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1/*
2** Algorithm: complex multiplication
3**
4** Performance: Bad accuracy, great speed.
5**
6** The simplest, way of generating trig values. Note, this method is
7** not stable, and errors accumulate rapidly.
8**
9** Computation: 2 *, 1 + per value.
10*/
11
12
13#include "m_fixed.h"
14
15
16#define TRIG_FAST
17
18#ifdef TRIG_FAST
19char mtrig_algorithm[] = "Simple";
20#define TRIG_VARS \
21 t_fixed t_c,t_s;
22#define TRIG_INIT(k,c,s) \
23 { \
24 t_c = fcostab[k]; \
25 t_s = fsintab[k]; \
26 c = itofix(1); \
27 s = 0; \
28 }
29#define TRIG_NEXT(k,c,s) \
30 { \
31 t_fixed t = c; \
32 c = mult(t,t_c) - mult(s,t_s); \
33 s = mult(t,t_s) + mult(s,t_c); \
34 }
35#define TRIG_23(k,c1,s1,c2,s2,c3,s3) \
36 { \
37 c2 = mult(c1,c1) - mult(s1,s1); \
38 s2 = (mult(c1,s1)<<2); \
39 c3 = mult(c2,c1) - mult(s2,s1); \
40 s3 = mult(c2,s1) + mult(s2,c1); \
41 }
42#endif
43#define TRIG_RESET(k,c,s)
44
45/*
46** Algorithm: O. Buneman's trig generator.
47**
48** Performance: Good accuracy, mediocre speed.
49**
50** Manipulates a log(n) table to stably create n evenly spaced trig
51** values. The newly generated values lay halfway between two
52** known values, and are calculated by appropriatelly scaling the
53** average of the known trig values appropriatelly according to the
54** angle between them. This process is inherently stable; and is
55** about as accurate as most trig library functions. The errors
56** caused by this code segment are primarily due to the less stable
57** method to calculate values for 2t and s 3t. Note: I believe this
58** algorithm is patented(!), see readme file for more details.
59**
60** Computation: 1 +, 1 *, much integer math, per trig value
61**
62*/
63
64#ifdef TRIG_GOOD
65#define TRIG_VARS \
66 int t_lam=0; \
67 double coswrk[TRIG_TABLE_SIZE],sinwrk[TRIG_TABLE_SIZE];
68#define TRIG_INIT(k,c,s) \
69 { \
70 int i; \
71 for (i=0 ; i<=k ; i++) \
72 {coswrk[i]=fcostab[i];sinwrk[i]=fsintab[i];} \
73 t_lam = 0; \
74 c = 1; \
75 s = 0; \
76 }
77#define TRIG_NEXT(k,c,s) \
78 { \
79 int i,j; \
80 (t_lam)++; \
81 for (i=0 ; !((1<<i)&t_lam) ; i++); \
82 i = k-i; \
83 s = sinwrk[i]; \
84 c = coswrk[i]; \
85 if (i>1) \
86 { \
87 for (j=k-i+2 ; (1<<j)&t_lam ; j++); \
88 j = k - j; \
89 sinwrk[i] = halsec[i] * (sinwrk[i-1] + sinwrk[j]); \
90 coswrk[i] = halsec[i] * (coswrk[i-1] + coswrk[j]); \
91 } \
92 }
93#endif
94
95
96#define TRIG_TAB_SIZE 22
97
98static long long halsec[TRIG_TAB_SIZE]= {1,2,3};
99
100#define FFTmult(x,y) mult(x,y)
101
102
103
104
105#include "d_imayer_tables.h"
106
107#define SQRT2 ftofix(1.414213562373095048801688724209698)
108
109
110void imayer_fht(t_fixed *fz, int n)
111{
112 int k,k1,k2,k3,k4,kx;
113 t_fixed *fi,*fn,*gi;
114 TRIG_VARS;
115
116 for (k1=1,k2=0;k1<n;k1++)
117 {
118 t_fixed aa;
119 for (k=n>>1; (!((k2^=k)&k)); k>>=1);
120 if (k1>k2)
121 {
122 aa=fz[k1];fz[k1]=fz[k2];fz[k2]=aa;
123 }
124 }
125 for ( k=0 ; (1<<k)<n ; k++ );
126 k &= 1;
127 if (k==0)
128 {
129 for (fi=fz,fn=fz+n;fi<fn;fi+=4)
130 {
131 t_fixed f0,f1,f2,f3;
132 f1 = fi[0 ]-fi[1 ];
133 f0 = fi[0 ]+fi[1 ];
134 f3 = fi[2 ]-fi[3 ];
135 f2 = fi[2 ]+fi[3 ];
136 fi[2 ] = (f0-f2);
137 fi[0 ] = (f0+f2);
138 fi[3 ] = (f1-f3);
139 fi[1 ] = (f1+f3);
140 }
141 }
142 else
143 {
144 for (fi=fz,fn=fz+n,gi=fi+1;fi<fn;fi+=8,gi+=8)
145 {
146 t_fixed bs1,bc1,bs2,bc2,bs3,bc3,bs4,bc4,
147 bg0,bf0,bf1,bg1,bf2,bg2,bf3,bg3;
148 bc1 = fi[0 ] - gi[0 ];
149 bs1 = fi[0 ] + gi[0 ];
150 bc2 = fi[2 ] - gi[2 ];
151 bs2 = fi[2 ] + gi[2 ];
152 bc3 = fi[4 ] - gi[4 ];
153 bs3 = fi[4 ] + gi[4 ];
154 bc4 = fi[6 ] - gi[6 ];
155 bs4 = fi[6 ] + gi[6 ];
156 bf1 = (bs1 - bs2);
157 bf0 = (bs1 + bs2);
158 bg1 = (bc1 - bc2);
159 bg0 = (bc1 + bc2);
160 bf3 = (bs3 - bs4);
161 bf2 = (bs3 + bs4);
162 bg3 = FFTmult(SQRT2,bc4);
163 bg2 = FFTmult(SQRT2,bc3);
164 fi[4 ] = bf0 - bf2;
165 fi[0 ] = bf0 + bf2;
166 fi[6 ] = bf1 - bf3;
167 fi[2 ] = bf1 + bf3;
168 gi[4 ] = bg0 - bg2;
169 gi[0 ] = bg0 + bg2;
170 gi[6 ] = bg1 - bg3;
171 gi[2 ] = bg1 + bg3;
172 }
173 }
174 if (n<16) return;
175
176 do
177 {
178 t_fixed s1,c1;
179 int ii;
180 k += 2;
181 k1 = 1 << k;
182 k2 = k1 << 1;
183 k4 = k2 << 1;
184 k3 = k2 + k1;
185 kx = k1 >> 1;
186 fi = fz;
187 gi = fi + kx;
188 fn = fz + n;
189 do
190 {
191 t_fixed g0,f0,f1,g1,f2,g2,f3,g3;
192 f1 = fi[0 ] - fi[k1];
193 f0 = fi[0 ] + fi[k1];
194 f3 = fi[k2] - fi[k3];
195 f2 = fi[k2] + fi[k3];
196 fi[k2] = f0 - f2;
197 fi[0 ] = f0 + f2;
198 fi[k3] = f1 - f3;
199 fi[k1] = f1 + f3;
200 g1 = gi[0 ] - gi[k1];
201 g0 = gi[0 ] + gi[k1];
202 g3 = FFTmult(SQRT2, gi[k3]);
203 g2 = FFTmult(SQRT2, gi[k2]);
204 gi[k2] = g0 - g2;
205 gi[0 ] = g0 + g2;
206 gi[k3] = g1 - g3;
207 gi[k1] = g1 + g3;
208 gi += k4;
209 fi += k4;
210 } while (fi<fn);
211 TRIG_INIT(k,c1,s1);
212 for (ii=1;ii<kx;ii++)
213 {
214 t_fixed c2,s2;
215 TRIG_NEXT(k,c1,s1);
216 c2 = FFTmult(c1,c1) - FFTmult(s1,s1);
217 s2 = 2*FFTmult(c1,s1);
218 fn = fz + n;
219 fi = fz +ii;
220 gi = fz +k1-ii;
221 do
222 {
223 t_fixed a,b,g0,f0,f1,g1,f2,g2,f3,g3;
224 b = FFTmult(s2,fi[k1]) - FFTmult(c2,gi[k1]);
225 a = FFTmult(c2,fi[k1]) + FFTmult(s2,gi[k1]);
226 f1 = fi[0 ] - a;
227 f0 = fi[0 ] + a;
228 g1 = gi[0 ] - b;
229 g0 = gi[0 ] + b;
230 b = FFTmult(s2,fi[k3]) - FFTmult(c2,gi[k3]);
231 a = FFTmult(c2,fi[k3]) + FFTmult(s2,gi[k3]);
232 f3 = fi[k2] - a;
233 f2 = fi[k2] + a;
234 g3 = gi[k2] - b;
235 g2 = gi[k2] + b;
236 b = FFTmult(s1,f2) - FFTmult(c1,g3);
237 a = FFTmult(c1,f2) + FFTmult(s1,g3);
238 fi[k2] = f0 - a;
239 fi[0 ] = f0 + a;
240 gi[k3] = g1 - b;
241 gi[k1] = g1 + b;
242 b = FFTmult(c1,g2) - FFTmult(s1,f3);
243 a = FFTmult(s1,g2) + FFTmult(c1,f3);
244 gi[k2] = g0 - a;
245 gi[0 ] = g0 + a;
246 fi[k3] = f1 - b;
247 fi[k1] = f1 + b;
248 gi += k4;
249 fi += k4;
250 } while (fi<fn);
251 }
252 TRIG_RESET(k,c1,s1);
253 } while (k4<n);
254}
255
256
257void imayer_fft(int n, t_fixed *real, t_fixed *imag)
258{
259 t_fixed a,b,c,d;
260 t_fixed q,r,s,t;
261 int i,j,k;
262 for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
263 a = real[i]; b = real[j]; q=a+b; r=a-b;
264 c = imag[i]; d = imag[j]; s=c+d; t=c-d;
265 real[i] = (q+t)>>1; real[j] = (q-t)>>1;
266 imag[i] = (s-r)>>1; imag[j] = (s+r)>>1;
267 }
268 imayer_fht(real,n);
269 imayer_fht(imag,n);
270}
271
272void imayer_ifft(int n, t_fixed *real, t_fixed *imag)
273{
274 t_fixed a,b,c,d;
275 t_fixed q,r,s,t;
276 int i,j,k;
277 imayer_fht(real,n);
278 imayer_fht(imag,n);
279 for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
280 a = real[i]; b = real[j]; q=a+b; r=a-b;
281 c = imag[i]; d = imag[j]; s=c+d; t=c-d;
282 imag[i] = (s+r)>>1; imag[j] = (s-r)>>1;
283 real[i] = (q-t)>>1; real[j] = (q+t)>>1;
284 }
285}
286
287void imayer_realfft(int n, t_fixed *real)
288{
289 t_fixed a,b,c,d;
290 int i,j,k;
291 imayer_fht(real,n);
292 for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
293 a = real[i];
294 b = real[j];
295 real[j] = (a-b)>>1;
296 real[i] = (a+b)>>1;
297 }
298}
299
300void imayer_realifft(int n, t_fixed *real)
301{
302 t_fixed a,b,c,d;
303 int i,j,k;
304 for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
305 a = real[i];
306 b = real[j];
307 real[j] = (a-b);
308 real[i] = (a+b);
309 }
310 imayer_fht(real,n);
311}
312
313
314
315#ifdef TEST
316
317static double dfcostab[TRIG_TAB_SIZE]=
318 {
319 .00000000000000000000000000000000000000000000000000,
320 .70710678118654752440084436210484903928483593768847,
321 .92387953251128675612818318939678828682241662586364,
322 .98078528040323044912618223613423903697393373089333,
323 .99518472667219688624483695310947992157547486872985,
324 .99879545620517239271477160475910069444320361470461,
325 .99969881869620422011576564966617219685006108125772,
326 .99992470183914454092164649119638322435060646880221,
327 .99998117528260114265699043772856771617391725094433,
328 .99999529380957617151158012570011989955298763362218,
329 .99999882345170190992902571017152601904826792288976,
330 .99999970586288221916022821773876567711626389934930,
331 .99999992646571785114473148070738785694820115568892,
332 .99999998161642929380834691540290971450507605124278,
333 .99999999540410731289097193313960614895889430318945,
334 .99999999885102682756267330779455410840053741619428,
335 .99999999971275670684941397221864177608908945791828,
336 .99999999992818917670977509588385049026048033310951
337 };
338static double dfsintab[TRIG_TAB_SIZE]=
339 {
340 1.0000000000000000000000000000000000000000000000000,
341 .70710678118654752440084436210484903928483593768846,
342 .38268343236508977172845998403039886676134456248561,
343 .19509032201612826784828486847702224092769161775195,
344 .09801714032956060199419556388864184586113667316749,
345 .04906767432741801425495497694268265831474536302574,
346 .02454122852291228803173452945928292506546611923944,
347 .01227153828571992607940826195100321214037231959176,
348 .00613588464915447535964023459037258091705788631738,
349 .00306795676296597627014536549091984251894461021344,
350 .00153398018628476561230369715026407907995486457522,
351 .00076699031874270452693856835794857664314091945205,
352 .00038349518757139558907246168118138126339502603495,
353 .00019174759731070330743990956198900093346887403385,
354 .00009587379909597734587051721097647635118706561284,
355 .00004793689960306688454900399049465887274686668768,
356 .00002396844980841821872918657716502182009476147489,
357 .00001198422490506970642152156159698898480473197753
358 };
359
360static double dhalsec[TRIG_TAB_SIZE]=
361 {
362 0,
363 0,
364 .54119610014619698439972320536638942006107206337801,
365 .50979557910415916894193980398784391368261849190893,
366 .50241928618815570551167011928012092247859337193963,
367 .50060299823519630134550410676638239611758632599591,
368 .50015063602065098821477101271097658495974913010340,
369 .50003765191554772296778139077905492847503165398345,
370 .50000941253588775676512870469186533538523133757983,
371 .50000235310628608051401267171204408939326297376426,
372 .50000058827484117879868526730916804925780637276181,
373 .50000014706860214875463798283871198206179118093251,
374 .50000003676714377807315864400643020315103490883972,
375 .50000000919178552207366560348853455333939112569380,
376 .50000000229794635411562887767906868558991922348920,
377 .50000000057448658687873302235147272458812263401372,
378 .50000000014362164661654736863252589967935073278768,
379 .50000000003590541164769084922906986545517021050714
380 };
381
382
383#include <stdio.h>
384
385
386int writetables()
387{
388 int i;
389
390 printf("/* Tables for fixed point lookup with %d bit precision*/\n\n",fix1);
391
392 printf("static int fsintab[TRIG_TAB_SIZE]= {\n");
393
394 for (i=0;i<TRIG_TAB_SIZE-1;i++)
395 printf("%ld, \n",ftofix(dfsintab[i]));
396 printf("%ld }; \n",ftofix(dfsintab[i]));
397
398
399 printf("\n\nstatic int fcostab[TRIG_TAB_SIZE]= {\n");
400
401 for (i=0;i<TRIG_TAB_SIZE-1;i++)
402 printf("%ld, \n",ftofix(dfcostab[i]));
403 printf("%ld }; \n",ftofix(dfcostab[i]));
404
405}
406
407
408#define OUTPUT \
409 fprintf(stderr,"Integer - Float\n");\
410 for (i=0;i<NP;i++)\
411 fprintf(stderr,"%f %f --> %f %f\n",fixtof(r[i]),fixtof(im[i]),\
412 fr[i],fim[i]);\
413 fprintf(stderr,"\n\n");
414
415
416
417int main()
418{
419 int i;
420 t_fixed r[256];
421 t_fixed im[256];
422 float fr[256];
423 float fim[256];
424
425
426#if 1
427 writetables();
428 exit(0);
429#endif
430
431
432#if 0
433 t_fixed c1,s1,c2,s2,c3,s3;
434 int k;
435 int i;
436
437 TRIG_VARS;
438
439 for (k=2;k<10;k+=2) {
440 TRIG_INIT(k,c1,s1);
441 for (i=0;i<8;i++) {
442 TRIG_NEXT(k,c1,s1);
443 TRIG_23(k,c1,s1,c2,s2,c3,s3);
444 printf("TRIG value k=%d,%d val1 = %f %f\n",k,i,fixtof(c1),fixtof(s1));
445 }
446 }
447#endif
448
449
450
451#if 1
452
453 #define NP 16
454
455 for (i=0;i<NP;i++) {
456 fr[i] = 0.;
457 r[i] = 0.;
458 fim[i] = 0.;
459 im[i] = 0;
460 }
461
462#if 0
463 for (i=0;i<NP;i++) {
464 if (i&1) {
465 fr[i] = 0.1*i;
466 r[i] = ftofix(0.1*i);
467 }
468 else {
469 fr[i] = 0.;
470 r[i] = 0.;
471 }
472 }
473#endif
474#if 0
475 for (i=0;i<NP;i++) {
476 fr[i] = 0.1;
477 r[i] = ftofix(0.1);
478 }
479#endif
480
481 r[1] = ftofix(0.1);
482 fr[1] = 0.1;
483
484
485
486 /* TEST RUN */
487
488 OUTPUT
489
490 imayer_fft(NP,r,im);
491 mayer_fft(NP,fr,fim);
492// imayer_fht(r,NP);
493// mayer_fht(fr,NP);
494
495#if 1
496 for (i=0;i<NP;i++) {
497 r[i] = mult(ftofix(0.01),r[i]);
498 fr[i] = 0.01*fr[i];
499 }
500#endif
501
502 OUTPUT
503
504
505 imayer_fft(NP,r,im);
506 mayer_fft(NP,fr,fim);
507
508 OUTPUT
509
510
511#endif
512
513
514}
515
516#endif
517/*
518** Algorithm: complex multiplication
519**
520** Performance: Bad accuracy, great speed.
