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mxfft.c
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/*
mxfft.c:
Copyright (C) 2002 Trevor Wishart, Keith Henderson
This file is part of Csound.
The Csound Library is free software; you can redistribute it
and/or modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
Csound 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 Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with Csound; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA
*/
/* This program converted from the FORTRAN routines by Singleton in
* Section 1.4 of "Programs for Digital Signal Processing", IEEE Press, 1979.
* Conversion by Trevor Wishart and Keith Henderson, York Univ.
*/
/*
static char *rcsid = "$Id$";
*/
/*
* $Log$
* Revision 1.15 2008-12-04 14:55:04 jpff
* Branch prediction
*
* Revision 1.14 2005/08/13 14:44:37 istvanv
* Minor code changes
*
* Revision 1.13 2005/08/12 19:01:23 istvanv
* Renamed ENVIRON to CSOUND
*
* Revision 1.12 2005/08/10 09:57:07 istvanv
* Use CSOUND* type for Csound instance pointers instead of void*
*
* Revision 1.11 2005/07/15 10:13:28 istvanv
* Removed cs.h
*
* Revision 1.10 2005/06/05 16:36:24 istvanv
* Minor code improvements
*
* Revision 1.9 2005/06/05 13:07:08 istvanv
* Added mxfft.c functions to API
*
* Revision 1.8 2005/05/28 13:00:02 istvanv
* Minor code changes (tabs etc.)
*
* Revision 1.7 2005/04/17 17:56:25 jpff
* Warnings
*
* Revision 1.6 2005/02/18 16:21:14 istvanv
* added csound pointer to csound->Malloc, auxalloc, and other functions
*
* Revision 1.5 2005/01/27 19:22:50 istvanv
* Merged changes from 4.24.1, including new localization system,
* timers, and allow use of underscore character in opcode names
*
* Revision 1.4 2004/09/27 05:52:31 jpff
* Minor coding
*
* Revision 1.3 2004/06/07 11:33:09 jpff
* line endings
*
* Revision 1.2 2004/05/31 15:53:06 jpff
* Removing warnings mainly
*
* Revision 1.1.1.1 2003/06/19 11:11:53 jpff
* Initial upload of sources
*
* Revision 1.2 2003/05/21 11:31:06 jpff
* Added Copyrigt notices
*
* Revision 3.4 1994/10/31 17:37:28 martin
* Starting with rcs
*
*/
#include "csoundCore.h"
#include <math.h>
#include <assert.h>
static void fft_(CSOUND *,MYFLT *, MYFLT *, int, int, int, int);
static void fftmx(MYFLT *, MYFLT *, int, int, int, int, int,
int*, MYFLT *, MYFLT *, MYFLT *, MYFLT *, int *, int[]);
static void reals_(CSOUND *,MYFLT *, MYFLT *, int, int);
/*
*-----------------------------------------------------------------------
* subroutine: fft
* multivariate complex fourier transform, computed in place
* using mixed-radix fast fourier transform algorithm.
*-----------------------------------------------------------------------
*
* this is the call from C:
* fft_(anal,banal,&one,&N2,&one,&mtwo);
* CHANGED TO:-
* fft_(csound,anal,banal,one,N2,one,mtwo);
*/
static void fft_(CSOUND *csound, MYFLT *a, MYFLT *b,
