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
split_radix_permutation(int i,int n,int inverse)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
ff_init_ff_cos_tabs(int index)88 av_cold void ff_init_ff_cos_tabs(int index)
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
is_second_half_of_fft32(int i,int n)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
fft_perm_avx(FFTContext * s)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
ff_fft_init(FFTContext * s,int nbits,int inverse)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 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 == 1)
174 if (ARCH_AARCH64) ff_fft_init_aarch64(s);
175 #endif
176 #if (ARCH_ARM == 1)
177 if (ARCH_ARM) ff_fft_init_arm(s);
178 #endif
179 #if (ARCH_PPC == 1)
180 if (ARCH_PPC) ff_fft_init_ppc(s);
181 #endif
182 #if (ARCH_X86 == 1)
183 if (ARCH_X86) ff_fft_init_x86(s);
184 #endif
185 if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc;
186 #if (HAVE_MIPSFPU == 1)
187 if (HAVE_MIPSFPU) ff_fft_init_mips(s);
188 #endif
189 #else
190 if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c;
191 #if (ARCH_ARM == 1)
192 if (ARCH_ARM) ff_fft_fixed_init_arm(s);
193 #endif
194 #endif
195 for(j=4; j<=nbits; j++) {
196 ff_init_ff_cos_tabs(j);
197 }
198 #endif /* FFT_FIXED_32 */
199
200
201 if (s->fft_permutation == FF_FFT_PERM_AVX) {
202 fft_perm_avx(s);
203 } else {
204 for(i=0; i<n; i++) {
205 j = i;
206 if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
207 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
208 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
209 }
210 }
211
212 return 0;
213 fail:
214 av_freep(&s->revtab);
215 av_freep(&s->tmp_buf);
216 return -1;
217 }
218
fft_permute_c(FFTContext * s,FFTComplex * z)219 static void fft_permute_c(FFTContext *s, FFTComplex *z)
220 {
221 int j, np;
222 const uint16_t *revtab = s->revtab;
223 np = 1 << s->nbits;
224 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
225 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
226 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
227 }
228
ff_fft_end(FFTContext * s)229 av_cold void ff_fft_end(FFTContext *s)
230 {
231 av_freep(&s->revtab);
232 av_freep(&s->tmp_buf);
233 }
234
235 #if FFT_FIXED_32
236
fft_calc_c(FFTContext * s,FFTComplex * z)237 static void fft_calc_c(FFTContext *s, FFTComplex *z) {
238
239 int nbits, i, n, num_transforms, offset, step;
240 int n4, n2, n34;
241 FFTSample tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;
