# Source code for _pytest.python_api

    import math
    import pprint
    from collections.abc import Collection
    from collections.abc import Sized
    from decimal import Decimal
    from numbers import Complex
    from types import TracebackType
    from typing import Any
    from typing import Callable
    from typing import cast
    from typing import ContextManager
    from typing import List
    from typing import Mapping
    from typing import Optional
    from typing import Pattern
    from typing import Sequence
    from typing import Tuple
    from typing import Type
    from typing import TYPE_CHECKING
    from typing import TypeVar
    from typing import Union

    if TYPE_CHECKING:
        from numpy import ndarray

    import _pytest._code
    from _pytest.compat import final
    from _pytest.compat import STRING_TYPES
    from _pytest.compat import overload
    from _pytest.outcomes import fail

    def _non_numeric_type_error(value, at: Optional[str]) -> TypeError:
        at_str = f" at {at}" if at else ""
        return TypeError(
            "cannot make approximate comparisons to non-numeric values: {!r} {}".format(
                value, at_str
            )
        )

    def _compare_approx(
        full_object: object,
        message_data: Sequence[Tuple[str, str, str]],
        number_of_elements: int,
        different_ids: Sequence[object],
        max_abs_diff: float,
        max_rel_diff: float,
    ) -> List[str]:
        message_list = list(message_data)
        message_list.insert(0, ("Index", "Obtained", "Expected"))
        max_sizes = [0, 0, 0]
        for index, obtained, expected in message_list:
            max_sizes[0] = max(max_sizes[0], len(index))
            max_sizes[1] = max(max_sizes[1], len(obtained))
            max_sizes[2] = max(max_sizes[2], len(expected))
        explanation = [
            f"comparison failed. Mismatched elements: {len(different_ids)} / {number_of_elements}:",
            f"Max absolute difference: {max_abs_diff}",
            f"Max relative difference: {max_rel_diff}",
        ] + [
            f"{indexes:<{max_sizes[0]}} | {obtained:<{max_sizes[1]}} | {expected:<{max_sizes[2]}}"
            for indexes, obtained, expected in message_list
        ]
        return explanation

    # builtin pytest.approx helper

    class ApproxBase:
        """Provide shared utilities for making approximate comparisons between
        numbers or sequences of numbers."""

        # Tell numpy to use our `__eq__` operator instead of its.
        __array_ufunc__ = None
        __array_priority__ = 100

        def __init__(self, expected, rel=None, abs=None, nan_ok: bool = False) -> None:
            __tracebackhide__ = True
            self.expected = expected
            self.abs = abs
            self.rel = rel
            self.nan_ok = nan_ok
            self._check_type()

        def __repr__(self) -> str:
            raise NotImplementedError

        def _repr_compare(self, other_side: Any) -> List[str]:
            return [
                "comparison failed",
                f"Obtained: {other_side}",
                f"Expected: {self}",
            ]

        def __eq__(self, actual) -> bool:
            return all(
                a == self._approx_scalar(x) for a, x in self._yield_comparisons(actual)
            )

        def __bool__(self):
            __tracebackhide__ = True
            raise AssertionError(
                "approx() is not supported in a boolean context.\nDid you mean: `assert a == approx(b)`?"
            )

        # Ignore type because of https://github.com/python/mypy/issues/4266.
        __hash__ = None  # type: ignore

        def __ne__(self, actual) -> bool:
            return not (actual == self)

        def _approx_scalar(self, x) -> "ApproxScalar":
            if isinstance(x, Decimal):
                return ApproxDecimal(x, rel=self.rel, abs=self.abs, nan_ok=self.nan_ok)
            return ApproxScalar(x, rel=self.rel, abs=self.abs, nan_ok=self.nan_ok)

        def _yield_comparisons(self, actual):
            """Yield all the pairs of numbers to be compared.

