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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
41COSTABLE(16);
42COSTABLE(32);
43COSTABLE(64);
44COSTABLE(128);
45COSTABLE(256);
46COSTABLE(512);
47COSTABLE(1024);
48COSTABLE(2048);
49COSTABLE(4096);
50COSTABLE(8192);
51COSTABLE(16384);
52COSTABLE(32768);
53COSTABLE(65536);
54COSTABLE(131072);
55#endif
56COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
57 NULL, NULL, NULL, NULL,
58 FFT_NAME(ff_cos_16),
59 FFT_NAME(ff_cos_32),
60 FFT_NAME(ff_cos_64),
61 FFT_NAME(ff_cos_128),
62 FFT_NAME(ff_cos_256),
63 FFT_NAME(ff_cos_512),
64 FFT_NAME(ff_cos_1024),
65 FFT_NAME(ff_cos_2048),
66 FFT_NAME(ff_cos_4096),
67 FFT_NAME(ff_cos_8192),
68 FFT_NAME(ff_cos_16384),
69 FFT_NAME(ff_cos_32768),
70 FFT_NAME(ff_cos_65536),
71 FFT_NAME(ff_cos_131072),
72};
73
74#endif /* FFT_FIXED_32 */
75
76static void fft_permute_c(FFTContext *s, FFTComplex *z);
77static void fft_calc_c(FFTContext *s, FFTComplex *z);
78
79static int split_radix_permutation(int i, int n, int inverse)
80{
81 int m;
82 if(n <= 2) return i&1;
83 m = n >> 1;
84 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
85 m >>= 1;
86 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
87 else return split_radix_permutation(i, m, inverse)*4 - 1;
88}
89
90av_cold void ff_init_ff_cos_tabs(int index)
91{
92#if (!CONFIG_HARDCODED_TABLES) && (!FFT_FIXED_32)
93 int i;
94 int m = 1<<index;
95 double freq = 2*M_PI/m;
96 FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
97 for(i=0; i<=m/4; i++)
98 tab[i] = FIX15(cos(i*freq));
99 for(i=1; i<m/4; i++)
100 tab[m/2-i] = tab[i];
101#endif
102}
103
104static const int avx_tab[] = {
105 0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
106};
107
108static int is_second_half_of_fft32(int i, int n)
109{
110 if (n <= 32)
111 return i >= 16;
112 else if (i < n/2)
113 return is_second_half_of_fft32(i, n/2);
114 else if (i < 3*n/4)
115 return is_second_half_of_fft32(i - n/2, n/4);
116 else
117 return is_second_half_of_fft32(i - 3*n/4, n/4);
118}
119
120static av_cold void fft_perm_avx(FFTContext *s)
121{
122 int i;
123 int n = 1 << s->nbits;
124
125 for (i = 0; i < n; i += 16) {
126 int k;
127 if (is_second_half_of_fft32(i, n)) {
128 for (k = 0; k < 16; k++)
129 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =
130 i + avx_tab[k];
131
132 } else {
133 for (k = 0; k < 16; k++) {
134 int j = i + k;
135 j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);
136 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;
137 }
138 }
139 }
140}
141
142av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