int nseg, int n, int nspn, int isn)
/* *a, pointer to array 'anal' */
/* *b; pointer to array 'banal' */
{
int32 nfac[17]; /* These are one bigger than needed */
/* because wish to use Fortran array */
/* index which runs 1 to n, not 0 to n */
int32 m = 0,
k,
kt,
jj,
j,
nf,
ntot,
maxf, maxp=-1;
/* work space pointers */
void *buf;
MYFLT *at, *ck, *bt, *sk;
int *np;
/* reduce the pointers to input arrays - by doing this, FFT uses FORTRAN
indexing but retains compatibility with C arrays */
a--; b--;
/*
* determine the factors of n
*/
k = nf = abs(n);
if (nf==1)
return;
nspn = abs(nf*nspn);
ntot = abs(nspn*nseg);
for (m=0; !(k%16); nfac[++m]=4,k/=16);
assert(m<16);
for (j=3,jj=9; jj<=k; j+=2,jj=j*j)
for (; !(k%jj); nfac[++m]=j,k/=jj);
if (k<=4) {
kt = m;
nfac[m+1] = k;
if (k != 1)
m++;
}
else {
if (k%4==0) {
nfac[++m]=2;
k/=4;
}
kt = m;
maxp = (kt+kt+2 > k-1 ? kt+kt+2 : k-1);
for (j=2; j<=k; j=1+((j+1)/2)*2)
if (k%j==0) {
nfac[++m]=j;
k/=j;
}
}
if (m <= kt+1)
maxp = m + kt + 1;
if (UNLIKELY(m+kt > 15)) {
csound->Warning(csound, Str("\nerror - fft parameter n has "
"more than 15 factors : %d"), n);
return;
}
if (kt!=0) {
j = kt;
while (j)
nfac[++m]=nfac[j--];
}
maxf = nfac[m-kt];
if (kt > 0 && maxf <nfac[kt])
maxf = nfac[kt];
/* allocate workspace - assume no errors! */
buf = calloc(sizeof(MYFLT) * 4 * maxf + sizeof(int) * maxp, (size_t) 1);
at = (MYFLT*) buf;
ck = (MYFLT*) at + (int) maxf;
bt = (MYFLT*) ck + (int) maxf;
sk = (MYFLT*) bt + (int) maxf;
np = (int*) ((void*) ((MYFLT*) sk + (int) maxf));
/* decrement pointers to allow FORTRAN type usage in fftmx */
at--; bt--; ck--; sk--; np--;
/* call fft driver */
fftmx(a, b, ntot, nf, nspn, isn, m, &kt, at, ck, bt, sk, np, nfac);
/* release working storage before returning - assume no problems */
free(buf);
}
/*
*-----------------------------------------------------------------------
* subroutine: fftmx
* called by subroutine 'fft' to compute mixed-radix fourier transform
*-----------------------------------------------------------------------
*/
static void fftmx(MYFLT *a, MYFLT *b,
int ntot, int n, int nspan, int isn, int m,
int *kt, MYFLT *at, MYFLT *ck, MYFLT *bt, MYFLT *sk,
int *np, int nfac[])
{
int i,inc,
j,jc,jf, jj,
k, k1, k2, k3=0, k4,
kk,klim,ks,kspan, kspnn,
lim,
maxf,mm,
nn,nt;
double aa, aj, ajm, ajp, ak, akm, akp,
bb, bj, bjm, bjp, bk, bkm, bkp,
c1, c2=0, c3=0, c72, cd,
dr,
rad,
sd, s1, s2=0, s3=0, s72, s120;
double xx; /****** ADDED APRIL 1991 *********/
inc=abs(isn);
nt = inc*ntot;
ks = inc*nspan;
/******************* REPLACED MARCH 29: ***********************
rad = atan(1.0);
**************************************************************/
rad = 0.785398163397448278900;
/******************* REPLACED MARCH 29: ***********************
s72 = rad/0.625;
c72 = cos(s72);
s72 = sin(s72);
**************************************************************/
c72 = 0.309016994374947451270;
