source: ntrip/trunk/BNC/newmat/newfft.cpp@ 2013

Last change on this file since 2013 was 2013, checked in by mervart, 13 years ago

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1/// \ingroup newmat
2///@{
3
4/// \file newfft.cpp
5/// Fast Fourier transform using Sande and Gentleman method.
6
7
8// This is originally by Sande and Gentleman in 1967! I have translated from
9// Fortran into C and a little bit of C++.
10
11// It takes about twice as long as fftw
12// (http://theory.lcs.mit.edu/~fftw/homepage.html)
13// but is much shorter than fftw and so despite its age
14// might represent a reasonable
15// compromise between speed and complexity.
16// If you really need the speed get fftw.
17
18
19// THIS SUBROUTINE WAS WRITTEN BY G.SANDE OF PRINCETON UNIVERSITY AND
20// W.M.GENTLMAN OF THE BELL TELEPHONE LAB. IT WAS BROUGHT TO LONDON
21// BY DR. M.D. GODFREY AT THE IMPERIAL COLLEGE AND WAS ADAPTED FOR
22// BURROUGHS 6700 BY D. R. BRILLINGER AND J. PEMBERTON
23// IT REPRESENTS THE STATE OF THE ART OF COMPUTING COMPLETE FINITE
24// DISCRETE FOURIER TRANSFORMS AS OF NOV.1967.
25// OTHER PROGRAMS REQUIRED.
26// ONLY THOSE SUBROUTINES INCLUDED HERE.
27// USAGE.
28// CALL AR1DFT(N,X,Y)
29// WHERE N IS THE NUMBER OF POINTS IN THE SEQUENCE .
30// X - IS A ONE-DIMENSIONAL ARRAY CONTAINING THE REAL
31// PART OF THE SEQUENCE.
32// Y - IS A ONE-DIMENSIONAL ARRAY CONTAINING THE
33// IMAGINARY PART OF THE SEQUENCE.
34// THE TRANSFORM IS RETURNED IN X AND Y.
35// METHOD
36// FOR A GENERAL DISCUSSION OF THESE TRANSFORMS AND OF
37// THE FAST METHOD FOR COMPUTING THEM, SEE GENTLEMAN AND SANDE,
38// @FAST FOURIER TRANSFORMS - FOR FUN AND PROFIT,@ 1966 FALL JOINT
39// COMPUTER CONFERENCE.
40// THIS PROGRAM COMPUTES THIS FOR A COMPLEX SEQUENCE Z(T) OF LENGTH
41// N WHOSE ELEMENTS ARE STORED AT(X(I) , Y(I)) AND RETURNS THE
42// TRANSFORM COEFFICIENTS AT (X(I), Y(I)).
43// DESCRIPTION
44// AR1DFT IS A HIGHLY MODULAR ROUTINE CAPABLE OF COMPUTING IN PLACE
45// THE COMPLETE FINITE DISCRETE FOURIER TRANSFORM OF A ONE-
46// DIMENSIONAL SEQUENCE OF RATHER GENERAL LENGTH N.
47// THE MAIN ROUTINE , AR1DFT ITSELF, FACTORS N. IT THEN CALLS ON
48// ON GR 1D FT TO COMPUTE THE ACTUAL TRANSFORMS, USING THESE FACTORS.
49// THIS GR 1D FT DOES, CALLING AT EACH STAGE ON THE APPROPRIATE KERN
50// EL R2FTK, R4FTK, R8FTK, R16FTK, R3FTK, R5FTK, OR RPFTK TO PERFORM
51// THE COMPUTATIONS FOR THIS PASS OVER THE SEQUENCE, DEPENDING ON
52// WHETHER THE CORRESPONDING FACTOR IS 2, 4, 8, 16, 3, 5, OR SOME
53// MORE GENERAL PRIME P. WHEN GR1DFT IS FINISHED THE TRANSFORM IS
54// COMPUTED, HOWEVER, THE RESULTS ARE STORED IN "DIGITS REVERSED"
55// ORDER. AR1DFT THEREFORE, CALLS UPON GR 1S FS TO SORT THEM OUT.
56// TO RETURN TO THE FACTORIZATION, SINGLETON HAS POINTED OUT THAT
57// THE TRANSFORMS ARE MORE EFFICIENT IF THE SAMPLE SIZE N, IS OF THE
58// FORM B*A**2 AND B CONSISTS OF A SINGLE FACTOR. IN SUCH A CASE
59// IF WE PROCESS THE FACTORS IN THE ORDER ABA THEN
60// THE REORDERING CAN BE DONE AS FAST IN PLACE, AS WITH SCRATCH
61// STORAGE. BUT AS B BECOMES MORE COMPLICATED, THE COST OF THE DIGIT
62// REVERSING DUE TO B PART BECOMES VERY EXPENSIVE IF WE TRY TO DO IT
63// IN PLACE. IN SUCH A CASE IT MIGHT BE BETTER TO USE EXTRA STORAGE
64// A ROUTINE TO DO THIS IS, HOWEVER, NOT INCLUDED HERE.
65// ANOTHER FEATURE INFLUENCING THE FACTORIZATION IS THAT FOR ANY FIXED
66// FACTOR N WE CAN PREPARE A SPECIAL KERNEL WHICH WILL COMPUTE
67// THAT STAGE OF THE TRANSFORM MORE EFFICIENTLY THAN WOULD A KERNEL
68// FOR GENERAL FACTORS, ESPECIALLY IF THE GENERAL KERNEL HAD TO BE
69// APPLIED SEVERAL TIMES. FOR EXAMPLE, FACTORS OF 4 ARE MORE
70// EFFICIENT THAN FACTORS OF 2, FACTORS OF 8 MORE EFFICIENT THAN 4,ETC
71// ON THE OTHER HAND DIMINISHING RETURNS RAPIDLY SET IN, ESPECIALLY
72// SINCE THE LENGTH OF THE KERNEL FOR A SPECIAL CASE IS ROUGHLY
73// PROPORTIONAL TO THE FACTOR IT DEALS WITH. HENCE THESE PROBABLY ARE
74// ALL THE KERNELS WE WISH TO HAVE.
75// RESTRICTIONS.
76// AN UNFORTUNATE FEATURE OF THE SORTING PROBLEM IS THAT THE MOST
77// EFFICIENT WAY TO DO IT IS WITH NESTED DO LOOPS, ONE FOR EACH
78// FACTOR. THIS PUTS A RESTRICTION ON N AS TO HOW MANY FACTORS IT
79// CAN HAVE. CURRENTLY THE LIMIT IS 16, BUT THE LIMIT CAN BE READILY
80// RAISED IF NECESSARY.
81// A SECOND RESTRICTION OF THE PROGRAM IS THAT LOCAL STORAGE OF THE
82// THE ORDER P**2 IS REQUIRED BY THE GENERAL KERNEL RPFTK, SO SOME
83// LIMIT MUST BE SET ON P. CURRENTLY THIS IS 19, BUT IT CAN BE INCRE
84// INCREASED BY TRIVIAL CHANGES.
85// OTHER COMMENTS.
86//(1) THE ROUTINE IS ADAPTED TO CHECK WHETHER A GIVEN N WILL MEET THE
87// ABOVE FACTORING REQUIREMENTS AN, IF NOT, TO RETURN THE NEXT HIGHER
88// NUMBER, NX, SAY, WHICH WILL MEET THESE REQUIREMENTS.
