Bug report

Bug description:

random.binomialvariate() can raise ZeroDivisionError when random() returns 0.0 in one of the paths.

            # Lib/random.py
            u = random()
            u -= 0.5
            us = 0.5 - _fabs(u)
            k = _floor((2.0 * a / us + b) * u + c) # <-- division by `us` which can be zero

Repro with a mock that forces random() to return zero:

import random
from unittest.mock import patch
with patch.object(random.Random, "random", side_effect=[0.0, 0.5, 0.5]):
    random.binomialvariate(100, 0.25)
#    k = _floor((2.0 * a / us + b) * u + c)
#                ~~~~~~~~^~~~
# ZeroDivisionError: division by zero

From what I've seen, it looks like the chance of random returning zero is about 1 in 2^53... But still, zero is a valid result and custom generators may return it more often.

CPython versions tested on:

3.12, 3.13, 3.14, 3.15

Operating systems tested on:

macOS

Linked PRs

gh-154001: Avoid division by zero in binomialvariate #154004
[3.15] gh-154001: Avoid division by zero in binomialvariate (GH-154004) #154050
[3.14] gh-154001: Avoid division by zero in binomialvariate (GH-154004) #154051
[3.13] gh-154001: Avoid division by zero in binomialvariate (GH-154004) #154052