aboutsummaryrefslogtreecommitdiff
path: root/externals/grill/vasp/source/mixfft.cpp
blob: 975e8cb1fea4ab431cb0af0a78cac91c4029331d (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588

#include <math.h>
#include <stdio.h>
#include <stdlib.h>

#ifdef _MSC_VER
#pragma warning(disable: 4244)
#endif

/************************************************************************
  fft(int n, double xRe[], double xIm[], double yRe[], double yIm[])
 ------------------------------------------------------------------------
  NOTE : This is copyrighted material, Not public domain. See below.
 ------------------------------------------------------------------------
  Input/output:
      int n          transformation length.
      double xRe[]   real part of input sequence.
      double xIm[]   imaginary part of input sequence.
      double yRe[]   real part of output sequence.
      double yIm[]   imaginary part of output sequence.
 ------------------------------------------------------------------------
  Function:
      The procedure performs a fast discrete Fourier transform (FFT) of
      a complex sequence, x, of an arbitrary length, n. The output, y,
      is also a complex sequence of length n.

      y[k] = sum(x[m]*exp(-i*2*pi*k*m/n), m=0..(n-1)), k=0,...,(n-1)

      The largest prime factor of n must be less than or equal to the
      constant maxPrimeFactor defined below.
 ------------------------------------------------------------------------
  Author:
      Jens Joergen Nielsen            For non-commercial use only.
      Bakkehusene 54                  A $100 fee must be paid if used
      DK-2970 Hoersholm               commercially. Please contact.
      DENMARK

      E-mail : jjn@get2net.dk   All rights reserved. October 2000.
      Homepage : http://home.get2net.dk/jjn
 ------------------------------------------------------------------------
  Implementation notes:
      The general idea is to factor the length of the DFT, n, into
      factors that are efficiently handled by the routines.

      A number of short DFT's are implemented with a minimum of
      arithmetical operations and using (almost) straight line code
      resulting in very fast execution when the factors of n belong
      to this set. Especially radix-10 is optimized.

      Prime factors, that are not in the set of short DFT's are handled
      with direct evaluation of the DFP expression.

      Please report any problems to the author. 
      Suggestions and improvements are welcomed.
 ------------------------------------------------------------------------
  Benchmarks:                   
      The Microsoft Visual C++ compiler was used with the following 
      compile options:
      /nologo /Gs /G2 /W4 /AH /Ox /D "NDEBUG" /D "_DOS" /FR
      and the FFTBENCH test executed on a 50MHz 486DX :
      
      Length  Time [s]  Accuracy [dB]

         128   0.0054     -314.8   
         256   0.0116     -309.8   
         512   0.0251     -290.8   
        1024   0.0567     -313.6   
        2048   0.1203     -306.4   
        4096   0.2600     -291.8   
        8192   0.5800     -305.1   
         100   0.0040     -278.5   
         200   0.0099     -280.3   
         500   0.0256     -278.5   
        1000   0.0540     -278.5   
        2000   0.1294     -280.6   
        5000   0.3300     -278.4   
       10000   0.7133     -278.5   
 ------------------------------------------------------------------------
  The following procedures are used :
      factorize       :  factor the transformation length.
      transTableSetup :  setup table with sofar-, actual-, and remainRadix.
      permute         :  permutation allows in-place calculations.
      twiddleTransf   :  twiddle multiplications and DFT's for one stage.
      initTrig        :  initialise sine/cosine table.
      fft_4           :  length 4 DFT, a la Nussbaumer.
      fft_5           :  length 5 DFT, a la Nussbaumer.
      fft_10          :  length 10 DFT using prime factor FFT.
      fft_odd         :  length n DFT, n odd.
*************************************************************************/

/************************************************************************

	changes by Thomas Grill:

	- introduced REAL type for numbers
	- made functions static
	- threw fft_n functions out of twiddleTransf
	  if feasible, these will be inlined by the compiler
	- changed log prints (to post)

************************************************************************/

#define REAL float
extern "C" void post(const char *c,...);

