ref: 9a9fa10c760b59e48c567d408de3878498755f84
dir: /libfaad/cfft.c/
/*
** FAAD - Freeware Advanced Audio Decoder
** Copyright (C) 2002 M. Bakker
**
** This program is free software; you can redistribute it and/or modify
** it under the terms of the GNU General Public License as published by
** the Free Software Foundation; either version 2 of the License, or
** (at your option) any later version.
**
** This program is distributed in the hope that it will be useful,
** but WITHOUT ANY WARRANTY; without even the implied warranty of
** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
** GNU General Public License for more details.
**
** You should have received a copy of the GNU General Public License
** along with this program; if not, write to the Free Software
** Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
**
** $Id: cfft.c,v 1.1 2002/07/14 19:11:11 menno Exp $
**/
/*
* Algorithmically based on Fortran-77 FFTPACK
* by Paul N. Swarztrauber(Version 4, 1985).
*/
/* isign is +1 for backward and -1 for forward transforms */
#include "common.h"
#include <stdlib.h>
#include "cfft.h"
/*----------------------------------------------------------------------
passf2, passf3, passf4, passf5, passf. Complex FFT passes fwd and bwd.
----------------------------------------------------------------------*/
static void passf2(uint16_t ido, uint16_t l1, real_t *cc, real_t *ch,
real_t *wa1, int8_t isign)
{
uint16_t i, k, ah, ac;
real_t ti2, tr2;
if (ido <= 2)
{
for (k = 0; k < l1; k++)
{
ah = k*ido;
ac = 2*k*ido;
ch[ah] = cc[ac] + cc[ac+ido];
ch[ah+ido*l1] = cc[ac] - cc[ac+ido];
ch[ah+1] = cc[ac+1] + cc[ac+ido+1];
ch[ah+ido*l1+1] = cc[ac+1] - cc[ac+ido+1];
}
} else {
for (k = 0; k < l1; k++)
{
for(i = 0; i < ido-1; i += 2)
{
ah = i + k*ido;
ac = i + 2*k*ido;
ch[ah] = cc[ac] + cc[ac+ido];
tr2 = cc[ac] - cc[ac+ido];
ch[ah+1] = cc[ac+1] + cc[ac+1+ido];
ti2 = cc[ac+1] - cc[ac+1+ido];
ch[ah+l1*ido+1] = wa1[i]*ti2 + isign*wa1[i+1]*tr2;
ch[ah+l1*ido] = wa1[i]*tr2 - isign*wa1[i+1]*ti2;
}
}
}
}
static void passf3(uint16_t ido, uint16_t l1, real_t *cc, real_t *ch,
real_t *wa1, real_t *wa2, int8_t isign)
{