89// THIS CAN BE ACCHIEVED BY A STATEMENT OF THE FORM
90// CALL FACTR(N,X,Y).
91// IF A DIFFERENT N, SAY NX, IS RETURNED THEN THE TRANSFORMS COULD BE
92// OBTAINED BY EXTENDING THE SIZE OF THE X-ARRAY AND Y-ARRAY TO NX,
93// AND SETTING X(I) = Y(I) = 0., FOR I = N+1, NX.
94//(2) IF THE SEQUENCE Z IS ONLY A REAL SEQUENCE, THEN THE IMAGINARY PART
95// Y(I)=0., THIS WILL RETURN THE COSINE TRANSFORM OF THE REAL SEQUENCE
96// IN X, AND THE SINE TRANSFORM IN Y.
97
98
99#define WANT_STREAM
100
101#define WANT_MATH
102
103#include "newmatap.h"
104
105#ifdef use_namespace
106namespace NEWMAT {
107#endif
108
109#ifdef DO_REPORT
110#define REPORT { static ExeCounter ExeCount(__LINE__,20); ++ExeCount; }
111#else
112#define REPORT {}
113#endif
114
115inline Real square(Real x) { return x*x; }
116inline int square(int x) { return x*x; }
117
118static void GR_1D_FS (int PTS, int N_SYM, int N_UN_SYM,
119 const SimpleIntArray& SYM, int P_SYM, const SimpleIntArray& UN_SYM,
120 Real* X, Real* Y);
121static void GR_1D_FT (int N, int N_FACTOR, const SimpleIntArray& FACTOR,
122 Real* X, Real* Y);
123static void R_P_FTK (int N, int M, int P, Real* X, Real* Y);
124static void R_2_FTK (int N, int M, Real* X0, Real* Y0, Real* X1, Real* Y1);
125static void R_3_FTK (int N, int M, Real* X0, Real* Y0, Real* X1, Real* Y1,
126 Real* X2, Real* Y2);
127static void R_4_FTK (int N, int M,
128 Real* X0, Real* Y0, Real* X1, Real* Y1,
129 Real* X2, Real* Y2, Real* X3, Real* Y3);
130static void R_5_FTK (int N, int M,
131 Real* X0, Real* Y0, Real* X1, Real* Y1, Real* X2, Real* Y2,
132 Real* X3, Real* Y3, Real* X4, Real* Y4);
133static void R_8_FTK (int N, int M,
134 Real* X0, Real* Y0, Real* X1, Real* Y1,
135 Real* X2, Real* Y2, Real* X3, Real* Y3,
136 Real* X4, Real* Y4, Real* X5, Real* Y5,
137 Real* X6, Real* Y6, Real* X7, Real* Y7);
138static void R_16_FTK (int N, int M,
139 Real* X0, Real* Y0, Real* X1, Real* Y1,
140 Real* X2, Real* Y2, Real* X3, Real* Y3,
141 Real* X4, Real* Y4, Real* X5, Real* Y5,
142 Real* X6, Real* Y6, Real* X7, Real* Y7,
143 Real* X8, Real* Y8, Real* X9, Real* Y9,
144 Real* X10, Real* Y10, Real* X11, Real* Y11,
145 Real* X12, Real* Y12, Real* X13, Real* Y13,
146 Real* X14, Real* Y14, Real* X15, Real* Y15);
147static int BitReverse(int x, int prod, int n, const SimpleIntArray& f);
148
149
150bool FFT_Controller::ar_1d_ft (int PTS, Real* X, Real *Y)
151{
152// ARBITRARY RADIX ONE DIMENSIONAL FOURIER TRANSFORM
153
154 REPORT
155
156 int F,J,N,NF,P,PMAX,P_SYM,P_TWO,Q,R,TWO_GRP;
157
158 // NP is maximum number of squared factors allows PTS up to 2**32 at least
159 // NQ is number of not-squared factors - increase if we increase PMAX
160 const int NP = 16, NQ = 10;
161 SimpleIntArray PP(NP), QQ(NQ);
162
163 TWO_GRP=16; PMAX=19;
164
165 // PMAX is the maximum factor size
166 // TWO_GRP is the maximum power of 2 handled as a single factor
167 // Doesn't take advantage of combining powers of 2 when calculating
168 // number of factors
169
170 if (PTS<=1) return true;
171 N=PTS; P_SYM=1; F=2; P=0; Q=0;
172
173 // P counts the number of squared factors
174 // Q counts the number of the rest
175 // R = 0 for no non-squared factors; 1 otherwise
176
177 // FACTOR holds all the factors - non-squared ones in the middle
178 // - length is 2*P+Q
179 // SYM also holds all the factors but with the non-squared ones
180 // multiplied together - length is 2*P+R
181 // PP holds the values of the squared factors - length is P
182 // QQ holds the values of the rest - length is Q
183
184 // P_SYM holds the product of the squared factors
185
186 // find the factors - load into PP and QQ
187 while (N > 1)
188 {
189 bool fail = true;
190 for (J=F; J<=PMAX; J++)
191 if (N % J == 0) { fail = false; F=J; break; }
192 if (fail || P >= NP || Q >= NQ) return false; // can't factor
193 N /= F;
194 if (N % F != 0) QQ[Q++] = F;
195 else { N /= F; PP[P++] = F; P_SYM *= F; }
196 }
197
198 R = (Q == 0) ? 0 : 1; // R = 0 if no not-squared factors, 1 otherwise
199
200 NF = 2*P + Q;
201 SimpleIntArray FACTOR(NF + 1), SYM(2*P + R);
