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lib/python3.12/site-packages/numpy/_core/__init__.py

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+"""
+This private module only contains stubs for interoperability with
+NumPy 2.0 pickled arrays. It may not be used by the end user.
+"""

lib/python3.12/site-packages/numpy/_core/_dtype.py

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+from numpy.core import _dtype
+
+_globals = globals()
+
+for item in _dtype.__dir__():
+    _globals[item] = getattr(_dtype, item)

lib/python3.12/site-packages/numpy/_core/_dtype_ctypes.py

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+from numpy.core import _dtype_ctypes
+
+_globals = globals()
+
+for item in _dtype_ctypes.__dir__():
+    _globals[item] = getattr(_dtype_ctypes, item)

lib/python3.12/site-packages/numpy/_core/_internal.py

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+from numpy.core import _internal
+
+_globals = globals()
+
+for item in _internal.__dir__():
+    _globals[item] = getattr(_internal, item)

lib/python3.12/site-packages/numpy/_core/_multiarray_umath.py

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+from numpy.core import _multiarray_umath
+
+_globals = globals()
+
+for item in _multiarray_umath.__dir__():
+    _globals[item] = getattr(_multiarray_umath, item)

lib/python3.12/site-packages/numpy/_core/multiarray.py

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+from numpy.core import multiarray
+
+_globals = globals()
+
+for item in multiarray.__dir__():
+    _globals[item] = getattr(multiarray, item)

lib/python3.12/site-packages/numpy/_core/umath.py

@@ -0,0 +1,6 @@
+from numpy.core import umath
+
+_globals = globals()
+
+for item in umath.__dir__():
+    _globals[item] = getattr(umath, item)

lib/python3.12/site-packages/numpy/array_api/__init__.py

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+"""
+A NumPy sub-namespace that conforms to the Python array API standard.
+
+This submodule accompanies NEP 47, which proposes its inclusion in NumPy. It
+is still considered experimental, and will issue a warning when imported.
+
+This is a proof-of-concept namespace that wraps the corresponding NumPy
+functions to give a conforming implementation of the Python array API standard
+(https://data-apis.github.io/array-api/latest/). The standard is currently in
+an RFC phase and comments on it are both welcome and encouraged. Comments
+should be made either at https://github.com/data-apis/array-api or at
+https://github.com/data-apis/consortium-feedback/discussions.
+
+NumPy already follows the proposed spec for the most part, so this module
+serves mostly as a thin wrapper around it. However, NumPy also implements a
+lot of behavior that is not included in the spec, so this serves as a
+restricted subset of the API. Only those functions that are part of the spec
+are included in this namespace, and all functions are given with the exact
+signature given in the spec, including the use of position-only arguments, and
+omitting any extra keyword arguments implemented by NumPy but not part of the
+spec. The behavior of some functions is also modified from the NumPy behavior
+to conform to the standard. Note that the underlying array object itself is
+wrapped in a wrapper Array() class, but is otherwise unchanged. This submodule
+is implemented in pure Python with no C extensions.
+
+The array API spec is designed as a "minimal API subset" and explicitly allows
+libraries to include behaviors not specified by it. But users of this module
+that intend to write portable code should be aware that only those behaviors
+that are listed in the spec are guaranteed to be implemented across libraries.
+Consequently, the NumPy implementation was chosen to be both conforming and
+minimal, so that users can use this implementation of the array API namespace
+and be sure that behaviors that it defines will be available in conforming
+namespaces from other libraries.
+
+A few notes about the current state of this submodule:
+
+- There is a test suite that tests modules against the array API standard at
+  https://github.com/data-apis/array-api-tests. The test suite is still a work
+  in progress, but the existing tests pass on this module, with a few
+  exceptions:
+
+  - DLPack support (see https://github.com/data-apis/array-api/pull/106) is
+    not included here, as it requires a full implementation in NumPy proper
+    first.
+
+  The test suite is not yet complete, and even the tests that exist are not
+  guaranteed to give a comprehensive coverage of the spec. Therefore, when
+  reviewing and using this submodule, you should refer to the standard
+  documents themselves. There are some tests in numpy.array_api.tests, but
+  they primarily focus on things that are not tested by the official array API
+  test suite.
+
+- There is a custom array object, numpy.array_api.Array, which is returned by
+  all functions in this module. All functions in the array API namespace
+  implicitly assume that they will only receive this object as input. The only
+  way to create instances of this object is to use one of the array creation
+  functions. It does not have a public constructor on the object itself. The
+  object is a small wrapper class around numpy.ndarray. The main purpose of it
+  is to restrict the namespace of the array object to only those dtypes and
+  only those methods that are required by the spec, as well as to limit/change
+  certain behavior that differs in the spec. In particular:
+
+  - The array API namespace does not have scalar objects, only 0-D arrays.
+    Operations on Array that would create a scalar in NumPy create a 0-D
+    array.
+
+  - Indexing: Only a subset of indices supported by NumPy are required by the
+    spec. The Array object restricts indexing to only allow those types of
+    indices that are required by the spec. See the docstring of the
+    numpy.array_api.Array._validate_indices helper function for more
+    information.
+
+  - Type promotion: Some type promotion rules are different in the spec. In
+    particular, the spec does not have any value-based casting. The spec also
+    does not require cross-kind casting, like integer -> floating-point. Only
+    those promotions that are explicitly required by the array API
+    specification are allowed in this module. See NEP 47 for more info.
+
+  - Functions do not automatically call asarray() on their input, and will not
+    work if the input type is not Array. The exception is array creation
+    functions, and Python operators on the Array object, which accept Python
+    scalars of the same type as the array dtype.
+
+- All functions include type annotations, corresponding to those given in the
+  spec (see _typing.py for definitions of some custom types). These do not
+  currently fully pass mypy due to some limitations in mypy.
+
+- Dtype objects are just the NumPy dtype objects, e.g., float64 =
+  np.dtype('float64'). The spec does not require any behavior on these dtype
+  objects other than that they be accessible by name and be comparable by
+  equality, but it was considered too much extra complexity to create custom
+  objects to represent dtypes.
+
+- All places where the implementations in this submodule are known to deviate
+  from their corresponding functions in NumPy are marked with "# Note:"
+  comments.
+
+Still TODO in this module are:
+
+- DLPack support for numpy.ndarray is still in progress. See
+  https://github.com/numpy/numpy/pull/19083.
+
+- The copy=False keyword argument to asarray() is not yet implemented. This
+  requires support in numpy.asarray() first.
+
+- Some functions are not yet fully tested in the array API test suite, and may
+  require updates that are not yet known until the tests are written.
+
+- The spec is still in an RFC phase and may still have minor updates, which
+  will need to be reflected here.
+
+- Complex number support in array API spec is planned but not yet finalized,
+  as are the fft extension and certain linear algebra functions such as eig
+  that require complex dtypes.
+
+"""
+
+import warnings
+
+warnings.warn(
+    "The numpy.array_api submodule is still experimental. See NEP 47.", stacklevel=2
+)
+
+__array_api_version__ = "2022.12"
+
+__all__ = ["__array_api_version__"]
+
+from ._constants import e, inf, nan, pi, newaxis
+
+__all__ += ["e", "inf", "nan", "pi", "newaxis"]
+
+from ._creation_functions import (
+    asarray,
+    arange,
+    empty,
+    empty_like,
+    eye,
+    from_dlpack,
+    full,
+    full_like,
+    linspace,
+    meshgrid,
+    ones,
+    ones_like,
+    tril,
+    triu,
+    zeros,
+    zeros_like,
+)
+
+__all__ += [
+    "asarray",
+    "arange",
+    "empty",
+    "empty_like",
+    "eye",
+    "from_dlpack",
+    "full",
+    "full_like",
+    "linspace",
+    "meshgrid",
+    "ones",
+    "ones_like",
+    "tril",
+    "triu",
+    "zeros",
+    "zeros_like",
+]
+
+from ._data_type_functions import (
+    astype,
+    broadcast_arrays,
+    broadcast_to,
+    can_cast,
+    finfo,
+    isdtype,
+    iinfo,
+    result_type,
+)
+
+__all__ += [
+    "astype",
+    "broadcast_arrays",
+    "broadcast_to",
+    "can_cast",
+    "finfo",
+    "iinfo",
+    "result_type",
+]
+
+from ._dtypes import (
+    int8,
+    int16,
+    int32,
+    int64,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+    float32,
+    float64,
+    complex64,
+    complex128,
+    bool,
+)
+
+__all__ += [
+    "int8",
+    "int16",
+    "int32",
+    "int64",
+    "uint8",
+    "uint16",
+    "uint32",
+    "uint64",
+    "float32",
+    "float64",
+    "bool",
+]
+
+from ._elementwise_functions import (
+    abs,
+    acos,
+    acosh,
+    add,
+    asin,
+    asinh,
+    atan,
+    atan2,
+    atanh,
+    bitwise_and,
+    bitwise_left_shift,
+    bitwise_invert,
+    bitwise_or,
+    bitwise_right_shift,
+    bitwise_xor,
+    ceil,
+    conj,
+    cos,
+    cosh,
+    divide,
+    equal,
+    exp,
+    expm1,
+    floor,
+    floor_divide,
+    greater,
+    greater_equal,
+    imag,
+    isfinite,
+    isinf,
+    isnan,
+    less,
+    less_equal,
+    log,
+    log1p,
+    log2,
+    log10,
+    logaddexp,
+    logical_and,
+    logical_not,
+    logical_or,
+    logical_xor,
+    multiply,
+    negative,
+    not_equal,
+    positive,
+    pow,
+    real,
+    remainder,
+    round,
+    sign,
+    sin,
+    sinh,
+    square,
+    sqrt,
+    subtract,
+    tan,
+    tanh,
+    trunc,
+)
+
+__all__ += [
+    "abs",
+    "acos",
+    "acosh",
+    "add",
+    "asin",
+    "asinh",
+    "atan",
+    "atan2",
+    "atanh",
+    "bitwise_and",
+    "bitwise_left_shift",
+    "bitwise_invert",
+    "bitwise_or",
+    "bitwise_right_shift",
+    "bitwise_xor",
+    "ceil",
+    "cos",
+    "cosh",
+    "divide",
+    "equal",
+    "exp",
+    "expm1",
+    "floor",
+    "floor_divide",
+    "greater",
+    "greater_equal",
+    "isfinite",
+    "isinf",
+    "isnan",
+    "less",
+    "less_equal",
+    "log",
+    "log1p",
+    "log2",
+    "log10",
+    "logaddexp",
+    "logical_and",
+    "logical_not",
+    "logical_or",
+    "logical_xor",
+    "multiply",
+    "negative",
+    "not_equal",
+    "positive",
+    "pow",
+    "remainder",
+    "round",
+    "sign",
+    "sin",
+    "sinh",
+    "square",
+    "sqrt",
+    "subtract",
+    "tan",
+    "tanh",
+    "trunc",
+]
+
+from ._indexing_functions import take
+
+__all__ += ["take"]
+
+# linalg is an extension in the array API spec, which is a sub-namespace. Only
+# a subset of functions in it are imported into the top-level namespace.
+from . import linalg
+
+__all__ += ["linalg"]
+
+from .linalg import matmul, tensordot, matrix_transpose, vecdot
+
+__all__ += ["matmul", "tensordot", "matrix_transpose", "vecdot"]
+
+from ._manipulation_functions import (
+    concat,
+    expand_dims,
+    flip,
+    permute_dims,
+    reshape,
+    roll,
+    squeeze,
+    stack,
+)
+
+__all__ += ["concat", "expand_dims", "flip", "permute_dims", "reshape", "roll", "squeeze", "stack"]
+
+from ._searching_functions import argmax, argmin, nonzero, where
+
+__all__ += ["argmax", "argmin", "nonzero", "where"]
+
+from ._set_functions import unique_all, unique_counts, unique_inverse, unique_values
+
+__all__ += ["unique_all", "unique_counts", "unique_inverse", "unique_values"]
+
+from ._sorting_functions import argsort, sort
+
+__all__ += ["argsort", "sort"]
+
+from ._statistical_functions import max, mean, min, prod, std, sum, var
+
+__all__ += ["max", "mean", "min", "prod", "std", "sum", "var"]
+
+from ._utility_functions import all, any
+
+__all__ += ["all", "any"]

lib/python3.12/site-packages/numpy/array_api/_array_object.py

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+"""
+Wrapper class around the ndarray object for the array API standard.
+
+The array API standard defines some behaviors differently than ndarray, in
+particular, type promotion rules are different (the standard has no
+value-based casting). The standard also specifies a more limited subset of
+array methods and functionalities than are implemented on ndarray. Since the
+goal of the array_api namespace is to be a minimal implementation of the array
+API standard, we need to define a separate wrapper class for the array_api
+namespace.
+
+The standard compliant class is only a wrapper class. It is *not* a subclass
+of ndarray.
+"""
+
+from __future__ import annotations
+
+import operator
+from enum import IntEnum
+from ._creation_functions import asarray
+from ._dtypes import (
+    _all_dtypes,
+    _boolean_dtypes,
+    _integer_dtypes,
+    _integer_or_boolean_dtypes,
+    _floating_dtypes,
+    _complex_floating_dtypes,
+    _numeric_dtypes,
+    _result_type,
+    _dtype_categories,
+)
+
+from typing import TYPE_CHECKING, Optional, Tuple, Union, Any, SupportsIndex
+import types
+
+if TYPE_CHECKING:
+    from ._typing import Any, PyCapsule, Device, Dtype
+    import numpy.typing as npt
+
+import numpy as np
+
+from numpy import array_api
+
+
+class Array:
+    """
+    n-d array object for the array API namespace.
+
+    See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
+    information.
+
+    This is a wrapper around numpy.ndarray that restricts the usage to only
+    those things that are required by the array API namespace. Note,
+    attributes on this object that start with a single underscore are not part
+    of the API specification and should only be used internally. This object
+    should not be constructed directly. Rather, use one of the creation
+    functions, such as asarray().
+
+    """
+    _array: np.ndarray[Any, Any]
+
+    # Use a custom constructor instead of __init__, as manually initializing
+    # this class is not supported API.
+    @classmethod
+    def _new(cls, x, /):
+        """
+        This is a private method for initializing the array API Array
+        object.
+
+        Functions outside of the array_api submodule should not use this
+        method. Use one of the creation functions instead, such as
+        ``asarray``.
+
+        """
+        obj = super().__new__(cls)
+        # Note: The spec does not have array scalars, only 0-D arrays.
+        if isinstance(x, np.generic):
+            # Convert the array scalar to a 0-D array
+            x = np.asarray(x)
+        if x.dtype not in _all_dtypes:
+            raise TypeError(
+                f"The array_api namespace does not support the dtype '{x.dtype}'"
+            )
+        obj._array = x
+        return obj
+
+    # Prevent Array() from working
+    def __new__(cls, *args, **kwargs):
+        raise TypeError(
+            "The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
+        )
+
+    # These functions are not required by the spec, but are implemented for
+    # the sake of usability.
+
+    def __str__(self: Array, /) -> str:
+        """
+        Performs the operation __str__.
+        """
+        return self._array.__str__().replace("array", "Array")
+
+    def __repr__(self: Array, /) -> str:
+        """
+        Performs the operation __repr__.
+        """
+        suffix = f", dtype={self.dtype.name})"
+        if 0 in self.shape:
+            prefix = "empty("
+            mid = str(self.shape)
+        else:
+            prefix = "Array("
+            mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
+        return prefix + mid + suffix
+
+    # This function is not required by the spec, but we implement it here for
+    # convenience so that np.asarray(np.array_api.Array) will work.
+    def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
+        """
+        Warning: this method is NOT part of the array API spec. Implementers
+        of other libraries need not include it, and users should not assume it
+        will be present in other implementations.
+
+        """
+        return np.asarray(self._array, dtype=dtype)
+
+    # These are various helper functions to make the array behavior match the
+    # spec in places where it either deviates from or is more strict than
+    # NumPy behavior
+
+    def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
+        """
+        Helper function for operators to only allow specific input dtypes
+
+        Use like
+
+            other = self._check_allowed_dtypes(other, 'numeric', '__add__')
+            if other is NotImplemented:
+                return other
+        """
+
+        if self.dtype not in _dtype_categories[dtype_category]:
+            raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
+        if isinstance(other, (int, complex, float, bool)):
+            other = self._promote_scalar(other)
+        elif isinstance(other, Array):
+            if other.dtype not in _dtype_categories[dtype_category]:
+                raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
+        else:
+            return NotImplemented
+
+        # This will raise TypeError for type combinations that are not allowed
+        # to promote in the spec (even if the NumPy array operator would
+        # promote them).
+        res_dtype = _result_type(self.dtype, other.dtype)
+        if op.startswith("__i"):
+            # Note: NumPy will allow in-place operators in some cases where
+            # the type promoted operator does not match the left-hand side
+            # operand. For example,
+
+            # >>> a = np.array(1, dtype=np.int8)
+            # >>> a += np.array(1, dtype=np.int16)
+
+            # The spec explicitly disallows this.
+            if res_dtype != self.dtype:
+                raise TypeError(
+                    f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
+                )
+
+        return other
+
+    # Helper function to match the type promotion rules in the spec
+    def _promote_scalar(self, scalar):
+        """
+        Returns a promoted version of a Python scalar appropriate for use with
+        operations on self.
+
+        This may raise an OverflowError in cases where the scalar is an
+        integer that is too large to fit in a NumPy integer dtype, or
+        TypeError when the scalar type is incompatible with the dtype of self.
+        """
+        # Note: Only Python scalar types that match the array dtype are
+        # allowed.
+        if isinstance(scalar, bool):
+            if self.dtype not in _boolean_dtypes:
+                raise TypeError(
+                    "Python bool scalars can only be promoted with bool arrays"
+                )
+        elif isinstance(scalar, int):
+            if self.dtype in _boolean_dtypes:
+                raise TypeError(
+                    "Python int scalars cannot be promoted with bool arrays"
+                )
+            if self.dtype in _integer_dtypes:
+                info = np.iinfo(self.dtype)
+                if not (info.min <= scalar <= info.max):
+                    raise OverflowError(
+                        "Python int scalars must be within the bounds of the dtype for integer arrays"
+                    )
+            # int + array(floating) is allowed
+        elif isinstance(scalar, float):
+            if self.dtype not in _floating_dtypes:
+                raise TypeError(
+                    "Python float scalars can only be promoted with floating-point arrays."
+                )
+        elif isinstance(scalar, complex):
+            if self.dtype not in _complex_floating_dtypes:
+                raise TypeError(
+                    "Python complex scalars can only be promoted with complex floating-point arrays."
+                )
+        else:
+            raise TypeError("'scalar' must be a Python scalar")
+
+        # Note: scalars are unconditionally cast to the same dtype as the
+        # array.
+
+        # Note: the spec only specifies integer-dtype/int promotion
+        # behavior for integers within the bounds of the integer dtype.
+        # Outside of those bounds we use the default NumPy behavior (either
+        # cast or raise OverflowError).
+        return Array._new(np.array(scalar, self.dtype))
+
+    @staticmethod
+    def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
+        """
+        Normalize inputs to two arg functions to fix type promotion rules
+
+        NumPy deviates from the spec type promotion rules in cases where one
+        argument is 0-dimensional and the other is not. For example:
+
+        >>> import numpy as np
+        >>> a = np.array([1.0], dtype=np.float32)
+        >>> b = np.array(1.0, dtype=np.float64)
+        >>> np.add(a, b) # The spec says this should be float64
+        array([2.], dtype=float32)
+
+        To fix this, we add a dimension to the 0-dimension array before passing it
+        through. This works because a dimension would be added anyway from
+        broadcasting, so the resulting shape is the same, but this prevents NumPy
+        from not promoting the dtype.
+        """
+        # Another option would be to use signature=(x1.dtype, x2.dtype, None),
+        # but that only works for ufuncs, so we would have to call the ufuncs
+        # directly in the operator methods. One should also note that this
+        # sort of trick wouldn't work for functions like searchsorted, which
+        # don't do normal broadcasting, but there aren't any functions like
+        # that in the array API namespace.
+        if x1.ndim == 0 and x2.ndim != 0:
+            # The _array[None] workaround was chosen because it is relatively
+            # performant. broadcast_to(x1._array, x2.shape) is much slower. We
+            # could also manually type promote x2, but that is more complicated
+            # and about the same performance as this.
+            x1 = Array._new(x1._array[None])
+        elif x2.ndim == 0 and x1.ndim != 0:
+            x2 = Array._new(x2._array[None])
+        return (x1, x2)
+
+    # Note: A large fraction of allowed indices are disallowed here (see the
+    # docstring below)
+    def _validate_index(self, key):
+        """
+        Validate an index according to the array API.
+
+        The array API specification only requires a subset of indices that are
+        supported by NumPy. This function will reject any index that is
+        allowed by NumPy but not required by the array API specification. We
+        always raise ``IndexError`` on such indices (the spec does not require
+        any specific behavior on them, but this makes the NumPy array API
+        namespace a minimal implementation of the spec). See
+        https://data-apis.org/array-api/latest/API_specification/indexing.html
+        for the full list of required indexing behavior
+
+        This function raises IndexError if the index ``key`` is invalid. It
+        only raises ``IndexError`` on indices that are not already rejected by
+        NumPy, as NumPy will already raise the appropriate error on such
+        indices. ``shape`` may be None, in which case, only cases that are
+        independent of the array shape are checked.
+
+        The following cases are allowed by NumPy, but not specified by the array
+        API specification:
+
+        - Indices to not include an implicit ellipsis at the end. That is,
+          every axis of an array must be explicitly indexed or an ellipsis
+          included. This behaviour is sometimes referred to as flat indexing.
+
+        - The start and stop of a slice may not be out of bounds. In
+          particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
+          following are allowed:
+
+          - ``i`` or ``j`` omitted (``None``).
+          - ``-n <= i <= max(0, n - 1)``.
+          - For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
+          - For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
+
+        - Boolean array indices are not allowed as part of a larger tuple
+          index.
+
+        - Integer array indices are not allowed (with the exception of 0-D
+          arrays, which are treated the same as scalars).
+
+        Additionally, it should be noted that indices that would return a
+        scalar in NumPy will return a 0-D array. Array scalars are not allowed
+        in the specification, only 0-D arrays. This is done in the
+        ``Array._new`` constructor, not this function.
+
+        """
+        _key = key if isinstance(key, tuple) else (key,)
+        for i in _key:
+            if isinstance(i, bool) or not (
+                isinstance(i, SupportsIndex)  # i.e. ints
+                or isinstance(i, slice)
+                or i == Ellipsis
+                or i is None
+                or isinstance(i, Array)
+                or isinstance(i, np.ndarray)
+            ):
+                raise IndexError(
+                    f"Single-axes index {i} has {type(i)=}, but only "
+                    "integers, slices (:), ellipsis (...), newaxis (None), "
+                    "zero-dimensional integer arrays and boolean arrays "
+                    "are specified in the Array API."
+                )
+
+        nonexpanding_key = []
+        single_axes = []
+        n_ellipsis = 0
+        key_has_mask = False
+        for i in _key:
+            if i is not None:
+                nonexpanding_key.append(i)
+                if isinstance(i, Array) or isinstance(i, np.ndarray):
+                    if i.dtype in _boolean_dtypes:
+                        key_has_mask = True
+                    single_axes.append(i)
+                else:
+                    # i must not be an array here, to avoid elementwise equals
+                    if i == Ellipsis:
+                        n_ellipsis += 1
+                    else:
+                        single_axes.append(i)
+
+        n_single_axes = len(single_axes)
+        if n_ellipsis > 1:
+            return  # handled by ndarray
+        elif n_ellipsis == 0:
+            # Note boolean masks must be the sole index, which we check for
+            # later on.
+            if not key_has_mask and n_single_axes < self.ndim:
+                raise IndexError(
+                    f"{self.ndim=}, but the multi-axes index only specifies "
+                    f"{n_single_axes} dimensions. If this was intentional, "
+                    "add a trailing ellipsis (...) which expands into as many "
+                    "slices (:) as necessary - this is what np.ndarray arrays "
+                    "implicitly do, but such flat indexing behaviour is not "
+                    "specified in the Array API."
+                )
+
+        if n_ellipsis == 0:
+            indexed_shape = self.shape
+        else:
+            ellipsis_start = None
+            for pos, i in enumerate(nonexpanding_key):
+                if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
+                    if i == Ellipsis:
+                        ellipsis_start = pos
+                        break
+            assert ellipsis_start is not None  # sanity check
+            ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
+            indexed_shape = (
+                self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
+            )
+        for i, side in zip(single_axes, indexed_shape):
+            if isinstance(i, slice):
+                if side == 0:
+                    f_range = "0 (or None)"
+                else:
+                    f_range = f"between -{side} and {side - 1} (or None)"
+                if i.start is not None:
+                    try:
+                        start = operator.index(i.start)
+                    except TypeError:
+                        pass  # handled by ndarray
+                    else:
+                        if not (-side <= start <= side):
+                            raise IndexError(
+                                f"Slice {i} contains {start=}, but should be "
+                                f"{f_range} for an axis of size {side} "
+                                "(out-of-bounds starts are not specified in "
+                                "the Array API)"
+                            )
+                if i.stop is not None:
+                    try:
+                        stop = operator.index(i.stop)
+                    except TypeError:
+                        pass  # handled by ndarray
+                    else:
+                        if not (-side <= stop <= side):
+                            raise IndexError(
+                                f"Slice {i} contains {stop=}, but should be "
+                                f"{f_range} for an axis of size {side} "
+                                "(out-of-bounds stops are not specified in "
+                                "the Array API)"
+                            )
+            elif isinstance(i, Array):
+                if i.dtype in _boolean_dtypes and len(_key) != 1:
+                    assert isinstance(key, tuple)  # sanity check
+                    raise IndexError(
+                        f"Single-axes index {i} is a boolean array and "
+                        f"{len(key)=}, but masking is only specified in the "
+                        "Array API when the array is the sole index."
+                    )
+                elif i.dtype in _integer_dtypes and i.ndim != 0:
+                    raise IndexError(
+                        f"Single-axes index {i} is a non-zero-dimensional "
+                        "integer array, but advanced integer indexing is not "
+                        "specified in the Array API."
+                    )
+            elif isinstance(i, tuple):
+                raise IndexError(
+                    f"Single-axes index {i} is a tuple, but nested tuple "
+                    "indices are not specified in the Array API."
+                )
+
+    # Everything below this line is required by the spec.
+
+    def __abs__(self: Array, /) -> Array:
+        """
+        Performs the operation __abs__.
+        """
+        if self.dtype not in _numeric_dtypes:
+            raise TypeError("Only numeric dtypes are allowed in __abs__")
+        res = self._array.__abs__()
+        return self.__class__._new(res)
+
+    def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __add__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__add__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__add__(other._array)
+        return self.__class__._new(res)
+
+    def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
+        """
+        Performs the operation __and__.
+        """
+        other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__and__(other._array)
+        return self.__class__._new(res)
+
+    def __array_namespace__(
+        self: Array, /, *, api_version: Optional[str] = None
+    ) -> types.ModuleType:
+        if api_version is not None and not api_version.startswith("2021."):
+            raise ValueError(f"Unrecognized array API version: {api_version!r}")
+        return array_api
+
+    def __bool__(self: Array, /) -> bool:
+        """
+        Performs the operation __bool__.
+        """
+        # Note: This is an error here.
+        if self._array.ndim != 0:
+            raise TypeError("bool is only allowed on arrays with 0 dimensions")
+        res = self._array.__bool__()
+        return res
+
+    def __complex__(self: Array, /) -> complex:
+        """
+        Performs the operation __complex__.
+        """
+        # Note: This is an error here.
+        if self._array.ndim != 0:
+            raise TypeError("complex is only allowed on arrays with 0 dimensions")
+        res = self._array.__complex__()
+        return res
+
+    def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
+        """
+        Performs the operation __dlpack__.
+        """
+        return self._array.__dlpack__(stream=stream)
+
+    def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
+        """
+        Performs the operation __dlpack_device__.
+        """
+        # Note: device support is required for this
+        return self._array.__dlpack_device__()
+
+    def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
+        """
+        Performs the operation __eq__.
+        """
+        # Even though "all" dtypes are allowed, we still require them to be
+        # promotable with each other.
+        other = self._check_allowed_dtypes(other, "all", "__eq__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__eq__(other._array)
+        return self.__class__._new(res)
+
+    def __float__(self: Array, /) -> float:
+        """
+        Performs the operation __float__.
+        """
+        # Note: This is an error here.
+        if self._array.ndim != 0:
+            raise TypeError("float is only allowed on arrays with 0 dimensions")
+        if self.dtype in _complex_floating_dtypes:
+            raise TypeError("float is not allowed on complex floating-point arrays")
+        res = self._array.__float__()
+        return res
+
+    def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __floordiv__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__floordiv__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__floordiv__(other._array)
+        return self.__class__._new(res)
+
+    def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __ge__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__ge__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__ge__(other._array)
+        return self.__class__._new(res)
+
+    def __getitem__(
+        self: Array,
+        key: Union[
+            int,
+            slice,
+            ellipsis,
+            Tuple[Union[int, slice, ellipsis, None], ...],
+            Array,
+        ],
+        /,
+    ) -> Array:
+        """
+        Performs the operation __getitem__.
+        """
+        # Note: Only indices required by the spec are allowed. See the
+        # docstring of _validate_index
+        self._validate_index(key)
+        if isinstance(key, Array):
+            # Indexing self._array with array_api arrays can be erroneous
+            key = key._array
+        res = self._array.__getitem__(key)
+        return self._new(res)
+
+    def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __gt__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__gt__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__gt__(other._array)
+        return self.__class__._new(res)
+
+    def __int__(self: Array, /) -> int:
+        """
+        Performs the operation __int__.
+        """
+        # Note: This is an error here.
+        if self._array.ndim != 0:
+            raise TypeError("int is only allowed on arrays with 0 dimensions")
+        if self.dtype in _complex_floating_dtypes:
+            raise TypeError("int is not allowed on complex floating-point arrays")
+        res = self._array.__int__()
+        return res
+
+    def __index__(self: Array, /) -> int:
+        """
+        Performs the operation __index__.
+        """
+        res = self._array.__index__()
+        return res
+
+    def __invert__(self: Array, /) -> Array:
+        """
+        Performs the operation __invert__.
+        """
+        if self.dtype not in _integer_or_boolean_dtypes:
+            raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
+        res = self._array.__invert__()
+        return self.__class__._new(res)
+
+    def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __le__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__le__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__le__(other._array)
+        return self.__class__._new(res)
+
+    def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
+        """
+        Performs the operation __lshift__.
+        """
+        other = self._check_allowed_dtypes(other, "integer", "__lshift__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__lshift__(other._array)
+        return self.__class__._new(res)
+
+    def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __lt__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__lt__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__lt__(other._array)
+        return self.__class__._new(res)
+
+    def __matmul__(self: Array, other: Array, /) -> Array:
+        """
+        Performs the operation __matmul__.
+        """
+        # matmul is not defined for scalars, but without this, we may get
+        # the wrong error message from asarray.
+        other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
+        if other is NotImplemented:
+            return other
+        res = self._array.__matmul__(other._array)
+        return self.__class__._new(res)
+
+    def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __mod__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__mod__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__mod__(other._array)
+        return self.__class__._new(res)
+
+    def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __mul__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__mul__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__mul__(other._array)
+        return self.__class__._new(res)
+
+    def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
+        """
+        Performs the operation __ne__.
+        """
+        other = self._check_allowed_dtypes(other, "all", "__ne__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__ne__(other._array)
+        return self.__class__._new(res)
+
+    def __neg__(self: Array, /) -> Array:
+        """
+        Performs the operation __neg__.
+        """
+        if self.dtype not in _numeric_dtypes:
+            raise TypeError("Only numeric dtypes are allowed in __neg__")
+        res = self._array.__neg__()
+        return self.__class__._new(res)
+
+    def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
+        """
+        Performs the operation __or__.
+        """
+        other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__or__(other._array)
+        return self.__class__._new(res)
+
+    def __pos__(self: Array, /) -> Array:
+        """
+        Performs the operation __pos__.
+        """
+        if self.dtype not in _numeric_dtypes:
+            raise TypeError("Only numeric dtypes are allowed in __pos__")
+        res = self._array.__pos__()
+        return self.__class__._new(res)
+
+    def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __pow__.
+        """
+        from ._elementwise_functions import pow
+
+        other = self._check_allowed_dtypes(other, "numeric", "__pow__")
+        if other is NotImplemented:
+            return other
+        # Note: NumPy's __pow__ does not follow type promotion rules for 0-d
+        # arrays, so we use pow() here instead.
+        return pow(self, other)
+
+    def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
+        """
+        Performs the operation __rshift__.
+        """
+        other = self._check_allowed_dtypes(other, "integer", "__rshift__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rshift__(other._array)
+        return self.__class__._new(res)
+
+    def __setitem__(
+        self,
+        key: Union[
+            int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
+        ],
+        value: Union[int, float, bool, Array],
+        /,
+    ) -> None:
+        """
+        Performs the operation __setitem__.
+        """
+        # Note: Only indices required by the spec are allowed. See the
+        # docstring of _validate_index
+        self._validate_index(key)
+        if isinstance(key, Array):
+            # Indexing self._array with array_api arrays can be erroneous
+            key = key._array
+        self._array.__setitem__(key, asarray(value)._array)
+
+    def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __sub__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__sub__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__sub__(other._array)
+        return self.__class__._new(res)
+
+    # PEP 484 requires int to be a subtype of float, but __truediv__ should
+    # not accept int.
+    def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
+        """
+        Performs the operation __truediv__.
+        """
+        other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__truediv__(other._array)
+        return self.__class__._new(res)
+
+    def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
+        """
+        Performs the operation __xor__.
+        """
+        other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__xor__(other._array)
+        return self.__class__._new(res)
+
+    def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __iadd__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
+        if other is NotImplemented:
+            return other
+        self._array.__iadd__(other._array)
+        return self
+
+    def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __radd__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__radd__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__radd__(other._array)
+        return self.__class__._new(res)
+
+    def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
+        """
+        Performs the operation __iand__.
+        """
+        other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
+        if other is NotImplemented:
+            return other
+        self._array.__iand__(other._array)
+        return self
+
+    def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
+        """
+        Performs the operation __rand__.
+        """
+        other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rand__(other._array)
+        return self.__class__._new(res)
+
+    def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __ifloordiv__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__ifloordiv__")
+        if other is NotImplemented:
+            return other
+        self._array.__ifloordiv__(other._array)
+        return self
+
+    def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __rfloordiv__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__rfloordiv__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rfloordiv__(other._array)
+        return self.__class__._new(res)
+
+    def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
+        """
+        Performs the operation __ilshift__.
+        """
+        other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
+        if other is NotImplemented:
+            return other
+        self._array.__ilshift__(other._array)
+        return self
+
+    def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
+        """
+        Performs the operation __rlshift__.
+        """
+        other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rlshift__(other._array)
+        return self.__class__._new(res)
+
+    def __imatmul__(self: Array, other: Array, /) -> Array:
+        """
+        Performs the operation __imatmul__.
+        """
+        # matmul is not defined for scalars, but without this, we may get
+        # the wrong error message from asarray.
+        other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
+        if other is NotImplemented:
+            return other
+        res = self._array.__imatmul__(other._array)
+        return self.__class__._new(res)
+
+    def __rmatmul__(self: Array, other: Array, /) -> Array:
+        """
+        Performs the operation __rmatmul__.
+        """
+        # matmul is not defined for scalars, but without this, we may get
+        # the wrong error message from asarray.
+        other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
+        if other is NotImplemented:
+            return other
+        res = self._array.__rmatmul__(other._array)
+        return self.__class__._new(res)
+
+    def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __imod__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__imod__")
+        if other is NotImplemented:
+            return other
+        self._array.__imod__(other._array)
+        return self
+
+    def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __rmod__.
+        """
+        other = self._check_allowed_dtypes(other, "real numeric", "__rmod__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rmod__(other._array)
+        return self.__class__._new(res)
+
+    def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __imul__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__imul__")
+        if other is NotImplemented:
+            return other
+        self._array.__imul__(other._array)
+        return self
+
+    def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __rmul__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rmul__(other._array)
+        return self.__class__._new(res)
+
+    def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
+        """
+        Performs the operation __ior__.
+        """
+        other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
+        if other is NotImplemented:
+            return other
+        self._array.__ior__(other._array)
+        return self
+
+    def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
+        """
+        Performs the operation __ror__.
+        """
+        other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__ror__(other._array)
+        return self.__class__._new(res)
+
+    def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __ipow__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
+        if other is NotImplemented:
+            return other
+        self._array.__ipow__(other._array)
+        return self
+
+    def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __rpow__.
+        """
+        from ._elementwise_functions import pow
+
+        other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
+        if other is NotImplemented:
+            return other
+        # Note: NumPy's __pow__ does not follow the spec type promotion rules
+        # for 0-d arrays, so we use pow() here instead.
+        return pow(other, self)
+
+    def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
+        """
+        Performs the operation __irshift__.
+        """
+        other = self._check_allowed_dtypes(other, "integer", "__irshift__")
+        if other is NotImplemented:
+            return other
+        self._array.__irshift__(other._array)
+        return self
+
+    def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
+        """
+        Performs the operation __rrshift__.
+        """
+        other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rrshift__(other._array)
+        return self.__class__._new(res)
+
+    def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __isub__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__isub__")
+        if other is NotImplemented:
+            return other
+        self._array.__isub__(other._array)
+        return self
+
+    def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
+        """
+        Performs the operation __rsub__.
+        """
+        other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rsub__(other._array)
+        return self.__class__._new(res)
+
+    def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
+        """
+        Performs the operation __itruediv__.
+        """
+        other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
+        if other is NotImplemented:
+            return other
+        self._array.__itruediv__(other._array)
+        return self
+
+    def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
+        """
+        Performs the operation __rtruediv__.
+        """
+        other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rtruediv__(other._array)
+        return self.__class__._new(res)
+
+    def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
+        """
+        Performs the operation __ixor__.
+        """
+        other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
+        if other is NotImplemented:
+            return other
+        self._array.__ixor__(other._array)
+        return self
+
+    def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
+        """
+        Performs the operation __rxor__.
+        """
+        other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
+        if other is NotImplemented:
+            return other
+        self, other = self._normalize_two_args(self, other)
+        res = self._array.__rxor__(other._array)
+        return self.__class__._new(res)
+
+    def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
+        if stream is not None:
+            raise ValueError("The stream argument to to_device() is not supported")
+        if device == 'cpu':
+            return self
+        raise ValueError(f"Unsupported device {device!r}")
+
+    @property
+    def dtype(self) -> Dtype:
+        """
+        Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
+
+        See its docstring for more information.
+        """
+        return self._array.dtype
+
+    @property
+    def device(self) -> Device:
+        return "cpu"
+
+    # Note: mT is new in array API spec (see matrix_transpose)
+    @property
+    def mT(self) -> Array:
+        from .linalg import matrix_transpose
+        return matrix_transpose(self)
+
+    @property
+    def ndim(self) -> int:
+        """
+        Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
+
+        See its docstring for more information.
+        """
+        return self._array.ndim
+
+    @property
+    def shape(self) -> Tuple[int, ...]:
+        """
+        Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
+
+        See its docstring for more information.
+        """
+        return self._array.shape
+
+    @property
+    def size(self) -> int:
+        """
+        Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
+
+        See its docstring for more information.
+        """
+        return self._array.size
+
+    @property
+    def T(self) -> Array:
+        """
+        Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
+
+        See its docstring for more information.
+        """
+        # Note: T only works on 2-dimensional arrays. See the corresponding
+        # note in the specification:
+        # https://data-apis.org/array-api/latest/API_specification/array_object.html#t
+        if self.ndim != 2:
+            raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
+        return self.__class__._new(self._array.T)