242 FFTComplex *tmpz;
243 const int fft_size = (1 << s->nbits);
244 int64_t accu;
245
246 num_transforms = (0x2aab >> (16 - s->nbits)) | 1;
247
248 for (n=0; n<num_transforms; n++){
249 offset = ff_fft_offsets_lut[n] << 2;
250 tmpz = z + offset;
251
252 tmp1 = tmpz[0].re + tmpz[1].re;
253 tmp5 = tmpz[2].re + tmpz[3].re;
254 tmp2 = tmpz[0].im + tmpz[1].im;
255 tmp6 = tmpz[2].im + tmpz[3].im;
256 tmp3 = tmpz[0].re - tmpz[1].re;
257 tmp8 = tmpz[2].im - tmpz[3].im;
258 tmp4 = tmpz[0].im - tmpz[1].im;
259 tmp7 = tmpz[2].re - tmpz[3].re;
260
261 tmpz[0].re = tmp1 + tmp5;
262 tmpz[2].re = tmp1 - tmp5;
263 tmpz[0].im = tmp2 + tmp6;
264 tmpz[2].im = tmp2 - tmp6;
265 tmpz[1].re = tmp3 + tmp8;
266 tmpz[3].re = tmp3 - tmp8;
267 tmpz[1].im = tmp4 - tmp7;
268 tmpz[3].im = tmp4 + tmp7;
269 }
270
271 if (fft_size < 8)
272 return;
273
274 num_transforms = (num_transforms >> 1) | 1;
275
276 for (n=0; n<num_transforms; n++){
277 offset = ff_fft_offsets_lut[n] << 3;
278 tmpz = z + offset;
279
280 tmp1 = tmpz[4].re + tmpz[5].re;
281 tmp3 = tmpz[6].re + tmpz[7].re;
282 tmp2 = tmpz[4].im + tmpz[5].im;
283 tmp4 = tmpz[6].im + tmpz[7].im;
284 tmp5 = tmp1 + tmp3;
285 tmp7 = tmp1 - tmp3;
286 tmp6 = tmp2 + tmp4;
287 tmp8 = tmp2 - tmp4;
288
289 tmp1 = tmpz[4].re - tmpz[5].re;
290 tmp2 = tmpz[4].im - tmpz[5].im;
291 tmp3 = tmpz[6].re - tmpz[7].re;
292 tmp4 = tmpz[6].im - tmpz[7].im;
293
294 tmpz[4].re = tmpz[0].re - tmp5;
295 tmpz[0].re = tmpz[0].re + tmp5;
296 tmpz[4].im = tmpz[0].im - tmp6;
297 tmpz[0].im = tmpz[0].im + tmp6;
298 tmpz[6].re = tmpz[2].re - tmp8;
299 tmpz[2].re = tmpz[2].re + tmp8;
300 tmpz[6].im = tmpz[2].im + tmp7;
301 tmpz[2].im = tmpz[2].im - tmp7;
302
303 accu = (int64_t)Q31(M_SQRT1_2)*(tmp1 + tmp2);
304 tmp5 = (int32_t)((accu + 0x40000000) >> 31);
305 accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 - tmp4);
306 tmp7 = (int32_t)((accu + 0x40000000) >> 31);
307 accu = (int64_t)Q31(M_SQRT1_2)*(tmp2 - tmp1);
308 tmp6 = (int32_t)((accu + 0x40000000) >> 31);
309 accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 + tmp4);
310 tmp8 = (int32_t)((accu + 0x40000000) >> 31);
311 tmp1 = tmp5 + tmp7;
312 tmp3 = tmp5 - tmp7;
313 tmp2 = tmp6 + tmp8;
314 tmp4 = tmp6 - tmp8;
315
316 tmpz[5].re = tmpz[1].re - tmp1;
317 tmpz[1].re = tmpz[1].re + tmp1;
318 tmpz[5].im = tmpz[1].im - tmp2;
319 tmpz[1].im = tmpz[1].im + tmp2;
320 tmpz[7].re = tmpz[3].re - tmp4;
321 tmpz[3].re = tmpz[3].re + tmp4;
322 tmpz[7].im = tmpz[3].im + tmp3;
323 tmpz[3].im = tmpz[3].im - tmp3;
324 }
325
