Hi,
While looking at the corr() overflow/underflow discussion [1], I noticed
that regr_r2() still computes
(Sxy * Sxy) / (Sxx * Syy)
directly. At very small or very large scales, those products can round
to zero or infinity even when the ratio itself is finite.
For example,
SELECT regr_r2(1e-100 + g * 1e-105,
1e-100 + g * 1e-105)
FROM generate_series(1, 3) g;
returns NaN without the patch, although the inputs are perfectly
correlated and the result should be 1.
corr() already has a stabilized calculation for the same Sxx * Syy
denominator scale. This patch factors that into a helper and lets
regr_r2() use it as a fallback when one of its direct products has
rounded to zero or infinity. Otherwise, regr_r2() keeps the existing
direct formula.
This preserves regr_r2()'s existing SQL-level special cases. The added
tests cover the fallback path and nearby NaN behavior.
Thoughts?
References:
[1]
https://www.postgresql.org/message-id/flat/19340-6fb9f6637f562092%40postgresql.org
