2 * Copyright (c) 2019 Lynne <dev@lynne.ee>
4 * Copyright (c) 2008 Loren Merritt
5 * Copyright (c) 2002 Fabrice Bellard
6 * Partly based on libdjbfft by D. J. Bernstein
8 * This file is part of FFmpeg.
10 * FFmpeg is free software; you can redistribute it and/or
11 * modify it under the terms of the GNU Lesser General Public
12 * License as published by the Free Software Foundation; either
13 * version 2.1 of the License, or (at your option) any later version.
15 * FFmpeg is distributed in the hope that it will be useful,
16 * but WITHOUT ANY WARRANTY; without even the implied warranty of
17 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
18 * Lesser General Public License for more details.
20 * You should have received a copy of the GNU Lesser General Public
21 * License along with FFmpeg; if not, write to the Free Software
22 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
25 /* All costabs for a type are defined here */
40 DECLARE_ALIGNED(32, FFTComplex, TX_NAME(ff_cos_53))[4];
42 static FFTSample * const cos_tabs[18] = {
57 TX_NAME(ff_cos_16384),
58 TX_NAME(ff_cos_32768),
59 TX_NAME(ff_cos_65536),
60 TX_NAME(ff_cos_131072),
63 static av_always_inline void init_cos_tabs_idx(int index)
66 double freq = 2*M_PI/m;
67 FFTSample *tab = cos_tabs[index];
68 for(int i = 0; i <= m/4; i++)
69 tab[i] = RESCALE(cos(i*freq));
70 for(int i = 1; i < m/4; i++)
71 tab[m/2 - i] = tab[i];
74 #define INIT_FF_COS_TABS_FUNC(index, size) \
75 static av_cold void init_cos_tabs_ ## size (void) \
77 init_cos_tabs_idx(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 av_cold void ff_init_53_tabs(void)
97 TX_NAME(ff_cos_53)[0] = (FFTComplex){ RESCALE(cos(2 * M_PI / 12)), RESCALE(cos(2 * M_PI / 12)) };
98 TX_NAME(ff_cos_53)[1] = (FFTComplex){ RESCALE(cos(2 * M_PI / 6)), RESCALE(cos(2 * M_PI / 6)) };
99 TX_NAME(ff_cos_53)[2] = (FFTComplex){ RESCALE(cos(2 * M_PI / 5)), RESCALE(sin(2 * M_PI / 5)) };
100 TX_NAME(ff_cos_53)[3] = (FFTComplex){ RESCALE(cos(2 * M_PI / 10)), RESCALE(sin(2 * M_PI / 10)) };
103 static CosTabsInitOnce cos_tabs_init_once[] = {
104 { ff_init_53_tabs, AV_ONCE_INIT },
108 { init_cos_tabs_16, AV_ONCE_INIT },
109 { init_cos_tabs_32, AV_ONCE_INIT },
110 { init_cos_tabs_64, AV_ONCE_INIT },
111 { init_cos_tabs_128, AV_ONCE_INIT },
112 { init_cos_tabs_256, AV_ONCE_INIT },
113 { init_cos_tabs_512, AV_ONCE_INIT },
114 { init_cos_tabs_1024, AV_ONCE_INIT },
115 { init_cos_tabs_2048, AV_ONCE_INIT },
116 { init_cos_tabs_4096, AV_ONCE_INIT },
117 { init_cos_tabs_8192, AV_ONCE_INIT },
118 { init_cos_tabs_16384, AV_ONCE_INIT },
119 { init_cos_tabs_32768, AV_ONCE_INIT },
120 { init_cos_tabs_65536, AV_ONCE_INIT },
121 { init_cos_tabs_131072, AV_ONCE_INIT },
124 static av_cold void init_cos_tabs(int index)
126 ff_thread_once(&cos_tabs_init_once[index].control,