326 step = 1 << ((MAX_LOG2_NFFT-4) - 4);
327 n4 = 4;
328
329 for (nbits=4; nbits<=s->nbits; nbits++){
330 n2 = 2*n4;
331 n34 = 3*n4;
332 num_transforms = (num_transforms >> 1) | 1;
333
334 for (n=0; n<num_transforms; n++){
335 const FFTSample *w_re_ptr = ff_w_tab_sr + step;
336 const FFTSample *w_im_ptr = ff_w_tab_sr + MAX_FFT_SIZE/(4*16) - step;
337 offset = ff_fft_offsets_lut[n] << nbits;
338 tmpz = z + offset;
339
340 tmp5 = tmpz[ n2].re + tmpz[n34].re;
341 tmp1 = tmpz[ n2].re - tmpz[n34].re;
342 tmp6 = tmpz[ n2].im + tmpz[n34].im;
343 tmp2 = tmpz[ n2].im - tmpz[n34].im;
344
345 tmpz[ n2].re = tmpz[ 0].re - tmp5;
346 tmpz[ 0].re = tmpz[ 0].re + tmp5;
347 tmpz[ n2].im = tmpz[ 0].im - tmp6;
348 tmpz[ 0].im = tmpz[ 0].im + tmp6;
349 tmpz[n34].re = tmpz[n4].re - tmp2;
350 tmpz[ n4].re = tmpz[n4].re + tmp2;
351 tmpz[n34].im = tmpz[n4].im + tmp1;
352 tmpz[ n4].im = tmpz[n4].im - tmp1;
353
354 for (i=1; i<n4; i++){
355 FFTSample w_re = w_re_ptr[0];
356 FFTSample w_im = w_im_ptr[0];
357 accu = (int64_t)w_re*tmpz[ n2+i].re;
358 accu += (int64_t)w_im*tmpz[ n2+i].im;
359 tmp1 = (int32_t)((accu + 0x40000000) >> 31);
360 accu = (int64_t)w_re*tmpz[ n2+i].im;
361 accu -= (int64_t)w_im*tmpz[ n2+i].re;
362 tmp2 = (int32_t)((accu + 0x40000000) >> 31);
363 accu = (int64_t)w_re*tmpz[n34+i].re;
364 accu -= (int64_t)w_im*tmpz[n34+i].im;
365 tmp3 = (int32_t)((accu + 0x40000000) >> 31);
366 accu = (int64_t)w_re*tmpz[n34+i].im;
367 accu += (int64_t)w_im*tmpz[n34+i].re;
368 tmp4 = (int32_t)((accu + 0x40000000) >> 31);
369
370 tmp5 = tmp1 + tmp3;
371 tmp1 = tmp1 - tmp3;
372 tmp6 = tmp2 + tmp4;
373 tmp2 = tmp2 - tmp4;
374
375 tmpz[ n2+i].re = tmpz[ i].re - tmp5;
376 tmpz[ i].re = tmpz[ i].re + tmp5;
377 tmpz[ n2+i].im = tmpz[ i].im - tmp6;
378 tmpz[ i].im = tmpz[ i].im + tmp6;
379 tmpz[n34+i].re = tmpz[n4+i].re - tmp2;
380 tmpz[ n4+i].re = tmpz[n4+i].re + tmp2;
381 tmpz[n34+i].im = tmpz[n4+i].im + tmp1;
382 tmpz[ n4+i].im = tmpz[n4+i].im - tmp1;
383
384 w_re_ptr += step;
385 w_im_ptr -= step;
386 }
387 }
388 step >>= 1;
389 n4 <<= 1;
390 }
391 }
392
393 #else /* FFT_FIXED_32 */
394
395 #define BUTTERFLIES(a0,a1,a2,a3) {\
396 BF(t3, t5, t5, t1);\
397 BF(a2.re, a0.re, a0.re, t5);\
398 BF(a3.im, a1.im, a1.im, t3);\
399 BF(t4, t6, t2, t6);\
400 BF(a3.re, a1.re, a1.re, t4);\
401 BF(a2.im, a0.im, a0.im, t6);\
402 }
403
404 // force loading all the inputs before storing any.
405 // this is slightly slower for small data, but avoids store->load aliasing
406 // for addresses separated by large powers of 2.
