1 //$ newfft.cpp
2
3 // This is originally by Sande and Gentleman in 1967! I have translated from
4 // Fortran into C and a little bit of C++.
5
6 // It takes about twice as long as fftw
7 // (http://theory.lcs.mit.edu/~fftw/homepage.html)
8 // but is much shorter than fftw and so despite its age
9 // might represent a reasonable
10 // compromise between speed and complexity.
11 // If you really need the speed get fftw.
12
13
14 // THIS SUBROUTINE WAS WRITTEN BY G.SANDE OF PRINCETON UNIVERSITY AND
15 // W.M.GENTLMAN OF THE BELL TELEPHONE LAB. IT WAS BROUGHT TO LONDON
16 // BY DR. M.D. GODFREY AT THE IMPERIAL COLLEGE AND WAS ADAPTED FOR
17 // BURROUGHS 6700 BY D. R. BRILLINGER AND J. PEMBERTON
18 // IT REPRESENTS THE STATE OF THE ART OF COMPUTING COMPLETE FINITE
19 // DISCRETE FOURIER TRANSFORMS AS OF NOV.1967.
20 // OTHER PROGRAMS REQUIRED.
21 // ONLY THOSE SUBROUTINES INCLUDED HERE.
22 // USAGE.
23 // CALL AR1DFT(N,X,Y)
24 // WHERE N IS THE NUMBER OF POINTS IN THE SEQUENCE .
25 // X - IS A ONE-DIMENSIONAL ARRAY CONTAINING THE REAL
26 // PART OF THE SEQUENCE.
27 // Y - IS A ONE-DIMENSIONAL ARRAY CONTAINING THE
28 // IMAGINARY PART OF THE SEQUENCE.
29 // THE TRANSFORM IS RETURNED IN X AND Y.
30 // METHOD
31 // FOR A GENERAL DISCUSSION OF THESE TRANSFORMS AND OF
32 // THE FAST METHOD FOR COMPUTING THEM, SEE GENTLEMAN AND SANDE,
33 // @FAST FOURIER TRANSFORMS - FOR FUN AND PROFIT,@ 1966 FALL JOINT
34 // COMPUTER CONFERENCE.
35 // THIS PROGRAM COMPUTES THIS FOR A COMPLEX SEQUENCE Z(T) OF LENGTH
36 // N WHOSE ELEMENTS ARE STORED AT(X(I) , Y(I)) AND RETURNS THE
37 // TRANSFORM COEFFICIENTS AT (X(I), Y(I)).
38 // DESCRIPTION
39 // AR1DFT IS A HIGHLY MODULAR ROUTINE CAPABLE OF COMPUTING IN PLACE
40 // THE COMPLETE FINITE DISCRETE FOURIER TRANSFORM OF A ONE-
41 // DIMENSIONAL SEQUENCE OF RATHER GENERAL LENGTH N.
42 // THE MAIN ROUTINE , AR1DFT ITSELF, FACTORS N. IT THEN CALLS ON
43 // ON GR 1D FT TO COMPUTE THE ACTUAL TRANSFORMS, USING THESE FACTORS.
44 // THIS GR 1D FT DOES, CALLING AT EACH STAGE ON THE APPROPRIATE KERN
45 // EL R2FTK, R4FTK, R8FTK, R16FTK, R3FTK, R5FTK, OR RPFTK TO PERFORM
46 // THE COMPUTATIONS FOR THIS PASS OVER THE SEQUENCE, DEPENDING ON
47 // WHETHER THE CORRESPONDING FACTOR IS 2, 4, 8, 16, 3, 5, OR SOME
48 // MORE GENERAL PRIME P. WHEN GR1DFT IS FINISHED THE TRANSFORM IS
49 // COMPUTED, HOWEVER, THE RESULTS ARE STORED IN "DIGITS REVERSED"
50 // ORDER. AR1DFT THEREFORE, CALLS UPON GR 1S FS TO SORT THEM OUT.
51 // TO RETURN TO THE FACTORIZATION, SINGLETON HAS POINTED OUT THAT
52 // THE TRANSFORMS ARE MORE EFFICIENT IF THE SAMPLE SIZE N, IS OF THE
53 // FORM B*A**2 AND B CONSISTS OF A SINGLE FACTOR. IN SUCH A CASE
54 // IF WE PROCESS THE FACTORS IN THE ORDER ABA THEN
55 // THE REORDERING CAN BE DONE AS FAST IN PLACE, AS WITH SCRATCH
56 // STORAGE. BUT AS B BECOMES MORE COMPLICATED, THE COST OF THE DIGIT
57 // REVERSING DUE TO B PART BECOMES VERY EXPENSIVE IF WE TRY TO DO IT
58 // IN PLACE. IN SUCH A CASE IT MIGHT BE BETTER TO USE EXTRA STORAGE
59 // A ROUTINE TO DO THIS IS, HOWEVER, NOT INCLUDED HERE.
60 // ANOTHER FEATURE INFLUENCING THE FACTORIZATION IS THAT FOR ANY FIXED
61 // FACTOR N WE CAN PREPARE A SPECIAL KERNEL WHICH WILL COMPUTE
62 // THAT STAGE OF THE TRANSFORM MORE EFFICIENTLY THAN WOULD A KERNEL
63 // FOR GENERAL FACTORS, ESPECIALLY IF THE GENERAL KERNEL HAD TO BE
64 // APPLIED SEVERAL TIMES. FOR EXAMPLE, FACTORS OF 4 ARE MORE
65 // EFFICIENT THAN FACTORS OF 2, FACTORS OF 8 MORE EFFICIENT THAN 4,ETC
66 // ON THE OTHER HAND DIMINISHING RETURNS RAPIDLY SET IN, ESPECIALLY
67 // SINCE THE LENGTH OF THE KERNEL FOR A SPECIAL CASE IS ROUGHLY
68 // PROPORTIONAL TO THE FACTOR IT DEALS WITH. HENCE THESE PROBABLY ARE
69 // ALL THE KERNELS WE WISH TO HAVE.
70 // RESTRICTIONS.
71 // AN UNFORTUNATE FEATURE OF THE SORTING PROBLEM IS THAT THE MOST
72 // EFFICIENT WAY TO DO IT IS WITH NESTED DO LOOPS, ONE FOR EACH
73 // FACTOR. THIS PUTS A RESTRICTION ON N AS TO HOW MANY FACTORS IT
74 // CAN HAVE. CURRENTLY THE LIMIT IS 16, BUT THE LIMIT CAN BE READILY
75 // RAISED IF NECESSARY.
76 // A SECOND RESTRICTION OF THE PROGRAM IS THAT LOCAL STORAGE OF THE
77 // THE ORDER P**2 IS REQUIRED BY THE GENERAL KERNEL RPFTK, SO SOME
78 // LIMIT MUST BE SET ON P. CURRENTLY THIS IS 19, BUT IT CAN BE INCRE
79 // INCREASED BY TRIVIAL CHANGES.
80 // OTHER COMMENTS.
81 //(1) THE ROUTINE IS ADAPTED TO CHECK WHETHER A GIVEN N WILL MEET THE
82 // ABOVE FACTORING REQUIREMENTS AN, IF NOT, TO RETURN THE NEXT HIGHER
83 // NUMBER, NX, SAY, WHICH WILL MEET THESE REQUIREMENTS.
84 // THIS CAN BE ACCHIEVED BY A STATEMENT OF THE FORM
85 // CALL FACTR(N,X,Y).
86 // IF A DIFFERENT N, SAY NX, IS RETURNED THEN THE TRANSFORMS COULD BE
87 // OBTAINED BY EXTENDING THE SIZE OF THE X-ARRAY AND Y-ARRAY TO NX,
88 // AND SETTING X(I) = Y(I) = 0., FOR I = N+1, NX.
