equal(ncu.ldexp(np.array(2., np.float32),
+                                      np.array(3, tp)), 16.)
+        assert_almost_equal(ncu.ldexp(np.array(2., np.float64),
+                                      np.array(3, tp)), 16.)
+        assert_almost_equal(ncu.ldexp(np.array(2., np.longdouble),
+                                      np.array(3, tp)), 16.)
+
+    def test_ldexp(self):
+        # The default Python int type should work
+        assert_almost_equal(ncu.ldexp(2., 3),  16.)
+        # The following int types should all be accepted
+        self._check_ldexp(np.int8)
+        self._check_ldexp(np.int16)
+        self._check_ldexp(np.int32)
+        self._check_ldexp('i')
+        self._check_ldexp('l')
+
+    def test_ldexp_overflow(self):
+        # silence warning emitted on overflow
+        with np.errstate(over="ignore"):
+            imax = np.iinfo(np.dtype('l')).max
+            imin = np.iinfo(np.dtype('l')).min
+            assert_equal(ncu.ldexp(2., imax), np.inf)
+            assert_equal(ncu.ldexp(2., imin), 0)
+
+
+class TestMaximum(_FilterInvalids):
+    def test_reduce(self):
+        dflt = np.typecodes['AllFloat']
+        dint = np.typecodes['AllInteger']
+        seq1 = np.arange(11)
+        seq2 = seq1[::-1]
+        func = np.maximum.reduce
+        for dt in dint:
+            tmp1 = seq1.astype(dt)
+            tmp2 = seq2.astype(dt)
+            assert_equal(func(tmp1), 10)
+            assert_equal(func(tmp2), 10)
+        for dt in dflt:
+            tmp1 = seq1.astype(dt)
+            tmp2 = seq2.astype(dt)
+            assert_equal(func(tmp1), 10)
+            assert_equal(func(tmp2), 10)
+            tmp1[::2] = np.nan
+            tmp2[::2] = np.nan
+            assert_equal(func(tmp1), np.nan)
+            assert_equal(func(tmp2), np.nan)
+
+    def test_reduce_complex(self):
+        assert_equal(np.maximum.reduce([1, 2j]), 1)
+        assert_equal(np.maximum.reduce([1 + 3j, 2j]), 1 + 3j)
+
+    def test_float_nans(self):
+        nan = np.nan
+        arg1 = np.array([0,   nan, nan])
+        arg2 = np.array([nan, 0,   nan])
+        out = np.array([nan, nan, nan])
+        assert_equal(np.maximum(arg1, arg2), out)
+
+    def test_object_nans(self):
+        # Multiple checks to give this a chance to
+        # fail if cmp is used instead of rich compare.
+        # Failure cannot be guaranteed.
+        for i in range(1):
+            x = np.array(float('nan'), object)
+            y = 1.0
+            z = np.array(float('nan'), object)
+            assert_(np.maximum(x, y) == 1.0)
+            assert_(np.maximum(z, y) == 1.0)
+
+    def test_complex_nans(self):
+        nan = np.nan
+        for cnan in [complex(nan, 0), complex(0, nan), complex(nan, nan)]:
+            arg1 = np.array([0, cnan, cnan], dtype=complex)
+            arg2 = np.array([cnan, 0, cnan], dtype=complex)
+            out = np.array([nan, nan, nan], dtype=complex)
+            assert_equal(np.maximum(arg1, arg2), out)
+
+    def test_object_array(self):
+        arg1 = np.arange(5, dtype=object)
+        arg2 = arg1 + 1
+        assert_equal(np.maximum(arg1, arg2), arg2)
+
+    def test_strided_array(self):
+        arr1 = np.array([-4.0,  1.0, 10.0,   0.0, np.nan, -np.nan, np.inf, -np.inf])
+        arr2 = np.array([-2.0, -1.0, np.nan, 1.0, 0.0,     np.nan, 1.0,    -3.0])  # noqa: E221
+        maxtrue = np.array([-2.0, 1.0, np.nan, 1.0, np.nan, np.nan, np.inf, -3.0])
+        out = np.ones(8)
+        out_maxtrue = np.array([-2.0, 1.0, 1.0, 10.0, 1.0, 1.0, np.nan, 1.0])
+        assert_equal(np.maximum(arr1, arr2), maxtrue)
+        assert_equal(np.maximum(arr1[::2], arr2[::2]), maxtrue[::2])
+        assert_equal(np.maximum(arr1[:4:], arr2[::2]), np.array([-2.0, np.nan, 10.0, 1.0]))
+        assert_equal(np.maximum(arr1[::3], arr2[:3:]), np.array([-2.0, 0.0, np.nan]))
+        assert_equal(np.maximum(arr1[:6:2], arr2[::3], out=out[::3]), np.array([-2.0, 10., np.nan]))
+        assert_equal(out, out_maxtrue)
+
+    def test_precision(self):
+        dtypes = [np.float16, np.float32, np.float64, np.longdouble]
+
+        for dt in dtypes:
+            dtmin = np.finfo(dt).min
+            dtmax = np.finfo(dt).max
+            d1 = dt(0.1)
+            d1_next = np.nextafter(d1, np.inf)
+
+            test_cases = [
+                # v1    v2          expected
+                (dtmin, -np.inf,    dtmin),
+                (dtmax, -np.inf,    dtmax),
+                (d1,    d1_next,    d1_next),
+                (dtmax, np.nan,     np.nan),
+            ]
+
+            for v1, v2, expected in test_cases:
+                assert_equal(np.maximum([v1], [v2]), [expected])
+                assert_equal(np.maximum.reduce([v1, v2]), expected)
+
+
+class TestMinimum(_FilterInvalids):
+    def test_reduce(self):
+        dflt = np.typecodes['AllFloat']
+        dint = np.typecodes['AllInteger']
+        seq1 = np.arange(11)
+        seq2 = seq1[::-1]
+        func = np.minimum.reduce
+        for dt in dint:
+            tmp1 = seq1.astype(dt)
+            tmp2 = seq2.astype(dt)
+            assert_equal(func(tmp1), 0)
+            assert_equal(func(tmp2), 0)
+        for dt in dflt:
+            tmp1 = seq1.astype(dt)
+            tmp2 = seq2.astype(dt)
+            assert_equal(func(tmp1), 0)
+            assert_equal(func(tmp2), 0)
+            tmp1[::2] = np.nan
+            tmp2[::2] = np.nan
+            assert_equal(func(tmp1), np.nan)
+            assert_equal(func(tmp2), np.nan)
+
+    def test_reduce_complex(self):
+        assert_equal(np.minimum.reduce([1, 2j]), 2j)
+        assert_equal(np.minimum.reduce([1 + 3j, 2j]), 2j)
+
+    def test_float_nans(self):
+        nan = np.nan
+        arg1 = np.array([0,   nan, nan])
+        arg2 = np.array([nan, 0,   nan])
+        out = np.array([nan, nan, nan])
+        assert_equal(np.minimum(arg1, arg2), out)
+
+    def test_object_nans(self):
+        # Multiple checks to give this a chance to
+        # fail if cmp is used instead of rich compare.
+        # Failure cannot be guaranteed.
+        for i in range(1):
+            x = np.array(float('nan'), object)
+            y = 1.0
+            z = np.array(float('nan'), object)
+            assert_(np.minimum(x, y) == 1.0)
+            assert_(np.minimum(z, y) == 1.0)
+
+    def test_complex_nans(self):
+        nan = np.nan
+        for cnan in [complex(nan, 0), complex(0, nan), complex(nan, nan)]:
+            arg1 = np.array([0, cnan, cnan], dtype=complex)
+            arg2 = np.array([cnan, 0, cnan], dtype=complex)
+            out = np.array([nan, nan, nan], dtype=complex)
+            assert_equal(np.minimum(arg1, arg2), out)
+
+    def test_object_array(self):
+        arg1 = np.arange(5, dtype=object)
+        arg2 = arg1 + 1
+        assert_equal(np.minimum(arg1, arg2), arg1)
+
+    def test_strided_array(self):
+        arr1 = np.array([-4.0, 1.0, 10.0,  0.0, np.nan, -np.nan, np.inf, -np.inf])
+        arr2 = np.array([-2.0, -1.0, np.nan, 1.0, 0.0,    np.nan, 1.0, -3.0])
+        mintrue = np.array([-4.0, -1.0, np.nan, 0.0, np.nan, np.nan, 1.0, -np.inf])
+        out = np.ones(8)
+        out_mintrue = np.array([-4.0, 1.0, 1.0, 1.0, 1.0, 1.0, np.nan, 1.0])
+        assert_equal(np.minimum(arr1, arr2), mintrue)
+        assert_equal(np.minimum(arr1[::2], arr2[::2]), mintrue[::2])
+        assert_equal(np.minimum(arr1[:4:], arr2[::2]), np.array([-4.0, np.nan, 0.0, 0.0]))
+        assert_equal(np.minimum(arr1[::3], arr2[:3:]), np.array([-4.0, -1.0, np.nan]))
+        assert_equal(np.minimum(arr1[:6:2], arr2[::3], out=out[::3]), np.array([-4.0, 1.0, np.nan]))
+        assert_equal(out, out_mintrue)
+
+    def test_precision(self):
+        dtypes = [np.float16, np.float32, np.float64, np.longdouble]
+
+        for dt in dtypes:
+            dtmin = np.finfo(dt).min
+            dtmax = np.finfo(dt).max
+            d1 = dt(0.1)
+            d1_next = np.nextafter(d1, np.inf)
+
+            test_cases = [
+                # v1    v2          expected
+                (dtmin, np.inf,     dtmin),
+                (dtmax, np.inf,     dtmax),
+                (d1,    d1_next,    d1),
+                (dtmin, np.nan,     np.nan),
+            ]
+
+            for v1, v2, expected in test_cases:
+                assert_equal(np.minimum([v1], [v2]), [expected])
+                assert_equal(np.minimum.reduce([v1, v2]), expected)
+
+
+class TestFmax(_FilterInvalids):
+    def test_reduce(self):
+        dflt = np.typecodes['AllFloat']
+        dint = np.typecodes['AllInteger']
+        seq1 = np.arange(11)
+        seq2 = seq1[::-1]
+        func = np.fmax.reduce
+        for dt in dint:
+            tmp1 = seq1.astype(dt)
+            tmp2 = seq2.astype(dt)
+            assert_equal(func(tmp1), 10)
+            assert_equal(func(tmp2), 10)
+        for dt in dflt:
+            tmp1 = seq1.astype(dt)
+            tmp2 = seq2.astype(dt)
+            assert_equal(func(tmp1), 10)
+            assert_equal(func(tmp2), 10)
+            tmp1[::2] = np.nan
+            tmp2[::2] = np.nan
+            assert_equal(func(tmp1), 9)
+            assert_equal(func(tmp2), 9)
+
+    def test_reduce_complex(self):
+        assert_equal(np.fmax.reduce([1, 2j]), 1)
+        assert_equal(np.fmax.reduce([1 + 3j, 2j]), 1 + 3j)
+
+    def test_float_nans(self):
+        nan = np.nan
+        arg1 = np.array([0,   nan, nan])
+        arg2 = np.array([nan, 0,   nan])
+        out = np.array([0,   0,   nan])
+        assert_equal(np.fmax(arg1, arg2), out)
+
+    def test_complex_nans(self):
+        nan = np.nan
+        for cnan in [complex(nan, 0), complex(0, nan), complex(nan, nan)]:
+            arg1 = np.array([0, cnan, cnan], dtype=complex)
+            arg2 = np.array([cnan, 0, cnan], dtype=complex)
+            out = np.array([0,    0, nan], dtype=complex)
+            assert_equal(np.fmax(arg1, arg2), out)
+
+    def test_precision(self):
+        dtypes = [np.float16, np.float32, np.float64, np.longdouble]
+
+        for dt in dtypes:
+            dtmin = np.finfo(dt).min
+            dtmax = np.finfo(dt).max
+            d1 = dt(0.1)
+            d1_next = np.nextafter(d1, np.inf)
+
+            test_cases = [
+                # v1    v2          expected
+                (dtmin, -np.inf,    dtmin),
+                (dtmax, -np.inf,    dtmax),
+                (d1,    d1_next,    d1_next),
+                (dtmax, np.nan,     dtmax),
+            ]
+
+            for v1, v2, expected in test_cases:
+                assert_equal(np.fmax([v1], [v2]), [expected])
+                assert_equal(np.fmax.reduce([v1, v2]), expected)
+
+
+class TestFmin(_FilterInvalids):
+    def test_reduce(self):
+        dflt = np.typecodes['AllFloat']
+        dint = np.typecodes['AllInteger']
+        seq1 = np.arange(11)
+        seq2 = seq1[::-1]
+        func = np.fmin.reduce
+        for dt in dint:
+            tmp1 = seq1.astype(dt)
+            tmp2 = seq2.astype(dt)
+            assert_equal(func(tmp1), 0)
+            assert_equal(func(tmp2), 0)
+        for dt in dflt:
+            tmp1 = seq1.astype(dt)
+            tmp2 = seq2.astype(dt)
+            assert_equal(func(tmp1), 0)
+            assert_equal(func(tmp2), 0)
+            tmp1[::2] = np.nan
+            tmp2[::2] = np.nan
+            assert_equal(func(tmp1), 1)
+            assert_equal(func(tmp2), 1)
+
+    def test_reduce_complex(self):
+        assert_equal(np.fmin.reduce([1, 2j]), 2j)
+        assert_equal(np.fmin.reduce([1 + 3j, 2j]), 2j)
+
+    def test_float_nans(self):
+        nan = np.nan
+        arg1 = np.array([0,   nan, nan])
+        arg2 = np.array([nan, 0,   nan])
+        out = np.array([0,   0,   nan])
+        assert_equal(np.fmin(arg1, arg2), out)
+
+    def test_complex_nans(self):
+        nan = np.nan
+        for cnan in [complex(nan, 0), complex(0, nan), complex(nan, nan)]:
+            arg1 = np.array([0, cnan, cnan], dtype=complex)
+            arg2 = np.array([cnan, 0, cnan], dtype=complex)
+            out = np.array([0,    0, nan], dtype=complex)
+            assert_equal(np.fmin(arg1, arg2), out)
+
+    def test_precision(self):
+        dtypes = [np.float16, np.float32, np.float64, np.longdouble]
+
+        for dt in dtypes:
+            dtmin = np.finfo(dt).min
+            dtmax = np.finfo(dt).max
+            d1 = dt(0.1)
+            d1_next = np.nextafter(d1, np.inf)
+
+            test_cases = [
+                # v1    v2          expected
+                (dtmin, np.inf,     dtmin),
+                (dtmax, np.inf,     dtmax),
+                (d1,    d1_next,    d1),
+                (dtmin, np.nan,     dtmin),
+            ]
+
+            for v1, v2, expected in test_cases:
+                assert_equal(np.fmin([v1], [v2]), [expected])
+                assert_equal(np.fmin.reduce([v1, v2]), expected)
+
+
+class TestBool:
+    def test_exceptions(self):
+        a = np.ones(1, dtype=np.bool)
+        assert_raises(TypeError, np.negative, a)
+        assert_raises(TypeError, np.positive, a)
+        assert_raises(TypeError, np.subtract, a, a)
+
+    def test_truth_table_logical(self):
+        # 2, 3 and 4 serves as true values
+        input1 = [0, 0, 3, 2]
+        input2 = [0, 4, 0, 2]
+
+        typecodes = (np.typecodes['AllFloat']
+                     + np.typecodes['AllInteger']
+                     + '?')     # boolean
+        for dtype in map(np.dtype, typecodes):
+            arg1 = np.asarray(input1, dtype=dtype)
+            arg2 = np.asarray(input2, dtype=dtype)
+
+            # OR
+            out = [False, True, True, True]
+            for func in (np.logical_or, np.maximum):
+                assert_equal(func(arg1, arg2).astype(bool), out)
+            # AND
+            out = [False, False, False, True]
+            for func in (np.logical_and, np.minimum):
+                assert_equal(func(arg1, arg2).astype(bool), out)
+            # XOR
+            out = [False, True, True, False]
+            for func in (np.logical_xor, np.not_equal):
+                assert_equal(func(arg1, arg2).astype(bool), out)
+
+    def test_truth_table_bitwise(self):
+        arg1 = [False, False, True, True]
+        arg2 = [False, True, False, True]
+
+        out = [False, True, True, True]
+        assert_equal(np.bitwise_or(arg1, arg2), out)
+
+        out = [False, False, False, True]
+        assert_equal(np.bitwise_and(arg1, arg2), out)
+
+        out = [False, True, True, False]
+        assert_equal(np.bitwise_xor(arg1, arg2), out)
+
+    def test_reduce(self):
+        none = np.array([0, 0, 0, 0], bool)
+        some = np.array([1, 0, 1, 1], bool)
+        every = np.array([1, 1, 1, 1], bool)
+        empty = np.array([], bool)
+
+        arrs = [none, some, every, empty]
+
+        for arr in arrs:
+            assert_equal(np.logical_and.reduce(arr), all(arr))
+
+        for arr in arrs:
+            assert_equal(np.logical_or.reduce(arr), any(arr))
+
+        for arr in arrs:
+            assert_equal(np.logical_xor.reduce(arr), arr.sum() % 2 == 1)
+
+
+class TestBitwiseUFuncs:
+
+    _all_ints_bits = [
+        np.dtype(c).itemsize * 8 for c in np.typecodes["AllInteger"]]
+    bitwise_types = [
+        np.dtype(c) for c in '?' + np.typecodes["AllInteger"] + 'O']
+    bitwise_bits = [
+        2,  # boolean type
+        *_all_ints_bits,  # All integers
+        max(_all_ints_bits) + 1,  # Object_ type
+    ]
+
+    def test_values(self):
+        for dt in self.bitwise_types:
+            zeros = np.array([0], dtype=dt)
+            ones = np.array([-1]).astype(dt)
+            msg = f"dt = '{dt.char}'"
+
+            assert_equal(np.bitwise_not(zeros), ones, err_msg=msg)
+            assert_equal(np.bitwise_not(ones), zeros, err_msg=msg)
+
+            assert_equal(np.bitwise_or(zeros, zeros), zeros, err_msg=msg)
+            assert_equal(np.bitwise_or(zeros, ones), ones, err_msg=msg)
+            assert_equal(np.bitwise_or(ones, zeros), ones, err_msg=msg)
+            assert_equal(np.bitwise_or(ones, ones), ones, err_msg=msg)
+
+            assert_equal(np.bitwise_xor(zeros, zeros), zeros, err_msg=msg)
+            assert_equal(np.bitwise_xor(zeros, ones), ones, err_msg=msg)
+            assert_equal(np.bitwise_xor(ones, zeros), ones, err_msg=msg)
+            assert_equal(np.bitwise_xor(ones, ones), zeros, err_msg=msg)
+
+            assert_equal(np.bitwise_and(zeros, zeros), zeros, err_msg=msg)
+            assert_equal(np.bitwise_and(zeros, ones), zeros, err_msg=msg)
+            assert_equal(np.bitwise_and(ones, zeros), zeros, err_msg=msg)
+            assert_equal(np.bitwise_and(ones, ones), ones, err_msg=msg)
+
+    def test_types(self):
+        for dt in self.bitwise_types:
+            zeros = np.array([0], dtype=dt)
+            ones = np.array([-1]).astype(dt)
+            msg = f"dt = '{dt.char}'"
+
+            assert_(np.bitwise_not(zeros).dtype == dt, msg)
+            assert_(np.bitwise_or(zeros, zeros).dtype == dt, msg)
+            assert_(np.bitwise_xor(zeros, zeros).dtype == dt, msg)
+            assert_(np.bitwise_and(zeros, zeros).dtype == dt, msg)
+
+    def test_identity(self):
+        assert_(np.bitwise_or.identity == 0, 'bitwise_or')
+        assert_(np.bitwise_xor.identity == 0, 'bitwise_xor')
+        assert_(np.bitwise_and.identity == -1, 'bitwise_and')
+
+    def test_reduction(self):
+        binary_funcs = (np.bitwise_or, np.bitwise_xor, np.bitwise_and)
+
+        for dt in self.bitwise_types:
+            zeros = np.array([0], dtype=dt)
+            ones = np.array([-1]).astype(dt)
+            for f in binary_funcs:
+                msg = f"dt: '{dt}', f: '{f}'"
+                assert_equal(f.reduce(zeros), zeros, err_msg=msg)
+                assert_equal(f.reduce(ones), ones, err_msg=msg)
+
+        # Test empty reduction, no object dtype
+        for dt in self.bitwise_types[:-1]:
+            # No object array types
+            empty = np.array([], dtype=dt)
+            for f in binary_funcs:
+                msg = f"dt: '{dt}', f: '{f}'"
+                tgt = np.array(f.identity).astype(dt)
+                res = f.reduce(empty)
+                assert_equal(res, tgt, err_msg=msg)
+                assert_(res.dtype == tgt.dtype, msg)
+
+        # Empty object arrays use the identity.  Note that the types may
+        # differ, the actual type used is determined by the assign_identity
+        # function and is not the same as the type returned by the identity
+        # method.