            This is used to implement the `__eq__` method.
            """
            raise NotImplementedError

        def _check_type(self) -> None:
            """Raise a TypeError if the expected value is not a valid type."""
            # This is only a concern if the expected value is a sequence.  In every
            # other case, the approx() function ensures that the expected value has
            # a numeric type.  For this reason, the default is to do nothing.  The
            # classes that deal with sequences should reimplement this method to
            # raise if there are any non-numeric elements in the sequence.

    def _recursive_sequence_map(f, x):
        """Recursively map a function over a sequence of arbitrary depth"""
        if isinstance(x, (list, tuple)):
            seq_type = type(x)
            return seq_type(_recursive_sequence_map(f, xi) for xi in x)
        else:
            return f(x)

    class ApproxNumpy(ApproxBase):
        """Perform approximate comparisons where the expected value is numpy array."""

        def __repr__(self) -> str:
            list_scalars = _recursive_sequence_map(
                self._approx_scalar, self.expected.tolist()
            )
            return f"approx({list_scalars!r})"

        def _repr_compare(self, other_side: "ndarray") -> List[str]:
            import itertools
            import math

            def get_value_from_nested_list(
                nested_list: List[Any], nd_index: Tuple[Any, ...]
            ) -> Any:
                """
                Helper function to get the value out of a nested list, given an n-dimensional index.
                This mimics numpy's indexing, but for raw nested python lists.
                """
                value: Any = nested_list
                for i in nd_index:
                    value = value[i]
                return value

            np_array_shape = self.expected.shape
            approx_side_as_seq = _recursive_sequence_map(
                self._approx_scalar, self.expected.tolist()
            )

            if np_array_shape != other_side.shape:
                return [
                    "Impossible to compare arrays with different shapes.",
                    f"Shapes: {np_array_shape} and {other_side.shape}",
                ]

            number_of_elements = self.expected.size
            max_abs_diff = -math.inf
            max_rel_diff = -math.inf
            different_ids = []
            for index in itertools.product(*(range(i) for i in np_array_shape)):
                approx_value = get_value_from_nested_list(approx_side_as_seq, index)
                other_value = get_value_from_nested_list(other_side, index)
                if approx_value != other_value:
                    abs_diff = abs(approx_value.expected - other_value)
                    max_abs_diff = max(max_abs_diff, abs_diff)
                    if other_value == 0.0:
                        max_rel_diff = math.inf
                    else:
                        max_rel_diff = max(max_rel_diff, abs_diff / abs(other_value))
                    different_ids.append(index)

            message_data = [
                (
                    str(index),
                    str(get_value_from_nested_list(other_side, index)),
                    str(get_value_from_nested_list(approx_side_as_seq, index)),
                )
                for index in different_ids
            ]
            return _compare_approx(
                self.expected,
                message_data,
                number_of_elements,
                different_ids,
                max_abs_diff,
                max_rel_diff,
            )

        def __eq__(self, actual) -> bool:
            import numpy as np

            # self.expected is supposed to always be an array here.

            if not np.isscalar(actual):
                try:
                    actual = np.asarray(actual)
                except Exception as e:
                    raise TypeError(f"cannot compare '{actual}' to numpy.ndarray") from e

            if not np.isscalar(actual) and actual.shape != self.expected.shape:
                return False

            return super().__eq__(actual)

        def _yield_comparisons(self, actual):
            import numpy as np

            # `actual` can either be a numpy array or a scalar, it is treated in
            # `__eq__` before being passed to `ApproxBase.__eq__`, which is the
            # only method that calls this one.

            if np.isscalar(actual):
                for i in np.ndindex(self.expected.shape):
                    yield actual, self.expected[i].item()
            else:
                for i in np.ndindex(self.expected.shape):
                    yield actual[i].item(), self.expected[i].item()

    class ApproxMapping(ApproxBase):
        """Perform approximate comparisons where the expected value is a mapping
        with numeric values (the keys can be anything)."""

        def __repr__(self) -> str:
            return "approx({!r})".format(
                {k: self._approx_scalar(v) for k, v in self.expected.items()}
            )

        def _repr_compare(self, other_side: Mapping[object, float]) -> List[str]:
            import math

            approx_side_as_map = {
                k: self._approx_scalar(v) for k, v in self.expected.items()
            }

            number_of_elements = len(approx_side_as_map)
            max_abs_diff = -math.inf
            max_rel_diff = -math.inf
            different_ids = []
            for (approx_key, approx_value), other_value in zip(
                approx_side_as_map.items(), other_side.values()
            ):
                if approx_value != other_value:
                    if approx_value.expected is not None and other_value is not None:
                        max_abs_diff = max(
                            max_abs_diff, abs(approx_value.expected - other_value)
                        )
                        if approx_value.expected == 0.0:
                            max_rel_diff = math.inf
                        else:
                            max_rel_diff = max(
                                max_rel_diff,
                                abs(
                                    (approx_value.expected - other_value)
                                    / approx_value.expected
                                ),
                            )
                    different_ids.append(approx_key)

            message_data = [
                (str(key), str(other_side[key]), str(approx_side_as_map[key]))
                for key in different_ids
            ]