89 //(2) IF THE SEQUENCE Z IS ONLY A REAL SEQUENCE, THEN THE IMAGINARY PART
90 // Y(I)=0., THIS WILL RETURN THE COSINE TRANSFORM OF THE REAL SEQUENCE
91 // IN X, AND THE SINE TRANSFORM IN Y.
92
93
94 #define WANT_STREAM
95
96 #define WANT_MATH
97
98 #include "newmatap.h"
99
100 #ifdef use_namespace
101 namespace NEWMAT {
102 #endif
103
104 #ifdef DO_REPORT
105 #define REPORT { static ExeCounter ExeCount(__LINE__,20); ++ExeCount; }
106 #else
107 #define REPORT {}
108 #endif
109
square(Real x)110 inline Real square(Real x) { return x*x; }
square(int x)111 inline int square(int x) { return x*x; }
112
113 static void GR_1D_FS (int PTS, int N_SYM, int N_UN_SYM,
114 const SimpleIntArray& SYM, int P_SYM, const SimpleIntArray& UN_SYM,
115 Real* X, Real* Y);
116 static void GR_1D_FT (int N, int N_FACTOR, const SimpleIntArray& FACTOR,
117 Real* X, Real* Y);
118 static void R_P_FTK (int N, int M, int P, Real* X, Real* Y);
119 static void R_2_FTK (int N, int M, Real* X0, Real* Y0, Real* X1, Real* Y1);
120 static void R_3_FTK (int N, int M, Real* X0, Real* Y0, Real* X1, Real* Y1,
121 Real* X2, Real* Y2);
122 static void R_4_FTK (int N, int M,
123 Real* X0, Real* Y0, Real* X1, Real* Y1,
124 Real* X2, Real* Y2, Real* X3, Real* Y3);
125 static void R_5_FTK (int N, int M,
126 Real* X0, Real* Y0, Real* X1, Real* Y1, Real* X2, Real* Y2,
127 Real* X3, Real* Y3, Real* X4, Real* Y4);
128 static void R_8_FTK (int N, int M,
129 Real* X0, Real* Y0, Real* X1, Real* Y1,
130 Real* X2, Real* Y2, Real* X3, Real* Y3,
131 Real* X4, Real* Y4, Real* X5, Real* Y5,
132 Real* X6, Real* Y6, Real* X7, Real* Y7);
133 static void R_16_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,
138 Real* X8, Real* Y8, Real* X9, Real* Y9,
139 Real* X10, Real* Y10, Real* X11, Real* Y11,
140 Real* X12, Real* Y12, Real* X13, Real* Y13,
141 Real* X14, Real* Y14, Real* X15, Real* Y15);
142 static int BitReverse(int x, int prod, int n, const SimpleIntArray& f);
143
144
ar_1d_ft(int PTS,Real * X,Real * Y)145 bool FFT_Controller::ar_1d_ft (int PTS, Real* X, Real *Y)
146 {
147 // ARBITRARY RADIX ONE DIMENSIONAL FOURIER TRANSFORM
148
149 REPORT
150
151 int F,J,N,NF,P,PMAX,P_SYM,P_TWO,Q,R,TWO_GRP;
152
153 // NP is maximum number of squared factors allows PTS up to 2**32 at least
154 // NQ is number of not-squared factors - increase if we increase PMAX
155 const int NP = 16, NQ = 10;
156 SimpleIntArray PP(NP), QQ(NQ);
157
158 TWO_GRP=16; PMAX=19;
159
160 // PMAX is the maximum factor size
161 // TWO_GRP is the maximum power of 2 handled as a single factor
162 // Doesn't take advantage of combining powers of 2 when calculating
163 // number of factors
164
165 if (PTS<=1) return true;
166 N=PTS; P_SYM=1; F=2; P=0; Q=0;
167
168 // P counts the number of squared factors
169 // Q counts the number of the rest
170 // R = 0 for no non-squared factors; 1 otherwise
171
172 // FACTOR holds all the factors - non-squared ones in the middle
173 // - length is 2*P+Q
174 // SYM also holds all the factors but with the non-squared ones
175 // multiplied together - length is 2*P+R
176 // PP holds the values of the squared factors - length is P
177 // QQ holds the values of the rest - length is Q
178
179 // P_SYM holds the product of the squared factors
180
181 // find the factors - load into PP and QQ
182 while (N > 1)
183 {
184 bool fail = true;
185 for (J=F; J<=PMAX; J++)
186 if (N % J == 0) { fail = false; F=J; break; }
187 if (fail || P >= NP || Q >= NQ) return false; // can't factor
188 N /= F;
189 if (N % F != 0) QQ[Q++] = F;
190 else { N /= F; PP[P++] = F; P_SYM *= F; }
191 }
192
193 R = (Q == 0) ? 0 : 1; // R = 0 if no not-squared factors, 1 otherwise
194
195 NF = 2*P + Q;
196 SimpleIntArray FACTOR(NF + 1), SYM(2*P + R);
197 FACTOR[NF] = 0; // we need this in the "combine powers of 2"
198
199 // load into SYM and FACTOR
200 for (J=0; J<P; J++)
201 { SYM[J]=FACTOR[J]=PP[P-1-J]; FACTOR[P+Q+J]=SYM[P+R+J]=PP[J]; }
202
203 if (Q>0)
204 {
205 REPORT
206 for (J=0; J<Q; J++) FACTOR[P+J]=QQ[J];
207 SYM[P]=PTS/square(P_SYM);
208 }
209
210 // combine powers of 2
211 P_TWO = 1;
212 for (J=0; J < NF; J++)
213 {
214 if (FACTOR[J]!=2) continue;
215 P_TWO=P_TWO*2; FACTOR[J]=1;