/************************************************************************/


#define  maxPrimeFactor        8000  // all static data should fit into 256kB of cache
#define  maxPrimeFactorDiv2    (maxPrimeFactor+1)/2
#define  maxFactorCount        100

static double  c3_1 = -1.5000000000000E+00;  /*  c3_1 = cos(2*pi/3)-1;          */
static double  c3_2 =  8.6602540378444E-01;  /*  c3_2 = sin(2*pi/3);            */
                                          
static double  u5   =  1.2566370614359E+00;  /*  u5   = 2*pi/5;                 */
static double  c5_1 = -1.2500000000000E+00;  /*  c5_1 = (cos(u5)+cos(2*u5))/2-1;*/
static double  c5_2 =  5.5901699437495E-01;  /*  c5_2 = (cos(u5)-cos(2*u5))/2;  */
static double  c5_3 = -9.5105651629515E-01;  /*  c5_3 = -sin(u5);               */
static double  c5_4 = -1.5388417685876E+00;  /*  c5_4 = -(sin(u5)+sin(2*u5));   */
static double  c5_5 =  3.6327126400268E-01;  /*  c5_5 = (sin(u5)-sin(2*u5));    */
static double  c8   =  7.0710678118655E-01;  /*  c8 = 1/sqrt(2);    */

static double   pi;
static int      groupOffset,dataOffset,blockOffset,adr;
static int      groupNo,dataNo,blockNo,twNo;
static double   omega;
static REAL tw_re,tw_im;
static REAL   twiddleRe[maxPrimeFactor], twiddleIm[maxPrimeFactor];
static REAL trigRe[maxPrimeFactor], trigIm[maxPrimeFactor];
static REAL zRe[maxPrimeFactor], zIm[maxPrimeFactor];
static REAL   vRe[maxPrimeFactorDiv2], vIm[maxPrimeFactorDiv2];
static REAL   wRe[maxPrimeFactorDiv2], wIm[maxPrimeFactorDiv2];


static void factorize(int n, int *nFact, int fact[])
{
    int i,j,k;
    int nRadix;
    int radices[7];
    int factors[maxFactorCount];

    nRadix    =  6;  
    radices[1]=  2;
    radices[2]=  3;
    radices[3]=  4;
    radices[4]=  5;
    radices[5]=  8;
    radices[6]= 10;

    if (n==1)
    {
        j=1;
        factors[1]=1;
    }
    else j=0;
    i=nRadix;
    while ((n>1) && (i>0))
    {
      if ((n % radices[i]) == 0)
      {
        n=n / radices[i];
        j=j+1;
        factors[j]=radices[i];
      }
      else  i=i-1;
    }
    if (factors[j] == 2)   /*substitute factors 2*8 with 4*4 */
    {   
      i = j-1;
      while ((i>0) && (factors[i] != 8)) i--;
      if (i>0)
      {
        factors[j] = 4;
        factors[i] = 4;
      }
    }
    if (n>1)
    {
        for (k=2; k<sqrt(n)+1; k++)
            while ((n % k) == 0)
            {
                n=n / k;
                j=j+1;
                factors[j]=k;
            }
        if (n>1)
        {
            j=j+1;
            factors[j]=n;
        }
    }               
    for (i=1; i<=j; i++)         
    {
      fact[i] = factors[j-i+1];
    }
    *nFact=j;
}   /* factorize */

/****************************************************************************
  After N is factored the parameters that control the stages are generated.
  For each stage we have:
    sofar   : the product of the radices so far.
    actual  : the radix handled in this stage.
    remain  : the product of the remaining radices.
 ****************************************************************************/

static bool transTableSetup(int sofar[], int actual[], int remain[],
                     int *nFact,
                     int *nPoints)
{
    int i;

    factorize(*nPoints, nFact, actual);
    if (actual[1] > maxPrimeFactor)
    {
		// T.Grill - replaced the printfs by a post
        post("FFT: Prime factor of FFT length is too large (%d) - aborted",actual[1]);
        return false;
    }

    remain[0]=*nPoints;
    sofar[1]=1;
    remain[1]=*nPoints / actual[1];
    for (i=2; i<=*nFact; i++)
    {
        sofar[i]=sofar[i-1]*actual[i-1];
        remain[i]=remain[i-1] / actual[i];
    }
	return true;
}   /* transTableSetup */