            return _compare_approx(
                self.expected,
                message_data,
                number_of_elements,
                different_ids,
                max_abs_diff,
                max_rel_diff,
            )

        def __eq__(self, actual) -> bool:
            try:
                if set(actual.keys()) != set(self.expected.keys()):
                    return False
            except AttributeError:
                return False

            return super().__eq__(actual)

        def _yield_comparisons(self, actual):
            for k in self.expected.keys():
                yield actual[k], self.expected[k]

        def _check_type(self) -> None:
            __tracebackhide__ = True
            for key, value in self.expected.items():
                if isinstance(value, type(self.expected)):
                    msg = "pytest.approx() does not support nested dictionaries: key={!r} value={!r}\n  full mapping={}"
                    raise TypeError(msg.format(key, value, pprint.pformat(self.expected)))

    class ApproxSequenceLike(ApproxBase):
        """Perform approximate comparisons where the expected value is a sequence of numbers."""

        def __repr__(self) -> str:
            seq_type = type(self.expected)
            if seq_type not in (tuple, list):
                seq_type = list
            return "approx({!r})".format(
                seq_type(self._approx_scalar(x) for x in self.expected)
            )

        def _repr_compare(self, other_side: Sequence[float]) -> List[str]:
            import math

            if len(self.expected) != len(other_side):
                return [
                    "Impossible to compare lists with different sizes.",
                    f"Lengths: {len(self.expected)} and {len(other_side)}",
                ]

            approx_side_as_map = _recursive_sequence_map(self._approx_scalar, self.expected)

            number_of_elements = len(approx_side_as_map)
            max_abs_diff = -math.inf
            max_rel_diff = -math.inf
            different_ids = []
            for i, (approx_value, other_value) in enumerate(
                zip(approx_side_as_map, other_side)
            ):
                if approx_value != other_value:
                    abs_diff = abs(approx_value.expected - other_value)
                    max_abs_diff = max(max_abs_diff, abs_diff)
                    if other_value == 0.0:
                        max_rel_diff = math.inf
                    else:
                        max_rel_diff = max(max_rel_diff, abs_diff / abs(other_value))
                    different_ids.append(i)

            message_data = [
                (str(i), str(other_side[i]), str(approx_side_as_map[i]))
                for i in different_ids
            ]

            return _compare_approx(
                self.expected,
                message_data,
                number_of_elements,
                different_ids,
                max_abs_diff,
                max_rel_diff,
            )

        def __eq__(self, actual) -> bool:
            try:
                if len(actual) != len(self.expected):
                    return False
            except TypeError:
                return False
            return super().__eq__(actual)

        def _yield_comparisons(self, actual):
            return zip(actual, self.expected)

        def _check_type(self) -> None:
            __tracebackhide__ = True
            for index, x in enumerate(self.expected):
                if isinstance(x, type(self.expected)):
                    msg = "pytest.approx() does not support nested data structures: {!r} at index {}\n  full sequence: {}"
                    raise TypeError(msg.format(x, index, pprint.pformat(self.expected)))

    class ApproxScalar(ApproxBase):
        """Perform approximate comparisons where the expected value is a single number."""

        # Using Real should be better than this Union, but not possible yet:
        # https://github.com/python/typeshed/pull/3108
        DEFAULT_ABSOLUTE_TOLERANCE: Union[float, Decimal] = 1e-12
        DEFAULT_RELATIVE_TOLERANCE: Union[float, Decimal] = 1e-6

        def __repr__(self) -> str:
            """Return a string communicating both the expected value and the
            tolerance for the comparison being made.

            For example, ``1.0 ± 1e-6``, ``(3+4j) ± 5e-6 ∠ ±180°``.
            """
            # Don't show a tolerance for values that aren't compared using
            # tolerances, i.e. non-numerics and infinities. Need to call abs to
            # handle complex numbers, e.g. (inf + 1j).
            if (not isinstance(self.expected, (Complex, Decimal))) or math.isinf(
                abs(self.expected)  # type: ignore[arg-type]
            ):
                return str(self.expected)

            # If a sensible tolerance can't be calculated, self.tolerance will
            # raise a ValueError.  In this case, display '???'.
            try:
                vetted_tolerance = f"{self.tolerance:.1e}"
                if (
                    isinstance(self.expected, Complex)
                    and self.expected.imag
                    and not math.isinf(self.tolerance)
                ):
                    vetted_tolerance += " ∠ ±180°"
            except ValueError:
                vetted_tolerance = "???"