s72 = 0.951056516295153531190;
/******************* REPLACED MARCH 29: ***********************
s120 = sqrt(0.75);
**************************************************************/
s120 = 0.866025403784438707600;
/* scale by 1/n for isn > 0 ( reverse transform ) */
if (isn < 0) {
s72 = -s72;
s120 = -s120;
rad = -rad;}
else {
ak = 1.0/(double)n;
for (j=1; j<=nt;j += inc) {
a[j] *= (MYFLT)ak;
b[j] *= (MYFLT)ak;
}
}
kspan = ks;
nn = nt - inc;
jc = ks/n;
/* sin, cos values are re-initialised each lim steps */
lim = 32;
klim = lim * jc;
i = 0;
jf = 0;
maxf = m - (*kt);
maxf = nfac[maxf];
if ((*kt) > 0 && maxf < nfac[*kt])
maxf = nfac[*kt];
/*
* compute Fourier transform
*/
lbl40:
dr = (8.0 * (double)jc)/((double)kspan);
/*************************** APRIL 1991 POW & POW2 not WORKING.. REPLACE *******
cd = 2.0 * (pow2 ( sin(0.5 * dr * rad)) );
*******************************************************************************/
xx = sin(0.5 * dr * rad);
cd = 2.0 * xx * xx;
sd = sin(dr * rad);
kk = 1;
if (nfac[++i]!=2) goto lbl110;
/*
* transform for factor of 2 (including rotation factor)
*/
kspan /= 2;
k1 = kspan + 2;
do {
do {
k2 = kk + kspan;
ak = a[k2];
bk = b[k2];
a[k2] = (a[kk]) - (MYFLT)ak;
b[k2] = (b[kk]) - (MYFLT)bk;
a[kk] = (a[kk]) + (MYFLT)ak;
b[kk] = (b[kk]) + (MYFLT)bk;
kk = k2 + kspan;
} while (kk <= nn);
kk -= nn;
} while (kk <= jc);
if (kk > kspan) goto lbl350;
lbl60:
c1 = 1.0 - cd;
s1 = sd;
mm = (k1/2 < klim ? k1/2 :klim);
goto lbl80;
lbl70:
ak = c1 - ((cd*c1)+(sd*s1));
s1 = ((sd*c1)-(cd*s1)) + s1;
c1 = ak;
lbl80:
do {
do {
k2 = kk + kspan;
ak = a[kk] - a[k2];
bk = b[kk] - b[k2];
a[kk] = a[kk] + a[k2];
b[kk] = b[kk] + b[k2];
a[k2] = (MYFLT)((c1 * ak) - (s1 * bk));
b[k2] = (MYFLT)((s1 * ak) + (c1 * bk));
kk = k2 + kspan;
} while (kk < nt);
k2 = kk - nt;
c1 = -c1;
kk = k1 - k2;
} while (kk > k2);
kk += jc;
if (kk <= mm) goto lbl70;
if (kk < k2) goto lbl90;
k1 += (inc + inc);
kk = ((k1-kspan)/2) + jc;
if (kk <= (jc+jc)) goto lbl60;
goto lbl40;
lbl90:
s1 = ((double)((kk-1)/jc)) * dr * rad;
c1 = cos(s1);
s1 = sin(s1);
mm = (k1/2 < mm+klim ? k1/2 : mm+klim);
goto lbl80;
/*
* transform for factor of 3 (optional code)
*/
lbl100:
k1 = kk + kspan;
k2 = k1 + kspan;
ak = a[kk];
bk = b[kk];
aj = a[k1] + a[k2];
bj = b[k1] + b[k2];
a[kk] = (MYFLT)(ak + aj);
b[kk] = (MYFLT)(bk + bj);
ak += (-0.5 * aj);
bk += (-0.5 * bj);
aj = (a[k1] - a[k2]) * s120;
bj = (b[k1] - b[k2]) * s120;
a[k1] = (MYFLT)(ak - bj);
b[k1] = (MYFLT)(bk + aj);
a[k2] = (MYFLT)(ak + bj);
b[k2] = (MYFLT)(bk - aj);
kk = k2 + kspan;
if (kk < nn) goto lbl100;
kk -= nn;
if (kk <= kspan) goto lbl100;
goto lbl290;
/*
* transform for factor of 4
*/
lbl110:
if (nfac[i] != 4) goto lbl230;
kspnn = kspan;
kspan = kspan/4;
lbl120:
c1 = 1.0;
s1 = 0;
mm = (kspan < klim ? kspan : klim);
goto lbl150;
lbl130:
c2 = c1 - ((cd*c1)+(sd*s1));
s1 = ((sd*c1)-(cd*s1)) + s1;
/*
* the following three statements compensate for truncation
