# Source code for hypothesis.strategies._internal.numbers

    # This file is part of Hypothesis, which may be found at
    # https://github.com/HypothesisWorks/hypothesis/
    #
    # Copyright the Hypothesis Authors.
    # Individual contributors are listed in AUTHORS.rst and the git log.
    #
    # This Source Code Form is subject to the terms of the Mozilla Public License,
    # v. 2.0. If a copy of the MPL was not distributed with this file, You can
    # obtain one at https://mozilla.org/MPL/2.0/.

    import math
    from decimal import Decimal
    from fractions import Fraction
    from typing import Literal, Optional, Union

    from hypothesis.control import reject
    from hypothesis.errors import InvalidArgument
    from hypothesis.internal.filtering import (
        get_float_predicate_bounds,
        get_integer_predicate_bounds,
    )
    from hypothesis.internal.floats import (
        SMALLEST_SUBNORMAL,
        float_of,
        float_to_int,
        int_to_float,
        is_negative,
        next_down,
        next_down_normal,
        next_up,
        next_up_normal,
        width_smallest_normals,
    )
    from hypothesis.internal.validation import (
        check_type,
        check_valid_bound,
        check_valid_interval,
    )
    from hypothesis.strategies._internal.misc import nothing
    from hypothesis.strategies._internal.strategies import (
        SampledFromStrategy,
        SearchStrategy,
    )
    from hypothesis.strategies._internal.utils import cacheable, defines_strategy

    # See https://github.com/python/mypy/issues/3186 - numbers.Real is wrong!
    Real = Union[int, float, Fraction, Decimal]

    class IntegersStrategy(SearchStrategy[int]):
        def __init__(self, start: Optional[int], end: Optional[int]) -> None:
            assert isinstance(start, int) or start is None
            assert isinstance(end, int) or end is None
            assert start is None or end is None or start <= end
            self.start = start
            self.end = end

        def __repr__(self):
            if self.start is None and self.end is None:
                return "integers()"
            if self.end is None:
                return f"integers(min_value={self.start})"
            if self.start is None:
                return f"integers(max_value={self.end})"
            return f"integers({self.start}, {self.end})"

        def do_draw(self, data):
            # For bounded integers, make the bounds and near-bounds more likely.
            weights = None
            if (
                self.end is not None
                and self.start is not None
                and self.end - self.start > 127
            ):
                weights = {
                    self.start: (2 / 128),
                    self.start + 1: (1 / 128),
                    self.end - 1: (1 / 128),
                    self.end: (2 / 128),
                }

            return data.draw_integer(
                min_value=self.start, max_value=self.end, weights=weights
            )

        def filter(self, condition):
            if condition is math.isfinite:
                return self
            if condition in [math.isinf, math.isnan]:
                return nothing()
            kwargs, pred = get_integer_predicate_bounds(condition)

            start, end = self.start, self.end
            if "min_value" in kwargs:
                start = max(kwargs["min_value"], -math.inf if start is None else start)
            if "max_value" in kwargs:
                end = min(kwargs["max_value"], math.inf if end is None else end)

            if start != self.start or end != self.end:
                if start is not None and end is not None and start > end:
                    return nothing()
                self = type(self)(start, end)
            if pred is None:
                return self
            return super().filter(pred)

    @cacheable
    @defines_strategy(force_reusable_values=True)
    def integers(
        min_value: Optional[int] = None,
        max_value: Optional[int] = None,
    ) -> SearchStrategy[int]:
        """Returns a strategy which generates integers.

        If min_value is not None then all values will be >= min_value. If
        max_value is not None then all values will be <= max_value

        Examples from this strategy will shrink towards zero, and negative values
        will also shrink towards positive (i.e. -n may be replaced by +n).
        """
        check_valid_bound(min_value, "min_value")
        check_valid_bound(max_value, "max_value")
        check_valid_interval(min_value, max_value, "min_value", "max_value")

        if min_value is not None:
            if min_value != int(min_value):
                raise InvalidArgument(
                    "min_value=%r of type %r cannot be exactly represented as an integer."
                    % (min_value, type(min_value))
                )
            min_value = int(min_value)
        if max_value is not None:
            if max_value != int(max_value):
                raise InvalidArgument(
                    "max_value=%r of type %r cannot be exactly represented as an integer."
                    % (max_value, type(max_value))
                )
            max_value = int(max_value)

        return IntegersStrategy(min_value, max_value)

    class FloatStrategy(SearchStrategy):
        """A strategy for floating point numbers."""