/****************************************************************************
  The sequence y is the permuted input sequence x so that the following
  transformations can be performed in-place, and the final result is the
  normal order.
 ****************************************************************************/

static void permute(int nPoint, int nFact,
             int fact[], int remain[],
             REAL xRe[], REAL xIm[],
             REAL yRe[], REAL yIm[])

{
    int i,j,k;
    int count[maxFactorCount]; 

    for (i=1; i<=nFact; i++) count[i]=0;
    k=0;
    for (i=0; i<=nPoint-2; i++)
    {
        yRe[i] = xRe[k];
        yIm[i] = xIm[k];
        j=1;
        k=k+remain[j];
        count[1] = count[1]+1;
        while (count[j] >= fact[j])
        {
            count[j]=0;
            k=k-remain[j-1]+remain[j+1];
            j=j+1;
            count[j]=count[j]+1;
        }
    }
    yRe[nPoint-1]=xRe[nPoint-1];
    yIm[nPoint-1]=xIm[nPoint-1];
}   /* permute */


/****************************************************************************
  Twiddle factor multiplications and transformations are performed on a
  group of data. The number of multiplications with 1 are reduced by skipping
  the twiddle multiplication of the first stage and of the first group of the
  following stages.
 ***************************************************************************/

static void initTrig(int radix)
{
    int i;
    double w,xre,xim,xre1,xim1;

    w=2*pi/radix;
    trigRe[0]=1; trigIm[0]=0;
    xre1=xre=cos(w); 
    xim1=xim=-sin(w);
    trigRe[1]=xre; trigIm[1]=xim;
    for (i=2; i<radix; i++)
    {
        trigRe[i] = xre1 = xre*trigRe[i-1] - xim*trigIm[i-1];
        trigIm[i] = xim1 = xim*trigRe[i-1] + xre*trigIm[i-1];
//        trigRe[i] = xre1 = xre*xre1 - xim*xim1;
//        trigIm[i] = xim1 = xim*xre1 + xre*xim1;
    }
}   /* initTrig */

static void fft_2(REAL aRe[], REAL aIm[])
{
	double gem;
	gem=zRe[0] + zRe[1];
	zRe[1]=zRe[0] -  zRe[1]; zRe[0]=gem;
	gem=zIm[0] + zIm[1];
	zIm[1]=zIm[0] - zIm[1]; zIm[0]=gem;
}

static void fft_3(REAL aRe[], REAL aIm[])
{
	REAL t1_re,t1_im;
    REAL  m2_re,m2_im; 
    REAL  m1_re,m1_im; 
    REAL  s1_re,s1_im; 
	t1_re=zRe[1] + zRe[2]; t1_im=zIm[1] + zIm[2];
	zRe[0]=zRe[0] + t1_re; zIm[0]=zIm[0] + t1_im;
	m1_re=c3_1*t1_re; m1_im=c3_1*t1_im;
	m2_re=c3_2*(zIm[1] - zIm[2]); 
	m2_im=c3_2*(zRe[2] -  zRe[1]);
	s1_re=zRe[0] + m1_re; s1_im=zIm[0] + m1_im;
	zRe[1]=s1_re + m2_re; zIm[1]=s1_im + m2_im;
	zRe[2]=s1_re - m2_re; zIm[2]=s1_im - m2_im;
}

static void fft_4(REAL aRe[], REAL aIm[])
{
    REAL t1_re,t1_im, t2_re,t2_im;
    REAL m2_re,m2_im, m3_re,m3_im;

    t1_re=aRe[0] + aRe[2]; t1_im=aIm[0] + aIm[2];
    t2_re=aRe[1] + aRe[3]; t2_im=aIm[1] + aIm[3];

    m2_re=aRe[0] - aRe[2]; m2_im=aIm[0] - aIm[2];
    m3_re=aIm[1] - aIm[3]; m3_im=aRe[3] - aRe[1];

