statistics.correlation() is inaccurate for tiny inputs #161259

Bug report

Originally discovered by @Broyojo, statistics.correlation() returns a wrong result when the sums of squared deviations are tiny, even though correlation is scale-invariant:

>>> import statistics
>>> statistics.correlation([1e-100, 2e-100, 3e-100], [1e-62, 2e-62, 3e-62])
0.8997827589086393

The expected result is 1.0. Normalizing both inputs by max(abs(...)) first gives 1.0.
P.S. The same problem applies to any nonzero product that is subnormal.

CPython versions tested on:

3.14, 3.15, 3.13

Operating systems tested on:

Windows, Linux

Linked PRs

• gh-161259: Fix statistics._sqrtprod() for subnormal products #161260