143{
144 int i, j, n;
145
146 s->revtab = NULL;
147 s->revtab32 = NULL;
148
149 if (nbits < 2 || nbits > 17)
150 goto fail;
151 s->nbits = nbits;
152 n = 1 << nbits;
153
154 if (nbits <= 16) {
155 s->revtab = av_malloc(n * sizeof(uint16_t));
156 if (!s->revtab)
157 goto fail;
158 } else {
159 s->revtab32 = av_malloc(n * sizeof(uint32_t));
160 if (!s->revtab32)
161 goto fail;
162 }
163 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
164 if (!s->tmp_buf)
165 goto fail;
166 s->inverse = inverse;
167 s->fft_permutation = FF_FFT_PERM_DEFAULT;
168
169 s->fft_permute = fft_permute_c;
170 s->fft_calc = fft_calc_c;
171#if CONFIG_MDCT
172 s->imdct_calc = ff_imdct_calc_c;
173 s->imdct_half = ff_imdct_half_c;
174 s->mdct_calc = ff_mdct_calc_c;
175#endif
176
177#if FFT_FIXED_32
178 {
179 int n=0;
180 ff_fft_lut_init(ff_fft_offsets_lut, 0, 1 << 17, &n);
181 }
182#else /* FFT_FIXED_32 */
183#if FFT_FLOAT
184 if (ARCH_AARCH64) ff_fft_init_aarch64(s);
185 if (ARCH_ARM) ff_fft_init_arm(s);
186 if (ARCH_PPC) ff_fft_init_ppc(s);
187 if (ARCH_X86) ff_fft_init_x86(s);
188 if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc;
189 if (HAVE_MIPSFPU) ff_fft_init_mips(s);
190#else
191 if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c;
192 if (ARCH_ARM) ff_fft_fixed_init_arm(s);
193#endif
194 for(j=4; j<=nbits; j++) {
195 ff_init_ff_cos_tabs(j);
196 }
197#endif /* FFT_FIXED_32 */
198
199
200 if (s->fft_permutation == FF_FFT_PERM_AVX) {
201 fft_perm_avx(s);
202 } else {
203 for(i=0; i<n; i++) {
204 int k;
205 j = i;
206 if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
207 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
208 k = -split_radix_permutation(i, n, s->inverse) & (n-1);
209 if (s->revtab)
210 s->revtab[k] = j;
211 if (s->revtab32)
212 s->revtab32[k] = j;
213 }
214 }
215
216 return 0;
217 fail:
218 av_freep(&s->revtab);
219 av_freep(&s->revtab32);
220 av_freep(&s->tmp_buf);
221 return -1;
222}
223
224static void fft_permute_c(FFTContext *s, FFTComplex *z)
225{
226 int j, np;
227 const uint16_t *revtab = s->revtab;
228 const uint32_t *revtab32 = s->revtab32;
229 np = 1 << s->nbits;
230 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
231 if (revtab) {
232 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
233 } else
234 for(j=0;j<np;j++) s->tmp_buf[revtab32[j]] = z[j];
235
236 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
237}
238
239av_cold void ff_fft_end(FFTContext *s)
240{
241 av_freep(&s->revtab);
242 av_freep(&s->revtab32);
243 av_freep(&s->tmp_buf);
244}
245
246#if FFT_FIXED_32
247
248static void fft_calc_c(FFTContext *s, FFTComplex *z) {
