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

[rajanarahul93]

Progresses #3677.

Description

What is the purpose of this pull request?

This pull request:

• Adds a C implementation for @stdlib/math/base/special/gammaincinv, including a Node-API addon, C examples, C benchmarks, native JS tests, and native JS benchmarks, fulfilling the requirements outlined in the related RFC. This implementation is a necessary prerequisite for adding a C implementation to @stdlib/stats/base/dists/invgamma/quantile.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• [RFC]: Add C implementation for @stdlib/stats/base/dists/invgamma/quantile #3677 (Blocked by this PR)

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.

No.

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

Disclosure

If you answered "yes" to using AI assistance, please provide a short disclosure indicating how you used AI assistance. This helps reviewers determine how much scrutiny to apply when reviewing your contribution. Example disclosures: "This PR was written primarily by Claude Code." or "I consulted ChatGPT to understand the codebase, but the proposed changes were fully authored manually by myself.".

Assisted by an AI (Gemini) to generate the C code translation, Node-API boilerplate, Makefiles, tests, benchmarks, documentation updates, and Git/build commands based on the existing JavaScript implementation and stdlib conventions. Local build verification was problematic due to environment issues, but the code structure follows project patterns.

---

@stdlib-js/reviewers

[stdlib-bot]

⚠️ Tracking Issue Closure Warning ⚠️

I noticed your PR description contains closing keywords ("Resolves", "Closes", or "Fixes") referencing a "Tracking Issue".

Why this matters:
Tracking issues should typically remain open until all related sub-issues are completed. GitHub automatically closes issues with such closing keywords when the PR is merged. For more information, see GitHub's documentation on using keywords in issues and pull requests.

Required action:
Use "Progresses" instead to reference the tracking issue without automatically closing it.

Thank you for your contribution to the project!

[gunjjoshi]

@rajanarahul93 Thank you for working on this. You'll need to spend some time in getting familiar with the packages in math/base/special/*. The current changes in this PR do not seem to be close to what is required to add the C implementation of a package. I would suggest to refer to old related PRs and trying it out yourself.

[rajanarahul93]

Thanks for the feedback, @gunjjoshi. I’ll go through similar past PRs and existing math/base/special packages to better understand the structure and requirements, then update this implementation accordingly.