202 FACTOR[NF] = 0; // we need this in the "combine powers of 2"
203
204 // load into SYM and FACTOR
205 for (J=0; J<P; J++)
206 { SYM[J]=FACTOR[J]=PP[P-1-J]; FACTOR[P+Q+J]=SYM[P+R+J]=PP[J]; }
207
208 if (Q>0)
209 {
210 REPORT
211 for (J=0; J<Q; J++) FACTOR[P+J]=QQ[J];
212 SYM[P]=PTS/square(P_SYM);
213 }
214
215 // combine powers of 2
216 P_TWO = 1;
217 for (J=0; J < NF; J++)
218 {
219 if (FACTOR[J]!=2) continue;
220 P_TWO=P_TWO*2; FACTOR[J]=1;
221 if (P_TWO<TWO_GRP && FACTOR[J+1]==2) continue;
222 FACTOR[J]=P_TWO; P_TWO=1;
223 }
224
225 if (P==0) R=0;
226 if (Q<=1) Q=0;
227
228 // do the analysis
229 GR_1D_FT(PTS,NF,FACTOR,X,Y); // the transform
230 GR_1D_FS(PTS,2*P+R,Q,SYM,P_SYM,QQ,X,Y); // the reshuffling
231
232 return true;
233
234}
235
236static void GR_1D_FS (int PTS, int N_SYM, int N_UN_SYM,
237 const SimpleIntArray& SYM, int P_SYM, const SimpleIntArray& UN_SYM,
238 Real* X, Real* Y)
239{
240// GENERAL RADIX ONE DIMENSIONAL FOURIER SORT
241
242// PTS = number of points
243// N_SYM = length of SYM
244// N_UN_SYM = length of UN_SYM
245// SYM: squared factors + product of non-squared factors + squared factors
246// P_SYM = product of squared factors (each included only once)
247// UN_SYM: not-squared factors
248
249 REPORT
250
251 Real T;
252 int JJ,KK,P_UN_SYM;
253
254 // I have replaced the multiple for-loop used by Sande-Gentleman code
255 // by the following code which does not limit the number of factors
256
257 if (N_SYM > 0)
258 {
259 REPORT
260 SimpleIntArray U(N_SYM);
261 for(MultiRadixCounter MRC(N_SYM, SYM, U); !MRC.Finish(); ++MRC)
262 {
263 if (MRC.Swap())
264 {
265 int P = MRC.Reverse(); int JJ = MRC.Counter(); Real T;
266 T=X[JJ]; X[JJ]=X[P]; X[P]=T; T=Y[JJ]; Y[JJ]=Y[P]; Y[P]=T;
267 }
268 }
269 }
270
271 int J,JL,K,L,M,MS;
272
273 // UN_SYM contains the non-squared factors
274 // I have replaced the Sande-Gentleman code as it runs into
275 // integer overflow problems
276 // My code (and theirs) would be improved by using a bit array
277 // as suggested by Van Loan
278
279 if (N_UN_SYM==0) { REPORT return; }
280 P_UN_SYM=PTS/square(P_SYM); JL=(P_UN_SYM-3)*P_SYM; MS=P_UN_SYM*P_SYM;
281
282 for (J = P_SYM; J<=JL; J+=P_SYM)
283 {
284 K=J;
285 do K = P_SYM * BitReverse(K / P_SYM, P_UN_SYM, N_UN_SYM, UN_SYM);
286 while (K<J);
287
288 if (K!=J)
289 {
290 REPORT
291 for (L=0; L<P_SYM; L++) for (M=L; M<PTS; M+=MS)
292 {
293 JJ=M+J; KK=M+K;
294 T=X[JJ]; X[JJ]=X[KK]; X[KK]=T; T=Y[JJ]; Y[JJ]=Y[KK]; Y[KK]=T;
295 }
296 }
297 }
298
299 return;
300}
301
302static void GR_1D_FT (int N, int N_FACTOR, const SimpleIntArray& FACTOR,
303 Real* X, Real* Y)
304{
305// GENERAL RADIX ONE DIMENSIONAL FOURIER TRANSFORM;
306
307 REPORT
308
309 int M = N;
310
311 for (int i = 0; i < N_FACTOR; i++)
312 {
313 int P = FACTOR[i]; M /= P;
314
315 switch(P)
316 {
317 case 1: REPORT break;
318 case 2: REPORT R_2_FTK (N,M,X,Y,X+M,Y+M); break;
319 case 3: REPORT R_3_FTK (N,M,X,Y,X+M,Y+M,X+2*M,Y+2*M); break;
320 case 4: REPORT R_4_FTK (N,M,X,Y,X+M,Y+M,X+2*M,Y+2*M,X+3*M,Y+3*M); break;
321 case 5:
322 REPORT
323 R_5_FTK (N,M,X,Y,X+M,Y+M,X+2*M,Y+2*M,X+3*M,Y+3*M,X+4*M,Y+4*M);
324 break;
325 case 8:
326 REPORT
327 R_8_FTK (N,M,X,Y,X+M,Y+M,X+2*M,Y+2*M,
328 X+3*M,Y+3*M,X+4*M,Y+4*M,X+5*M,Y+5*M,
329 X+6*M,Y+6*M,X+7*M,Y+7*M);
330 break;
331 case 16:
332 REPORT
333 R_16_FTK (N,M,X,Y,X+M,Y+M,X+2*M,Y+2*M,
334 X+3*M,Y+3*M,X+4*M,Y+4*M,X+5*M,Y+5*M,
335 X+6*M,Y+6*M,X+7*M,Y+7*M,X+8*M,Y+8*M,
336 X+9*M,Y+9*M,X+10*M,Y+10*M,X+11*M,Y+11*M,
337 X+12*M,Y+12*M,X+13*M,Y+13*M,X+14*M,Y+14*M,
338 X+15*M,Y+15*M);
339 break;
340 default: REPORT R_P_FTK (N,M,P,X,Y); break;
341 }
342 }
343
344}
345
346static void R_P_FTK (int N, int M, int P, Real* X, Real* Y)
347// RADIX PRIME FOURIER TRANSFORM KERNEL;
348// X and Y are treated as M * P matrices with Fortran storage
349{
350 REPORT
351 bool NO_FOLD,ZERO;
352 Real ANGLE,IS,IU,RS,RU,T,TWOPI,XT,YT;
353 int J,JJ,K0,K,M_OVER_2,MP,PM,PP,U,V;
354
355 Real AA [9][9], BB [9][9];
356 Real A [18], B [18], C [18], S [18];
357 Real IA [9], IB [9], RA [9], RB [9];
358