+        for f in binary_funcs:
+            msg = f"dt: '{f}'"
+            empty = np.array([], dtype=object)
+            tgt = f.identity
+            res = f.reduce(empty)
+            assert_equal(res, tgt, err_msg=msg)
+
+        # Non-empty object arrays do not use the identity
+        for f in binary_funcs:
+            msg = f"dt: '{f}'"
+            btype = np.array([True], dtype=object)
+            assert_(type(f.reduce(btype)) is bool, msg)
+
+    @pytest.mark.parametrize("input_dtype_obj, bitsize",
+            zip(bitwise_types, bitwise_bits))
+    def test_bitwise_count(self, input_dtype_obj, bitsize):
+        input_dtype = input_dtype_obj.type
+
+        for i in range(1, bitsize):
+            num = 2**i - 1
+            msg = f"bitwise_count for {num}"
+            assert i == np.bitwise_count(input_dtype(num)), msg
+            if np.issubdtype(
+                input_dtype, np.signedinteger) or input_dtype == np.object_:
+                assert i == np.bitwise_count(input_dtype(-num)), msg
+
+        a = np.array([2**i - 1 for i in range(1, bitsize)], dtype=input_dtype)
+        bitwise_count_a = np.bitwise_count(a)
+        expected = np.arange(1, bitsize, dtype=input_dtype)
+
+        msg = f"array bitwise_count for {input_dtype}"
+        assert all(bitwise_count_a == expected), msg
+
+
+class TestInt:
+    def test_logical_not(self):
+        x = np.ones(10, dtype=np.int16)
+        o = np.ones(10 * 2, dtype=bool)
+        tgt = o.copy()
+        tgt[::2] = False
+        os = o[::2]
+        assert_array_equal(np.logical_not(x, out=os), False)
+        assert_array_equal(o, tgt)
+
+
+class TestFloatingPoint:
+    def test_floating_point(self):
+        assert_equal(ncu.FLOATING_POINT_SUPPORT, 1)
+
+
+class TestDegrees:
+    def test_degrees(self):
+        assert_almost_equal(ncu.degrees(np.pi), 180.0)
+        assert_almost_equal(ncu.degrees(-0.5 * np.pi), -90.0)
+
+
+class TestRadians:
+    def test_radians(self):
+        assert_almost_equal(ncu.radians(180.0), np.pi)
+        assert_almost_equal(ncu.radians(-90.0), -0.5 * np.pi)
+
+
+class TestHeavside:
+    def test_heaviside(self):
+        x = np.array([[-30.0, -0.1, 0.0, 0.2], [7.5, np.nan, np.inf, -np.inf]])
+        expectedhalf = np.array([[0.0, 0.0, 0.5, 1.0], [1.0, np.nan, 1.0, 0.0]])
+        expected1 = expectedhalf.copy()
+        expected1[0, 2] = 1
+
+        h = ncu.heaviside(x, 0.5)
+        assert_equal(h, expectedhalf)
+
+        h = ncu.heaviside(x, 1.0)
+        assert_equal(h, expected1)
+
+        x = x.astype(np.float32)
+
+        h = ncu.heaviside(x, np.float32(0.5))
+        assert_equal(h, expectedhalf.astype(np.float32))
+
+        h = ncu.heaviside(x, np.float32(1.0))
+        assert_equal(h, expected1.astype(np.float32))
+
+
+class TestSign:
+    def test_sign(self):
+        a = np.array([np.inf, -np.inf, np.nan, 0.0, 3.0, -3.0])
+        out = np.zeros(a.shape)
+        tgt = np.array([1., -1., np.nan, 0.0, 1.0, -1.0])
+
+        with np.errstate(invalid='ignore'):
+            res = ncu.sign(a)
+            assert_equal(res, tgt)
+            res = ncu.sign(a, out)
+            assert_equal(res, tgt)
+            assert_equal(out, tgt)
+
+    def test_sign_complex(self):
+        a = np.array([
+            np.inf, -np.inf, complex(0, np.inf), complex(0, -np.inf),
+            complex(np.inf, np.inf), complex(np.inf, -np.inf),  # nan
+            np.nan, complex(0, np.nan), complex(np.nan, np.nan),  # nan
+            0.0,  # 0.
+            3.0, -3.0, -2j, 3.0 + 4.0j, -8.0 + 6.0j
+        ])
+        out = np.zeros(a.shape, a.dtype)
+        tgt = np.array([
+            1., -1., 1j, -1j,
+            ] + [complex(np.nan, np.nan)] * 5 + [
+            0.0,
+            1.0, -1.0, -1j, 0.6 + 0.8j, -0.8 + 0.6j])
+
+        with np.errstate(invalid='ignore'):
+            res = ncu.sign(a)
+            assert_equal(res, tgt)
+            res = ncu.sign(a, out)
+            assert_(res is out)
+            assert_equal(res, tgt)
+
+    def test_sign_dtype_object(self):
+        # In reference to github issue #6229
+
+        foo = np.array([-.1, 0, .1])
+        a = np.sign(foo.astype(object))
+        b = np.sign(foo)
+
+        assert_array_equal(a, b)
+
+    def test_sign_dtype_nan_object(self):
+        # In reference to github issue #6229
+        def test_nan():
+            foo = np.array([np.nan])
+            # FIXME: a not used
+            a = np.sign(foo.astype(object))
+
+        assert_raises(TypeError, test_nan)
+
+class TestMinMax:
+    def test_minmax_blocked(self):
+        # simd tests on max/min, test all alignments, slow but important
+        # for 2 * vz + 2 * (vs - 1) + 1 (unrolled once)
+        for dt, sz in [(np.float32, 15), (np.float64, 7)]:
+            for out, inp, msg in _gen_alignment_data(dtype=dt, type='unary',
+                                                     max_size=sz):
+                for i in range(inp.size):
+                    inp[:] = np.arange(inp.size, dtype=dt)
+                    inp[i] = np.nan
+                    emsg = lambda: f'{inp!r}\n{msg}'
+                    with suppress_warnings() as sup:
+                        sup.filter(RuntimeWarning,
+                                   "invalid value encountered in reduce")
+                        assert_(np.isnan(inp.max()), msg=emsg)
+                        assert_(np.isnan(inp.min()), msg=emsg)
+
+                    inp[i] = 1e10
+                    assert_equal(inp.max(), 1e10, err_msg=msg)
+                    inp[i] = -1e10
+                    assert_equal(inp.min(), -1e10, err_msg=msg)
+
+    def test_lower_align(self):
+        # check data that is not aligned to element size
+        # i.e doubles are aligned to 4 bytes on i386
+        d = np.zeros(23 * 8, dtype=np.int8)[4:-4].view(np.float64)
+        assert_equal(d.max(), d[0])
+        assert_equal(d.min(), d[0])
+
+    def test_reduce_reorder(self):
+        # gh 10370, 11029 Some compilers reorder the call to npy_getfloatstatus
+        # and put it before the call to an intrinsic function that causes
+        # invalid status to be set. Also make sure warnings are not emitted
+        for n in (2, 4, 8, 16, 32):
+            for dt in (np.float32, np.float16, np.complex64):
+                for r in np.diagflat(np.array([np.nan] * n, dtype=dt)):
+                    assert_equal(np.min(r), np.nan)
+
+    def test_minimize_no_warns(self):
+        a = np.minimum(np.nan, 1)
+        assert_equal(a, np.nan)
+
+
+class TestAbsoluteNegative:
+    def test_abs_neg_blocked(self):
+        # simd tests on abs, test all alignments for vz + 2 * (vs - 1) + 1
+        for dt, sz in [(np.float32, 11), (np.float64, 5)]:
+            for out, inp, msg in _gen_alignment_data(dtype=dt, type='unary',
+                                                     max_size=sz):
+                tgt = [ncu.absolute(i) for i in inp]
+                np.absolute(inp, out=out)
+                assert_equal(out, tgt, err_msg=msg)
+                assert_((out >= 0).all())
+
+                tgt = [-1 * (i) for i in inp]
+                np.negative(inp, out=out)
+                assert_equal(out, tgt, err_msg=msg)
+
+                for v in [np.nan, -np.inf, np.inf]:
+                    for i in range(inp.size):
+                        d = np.arange(inp.size, dtype=dt)
+                        inp[:] = -d
+                        inp[i] = v
+                        d[i] = -v if v == -np.inf else v
+                        assert_array_equal(np.abs(inp), d, err_msg=msg)
+                        np.abs(inp, out=out)
+                        assert_array_equal(out, d, err_msg=msg)
+
+                        assert_array_equal(-inp, -1 * inp, err_msg=msg)
+                        d = -1 * inp
+                        np.negative(inp, out=out)
+                        assert_array_equal(out, d, err_msg=msg)
+
+    def test_lower_align(self):
+        # check data that is not aligned to element size
+        # i.e doubles are aligned to 4 bytes on i386
+        d = np.zeros(23 * 8, dtype=np.int8)[4:-4].view(np.float64)
+        assert_equal(np.abs(d), d)
+        assert_equal(np.negative(d), -d)
+        np.negative(d, out=d)
+        np.negative(np.ones_like(d), out=d)
+        np.abs(d, out=d)
+        np.abs(np.ones_like(d), out=d)
+
+    @pytest.mark.parametrize("dtype", ['d', 'f', 'int32', 'int64'])
+    @pytest.mark.parametrize("big", [True, False])
+    def test_noncontiguous(self, dtype, big):
+        data = np.array([-1.0, 1.0, -0.0, 0.0, 2.2251e-308, -2.5, 2.5, -6,
+                            6, -2.2251e-308, -8, 10], dtype=dtype)
+        expect = np.array([1.0, -1.0, 0.0, -0.0, -2.2251e-308, 2.5, -2.5, 6,
+                            -6, 2.2251e-308, 8, -10], dtype=dtype)
+        if big:
+            data = np.repeat(data, 10)
+            expect = np.repeat(expect, 10)
+        out = np.ndarray(data.shape, dtype=dtype)
+        ncontig_in = data[1::2]
+        ncontig_out = out[1::2]
+        contig_in = np.array(ncontig_in)
+        # contig in, contig out
+        assert_array_equal(np.negative(contig_in), expect[1::2])
+        # contig in, ncontig out
+        assert_array_equal(np.negative(contig_in, out=ncontig_out),
+                                expect[1::2])
+        # ncontig in, contig out
+        assert_array_equal(np.negative(ncontig_in), expect[1::2])
+        # ncontig in, ncontig out
+        assert_array_equal(np.negative(ncontig_in, out=ncontig_out),
+                                expect[1::2])
+        # contig in, contig out, nd stride
+        data_split = np.array(np.array_split(data, 2))
+        expect_split = np.array(np.array_split(expect, 2))
+        assert_equal(np.negative(data_split), expect_split)
+
+
+class TestPositive:
+    def test_valid(self):
+        valid_dtypes = [int, float, complex, object]
+        for dtype in valid_dtypes:
+            x = np.arange(5, dtype=dtype)
+            result = np.positive(x)
+            assert_equal(x, result, err_msg=str(dtype))
+
+    def test_invalid(self):
+        with assert_raises(TypeError):
+            np.positive(True)
+        with assert_raises(TypeError):
+            np.positive(np.datetime64('2000-01-01'))
+        with assert_raises(TypeError):
+            np.positive(np.array(['foo'], dtype=str))
+        with assert_raises(TypeError):
+            np.positive(np.array(['bar'], dtype=object))
+
+
+class TestSpecialMethods:
+    def test_wrap(self):
+
+        class with_wrap:
+            def __array__(self, dtype=None, copy=None):
+                return np.zeros(1)
+
+            def __array_wrap__(self, arr, context, return_scalar):
+                r = with_wrap()
+                r.arr = arr
+                r.context = context
+                return r
+
+        a = with_wrap()
+        x = ncu.minimum(a, a)
+        assert_equal(x.arr, np.zeros(1))
+        func, args, i = x.context
+        assert_(func is ncu.minimum)
+        assert_equal(len(args), 2)
+        assert_equal(args[0], a)
+        assert_equal(args[1], a)
+        assert_equal(i, 0)
+
+    def test_wrap_out(self):
+        # Calling convention for out should not affect how special methods are
+        # called
+
+        class StoreArrayPrepareWrap(np.ndarray):
+            _wrap_args = None
+            _prepare_args = None
+
+            def __new__(cls):
+                return np.zeros(()).view(cls)
+
+            def __array_wrap__(self, obj, context, return_scalar):
+                self._wrap_args = context[1]
+                return obj
+
+            @property
+            def args(self):
+                # We need to ensure these are fetched at the same time, before
+                # any other ufuncs are called by the assertions
+                return self._wrap_args
+
+            def __repr__(self):
+                return "a"  # for short test output
+
+        def do_test(f_call, f_expected):
+            a = StoreArrayPrepareWrap()
+
+            f_call(a)
+
+            w = a.args
+            expected = f_expected(a)
+            try:
+                assert w == expected
+            except AssertionError as e:
+                # assert_equal produces truly useless error messages
+                raise AssertionError("\n".join([
+                    "Bad arguments passed in ufunc call",
+                    f" expected:              {expected}",
+                    f" __array_wrap__ got:    {w}"
+                ]))
+
+        # method not on the out argument
+        do_test(lambda a: np.add(a, 0), lambda a: (a, 0))
+        do_test(lambda a: np.add(a, 0, None), lambda a: (a, 0))
+        do_test(lambda a: np.add(a, 0, out=None), lambda a: (a, 0))
+        do_test(lambda a: np.add(a, 0, out=(None,)), lambda a: (a, 0))
+
+        # method on the out argument
+        do_test(lambda a: np.add(0, 0, a), lambda a: (0, 0, a))
+        do_test(lambda a: np.add(0, 0, out=a), lambda a: (0, 0, a))
+        do_test(lambda a: np.add(0, 0, out=(a,)), lambda a: (0, 0, a))
+
+        # Also check the where mask handling:
+        do_test(lambda a: np.add(a, 0, where=False), lambda a: (a, 0))
+        do_test(lambda a: np.add(0, 0, a, where=False), lambda a: (0, 0, a))
+
+    def test_wrap_with_iterable(self):
+        # test fix for bug #1026:
+
+        class with_wrap(np.ndarray):
+            __array_priority__ = 10
+
+            def __new__(cls):
+                return np.asarray(1).view(cls).copy()
+
+            def __array_wrap__(self, arr, context, return_scalar):
+                return arr.view(type(self))
+
+        a = with_wrap()
+        x = ncu.multiply(a, (1, 2, 3))
+        assert_(isinstance(x, with_wrap))
+        assert_array_equal(x, np.array((1, 2, 3)))
+
+    def test_priority_with_scalar(self):
+        # test fix for bug #826:
+
+        class A(np.ndarray):
+            __array_priority__ = 10
+
+            def __new__(cls):
+                return np.asarray(1.0, 'float64').view(cls).copy()
+
+        a = A()
+        x = np.float64(1) * a
+        assert_(isinstance(x, A))
+        assert_array_equal(x, np.array(1))
+
+    def test_priority(self):
+
+        class A:
+            def __array__(self, dtype=None, copy=None):
+                return np.zeros(1)
+
+            def __array_wrap__(self, arr, context, return_scalar):
+                r = type(self)()
+                r.arr = arr
+                r.context = context
+                return r
+
+        class B(A):
+            __array_priority__ = 20.
+
+        class C(A):
+            __array_priority__ = 40.
+
+        x = np.zeros(1)
+        a = A()
+        b = B()
+        c = C()
+        f = ncu.minimum
+        assert_(type(f(x, x)) is np.ndarray)
+        assert_(type(f(x, a)) is A)
+        assert_(type(f(x, b)) is B)
+        assert_(type(f(x, c)) is C)
+        assert_(type(f(a, x)) is A)
+        assert_(type(f(b, x)) is B)
+        assert_(type(f(c, x)) is C)
+
+        assert_(type(f(a, a)) is A)
+        assert_(type(f(a, b)) is B)
+        assert_(type(f(b, a)) is B)
+        assert_(type(f(b, b)) is B)
+        assert_(type(f(b, c)) is C)
+        assert_(type(f(c, b)) is C)
+        assert_(type(f(c, c)) is C)
+
+        assert_(type(ncu.exp(a) is A))
+        assert_(type(ncu.exp(b) is B))
+        assert_(type(ncu.exp(c) is C))
+
+    def test_failing_wrap(self):
+
+        class A:
+            def __array__(self, dtype=None, copy=None):
+                return np.zeros(2)
+
+            def __array_wrap__(self, arr, context, return_scalar):
+                raise RuntimeError
+
+        a = A()
+        assert_raises(RuntimeError, ncu.maximum, a, a)
+        assert_raises(RuntimeError, ncu.maximum.reduce, a)
+
+    def test_failing_out_wrap(self):
+
+        singleton = np.array([1.0])
+
+        class Ok(np.ndarray):
+            def __array_wrap__(self, obj, context, return_scalar):
+                return singleton
+
+        class Bad(np.ndarray):
+            def __array_wrap__(self, obj, context, return_scalar):
+                raise RuntimeError
+
+        ok = np.empty(1).view(Ok)
+        bad = np.empty(1).view(Bad)
+        # double-free (segfault) of "ok" if "bad" raises an exception
+        for i in range(10):
+            assert_raises(RuntimeError, ncu.frexp, 1, ok, bad)
+
+    def test_none_wrap(self):
+        # Tests that issue #8507 is resolved. Previously, this would segfault
+
+        class A:
+            def __array__(self, dtype=None, copy=None):
+                return np.zeros(1)
+
+            def __array_wrap__(self, arr, context=None, return_scalar=False):
+                return None
+
+        a = A()
+        assert_equal(ncu.maximum(a, a), None)
+
+    def test_default_prepare(self):
+
+        class with_wrap:
+            __array_priority__ = 10
+
+            def __array__(self, dtype=None, copy=None):
+                return np.zeros(1)
+
+            def __array_wrap__(self, arr, context, return_scalar):
+                return arr
+
+        a = with_wrap()
+        x = ncu.minimum(a, a)
+        assert_equal(x, np.zeros(1))
+        assert_equal(type(x), np.ndarray)
+
+    def test_array_too_many_args(self):
+
+        class A:
+            def __array__(self, dtype, context, copy=None):
+                return np.zeros(1)
+
+        a = A()
+        assert_raises_regex(TypeError, '2 required positional', np.sum, a)
+
+    def test_ufunc_override(self):
+        # check override works even with instance with high priority.
+        class A:
+            def __array_ufunc__(self, func, method, *inputs, **kwargs):
+                return self, func, method, inputs, kwargs
+
+        class MyNDArray(np.ndarray):
+            __array_priority__ = 100
+
+        a = A()
+        b = np.array([1]).view(MyNDArray)
+        res0 = np.multiply(a, b)
+        res1 = np.multiply(b, b, out=a)
+
+        # self
+        assert_equal(res0[0], a)
+        assert_equal(res1[0], a)
+        assert_equal(res0[1], np.multiply)
+        assert_equal(res1[1], np.multiply)
+        assert_equal(res0[2], '__call__')
+        assert_equal(res1[2], '__call__')
+        assert_equal(res0[3], (a, b))
+        assert_equal(res1[3], (b, b))
+        assert_equal(res0[4], {})
+        assert_equal(res1[4], {'out': (a,)})
+
+    def test_ufunc_override_mro(self):
+
+        # Some multi arg functions for testing.
+        def tres_mul(a, b, c):
+            return a * b * c
+
+        def quatro_mul(a, b, c, d):
+            return a * b * c * d
+
+        # Make these into ufuncs.