* error. if rounded arithmetic is used, substitute
* c1=c2
*
* c1 = (0.5/(pow2(c2)+pow2(s1))) + 0.5;
* s1 = c1*s1;
* c1 = c1*c2;
*/
c1 = c2;
lbl140:
c2 = (c1 * c1) - (s1 * s1);
s2 = c1 * s1 * 2.0;
c3 = (c2 * c1) - (s2 * s1);
s3 = (c2 * s1) + (s2 * c1);
lbl150:
k1 = kk + kspan;
k2 = k1 + kspan;
k3 = k2 + kspan;
akp = a[kk] + a[k2];
akm = a[kk] - a[k2];
ajp = a[k1] + a[k3];
ajm = a[k1] - a[k3];
a[kk] = (MYFLT)(akp + ajp);
ajp = akp - ajp;
bkp = b[kk] + b[k2];
bkm = b[kk] - b[k2];
bjp = b[k1] + b[k3];
bjm = b[k1] - b[k3];
b[kk] = (MYFLT)(bkp + bjp);
bjp = bkp - bjp;
if (isn < 0) goto lbl180;
akp = akm - bjm;
akm = akm + bjm;
bkp = bkm + ajm;
bkm = bkm - ajm;
if (s1 == 0.0) goto lbl190;
lbl160:
a[k1] = (MYFLT)((akp*c1) - (bkp*s1));
b[k1] = (MYFLT)((akp*s1) + (bkp*c1));
a[k2] = (MYFLT)((ajp*c2) - (bjp*s2));
b[k2] = (MYFLT)((ajp*s2) + (bjp*c2));
a[k3] = (MYFLT)((akm*c3) - (bkm*s3));
b[k3] = (MYFLT)((akm*s3) + (bkm*c3));
kk = k3 + kspan;
if (kk <= nt) goto lbl150;
lbl170:
kk -= (nt - jc);
if (kk <= mm) goto lbl130;
if (kk < kspan) goto lbl200;
kk -= (kspan - inc);
if (kk <= jc) goto lbl120;
if (kspan==jc) goto lbl350;
goto lbl40;
lbl180:
akp = akm + bjm;
akm = akm - bjm;
bkp = bkm - ajm;
bkm = bkm + ajm;
if (s1 != 0.0) goto lbl160;
lbl190:
a[k1] = (MYFLT)akp;
b[k1] = (MYFLT)bkp;
a[k2] = (MYFLT)ajp;
b[k2] = (MYFLT)bjp;
a[k3] = (MYFLT)akm;
b[k3] = (MYFLT)bkm;
kk = k3 + kspan;
if (kk <= nt) goto lbl150;
goto lbl170;
lbl200:
s1 = ((double)((kk-1)/jc)) * dr * rad;
c1 = cos(s1);
s1 = sin(s1);
mm = (kspan < mm+klim ? kspan : mm+klim);
goto lbl140;
/*
* transform for factor of 5 (optional code)
*/
lbl210:
c2 = (c72*c72) - (s72*s72);
s2 = 2.0 * c72 * s72;
lbl220:
k1 = kk + kspan;
k2 = k1 + kspan;
k3 = k2 + kspan;
k4 = k3 + kspan;
akp = a[k1] + a[k4];
akm = a[k1] - a[k4];
bkp = b[k1] + b[k4];
bkm = b[k1] - b[k4];
ajp = a[k2] + a[k3];
ajm = a[k2] - a[k3];
bjp = b[k2] + b[k3];
bjm = b[k2] - b[k3];
aa = a[kk];
bb = b[kk];
a[kk] = (MYFLT)(aa + akp + ajp);
b[kk] = (MYFLT)(bb + bkp + bjp);
ak = (akp*c72) + (ajp*c2) + aa;
bk = (bkp*c72) + (bjp*c2) + bb;
aj = (akm*s72) + (ajm*s2);
bj = (bkm*s72) + (bjm*s2);
a[k1] = (MYFLT)(ak - bj);
a[k4] = (MYFLT)(ak + bj);
b[k1] = (MYFLT)(bk + aj);
b[k4] = (MYFLT)(bk - aj);
ak = (akp*c2) + (ajp*c72) + aa;
bk = (bkp*c2) + (bjp*c72) + bb;
aj = (akm*s2) - (ajm*s72);
bj = (bkm*s2) - (bjm*s72);
a[k2] = (MYFLT)(ak - bj);
a[k3] = (MYFLT)(ak + bj);
b[k2] = (MYFLT)(bk + aj);
b[k3] = (MYFLT)(bk - aj);
kk = k4 + kspan;
if (kk < nn) goto lbl220;
kk -= nn;
if (kk <= kspan) goto lbl220;
goto lbl290;
/*
* transform for odd factors
*/
lbl230:
k = nfac[i];
kspnn = kspan;
kspan /= k;
if (k==3) goto lbl100;
if (k==5) goto lbl210;
if (k==jf) goto lbl250;
jf = k;
s1 = rad/(((double)(k))/8.0);
c1 = cos(s1);
s1 = sin(s1);
ck[jf] = FL(1.0);
sk[jf] = FL(0.0);
for (j=1; j<k ; j++) {
ck[j] = (MYFLT)((ck[k])*c1 + (sk[k])*s1);
