ref: e7a86f9e7d40a6d6354453109fc1c8b6852b0a38
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 1.10 2002/11/28 18:48:29 menno Exp $
**/
/*
* Algorithmically based on Fortran-77 FFTPACK
* by Paul N. Swarztrauber(Version 4, 1985).
*
* Does even sized fft only
*/
/* isign is +1 for backward and -1 for forward transforms */
#include "common.h"
#include "structs.h"
#include <stdlib.h>
#ifdef _WIN32_WCE
#define assert(x)
#else
#include <assert.h>
#endif
#include "cfft.h"
#include "cfft_tab.h"
/*----------------------------------------------------------------------
passf2, passf3, passf4, passf5. Complex FFT passes fwd and bwd.
----------------------------------------------------------------------*/
static void passf2(uint16_t ido, uint16_t l1, complex_t *cc, complex_t *ch,
complex_t *wa, int8_t isign)
{
uint16_t i, k, ah, ac;
if (ido == 1)
{
for (k = 0; k < l1; k++)
{
ah = 2*k;
ac = 4*k;
RE(ch[ah]) = RE(cc[ac]) + RE(cc[ac+1]);
IM(ch[ah]) = IM(cc[ac]) + IM(cc[ac+1]);
RE(ch[ah+l1]) = RE(cc[ac]) - RE(cc[ac+1]);
IM(ch[ah+l1]) = IM(cc[ac]) - IM(cc[ac+1]);
}
} else {
for (k = 0; k < l1; k++)
{
ah = k*ido;
ac = 2*k*ido;
for (i = 0; i < ido; i++)
{
complex_t t2;
RE(ch[ah]) = RE(cc[ac]) + RE(cc[ac+ido]);
IM(ch[ah]) = IM(cc[ac]) + IM(cc[ac+ido]);
RE(t2) = RE(cc[ac]) - RE(cc[ac+ido]);
IM(t2) = IM(cc[ac]) - IM(cc[ac+ido]);
RE(ch[ah+l1*ido]) = MUL_R_C(RE(t2),RE(wa[i])) - MUL_R_C(IM(t2),IM(wa[i]))*isign;
IM(ch[ah+l1*ido]) = MUL_R_C(IM(t2),RE(wa[i])) + MUL_R_C(RE(t2),IM(wa[i]))*isign;
ah++;
ac++;
}
}
}
}
static void passf3(uint16_t ido, uint16_t l1, complex_t *cc, complex_t *ch,
complex_t *wa1, complex_t *wa2, int8_t isign)
{
static real_t taur = COEF_CONST(-0.5);
static real_t taui = COEF_CONST(0.866025403784439);
uint16_t i, k, ac, ah;
complex_t c2, c3, d2, d3, t2;
if (ido == 1)
{
for (k = 0; k < l1; k++)
{
ac = 3*k+1;
ah = k;
RE(t2) = RE(cc[ac]) + RE(cc[ac+1]);
IM(t2) = IM(cc[ac]) + IM(cc[ac+1]);
RE(c2) = RE(cc[ac-1]) + MUL_R_C(RE(t2),taur);
IM(c2) = IM(cc[ac-1]) + MUL_R_C(IM(t2),taur);
RE(ch[ah]) = RE(cc[ac-1]) + RE(t2);
IM(ch[ah]) = IM(cc[ac-1]) + IM(t2);
RE(c3) = MUL_R_C((RE(cc[ac]) - RE(cc[ac+1])), taui)*isign;
IM(c3) = MUL_R_C((IM(cc[ac]) - IM(cc[ac+1])), taui)*isign;
RE(ch[ah+l1]) = RE(c2) - IM(c3);
IM(ch[ah+l1]) = IM(c2) + RE(c3);