+        three_mul_ufunc = np.frompyfunc(tres_mul, 3, 1)
+        four_mul_ufunc = np.frompyfunc(quatro_mul, 4, 1)
+
+        class A:
+            def __array_ufunc__(self, func, method, *inputs, **kwargs):
+                return "A"
+
+        class ASub(A):
+            def __array_ufunc__(self, func, method, *inputs, **kwargs):
+                return "ASub"
+
+        class B:
+            def __array_ufunc__(self, func, method, *inputs, **kwargs):
+                return "B"
+
+        class C:
+            def __init__(self):
+                self.count = 0
+
+            def __array_ufunc__(self, func, method, *inputs, **kwargs):
+                self.count += 1
+                return NotImplemented
+
+        class CSub(C):
+            def __array_ufunc__(self, func, method, *inputs, **kwargs):
+                self.count += 1
+                return NotImplemented
+
+        a = A()
+        a_sub = ASub()
+        b = B()
+        c = C()
+
+        # Standard
+        res = np.multiply(a, a_sub)
+        assert_equal(res, "ASub")
+        res = np.multiply(a_sub, b)
+        assert_equal(res, "ASub")
+
+        # With 1 NotImplemented
+        res = np.multiply(c, a)
+        assert_equal(res, "A")
+        assert_equal(c.count, 1)
+        # Check our counter works, so we can trust tests below.
+        res = np.multiply(c, a)
+        assert_equal(c.count, 2)
+
+        # Both NotImplemented.
+        c = C()
+        c_sub = CSub()
+        assert_raises(TypeError, np.multiply, c, c_sub)
+        assert_equal(c.count, 1)
+        assert_equal(c_sub.count, 1)
+        c.count = c_sub.count = 0
+        assert_raises(TypeError, np.multiply, c_sub, c)
+        assert_equal(c.count, 1)
+        assert_equal(c_sub.count, 1)
+        c.count = 0
+        assert_raises(TypeError, np.multiply, c, c)
+        assert_equal(c.count, 1)
+        c.count = 0
+        assert_raises(TypeError, np.multiply, 2, c)
+        assert_equal(c.count, 1)
+
+        # Ternary testing.
+        assert_equal(three_mul_ufunc(a, 1, 2), "A")
+        assert_equal(three_mul_ufunc(1, a, 2), "A")
+        assert_equal(three_mul_ufunc(1, 2, a), "A")
+
+        assert_equal(three_mul_ufunc(a, a, 6), "A")
+        assert_equal(three_mul_ufunc(a, 2, a), "A")
+        assert_equal(three_mul_ufunc(a, 2, b), "A")
+        assert_equal(three_mul_ufunc(a, 2, a_sub), "ASub")
+        assert_equal(three_mul_ufunc(a, a_sub, 3), "ASub")
+        c.count = 0
+        assert_equal(three_mul_ufunc(c, a_sub, 3), "ASub")
+        assert_equal(c.count, 1)
+        c.count = 0
+        assert_equal(three_mul_ufunc(1, a_sub, c), "ASub")
+        assert_equal(c.count, 0)
+
+        c.count = 0
+        assert_equal(three_mul_ufunc(a, b, c), "A")
+        assert_equal(c.count, 0)
+        c_sub.count = 0
+        assert_equal(three_mul_ufunc(a, b, c_sub), "A")
+        assert_equal(c_sub.count, 0)
+        assert_equal(three_mul_ufunc(1, 2, b), "B")
+
+        assert_raises(TypeError, three_mul_ufunc, 1, 2, c)
+        assert_raises(TypeError, three_mul_ufunc, c_sub, 2, c)
+        assert_raises(TypeError, three_mul_ufunc, c_sub, 2, 3)
+
+        # Quaternary testing.
+        assert_equal(four_mul_ufunc(a, 1, 2, 3), "A")
+        assert_equal(four_mul_ufunc(1, a, 2, 3), "A")
+        assert_equal(four_mul_ufunc(1, 1, a, 3), "A")
+        assert_equal(four_mul_ufunc(1, 1, 2, a), "A")
+
+        assert_equal(four_mul_ufunc(a, b, 2, 3), "A")
+        assert_equal(four_mul_ufunc(1, a, 2, b), "A")
+        assert_equal(four_mul_ufunc(b, 1, a, 3), "B")
+        assert_equal(four_mul_ufunc(a_sub, 1, 2, a), "ASub")
+        assert_equal(four_mul_ufunc(a, 1, 2, a_sub), "ASub")
+
+        c = C()
+        c_sub = CSub()
+        assert_raises(TypeError, four_mul_ufunc, 1, 2, 3, c)
+        assert_equal(c.count, 1)
+        c.count = 0
+        assert_raises(TypeError, four_mul_ufunc, 1, 2, c_sub, c)
+        assert_equal(c_sub.count, 1)
+        assert_equal(c.count, 1)
+        c2 = C()
+        c.count = c_sub.count = 0
+        assert_raises(TypeError, four_mul_ufunc, 1, c, c_sub, c2)
+        assert_equal(c_sub.count, 1)
+        assert_equal(c.count, 1)
+        assert_equal(c2.count, 0)
+        c.count = c2.count = c_sub.count = 0
+        assert_raises(TypeError, four_mul_ufunc, c2, c, c_sub, c)
+        assert_equal(c_sub.count, 1)
+        assert_equal(c.count, 0)
+        assert_equal(c2.count, 1)
+
+    def test_ufunc_override_methods(self):
+
+        class A:
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+                return self, ufunc, method, inputs, kwargs
+
+        # __call__
+        a = A()
+        with assert_raises(TypeError):
+            np.multiply.__call__(1, a, foo='bar', answer=42)
+        res = np.multiply.__call__(1, a, subok='bar', where=42)
+        assert_equal(res[0], a)
+        assert_equal(res[1], np.multiply)
+        assert_equal(res[2], '__call__')
+        assert_equal(res[3], (1, a))
+        assert_equal(res[4], {'subok': 'bar', 'where': 42})
+
+        # __call__, wrong args
+        assert_raises(TypeError, np.multiply, a)
+        assert_raises(TypeError, np.multiply, a, a, a, a)
+        assert_raises(TypeError, np.multiply, a, a, sig='a', signature='a')
+        assert_raises(TypeError, ncu_tests.inner1d, a, a, axis=0, axes=[0, 0])
+
+        # reduce, positional args
+        res = np.multiply.reduce(a, 'axis0', 'dtype0', 'out0', 'keep0')
+        assert_equal(res[0], a)
+        assert_equal(res[1], np.multiply)
+        assert_equal(res[2], 'reduce')
+        assert_equal(res[3], (a,))
+        assert_equal(res[4], {'dtype': 'dtype0',
+                              'out': ('out0',),
+                              'keepdims': 'keep0',
+                              'axis': 'axis0'})
+
+        # reduce, kwargs
+        res = np.multiply.reduce(a, axis='axis0', dtype='dtype0', out='out0',
+                                 keepdims='keep0', initial='init0',
+                                 where='where0')
+        assert_equal(res[0], a)
+        assert_equal(res[1], np.multiply)
+        assert_equal(res[2], 'reduce')
+        assert_equal(res[3], (a,))
+        assert_equal(res[4], {'dtype': 'dtype0',
+                              'out': ('out0',),
+                              'keepdims': 'keep0',
+                              'axis': 'axis0',
+                              'initial': 'init0',
+                              'where': 'where0'})
+
+        # reduce, output equal to None removed, but not other explicit ones,
+        # even if they are at their default value.
+        res = np.multiply.reduce(a, 0, None, None, False)
+        assert_equal(res[4], {'axis': 0, 'dtype': None, 'keepdims': False})
+        res = np.multiply.reduce(a, out=None, axis=0, keepdims=True)
+        assert_equal(res[4], {'axis': 0, 'keepdims': True})
+        res = np.multiply.reduce(a, None, out=(None,), dtype=None)
+        assert_equal(res[4], {'axis': None, 'dtype': None})
+        res = np.multiply.reduce(a, 0, None, None, False, 2, True)
+        assert_equal(res[4], {'axis': 0, 'dtype': None, 'keepdims': False,
+                              'initial': 2, 'where': True})
+        # np._NoValue ignored for initial
+        res = np.multiply.reduce(a, 0, None, None, False,
+                                 np._NoValue, True)
+        assert_equal(res[4], {'axis': 0, 'dtype': None, 'keepdims': False,
+                              'where': True})
+        # None kept for initial, True for where.
+        res = np.multiply.reduce(a, 0, None, None, False, None, True)
+        assert_equal(res[4], {'axis': 0, 'dtype': None, 'keepdims': False,
+                              'initial': None, 'where': True})
+
+        # reduce, wrong args
+        assert_raises(ValueError, np.multiply.reduce, a, out=())
+        assert_raises(ValueError, np.multiply.reduce, a, out=('out0', 'out1'))
+        assert_raises(TypeError, np.multiply.reduce, a, 'axis0', axis='axis0')
+
+        # accumulate, pos args
+        res = np.multiply.accumulate(a, 'axis0', 'dtype0', 'out0')
+        assert_equal(res[0], a)
+        assert_equal(res[1], np.multiply)
+        assert_equal(res[2], 'accumulate')
+        assert_equal(res[3], (a,))
+        assert_equal(res[4], {'dtype': 'dtype0',
+                              'out': ('out0',),
+                              'axis': 'axis0'})
+
+        # accumulate, kwargs
+        res = np.multiply.accumulate(a, axis='axis0', dtype='dtype0',
+                                     out='out0')
+        assert_equal(res[0], a)
+        assert_equal(res[1], np.multiply)
+        assert_equal(res[2], 'accumulate')
+        assert_equal(res[3], (a,))
+        assert_equal(res[4], {'dtype': 'dtype0',
+                              'out': ('out0',),
+                              'axis': 'axis0'})
+
+        # accumulate, output equal to None removed.
+        res = np.multiply.accumulate(a, 0, None, None)
+        assert_equal(res[4], {'axis': 0, 'dtype': None})
+        res = np.multiply.accumulate(a, out=None, axis=0, dtype='dtype1')
+        assert_equal(res[4], {'axis': 0, 'dtype': 'dtype1'})
+        res = np.multiply.accumulate(a, None, out=(None,), dtype=None)
+        assert_equal(res[4], {'axis': None, 'dtype': None})
+
+        # accumulate, wrong args
+        assert_raises(ValueError, np.multiply.accumulate, a, out=())
+        assert_raises(ValueError, np.multiply.accumulate, a,
+                      out=('out0', 'out1'))
+        assert_raises(TypeError, np.multiply.accumulate, a,
+                      'axis0', axis='axis0')
+
+        # reduceat, pos args
+        res = np.multiply.reduceat(a, [4, 2], 'axis0', 'dtype0', 'out0')
+        assert_equal(res[0], a)
+        assert_equal(res[1], np.multiply)
+        assert_equal(res[2], 'reduceat')
+        assert_equal(res[3], (a, [4, 2]))
+        assert_equal(res[4], {'dtype': 'dtype0',
+                              'out': ('out0',),
+                              'axis': 'axis0'})
+
+        # reduceat, kwargs
+        res = np.multiply.reduceat(a, [4, 2], axis='axis0', dtype='dtype0',
+                                   out='out0')
+        assert_equal(res[0], a)
+        assert_equal(res[1], np.multiply)
+        assert_equal(res[2], 'reduceat')
+        assert_equal(res[3], (a, [4, 2]))
+        assert_equal(res[4], {'dtype': 'dtype0',
+                              'out': ('out0',),
+                              'axis': 'axis0'})
+
+        # reduceat, output equal to None removed.
+        res = np.multiply.reduceat(a, [4, 2], 0, None, None)
+        assert_equal(res[4], {'axis': 0, 'dtype': None})
+        res = np.multiply.reduceat(a, [4, 2], axis=None, out=None, dtype='dt')
+        assert_equal(res[4], {'axis': None, 'dtype': 'dt'})
+        res = np.multiply.reduceat(a, [4, 2], None, None, out=(None,))
+        assert_equal(res[4], {'axis': None, 'dtype': None})
+
+        # reduceat, wrong args
+        assert_raises(ValueError, np.multiply.reduce, a, [4, 2], out=())
+        assert_raises(ValueError, np.multiply.reduce, a, [4, 2],
+                      out=('out0', 'out1'))
+        assert_raises(TypeError, np.multiply.reduce, a, [4, 2],
+                      'axis0', axis='axis0')
+
+        # outer
+        res = np.multiply.outer(a, 42)
+        assert_equal(res[0], a)
+        assert_equal(res[1], np.multiply)
+        assert_equal(res[2], 'outer')
+        assert_equal(res[3], (a, 42))
+        assert_equal(res[4], {})
+
+        # outer, wrong args
+        assert_raises(TypeError, np.multiply.outer, a)
+        assert_raises(TypeError, np.multiply.outer, a, a, a, a)
+        assert_raises(TypeError, np.multiply.outer, a, a, sig='a', signature='a')
+
+        # at
+        res = np.multiply.at(a, [4, 2], 'b0')
+        assert_equal(res[0], a)
+        assert_equal(res[1], np.multiply)
+        assert_equal(res[2], 'at')
+        assert_equal(res[3], (a, [4, 2], 'b0'))
+
+        # at, wrong args
+        assert_raises(TypeError, np.multiply.at, a)
+        assert_raises(TypeError, np.multiply.at, a, a, a, a)
+
+    def test_ufunc_override_out(self):
+
+        class A:
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+                return kwargs
+
+        class B:
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+                return kwargs
+
+        a = A()
+        b = B()
+        res0 = np.multiply(a, b, 'out_arg')
+        res1 = np.multiply(a, b, out='out_arg')
+        res2 = np.multiply(2, b, 'out_arg')
+        res3 = np.multiply(3, b, out='out_arg')
+        res4 = np.multiply(a, 4, 'out_arg')
+        res5 = np.multiply(a, 5, out='out_arg')
+
+        assert_equal(res0['out'][0], 'out_arg')
+        assert_equal(res1['out'][0], 'out_arg')
+        assert_equal(res2['out'][0], 'out_arg')
+        assert_equal(res3['out'][0], 'out_arg')
+        assert_equal(res4['out'][0], 'out_arg')
+        assert_equal(res5['out'][0], 'out_arg')
+
+        # ufuncs with multiple output modf and frexp.
+        res6 = np.modf(a, 'out0', 'out1')
+        res7 = np.frexp(a, 'out0', 'out1')
+        assert_equal(res6['out'][0], 'out0')
+        assert_equal(res6['out'][1], 'out1')
+        assert_equal(res7['out'][0], 'out0')
+        assert_equal(res7['out'][1], 'out1')
+
+        # While we're at it, check that default output is never passed on.
+        assert_(np.sin(a, None) == {})
+        assert_(np.sin(a, out=None) == {})
+        assert_(np.sin(a, out=(None,)) == {})
+        assert_(np.modf(a, None) == {})
+        assert_(np.modf(a, None, None) == {})
+        assert_(np.modf(a, out=(None, None)) == {})
+        with assert_raises(TypeError):
+            # Out argument must be tuple, since there are multiple outputs.
+            np.modf(a, out=None)
+
+        # don't give positional and output argument, or too many arguments.
+        # wrong number of arguments in the tuple is an error too.
+        assert_raises(TypeError, np.multiply, a, b, 'one', out='two')
+        assert_raises(TypeError, np.multiply, a, b, 'one', 'two')
+        assert_raises(ValueError, np.multiply, a, b, out=('one', 'two'))
+        assert_raises(TypeError, np.multiply, a, out=())
+        assert_raises(TypeError, np.modf, a, 'one', out=('two', 'three'))
+        assert_raises(TypeError, np.modf, a, 'one', 'two', 'three')
+        assert_raises(ValueError, np.modf, a, out=('one', 'two', 'three'))
+        assert_raises(ValueError, np.modf, a, out=('one',))
+
+    def test_ufunc_override_where(self):
+
+        class OverriddenArrayOld(np.ndarray):
+
+            def _unwrap(self, objs):
+                cls = type(self)
+                result = []
+                for obj in objs:
+                    if isinstance(obj, cls):
+                        obj = np.array(obj)
+                    elif type(obj) != np.ndarray:
+                        return NotImplemented
+                    result.append(obj)
+                return result
+
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+
+                inputs = self._unwrap(inputs)
+                if inputs is NotImplemented:
+                    return NotImplemented
+
+                kwargs = kwargs.copy()
+                if "out" in kwargs:
+                    kwargs["out"] = self._unwrap(kwargs["out"])
+                    if kwargs["out"] is NotImplemented:
+                        return NotImplemented
+
+                r = super().__array_ufunc__(ufunc, method, *inputs, **kwargs)
+                if r is not NotImplemented:
+                    r = r.view(type(self))
+
+                return r
+
+        class OverriddenArrayNew(OverriddenArrayOld):
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+
+                kwargs = kwargs.copy()
+                if "where" in kwargs:
+                    kwargs["where"] = self._unwrap((kwargs["where"], ))
+                    if kwargs["where"] is NotImplemented:
+                        return NotImplemented
+                    else:
+                        kwargs["where"] = kwargs["where"][0]
+
+                r = super().__array_ufunc__(ufunc, method, *inputs, **kwargs)
+                if r is not NotImplemented:
+                    r = r.view(type(self))
+
+                return r
+
+        ufunc = np.negative
+
+        array = np.array([1, 2, 3])
+        where = np.array([True, False, True])
+        expected = ufunc(array, where=where)
+
+        with pytest.raises(TypeError):
+            ufunc(array, where=where.view(OverriddenArrayOld))
+
+        result_1 = ufunc(
+            array,
+            where=where.view(OverriddenArrayNew)
+        )
+        assert isinstance(result_1, OverriddenArrayNew)
+        assert np.all(np.array(result_1) == expected, where=where)
+
+        result_2 = ufunc(
+            array.view(OverriddenArrayNew),
+            where=where.view(OverriddenArrayNew)
+        )
+        assert isinstance(result_2, OverriddenArrayNew)
+        assert np.all(np.array(result_2) == expected, where=where)
+
+    def test_ufunc_override_exception(self):
+
+        class A:
+            def __array_ufunc__(self, *a, **kwargs):
+                raise ValueError("oops")
+
+        a = A()
+        assert_raises(ValueError, np.negative, 1, out=a)
+        assert_raises(ValueError, np.negative, a)
+        assert_raises(ValueError, np.divide, 1., a)
+
+    def test_ufunc_override_not_implemented(self):
+
+        class A:
+            def __array_ufunc__(self, *args, **kwargs):
+                return NotImplemented
+
+        msg = ("operand type(s) all returned NotImplemented from "
+               "__array_ufunc__(<ufunc 'negative'>, '__call__', <*>): 'A'")
+        with assert_raises_regex(TypeError, fnmatch.translate(msg)):
+            np.negative(A())
+
+        msg = ("operand type(s) all returned NotImplemented from "
+               "__array_ufunc__(<ufunc 'add'>, '__call__', <*>, <object *>, "
+               "out=(1,)): 'A', 'object', 'int'")
+        with assert_raises_regex(TypeError, fnmatch.translate(msg)):
+            np.add(A(), object(), out=1)
+
+    def test_ufunc_override_disabled(self):
+
+        class OptOut:
+            __array_ufunc__ = None
+
+        opt_out = OptOut()
+
+        # ufuncs always raise
+        msg = "operand 'OptOut' does not support ufuncs"
+        with assert_raises_regex(TypeError, msg):
+            np.add(opt_out, 1)
+        with assert_raises_regex(TypeError, msg):
+            np.add(1, opt_out)
+        with assert_raises_regex(TypeError, msg):
+            np.negative(opt_out)
+
+        # opt-outs still hold even when other arguments have pathological
+        # __array_ufunc__ implementations
+
+        class GreedyArray:
+            def __array_ufunc__(self, *args, **kwargs):
+                return self
+
+        greedy = GreedyArray()
+        assert_(np.negative(greedy) is greedy)
+        with assert_raises_regex(TypeError, msg):
+            np.add(greedy, opt_out)
+        with assert_raises_regex(TypeError, msg):
+            np.add(greedy, 1, out=opt_out)
+
+    def test_gufunc_override(self):
+        # gufunc are just ufunc instances, but follow a different path,
+        # so check __array_ufunc__ overrides them properly.
+        class A:
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+                return self, ufunc, method, inputs, kwargs
+
+        inner1d = ncu_tests.inner1d
+        a = A()
+        res = inner1d(a, a)
+        assert_equal(res[0], a)
+        assert_equal(res[1], inner1d)
+        assert_equal(res[2], '__call__')
+        assert_equal(res[3], (a, a))
+        assert_equal(res[4], {})
+
+        res = inner1d(1, 1, out=a)
+        assert_equal(res[0], a)
+        assert_equal(res[1], inner1d)
+        assert_equal(res[2], '__call__')
+        assert_equal(res[3], (1, 1))
+        assert_equal(res[4], {'out': (a,)})
+
+        # wrong number of arguments in the tuple is an error too.