lib/python3.12/site-packages/numpy/array_api/_constants.py

@@ -0,0 +1,7 @@
+import numpy as np
+
+e = np.e
+inf = np.inf
+nan = np.nan
+pi = np.pi
+newaxis = np.newaxis

lib/python3.12/site-packages/numpy/array_api/_creation_functions.py

@@ -0,0 +1,351 @@
+from __future__ import annotations
+
+
+from typing import TYPE_CHECKING, List, Optional, Tuple, Union
+
+if TYPE_CHECKING:
+    from ._typing import (
+        Array,
+        Device,
+        Dtype,
+        NestedSequence,
+        SupportsBufferProtocol,
+    )
+    from collections.abc import Sequence
+from ._dtypes import _all_dtypes
+
+import numpy as np
+
+
+def _check_valid_dtype(dtype):
+    # Note: Only spelling dtypes as the dtype objects is supported.
+
+    # We use this instead of "dtype in _all_dtypes" because the dtype objects
+    # define equality with the sorts of things we want to disallow.
+    for d in (None,) + _all_dtypes:
+        if dtype is d:
+            return
+    raise ValueError("dtype must be one of the supported dtypes")
+
+
+def asarray(
+    obj: Union[
+        Array,
+        bool,
+        int,
+        float,
+        NestedSequence[bool | int | float],
+        SupportsBufferProtocol,
+    ],
+    /,
+    *,
+    dtype: Optional[Dtype] = None,
+    device: Optional[Device] = None,
+    copy: Optional[Union[bool, np._CopyMode]] = None,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.asarray <numpy.asarray>`.
+
+    See its docstring for more information.
+    """
+    # _array_object imports in this file are inside the functions to avoid
+    # circular imports
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    if copy in (False, np._CopyMode.IF_NEEDED):
+        # Note: copy=False is not yet implemented in np.asarray
+        raise NotImplementedError("copy=False is not yet implemented")
+    if isinstance(obj, Array):
+        if dtype is not None and obj.dtype != dtype:
+            copy = True
+        if copy in (True, np._CopyMode.ALWAYS):
+            return Array._new(np.array(obj._array, copy=True, dtype=dtype))
+        return obj
+    if dtype is None and isinstance(obj, int) and (obj > 2 ** 64 or obj < -(2 ** 63)):
+        # Give a better error message in this case. NumPy would convert this
+        # to an object array. TODO: This won't handle large integers in lists.
+        raise OverflowError("Integer out of bounds for array dtypes")
+    res = np.asarray(obj, dtype=dtype)
+    return Array._new(res)
+
+
+def arange(
+    start: Union[int, float],
+    /,
+    stop: Optional[Union[int, float]] = None,
+    step: Union[int, float] = 1,
+    *,
+    dtype: Optional[Dtype] = None,
+    device: Optional[Device] = None,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.arange <numpy.arange>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    return Array._new(np.arange(start, stop=stop, step=step, dtype=dtype))
+
+
+def empty(
+    shape: Union[int, Tuple[int, ...]],
+    *,
+    dtype: Optional[Dtype] = None,
+    device: Optional[Device] = None,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.empty <numpy.empty>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    return Array._new(np.empty(shape, dtype=dtype))
+
+
+def empty_like(
+    x: Array, /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.empty_like <numpy.empty_like>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    return Array._new(np.empty_like(x._array, dtype=dtype))
+
+
+def eye(
+    n_rows: int,
+    n_cols: Optional[int] = None,
+    /,
+    *,
+    k: int = 0,
+    dtype: Optional[Dtype] = None,
+    device: Optional[Device] = None,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.eye <numpy.eye>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    return Array._new(np.eye(n_rows, M=n_cols, k=k, dtype=dtype))
+
+
+def from_dlpack(x: object, /) -> Array:
+    from ._array_object import Array
+
+    return Array._new(np.from_dlpack(x))
+
+
+def full(
+    shape: Union[int, Tuple[int, ...]],
+    fill_value: Union[int, float],
+    *,
+    dtype: Optional[Dtype] = None,
+    device: Optional[Device] = None,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.full <numpy.full>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    if isinstance(fill_value, Array) and fill_value.ndim == 0:
+        fill_value = fill_value._array
+    res = np.full(shape, fill_value, dtype=dtype)
+    if res.dtype not in _all_dtypes:
+        # This will happen if the fill value is not something that NumPy
+        # coerces to one of the acceptable dtypes.
+        raise TypeError("Invalid input to full")
+    return Array._new(res)
+
+
+def full_like(
+    x: Array,
+    /,
+    fill_value: Union[int, float],
+    *,
+    dtype: Optional[Dtype] = None,
+    device: Optional[Device] = None,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.full_like <numpy.full_like>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    res = np.full_like(x._array, fill_value, dtype=dtype)
+    if res.dtype not in _all_dtypes:
+        # This will happen if the fill value is not something that NumPy
+        # coerces to one of the acceptable dtypes.
+        raise TypeError("Invalid input to full_like")
+    return Array._new(res)
+
+
+def linspace(
+    start: Union[int, float],
+    stop: Union[int, float],
+    /,
+    num: int,
+    *,
+    dtype: Optional[Dtype] = None,
+    device: Optional[Device] = None,
+    endpoint: bool = True,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.linspace <numpy.linspace>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    return Array._new(np.linspace(start, stop, num, dtype=dtype, endpoint=endpoint))
+
+
+def meshgrid(*arrays: Array, indexing: str = "xy") -> List[Array]:
+    """
+    Array API compatible wrapper for :py:func:`np.meshgrid <numpy.meshgrid>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    # Note: unlike np.meshgrid, only inputs with all the same dtype are
+    # allowed
+
+    if len({a.dtype for a in arrays}) > 1:
+        raise ValueError("meshgrid inputs must all have the same dtype")
+
+    return [
+        Array._new(array)
+        for array in np.meshgrid(*[a._array for a in arrays], indexing=indexing)
+    ]
+
+
+def ones(
+    shape: Union[int, Tuple[int, ...]],
+    *,
+    dtype: Optional[Dtype] = None,
+    device: Optional[Device] = None,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.ones <numpy.ones>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    return Array._new(np.ones(shape, dtype=dtype))
+
+
+def ones_like(
+    x: Array, /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.ones_like <numpy.ones_like>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    return Array._new(np.ones_like(x._array, dtype=dtype))
+
+
+def tril(x: Array, /, *, k: int = 0) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.tril <numpy.tril>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    if x.ndim < 2:
+        # Note: Unlike np.tril, x must be at least 2-D
+        raise ValueError("x must be at least 2-dimensional for tril")
+    return Array._new(np.tril(x._array, k=k))
+
+
+def triu(x: Array, /, *, k: int = 0) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.triu <numpy.triu>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    if x.ndim < 2:
+        # Note: Unlike np.triu, x must be at least 2-D
+        raise ValueError("x must be at least 2-dimensional for triu")
+    return Array._new(np.triu(x._array, k=k))
+
+
+def zeros(
+    shape: Union[int, Tuple[int, ...]],
+    *,
+    dtype: Optional[Dtype] = None,
+    device: Optional[Device] = None,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.zeros <numpy.zeros>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    return Array._new(np.zeros(shape, dtype=dtype))
+
+
+def zeros_like(
+    x: Array, /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.zeros_like <numpy.zeros_like>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    _check_valid_dtype(dtype)
+    if device not in ["cpu", None]:
+        raise ValueError(f"Unsupported device {device!r}")
+    return Array._new(np.zeros_like(x._array, dtype=dtype))

