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fft.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 CONFIG_FFT_FIXED_32
36 #include "fft_table.h"
37 #else /* CONFIG_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 /* CONFIG_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 
88 av_cold void ff_init_ff_cos_tabs(int index)
89 {
90 #if (!CONFIG_HARDCODED_TABLES) && (!CONFIG_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 
118 static av_cold void fft_perm_avx(FFTContext *s)
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 
140 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
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;
156  s->fft_permutation = FF_FFT_PERM_DEFAULT;
157 
158  s->fft_permute = fft_permute_c;
159  s->fft_calc = fft_calc_c;
160 #if CONFIG_MDCT
161  s->imdct_calc = ff_imdct_calc_c;
162  s->imdct_half = ff_imdct_half_c;
163  s->mdct_calc = ff_mdct_calc_c;
164 #endif
165 
166 #if CONFIG_FFT_FIXED_32
167  {
168  int n=0;
169  ff_fft_lut_init(fft_offsets_lut, 0, 1 << 16, &n);
170  }
171 #else /* CONFIG_FFT_FIXED_32 */
172 #if CONFIG_FFT_FLOAT
173  if (ARCH_ARM) ff_fft_init_arm(s);
174  if (ARCH_PPC) ff_fft_init_ppc(s);
175  if (ARCH_X86) ff_fft_init_x86(s);
176  if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc;
177  if (HAVE_MIPSFPU) ff_fft_init_mips(s);
178 #else
179  if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c;
180  if (ARCH_ARM) ff_fft_fixed_init_arm(s);
181 #endif
182  for(j=4; j<=nbits; j++) {
183  ff_init_ff_cos_tabs(j);
184  }
185 #endif /* CONFIG_FFT_FIXED_32 */
186 
187 
188  if (s->fft_permutation == FF_FFT_PERM_AVX) {
189  fft_perm_avx(s);
190  } else {
191  for(i=0; i<n; i++) {
192  j = i;
193  if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
194  j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
195  s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
196  }
197  }
198 
199  return 0;
200  fail:
201  av_freep(&s->revtab);
202  av_freep(&s->tmp_buf);
203  return -1;
204 }
205 
206 static void fft_permute_c(FFTContext *s, FFTComplex *z)
207 {
208  int j, np;
209  const uint16_t *revtab = s->revtab;
210  np = 1 << s->nbits;
211  /* TODO: handle split-radix permute in a more optimal way, probably in-place */
212  for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
213  memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
214 }
215 
216 av_cold void ff_fft_end(FFTContext *s)
217 {
218  av_freep(&s->revtab);
219  av_freep(&s->tmp_buf);
220 }
221 
222 #if CONFIG_FFT_FIXED_32
223 
224 static void fft_calc_c(FFTContext *s, FFTComplex *z) {
225 
226  int nbits, i, n, num_transforms, offset, step;
