3 * Copyright (c) 2008 Loren Merritt
4 * Copyright (c) 2002 Fabrice Bellard
5 * Partly based on libdjbfft by D. J. Bernstein
7 * This file is part of FFmpeg.
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.
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.
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
26 * FFT/IFFT transforms.
31 #include "libavutil/mathematics.h"
32 #include "libavutil/thread.h"
34 #include "fft-internal.h"
37 #include "fft_table.h"
38 #else /* FFT_FIXED_32 */
40 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
41 #if !CONFIG_HARDCODED_TABLES
57 static av_cold void init_ff_cos_tabs(int index)
61 double freq = 2*M_PI/m;
62 FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
64 tab[i] = FIX15(cos(i*freq));
69 typedef struct CosTabsInitOnce {
74 #define INIT_FF_COS_TABS_FUNC(index, size) \
75 static av_cold void init_ff_cos_tabs_ ## size (void)\
77 init_ff_cos_tabs(index); \
80 INIT_FF_COS_TABS_FUNC(4, 16)
81 INIT_FF_COS_TABS_FUNC(5, 32)
82 INIT_FF_COS_TABS_FUNC(6, 64)
83 INIT_FF_COS_TABS_FUNC(7, 128)
84 INIT_FF_COS_TABS_FUNC(8, 256)
85 INIT_FF_COS_TABS_FUNC(9, 512)
86 INIT_FF_COS_TABS_FUNC(10, 1024)
87 INIT_FF_COS_TABS_FUNC(11, 2048)
88 INIT_FF_COS_TABS_FUNC(12, 4096)
89 INIT_FF_COS_TABS_FUNC(13, 8192)
90 INIT_FF_COS_TABS_FUNC(14, 16384)
91 INIT_FF_COS_TABS_FUNC(15, 32768)
92 INIT_FF_COS_TABS_FUNC(16, 65536)
93 INIT_FF_COS_TABS_FUNC(17, 131072)
95 static CosTabsInitOnce cos_tabs_init_once[] = {
100 { init_ff_cos_tabs_16, AV_ONCE_INIT },
101 { init_ff_cos_tabs_32, AV_ONCE_INIT },
102 { init_ff_cos_tabs_64, AV_ONCE_INIT },
103 { init_ff_cos_tabs_128, AV_ONCE_INIT },
104 { init_ff_cos_tabs_256, AV_ONCE_INIT },
105 { init_ff_cos_tabs_512, AV_ONCE_INIT },
106 { init_ff_cos_tabs_1024, AV_ONCE_INIT },
107 { init_ff_cos_tabs_2048, AV_ONCE_INIT },
108 { init_ff_cos_tabs_4096, AV_ONCE_INIT },
109 { init_ff_cos_tabs_8192, AV_ONCE_INIT },
110 { init_ff_cos_tabs_16384, AV_ONCE_INIT },
111 { init_ff_cos_tabs_32768, AV_ONCE_INIT },
112 { init_ff_cos_tabs_65536, AV_ONCE_INIT },
113 { init_ff_cos_tabs_131072, AV_ONCE_INIT },
116 av_cold void ff_init_ff_cos_tabs(int index)
118 ff_thread_once(&cos_tabs_init_once[index].control, cos_tabs_init_once[index].func);
121 COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
122 NULL, NULL, NULL, NULL,
126 FFT_NAME(ff_cos_128),
127 FFT_NAME(ff_cos_256),
128 FFT_NAME(ff_cos_512),
129 FFT_NAME(ff_cos_1024),
130 FFT_NAME(ff_cos_2048),
131 FFT_NAME(ff_cos_4096),
132 FFT_NAME(ff_cos_8192),
133 FFT_NAME(ff_cos_16384),
134 FFT_NAME(ff_cos_32768),
135 FFT_NAME(ff_cos_65536),
136 FFT_NAME(ff_cos_131072),
139 #endif /* FFT_FIXED_32 */
141 static void fft_permute_c(FFTContext *s, FFTComplex *z);
142 static void fft_calc_c(FFTContext *s, FFTComplex *z);
144 static int split_radix_permutation(int i, int n, int inverse)
147 if(n <= 2) return i&1;
149 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
151 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
152 else return split_radix_permutation(i, m, inverse)*4 - 1;
156 static const int avx_tab[] = {
157 0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
160 static int is_second_half_of_fft32(int i, int n)
165 return is_second_half_of_fft32(i, n/2);
167 return is_second_half_of_fft32(i - n/2, n/4);
169 return is_second_half_of_fft32(i - 3*n/4, n/4);
