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# Source code for torch.distributions.gumbel

    import math
    from numbers import Number

    import torch
    from torch.distributions import constraints
    from torch.distributions.transformed_distribution import TransformedDistribution
    from torch.distributions.transforms import AffineTransform, ExpTransform
    from torch.distributions.uniform import Uniform
    from torch.distributions.utils import broadcast_all, euler_constant

    __all__ = ["Gumbel"]

    class Gumbel(TransformedDistribution):
        r"""
        Samples from a Gumbel Distribution.

        Examples::

            >>> # xdoctest: +IGNORE_WANT("non-deterinistic")
            >>> m = Gumbel(torch.tensor([1.0]), torch.tensor([2.0]))
            >>> m.sample()  # sample from Gumbel distribution with loc=1, scale=2
            tensor([ 1.0124])

        Args:
            loc (float or Tensor): Location parameter of the distribution
            scale (float or Tensor): Scale parameter of the distribution
        """
        arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
        support = constraints.real

        def __init__(self, loc, scale, validate_args=None):
            self.loc, self.scale = broadcast_all(loc, scale)
            finfo = torch.finfo(self.loc.dtype)
            if isinstance(loc, Number) and isinstance(scale, Number):
                base_dist = Uniform(finfo.tiny, 1 - finfo.eps, validate_args=validate_args)
            else:
                base_dist = Uniform(
                    torch.full_like(self.loc, finfo.tiny),
                    torch.full_like(self.loc, 1 - finfo.eps),
                    validate_args=validate_args,
                )
            transforms = [
                ExpTransform().inv,
                AffineTransform(loc=0, scale=-torch.ones_like(self.scale)),
                ExpTransform().inv,
                AffineTransform(loc=loc, scale=-self.scale),
            ]
            super().__init__(base_dist, transforms, validate_args=validate_args)

        def expand(self, batch_shape, _instance=None):
            new = self._get_checked_instance(Gumbel, _instance)
            new.loc = self.loc.expand(batch_shape)
            new.scale = self.scale.expand(batch_shape)
            return super().expand(batch_shape, _instance=new)

        # Explicitly defining the log probability function for Gumbel due to precision issues
        def log_prob(self, value):
            if self._validate_args:
                self._validate_sample(value)
            y = (self.loc - value) / self.scale
            return (y - y.exp()) - self.scale.log()

        @property
        def mean(self):
            return self.loc + self.scale * euler_constant

        @property
        def mode(self):
            return self.loc

        @property
        def stddev(self):
            return (math.pi / math.sqrt(6)) * self.scale

        @property
        def variance(self):
            return self.stddev.pow(2)

        def entropy(self):
            return self.scale.log() + (1 + euler_constant)

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