407 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
408 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
409 BF(t3, t5, t5, t1);\
410 BF(a2.re, a0.re, r0, t5);\
411 BF(a3.im, a1.im, i1, t3);\
412 BF(t4, t6, t2, t6);\
413 BF(a3.re, a1.re, r1, t4);\
414 BF(a2.im, a0.im, i0, t6);\
415 }
416
417 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
418 CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
419 CMUL(t5, t6, a3.re, a3.im, wre, wim);\
420 BUTTERFLIES(a0,a1,a2,a3)\
421 }
422
423 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
424 t1 = a2.re;\
425 t2 = a2.im;\
426 t5 = a3.re;\
427 t6 = a3.im;\
428 BUTTERFLIES(a0,a1,a2,a3)\
429 }
430
431 /* z[0...8n-1], w[1...2n-1] */
432 #define PASS(name)\
433 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
434 {\
435 FFTDouble t1, t2, t3, t4, t5, t6;\
436 int o1 = 2*n;\
437 int o2 = 4*n;\
438 int o3 = 6*n;\
439 const FFTSample *wim = wre+o1;\
440 n--;\
441 \
442 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
443 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
444 do {\
445 z += 2;\
446 wre += 2;\
447 wim -= 2;\
448 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
449 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
450 } while(--n);\
451 }
452
453 PASS(pass)
454 #undef BUTTERFLIES
455 #define BUTTERFLIES BUTTERFLIES_BIG
PASS(pass_big)456 PASS(pass_big)
457
458 #define DECL_FFT(n,n2,n4)\
459 static void fft##n(FFTComplex *z)\
460 {\
461 fft##n2(z);\
462 fft##n4(z+n4*2);\
463 fft##n4(z+n4*3);\
464 pass(z,FFT_NAME(ff_cos_##n),n4/2);\
465 }
466
467 static void fft4(FFTComplex *z)
468 {
469 FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
470
471 BF(t3, t1, z[0].re, z[1].re);
472 BF(t8, t6, z[3].re, z[2].re);
473 BF(z[2].re, z[0].re, t1, t6);
474 BF(t4, t2, z[0].im, z[1].im);
475 BF(t7, t5, z[2].im, z[3].im);
476 BF(z[3].im, z[1].im, t4, t8);
477 BF(z[3].re, z[1].re, t3, t7);
478 BF(z[2].im, z[0].im, t2, t5);
479 }
480
fft8(FFTComplex * z)481 static void fft8(FFTComplex *z)
482 {
483 FFTDouble t1, t2, t3, t4, t5, t6;
484
485 fft4(z);
486
487 BF(t1, z[5].re, z[4].re, -z[5].re);
488 BF(t2, z[5].im, z[4].im, -z[5].im);
489 BF(t5, z[7].re, z[6].re, -z[7].re);
490 BF(t6, z[7].im, z[6].im, -z[7].im);
491
492 BUTTERFLIES(z[0],z[2],z[4],z[6]);
493 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
494 }
495
496 #if !CONFIG_SMALL
fft16(FFTComplex * z)497 static void fft16(FFTComplex *z)
498 {
499 FFTDouble t1, t2, t3, t4, t5, t6;
500 FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
501 FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
502
503 fft8(z);
504 fft4(z+8);
505 fft4(z+12);
506
507 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
508 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
509 TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
510 TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
511 }
512 #else
513 DECL_FFT(16,8,4)
514 #endif
515 DECL_FFT(32,16,8)
516 DECL_FFT(64,32,16)
517 DECL_FFT(128,64,32)
518 DECL_FFT(256,128,64)
519 DECL_FFT(512,256,128)
520 #if !CONFIG_SMALL
521 #define pass pass_big
522 #endif
523 DECL_FFT(1024,512,256)
524 DECL_FFT(2048,1024,512)
525 DECL_FFT(4096,2048,1024)
526 DECL_FFT(8192,4096,2048)
527 DECL_FFT(16384,8192,4096)
528 DECL_FFT(32768,16384,8192)
529 DECL_FFT(65536,32768,16384)
530
531 static void (* const fft_dispatch[])(FFTComplex*) = {
532 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
533 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
534 };
535
fft_calc_c(FFTContext * s,FFTComplex * z)536 static void fft_calc_c(FFTContext *s, FFTComplex *z)
537 {
538 fft_dispatch[s->nbits-2](z);
539 }
540 #endif /* FFT_FIXED_32 */
541