359 TWOPI=8.0*atan(1.0);
360 M_OVER_2=M/2+1; MP=M*P; PP=P/2; PM=P-1;
361
362 for (U=0; U<PP; U++)
363 {
364 ANGLE=TWOPI*Real(U+1)/Real(P);
365 JJ=P-U-2;
366 A[U]=cos(ANGLE); B[U]=sin(ANGLE);
367 A[JJ]=A[U]; B[JJ]= -B[U];
368 }
369
370 for (U=1; U<=PP; U++)
371 {
372 for (V=1; V<=PP; V++)
373 { JJ=U*V-U*V/P*P; AA[V-1][U-1]=A[JJ-1]; BB[V-1][U-1]=B[JJ-1]; }
374 }
375
376 for (J=0; J<M_OVER_2; J++)
377 {
378 NO_FOLD = (J==0 || 2*J==M);
379 K0=J;
380 ANGLE=TWOPI*Real(J)/Real(MP); ZERO=ANGLE==0.0;
381 C[0]=cos(ANGLE); S[0]=sin(ANGLE);
382 for (U=1; U<PM; U++)
383 {
384 C[U]=C[U-1]*C[0]-S[U-1]*S[0];
385 S[U]=S[U-1]*C[0]+C[U-1]*S[0];
386 }
387 goto L700;
388 L500:
389 REPORT
390 if (NO_FOLD) { REPORT goto L1500; }
391 REPORT
392 NO_FOLD=true; K0=M-J;
393 for (U=0; U<PM; U++)
394 { T=C[U]*A[U]+S[U]*B[U]; S[U]= -S[U]*A[U]+C[U]*B[U]; C[U]=T; }
395 L700:
396 REPORT
397 for (K=K0; K<N; K+=MP)
398 {
399 XT=X[K]; YT=Y[K];
400 for (U=1; U<=PP; U++)
401 {
402 RA[U-1]=XT; IA[U-1]=YT;
403 RB[U-1]=0.0; IB[U-1]=0.0;
404 }
405 for (U=1; U<=PP; U++)
406 {
407 JJ=P-U;
408 RS=X[K+M*U]+X[K+M*JJ]; IS=Y[K+M*U]+Y[K+M*JJ];
409 RU=X[K+M*U]-X[K+M*JJ]; IU=Y[K+M*U]-Y[K+M*JJ];
410 XT=XT+RS; YT=YT+IS;
411 for (V=0; V<PP; V++)
412 {
413 RA[V]=RA[V]+RS*AA[V][U-1]; IA[V]=IA[V]+IS*AA[V][U-1];
414 RB[V]=RB[V]+RU*BB[V][U-1]; IB[V]=IB[V]+IU*BB[V][U-1];
415 }
416 }
417 X[K]=XT; Y[K]=YT;
418 for (U=1; U<=PP; U++)
419 {
420 if (!ZERO)
421 {
422 REPORT
423 XT=RA[U-1]+IB[U-1]; YT=IA[U-1]-RB[U-1];
424 X[K+M*U]=XT*C[U-1]+YT*S[U-1]; Y[K+M*U]=YT*C[U-1]-XT*S[U-1];
425 JJ=P-U;
426 XT=RA[U-1]-IB[U-1]; YT=IA[U-1]+RB[U-1];
427 X[K+M*JJ]=XT*C[JJ-1]+YT*S[JJ-1];
428 Y[K+M*JJ]=YT*C[JJ-1]-XT*S[JJ-1];
429 }
430 else
431 {
432 REPORT
433 X[K+M*U]=RA[U-1]+IB[U-1]; Y[K+M*U]=IA[U-1]-RB[U-1];
434 JJ=P-U;
435 X[K+M*JJ]=RA[U-1]-IB[U-1]; Y[K+M*JJ]=IA[U-1]+RB[U-1];
436 }
437 }
438 }
439 goto L500;
440L1500: ;
441 }
442 return;
443}
444
445static void R_2_FTK (int N, int M, Real* X0, Real* Y0, Real* X1, Real* Y1)
446// RADIX TWO FOURIER TRANSFORM KERNEL;
447{
448 REPORT
449 bool NO_FOLD,ZERO;
450 int J,K,K0,M2,M_OVER_2;
451 Real ANGLE,C,IS,IU,RS,RU,S,TWOPI;
452
453 M2=M*2; M_OVER_2=M/2+1;
454 TWOPI=8.0*atan(1.0);
455
456 for (J=0; J<M_OVER_2; J++)
457 {
458 NO_FOLD = (J==0 || 2*J==M);
459 K0=J;
460 ANGLE=TWOPI*Real(J)/Real(M2); ZERO=ANGLE==0.0;
461 C=cos(ANGLE); S=sin(ANGLE);
462 goto L200;
463 L100:
464 REPORT
465 if (NO_FOLD) { REPORT goto L600; }
466 REPORT
467 NO_FOLD=true; K0=M-J; C= -C;
468 L200:
469 REPORT
470 for (K=K0; K<N; K+=M2)
471 {
472 RS=X0[K]+X1[K]; IS=Y0[K]+Y1[K];
473 RU=X0[K]-X1[K]; IU=Y0[K]-Y1[K];
474 X0[K]=RS; Y0[K]=IS;
475 if (!ZERO) { X1[K]=RU*C+IU*S; Y1[K]=IU*C-RU*S; }
476 else { X1[K]=RU; Y1[K]=IU; }
477 }
478 goto L100;
479 L600: ;
480 }
481
482 return;
483}
484
485static void R_3_FTK (int N, int M, Real* X0, Real* Y0, Real* X1, Real* Y1,
486 Real* X2, Real* Y2)
487// RADIX THREE FOURIER TRANSFORM KERNEL
488{
489 REPORT
490 bool NO_FOLD,ZERO;
491 int J,K,K0,M3,M_OVER_2;
492 Real ANGLE,A,B,C1,C2,S1,S2,T,TWOPI;
493 Real I0,I1,I2,IA,IB,IS,R0,R1,R2,RA,RB,RS;
494
495 M3=M*3; M_OVER_2=M/2+1; TWOPI=8.0*atan(1.0);
496 A=cos(TWOPI/3.0); B=sin(TWOPI/3.0);
497
498 for (J=0; J<M_OVER_2; J++)
499 {
500 NO_FOLD = (J==0 || 2*J==M);
501 K0=J;
502 ANGLE=TWOPI*Real(J)/Real(M3); ZERO=ANGLE==0.0;
503 C1=cos(ANGLE); S1=sin(ANGLE);
504 C2=C1*C1-S1*S1; S2=S1*C1+C1*S1;
505 goto L200;
506 L100:
507 REPORT
508 if (NO_FOLD) { REPORT goto L600; }
509 REPORT
510 NO_FOLD=true; K0=M-J;
511 T=C1*A+S1*B; S1=C1*B-S1*A; C1=T;
512 T=C2*A-S2*B; S2= -C2*B-S2*A; C2=T;
513 L200:
514 REPORT
515 for (K=K0; K<N; K+=M3)
516 {
517 R0 = X0[K]; I0 = Y0[K];
518 RS=X1[K]+X2[K]; IS=Y1[K]+Y2[K];
519 X0[K]=R0+RS; Y0[K]=I0+IS;
520 RA=R0+RS*A; IA=I0+IS*A;
521 RB=(X1[K]-X2[K])*B; IB=(Y1[K]-Y2[K])*B;
522 if (!ZERO)
523 {
524 REPORT
525 R1=RA+IB; I1=IA-RB; R2=RA-IB; I2=IA+RB;
526 X1[K]=R1*C1+I1*S1; Y1[K]=I1*C1-R1*S1;
527 X2[K]=R2*C2+I2*S2; Y2[K]=I2*C2-R2*S2;
528 }
529 else { REPORT X1[K]=RA+IB; Y1[K]=IA-RB; X2[K]=RA-IB; Y2[K]=IA+RB; }
530 }
531 goto L100;
532 L600: ;
533 }
