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

[Planeshifter]

Progresses #649.

Description

What is the purpose of this pull request?

This pull request:

• adds a C implementation for math/base/special/polygamma
• adds native bindings, tests, benchmarks, and examples
• updates the package documentation to document the C API
• extends scripts/evalpoly.js to also generate the compiled polynomial evaluation functions in src/main.c

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• [RFC]: Add C implementations to base special math functions (tracking issue) #649

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.

Implementation notes:

• The C API is double stdlib_base_polygamma( const int32_t n, const double x ), following the integer-order convention used elsewhere (e.g., ldexp, falling-factorial) and Boost's polygamma(int, T). Non-integer n validation remains on the JS side, matching existing precedent.
• The port was validated bit-identical to the JS implementation at 167,037 points (all fixtures plus systematic sweeps across every dispatch regime and 100k+ random pairs) when compiled with -ffp-contract=off, with zero NaN/Infinity/sign mismatches.
• For n >= 13, the cotangent-polynomial table is built via a heap-allocated ping-pong buffer pair (freed before return), as rows can reach ~10⁶ doubles for reachable inputs; a NULL allocation returns NaN.
• With default floating-point contraction (FMA) on arm64, some exponent-amplified regimes drift from the JS results; the ULP tolerances in test/test.native.js (per RFC [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352) were measured accordingly, with the C and JS minima coinciding at every test site.
• C lint tasks may report missing_dependencies 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

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.".

This PR was written by Claude Code under my direction and guidance, including the C implementation, tests, benchmarks, and documentation. The port was adversarially reviewed and numerically validated against the existing JS implementation (bit-identical at 167,037 validation points), with all design decisions and validation results reviewed by me.

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/polygamma	$\\color{red}1333/1385$ $\\color{green}+96.25\\%$	$\\color{red}130/157$ $\\color{green}+82.80\\%$	$\\color{green}17/17$ $\\color{green}+100.00\\%$	$\\color{red}1333/1385$ $\\color{green}+96.25\\%$

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