            return f"{self.expected} ± {vetted_tolerance}"

        def __eq__(self, actual) -> bool:
            """Return whether the given value is equal to the expected value
            within the pre-specified tolerance."""
            asarray = _as_numpy_array(actual)
            if asarray is not None:
                # Call ``__eq__()`` manually to prevent infinite-recursion with
                # numpy<1.13.  See #3748.
                return all(self.__eq__(a) for a in asarray.flat)

            # Short-circuit exact equality.
            if actual == self.expected:
                return True

            # If either type is non-numeric, fall back to strict equality.
            # NB: we need Complex, rather than just Number, to ensure that __abs__,
            # __sub__, and __float__ are defined.
            if not (
                isinstance(self.expected, (Complex, Decimal))
                and isinstance(actual, (Complex, Decimal))
            ):
                return False

            # Allow the user to control whether NaNs are considered equal to each
            # other or not.  The abs() calls are for compatibility with complex
            # numbers.
            if math.isnan(abs(self.expected)):  # type: ignore[arg-type]
                return self.nan_ok and math.isnan(abs(actual))  # type: ignore[arg-type]

            # Infinity shouldn't be approximately equal to anything but itself, but
            # if there's a relative tolerance, it will be infinite and infinity
            # will seem approximately equal to everything.  The equal-to-itself
            # case would have been short circuited above, so here we can just
            # return false if the expected value is infinite.  The abs() call is
            # for compatibility with complex numbers.
            if math.isinf(abs(self.expected)):  # type: ignore[arg-type]
                return False

            # Return true if the two numbers are within the tolerance.
            result: bool = abs(self.expected - actual) <= self.tolerance
            return result

        # Ignore type because of https://github.com/python/mypy/issues/4266.
        __hash__ = None  # type: ignore

        @property
        def tolerance(self):
            """Return the tolerance for the comparison.

            This could be either an absolute tolerance or a relative tolerance,
            depending on what the user specified or which would be larger.
            """

            def set_default(x, default):
                return x if x is not None else default

            # Figure out what the absolute tolerance should be.  ``self.abs`` is
            # either None or a value specified by the user.
            absolute_tolerance = set_default(self.abs, self.DEFAULT_ABSOLUTE_TOLERANCE)

            if absolute_tolerance < 0:
                raise ValueError(
                    f"absolute tolerance can't be negative: {absolute_tolerance}"
                )
            if math.isnan(absolute_tolerance):
                raise ValueError("absolute tolerance can't be NaN.")

            # If the user specified an absolute tolerance but not a relative one,
            # just return the absolute tolerance.
            if self.rel is None:
                if self.abs is not None:
                    return absolute_tolerance

            # Figure out what the relative tolerance should be.  ``self.rel`` is
            # either None or a value specified by the user.  This is done after
            # we've made sure the user didn't ask for an absolute tolerance only,
            # because we don't want to raise errors about the relative tolerance if
            # we aren't even going to use it.
            relative_tolerance = set_default(
                self.rel, self.DEFAULT_RELATIVE_TOLERANCE
            ) * abs(self.expected)

            if relative_tolerance < 0:
                raise ValueError(
                    f"relative tolerance can't be negative: {relative_tolerance}"
                )
            if math.isnan(relative_tolerance):
                raise ValueError("relative tolerance can't be NaN.")

            # Return the larger of the relative and absolute tolerances.
            return max(relative_tolerance, absolute_tolerance)

    class ApproxDecimal(ApproxScalar):
        """Perform approximate comparisons where the expected value is a Decimal."""

        DEFAULT_ABSOLUTE_TOLERANCE = Decimal("1e-12")
        DEFAULT_RELATIVE_TOLERANCE = Decimal("1e-6")

    def approx(expected, rel=None, abs=None, nan_ok: bool = False) -> ApproxBase:
        """Assert that two numbers (or two ordered sequences of numbers) are equal to each other
        within some tolerance.

        Due to the :doc:`python:tutorial/floatingpoint`, numbers that we
        would intuitively expect to be equal are not always so::

            >>> 0.1 + 0.2 == 0.3
            False

        This problem is commonly encountered when writing tests, e.g. when making
        sure that floating-point values are what you expect them to be.  One way to
        deal with this problem is to assert that two floating-point numbers are
        equal to within some appropriate tolerance::

            >>> abs((0.1 + 0.2) - 0.3) < 1e-6
            True

        However, comparisons like this are tedious to write and difficult to
        understand.  Furthermore, absolute comparisons like the one above are
        usually discouraged because there's no tolerance that works well for all
        situations.  ``1e-6`` is good for numbers around ``1``, but too small for
        very big numbers and too big for very small ones.  It's better to express
        the tolerance as a fraction of the expected value, but relative comparisons
        like that are even more difficult to write correctly and concisely.