227  int n4, n2, n34;
228  FFTSample tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;
229  FFTComplex *tmpz;
230  FFTSample w_re, w_im;
231  FFTSample *w_re_ptr, *w_im_ptr;
232  const int fft_size = (1 << s->nbits);
233  int64_t accu;
234 
235  num_transforms = (0x2aab >> (16 - s->nbits)) | 1;
236 
237  for (n=0; n<num_transforms; n++){
238  offset = fft_offsets_lut[n] << 2;
239  tmpz = z + offset;
240 
241  tmp1 = tmpz[0].re + tmpz[1].re;
242  tmp5 = tmpz[2].re + tmpz[3].re;
243  tmp2 = tmpz[0].im + tmpz[1].im;
244  tmp6 = tmpz[2].im + tmpz[3].im;
245  tmp3 = tmpz[0].re - tmpz[1].re;
246  tmp8 = tmpz[2].im - tmpz[3].im;
247  tmp4 = tmpz[0].im - tmpz[1].im;
248  tmp7 = tmpz[2].re - tmpz[3].re;
249 
250  tmpz[0].re = tmp1 + tmp5;
251  tmpz[2].re = tmp1 - tmp5;
252  tmpz[0].im = tmp2 + tmp6;
253  tmpz[2].im = tmp2 - tmp6;
254  tmpz[1].re = tmp3 + tmp8;
255  tmpz[3].re = tmp3 - tmp8;
256  tmpz[1].im = tmp4 - tmp7;
257  tmpz[3].im = tmp4 + tmp7;
258  }
259 
260  if (fft_size < 8)
261  return;
262 
263  num_transforms = (num_transforms >> 1) | 1;
264 
265  for (n=0; n<num_transforms; n++){
266  offset = fft_offsets_lut[n] << 3;
267  tmpz = z + offset;
268 
269  tmp1 = tmpz[4].re + tmpz[5].re;
270  tmp3 = tmpz[6].re + tmpz[7].re;
271  tmp2 = tmpz[4].im + tmpz[5].im;
272  tmp4 = tmpz[6].im + tmpz[7].im;
273  tmp5 = tmp1 + tmp3;
274  tmp7 = tmp1 - tmp3;
275  tmp6 = tmp2 + tmp4;
276  tmp8 = tmp2 - tmp4;
277 
278  tmp1 = tmpz[4].re - tmpz[5].re;
279  tmp2 = tmpz[4].im - tmpz[5].im;
280  tmp3 = tmpz[6].re - tmpz[7].re;
281  tmp4 = tmpz[6].im - tmpz[7].im;
282 
283  tmpz[4].re = tmpz[0].re - tmp5;
284  tmpz[0].re = tmpz[0].re + tmp5;
285  tmpz[4].im = tmpz[0].im - tmp6;
286  tmpz[0].im = tmpz[0].im + tmp6;
287  tmpz[6].re = tmpz[2].re - tmp8;
288  tmpz[2].re = tmpz[2].re + tmp8;
289  tmpz[6].im = tmpz[2].im + tmp7;
290  tmpz[2].im = tmpz[2].im - tmp7;
291 
292  accu = (int64_t)Q31(M_SQRT1_2)*(tmp1 + tmp2);
293  tmp5 = (int32_t)((accu + 0x40000000) >> 31);
294  accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 - tmp4);
295  tmp7 = (int32_t)((accu + 0x40000000) >> 31);
296  accu = (int64_t)Q31(M_SQRT1_2)*(tmp2 - tmp1);
297  tmp6 = (int32_t)((accu + 0x40000000) >> 31);
298  accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 + tmp4);
299  tmp8 = (int32_t)((accu + 0x40000000) >> 31);
300  tmp1 = tmp5 + tmp7;
301  tmp3 = tmp5 - tmp7;
302  tmp2 = tmp6 + tmp8;
303  tmp4 = tmp6 - tmp8;
304 
305  tmpz[5].re = tmpz[1].re - tmp1;
306  tmpz[1].re = tmpz[1].re + tmp1;
307  tmpz[5].im = tmpz[1].im - tmp2;
308  tmpz[1].im = tmpz[1].im + tmp2;
309  tmpz[7].re = tmpz[3].re - tmp4;
310  tmpz[3].re = tmpz[3].re + tmp4;