lib/python3.12/site-packages/numpy/array_api/_data_type_functions.py

@@ -0,0 +1,197 @@
+from __future__ import annotations
+
+from ._array_object import Array
+from ._dtypes import (
+    _all_dtypes,
+    _boolean_dtypes,
+    _signed_integer_dtypes,
+    _unsigned_integer_dtypes,
+    _integer_dtypes,
+    _real_floating_dtypes,
+    _complex_floating_dtypes,
+    _numeric_dtypes,
+    _result_type,
+)
+
+from dataclasses import dataclass
+from typing import TYPE_CHECKING, List, Tuple, Union
+
+if TYPE_CHECKING:
+    from ._typing import Dtype
+    from collections.abc import Sequence
+
+import numpy as np
+
+
+# Note: astype is a function, not an array method as in NumPy.
+def astype(x: Array, dtype: Dtype, /, *, copy: bool = True) -> Array:
+    if not copy and dtype == x.dtype:
+        return x
+    return Array._new(x._array.astype(dtype=dtype, copy=copy))
+
+
+def broadcast_arrays(*arrays: Array) -> List[Array]:
+    """
+    Array API compatible wrapper for :py:func:`np.broadcast_arrays <numpy.broadcast_arrays>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    return [
+        Array._new(array) for array in np.broadcast_arrays(*[a._array for a in arrays])
+    ]
+
+
+def broadcast_to(x: Array, /, shape: Tuple[int, ...]) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.broadcast_to <numpy.broadcast_to>`.
+
+    See its docstring for more information.
+    """
+    from ._array_object import Array
+
+    return Array._new(np.broadcast_to(x._array, shape))
+
+
+def can_cast(from_: Union[Dtype, Array], to: Dtype, /) -> bool:
+    """
+    Array API compatible wrapper for :py:func:`np.can_cast <numpy.can_cast>`.
+
+    See its docstring for more information.
+    """
+    if isinstance(from_, Array):
+        from_ = from_.dtype
+    elif from_ not in _all_dtypes:
+        raise TypeError(f"{from_=}, but should be an array_api array or dtype")
+    if to not in _all_dtypes:
+        raise TypeError(f"{to=}, but should be a dtype")
+    # Note: We avoid np.can_cast() as it has discrepancies with the array API,
+    # since NumPy allows cross-kind casting (e.g., NumPy allows bool -> int8).
+    # See https://github.com/numpy/numpy/issues/20870
+    try:
+        # We promote `from_` and `to` together. We then check if the promoted
+        # dtype is `to`, which indicates if `from_` can (up)cast to `to`.
+        dtype = _result_type(from_, to)
+        return to == dtype
+    except TypeError:
+        # _result_type() raises if the dtypes don't promote together
+        return False
+
+
+# These are internal objects for the return types of finfo and iinfo, since
+# the NumPy versions contain extra data that isn't part of the spec.
+@dataclass
+class finfo_object:
+    bits: int
+    # Note: The types of the float data here are float, whereas in NumPy they
+    # are scalars of the corresponding float dtype.
+    eps: float
+    max: float
+    min: float
+    smallest_normal: float
+    dtype: Dtype
+
+
+@dataclass
+class iinfo_object:
+    bits: int
+    max: int
+    min: int
+    dtype: Dtype
+
+
+def finfo(type: Union[Dtype, Array], /) -> finfo_object:
+    """
+    Array API compatible wrapper for :py:func:`np.finfo <numpy.finfo>`.
+
+    See its docstring for more information.
+    """
+    fi = np.finfo(type)
+    # Note: The types of the float data here are float, whereas in NumPy they
+    # are scalars of the corresponding float dtype.
+    return finfo_object(
+        fi.bits,
+        float(fi.eps),
+        float(fi.max),
+        float(fi.min),
+        float(fi.smallest_normal),
+        fi.dtype,
+    )
+
+
+def iinfo(type: Union[Dtype, Array], /) -> iinfo_object:
+    """
+    Array API compatible wrapper for :py:func:`np.iinfo <numpy.iinfo>`.
+
+    See its docstring for more information.
+    """
+    ii = np.iinfo(type)
+    return iinfo_object(ii.bits, ii.max, ii.min, ii.dtype)
+
+
+# Note: isdtype is a new function from the 2022.12 array API specification.
+def isdtype(
+    dtype: Dtype, kind: Union[Dtype, str, Tuple[Union[Dtype, str], ...]]
+) -> bool:
+    """
+    Returns a boolean indicating whether a provided dtype is of a specified data type ``kind``.
+
+    See
+    https://data-apis.org/array-api/latest/API_specification/generated/array_api.isdtype.html
+    for more details
+    """
+    if isinstance(kind, tuple):
+        # Disallow nested tuples
+        if any(isinstance(k, tuple) for k in kind):
+            raise TypeError("'kind' must be a dtype, str, or tuple of dtypes and strs")
+        return any(isdtype(dtype, k) for k in kind)
+    elif isinstance(kind, str):
+        if kind == 'bool':
+            return dtype in _boolean_dtypes
+        elif kind == 'signed integer':
+            return dtype in _signed_integer_dtypes
+        elif kind == 'unsigned integer':
+            return dtype in _unsigned_integer_dtypes
+        elif kind == 'integral':
+            return dtype in _integer_dtypes
+        elif kind == 'real floating':
+            return dtype in _real_floating_dtypes
+        elif kind == 'complex floating':
+            return dtype in _complex_floating_dtypes
+        elif kind == 'numeric':
+            return dtype in _numeric_dtypes
+        else:
+            raise ValueError(f"Unrecognized data type kind: {kind!r}")
+    elif kind in _all_dtypes:
+        return dtype == kind
+    else:
+        raise TypeError(f"'kind' must be a dtype, str, or tuple of dtypes and strs, not {type(kind).__name__}")
+
+def result_type(*arrays_and_dtypes: Union[Array, Dtype]) -> Dtype:
+    """
+    Array API compatible wrapper for :py:func:`np.result_type <numpy.result_type>`.
+
+    See its docstring for more information.
+    """
+    # Note: we use a custom implementation that gives only the type promotions
+    # required by the spec rather than using np.result_type. NumPy implements
+    # too many extra type promotions like int64 + uint64 -> float64, and does
+    # value-based casting on scalar arrays.
+    A = []
+    for a in arrays_and_dtypes:
+        if isinstance(a, Array):
+            a = a.dtype
+        elif isinstance(a, np.ndarray) or a not in _all_dtypes:
+            raise TypeError("result_type() inputs must be array_api arrays or dtypes")
+        A.append(a)
+
+    if len(A) == 0:
+        raise ValueError("at least one array or dtype is required")
+    elif len(A) == 1:
+        return A[0]
+    else:
+        t = A[0]
+        for t2 in A[1:]:
+            t = _result_type(t, t2)
+        return t

lib/python3.12/site-packages/numpy/array_api/_dtypes.py

@@ -0,0 +1,180 @@
+import numpy as np
+
+# Note: we use dtype objects instead of dtype classes. The spec does not
+# require any behavior on dtypes other than equality.
+int8 = np.dtype("int8")
+int16 = np.dtype("int16")
+int32 = np.dtype("int32")
+int64 = np.dtype("int64")
+uint8 = np.dtype("uint8")
+uint16 = np.dtype("uint16")
+uint32 = np.dtype("uint32")
+uint64 = np.dtype("uint64")
+float32 = np.dtype("float32")
+float64 = np.dtype("float64")
+complex64 = np.dtype("complex64")
+complex128 = np.dtype("complex128")
+# Note: This name is changed
+bool = np.dtype("bool")
+
+_all_dtypes = (
+    int8,
+    int16,
+    int32,
+    int64,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+    float32,
+    float64,
+    complex64,
+    complex128,
+    bool,
+)
+_boolean_dtypes = (bool,)
+_real_floating_dtypes = (float32, float64)
+_floating_dtypes = (float32, float64, complex64, complex128)
+_complex_floating_dtypes = (complex64, complex128)
+_integer_dtypes = (int8, int16, int32, int64, uint8, uint16, uint32, uint64)
+_signed_integer_dtypes = (int8, int16, int32, int64)
+_unsigned_integer_dtypes = (uint8, uint16, uint32, uint64)
+_integer_or_boolean_dtypes = (
+    bool,
+    int8,
+    int16,
+    int32,
+    int64,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+)
+_real_numeric_dtypes = (
+    float32,
+    float64,
+    int8,
+    int16,
+    int32,
+    int64,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+)
+_numeric_dtypes = (
+    float32,
+    float64,
+    complex64,
+    complex128,
+    int8,
+    int16,
+    int32,
+    int64,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+)
+
+_dtype_categories = {
+    "all": _all_dtypes,
+    "real numeric": _real_numeric_dtypes,
+    "numeric": _numeric_dtypes,
+    "integer": _integer_dtypes,
+    "integer or boolean": _integer_or_boolean_dtypes,
+    "boolean": _boolean_dtypes,
+    "real floating-point": _floating_dtypes,
+    "complex floating-point": _complex_floating_dtypes,
+    "floating-point": _floating_dtypes,
+}
+
+
+# Note: the spec defines a restricted type promotion table compared to NumPy.
+# In particular, cross-kind promotions like integer + float or boolean +
+# integer are not allowed, even for functions that accept both kinds.
+# Additionally, NumPy promotes signed integer + uint64 to float64, but this
+# promotion is not allowed here. To be clear, Python scalar int objects are
+# allowed to promote to floating-point dtypes, but only in array operators
+# (see Array._promote_scalar) method in _array_object.py.
+_promotion_table = {
+    (int8, int8): int8,
+    (int8, int16): int16,
+    (int8, int32): int32,
+    (int8, int64): int64,
+    (int16, int8): int16,
+    (int16, int16): int16,
+    (int16, int32): int32,
+    (int16, int64): int64,
+    (int32, int8): int32,
+    (int32, int16): int32,
+    (int32, int32): int32,
+    (int32, int64): int64,
+    (int64, int8): int64,
+    (int64, int16): int64,
+    (int64, int32): int64,
+    (int64, int64): int64,
+    (uint8, uint8): uint8,
+    (uint8, uint16): uint16,
+    (uint8, uint32): uint32,
+    (uint8, uint64): uint64,
+    (uint16, uint8): uint16,
+    (uint16, uint16): uint16,
+    (uint16, uint32): uint32,
+    (uint16, uint64): uint64,
+    (uint32, uint8): uint32,
+    (uint32, uint16): uint32,
+    (uint32, uint32): uint32,
+    (uint32, uint64): uint64,
+    (uint64, uint8): uint64,
+    (uint64, uint16): uint64,
+    (uint64, uint32): uint64,
+    (uint64, uint64): uint64,
+    (int8, uint8): int16,
+    (int8, uint16): int32,
+    (int8, uint32): int64,
+    (int16, uint8): int16,
+    (int16, uint16): int32,
+    (int16, uint32): int64,
+    (int32, uint8): int32,
+    (int32, uint16): int32,
+    (int32, uint32): int64,
+    (int64, uint8): int64,
+    (int64, uint16): int64,
+    (int64, uint32): int64,
+    (uint8, int8): int16,
+    (uint16, int8): int32,
+    (uint32, int8): int64,
+    (uint8, int16): int16,
+    (uint16, int16): int32,
+    (uint32, int16): int64,
+    (uint8, int32): int32,
+    (uint16, int32): int32,
+    (uint32, int32): int64,
+    (uint8, int64): int64,
+    (uint16, int64): int64,
+    (uint32, int64): int64,
+    (float32, float32): float32,
+    (float32, float64): float64,
+    (float64, float32): float64,
+    (float64, float64): float64,
+    (complex64, complex64): complex64,
+    (complex64, complex128): complex128,
+    (complex128, complex64): complex128,
+    (complex128, complex128): complex128,
+    (float32, complex64): complex64,
+    (float32, complex128): complex128,
+    (float64, complex64): complex128,
+    (float64, complex128): complex128,
+    (complex64, float32): complex64,
+    (complex64, float64): complex128,
+    (complex128, float32): complex128,
+    (complex128, float64): complex128,
+    (bool, bool): bool,
+}
+
+
+def _result_type(type1, type2):
+    if (type1, type2) in _promotion_table:
+        return _promotion_table[type1, type2]
+    raise TypeError(f"{type1} and {type2} cannot be type promoted together")

