feat: add fft/base/fftpack/rfftf

[gunjjoshi]

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Resolves None.

Description

What is the purpose of this pull request?

This pull request:

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

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This pull request has the following related issues:

None.

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No.

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• 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?

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• Test/benchmark generation
• Documentation (including examples)
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Used AI to understand the implementation, reason about specific choices and to help write equations and explanations in implementation comments. Also referred it to understand the working of FFTs.

---

@stdlib-js/reviewers

[gunjjoshi]

Opened this draft PR to discuss the implementation or ask questions, if any, and to track progress.

[gunjjoshi]

I could have used math/base/special/sin and math/base/special/cos here, but instead I have hardcoded the exact constants used in pffft (Ref: https://github.com/marton78/pffft/blob/master/src/fftpack.c#L1308), to be as close as possible, to the actual results. Using math/base/special/sin and math/base/special/cos leads to slightly off results. If we are fine with that, I'll replace these hardcoded constants with stdlib functions.

[gunjjoshi]

Not must difference for sin, but there is some difference for cos:

In [5]: var cos = require('@stdlib/math/base/special/cos')
Out[5]: [Function: cos]

In [6]: cos((2*pi)/3)
Out[6]: -0.4999999999999998

In [7]: var cos = require('@stdlib/math/base/special/cosf')
Out[7]: [Function: cosf]

In [8]: var pi = require('@stdlib/constants/float32/pi')
Out[8]: 3.1415927410125732

In [9]: cos((2*pi)/3)
Out[9]: -0.5000000596046448

In [10]: