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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None.

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• Read, understood, and followed the contributing guidelines.

AI Assistance

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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]: 

[kgryte]

Yes, that seems reasonable to me. Better to use exact values. However, instead of cos and sin, for multiple of pi, one should use sinpi and cospi which will give you more accurate results.

[gunjjoshi]

Thanks, I've now replaced the use of hardcoded constants by sinpi and cospi in 5f3fc63.

[kgryte]

Given that these are one time computations, it is probably preferable to just hard code the constants. My point about using sinpi and cospi is, if one were to perform computation, those should be used when what you are wanting to evaluate is a multiple of pi.

[gunjjoshi]

/stdlib merge

[gunjjoshi]

Will keep on updating this as we add more directories.

[gunjjoshi]

These are some initial tests that I could think of. Let me know if there are any suggestions to add more.

[gunjjoshi]

The failing CI tests should pass once we merge #11467.