172 static av_cold void fft_perm_avx(FFTContext *s)
175 int n = 1 << s->nbits;
177 for (i = 0; i < n; i += 16) {
179 if (is_second_half_of_fft32(i, n)) {
180 for (k = 0; k < 16; k++)
181 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =
185 for (k = 0; k < 16; k++) {
187 j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);
188 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;
194 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
201 if (nbits < 2 || nbits > 17)
207 s->revtab = av_malloc(n * sizeof(uint16_t));
211 s->revtab32 = av_malloc(n * sizeof(uint32_t));
215 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
218 s->inverse = inverse;
219 s->fft_permutation = FF_FFT_PERM_DEFAULT;
221 s->fft_permute = fft_permute_c;
222 s->fft_calc = fft_calc_c;
224 s->imdct_calc = ff_imdct_calc_c;
225 s->imdct_half = ff_imdct_half_c;
226 s->mdct_calc = ff_mdct_calc_c;
231 #else /* FFT_FIXED_32 */
233 if (ARCH_AARCH64) ff_fft_init_aarch64(s);
234 if (ARCH_ARM) ff_fft_init_arm(s);
235 if (ARCH_PPC) ff_fft_init_ppc(s);
236 if (ARCH_X86) ff_fft_init_x86(s);
237 if (HAVE_MIPSFPU) ff_fft_init_mips(s);
239 for(j=4; j<=nbits; j++) {
240 ff_init_ff_cos_tabs(j);
242 #endif /* FFT_FIXED_32 */
245 if (ARCH_X86 && FFT_FLOAT && s->fft_permutation == FF_FFT_PERM_AVX) {
248 #define PROCESS_FFT_PERM_SWAP_LSBS(num) do {\
249 for(i = 0; i < n; i++) {\
252 j = (j & ~3) | ((j >> 1) & 1) | ((j << 1) & 2);\
253 k = -split_radix_permutation(i, n, s->inverse) & (n - 1);\
254 s->revtab##num[k] = j;\
258 #define PROCESS_FFT_PERM_DEFAULT(num) do {\
259 for(i = 0; i < n; i++) {\
262 k = -split_radix_permutation(i, n, s->inverse) & (n - 1);\
263 s->revtab##num[k] = j;\
267 #define SPLIT_RADIX_PERMUTATION(num) do { \
268 if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS) {\
269 PROCESS_FFT_PERM_SWAP_LSBS(num) \
271 PROCESS_FFT_PERM_DEFAULT(num) \
276 SPLIT_RADIX_PERMUTATION()
278 SPLIT_RADIX_PERMUTATION(32)
280 #undef PROCESS_FFT_PERM_DEFAULT
281 #undef PROCESS_FFT_PERM_SWAP_LSBS
282 #undef SPLIT_RADIX_PERMUTATION
287 av_freep(&s->revtab);
288 av_freep(&s->revtab32);
289 av_freep(&s->tmp_buf);
293 static void fft_permute_c(FFTContext *s, FFTComplex *z)
296 const uint16_t *revtab = s->revtab;
297 const uint32_t *revtab32 = s->revtab32;
299 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
301 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
303 for(j=0;j<np;j++) s->tmp_buf[revtab32[j]] = z[j];
305 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
308 av_cold void ff_fft_end(FFTContext *s)
310 av_freep(&s->revtab);
311 av_freep(&s->revtab32);
312 av_freep(&s->tmp_buf);
317 static void fft_calc_c(FFTContext *s, FFTComplex *z) {
319 int nbits, i, n, num_transforms, offset, step;
321 unsigned tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;
323 const int fft_size = (1 << s->nbits);
326 num_transforms = (0x2aab >> (16 - s->nbits)) | 1;
328 for (n=0; n<num_transforms; n++){
329 offset = ff_fft_offsets_lut[n] << 2;
332 tmp1 = tmpz[0].re + (unsigned)tmpz[1].re;
333 tmp5 = tmpz[2].re + (unsigned)tmpz[3].re;
334 tmp2 = tmpz[0].im + (unsigned)tmpz[1].im;
335 tmp6 = tmpz[2].im + (unsigned)tmpz[3].im;
336 tmp3 = tmpz[0].re - (unsigned)tmpz[1].re;
337 tmp8 = tmpz[2].im - (unsigned)tmpz[3].im;
338 tmp4 = tmpz[0].im - (unsigned)tmpz[1].im;
339 tmp7 = tmpz[2].re - (unsigned)tmpz[3].re;
341 tmpz[0].re = tmp1 + tmp5;