249
250 int nbits, i, n, num_transforms, offset, step;
251 int n4, n2, n34;
252 FFTSample tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;
253 FFTComplex *tmpz;
254 const int fft_size = (1 << s->nbits);
255 int64_t accu;
256
257 num_transforms = (0x2aab >> (16 - s->nbits)) | 1;
258
259 for (n=0; n<num_transforms; n++){
260 offset = ff_fft_offsets_lut[n] << 2;
261 tmpz = z + offset;
262
263 tmp1 = tmpz[0].re + tmpz[1].re;
264 tmp5 = tmpz[2].re + tmpz[3].re;
265 tmp2 = tmpz[0].im + tmpz[1].im;
266 tmp6 = tmpz[2].im + tmpz[3].im;
267 tmp3 = tmpz[0].re - tmpz[1].re;
268 tmp8 = tmpz[2].im - tmpz[3].im;
269 tmp4 = tmpz[0].im - tmpz[1].im;
270 tmp7 = tmpz[2].re - tmpz[3].re;
271
272 tmpz[0].re = tmp1 + tmp5;
273 tmpz[2].re = tmp1 - tmp5;
274 tmpz[0].im = tmp2 + tmp6;
275 tmpz[2].im = tmp2 - tmp6;
276 tmpz[1].re = tmp3 + tmp8;
277 tmpz[3].re = tmp3 - tmp8;
278 tmpz[1].im = tmp4 - tmp7;
279 tmpz[3].im = tmp4 + tmp7;
280 }
281
282 if (fft_size < 8)
283 return;
284
285 num_transforms = (num_transforms >> 1) | 1;
286
287 for (n=0; n<num_transforms; n++){
288 offset = ff_fft_offsets_lut[n] << 3;
289 tmpz = z + offset;
290
291 tmp1 = tmpz[4].re + tmpz[5].re;
292 tmp3 = tmpz[6].re + tmpz[7].re;
293 tmp2 = tmpz[4].im + tmpz[5].im;
294 tmp4 = tmpz[6].im + tmpz[7].im;
295 tmp5 = tmp1 + tmp3;
296 tmp7 = tmp1 - tmp3;
297 tmp6 = tmp2 + tmp4;
298 tmp8 = tmp2 - tmp4;
299
300 tmp1 = tmpz[4].re - tmpz[5].re;
301 tmp2 = tmpz[4].im - tmpz[5].im;
302 tmp3 = tmpz[6].re - tmpz[7].re;
303 tmp4 = tmpz[6].im - tmpz[7].im;
304
305 tmpz[4].re = tmpz[0].re - tmp5;
306 tmpz[0].re = tmpz[0].re + tmp5;
307 tmpz[4].im = tmpz[0].im - tmp6;
308 tmpz[0].im = tmpz[0].im + tmp6;
309 tmpz[6].re = tmpz[2].re - tmp8;
310 tmpz[2].re = tmpz[2].re + tmp8;
311 tmpz[6].im = tmpz[2].im + tmp7;
312 tmpz[2].im = tmpz[2].im - tmp7;
313
314 accu = (int64_t)Q31(M_SQRT1_2)*(tmp1 + tmp2);
315 tmp5 = (int32_t)((accu + 0x40000000) >> 31);
316 accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 - tmp4);
317 tmp7 = (int32_t)((accu + 0x40000000) >> 31);
318 accu = (int64_t)Q31(M_SQRT1_2)*(tmp2 - tmp1);
319 tmp6 = (int32_t)((accu + 0x40000000) >> 31);
320 accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 + tmp4);
321 tmp8 = (int32_t)((accu + 0x40000000) >> 31);
322 tmp1 = tmp5 + tmp7;
323 tmp3 = tmp5 - tmp7;
324 tmp2 = tmp6 + tmp8;
325 tmp4 = tmp6 - tmp8;
326
327 tmpz[5].re = tmpz[1].re - tmp1;
328 tmpz[1].re = tmpz[1].re + tmp1;
329 tmpz[5].im = tmpz[1].im - tmp2;
330 tmpz[1].im = tmpz[1].im + tmp2;
331 tmpz[7].re = tmpz[3].re - tmp4;
332 tmpz[3].re = tmpz[3].re + tmp4;