534
535 return;
536}
537
538static void R_4_FTK (int N, int M,
539 Real* X0, Real* Y0, Real* X1, Real* Y1,
540 Real* X2, Real* Y2, Real* X3, Real* Y3)
541// RADIX FOUR FOURIER TRANSFORM KERNEL
542{
543 REPORT
544 bool NO_FOLD,ZERO;
545 int J,K,K0,M4,M_OVER_2;
546 Real ANGLE,C1,C2,C3,S1,S2,S3,T,TWOPI;
547 Real I1,I2,I3,IS0,IS1,IU0,IU1,R1,R2,R3,RS0,RS1,RU0,RU1;
548
549 M4=M*4; M_OVER_2=M/2+1;
550 TWOPI=8.0*atan(1.0);
551
552 for (J=0; J<M_OVER_2; J++)
553 {
554 NO_FOLD = (J==0 || 2*J==M);
555 K0=J;
556 ANGLE=TWOPI*Real(J)/Real(M4); ZERO=ANGLE==0.0;
557 C1=cos(ANGLE); S1=sin(ANGLE);
558 C2=C1*C1-S1*S1; S2=S1*C1+C1*S1;
559 C3=C2*C1-S2*S1; S3=S2*C1+C2*S1;
560 goto L200;
561 L100:
562 REPORT
563 if (NO_FOLD) { REPORT goto L600; }
564 REPORT
565 NO_FOLD=true; K0=M-J;
566 T=C1; C1=S1; S1=T;
567 C2= -C2;
568 T=C3; C3= -S3; S3= -T;
569 L200:
570 REPORT
571 for (K=K0; K<N; K+=M4)
572 {
573 RS0=X0[K]+X2[K]; IS0=Y0[K]+Y2[K];
574 RU0=X0[K]-X2[K]; IU0=Y0[K]-Y2[K];
575 RS1=X1[K]+X3[K]; IS1=Y1[K]+Y3[K];
576 RU1=X1[K]-X3[K]; IU1=Y1[K]-Y3[K];
577 X0[K]=RS0+RS1; Y0[K]=IS0+IS1;
578 if (!ZERO)
579 {
580 REPORT
581 R1=RU0+IU1; I1=IU0-RU1;
582 R2=RS0-RS1; I2=IS0-IS1;
583 R3=RU0-IU1; I3=IU0+RU1;
584 X2[K]=R1*C1+I1*S1; Y2[K]=I1*C1-R1*S1;
585 X1[K]=R2*C2+I2*S2; Y1[K]=I2*C2-R2*S2;
586 X3[K]=R3*C3+I3*S3; Y3[K]=I3*C3-R3*S3;
587 }
588 else
589 {
590 REPORT
591 X2[K]=RU0+IU1; Y2[K]=IU0-RU1;
592 X1[K]=RS0-RS1; Y1[K]=IS0-IS1;
593 X3[K]=RU0-IU1; Y3[K]=IU0+RU1;
594 }
595 }
596 goto L100;
597 L600: ;
598 }
599
600 return;
601}
602
603static void R_5_FTK (int N, int M,
604 Real* X0, Real* Y0, Real* X1, Real* Y1, Real* X2, Real* Y2,
605 Real* X3, Real* Y3, Real* X4, Real* Y4)
606// RADIX FIVE FOURIER TRANSFORM KERNEL
607
608{
609 REPORT
610 bool NO_FOLD,ZERO;
611 int J,K,K0,M5,M_OVER_2;
612 Real ANGLE,A1,A2,B1,B2,C1,C2,C3,C4,S1,S2,S3,S4,T,TWOPI;
613 Real R0,R1,R2,R3,R4,RA1,RA2,RB1,RB2,RS1,RS2,RU1,RU2;
614 Real I0,I1,I2,I3,I4,IA1,IA2,IB1,IB2,IS1,IS2,IU1,IU2;
615
616 M5=M*5; M_OVER_2=M/2+1;
617 TWOPI=8.0*atan(1.0);
618 A1=cos(TWOPI/5.0); B1=sin(TWOPI/5.0);
619 A2=cos(2.0*TWOPI/5.0); B2=sin(2.0*TWOPI/5.0);
620
621 for (J=0; J<M_OVER_2; J++)
622 {
623 NO_FOLD = (J==0 || 2*J==M);
624 K0=J;
625 ANGLE=TWOPI*Real(J)/Real(M5); ZERO=ANGLE==0.0;
626 C1=cos(ANGLE); S1=sin(ANGLE);
627 C2=C1*C1-S1*S1; S2=S1*C1+C1*S1;
628 C3=C2*C1-S2*S1; S3=S2*C1+C2*S1;
629 C4=C2*C2-S2*S2; S4=S2*C2+C2*S2;
630 goto L200;
631 L100:
632 REPORT
633 if (NO_FOLD) { REPORT goto L600; }
634 REPORT
635 NO_FOLD=true; K0=M-J;
636 T=C1*A1+S1*B1; S1=C1*B1-S1*A1; C1=T;
637 T=C2*A2+S2*B2; S2=C2*B2-S2*A2; C2=T;
638 T=C3*A2-S3*B2; S3= -C3*B2-S3*A2; C3=T;
639 T=C4*A1-S4*B1; S4= -C4*B1-S4*A1; C4=T;
640 L200:
641 REPORT
642 for (K=K0; K<N; K+=M5)
643 {
644 R0=X0[K]; I0=Y0[K];
645 RS1=X1[K]+X4[K]; IS1=Y1[K]+Y4[K];
646 RU1=X1[K]-X4[K]; IU1=Y1[K]-Y4[K];
647 RS2=X2[K]+X3[K]; IS2=Y2[K]+Y3[K];
648 RU2=X2[K]-X3[K]; IU2=Y2[K]-Y3[K];
649 X0[K]=R0+RS1+RS2; Y0[K]=I0+IS1+IS2;
650 RA1=R0+RS1*A1+RS2*A2; IA1=I0+IS1*A1+IS2*A2;
651 RA2=R0+RS1*A2+RS2*A1; IA2=I0+IS1*A2+IS2*A1;
652 RB1=RU1*B1+RU2*B2; IB1=IU1*B1+IU2*B2;
653 RB2=RU1*B2-RU2*B1; IB2=IU1*B2-IU2*B1;
654 if (!ZERO)
655 {
656 REPORT
657 R1=RA1+IB1; I1=IA1-RB1;
658 R2=RA2+IB2; I2=IA2-RB2;
659 R3=RA2-IB2; I3=IA2+RB2;
660 R4=RA1-IB1; I4=IA1+RB1;
661 X1[K]=R1*C1+I1*S1; Y1[K]=I1*C1-R1*S1;
662 X2[K]=R2*C2+I2*S2; Y2[K]=I2*C2-R2*S2;
663 X3[K]=R3*C3+I3*S3; Y3[K]=I3*C3-R3*S3;
664 X4[K]=R4*C4+I4*S4; Y4[K]=I4*C4-R4*S4;
665 }
666 else
667 {
668 REPORT
669 X1[K]=RA1+IB1; Y1[K]=IA1-RB1;
670 X2[K]=RA2+IB2; Y2[K]=IA2-RB2;
671 X3[K]=RA2-IB2; Y3[K]=IA2+RB2;
672 X4[K]=RA1-IB1; Y4[K]=IA1+RB1;
673 }
674 }
675 goto L100;
676 L600: ;
677 }
678
679 return;
680}
681
682static void R_8_FTK (int N, int M,
683 Real* X0, Real* Y0, Real* X1, Real* Y1,
684 Real* X2, Real* Y2, Real* X3, Real* Y3,
685 Real* X4, Real* Y4, Real* X5, Real* Y5,
686 Real* X6, Real* Y6, Real* X7, Real* Y7)
687// RADIX EIGHT FOURIER TRANSFORM KERNEL
688{
689 REPORT
690 bool NO_FOLD,ZERO;
691 int J,K,K0,M8,M_OVER_2;
692 Real ANGLE,C1,C2,C3,C4,C5,C6,C7,E,S1,S2,S3,S4,S5,S6,S7,T,TWOPI;