lib/python3.12/site-packages/numpy/array_api/_elementwise_functions.py

@@ -0,0 +1,765 @@
+from __future__ import annotations
+
+from ._dtypes import (
+    _boolean_dtypes,
+    _floating_dtypes,
+    _real_floating_dtypes,
+    _complex_floating_dtypes,
+    _integer_dtypes,
+    _integer_or_boolean_dtypes,
+    _real_numeric_dtypes,
+    _numeric_dtypes,
+    _result_type,
+)
+from ._array_object import Array
+
+import numpy as np
+
+
+def abs(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.abs <numpy.abs>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in abs")
+    return Array._new(np.abs(x._array))
+
+
+# Note: the function name is different here
+def acos(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.arccos <numpy.arccos>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in acos")
+    return Array._new(np.arccos(x._array))
+
+
+# Note: the function name is different here
+def acosh(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.arccosh <numpy.arccosh>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in acosh")
+    return Array._new(np.arccosh(x._array))
+
+
+def add(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.add <numpy.add>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in add")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.add(x1._array, x2._array))
+
+
+# Note: the function name is different here
+def asin(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.arcsin <numpy.arcsin>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in asin")
+    return Array._new(np.arcsin(x._array))
+
+
+# Note: the function name is different here
+def asinh(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.arcsinh <numpy.arcsinh>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in asinh")
+    return Array._new(np.arcsinh(x._array))
+
+
+# Note: the function name is different here
+def atan(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.arctan <numpy.arctan>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in atan")
+    return Array._new(np.arctan(x._array))
+
+
+# Note: the function name is different here
+def atan2(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.arctan2 <numpy.arctan2>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _real_floating_dtypes or x2.dtype not in _real_floating_dtypes:
+        raise TypeError("Only real floating-point dtypes are allowed in atan2")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.arctan2(x1._array, x2._array))
+
+
+# Note: the function name is different here
+def atanh(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.arctanh <numpy.arctanh>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in atanh")
+    return Array._new(np.arctanh(x._array))
+
+
+def bitwise_and(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.bitwise_and <numpy.bitwise_and>`.
+
+    See its docstring for more information.
+    """
+    if (
+        x1.dtype not in _integer_or_boolean_dtypes
+        or x2.dtype not in _integer_or_boolean_dtypes
+    ):
+        raise TypeError("Only integer or boolean dtypes are allowed in bitwise_and")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.bitwise_and(x1._array, x2._array))
+
+
+# Note: the function name is different here
+def bitwise_left_shift(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.left_shift <numpy.left_shift>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _integer_dtypes or x2.dtype not in _integer_dtypes:
+        raise TypeError("Only integer dtypes are allowed in bitwise_left_shift")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    # Note: bitwise_left_shift is only defined for x2 nonnegative.
+    if np.any(x2._array < 0):
+        raise ValueError("bitwise_left_shift(x1, x2) is only defined for x2 >= 0")
+    return Array._new(np.left_shift(x1._array, x2._array))
+
+
+# Note: the function name is different here
+def bitwise_invert(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.invert <numpy.invert>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _integer_or_boolean_dtypes:
+        raise TypeError("Only integer or boolean dtypes are allowed in bitwise_invert")
+    return Array._new(np.invert(x._array))
+
+
+def bitwise_or(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.bitwise_or <numpy.bitwise_or>`.
+
+    See its docstring for more information.
+    """
+    if (
+        x1.dtype not in _integer_or_boolean_dtypes
+        or x2.dtype not in _integer_or_boolean_dtypes
+    ):
+        raise TypeError("Only integer or boolean dtypes are allowed in bitwise_or")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.bitwise_or(x1._array, x2._array))
+
+
+# Note: the function name is different here
+def bitwise_right_shift(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.right_shift <numpy.right_shift>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _integer_dtypes or x2.dtype not in _integer_dtypes:
+        raise TypeError("Only integer dtypes are allowed in bitwise_right_shift")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    # Note: bitwise_right_shift is only defined for x2 nonnegative.
+    if np.any(x2._array < 0):
+        raise ValueError("bitwise_right_shift(x1, x2) is only defined for x2 >= 0")
+    return Array._new(np.right_shift(x1._array, x2._array))
+
+
+def bitwise_xor(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.bitwise_xor <numpy.bitwise_xor>`.
+
+    See its docstring for more information.
+    """
+    if (
+        x1.dtype not in _integer_or_boolean_dtypes
+        or x2.dtype not in _integer_or_boolean_dtypes
+    ):
+        raise TypeError("Only integer or boolean dtypes are allowed in bitwise_xor")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.bitwise_xor(x1._array, x2._array))
+
+
+def ceil(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.ceil <numpy.ceil>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in ceil")
+    if x.dtype in _integer_dtypes:
+        # Note: The return dtype of ceil is the same as the input
+        return x
+    return Array._new(np.ceil(x._array))
+
+
+def conj(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.conj <numpy.conj>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _complex_floating_dtypes:
+        raise TypeError("Only complex floating-point dtypes are allowed in conj")
+    return Array._new(np.conj(x))
+
+
+def cos(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.cos <numpy.cos>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in cos")
+    return Array._new(np.cos(x._array))
+
+
+def cosh(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.cosh <numpy.cosh>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in cosh")
+    return Array._new(np.cosh(x._array))
+
+
+def divide(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.divide <numpy.divide>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _floating_dtypes or x2.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in divide")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.divide(x1._array, x2._array))
+
+
+def equal(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.equal <numpy.equal>`.
+
+    See its docstring for more information.
+    """
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.equal(x1._array, x2._array))
+
+
+def exp(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.exp <numpy.exp>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in exp")
+    return Array._new(np.exp(x._array))
+
+
+def expm1(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.expm1 <numpy.expm1>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in expm1")
+    return Array._new(np.expm1(x._array))
+
+
+def floor(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.floor <numpy.floor>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in floor")
+    if x.dtype in _integer_dtypes:
+        # Note: The return dtype of floor is the same as the input
+        return x
+    return Array._new(np.floor(x._array))
+
+
+def floor_divide(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.floor_divide <numpy.floor_divide>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _real_numeric_dtypes or x2.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in floor_divide")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.floor_divide(x1._array, x2._array))
+
+
+def greater(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.greater <numpy.greater>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _real_numeric_dtypes or x2.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in greater")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.greater(x1._array, x2._array))
+
+
+def greater_equal(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.greater_equal <numpy.greater_equal>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _real_numeric_dtypes or x2.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in greater_equal")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.greater_equal(x1._array, x2._array))
+
+
+def imag(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.imag <numpy.imag>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _complex_floating_dtypes:
+        raise TypeError("Only complex floating-point dtypes are allowed in imag")
+    return Array._new(np.imag(x))
+
+
+def isfinite(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.isfinite <numpy.isfinite>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in isfinite")
+    return Array._new(np.isfinite(x._array))
+
+
+def isinf(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.isinf <numpy.isinf>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in isinf")
+    return Array._new(np.isinf(x._array))
+
+
+def isnan(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.isnan <numpy.isnan>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in isnan")
+    return Array._new(np.isnan(x._array))
+
+
+def less(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.less <numpy.less>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _real_numeric_dtypes or x2.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in less")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.less(x1._array, x2._array))
+
+
+def less_equal(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.less_equal <numpy.less_equal>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _real_numeric_dtypes or x2.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in less_equal")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.less_equal(x1._array, x2._array))
+
+
+def log(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.log <numpy.log>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in log")
+    return Array._new(np.log(x._array))
+
+
+def log1p(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.log1p <numpy.log1p>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in log1p")
+    return Array._new(np.log1p(x._array))
+
+
+def log2(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.log2 <numpy.log2>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in log2")
+    return Array._new(np.log2(x._array))
+
+
+def log10(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.log10 <numpy.log10>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in log10")
+    return Array._new(np.log10(x._array))
+
+
+def logaddexp(x1: Array, x2: Array) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.logaddexp <numpy.logaddexp>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _real_floating_dtypes or x2.dtype not in _real_floating_dtypes:
+        raise TypeError("Only real floating-point dtypes are allowed in logaddexp")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.logaddexp(x1._array, x2._array))
+
+
+def logical_and(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.logical_and <numpy.logical_and>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _boolean_dtypes or x2.dtype not in _boolean_dtypes:
+        raise TypeError("Only boolean dtypes are allowed in logical_and")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.logical_and(x1._array, x2._array))
+
+
+def logical_not(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.logical_not <numpy.logical_not>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _boolean_dtypes:
+        raise TypeError("Only boolean dtypes are allowed in logical_not")
+    return Array._new(np.logical_not(x._array))
+
+
+def logical_or(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.logical_or <numpy.logical_or>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _boolean_dtypes or x2.dtype not in _boolean_dtypes:
+        raise TypeError("Only boolean dtypes are allowed in logical_or")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.logical_or(x1._array, x2._array))
+
+
+def logical_xor(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.logical_xor <numpy.logical_xor>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _boolean_dtypes or x2.dtype not in _boolean_dtypes:
+        raise TypeError("Only boolean dtypes are allowed in logical_xor")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.logical_xor(x1._array, x2._array))
+
+
+def multiply(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.multiply <numpy.multiply>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in multiply")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.multiply(x1._array, x2._array))
+
+
+def negative(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.negative <numpy.negative>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in negative")
+    return Array._new(np.negative(x._array))
+
+
+def not_equal(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.not_equal <numpy.not_equal>`.
+
+    See its docstring for more information.
+    """
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.not_equal(x1._array, x2._array))
+
+
+def positive(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.positive <numpy.positive>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in positive")
+    return Array._new(np.positive(x._array))
+
+
+# Note: the function name is different here
+def pow(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.power <numpy.power>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in pow")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.power(x1._array, x2._array))
+
+
+def real(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.real <numpy.real>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _complex_floating_dtypes:
+        raise TypeError("Only complex floating-point dtypes are allowed in real")
+    return Array._new(np.real(x))
+
+
+def remainder(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.remainder <numpy.remainder>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _real_numeric_dtypes or x2.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in remainder")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.remainder(x1._array, x2._array))
+
+
+def round(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.round <numpy.round>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in round")
+    return Array._new(np.round(x._array))
+
+
+def sign(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.sign <numpy.sign>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in sign")
+    return Array._new(np.sign(x._array))
+
+
+def sin(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.sin <numpy.sin>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in sin")
+    return Array._new(np.sin(x._array))
+
+
+def sinh(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.sinh <numpy.sinh>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in sinh")
+    return Array._new(np.sinh(x._array))
+
+
+def square(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.square <numpy.square>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in square")
+    return Array._new(np.square(x._array))
+
+
+def sqrt(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.sqrt <numpy.sqrt>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in sqrt")
+    return Array._new(np.sqrt(x._array))
+
+
+def subtract(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.subtract <numpy.subtract>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in subtract")
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.subtract(x1._array, x2._array))
+
+
+def tan(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.tan <numpy.tan>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in tan")
+    return Array._new(np.tan(x._array))
+
+
+def tanh(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.tanh <numpy.tanh>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _floating_dtypes:
+        raise TypeError("Only floating-point dtypes are allowed in tanh")
+    return Array._new(np.tanh(x._array))
+
+
+def trunc(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.trunc <numpy.trunc>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in trunc")
+    if x.dtype in _integer_dtypes:
+        # Note: The return dtype of trunc is the same as the input
+        return x
+    return Array._new(np.trunc(x._array))

lib/python3.12/site-packages/numpy/array_api/_indexing_functions.py

@@ -0,0 +1,20 @@
+from __future__ import annotations
+
+from ._array_object import Array
+from ._dtypes import _integer_dtypes
+
+import numpy as np
+
+def take(x: Array, indices: Array, /, *, axis: Optional[int] = None) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.take <numpy.take>`.
+
+    See its docstring for more information.
+    """
+    if axis is None and x.ndim != 1:
+        raise ValueError("axis must be specified when ndim > 1")
+    if indices.dtype not in _integer_dtypes:
+        raise TypeError("Only integer dtypes are allowed in indexing")
+    if indices.ndim != 1:
+        raise ValueError("Only 1-dim indices array is supported")
+    return Array._new(np.take(x._array, indices._array, axis=axis))

lib/python3.12/site-packages/numpy/array_api/_manipulation_functions.py

@@ -0,0 +1,112 @@
+from __future__ import annotations
+
+from ._array_object import Array
+from ._data_type_functions import result_type
+
+from typing import List, Optional, Tuple, Union
+
+import numpy as np
+
+# Note: the function name is different here
+def concat(
+    arrays: Union[Tuple[Array, ...], List[Array]], /, *, axis: Optional[int] = 0
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.concatenate <numpy.concatenate>`.
+
+    See its docstring for more information.
+    """
+    # Note: Casting rules here are different from the np.concatenate default
+    # (no for scalars with axis=None, no cross-kind casting)
+    dtype = result_type(*arrays)
+    arrays = tuple(a._array for a in arrays)
+    return Array._new(np.concatenate(arrays, axis=axis, dtype=dtype))
+
+
+def expand_dims(x: Array, /, *, axis: int) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.expand_dims <numpy.expand_dims>`.
+
+    See its docstring for more information.
+    """
+    return Array._new(np.expand_dims(x._array, axis))
+
+
+def flip(x: Array, /, *, axis: Optional[Union[int, Tuple[int, ...]]] = None) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.flip <numpy.flip>`.
+
+    See its docstring for more information.
+    """
+    return Array._new(np.flip(x._array, axis=axis))
+
+
+# Note: The function name is different here (see also matrix_transpose).
+# Unlike transpose(), the axes argument is required.
+def permute_dims(x: Array, /, axes: Tuple[int, ...]) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.transpose <numpy.transpose>`.
+
+    See its docstring for more information.
+    """
+    return Array._new(np.transpose(x._array, axes))
+
+
+# Note: the optional argument is called 'shape', not 'newshape'
+def reshape(x: Array, 
+            /, 
+            shape: Tuple[int, ...],
+            *,
+            copy: Optional[Bool] = None) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.reshape <numpy.reshape>`.
+
+    See its docstring for more information.
+    """
+
+    data = x._array
+    if copy:
+        data = np.copy(data)
+
+    reshaped = np.reshape(data, shape)
+
+    if copy is False and not np.shares_memory(data, reshaped):
+        raise AttributeError("Incompatible shape for in-place modification.")
+
+    return Array._new(reshaped)
+
+
+def roll(
+    x: Array,
+    /,
+    shift: Union[int, Tuple[int, ...]],
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.roll <numpy.roll>`.
+
+    See its docstring for more information.
+    """
+    return Array._new(np.roll(x._array, shift, axis=axis))
+
+
+def squeeze(x: Array, /, axis: Union[int, Tuple[int, ...]]) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.squeeze <numpy.squeeze>`.
+
+    See its docstring for more information.
+    """
+    return Array._new(np.squeeze(x._array, axis=axis))
+
+
+def stack(arrays: Union[Tuple[Array, ...], List[Array]], /, *, axis: int = 0) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.stack <numpy.stack>`.
+
+    See its docstring for more information.
+    """
+    # Call result type here just to raise on disallowed type combinations
+    result_type(*arrays)
+    arrays = tuple(a._array for a in arrays)
+    return Array._new(np.stack(arrays, axis=axis))

