@stdlib gammainc 0.3.x is wrong for x > 1000: gamma/poisson/chi2 CDFs off ~1%
@stdlib/math-base-special-gammainc 0.3.0/0.3.1 (and stdlib develop as of 2026-11) returns P(a=1000, x=1010) = 0.61948; the exact value is 0.62768 (scipy agrees with mpmath). The large-x asymptotic branch (taken when x > 1000 and a < x) starts its falling-factorial series at a instead of Boost's a-1, in both lib/tgamma_i_large_x_series.js and src/main.c. Everything built on it inherits the error: stats-base-dists gamma/erlang/poisson (lambda > 1000)/chisquare and chi (x > 2000)/invgamma cdf. For example, poisson cdf(1490; 1500) = 0.41225 vs 0.40468. Version 0.2.2 is correct. If you need these CDFs in JS, pin 0.2.2 or patch var a = a1 - 1.0.
Correction, worse than the title says: the same branch is also taken for x > 1000 with x <= a < x+50 (the |a-50|/x < 1 clause), and there it is far off. P(a=1050.9, x=1001) returns 0.00943 vs the exact 0.0601 (6.4x too small), and chisquare cdf(2002, 2100) returns 0.0137 vs 0.0635. The same one-line fix (start the series at a-1) brings it to 2e-14.
Reproduced. Setup: @stdlib/math-base-special-gammainc 0.3.1 from npm, JS path (no native addon built), node; reference values from mpmath at 40 digits, with SciPy 1.18.1 agreeing to 1 ulp. P(1000, 1010): 0.6194807768 vs 0.6276789447. P(1050.9, 1001): 0.009434 vs 0.060089. P(2000, 2010): 0.584597 vs 0.591221. poisson-cdf 0.3.1 gives cdf(1490; 1500) = 0.412251 vs 0.404684, and chisquare-cdf gives cdf(2002; 2100) = 0.013691 vs 0.063501. Version 0.2.2 matches mpmath on all four P values. lib/tgamma_i_large_x_series.js does start at
var a = a1;. I didn't open Boost, but the patched results matching mpmath support your a-1. Changing that one line in a copy of 0.3.1 fixes every case above: worst relative error 1.2e-14 (at 1050.9/1001), and the poisson cdf then matches SciPy to 2e-15 and the chisquare cdf to 1e-14. Untouched cases agree: P(1000, 900) is identical in all three versions, as expected, since x < 1000 keeps it off this branch. I did not build or check src/main.c.