static real_t taur = -0.5;
static real_t taui = 0.866025403784439;
uint16_t i, k, ac, ah;
real_t ci2, ci3, di2, di3, cr2, cr3, dr2, dr3, ti2, tr2;
if (ido == 2)
{
for (k = 1; k <= l1; k++)
{
ac = (3*k-2) * ido;
tr2 = cc[ac] + cc[ac+ido];
cr2 = cc[ac-ido] + taur*tr2;
ah = (k-1) * ido;
ch[ah] = cc[ac-ido] + tr2;
ti2 = cc[ac+1] + cc[ac+ido+1];
ci2 = cc[ac-ido+1] + taur*ti2;
ch[ah+1] = cc[ac-ido+1] + ti2;
cr3 = isign * taui * (cc[ac] - cc[ac+ido]);
ci3 = isign * taui * (cc[ac+1] - cc[ac+ido+1]);
ch[ah+l1*ido] = cr2 - ci3;
ch[ah+2*l1*ido] = cr2 + ci3;
ch[ah+l1*ido+1] = ci2 + cr3;
ch[ah+2*l1*ido+1] = ci2 - cr3;
}
} else {
for (k = 1; k <= l1; k++)
{
for (i = 0; i < ido-1; i += 2)
{
ac = i + (3*k-2) * ido;
tr2 = cc[ac] + cc[ac+ido];
cr2 = cc[ac-ido] + taur*tr2;
ah = i + (k-1) * ido;
ch[ah] = cc[ac-ido] + tr2;
ti2 = cc[ac+1] + cc[ac+ido+1];
ci2 = cc[ac-ido+1] + taur*ti2;
ch[ah+1] = cc[ac-ido+1] + ti2;
cr3 = isign * taui * (cc[ac] - cc[ac+ido]);
ci3 = isign * taui * (cc[ac+1] - cc[ac+ido+1]);
dr2 = cr2 - ci3;
dr3 = cr2 + ci3;
di2 = ci2 + cr3;
di3 = ci2 - cr3;
ch[ah+l1*ido+1] = wa1[i]*di2 + isign*wa1[i+1]*dr2;
ch[ah+l1*ido] = wa1[i]*dr2 - isign*wa1[i+1]*di2;
ch[ah+2*l1*ido+1] = wa2[i]*di3 + isign*wa2[i+1]*dr3;
ch[ah+2*l1*ido] = wa2[i]*dr3 - isign*wa2[i+1]*di3;
}
}
}
}
static void passf4(uint16_t ido, uint16_t l1, real_t *cc, real_t *ch,
real_t *wa1, real_t *wa2, real_t *wa3, int8_t isign)
{
uint16_t i, k, ac, ah;
real_t ci2, ci3, ci4, cr2, cr3, cr4, ti1, ti2, ti3, ti4, tr1, tr2,
tr3, tr4;
if (ido == 2)
{
for (k = 0; k < l1; k++)
{
ac = 4*k*ido + 1;
ti1 = cc[ac] - cc[ac+2*ido];
ti2 = cc[ac] + cc[ac+2*ido];
tr4 = cc[ac+3*ido] - cc[ac+ido];
ti3 = cc[ac+ido] + cc[ac+3*ido];
tr1 = cc[ac-1] - cc[ac+2*ido-1];
tr2 = cc[ac-1] + cc[ac+2*ido-1];
ti4 = cc[ac+ido-1] - cc[ac+3*ido-1];
tr3 = cc[ac+ido-1] + cc[ac+3*ido-1];
ah = k*ido;
ch[ah] = tr2 + tr3;
ch[ah+2*l1*ido] = tr2 - tr3;
ch[ah+1] = ti2 + ti3;
ch[ah+2*l1*ido+1] = ti2 - ti3;
ch[ah+l1*ido] = tr1 + isign*tr4;
ch[ah+3*l1*ido] = tr1 - isign*tr4;
ch[ah+l1*ido+1] = ti1 + isign*ti4;
ch[ah+3*l1*ido+1] = ti1 - isign*ti4;
}
} else {
for (k = 0; k < l1; k++)
{
for (i = 0; i < ido-1; i += 2)
