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"
33 #include "fft-internal.h"
36 #include "fft_table.h"
37 #else /* FFT_FIXED_32 */
39 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
40 #if !CONFIG_HARDCODED_TABLES
56 COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
57 NULL, NULL, NULL, NULL,
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),
74 #endif /* FFT_FIXED_32 */
76 static void fft_permute_c(FFTContext *s, FFTComplex *z);
77 static void fft_calc_c(FFTContext *s, FFTComplex *z);
79 static int split_radix_permutation(int i, int n, int inverse)
82 if(n <= 2) return i&1;
84 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
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;
90 av_cold void ff_init_ff_cos_tabs(int index)
92 #if (!CONFIG_HARDCODED_TABLES) && (!FFT_FIXED_32)
95 double freq = 2*M_PI/m;
96 FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
98 tab[i] = FIX15(cos(i*freq));
104 static const int avx_tab[] = {
105 0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
108 static int is_second_half_of_fft32(int i, int n)
113 return is_second_half_of_fft32(i, n/2);
115 return is_second_half_of_fft32(i - n/2, n/4);
117 return is_second_half_of_fft32(i - 3*n/4, n/4);
120 static av_cold void fft_perm_avx(FFTContext *s)
123 int n = 1 << s->nbits;
125 for (i = 0; i < n; i += 16) {
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)] =
133 for (k = 0; k < 16; 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;
142 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
146 if (nbits < 2 || nbits > 17)
151 s->revtab = av_malloc(n * sizeof(uint16_t));
154 s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
157 s->inverse = inverse;
158 s->fft_permutation = FF_FFT_PERM_DEFAULT;
160 s->fft_permute = fft_permute_c;
161 s->fft_calc = fft_calc_c;
163 s->imdct_calc = ff_imdct_calc_c;
164 s->imdct_half = ff_imdct_half_c;
165 s->mdct_calc = ff_mdct_calc_c;
171 ff_fft_lut_init(ff_fft_offsets_lut, 0, 1 << 17, &n);
173 #else /* FFT_FIXED_32 */
175 if (ARCH_AARCH64) ff_fft_init_aarch64(s);
176 if (ARCH_ARM) ff_fft_init_arm(s);
177 if (ARCH_PPC) ff_fft_init_ppc(s);
178 if (ARCH_X86) ff_fft_init_x86(s);
179 if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc;
180 if (HAVE_MIPSFPU) ff_fft_init_mips(s);
182 if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c;
183 if (ARCH_ARM) ff_fft_fixed_init_arm(s);
185 for(j=4; j<=nbits; j++) {
186 ff_init_ff_cos_tabs(j);
188 #endif /* FFT_FIXED_32 */
191 if (s->fft_permutation == FF_FFT_PERM_AVX) {
196 if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
197 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
198 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
204 av_freep(&s->revtab);
205 av_freep(&s->tmp_buf);
209 static void fft_permute_c(FFTContext *s, FFTComplex *z)
212 const uint16_t *revtab = s->revtab;
214 /* TODO: handle split-radix permute in a more optimal way, probably in-place */
215 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
216 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
219 av_cold void ff_fft_end(FFTContext *s)
221 av_freep(&s->revtab);
222 av_freep(&s->tmp_buf);
227 static void fft_calc_c(FFTContext *s, FFTComplex *z) {
229 int nbits, i, n, num_transforms, offset, step;
231 FFTSample tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;
233 const int fft_size = (1 << s->nbits);
236 num_transforms = (0x2aab >> (16 - s->nbits)) | 1;
238 for (n=0; n<num_transforms; n++){
239 offset = ff_fft_offsets_lut[n] << 2;
242 tmp1 = tmpz[0].re + tmpz[1].re;
243 tmp5 = tmpz[2].re + tmpz[3].re;
244 tmp2 = tmpz[0].im + tmpz[1].im;
245 tmp6 = tmpz[2].im + tmpz[3].im;
246 tmp3 = tmpz[0].re - tmpz[1].re;
247 tmp8 = tmpz[2].im - tmpz[3].im;
248 tmp4 = tmpz[0].im - tmpz[1].im;
249 tmp7 = tmpz[2].re - tmpz[3].re;
251 tmpz[0].re = tmp1 + tmp5;
252 tmpz[2].re = tmp1 - tmp5;
253 tmpz[0].im = tmp2 + tmp6;
254 tmpz[2].im = tmp2 - tmp6;
255 tmpz[1].re = tmp3 + tmp8;
256 tmpz[3].re = tmp3 - tmp8;
257 tmpz[1].im = tmp4 - tmp7;
258 tmpz[3].im = tmp4 + tmp7;
264 num_transforms = (num_transforms >> 1) | 1;
266 for (n=0; n<num_transforms; n++){
267 offset = ff_fft_offsets_lut[n] << 3;
270 tmp1 = tmpz[4].re + tmpz[5].re;