+        assert_raises(TypeError, inner1d, a, out='two')
+        assert_raises(TypeError, inner1d, a, a, 'one', out='two')
+        assert_raises(TypeError, inner1d, a, a, 'one', 'two')
+        assert_raises(ValueError, inner1d, a, a, out=('one', 'two'))
+        assert_raises(ValueError, inner1d, a, a, out=())
+
+    def test_ufunc_override_with_super(self):
+        # NOTE: this class is used in doc/source/user/basics.subclassing.rst
+        # if you make any changes here, do update it there too.
+        class A(np.ndarray):
+            def __array_ufunc__(self, ufunc, method, *inputs, out=None, **kwargs):
+                args = []
+                in_no = []
+                for i, input_ in enumerate(inputs):
+                    if isinstance(input_, A):
+                        in_no.append(i)
+                        args.append(input_.view(np.ndarray))
+                    else:
+                        args.append(input_)
+
+                outputs = out
+                out_no = []
+                if outputs:
+                    out_args = []
+                    for j, output in enumerate(outputs):
+                        if isinstance(output, A):
+                            out_no.append(j)
+                            out_args.append(output.view(np.ndarray))
+                        else:
+                            out_args.append(output)
+                    kwargs['out'] = tuple(out_args)
+                else:
+                    outputs = (None,) * ufunc.nout
+
+                info = {}
+                if in_no:
+                    info['inputs'] = in_no
+                if out_no:
+                    info['outputs'] = out_no
+
+                results = super().__array_ufunc__(ufunc, method,
+                                                  *args, **kwargs)
+                if results is NotImplemented:
+                    return NotImplemented
+
+                if method == 'at':
+                    if isinstance(inputs[0], A):
+                        inputs[0].info = info
+                    return
+
+                if ufunc.nout == 1:
+                    results = (results,)
+
+                results = tuple((np.asarray(result).view(A)
+                                 if output is None else output)
+                                for result, output in zip(results, outputs))
+                if results and isinstance(results[0], A):
+                    results[0].info = info
+
+                return results[0] if len(results) == 1 else results
+
+        class B:
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+                if any(isinstance(input_, A) for input_ in inputs):
+                    return "A!"
+                else:
+                    return NotImplemented
+
+        d = np.arange(5.)
+        # 1 input, 1 output
+        a = np.arange(5.).view(A)
+        b = np.sin(a)
+        check = np.sin(d)
+        assert_(np.all(check == b))
+        assert_equal(b.info, {'inputs': [0]})
+        b = np.sin(d, out=(a,))
+        assert_(np.all(check == b))
+        assert_equal(b.info, {'outputs': [0]})
+        assert_(b is a)
+        a = np.arange(5.).view(A)
+        b = np.sin(a, out=a)
+        assert_(np.all(check == b))
+        assert_equal(b.info, {'inputs': [0], 'outputs': [0]})
+
+        # 1 input, 2 outputs
+        a = np.arange(5.).view(A)
+        b1, b2 = np.modf(a)
+        assert_equal(b1.info, {'inputs': [0]})
+        b1, b2 = np.modf(d, out=(None, a))
+        assert_(b2 is a)
+        assert_equal(b1.info, {'outputs': [1]})
+        a = np.arange(5.).view(A)
+        b = np.arange(5.).view(A)
+        c1, c2 = np.modf(a, out=(a, b))
+        assert_(c1 is a)
+        assert_(c2 is b)
+        assert_equal(c1.info, {'inputs': [0], 'outputs': [0, 1]})
+
+        # 2 input, 1 output
+        a = np.arange(5.).view(A)
+        b = np.arange(5.).view(A)
+        c = np.add(a, b, out=a)
+        assert_(c is a)
+        assert_equal(c.info, {'inputs': [0, 1], 'outputs': [0]})
+        # some tests with a non-ndarray subclass
+        a = np.arange(5.)
+        b = B()
+        assert_(a.__array_ufunc__(np.add, '__call__', a, b) is NotImplemented)
+        assert_(b.__array_ufunc__(np.add, '__call__', a, b) is NotImplemented)
+        assert_raises(TypeError, np.add, a, b)
+        a = a.view(A)
+        assert_(a.__array_ufunc__(np.add, '__call__', a, b) is NotImplemented)
+        assert_(b.__array_ufunc__(np.add, '__call__', a, b) == "A!")
+        assert_(np.add(a, b) == "A!")
+        # regression check for gh-9102 -- tests ufunc.reduce implicitly.
+        d = np.array([[1, 2, 3], [1, 2, 3]])
+        a = d.view(A)
+        c = a.any()
+        check = d.any()
+        assert_equal(c, check)
+        assert_(c.info, {'inputs': [0]})
+        c = a.max()
+        check = d.max()
+        assert_equal(c, check)
+        assert_(c.info, {'inputs': [0]})
+        b = np.array(0).view(A)
+        c = a.max(out=b)
+        assert_equal(c, check)
+        assert_(c is b)
+        assert_(c.info, {'inputs': [0], 'outputs': [0]})
+        check = a.max(axis=0)
+        b = np.zeros_like(check).view(A)
+        c = a.max(axis=0, out=b)
+        assert_equal(c, check)
+        assert_(c is b)
+        assert_(c.info, {'inputs': [0], 'outputs': [0]})
+        # simple explicit tests of reduce, accumulate, reduceat
+        check = np.add.reduce(d, axis=1)
+        c = np.add.reduce(a, axis=1)
+        assert_equal(c, check)
+        assert_(c.info, {'inputs': [0]})
+        b = np.zeros_like(c)
+        c = np.add.reduce(a, 1, None, b)
+        assert_equal(c, check)
+        assert_(c is b)
+        assert_(c.info, {'inputs': [0], 'outputs': [0]})
+        check = np.add.accumulate(d, axis=0)
+        c = np.add.accumulate(a, axis=0)
+        assert_equal(c, check)
+        assert_(c.info, {'inputs': [0]})
+        b = np.zeros_like(c)
+        c = np.add.accumulate(a, 0, None, b)
+        assert_equal(c, check)
+        assert_(c is b)
+        assert_(c.info, {'inputs': [0], 'outputs': [0]})
+        indices = [0, 2, 1]
+        check = np.add.reduceat(d, indices, axis=1)
+        c = np.add.reduceat(a, indices, axis=1)
+        assert_equal(c, check)
+        assert_(c.info, {'inputs': [0]})
+        b = np.zeros_like(c)
+        c = np.add.reduceat(a, indices, 1, None, b)
+        assert_equal(c, check)
+        assert_(c is b)
+        assert_(c.info, {'inputs': [0], 'outputs': [0]})
+        # and a few tests for at
+        d = np.array([[1, 2, 3], [1, 2, 3]])
+        check = d.copy()
+        a = d.copy().view(A)
+        np.add.at(check, ([0, 1], [0, 2]), 1.)
+        np.add.at(a, ([0, 1], [0, 2]), 1.)
+        assert_equal(a, check)
+        assert_(a.info, {'inputs': [0]})
+        b = np.array(1.).view(A)
+        a = d.copy().view(A)
+        np.add.at(a, ([0, 1], [0, 2]), b)
+        assert_equal(a, check)
+        assert_(a.info, {'inputs': [0, 2]})
+
+    def test_array_ufunc_direct_call(self):
+        # This is mainly a regression test for gh-24023 (shouldn't segfault)
+        a = np.array(1)
+        with pytest.raises(TypeError):
+            a.__array_ufunc__()
+
+        # No kwargs means kwargs may be NULL on the C-level
+        with pytest.raises(TypeError):
+            a.__array_ufunc__(1, 2)
+
+        # And the same with a valid call:
+        res = a.__array_ufunc__(np.add, "__call__", a, a)
+        assert_array_equal(res, a + a)
+
+    def test_ufunc_docstring(self):
+        original_doc = np.add.__doc__
+        new_doc = "new docs"
+        expected_dict = (
+            {} if IS_PYPY else {"__module__": "numpy", "__qualname__": "add"}
+        )
+
+        np.add.__doc__ = new_doc
+        assert np.add.__doc__ == new_doc
+        assert np.add.__dict__["__doc__"] == new_doc
+
+        del np.add.__doc__
+        assert np.add.__doc__ == original_doc
+        assert np.add.__dict__ == expected_dict
+
+        np.add.__dict__["other"] = 1
+        np.add.__dict__["__doc__"] = new_doc
+        assert np.add.__doc__ == new_doc
+
+        del np.add.__dict__["__doc__"]
+        assert np.add.__doc__ == original_doc
+        del np.add.__dict__["other"]
+        assert np.add.__dict__ == expected_dict
+
+
+class TestChoose:
+    def test_mixed(self):
+        c = np.array([True, True])
+        a = np.array([True, True])
+        assert_equal(np.choose(c, (a, 1)), np.array([1, 1]))
+
+
+class TestRationalFunctions:
+    def test_lcm(self):
+        self._test_lcm_inner(np.int16)
+        self._test_lcm_inner(np.uint16)
+
+    def test_lcm_object(self):
+        self._test_lcm_inner(np.object_)
+
+    def test_gcd(self):
+        self._test_gcd_inner(np.int16)
+        self._test_lcm_inner(np.uint16)
+
+    def test_gcd_object(self):
+        self._test_gcd_inner(np.object_)
+
+    def _test_lcm_inner(self, dtype):
+        # basic use
+        a = np.array([12, 120], dtype=dtype)
+        b = np.array([20, 200], dtype=dtype)
+        assert_equal(np.lcm(a, b), [60, 600])
+
+        if not issubclass(dtype, np.unsignedinteger):
+            # negatives are ignored
+            a = np.array([12, -12,  12, -12], dtype=dtype)
+            b = np.array([20,  20, -20, -20], dtype=dtype)
+            assert_equal(np.lcm(a, b), [60] * 4)
+
+        # reduce
+        a = np.array([3, 12, 20], dtype=dtype)
+        assert_equal(np.lcm.reduce([3, 12, 20]), 60)
+
+        # broadcasting, and a test including 0
+        a = np.arange(6).astype(dtype)
+        b = 20
+        assert_equal(np.lcm(a, b), [0, 20, 20, 60, 20, 20])
+
+    def _test_gcd_inner(self, dtype):
+        # basic use
+        a = np.array([12, 120], dtype=dtype)
+        b = np.array([20, 200], dtype=dtype)
+        assert_equal(np.gcd(a, b), [4, 40])
+
+        if not issubclass(dtype, np.unsignedinteger):
+            # negatives are ignored
+            a = np.array([12, -12,  12, -12], dtype=dtype)
+            b = np.array([20,  20, -20, -20], dtype=dtype)
+            assert_equal(np.gcd(a, b), [4] * 4)
+
+        # reduce
+        a = np.array([15, 25, 35], dtype=dtype)
+        assert_equal(np.gcd.reduce(a), 5)
+
+        # broadcasting, and a test including 0
+        a = np.arange(6).astype(dtype)
+        b = 20
+        assert_equal(np.gcd(a, b), [20,  1,  2,  1,  4,  5])
+
+    def test_lcm_overflow(self):
+        # verify that we don't overflow when a*b does overflow
+        big = np.int32(np.iinfo(np.int32).max // 11)
+        a = 2 * big
+        b = 5 * big
+        assert_equal(np.lcm(a, b), 10 * big)
+
+    def test_gcd_overflow(self):
+        for dtype in (np.int32, np.int64):
+            # verify that we don't overflow when taking abs(x)
+            # not relevant for lcm, where the result is unrepresentable anyway
+            a = dtype(np.iinfo(dtype).min)  # negative power of two
+            q = -(a // 4)
+            assert_equal(np.gcd(a,  q * 3), q)
+            assert_equal(np.gcd(a, -q * 3), q)
+
+    def test_decimal(self):
+        from decimal import Decimal
+        a = np.array([1,  1, -1, -1]) * Decimal('0.20')
+        b = np.array([1, -1,  1, -1]) * Decimal('0.12')
+
+        assert_equal(np.gcd(a, b), 4 * [Decimal('0.04')])
+        assert_equal(np.lcm(a, b), 4 * [Decimal('0.60')])
+
+    def test_float(self):
+        # not well-defined on float due to rounding errors
+        assert_raises(TypeError, np.gcd, 0.3, 0.4)
+        assert_raises(TypeError, np.lcm, 0.3, 0.4)
+
+    def test_huge_integers(self):
+        # Converting to an array first is a bit different as it means we
+        # have an explicit object dtype:
+        assert_equal(np.array(2**200), 2**200)
+        # Special promotion rules should ensure that this also works for
+        # two Python integers (even if slow).
+        # (We do this for comparisons, as the result is always bool and
+        # we also special case array comparisons with Python integers)
+        np.equal(2**200, 2**200)
+
+        # But, we cannot do this when it would affect the result dtype:
+        with pytest.raises(OverflowError):
+            np.gcd(2**100, 3**100)
+
+        # Asking for `object` explicitly is fine, though:
+        assert np.gcd(2**100, 3**100, dtype=object) == 1
+
+        # As of now, the below work, because it is using arrays (which
+        # will be object arrays)
+        a = np.array(2**100 * 3**5)
+        b = np.array([2**100 * 5**7, 2**50 * 3**10])
+        assert_equal(np.gcd(a, b), [2**100,               2**50 * 3**5])
+        assert_equal(np.lcm(a, b), [2**100 * 3**5 * 5**7, 2**100 * 3**10])
+
+    def test_inf_and_nan(self):
+        inf = np.array([np.inf], dtype=np.object_)
+        assert_raises(ValueError, np.gcd, inf, 1)
+        assert_raises(ValueError, np.gcd, 1, inf)
+        assert_raises(ValueError, np.gcd, np.nan, inf)
+        assert_raises(TypeError, np.gcd, 4, float(np.inf))
+
+
+class TestRoundingFunctions:
+
+    def test_object_direct(self):
+        """ test direct implementation of these magic methods """
+        class C:
+            def __floor__(self):
+                return 1
+
+            def __ceil__(self):
+                return 2
+
+            def __trunc__(self):
+                return 3
+
+        arr = np.array([C(), C()])
+        assert_equal(np.floor(arr), [1, 1])
+        assert_equal(np.ceil(arr),  [2, 2])
+        assert_equal(np.trunc(arr), [3, 3])
+
+    def test_object_indirect(self):
+        """ test implementations via __float__ """
+        class C:
+            def __float__(self):
+                return -2.5
+
+        arr = np.array([C(), C()])
+        assert_equal(np.floor(arr), [-3, -3])
+        assert_equal(np.ceil(arr),  [-2, -2])
+        with pytest.raises(TypeError):
+            np.trunc(arr)  # consistent with math.trunc
+
+    def test_fraction(self):
+        f = Fraction(-4, 3)
+        assert_equal(np.floor(f), -2)
+        assert_equal(np.ceil(f), -1)
+        assert_equal(np.trunc(f), -1)
+
+    @pytest.mark.parametrize('func', [np.floor, np.ceil, np.trunc])
+    @pytest.mark.parametrize('dtype', [np.bool, np.float64, np.float32,
+                                       np.int64, np.uint32])
+    def test_output_dtype(self, func, dtype):
+        arr = np.array([-2, 0, 4, 8]).astype(dtype)
+        result = func(arr)
+        assert_equal(arr, result)
+        assert result.dtype == dtype
+
+
+class TestComplexFunctions:
+    funcs = [np.arcsin,  np.arccos,  np.arctan, np.arcsinh, np.arccosh,
+             np.arctanh, np.sin,     np.cos,    np.tan,     np.exp,
+             np.exp2,    np.log,     np.sqrt,   np.log10,   np.log2,
+             np.log1p]
+
+    def test_it(self):
+        for f in self.funcs:
+            if f is np.arccosh:
+                x = 1.5
+            else:
+                x = .5
+            fr = f(x)
+            fz = f(complex(x))
+            assert_almost_equal(fz.real, fr, err_msg=f'real part {f}')
+            assert_almost_equal(fz.imag, 0., err_msg=f'imag part {f}')
+
+    @pytest.mark.xfail(IS_WASM, reason="doesn't work")
+    def test_precisions_consistent(self):
+        z = 1 + 1j
+        for f in self.funcs:
+            fcf = f(np.csingle(z))
+            fcd = f(np.cdouble(z))
+            fcl = f(np.clongdouble(z))
+            assert_almost_equal(fcf, fcd, decimal=6, err_msg=f'fch-fcd {f}')
+            assert_almost_equal(fcl, fcd, decimal=15, err_msg=f'fch-fcl {f}')
+
+    @pytest.mark.xfail(IS_WASM, reason="doesn't work")
+    def test_branch_cuts(self):
+        # check branch cuts and continuity on them
+        _check_branch_cut(np.log,   -0.5, 1j, 1, -1, True)  # noqa: E221
+        _check_branch_cut(np.log2,  -0.5, 1j, 1, -1, True)  # noqa: E221
+        _check_branch_cut(np.log10, -0.5, 1j, 1, -1, True)
+        _check_branch_cut(np.log1p, -1.5, 1j, 1, -1, True)
+        _check_branch_cut(np.sqrt,  -0.5, 1j, 1, -1, True)  # noqa: E221
+
+        _check_branch_cut(np.arcsin, [ -2, 2],   [1j, 1j], 1, -1, True)
+        _check_branch_cut(np.arccos, [ -2, 2],   [1j, 1j], 1, -1, True)
+        _check_branch_cut(np.arctan, [0 - 2j, 2j],  [1,  1], -1, 1, True)
+
+        _check_branch_cut(np.arcsinh, [0 - 2j,  2j], [1,   1], -1, 1, True)
+        _check_branch_cut(np.arccosh, [ -1, 0.5], [1j,  1j], 1, -1, True)
+        _check_branch_cut(np.arctanh, [ -2,   2], [1j, 1j], 1, -1, True)
+
+        # check against bogus branch cuts: assert continuity between quadrants
+        _check_branch_cut(np.arcsin, [0 - 2j, 2j], [ 1,  1], 1, 1)
+        _check_branch_cut(np.arccos, [0 - 2j, 2j], [ 1,  1], 1, 1)
+        _check_branch_cut(np.arctan, [ -2,  2], [1j, 1j], 1, 1)
+
+        _check_branch_cut(np.arcsinh, [ -2,  2, 0], [1j, 1j, 1], 1, 1)
+        _check_branch_cut(np.arccosh, [0 - 2j, 2j, 2], [1,  1,  1j], 1, 1)
+        _check_branch_cut(np.arctanh, [0 - 2j, 2j, 0], [1,  1,  1j], 1, 1)
+
+    @pytest.mark.xfail(IS_WASM, reason="doesn't work")
+    def test_branch_cuts_complex64(self):
+        # check branch cuts and continuity on them
+        _check_branch_cut(np.log,   -0.5, 1j, 1, -1, True, np.complex64)  # noqa: E221
+        _check_branch_cut(np.log2,  -0.5, 1j, 1, -1, True, np.complex64)  # noqa: E221
+        _check_branch_cut(np.log10, -0.5, 1j, 1, -1, True, np.complex64)
+        _check_branch_cut(np.log1p, -1.5, 1j, 1, -1, True, np.complex64)
+        _check_branch_cut(np.sqrt,  -0.5, 1j, 1, -1, True, np.complex64)  # noqa: E221
+
+        _check_branch_cut(np.arcsin, [ -2, 2],   [1j, 1j], 1, -1, True, np.complex64)
+        _check_branch_cut(np.arccos, [ -2, 2],   [1j, 1j], 1, -1, True, np.complex64)
+        _check_branch_cut(np.arctan, [0 - 2j, 2j],  [1,  1], -1, 1, True, np.complex64)
+
+        _check_branch_cut(np.arcsinh, [0 - 2j,  2j], [1,   1], -1, 1, True, np.complex64)
+        _check_branch_cut(np.arccosh, [ -1, 0.5], [1j,  1j], 1, -1, True, np.complex64)
+        _check_branch_cut(np.arctanh, [ -2,   2], [1j, 1j], 1, -1, True, np.complex64)
+
+        # check against bogus branch cuts: assert continuity between quadrants
+        _check_branch_cut(np.arcsin, [0 - 2j, 2j], [ 1,  1], 1, 1, False, np.complex64)
+        _check_branch_cut(np.arccos, [0 - 2j, 2j], [ 1,  1], 1, 1, False, np.complex64)
+        _check_branch_cut(np.arctan, [ -2,  2], [1j, 1j], 1, 1, False, np.complex64)
+
+        _check_branch_cut(np.arcsinh, [ -2,  2, 0], [1j, 1j, 1], 1, 1, False, np.complex64)
+        _check_branch_cut(np.arccosh, [0 - 2j, 2j, 2], [1,  1,  1j], 1, 1, False, np.complex64)
+        _check_branch_cut(np.arctanh, [0 - 2j, 2j, 0], [1,  1,  1j], 1, 1, False, np.complex64)
+
+    def test_against_cmath(self):
+        import cmath
+
+        points = [-1 - 1j, -1 + 1j, +1 - 1j, +1 + 1j]
+        name_map = {'arcsin': 'asin', 'arccos': 'acos', 'arctan': 'atan',
+                    'arcsinh': 'asinh', 'arccosh': 'acosh', 'arctanh': 'atanh'}
+        atol = 4 * np.finfo(complex).eps
+        for func in self.funcs:
+            fname = func.__name__.split('.')[-1]
+            cname = name_map.get(fname, fname)
+            try:
+                cfunc = getattr(cmath, cname)
+            except AttributeError:
+                continue
+            for p in points:
+                a = complex(func(np.complex128(p)))
+                b = cfunc(p)
+                assert_(
+                    abs(a - b) < atol,
+                    f"{fname} {p}: {a}; cmath: {b}"
+                )
+
+    @pytest.mark.xfail(
+        # manylinux2014 uses glibc2.17
+        _glibc_older_than("2.18"),
+        reason="Older glibc versions are imprecise (maybe passes with SIMD?)"