216 if (P_TWO<TWO_GRP && FACTOR[J+1]==2) continue;
217 FACTOR[J]=P_TWO; P_TWO=1;
218 }
219
220 if (P==0) R=0;
221 if (Q<=1) Q=0;
222
223 // do the analysis
224 GR_1D_FT(PTS,NF,FACTOR,X,Y); // the transform
225 GR_1D_FS(PTS,2*P+R,Q,SYM,P_SYM,QQ,X,Y); // the reshuffling
226
227 return true;
228
229 }
230
GR_1D_FS(int PTS,int N_SYM,int N_UN_SYM,const SimpleIntArray & SYM,int P_SYM,const SimpleIntArray & UN_SYM,Real * X,Real * Y)231 static void GR_1D_FS (int PTS, int N_SYM, int N_UN_SYM,
232 const SimpleIntArray& SYM, int P_SYM, const SimpleIntArray& UN_SYM,
233 Real* X, Real* Y)
234 {
235 // GENERAL RADIX ONE DIMENSIONAL FOURIER SORT
236
237 // PTS = number of points
238 // N_SYM = length of SYM
239 // N_UN_SYM = length of UN_SYM
240 // SYM: squared factors + product of non-squared factors + squared factors
241 // P_SYM = product of squared factors (each included only once)
242 // UN_SYM: not-squared factors
243
244 REPORT
245
246 Real T;
247 int JJ,KK,P_UN_SYM;
248
249 // I have replaced the multiple for-loop used by Sande-Gentleman code
250 // by the following code which does not limit the number of factors
251
252 if (N_SYM > 0)
253 {
254 REPORT
255 SimpleIntArray U(N_SYM);
256 for(MultiRadixCounter MRC(N_SYM, SYM, U); !MRC.Finish(); ++MRC)
257 {
258 if (MRC.Swap())
259 {
260 int P = MRC.Reverse(); int JJ = MRC.Counter(); Real T;
261 T=X[JJ]; X[JJ]=X[P]; X[P]=T; T=Y[JJ]; Y[JJ]=Y[P]; Y[P]=T;
262 }
263 }
264 }
265
266 int J,JL,K,L,M,MS;
267
268 // UN_SYM contains the non-squared factors
269 // I have replaced the Sande-Gentleman code as it runs into
270 // integer overflow problems
271 // My code (and theirs) would be improved by using a bit array
272 // as suggested by Van Loan
273
274 if (N_UN_SYM==0) { REPORT return; }
275 P_UN_SYM=PTS/square(P_SYM); JL=(P_UN_SYM-3)*P_SYM; MS=P_UN_SYM*P_SYM;
276
277 for (J = P_SYM; J<=JL; J+=P_SYM)
278 {
279 K=J;
280 do K = P_SYM * BitReverse(K / P_SYM, P_UN_SYM, N_UN_SYM, UN_SYM);
281 while (K<J);
282
283 if (K!=J)
284 {
285 REPORT
286 for (L=0; L<P_SYM; L++) for (M=L; M<PTS; M+=MS)
287 {
288 JJ=M+J; KK=M+K;
289 T=X[JJ]; X[JJ]=X[KK]; X[KK]=T; T=Y[JJ]; Y[JJ]=Y[KK]; Y[KK]=T;
290 }
291 }
292 }
293
294 return;
295 }
296
GR_1D_FT(int N,int N_FACTOR,const SimpleIntArray & FACTOR,Real * X,Real * Y)297 static void GR_1D_FT (int N, int N_FACTOR, const SimpleIntArray& FACTOR,
298 Real* X, Real* Y)
299 {
300 // GENERAL RADIX ONE DIMENSIONAL FOURIER TRANSFORM;
301
302 REPORT
303
304 int M = N;
305
306 for (int i = 0; i < N_FACTOR; i++)
307 {
308 int P = FACTOR[i]; M /= P;
309
310 switch(P)
311 {
312 case 1: REPORT break;
313 case 2: REPORT R_2_FTK (N,M,X,Y,X+M,Y+M); break;
314 case 3: REPORT R_3_FTK (N,M,X,Y,X+M,Y+M,X+2*M,Y+2*M); break;
315 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;
316 case 5:
317 REPORT
318 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);
319 break;
320 case 8:
321 REPORT
322 R_8_FTK (N,M,X,Y,X+M,Y+M,X+2*M,Y+2*M,
323 X+3*M,Y+3*M,X+4*M,Y+4*M,X+5*M,Y+5*M,
324 X+6*M,Y+6*M,X+7*M,Y+7*M);
325 break;
326 case 16:
327 REPORT
328 R_16_FTK (N,M,X,Y,X+M,Y+M,X+2*M,Y+2*M,
329 X+3*M,Y+3*M,X+4*M,Y+4*M,X+5*M,Y+5*M,
330 X+6*M,Y+6*M,X+7*M,Y+7*M,X+8*M,Y+8*M,
331 X+9*M,Y+9*M,X+10*M,Y+10*M,X+11*M,Y+11*M,
332 X+12*M,Y+12*M,X+13*M,Y+13*M,X+14*M,Y+14*M,
333 X+15*M,Y+15*M);
334 break;
335 default: REPORT R_P_FTK (N,M,P,X,Y); break;
336 }
337 }
338
339 }
340
R_P_FTK(int N,int M,int P,Real * X,Real * Y)341 static void R_P_FTK (int N, int M, int P, Real* X, Real* Y)
342 // RADIX PRIME FOURIER TRANSFORM KERNEL;
343 // X and Y are treated as M * P matrices with Fortran storage
344 {
345 REPORT
346 bool NO_FOLD,ZERO;
347 Real ANGLE,IS,IU,RS,RU,T,TWOPI,XT,YT;
348 int J,JJ,K0,K,M_OVER_2,MP,PM,PP,U,V;
349
350 Real AA [9][9], BB [9][9];
351 Real A [18], B [18], C [18], S [18];
352 Real IA [9], IB [9], RA [9], RB [9];
353
354 TWOPI=8.0*atan(1.0);
355 M_OVER_2=M/2+1; MP=M*P; PP=P/2; PM=P-1;
356
357 for (U=0; U<PP; U++)
358 {
359 ANGLE=TWOPI*Real(U+1)/Real(P);
360 JJ=P-U-2;
361 A[U]=cos(ANGLE); B[U]=sin(ANGLE);
362 A[JJ]=A[U]; B[JJ]= -B[U];
363 }
364
365 for (U=1; U<=PP; U++)
366 {
367 for (V=1; V<=PP; V++)
368 { JJ=U*V-U*V/P*P; AA[V-1][U-1]=A[JJ-1]; BB[V-1][U-1]=B[JJ-1]; }
