The function `rnn_fft_impl` appears to implement a multi-stage Radix-N Fast...

September 2, 2025 at 07:39 AM

void rnn_fft_impl(const kiss_fft_state *st,kiss_fft_cpx *fout)
{
    int m2, m;
    int p;
    int L;
    int fstride[MAXFACTORS];
    int i;
    int shift;

    /* st->shift can be -1 */
    shift = st->shift>0 ? st->shift : 0;

    fstride[0] = 1;
    L=0;
    do {
       p = st->factors[2*L];
       m = st->factors[2*L+1];
       fstride[L+1] = fstride[L]*p;
       L++;
    } while(m!=1);
    m = st->factors[2*L-1];
    for (i=L-1;i>=0;i--)
    {
       if (i!=0)
          m2 = st->factors[2*i-1];
       else
          m2 = 1;
       switch (st->factors[2*i])
       {
       case 2:
          kf_bfly2(fout, m, fstride[i]);
          break;
       case 4:
          kf_bfly4(fout,fstride[i]<<shift,st,m, fstride[i], m2);
          break;
 #ifndef RADIX_TWO_ONLY
       case 3:
          kf_bfly3(fout,fstride[i]<<shift,st,m, fstride[i], m2);
          break;
       case 5:
          kf_bfly5(fout,fstride[i]<<shift,st,m, fstride[i], m2);
          break;
 #endif
       }
       m = m2;
    }
}

The function rnn_fft_impl appears to implement a multi-stage Radix-N Fast Fourier Transform (FFT) algorithm. This type of FFT algorithm is used to efficiently compute the discrete Fourier transform (DFT) of a sequence. Let's break down what this specific code does:

General Purpose

rnn_fft_impl is designed to compute an FFT on a given input sequence represented by complex numbers. It performs the transformations in stages based on factors of the FFT size, using Radix algorithms (like Radix-2, Radix-3, Radix-4, etc.). The algorithm appears to be flexible to support multiple radix factors to optimize for different input sizes.

Key Variables

st: A structure (kiss_fft_state) that contains the configuration/state for the FFT. This includes:
- st->factors: The decomposition (factorization) of the FFT size into smaller factors (e.g., for size 12, factors might be [3, 4] for a Radix-3 followed by a Radix-4).
- st->shift: An optional shift value, possibly used for scaling or precision adjustments during the FFT.
fout: The complex output array that will hold the Fourier-transformed data.
Other variables:
- factors: Used for stage-wise processing, where the input data is progressively split and transformed.
- fstride: Array of strides to compute offsets during butterfly operations.
- shift: Adjusts the stride for scaling or precision.

Algorithm Steps

1. Generate Stride Array (`fstride`)

The fstride array stores the multiplicative step sizes (strides) for each stage of the FFT computation.

It is initialized with fstride[0] = 1.
The strides are calculated based on the factors (st->factors) of the FFT size:
- p is the radix of the current stage.
- m is the size of the current stage.
- The function computes strides for subsequent stages as fstride[L+1] = fstride[L] * p.

2. Process Each Stage (Radix Computation)

The bulk of the FFT computation happens in this loop:

for (i=L-1; i>=0; i--)

This loop processes the FFT stages in reverse order (starting with the finest decomposition and moving to the coarsest).

Key steps for each stage:

Determine the size of the current stage (m) and the next stage (m2).
Use the corresponding Radix operation (butterfly computations) for the current stage:
- case 2: Radix-2 FFT using kf_bfly2.
- case 4: Radix-4 FFT using kf_bfly4.
- case 3: Radix-3 FFT using kf_bfly3 (if supported, excluded in RADIX_TWO_ONLY mode).
- case 5: Radix-5 FFT using kf_bfly5 (if supported).
The butterfly calculations involve reorganizing and combining portions of the input/output arrays (fout), based on the stride and radix.
- kf_bfly* are helper functions that implement specific radix-based FFT operations.

3. Update Size (`m`) for Next Stage

At the end of each stage, m is updated to m2 (the size of the subsequent stage).

Summary

In essence, the function:

Decomposes the FFT computation into stages based on the factorization of the FFT size (st->factors).
Computes the FFT stage by stage, using appropriate Radix-based butterfly operations to efficiently perform the transform.
Produces the output in the array fout.

The implementation supports multi-radix FFT (Radix-2, Radix-3, Radix-4, Radix-5), which allows it to adapt to different input lengths in an efficient manner. It also appears to be part of a larger library (likely the KISS FFT library or something similar).

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