        The ``approx`` class performs floating-point comparisons using a syntax
        that's as intuitive as possible::

            >>> from pytest import approx
            >>> 0.1 + 0.2 == approx(0.3)
            True

        The same syntax also works for ordered sequences of numbers::

            >>> (0.1 + 0.2, 0.2 + 0.4) == approx((0.3, 0.6))
            True

        ``numpy`` arrays::

            >>> import numpy as np                                                          # doctest: +SKIP
            >>> np.array([0.1, 0.2]) + np.array([0.2, 0.4]) == approx(np.array([0.3, 0.6])) # doctest: +SKIP
            True

        And for a ``numpy`` array against a scalar::

            >>> import numpy as np                                         # doctest: +SKIP
            >>> np.array([0.1, 0.2]) + np.array([0.2, 0.1]) == approx(0.3) # doctest: +SKIP
            True

        Only ordered sequences are supported, because ``approx`` needs
        to infer the relative position of the sequences without ambiguity. This means
        ``sets`` and other unordered sequences are not supported.

        Finally, dictionary *values* can also be compared::

            >>> {'a': 0.1 + 0.2, 'b': 0.2 + 0.4} == approx({'a': 0.3, 'b': 0.6})
            True

        The comparison will be true if both mappings have the same keys and their
        respective values match the expected tolerances.

        **Tolerances**

        By default, ``approx`` considers numbers within a relative tolerance of
        ``1e-6`` (i.e. one part in a million) of its expected value to be equal.
        This treatment would lead to surprising results if the expected value was
        ``0.0``, because nothing but ``0.0`` itself is relatively close to ``0.0``.
        To handle this case less surprisingly, ``approx`` also considers numbers
        within an absolute tolerance of ``1e-12`` of its expected value to be
        equal.  Infinity and NaN are special cases.  Infinity is only considered
        equal to itself, regardless of the relative tolerance.  NaN is not
        considered equal to anything by default, but you can make it be equal to
        itself by setting the ``nan_ok`` argument to True.  (This is meant to
        facilitate comparing arrays that use NaN to mean "no data".)

        Both the relative and absolute tolerances can be changed by passing
        arguments to the ``approx`` constructor::

            >>> 1.0001 == approx(1)
            False
            >>> 1.0001 == approx(1, rel=1e-3)
            True
            >>> 1.0001 == approx(1, abs=1e-3)
            True

        If you specify ``abs`` but not ``rel``, the comparison will not consider
        the relative tolerance at all.  In other words, two numbers that are within
        the default relative tolerance of ``1e-6`` will still be considered unequal
        if they exceed the specified absolute tolerance.  If you specify both
        ``abs`` and ``rel``, the numbers will be considered equal if either
        tolerance is met::

            >>> 1 + 1e-8 == approx(1)
            True
            >>> 1 + 1e-8 == approx(1, abs=1e-12)
            False
            >>> 1 + 1e-8 == approx(1, rel=1e-6, abs=1e-12)
            True

        You can also use ``approx`` to compare nonnumeric types, or dicts and
        sequences containing nonnumeric types, in which case it falls back to
        strict equality. This can be useful for comparing dicts and sequences that
        can contain optional values::

            >>> {"required": 1.0000005, "optional": None} == approx({"required": 1, "optional": None})
            True
            >>> [None, 1.0000005] == approx([None,1])
            True
            >>> ["foo", 1.0000005] == approx([None,1])
            False

        If you're thinking about using ``approx``, then you might want to know how
        it compares to other good ways of comparing floating-point numbers.  All of
        these algorithms are based on relative and absolute tolerances and should
        agree for the most part, but they do have meaningful differences:

        - ``math.isclose(a, b, rel_tol=1e-9, abs_tol=0.0)``:  True if the relative
          tolerance is met w.r.t. either ``a`` or ``b`` or if the absolute
          tolerance is met.  Because the relative tolerance is calculated w.r.t.
          both ``a`` and ``b``, this test is symmetric (i.e.  neither ``a`` nor
          ``b`` is a "reference value").  You have to specify an absolute tolerance
          if you want to compare to ``0.0`` because there is no tolerance by
          default.  More information: :py:func:`math.isclose`.