342 tmpz[2].re = tmp1 - tmp5;
343 tmpz[0].im = tmp2 + tmp6;
344 tmpz[2].im = tmp2 - tmp6;
345 tmpz[1].re = tmp3 + tmp8;
346 tmpz[3].re = tmp3 - tmp8;
347 tmpz[1].im = tmp4 - tmp7;
348 tmpz[3].im = tmp4 + tmp7;
354 num_transforms = (num_transforms >> 1) | 1;
356 for (n=0; n<num_transforms; n++){
357 offset = ff_fft_offsets_lut[n] << 3;
360 tmp1 = tmpz[4].re + (unsigned)tmpz[5].re;
361 tmp3 = tmpz[6].re + (unsigned)tmpz[7].re;
362 tmp2 = tmpz[4].im + (unsigned)tmpz[5].im;
363 tmp4 = tmpz[6].im + (unsigned)tmpz[7].im;
369 tmp1 = tmpz[4].re - (unsigned)tmpz[5].re;
370 tmp2 = tmpz[4].im - (unsigned)tmpz[5].im;
371 tmp3 = tmpz[6].re - (unsigned)tmpz[7].re;
372 tmp4 = tmpz[6].im - (unsigned)tmpz[7].im;
374 tmpz[4].re = tmpz[0].re - tmp5;
375 tmpz[0].re = tmpz[0].re + tmp5;
376 tmpz[4].im = tmpz[0].im - tmp6;
377 tmpz[0].im = tmpz[0].im + tmp6;
378 tmpz[6].re = tmpz[2].re - tmp8;
379 tmpz[2].re = tmpz[2].re + tmp8;
380 tmpz[6].im = tmpz[2].im + tmp7;
381 tmpz[2].im = tmpz[2].im - tmp7;
383 accu = (int64_t)Q31(M_SQRT1_2)*(int)(tmp1 + tmp2);
384 tmp5 = (int32_t)((accu + 0x40000000) >> 31);
385 accu = (int64_t)Q31(M_SQRT1_2)*(int)(tmp3 - tmp4);
386 tmp7 = (int32_t)((accu + 0x40000000) >> 31);
387 accu = (int64_t)Q31(M_SQRT1_2)*(int)(tmp2 - tmp1);
388 tmp6 = (int32_t)((accu + 0x40000000) >> 31);
389 accu = (int64_t)Q31(M_SQRT1_2)*(int)(tmp3 + tmp4);
390 tmp8 = (int32_t)((accu + 0x40000000) >> 31);
396 tmpz[5].re = tmpz[1].re - tmp1;
397 tmpz[1].re = tmpz[1].re + tmp1;
398 tmpz[5].im = tmpz[1].im - tmp2;
399 tmpz[1].im = tmpz[1].im + tmp2;
400 tmpz[7].re = tmpz[3].re - tmp4;
401 tmpz[3].re = tmpz[3].re + tmp4;
402 tmpz[7].im = tmpz[3].im + tmp3;
403 tmpz[3].im = tmpz[3].im - tmp3;
406 step = 1 << ((MAX_LOG2_NFFT-4) - 4);
409 for (nbits=4; nbits<=s->nbits; nbits++){
412 num_transforms = (num_transforms >> 1) | 1;
414 for (n=0; n<num_transforms; n++){
415 const FFTSample *w_re_ptr = ff_w_tab_sr + step;
416 const FFTSample *w_im_ptr = ff_w_tab_sr + MAX_FFT_SIZE/(4*16) - step;
417 offset = ff_fft_offsets_lut[n] << nbits;
420 tmp5 = tmpz[ n2].re + (unsigned)tmpz[n34].re;
421 tmp1 = tmpz[ n2].re - (unsigned)tmpz[n34].re;
422 tmp6 = tmpz[ n2].im + (unsigned)tmpz[n34].im;
423 tmp2 = tmpz[ n2].im - (unsigned)tmpz[n34].im;
425 tmpz[ n2].re = tmpz[ 0].re - tmp5;
426 tmpz[ 0].re = tmpz[ 0].re + tmp5;
427 tmpz[ n2].im = tmpz[ 0].im - tmp6;
428 tmpz[ 0].im = tmpz[ 0].im + tmp6;
429 tmpz[n34].re = tmpz[n4].re - tmp2;
430 tmpz[ n4].re = tmpz[n4].re + tmp2;
431 tmpz[n34].im = tmpz[n4].im + tmp1;
432 tmpz[ n4].im = tmpz[n4].im - tmp1;
434 for (i=1; i<n4; i++){
435 FFTSample w_re = w_re_ptr[0];
436 FFTSample w_im = w_im_ptr[0];
437 accu = (int64_t)w_re*tmpz[ n2+i].re;
438 accu += (int64_t)w_im*tmpz[ n2+i].im;
439 tmp1 = (int32_t)((accu + 0x40000000) >> 31);
440 accu = (int64_t)w_re*tmpz[ n2+i].im;
441 accu -= (int64_t)w_im*tmpz[ n2+i].re;
442 tmp2 = (int32_t)((accu + 0x40000000) >> 31);
443 accu = (int64_t)w_re*tmpz[n34+i].re;
444 accu -= (int64_t)w_im*tmpz[n34+i].im;
445 tmp3 = (int32_t)((accu + 0x40000000) >> 31);
446 accu = (int64_t)w_re*tmpz[n34+i].im;
447 accu += (int64_t)w_im*tmpz[n34+i].re;
448 tmp4 = (int32_t)((accu + 0x40000000) >> 31);
455 tmpz[ n2+i].re = tmpz[ i].re - tmp5;
456 tmpz[ i].re = tmpz[ i].re + tmp5;
457 tmpz[ n2+i].im = tmpz[ i].im - tmp6;
458 tmpz[ i].im = tmpz[ i].im + tmp6;
