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

[Om-A-osc]

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type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:

• task: lint_filenames
  status: passed
• task: lint_editorconfig
  status: passed
• task: lint_markdown
  status: passed
• task: lint_package_json
  status: passed
• task: lint_repl_help
  status: na
• task: lint_javascript_src
  status: passed
• task: lint_javascript_cli
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• task: lint_javascript_examples
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• task: lint_javascript_tests
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• task: lint_javascript_benchmarks
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• task: lint_python
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• task: lint_r
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• task: lint_c_src
  status: missing_dependencies
• task: lint_c_examples
  status: missing_dependencies
• task: lint_c_benchmarks
  status: missing_dependencies
• task: lint_c_tests_fixtures
  status: na
• task: lint_shell
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• task: lint_typescript_declarations
  status: passed
• task: lint_typescript_tests
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• task: lint_license_headers
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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	$\color{red}1637/1868$ $\color{green}+0.00%$	$\color{red}127/156$ $\color{green}+0.00%$	$\color{red}15/24$ $\color{green}+0.00%$	$\color{red}1637/1868$ $\color{green}+0.00%$

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