        - ``numpy.isclose(a, b, rtol=1e-5, atol=1e-8)``: True if the difference
          between ``a`` and ``b`` is less that the sum of the relative tolerance
          w.r.t. ``b`` and the absolute tolerance.  Because the relative tolerance
          is only calculated w.r.t. ``b``, this test is asymmetric and you can
          think of ``b`` as the reference value.  Support for comparing sequences
          is provided by :py:func:`numpy.allclose`.  More information:
          :std:doc:`numpy:reference/generated/numpy.isclose`.

        - ``unittest.TestCase.assertAlmostEqual(a, b)``: True if ``a`` and ``b``
          are within an absolute tolerance of ``1e-7``.  No relative tolerance is
          considered , so this function is not appropriate for very large or very
          small numbers.  Also, it's only available in subclasses of ``unittest.TestCase``
          and it's ugly because it doesn't follow PEP8.  More information:
          :py:meth:`unittest.TestCase.assertAlmostEqual`.

        - ``a == pytest.approx(b, rel=1e-6, abs=1e-12)``: True if the relative
          tolerance is met w.r.t. ``b`` or if the absolute tolerance is met.
          Because the relative tolerance is only calculated w.r.t. ``b``, this test
          is asymmetric and you can think of ``b`` as the reference value.  In the
          special case that you explicitly specify an absolute tolerance but not a
          relative tolerance, only the absolute tolerance is considered.

        .. note::

            ``approx`` can handle numpy arrays, but we recommend the
            specialised test helpers in :std:doc:`numpy:reference/routines.testing`
            if you need support for comparisons, NaNs, or ULP-based tolerances.

            To match strings using regex, you can use
            `Matches <https://github.com/asottile/re-assert#re_assertmatchespattern-str-args-kwargs>`_
            from the
            `re_assert package <https://github.com/asottile/re-assert>`_.

        .. warning::

           .. versionchanged:: 3.2

           In order to avoid inconsistent behavior, :py:exc:`TypeError` is
           raised for ``>``, ``>=``, ``<`` and ``<=`` comparisons.
           The example below illustrates the problem::

               assert approx(0.1) > 0.1 + 1e-10  # calls approx(0.1).__gt__(0.1 + 1e-10)
               assert 0.1 + 1e-10 > approx(0.1)  # calls approx(0.1).__lt__(0.1 + 1e-10)

           In the second example one expects ``approx(0.1).__le__(0.1 + 1e-10)``
           to be called. But instead, ``approx(0.1).__lt__(0.1 + 1e-10)`` is used to
           comparison. This is because the call hierarchy of rich comparisons
           follows a fixed behavior. More information: :py:meth:`object.__ge__`

        .. versionchanged:: 3.7.1
           ``approx`` raises ``TypeError`` when it encounters a dict value or
           sequence element of nonnumeric type.

        .. versionchanged:: 6.1.0
           ``approx`` falls back to strict equality for nonnumeric types instead
           of raising ``TypeError``.
        """

        # Delegate the comparison to a class that knows how to deal with the type
        # of the expected value (e.g. int, float, list, dict, numpy.array, etc).
        #
        # The primary responsibility of these classes is to implement ``__eq__()``
        # and ``__repr__()``.  The former is used to actually check if some
        # "actual" value is equivalent to the given expected value within the
        # allowed tolerance.  The latter is used to show the user the expected
        # value and tolerance, in the case that a test failed.
        #
        # The actual logic for making approximate comparisons can be found in
        # ApproxScalar, which is used to compare individual numbers.  All of the
        # other Approx classes eventually delegate to this class.  The ApproxBase
        # class provides some convenient methods and overloads, but isn't really
        # essential.

        __tracebackhide__ = True

        if isinstance(expected, Decimal):
            cls: Type[ApproxBase] = ApproxDecimal
        elif isinstance(expected, Mapping):
            cls = ApproxMapping
        elif _is_numpy_array(expected):
            expected = _as_numpy_array(expected)
            cls = ApproxNumpy
        elif (
            hasattr(expected, "__getitem__")
            and isinstance(expected, Sized)
            # Type ignored because the error is wrong -- not unreachable.
            and not isinstance(expected, STRING_TYPES)  # type: ignore[unreachable]
        ):
            cls = ApproxSequenceLike
        elif (
            isinstance(expected, Collection)
            # Type ignored because the error is wrong -- not unreachable.
            and not isinstance(expected, STRING_TYPES)  # type: ignore[unreachable]
        ):
            msg = f"pytest.approx() only supports ordered sequences, but got: {repr(expected)}"
            raise TypeError(msg)
        else:
            cls = ApproxScalar