sk[j] = (MYFLT)((ck[k])*s1 - (sk[k])*c1);
k--;
ck[k] = ck[j];
sk[k] = -(sk[j]);
}
lbl250:
k1 = kk;
k2 = kk + kspnn;
aa = a[kk];
bb = b[kk];
ak = aa;
bk = bb;
j = 1;
k1 += kspan;
do {
k2 -= kspan;
j++;
at[j] = a[k1] + a[k2];
ak = at[j] + ak;
bt[j] = b[k1] + b[k2];
bk = bt[j] + bk;
j++;
at[j] = a[k1] - a[k2];
bt[j] = b[k1] - b[k2];
k1 += kspan;
} while (k1 < k2);
a[kk] = (MYFLT)ak;
b[kk] = (MYFLT)bk;
k1 = kk;
k2 = kk + kspnn;
j = 1;
lbl270:
k1 += kspan;
k2 -= kspan;
jj = j;
ak = aa;
bk = bb;
aj = 0.0;
bj = 0.0;
k = 1;
do {
k++;
ak = (at[k] * ck[jj]) + ak;
bk = (bt[k] * ck[jj]) + bk;
k++;
aj = (at[k] * sk[jj]) + aj;
bj = (bt[k] * sk[jj]) + bj;
jj += j;
if (jj > jf)
jj -= jf;
} while (k < jf);
k = jf - j;
a[k1] = (MYFLT)(ak - bj);
b[k1] = (MYFLT)(bk + aj);
a[k2] = (MYFLT)(ak + bj);
b[k2] = (MYFLT)(bk - aj);
j++;
if (j < k) goto lbl270;
kk += kspnn;
if (kk <= nn) goto lbl250;
kk -= nn;
if (kk<=kspan) goto lbl250;
/*
* multiply by rotation factor (except for factors of 2 and 4)
*/
lbl290:
if (i==m) goto lbl350;
kk = jc + 1;
lbl300:
c2 = 1.0 - cd;
s1 = sd;
mm = (kspan < klim ? kspan : klim);
goto lbl320;
lbl310:
c2 = c1 - ((cd*c1) + (sd*s1));
s1 = s1 + ((sd*c1) - (cd*s1));
lbl320:
c1 = c2;
s2 = s1;
kk += kspan;
lbl330:
ak = a[kk];
a[kk] = (MYFLT)((c2*ak) - (s2 * b[kk]));
b[kk] = (MYFLT)((s2*ak) + (c2 * b[kk]));
kk += kspnn;
if (kk <= nt) goto lbl330;
ak = s1*s2;
s2 = (s1*c2) + (c1*s2);
c2 = (c1*c2) - ak;
kk -= (nt - kspan);
if (kk <= kspnn) goto lbl330;
kk -= (kspnn - jc);
if (kk <= mm) goto lbl310;
if (kk < kspan) goto lbl340;
kk -= (kspan - jc - inc);
if (kk <= (jc+jc)) goto lbl300;
goto lbl40;
lbl340:
s1 = ((double)((kk-1)/jc)) * dr * rad;
c2 = cos(s1);
s1 = sin(s1);
mm = (kspan < mm+klim ? kspan :mm+klim);
goto lbl320;
/*
* permute the results to normal order---done in two stages
* permutation for square factors of n
*/
lbl350:
np[1] = ks;
if (!(*kt)) goto lbl440;
k = *kt + *kt + 1;
if (m < k)
k--;
np[k+1] = jc;
for (j=1; j < k; j++,k--) {
np[j+1] = np[j] / nfac[j];
np[k] = np[k+1] * nfac[j];
}
k3 = np[k+1];
kspan = np[2];
kk = jc + 1;
k2 = kspan + 1;
j = 1;
if (n != ntot) goto lbl400;
/*
* permutation for single-variate transform (optional code)
*/
lbl370:
do {
ak = a[kk];
a[kk] = a[k2];
a[k2] = (MYFLT)ak;
bk = b[kk];
b[kk] = b[k2];
b[k2] = (MYFLT)bk;
kk += inc;
k2 += kspan;
} while (k2 < ks);
lbl380:
do {
k2 -= np[j++];
k2 += np[j+1];
} while (k2 > np[j]);
j = 1;
lbl390:
if (kk < k2) {
goto lbl370;
}
kk += inc;
k2 += kspan;
if (k2 < ks) goto lbl390;
if (kk < ks) goto lbl380;
jc = k3;
goto lbl440;
/*
* permutation for multivariate transform
*/
lbl400:
do {
do {
k = kk + jc;
do {
ak = a[kk];
a[kk] = a[k2];
a[k2] = (MYFLT)ak;
bk = b[kk];
b[kk] = b[k2];
b[k2] = (MYFLT)bk;
kk += inc;
k2 += inc;
} while (kk < k);
kk += (ks - jc);
k2 += (ks - jc);
} while (kk < nt);
k2 -= (nt - kspan);
kk -= (nt - jc);
} while (k2 < ks);
lbl420:
do {
k2 -= np[j++];