    aRe[0]=t1_re + t2_re; aIm[0]=t1_im + t2_im;
    aRe[2]=t1_re - t2_re; aIm[2]=t1_im - t2_im;
    aRe[1]=m2_re + m3_re; aIm[1]=m2_im + m3_im;
    aRe[3]=m2_re - m3_re; aIm[3]=m2_im - m3_im;
}   /* fft_4 */


static void fft_5(REAL aRe[], REAL aIm[])
{    
    REAL t1_re,t1_im, t2_re,t2_im, t3_re,t3_im;
    REAL t4_re,t4_im, t5_re,t5_im;
    REAL m2_re,m2_im, m3_re,m3_im, m4_re,m4_im;
    REAL m1_re,m1_im, m5_re,m5_im;
    REAL s1_re,s1_im, s2_re,s2_im, s3_re,s3_im;
    REAL s4_re,s4_im, s5_re,s5_im;

    t1_re=aRe[1] + aRe[4]; t1_im=aIm[1] + aIm[4];
    t2_re=aRe[2] + aRe[3]; t2_im=aIm[2] + aIm[3];
    t3_re=aRe[1] - aRe[4]; t3_im=aIm[1] - aIm[4];
    t4_re=aRe[3] - aRe[2]; t4_im=aIm[3] - aIm[2];
    t5_re=t1_re + t2_re; t5_im=t1_im + t2_im;
    aRe[0]=aRe[0] + t5_re; aIm[0]=aIm[0] + t5_im;
    m1_re=c5_1*t5_re; m1_im=c5_1*t5_im;
    m2_re=c5_2*(t1_re - t2_re); m2_im=c5_2*(t1_im - t2_im);

    m3_re=-c5_3*(t3_im + t4_im); m3_im=c5_3*(t3_re + t4_re);
    m4_re=-c5_4*t4_im; m4_im=c5_4*t4_re;
    m5_re=-c5_5*t3_im; m5_im=c5_5*t3_re;

    s3_re=m3_re - m4_re; s3_im=m3_im - m4_im;
    s5_re=m3_re + m5_re; s5_im=m3_im + m5_im;
    s1_re=aRe[0] + m1_re; s1_im=aIm[0] + m1_im;
    s2_re=s1_re + m2_re; s2_im=s1_im + m2_im;
    s4_re=s1_re - m2_re; s4_im=s1_im - m2_im;

    aRe[1]=s2_re + s3_re; aIm[1]=s2_im + s3_im;
    aRe[2]=s4_re + s5_re; aIm[2]=s4_im + s5_im;
    aRe[3]=s4_re - s5_re; aIm[3]=s4_im - s5_im;
    aRe[4]=s2_re - s3_re; aIm[4]=s2_im - s3_im;
}   /* fft_5 */

static void fft_8()
{
    REAL aRe[4], aIm[4], bRe[4], bIm[4], gem;

    aRe[0] = zRe[0];    bRe[0] = zRe[1];
    aRe[1] = zRe[2];    bRe[1] = zRe[3];
    aRe[2] = zRe[4];    bRe[2] = zRe[5];
    aRe[3] = zRe[6];    bRe[3] = zRe[7];

    aIm[0] = zIm[0];    bIm[0] = zIm[1];
    aIm[1] = zIm[2];    bIm[1] = zIm[3];
    aIm[2] = zIm[4];    bIm[2] = zIm[5];
    aIm[3] = zIm[6];    bIm[3] = zIm[7];

    fft_4(aRe, aIm); fft_4(bRe, bIm);

    gem    = c8*(bRe[1] + bIm[1]);
    bIm[1] = c8*(bIm[1] - bRe[1]);
    bRe[1] = gem;
    gem    = bIm[2];
    bIm[2] =-bRe[2];
    bRe[2] = gem;
    gem    = c8*(bIm[3] - bRe[3]);
    bIm[3] =-c8*(bRe[3] + bIm[3]);
    bRe[3] = gem;
    