369 }
370
371 for (J=0; J<M_OVER_2; J++)
372 {
373 NO_FOLD = (J==0 || 2*J==M);
374 K0=J;
375 ANGLE=TWOPI*Real(J)/Real(MP); ZERO=ANGLE==0.0;
376 C[0]=cos(ANGLE); S[0]=sin(ANGLE);
377 for (U=1; U<PM; U++)
378 {
379 C[U]=C[U-1]*C[0]-S[U-1]*S[0];
380 S[U]=S[U-1]*C[0]+C[U-1]*S[0];
381 }
382 goto L700;
383 L500:
384 REPORT
385 if (NO_FOLD) { REPORT goto L1500; }
386 REPORT
387 NO_FOLD=true; K0=M-J;
388 for (U=0; U<PM; U++)
389 { T=C[U]*A[U]+S[U]*B[U]; S[U]= -S[U]*A[U]+C[U]*B[U]; C[U]=T; }
390 L700:
391 REPORT
392 for (K=K0; K<N; K+=MP)
393 {
394 XT=X[K]; YT=Y[K];
395 for (U=1; U<=PP; U++)
396 {
397 RA[U-1]=XT; IA[U-1]=YT;
398 RB[U-1]=0.0; IB[U-1]=0.0;
399 }
400 for (U=1; U<=PP; U++)
401 {
402 JJ=P-U;
403 RS=X[K+M*U]+X[K+M*JJ]; IS=Y[K+M*U]+Y[K+M*JJ];
404 RU=X[K+M*U]-X[K+M*JJ]; IU=Y[K+M*U]-Y[K+M*JJ];
405 XT=XT+RS; YT=YT+IS;
406 for (V=0; V<PP; V++)
407 {
408 RA[V]=RA[V]+RS*AA[V][U-1]; IA[V]=IA[V]+IS*AA[V][U-1];
409 RB[V]=RB[V]+RU*BB[V][U-1]; IB[V]=IB[V]+IU*BB[V][U-1];
410 }
411 }
412 X[K]=XT; Y[K]=YT;
413 for (U=1; U<=PP; U++)
414 {
415 if (!ZERO)
416 {
417 REPORT
418 XT=RA[U-1]+IB[U-1]; YT=IA[U-1]-RB[U-1];
419 X[K+M*U]=XT*C[U-1]+YT*S[U-1]; Y[K+M*U]=YT*C[U-1]-XT*S[U-1];
420 JJ=P-U;
421 XT=RA[U-1]-IB[U-1]; YT=IA[U-1]+RB[U-1];
422 X[K+M*JJ]=XT*C[JJ-1]+YT*S[JJ-1];
423 Y[K+M*JJ]=YT*C[JJ-1]-XT*S[JJ-1];
424 }
425 else
426 {
427 REPORT
428 X[K+M*U]=RA[U-1]+IB[U-1]; Y[K+M*U]=IA[U-1]-RB[U-1];
429 JJ=P-U;
430 X[K+M*JJ]=RA[U-1]-IB[U-1]; Y[K+M*JJ]=IA[U-1]+RB[U-1];
431 }
432 }
433 }
434 goto L500;
435 L1500: ;
436 }
437 return;
438 }
439
R_2_FTK(int N,int M,Real * X0,Real * Y0,Real * X1,Real * Y1)440 static void R_2_FTK (int N, int M, Real* X0, Real* Y0, Real* X1, Real* Y1)
441 // RADIX TWO FOURIER TRANSFORM KERNEL;
442 {
443 REPORT
444 bool NO_FOLD,ZERO;
445 int J,K,K0,M2,M_OVER_2;
446 Real ANGLE,C,IS,IU,RS,RU,S,TWOPI;
447
448 M2=M*2; M_OVER_2=M/2+1;
449 TWOPI=8.0*atan(1.0);
450
451 for (J=0; J<M_OVER_2; J++)
452 {
453 NO_FOLD = (J==0 || 2*J==M);
454 K0=J;
455 ANGLE=TWOPI*Real(J)/Real(M2); ZERO=ANGLE==0.0;
456 C=cos(ANGLE); S=sin(ANGLE);
457 goto L200;
458 L100:
459 REPORT
460 if (NO_FOLD) { REPORT goto L600; }
461 REPORT
462 NO_FOLD=true; K0=M-J; C= -C;
463 L200:
464 REPORT
465 for (K=K0; K<N; K+=M2)
466 {
467 RS=X0[K]+X1[K]; IS=Y0[K]+Y1[K];
468 RU=X0[K]-X1[K]; IU=Y0[K]-Y1[K];
469 X0[K]=RS; Y0[K]=IS;
470 if (!ZERO) { X1[K]=RU*C+IU*S; Y1[K]=IU*C-RU*S; }
471 else { X1[K]=RU; Y1[K]=IU; }
472 }
473 goto L100;
474 L600: ;
475 }
476
477 return;
478 }
479
R_3_FTK(int N,int M,Real * X0,Real * Y0,Real * X1,Real * Y1,Real * X2,Real * Y2)480 static void R_3_FTK (int N, int M, Real* X0, Real* Y0, Real* X1, Real* Y1,
481 Real* X2, Real* Y2)
482 // RADIX THREE FOURIER TRANSFORM KERNEL
483 {
484 REPORT
485 bool NO_FOLD,ZERO;
486 int J,K,K0,M3,M_OVER_2;
487 Real ANGLE,A,B,C1,C2,S1,S2,T,TWOPI;
488 Real I0,I1,I2,IA,IB,IS,R0,R1,R2,RA,RB,RS;
489
490 M3=M*3; M_OVER_2=M/2+1; TWOPI=8.0*atan(1.0);
491 A=cos(TWOPI/3.0); B=sin(TWOPI/3.0);
492
493 for (J=0; J<M_OVER_2; J++)
494 {
495 NO_FOLD = (J==0 || 2*J==M);
496 K0=J;
497 ANGLE=TWOPI*Real(J)/Real(M3); ZERO=ANGLE==0.0;
498 C1=cos(ANGLE); S1=sin(ANGLE);
499 C2=C1*C1-S1*S1; S2=S1*C1+C1*S1;
500 goto L200;
501 L100:
502 REPORT
503 if (NO_FOLD) { REPORT goto L600; }
504 REPORT
505 NO_FOLD=true; K0=M-J;
506 T=C1*A+S1*B; S1=C1*B-S1*A; C1=T;
507 T=C2*A-S2*B; S2= -C2*B-S2*A; C2=T;
508 L200:
509 REPORT
510 for (K=K0; K<N; K+=M3)
511 {
512 R0 = X0[K]; I0 = Y0[K];
513 RS=X1[K]+X2[K]; IS=Y1[K]+Y2[K];
514 X0[K]=R0+RS; Y0[K]=I0+IS;
515 RA=R0+RS*A; IA=I0+IS*A;
516 RB=(X1[K]-X2[K])*B; IB=(Y1[K]-Y2[K])*B;
517 if (!ZERO)
518 {
519 REPORT
520 R1=RA+IB; I1=IA-RB; R2=RA-IB; I2=IA+RB;
521 X1[K]=R1*C1+I1*S1; Y1[K]=I1*C1-R1*S1;
522 X2[K]=R2*C2+I2*S2; Y2[K]=I2*C2-R2*S2;
523 }
524 else { REPORT X1[K]=RA+IB; Y1[K]=IA-RB; X2[K]=RA-IB; Y2[K]=IA+RB; }
525 }
526 goto L100;
527 L600: ;
528 }
529
530 return;
531 }
532
R_4_FTK(int N,int M,Real * X0,Real * Y0,Real * X1,Real * Y1,Real * X2,Real * Y2,Real * X3,Real * Y3)533 static void R_4_FTK (int N, int M,
534 Real* X0, Real* Y0, Real* X1, Real* Y1,
535 Real* X2, Real* Y2, Real* X3, Real* Y3)
536 // RADIX FOUR FOURIER TRANSFORM KERNEL
537 {
538 REPORT
539 bool NO_FOLD,ZERO;
540 int J,K,K0,M4,M_OVER_2;
541 Real ANGLE,C1,C2,C3,S1,S2,S3,T,TWOPI;
542 Real I1,I2,I3,IS0,IS1,IU0,IU1,R1,R2,R3,RS0,RS1,RU0,RU1;
543
544 M4=M*4; M_OVER_2=M/2+1;
545 TWOPI=8.0*atan(1.0);
546
547 for (J=0; J<M_OVER_2; J++)
548 {
549 NO_FOLD = (J==0 || 2*J==M);
550 K0=J;
551 ANGLE=TWOPI*Real(J)/Real(M4); ZERO=ANGLE==0.0;
552 C1=cos(ANGLE); S1=sin(ANGLE);
553 C2=C1*C1-S1*S1; S2=S1*C1+C1*S1;
554 C3=C2*C1-S2*S1; S3=S2*C1+C2*S1;
555 goto L200;
556 L100:
557 REPORT
558 if (NO_FOLD) { REPORT goto L600; }
559 REPORT
560 NO_FOLD=true; K0=M-J;
561 T=C1; C1=S1; S1=T;
562 C2= -C2;
563 T=C3; C3= -S3; S3= -T;
564 L200:
565 REPORT
566 for (K=K0; K<N; K+=M4)
567 {
568 RS0=X0[K]+X2[K]; IS0=Y0[K]+Y2[K];
569 RU0=X0[K]-X2[K]; IU0=Y0[K]-Y2[K];
570 RS1=X1[K]+X3[K]; IS1=Y1[K]+Y3[K];
571 RU1=X1[K]-X3[K]; IU1=Y1[K]-Y3[K];
572 X0[K]=RS0+RS1; Y0[K]=IS0+IS1;
573 if (!ZERO)
574 {
575 REPORT
576 R1=RU0+IU1; I1=IU0-RU1;
577 R2=RS0-RS1; I2=IS0-IS1;
578 R3=RU0-IU1; I3=IU0+RU1;
579 X2[K]=R1*C1+I1*S1; Y2[K]=I1*C1-R1*S1;
580 X1[K]=R2*C2+I2*S2; Y1[K]=I2*C2-R2*S2;
581 X3[K]=R3*C3+I3*S3; Y3[K]=I3*C3-R3*S3;
582 }
583 else
584 {
585 REPORT
586 X2[K]=RU0+IU1; Y2[K]=IU0-RU1;
587 X1[K]=RS0-RS1; Y1[K]=IS0-IS1;
588 X3[K]=RU0-IU1; Y3[K]=IU0+RU1;
589 }
590 }
591 goto L100;
592 L600: ;
593 }
594
595 return;
596 }
597
R_5_FTK(int N,int M,Real * X0,Real * Y0,Real * X1,Real * Y1,Real * X2,Real * Y2,Real * X3,Real * Y3,Real * X4,Real * Y4)598 static void R_5_FTK (int N, int M,
599 Real* X0, Real* Y0, Real* X1, Real* Y1, Real* X2, Real* Y2,
600 Real* X3, Real* Y3, Real* X4, Real* Y4)
601 // RADIX FIVE FOURIER TRANSFORM KERNEL
602
603 {
604 REPORT
605 bool NO_FOLD,ZERO;
606 int J,K,K0,M5,M_OVER_2;
607 Real ANGLE,A1,A2,B1,B2,C1,C2,C3,C4,S1,S2,S3,S4,T,TWOPI;
608 Real R0,R1,R2,R3,R4,RA1,RA2,RB1,RB2,RS1,RS2,RU1,RU2;
609 Real I0,I1,I2,I3,I4,IA1,IA2,IB1,IB2,IS1,IS2,IU1,IU2;
610
611 M5=M*5; M_OVER_2=M/2+1;
612 TWOPI=8.0*atan(1.0);
613 A1=cos(TWOPI/5.0); B1=sin(TWOPI/5.0);
614 A2=cos(2.0*TWOPI/5.0); B2=sin(2.0*TWOPI/5.0);
615
616 for (J=0; J<M_OVER_2; J++)
617 {
618 NO_FOLD = (J==0 || 2*J==M);
619 K0=J;
620 ANGLE=TWOPI*Real(J)/Real(M5); ZERO=ANGLE==0.0;
621 C1=cos(ANGLE); S1=sin(ANGLE);
622 C2=C1*C1-S1*S1; S2=S1*C1+C1*S1;
623 C3=C2*C1-S2*S1; S3=S2*C1+C2*S1;
624 C4=C2*C2-S2*S2; S4=S2*C2+C2*S2;
625 goto L200;
626 L100:
627 REPORT
628 if (NO_FOLD) { REPORT goto L600; }
629 REPORT
630 NO_FOLD=true; K0=M-J;
631 T=C1*A1+S1*B1; S1=C1*B1-S1*A1; C1=T;
632 T=C2*A2+S2*B2; S2=C2*B2-S2*A2; C2=T;
633 T=C3*A2-S3*B2; S3= -C3*B2-S3*A2; C3=T;
634 T=C4*A1-S4*B1; S4= -C4*B1-S4*A1; C4=T;
635 L200:
636 REPORT
637 for (K=K0; K<N; K+=M5)
638 {
639 R0=X0[K]; I0=Y0[K];
640 RS1=X1[K]+X4[K]; IS1=Y1[K]+Y4[K];
641 RU1=X1[K]-X4[K]; IU1=Y1[K]-Y4[K];
642 RS2=X2[K]+X3[K]; IS2=Y2[K]+Y3[K];
643 RU2=X2[K]-X3[K]; IU2=Y2[K]-Y3[K];
644 X0[K]=R0+RS1+RS2; Y0[K]=I0+IS1+IS2;
645 RA1=R0+RS1*A1+RS2*A2; IA1=I0+IS1*A1+IS2*A2;
646 RA2=R0+RS1*A2+RS2*A1; IA2=I0+IS1*A2+IS2*A1;
647 RB1=RU1*B1+RU2*B2; IB1=IU1*B1+IU2*B2;
648 RB2=RU1*B2-RU2*B1; IB2=IU1*B2-IU2*B1;
649 if (!ZERO)
650 {
651 REPORT
652 R1=RA1+IB1; I1=IA1-RB1;
653 R2=RA2+IB2; I2=IA2-RB2;
654 R3=RA2-IB2; I3=IA2+RB2;
655 R4=RA1-IB1; I4=IA1+RB1;
656 X1[K]=R1*C1+I1*S1; Y1[K]=I1*C1-R1*S1;
657 X2[K]=R2*C2+I2*S2; Y2[K]=I2*C2-R2*S2;
658 X3[K]=R3*C3+I3*S3; Y3[K]=I3*C3-R3*S3;
659 X4[K]=R4*C4+I4*S4; Y4[K]=I4*C4-R4*S4;
660 }
661 else
662 {
663 REPORT
664 X1[K]=RA1+IB1; Y1[K]=IA1-RB1;
665 X2[K]=RA2+IB2; Y2[K]=IA2-RB2;
666 X3[K]=RA2-IB2; Y3[K]=IA2+RB2;
667 X4[K]=RA1-IB1; Y4[K]=IA1+RB1;
668 }
669 }
670 goto L100;
671 L600: ;
672 }
673
674 return;
675 }
676
R_8_FTK(int N,int M,Real * X0,Real * Y0,Real * X1,Real * Y1,Real * X2,Real * Y2,Real * X3,Real * Y3,Real * X4,Real * Y4,Real * X5,Real * Y5,Real * X6,Real * Y6,Real * X7,Real * Y7)677 static void R_8_FTK (int N, int M,
678 Real* X0, Real* Y0, Real* X1, Real* Y1,
679 Real* X2, Real* Y2, Real* X3, Real* Y3,
680 Real* X4, Real* Y4, Real* X5, Real* Y5,
681 Real* X6, Real* Y6, Real* X7, Real* Y7)
682 // RADIX EIGHT FOURIER TRANSFORM KERNEL
683 {
684 REPORT
685 bool NO_FOLD,ZERO;
686 int J,K,K0,M8,M_OVER_2;
687 Real ANGLE,C1,C2,C3,C4,C5,C6,C7,E,S1,S2,S3,S4,S5,S6,S7,T,TWOPI;