        def __init__(
            self,
            *,
            min_value: float,
            max_value: float,
            allow_nan: bool,
            # The smallest nonzero number we can represent is usually a subnormal, but may
            # be the smallest normal if we're running in unsafe denormals-are-zero mode.
            # While that's usually an explicit error, we do need to handle the case where
            # the user passes allow_subnormal=False.
            smallest_nonzero_magnitude: float = SMALLEST_SUBNORMAL,
        ):
            super().__init__()
            assert isinstance(allow_nan, bool)
            assert smallest_nonzero_magnitude >= 0.0, "programmer error if this is negative"
            if smallest_nonzero_magnitude == 0.0:  # pragma: no cover
                raise FloatingPointError(
                    "Got allow_subnormal=True, but we can't represent subnormal floats "
                    "right now, in violation of the IEEE-754 floating-point "
                    "specification.  This is usually because something was compiled with "
                    "-ffast-math or a similar option, which sets global processor state.  "
                    "See https://simonbyrne.github.io/notes/fastmath/ for a more detailed "
                    "writeup - and good luck!"
                )
            self.min_value = min_value
            self.max_value = max_value
            self.allow_nan = allow_nan
            self.smallest_nonzero_magnitude = smallest_nonzero_magnitude

        def __repr__(self):
            return (
                f"{self.__class__.__name__}({self.min_value=}, {self.max_value=}, "
                f"{self.allow_nan=}, {self.smallest_nonzero_magnitude=})"
            ).replace("self.", "")

        def do_draw(self, data):
            return data.draw_float(
                min_value=self.min_value,
                max_value=self.max_value,
                allow_nan=self.allow_nan,
                smallest_nonzero_magnitude=self.smallest_nonzero_magnitude,
            )

        def filter(self, condition):
            # Handle a few specific weird cases.
            if condition is math.isfinite:
                return FloatStrategy(
                    min_value=max(self.min_value, next_up(float("-inf"))),
                    max_value=min(self.max_value, next_down(float("inf"))),
                    allow_nan=False,
                    smallest_nonzero_magnitude=self.smallest_nonzero_magnitude,
                )
            if condition is math.isinf:
                if permitted_infs := [
                    x
                    for x in (-math.inf, math.inf)
                    if self.min_value <= x <= self.max_value
                ]:
                    return SampledFromStrategy(permitted_infs)
                return nothing()
            if condition is math.isnan:
                if not self.allow_nan:
                    return nothing()
                return NanStrategy()

            kwargs, pred = get_float_predicate_bounds(condition)
            if not kwargs:
                return super().filter(pred)
            min_bound = max(kwargs.get("min_value", -math.inf), self.min_value)
            max_bound = min(kwargs.get("max_value", math.inf), self.max_value)

            # Adjustments for allow_subnormal=False, if any need to be made
            if -self.smallest_nonzero_magnitude < min_bound < 0:
                min_bound = -0.0
            elif 0 < min_bound < self.smallest_nonzero_magnitude:
                min_bound = self.smallest_nonzero_magnitude
            if -self.smallest_nonzero_magnitude < max_bound < 0:
                max_bound = -self.smallest_nonzero_magnitude
            elif 0 < max_bound < self.smallest_nonzero_magnitude:
                max_bound = 0.0

            if min_bound > max_bound:
                return nothing()
            if (
                min_bound > self.min_value
                or self.max_value > max_bound
                or (self.allow_nan and (-math.inf < min_bound or max_bound < math.inf))
            ):
                self = type(self)(
                    min_value=min_bound,
                    max_value=max_bound,
                    allow_nan=False,
                    smallest_nonzero_magnitude=self.smallest_nonzero_magnitude,
                )
            if pred is None:
                return self
            return super().filter(pred)

    @cacheable
    @defines_strategy(force_reusable_values=True)
    def floats(
        min_value: Optional[Real] = None,
        max_value: Optional[Real] = None,
        *,
        allow_nan: Optional[bool] = None,
        allow_infinity: Optional[bool] = None,
        allow_subnormal: Optional[bool] = None,
        width: Literal[16, 32, 64] = 64,
        exclude_min: bool = False,
        exclude_max: bool = False,
    ) -> SearchStrategy[float]:
        """Returns a strategy which generates floats.

        - If min_value is not None, all values will be ``>= min_value``
          (or ``> min_value`` if ``exclude_min``).
        - If max_value is not None, all values will be ``<= max_value``
          (or ``< max_value`` if ``exclude_max``).
        - If min_value or max_value is not None, it is an error to enable
          allow_nan.
        - If both min_value and max_value are not None, it is an error to enable
          allow_infinity.
        - If inferred values range does not include subnormal values, it is an error
          to enable allow_subnormal.

        Where not explicitly ruled out by the bounds,
        :wikipedia:`subnormals <Subnormal_number>`, infinities, and NaNs are possible
        values generated by this strategy.