333 tmpz[7].im = tmpz[3].im + tmp3;
334 tmpz[3].im = tmpz[3].im - tmp3;
335 }
336
337 step = 1 << ((MAX_LOG2_NFFT-4) - 4);
338 n4 = 4;
339
340 for (nbits=4; nbits<=s->nbits; nbits++){
341 n2 = 2*n4;
342 n34 = 3*n4;
343 num_transforms = (num_transforms >> 1) | 1;
344
345 for (n=0; n<num_transforms; n++){
346 const FFTSample *w_re_ptr = ff_w_tab_sr + step;
347 const FFTSample *w_im_ptr = ff_w_tab_sr + MAX_FFT_SIZE/(4*16) - step;
348 offset = ff_fft_offsets_lut[n] << nbits;
349 tmpz = z + offset;
350
351 tmp5 = tmpz[ n2].re + tmpz[n34].re;
352 tmp1 = tmpz[ n2].re - tmpz[n34].re;
353 tmp6 = tmpz[ n2].im + tmpz[n34].im;
354 tmp2 = tmpz[ n2].im - tmpz[n34].im;
355
356 tmpz[ n2].re = tmpz[ 0].re - tmp5;
357 tmpz[ 0].re = tmpz[ 0].re + tmp5;
358 tmpz[ n2].im = tmpz[ 0].im - tmp6;
359 tmpz[ 0].im = tmpz[ 0].im + tmp6;
360 tmpz[n34].re = tmpz[n4].re - tmp2;
361 tmpz[ n4].re = tmpz[n4].re + tmp2;
362 tmpz[n34].im = tmpz[n4].im + tmp1;
363 tmpz[ n4].im = tmpz[n4].im - tmp1;
364
365 for (i=1; i<n4; i++){
366 FFTSample w_re = w_re_ptr[0];
367 FFTSample w_im = w_im_ptr[0];
368 accu = (int64_t)w_re*tmpz[ n2+i].re;
369 accu += (int64_t)w_im*tmpz[ n2+i].im;
370 tmp1 = (int32_t)((accu + 0x40000000) >> 31);
371 accu = (int64_t)w_re*tmpz[ n2+i].im;
372 accu -= (int64_t)w_im*tmpz[ n2+i].re;
373 tmp2 = (int32_t)((accu + 0x40000000) >> 31);
374 accu = (int64_t)w_re*tmpz[n34+i].re;
375 accu -= (int64_t)w_im*tmpz[n34+i].im;
376 tmp3 = (int32_t)((accu + 0x40000000) >> 31);
377 accu = (int64_t)w_re*tmpz[n34+i].im;
378 accu += (int64_t)w_im*tmpz[n34+i].re;
379 tmp4 = (int32_t)((accu + 0x40000000) >> 31);
380
381 tmp5 = tmp1 + tmp3;
382 tmp1 = tmp1 - tmp3;
383 tmp6 = tmp2 + tmp4;
384 tmp2 = tmp2 - tmp4;
385
386 tmpz[ n2+i].re = tmpz[ i].re - tmp5;
387 tmpz[ i].re = tmpz[ i].re + tmp5;
388 tmpz[ n2+i].im = tmpz[ i].im - tmp6;
389 tmpz[ i].im = tmpz[ i].im + tmp6;
390 tmpz[n34+i].re = tmpz[n4+i].re - tmp2;
391 tmpz[ n4+i].re = tmpz[n4+i].re + tmp2;
392 tmpz[n34+i].im = tmpz[n4+i].im + tmp1;
393 tmpz[ n4+i].im = tmpz[n4+i].im - tmp1;
394
395 w_re_ptr += step;
396 w_im_ptr -= step;
397 }
398 }
399 step >>= 1;
400 n4 <<= 1;
401 }
402}
403
404#else /* FFT_FIXED_32 */
405
406#define BUTTERFLIES(a0,a1,a2,a3) {\
407 BF(t3, t5, t5, t1);\
408 BF(a2.re, a0.re, a0.re, t5);\
409 BF(a3.im, a1.im, a1.im, t3);\
410 BF(t4, t6, t2, t6);\
411 BF(a3.re, a1.re, a1.re, t4);\
412 BF(a2.im, a0.im, a0.im, t6);\
413}
414
415// force loading all the inputs before storing any.
416// this is slightly slower for small data, but avoids store->load aliasing
417// for addresses separated by large powers of 2.