459 tmpz[n34+i].re = tmpz[n4+i].re - tmp2;
460 tmpz[ n4+i].re = tmpz[n4+i].re + tmp2;
461 tmpz[n34+i].im = tmpz[n4+i].im + tmp1;
462 tmpz[ n4+i].im = tmpz[n4+i].im - tmp1;
473 #else /* FFT_FIXED_32 */
475 #define BUTTERFLIES(a0,a1,a2,a3) {\
477 BF(a2.re, a0.re, a0.re, t5);\
478 BF(a3.im, a1.im, a1.im, t3);\
480 BF(a3.re, a1.re, a1.re, t4);\
481 BF(a2.im, a0.im, a0.im, t6);\
484 // force loading all the inputs before storing any.
485 // this is slightly slower for small data, but avoids store->load aliasing
486 // for addresses separated by large powers of 2.
487 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
488 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
490 BF(a2.re, a0.re, r0, t5);\
491 BF(a3.im, a1.im, i1, t3);\
493 BF(a3.re, a1.re, r1, t4);\
494 BF(a2.im, a0.im, i0, t6);\
497 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
498 CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
499 CMUL(t5, t6, a3.re, a3.im, wre, wim);\
500 BUTTERFLIES(a0,a1,a2,a3)\
503 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
508 BUTTERFLIES(a0,a1,a2,a3)\
511 /* z[0...8n-1], w[1...2n-1] */
513 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
515 FFTDouble t1, t2, t3, t4, t5, t6;\
519 const FFTSample *wim = wre+o1;\
522 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
523 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
528 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
529 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
536 #define BUTTERFLIES BUTTERFLIES_BIG
540 #define DECL_FFT(n,n2,n4)\
541 static void fft##n(FFTComplex *z)\
546 pass(z,FFT_NAME(ff_cos_##n),n4/2);\
549 static void fft4(FFTComplex *z)
551 FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
553 BF(t3, t1, z[0].re, z[1].re);
554 BF(t8, t6, z[3].re, z[2].re);
555 BF(z[2].re, z[0].re, t1, t6);
556 BF(t4, t2, z[0].im, z[1].im);
557 BF(t7, t5, z[2].im, z[3].im);
558 BF(z[3].im, z[1].im, t4, t8);
559 BF(z[3].re, z[1].re, t3, t7);
560 BF(z[2].im, z[0].im, t2, t5);
563 static void fft8(FFTComplex *z)
565 FFTDouble t1, t2, t3, t4, t5, t6;
569 BF(t1, z[5].re, z[4].re, -z[5].re);
570 BF(t2, z[5].im, z[4].im, -z[5].im);
571 BF(t5, z[7].re, z[6].re, -z[7].re);
572 BF(t6, z[7].im, z[6].im, -z[7].im);
574 BUTTERFLIES(z[0],z[2],z[4],z[6]);
575 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
579 static void fft16(FFTComplex *z)
581 FFTDouble t1, t2, t3, t4, t5, t6;
582 FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
583 FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
589 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
590 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
591 TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
592 TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
601 DECL_FFT(512,256,128)
603 #define pass pass_big
605 DECL_FFT(1024,512,256)
606 DECL_FFT(2048,1024,512)
607 DECL_FFT(4096,2048,1024)
608 DECL_FFT(8192,4096,2048)
609 DECL_FFT(16384,8192,4096)
610 DECL_FFT(32768,16384,8192)
611 DECL_FFT(65536,32768,16384)
612 DECL_FFT(131072,65536,32768)
614 static void (* const fft_dispatch[])(FFTComplex*) = {
615 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
616 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, fft131072
619 static void fft_calc_c(FFTContext *s, FFTComplex *z)
621 fft_dispatch[s->nbits-2](z);
623 #endif /* FFT_FIXED_32 */