        The width argument specifies the maximum number of bits of precision
        required to represent the generated float. Valid values are 16, 32, or 64.
        Passing ``width=32`` will still use the builtin 64-bit :class:`~python:float` class,
        but always for values which can be exactly represented as a 32-bit float.

        The exclude_min and exclude_max argument can be used to generate numbers
        from open or half-open intervals, by excluding the respective endpoints.
        Excluding either signed zero will also exclude the other.
        Attempting to exclude an endpoint which is None will raise an error;
        use ``allow_infinity=False`` to generate finite floats.  You can however
        use e.g. ``min_value=-math.inf, exclude_min=True`` to exclude only
        one infinite endpoint.

        Examples from this strategy have a complicated and hard to explain
        shrinking behaviour, but it tries to improve "human readability". Finite
        numbers will be preferred to infinity and infinity will be preferred to
        NaN.
        """
        check_type(bool, exclude_min, "exclude_min")
        check_type(bool, exclude_max, "exclude_max")

        if allow_nan is None:
            allow_nan = bool(min_value is None and max_value is None)
        elif allow_nan and (min_value is not None or max_value is not None):
            raise InvalidArgument(f"Cannot have {allow_nan=}, with min_value or max_value")

        if width not in (16, 32, 64):
            raise InvalidArgument(
                f"Got {width=}, but the only valid values "
                "are the integers 16, 32, and 64."
            )

        check_valid_bound(min_value, "min_value")
        check_valid_bound(max_value, "max_value")

        if math.copysign(1.0, -0.0) == 1.0:  # pragma: no cover
            raise FloatingPointError(
                "Your Python install can't represent -0.0, which is required by the "
                "IEEE-754 floating-point specification.  This is probably because it was "
                "compiled with an unsafe option like -ffast-math; for a more detailed "
                "explanation see https://simonbyrne.github.io/notes/fastmath/"
            )
        if allow_subnormal and next_up(0.0, width=width) == 0:  # pragma: no cover
            # Not worth having separate CI envs and dependencies just to cover this branch;
            # discussion in https://github.com/HypothesisWorks/hypothesis/issues/3092
            #
            # Erroring out here ensures that the database contents are interpreted
            # consistently - which matters for such a foundational strategy, even if it's
            # not always true for all user-composed strategies further up the stack.
            from _hypothesis_ftz_detector import identify_ftz_culprits

            try:
                ftz_pkg = identify_ftz_culprits()
            except Exception:
                ftz_pkg = None
            if ftz_pkg:
                ftz_msg = (
                    f"This seems to be because the `{ftz_pkg}` package was compiled with "
                    f"-ffast-math or a similar option, which sets global processor state "
                    f"- see https://simonbyrne.github.io/notes/fastmath/ for details.  "
                    f"If you don't know why {ftz_pkg} is installed, `pipdeptree -rp "
                    f"{ftz_pkg}` will show which packages depend on it."
                )
            else:
                ftz_msg = (
                    "This is usually because something was compiled with -ffast-math "
                    "or a similar option, which sets global processor state.  See "
                    "https://simonbyrne.github.io/notes/fastmath/ for a more detailed "
                    "writeup - and good luck!"
                )
            raise FloatingPointError(
                f"Got {allow_subnormal=}, but we can't represent "
                f"subnormal floats right now, in violation of the IEEE-754 floating-point "
                f"specification.  {ftz_msg}"
            )

        min_arg, max_arg = min_value, max_value
        if min_value is not None:
            min_value = float_of(min_value, width)
            assert isinstance(min_value, float)
        if max_value is not None:
            max_value = float_of(max_value, width)
            assert isinstance(max_value, float)

        if min_value != min_arg:
            raise InvalidArgument(
                f"min_value={min_arg!r} cannot be exactly represented as a float "
                f"of width {width} - use {min_value=} instead."
            )
        if max_value != max_arg:
            raise InvalidArgument(
                f"max_value={max_arg!r} cannot be exactly represented as a float "
                f"of width {width} - use {max_value=} instead."
            )

        if exclude_min and (min_value is None or min_value == math.inf):
            raise InvalidArgument(f"Cannot exclude {min_value=}")
        if exclude_max and (max_value is None or max_value == -math.inf):
            raise InvalidArgument(f"Cannot exclude {max_value=}")