521**
522** The simplest, way of generating trig values. Note, this method is
523** not stable, and errors accumulate rapidly.
524**
525** Computation: 2 *, 1 + per value.
526*/
527
528
529#include "m_fixed.h"
530
531
532#define TRIG_FAST
533
534#ifdef TRIG_FAST
535char mtrig_algorithm[] = "Simple";
536#define TRIG_VARS \
537 t_fixed t_c,t_s;
538#define TRIG_INIT(k,c,s) \
539 { \
540 t_c = fcostab[k]; \
541 t_s = fsintab[k]; \
542 c = itofix(1); \
543 s = 0; \
544 }
545#define TRIG_NEXT(k,c,s) \
546 { \
547 t_fixed t = c; \
548 c = mult(t,t_c) - mult(s,t_s); \
549 s = mult(t,t_s) + mult(s,t_c); \
550 }
551#define TRIG_23(k,c1,s1,c2,s2,c3,s3) \
552 { \
553 c2 = mult(c1,c1) - mult(s1,s1); \
554 s2 = (mult(c1,s1)<<2); \
555 c3 = mult(c2,c1) - mult(s2,s1); \
556 s3 = mult(c2,s1) + mult(s2,c1); \
557 }
558#endif
559#define TRIG_RESET(k,c,s)
560
561/*
562** Algorithm: O. Buneman's trig generator.
563**
564** Performance: Good accuracy, mediocre speed.
565**
566** Manipulates a log(n) table to stably create n evenly spaced trig
567** values. The newly generated values lay halfway between two
568** known values, and are calculated by appropriatelly scaling the
569** average of the known trig values appropriatelly according to the
570** angle between them. This process is inherently stable; and is
571** about as accurate as most trig library functions. The errors
572** caused by this code segment are primarily due to the less stable
573** method to calculate values for 2t and s 3t. Note: I believe this
574** algorithm is patented(!), see readme file for more details.
575**
576** Computation: 1 +, 1 *, much integer math, per trig value
577**
578*/
579
580#ifdef TRIG_GOOD
581#define TRIG_VARS \
582 int t_lam=0; \
583 double coswrk[TRIG_TABLE_SIZE],sinwrk[TRIG_TABLE_SIZE];
584#define TRIG_INIT(k,c,s) \
585 { \
586 int i; \
587 for (i=0 ; i<=k ; i++) \
588 {coswrk[i]=fcostab[i];sinwrk[i]=fsintab[i];} \
589 t_lam = 0; \
590 c = 1; \
591 s = 0; \
592 }
593#define TRIG_NEXT(k,c,s) \
594 { \
595 int i,j; \
596 (t_lam)++; \
597 for (i=0 ; !((1<<i)&t_lam) ; i++); \
598 i = k-i; \
599 s = sinwrk[i]; \
600 c = coswrk[i]; \
601 if (i>1) \
602 { \
603 for (j=k-i+2 ; (1<<j)&t_lam ; j++); \
604 j = k - j; \
605 sinwrk[i] = halsec[i] * (sinwrk[i-1] + sinwrk[j]); \
606 coswrk[i] = halsec[i] * (coswrk[i-1] + coswrk[j]); \
607 } \
608 }
609#endif
610
611
612#define TRIG_TAB_SIZE 22
613
614static long long halsec[TRIG_TAB_SIZE]= {1,2,3};
615
616#define FFTmult(x,y) mult(x,y)
617
618
619
620
621#include "d_imayer_tables.h"
622
623#define SQRT2 ftofix(1.414213562373095048801688724209698)
624
625
626void imayer_fht(t_fixed *fz, int n)
627{
628 int k,k1,k2,k3,k4,kx;
629 t_fixed *fi,*fn,*gi;
630 TRIG_VARS;
631
632 for (k1=1,k2=0;k1<n;k1++)
633 {
634 t_fixed aa;
635 for (k=n>>1; (!((k2^=k)&k)); k>>=1);
636 if (k1>k2)
637 {
638 aa=fz[k1];fz[k1]=fz[k2];fz[k2]=aa;
639 }
640 }
641 for ( k=0 ; (1<<k)<n ; k++ );
642 k &= 1;
643 if (k==0)
644 {
645 for (fi=fz,fn=fz+n;fi<fn;fi+=4)
646 {
647 t_fixed f0,f1,f2,f3;
648 f1 = fi[0 ]-fi[1 ];
649 f0 = fi[0 ]+fi[1 ];
650 f3 = fi[2 ]-fi[3 ];
651 f2 = fi[2 ]+fi[3 ];
652 fi[2 ] = (f0-f2);