418#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
419 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
420 BF(t3, t5, t5, t1);\
421 BF(a2.re, a0.re, r0, t5);\
422 BF(a3.im, a1.im, i1, t3);\
423 BF(t4, t6, t2, t6);\
424 BF(a3.re, a1.re, r1, t4);\
425 BF(a2.im, a0.im, i0, t6);\
426}
427
428#define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
429 CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
430 CMUL(t5, t6, a3.re, a3.im, wre, wim);\
431 BUTTERFLIES(a0,a1,a2,a3)\
432}
433
434#define TRANSFORM_ZERO(a0,a1,a2,a3) {\
435 t1 = a2.re;\
436 t2 = a2.im;\
437 t5 = a3.re;\
438 t6 = a3.im;\
439 BUTTERFLIES(a0,a1,a2,a3)\
440}
441
442/* z[0...8n-1], w[1...2n-1] */
443#define PASS(name)\
444static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
445{\
446 FFTDouble t1, t2, t3, t4, t5, t6;\
447 int o1 = 2*n;\
448 int o2 = 4*n;\
449 int o3 = 6*n;\
450 const FFTSample *wim = wre+o1;\
451 n--;\
452\
453 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
454 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
455 do {\
456 z += 2;\
457 wre += 2;\
458 wim -= 2;\
459 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
460 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
461 } while(--n);\
462}
463
464PASS(pass)
465#undef BUTTERFLIES
466#define BUTTERFLIES BUTTERFLIES_BIG
467PASS(pass_big)
468
469#define DECL_FFT(n,n2,n4)\
470static void fft##n(FFTComplex *z)\
471{\
472 fft##n2(z);\
473 fft##n4(z+n4*2);\
474 fft##n4(z+n4*3);\
475 pass(z,FFT_NAME(ff_cos_##n),n4/2);\
476}
477
478static void fft4(FFTComplex *z)
479{
480 FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
481
482 BF(t3, t1, z[0].re, z[1].re);
483 BF(t8, t6, z[3].re, z[2].re);
484 BF(z[2].re, z[0].re, t1, t6);
485 BF(t4, t2, z[0].im, z[1].im);
486 BF(t7, t5, z[2].im, z[3].im);
487 BF(z[3].im, z[1].im, t4, t8);
488 BF(z[3].re, z[1].re, t3, t7);
489 BF(z[2].im, z[0].im, t2, t5);
490}
491
492static void fft8(FFTComplex *z)
493{
494 FFTDouble t1, t2, t3, t4, t5, t6;
495
496 fft4(z);
497
498 BF(t1, z[5].re, z[4].re, -z[5].re);
499 BF(t2, z[5].im, z[4].im, -z[5].im);
500 BF(t5, z[7].re, z[6].re, -z[7].re);
501 BF(t6, z[7].im, z[6].im, -z[7].im);
502
503 BUTTERFLIES(z[0],z[2],z[4],z[6]);
504 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
505}
506
507#if !CONFIG_SMALL
508static void fft16(FFTComplex *z)
509{
510 FFTDouble t1, t2, t3, t4, t5, t6;
511 FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
512 FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
513
514 fft8(z);
515 fft4(z+8);
516 fft4(z+12);
517
518 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
519 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
520 TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
521 TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
522}
523#else
524DECL_FFT(16,8,4)
525#endif
526DECL_FFT(32,16,8)
527DECL_FFT(64,32,16)
528DECL_FFT(128,64,32)
529DECL_FFT(256,128,64)
530DECL_FFT(512,256,128)
531#if !CONFIG_SMALL
532#define pass pass_big
533#endif
534DECL_FFT(1024,512,256)
535DECL_FFT(2048,1024,512)
536DECL_FFT(4096,2048,1024)
537DECL_FFT(8192,4096,2048)
538DECL_FFT(16384,8192,4096)
539DECL_FFT(32768,16384,8192)
540DECL_FFT(65536,32768,16384)
541DECL_FFT(131072,65536,32768)
542
543static void (* const fft_dispatch[])(FFTComplex*) = {
544 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
545 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, fft131072
546};
547
548static void fft_calc_c(FFTContext *s, FFTComplex *z)
549{
550 fft_dispatch[s->nbits-2](z);
551}
552#endif /* FFT_FIXED_32 */
553
generated by cgit at 2024-05-17 06:30:31 (GMT)