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fft_template.c
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1 /*
2  * FFT/IFFT transforms
3  * Copyright (c) 2008 Loren Merritt
4  * Copyright (c) 2002 Fabrice Bellard
5  * Partly based on libdjbfft by D. J. Bernstein
6  *
7  * This file is part of FFmpeg.
8  *
9  * FFmpeg is free software; you can redistribute it and/or
10  * modify it under the terms of the GNU Lesser General Public
11  * License as published by the Free Software Foundation; either
12  * version 2.1 of the License, or (at your option) any later version.
13  *
14  * FFmpeg is distributed in the hope that it will be useful,
15  * but WITHOUT ANY WARRANTY; without even the implied warranty of
16  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
17  * Lesser General Public License for more details.
18  *
19  * You should have received a copy of the GNU Lesser General Public
20  * License along with FFmpeg; if not, write to the Free Software
21  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
22  */
23 
24 /**
25  * @file
26  * FFT/IFFT transforms.
27  */
28 
29 #include <stdlib.h>
30 #include <string.h>
31 #include "libavutil/mathematics.h"
32 #include "fft.h"
33 #include "fft-internal.h"
34 
35 #if FFT_FIXED_32
36 #include "fft_table.h"
37 #else /* FFT_FIXED_32 */
38 
39 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
40 #if !CONFIG_HARDCODED_TABLES
41 COSTABLE(16);
42 COSTABLE(32);
43 COSTABLE(64);
44 COSTABLE(128);
45 COSTABLE(256);
46 COSTABLE(512);
47 COSTABLE(1024);
48 COSTABLE(2048);
49 COSTABLE(4096);
50 COSTABLE(8192);
51 COSTABLE(16384);
52 COSTABLE(32768);
53 COSTABLE(65536);
54 #endif
55 COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
56  NULL, NULL, NULL, NULL,
57  FFT_NAME(ff_cos_16),
58  FFT_NAME(ff_cos_32),
59  FFT_NAME(ff_cos_64),
60  FFT_NAME(ff_cos_128),
61  FFT_NAME(ff_cos_256),
62  FFT_NAME(ff_cos_512),
63  FFT_NAME(ff_cos_1024),
64  FFT_NAME(ff_cos_2048),
65  FFT_NAME(ff_cos_4096),
66  FFT_NAME(ff_cos_8192),
67  FFT_NAME(ff_cos_16384),
68  FFT_NAME(ff_cos_32768),
69  FFT_NAME(ff_cos_65536),
70 };
71 
72 #endif /* FFT_FIXED_32 */
73 
74 static void fft_permute_c(FFTContext *s, FFTComplex *z);
75 static void fft_calc_c(FFTContext *s, FFTComplex *z);
76 
77 static int split_radix_permutation(int i, int n, int inverse)
78 {
79  int m;
80  if(n <= 2) return i&1;
81  m = n >> 1;
82  if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
83  m >>= 1;
84  if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
85  else return split_radix_permutation(i, m, inverse)*4 - 1;
86 }
87 
89 {
90 #if (!CONFIG_HARDCODED_TABLES) && (!FFT_FIXED_32)
91  int i;
92  int m = 1<<index;
93  double freq = 2*M_PI/m;
94  FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
