statistics.quantiles produces infinite cut points from finite inputs with representable results

[augusto-rehfeldt]

Bug report

Bug description:

Documented behaviour: The statistics.quantiles documentation states: "The cut points are linearly interpolated from the two nearest data points." For method='exclusive', it states: "The portion of the population falling below the i-th of m sorted data points is computed as i / (m + 1)." With two observations, these rules place them at probabilities 1/3 and 2/3 and determine the stated quartiles.

Expected: For a=6e307, approximately [-9e307, 0.0, 9e307], all finite.

Actual: [-inf, 0.0, inf]

import statistics
import math

a = 6e307
data = [-a, a]
if len(data) < 2 or not all(math.isfinite(x) for x in data):
    print("REFUTATION REJECTED: invalid input")
else:
    actual = statistics.quantiles(data, n=4, method="exclusive")
    # Interpolate/extrapolate between (-a, 1/3) and (a, 2/3).
    expected = [a * (3 * i / 2 - 3) for i in range(1, 4)]
    if len(actual) != 3 or any(
        not math.isfinite(x) or not math.isclose(x, y, rel_tol=1e-14, abs_tol=0.0)
        for x, y in zip(actual, expected)
    ):
        print("REFUTATION CONFIRMED:", data, "actual:", actual, "expected:", expected)
    else:
        print("REFUTATION REJECTED: actual matches documented expectation")

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

REFUTATION CONFIRMED: [-6e+307, 6e+307] actual: [-inf, 0.0, inf] expected: [-8.999999999999999e+307, 0.0, 8.999999999999999e+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-20261003-154526-c4

CPython versions tested on:

3.14

Operating systems tested on:

Windows

[ZeroIntensity]

See #158748 (comment).