k2 += np[j+1];
} while (k2 > np[j]);
j = 1;
lbl430:
if (kk < k2) goto lbl400;
kk += jc;
k2 += kspan;
if (k2 < ks) goto lbl430;
if (kk < ks) goto lbl420;
jc = k3;
lbl440:
if ((2*(*kt))+1 >= m)
return;
kspnn = *(np + *(kt) + 1);
j = m - *kt;
nfac[j+1] = 1;
lbl450:
nfac[j] = nfac[j] * nfac[j+1];
j--;
if (j != *kt) goto lbl450;
*kt = *(kt) + 1;
nn = nfac[*kt] - 1;
jj = 0;
j = 0;
goto lbl480;
lbl460:
jj -= k2;
k2 = kk;
kk = nfac[++k];
lbl470:
jj += kk;
if (jj >= k2) goto lbl460;
np[j] = jj;
lbl480:
k2 = nfac[*kt];
k = *kt + 1;
kk = nfac[k];
j++;
if (j <= nn) goto lbl470;
/* Determine permutation cycles of length greater than 1 */
j = 0;
goto lbl500;
lbl490:
k = kk;
kk = np[k];
np[k] = -kk;
if (kk != j) goto lbl490;
k3 = kk;
lbl500:
kk = np[++j];
if (kk < 0) goto lbl500;
if (kk != j) goto lbl490;
np[j] = -j;
if (j != nn) goto lbl500;
maxf *= inc;
/* Perform reordering following permutation cycles */
goto lbl570;
lbl510:
j--;
if (np[j] < 0) goto lbl510;
jj = jc;
lbl520:
kspan = jj;
if (jj > maxf)
kspan = maxf;
jj -= kspan;
k = np[j];
kk = (jc*k) + i + jj;
k1 = kk + kspan;
k2 = 0;
lbl530:
k2++;
at[k2] = a[k1];
bt[k2] = b[k1];
k1 -= inc;
if (k1 != kk) goto lbl530;
lbl540:
k1 = kk + kspan;
k2 = k1 - (jc * (k + np[k]));
k = -(np[k]);
lbl550:
a[k1] = a[k2];
b[k1] = b[k2];
k1 -= inc;
k2 -= inc;
if (k1 != kk) goto lbl550;
kk = k2;
if (k != j) goto lbl540;
k1 = kk + kspan;
k2 = 0;
lbl560:
k2++;
a[k1] = at[k2];
b[k1] = bt[k2];
k1 -= inc;
if (k1 != kk) goto lbl560;
if (jj) goto lbl520;
if (j != 1) goto lbl510;
lbl570:
j = k3 + 1;
nt -= kspnn;
i = nt - inc + 1;
if (nt >= 0) goto lbl510;
return;
}
/*
*-----------------------------------------------------------------------
* subroutine:
* reals
* used with 'fft' to compute fourier transform or inverse for real data
*-----------------------------------------------------------------------
* this is the call from C:
*
* reals_(anal,banal,N2,mtwo);
* which has been changed from CARL call
* reals_(csound,anal,banal,&N2,&mtwo);
*/
static void reals_(CSOUND *csound, MYFLT *a, MYFLT *b, int n, int isn)
/* *a, a refers to an array of floats 'anal' */
/* *b; b refers to an array of floats 'banal' */
/* See IEEE book for a long comment here on usage */
{
int inc,
j,
k,
lim,
mm,ml,
nf,nk,nh;
double aa,ab,
ba,bb,
cd,cn,
dr,
em,
rad,re,
sd,sn;
double xx; /******* ADDED APRIL 1991 ******/
/* adjust input array pointers (called from C) */
a--; b--;
inc = abs(isn);
nf = abs(n);
nk = (nf*inc) + 2;
nh = nk/2;
/*****************************
rad = atan((double)1.0);
******************************/
rad = 0.785398163397448278900;
dr = -4.0/(double)(nf);
/********************************** POW2 REMOVED APRIL 1991 *****************
cd = 2.0 * (pow2(sin((double)0.5 * dr * rad)));
*****************************************************************************/
xx = sin((double)0.5 * dr * rad);
cd = 2.0 * xx * xx;
sd = sin(dr * rad);
/*
