feat: add fft/base/fftpack/rffti

[gunjjoshi]

Resolves None.

Description

What is the purpose of this pull request?

This pull request:

• adds fft/base/fftpack/rffti, which is a part of fftpack.
• is an extension of feat: add initial implementation of fft/base/fftpack #4121.

Related Issues

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This pull request has the following related issues:

None.

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No.

Other

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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

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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

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.".

Used AI to understand how we generate C fixtures using FFTPACK.

---

@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
fft/base/fftpack/rffti	$\color{green}404/404$ $\color{green}+100.00%$	$\color{green}12/12$ $\color{green}+100.00%$	$\color{green}2/2$ $\color{green}+100.00%$	$\color{green}404/404$ $\color{green}+100.00%$

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

[kgryte]

I suggest going ahead and migrating to use @stdlib/assert/is-almost-same-value in order to measure differences in units of ULPs, rather than, here, where we compute an epsilon difference.

[kgryte]

Suggested change

	var workspace;
	var N;
	var nf;
	var i;
	var j;
	N = 8;
	workspace = new Float64Array( ( 2*N ) + 34 );
	rffti( N, workspace, 1, 0 );
	console.log( 'Sequence length: %d', N );
	console.log( 'Twiddle factors:' );
	for ( i = N; i < 2*N; i++ ) {
	console.log( ' workspace[%d] = %d', i, workspace[ i ] );
	}
	console.log( 'Factorization:' );
	nf = workspace[ ( 2*N ) + 1 ];
	console.log( ' number of factors: %d', nf );
	for ( j = 0; j < nf; j++ ) {
	console.log( ' factor[%d]: %d', j, workspace[ ( 2*N ) + 2 + j ] );
	}
	var N = 8;
	var workspace = new Float64Array( ( 2*N ) + 34 );
	rffti( N, workspace, 1, 0 );
	console.log( 'Sequence length: %d', N );
	console.log( 'Twiddle factors:' );
	var i;
	for ( i = N; i < 2*N; i++ ) {
	console.log( ' workspace[%d] = %d', i, workspace[ i ] );
	}
	console.log( 'Factorization:' );
	var nf = workspace[ ( 2*N ) + 1 ];
	console.log( ' number of factors: %d', nf );
	for ( i = 0; i < nf; i++ ) {
	console.log( ' factor[%d]: %d', i, workspace[ ( 2*N ) + 2 + i ] );
	}

[kgryte]

This may also apply to your example file.

[kgryte]

Suggested change

	The workspace array is divided into three sections: scratch/workspace
	(indices 0 to N-1), twiddle factors (indices N to 2N-1), and radix factor
	table (indices 2N onwards).
	The workspace array is divided into three sections:
	1. scratch/workspace: the section range from indices 0 to N-1 and is used while performing transforms. This section is not updated during initialization.
	2. twiddle factors (indices N to 2N-1)
	3. radix factor table (indices 2N onwards).