+    )
+    @pytest.mark.xfail(IS_WASM, reason="doesn't work")
+    @pytest.mark.parametrize('dtype', [
+        np.complex64, np.complex128, np.clongdouble
+    ])
+    def test_loss_of_precision(self, dtype):
+        """Check loss of precision in complex arc* functions"""
+        if dtype is np.clongdouble and platform.machine() != 'x86_64':
+            # Failures on musllinux, aarch64, s390x, ppc64le (see gh-17554)
+            pytest.skip('Only works reliably for x86-64 and recent glibc')
+
+        # Check against known-good functions
+
+        info = np.finfo(dtype)
+        real_dtype = dtype(0.).real.dtype
+        eps = info.eps
+
+        def check(x, rtol):
+            x = x.astype(real_dtype)
+
+            z = x.astype(dtype)
+            d = np.absolute(np.arcsinh(x) / np.arcsinh(z).real - 1)
+            assert_(np.all(d < rtol), (np.argmax(d), x[np.argmax(d)], d.max(),
+                                      'arcsinh'))
+
+            z = (1j * x).astype(dtype)
+            d = np.absolute(np.arcsinh(x) / np.arcsin(z).imag - 1)
+            assert_(np.all(d < rtol), (np.argmax(d), x[np.argmax(d)], d.max(),
+                                      'arcsin'))
+
+            z = x.astype(dtype)
+            d = np.absolute(np.arctanh(x) / np.arctanh(z).real - 1)
+            assert_(np.all(d < rtol), (np.argmax(d), x[np.argmax(d)], d.max(),
+                                      'arctanh'))
+
+            z = (1j * x).astype(dtype)
+            d = np.absolute(np.arctanh(x) / np.arctan(z).imag - 1)
+            assert_(np.all(d < rtol), (np.argmax(d), x[np.argmax(d)], d.max(),
+                                      'arctan'))
+
+        # The switchover was chosen as 1e-3; hence there can be up to
+        # ~eps/1e-3 of relative cancellation error before it
+
+        x_series = np.logspace(-20, -3.001, 200)
+        x_basic = np.logspace(-2.999, 0, 10, endpoint=False)
+
+        if dtype is np.clongdouble:
+            if bad_arcsinh():
+                pytest.skip("Trig functions of np.clongdouble values known "
+                            "to be inaccurate on aarch64 and PPC for some "
+                            "compilation configurations.")
+            # It's not guaranteed that the system-provided arc functions
+            # are accurate down to a few epsilons. (Eg. on Linux 64-bit)
+            # So, give more leeway for long complex tests here:
+            check(x_series, 50.0 * eps)
+        else:
+            check(x_series, 2.1 * eps)
+        check(x_basic, 2.0 * eps / 1e-3)
+
+        # Check a few points
+
+        z = np.array([1e-5 * (1 + 1j)], dtype=dtype)
+        p = 9.999999999333333333e-6 + 1.000000000066666666e-5j
+        d = np.absolute(1 - np.arctanh(z) / p)
+        assert_(np.all(d < 1e-15))
+
+        p = 1.0000000000333333333e-5 + 9.999999999666666667e-6j
+        d = np.absolute(1 - np.arcsinh(z) / p)
+        assert_(np.all(d < 1e-15))
+
+        p = 9.999999999333333333e-6j + 1.000000000066666666e-5
+        d = np.absolute(1 - np.arctan(z) / p)
+        assert_(np.all(d < 1e-15))
+
+        p = 1.0000000000333333333e-5j + 9.999999999666666667e-6
+        d = np.absolute(1 - np.arcsin(z) / p)
+        assert_(np.all(d < 1e-15))
+
+        # Check continuity across switchover points
+
+        def check(func, z0, d=1):
+            z0 = np.asarray(z0, dtype=dtype)
+            zp = z0 + abs(z0) * d * eps * 2
+            zm = z0 - abs(z0) * d * eps * 2
+            assert_(np.all(zp != zm), (zp, zm))
+
+            # NB: the cancellation error at the switchover is at least eps
+            good = (abs(func(zp) - func(zm)) < 2 * eps)
+            assert_(np.all(good), (func, z0[~good]))
+
+        for func in (np.arcsinh, np.arcsinh, np.arcsin, np.arctanh, np.arctan):
+            pts = [rp + 1j * ip for rp in (-1e-3, 0, 1e-3) for ip in (-1e-3, 0, 1e-3)
+                   if rp != 0 or ip != 0]
+            check(func, pts, 1)
+            check(func, pts, 1j)
+            check(func, pts, 1 + 1j)
+
+    @np.errstate(all="ignore")
+    def test_promotion_corner_cases(self):
+        for func in self.funcs:
+            assert func(np.float16(1)).dtype == np.float16
+            # Integer to low precision float promotion is a dubious choice:
+            assert func(np.uint8(1)).dtype == np.float16
+            assert func(np.int16(1)).dtype == np.float32
+
+
+class TestAttributes:
+    def test_attributes(self):
+        add = ncu.add
+        assert_equal(add.__name__, 'add')
+        assert_(add.ntypes >= 18)  # don't fail if types added
+        assert_('ii->i' in add.types)
+        assert_equal(add.nin, 2)
+        assert_equal(add.nout, 1)
+        assert_equal(add.identity, 0)
+
+    def test_doc(self):
+        # don't bother checking the long list of kwargs, which are likely to
+        # change
+        assert_(ncu.add.__doc__.startswith(
+            "add(x1, x2, /, out=None, *, where=True"))
+        assert_(ncu.frexp.__doc__.startswith(
+            "frexp(x[, out1, out2], / [, out=(None, None)], *, where=True"))
+
+
+class TestSubclass:
+
+    def test_subclass_op(self):
+
+        class simple(np.ndarray):
+            def __new__(subtype, shape):
+                self = np.ndarray.__new__(subtype, shape, dtype=object)
+                self.fill(0)
+                return self
+
+        a = simple((3, 4))
+        assert_equal(a + a, a)
+
+
+class TestFrompyfunc:
+
+    def test_identity(self):
+        def mul(a, b):
+            return a * b
+
+        # with identity=value
+        mul_ufunc = np.frompyfunc(mul, nin=2, nout=1, identity=1)
+        assert_equal(mul_ufunc.reduce([2, 3, 4]), 24)
+        assert_equal(mul_ufunc.reduce(np.ones((2, 2)), axis=(0, 1)), 1)
+        assert_equal(mul_ufunc.reduce([]), 1)
+
+        # with identity=None (reorderable)
+        mul_ufunc = np.frompyfunc(mul, nin=2, nout=1, identity=None)
+        assert_equal(mul_ufunc.reduce([2, 3, 4]), 24)
+        assert_equal(mul_ufunc.reduce(np.ones((2, 2)), axis=(0, 1)), 1)
+        assert_raises(ValueError, lambda: mul_ufunc.reduce([]))
+
+        # with no identity (not reorderable)
+        mul_ufunc = np.frompyfunc(mul, nin=2, nout=1)
+        assert_equal(mul_ufunc.reduce([2, 3, 4]), 24)
+        assert_raises(ValueError, lambda: mul_ufunc.reduce(np.ones((2, 2)), axis=(0, 1)))
+        assert_raises(ValueError, lambda: mul_ufunc.reduce([]))
+
+
+def _check_branch_cut(f, x0, dx, re_sign=1, im_sign=-1, sig_zero_ok=False,
+                      dtype=complex):
+    """
+    Check for a branch cut in a function.
+
+    Assert that `x0` lies on a branch cut of function `f` and `f` is
+    continuous from the direction `dx`.
+
+    Parameters
+    ----------
+    f : func
+        Function to check
+    x0 : array-like
+        Point on branch cut
+    dx : array-like
+        Direction to check continuity in
+    re_sign, im_sign : {1, -1}
+        Change of sign of the real or imaginary part expected
+    sig_zero_ok : bool
+        Whether to check if the branch cut respects signed zero (if applicable)
+    dtype : dtype
+        Dtype to check (should be complex)
+
+    """
+    x0 = np.atleast_1d(x0).astype(dtype)
+    dx = np.atleast_1d(dx).astype(dtype)
+
+    if np.dtype(dtype).char == 'F':
+        scale = np.finfo(dtype).eps * 1e2
+        atol = np.float32(1e-2)
+    else:
+        scale = np.finfo(dtype).eps * 1e3
+        atol = 1e-4
+
+    y0 = f(x0)
+    yp = f(x0 + dx * scale * np.absolute(x0) / np.absolute(dx))
+    ym = f(x0 - dx * scale * np.absolute(x0) / np.absolute(dx))
+
+    assert_(np.all(np.absolute(y0.real - yp.real) < atol), (y0, yp))
+    assert_(np.all(np.absolute(y0.imag - yp.imag) < atol), (y0, yp))
+    assert_(np.all(np.absolute(y0.real - ym.real * re_sign) < atol), (y0, ym))
+    assert_(np.all(np.absolute(y0.imag - ym.imag * im_sign) < atol), (y0, ym))
+
+    if sig_zero_ok:
+        # check that signed zeros also work as a displacement
+        jr = (x0.real == 0) & (dx.real != 0)
+        ji = (x0.imag == 0) & (dx.imag != 0)
+        if np.any(jr):
+            x = x0[jr]
+            x.real = ncu.NZERO
+            ym = f(x)
+            assert_(np.all(np.absolute(y0[jr].real - ym.real * re_sign) < atol), (y0[jr], ym))
+            assert_(np.all(np.absolute(y0[jr].imag - ym.imag * im_sign) < atol), (y0[jr], ym))
+
+        if np.any(ji):
+            x = x0[ji]
+            x.imag = ncu.NZERO
+            ym = f(x)
+            assert_(np.all(np.absolute(y0[ji].real - ym.real * re_sign) < atol), (y0[ji], ym))
+            assert_(np.all(np.absolute(y0[ji].imag - ym.imag * im_sign) < atol), (y0[ji], ym))
+
+def test_copysign():
+    assert_(np.copysign(1, -1) == -1)
+    with np.errstate(divide="ignore"):
+        assert_(1 / np.copysign(0, -1) < 0)
+        assert_(1 / np.copysign(0, 1) > 0)
+    assert_(np.signbit(np.copysign(np.nan, -1)))
+    assert_(not np.signbit(np.copysign(np.nan, 1)))
+
+def _test_nextafter(t):
+    one = t(1)
+    two = t(2)
+    zero = t(0)
+    eps = np.finfo(t).eps
+    assert_(np.nextafter(one, two) - one == eps)
+    assert_(np.nextafter(one, zero) - one < 0)
+    assert_(np.isnan(np.nextafter(np.nan, one)))
+    assert_(np.isnan(np.nextafter(one, np.nan)))
+    assert_(np.nextafter(one, one) == one)
+
+def test_nextafter():
+    return _test_nextafter(np.float64)
+
+
+def test_nextafterf():
+    return _test_nextafter(np.float32)
+
+
+@pytest.mark.skipif(np.finfo(np.double) == np.finfo(np.longdouble),
+                    reason="long double is same as double")
+@pytest.mark.xfail(condition=platform.machine().startswith("ppc64"),
+                    reason="IBM double double")
+def test_nextafterl():
+    return _test_nextafter(np.longdouble)
+
+
+def test_nextafter_0():
+    for t, direction in itertools.product(np._core.sctypes['float'], (1, -1)):
+        # The value of tiny for double double is NaN, so we need to pass the
+        # assert
+        with suppress_warnings() as sup:
+            sup.filter(UserWarning)
+            if not np.isnan(np.finfo(t).tiny):
+                tiny = np.finfo(t).tiny
+                assert_(
+                    0. < direction * np.nextafter(t(0), t(direction)) < tiny)
+        assert_equal(np.nextafter(t(0), t(direction)) / t(2.1), direction * 0.0)
+
+def _test_spacing(t):
+    one = t(1)
+    eps = np.finfo(t).eps
+    nan = t(np.nan)
+    inf = t(np.inf)
+    with np.errstate(invalid='ignore'):
+        assert_equal(np.spacing(one), eps)
+        assert_(np.isnan(np.spacing(nan)))
+        assert_(np.isnan(np.spacing(inf)))
+        assert_(np.isnan(np.spacing(-inf)))
+        assert_(np.spacing(t(1e30)) != 0)
+
+def test_spacing():
+    return _test_spacing(np.float64)
+
+def test_spacingf():
+    return _test_spacing(np.float32)
+
+
+@pytest.mark.skipif(np.finfo(np.double) == np.finfo(np.longdouble),
+                    reason="long double is same as double")
+@pytest.mark.xfail(condition=platform.machine().startswith("ppc64"),
+                    reason="IBM double double")
+def test_spacingl():
+    return _test_spacing(np.longdouble)
+
+def test_spacing_gfortran():
+    # Reference from this fortran file, built with gfortran 4.3.3 on linux
+    # 32bits:
+    #       PROGRAM test_spacing
+    #        INTEGER, PARAMETER :: SGL = SELECTED_REAL_KIND(p=6, r=37)
+    #        INTEGER, PARAMETER :: DBL = SELECTED_REAL_KIND(p=13, r=200)
+    #
+    #        WRITE(*,*) spacing(0.00001_DBL)
+    #        WRITE(*,*) spacing(1.0_DBL)
+    #        WRITE(*,*) spacing(1000._DBL)
+    #        WRITE(*,*) spacing(10500._DBL)
+    #
+    #        WRITE(*,*) spacing(0.00001_SGL)
+    #        WRITE(*,*) spacing(1.0_SGL)
+    #        WRITE(*,*) spacing(1000._SGL)
+    #        WRITE(*,*) spacing(10500._SGL)
+    #       END PROGRAM
+    ref = {np.float64: [1.69406589450860068E-021,
+                        2.22044604925031308E-016,
+                        1.13686837721616030E-013,
+                        1.81898940354585648E-012],
+           np.float32: [9.09494702E-13,
+                        1.19209290E-07,
+                        6.10351563E-05,
+                        9.76562500E-04]}
+
+    for dt, dec_ in zip([np.float32, np.float64], (10, 20)):
+        x = np.array([1e-5, 1, 1000, 10500], dtype=dt)
+        assert_array_almost_equal(np.spacing(x), ref[dt], decimal=dec_)
+
+def test_nextafter_vs_spacing():
+    # XXX: spacing does not handle long double yet
+    for t in [np.float32, np.float64]:
+        for _f in [1, 1e-5, 1000]:
+            f = t(_f)
+            f1 = t(_f + 1)
+            assert_(np.nextafter(f, f1) - f == np.spacing(f))
+
+def test_pos_nan():
+    """Check np.nan is a positive nan."""
+    assert_(np.signbit(np.nan) == 0)
+
+def test_reduceat():
+    """Test bug in reduceat when structured arrays are not copied."""
+    db = np.dtype([('name', 'S11'), ('time', np.int64), ('value', np.float32)])
+    a = np.empty([100], dtype=db)
+    a['name'] = 'Simple'
+    a['time'] = 10
+    a['value'] = 100
+    indx = [0, 7, 15, 25]
+
+    h2 = []
+    val1 = indx[0]
+    for val2 in indx[1:]:
+        h2.append(np.add.reduce(a['value'][val1:val2]))
+        val1 = val2
+    h2.append(np.add.reduce(a['value'][val1:]))
+    h2 = np.array(h2)
+
+    # test buffered -- this should work
+    h1 = np.add.reduceat(a['value'], indx)
+    assert_array_almost_equal(h1, h2)
+
+    # This is when the error occurs.
+    # test no buffer
+    np.setbufsize(32)
+    h1 = np.add.reduceat(a['value'], indx)
+    np.setbufsize(ncu.UFUNC_BUFSIZE_DEFAULT)
+    assert_array_almost_equal(h1, h2)
+
+def test_reduceat_empty():
+    """Reduceat should work with empty arrays"""
+    indices = np.array([], 'i4')
+    x = np.array([], 'f8')
+    result = np.add.reduceat(x, indices)
+    assert_equal(result.dtype, x.dtype)
+    assert_equal(result.shape, (0,))
+    # Another case with a slightly different zero-sized shape
+    x = np.ones((5, 2))
+    result = np.add.reduceat(x, [], axis=0)
+    assert_equal(result.dtype, x.dtype)
+    assert_equal(result.shape, (0, 2))
+    result = np.add.reduceat(x, [], axis=1)
+    assert_equal(result.dtype, x.dtype)
+    assert_equal(result.shape, (5, 0))
+
+def test_complex_nan_comparisons():
+    nans = [complex(np.nan, 0), complex(0, np.nan), complex(np.nan, np.nan)]
+    fins = [complex(1, 0), complex(-1, 0), complex(0, 1), complex(0, -1),
+            complex(1, 1), complex(-1, -1), complex(0, 0)]
+
+    with np.errstate(invalid='ignore'):
+        for x in nans + fins:
+            x = np.array([x])
+            for y in nans + fins:
+                y = np.array([y])
+
+                if np.isfinite(x) and np.isfinite(y):
+                    continue
+
+                assert_equal(x < y, False, err_msg=f"{x!r} < {y!r}")
+                assert_equal(x > y, False, err_msg=f"{x!r} > {y!r}")
+                assert_equal(x <= y, False, err_msg=f"{x!r} <= {y!r}")
+                assert_equal(x >= y, False, err_msg=f"{x!r} >= {y!r}")
+                assert_equal(x == y, False, err_msg=f"{x!r} == {y!r}")
+
+
+def test_rint_big_int():
+    # np.rint bug for large integer values on Windows 32-bit and MKL
+    # https://github.com/numpy/numpy/issues/6685
+    val = 4607998452777363968
+    # This is exactly representable in floating point
+    assert_equal(val, int(float(val)))
+    # Rint should not change the value
+    assert_equal(val, np.rint(val))
+
+
+@pytest.mark.parametrize('ftype', [np.float32, np.float64])
+def test_memoverlap_accumulate(ftype):
+    # Reproduces bug https://github.com/numpy/numpy/issues/15597
+    arr = np.array([0.61, 0.60, 0.77, 0.41, 0.19], dtype=ftype)
+    out_max = np.array([0.61, 0.61, 0.77, 0.77, 0.77], dtype=ftype)
+    out_min = np.array([0.61, 0.60, 0.60, 0.41, 0.19], dtype=ftype)
+    assert_equal(np.maximum.accumulate(arr), out_max)
+    assert_equal(np.minimum.accumulate(arr), out_min)
+
+@pytest.mark.parametrize("ufunc, dtype", [
+    (ufunc, t[0])
+    for ufunc in UFUNCS_BINARY_ACC
+    for t in ufunc.types
+    if t[-1] == '?' and t[0] not in 'DFGMmO'
+])
+def test_memoverlap_accumulate_cmp(ufunc, dtype):
+    if ufunc.signature:
+        pytest.skip('For generic signatures only')
+    for size in (2, 8, 32, 64, 128, 256):
+        arr = np.array([0, 1, 1] * size, dtype=dtype)
+        acc = ufunc.accumulate(arr, dtype='?')