lib/python3.12/site-packages/numpy/array_api/_searching_functions.py

@@ -0,0 +1,51 @@
+from __future__ import annotations
+
+from ._array_object import Array
+from ._dtypes import _result_type, _real_numeric_dtypes
+
+from typing import Optional, Tuple
+
+import numpy as np
+
+
+def argmax(x: Array, /, *, axis: Optional[int] = None, keepdims: bool = False) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.argmax <numpy.argmax>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in argmax")
+    return Array._new(np.asarray(np.argmax(x._array, axis=axis, keepdims=keepdims)))
+
+
+def argmin(x: Array, /, *, axis: Optional[int] = None, keepdims: bool = False) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.argmin <numpy.argmin>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in argmin")
+    return Array._new(np.asarray(np.argmin(x._array, axis=axis, keepdims=keepdims)))
+
+
+def nonzero(x: Array, /) -> Tuple[Array, ...]:
+    """
+    Array API compatible wrapper for :py:func:`np.nonzero <numpy.nonzero>`.
+
+    See its docstring for more information.
+    """
+    return tuple(Array._new(i) for i in np.nonzero(x._array))
+
+
+def where(condition: Array, x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.where <numpy.where>`.
+
+    See its docstring for more information.
+    """
+    # Call result type here just to raise on disallowed type combinations
+    _result_type(x1.dtype, x2.dtype)
+    x1, x2 = Array._normalize_two_args(x1, x2)
+    return Array._new(np.where(condition._array, x1._array, x2._array))

lib/python3.12/site-packages/numpy/array_api/_set_functions.py

@@ -0,0 +1,106 @@
+from __future__ import annotations
+
+from ._array_object import Array
+
+from typing import NamedTuple
+
+import numpy as np
+
+# Note: np.unique() is split into four functions in the array API:
+# unique_all, unique_counts, unique_inverse, and unique_values (this is done
+# to remove polymorphic return types).
+
+# Note: The various unique() functions are supposed to return multiple NaNs.
+# This does not match the NumPy behavior, however, this is currently left as a
+# TODO in this implementation as this behavior may be reverted in np.unique().
+# See https://github.com/numpy/numpy/issues/20326.
+
+# Note: The functions here return a namedtuple (np.unique() returns a normal
+# tuple).
+
+class UniqueAllResult(NamedTuple):
+    values: Array
+    indices: Array
+    inverse_indices: Array
+    counts: Array
+
+
+class UniqueCountsResult(NamedTuple):
+    values: Array
+    counts: Array
+
+
+class UniqueInverseResult(NamedTuple):
+    values: Array
+    inverse_indices: Array
+
+
+def unique_all(x: Array, /) -> UniqueAllResult:
+    """
+    Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`.
+
+    See its docstring for more information.
+    """
+    values, indices, inverse_indices, counts = np.unique(
+        x._array,
+        return_counts=True,
+        return_index=True,
+        return_inverse=True,
+        equal_nan=False,
+    )
+    # np.unique() flattens inverse indices, but they need to share x's shape
+    # See https://github.com/numpy/numpy/issues/20638
+    inverse_indices = inverse_indices.reshape(x.shape)
+    return UniqueAllResult(
+        Array._new(values),
+        Array._new(indices),
+        Array._new(inverse_indices),
+        Array._new(counts),
+    )
+
+
+def unique_counts(x: Array, /) -> UniqueCountsResult:
+    res = np.unique(
+        x._array,
+        return_counts=True,
+        return_index=False,
+        return_inverse=False,
+        equal_nan=False,
+    )
+
+    return UniqueCountsResult(*[Array._new(i) for i in res])
+
+
+def unique_inverse(x: Array, /) -> UniqueInverseResult:
+    """
+    Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`.
+
+    See its docstring for more information.
+    """
+    values, inverse_indices = np.unique(
+        x._array,
+        return_counts=False,
+        return_index=False,
+        return_inverse=True,
+        equal_nan=False,
+    )
+    # np.unique() flattens inverse indices, but they need to share x's shape
+    # See https://github.com/numpy/numpy/issues/20638
+    inverse_indices = inverse_indices.reshape(x.shape)
+    return UniqueInverseResult(Array._new(values), Array._new(inverse_indices))
+
+
+def unique_values(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`.
+
+    See its docstring for more information.
+    """
+    res = np.unique(
+        x._array,
+        return_counts=False,
+        return_index=False,
+        return_inverse=False,
+        equal_nan=False,
+    )
+    return Array._new(res)

lib/python3.12/site-packages/numpy/array_api/_sorting_functions.py

@@ -0,0 +1,54 @@
+from __future__ import annotations
+
+from ._array_object import Array
+from ._dtypes import _real_numeric_dtypes
+
+import numpy as np
+
+
+# Note: the descending keyword argument is new in this function
+def argsort(
+    x: Array, /, *, axis: int = -1, descending: bool = False, stable: bool = True
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.argsort <numpy.argsort>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in argsort")
+    # Note: this keyword argument is different, and the default is different.
+    kind = "stable" if stable else "quicksort"
+    if not descending:
+        res = np.argsort(x._array, axis=axis, kind=kind)
+    else:
+        # As NumPy has no native descending sort, we imitate it here. Note that
+        # simply flipping the results of np.argsort(x._array, ...) would not
+        # respect the relative order like it would in native descending sorts.
+        res = np.flip(
+            np.argsort(np.flip(x._array, axis=axis), axis=axis, kind=kind),
+            axis=axis,
+        )
+        # Rely on flip()/argsort() to validate axis
+        normalised_axis = axis if axis >= 0 else x.ndim + axis
+        max_i = x.shape[normalised_axis] - 1
+        res = max_i - res
+    return Array._new(res)
+
+# Note: the descending keyword argument is new in this function
+def sort(
+    x: Array, /, *, axis: int = -1, descending: bool = False, stable: bool = True
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.sort <numpy.sort>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in sort")
+    # Note: this keyword argument is different, and the default is different.
+    kind = "stable" if stable else "quicksort"
+    res = np.sort(x._array, axis=axis, kind=kind)
+    if descending:
+        res = np.flip(res, axis=axis)
+    return Array._new(res)

lib/python3.12/site-packages/numpy/array_api/_statistical_functions.py

@@ -0,0 +1,122 @@
+from __future__ import annotations
+
+from ._dtypes import (
+    _real_floating_dtypes,
+    _real_numeric_dtypes,
+    _numeric_dtypes,
+)
+from ._array_object import Array
+from ._dtypes import float32, float64, complex64, complex128
+
+from typing import TYPE_CHECKING, Optional, Tuple, Union
+
+if TYPE_CHECKING:
+    from ._typing import Dtype
+
+import numpy as np
+
+
+def max(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    keepdims: bool = False,
+) -> Array:
+    if x.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in max")
+    return Array._new(np.max(x._array, axis=axis, keepdims=keepdims))
+
+
+def mean(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    keepdims: bool = False,
+) -> Array:
+    if x.dtype not in _real_floating_dtypes:
+        raise TypeError("Only real floating-point dtypes are allowed in mean")
+    return Array._new(np.mean(x._array, axis=axis, keepdims=keepdims))
+
+
+def min(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    keepdims: bool = False,
+) -> Array:
+    if x.dtype not in _real_numeric_dtypes:
+        raise TypeError("Only real numeric dtypes are allowed in min")
+    return Array._new(np.min(x._array, axis=axis, keepdims=keepdims))
+
+
+def prod(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    dtype: Optional[Dtype] = None,
+    keepdims: bool = False,
+) -> Array:
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in prod")
+    # Note: sum() and prod() always upcast for dtype=None. `np.prod` does that
+    # for integers, but not for float32 or complex64, so we need to
+    # special-case it here
+    if dtype is None:
+        if x.dtype == float32:
+            dtype = float64
+        elif x.dtype == complex64:
+            dtype = complex128
+    return Array._new(np.prod(x._array, dtype=dtype, axis=axis, keepdims=keepdims))
+
+
+def std(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    correction: Union[int, float] = 0.0,
+    keepdims: bool = False,
+) -> Array:
+    # Note: the keyword argument correction is different here
+    if x.dtype not in _real_floating_dtypes:
+        raise TypeError("Only real floating-point dtypes are allowed in std")
+    return Array._new(np.std(x._array, axis=axis, ddof=correction, keepdims=keepdims))
+
+
+def sum(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    dtype: Optional[Dtype] = None,
+    keepdims: bool = False,
+) -> Array:
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError("Only numeric dtypes are allowed in sum")
+    # Note: sum() and prod() always upcast for dtype=None. `np.sum` does that
+    # for integers, but not for float32 or complex64, so we need to
+    # special-case it here
+    if dtype is None:
+        if x.dtype == float32:
+            dtype = float64
+        elif x.dtype == complex64:
+            dtype = complex128
+    return Array._new(np.sum(x._array, axis=axis, dtype=dtype, keepdims=keepdims))
+
+
+def var(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    correction: Union[int, float] = 0.0,
+    keepdims: bool = False,
+) -> Array:
+    # Note: the keyword argument correction is different here
+    if x.dtype not in _real_floating_dtypes:
+        raise TypeError("Only real floating-point dtypes are allowed in var")
+    return Array._new(np.var(x._array, axis=axis, ddof=correction, keepdims=keepdims))

lib/python3.12/site-packages/numpy/array_api/_typing.py

@@ -0,0 +1,76 @@
+"""
+This file defines the types for type annotations.
+
+These names aren't part of the module namespace, but they are used in the
+annotations in the function signatures. The functions in the module are only
+valid for inputs that match the given type annotations.
+"""
+
+from __future__ import annotations
+
+__all__ = [
+    "Array",
+    "Device",
+    "Dtype",
+    "SupportsDLPack",
+    "SupportsBufferProtocol",
+    "PyCapsule",
+]
+
+import sys
+
+from typing import (
+    Any,
+    Literal,
+    Sequence,
+    Type,
+    Union,
+    TypeVar,
+    Protocol,
+)
+
+from ._array_object import Array
+from numpy import (
+    dtype,
+    int8,
+    int16,
+    int32,
+    int64,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+    float32,
+    float64,
+)
+
+_T_co = TypeVar("_T_co", covariant=True)
+
+class NestedSequence(Protocol[_T_co]):
+    def __getitem__(self, key: int, /) -> _T_co | NestedSequence[_T_co]: ...
+    def __len__(self, /) -> int: ...
+
+Device = Literal["cpu"]
+
+Dtype = dtype[Union[
+    int8,
+    int16,
+    int32,
+    int64,
+    uint8,
+    uint16,
+    uint32,
+    uint64,
+    float32,
+    float64,
+]]
+
+if sys.version_info >= (3, 12):
+    from collections.abc import Buffer as SupportsBufferProtocol
+else:
+    SupportsBufferProtocol = Any
+
+PyCapsule = Any
+
+class SupportsDLPack(Protocol):
+    def __dlpack__(self, /, *, stream: None = ...) -> PyCapsule: ...

lib/python3.12/site-packages/numpy/array_api/_utility_functions.py

@@ -0,0 +1,37 @@
+from __future__ import annotations
+
+from ._array_object import Array
+
+from typing import Optional, Tuple, Union
+
+import numpy as np
+
+
+def all(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    keepdims: bool = False,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.all <numpy.all>`.
+
+    See its docstring for more information.
+    """
+    return Array._new(np.asarray(np.all(x._array, axis=axis, keepdims=keepdims)))
+
+
+def any(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    keepdims: bool = False,
+) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.any <numpy.any>`.
+
+    See its docstring for more information.
+    """
+    return Array._new(np.asarray(np.any(x._array, axis=axis, keepdims=keepdims)))

