blob: a78b9370f4946fb9a3c75abbe6c073aad5f872a2 [file] [log] [blame]
/*
** Algorithm: complex multiplication
**
** Performance: Bad accuracy, great speed.
**
** The simplest, way of generating trig values. Note, this method is
** not stable, and errors accumulate rapidly.
**
** Computation: 2 *, 1 + per value.
*/
#include "m_pd.h"
#include "m_fixed.h"
#define TRIG_FAST
#ifdef TRIG_FAST
char mtrig_algorithm[] = "Simple";
#define TRIG_VARS \
t_fixed t_c,t_s;
#define TRIG_INIT(k,c,s) \
{ \
t_c = fcostab[k]; \
t_s = fsintab[k]; \
c = itofix(1); \
s = 0; \
}
#define TRIG_NEXT(k,c,s) \
{ \
t_fixed t = c; \
c = mult(t,t_c) - mult(s,t_s); \
s = mult(t,t_s) + mult(s,t_c); \
}
#define TRIG_23(k,c1,s1,c2,s2,c3,s3) \
{ \
c2 = mult(c1,c1) - mult(s1,s1); \
s2 = (mult(c1,s1)<<2); \
c3 = mult(c2,c1) - mult(s2,s1); \
s3 = mult(c2,s1) + mult(s2,c1); \
}
#endif
#define TRIG_RESET(k,c,s)
/*
** Algorithm: O. Buneman's trig generator.
**
** Performance: Good accuracy, mediocre speed.
**
** Manipulates a log(n) table to stably create n evenly spaced trig
** values. The newly generated values lay halfway between two
** known values, and are calculated by appropriatelly scaling the
** average of the known trig values appropriatelly according to the
** angle between them. This process is inherently stable; and is
** about as accurate as most trig library functions. The errors
** caused by this code segment are primarily due to the less stable
** method to calculate values for 2t and s 3t. Note: I believe this
** algorithm is patented(!), see readme file for more details.
**
** Computation: 1 +, 1 *, much integer math, per trig value
**
*/
#ifdef TRIG_GOOD
#define TRIG_VARS \
int t_lam=0; \
double coswrk[TRIG_TABLE_SIZE],sinwrk[TRIG_TABLE_SIZE];
#define TRIG_INIT(k,c,s) \
{ \
int i; \
for (i=0 ; i<=k ; i++) \
{coswrk[i]=fcostab[i];sinwrk[i]=fsintab[i];} \
t_lam = 0; \
c = 1; \
s = 0; \
}
#define TRIG_NEXT(k,c,s) \
{ \
int i,j; \
(t_lam)++; \
for (i=0 ; !((1<<i)&t_lam) ; i++); \
i = k-i; \
s = sinwrk[i]; \
c = coswrk[i]; \
if (i>1) \
{ \
for (j=k-i+2 ; (1<<j)&t_lam ; j++); \
j = k - j; \
sinwrk[i] = halsec[i] * (sinwrk[i-1] + sinwrk[j]); \
coswrk[i] = halsec[i] * (coswrk[i-1] + coswrk[j]); \
} \
}
#endif
#define TRIG_TAB_SIZE 22
#ifndef ROCKBOX
static long long halsec[TRIG_TAB_SIZE]= {1,2,3};
#endif
#define FFTmult(x,y) mult(x,y)
#include "d_imayer_tables.h"
#define SQRT2 ftofix(1.414213562373095048801688724209698)
void imayer_fht(t_fixed *fz, int n)
{
int k,k1,k2,k3,k4,kx;
t_fixed *fi,*fn,*gi;
TRIG_VARS;
for (k1=1,k2=0;k1<n;k1++)
{
t_fixed aa;
for (k=n>>1; (!((k2^=k)&k)); k>>=1);
if (k1>k2)
{
aa=fz[k1];fz[k1]=fz[k2];fz[k2]=aa;
}
}
for ( k=0 ; (1<<k)<n ; k++ );
k &= 1;