        return cls(expected, rel, abs, nan_ok)

    def _is_numpy_array(obj: object) -> bool:
        """
        Return true if the given object is implicitly convertible to ndarray,
        and numpy is already imported.
        """
        return _as_numpy_array(obj) is not None

    def _as_numpy_array(obj: object) -> Optional["ndarray"]:
        """
        Return an ndarray if the given object is implicitly convertible to ndarray,
        and numpy is already imported, otherwise None.
        """
        import sys

        np: Any = sys.modules.get("numpy")
        if np is not None:
            # avoid infinite recursion on numpy scalars, which have __array__
            if np.isscalar(obj):
                return None
            elif isinstance(obj, np.ndarray):
                return obj
            elif hasattr(obj, "__array__") or hasattr("obj", "__array_interface__"):
                return np.asarray(obj)
        return None

    # builtin pytest.raises helper

    E = TypeVar("E", bound=BaseException)

    @overload
    def raises(
        expected_exception: Union[Type[E], Tuple[Type[E], ...]],
        *,
        match: Optional[Union[str, Pattern[str]]] = ...,
    ) -> "RaisesContext[E]":
        ...

    @overload
    def raises(  # noqa: F811
        expected_exception: Union[Type[E], Tuple[Type[E], ...]],
        func: Callable[..., Any],
        *args: Any,
        **kwargs: Any,
    ) -> _pytest._code.ExceptionInfo[E]:
        ...

    def raises(  # noqa: F811
        expected_exception: Union[Type[E], Tuple[Type[E], ...]], *args: Any, **kwargs: Any
    ) -> Union["RaisesContext[E]", _pytest._code.ExceptionInfo[E]]:
        r"""Assert that a code block/function call raises an exception.

        :param typing.Type[E] | typing.Tuple[typing.Type[E], ...] expected_exception:
            The expected exception type, or a tuple if one of multiple possible
            exception types are expected.
        :kwparam str | typing.Pattern[str] | None match:
            If specified, a string containing a regular expression,
            or a regular expression object, that is tested against the string
            representation of the exception using :func:`re.search`.

            To match a literal string that may contain :ref:`special characters
            <re-syntax>`, the pattern can first be escaped with :func:`re.escape`.

            (This is only used when :py:func:`pytest.raises` is used as a context manager,
            and passed through to the function otherwise.
            When using :py:func:`pytest.raises` as a function, you can use:
            ``pytest.raises(Exc, func, match="passed on").match("my pattern")``.)

        .. currentmodule:: _pytest._code

        Use ``pytest.raises`` as a context manager, which will capture the exception of the given
        type::

            >>> import pytest
            >>> with pytest.raises(ZeroDivisionError):
            ...    1/0

        If the code block does not raise the expected exception (``ZeroDivisionError`` in the example
        above), or no exception at all, the check will fail instead.

        You can also use the keyword argument ``match`` to assert that the
        exception matches a text or regex::

            >>> with pytest.raises(ValueError, match='must be 0 or None'):
            ...     raise ValueError("value must be 0 or None")

            >>> with pytest.raises(ValueError, match=r'must be \d+$'):
            ...     raise ValueError("value must be 42")

        The context manager produces an :class:`ExceptionInfo` object which can be used to inspect the
        details of the captured exception::

            >>> with pytest.raises(ValueError) as exc_info:
            ...     raise ValueError("value must be 42")
            >>> assert exc_info.type is ValueError
            >>> assert exc_info.value.args[0] == "value must be 42"

        .. note::

           When using ``pytest.raises`` as a context manager, it's worthwhile to
           note that normal context manager rules apply and that the exception
           raised *must* be the final line in the scope of the context manager.
           Lines of code after that, within the scope of the context manager will
           not be executed. For example::

               >>> value = 15
               >>> with pytest.raises(ValueError) as exc_info:
               ...     if value > 10:
               ...         raise ValueError("value must be <= 10")
               ...     assert exc_info.type is ValueError  # this will not execute

           Instead, the following approach must be taken (note the difference in
           scope)::

               >>> with pytest.raises(ValueError) as exc_info:
               ...     if value > 10:
               ...         raise ValueError("value must be <= 10")
               ...
               >>> assert exc_info.type is ValueError

        **Using with** ``pytest.mark.parametrize``

        When using :ref:`pytest.mark.parametrize ref`
        it is possible to parametrize tests such that
        some runs raise an exception and others do not.

