feat: add C implementation for stats/base/dists/studentized-range/cdf

[nirmaljb]

Resolves #3887.

Description

What is the purpose of this pull request?

This pull request:

• Adds a C implementation of the studentized-range cumulative distribution function (CDF).
• Includes benchmarks for the C implementation.
• Provides examples demonstrating the usage of the studentized-range CDF 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/studentized-range/cdf #3887

Questions

Any questions for reviewers of this pull request?

No.

Other

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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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• 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

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/studentized-range/cdf	$\color{red}709/769$ $\color{green}+0.00%$	$\color{red}70/87$ $\color{green}+0.00%$	$\color{green}10/10$ $\color{green}+0.00%$	$\color{red}709/769$ $\color{green}+0.00%$

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

[Planeshifter]

Thanks for your contribution! Left round of feedback.

[Planeshifter]

The native wrapper doesn't default nranges to 1 when undefined. Calling cdf(q, r, v) with three arguments forwards undefined to the addon (coerced to NaN), causing stdlib_base_is_positive_integer(NaN) to return false and the CDF to return NaN. This breaks parity with lib/main.js and contradicts the 3-arg JSDoc examples which claim ~0.0644.

Suggested change

	function cdf( q, r, v, nranges ) {
	return addon( q, r, v, nranges );
	}
	function cdf( q, r, v, nranges ) {
	if ( nranges === void 0 ) {
	nranges = 1;
	}
	return addon( q, r, v, nranges );
	}

[Planeshifter]

This example passes 5 arguments, but cdf only accepts 4 (q, r, v, nranges). Drop the trailing 1.0.

Suggested change

	* var y = cdf( 0.5, 3.0, 2.0, 2, 1.0 );
	* var y = cdf( 0.5, 3.0, 2.0, 2 );

[Planeshifter]

This is the else-branch of if ( zabs > 37.0 ), so it's the |z| <= 37 case.

Suggested change

	// Case: |z| >= 37
	// Case: |z| <= 37

[Planeshifter]

These file-scope scalars are immutable — mark them static const double to match stdlib's C conventions.

[Planeshifter]

Use @return (no trailing s) in C JSDoc to match stdlib convention. Update all occurrences in this file (apnorm, fint, gaussLegreQuadrature, prangeVInf, f26, gausslegdquad, and the main function).

[Planeshifter]

Missing space after for. Every other loop in this file has one.

Suggested change

	for( j = 0; j < n; j++ ) {
	for ( j = 0; j < n; j++ ) {

[Planeshifter]

Use the fully qualified C symbol in the @example block.

Suggested change

	* double y = cdf( 0.5, 3.0, 2.0, 2 );
	* // returns ~0.01
	* double y = stdlib_base_dists_studentized_range_cdf( 0.5, 3.0, 2.0, 1.0 );
	* // returns ~0.0644