_kiss_fft_guts.h

#ifndef KISS_FFT_GUTS_H
#define KISS_FFT_GUTS_H
/*
Copyright (c) 2003-2010, Mark Borgerding
Copyright (c) 2020-2021, Bernd Porr

All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
    * Neither the author nor the names of any contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/

#include <limits.h>

#define MAXFACTORS 32
/* e.g. an fft of length 128 has 4 factors 
 as far as kissfft is concerned
 4*4*4*2
 */

struct kiss_fft_state{
    int nfft;
    int inverse;
    int factors[2*MAXFACTORS];
    kiss_fft_cpx twiddles[1];
};

/*
  Explanation of macros dealing with complex math:

   C_MUL(m,a,b)         : m = a*b
   C_SUB( res, a,b)     : res = a - b
   C_SUBFROM( res , a)  : res -= a
   C_ADDTO( res , a)    : res += a
 * */


#define S_MUL(a,b) ( (a)*(b) )

#define C_MUL(m,a,b) \
    { (m).r = (a).r*(b).r - (a).i*(b).i;\
      (m).i = (a).r*(b).i + (a).i*(b).r; }

#define C_MULBYSCALAR( c, s )		\
    { (c).r *= (s);\
      (c).i *= (s); }

#define C_ADD( res, a,b)\
    { \
	    (res).r=(a).r+(b).r;  (res).i=(a).i+(b).i; \
    }

#define C_SUB( res, a,b)			\
    { \
	    (res).r=(a).r-(b).r;  (res).i=(a).i-(b).i; \
    }

#define C_ADDTO( res , a)			\
    { \
	    (res).r += (a).r;  (res).i += (a).i;\
    }

#define C_SUBFROM( res , a)\
    {\
	    (res).r -= (a).r;  (res).i -= (a).i; \
    }


#define HALF_OF(x) ((x)*.5)


#define  kf_cexp(x,phase) \
	{ \
		(x)->r = cos(phase);\
		(x)->i = sin(phase);\
	}


/* a debugging function */
#define pcpx(c)\
    fprintf(stderr,"%g + %gi\n",(double)((c)->r),(double)((c)->i) )



static void kf_bfly2(
        kiss_fft_cpx *Fout,
        const size_t fstride,
        const kiss_fft_cfg st,
        int m
) {
    kiss_fft_cpx *Fout2;
    kiss_fft_cpx *tw1 = st->twiddles;
    kiss_fft_cpx t;
    Fout2 = Fout + m;
    do {
        C_MUL (t, *Fout2, *tw1);
        tw1 += fstride;
        C_SUB(*Fout2, *Fout, t);
        C_ADDTO(*Fout, t);
        ++Fout2;
        ++Fout;
    } while (--m);
}

static void kf_bfly4(
        kiss_fft_cpx *Fout,
        const size_t fstride,
        const kiss_fft_cfg st,
        const size_t m
) {
    kiss_fft_cpx *tw1, *tw2, *tw3;
    kiss_fft_cpx scratch[6];
    size_t k = m;
    const size_t m2 = 2 * m;
    const size_t m3 = 3 * m;


    tw3 = tw2 = tw1 = st->twiddles;

    do {
        C_MUL(scratch[0], Fout[m], *tw1);
        C_MUL(scratch[1], Fout[m2], *tw2);
        C_MUL(scratch[2], Fout[m3], *tw3);

        C_SUB(scratch[5], *Fout, scratch[1]);
        C_ADDTO(*Fout, scratch[1]);
        C_ADD(scratch[3], scratch[0], scratch[2]);
        C_SUB(scratch[4], scratch[0], scratch[2]);
        C_SUB(Fout[m2], *Fout, scratch[3]);
        tw1 += fstride;
        tw2 += fstride * 2;
        tw3 += fstride * 3;
        C_ADDTO(*Fout, scratch[3]);

        if (st->inverse) {
            Fout[m].r = scratch[5].r - scratch[4].i;
            Fout[m].i = scratch[5].i + scratch[4].r;
            Fout[m3].r = scratch[5].r + scratch[4].i;
            Fout[m3].i = scratch[5].i - scratch[4].r;
        } else {
            Fout[m].r = scratch[5].r + scratch[4].i;
            Fout[m].i = scratch[5].i - scratch[4].r;
            Fout[m3].r = scratch[5].r - scratch[4].i;
            Fout[m3].i = scratch[5].i + scratch[4].r;
        }
        ++Fout;
    } while (--k);
}

static void kf_bfly3(
        kiss_fft_cpx *Fout,
        const size_t fstride,
        const kiss_fft_cfg st,
        size_t m
) {
    size_t k = m;
    const size_t m2 = 2 * m;
    kiss_fft_cpx *tw1, *tw2;
    kiss_fft_cpx scratch[5];
    kiss_fft_cpx epi3;
    epi3 = st->twiddles[fstride * m];

    tw1 = tw2 = st->twiddles;

    do {
        C_MUL(scratch[1], Fout[m], *tw1);
        C_MUL(scratch[2], Fout[m2], *tw2);

        C_ADD(scratch[3], scratch[1], scratch[2]);
        C_SUB(scratch[0], scratch[1], scratch[2]);
        tw1 += fstride;
        tw2 += fstride * 2;

        Fout[m].r = Fout->r - HALF_OF(scratch[3].r);
        Fout[m].i = Fout->i - HALF_OF(scratch[3].i);

        C_MULBYSCALAR(scratch[0], epi3.i);

        C_ADDTO(*Fout, scratch[3]);

        Fout[m2].r = Fout[m].r + scratch[0].i;
        Fout[m2].i = Fout[m].i - scratch[0].r;

        Fout[m].r -= scratch[0].i;
        Fout[m].i += scratch[0].r;

