statistics.covariance overflows when the final covariance is representable

[augusto-rehfeldt]

Bug report

Bug description:

Documented behaviour: "Return the sample covariance of two inputs x and y." — statistics.covariance docstring.

Expected: A finite sample covariance approximately equal to 6.533333333333333e+307 for the reproduced input.

Actual: statistics.covariance(x, x) returns inf.

import statistics, math
from fractions import Fraction

x = [-7e153, -7e153, 7e153, 7e153]
y = x.copy()
if len(x) != len(y) or len(x) < 2 or not all(map(math.isfinite, x + y)):
    print("REFUTATION REJECTED: invalid input")
else:
    n = len(x)
    u, v = list(map(Fraction, x)), list(map(Fraction, y))
    expected = float((sum(a*b for a, b in zip(u, v)) - sum(u)*sum(v)/n)/(n-1))
    try:
        actual = statistics.covariance(x, y)
        broken = not math.isfinite(actual) or not math.isclose(actual, expected, rel_tol=1e-14)
    except Exception as e:
        actual, broken = repr(e), True
    if broken:
        print("REFUTATION CONFIRMED:", (x, y), "actual:", actual, "expected:", expected)
    else:
        print("REFUTATION REJECTED: sample covariance agrees with exact reference")

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

REFUTATION CONFIRMED: ([-7e+153, -7e+153, 7e+153, 7e+153], [-7e+153, -7e+153, 7e+153, 7e+153]) actual: inf expected: 6.533333333333333e+307

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-20261003-185112-c4

CPython versions tested on:

3.14

Operating systems tested on:

Windows

[ZeroIntensity]

See #158748 (comment).