+        acc_u8 = acc.view(np.uint8)
+        exp = np.array(list(itertools.accumulate(arr, ufunc)), dtype=np.uint8)
+        assert_equal(exp, acc_u8)
+
+@pytest.mark.parametrize("ufunc, dtype", [
+    (ufunc, t[0])
+    for ufunc in UFUNCS_BINARY_ACC
+    for t in ufunc.types
+    if t[0] == t[1] and t[0] == t[-1] and t[0] not in 'DFGMmO?'
+])
+def test_memoverlap_accumulate_symmetric(ufunc, dtype):
+    if ufunc.signature:
+        pytest.skip('For generic signatures only')
+    with np.errstate(all='ignore'):
+        for size in (2, 8, 32, 64, 128, 256):
+            arr = np.array([0, 1, 2] * size).astype(dtype)
+            acc = ufunc.accumulate(arr, dtype=dtype)
+            exp = np.array(list(itertools.accumulate(arr, ufunc)), dtype=dtype)
+            assert_equal(exp, acc)
+
+def test_signaling_nan_exceptions():
+    with assert_no_warnings():
+        a = np.ndarray(shape=(), dtype='float32', buffer=b'\x00\xe0\xbf\xff')
+        np.isnan(a)
+
+@pytest.mark.parametrize("arr", [
+    np.arange(2),
+    np.matrix([0, 1]),
+    np.matrix([[0, 1], [2, 5]]),
+    ])
+def test_outer_subclass_preserve(arr):
+    # for gh-8661
+    class foo(np.ndarray):
+        pass
+    actual = np.multiply.outer(arr.view(foo), arr.view(foo))
+    assert actual.__class__.__name__ == 'foo'
+
+def test_outer_bad_subclass():
+    class BadArr1(np.ndarray):
+        def __array_finalize__(self, obj):
+            # The outer call reshapes to 3 dims, try to do a bad reshape.
+            if self.ndim == 3:
+                self.shape = self.shape + (1,)
+
+    class BadArr2(np.ndarray):
+        def __array_finalize__(self, obj):
+            if isinstance(obj, BadArr2):
+                # outer inserts 1-sized dims. In that case disturb them.
+                if self.shape[-1] == 1:
+                    self.shape = self.shape[::-1]
+
+    for cls in [BadArr1, BadArr2]:
+        arr = np.ones((2, 3)).view(cls)
+        with assert_raises(TypeError) as a:
+            # The first array gets reshaped (not the second one)
+            np.add.outer(arr, [1, 2])
+
+        # This actually works, since we only see the reshaping error:
+        arr = np.ones((2, 3)).view(cls)
+        assert type(np.add.outer([1, 2], arr)) is cls
+
+def test_outer_exceeds_maxdims():
+    deep = np.ones((1,) * 33)
+    with assert_raises(ValueError):
+        np.add.outer(deep, deep)
+
+def test_bad_legacy_ufunc_silent_errors():
+    # legacy ufuncs can't report errors and NumPy can't check if the GIL
+    # is released.  So NumPy has to check after the GIL is released just to
+    # cover all bases.  `np.power` uses/used to use this.
+    arr = np.arange(3).astype(np.float64)
+
+    with pytest.raises(RuntimeError, match=r"How unexpected :\)!"):
+        ncu_tests.always_error(arr, arr)
+
+    with pytest.raises(RuntimeError, match=r"How unexpected :\)!"):
+        # not contiguous means the fast-path cannot be taken
+        non_contig = arr.repeat(20).reshape(-1, 6)[:, ::2]
+        ncu_tests.always_error(non_contig, arr)
+
+    with pytest.raises(RuntimeError, match=r"How unexpected :\)!"):
+        ncu_tests.always_error.outer(arr, arr)
+
+    with pytest.raises(RuntimeError, match=r"How unexpected :\)!"):
+        ncu_tests.always_error.reduce(arr)
+
+    with pytest.raises(RuntimeError, match=r"How unexpected :\)!"):
+        ncu_tests.always_error.reduceat(arr, [0, 1])
+
+    with pytest.raises(RuntimeError, match=r"How unexpected :\)!"):
+        ncu_tests.always_error.accumulate(arr)
+
+    with pytest.raises(RuntimeError, match=r"How unexpected :\)!"):
+        ncu_tests.always_error.at(arr, [0, 1, 2], arr)
+
+
+@pytest.mark.parametrize('x1', [np.arange(3.0), [0.0, 1.0, 2.0]])
+def test_bad_legacy_gufunc_silent_errors(x1):
+    # Verify that an exception raised in a gufunc loop propagates correctly.
+    # The signature of always_error_gufunc is '(i),()->()'.
+    with pytest.raises(RuntimeError, match=r"How unexpected :\)!"):
+        ncu_tests.always_error_gufunc(x1, 0.0)
+
+
+class TestAddDocstring:
+    @pytest.mark.skipif(sys.flags.optimize == 2, reason="Python running -OO")
+    @pytest.mark.skipif(IS_PYPY, reason="PyPy does not modify tp_doc")
+    def test_add_same_docstring(self):
+        # test for attributes (which are C-level defined)
+        ncu.add_docstring(np.ndarray.flat, np.ndarray.flat.__doc__)
+
+        # And typical functions:
+        def func():
+            """docstring"""
+            return
+
+        ncu.add_docstring(func, func.__doc__)
+
+    @pytest.mark.skipif(sys.flags.optimize == 2, reason="Python running -OO")
+    def test_different_docstring_fails(self):
+        # test for attributes (which are C-level defined)
+        with assert_raises(RuntimeError):
+            ncu.add_docstring(np.ndarray.flat, "different docstring")
+
+        # And typical functions:
+        def func():
+            """docstring"""
+            return
+
+        with assert_raises(RuntimeError):
+            ncu.add_docstring(func, "different docstring")
+
+
+class TestAdd_newdoc_ufunc:
+    @pytest.mark.filterwarnings("ignore:_add_newdoc_ufunc:DeprecationWarning")
+    def test_ufunc_arg(self):
+        assert_raises(TypeError, ncu._add_newdoc_ufunc, 2, "blah")
+        assert_raises(ValueError, ncu._add_newdoc_ufunc, np.add, "blah")
+
+    @pytest.mark.filterwarnings("ignore:_add_newdoc_ufunc:DeprecationWarning")
+    def test_string_arg(self):
+        assert_raises(TypeError, ncu._add_newdoc_ufunc, np.add, 3)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_umath_accuracy.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_umath_accuracy.py
new file mode 100644
index 0000000..5707e92
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_umath_accuracy.py
@@ -0,0 +1,124 @@
+import os
+import sys
+from ctypes import POINTER, c_double, c_float, c_int, c_longlong, cast, pointer
+from os import path
+
+import pytest
+from numpy._core._multiarray_umath import __cpu_features__
+
+import numpy as np
+from numpy.testing import assert_array_max_ulp
+from numpy.testing._private.utils import _glibc_older_than
+
+UNARY_UFUNCS = [obj for obj in np._core.umath.__dict__.values() if
+        isinstance(obj, np.ufunc)]
+UNARY_OBJECT_UFUNCS = [uf for uf in UNARY_UFUNCS if "O->O" in uf.types]
+
+# Remove functions that do not support `floats`
+UNARY_OBJECT_UFUNCS.remove(np.invert)
+UNARY_OBJECT_UFUNCS.remove(np.bitwise_count)
+
+IS_AVX = __cpu_features__.get('AVX512F', False) or \
+        (__cpu_features__.get('FMA3', False) and __cpu_features__.get('AVX2', False))
+
+IS_AVX512FP16 = __cpu_features__.get('AVX512FP16', False)
+
+# only run on linux with AVX, also avoid old glibc (numpy/numpy#20448).
+runtest = (sys.platform.startswith('linux')
+           and IS_AVX and not _glibc_older_than("2.17"))
+platform_skip = pytest.mark.skipif(not runtest,
+                                   reason="avoid testing inconsistent platform "
+                                   "library implementations")
+
+# convert string to hex function taken from:
+# https://stackoverflow.com/questions/1592158/convert-hex-to-float #
+def convert(s, datatype="np.float32"):
+    i = int(s, 16)                   # convert from hex to a Python int
+    if (datatype == "np.float64"):
+        cp = pointer(c_longlong(i))           # make this into a c long long integer
+        fp = cast(cp, POINTER(c_double))  # cast the int pointer to a double pointer
+    else:
+        cp = pointer(c_int(i))           # make this into a c integer
+        fp = cast(cp, POINTER(c_float))  # cast the int pointer to a float pointer
+
+    return fp.contents.value         # dereference the pointer, get the float
+
+
+str_to_float = np.vectorize(convert)
+
+class TestAccuracy:
+    @platform_skip
+    def test_validate_transcendentals(self):
+        with np.errstate(all='ignore'):
+            data_dir = path.join(path.dirname(__file__), 'data')
+            files = os.listdir(data_dir)
+            files = list(filter(lambda f: f.endswith('.csv'), files))
+            for filename in files:
+                filepath = path.join(data_dir, filename)
+                with open(filepath) as fid:
+                    file_without_comments = (
+                        r for r in fid if r[0] not in ('$', '#')
+                    )
+                    data = np.genfromtxt(file_without_comments,
+                                         dtype=('|S39', '|S39', '|S39', int),
+                                         names=('type', 'input', 'output', 'ulperr'),
+                                         delimiter=',',
+                                         skip_header=1)
+                    npname = path.splitext(filename)[0].split('-')[3]
+                    npfunc = getattr(np, npname)
+                    for datatype in np.unique(data['type']):
+                        data_subset = data[data['type'] == datatype]
+                        inval = np.array(str_to_float(data_subset['input'].astype(str), data_subset['type'].astype(str)), dtype=eval(datatype))
+                        outval = np.array(str_to_float(data_subset['output'].astype(str), data_subset['type'].astype(str)), dtype=eval(datatype))
+                        perm = np.random.permutation(len(inval))
+                        inval = inval[perm]
+                        outval = outval[perm]
+                        maxulperr = data_subset['ulperr'].max()
+                        assert_array_max_ulp(npfunc(inval), outval, maxulperr)
+
+    @pytest.mark.skipif(IS_AVX512FP16,
+            reason="SVML FP16 have slightly higher ULP errors")
+    @pytest.mark.parametrize("ufunc", UNARY_OBJECT_UFUNCS)
+    def test_validate_fp16_transcendentals(self, ufunc):
+        with np.errstate(all='ignore'):
+            arr = np.arange(65536, dtype=np.int16)
+            datafp16 = np.frombuffer(arr.tobytes(), dtype=np.float16)
+            datafp32 = datafp16.astype(np.float32)
+            assert_array_max_ulp(ufunc(datafp16), ufunc(datafp32),
+                    maxulp=1, dtype=np.float16)
+
+    @pytest.mark.skipif(not IS_AVX512FP16,
+                               reason="lower ULP only apply for SVML FP16")
+    def test_validate_svml_fp16(self):
+        max_ulp_err = {
+                "arccos": 2.54,
+                "arccosh": 2.09,
+                "arcsin": 3.06,
+                "arcsinh": 1.51,
+                "arctan": 2.61,
+                "arctanh": 1.88,
+                "cbrt": 1.57,
+                "cos": 1.43,
+                "cosh": 1.33,
+                "exp2": 1.33,
+                "exp": 1.27,
+                "expm1": 0.53,
+                "log": 1.80,
+                "log10": 1.27,
+                "log1p": 1.88,
+                "log2": 1.80,
+                "sin": 1.88,
+                "sinh": 2.05,
+                "tan": 2.26,
+                "tanh": 3.00,
+                }
+
+        with np.errstate(all='ignore'):
+            arr = np.arange(65536, dtype=np.int16)
+            datafp16 = np.frombuffer(arr.tobytes(), dtype=np.float16)
+            datafp32 = datafp16.astype(np.float32)
+            for func in max_ulp_err:
+                ufunc = getattr(np, func)
+                ulp = np.ceil(max_ulp_err[func])
+                assert_array_max_ulp(ufunc(datafp16), ufunc(datafp32),
+                        maxulp=ulp, dtype=np.float16)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_umath_complex.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_umath_complex.py
new file mode 100644
index 0000000..a97af47
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_umath_complex.py
@@ -0,0 +1,626 @@
+import platform
+import sys
+
+# import the c-extension module directly since _arg is not exported via umath
+import numpy._core._multiarray_umath as ncu
+import pytest
+
+import numpy as np
+from numpy.testing import (
+    assert_almost_equal,
+    assert_array_equal,
+    assert_array_max_ulp,
+    assert_equal,
+    assert_raises,
+)
+
+# TODO: branch cuts (use Pauli code)
+# TODO: conj 'symmetry'
+# TODO: FPU exceptions
+
+# At least on Windows the results of many complex functions are not conforming
+# to the C99 standard. See ticket 1574.
+# Ditto for Solaris (ticket 1642) and OS X on PowerPC.
+# FIXME: this will probably change when we require full C99 compatibility
+with np.errstate(all='ignore'):
+    functions_seem_flaky = ((np.exp(complex(np.inf, 0)).imag != 0)
+                            or (np.log(complex(ncu.NZERO, 0)).imag != np.pi))
+# TODO: replace with a check on whether platform-provided C99 funcs are used
+xfail_complex_tests = (not sys.platform.startswith('linux') or functions_seem_flaky)
+
+# TODO This can be xfail when the generator functions are got rid of.
+platform_skip = pytest.mark.skipif(xfail_complex_tests,
+                                   reason="Inadequate C99 complex support")
+
+
+class TestCexp:
+    def test_simple(self):
+        check = check_complex_value
+        f = np.exp
+
+        check(f, 1, 0, np.exp(1), 0, False)
+        check(f, 0, 1, np.cos(1), np.sin(1), False)
+
+        ref = np.exp(1) * complex(np.cos(1), np.sin(1))
+        check(f, 1, 1, ref.real, ref.imag, False)
+
+    @platform_skip
+    def test_special_values(self):
+        # C99: Section G 6.3.1
+
+        check = check_complex_value
+        f = np.exp
+
+        # cexp(+-0 + 0i) is 1 + 0i
+        check(f, ncu.PZERO, 0, 1, 0, False)
+        check(f, ncu.NZERO, 0, 1, 0, False)
+
+        # cexp(x + infi) is nan + nani for finite x and raises 'invalid' FPU
+        # exception
+        check(f,  1, np.inf, np.nan, np.nan)
+        check(f, -1, np.inf, np.nan, np.nan)
+        check(f,  0, np.inf, np.nan, np.nan)
+
+        # cexp(inf + 0i) is inf + 0i
+        check(f,  np.inf, 0, np.inf, 0)
+
+        # cexp(-inf + yi) is +0 * (cos(y) + i sin(y)) for finite y
+        check(f, -np.inf, 1, ncu.PZERO, ncu.PZERO)
+        check(f, -np.inf, 0.75 * np.pi, ncu.NZERO, ncu.PZERO)
+
+        # cexp(inf + yi) is +inf * (cos(y) + i sin(y)) for finite y
+        check(f,  np.inf, 1, np.inf, np.inf)
+        check(f,  np.inf, 0.75 * np.pi, -np.inf, np.inf)
+
+        # cexp(-inf + inf i) is +-0 +- 0i (signs unspecified)
+        def _check_ninf_inf(dummy):
+            msgform = "cexp(-inf, inf) is (%f, %f), expected (+-0, +-0)"
+            with np.errstate(invalid='ignore'):
+                z = f(np.array(complex(-np.inf, np.inf)))
+                if z.real != 0 or z.imag != 0:
+                    raise AssertionError(msgform % (z.real, z.imag))
+
+        _check_ninf_inf(None)
+
+        # cexp(inf + inf i) is +-inf + NaNi and raised invalid FPU ex.
+        def _check_inf_inf(dummy):
+            msgform = "cexp(inf, inf) is (%f, %f), expected (+-inf, nan)"
+            with np.errstate(invalid='ignore'):
+                z = f(np.array(complex(np.inf, np.inf)))
+                if not np.isinf(z.real) or not np.isnan(z.imag):
+                    raise AssertionError(msgform % (z.real, z.imag))
+
+        _check_inf_inf(None)
+
+        # cexp(-inf + nan i) is +-0 +- 0i
+        def _check_ninf_nan(dummy):
+            msgform = "cexp(-inf, nan) is (%f, %f), expected (+-0, +-0)"
+            with np.errstate(invalid='ignore'):
+                z = f(np.array(complex(-np.inf, np.nan)))
+                if z.real != 0 or z.imag != 0:
+                    raise AssertionError(msgform % (z.real, z.imag))
+
+        _check_ninf_nan(None)
+
+        # cexp(inf + nan i) is +-inf + nan
+        def _check_inf_nan(dummy):
+            msgform = "cexp(-inf, nan) is (%f, %f), expected (+-inf, nan)"
+            with np.errstate(invalid='ignore'):
+                z = f(np.array(complex(np.inf, np.nan)))
+                if not np.isinf(z.real) or not np.isnan(z.imag):
+                    raise AssertionError(msgform % (z.real, z.imag))
+
+        _check_inf_nan(None)
+
+        # cexp(nan + yi) is nan + nani for y != 0 (optional: raises invalid FPU
+        # ex)
+        check(f, np.nan, 1, np.nan, np.nan)
+        check(f, np.nan, -1, np.nan, np.nan)
+
+        check(f, np.nan,  np.inf, np.nan, np.nan)
+        check(f, np.nan, -np.inf, np.nan, np.nan)
+
+        # cexp(nan + nani) is nan + nani
+        check(f, np.nan, np.nan, np.nan, np.nan)
+
+    # TODO This can be xfail when the generator functions are got rid of.
+    @pytest.mark.skip(reason="cexp(nan + 0I) is wrong on most platforms")
+    def test_special_values2(self):
+        # XXX: most implementations get it wrong here (including glibc <= 2.10)
+        # cexp(nan + 0i) is nan + 0i
+        check = check_complex_value
+        f = np.exp
+
+        check(f, np.nan, 0, np.nan, 0)
+
+class TestClog:
+    def test_simple(self):
+        x = np.array([1 + 0j, 1 + 2j])
+        y_r = np.log(np.abs(x)) + 1j * np.angle(x)
+        y = np.log(x)
+        assert_almost_equal(y, y_r)
+
+    @platform_skip
+    @pytest.mark.skipif(platform.machine() == "armv5tel", reason="See gh-413.")
+    def test_special_values(self):
+        xl = []
+        yl = []
+
+        # From C99 std (Sec 6.3.2)
+        # XXX: check exceptions raised
+        # --- raise for invalid fails.
+
+        # clog(-0 + i0) returns -inf + i pi and raises the 'divide-by-zero'
+        # floating-point exception.
+        with np.errstate(divide='raise'):
+            x = np.array([ncu.NZERO], dtype=complex)
+            y = complex(-np.inf, np.pi)
+            assert_raises(FloatingPointError, np.log, x)
+        with np.errstate(divide='ignore'):
+            assert_almost_equal(np.log(x), y)
+
+        xl.append(x)
+        yl.append(y)
+
+        # clog(+0 + i0) returns -inf + i0 and raises the 'divide-by-zero'
+        # floating-point exception.
+        with np.errstate(divide='raise'):
+            x = np.array([0], dtype=complex)
+            y = complex(-np.inf, 0)
+            assert_raises(FloatingPointError, np.log, x)
+        with np.errstate(divide='ignore'):
+            assert_almost_equal(np.log(x), y)
+
+        xl.append(x)
+        yl.append(y)
+
+        # clog(x + i inf returns +inf + i pi /2, for finite x.
+        x = np.array([complex(1, np.inf)], dtype=complex)
+        y = complex(np.inf, 0.5 * np.pi)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        x = np.array([complex(-1, np.inf)], dtype=complex)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        # clog(x + iNaN) returns NaN + iNaN and optionally raises the
+        # 'invalid' floating- point exception, for finite x.
+        with np.errstate(invalid='raise'):
+            x = np.array([complex(1., np.nan)], dtype=complex)
+            y = complex(np.nan, np.nan)
+            #assert_raises(FloatingPointError, np.log, x)
+        with np.errstate(invalid='ignore'):
+            assert_almost_equal(np.log(x), y)
+
+        xl.append(x)
+        yl.append(y)
+
+        with np.errstate(invalid='raise'):
+            x = np.array([np.inf + 1j * np.nan], dtype=complex)
+            #assert_raises(FloatingPointError, np.log, x)
+        with np.errstate(invalid='ignore'):
+            assert_almost_equal(np.log(x), y)
+
+        xl.append(x)
+        yl.append(y)
+
+        # clog(- inf + iy) returns +inf + ipi , for finite positive-signed y.