if (k==0)
{
for (fi=fz,fn=fz+n;fi<fn;fi+=4)
{
t_fixed f0,f1,f2,f3;
f1 = fi[0 ]-fi[1 ];
f0 = fi[0 ]+fi[1 ];
f3 = fi[2 ]-fi[3 ];
f2 = fi[2 ]+fi[3 ];
fi[2 ] = (f0-f2);
fi[0 ] = (f0+f2);
fi[3 ] = (f1-f3);
fi[1 ] = (f1+f3);
}
}
else
{
for (fi=fz,fn=fz+n,gi=fi+1;fi<fn;fi+=8,gi+=8)
{
t_fixed bs1,bc1,bs2,bc2,bs3,bc3,bs4,bc4,
bg0,bf0,bf1,bg1,bf2,bg2,bf3,bg3;
bc1 = fi[0 ] - gi[0 ];
bs1 = fi[0 ] + gi[0 ];
bc2 = fi[2 ] - gi[2 ];
bs2 = fi[2 ] + gi[2 ];
bc3 = fi[4 ] - gi[4 ];
bs3 = fi[4 ] + gi[4 ];
bc4 = fi[6 ] - gi[6 ];
bs4 = fi[6 ] + gi[6 ];
bf1 = (bs1 - bs2);
bf0 = (bs1 + bs2);
bg1 = (bc1 - bc2);
bg0 = (bc1 + bc2);
bf3 = (bs3 - bs4);
bf2 = (bs3 + bs4);
bg3 = FFTmult(SQRT2,bc4);
bg2 = FFTmult(SQRT2,bc3);
fi[4 ] = bf0 - bf2;
fi[0 ] = bf0 + bf2;
fi[6 ] = bf1 - bf3;
fi[2 ] = bf1 + bf3;
gi[4 ] = bg0 - bg2;
gi[0 ] = bg0 + bg2;
gi[6 ] = bg1 - bg3;
gi[2 ] = bg1 + bg3;
}
}
if (n<16) return;
do
{
t_fixed s1,c1;
int ii;
k += 2;
k1 = 1 << k;
k2 = k1 << 1;
k4 = k2 << 1;
k3 = k2 + k1;
kx = k1 >> 1;
fi = fz;
gi = fi + kx;
fn = fz + n;
do
{
t_fixed g0,f0,f1,g1,f2,g2,f3,g3;
f1 = fi[0 ] - fi[k1];
f0 = fi[0 ] + fi[k1];
f3 = fi[k2] - fi[k3];
f2 = fi[k2] + fi[k3];
fi[k2] = f0 - f2;
fi[0 ] = f0 + f2;
fi[k3] = f1 - f3;
fi[k1] = f1 + f3;
g1 = gi[0 ] - gi[k1];
g0 = gi[0 ] + gi[k1];
g3 = FFTmult(SQRT2, gi[k3]);
g2 = FFTmult(SQRT2, gi[k2]);
gi[k2] = g0 - g2;
gi[0 ] = g0 + g2;
gi[k3] = g1 - g3;
gi[k1] = g1 + g3;
gi += k4;
fi += k4;
} while (fi<fn);
TRIG_INIT(k,c1,s1);
for (ii=1;ii<kx;ii++)
{
t_fixed c2,s2;
TRIG_NEXT(k,c1,s1);
c2 = FFTmult(c1,c1) - FFTmult(s1,s1);
s2 = 2*FFTmult(c1,s1);
fn = fz + n;
fi = fz +ii;
gi = fz +k1-ii;
do
{
t_fixed a,b,g0,f0,f1,g1,f2,g2,f3,g3;
b = FFTmult(s2,fi[k1]) - FFTmult(c2,gi[k1]);
a = FFTmult(c2,fi[k1]) + FFTmult(s2,gi[k1]);
f1 = fi[0 ] - a;
f0 = fi[0 ] + a;
g1 = gi[0 ] - b;
g0 = gi[0 ] + b;
b = FFTmult(s2,fi[k3]) - FFTmult(c2,gi[k3]);
a = FFTmult(c2,fi[k3]) + FFTmult(s2,gi[k3]);
f3 = fi[k2] - a;
f2 = fi[k2] + a;
g3 = gi[k2] - b;
g2 = gi[k2] + b;
b = FFTmult(s1,f2) - FFTmult(c1,g3);
a = FFTmult(c1,f2) + FFTmult(s1,g3);
fi[k2] = f0 - a;
fi[0 ] = f0 + a;
gi[k3] = g1 - b;
gi[k1] = g1 + b;
b = FFTmult(c1,g2) - FFTmult(s1,f3);
a = FFTmult(s1,g2) + FFTmult(c1,f3);
gi[k2] = g0 - a;
gi[0 ] = g0 + a;
fi[k3] = f1 - b;
fi[k1] = f1 + b;
gi += k4;
fi += k4;
} while (fi<fn);
}
TRIG_RESET(k,c1,s1);
} while (k4<n);
}
void imayer_fft(int n, t_fixed *real, t_fixed *imag)
{
t_fixed a,b,c,d;
t_fixed q,r,s,t;
int i,j,k;
for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
a = real[i]; b = real[j]; q=a+b; r=a-b;
c = imag[i]; d = imag[j]; s=c+d; t=c-d;
real[i] = (q+t)>>1; real[j] = (q-t)>>1;
imag[i] = (s-r)>>1; imag[j] = (s+r)>>1;
}
imayer_fht(real,n);
