feat: add C implementation for math/base/special/gammaincinv

[Om-A-osc]

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Description

What is the purpose of this pull request?

This pull request adds a C implementation for the @stdlib/math/base/special/gammaincinv function and integrates it into the existing native interface.

Specifically, this PR:

• Adds a C implementation of the inverse incomplete gamma function (stdlib_base_gammaincinv)
• Adds C benchmarks for performance evaluation
• Adds C usage examples
• Updates the C API documentation in the README
• Updates and extends native tests to validate correctness and edge cases

Once merged, this implementation will enable adding native C implementations for:

• @stdlib/stats/base/dists/gamma/quantile
• @stdlib/stats/base/dists/erlang/quantile
• and others

thereby improving performance and native coverage for distribution quantile functions.

Related Issues

Does this pull request have any related issues?

• NO

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.

C lint tasks report missing_dependencies, which is expected in environments where the required native tooling is not installed.

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

Disclosure

Not applicable.

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@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/gammaincinv	$\\color{red}1647/1872$ $\\color{green}+0.00\\%$	$\\color{red}129/160$ $\\color{green}+0.00\\%$	$\\color{red}16/24$ $\\color{green}+0.00\\%$	$\\color{red}1647/1872$ $\\color{green}+0.00\\%$

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

[Planeshifter]

Looks good to me now after significant refactoring. Mainly, the C implementation was not faithful to the JavaScript implementation. These have now been aligned.

Thanks, @Om-A-osc!

[stdlib-bot]

PR Commit Message

feat: add C implementation for `math/base/special/gammaincinv`

PR-URL: https://github.com/stdlib-js/stdlib/pull/9982

Co-authored-by: Philipp Burckhardt <pburckhardt@outlook.com>
Reviewed-by: Philipp Burckhardt <pburckhardt@outlook.com>

Please review the above commit message and make any necessary adjustments.