95  for(i=0; i<=m/4; i++)
96  tab[i] = FIX15(cos(i*freq));
97  for(i=1; i<m/4; i++)
98  tab[m/2-i] = tab[i];
99 #endif
100 }
101 
102 static const int avx_tab[] = {
103  0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
104 };
105 
106 static int is_second_half_of_fft32(int i, int n)
107 {
108  if (n <= 32)
109  return i >= 16;
110  else if (i < n/2)
111  return is_second_half_of_fft32(i, n/2);
112  else if (i < 3*n/4)
113  return is_second_half_of_fft32(i - n/2, n/4);
114  else
115  return is_second_half_of_fft32(i - 3*n/4, n/4);
116 }
117 
119 {
120  int i;
121  int n = 1 << s->nbits;
122 
123  for (i = 0; i < n; i += 16) {
124  int k;
125  if (is_second_half_of_fft32(i, n)) {
126  for (k = 0; k < 16; k++)
127  s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =
128  i + avx_tab[k];
129 
130  } else {
131  for (k = 0; k < 16; k++) {
132  int j = i + k;
133  j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);
134  s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;
135  }
136  }
137  }
138 }
139 
141 {
142  int i, j, n;
143 
144  if (nbits < 2 || nbits > 16)
145  goto fail;
146  s->nbits = nbits;
147  n = 1 << nbits;
148 
149  s->revtab = av_malloc(n * sizeof(uint16_t));
150  if (!s->revtab)
151  goto fail;
152  s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
153  if (!s->tmp_buf)
154  goto fail;
155  s->inverse = inverse;
157 
159  s->fft_calc = fft_calc_c;
160 #if CONFIG_MDCT
164 #endif
165 
166 #if FFT_FIXED_32
167  {
168  int n=0;
169  ff_fft_lut_init(ff_fft_offsets_lut, 0, 1 << 16, &n);
170  }
171 #else /* FFT_FIXED_32 */
172 #if FFT_FLOAT
173  if (ARCH_AARCH64) ff_fft_init_aarch64(s);
174  if (ARCH_ARM) ff_fft_init_arm(s);
175  if (ARCH_PPC) ff_fft_init_ppc(s);
176  if (ARCH_X86) ff_fft_init_x86(s);
177  if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc;
178  if (HAVE_MIPSFPU) ff_fft_init_mips(s);
179 #else
180  if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c;
181  if (ARCH_ARM) ff_fft_fixed_init_arm(s);
182 #endif
183  for(j=4; j<=nbits; j++) {
185  }
186 #endif /* FFT_FIXED_32 */
187 
188 
189  if (s->fft_permutation == FF_FFT_PERM_AVX) {
190  fft_perm_avx(s);
191  } else {
192  for(i=0; i<n; i++) {
193  j = i;
195  j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
196  s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
197  }
198  }
199 
200  return 0;
201  fail:
202  av_freep(&s->revtab);
203  av_freep(&s->tmp_buf);
204  return -1;
205 }
206 
208 {
209  int j, np;
210  const uint16_t *revtab = s->revtab;
211  np = 1 << s->nbits;
212  /* TODO: handle split-radix permute in a more optimal way, probably in-place */
213  for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
214  memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
