feat: add initial implementaion of fft/base/fftpack

[gunjjoshi]

Progresses #3131

Description

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This pull request:

• adds fft/base/fftpack.

Related Issues

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This pull request:

• progresses [RFC]: signal process related algorithms like fft family #3131.

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No.

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• Read, understood, and followed the contributing guidelines.

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@stdlib-js/reviewers

[kgryte]

Just checking. Seems a little strange to be mutating a variable in the parent scope.

[gunjjoshi]

In the reference implementation, these constants are multiplied with fsign at the time of declaration itself. But, as fsign comes as an argument to the passfb5 function, we can't use it in the // VARIABLES // section.

[gunjjoshi]

Should I move these declarations inside the function, similar to the reference implementation?

[gunjjoshi]

I had a confusion here. If we see the reference implementations of cosqf and cosqf1, cosqf calls cosqf1 here, and passes pointers to the wsave arrays, as cosqf1 accepts pointers to that array.
But in the current JS implementation in this PR, I am passing a single element of the array here, while cosqf1 takes an entire array as an argument here. This might not be the right approach. Is there any other way to achieve the same behavior as shown in the reference C implementation?

[gunjjoshi]

Should I follow something like what we are doing in the C and JS implementations of modf?

[kgryte]

@gunjjoshi It's a little hard to follow what you are asking given the various links. Can you provide relevant snippets in a single comment so we can see what you are referencing in one view?

[gunjjoshi]

@kgryte Ahh, sorry for the confusion.

This is the cosqf1 function:

static void cosqf1(integer n, real *x, real *w, real *xh)

This cosqf1 is used within the cosqf function as:

cosqf1(n, &x[1], &wsave[1], &wsave[n + 1]);

In order to replicate this same behavior in JS, currently, what I'm doing is:

cosqf1:

function cosqf1( n, x, w, xh )

where n is a number, while x, w and xh are Float64Arrays.

And, while calling this cosqf1 from cosqf, we are currently using it as:

cosqf1( n, x[ 1 - 1 ], wsave[ 1 - 1 ], wsave[ n + 1 - 1 ] );

But in this JS version, instead of passing arrays, I am currently passing single elements, such as wsave[ n + 1 - 1 ].
This seems to be wrong. Is there any other way of passing arrays here, but from a specific index (something like a subarray)?

I think this problem might be summed up as, how should we replicate the logic of passing subarrays (using pointers) in C, for the JS implementation?

[kgryte]

@gunjjoshi What about providing an array and then offsets, similar in concept to the ndarray APIs we have. E.g.,

xptr = ...;
wptr = ...;
xhptr = ...;

cosqf1(n, x, xptr, wsave, wptr, xhptr ); // =>cosqf1( n: number, x: Float64Array, xptr: number, wsave: Float64Array, wptr: number, xhptr: number )

where the *ptr variables are indices into the respective arrays.

Another alternative is that you pass down slices which has more overhead due to object creation.

cosqf1( n, x.slice( 1 ), wsave.slice( 1 ), wsave.slice( n+1 ) )

[gunjjoshi]

Thanks, @kgryte, I'll go with the first method!