ref: 8803428fda6667b186eae4f20060744ed357e5a8
dir: /kiss_fft.c/
/*
Copyright (c) 2003-2010, Mark Borgerding
Copyright (c) 2017, 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 <u.h>
#include <libc.h>
#include "_kiss_fft_guts.h"
/* The guts header contains all the multiplication and addition macros that are defined for
fixed or floating point complex numbers. It also delares the kf_ internal functions.
*/
static void kf_bfly2(
kiss_fft_cpx *Fout,
const usize 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_FIXDIV(*Fout, 2); C_FIXDIV(*Fout2, 2);
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 usize fstride,
const kiss_fft_cfg *st,
const usize m
) {
kiss_fft_cpx *tw1, *tw2, *tw3;
kiss_fft_cpx scratch[6];
usize k = m;
const usize m2 = 2 * m;
const usize m3 = 3 * m;
tw3 = tw2 = tw1 = st->twiddles;
do {
C_FIXDIV(*Fout, 4); C_FIXDIV(Fout[m], 4); C_FIXDIV(Fout[m2], 4); C_FIXDIV(Fout[m3], 4);
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 usize fstride,
const kiss_fft_cfg *st,
usize m
) {
usize k = m;
const usize 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_FIXDIV(*Fout, 3); C_FIXDIV(Fout[m], 3); C_FIXDIV(Fout[m2], 3);
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 usize 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) {
C_FIXDIV(*Fout0, 5); C_FIXDIV(*Fout1, 5); C_FIXDIV(*Fout2, 5); C_FIXDIV(*Fout3,
5); C_FIXDIV(*Fout4,
5);
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 usize 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;
int Norig = st->nfft;
kiss_fft_cpx *scratch = (kiss_fft_cpx *) KISS_FFT_TMP_ALLOC(sizeof(kiss_fft_cpx) * p);
for (u = 0; u < m; ++u) {
k = u;
for (q1 = 0; q1 < p; ++q1) {
scratch[q1] = Fout[k];
C_FIXDIV(scratch[q1], p);
k += m;
}
k = u;
for (q1 = 0; q1 < p; ++q1) {
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;
}
}
KISS_FFT_TMP_FREE(scratch);
}
static
void kf_work(
kiss_fft_cpx *Fout,
const kiss_fft_cpx *f,
const usize 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;
}
}
/* facbuf is populated by p1,m1,p2,m2, ...
where
p[i] * m[i] = m[i-1]
m0 = n */
static
void kf_factor(int n, int *facbuf) {
int p = 4;
double floor_sqrt;
floor_sqrt = floor(sqrt((double) n));
/*factor out powers of 4, powers of 2, then any remaining primes */
do {
while (n % p) {
switch (p) {
case 4:
p = 2;
break;
case 2:
p = 3;
break;
default:
p += 2;
break;
}
if (p > floor_sqrt)
p = n; /* no more factors, skip to end */
}
n /= p;
*facbuf++ = p;
*facbuf++ = n;
} while (n > 1);
}
/*
*
* User-callable function to allocate all necessary storage space for the fft.
*
* The return value is a contiguous block of memory, allocated with malloc. As such,
* It can be freed with free(), rather than a kiss_fft-specific function.
* */
kiss_fft_cfg *kiss_fft_alloc(int nfft, int inverse_fft, void *mem, usize *lenmem) {
kiss_fft_cfg *st = nil;
usize memneeded = sizeof(struct kiss_fft_state)
+ sizeof(kiss_fft_cpx) * (nfft - 1); /* twiddle factors*/
if (lenmem == nil) {
st = (kiss_fft_cfg*) KISS_FFT_MALLOC(memneeded);
} else {
if (mem != nil && *lenmem >= memneeded)
st = (kiss_fft_cfg*) mem;
*lenmem = memneeded;
}
if (st) {
int i;
st->nfft = nfft;
st->inverse = inverse_fft;
for (i = 0; i < nfft; ++i) {
double phase = -2.0 * PI * ((double)i) / ((double)nfft);
if (st->inverse)
phase *= -1;
kf_cexp(st->twiddles + i, phase);
}
kf_factor(nfft, st->factors);
}
return st;
}
void kiss_fft_stride(kiss_fft_cfg *st, const kiss_fft_cpx *fin, kiss_fft_cpx *fout, int in_stride) {
int j;
if (fin == fout) {
//NOTE: this is not really an in-place FFT algorithm.
//It just performs an out-of-place FFT into a temp buffer
kiss_fft_cpx *tmpbuf = (kiss_fft_cpx *) KISS_FFT_TMP_ALLOC(sizeof(kiss_fft_cpx) * st->nfft);
kf_work(tmpbuf, fin, 1, in_stride, st->factors, st);
memcpy(fout, tmpbuf, sizeof(kiss_fft_cpx) * st->nfft);
KISS_FFT_TMP_FREE(tmpbuf);
} else {
kf_work(fout, fin, 1, in_stride, st->factors, st);
}
if (st->inverse) {
for (j = 0; j < st->nfft; j++) {
fout[j].r /= st->nfft;
fout[j].i /= st->nfft;
}
}
}
void kiss_fft(kiss_fft_cfg *cfg, const kiss_fft_cpx *fin, kiss_fft_cpx *fout) {
kiss_fft_stride(cfg, fin, fout, 1);
}
int kiss_fft_next_fast_size(int n) {
while (1) {
int m = n;
while ((m % 2) == 0) m /= 2;
while ((m % 3) == 0) m /= 3;
while ((m % 5) == 0) m /= 5;
if (m <= 1)
break; /* n is completely factorable by twos, threes, and fives */
n++;
}
return n;
}