215 }
216 
218 {
219  av_freep(&s->revtab);
220  av_freep(&s->tmp_buf);
221 }
222 
223 #if FFT_FIXED_32
224 
225 static void fft_calc_c(FFTContext *s, FFTComplex *z) {
226 
227  int nbits, i, n, num_transforms, offset, step;
228  int n4, n2, n34;
229  FFTSample tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;
230  FFTComplex *tmpz;
231  const int fft_size = (1 << s->nbits);
232  int64_t accu;
233 
234  num_transforms = (0x2aab >> (16 - s->nbits)) | 1;
235 
236  for (n=0; n<num_transforms; n++){
237  offset = ff_fft_offsets_lut[n] << 2;
238  tmpz = z + offset;
239 
240  tmp1 = tmpz[0].re + tmpz[1].re;
241  tmp5 = tmpz[2].re + tmpz[3].re;
242  tmp2 = tmpz[0].im + tmpz[1].im;
243  tmp6 = tmpz[2].im + tmpz[3].im;
244  tmp3 = tmpz[0].re - tmpz[1].re;
245  tmp8 = tmpz[2].im - tmpz[3].im;
246  tmp4 = tmpz[0].im - tmpz[1].im;
247  tmp7 = tmpz[2].re - tmpz[3].re;
248 
249  tmpz[0].re = tmp1 + tmp5;
250  tmpz[2].re = tmp1 - tmp5;
251  tmpz[0].im = tmp2 + tmp6;
252  tmpz[2].im = tmp2 - tmp6;
253  tmpz[1].re = tmp3 + tmp8;
254  tmpz[3].re = tmp3 - tmp8;
255  tmpz[1].im = tmp4 - tmp7;
256  tmpz[3].im = tmp4 + tmp7;
257  }
258 
259  if (fft_size < 8)
260  return;
261 
262  num_transforms = (num_transforms >> 1) | 1;
263 
264  for (n=0; n<num_transforms; n++){
265  offset = ff_fft_offsets_lut[n] << 3;
266  tmpz = z + offset;
267 
268  tmp1 = tmpz[4].re + tmpz[5].re;
269  tmp3 = tmpz[6].re + tmpz[7].re;
270  tmp2 = tmpz[4].im + tmpz[5].im;
271  tmp4 = tmpz[6].im + tmpz[7].im;
272  tmp5 = tmp1 + tmp3;
273  tmp7 = tmp1 - tmp3;
274  tmp6 = tmp2 + tmp4;
275  tmp8 = tmp2 - tmp4;
276 
277  tmp1 = tmpz[4].re - tmpz[5].re;
278  tmp2 = tmpz[4].im - tmpz[5].im;
279  tmp3 = tmpz[6].re - tmpz[7].re;
280  tmp4 = tmpz[6].im - tmpz[7].im;
281 
282  tmpz[4].re = tmpz[0].re - tmp5;
283  tmpz[0].re = tmpz[0].re + tmp5;
284  tmpz[4].im = tmpz[0].im - tmp6;
285  tmpz[0].im = tmpz[0].im + tmp6;
286  tmpz[6].re = tmpz[2].re - tmp8;
287  tmpz[2].re = tmpz[2].re + tmp8;
288  tmpz[6].im = tmpz[2].im + tmp7;
289  tmpz[2].im = tmpz[2].im - tmp7;
290 
291  accu = (int64_t)Q31(M_SQRT1_2)*(tmp1 + tmp2);
292  tmp5 = (int32_t)((accu + 0x40000000) >> 31);
293  accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 - tmp4);
294  tmp7 = (int32_t)((accu + 0x40000000) >> 31);
295  accu = (int64_t)Q31(M_SQRT1_2)*(tmp2 - tmp1);
296  tmp6 = (int32_t)((accu + 0x40000000) >> 31);
297  accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 + tmp4);
298  tmp8 = (int32_t)((accu + 0x40000000) >> 31);
299  tmp1 = tmp5 + tmp7;
300  tmp3 = tmp5 - tmp7;
301  tmp2 = tmp6 + tmp8;
302  tmp4 = tmp6 - tmp8;
303 
304  tmpz[5].re = tmpz[1].re - tmp1;
305  tmpz[1].re = tmpz[1].re + tmp1;
306  tmpz[5].im = tmpz[1].im - tmp2;
307  tmpz[1].im = tmpz[1].im + tmp2;