693 Real R1,R2,R3,R4,R5,R6,R7,RS0,RS1,RS2,RS3,RU0,RU1,RU2,RU3;
694 Real I1,I2,I3,I4,I5,I6,I7,IS0,IS1,IS2,IS3,IU0,IU1,IU2,IU3;
695 Real RSS0,RSS1,RSU0,RSU1,RUS0,RUS1,RUU0,RUU1;
696 Real ISS0,ISS1,ISU0,ISU1,IUS0,IUS1,IUU0,IUU1;
697
698 M8=M*8; M_OVER_2=M/2+1;
699 TWOPI=8.0*atan(1.0); E=cos(TWOPI/8.0);
700
701 for (J=0;J<M_OVER_2;J++)
702 {
703 NO_FOLD= (J==0 || 2*J==M);
704 K0=J;
705 ANGLE=TWOPI*Real(J)/Real(M8); ZERO=ANGLE==0.0;
706 C1=cos(ANGLE); S1=sin(ANGLE);
707 C2=C1*C1-S1*S1; S2=C1*S1+S1*C1;
708 C3=C2*C1-S2*S1; S3=S2*C1+C2*S1;
709 C4=C2*C2-S2*S2; S4=S2*C2+C2*S2;
710 C5=C4*C1-S4*S1; S5=S4*C1+C4*S1;
711 C6=C4*C2-S4*S2; S6=S4*C2+C4*S2;
712 C7=C4*C3-S4*S3; S7=S4*C3+C4*S3;
713 goto L200;
714 L100:
715 REPORT
716 if (NO_FOLD) { REPORT goto L600; }
717 REPORT
718 NO_FOLD=true; K0=M-J;
719 T=(C1+S1)*E; S1=(C1-S1)*E; C1=T;
720 T=S2; S2=C2; C2=T;
721 T=(-C3+S3)*E; S3=(C3+S3)*E; C3=T;
722 C4= -C4;
723 T= -(C5+S5)*E; S5=(-C5+S5)*E; C5=T;
724 T= -S6; S6= -C6; C6=T;
725 T=(C7-S7)*E; S7= -(C7+S7)*E; C7=T;
726 L200:
727 REPORT
728 for (K=K0; K<N; K+=M8)
729 {
730 RS0=X0[K]+X4[K]; IS0=Y0[K]+Y4[K];
731 RU0=X0[K]-X4[K]; IU0=Y0[K]-Y4[K];
732 RS1=X1[K]+X5[K]; IS1=Y1[K]+Y5[K];
733 RU1=X1[K]-X5[K]; IU1=Y1[K]-Y5[K];
734 RS2=X2[K]+X6[K]; IS2=Y2[K]+Y6[K];
735 RU2=X2[K]-X6[K]; IU2=Y2[K]-Y6[K];
736 RS3=X3[K]+X7[K]; IS3=Y3[K]+Y7[K];
737 RU3=X3[K]-X7[K]; IU3=Y3[K]-Y7[K];
738 RSS0=RS0+RS2; ISS0=IS0+IS2;
739 RSU0=RS0-RS2; ISU0=IS0-IS2;
740 RSS1=RS1+RS3; ISS1=IS1+IS3;
741 RSU1=RS1-RS3; ISU1=IS1-IS3;
742 RUS0=RU0-IU2; IUS0=IU0+RU2;
743 RUU0=RU0+IU2; IUU0=IU0-RU2;
744 RUS1=RU1-IU3; IUS1=IU1+RU3;
745 RUU1=RU1+IU3; IUU1=IU1-RU3;
746 T=(RUS1+IUS1)*E; IUS1=(IUS1-RUS1)*E; RUS1=T;
747 T=(RUU1+IUU1)*E; IUU1=(IUU1-RUU1)*E; RUU1=T;
748 X0[K]=RSS0+RSS1; Y0[K]=ISS0+ISS1;
749 if (!ZERO)
750 {
751 REPORT
752 R1=RUU0+RUU1; I1=IUU0+IUU1;
753 R2=RSU0+ISU1; I2=ISU0-RSU1;
754 R3=RUS0+IUS1; I3=IUS0-RUS1;
755 R4=RSS0-RSS1; I4=ISS0-ISS1;
756 R5=RUU0-RUU1; I5=IUU0-IUU1;
757 R6=RSU0-ISU1; I6=ISU0+RSU1;
758 R7=RUS0-IUS1; I7=IUS0+RUS1;
759 X4[K]=R1*C1+I1*S1; Y4[K]=I1*C1-R1*S1;
760 X2[K]=R2*C2+I2*S2; Y2[K]=I2*C2-R2*S2;
761 X6[K]=R3*C3+I3*S3; Y6[K]=I3*C3-R3*S3;
762 X1[K]=R4*C4+I4*S4; Y1[K]=I4*C4-R4*S4;
763 X5[K]=R5*C5+I5*S5; Y5[K]=I5*C5-R5*S5;
764 X3[K]=R6*C6+I6*S6; Y3[K]=I6*C6-R6*S6;
765 X7[K]=R7*C7+I7*S7; Y7[K]=I7*C7-R7*S7;
766 }
767 else
768 {
769 REPORT
770 X4[K]=RUU0+RUU1; Y4[K]=IUU0+IUU1;
771 X2[K]=RSU0+ISU1; Y2[K]=ISU0-RSU1;
772 X6[K]=RUS0+IUS1; Y6[K]=IUS0-RUS1;
773 X1[K]=RSS0-RSS1; Y1[K]=ISS0-ISS1;
774 X5[K]=RUU0-RUU1; Y5[K]=IUU0-IUU1;
775 X3[K]=RSU0-ISU1; Y3[K]=ISU0+RSU1;
776 X7[K]=RUS0-IUS1; Y7[K]=IUS0+RUS1;
777 }
778 }
779 goto L100;
780 L600: ;
781 }
782
783 return;
784}
785
786static void R_16_FTK (int N, int M,
787 Real* X0, Real* Y0, Real* X1, Real* Y1,
788 Real* X2, Real* Y2, Real* X3, Real* Y3,
789 Real* X4, Real* Y4, Real* X5, Real* Y5,
790 Real* X6, Real* Y6, Real* X7, Real* Y7,
791 Real* X8, Real* Y8, Real* X9, Real* Y9,
792 Real* X10, Real* Y10, Real* X11, Real* Y11,
793 Real* X12, Real* Y12, Real* X13, Real* Y13,
794 Real* X14, Real* Y14, Real* X15, Real* Y15)
795// RADIX SIXTEEN FOURIER TRANSFORM KERNEL
796{
797 REPORT
798 bool NO_FOLD,ZERO;
799 int J,K,K0,M16,M_OVER_2;
800 Real ANGLE,EI1,ER1,E2,EI3,ER3,EI5,ER5,T,TWOPI;
801 Real RS0,RS1,RS2,RS3,RS4,RS5,RS6,RS7;
802 Real IS0,IS1,IS2,IS3,IS4,IS5,IS6,IS7;
803 Real RU0,RU1,RU2,RU3,RU4,RU5,RU6,RU7;
804 Real IU0,IU1,IU2,IU3,IU4,IU5,IU6,IU7;
805 Real RUS0,RUS1,RUS2,RUS3,RUU0,RUU1,RUU2,RUU3;
806 Real ISS0,ISS1,ISS2,ISS3,ISU0,ISU1,ISU2,ISU3;
807 Real RSS0,RSS1,RSS2,RSS3,RSU0,RSU1,RSU2,RSU3;
808 Real IUS0,IUS1,IUS2,IUS3,IUU0,IUU1,IUU2,IUU3;
809 Real RSSS0,RSSS1,RSSU0,RSSU1,RSUS0,RSUS1,RSUU0,RSUU1;
810 Real ISSS0,ISSS1,ISSU0,ISSU1,ISUS0,ISUS1,ISUU0,ISUU1;
811 Real RUSS0,RUSS1,RUSU0,RUSU1,RUUS0,RUUS1,RUUU0,RUUU1;
812 Real IUSS0,IUSS1,IUSU0,IUSU1,IUUS0,IUUS1,IUUU0,IUUU1;
813 Real R1,R2,R3,R4,R5,R6,R7,R8,R9,R10,R11,R12,R13,R14,R15;
814 Real I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,I11,I12,I13,I14,I15;
815 Real C1,C2,C3,C4,C5,C6,C7,C8,C9,C10,C11,C12,C13,C14,C15;