653 fi[0 ] = (f0+f2);
654 fi[3 ] = (f1-f3);
655 fi[1 ] = (f1+f3);
656 }
657 }
658 else
659 {
660 for (fi=fz,fn=fz+n,gi=fi+1;fi<fn;fi+=8,gi+=8)
661 {
662 t_fixed bs1,bc1,bs2,bc2,bs3,bc3,bs4,bc4,
663 bg0,bf0,bf1,bg1,bf2,bg2,bf3,bg3;
664 bc1 = fi[0 ] - gi[0 ];
665 bs1 = fi[0 ] + gi[0 ];
666 bc2 = fi[2 ] - gi[2 ];
667 bs2 = fi[2 ] + gi[2 ];
668 bc3 = fi[4 ] - gi[4 ];
669 bs3 = fi[4 ] + gi[4 ];
670 bc4 = fi[6 ] - gi[6 ];
671 bs4 = fi[6 ] + gi[6 ];
672 bf1 = (bs1 - bs2);
673 bf0 = (bs1 + bs2);
674 bg1 = (bc1 - bc2);
675 bg0 = (bc1 + bc2);
676 bf3 = (bs3 - bs4);
677 bf2 = (bs3 + bs4);
678 bg3 = FFTmult(SQRT2,bc4);
679 bg2 = FFTmult(SQRT2,bc3);
680 fi[4 ] = bf0 - bf2;
681 fi[0 ] = bf0 + bf2;
682 fi[6 ] = bf1 - bf3;
683 fi[2 ] = bf1 + bf3;
684 gi[4 ] = bg0 - bg2;
685 gi[0 ] = bg0 + bg2;
686 gi[6 ] = bg1 - bg3;
687 gi[2 ] = bg1 + bg3;
688 }
689 }
690 if (n<16) return;
691
692 do
693 {
694 t_fixed s1,c1;
695 int ii;
696 k += 2;
697 k1 = 1 << k;
698 k2 = k1 << 1;
699 k4 = k2 << 1;
700 k3 = k2 + k1;
701 kx = k1 >> 1;
702 fi = fz;
703 gi = fi + kx;
704 fn = fz + n;
705 do
706 {
707 t_fixed g0,f0,f1,g1,f2,g2,f3,g3;
708 f1 = fi[0 ] - fi[k1];
709 f0 = fi[0 ] + fi[k1];
710 f3 = fi[k2] - fi[k3];
711 f2 = fi[k2] + fi[k3];
712 fi[k2] = f0 - f2;
713 fi[0 ] = f0 + f2;
714 fi[k3] = f1 - f3;
715 fi[k1] = f1 + f3;
716 g1 = gi[0 ] - gi[k1];
717 g0 = gi[0 ] + gi[k1];
718 g3 = FFTmult(SQRT2, gi[k3]);
719 g2 = FFTmult(SQRT2, gi[k2]);
720 gi[k2] = g0 - g2;
721 gi[0 ] = g0 + g2;
722 gi[k3] = g1 - g3;
723 gi[k1] = g1 + g3;
724 gi += k4;
725 fi += k4;
726 } while (fi<fn);
727 TRIG_INIT(k,c1,s1);
728 for (ii=1;ii<kx;ii++)
729 {
730 t_fixed c2,s2;
731 TRIG_NEXT(k,c1,s1);
732 c2 = FFTmult(c1,c1) - FFTmult(s1,s1);
733 s2 = 2*FFTmult(c1,s1);
734 fn = fz + n;
735 fi = fz +ii;
736 gi = fz +k1-ii;
737 do
738 {
739 t_fixed a,b,g0,f0,f1,g1,f2,g2,f3,g3;
740 b = FFTmult(s2,fi[k1]) - FFTmult(c2,gi[k1]);
741 a = FFTmult(c2,fi[k1]) + FFTmult(s2,gi[k1]);
742 f1 = fi[0 ] - a;
743 f0 = fi[0 ] + a;
744 g1 = gi[0 ] - b;
745 g0 = gi[0 ] + b;
746 b = FFTmult(s2,fi[k3]) - FFTmult(c2,gi[k3]);
747 a = FFTmult(c2,fi[k3]) + FFTmult(s2,gi[k3]);
748 f3 = fi[k2] - a;
749 f2 = fi[k2] + a;
750 g3 = gi[k2] - b;
751 g2 = gi[k2] + b;
752 b = FFTmult(s1,f2) - FFTmult(c1,g3);
753 a = FFTmult(c1,f2) + FFTmult(s1,g3);
754 fi[k2] = f0 - a;
755 fi[0 ] = f0 + a;
756 gi[k3] = g1 - b;
757 gi[k1] = g1 + b;
758 b = FFTmult(c1,g2) - FFTmult(s1,f3);
759 a = FFTmult(s1,g2) + FFTmult(c1,f3);
760 gi[k2] = g0 - a;
761 gi[0 ] = g0 + a;
762 fi[k3] = f1 - b;
763 fi[k1] = f1 + b;
764 gi += k4;
765 fi += k4;
766 } while (fi<fn);
767 }
768 TRIG_RESET(k,c1,s1);
769 } while (k4<n);
770}
771
772
773void imayer_fft(int n, t_fixed *real, t_fixed *imag)
774{
775 t_fixed a,b,c,d;
776 t_fixed q,r,s,t;
777 int i,j,k;
778 for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
779 a = real[i]; b = real[j]; q=a+b; r=a-b;
780 c = imag[i]; d = imag[j]; s=c+d; t=c-d;
781 real[i] = (q+t)>>1; real[j] = (q-t)>>1;
782 imag[i] = (s-r)>>1; imag[j] = (s+r)>>1;
783 }
784 imayer_fht(real,n);
785 imayer_fht(imag,n);
786}
787
788void imayer_ifft(int n, t_fixed *real, t_fixed *imag)