308  tmpz[7].re = tmpz[3].re - tmp4;
309  tmpz[3].re = tmpz[3].re + tmp4;
310  tmpz[7].im = tmpz[3].im + tmp3;
311  tmpz[3].im = tmpz[3].im - tmp3;
312  }
313 
314  step = 1 << ((MAX_LOG2_NFFT-4) - 4);
315  n4 = 4;
316 
317  for (nbits=4; nbits<=s->nbits; nbits++){
318  n2 = 2*n4;
319  n34 = 3*n4;
320  num_transforms = (num_transforms >> 1) | 1;
321 
322  for (n=0; n<num_transforms; n++){
323  const FFTSample *w_re_ptr = ff_w_tab_sr + step;
324  const FFTSample *w_im_ptr = ff_w_tab_sr + MAX_FFT_SIZE/(4*16) - step;
325  offset = ff_fft_offsets_lut[n] << nbits;
326  tmpz = z + offset;
327 
328  tmp5 = tmpz[ n2].re + tmpz[n34].re;
329  tmp1 = tmpz[ n2].re - tmpz[n34].re;
330  tmp6 = tmpz[ n2].im + tmpz[n34].im;
331  tmp2 = tmpz[ n2].im - tmpz[n34].im;
332 
333  tmpz[ n2].re = tmpz[ 0].re - tmp5;
334  tmpz[ 0].re = tmpz[ 0].re + tmp5;
335  tmpz[ n2].im = tmpz[ 0].im - tmp6;
336  tmpz[ 0].im = tmpz[ 0].im + tmp6;
337  tmpz[n34].re = tmpz[n4].re - tmp2;
338  tmpz[ n4].re = tmpz[n4].re + tmp2;
339  tmpz[n34].im = tmpz[n4].im + tmp1;
340  tmpz[ n4].im = tmpz[n4].im - tmp1;
341 
342  for (i=1; i<n4; i++){
343  FFTSample w_re = w_re_ptr[0];
344  FFTSample w_im = w_im_ptr[0];
345  accu = (int64_t)w_re*tmpz[ n2+i].re;
346  accu += (int64_t)w_im*tmpz[ n2+i].im;
347  tmp1 = (int32_t)((accu + 0x40000000) >> 31);
348  accu = (int64_t)w_re*tmpz[ n2+i].im;
349  accu -= (int64_t)w_im*tmpz[ n2+i].re;
350  tmp2 = (int32_t)((accu + 0x40000000) >> 31);
351  accu = (int64_t)w_re*tmpz[n34+i].re;
352  accu -= (int64_t)w_im*tmpz[n34+i].im;
353  tmp3 = (int32_t)((accu + 0x40000000) >> 31);
354  accu = (int64_t)w_re*tmpz[n34+i].im;
355  accu += (int64_t)w_im*tmpz[n34+i].re;
356  tmp4 = (int32_t)((accu + 0x40000000) >> 31);
357 
358  tmp5 = tmp1 + tmp3;
359  tmp1 = tmp1 - tmp3;
360  tmp6 = tmp2 + tmp4;
361  tmp2 = tmp2 - tmp4;
362 
363  tmpz[ n2+i].re = tmpz[ i].re - tmp5;
364  tmpz[ i].re = tmpz[ i].re + tmp5;
365  tmpz[ n2+i].im = tmpz[ i].im - tmp6;
366  tmpz[ i].im = tmpz[ i].im + tmp6;
367  tmpz[n34+i].re = tmpz[n4+i].re - tmp2;
368  tmpz[ n4+i].re = tmpz[n4+i].re + tmp2;
369  tmpz[n34+i].im = tmpz[n4+i].im + tmp1;
370  tmpz[ n4+i].im = tmpz[n4+i].im - tmp1;
371 
372  w_re_ptr += step;
373  w_im_ptr -= step;
374  }
375  }
376  step >>= 1;
377  n4 <<= 1;
378  }
379 }
380 
381 #else /* FFT_FIXED_32 */
382 
383 #define BUTTERFLIES(a0,a1,a2,a3) {\
384  BF(t3, t5, t5, t1);\
385  BF(a2.re, a0.re, a0.re, t5);\
386  BF(a3.im, a1.im, a1.im, t3);\
387  BF(t4, t6, t2, t6);\
388  BF(a3.re, a1.re, a1.re, t4);\
389  BF(a2.im, a0.im, a0.im, t6);\
390 }
391 
392 // force loading all the inputs before storing any.
393 // this is slightly slower for small data, but avoids store->load aliasing
394 // for addresses separated by large powers of 2.