{
ac = i + 1 + 4*k*ido;
ti1 = cc[ac] - cc[ac+2*ido];
ti2 = cc[ac] + cc[ac+2*ido];
ti3 = cc[ac+ido] + cc[ac+3*ido];
tr4 = cc[ac+3*ido] - cc[ac+ido];
tr1 = cc[ac-1] - cc[ac+2*ido-1];
tr2 = cc[ac-1] + cc[ac+2*ido-1];
ti4 = cc[ac+ido-1] - cc[ac+3*ido-1];
tr3 = cc[ac+ido-1] + cc[ac+3*ido-1];
ah = i + k*ido;
ch[ah] = tr2 + tr3;
cr3 = tr2 - tr3;
ch[ah+1] = ti2 + ti3;
ci3 = ti2 - ti3;
cr2 = tr1 + isign*tr4;
cr4 = tr1 - isign*tr4;
ci2 = ti1 + isign*ti4;
ci4 = ti1 - isign*ti4;
ch[ah+l1*ido] = wa1[i]*cr2 - isign*wa1[i+1]*ci2;
ch[ah+l1*ido+1] = wa1[i]*ci2 + isign*wa1[i+1]*cr2;
ch[ah+2*l1*ido] = wa2[i]*cr3 - isign*wa2[i+1]*ci3;
ch[ah+2*l1*ido+1] = wa2[i]*ci3 + isign*wa2[i+1]*cr3;
ch[ah+3*l1*ido] = wa3[i]*cr4 - isign*wa3[i+1]*ci4;
ch[ah+3*l1*ido+1] = wa3[i]*ci4 + isign*wa3[i+1]*cr4;
}
}
}
}
static void passf5(uint16_t ido, uint16_t l1, real_t *cc, real_t *ch,
real_t *wa1, real_t *wa2, real_t *wa3, real_t *wa4,
int8_t isign)
{
static real_t tr11 = 0.309016994374947;
static real_t ti11 = 0.951056516295154;
static real_t tr12 = -0.809016994374947;
static real_t ti12 = 0.587785252292473;
uint16_t i, k, ac, ah;
real_t ci2, ci3, ci4, ci5, di3, di4, di5, di2, cr2, cr3, cr5, cr4,
ti2, ti3, ti4, ti5, dr3, dr4, dr5, dr2, tr2, tr3, tr4, tr5;
if (ido == 2)
{
for (k = 1; k <= l1; ++k)
{
ac = (5*k-4) * ido + 1;
ti5 = cc[ac] - cc[ac+3*ido];
ti2 = cc[ac] + cc[ac+3*ido];
ti4 = cc[ac+ido] - cc[ac+2*ido];
ti3 = cc[ac+ido] + cc[ac+2*ido];
tr5 = cc[ac-1] - cc[ac+3*ido-1];
tr2 = cc[ac-1] + cc[ac+3*ido-1];
tr4 = cc[ac+ido-1] - cc[ac+2*ido-1];
tr3 = cc[ac+ido-1] + cc[ac+2*ido-1];
ah = (k-1) * ido;
ch[ah] = cc[ac-ido-1] + tr2 + tr3;
ch[ah+1] = cc[ac-ido] + ti2 + ti3;
cr2 = cc[ac-ido-1] + tr11*tr2 + tr12*tr3;
ci2 = cc[ac-ido] + tr11*ti2 + tr12*ti3;
cr3 = cc[ac-ido-1] + tr12*tr2 + tr11*tr3;
ci3 = cc[ac-ido] + tr12*ti2 + tr11*ti3;
cr5 = isign * (ti11*tr5 + ti12*tr4);
ci5 = isign * (ti11*ti5 + ti12*ti4);
cr4 = isign * (ti12*tr5 - ti11*tr4);
ci4 = isign * (ti12*ti5 - ti11*ti4);
ch[ah+l1*ido] = cr2 - ci5;
ch[ah+4*l1*ido] = cr2 + ci5;
ch[ah+l1*ido+1] = ci2 + cr5;
ch[ah+2*l1*ido+1]=ci3 + cr4;
ch[ah+2*l1*ido] = cr3 - ci4;