lib/python3.12/site-packages/numpy/array_api/linalg.py

@@ -0,0 +1,466 @@
+from __future__ import annotations
+
+from ._dtypes import (
+    _floating_dtypes,
+    _numeric_dtypes,
+    float32,
+    float64,
+    complex64,
+    complex128
+)
+from ._manipulation_functions import reshape
+from ._elementwise_functions import conj
+from ._array_object import Array
+
+from ..core.numeric import normalize_axis_tuple
+
+from typing import TYPE_CHECKING
+if TYPE_CHECKING:
+    from ._typing import Literal, Optional, Sequence, Tuple, Union, Dtype
+
+from typing import NamedTuple
+
+import numpy.linalg
+import numpy as np
+
+class EighResult(NamedTuple):
+    eigenvalues: Array
+    eigenvectors: Array
+
+class QRResult(NamedTuple):
+    Q: Array
+    R: Array
+
+class SlogdetResult(NamedTuple):
+    sign: Array
+    logabsdet: Array
+
+class SVDResult(NamedTuple):
+    U: Array
+    S: Array
+    Vh: Array
+
+# Note: the inclusion of the upper keyword is different from
+# np.linalg.cholesky, which does not have it.
+def cholesky(x: Array, /, *, upper: bool = False) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.cholesky <numpy.linalg.cholesky>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.cholesky.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in cholesky')
+    L = np.linalg.cholesky(x._array)
+    if upper:
+        U = Array._new(L).mT
+        if U.dtype in [complex64, complex128]:
+            U = conj(U)
+        return U
+    return Array._new(L)
+
+# Note: cross is the numpy top-level namespace, not np.linalg
+def cross(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.cross <numpy.cross>`.
+
+    See its docstring for more information.
+    """
+    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
+        raise TypeError('Only numeric dtypes are allowed in cross')
+    # Note: this is different from np.cross(), which broadcasts
+    if x1.shape != x2.shape:
+        raise ValueError('x1 and x2 must have the same shape')
+    if x1.ndim == 0:
+        raise ValueError('cross() requires arrays of dimension at least 1')
+    # Note: this is different from np.cross(), which allows dimension 2
+    if x1.shape[axis] != 3:
+        raise ValueError('cross() dimension must equal 3')
+    return Array._new(np.cross(x1._array, x2._array, axis=axis))
+
+def det(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.det <numpy.linalg.det>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.det.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in det')
+    return Array._new(np.linalg.det(x._array))
+
+# Note: diagonal is the numpy top-level namespace, not np.linalg
+def diagonal(x: Array, /, *, offset: int = 0) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.diagonal <numpy.diagonal>`.
+
+    See its docstring for more information.
+    """
+    # Note: diagonal always operates on the last two axes, whereas np.diagonal
+    # operates on the first two axes by default
+    return Array._new(np.diagonal(x._array, offset=offset, axis1=-2, axis2=-1))
+
+
+def eigh(x: Array, /) -> EighResult:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.eigh <numpy.linalg.eigh>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.eigh.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in eigh')
+
+    # Note: the return type here is a namedtuple, which is different from
+    # np.eigh, which only returns a tuple.
+    return EighResult(*map(Array._new, np.linalg.eigh(x._array)))
+
+
+def eigvalsh(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.eigvalsh <numpy.linalg.eigvalsh>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.eigvalsh.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in eigvalsh')
+
+    return Array._new(np.linalg.eigvalsh(x._array))
+
+def inv(x: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.inv <numpy.linalg.inv>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.inv.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in inv')
+
+    return Array._new(np.linalg.inv(x._array))
+
+
+# Note: matmul is the numpy top-level namespace but not in np.linalg
+def matmul(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.matmul <numpy.matmul>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to numeric dtypes only is different from
+    # np.matmul.
+    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
+        raise TypeError('Only numeric dtypes are allowed in matmul')
+
+    return Array._new(np.matmul(x1._array, x2._array))
+
+
+# Note: the name here is different from norm(). The array API norm is split
+# into matrix_norm and vector_norm().
+
+# The type for ord should be Optional[Union[int, float, Literal[np.inf,
+# -np.inf, 'fro', 'nuc']]], but Literal does not support floating-point
+# literals.
+def matrix_norm(x: Array, /, *, keepdims: bool = False, ord: Optional[Union[int, float, Literal['fro', 'nuc']]] = 'fro') -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.norm.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in matrix_norm')
+
+    return Array._new(np.linalg.norm(x._array, axis=(-2, -1), keepdims=keepdims, ord=ord))
+
+
+def matrix_power(x: Array, n: int, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.matrix_power <numpy.matrix_power>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.matrix_power.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed for the first argument of matrix_power')
+
+    # np.matrix_power already checks if n is an integer
+    return Array._new(np.linalg.matrix_power(x._array, n))
+
+# Note: the keyword argument name rtol is different from np.linalg.matrix_rank
+def matrix_rank(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.matrix_rank <numpy.matrix_rank>`.
+
+    See its docstring for more information.
+    """
+    # Note: this is different from np.linalg.matrix_rank, which supports 1
+    # dimensional arrays.
+    if x.ndim < 2:
+        raise np.linalg.LinAlgError("1-dimensional array given. Array must be at least two-dimensional")
+    S = np.linalg.svd(x._array, compute_uv=False)
+    if rtol is None:
+        tol = S.max(axis=-1, keepdims=True) * max(x.shape[-2:]) * np.finfo(S.dtype).eps
+    else:
+        if isinstance(rtol, Array):
+            rtol = rtol._array
+        # Note: this is different from np.linalg.matrix_rank, which does not multiply
+        # the tolerance by the largest singular value.
+        tol = S.max(axis=-1, keepdims=True)*np.asarray(rtol)[..., np.newaxis]
+    return Array._new(np.count_nonzero(S > tol, axis=-1))
+
+
+# Note: this function is new in the array API spec. Unlike transpose, it only
+# transposes the last two axes.
+def matrix_transpose(x: Array, /) -> Array:
+    if x.ndim < 2:
+        raise ValueError("x must be at least 2-dimensional for matrix_transpose")
+    return Array._new(np.swapaxes(x._array, -1, -2))
+
+# Note: outer is the numpy top-level namespace, not np.linalg
+def outer(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.outer <numpy.outer>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to numeric dtypes only is different from
+    # np.outer.
+    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
+        raise TypeError('Only numeric dtypes are allowed in outer')
+
+    # Note: the restriction to only 1-dim arrays is different from np.outer
+    if x1.ndim != 1 or x2.ndim != 1:
+        raise ValueError('The input arrays to outer must be 1-dimensional')
+
+    return Array._new(np.outer(x1._array, x2._array))
+
+# Note: the keyword argument name rtol is different from np.linalg.pinv
+def pinv(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.pinv <numpy.linalg.pinv>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.pinv.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in pinv')
+
+    # Note: this is different from np.linalg.pinv, which does not multiply the
+    # default tolerance by max(M, N).
+    if rtol is None:
+        rtol = max(x.shape[-2:]) * np.finfo(x.dtype).eps
+    return Array._new(np.linalg.pinv(x._array, rcond=rtol))
+
+def qr(x: Array, /, *, mode: Literal['reduced', 'complete'] = 'reduced') -> QRResult:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.qr <numpy.linalg.qr>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.qr.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in qr')
+
+    # Note: the return type here is a namedtuple, which is different from
+    # np.linalg.qr, which only returns a tuple.
+    return QRResult(*map(Array._new, np.linalg.qr(x._array, mode=mode)))
+
+def slogdet(x: Array, /) -> SlogdetResult:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.slogdet <numpy.linalg.slogdet>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.slogdet.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in slogdet')
+
+    # Note: the return type here is a namedtuple, which is different from
+    # np.linalg.slogdet, which only returns a tuple.
+    return SlogdetResult(*map(Array._new, np.linalg.slogdet(x._array)))
+
+# Note: unlike np.linalg.solve, the array API solve() only accepts x2 as a
+# vector when it is exactly 1-dimensional. All other cases treat x2 as a stack
+# of matrices. The np.linalg.solve behavior of allowing stacks of both
+# matrices and vectors is ambiguous c.f.
+# https://github.com/numpy/numpy/issues/15349 and
+# https://github.com/data-apis/array-api/issues/285.
+
+# To workaround this, the below is the code from np.linalg.solve except
+# only calling solve1 in the exactly 1D case.
+def _solve(a, b):
+    from ..linalg.linalg import (_makearray, _assert_stacked_2d,
+                                 _assert_stacked_square, _commonType,
+                                 isComplexType, get_linalg_error_extobj,
+                                 _raise_linalgerror_singular)
+    from ..linalg import _umath_linalg
+
+    a, _ = _makearray(a)
+    _assert_stacked_2d(a)
+    _assert_stacked_square(a)
+    b, wrap = _makearray(b)
+    t, result_t = _commonType(a, b)
+
+    # This part is different from np.linalg.solve
+    if b.ndim == 1:
+        gufunc = _umath_linalg.solve1
+    else:
+        gufunc = _umath_linalg.solve
+
+    # This does nothing currently but is left in because it will be relevant
+    # when complex dtype support is added to the spec in 2022.
+    signature = 'DD->D' if isComplexType(t) else 'dd->d'
+    with np.errstate(call=_raise_linalgerror_singular, invalid='call',
+                     over='ignore', divide='ignore', under='ignore'):
+        r = gufunc(a, b, signature=signature)
+
+    return wrap(r.astype(result_t, copy=False))
+
+def solve(x1: Array, x2: Array, /) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.solve <numpy.linalg.solve>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.solve.
+    if x1.dtype not in _floating_dtypes or x2.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in solve')
+
+    return Array._new(_solve(x1._array, x2._array))
+
+def svd(x: Array, /, *, full_matrices: bool = True) -> SVDResult:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.svd <numpy.linalg.svd>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.svd.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in svd')
+
+    # Note: the return type here is a namedtuple, which is different from
+    # np.svd, which only returns a tuple.
+    return SVDResult(*map(Array._new, np.linalg.svd(x._array, full_matrices=full_matrices)))
+
+# Note: svdvals is not in NumPy (but it is in SciPy). It is equivalent to
+# np.linalg.svd(compute_uv=False).
+def svdvals(x: Array, /) -> Union[Array, Tuple[Array, ...]]:
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in svdvals')
+    return Array._new(np.linalg.svd(x._array, compute_uv=False))
+
+# Note: tensordot is the numpy top-level namespace but not in np.linalg
+
+# Note: axes must be a tuple, unlike np.tensordot where it can be an array or array-like.
+def tensordot(x1: Array, x2: Array, /, *, axes: Union[int, Tuple[Sequence[int], Sequence[int]]] = 2) -> Array:
+    # Note: the restriction to numeric dtypes only is different from
+    # np.tensordot.
+    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
+        raise TypeError('Only numeric dtypes are allowed in tensordot')
+
+    return Array._new(np.tensordot(x1._array, x2._array, axes=axes))
+
+# Note: trace is the numpy top-level namespace, not np.linalg
+def trace(x: Array, /, *, offset: int = 0, dtype: Optional[Dtype] = None) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.trace <numpy.trace>`.
+
+    See its docstring for more information.
+    """
+    if x.dtype not in _numeric_dtypes:
+        raise TypeError('Only numeric dtypes are allowed in trace')
+
+    # Note: trace() works the same as sum() and prod() (see
+    # _statistical_functions.py)
+    if dtype is None:
+        if x.dtype == float32:
+            dtype = float64
+        elif x.dtype == complex64:
+            dtype = complex128
+    # Note: trace always operates on the last two axes, whereas np.trace
+    # operates on the first two axes by default
+    return Array._new(np.asarray(np.trace(x._array, offset=offset, axis1=-2, axis2=-1, dtype=dtype)))
+
+# Note: vecdot is not in NumPy
+def vecdot(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
+    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
+        raise TypeError('Only numeric dtypes are allowed in vecdot')
+    ndim = max(x1.ndim, x2.ndim)
+    x1_shape = (1,)*(ndim - x1.ndim) + tuple(x1.shape)
+    x2_shape = (1,)*(ndim - x2.ndim) + tuple(x2.shape)
+    if x1_shape[axis] != x2_shape[axis]:
+        raise ValueError("x1 and x2 must have the same size along the given axis")
+
+    x1_, x2_ = np.broadcast_arrays(x1._array, x2._array)
+    x1_ = np.moveaxis(x1_, axis, -1)
+    x2_ = np.moveaxis(x2_, axis, -1)
+
+    res = x1_[..., None, :] @ x2_[..., None]
+    return Array._new(res[..., 0, 0])
+
+
+# Note: the name here is different from norm(). The array API norm is split
+# into matrix_norm and vector_norm().
+
+# The type for ord should be Optional[Union[int, float, Literal[np.inf,
+# -np.inf]]] but Literal does not support floating-point literals.
+def vector_norm(x: Array, /, *, axis: Optional[Union[int, Tuple[int, ...]]] = None, keepdims: bool = False, ord: Optional[Union[int, float]] = 2) -> Array:
+    """
+    Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`.
+
+    See its docstring for more information.
+    """
+    # Note: the restriction to floating-point dtypes only is different from
+    # np.linalg.norm.
+    if x.dtype not in _floating_dtypes:
+        raise TypeError('Only floating-point dtypes are allowed in norm')
+
+    # np.linalg.norm tries to do a matrix norm whenever axis is a 2-tuple or
+    # when axis=None and the input is 2-D, so to force a vector norm, we make
+    # it so the input is 1-D (for axis=None), or reshape so that norm is done
+    # on a single dimension.
+    a = x._array
+    if axis is None:
+        # Note: np.linalg.norm() doesn't handle 0-D arrays
+        a = a.ravel()
+        _axis = 0
+    elif isinstance(axis, tuple):
+        # Note: The axis argument supports any number of axes, whereas
+        # np.linalg.norm() only supports a single axis for vector norm.
+        normalized_axis = normalize_axis_tuple(axis, x.ndim)
+        rest = tuple(i for i in range(a.ndim) if i not in normalized_axis)
+        newshape = axis + rest
+        a = np.transpose(a, newshape).reshape(
+            (np.prod([a.shape[i] for i in axis], dtype=int), *[a.shape[i] for i in rest]))
+        _axis = 0
+    else:
+        _axis = axis
+
+    res = Array._new(np.linalg.norm(a, axis=_axis, ord=ord))
+
+    if keepdims:
+        # We can't reuse np.linalg.norm(keepdims) because of the reshape hacks
+        # above to avoid matrix norm logic.
+        shape = list(x.shape)
+        _axis = normalize_axis_tuple(range(x.ndim) if axis is None else axis, x.ndim)
+        for i in _axis:
+            shape[i] = 1
+        res = reshape(res, tuple(shape))
+
+    return res
+
+__all__ = ['cholesky', 'cross', 'det', 'diagonal', 'eigh', 'eigvalsh', 'inv', 'matmul', 'matrix_norm', 'matrix_power', 'matrix_rank', 'matrix_transpose', 'outer', 'pinv', 'qr', 'slogdet', 'solve', 'svd', 'svdvals', 'tensordot', 'trace', 'vecdot', 'vector_norm']

lib/python3.12/site-packages/numpy/array_api/setup.py

@@ -0,0 +1,12 @@
+def configuration(parent_package="", top_path=None):
+    from numpy.distutils.misc_util import Configuration
+
+    config = Configuration("array_api", parent_package, top_path)
+    config.add_subpackage("tests")
+    return config
+
+
+if __name__ == "__main__":
+    from numpy.distutils.core import setup
+
+    setup(configuration=configuration)

lib/python3.12/site-packages/numpy/array_api/tests/__init__.py

@@ -0,0 +1,7 @@
+"""
+Tests for the array API namespace.
+
+Note, full compliance with the array API can be tested with the official array API test
+suite https://github.com/data-apis/array-api-tests. This test suite primarily
+focuses on those things that are not tested by the official test suite.
+"""