816 Real S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,S13,S14,S15;
817
818 M16=M*16; M_OVER_2=M/2+1;
819 TWOPI=8.0*atan(1.0);
820 ER1=cos(TWOPI/16.0); EI1=sin(TWOPI/16.0);
821 E2=cos(TWOPI/8.0);
822 ER3=cos(3.0*TWOPI/16.0); EI3=sin(3.0*TWOPI/16.0);
823 ER5=cos(5.0*TWOPI/16.0); EI5=sin(5.0*TWOPI/16.0);
824
825 for (J=0; J<M_OVER_2; J++)
826 {
827 NO_FOLD = (J==0 || 2*J==M);
828 K0=J;
829 ANGLE=TWOPI*Real(J)/Real(M16);
830 ZERO=ANGLE==0.0;
831 C1=cos(ANGLE); S1=sin(ANGLE);
832 C2=C1*C1-S1*S1; S2=C1*S1+S1*C1;
833 C3=C2*C1-S2*S1; S3=S2*C1+C2*S1;
834 C4=C2*C2-S2*S2; S4=S2*C2+C2*S2;
835 C5=C4*C1-S4*S1; S5=S4*C1+C4*S1;
836 C6=C4*C2-S4*S2; S6=S4*C2+C4*S2;
837 C7=C4*C3-S4*S3; S7=S4*C3+C4*S3;
838 C8=C4*C4-S4*S4; S8=C4*S4+S4*C4;
839 C9=C8*C1-S8*S1; S9=S8*C1+C8*S1;
840 C10=C8*C2-S8*S2; S10=S8*C2+C8*S2;
841 C11=C8*C3-S8*S3; S11=S8*C3+C8*S3;
842 C12=C8*C4-S8*S4; S12=S8*C4+C8*S4;
843 C13=C8*C5-S8*S5; S13=S8*C5+C8*S5;
844 C14=C8*C6-S8*S6; S14=S8*C6+C8*S6;
845 C15=C8*C7-S8*S7; S15=S8*C7+C8*S7;
846 goto L200;
847 L100:
848 REPORT
849 if (NO_FOLD) { REPORT goto L600; }
850 REPORT
851 NO_FOLD=true; K0=M-J;
852 T=C1*ER1+S1*EI1; S1= -S1*ER1+C1*EI1; C1=T;
853 T=(C2+S2)*E2; S2=(C2-S2)*E2; C2=T;
854 T=C3*ER3+S3*EI3; S3= -S3*ER3+C3*EI3; C3=T;
855 T=S4; S4=C4; C4=T;
856 T=S5*ER1-C5*EI1; S5=C5*ER1+S5*EI1; C5=T;
857 T=(-C6+S6)*E2; S6=(C6+S6)*E2; C6=T;
858 T=S7*ER3-C7*EI3; S7=C7*ER3+S7*EI3; C7=T;
859 C8= -C8;
860 T= -(C9*ER1+S9*EI1); S9=S9*ER1-C9*EI1; C9=T;
861 T= -(C10+S10)*E2; S10=(-C10+S10)*E2; C10=T;
862 T= -(C11*ER3+S11*EI3); S11=S11*ER3-C11*EI3; C11=T;
863 T= -S12; S12= -C12; C12=T;
864 T= -S13*ER1+C13*EI1; S13= -(C13*ER1+S13*EI1); C13=T;
865 T=(C14-S14)*E2; S14= -(C14+S14)*E2; C14=T;
866 T= -S15*ER3+C15*EI3; S15= -(C15*ER3+S15*EI3); C15=T;
867 L200:
868 REPORT
869 for (K=K0; K<N; K+=M16)
870 {
871 RS0=X0[K]+X8[K]; IS0=Y0[K]+Y8[K];
872 RU0=X0[K]-X8[K]; IU0=Y0[K]-Y8[K];
873 RS1=X1[K]+X9[K]; IS1=Y1[K]+Y9[K];
874 RU1=X1[K]-X9[K]; IU1=Y1[K]-Y9[K];
875 RS2=X2[K]+X10[K]; IS2=Y2[K]+Y10[K];
876 RU2=X2[K]-X10[K]; IU2=Y2[K]-Y10[K];
877 RS3=X3[K]+X11[K]; IS3=Y3[K]+Y11[K];
878 RU3=X3[K]-X11[K]; IU3=Y3[K]-Y11[K];
879 RS4=X4[K]+X12[K]; IS4=Y4[K]+Y12[K];
880 RU4=X4[K]-X12[K]; IU4=Y4[K]-Y12[K];
881 RS5=X5[K]+X13[K]; IS5=Y5[K]+Y13[K];
882 RU5=X5[K]-X13[K]; IU5=Y5[K]-Y13[K];
883 RS6=X6[K]+X14[K]; IS6=Y6[K]+Y14[K];
884 RU6=X6[K]-X14[K]; IU6=Y6[K]-Y14[K];
885 RS7=X7[K]+X15[K]; IS7=Y7[K]+Y15[K];
886 RU7=X7[K]-X15[K]; IU7=Y7[K]-Y15[K];
887 RSS0=RS0+RS4; ISS0=IS0+IS4;
888 RSS1=RS1+RS5; ISS1=IS1+IS5;
889 RSS2=RS2+RS6; ISS2=IS2+IS6;
890 RSS3=RS3+RS7; ISS3=IS3+IS7;
891 RSU0=RS0-RS4; ISU0=IS0-IS4;
892 RSU1=RS1-RS5; ISU1=IS1-IS5;
893 RSU2=RS2-RS6; ISU2=IS2-IS6;
894 RSU3=RS3-RS7; ISU3=IS3-IS7;
895 RUS0=RU0-IU4; IUS0=IU0+RU4;
896 RUS1=RU1-IU5; IUS1=IU1+RU5;
897 RUS2=RU2-IU6; IUS2=IU2+RU6;
898 RUS3=RU3-IU7; IUS3=IU3+RU7;
899 RUU0=RU0+IU4; IUU0=IU0-RU4;
900 RUU1=RU1+IU5; IUU1=IU1-RU5;
901 RUU2=RU2+IU6; IUU2=IU2-RU6;
902 RUU3=RU3+IU7; IUU3=IU3-RU7;
903 T=(RSU1+ISU1)*E2; ISU1=(ISU1-RSU1)*E2; RSU1=T;
904 T=(RSU3+ISU3)*E2; ISU3=(ISU3-RSU3)*E2; RSU3=T;
905 T=RUS1*ER3+IUS1*EI3; IUS1=IUS1*ER3-RUS1*EI3; RUS1=T;
906 T=(RUS2+IUS2)*E2; IUS2=(IUS2-RUS2)*E2; RUS2=T;
907 T=RUS3*ER5+IUS3*EI5; IUS3=IUS3*ER5-RUS3*EI5; RUS3=T;
908 T=RUU1*ER1+IUU1*EI1; IUU1=IUU1*ER1-RUU1*EI1; RUU1=T;
909 T=(RUU2+IUU2)*E2; IUU2=(IUU2-RUU2)*E2; RUU2=T;
910 T=RUU3*ER3+IUU3*EI3; IUU3=IUU3*ER3-RUU3*EI3; RUU3=T;
911 RSSS0=RSS0+RSS2; ISSS0=ISS0+ISS2;
912 RSSS1=RSS1+RSS3; ISSS1=ISS1+ISS3;
913 RSSU0=RSS0-RSS2; ISSU0=ISS0-ISS2;
914 RSSU1=RSS1-RSS3; ISSU1=ISS1-ISS3;
915 RSUS0=RSU0-ISU2; ISUS0=ISU0+RSU2;
916 RSUS1=RSU1-ISU3; ISUS1=ISU1+RSU3;
917 RSUU0=RSU0+ISU2; ISUU0=ISU0-RSU2;
918 RSUU1=RSU1+ISU3; ISUU1=ISU1-RSU3;
919 RUSS0=RUS0-IUS2; IUSS0=IUS0+RUS2;
920 RUSS1=RUS1-IUS3; IUSS1=IUS1+RUS3;
921 RUSU0=RUS0+IUS2; IUSU0=IUS0-RUS2;
922 RUSU1=RUS1+IUS3; IUSU1=IUS1-RUS3;
923 RUUS0=RUU0+RUU2; IUUS0=IUU0+IUU2;
924 RUUS1=RUU1+RUU3; IUUS1=IUU1+IUU3;
925 RUUU0=RUU0-RUU2; IUUU0=IUU0-IUU2;
926 RUUU1=RUU1-RUU3; IUUU1=IUU1-IUU3;
927 X0[K]=RSSS0+RSSS1; Y0[K]=ISSS0+ISSS1;