imayer_fht(imag,n);
}
void imayer_ifft(int n, t_fixed *real, t_fixed *imag)
{
t_fixed a,b,c,d;
t_fixed q,r,s,t;
int i,j,k;
imayer_fht(real,n);
imayer_fht(imag,n);
for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
a = real[i]; b = real[j]; q=a+b; r=a-b;
c = imag[i]; d = imag[j]; s=c+d; t=c-d;
imag[i] = (s+r)>>1; imag[j] = (s-r)>>1;
real[i] = (q-t)>>1; real[j] = (q+t)>>1;
}
}
void imayer_realfft(int n, t_fixed *real)
{
#ifdef ROCKBOX
t_fixed a,b;
#else
t_fixed a,b,c,d;
#endif
int i,j,k;
imayer_fht(real,n);
for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
a = real[i];
b = real[j];
real[j] = (a-b)>>1;
real[i] = (a+b)>>1;
}
}
void imayer_realifft(int n, t_fixed *real)
{
#ifdef ROCKBOX
t_fixed a,b;
#else
t_fixed a,b,c,d;
#endif
int i,j,k;
for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
a = real[i];
b = real[j];
real[j] = (a-b);
real[i] = (a+b);
}
imayer_fht(real,n);
}
#ifdef TEST
static double dfcostab[TRIG_TAB_SIZE]=
{
.00000000000000000000000000000000000000000000000000,
.70710678118654752440084436210484903928483593768847,
.92387953251128675612818318939678828682241662586364,
.98078528040323044912618223613423903697393373089333,
.99518472667219688624483695310947992157547486872985,
.99879545620517239271477160475910069444320361470461,
.99969881869620422011576564966617219685006108125772,
.99992470183914454092164649119638322435060646880221,
.99998117528260114265699043772856771617391725094433,
.99999529380957617151158012570011989955298763362218,
.99999882345170190992902571017152601904826792288976,
.99999970586288221916022821773876567711626389934930,
.99999992646571785114473148070738785694820115568892,
.99999998161642929380834691540290971450507605124278,
.99999999540410731289097193313960614895889430318945,
.99999999885102682756267330779455410840053741619428,
.99999999971275670684941397221864177608908945791828,
.99999999992818917670977509588385049026048033310951
};
static double dfsintab[TRIG_TAB_SIZE]=
{
1.0000000000000000000000000000000000000000000000000,
.70710678118654752440084436210484903928483593768846,
.38268343236508977172845998403039886676134456248561,
.19509032201612826784828486847702224092769161775195,
.09801714032956060199419556388864184586113667316749,
.04906767432741801425495497694268265831474536302574,
.02454122852291228803173452945928292506546611923944,
.01227153828571992607940826195100321214037231959176,
.00613588464915447535964023459037258091705788631738,
.00306795676296597627014536549091984251894461021344,
.00153398018628476561230369715026407907995486457522,
.00076699031874270452693856835794857664314091945205,
.00038349518757139558907246168118138126339502603495,
.00019174759731070330743990956198900093346887403385,