ch[ah+3*l1*ido] = cr3 + ci4;
ch[ah+3*l1*ido+1] = ci3 - cr4;
ch[ah+4*l1*ido+1] = ci2 - cr5;
}
} else {
for (k = 1; k <= l1; k++)
{
for (i = 0; i < ido-1; i += 2)
{
ac = i + 1 + (k*5-4) * ido;
ti5 = cc[ac] - cc[ac+3*ido];
ti2 = cc[ac] + cc[ac+3*ido];
ti4 = cc[ac+ido] - cc[ac+2*ido];
ti3 = cc[ac+ido] + cc[ac+2*ido];
tr5 = cc[ac-1] - cc[ac+3*ido-1];
tr2 = cc[ac-1] + cc[ac+3*ido-1];
tr4 = cc[ac+ido-1] - cc[ac+2*ido-1];
tr3 = cc[ac+ido-1] + cc[ac+2*ido-1];
ah = i + (k-1) * ido;
ch[ah] = cc[ac-ido-1] + tr2 + tr3;
ch[ah+1] = cc[ac-ido] + ti2 + ti3;
cr2 = cc[ac-ido-1] + tr11*tr2 + tr12*tr3;
ci2 = cc[ac-ido] + tr11*ti2 + tr12*ti3;
cr3 = cc[ac-ido-1] + tr12*tr2 + tr11*tr3;
ci3 = cc[ac-ido] + tr12*ti2 + tr11*ti3;
cr5 = isign * (ti11*tr5 + ti12*tr4);
ci5 = isign * (ti11*ti5 + ti12*ti4);
cr4 = isign * (ti12*tr5 - ti11*tr4);
ci4 = isign * (ti12*ti5 - ti11*ti4);
dr3 = cr3 - ci4;
dr4 = cr3 + ci4;
di3 = ci3 + cr4;
di4 = ci3 - cr4;
dr5 = cr2 + ci5;
dr2 = cr2 - ci5;
di5 = ci2 - cr5;
di2 = ci2 + cr5;
ch[ah+l1*ido] = wa1[i]*dr2 - isign*wa1[i+1]*di2;
ch[ah+l1*ido+1] = wa1[i]*di2 + isign*wa1[i+1]*dr2;
ch[ah+2*l1*ido] = wa2[i]*dr3 - isign*wa2[i+1]*di3;
ch[ah+2*l1*ido+1] = wa2[i]*di3 + isign*wa2[i+1]*dr3;
ch[ah+3*l1*ido] = wa3[i]*dr4 - isign*wa3[i+1]*di4;
ch[ah+3*l1*ido+1] = wa3[i]*di4 + isign*wa3[i+1]*dr4;
ch[ah+4*l1*ido] = wa4[i]*dr5 - isign*wa4[i+1]*di5;
ch[ah+4*l1*ido+1] = wa4[i]*di5 + isign*wa4[i+1]*dr5;
}
}
}
}
static void passf(uint16_t *nac, uint16_t ido, uint16_t ip, uint16_t l1,
uint16_t idl1, real_t *cc, real_t *ch, real_t *wa,
int8_t isign)
{
uint16_t idij, idlj, idot, ipph, i, j, k, l, jc, lc, ik, nt, idj, idl;
uint16_t inc, idp;
real_t wai, war;
idot = ido / 2;
nt = ip*idl1;
ipph = (ip+1) / 2;
idp = ip*ido;
if (ido >= l1)
{
for (j = 1; j < ipph; j++)
{
jc = ip - j;
for (k = 0; k < l1; k++)
{
for (i = 0; i < ido; i++)
{
ch[i+(k+j*l1)*ido] = cc[i+(j+k*ip)*ido] + cc[i+(jc+k*ip)*ido];
ch[i+(k+jc*l1)*ido] = cc[i+(j+k*ip)*ido] - cc[i+(jc+k*ip)*ido];
}
}
}
for (k = 0; k < l1; k++)
{
for (i = 0; i < ido; i++)
ch[i+k*ido] = cc[i+k*ip*ido];
}
} else {
for (j = 1; j < ipph; j++)
{
jc = ip - j;
for (i = 0; i < ido; i++)
{