928 if (!ZERO)
929 {
930 REPORT
931 R1=RUUS0+RUUS1; I1=IUUS0+IUUS1;
932 R2=RSUU0+RSUU1; I2=ISUU0+ISUU1;
933 R3=RUSU0+RUSU1; I3=IUSU0+IUSU1;
934 R4=RSSU0+ISSU1; I4=ISSU0-RSSU1;
935 R5=RUUU0+IUUU1; I5=IUUU0-RUUU1;
936 R6=RSUS0+ISUS1; I6=ISUS0-RSUS1;
937 R7=RUSS0+IUSS1; I7=IUSS0-RUSS1;
938 R8=RSSS0-RSSS1; I8=ISSS0-ISSS1;
939 R9=RUUS0-RUUS1; I9=IUUS0-IUUS1;
940 R10=RSUU0-RSUU1; I10=ISUU0-ISUU1;
941 R11=RUSU0-RUSU1; I11=IUSU0-IUSU1;
942 R12=RSSU0-ISSU1; I12=ISSU0+RSSU1;
943 R13=RUUU0-IUUU1; I13=IUUU0+RUUU1;
944 R14=RSUS0-ISUS1; I14=ISUS0+RSUS1;
945 R15=RUSS0-IUSS1; I15=IUSS0+RUSS1;
946 X8[K]=R1*C1+I1*S1; Y8[K]=I1*C1-R1*S1;
947 X4[K]=R2*C2+I2*S2; Y4[K]=I2*C2-R2*S2;
948 X12[K]=R3*C3+I3*S3; Y12[K]=I3*C3-R3*S3;
949 X2[K]=R4*C4+I4*S4; Y2[K]=I4*C4-R4*S4;
950 X10[K]=R5*C5+I5*S5; Y10[K]=I5*C5-R5*S5;
951 X6[K]=R6*C6+I6*S6; Y6[K]=I6*C6-R6*S6;
952 X14[K]=R7*C7+I7*S7; Y14[K]=I7*C7-R7*S7;
953 X1[K]=R8*C8+I8*S8; Y1[K]=I8*C8-R8*S8;
954 X9[K]=R9*C9+I9*S9; Y9[K]=I9*C9-R9*S9;
955 X5[K]=R10*C10+I10*S10; Y5[K]=I10*C10-R10*S10;
956 X13[K]=R11*C11+I11*S11; Y13[K]=I11*C11-R11*S11;
957 X3[K]=R12*C12+I12*S12; Y3[K]=I12*C12-R12*S12;
958 X11[K]=R13*C13+I13*S13; Y11[K]=I13*C13-R13*S13;
959 X7[K]=R14*C14+I14*S14; Y7[K]=I14*C14-R14*S14;
960 X15[K]=R15*C15+I15*S15; Y15[K]=I15*C15-R15*S15;
961 }
962 else
963 {
964 REPORT
965 X8[K]=RUUS0+RUUS1; Y8[K]=IUUS0+IUUS1;
966 X4[K]=RSUU0+RSUU1; Y4[K]=ISUU0+ISUU1;
967 X12[K]=RUSU0+RUSU1; Y12[K]=IUSU0+IUSU1;
968 X2[K]=RSSU0+ISSU1; Y2[K]=ISSU0-RSSU1;
969 X10[K]=RUUU0+IUUU1; Y10[K]=IUUU0-RUUU1;
970 X6[K]=RSUS0+ISUS1; Y6[K]=ISUS0-RSUS1;
971 X14[K]=RUSS0+IUSS1; Y14[K]=IUSS0-RUSS1;
972 X1[K]=RSSS0-RSSS1; Y1[K]=ISSS0-ISSS1;
973 X9[K]=RUUS0-RUUS1; Y9[K]=IUUS0-IUUS1;
974 X5[K]=RSUU0-RSUU1; Y5[K]=ISUU0-ISUU1;
975 X13[K]=RUSU0-RUSU1; Y13[K]=IUSU0-IUSU1;
976 X3[K]=RSSU0-ISSU1; Y3[K]=ISSU0+RSSU1;
977 X11[K]=RUUU0-IUUU1; Y11[K]=IUUU0+RUUU1;
978 X7[K]=RSUS0-ISUS1; Y7[K]=ISUS0+RSUS1;
979 X15[K]=RUSS0-IUSS1; Y15[K]=IUSS0+RUSS1;
980 }
981 }
982 goto L100;
983 L600: ;
984 }
985
986 return;
987}
988
989// can the number of points be factorised sufficiently
990// for the fft to run
991
992bool FFT_Controller::CanFactor(int PTS)
993{
994 REPORT
995 const int NP = 16, NQ = 10, PMAX=19;
996
997 if (PTS<=1) { REPORT return true; }
998
999 int N = PTS, F = 2, P = 0, Q = 0;
1000
1001 while (N > 1)
1002 {
1003 bool fail = true;
1004 for (int J = F; J <= PMAX; J++)
1005 if (N % J == 0) { fail = false; F=J; break; }
1006 if (fail || P >= NP || Q >= NQ) { REPORT return false; }
1007 N /= F;
1008 if (N % F != 0) Q++; else { N /= F; P++; }
1009 }
1010
1011 return true; // can factorise
1012
1013}
1014
1015bool FFT_Controller::OnlyOldFFT; // static variable
1016
1017// **************************** multi radix counter **********************
1018
1019MultiRadixCounter::MultiRadixCounter(int nx, const SimpleIntArray& rx,
1020 SimpleIntArray& vx)
1021 : Radix(rx), Value(vx), n(nx), reverse(0),
1022 product(1), counter(0), finish(false)
1023{
1024 REPORT for (int k = 0; k < n; k++) { Value[k] = 0; product *= Radix[k]; }
1025}
1026
1027void MultiRadixCounter::operator++()
1028{
1029 REPORT
1030 counter++; int p = product;
1031 for (int k = 0; k < n; k++)
1032 {
1033 Value[k]++; int p1 = p / Radix[k]; reverse += p1;
1034 if (Value[k] == Radix[k]) { REPORT Value[k] = 0; reverse -= p; p = p1; }
1035 else { REPORT return; }
1036 }
1037 finish = true;
1038}
1039
1040
1041static int BitReverse(int x, int prod, int n, const SimpleIntArray& f)
1042{
1043 // x = c[0]+f[0]*(c[1]+f[1]*(c[2]+...
1044 // return c[n-1]+f[n-1]*(c[n-2]+f[n-2]*(c[n-3]+...
1045 // prod is the product of the f[i]
1046 // n is the number of f[i] (don't assume f has the correct length)
1047
1048 REPORT
1049 const int* d = f.Data() + n; int sum = 0; int q = 1;
1050 while (n--)
1051 {
1052 prod /= *(--d);
1053 int c = x / prod; x-= c * prod;
1054 sum += q * c; q *= *d;
1055 }
1056 return sum;
1057}
1058
1059
1060#ifdef use_namespace
1061}
1062#endif
1063
1064///@}
1065
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