789{
790 t_fixed a,b,c,d;
791 t_fixed q,r,s,t;
792 int i,j,k;
793 imayer_fht(real,n);
794 imayer_fht(imag,n);
795 for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
796 a = real[i]; b = real[j]; q=a+b; r=a-b;
797 c = imag[i]; d = imag[j]; s=c+d; t=c-d;
798 imag[i] = (s+r)>>1; imag[j] = (s-r)>>1;
799 real[i] = (q-t)>>1; real[j] = (q+t)>>1;
800 }
801}
802
803void imayer_realfft(int n, t_fixed *real)
804{
805 t_fixed a,b,c,d;
806 int i,j,k;
807 imayer_fht(real,n);
808 for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
809 a = real[i];
810 b = real[j];
811 real[j] = (a-b)>>1;
812 real[i] = (a+b)>>1;
813 }
814}
815
816void imayer_realifft(int n, t_fixed *real)
817{
818 t_fixed a,b,c,d;
819 int i,j,k;
820 for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
821 a = real[i];
822 b = real[j];
823 real[j] = (a-b);
824 real[i] = (a+b);
825 }
826 imayer_fht(real,n);
827}
828
829
830
831#ifdef TEST
832
833static double dfcostab[TRIG_TAB_SIZE]=
834 {
835 .00000000000000000000000000000000000000000000000000,
836 .70710678118654752440084436210484903928483593768847,
837 .92387953251128675612818318939678828682241662586364,
838 .98078528040323044912618223613423903697393373089333,
839 .99518472667219688624483695310947992157547486872985,
840 .99879545620517239271477160475910069444320361470461,
841 .99969881869620422011576564966617219685006108125772,
842 .99992470183914454092164649119638322435060646880221,
843 .99998117528260114265699043772856771617391725094433,
844 .99999529380957617151158012570011989955298763362218,
845 .99999882345170190992902571017152601904826792288976,
846 .99999970586288221916022821773876567711626389934930,
847 .99999992646571785114473148070738785694820115568892,
848 .99999998161642929380834691540290971450507605124278,
849 .99999999540410731289097193313960614895889430318945,
850 .99999999885102682756267330779455410840053741619428,
851 .99999999971275670684941397221864177608908945791828,
852 .99999999992818917670977509588385049026048033310951
853 };
854static double dfsintab[TRIG_TAB_SIZE]=
855 {
856 1.0000000000000000000000000000000000000000000000000,
857 .70710678118654752440084436210484903928483593768846,
858 .38268343236508977172845998403039886676134456248561,
859 .19509032201612826784828486847702224092769161775195,
860 .09801714032956060199419556388864184586113667316749,
861 .04906767432741801425495497694268265831474536302574,
862 .02454122852291228803173452945928292506546611923944,
863 .01227153828571992607940826195100321214037231959176,
864 .00613588464915447535964023459037258091705788631738,
865 .00306795676296597627014536549091984251894461021344,
866 .00153398018628476561230369715026407907995486457522,
867 .00076699031874270452693856835794857664314091945205,
868 .00038349518757139558907246168118138126339502603495,
869 .00019174759731070330743990956198900093346887403385,
870 .00009587379909597734587051721097647635118706561284,
871 .00004793689960306688454900399049465887274686668768,
872 .00002396844980841821872918657716502182009476147489,
873 .00001198422490506970642152156159698898480473197753
874 };
875
876static double dhalsec[TRIG_TAB_SIZE]=
877 {