311  tmpz[7].im = tmpz[3].im + tmp3;
312  tmpz[3].im = tmpz[3].im - tmp3;
313  }
314 
315  step = 1 << ((MAX_LOG2_NFFT-4) - 4);
316  n4 = 4;
317 
318  for (nbits=4; nbits<=s->nbits; nbits++){
319  n2 = 2*n4;
320  n34 = 3*n4;
321  num_transforms = (num_transforms >> 1) | 1;
322 
323  for (n=0; n<num_transforms; n++){
324  offset = fft_offsets_lut[n] << nbits;
325  tmpz = z + offset;
326 
327  tmp5 = tmpz[ n2].re + tmpz[n34].re;
328  tmp1 = tmpz[ n2].re - tmpz[n34].re;
329  tmp6 = tmpz[ n2].im + tmpz[n34].im;
330  tmp2 = tmpz[ n2].im - tmpz[n34].im;
331 
332  tmpz[ n2].re = tmpz[ 0].re - tmp5;
333  tmpz[ 0].re = tmpz[ 0].re + tmp5;
334  tmpz[ n2].im = tmpz[ 0].im - tmp6;
335  tmpz[ 0].im = tmpz[ 0].im + tmp6;
336  tmpz[n34].re = tmpz[n4].re - tmp2;
337  tmpz[ n4].re = tmpz[n4].re + tmp2;
338  tmpz[n34].im = tmpz[n4].im + tmp1;
339  tmpz[ n4].im = tmpz[n4].im - tmp1;
340 
341  w_re_ptr = w_tab_sr + step;
342  w_im_ptr = w_tab_sr + MAX_FFT_SIZE/(4*16) - step;
343 
344  for (i=1; i<n4; i++){
345  w_re = w_re_ptr[0];
346  w_im = w_im_ptr[0];
347  accu = (int64_t)w_re*tmpz[ n2+i].re;
348  accu += (int64_t)w_im*tmpz[ n2+i].im;
349  tmp1 = (int32_t)((accu + 0x40000000) >> 31);
350  accu = (int64_t)w_re*tmpz[ n2+i].im;
351  accu -= (int64_t)w_im*tmpz[ n2+i].re;
352  tmp2 = (int32_t)((accu + 0x40000000) >> 31);
353  accu = (int64_t)w_re*tmpz[n34+i].re;
354  accu -= (int64_t)w_im*tmpz[n34+i].im;
355  tmp3 = (int32_t)((accu + 0x40000000) >> 31);
356  accu = (int64_t)w_re*tmpz[n34+i].im;
357  accu += (int64_t)w_im*tmpz[n34+i].re;
358  tmp4 = (int32_t)((accu + 0x40000000) >> 31);
359 
360  tmp5 = tmp1 + tmp3;
361  tmp1 = tmp1 - tmp3;
362  tmp6 = tmp2 + tmp4;
363  tmp2 = tmp2 - tmp4;
364 
365  tmpz[ n2+i].re = tmpz[ i].re - tmp5;
366  tmpz[ i].re = tmpz[ i].re + tmp5;
367  tmpz[ n2+i].im = tmpz[ i].im - tmp6;
368  tmpz[ i].im = tmpz[ i].im + tmp6;
369  tmpz[n34+i].re = tmpz[n4+i].re - tmp2;
370  tmpz[ n4+i].re = tmpz[n4+i].re + tmp2;
371  tmpz[n34+i].im = tmpz[n4+i].im + tmp1;
372  tmpz[ n4+i].im = tmpz[n4+i].im - tmp1;
373 
374  w_re_ptr += step;
375  w_im_ptr -= step;
376  }
377  }
378  step >>= 1;
379  n4 <<= 1;
380  }
381 }
382 
383 #else /* CONFIG_FFT_FIXED_32 */
384 
385 #define BUTTERFLIES(a0,a1,a2,a3) {\
386  BF(t3, t5, t5, t1);\
387  BF(a2.re, a0.re, a0.re, t5);\
388  BF(a3.im, a1.im, a1.im, t3);\
389  BF(t4, t6, t2, t6);\
390  BF(a3.re, a1.re, a1.re, t4);\
391  BF(a2.im, a0.im, a0.im, t6);\
392 }
393 
394 // force loading all the inputs before storing any.
395 // this is slightly slower for small data, but avoids store->load aliasing
396 // for addresses separated by large powers of 2.