RE(ch[ah+2*l1]) = RE(c2) + IM(c3);
IM(ch[ah+2*l1]) = IM(c2) - RE(c3);
}
} else {
for (k = 0; k < l1; k++)
{
for (i = 0; i < ido; i++)
{
ac = i + (3*k+1)*ido;
ah = i + k * ido;
RE(t2) = RE(cc[ac]) + RE(cc[ac+ido]);
RE(c2) = RE(cc[ac-ido]) + MUL_R_C(RE(t2),taur);
IM(t2) = IM(cc[ac]) + IM(cc[ac+ido]);
IM(c2) = IM(cc[ac-ido]) + MUL_R_C(IM(t2),taur);
RE(ch[ah]) = RE(cc[ac-ido]) + RE(t2);
IM(ch[ah]) = IM(cc[ac-ido]) + IM(t2);
RE(c3) = MUL_R_C((RE(cc[ac]) - RE(cc[ac+ido])), taui)*isign;
IM(c3) = MUL_R_C((IM(cc[ac]) - IM(cc[ac+ido])), taui)*isign;
RE(d2) = RE(c2) - IM(c3);
IM(d3) = IM(c2) - RE(c3);
RE(d3) = RE(c2) + IM(c3);
IM(d2) = IM(c2) + RE(c3);
RE(ch[ah+l1*ido]) = MUL_R_C(RE(d2),RE(wa1[i])) - MUL_R_C(IM(d2),IM(wa1[i]))*isign;
IM(ch[ah+l1*ido]) = MUL_R_C(IM(d2),RE(wa1[i])) + MUL_R_C(RE(d2),IM(wa1[i]))*isign;
RE(ch[ah+l1*2*ido]) = MUL_R_C(RE(d3),RE(wa2[i])) - MUL_R_C(IM(d3),IM(wa2[i]))*isign;
IM(ch[ah+l1*2*ido]) = MUL_R_C(IM(d3),RE(wa2[i])) + MUL_R_C(RE(d3),IM(wa2[i]))*isign;
}
}
}
}
static void passf4(uint16_t ido, uint16_t l1, complex_t *cc, complex_t *ch,
complex_t *wa1, complex_t *wa2, complex_t *wa3, int8_t isign)
{
uint16_t i, k, ac, ah;
complex_t c2, c3, c4, t1, t2, t3, t4;
if (ido == 1)
{
for (k = 0; k < l1; k++)
{
ac = 4*k;
ah = k;
RE(t2) = RE(cc[ac]) + RE(cc[ac+2]);
IM(t2) = IM(cc[ac]) + IM(cc[ac+2]);
RE(t3) = RE(cc[ac+1]) + RE(cc[ac+3]);
IM(t3) = IM(cc[ac+1]) + IM(cc[ac+3]);
RE(t1) = RE(cc[ac]) - RE(cc[ac+2]);
IM(t1) = IM(cc[ac]) - IM(cc[ac+2]);
RE(t4) = IM(cc[ac+3]) - IM(cc[ac+1]);
IM(t4) = RE(cc[ac+1]) - RE(cc[ac+3]);
RE(ch[ah]) = RE(t2) + RE(t3);
IM(ch[ah]) = IM(t2) + IM(t3);
RE(ch[ah+l1]) = RE(t1) + RE(t4)*isign;
IM(ch[ah+l1]) = IM(t1) + IM(t4)*isign;
RE(ch[ah+2*l1]) = RE(t2) - RE(t3);
IM(ch[ah+2*l1]) = IM(t2) - IM(t3);
RE(ch[ah+3*l1]) = RE(t1) - RE(t4)*isign;
IM(ch[ah+3*l1]) = IM(t1) - IM(t4)*isign;
}
} else {
for (k = 0; k < l1; k++)
{
for (i = 0; i < ido; i++)
{
ac = i + 4*k*ido;
ah = i + k*ido;
RE(t2) = RE(cc[ac]) + RE(cc[ac+2*ido]);
IM(t2) = IM(cc[ac]) + IM(cc[ac+2*ido]);
RE(t3) = RE(cc[ac+ido]) + RE(cc[ac+3*ido]);
IM(t3) = IM(cc[ac+ido]) + IM(cc[ac+3*ido]);
RE(t1) = RE(cc[ac]) - RE(cc[ac+2*ido]);
IM(t1) = IM(cc[ac]) - IM(cc[ac+2*ido]);
RE(t4) = IM(cc[ac+3*ido]) - IM(cc[ac+ido]);
IM(t4) = RE(cc[ac+ido]) - RE(cc[ac+3*ido]);