878 0,
879 0,
880 .54119610014619698439972320536638942006107206337801,
881 .50979557910415916894193980398784391368261849190893,
882 .50241928618815570551167011928012092247859337193963,
883 .50060299823519630134550410676638239611758632599591,
884 .50015063602065098821477101271097658495974913010340,
885 .50003765191554772296778139077905492847503165398345,
886 .50000941253588775676512870469186533538523133757983,
887 .50000235310628608051401267171204408939326297376426,
888 .50000058827484117879868526730916804925780637276181,
889 .50000014706860214875463798283871198206179118093251,
890 .50000003676714377807315864400643020315103490883972,
891 .50000000919178552207366560348853455333939112569380,
892 .50000000229794635411562887767906868558991922348920,
893 .50000000057448658687873302235147272458812263401372,
894 .50000000014362164661654736863252589967935073278768,
895 .50000000003590541164769084922906986545517021050714
896 };
897
898
899#include <stdio.h>
900
901
902int writetables()
903{
904 int i;
905
906 printf("/* Tables for fixed point lookup with %d bit precision*/\n\n",fix1);
907
908 printf("static int fsintab[TRIG_TAB_SIZE]= {\n");
909
910 for (i=0;i<TRIG_TAB_SIZE-1;i++)
911 printf("%ld, \n",ftofix(dfsintab[i]));
912 printf("%ld }; \n",ftofix(dfsintab[i]));
913
914
915 printf("\n\nstatic int fcostab[TRIG_TAB_SIZE]= {\n");
916
917 for (i=0;i<TRIG_TAB_SIZE-1;i++)
918 printf("%ld, \n",ftofix(dfcostab[i]));
919 printf("%ld }; \n",ftofix(dfcostab[i]));
920
921}
922
923
924#define OUTPUT \
925 fprintf(stderr,"Integer - Float\n");\
926 for (i=0;i<NP;i++)\
927 fprintf(stderr,"%f %f --> %f %f\n",fixtof(r[i]),fixtof(im[i]),\
928 fr[i],fim[i]);\
929 fprintf(stderr,"\n\n");
930
931
932
933int main()
934{
935 int i;
936 t_fixed r[256];
937 t_fixed im[256];
938 float fr[256];
939 float fim[256];
940
941
942#if 1
943 writetables();
944 exit(0);
945#endif
946
947
948#if 0
949 t_fixed c1,s1,c2,s2,c3,s3;
950 int k;
951 int i;
952
953 TRIG_VARS;
954
955 for (k=2;k<10;k+=2) {
956 TRIG_INIT(k,c1,s1);
957 for (i=0;i<8;i++) {
958 TRIG_NEXT(k,c1,s1);
959 TRIG_23(k,c1,s1,c2,s2,c3,s3);
960 printf("TRIG value k=%d,%d val1 = %f %f\n",k,i,fixtof(c1),fixtof(s1));
961 }
962 }
963#endif
964
965
966
967#if 1
968
969 #define NP 16
970
971 for (i=0;i<NP;i++) {
972 fr[i] = 0.;
973 r[i] = 0.;
974 fim[i] = 0.;
975 im[i] = 0;
976 }
977
978#if 0
979 for (i=0;i<NP;i++) {
980 if (i&1) {
981 fr[i] = 0.1*i;
982 r[i] = ftofix(0.1*i);
983 }
984 else {
985 fr[i] = 0.;
986 r[i] = 0.;
987 }
988 }
989#endif
990#if 0
991 for (i=0;i<NP;i++) {
992 fr[i] = 0.1;
993 r[i] = ftofix(0.1);
994 }
995#endif
996
997 r[1] = ftofix(0.1);
998 fr[1] = 0.1;
999
1000
1001
1002 /* TEST RUN */
1003
1004 OUTPUT
1005
1006 imayer_fft(NP,r,im);
1007 mayer_fft(NP,fr,fim);
1008// imayer_fht(r,NP);
1009// mayer_fht(fr,NP);
1010
1011#if 1
1012 for (i=0;i<NP;i++) {
1013 r[i] = mult(ftofix(0.01),r[i]);
1014 fr[i] = 0.01*fr[i];
1015 }
1016#endif
1017
1018 OUTPUT
1019
1020
1021 imayer_fft(NP,r,im);
1022 mayer_fft(NP,fr,fim);
1023
1024 OUTPUT
1025
1026
1027#endif
1028
1029
1030}
1031
1032#endif
generated by cgit v1.2.3 (git 2.39.1) at 2024-09-12 17:47:40 +0000