random.vonmisesvariate raises ZeroDivisionError for large finite kappa

[augusto-rehfeldt]

Bug report

Bug description:

Documented behaviour: Random.vonmisesvariate docstring: "mu is the mean angle, expressed in radians between 0 and 2*pi, and kappa is the concentration parameter, which must be greater than or equal to zero." Random class docstring explicitly permits subclassing to "use a different basic generator of your own devising" by overriding random() and the state methods.

Expected: Return a finite circular sample without raising an exception.

Actual: ZeroDivisionError: division by zero

import math
import random

mu, kappa = 0.0, 1e20
values = (1.0 - 2**-53, 0.5, 0.5, 0.5)
input_ = dict(mu=mu, kappa=kappa, random_values=values)

class R(random.Random):
    def random(self):
        return next(self.values, 0.5)

valid = (math.isfinite(mu) and 0 <= mu <= math.tau
         and math.isfinite(kappa) and kappa >= 0
         and all(0 <= x < 1 for x in values))
if not valid:
    print("REFUTATION REJECTED:", "input violates documented domain", input_)
else:
    r = R()
    r.values = iter(values)
    expected = f"finite circular sample in [0, {2 * math.pi}] without an exception"
    try:
        actual = r.vonmisesvariate(mu, kappa)
        broken = not (math.isfinite(actual) and 0 <= actual <= 2 * math.pi)
    except Exception as e:
        actual = (type(e).__name__, str(e))
        broken = True
    if broken:
        print("REFUTATION CONFIRMED:", input_, "actual:", actual, "expected:", expected)
    else:
        print("REFUTATION REJECTED:", "call returned a valid sample", actual)

Output on Python 3.14.6 (Windows-11-10.0.26220-SP0), standard library random:

REFUTATION CONFIRMED: {'mu': 0.0, 'kappa': 1e+20, 'random_values': (0.9999999999999999, 0.5, 0.5, 0.5)} actual: ('ZeroDivisionError', 'division by zero') expected: finite circular sample in [0, 6.283185307179586] without an exception

This report was found and written by an automated property-testing tool I run (bugforge). The reproducer above was executed and its output is pasted unedited; no person reviewed the report before it was filed. The search script is in https://github.com/augusto-rehfeldt/bugforge-results/tree/main/random-20261003-034345-c2

CPython versions tested on:

3.14

Operating systems tested on:

Windows

[ZeroIntensity]

See #158748 (comment).