395 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
396  FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
397  BF(t3, t5, t5, t1);\
398  BF(a2.re, a0.re, r0, t5);\
399  BF(a3.im, a1.im, i1, t3);\
400  BF(t4, t6, t2, t6);\
401  BF(a3.re, a1.re, r1, t4);\
402  BF(a2.im, a0.im, i0, t6);\
403 }
404 
405 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
406  CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
407  CMUL(t5, t6, a3.re, a3.im, wre, wim);\
408  BUTTERFLIES(a0,a1,a2,a3)\
409 }
410 
411 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
412  t1 = a2.re;\
413  t2 = a2.im;\
414  t5 = a3.re;\
415  t6 = a3.im;\
416  BUTTERFLIES(a0,a1,a2,a3)\
417 }
418 
419 /* z[0...8n-1], w[1...2n-1] */
420 #define PASS(name)\
421 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
422 {\
423  FFTDouble t1, t2, t3, t4, t5, t6;\
424  int o1 = 2*n;\
425  int o2 = 4*n;\
426  int o3 = 6*n;\
427  const FFTSample *wim = wre+o1;\
428  n--;\
429 \
430  TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
431  TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
432  do {\
433  z += 2;\
434  wre += 2;\
435  wim -= 2;\
436  TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
437  TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
438  } while(--n);\
439 }
440 
441 PASS(pass)
442 #undef BUTTERFLIES
443 #define BUTTERFLIES BUTTERFLIES_BIG
444 PASS(pass_big)
445 
446 #define DECL_FFT(n,n2,n4)\
447 static void fft##n(FFTComplex *z)\
448 {\
449  fft##n2(z);\
450  fft##n4(z+n4*2);\
451  fft##n4(z+n4*3);\
452  pass(z,FFT_NAME(ff_cos_##n),n4/2);\
453 }
454 
455 static void fft4(FFTComplex *z)
456 {
457  FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
458 
459  BF(t3, t1, z[0].re, z[1].re);
460  BF(t8, t6, z[3].re, z[2].re);
461  BF(z[2].re, z[0].re, t1, t6);
462  BF(t4, t2, z[0].im, z[1].im);
463  BF(t7, t5, z[2].im, z[3].im);
464  BF(z[3].im, z[1].im, t4, t8);
465  BF(z[3].re, z[1].re, t3, t7);
466  BF(z[2].im, z[0].im, t2, t5);
467 }
468 
469 static void fft8(FFTComplex *z)
470 {
471  FFTDouble t1, t2, t3, t4, t5, t6;
472 
473  fft4(z);
474 
475  BF(t1, z[5].re, z[4].re, -z[5].re);
476  BF(t2, z[5].im, z[4].im, -z[5].im);
477  BF(t5, z[7].re, z[6].re, -z[7].re);
478  BF(t6, z[7].im, z[6].im, -z[7].im);
479 
480  BUTTERFLIES(z[0],z[2],z[4],z[6]);
481  TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
482 }
483 
484 #if !CONFIG_SMALL
485 static void fft16(FFTComplex *z)
486 {
487  FFTDouble t1, t2, t3, t4, t5, t6;
488  FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
489  FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
490 
491  fft8(z);
492  fft4(z+8);
493  fft4(z+12);
494 
495  TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
496  TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
497  TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
498  TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
499 }
500 #else
501 DECL_FFT(16,8,4)
502 #endif
503 DECL_FFT(32,16,8)
504 DECL_FFT(64,32,16)
505 DECL_FFT(128,64,32)
506 DECL_FFT(256,128,64)
507 DECL_FFT(512,256,128)
508 #if !CONFIG_SMALL
509 #define pass pass_big
510 #endif
511 DECL_FFT(1024,512,256)
512 DECL_FFT(2048,1024,512)
513 DECL_FFT(4096,2048,1024)
514 DECL_FFT(8192,4096,2048)
515 DECL_FFT(16384,8192,4096)
516 DECL_FFT(32768,16384,8192)
517 DECL_FFT(65536,32768,16384)
518 
519 static void (* const fft_dispatch[])(FFTComplex*) = {
520  fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
521  fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
522 };
523 
524 static void fft_calc_c(FFTContext *s, FFTComplex *z)
525 {
526  fft_dispatch[s->nbits-2](z);
527 }
528 #endif /* FFT_FIXED_32 */