for (k = 0; k < l1; k++)
{
ch[i+(k+j*l1)*ido] = cc[i+(j+k*ip)*ido] + cc[i+(jc+k*ip)*ido];
ch[i+(k+jc*l1)*ido] = cc[i+(j+k*ip)*ido] - cc[i+(jc+k*ip)*ido];
}
}
}
for (i = 0; i < ido; i++)
{
for (k = 0; k < l1; k++)
ch[i+k*ido] = cc[i+k*ip*ido];
}
}
idl = 2 - ido;
inc = 0;
for (l = 1; l < ipph; l++)
{
lc = ip - l;
idl += ido;
for (ik = 0; ik < idl1; ik++)
{
cc[ik+l*idl1] = ch[ik] + wa[idl-2]*ch[ik+idl1];
cc[ik+lc*idl1] = isign*wa[idl-1]*ch[ik+(ip-1)*idl1];
}
idlj = idl;
inc += ido;
for (j = 2; j < ipph; j++)
{
jc = ip - j;
idlj += inc;
if (idlj > idp)
idlj -= idp;
war = wa[idlj-2];
wai = wa[idlj-1];
for (ik = 0; ik < idl1; ik++)
{
cc[ik+l*idl1] += war*ch[ik+j*idl1];
cc[ik+lc*idl1] += isign*wai*ch[ik+jc*idl1];
}
}
}
for (j = 1; j < ipph; j++)
{
for (ik = 0; ik < idl1; ik++)
ch[ik] += ch[ik+j*idl1];
}
for (j = 1; j < ipph; j++)
{
jc = ip - j;
for (ik = 1; ik < idl1; ik += 2)
{
ch[ik-1+j*idl1] = cc[ik-1+j*idl1] - cc[ik+jc*idl1];
ch[ik-1+jc*idl1] = cc[ik-1+j*idl1] + cc[ik+jc*idl1];
ch[ik+j*idl1] = cc[ik+j*idl1] + cc[ik-1+jc*idl1];
ch[ik+jc*idl1] = cc[ik+j*idl1] - cc[ik-1+jc*idl1];
}
}
*nac = 1;
if (ido == 2)
return;
*nac = 0;
for (ik = 0; ik < idl1; ik++)
cc[ik] = ch[ik];
for (j = 1; j < ip; j++)
{
for (k = 0; k < l1; k++)
{
cc[(k+j*l1)*ido+0] = ch[(k+j*l1)*ido+0];
cc[(k+j*l1)*ido+1] = ch[(k+j*l1)*ido+1];
}
}
if (idot <= l1)
{
idij = 0;
for (j = 1; j < ip; j++)
{
idij += 2;
for (i = 3; i < ido; i += 2)
{
idij += 2;
for (k = 0; k < l1; k++)
{
cc[i-1+(k+j*l1)*ido] = wa[idij-2] * ch[i-1+(k+j*l1)*ido] -
isign * wa[idij-1] * ch[i+(k+j*l1)*ido];
cc[i+(k+j*l1)*ido] = wa[idij-2] * ch[i+(k+j*l1)*ido] +
isign * wa[idij-1] * ch[i-1+(k+j*l1)*ido];
}
}
}
} else {
idj = 2 - ido;
for (j = 1; j < ip; j++)
{
idj += ido;
for (k = 0; k < l1; k++)
{
idij = idj;
for (i = 3; i < ido; i += 2)
{
idij += 2;
cc[i-1+(k+j*l1)*ido] = wa[idij-2] * ch[i-1+(k+j*l1)*ido] -
isign * wa[idij-1] * ch[i+(k+j*l1)*ido];
cc[i+(k+j*l1)*ido] = wa[idij-2] * ch[i+(k+j*l1)*ido] +
isign * wa[idij-1] * ch[i-1+(k+j*l1)*ido];
}
}
}
}
}
/*----------------------------------------------------------------------
cfftf1, cfftf, cfftb, cffti1, cffti. Complex FFTs.