lib/python3.12/site-packages/numpy/array_api/tests/test_array_object.py

@@ -0,0 +1,395 @@
+import operator
+
+from numpy.testing import assert_raises, suppress_warnings
+import numpy as np
+import pytest
+
+from .. import ones, asarray, reshape, result_type, all, equal
+from .._array_object import Array
+from .._dtypes import (
+    _all_dtypes,
+    _boolean_dtypes,
+    _real_floating_dtypes,
+    _floating_dtypes,
+    _complex_floating_dtypes,
+    _integer_dtypes,
+    _integer_or_boolean_dtypes,
+    _real_numeric_dtypes,
+    _numeric_dtypes,
+    int8,
+    int16,
+    int32,
+    int64,
+    uint64,
+    bool as bool_,
+)
+
+
+def test_validate_index():
+    # The indexing tests in the official array API test suite test that the
+    # array object correctly handles the subset of indices that are required
+    # by the spec. But the NumPy array API implementation specifically
+    # disallows any index not required by the spec, via Array._validate_index.
+    # This test focuses on testing that non-valid indices are correctly
+    # rejected. See
+    # https://data-apis.org/array-api/latest/API_specification/indexing.html
+    # and the docstring of Array._validate_index for the exact indexing
+    # behavior that should be allowed. This does not test indices that are
+    # already invalid in NumPy itself because Array will generally just pass
+    # such indices directly to the underlying np.ndarray.
+
+    a = ones((3, 4))
+
+    # Out of bounds slices are not allowed
+    assert_raises(IndexError, lambda: a[:4])
+    assert_raises(IndexError, lambda: a[:-4])
+    assert_raises(IndexError, lambda: a[:3:-1])
+    assert_raises(IndexError, lambda: a[:-5:-1])
+    assert_raises(IndexError, lambda: a[4:])
+    assert_raises(IndexError, lambda: a[-4:])
+    assert_raises(IndexError, lambda: a[4::-1])
+    assert_raises(IndexError, lambda: a[-4::-1])
+
+    assert_raises(IndexError, lambda: a[...,:5])
+    assert_raises(IndexError, lambda: a[...,:-5])
+    assert_raises(IndexError, lambda: a[...,:5:-1])
+    assert_raises(IndexError, lambda: a[...,:-6:-1])
+    assert_raises(IndexError, lambda: a[...,5:])
+    assert_raises(IndexError, lambda: a[...,-5:])
+    assert_raises(IndexError, lambda: a[...,5::-1])
+    assert_raises(IndexError, lambda: a[...,-5::-1])
+
+    # Boolean indices cannot be part of a larger tuple index
+    assert_raises(IndexError, lambda: a[a[:,0]==1,0])
+    assert_raises(IndexError, lambda: a[a[:,0]==1,...])
+    assert_raises(IndexError, lambda: a[..., a[0]==1])
+    assert_raises(IndexError, lambda: a[[True, True, True]])
+    assert_raises(IndexError, lambda: a[(True, True, True),])
+
+    # Integer array indices are not allowed (except for 0-D)
+    idx = asarray([[0, 1]])
+    assert_raises(IndexError, lambda: a[idx])
+    assert_raises(IndexError, lambda: a[idx,])
+    assert_raises(IndexError, lambda: a[[0, 1]])
+    assert_raises(IndexError, lambda: a[(0, 1), (0, 1)])
+    assert_raises(IndexError, lambda: a[[0, 1]])
+    assert_raises(IndexError, lambda: a[np.array([[0, 1]])])
+
+    # Multiaxis indices must contain exactly as many indices as dimensions
+    assert_raises(IndexError, lambda: a[()])
+    assert_raises(IndexError, lambda: a[0,])
+    assert_raises(IndexError, lambda: a[0])
+    assert_raises(IndexError, lambda: a[:])
+
+def test_operators():
+    # For every operator, we test that it works for the required type
+    # combinations and raises TypeError otherwise
+    binary_op_dtypes = {
+        "__add__": "numeric",
+        "__and__": "integer_or_boolean",
+        "__eq__": "all",
+        "__floordiv__": "real numeric",
+        "__ge__": "real numeric",
+        "__gt__": "real numeric",
+        "__le__": "real numeric",
+        "__lshift__": "integer",
+        "__lt__": "real numeric",
+        "__mod__": "real numeric",
+        "__mul__": "numeric",
+        "__ne__": "all",
+        "__or__": "integer_or_boolean",
+        "__pow__": "numeric",
+        "__rshift__": "integer",
+        "__sub__": "numeric",
+        "__truediv__": "floating",
+        "__xor__": "integer_or_boolean",
+    }
+    # Recompute each time because of in-place ops
+    def _array_vals():
+        for d in _integer_dtypes:
+            yield asarray(1, dtype=d)
+        for d in _boolean_dtypes:
+            yield asarray(False, dtype=d)
+        for d in _floating_dtypes:
+            yield asarray(1.0, dtype=d)
+
+
+    BIG_INT = int(1e30)
+    for op, dtypes in binary_op_dtypes.items():
+        ops = [op]
+        if op not in ["__eq__", "__ne__", "__le__", "__ge__", "__lt__", "__gt__"]:
+            rop = "__r" + op[2:]
+            iop = "__i" + op[2:]
+            ops += [rop, iop]
+        for s in [1, 1.0, 1j, BIG_INT, False]:
+            for _op in ops:
+                for a in _array_vals():
+                    # Test array op scalar. From the spec, the following combinations
+                    # are supported:
+
+                    # - Python bool for a bool array dtype,
+                    # - a Python int within the bounds of the given dtype for integer array dtypes,
+                    # - a Python int or float for real floating-point array dtypes
+                    # - a Python int, float, or complex for complex floating-point array dtypes
+
+                    if ((dtypes == "all"
+                         or dtypes == "numeric" and a.dtype in _numeric_dtypes
+                         or dtypes == "real numeric" and a.dtype in _real_numeric_dtypes
+                         or dtypes == "integer" and a.dtype in _integer_dtypes
+                         or dtypes == "integer_or_boolean" and a.dtype in _integer_or_boolean_dtypes
+                         or dtypes == "boolean" and a.dtype in _boolean_dtypes
+                         or dtypes == "floating" and a.dtype in _floating_dtypes
+                        )
+                        # bool is a subtype of int, which is why we avoid
+                        # isinstance here.
+                        and (a.dtype in _boolean_dtypes and type(s) == bool
+                             or a.dtype in _integer_dtypes and type(s) == int
+                             or a.dtype in _real_floating_dtypes and type(s) in [float, int]
+                             or a.dtype in _complex_floating_dtypes and type(s) in [complex, float, int]
+                        )):
+                        if a.dtype in _integer_dtypes and s == BIG_INT:
+                            assert_raises(OverflowError, lambda: getattr(a, _op)(s))
+                        else:
+                            # Only test for no error
+                            with suppress_warnings() as sup:
+                                # ignore warnings from pow(BIG_INT)
+                                sup.filter(RuntimeWarning,
+                                           "invalid value encountered in power")
+                                getattr(a, _op)(s)
+                    else:
+                        assert_raises(TypeError, lambda: getattr(a, _op)(s))
+
+                # Test array op array.
+                for _op in ops:
+                    for x in _array_vals():
+                        for y in _array_vals():
+                            # See the promotion table in NEP 47 or the array
+                            # API spec page on type promotion. Mixed kind
+                            # promotion is not defined.
+                            if (x.dtype == uint64 and y.dtype in [int8, int16, int32, int64]
+                                or y.dtype == uint64 and x.dtype in [int8, int16, int32, int64]
+                                or x.dtype in _integer_dtypes and y.dtype not in _integer_dtypes
+                                or y.dtype in _integer_dtypes and x.dtype not in _integer_dtypes
+                                or x.dtype in _boolean_dtypes and y.dtype not in _boolean_dtypes
+                                or y.dtype in _boolean_dtypes and x.dtype not in _boolean_dtypes
+                                or x.dtype in _floating_dtypes and y.dtype not in _floating_dtypes
+                                or y.dtype in _floating_dtypes and x.dtype not in _floating_dtypes
+                                ):
+                                assert_raises(TypeError, lambda: getattr(x, _op)(y))
+                            # Ensure in-place operators only promote to the same dtype as the left operand.
+                            elif (
+                                _op.startswith("__i")
+                                and result_type(x.dtype, y.dtype) != x.dtype
+                            ):
+                                assert_raises(TypeError, lambda: getattr(x, _op)(y))
+                            # Ensure only those dtypes that are required for every operator are allowed.
+                            elif (dtypes == "all" and (x.dtype in _boolean_dtypes and y.dtype in _boolean_dtypes
+                                                      or x.dtype in _numeric_dtypes and y.dtype in _numeric_dtypes)
+                                or (dtypes == "real numeric" and x.dtype in _real_numeric_dtypes and y.dtype in _real_numeric_dtypes)
+                                or (dtypes == "numeric" and x.dtype in _numeric_dtypes and y.dtype in _numeric_dtypes)
+                                or dtypes == "integer" and x.dtype in _integer_dtypes and y.dtype in _integer_dtypes
+                                or dtypes == "integer_or_boolean" and (x.dtype in _integer_dtypes and y.dtype in _integer_dtypes
+                                                                       or x.dtype in _boolean_dtypes and y.dtype in _boolean_dtypes)
+                                or dtypes == "boolean" and x.dtype in _boolean_dtypes and y.dtype in _boolean_dtypes
+                                or dtypes == "floating" and x.dtype in _floating_dtypes and y.dtype in _floating_dtypes
+                            ):
+                                getattr(x, _op)(y)
+                            else:
+                                assert_raises(TypeError, lambda: getattr(x, _op)(y))
+
+    unary_op_dtypes = {
+        "__abs__": "numeric",
+        "__invert__": "integer_or_boolean",
+        "__neg__": "numeric",
+        "__pos__": "numeric",
+    }
+    for op, dtypes in unary_op_dtypes.items():
+        for a in _array_vals():
+            if (
+                dtypes == "numeric"
+                and a.dtype in _numeric_dtypes
+                or dtypes == "integer_or_boolean"
+                and a.dtype in _integer_or_boolean_dtypes
+            ):
+                # Only test for no error
+                getattr(a, op)()
+            else:
+                assert_raises(TypeError, lambda: getattr(a, op)())
+
+    # Finally, matmul() must be tested separately, because it works a bit
+    # different from the other operations.
+    def _matmul_array_vals():
+        for a in _array_vals():
+            yield a
+        for d in _all_dtypes:
+            yield ones((3, 4), dtype=d)
+            yield ones((4, 2), dtype=d)
+            yield ones((4, 4), dtype=d)
+
+    # Scalars always error
+    for _op in ["__matmul__", "__rmatmul__", "__imatmul__"]:
+        for s in [1, 1.0, False]:
+            for a in _matmul_array_vals():
+                if (type(s) in [float, int] and a.dtype in _floating_dtypes
+                    or type(s) == int and a.dtype in _integer_dtypes):
+                    # Type promotion is valid, but @ is not allowed on 0-D
+                    # inputs, so the error is a ValueError
+                    assert_raises(ValueError, lambda: getattr(a, _op)(s))
+                else:
+                    assert_raises(TypeError, lambda: getattr(a, _op)(s))
+
+    for x in _matmul_array_vals():
+        for y in _matmul_array_vals():
+            if (x.dtype == uint64 and y.dtype in [int8, int16, int32, int64]
+                or y.dtype == uint64 and x.dtype in [int8, int16, int32, int64]
+                or x.dtype in _integer_dtypes and y.dtype not in _integer_dtypes
+                or y.dtype in _integer_dtypes and x.dtype not in _integer_dtypes
+                or x.dtype in _floating_dtypes and y.dtype not in _floating_dtypes
+                or y.dtype in _floating_dtypes and x.dtype not in _floating_dtypes
+                or x.dtype in _boolean_dtypes
+                or y.dtype in _boolean_dtypes
+                ):
+                assert_raises(TypeError, lambda: x.__matmul__(y))
+                assert_raises(TypeError, lambda: y.__rmatmul__(x))
+                assert_raises(TypeError, lambda: x.__imatmul__(y))
+            elif x.shape == () or y.shape == () or x.shape[1] != y.shape[0]:
+                assert_raises(ValueError, lambda: x.__matmul__(y))
+                assert_raises(ValueError, lambda: y.__rmatmul__(x))
+                if result_type(x.dtype, y.dtype) != x.dtype:
+                    assert_raises(TypeError, lambda: x.__imatmul__(y))
+                else:
+                    assert_raises(ValueError, lambda: x.__imatmul__(y))
+            else:
+                x.__matmul__(y)
+                y.__rmatmul__(x)
+                if result_type(x.dtype, y.dtype) != x.dtype:
+                    assert_raises(TypeError, lambda: x.__imatmul__(y))
+                elif y.shape[0] != y.shape[1]:
+                    # This one fails because x @ y has a different shape from x
+                    assert_raises(ValueError, lambda: x.__imatmul__(y))
+                else:
+                    x.__imatmul__(y)
+
+
+def test_python_scalar_construtors():
+    b = asarray(False)
+    i = asarray(0)
+    f = asarray(0.0)
+    c = asarray(0j)
+
+    assert bool(b) == False
+    assert int(i) == 0
+    assert float(f) == 0.0
+    assert operator.index(i) == 0
+
+    # bool/int/float/complex should only be allowed on 0-D arrays.
+    assert_raises(TypeError, lambda: bool(asarray([False])))
+    assert_raises(TypeError, lambda: int(asarray([0])))
+    assert_raises(TypeError, lambda: float(asarray([0.0])))
+    assert_raises(TypeError, lambda: complex(asarray([0j])))
+    assert_raises(TypeError, lambda: operator.index(asarray([0])))
+
+    # bool should work on all types of arrays
+    assert bool(b) is bool(i) is bool(f) is bool(c) is False
+
+    # int should fail on complex arrays
+    assert int(b) == int(i) == int(f) == 0
+    assert_raises(TypeError, lambda: int(c))
+
+    # float should fail on complex arrays
+    assert float(b) == float(i) == float(f) == 0.0
+    assert_raises(TypeError, lambda: float(c))
+
+    # complex should work on all types of arrays
+    assert complex(b) == complex(i) == complex(f) == complex(c) == 0j
+
+    # index should only work on integer arrays
+    assert operator.index(i) == 0
+    assert_raises(TypeError, lambda: operator.index(b))
+    assert_raises(TypeError, lambda: operator.index(f))
+    assert_raises(TypeError, lambda: operator.index(c))
+
+
+def test_device_property():
+    a = ones((3, 4))
+    assert a.device == 'cpu'
+
+    assert all(equal(a.to_device('cpu'), a))
+    assert_raises(ValueError, lambda: a.to_device('gpu'))
+
+    assert all(equal(asarray(a, device='cpu'), a))
+    assert_raises(ValueError, lambda: asarray(a, device='gpu'))
+
+def test_array_properties():
+    a = ones((1, 2, 3))
+    b = ones((2, 3))
+    assert_raises(ValueError, lambda: a.T)
+
+    assert isinstance(b.T, Array)
+    assert b.T.shape == (3, 2)
+
+    assert isinstance(a.mT, Array)
+    assert a.mT.shape == (1, 3, 2)
+    assert isinstance(b.mT, Array)
+    assert b.mT.shape == (3, 2)
+
+def test___array__():
+    a = ones((2, 3), dtype=int16)
+    assert np.asarray(a) is a._array
+    b = np.asarray(a, dtype=np.float64)
+    assert np.all(np.equal(b, np.ones((2, 3), dtype=np.float64)))
+    assert b.dtype == np.float64
+
+def test_allow_newaxis():
+    a = ones(5)
+    indexed_a = a[None, :]
+    assert indexed_a.shape == (1, 5)
+
+def test_disallow_flat_indexing_with_newaxis():
+    a = ones((3, 3, 3))
+    with pytest.raises(IndexError):
+        a[None, 0, 0]
+
+def test_disallow_mask_with_newaxis():
+    a = ones((3, 3, 3))
+    with pytest.raises(IndexError):
+        a[None, asarray(True)]
+
+@pytest.mark.parametrize("shape", [(), (5,), (3, 3, 3)])
+@pytest.mark.parametrize("index", ["string", False, True])
+def test_error_on_invalid_index(shape, index):
+    a = ones(shape)
+    with pytest.raises(IndexError):
+        a[index]
+
+def test_mask_0d_array_without_errors():
+    a = ones(())
+    a[asarray(True)]
+
+@pytest.mark.parametrize(
+    "i", [slice(5), slice(5, 0), asarray(True), asarray([0, 1])]
+)
+def test_error_on_invalid_index_with_ellipsis(i):
+    a = ones((3, 3, 3))
+    with pytest.raises(IndexError):
+        a[..., i]
+    with pytest.raises(IndexError):
+        a[i, ...]
+
+def test_array_keys_use_private_array():
+    """
+    Indexing operations convert array keys before indexing the internal array
+
+    Fails when array_api array keys are not converted into NumPy-proper arrays
+    in __getitem__(). This is achieved by passing array_api arrays with 0-sized
+    dimensions, which NumPy-proper treats erroneously - not sure why!
+
+    TODO: Find and use appropriate __setitem__() case.
+    """
+    a = ones((0, 0), dtype=bool_)
+    assert a[a].shape == (0,)
+
+    a = ones((0,), dtype=bool_)
+    key = ones((0, 0), dtype=bool_)
+    with pytest.raises(IndexError):
+        a[key]