feat: add C implementation for stats/base/dists/negative-binomial/logpmf

[nirmaljb]

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Resolves #3762.

Description

What is the purpose of this pull request?

This pull request:

• Adds a C implementation of the negative binomial logpmf.
• Includes benchmarks for the C implementation.
• Provides examples demonstrating the usage of the negative binomial logpmf in C.

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/negative-binomial/logpmf #3762

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

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• Yes
• No

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

Disclosure

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/negative-binomial/logpmf	$\color{red}618/661$ $\color{green}+0.00%$	$\color{red}47/53$ $\color{green}+0.00%$	$\color{green}6/6$ $\color{green}+0.00%$	$\color{red}618/661$ $\color{green}+0.00%$

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

[Planeshifter]

The header stdlib/math/base/special/sqrt.h is included and @stdlib/math/base/special/sqrt is listed as a dependency, yet the raw sqrt() from libc is called instead of stdlib_base_sqrt.

Suggested change

	result *= sqrt( bgh / STDLIB_CONSTANT_FLOAT64_E );
	result *= sqrt( agh / cgh );
	result *= stdlib_base_sqrt( bgh / STDLIB_CONSTANT_FLOAT64_E );
	result *= stdlib_base_sqrt( agh / cgh );

[Planeshifter]

Drop the trailing semicolon — stdlib convention omits it, as in beta/logpdf/src/addon.c, gamma/logpdf/src/addon.c, etc.

Suggested change

	STDLIB_MATH_BASE_NAPI_MODULE_DDD_D( stdlib_base_dists_negative_binomial_logpmf );
	STDLIB_MATH_BASE_NAPI_MODULE_DDD_D( stdlib_base_dists_negative_binomial_logpmf )

[Planeshifter]

Missing @private tag. Add it to match the convention used by all other native.js wrappers.

[Planeshifter]

example.c calls stdlib_base_ceil, but @stdlib/math/base/special/ceil is absent from the examples conf dependencies here. Add it so the example builds correctly.

[Planeshifter]

logpmf requires a non-negative integer x; random_uniform( 1.0, 100.0 ) produces non-integers, causing every call to return -Infinity — the actual algorithm is never exercised. The y != y guard does not catch -Infinity. Wrap the result in stdlib_base_ceil() and add the corresponding include and manifest dependency, matching poisson/logpmf/benchmark/c/benchmark.c.

[Planeshifter]

This JSDoc block is copied verbatim from the JS source: it uses {type} braces, dash separators, @private, and @returns. Rewrite in C JSDoc style — no type braces, no leading dash, @return (singular), space-aligned parameter descriptions.

[Planeshifter]

The @param and @returns tags use tab characters before the parameter name rather than space alignment, and @returns should be @return (singular). Also remove the - separator between parameter name and description. Same issue applies to the JSDoc block on lines 252–256. Follow the C JSDoc convention used throughout the rest of the codebase.