RE(ch[ah]) = RE(t2) + RE(t3);
IM(ch[ah]) = IM(t2) + IM(t3);
RE(c2) = RE(t1) + RE(t4)*isign;
IM(c2) = IM(t1) + IM(t4)*isign;
RE(c3) = RE(t2) - RE(t3);
IM(c3) = IM(t2) - IM(t3);
RE(c4) = RE(t1) - RE(t4)*isign;
IM(c4) = IM(t1) - IM(t4)*isign;
RE(ch[ah+l1*ido]) = MUL_R_C(RE(c2),RE(wa1[i])) - MUL_R_C(IM(c2),IM(wa1[i]))*isign;
IM(ch[ah+l1*ido]) = MUL_R_C(IM(c2),RE(wa1[i])) + MUL_R_C(RE(c2),IM(wa1[i]))*isign;
RE(ch[ah+2*l1*ido]) = MUL_R_C(RE(c3),RE(wa2[i])) - MUL_R_C(IM(c3),IM(wa2[i]))*isign;
IM(ch[ah+2*l1*ido]) = MUL_R_C(IM(c3),RE(wa2[i])) + MUL_R_C(RE(c3),IM(wa2[i]))*isign;
RE(ch[ah+3*l1*ido]) = MUL_R_C(RE(c4),RE(wa3[i])) - MUL_R_C(IM(c4),IM(wa3[i]))*isign;
IM(ch[ah+3*l1*ido]) = MUL_R_C(IM(c4),RE(wa3[i])) + MUL_R_C(RE(c4),IM(wa3[i]))*isign;
}
}
}
}
static void passf5(uint16_t ido, uint16_t l1, complex_t *cc, complex_t *ch,
complex_t *wa1, complex_t *wa2, complex_t *wa3, complex_t *wa4,
int8_t isign)
{
static real_t tr11 = COEF_CONST(0.309016994374947);
static real_t ti11 = COEF_CONST(0.951056516295154);
static real_t tr12 = COEF_CONST(-0.809016994374947);
static real_t ti12 = COEF_CONST(0.587785252292473);
uint16_t i, k, ac, ah;
complex_t c2, c3, c4, c5, d3, d4, d5, d2, t2, t3, t4, t5;
if (ido == 1)
{
for (k = 0; k < l1; k++)
{
ac = 5*k + 1;
ah = k;
RE(t2) = RE(cc[ac]) + RE(cc[ac+3]);
IM(t2) = IM(cc[ac]) + IM(cc[ac+3]);
RE(t3) = RE(cc[ac+1]) + RE(cc[ac+2]);
IM(t3) = IM(cc[ac+1]) + IM(cc[ac+2]);
RE(t4) = RE(cc[ac+1]) - RE(cc[ac+2]);
IM(t4) = IM(cc[ac+1]) - IM(cc[ac+2]);
RE(t5) = RE(cc[ac]) - RE(cc[ac+3]);
IM(t5) = IM(cc[ac]) - IM(cc[ac+3]);
RE(ch[ah]) = RE(cc[ac-1]) + RE(t2) + RE(t3);
IM(ch[ah]) = IM(cc[ac-1]) + IM(t2) + IM(t3);
RE(c2) = RE(cc[ac-1]) + MUL_R_C(RE(t2),tr11) + MUL_R_C(RE(t3),tr12);
IM(c2) = IM(cc[ac-1]) + MUL_R_C(IM(t2),tr11) + MUL_R_C(IM(t3),tr12);
RE(c3) = RE(cc[ac-1]) + MUL_R_C(RE(t2),tr12) + MUL_R_C(RE(t3),tr11);
IM(c3) = IM(cc[ac-1]) + MUL_R_C(IM(t2),tr12) + MUL_R_C(IM(t3),tr11);
RE(c4) = (MUL_R_C(RE(t5),ti12)*isign - MUL_R_C(RE(t4),ti11));
IM(c4) = (MUL_R_C(IM(t5),ti12)*isign - MUL_R_C(IM(t4),ti11));
RE(c5) = (MUL_R_C(RE(t5),ti11)*isign + MUL_R_C(RE(t4),ti12));
IM(c5) = (MUL_R_C(IM(t5),ti11)*isign + MUL_R_C(IM(t4),ti12));
RE(ch[ah+l1]) = RE(c2) - IM(c5);
IM(ch[ah+l1]) = IM(c2) + RE(c5);
RE(ch[ah+2*l1]) = RE(c3) - IM(c4);