    zRe[0] = aRe[0] + bRe[0]; zRe[4] = aRe[0] - bRe[0];
    zRe[1] = aRe[1] + bRe[1]; zRe[5] = aRe[1] - bRe[1];
    zRe[2] = aRe[2] + bRe[2]; zRe[6] = aRe[2] - bRe[2];
    zRe[3] = aRe[3] + bRe[3]; zRe[7] = aRe[3] - bRe[3];

    zIm[0] = aIm[0] + bIm[0]; zIm[4] = aIm[0] - bIm[0];
    zIm[1] = aIm[1] + bIm[1]; zIm[5] = aIm[1] - bIm[1];
    zIm[2] = aIm[2] + bIm[2]; zIm[6] = aIm[2] - bIm[2];
    zIm[3] = aIm[3] + bIm[3]; zIm[7] = aIm[3] - bIm[3];
}   /* fft_8 */

static void fft_10()
{
    REAL aRe[5], aIm[5], bRe[5], bIm[5];

    aRe[0] = zRe[0];    bRe[0] = zRe[5];
    aRe[1] = zRe[2];    bRe[1] = zRe[7];
    aRe[2] = zRe[4];    bRe[2] = zRe[9];
    aRe[3] = zRe[6];    bRe[3] = zRe[1];
    aRe[4] = zRe[8];    bRe[4] = zRe[3];

    aIm[0] = zIm[0];    bIm[0] = zIm[5];
    aIm[1] = zIm[2];    bIm[1] = zIm[7];
    aIm[2] = zIm[4];    bIm[2] = zIm[9];
    aIm[3] = zIm[6];    bIm[3] = zIm[1];
    aIm[4] = zIm[8];    bIm[4] = zIm[3];

    fft_5(aRe, aIm); fft_5(bRe, bIm);

    zRe[0] = aRe[0] + bRe[0]; zRe[5] = aRe[0] - bRe[0];
    zRe[6] = aRe[1] + bRe[1]; zRe[1] = aRe[1] - bRe[1];
    zRe[2] = aRe[2] + bRe[2]; zRe[7] = aRe[2] - bRe[2];
    zRe[8] = aRe[3] + bRe[3]; zRe[3] = aRe[3] - bRe[3];
    zRe[4] = aRe[4] + bRe[4]; zRe[9] = aRe[4] - bRe[4];

    zIm[0] = aIm[0] + bIm[0]; zIm[5] = aIm[0] - bIm[0];
    zIm[6] = aIm[1] + bIm[1]; zIm[1] = aIm[1] - bIm[1];
    zIm[2] = aIm[2] + bIm[2]; zIm[7] = aIm[2] - bIm[2];
    zIm[8] = aIm[3] + bIm[3]; zIm[3] = aIm[3] - bIm[3];
    zIm[4] = aIm[4] + bIm[4]; zIm[9] = aIm[4] - bIm[4];
}   /* fft_10 */

static void fft_odd(int radix)
{
    REAL  rere, reim, imre, imim;
    int     i,j,k,n,max;

    n = radix;
    max = (n + 1)/2;
    for (j=1; j < max; j++)
    {
      vRe[j] = zRe[j] + zRe[n-j];
      vIm[j] = zIm[j] - zIm[n-j];
      wRe[j] = zRe[j] - zRe[n-j];
      wIm[j] = zIm[j] + zIm[n-j];
    }

    for (j=1; j < max; j++)
    {
        zRe[j]=zRe[0]; 
        zIm[j]=zIm[0];
        zRe[n-j]=zRe[0]; 
        zIm[n-j]=zIm[0];
        k=j;
        for (i=1; i < max; i++)
        {
            rere = trigRe[k] * vRe[i];
            imim = trigIm[k] * vIm[i];
            reim = trigRe[k] * wIm[i];
            imre = trigIm[k] * wRe[i];
            
            zRe[n-j] += rere + imim;
            zIm[n-j] += reim - imre;
            zRe[j]   += rere - imim;
            zIm[j]   += reim + imre;

            k = k + j;
            if (k >= n)  k = k - n;
        }
    }
    for (j=1; j < max; j++)
    {
        zRe[0]=zRe[0] + vRe[j]; 
        zIm[0]=zIm[0] + wIm[j];
    }
}   /* fft_odd */


static void twiddleTransf(int sofarRadix, int radix, int remainRadix,
                    REAL yRe[], REAL yIm[])