+        x = np.array([-np.inf + 1j], dtype=complex)
+        y = complex(np.inf, np.pi)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        # clog(+ inf + iy) returns +inf + i0, for finite positive-signed y.
+        x = np.array([np.inf + 1j], dtype=complex)
+        y = complex(np.inf, 0)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        # clog(- inf + i inf) returns +inf + i3pi /4.
+        x = np.array([complex(-np.inf, np.inf)], dtype=complex)
+        y = complex(np.inf, 0.75 * np.pi)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        # clog(+ inf + i inf) returns +inf + ipi /4.
+        x = np.array([complex(np.inf, np.inf)], dtype=complex)
+        y = complex(np.inf, 0.25 * np.pi)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        # clog(+/- inf + iNaN) returns +inf + iNaN.
+        x = np.array([complex(np.inf, np.nan)], dtype=complex)
+        y = complex(np.inf, np.nan)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        x = np.array([complex(-np.inf, np.nan)], dtype=complex)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        # clog(NaN + iy) returns NaN + iNaN and optionally raises the
+        # 'invalid' floating-point exception, for finite y.
+        x = np.array([complex(np.nan, 1)], dtype=complex)
+        y = complex(np.nan, np.nan)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        # clog(NaN + i inf) returns +inf + iNaN.
+        x = np.array([complex(np.nan, np.inf)], dtype=complex)
+        y = complex(np.inf, np.nan)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        # clog(NaN + iNaN) returns NaN + iNaN.
+        x = np.array([complex(np.nan, np.nan)], dtype=complex)
+        y = complex(np.nan, np.nan)
+        assert_almost_equal(np.log(x), y)
+        xl.append(x)
+        yl.append(y)
+
+        # clog(conj(z)) = conj(clog(z)).
+        xa = np.array(xl, dtype=complex)
+        ya = np.array(yl, dtype=complex)
+        with np.errstate(divide='ignore'):
+            for i in range(len(xa)):
+                assert_almost_equal(np.log(xa[i].conj()), ya[i].conj())
+
+
+class TestCsqrt:
+
+    def test_simple(self):
+        # sqrt(1)
+        check_complex_value(np.sqrt, 1, 0, 1, 0)
+
+        # sqrt(1i)
+        rres = 0.5 * np.sqrt(2)
+        ires = rres
+        check_complex_value(np.sqrt, 0, 1, rres, ires, False)
+
+        # sqrt(-1)
+        check_complex_value(np.sqrt, -1, 0, 0, 1)
+
+    def test_simple_conjugate(self):
+        ref = np.conj(np.sqrt(complex(1, 1)))
+
+        def f(z):
+            return np.sqrt(np.conj(z))
+
+        check_complex_value(f, 1, 1, ref.real, ref.imag, False)
+
+    #def test_branch_cut(self):
+    #    _check_branch_cut(f, -1, 0, 1, -1)
+
+    @platform_skip
+    def test_special_values(self):
+        # C99: Sec G 6.4.2
+
+        check = check_complex_value
+        f = np.sqrt
+
+        # csqrt(+-0 + 0i) is 0 + 0i
+        check(f, ncu.PZERO, 0, 0, 0)
+        check(f, ncu.NZERO, 0, 0, 0)
+
+        # csqrt(x + infi) is inf + infi for any x (including NaN)
+        check(f,  1, np.inf, np.inf, np.inf)
+        check(f, -1, np.inf, np.inf, np.inf)
+
+        check(f, ncu.PZERO, np.inf, np.inf, np.inf)
+        check(f, ncu.NZERO, np.inf, np.inf, np.inf)
+        check(f,    np.inf, np.inf, np.inf, np.inf)
+        check(f,   -np.inf, np.inf, np.inf, np.inf)  # noqa: E221
+        check(f,   -np.nan, np.inf, np.inf, np.inf)  # noqa: E221
+
+        # csqrt(x + nani) is nan + nani for any finite x
+        check(f,  1, np.nan, np.nan, np.nan)
+        check(f, -1, np.nan, np.nan, np.nan)
+        check(f,  0, np.nan, np.nan, np.nan)
+
+        # csqrt(-inf + yi) is +0 + infi for any finite y > 0
+        check(f, -np.inf, 1, ncu.PZERO, np.inf)
+
+        # csqrt(inf + yi) is +inf + 0i for any finite y > 0
+        check(f, np.inf, 1, np.inf, ncu.PZERO)
+
+        # csqrt(-inf + nani) is nan +- infi (both +i infi are valid)
+        def _check_ninf_nan(dummy):
+            msgform = "csqrt(-inf, nan) is (%f, %f), expected (nan, +-inf)"
+            z = np.sqrt(np.array(complex(-np.inf, np.nan)))
+            # FIXME: ugly workaround for isinf bug.
+            with np.errstate(invalid='ignore'):
+                if not (np.isnan(z.real) and np.isinf(z.imag)):
+                    raise AssertionError(msgform % (z.real, z.imag))
+
+        _check_ninf_nan(None)
+
+        # csqrt(+inf + nani) is inf + nani
+        check(f, np.inf, np.nan, np.inf, np.nan)
+
+        # csqrt(nan + yi) is nan + nani for any finite y (infinite handled in x
+        # + nani)
+        check(f, np.nan,       0, np.nan, np.nan)
+        check(f, np.nan,       1, np.nan, np.nan)
+        check(f, np.nan,  np.nan, np.nan, np.nan)
+
+        # XXX: check for conj(csqrt(z)) == csqrt(conj(z)) (need to fix branch
+        # cuts first)
+
+class TestCpow:
+    def setup_method(self):
+        self.olderr = np.seterr(invalid='ignore')
+
+    def teardown_method(self):
+        np.seterr(**self.olderr)
+
+    def test_simple(self):
+        x = np.array([1 + 1j, 0 + 2j, 1 + 2j, np.inf, np.nan])
+        y_r = x ** 2
+        y = np.power(x, 2)
+        assert_almost_equal(y, y_r)
+
+    def test_scalar(self):
+        x = np.array([1, 1j,         2,  2.5 + .37j, np.inf, np.nan])
+        y = np.array([1, 1j, -0.5 + 1.5j, -0.5 + 1.5j,      2,      3])
+        lx = list(range(len(x)))
+
+        # Hardcode the expected `builtins.complex` values,
+        # as complex exponentiation is broken as of bpo-44698
+        p_r = [
+            1 + 0j,
+            0.20787957635076193 + 0j,
+            0.35812203996480685 + 0.6097119028618724j,
+            0.12659112128185032 + 0.48847676699581527j,
+            complex(np.inf, np.nan),
+            complex(np.nan, np.nan),
+        ]
+
+        n_r = [x[i] ** y[i] for i in lx]
+        for i in lx:
+            assert_almost_equal(n_r[i], p_r[i], err_msg='Loop %d\n' % i)
+
+    def test_array(self):
+        x = np.array([1, 1j,         2,  2.5 + .37j, np.inf, np.nan])
+        y = np.array([1, 1j, -0.5 + 1.5j, -0.5 + 1.5j,      2,      3])
+        lx = list(range(len(x)))
+
+        # Hardcode the expected `builtins.complex` values,
+        # as complex exponentiation is broken as of bpo-44698
+        p_r = [
+            1 + 0j,
+            0.20787957635076193 + 0j,
+            0.35812203996480685 + 0.6097119028618724j,
+            0.12659112128185032 + 0.48847676699581527j,
+            complex(np.inf, np.nan),
+            complex(np.nan, np.nan),
+        ]
+
+        n_r = x ** y
+        for i in lx:
+            assert_almost_equal(n_r[i], p_r[i], err_msg='Loop %d\n' % i)
+
+class TestCabs:
+    def setup_method(self):
+        self.olderr = np.seterr(invalid='ignore')
+
+    def teardown_method(self):
+        np.seterr(**self.olderr)
+
+    def test_simple(self):
+        x = np.array([1 + 1j, 0 + 2j, 1 + 2j, np.inf, np.nan])
+        y_r = np.array([np.sqrt(2.), 2, np.sqrt(5), np.inf, np.nan])
+        y = np.abs(x)
+        assert_almost_equal(y, y_r)
+
+    def test_fabs(self):
+        # Test that np.abs(x +- 0j) == np.abs(x) (as mandated by C99 for cabs)
+        x = np.array([1 + 0j], dtype=complex)
+        assert_array_equal(np.abs(x), np.real(x))
+
+        x = np.array([complex(1, ncu.NZERO)], dtype=complex)
+        assert_array_equal(np.abs(x), np.real(x))
+
+        x = np.array([complex(np.inf, ncu.NZERO)], dtype=complex)
+        assert_array_equal(np.abs(x), np.real(x))
+
+        x = np.array([complex(np.nan, ncu.NZERO)], dtype=complex)
+        assert_array_equal(np.abs(x), np.real(x))
+
+    def test_cabs_inf_nan(self):
+        x, y = [], []
+
+        # cabs(+-nan + nani) returns nan
+        x.append(np.nan)
+        y.append(np.nan)
+        check_real_value(np.abs,  np.nan, np.nan, np.nan)
+
+        x.append(np.nan)
+        y.append(-np.nan)
+        check_real_value(np.abs, -np.nan, np.nan, np.nan)
+
+        # According to C99 standard, if exactly one of the real/part is inf and
+        # the other nan, then cabs should return inf
+        x.append(np.inf)
+        y.append(np.nan)
+        check_real_value(np.abs,  np.inf, np.nan, np.inf)
+
+        x.append(-np.inf)
+        y.append(np.nan)
+        check_real_value(np.abs, -np.inf, np.nan, np.inf)
+
+        # cabs(conj(z)) == conj(cabs(z)) (= cabs(z))
+        def f(a):
+            return np.abs(np.conj(a))
+
+        def g(a, b):
+            return np.abs(complex(a, b))
+
+        xa = np.array(x, dtype=complex)
+        assert len(xa) == len(x) == len(y)
+        for xi, yi in zip(x, y):
+            ref = g(xi, yi)
+            check_real_value(f, xi, yi, ref)
+
+class TestCarg:
+    def test_simple(self):
+        check_real_value(ncu._arg, 1, 0, 0, False)
+        check_real_value(ncu._arg, 0, 1, 0.5 * np.pi, False)
+
+        check_real_value(ncu._arg, 1, 1, 0.25 * np.pi, False)
+        check_real_value(ncu._arg, ncu.PZERO, ncu.PZERO, ncu.PZERO)
+
+    # TODO This can be xfail when the generator functions are got rid of.
+    @pytest.mark.skip(
+        reason="Complex arithmetic with signed zero fails on most platforms")
+    def test_zero(self):
+        # carg(-0 +- 0i) returns +- pi
+        check_real_value(ncu._arg, ncu.NZERO, ncu.PZERO,  np.pi, False)
+        check_real_value(ncu._arg, ncu.NZERO, ncu.NZERO, -np.pi, False)
+
+        # carg(+0 +- 0i) returns +- 0
+        check_real_value(ncu._arg, ncu.PZERO, ncu.PZERO, ncu.PZERO)
+        check_real_value(ncu._arg, ncu.PZERO, ncu.NZERO, ncu.NZERO)
+
+        # carg(x +- 0i) returns +- 0 for x > 0
+        check_real_value(ncu._arg, 1, ncu.PZERO, ncu.PZERO, False)
+        check_real_value(ncu._arg, 1, ncu.NZERO, ncu.NZERO, False)
+
+        # carg(x +- 0i) returns +- pi for x < 0
+        check_real_value(ncu._arg, -1, ncu.PZERO,  np.pi, False)
+        check_real_value(ncu._arg, -1, ncu.NZERO, -np.pi, False)
+
+        # carg(+- 0 + yi) returns pi/2 for y > 0
+        check_real_value(ncu._arg, ncu.PZERO, 1, 0.5 * np.pi, False)
+        check_real_value(ncu._arg, ncu.NZERO, 1, 0.5 * np.pi, False)
+
+        # carg(+- 0 + yi) returns -pi/2 for y < 0
+        check_real_value(ncu._arg, ncu.PZERO, -1, 0.5 * np.pi, False)
+        check_real_value(ncu._arg, ncu.NZERO, -1, -0.5 * np.pi, False)
+
+    #def test_branch_cuts(self):
+    #    _check_branch_cut(ncu._arg, -1, 1j, -1, 1)
+
+    def test_special_values(self):
+        # carg(-np.inf +- yi) returns +-pi for finite y > 0
+        check_real_value(ncu._arg, -np.inf,  1,  np.pi, False)
+        check_real_value(ncu._arg, -np.inf, -1, -np.pi, False)
+
+        # carg(np.inf +- yi) returns +-0 for finite y > 0
+        check_real_value(ncu._arg, np.inf,  1, ncu.PZERO, False)
+        check_real_value(ncu._arg, np.inf, -1, ncu.NZERO, False)
+
+        # carg(x +- np.infi) returns +-pi/2 for finite x
+        check_real_value(ncu._arg, 1,  np.inf,  0.5 * np.pi, False)
+        check_real_value(ncu._arg, 1, -np.inf, -0.5 * np.pi, False)
+
+        # carg(-np.inf +- np.infi) returns +-3pi/4
+        check_real_value(ncu._arg, -np.inf,  np.inf,  0.75 * np.pi, False)
+        check_real_value(ncu._arg, -np.inf, -np.inf, -0.75 * np.pi, False)
+
+        # carg(np.inf +- np.infi) returns +-pi/4
+        check_real_value(ncu._arg, np.inf,  np.inf,  0.25 * np.pi, False)
+        check_real_value(ncu._arg, np.inf, -np.inf, -0.25 * np.pi, False)
+
+        # carg(x + yi) returns np.nan if x or y is nan
+        check_real_value(ncu._arg, np.nan,      0, np.nan, False)
+        check_real_value(ncu._arg,      0, np.nan, np.nan, False)
+
+        check_real_value(ncu._arg, np.nan, np.inf, np.nan, False)
+        check_real_value(ncu._arg, np.inf, np.nan, np.nan, False)
+
+
+def check_real_value(f, x1, y1, x, exact=True):
+    z1 = np.array([complex(x1, y1)])
+    if exact:
+        assert_equal(f(z1), x)
+    else:
+        assert_almost_equal(f(z1), x)
+
+
+def check_complex_value(f, x1, y1, x2, y2, exact=True):
+    z1 = np.array([complex(x1, y1)])
+    z2 = complex(x2, y2)
+    with np.errstate(invalid='ignore'):
+        if exact:
+            assert_equal(f(z1), z2)
+        else:
+            assert_almost_equal(f(z1), z2)
+
+class TestSpecialComplexAVX:
+    @pytest.mark.parametrize("stride", [-4, -2, -1, 1, 2, 4])
+    @pytest.mark.parametrize("astype", [np.complex64, np.complex128])
+    def test_array(self, stride, astype):
+        arr = np.array([complex(np.nan, np.nan),
+                        complex(np.nan, np.inf),
+                        complex(np.inf, np.nan),
+                        complex(np.inf, np.inf),
+                        complex(0.,     np.inf),
+                        complex(np.inf, 0.),
+                        complex(0.,     0.),
+                        complex(0.,     np.nan),
+                        complex(np.nan, 0.)], dtype=astype)
+        abs_true = np.array([np.nan, np.inf, np.inf, np.inf, np.inf, np.inf, 0., np.nan, np.nan], dtype=arr.real.dtype)
+        sq_true = np.array([complex(np.nan,  np.nan),
+                            complex(np.nan,  np.nan),
+                            complex(np.nan,  np.nan),
+                            complex(np.nan,  np.inf),
+                            complex(-np.inf, np.nan),
+                            complex(np.inf,  np.nan),
+                            complex(0.,      0.),
+                            complex(np.nan,  np.nan),
+                            complex(np.nan,  np.nan)], dtype=astype)
+        with np.errstate(invalid='ignore'):
+            assert_equal(np.abs(arr[::stride]), abs_true[::stride])
+            assert_equal(np.square(arr[::stride]), sq_true[::stride])
+
+class TestComplexAbsoluteAVX:
+    @pytest.mark.parametrize("arraysize", [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 18, 19])
+    @pytest.mark.parametrize("stride", [-4, -3, -2, -1, 1, 2, 3, 4])
+    @pytest.mark.parametrize("astype", [np.complex64, np.complex128])
+    # test to ensure masking and strides work as intended in the AVX implementation
+    def test_array(self, arraysize, stride, astype):
+        arr = np.ones(arraysize, dtype=astype)
+        abs_true = np.ones(arraysize, dtype=arr.real.dtype)
+        assert_equal(np.abs(arr[::stride]), abs_true[::stride])
+
+# Testcase taken as is from https://github.com/numpy/numpy/issues/16660
+class TestComplexAbsoluteMixedDTypes:
+    @pytest.mark.parametrize("stride", [-4, -3, -2, -1, 1, 2, 3, 4])
+    @pytest.mark.parametrize("astype", [np.complex64, np.complex128])
+    @pytest.mark.parametrize("func", ['abs', 'square', 'conjugate'])
+    def test_array(self, stride, astype, func):
+        dtype = [('template_id', '<i8'), ('bank_chisq', '<f4'),
+                 ('bank_chisq_dof', '<i8'), ('chisq', '<f4'), ('chisq_dof', '<i8'),
+                 ('cont_chisq', '<f4'), ('psd_var_val', '<f4'), ('sg_chisq', '<f4'),
+                 ('mycomplex', astype), ('time_index', '<i8')]
+        vec = np.array([
+                (0, 0., 0, -31.666483, 200, 0., 0.,  1.      ,  3.0 + 4.0j  ,  613090),   # noqa: E203,E501
+                (1, 0., 0, 260.91525 ,  42, 0., 0.,  1.      ,  5.0 + 12.0j ,  787315),   # noqa: E203,E501
+                (1, 0., 0,  52.15155 ,  42, 0., 0.,  1.      ,  8.0 + 15.0j ,  806641),   # noqa: E203,E501
+                (1, 0., 0,  52.430195,  42, 0., 0.,  1.      ,  7.0 + 24.0j , 1363540),   # noqa: E203,E501
+                (2, 0., 0, 304.43646 ,  58, 0., 0.,  1.      ,  20.0 + 21.0j,  787323),   # noqa: E203,E501
+                (3, 0., 0, 299.42108 ,  52, 0., 0.,  1.      ,  12.0 + 35.0j,  787332),   # noqa: E203,E501
+                (4, 0., 0,  39.4836  ,  28, 0., 0.,  9.182192,  9.0 + 40.0j ,  787304),   # noqa: E203,E501
+                (4, 0., 0,  76.83787 ,  28, 0., 0.,  1.      ,  28.0 + 45.0j, 1321869),   # noqa: E203,E501
+                (5, 0., 0, 143.26366 ,  24, 0., 0., 10.996129,  11.0 + 60.0j,  787299)],  # noqa: E203,E501
+            dtype=dtype)
+        myfunc = getattr(np, func)
+        a = vec['mycomplex']
+        g = myfunc(a[::stride])
+
+        b = vec['mycomplex'].copy()
+        h = myfunc(b[::stride])
+
+        assert_array_max_ulp(h.real, g.real, 1)
+        assert_array_max_ulp(h.imag, g.imag, 1)
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_unicode.py b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_unicode.py
new file mode 100644
index 0000000..9fdc55b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/tests/test_unicode.py
@@ -0,0 +1,368 @@
+
+import numpy as np
+from numpy.testing import assert_, assert_array_equal, assert_equal
+
+
+def buffer_length(arr):
+    if isinstance(arr, str):
+        if not arr:
+            charmax = 0
+        else:
+            charmax = max(ord(c) for c in arr)
+        if charmax < 256:
+            size = 1
+        elif charmax < 65536:
+            size = 2
+        else:
+            size = 4
+        return size * len(arr)
+    v = memoryview(arr)
+    if v.shape is None:
+        return len(v) * v.itemsize
+    else:
+        return np.prod(v.shape) * v.itemsize
+
+
+# In both cases below we need to make sure that the byte swapped value (as
+# UCS4) is still a valid unicode:
+# Value that can be represented in UCS2 interpreters
+ucs2_value = '\u0900'
+# Value that cannot be represented in UCS2 interpreters (but can in UCS4)
+ucs4_value = '\U00100900'
+
+
+def test_string_cast():
+    str_arr = np.array(["1234", "1234\0\0"], dtype='S')
+    uni_arr1 = str_arr.astype('>U')
+    uni_arr2 = str_arr.astype('<U')
+
+    assert_array_equal(str_arr != uni_arr1, np.ones(2, dtype=bool))
+    assert_array_equal(uni_arr1 != str_arr, np.ones(2, dtype=bool))