688 Real R1,R2,R3,R4,R5,R6,R7,RS0,RS1,RS2,RS3,RU0,RU1,RU2,RU3;
689 Real I1,I2,I3,I4,I5,I6,I7,IS0,IS1,IS2,IS3,IU0,IU1,IU2,IU3;
690 Real RSS0,RSS1,RSU0,RSU1,RUS0,RUS1,RUU0,RUU1;
691 Real ISS0,ISS1,ISU0,ISU1,IUS0,IUS1,IUU0,IUU1;
692
693 M8=M*8; M_OVER_2=M/2+1;
694 TWOPI=8.0*atan(1.0); E=cos(TWOPI/8.0);
695
696 for (J=0;J<M_OVER_2;J++)
697 {
698 NO_FOLD= (J==0 || 2*J==M);
699 K0=J;
700 ANGLE=TWOPI*Real(J)/Real(M8); ZERO=ANGLE==0.0;
701 C1=cos(ANGLE); S1=sin(ANGLE);
702 C2=C1*C1-S1*S1; S2=C1*S1+S1*C1;
703 C3=C2*C1-S2*S1; S3=S2*C1+C2*S1;
704 C4=C2*C2-S2*S2; S4=S2*C2+C2*S2;
705 C5=C4*C1-S4*S1; S5=S4*C1+C4*S1;
706 C6=C4*C2-S4*S2; S6=S4*C2+C4*S2;
707 C7=C4*C3-S4*S3; S7=S4*C3+C4*S3;
708 goto L200;
709 L100:
710 REPORT
711 if (NO_FOLD) { REPORT goto L600; }
712 REPORT
713 NO_FOLD=true; K0=M-J;
714 T=(C1+S1)*E; S1=(C1-S1)*E; C1=T;
715 T=S2; S2=C2; C2=T;
716 T=(-C3+S3)*E; S3=(C3+S3)*E; C3=T;
717 C4= -C4;
718 T= -(C5+S5)*E; S5=(-C5+S5)*E; C5=T;
719 T= -S6; S6= -C6; C6=T;
720 T=(C7-S7)*E; S7= -(C7+S7)*E; C7=T;
721 L200:
722 REPORT
723 for (K=K0; K<N; K+=M8)
724 {
725 RS0=X0[K]+X4[K]; IS0=Y0[K]+Y4[K];
726 RU0=X0[K]-X4[K]; IU0=Y0[K]-Y4[K];
727 RS1=X1[K]+X5[K]; IS1=Y1[K]+Y5[K];
728 RU1=X1[K]-X5[K]; IU1=Y1[K]-Y5[K];
729 RS2=X2[K]+X6[K]; IS2=Y2[K]+Y6[K];
730 RU2=X2[K]-X6[K]; IU2=Y2[K]-Y6[K];
731 RS3=X3[K]+X7[K]; IS3=Y3[K]+Y7[K];
732 RU3=X3[K]-X7[K]; IU3=Y3[K]-Y7[K];
733 RSS0=RS0+RS2; ISS0=IS0+IS2;
734 RSU0=RS0-RS2; ISU0=IS0-IS2;
735 RSS1=RS1+RS3; ISS1=IS1+IS3;
736 RSU1=RS1-RS3; ISU1=IS1-IS3;
737 RUS0=RU0-IU2; IUS0=IU0+RU2;
738 RUU0=RU0+IU2; IUU0=IU0-RU2;
739 RUS1=RU1-IU3; IUS1=IU1+RU3;
740 RUU1=RU1+IU3; IUU1=IU1-RU3;
741 T=(RUS1+IUS1)*E; IUS1=(IUS1-RUS1)*E; RUS1=T;
742 T=(RUU1+IUU1)*E; IUU1=(IUU1-RUU1)*E; RUU1=T;
743 X0[K]=RSS0+RSS1; Y0[K]=ISS0+ISS1;
744 if (!ZERO)
745 {
746 REPORT
747 R1=RUU0+RUU1; I1=IUU0+IUU1;
748 R2=RSU0+ISU1; I2=ISU0-RSU1;
749 R3=RUS0+IUS1; I3=IUS0-RUS1;
750 R4=RSS0-RSS1; I4=ISS0-ISS1;
751 R5=RUU0-RUU1; I5=IUU0-IUU1;
752 R6=RSU0-ISU1; I6=ISU0+RSU1;
753 R7=RUS0-IUS1; I7=IUS0+RUS1;
754 X4[K]=R1*C1+I1*S1; Y4[K]=I1*C1-R1*S1;
755 X2[K]=R2*C2+I2*S2; Y2[K]=I2*C2-R2*S2;
756 X6[K]=R3*C3+I3*S3; Y6[K]=I3*C3-R3*S3;
757 X1[K]=R4*C4+I4*S4; Y1[K]=I4*C4-R4*S4;
758 X5[K]=R5*C5+I5*S5; Y5[K]=I5*C5-R5*S5;
759 X3[K]=R6*C6+I6*S6; Y3[K]=I6*C6-R6*S6;
760 X7[K]=R7*C7+I7*S7; Y7[K]=I7*C7-R7*S7;
761 }
762 else
763 {
764 REPORT
765 X4[K]=RUU0+RUU1; Y4[K]=IUU0+IUU1;
766 X2[K]=RSU0+ISU1; Y2[K]=ISU0-RSU1;
767 X6[K]=RUS0+IUS1; Y6[K]=IUS0-RUS1;
768 X1[K]=RSS0-RSS1; Y1[K]=ISS0-ISS1;
769 X5[K]=RUU0-RUU1; Y5[K]=IUU0-IUU1;
770 X3[K]=RSU0-ISU1; Y3[K]=ISU0+RSU1;
771 X7[K]=RUS0-IUS1; Y7[K]=IUS0+RUS1;
772 }
773 }
774 goto L100;
775 L600: ;
776 }
777
778 return;
779 }
780
R_16_FTK(int N,int M,Real * X0,Real * Y0,Real * X1,Real * Y1,Real * X2,Real * Y2,Real * X3,Real * Y3,Real * X4,Real * Y4,Real * X5,Real * Y5,Real * X6,Real * Y6,Real * X7,Real * Y7,Real * X8,Real * Y8,Real * X9,Real * Y9,Real * X10,Real * Y10,Real * X11,Real * Y11,Real * X12,Real * Y12,Real * X13,Real * Y13,Real * X14,Real * Y14,Real * X15,Real * Y15)781 static void R_16_FTK (int N, int M,
782 Real* X0, Real* Y0, Real* X1, Real* Y1,
783 Real* X2, Real* Y2, Real* X3, Real* Y3,
784 Real* X4, Real* Y4, Real* X5, Real* Y5,
785 Real* X6, Real* Y6, Real* X7, Real* Y7,
786 Real* X8, Real* Y8, Real* X9, Real* Y9,
787 Real* X10, Real* Y10, Real* X11, Real* Y11,
788 Real* X12, Real* Y12, Real* X13, Real* Y13,
789 Real* X14, Real* Y14, Real* X15, Real* Y15)
790 // RADIX SIXTEEN FOURIER TRANSFORM KERNEL
791 {
792 REPORT
793 bool NO_FOLD,ZERO;
794 int J,K,K0,M16,M_OVER_2;
795 Real ANGLE,EI1,ER1,E2,EI3,ER3,EI5,ER5,T,TWOPI;
796 Real RS0,RS1,RS2,RS3,RS4,RS5,RS6,RS7;
797 Real IS0,IS1,IS2,IS3,IS4,IS5,IS6,IS7;
798 Real RU0,RU1,RU2,RU3,RU4,RU5,RU6,RU7;
799 Real IU0,IU1,IU2,IU3,IU4,IU5,IU6,IU7;
800 Real RUS0,RUS1,RUS2,RUS3,RUU0,RUU1,RUU2,RUU3;
801 Real ISS0,ISS1,ISS2,ISS3,ISU0,ISU1,ISU2,ISU3;
802 Real RSS0,RSS1,RSS2,RSS3,RSU0,RSU1,RSU2,RSU3;
803 Real IUS0,IUS1,IUS2,IUS3,IUU0,IUU1,IUU2,IUU3;
804 Real RSSS0,RSSS1,RSSU0,RSSU1,RSUS0,RSUS1,RSUU0,RSUU1;
805 Real ISSS0,ISSS1,ISSU0,ISSU1,ISUS0,ISUS1,ISUU0,ISUU1;
806 Real RUSS0,RUSS1,RUSU0,RUSU1,RUUS0,RUUS1,RUUU0,RUUU1;
807 Real IUSS0,IUSS1,IUSU0,IUSU1,IUUS0,IUUS1,IUUU0,IUUU1;