IM(ch[ah+2*l1]) = IM(c3) + RE(c4);
RE(ch[ah+3*l1]) = RE(c3) + IM(c4);
IM(ch[ah+3*l1]) = IM(c3) - RE(c4);
RE(ch[ah+4*l1]) = RE(c2) + IM(c5);
IM(ch[ah+4*l1]) = IM(c2) - RE(c5);
}
} else {
for (k = 0; k < l1; k++)
{
for (i = 0; i < ido; i++)
{
ac = i + (k*5 + 1) * ido;
ah = i + k * ido;
RE(t2) = RE(cc[ac]) + RE(cc[ac+3*ido]);
IM(t2) = IM(cc[ac]) + IM(cc[ac+3*ido]);
RE(t3) = RE(cc[ac+ido]) + RE(cc[ac+2*ido]);
IM(t3) = IM(cc[ac+ido]) + IM(cc[ac+2*ido]);
RE(t4) = RE(cc[ac+ido]) - RE(cc[ac+2*ido]);
IM(t4) = IM(cc[ac+ido]) - IM(cc[ac+2*ido]);
RE(t5) = RE(cc[ac]) - RE(cc[ac+3*ido]);
IM(t5) = IM(cc[ac]) - IM(cc[ac+3*ido]);
RE(ch[ah]) = RE(cc[ac-ido]) + RE(t2) + RE(t3);
IM(ch[ah]) = IM(cc[ac-ido]) + IM(t2) + IM(t3);
RE(c2) = RE(cc[ac-ido]) + MUL_R_C(RE(t2),tr11) + MUL_R_C(RE(t3),tr12);
IM(c2) = IM(cc[ac-ido]) + MUL_R_C(IM(t2),tr11) + MUL_R_C(IM(t3),tr12);
RE(c3) = RE(cc[ac-ido]) + MUL_R_C(RE(t2),tr12) + MUL_R_C(RE(t3),tr11);
IM(c3) = IM(cc[ac-ido]) + MUL_R_C(IM(t2),tr12) + MUL_R_C(IM(t3),tr11);
RE(c4) = (MUL_R_C(RE(t5),ti12)*isign - MUL_R_C(RE(t4),ti11));
IM(c4) = (MUL_R_C(IM(t5),ti12)*isign - MUL_R_C(IM(t4),ti11));
RE(c5) = (MUL_R_C(RE(t5),ti11)*isign + MUL_R_C(RE(t4),ti12));
IM(c5) = (MUL_R_C(IM(t5),ti11)*isign + MUL_R_C(IM(t4),ti12));
IM(d2) = IM(c2) + RE(c5);
IM(d3) = IM(c3) + RE(c4);
RE(d4) = RE(c3) + IM(c4);
RE(d5) = RE(c2) + IM(c5);
RE(d2) = RE(c2) - IM(c5);
IM(d5) = IM(c2) - RE(c5);
RE(d3) = RE(c3) - IM(c4);
IM(d4) = IM(c3) - RE(c4);
RE(ch[ah+l1*ido]) = MUL_R_C(RE(d2),RE(wa1[i])) - MUL_R_C(IM(d2),IM(wa1[i]))*isign;
IM(ch[ah+l1*ido]) = MUL_R_C(IM(d2),RE(wa1[i])) + MUL_R_C(RE(d2),IM(wa1[i]))*isign;
RE(ch[ah+2*l1*ido]) = MUL_R_C(RE(d3),RE(wa2[i])) - MUL_R_C(IM(d3),IM(wa2[i]))*isign;
IM(ch[ah+2*l1*ido]) = MUL_R_C(IM(d3),RE(wa2[i])) + MUL_R_C(RE(d3),IM(wa2[i]))*isign;
RE(ch[ah+3*l1*ido]) = MUL_R_C(RE(d4),RE(wa3[i])) - MUL_R_C(IM(d4),IM(wa3[i]))*isign;
IM(ch[ah+3*l1*ido]) = MUL_R_C(IM(d4),RE(wa3[i])) + MUL_R_C(RE(d4),IM(wa3[i]))*isign;
RE(ch[ah+4*l1*ido]) = MUL_R_C(RE(d5),RE(wa4[i])) - MUL_R_C(IM(d5),IM(wa4[i]))*isign;
IM(ch[ah+4*l1*ido]) = MUL_R_C(IM(d5),RE(wa4[i])) + MUL_R_C(RE(d5),IM(wa4[i]))*isign;
}
}
}
}
/*----------------------------------------------------------------------
cfftf1, cfftf, cfftb, cffti1, cffti. Complex FFTs.