+    assert_array_equal(str_arr == uni_arr1, np.zeros(2, dtype=bool))
+    assert_array_equal(uni_arr1 == str_arr, np.zeros(2, dtype=bool))
+
+    assert_array_equal(uni_arr1, uni_arr2)
+
+
+############################################################
+#    Creation tests
+############################################################
+
+class CreateZeros:
+    """Check the creation of zero-valued arrays"""
+
+    def content_check(self, ua, ua_scalar, nbytes):
+
+        # Check the length of the unicode base type
+        assert_(int(ua.dtype.str[2:]) == self.ulen)
+        # Check the length of the data buffer
+        assert_(buffer_length(ua) == nbytes)
+        # Small check that data in array element is ok
+        assert_(ua_scalar == '')
+        # Encode to ascii and double check
+        assert_(ua_scalar.encode('ascii') == b'')
+        # Check buffer lengths for scalars
+        assert_(buffer_length(ua_scalar) == 0)
+
+    def test_zeros0D(self):
+        # Check creation of 0-dimensional objects
+        ua = np.zeros((), dtype=f'U{self.ulen}')
+        self.content_check(ua, ua[()], 4 * self.ulen)
+
+    def test_zerosSD(self):
+        # Check creation of single-dimensional objects
+        ua = np.zeros((2,), dtype=f'U{self.ulen}')
+        self.content_check(ua, ua[0], 4 * self.ulen * 2)
+        self.content_check(ua, ua[1], 4 * self.ulen * 2)
+
+    def test_zerosMD(self):
+        # Check creation of multi-dimensional objects
+        ua = np.zeros((2, 3, 4), dtype=f'U{self.ulen}')
+        self.content_check(ua, ua[0, 0, 0], 4 * self.ulen * 2 * 3 * 4)
+        self.content_check(ua, ua[-1, -1, -1], 4 * self.ulen * 2 * 3 * 4)
+
+
+class TestCreateZeros_1(CreateZeros):
+    """Check the creation of zero-valued arrays (size 1)"""
+    ulen = 1
+
+
+class TestCreateZeros_2(CreateZeros):
+    """Check the creation of zero-valued arrays (size 2)"""
+    ulen = 2
+
+
+class TestCreateZeros_1009(CreateZeros):
+    """Check the creation of zero-valued arrays (size 1009)"""
+    ulen = 1009
+
+
+class CreateValues:
+    """Check the creation of unicode arrays with values"""
+
+    def content_check(self, ua, ua_scalar, nbytes):
+
+        # Check the length of the unicode base type
+        assert_(int(ua.dtype.str[2:]) == self.ulen)
+        # Check the length of the data buffer
+        assert_(buffer_length(ua) == nbytes)
+        # Small check that data in array element is ok
+        assert_(ua_scalar == self.ucs_value * self.ulen)
+        # Encode to UTF-8 and double check
+        assert_(ua_scalar.encode('utf-8') ==
+                        (self.ucs_value * self.ulen).encode('utf-8'))
+        # Check buffer lengths for scalars
+        if self.ucs_value == ucs4_value:
+            # In UCS2, the \U0010FFFF will be represented using a
+            # surrogate *pair*
+            assert_(buffer_length(ua_scalar) == 2 * 2 * self.ulen)
+        else:
+            # In UCS2, the \uFFFF will be represented using a
+            # regular 2-byte word
+            assert_(buffer_length(ua_scalar) == 2 * self.ulen)
+
+    def test_values0D(self):
+        # Check creation of 0-dimensional objects with values
+        ua = np.array(self.ucs_value * self.ulen, dtype=f'U{self.ulen}')
+        self.content_check(ua, ua[()], 4 * self.ulen)
+
+    def test_valuesSD(self):
+        # Check creation of single-dimensional objects with values
+        ua = np.array([self.ucs_value * self.ulen] * 2, dtype=f'U{self.ulen}')
+        self.content_check(ua, ua[0], 4 * self.ulen * 2)
+        self.content_check(ua, ua[1], 4 * self.ulen * 2)
+
+    def test_valuesMD(self):
+        # Check creation of multi-dimensional objects with values
+        ua = np.array([[[self.ucs_value * self.ulen] * 2] * 3] * 4, dtype=f'U{self.ulen}')
+        self.content_check(ua, ua[0, 0, 0], 4 * self.ulen * 2 * 3 * 4)
+        self.content_check(ua, ua[-1, -1, -1], 4 * self.ulen * 2 * 3 * 4)
+
+
+class TestCreateValues_1_UCS2(CreateValues):
+    """Check the creation of valued arrays (size 1, UCS2 values)"""
+    ulen = 1
+    ucs_value = ucs2_value
+
+
+class TestCreateValues_1_UCS4(CreateValues):
+    """Check the creation of valued arrays (size 1, UCS4 values)"""
+    ulen = 1
+    ucs_value = ucs4_value
+
+
+class TestCreateValues_2_UCS2(CreateValues):
+    """Check the creation of valued arrays (size 2, UCS2 values)"""
+    ulen = 2
+    ucs_value = ucs2_value
+
+
+class TestCreateValues_2_UCS4(CreateValues):
+    """Check the creation of valued arrays (size 2, UCS4 values)"""
+    ulen = 2
+    ucs_value = ucs4_value
+
+
+class TestCreateValues_1009_UCS2(CreateValues):
+    """Check the creation of valued arrays (size 1009, UCS2 values)"""
+    ulen = 1009
+    ucs_value = ucs2_value
+
+
+class TestCreateValues_1009_UCS4(CreateValues):
+    """Check the creation of valued arrays (size 1009, UCS4 values)"""
+    ulen = 1009
+    ucs_value = ucs4_value
+
+
+############################################################
+#    Assignment tests
+############################################################
+
+class AssignValues:
+    """Check the assignment of unicode arrays with values"""
+
+    def content_check(self, ua, ua_scalar, nbytes):
+
+        # Check the length of the unicode base type
+        assert_(int(ua.dtype.str[2:]) == self.ulen)
+        # Check the length of the data buffer
+        assert_(buffer_length(ua) == nbytes)
+        # Small check that data in array element is ok
+        assert_(ua_scalar == self.ucs_value * self.ulen)
+        # Encode to UTF-8 and double check
+        assert_(ua_scalar.encode('utf-8') ==
+                        (self.ucs_value * self.ulen).encode('utf-8'))
+        # Check buffer lengths for scalars
+        if self.ucs_value == ucs4_value:
+            # In UCS2, the \U0010FFFF will be represented using a
+            # surrogate *pair*
+            assert_(buffer_length(ua_scalar) == 2 * 2 * self.ulen)
+        else:
+            # In UCS2, the \uFFFF will be represented using a
+            # regular 2-byte word
+            assert_(buffer_length(ua_scalar) == 2 * self.ulen)
+
+    def test_values0D(self):
+        # Check assignment of 0-dimensional objects with values
+        ua = np.zeros((), dtype=f'U{self.ulen}')
+        ua[()] = self.ucs_value * self.ulen
+        self.content_check(ua, ua[()], 4 * self.ulen)
+
+    def test_valuesSD(self):
+        # Check assignment of single-dimensional objects with values
+        ua = np.zeros((2,), dtype=f'U{self.ulen}')
+        ua[0] = self.ucs_value * self.ulen
+        self.content_check(ua, ua[0], 4 * self.ulen * 2)
+        ua[1] = self.ucs_value * self.ulen
+        self.content_check(ua, ua[1], 4 * self.ulen * 2)
+
+    def test_valuesMD(self):
+        # Check assignment of multi-dimensional objects with values
+        ua = np.zeros((2, 3, 4), dtype=f'U{self.ulen}')
+        ua[0, 0, 0] = self.ucs_value * self.ulen
+        self.content_check(ua, ua[0, 0, 0], 4 * self.ulen * 2 * 3 * 4)
+        ua[-1, -1, -1] = self.ucs_value * self.ulen
+        self.content_check(ua, ua[-1, -1, -1], 4 * self.ulen * 2 * 3 * 4)
+
+
+class TestAssignValues_1_UCS2(AssignValues):
+    """Check the assignment of valued arrays (size 1, UCS2 values)"""
+    ulen = 1
+    ucs_value = ucs2_value
+
+
+class TestAssignValues_1_UCS4(AssignValues):
+    """Check the assignment of valued arrays (size 1, UCS4 values)"""
+    ulen = 1
+    ucs_value = ucs4_value
+
+
+class TestAssignValues_2_UCS2(AssignValues):
+    """Check the assignment of valued arrays (size 2, UCS2 values)"""
+    ulen = 2
+    ucs_value = ucs2_value
+
+
+class TestAssignValues_2_UCS4(AssignValues):
+    """Check the assignment of valued arrays (size 2, UCS4 values)"""
+    ulen = 2
+    ucs_value = ucs4_value
+
+
+class TestAssignValues_1009_UCS2(AssignValues):
+    """Check the assignment of valued arrays (size 1009, UCS2 values)"""
+    ulen = 1009
+    ucs_value = ucs2_value
+
+
+class TestAssignValues_1009_UCS4(AssignValues):
+    """Check the assignment of valued arrays (size 1009, UCS4 values)"""
+    ulen = 1009
+    ucs_value = ucs4_value
+
+
+############################################################
+#    Byteorder tests
+############################################################
+
+class ByteorderValues:
+    """Check the byteorder of unicode arrays in round-trip conversions"""
+
+    def test_values0D(self):
+        # Check byteorder of 0-dimensional objects
+        ua = np.array(self.ucs_value * self.ulen, dtype=f'U{self.ulen}')
+        ua2 = ua.view(ua.dtype.newbyteorder())
+        # This changes the interpretation of the data region (but not the
+        #  actual data), therefore the returned scalars are not
+        #  the same (they are byte-swapped versions of each other).
+        assert_(ua[()] != ua2[()])
+        ua3 = ua2.view(ua2.dtype.newbyteorder())
+        # Arrays must be equal after the round-trip
+        assert_equal(ua, ua3)
+
+    def test_valuesSD(self):
+        # Check byteorder of single-dimensional objects
+        ua = np.array([self.ucs_value * self.ulen] * 2, dtype=f'U{self.ulen}')
+        ua2 = ua.view(ua.dtype.newbyteorder())
+        assert_((ua != ua2).all())
+        assert_(ua[-1] != ua2[-1])
+        ua3 = ua2.view(ua2.dtype.newbyteorder())
+        # Arrays must be equal after the round-trip
+        assert_equal(ua, ua3)
+
+    def test_valuesMD(self):
+        # Check byteorder of multi-dimensional objects
+        ua = np.array([[[self.ucs_value * self.ulen] * 2] * 3] * 4,
+                      dtype=f'U{self.ulen}')
+        ua2 = ua.view(ua.dtype.newbyteorder())
+        assert_((ua != ua2).all())
+        assert_(ua[-1, -1, -1] != ua2[-1, -1, -1])
+        ua3 = ua2.view(ua2.dtype.newbyteorder())
+        # Arrays must be equal after the round-trip
+        assert_equal(ua, ua3)
+
+    def test_values_cast(self):
+        # Check byteorder of when casting the array for a strided and
+        # contiguous array:
+        test1 = np.array([self.ucs_value * self.ulen] * 2, dtype=f'U{self.ulen}')
+        test2 = np.repeat(test1, 2)[::2]
+        for ua in (test1, test2):
+            ua2 = ua.astype(dtype=ua.dtype.newbyteorder())
+            assert_((ua == ua2).all())
+            assert_(ua[-1] == ua2[-1])
+            ua3 = ua2.astype(dtype=ua.dtype)
+            # Arrays must be equal after the round-trip
+            assert_equal(ua, ua3)
+
+    def test_values_updowncast(self):
+        # Check byteorder of when casting the array to a longer and shorter
+        # string length for strided and contiguous arrays
+        test1 = np.array([self.ucs_value * self.ulen] * 2, dtype=f'U{self.ulen}')
+        test2 = np.repeat(test1, 2)[::2]
+        for ua in (test1, test2):
+            # Cast to a longer type with zero padding
+            longer_type = np.dtype(f'U{self.ulen + 1}').newbyteorder()
+            ua2 = ua.astype(dtype=longer_type)
+            assert_((ua == ua2).all())
+            assert_(ua[-1] == ua2[-1])
+            # Cast back again with truncating:
+            ua3 = ua2.astype(dtype=ua.dtype)
+            # Arrays must be equal after the round-trip
+            assert_equal(ua, ua3)
+
+
+class TestByteorder_1_UCS2(ByteorderValues):
+    """Check the byteorder in unicode (size 1, UCS2 values)"""
+    ulen = 1
+    ucs_value = ucs2_value
+
+
+class TestByteorder_1_UCS4(ByteorderValues):
+    """Check the byteorder in unicode (size 1, UCS4 values)"""
+    ulen = 1
+    ucs_value = ucs4_value
+
+
+class TestByteorder_2_UCS2(ByteorderValues):
+    """Check the byteorder in unicode (size 2, UCS2 values)"""
+    ulen = 2
+    ucs_value = ucs2_value
+
+
+class TestByteorder_2_UCS4(ByteorderValues):
+    """Check the byteorder in unicode (size 2, UCS4 values)"""
+    ulen = 2
+    ucs_value = ucs4_value
+
+
+class TestByteorder_1009_UCS2(ByteorderValues):
+    """Check the byteorder in unicode (size 1009, UCS2 values)"""
+    ulen = 1009
+    ucs_value = ucs2_value
+
+
+class TestByteorder_1009_UCS4(ByteorderValues):
+    """Check the byteorder in unicode (size 1009, UCS4 values)"""
+    ulen = 1009
+    ucs_value = ucs4_value
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/umath.py b/.venv/lib/python3.12/site-packages/numpy/_core/umath.py
new file mode 100644
index 0000000..94f97c0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/umath.py
@@ -0,0 +1,60 @@
+"""
+Create the numpy._core.umath namespace for backward compatibility. In v1.16
+the multiarray and umath c-extension modules were merged into a single
+_multiarray_umath extension module. So we replicate the old namespace
+by importing from the extension module.
+
+"""
+
+import numpy
+
+from . import _multiarray_umath
+from ._multiarray_umath import *
+
+# These imports are needed for backward compatibility,
+# do not change them. issue gh-11862
+# _ones_like is semi-public, on purpose not added to __all__
+# These imports are needed for the strip & replace implementations
+from ._multiarray_umath import (
+    _UFUNC_API,
+    _add_newdoc_ufunc,
+    _center,
+    _expandtabs,
+    _expandtabs_length,
+    _extobj_contextvar,
+    _get_extobj_dict,
+    _ljust,
+    _lstrip_chars,
+    _lstrip_whitespace,
+    _make_extobj,
+    _ones_like,
+    _partition,
+    _partition_index,
+    _replace,
+    _rjust,
+    _rpartition,
+    _rpartition_index,
+    _rstrip_chars,
+    _rstrip_whitespace,
+    _slice,
+    _strip_chars,
+    _strip_whitespace,
+    _zfill,
+)
+
+__all__ = [
+    'absolute', 'add',
+    'arccos', 'arccosh', 'arcsin', 'arcsinh', 'arctan', 'arctan2', 'arctanh',
+    'bitwise_and', 'bitwise_or', 'bitwise_xor', 'cbrt', 'ceil', 'conj',
+    'conjugate', 'copysign', 'cos', 'cosh', 'bitwise_count', 'deg2rad',
+    'degrees', 'divide', 'divmod', 'e', 'equal', 'euler_gamma', 'exp', 'exp2',
+    'expm1', 'fabs', 'floor', 'floor_divide', 'float_power', 'fmax', 'fmin',
+    'fmod', 'frexp', 'frompyfunc', 'gcd', 'greater', 'greater_equal',
+    'heaviside', 'hypot', 'invert', 'isfinite', 'isinf', 'isnan', 'isnat',
+    'lcm', 'ldexp', 'left_shift', 'less', 'less_equal', 'log', 'log10',
+    'log1p', 'log2', 'logaddexp', 'logaddexp2', 'logical_and', 'logical_not',
+    'logical_or', 'logical_xor', 'matvec', 'maximum', 'minimum', 'mod', 'modf',
+    'multiply', 'negative', 'nextafter', 'not_equal', 'pi', 'positive',
+    'power', 'rad2deg', 'radians', 'reciprocal', 'remainder', 'right_shift',
+    'rint', 'sign', 'signbit', 'sin', 'sinh', 'spacing', 'sqrt', 'square',
+    'subtract', 'tan', 'tanh', 'true_divide', 'trunc', 'vecdot', 'vecmat']
diff --git a/.venv/lib/python3.12/site-packages/numpy/_core/umath.pyi b/.venv/lib/python3.12/site-packages/numpy/_core/umath.pyi
new file mode 100644
index 0000000..d9f0d38
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/_core/umath.pyi
@@ -0,0 +1,197 @@
+from numpy import (
+    absolute,
+    add,
+    arccos,
+    arccosh,
+    arcsin,
+    arcsinh,
+    arctan,
+    arctan2,
+    arctanh,
+    bitwise_and,
+    bitwise_count,
+    bitwise_or,
+    bitwise_xor,
+    cbrt,
+    ceil,
+    conj,
+    conjugate,
+    copysign,
+    cos,
+    cosh,
+    deg2rad,
+    degrees,
+    divide,
+    divmod,
+    e,
+    equal,
+    euler_gamma,
+    exp,
+    exp2,
+    expm1,
+    fabs,
+    float_power,
+    floor,
+    floor_divide,
+    fmax,
+    fmin,
+    fmod,
+    frexp,
+    frompyfunc,
+    gcd,
+    greater,
+    greater_equal,
+    heaviside,
+    hypot,
+    invert,
+    isfinite,
+    isinf,
+    isnan,
+    isnat,
+    lcm,
+    ldexp,
+    left_shift,
+    less,
+    less_equal,
+    log,
+    log1p,
+    log2,
+    log10,
+    logaddexp,
+    logaddexp2,
+    logical_and,
+    logical_not,
+    logical_or,
+    logical_xor,
+    matvec,
+    maximum,
+    minimum,
+    mod,
+    modf,
+    multiply,
+    negative,
+    nextafter,
+    not_equal,
+    pi,
+    positive,
+    power,
+    rad2deg,
+    radians,
+    reciprocal,
+    remainder,
+    right_shift,
+    rint,
+    sign,
+    signbit,
+    sin,
+    sinh,
+    spacing,
+    sqrt,
+    square,
+    subtract,
+    tan,
+    tanh,
+    true_divide,
+    trunc,
+    vecdot,
+    vecmat,
+)
+
+__all__ = [
+    "absolute",
+    "add",
+    "arccos",
+    "arccosh",
+    "arcsin",
+    "arcsinh",
+    "arctan",
+    "arctan2",
+    "arctanh",
+    "bitwise_and",
+    "bitwise_count",
+    "bitwise_or",
+    "bitwise_xor",
+    "cbrt",
+    "ceil",
+    "conj",
+    "conjugate",
+    "copysign",
+    "cos",
+    "cosh",
+    "deg2rad",
+    "degrees",
+    "divide",
+    "divmod",
+    "e",
+    "equal",
+    "euler_gamma",
+    "exp",
+    "exp2",
+    "expm1",
+    "fabs",
+    "float_power",
+    "floor",
+    "floor_divide",
+    "fmax",
+    "fmin",
+    "fmod",
+    "frexp",
+    "frompyfunc",
+    "gcd",
+    "greater",
+    "greater_equal",
+    "heaviside",
+    "hypot",
+    "invert",
+    "isfinite",
+    "isinf",
+    "isnan",
+    "isnat",
+    "lcm",
+    "ldexp",
+    "left_shift",
+    "less",
+    "less_equal",
+    "log",
+    "log1p",
+    "log2",
+    "log10",
+    "logaddexp",
+    "logaddexp2",
+    "logical_and",
+    "logical_not",
+    "logical_or",
+    "logical_xor",
+    "matvec",
+    "maximum",
+    "minimum",
+    "mod",
+    "modf",
+    "multiply",
+    "negative",
+    "nextafter",
+    "not_equal",
+    "pi",
+    "positive",
+    "power",
+    "rad2deg",
+    "radians",
+    "reciprocal",
+    "remainder",
+    "right_shift",
+    "rint",
+    "sign",
+    "signbit",
+    "sin",
+    "sinh",
+    "spacing",
+    "sqrt",
+    "square",
+    "subtract",
+    "tan",
+    "tanh",
+    "true_divide",
+    "trunc",
+    "vecdot",
+    "vecmat",
+]