808 Real R1,R2,R3,R4,R5,R6,R7,R8,R9,R10,R11,R12,R13,R14,R15;
809 Real I1,I2,I3,I4,I5,I6,I7,I8,I9,I10,I11,I12,I13,I14,I15;
810 Real C1,C2,C3,C4,C5,C6,C7,C8,C9,C10,C11,C12,C13,C14,C15;
811 Real S1,S2,S3,S4,S5,S6,S7,S8,S9,S10,S11,S12,S13,S14,S15;
812
813 M16=M*16; M_OVER_2=M/2+1;
814 TWOPI=8.0*atan(1.0);
815 ER1=cos(TWOPI/16.0); EI1=sin(TWOPI/16.0);
816 E2=cos(TWOPI/8.0);
817 ER3=cos(3.0*TWOPI/16.0); EI3=sin(3.0*TWOPI/16.0);
818 ER5=cos(5.0*TWOPI/16.0); EI5=sin(5.0*TWOPI/16.0);
819
820 for (J=0; J<M_OVER_2; J++)
821 {
822 NO_FOLD = (J==0 || 2*J==M);
823 K0=J;
824 ANGLE=TWOPI*Real(J)/Real(M16);
825 ZERO=ANGLE==0.0;
826 C1=cos(ANGLE); S1=sin(ANGLE);
827 C2=C1*C1-S1*S1; S2=C1*S1+S1*C1;
828 C3=C2*C1-S2*S1; S3=S2*C1+C2*S1;
829 C4=C2*C2-S2*S2; S4=S2*C2+C2*S2;
830 C5=C4*C1-S4*S1; S5=S4*C1+C4*S1;
831 C6=C4*C2-S4*S2; S6=S4*C2+C4*S2;
832 C7=C4*C3-S4*S3; S7=S4*C3+C4*S3;
833 C8=C4*C4-S4*S4; S8=C4*S4+S4*C4;
834 C9=C8*C1-S8*S1; S9=S8*C1+C8*S1;
835 C10=C8*C2-S8*S2; S10=S8*C2+C8*S2;
836 C11=C8*C3-S8*S3; S11=S8*C3+C8*S3;
837 C12=C8*C4-S8*S4; S12=S8*C4+C8*S4;
838 C13=C8*C5-S8*S5; S13=S8*C5+C8*S5;
839 C14=C8*C6-S8*S6; S14=S8*C6+C8*S6;
840 C15=C8*C7-S8*S7; S15=S8*C7+C8*S7;
841 goto L200;
842 L100:
843 REPORT
844 if (NO_FOLD) { REPORT goto L600; }
845 REPORT
846 NO_FOLD=true; K0=M-J;
847 T=C1*ER1+S1*EI1; S1= -S1*ER1+C1*EI1; C1=T;
848 T=(C2+S2)*E2; S2=(C2-S2)*E2; C2=T;
849 T=C3*ER3+S3*EI3; S3= -S3*ER3+C3*EI3; C3=T;
850 T=S4; S4=C4; C4=T;
851 T=S5*ER1-C5*EI1; S5=C5*ER1+S5*EI1; C5=T;
852 T=(-C6+S6)*E2; S6=(C6+S6)*E2; C6=T;
853 T=S7*ER3-C7*EI3; S7=C7*ER3+S7*EI3; C7=T;
854 C8= -C8;
855 T= -(C9*ER1+S9*EI1); S9=S9*ER1-C9*EI1; C9=T;
856 T= -(C10+S10)*E2; S10=(-C10+S10)*E2; C10=T;
857 T= -(C11*ER3+S11*EI3); S11=S11*ER3-C11*EI3; C11=T;
858 T= -S12; S12= -C12; C12=T;
859 T= -S13*ER1+C13*EI1; S13= -(C13*ER1+S13*EI1); C13=T;
860 T=(C14-S14)*E2; S14= -(C14+S14)*E2; C14=T;
861 T= -S15*ER3+C15*EI3; S15= -(C15*ER3+S15*EI3); C15=T;
862 L200:
863 REPORT
864 for (K=K0; K<N; K+=M16)
865 {
866 RS0=X0[K]+X8[K]; IS0=Y0[K]+Y8[K];
867 RU0=X0[K]-X8[K]; IU0=Y0[K]-Y8[K];
868 RS1=X1[K]+X9[K]; IS1=Y1[K]+Y9[K];
869 RU1=X1[K]-X9[K]; IU1=Y1[K]-Y9[K];
870 RS2=X2[K]+X10[K]; IS2=Y2[K]+Y10[K];
871 RU2=X2[K]-X10[K]; IU2=Y2[K]-Y10[K];
872 RS3=X3[K]+X11[K]; IS3=Y3[K]+Y11[K];
873 RU3=X3[K]-X11[K]; IU3=Y3[K]-Y11[K];
874 RS4=X4[K]+X12[K]; IS4=Y4[K]+Y12[K];
875 RU4=X4[K]-X12[K]; IU4=Y4[K]-Y12[K];
876 RS5=X5[K]+X13[K]; IS5=Y5[K]+Y13[K];
877 RU5=X5[K]-X13[K]; IU5=Y5[K]-Y13[K];
878 RS6=X6[K]+X14[K]; IS6=Y6[K]+Y14[K];
879 RU6=X6[K]-X14[K]; IU6=Y6[K]-Y14[K];
880 RS7=X7[K]+X15[K]; IS7=Y7[K]+Y15[K];
881 RU7=X7[K]-X15[K]; IU7=Y7[K]-Y15[K];
882 RSS0=RS0+RS4; ISS0=IS0+IS4;
883 RSS1=RS1+RS5; ISS1=IS1+IS5;
884 RSS2=RS2+RS6; ISS2=IS2+IS6;
885 RSS3=RS3+RS7; ISS3=IS3+IS7;
886 RSU0=RS0-RS4; ISU0=IS0-IS4;
887 RSU1=RS1-RS5; ISU1=IS1-IS5;
888 RSU2=RS2-RS6; ISU2=IS2-IS6;
889 RSU3=RS3-RS7; ISU3=IS3-IS7;
890 RUS0=RU0-IU4; IUS0=IU0+RU4;
891 RUS1=RU1-IU5; IUS1=IU1+RU5;
892 RUS2=RU2-IU6; IUS2=IU2+RU6;
893 RUS3=RU3-IU7; IUS3=IU3+RU7;
894 RUU0=RU0+IU4; IUU0=IU0-RU4;
895 RUU1=RU1+IU5; IUU1=IU1-RU5;
896 RUU2=RU2+IU6; IUU2=IU2-RU6;
897 RUU3=RU3+IU7; IUU3=IU3-RU7;
898 T=(RSU1+ISU1)*E2; ISU1=(ISU1-RSU1)*E2; RSU1=T;
899 T=(RSU3+ISU3)*E2; ISU3=(ISU3-RSU3)*E2; RSU3=T;
900 T=RUS1*ER3+IUS1*EI3; IUS1=IUS1*ER3-RUS1*EI3; RUS1=T;
901 T=(RUS2+IUS2)*E2; IUS2=(IUS2-RUS2)*E2; RUS2=T;
902 T=RUS3*ER5+IUS3*EI5; IUS3=IUS3*ER5-RUS3*EI5; RUS3=T;
903 T=RUU1*ER1+IUU1*EI1; IUU1=IUU1*ER1-RUU1*EI1; RUU1=T;
904 T=(RUU2+IUU2)*E2; IUU2=(IUU2-RUU2)*E2; RUU2=T;
905 T=RUU3*ER3+IUU3*EI3; IUU3=IUU3*ER3-RUU3*EI3; RUU3=T;
906 RSSS0=RSS0+RSS2; ISSS0=ISS0+ISS2;
907 RSSS1=RSS1+RSS3; ISSS1=ISS1+ISS3;
908 RSSU0=RSS0-RSS2; ISSU0=ISS0-ISS2;
909 RSSU1=RSS1-RSS3; ISSU1=ISS1-ISS3;
910 RSUS0=RSU0-ISU2; ISUS0=ISU0+RSU2;
911 RSUS1=RSU1-ISU3; ISUS1=ISU1+RSU3;
912 RSUU0=RSU0+ISU2; ISUU0=ISU0-RSU2;
913 RSUU1=RSU1+ISU3; ISUU1=ISU1-RSU3;
914 RUSS0=RUS0-IUS2; IUSS0=IUS0+RUS2;
915 RUSS1=RUS1-IUS3; IUSS1=IUS1+RUS3;
916 RUSU0=RUS0+IUS2; IUSU0=IUS0-RUS2;
917 RUSU1=RUS1+IUS3; IUSU1=IUS1-RUS3;
918 RUUS0=RUU0+RUU2; IUUS0=IUU0+IUU2;
919 RUUS1=RUU1+RUU3; IUUS1=IUU1+IUU3;
920 RUUU0=RUU0-RUU2; IUUU0=IUU0-IUU2;
921 RUUU1=RUU1-RUU3; IUUU1=IUU1-IUU3;