        assumed_allow_subnormal = allow_subnormal is None or allow_subnormal
        if min_value is not None and (
            exclude_min or (min_arg is not None and min_value < min_arg)
        ):
            min_value = next_up_normal(
                min_value, width, allow_subnormal=assumed_allow_subnormal
            )
            if min_value == min_arg:
                assert min_value == min_arg == 0
                assert is_negative(min_arg)
                assert not is_negative(min_value)
                min_value = next_up_normal(
                    min_value, width, allow_subnormal=assumed_allow_subnormal
                )
            assert min_value > min_arg  # type: ignore
        if max_value is not None and (
            exclude_max or (max_arg is not None and max_value > max_arg)
        ):
            max_value = next_down_normal(
                max_value, width, allow_subnormal=assumed_allow_subnormal
            )
            if max_value == max_arg:
                assert max_value == max_arg == 0
                assert is_negative(max_value)
                assert not is_negative(max_arg)
                max_value = next_down_normal(
                    max_value, width, allow_subnormal=assumed_allow_subnormal
                )
            assert max_value < max_arg  # type: ignore

        if min_value == -math.inf:
            min_value = None
        if max_value == math.inf:
            max_value = None

        bad_zero_bounds = (
            min_value == max_value == 0
            and is_negative(max_value)
            and not is_negative(min_value)
        )
        if (
            min_value is not None
            and max_value is not None
            and (min_value > max_value or bad_zero_bounds)
        ):
            # This is a custom alternative to check_valid_interval, because we want
            # to include the bit-width and exclusion information in the message.
            msg = (
                "There are no %s-bit floating-point values between min_value=%r "
                "and max_value=%r" % (width, min_arg, max_arg)
            )
            if exclude_min or exclude_max:
                msg += f", {exclude_min=} and {exclude_max=}"
            raise InvalidArgument(msg)

        if allow_infinity is None:
            allow_infinity = bool(min_value is None or max_value is None)
        elif allow_infinity:
            if min_value is not None and max_value is not None:
                raise InvalidArgument(
                    f"Cannot have {allow_infinity=}, with both min_value and max_value"
                )
        elif min_value == math.inf:
            if min_arg == math.inf:
                raise InvalidArgument("allow_infinity=False excludes min_value=inf")
            raise InvalidArgument(
                f"exclude_min=True turns min_value={min_arg!r} into inf, "
                "but allow_infinity=False"
            )
        elif max_value == -math.inf:
            if max_arg == -math.inf:
                raise InvalidArgument("allow_infinity=False excludes max_value=-inf")
            raise InvalidArgument(
                f"exclude_max=True turns max_value={max_arg!r} into -inf, "
                "but allow_infinity=False"
            )

        smallest_normal = width_smallest_normals[width]
        if allow_subnormal is None:
            if min_value is not None and max_value is not None:
                if min_value == max_value:
                    allow_subnormal = -smallest_normal < min_value < smallest_normal
                else:
                    allow_subnormal = (
                        min_value < smallest_normal and max_value > -smallest_normal
                    )
            elif min_value is not None:
                allow_subnormal = min_value < smallest_normal
            elif max_value is not None:
                allow_subnormal = max_value > -smallest_normal
            else:
                allow_subnormal = True
        if allow_subnormal:
            if min_value is not None and min_value >= smallest_normal:
                raise InvalidArgument(
                    f"allow_subnormal=True, but minimum value {min_value} "
                    f"excludes values below float{width}'s "
                    f"smallest positive normal {smallest_normal}"
                )
            if max_value is not None and max_value <= -smallest_normal:
                raise InvalidArgument(
                    f"allow_subnormal=True, but maximum value {max_value} "
                    f"excludes values above float{width}'s "
                    f"smallest negative normal {-smallest_normal}"
                )

        if min_value is None:
            min_value = float("-inf")
        if max_value is None:
            max_value = float("inf")
        if not allow_infinity:
            min_value = max(min_value, next_up(float("-inf")))
            max_value = min(max_value, next_down(float("inf")))
        assert isinstance(min_value, float)
        assert isinstance(max_value, float)
        smallest_nonzero_magnitude = (
            SMALLEST_SUBNORMAL if allow_subnormal else smallest_normal
        )
        result: SearchStrategy = FloatStrategy(
            min_value=min_value,
            max_value=max_value,
            allow_nan=allow_nan,
            smallest_nonzero_magnitude=smallest_nonzero_magnitude,
        )

        if width < 64:

            def downcast(x):
                try:
                    return float_of(x, width)
                except OverflowError:  # pragma: no cover
                    reject()

            result = result.map(downcast)
        return result

    class NanStrategy(SearchStrategy):
        """Strategy for sampling the space of nan float values."""

        def do_draw(self, data):
            # Nans must have all exponent bits and the first mantissa bit set, so
            # we generate by taking 64 random bits and setting the required ones.
            sign_bit = int(data.draw_boolean()) << 63
            nan_bits = float_to_int(math.nan)
            mantissa_bits = data.draw_integer(0, 2**52 - 1)
            return int_to_float(sign_bit | nan_bits | mantissa_bits)