        ++Fout;
    } while (--k);
}

static void kf_bfly5(
        kiss_fft_cpx *Fout,
        const size_t fstride,
        const kiss_fft_cfg st,
        int m
) {
    kiss_fft_cpx *Fout0, *Fout1, *Fout2, *Fout3, *Fout4;
    int u;
    kiss_fft_cpx scratch[13];
    kiss_fft_cpx *twiddles = st->twiddles;
    kiss_fft_cpx *tw;
    kiss_fft_cpx ya, yb;
    ya = twiddles[fstride * m];
    yb = twiddles[fstride * 2 * m];

    Fout0 = Fout;
    Fout1 = Fout0 + m;
    Fout2 = Fout0 + 2 * m;
    Fout3 = Fout0 + 3 * m;
    Fout4 = Fout0 + 4 * m;

    tw = st->twiddles;
    for (u = 0; u < m; ++u) {
        scratch[0] = *Fout0;

        C_MUL(scratch[1], *Fout1, tw[u * fstride]);
        C_MUL(scratch[2], *Fout2, tw[2 * u * fstride]);
        C_MUL(scratch[3], *Fout3, tw[3 * u * fstride]);
        C_MUL(scratch[4], *Fout4, tw[4 * u * fstride]);

        C_ADD(scratch[7], scratch[1], scratch[4]);
        C_SUB(scratch[10], scratch[1], scratch[4]);
        C_ADD(scratch[8], scratch[2], scratch[3]);
        C_SUB(scratch[9], scratch[2], scratch[3]);

        Fout0->r += scratch[7].r + scratch[8].r;
        Fout0->i += scratch[7].i + scratch[8].i;

        scratch[5].r = scratch[0].r + S_MUL(scratch[7].r, ya.r) + S_MUL(scratch[8].r, yb.r);
        scratch[5].i = scratch[0].i + S_MUL(scratch[7].i, ya.r) + S_MUL(scratch[8].i, yb.r);

        scratch[6].r = S_MUL(scratch[10].i, ya.i) + S_MUL(scratch[9].i, yb.i);
        scratch[6].i = -S_MUL(scratch[10].r, ya.i) - S_MUL(scratch[9].r, yb.i);

        C_SUB(*Fout1, scratch[5], scratch[6]);
        C_ADD(*Fout4, scratch[5], scratch[6]);

        scratch[11].r = scratch[0].r + S_MUL(scratch[7].r, yb.r) + S_MUL(scratch[8].r, ya.r);
        scratch[11].i = scratch[0].i + S_MUL(scratch[7].i, yb.r) + S_MUL(scratch[8].i, ya.r);
        scratch[12].r = -S_MUL(scratch[10].i, yb.i) + S_MUL(scratch[9].i, ya.i);
        scratch[12].i = S_MUL(scratch[10].r, yb.i) - S_MUL(scratch[9].r, ya.i);

        C_ADD(*Fout2, scratch[11], scratch[12]);
        C_SUB(*Fout3, scratch[11], scratch[12]);

        ++Fout0;
        ++Fout1;
        ++Fout2;
        ++Fout3;
        ++Fout4;
    }
}

/* perform the butterfly for one stage of a mixed radix FFT */
static void kf_bfly_generic(
        kiss_fft_cpx *Fout,
        const size_t fstride,
        const kiss_fft_cfg st,
        int m,
        int p
) {
    int u, k, q1, q;
    kiss_fft_cpx *twiddles = st->twiddles;
    kiss_fft_cpx t;
    long unsigned int Norig = st->nfft;

    kiss_fft_cpx *scratch = (kiss_fft_cpx *) malloc(sizeof(kiss_fft_cpx) * p);

    for (u = 0; u < m; ++u) {
        k = u;
        for (q1 = 0; q1 < p; ++q1) {
            scratch[q1] = Fout[k];
            k += m;
        }

        k = u;
        for (q1 = 0; q1 < p; ++q1) {
            long unsigned int twidx = 0;
            Fout[k] = scratch[0];
            for (q = 1; q < p; ++q) {
                twidx += fstride * k;
                if (twidx >= Norig) twidx -= Norig;
                C_MUL(t, scratch[q], twiddles[twidx]);
                C_ADDTO(Fout[k], t);
            }
            k += m;
        }
    }
    free(scratch);
}


static
void kf_work(
        kiss_fft_cpx *Fout,
        const kiss_fft_cpx *f,
        const size_t fstride,
        int in_stride,
        int *factors,
        const kiss_fft_cfg st
) {
    kiss_fft_cpx *Fout_beg = Fout;
    const int p = *factors++; /* the radix  */
    const int m = *factors++; /* stage's fft length/p */
    const kiss_fft_cpx *Fout_end = Fout + p * m;

    if (m == 1) {
        do {
            *Fout = *f;
            f += fstride * in_stride;
        } while (++Fout != Fout_end);
    } else {
        do {
            // recursive call:
            // DFT of size m*p performed by doing
            // p instances of smaller DFTs of size m, 
            // each one takes a decimated version of the input
            kf_work(Fout, f, fstride * p, in_stride, factors, st);
            f += fstride * in_stride;
        } while ((Fout += m) != Fout_end);
    }

    Fout = Fout_beg;

    // recombine the p smaller DFTs 
    switch (p) {
        case 2:
            kf_bfly2(Fout, fstride, st, m);
            break;
        case 3:
            kf_bfly3(Fout, fstride, st, m);
            break;
        case 4:
            kf_bfly4(Fout, fstride, st, m);
            break;
        case 5:
            kf_bfly5(Fout, fstride, st, m);
            break;
        default:
            kf_bfly_generic(Fout, fstride, st, m, p);
            break;
    }
}




#endif