{   /* twiddleTransf */ 
    double cosw, sinw, gem;

    initTrig(radix);
    omega = 2*pi/(double)(sofarRadix*radix);
    cosw =  cos(omega);
    sinw = -sin(omega);
    tw_re = 1.0;
    tw_im = 0;
    dataOffset=0;
    groupOffset=dataOffset;
    adr=groupOffset;
    for (dataNo=0; dataNo<sofarRadix; dataNo++)
    {
        if (sofarRadix>1)
        {
            twiddleRe[0] = 1.0; 
            twiddleIm[0] = 0.0;
            twiddleRe[1] = tw_re;
            twiddleIm[1] = tw_im;
            for (twNo=2; twNo<radix; twNo++)
            {
                twiddleRe[twNo]=tw_re*twiddleRe[twNo-1]
                               - tw_im*twiddleIm[twNo-1];
                twiddleIm[twNo]=tw_im*twiddleRe[twNo-1]
                               + tw_re*twiddleIm[twNo-1];
            }
            gem   = cosw*tw_re - sinw*tw_im;
            tw_im = sinw*tw_re + cosw*tw_im;
            tw_re = gem;                      
        }
        for (groupNo=0; groupNo<remainRadix; groupNo++)
        {
            if ((sofarRadix>1) && (dataNo > 0))
            {
                zRe[0]=yRe[adr];
                zIm[0]=yIm[adr];
                blockNo=1;
                do {
                    adr = adr + sofarRadix;
                    zRe[blockNo]=  twiddleRe[blockNo] * yRe[adr]
                                 - twiddleIm[blockNo] * yIm[adr];
                    zIm[blockNo]=  twiddleRe[blockNo] * yIm[adr]
                                 + twiddleIm[blockNo] * yRe[adr]; 
                    
                    blockNo++;
                } while (blockNo < radix);
            }
            else
                for (blockNo=0; blockNo<radix; blockNo++)
                {
                   zRe[blockNo]=yRe[adr];
                   zIm[blockNo]=yIm[adr];
                   adr=adr+sofarRadix;
                }
            switch(radix) {
			// T.Grill - replaced the inlined code by their function counterparts
			  case  2  : fft_2(zRe,zIm); break;
			  case  3  : fft_3(zRe,zIm); break;
              case  4  : fft_4(zRe,zIm); break;
              case  5  : fft_5(zRe,zIm); break;
              case  8  : fft_8(); break;
              case 10  : fft_10(); break;
              default  : fft_odd(radix); break;
            }
            adr=groupOffset;
            for (blockNo=0; blockNo<radix; blockNo++)
            {
                yRe[adr]=zRe[blockNo]; yIm[adr]=zIm[blockNo];
                adr=adr+sofarRadix;
            }
            groupOffset=groupOffset+sofarRadix*radix;
            adr=groupOffset;
        }
        dataOffset=dataOffset+1;
        groupOffset=dataOffset;
        adr=groupOffset;
    }
}   /* twiddleTransf */

bool mixfft(int n, REAL *xRe, REAL *xIm,REAL *yRe, REAL *yIm)
{
    int   sofarRadix[maxFactorCount], 
          actualRadix[maxFactorCount], 
          remainRadix[maxFactorCount];
    int   nFactor;
    int   count;

    pi = 4*atan(1);    

    if(!transTableSetup(sofarRadix, actualRadix, remainRadix, &nFactor, &n)) return false;
    permute(n, nFactor, actualRadix, remainRadix, xRe, xIm, yRe, yIm);

    for (count=1; count<=nFactor; count++)
      twiddleTransf(sofarRadix[count], actualRadix[count], remainRadix[count], 
                    yRe, yIm);
	return true;
}   /* fft */