397 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
398  FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
399  BF(t3, t5, t5, t1);\
400  BF(a2.re, a0.re, r0, t5);\
401  BF(a3.im, a1.im, i1, t3);\
402  BF(t4, t6, t2, t6);\
403  BF(a3.re, a1.re, r1, t4);\
404  BF(a2.im, a0.im, i0, t6);\
405 }
406 
407 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
408  CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
409  CMUL(t5, t6, a3.re, a3.im, wre, wim);\
410  BUTTERFLIES(a0,a1,a2,a3)\
411 }
412 
413 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
414  t1 = a2.re;\
415  t2 = a2.im;\
416  t5 = a3.re;\
417  t6 = a3.im;\
418  BUTTERFLIES(a0,a1,a2,a3)\
419 }
420 
421 /* z[0...8n-1], w[1...2n-1] */
422 #define PASS(name)\
423 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
424 {\
425  FFTDouble t1, t2, t3, t4, t5, t6;\
426  int o1 = 2*n;\
427  int o2 = 4*n;\
428  int o3 = 6*n;\
429  const FFTSample *wim = wre+o1;\
430  n--;\
431 \
432  TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
433  TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
434  do {\
435  z += 2;\
436  wre += 2;\
437  wim -= 2;\
438  TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
439  TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
440  } while(--n);\
441 }
442 
443 PASS(pass)
444 #undef BUTTERFLIES
445 #define BUTTERFLIES BUTTERFLIES_BIG
446 PASS(pass_big)
447 
448 #define DECL_FFT(n,n2,n4)\
449 static void fft##n(FFTComplex *z)\
450 {\
451  fft##n2(z);\
452  fft##n4(z+n4*2);\
453  fft##n4(z+n4*3);\
454  pass(z,FFT_NAME(ff_cos_##n),n4/2);\
455 }
456 
457 static void fft4(FFTComplex *z)
458 {
459  FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
460 
461  BF(t3, t1, z[0].re, z[1].re);
462  BF(t8, t6, z[3].re, z[2].re);
463  BF(z[2].re, z[0].re, t1, t6);
464  BF(t4, t2, z[0].im, z[1].im);
465  BF(t7, t5, z[2].im, z[3].im);
466  BF(z[3].im, z[1].im, t4, t8);
467  BF(z[3].re, z[1].re, t3, t7);
468  BF(z[2].im, z[0].im, t2, t5);
469 }
470 
471 static void fft8(FFTComplex *z)
472 {
473  FFTDouble t1, t2, t3, t4, t5, t6;
474 
475  fft4(z);
476 
477  BF(t1, z[5].re, z[4].re, -z[5].re);
478  BF(t2, z[5].im, z[4].im, -z[5].im);
479  BF(t5, z[7].re, z[6].re, -z[7].re);
480  BF(t6, z[7].im, z[6].im, -z[7].im);
481 
482  BUTTERFLIES(z[0],z[2],z[4],z[6]);
483  TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
484 }
485 
486 #if !CONFIG_SMALL
487 static void fft16(FFTComplex *z)
488 {
489  FFTDouble t1, t2, t3, t4, t5, t6;
490  FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
491  FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
492 
493  fft8(z);
494  fft4(z+8);
495  fft4(z+12);
496 
497  TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
498  TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
499  TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
500  TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
501 }
502 #else
503 DECL_FFT(16,8,4)
504 #endif
505 DECL_FFT(32,16,8)
506 DECL_FFT(64,32,16)
507 DECL_FFT(128,64,32)
508 DECL_FFT(256,128,64)
509 DECL_FFT(512,256,128)
510 #if !CONFIG_SMALL
511 #define pass pass_big
512 #endif
513 DECL_FFT(1024,512,256)
514 DECL_FFT(2048,1024,512)
515 DECL_FFT(4096,2048,1024)
516 DECL_FFT(8192,4096,2048)
517 DECL_FFT(16384,8192,4096)
518 DECL_FFT(32768,16384,8192)
519 DECL_FFT(65536,32768,16384)
520 
521 static void (* const fft_dispatch[])(FFTComplex*) = {
522  fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
523  fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
524 };
525 
526 static void fft_calc_c(FFTContext *s, FFTComplex *z)
527 {
528  fft_dispatch[s->nbits-2](z);
529 }
530 #endif /* CONFIG_FFT_FIXED_32 */
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