922 X0[K]=RSSS0+RSSS1; Y0[K]=ISSS0+ISSS1;
923 if (!ZERO)
924 {
925 REPORT
926 R1=RUUS0+RUUS1; I1=IUUS0+IUUS1;
927 R2=RSUU0+RSUU1; I2=ISUU0+ISUU1;
928 R3=RUSU0+RUSU1; I3=IUSU0+IUSU1;
929 R4=RSSU0+ISSU1; I4=ISSU0-RSSU1;
930 R5=RUUU0+IUUU1; I5=IUUU0-RUUU1;
931 R6=RSUS0+ISUS1; I6=ISUS0-RSUS1;
932 R7=RUSS0+IUSS1; I7=IUSS0-RUSS1;
933 R8=RSSS0-RSSS1; I8=ISSS0-ISSS1;
934 R9=RUUS0-RUUS1; I9=IUUS0-IUUS1;
935 R10=RSUU0-RSUU1; I10=ISUU0-ISUU1;
936 R11=RUSU0-RUSU1; I11=IUSU0-IUSU1;
937 R12=RSSU0-ISSU1; I12=ISSU0+RSSU1;
938 R13=RUUU0-IUUU1; I13=IUUU0+RUUU1;
939 R14=RSUS0-ISUS1; I14=ISUS0+RSUS1;
940 R15=RUSS0-IUSS1; I15=IUSS0+RUSS1;
941 X8[K]=R1*C1+I1*S1; Y8[K]=I1*C1-R1*S1;
942 X4[K]=R2*C2+I2*S2; Y4[K]=I2*C2-R2*S2;
943 X12[K]=R3*C3+I3*S3; Y12[K]=I3*C3-R3*S3;
944 X2[K]=R4*C4+I4*S4; Y2[K]=I4*C4-R4*S4;
945 X10[K]=R5*C5+I5*S5; Y10[K]=I5*C5-R5*S5;
946 X6[K]=R6*C6+I6*S6; Y6[K]=I6*C6-R6*S6;
947 X14[K]=R7*C7+I7*S7; Y14[K]=I7*C7-R7*S7;
948 X1[K]=R8*C8+I8*S8; Y1[K]=I8*C8-R8*S8;
949 X9[K]=R9*C9+I9*S9; Y9[K]=I9*C9-R9*S9;
950 X5[K]=R10*C10+I10*S10; Y5[K]=I10*C10-R10*S10;
951 X13[K]=R11*C11+I11*S11; Y13[K]=I11*C11-R11*S11;
952 X3[K]=R12*C12+I12*S12; Y3[K]=I12*C12-R12*S12;
953 X11[K]=R13*C13+I13*S13; Y11[K]=I13*C13-R13*S13;
954 X7[K]=R14*C14+I14*S14; Y7[K]=I14*C14-R14*S14;
955 X15[K]=R15*C15+I15*S15; Y15[K]=I15*C15-R15*S15;
956 }
957 else
958 {
959 REPORT
960 X8[K]=RUUS0+RUUS1; Y8[K]=IUUS0+IUUS1;
961 X4[K]=RSUU0+RSUU1; Y4[K]=ISUU0+ISUU1;
962 X12[K]=RUSU0+RUSU1; Y12[K]=IUSU0+IUSU1;
963 X2[K]=RSSU0+ISSU1; Y2[K]=ISSU0-RSSU1;
964 X10[K]=RUUU0+IUUU1; Y10[K]=IUUU0-RUUU1;
965 X6[K]=RSUS0+ISUS1; Y6[K]=ISUS0-RSUS1;
966 X14[K]=RUSS0+IUSS1; Y14[K]=IUSS0-RUSS1;
967 X1[K]=RSSS0-RSSS1; Y1[K]=ISSS0-ISSS1;
968 X9[K]=RUUS0-RUUS1; Y9[K]=IUUS0-IUUS1;
969 X5[K]=RSUU0-RSUU1; Y5[K]=ISUU0-ISUU1;
970 X13[K]=RUSU0-RUSU1; Y13[K]=IUSU0-IUSU1;
971 X3[K]=RSSU0-ISSU1; Y3[K]=ISSU0+RSSU1;
972 X11[K]=RUUU0-IUUU1; Y11[K]=IUUU0+RUUU1;
973 X7[K]=RSUS0-ISUS1; Y7[K]=ISUS0+RSUS1;
974 X15[K]=RUSS0-IUSS1; Y15[K]=IUSS0+RUSS1;
975 }
976 }
977 goto L100;
978 L600: ;
979 }
980
981 return;
982 }
983
984 // can the number of points be factorised sufficiently
985 // for the fft to run
986
CanFactor(int PTS)987 bool FFT_Controller::CanFactor(int PTS)
988 {
989 REPORT
990 const int NP = 16, NQ = 10, PMAX=19;
991
992 if (PTS<=1) { REPORT return true; }
993
994 int N = PTS, F = 2, P = 0, Q = 0;
995
996 while (N > 1)
997 {
998 bool fail = true;
999 for (int J = F; J <= PMAX; J++)
1000 if (N % J == 0) { fail = false; F=J; break; }
1001 if (fail || P >= NP || Q >= NQ) { REPORT return false; }
1002 N /= F;
1003 if (N % F != 0) Q++; else { N /= F; P++; }
1004 }
1005
1006 return true; // can factorise
1007
1008 }
1009
1010 bool FFT_Controller::OnlyOldFFT; // static variable
1011
1012 // **************************** multi radix counter **********************
1013
MultiRadixCounter(int nx,const SimpleIntArray & rx,SimpleIntArray & vx)1014 MultiRadixCounter::MultiRadixCounter(int nx, const SimpleIntArray& rx,
1015 SimpleIntArray& vx)
1016 : Radix(rx), Value(vx), n(nx), reverse(0),
1017 product(1), counter(0), finish(false)
1018 {
1019 REPORT for (int k = 0; k < n; k++) { Value[k] = 0; product *= Radix[k]; }
1020 }
1021
1022 void MultiRadixCounter::operator++()
1023 {
1024 REPORT
1025 counter++; int p = product;
1026 for (int k = 0; k < n; k++)
1027 {
1028 Value[k]++; int p1 = p / Radix[k]; reverse += p1;
1029 if (Value[k] == Radix[k]) { REPORT Value[k] = 0; reverse -= p; p = p1; }
1030 else { REPORT return; }
1031 }
1032 finish = true;
1033 }
1034
1035
BitReverse(int x,int prod,int n,const SimpleIntArray & f)1036 static int BitReverse(int x, int prod, int n, const SimpleIntArray& f)
1037 {
1038 // x = c[0]+f[0]*(c[1]+f[1]*(c[2]+...
1039 // return c[n-1]+f[n-1]*(c[n-2]+f[n-2]*(c[n-3]+...
1040 // prod is the product of the f[i]
1041 // n is the number of f[i] (don't assume f has the correct length)
1042
1043 REPORT
1044 const int* d = f.Data() + n; int sum = 0; int q = 1;
1045 while (n--)
1046 {
1047 prod /= *(--d);
1048 int c = x / prod; x-= c * prod;
1049 sum += q * c; q *= *d;
1050 }
1051 return sum;
1052 }
1053
1054
1055 #ifdef use_namespace
1056 }
1057 #endif
1058
1059
1060