[manit2004]

Resolves #16533.

Description

What is the purpose of this pull request?

This pull request:

• Fixes an off-by-one in the large-x asymptotic series used by math/base/special/gammainc. The expansion is 1 + (a-1)/x + (a-1)(a-2)/x² + ..., so the falling factorial has to start at a-1 (Boost does a_poch( a - 1 )), but both the JS and C implementations started at a.
• Adds regression tests for gammainc and for poisson/cdf and chisquare/cdf, which are affected through it. The existing fixtures pass with or without the fix, which is why this went unnoticed.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• [BUG]: math/base/special/gammainc is off by up to 0.03 for x > 1000 when a is close to x #16533

Reference Packages

Did the content of this pull request follow one or more existing packages? Answering is optional.

This pull request followed these packages:

• None, this is a bug fix.

Questions

Any questions for reviewers of this pull request?

No.

Other

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

Call	Before	After	Expected (mpmath, 60 digits)
gammainc( 1367.3436948118986, 1409.203708740708 )	0.09952119051642438	0.13190499189857297	0.13190499189857088
gammainc( 1001, 1000.5, true, true )	0.501850998882592	0.48949191460024466	0.48949191460024505
poisson cdf( 999, 1001 )	0.49530155533410974	0.48318854707021264	0.4831885470702138
chisquare cdf( 2500, 2400 )	0.9231500432608719	0.9241270884571918	0.9241270884571916

The new tests fail on the unfixed code and pass with the fix, for both the JS and native implementations (I rebuilt the three add-ons with and without the C change).

I also compared against SciPy on 20,000 points (x from 1e3 to 1e6, a near x). Points with a relative error above 1e-8 went from 13,130 to 40. The remaining 40 are around x ≈ 975000, with a worst relative error of 4.68e-6. I haven't looked into those, and they may be a separate issue.

Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines.

AI Assistance

When authoring the changes proposed in this PR, did you use any kind of AI assistance?

• Yes
• No

If you answered "yes" above, how did you use AI assistance?

• Code generation (e.g., when writing an implementation or fixing a bug)
• Test/benchmark generation
• Documentation (including examples)
• Research and understanding

---

@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/gammainc	$\\color{red}1794/1978$ $\\color{green}+90.70\\%$	$\\color{red}133/161$ $\\color{green}+82.61\\%$	$\\color{red}24/28$ $\\color{green}+85.71\\%$	$\\color{red}1794/1978$ $\\color{green}+90.70\\%$
stats/base/dists/chisquare/cdf	$\\color{green}241/241$ $\\color{green}+100.00\\%$	$\\color{green}7/7$ $\\color{green}+100.00\\%$	$\\color{green}3/3$ $\\color{green}+100.00\\%$	$\\color{green}241/241$ $\\color{green}+100.00\\%$
stats/base/dists/poisson/cdf	$\\color{green}286/286$ $\\color{green}+100.00\\%$	$\\color{green}28/28$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}286/286$ $\\color{green}+100.00\\%$

The above coverage report was generated for the changes in this PR.

[kgryte]

@anandkaranubc Would you mind taking a first look at this? Cheers!