        See :ref:`parametrizing_conditional_raising` for an example.

        **Legacy form**

        It is possible to specify a callable by passing a to-be-called lambda::

            >>> raises(ZeroDivisionError, lambda: 1/0)
            <ExceptionInfo ...>

        or you can specify an arbitrary callable with arguments::

            >>> def f(x): return 1/x
            ...
            >>> raises(ZeroDivisionError, f, 0)
            <ExceptionInfo ...>
            >>> raises(ZeroDivisionError, f, x=0)
            <ExceptionInfo ...>

        The form above is fully supported but discouraged for new code because the
        context manager form is regarded as more readable and less error-prone.

        .. note::
            Similar to caught exception objects in Python, explicitly clearing
            local references to returned ``ExceptionInfo`` objects can
            help the Python interpreter speed up its garbage collection.

            Clearing those references breaks a reference cycle
            (``ExceptionInfo`` --> caught exception --> frame stack raising
            the exception --> current frame stack --> local variables -->
            ``ExceptionInfo``) which makes Python keep all objects referenced
            from that cycle (including all local variables in the current
            frame) alive until the next cyclic garbage collection run.
            More detailed information can be found in the official Python
            documentation for :ref:`the try statement <python:try>`.
        """
        __tracebackhide__ = True

        if not expected_exception:
            raise ValueError(
                f"Expected an exception type or a tuple of exception types, but got `{expected_exception!r}`. "
                f"Raising exceptions is already understood as failing the test, so you don't need "
                f"any special code to say 'this should never raise an exception'."
            )
        if isinstance(expected_exception, type):
            expected_exceptions: Tuple[Type[E], ...] = (expected_exception,)
        else:
            expected_exceptions = expected_exception
        for exc in expected_exceptions:
            if not isinstance(exc, type) or not issubclass(exc, BaseException):
                msg = "expected exception must be a BaseException type, not {}"  # type: ignore[unreachable]
                not_a = exc.__name__ if isinstance(exc, type) else type(exc).__name__
                raise TypeError(msg.format(not_a))

        message = f"DID NOT RAISE {expected_exception}"

        if not args:
            match: Optional[Union[str, Pattern[str]]] = kwargs.pop("match", None)
            if kwargs:
                msg = "Unexpected keyword arguments passed to pytest.raises: "
                msg += ", ".join(sorted(kwargs))
                msg += "\nUse context-manager form instead?"
                raise TypeError(msg)
            return RaisesContext(expected_exception, message, match)
        else:
            func = args[0]
            if not callable(func):
                raise TypeError(f"{func!r} object (type: {type(func)}) must be callable")
            try:
                func(*args[1:], **kwargs)
            except expected_exception as e:
                return _pytest._code.ExceptionInfo.from_exception(e)
        fail(message)

    # This doesn't work with mypy for now. Use fail.Exception instead.
    raises.Exception = fail.Exception  # type: ignore

    @final
    class RaisesContext(ContextManager[_pytest._code.ExceptionInfo[E]]):
        def __init__(
            self,
            expected_exception: Union[Type[E], Tuple[Type[E], ...]],
            message: str,
            match_expr: Optional[Union[str, Pattern[str]]] = None,
        ) -> None:
            self.expected_exception = expected_exception
            self.message = message
            self.match_expr = match_expr
            self.excinfo: Optional[_pytest._code.ExceptionInfo[E]] = None

        def __enter__(self) -> _pytest._code.ExceptionInfo[E]:
            self.excinfo = _pytest._code.ExceptionInfo.for_later()
            return self.excinfo

        def __exit__(
            self,
            exc_type: Optional[Type[BaseException]],
            exc_val: Optional[BaseException],
            exc_tb: Optional[TracebackType],
        ) -> bool:
            __tracebackhide__ = True
            if exc_type is None:
                fail(self.message)
            assert self.excinfo is not None
            if not issubclass(exc_type, self.expected_exception):
                return False
            # Cast to narrow the exception type now that it's verified.
            exc_info = cast(Tuple[Type[E], E, TracebackType], (exc_type, exc_val, exc_tb))
            self.excinfo.fill_unfilled(exc_info)
            if self.match_expr is not None:
                self.excinfo.match(self.match_expr)
            return True