271 tmp3 = tmpz[6].re + tmpz[7].re;
272 tmp2 = tmpz[4].im + tmpz[5].im;
273 tmp4 = tmpz[6].im + tmpz[7].im;
279 tmp1 = tmpz[4].re - tmpz[5].re;
280 tmp2 = tmpz[4].im - tmpz[5].im;
281 tmp3 = tmpz[6].re - tmpz[7].re;
282 tmp4 = tmpz[6].im - tmpz[7].im;
284 tmpz[4].re = tmpz[0].re - tmp5;
285 tmpz[0].re = tmpz[0].re + tmp5;
286 tmpz[4].im = tmpz[0].im - tmp6;
287 tmpz[0].im = tmpz[0].im + tmp6;
288 tmpz[6].re = tmpz[2].re - tmp8;
289 tmpz[2].re = tmpz[2].re + tmp8;
290 tmpz[6].im = tmpz[2].im + tmp7;
291 tmpz[2].im = tmpz[2].im - tmp7;
293 accu = (int64_t)Q31(M_SQRT1_2)*(tmp1 + tmp2);
294 tmp5 = (int32_t)((accu + 0x40000000) >> 31);
295 accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 - tmp4);
296 tmp7 = (int32_t)((accu + 0x40000000) >> 31);
297 accu = (int64_t)Q31(M_SQRT1_2)*(tmp2 - tmp1);
298 tmp6 = (int32_t)((accu + 0x40000000) >> 31);
299 accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 + tmp4);
300 tmp8 = (int32_t)((accu + 0x40000000) >> 31);
306 tmpz[5].re = tmpz[1].re - tmp1;
307 tmpz[1].re = tmpz[1].re + tmp1;
308 tmpz[5].im = tmpz[1].im - tmp2;
309 tmpz[1].im = tmpz[1].im + tmp2;
310 tmpz[7].re = tmpz[3].re - tmp4;
311 tmpz[3].re = tmpz[3].re + tmp4;
312 tmpz[7].im = tmpz[3].im + tmp3;
313 tmpz[3].im = tmpz[3].im - tmp3;
316 step = 1 << ((MAX_LOG2_NFFT-4) - 4);
319 for (nbits=4; nbits<=s->nbits; nbits++){
322 num_transforms = (num_transforms >> 1) | 1;
324 for (n=0; n<num_transforms; n++){
325 const FFTSample *w_re_ptr = ff_w_tab_sr + step;
326 const FFTSample *w_im_ptr = ff_w_tab_sr + MAX_FFT_SIZE/(4*16) - step;
327 offset = ff_fft_offsets_lut[n] << nbits;
330 tmp5 = tmpz[ n2].re + tmpz[n34].re;
331 tmp1 = tmpz[ n2].re - tmpz[n34].re;
332 tmp6 = tmpz[ n2].im + tmpz[n34].im;
333 tmp2 = tmpz[ n2].im - tmpz[n34].im;
335 tmpz[ n2].re = tmpz[ 0].re - tmp5;
336 tmpz[ 0].re = tmpz[ 0].re + tmp5;
337 tmpz[ n2].im = tmpz[ 0].im - tmp6;
338 tmpz[ 0].im = tmpz[ 0].im + tmp6;
339 tmpz[n34].re = tmpz[n4].re - tmp2;
340 tmpz[ n4].re = tmpz[n4].re + tmp2;
341 tmpz[n34].im = tmpz[n4].im + tmp1;
342 tmpz[ n4].im = tmpz[n4].im - tmp1;
344 for (i=1; i<n4; i++){
345 FFTSample w_re = w_re_ptr[0];
346 FFTSample 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);
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;
383 #else /* FFT_FIXED_32 */
385 #define BUTTERFLIES(a0,a1,a2,a3) {\
387 BF(a2.re, a0.re, a0.re, t5);\
388 BF(a3.im, a1.im, a1.im, t3);\
390 BF(a3.re, a1.re, a1.re, t4);\
391 BF(a2.im, a0.im, a0.im, t6);\
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;\
400 BF(a2.re, a0.re, r0, t5);\
401 BF(a3.im, a1.im, i1, t3);\
403 BF(a3.re, a1.re, r1, t4);\
404 BF(a2.im, a0.im, i0, t6);\
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)\
413 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
418 BUTTERFLIES(a0,a1,a2,a3)\
421 /* z[0...8n-1], w[1...2n-1] */
423 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
425 FFTDouble t1, t2, t3, t4, t5, t6;\
429 const FFTSample *wim = wre+o1;\
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]);\
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]);\
445 #define BUTTERFLIES BUTTERFLIES_BIG
448 #define DECL_FFT(n,n2,n4)\
449 static void fft##n(FFTComplex *z)\
454 pass(z,FFT_NAME(ff_cos_##n),n4/2);\
457 static void fft4(FFTComplex *z)
459 FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
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);
471 static void fft8(FFTComplex *z)
473 FFTDouble t1, t2, t3, t4, t5, t6;
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);
482 BUTTERFLIES(z[0],z[2],z[4],z[6]);
483 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
487 static void fft16(FFTComplex *z)
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];
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);
509 DECL_FFT(512,256,128)
511 #define pass pass_big
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 DECL_FFT(131072,65536,32768)
522 static void (* const fft_dispatch[])(FFTComplex*) = {
523 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
524 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, fft131072
527 static void fft_calc_c(FFTContext *s, FFTComplex *z)
529 fft_dispatch[s->nbits-2](z);
531 #endif /* FFT_FIXED_32 */