----------------------------------------------------------------------*/
INLINE void cfftf1(uint16_t n, real_t *c, real_t *ch, real_t *wa,
uint16_t *ifac, int8_t isign)
{
uint16_t idot, i;
uint16_t k1, l1, l2;
uint16_t na, nf, ip, iw, ix2, ix3, ix4, nac, ido, idl1;
nf = ifac[1];
na = 0;
l1 = 1;
iw = 0;
for (k1 = 2; k1 <= nf+1; k1++)
{
ip = ifac[k1];
l2 = ip*l1;
ido = n / l2;
idot = ido+ido;
idl1 = idot*l1;
switch (ip)
{
case 2:
if (na == 0)
passf2(idot, l1, c, ch, &wa[iw], isign);
else
passf2(idot, l1, ch, c, &wa[iw], isign);
na = 1 - na;
break;
case 3:
ix2 = iw + idot;
if (na == 0)
passf3(idot, l1, c, ch, &wa[iw], &wa[ix2], isign);
else
passf3(idot, l1, ch, c, &wa[iw], &wa[ix2], isign);
na = 1 - na;
break;
case 4:
ix2 = iw + idot;
ix3 = ix2 + idot;
if (na == 0)
passf4(idot, l1, c, ch, &wa[iw], &wa[ix2], &wa[ix3], isign);
else
passf4(idot, l1, ch, c, &wa[iw], &wa[ix2], &wa[ix3], isign);
na = 1 - na;
break;
case 5:
ix2 = iw + idot;
ix3 = ix2 + idot;
ix4 = ix3 + idot;
if (na == 0)
passf5(idot, l1, c, ch, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], isign);
else
passf5(idot, l1, ch, c, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], isign);
na = 1 - na;
break;
default:
if (na == 0)
passf(&nac, idot, ip, l1, idl1, c, ch, &wa[iw], isign);
else
passf(&nac, idot, ip, l1, idl1, ch, c, &wa[iw], isign);
if (nac != 0)
na = 1 - na;
break;
}
l1 = l2;
iw += (ip-1) * idot;
}
if (na == 0)
return;
for (i = 0; i < 2*n; i++)
c[i] = ch[i];
}
void cfftf(cfft_info cfft, real_t *c)
{
cfftf1(cfft.n, c, cfft.work, cfft.tab, cfft.ifac, -1);
}
void cfftb(cfft_info cfft, real_t *c)
{
cfftf1(cfft.n, c, cfft.work, cfft.tab, cfft.ifac, +1);
}
static void cffti1(uint16_t n, real_t *wa, uint16_t *ifac)
{
static uint16_t ntryh[4] = {3, 4, 2, 5};
real_t arg, argh, argld, fi;
uint16_t idot, ntry, i, j;
uint16_t i1, k1, l1, l2, ib;
uint16_t ld, ii, nf, ip, nl, nq, nr;
uint16_t ido, ipm;
nl = n;
nf = 0;
j = 0;
startloop:
j++;
if (j <= 4)
ntry = ntryh[j-1];
else
ntry += 2;
do
{
nq = nl / ntry;
nr = nl - ntry*nq;
if (nr != 0)
goto startloop;
nf++;
ifac[nf+1] = ntry;
nl = nq;
if (ntry == 2 && nf != 1)
{
for (i = 2; i <= nf; i++)
{
ib = nf - i + 2;
ifac[ib+1] = ifac[ib];
}
ifac[2] = 2;
}
} while (nl != 1);
ifac[0] = n;
ifac[1] = nf;
argh = 2*M_PI / (real_t)n;
i = 1;
l1 = 1;
for (k1 = 1; k1 <= nf; k1++)
{
ip = ifac[k1+1];
ld = 0;
l2 = l1*ip;
ido = n / l2;
idot = ido + ido + 2;
ipm = ip - 1;
for (j = 1; j <= ipm; j++)
{
i1 = i;
wa[i-1] = 1;
wa[i] = 0;
ld += l1;
fi = 0;
argld = ld*argh;
for (ii = 4; ii <= idot; ii += 2)
{
i += 2;
fi += 1;
arg = fi*argld;
wa[i-1] = cos(arg);
wa[i] = sin(arg);
}
if (ip > 5)
{
wa[i1-1] = wa[i-1];
wa[i1] = wa[i];
}
}
l1 = l2;
}
}
cfft_info cffti(uint16_t n)
{
cfft_info cfft;
cfft.n = n;
cfft.work = malloc(2*n*sizeof(real_t));
cfft.tab = malloc(2*n*sizeof(real_t));
cffti1(n, cfft.tab, cfft.ifac);
return cfft;
}
void cfftu(cfft_info cfft)
{
if (cfft.work) free(cfft.work);
if (cfft.tab) free(cfft.tab);
}