.00009587379909597734587051721097647635118706561284,
.00004793689960306688454900399049465887274686668768,
.00002396844980841821872918657716502182009476147489,
.00001198422490506970642152156159698898480473197753
};
static double dhalsec[TRIG_TAB_SIZE]=
{
0,
0,
.54119610014619698439972320536638942006107206337801,
.50979557910415916894193980398784391368261849190893,
.50241928618815570551167011928012092247859337193963,
.50060299823519630134550410676638239611758632599591,
.50015063602065098821477101271097658495974913010340,
.50003765191554772296778139077905492847503165398345,
.50000941253588775676512870469186533538523133757983,
.50000235310628608051401267171204408939326297376426,
.50000058827484117879868526730916804925780637276181,
.50000014706860214875463798283871198206179118093251,
.50000003676714377807315864400643020315103490883972,
.50000000919178552207366560348853455333939112569380,
.50000000229794635411562887767906868558991922348920,
.50000000057448658687873302235147272458812263401372,
.50000000014362164661654736863252589967935073278768,
.50000000003590541164769084922906986545517021050714
};
#include <stdio.h>
int writetables()
{
int i;
printf("/* Tables for fixed point lookup with %d bit precision*/\n\n",fix1);
printf("static int fsintab[TRIG_TAB_SIZE]= {\n");
for (i=0;i<TRIG_TAB_SIZE-1;i++)
printf("%ld, \n",ftofix(dfsintab[i]));
printf("%ld }; \n",ftofix(dfsintab[i]));
printf("\n\nstatic int fcostab[TRIG_TAB_SIZE]= {\n");
for (i=0;i<TRIG_TAB_SIZE-1;i++)
printf("%ld, \n",ftofix(dfcostab[i]));
printf("%ld }; \n",ftofix(dfcostab[i]));
}
#define OUTPUT \
fprintf(stderr,"Integer - Float\n");\
for (i=0;i<NP;i++)\
fprintf(stderr,"%f %f --> %f %f\n",fixtof(r[i]),fixtof(im[i]),\
fr[i],fim[i]);\
fprintf(stderr,"\n\n");
int main()
{
int i;
t_fixed r[256];
t_fixed im[256];
float fr[256];
float fim[256];
#if 1
writetables();
exit(0);
#endif
#if 0
t_fixed c1,s1,c2,s2,c3,s3;
int k;
int i;
TRIG_VARS;
for (k=2;k<10;k+=2) {
TRIG_INIT(k,c1,s1);
for (i=0;i<8;i++) {
TRIG_NEXT(k,c1,s1);
TRIG_23(k,c1,s1,c2,s2,c3,s3);
printf("TRIG value k=%d,%d val1 = %f %f\n",k,i,fixtof(c1),fixtof(s1));
}
}
#endif
#if 1
#define NP 16
for (i=0;i<NP;i++) {
fr[i] = 0.;
r[i] = 0.;
fim[i] = 0.;
im[i] = 0;
}
#if 0
for (i=0;i<NP;i++) {
if (i&1) {
fr[i] = 0.1*i;
r[i] = ftofix(0.1*i);
}
else {
fr[i] = 0.;
r[i] = 0.;
}
}
#endif
#if 0
for (i=0;i<NP;i++) {
fr[i] = 0.1;
r[i] = ftofix(0.1);
}
#endif
r[1] = ftofix(0.1);
fr[1] = 0.1;
/* TEST RUN */
OUTPUT
imayer_fft(NP,r,im);
mayer_fft(NP,fr,fim);
// imayer_fht(r,NP);
// mayer_fht(fr,NP);
#if 1
for (i=0;i<NP;i++) {
r[i] = mult(ftofix(0.01),r[i]);
fr[i] = 0.01*fr[i];
}
#endif
OUTPUT
imayer_fft(NP,r,im);
mayer_fft(NP,fr,fim);
OUTPUT
#endif
}
#endif