[Sad Catapella N2][Numerical correctness] Linear interpolation percentile overflows between finite extreme values #32

Baseline and classification

Normalization Batch 2, commit f784c95e3049483f87466150ffc5764375fa631d. Confirmed formula overflow via isolated NumPy arithmetic probe, not a repository test.

Evidence

• _linear_percentile, lines 376–396 forms difference = above - below and then interpolates, without guarding finite endpoint values whose subtraction exceeds float64 range.
• Called by PooledHistogram.linear_percentile() and WeightedHistogram.linear_percentile(), including RGB percentile fitting.
• Pooling tests do not cover extreme opposite-sign finite endpoints; weighted tests use ordinary uint16 intensities.

Minimal counterexample

An exact conceptual distribution containing only [-1e308, +1e308] has NumPy type-7 50th percentile 0. Inside _linear_percentile, above - below overflows to infinity, so the interpolation gives a nonfinite result. Independent NumPy arithmetic with those endpoints reproduced inf.

Impact / scope

Incorrect linear percentiles for fully finite data, and potentially an invalid normalization scale. Normal scientific RGB uint8/16 input cannot reach this numeric range, but linear_percentile is a public API that accepts float64 pooled data; a robust implementation must not silently return nonfinite results from finite, mathematically representable interpolations.

Fix and acceptance

Compute an overflow-safe convex combination, chosen to preserve bit-identical outputs for the existing normal-range CSBDeep/StarDist parity test (or document a scientific precision policy if strict parity cannot be preserved at extremes). Reject truly nonrepresentable results explicitly. Test ±1e308, mixed signs, subnormal endpoints, adjacent floats, q=0/50/100, arbitrary positive weights, and cases with widely different counts; compare to a high-precision reference. Do not introduce Numba before numerical semantics and parity are proven.