statistics.harmonic_mean returns zero for identical positive subnormal floats

[augusto-rehfeldt]

Bug report

Bug description:

Documented behaviour: The harmonic_mean docstring states: "The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the data." For identical positive observations, this is the observation itself.

Expected: 1e-320

Actual: 0.0

import math
import statistics
from fractions import Fraction

data = [1e-320, 1e-320]
if len(data) < 2 or not all(math.isfinite(x) and x > 0 for x in data):
    print("REFUTATION REJECTED: invalid input")
else:
    expected = float(len(data) / sum(1 / Fraction(x) for x in data))
    actual = statistics.harmonic_mean(data)
    if actual != expected:
        print(f"REFUTATION CONFIRMED: input={data!r}, actual={actual!r}, expected={expected!r}")
    else:
        print("REFUTATION REJECTED: actual equals documented expectation")

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

REFUTATION CONFIRMED: input=[1e-320, 1e-320], actual=0.0, expected=1e-320

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/statistics-20261003-081656-c3

CPython versions tested on:

3.14

Operating systems tested on:

Windows

[ZeroIntensity]

See #158748 (comment).