----------------------------------------------------------------------*/
INLINE void cfftf1(uint16_t n, complex_t *c, complex_t *ch,
uint16_t *ifac, complex_t *wa, int8_t isign)
{
uint16_t i;
uint16_t k1, l1, l2;
uint16_t na, nf, ip, iw, ix2, ix3, ix4, 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;
idl1 = ido*l1;
switch (ip)
{
case 2:
if (na == 0)
passf2(ido, l1, c, ch, &wa[iw], isign);
else
passf2(ido, l1, ch, c, &wa[iw], isign);
na = 1 - na;
break;
case 3:
ix2 = iw + ido;
if (na == 0)
passf3(ido, l1, c, ch, &wa[iw], &wa[ix2], isign);
else
passf3(ido, l1, ch, c, &wa[iw], &wa[ix2], isign);
na = 1 - na;
break;
case 4:
ix2 = iw + ido;
ix3 = ix2 + ido;
if (na == 0)
passf4(ido, l1, c, ch, &wa[iw], &wa[ix2], &wa[ix3], isign);
else
passf4(ido, l1, ch, c, &wa[iw], &wa[ix2], &wa[ix3], isign);
na = 1 - na;
break;
case 5:
ix2 = iw + ido;
ix3 = ix2 + ido;
ix4 = ix3 + ido;
if (na == 0)
passf5(ido, l1, c, ch, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], isign);
else
passf5(ido, l1, ch, c, &wa[iw], &wa[ix2], &wa[ix3], &wa[ix4], isign);
na = 1 - na;
break;
}
l1 = l2;
iw += (ip-1) * ido;
}
if (na == 0)
return;
for (i = 0; i < n; i++)
{
RE(c[i]) = RE(ch[i]);
IM(c[i]) = IM(ch[i]);
}
}
void cfftf(cfft_info *cfft, complex_t *c)
{
cfftf1(cfft->n, c, cfft->work, cfft->ifac, cfft->tab, -1);
}
void cfftb(cfft_info *cfft, complex_t *c)
{
cfftf1(cfft->n, c, cfft->work, cfft->ifac, cfft->tab, +1);
}
static void cffti1(uint16_t n, complex_t *wa, uint16_t *ifac)
{
static uint16_t ntryh[4] = {3, 4, 2, 5};
#ifndef FIXED_POINT
real_t arg, argh, argld, fi;
uint16_t ido, ipm;
uint16_t i1, k1, l1, l2;
uint16_t ld, ii, ip;
#endif
uint16_t ntry, i, j;
uint16_t ib;
uint16_t nf, nl, nq, nr;
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;
#ifndef FIXED_POINT
argh = 2.0*M_PI / (real_t)n;
i = 0;
l1 = 1;
for (k1 = 1; k1 <= nf; k1++)
{
ip = ifac[k1+1];
ld = 0;
l2 = l1*ip;
ido = n / l2;
ipm = ip - 1;
for (j = 0; j < ipm; j++)
{
i1 = i;
RE(wa[i]) = 1.0;
IM(wa[i]) = 0.0;
ld += l1;
fi = 0;
argld = ld*argh;
for (ii = 0; ii < ido; ii++)
{
i++;
fi++;
arg = fi * argld;
RE(wa[i]) = cos(arg);
IM(wa[i]) = sin(arg);
}
if (ip > 5)
{
RE(wa[i1]) = RE(wa[i]);
IM(wa[i1]) = IM(wa[i]);
}
}
l1 = l2;
}
#endif
}
cfft_info *cffti(uint16_t n)
{
cfft_info *cfft = (cfft_info*)malloc(sizeof(cfft_info));
cfft->n = n;
cfft->work = (complex_t*)malloc(n*sizeof(complex_t));
#ifndef FIXED_POINT
cfft->tab = (complex_t*)malloc(n*sizeof(complex_t));
cffti1(n, cfft->tab, cfft->ifac);
#else
cffti1(n, NULL, cfft->ifac);
switch (n)
{
case 60: cfft->tab = cfft_tab_60; break;
case 64: cfft->tab = cfft_tab_64; break;
case 480: cfft->tab = cfft_tab_480; break;
case 512: cfft->tab = cfft_tab_512; break;
#ifdef LD_DEC
case 240: cfft->tab = cfft_tab_240; break;
case 256: cfft->tab = cfft_tab_256; break;
#endif
}
#endif
return cfft;
}
void cfftu(cfft_info *cfft)
{
if (cfft->work) free(cfft->work);
#ifndef FIXED_POINT
if (cfft->tab) free(cfft->tab);
#endif
if (cfft) free(cfft);
}