127 cos_tabs_init_once[index].func);
130 static av_always_inline void fft3(FFTComplex *out, FFTComplex *in,
135 BF(tmp[0].re, tmp[1].im, in[1].im, in[2].im);
136 BF(tmp[0].im, tmp[1].re, in[1].re, in[2].re);
138 out[0*stride].re = in[0].re + tmp[1].re;
139 out[0*stride].im = in[0].im + tmp[1].im;
141 tmp[0].re = MUL(TX_NAME(ff_cos_53)[0].re, tmp[0].re);
142 tmp[0].im = MUL(TX_NAME(ff_cos_53)[0].im, tmp[0].im);
143 tmp[1].re = MUL(TX_NAME(ff_cos_53)[1].re, tmp[1].re);
144 tmp[1].im = MUL(TX_NAME(ff_cos_53)[1].re, tmp[1].im);
146 out[1*stride].re = in[0].re - tmp[1].re + tmp[0].re;
147 out[1*stride].im = in[0].im - tmp[1].im - tmp[0].im;
148 out[2*stride].re = in[0].re - tmp[1].re - tmp[0].re;
149 out[2*stride].im = in[0].im - tmp[1].im + tmp[0].im;
152 #define DECL_FFT5(NAME, D0, D1, D2, D3, D4) \
153 static av_always_inline void NAME(FFTComplex *out, FFTComplex *in, \
156 FFTComplex z0[4], t[6]; \
158 BF(t[1].im, t[0].re, in[1].re, in[4].re); \
159 BF(t[1].re, t[0].im, in[1].im, in[4].im); \
160 BF(t[3].im, t[2].re, in[2].re, in[3].re); \
161 BF(t[3].re, t[2].im, in[2].im, in[3].im); \
163 out[D0*stride].re = in[0].re + t[0].re + t[2].re; \
164 out[D0*stride].im = in[0].im + t[0].im + t[2].im; \
166 SMUL(t[4].re, t[0].re, TX_NAME(ff_cos_53)[2].re, TX_NAME(ff_cos_53)[3].re, t[2].re, t[0].re); \
167 SMUL(t[4].im, t[0].im, TX_NAME(ff_cos_53)[2].re, TX_NAME(ff_cos_53)[3].re, t[2].im, t[0].im); \
168 CMUL(t[5].re, t[1].re, TX_NAME(ff_cos_53)[2].im, TX_NAME(ff_cos_53)[3].im, t[3].re, t[1].re); \
169 CMUL(t[5].im, t[1].im, TX_NAME(ff_cos_53)[2].im, TX_NAME(ff_cos_53)[3].im, t[3].im, t[1].im); \
171 BF(z0[0].re, z0[3].re, t[0].re, t[1].re); \
172 BF(z0[0].im, z0[3].im, t[0].im, t[1].im); \
173 BF(z0[2].re, z0[1].re, t[4].re, t[5].re); \
174 BF(z0[2].im, z0[1].im, t[4].im, t[5].im); \
176 out[D1*stride].re = in[0].re + z0[3].re; \
177 out[D1*stride].im = in[0].im + z0[0].im; \
178 out[D2*stride].re = in[0].re + z0[2].re; \
179 out[D2*stride].im = in[0].im + z0[1].im; \
180 out[D3*stride].re = in[0].re + z0[1].re; \
181 out[D3*stride].im = in[0].im + z0[2].im; \
182 out[D4*stride].re = in[0].re + z0[0].re; \
183 out[D4*stride].im = in[0].im + z0[3].im; \
186 DECL_FFT5(fft5, 0, 1, 2, 3, 4)
187 DECL_FFT5(fft5_m1, 0, 6, 12, 3, 9)
188 DECL_FFT5(fft5_m2, 10, 1, 7, 13, 4)
189 DECL_FFT5(fft5_m3, 5, 11, 2, 8, 14)
191 static av_always_inline void fft15(FFTComplex *out, FFTComplex *in,
196 for (int i = 0; i < 5; i++)
197 fft3(tmp + i, in + i*3, 5);
199 fft5_m1(out, tmp + 0, stride);
200 fft5_m2(out, tmp + 5, stride);
201 fft5_m3(out, tmp + 10, stride);
204 #define BUTTERFLIES(a0,a1,a2,a3) {\
206 BF(a2.re, a0.re, a0.re, t5);\
207 BF(a3.im, a1.im, a1.im, t3);\
209 BF(a3.re, a1.re, a1.re, t4);\
210 BF(a2.im, a0.im, a0.im, t6);\
213 // force loading all the inputs before storing any.