* sin,cos values are re-initialised each lim steps
*/
lim = 32;
mm = lim;
ml = 0;
sn = 0.0;
if (isn<0) {
cn = 1.0;
a[nk-1] = a[1];
b[nk-1] = b[1]; }
else {
cn = -1.0;
sd = -sd;
}
for (j=1;j<=nh;j+=inc) {
k = nk - j;
aa = a[j] + a[k];
ab = a[j] - a[k];
ba = b[j] + b[k];
bb = b[j] - b[k];
re = (cn*ba) + (sn*ab);
em = (sn*ba) - (cn*ab);
b[k] = (MYFLT)((em-bb)*0.5);
b[j] = (MYFLT)((em+bb)*0.5);
a[k] = (MYFLT)((aa-re)*0.5);
a[j] = (MYFLT)((aa+re)*0.5);
ml++;
if (ml!=mm) {
aa = cn - ((cd*cn)+(sd*sn));
sn = ((sd*cn) - (cd*sn)) + sn;
cn = aa;}
else {
mm +=lim;
sn = ((MYFLT)ml) * dr * rad;
cn = cos(sn);
if (isn>0)
cn = -cn;
sn = sin(sn);
}
}
return;
}
/**
* Compute in-place real FFT, allowing non power of two FFT sizes.
*
* buf: array of FFTsize + 2 MYFLT values; output is in interleaved
* real/imaginary format (note: the real part of the Nyquist
* frequency is stored in buf[FFTsize], and not in buf[1]).
* FFTsize: FFT length in samples; not required to be an integer power of two,
* but should be even and not have too many factors.
*/
void csoundRealFFTnp2(CSOUND *csound, MYFLT *buf, int FFTsize)
{
if (!(FFTsize & (FFTsize - 1))) {
/* if FFT size is power of two: */
csound->RealFFT(csound, buf, FFTsize);
buf[FFTsize] = buf[1];
}
else {
if (UNLIKELY(FFTsize < 2 || (FFTsize & 1))) {
csound->Warning(csound,
Str("csoundRealFFTnp2(): invalid FFT size, %d"), FFTsize);
return;
}
buf[FFTsize] = buf[FFTsize + 1] = FL(0.0);
fft_(csound, buf, &(buf[1]), 1, (FFTsize >> 1), 1, -2);
reals_(csound, buf, &(buf[1]), (FFTsize >> 1), -2);
}
buf[1] = buf[FFTsize + 1] = FL(0.0);
}
/**
* Compute in-place inverse real FFT, allowing non power of two FFT sizes.
* The output does not need to be scaled.
*
* buf: array of FFTsize + 2 MYFLT values, in interleaved real/imaginary
* format (note: the real part of the Nyquist frequency is stored
* in buf[FFTsize], and not in buf[1]).
* FFTsize: FFT length in samples; not required to be an integer power of two,
* but should be even and not have too many factors.
*/
void csoundInverseRealFFTnp2(CSOUND *csound, MYFLT *buf, int FFTsize)
{
if (UNLIKELY(FFTsize < 2 || (FFTsize & 1))){
csound->Warning(csound, Str("csoundInverseRealFFTnp2(): invalid FFT size"));
return;
}
buf[1] = buf[FFTsize + 1] = FL(0.0);
reals_(csound, buf, &(buf[1]), (FFTsize >> 1), 2);
fft_(csound, buf, &(buf[1]), 1, (FFTsize >> 1), 1, 2);
buf[FFTsize] = buf[FFTsize + 1] = FL(0.0);
}
void csoundInverseComplexFFTnp2(CSOUND *csound, MYFLT *buf, int FFTsize)
{
if (UNLIKELY(FFTsize < 2 || (FFTsize & 1))){
csound->Warning(csound, Str("csoundInverseRealFFTnp2(): invalid FFT size"));
return;
}
fft_(csound, buf, buf, 1, FFTsize, 1, 2);
}
void csoundComplexFFTnp2(CSOUND *csound, MYFLT *buf, int FFTsize)
{
if (UNLIKELY(FFTsize < 2 || (FFTsize & 1))) {
csound->Warning(csound, Str("csoundRealFFTnp2(): invalid FFT size"));
return;
}
fft_(csound, buf, buf, 1, FFTsize, 1, -2);
}