214 // this is slightly slower for small data, but avoids store->load aliasing
215 // for addresses separated by large powers of 2.
216 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
217 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
219 BF(a2.re, a0.re, r0, t5);\
220 BF(a3.im, a1.im, i1, t3);\
222 BF(a3.re, a1.re, r1, t4);\
223 BF(a2.im, a0.im, i0, t6);\
226 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
227 CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
228 CMUL(t5, t6, a3.re, a3.im, wre, wim);\
229 BUTTERFLIES(a0,a1,a2,a3)\
232 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
237 BUTTERFLIES(a0,a1,a2,a3)\
240 /* z[0...8n-1], w[1...2n-1] */
242 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
244 FFTSample t1, t2, t3, t4, t5, t6;\
248 const FFTSample *wim = wre+o1;\
251 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
252 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
257 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
258 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
264 #define BUTTERFLIES BUTTERFLIES_BIG
267 #define DECL_FFT(n,n2,n4)\
268 static void fft##n(FFTComplex *z)\
273 pass(z,TX_NAME(ff_cos_##n),n4/2);\
276 static void fft4(FFTComplex *z)
278 FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
280 BF(t3, t1, z[0].re, z[1].re);
281 BF(t8, t6, z[3].re, z[2].re);
282 BF(z[2].re, z[0].re, t1, t6);
283 BF(t4, t2, z[0].im, z[1].im);
284 BF(t7, t5, z[2].im, z[3].im);
285 BF(z[3].im, z[1].im, t4, t8);
286 BF(z[3].re, z[1].re, t3, t7);
287 BF(z[2].im, z[0].im, t2, t5);
290 static void fft8(FFTComplex *z)
292 FFTSample t1, t2, t3, t4, t5, t6;
296 BF(t1, z[5].re, z[4].re, -z[5].re);
297 BF(t2, z[5].im, z[4].im, -z[5].im);
298 BF(t5, z[7].re, z[6].re, -z[7].re);
299 BF(t6, z[7].im, z[6].im, -z[7].im);
301 BUTTERFLIES(z[0],z[2],z[4],z[6]);
302 TRANSFORM(z[1],z[3],z[5],z[7],RESCALE(M_SQRT1_2),RESCALE(M_SQRT1_2));
305 static void fft16(FFTComplex *z)
307 FFTSample t1, t2, t3, t4, t5, t6;
308 FFTSample cos_16_1 = TX_NAME(ff_cos_16)[1];
309 FFTSample cos_16_3 = TX_NAME(ff_cos_16)[3];
315 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
316 TRANSFORM(z[2],z[6],z[10],z[14],RESCALE(M_SQRT1_2),RESCALE(M_SQRT1_2));
317 TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
318 TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
325 DECL_FFT(512,256,128)
326 #define pass pass_big
327 DECL_FFT(1024,512,256)
328 DECL_FFT(2048,1024,512)
329 DECL_FFT(4096,2048,1024)
330 DECL_FFT(8192,4096,2048)
331 DECL_FFT(16384,8192,4096)
332 DECL_FFT(32768,16384,8192)
333 DECL_FFT(65536,32768,16384)
334 DECL_FFT(131072,65536,32768)
336 static void (* const fft_dispatch[])(FFTComplex*) = {
337 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
338 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, fft131072
341 #define DECL_COMP_FFT(N) \
342 static void compound_fft_##N##xM(AVTXContext *s, void *_out, \
343 void *_in, ptrdiff_t stride) \
345 const int m = s->m, *in_map = s->pfatab, *out_map = in_map + N*m; \
346 FFTComplex *in = _in; \
347 FFTComplex *out = _out; \
348 FFTComplex fft##N##in[N]; \
349 void (*fftp)(FFTComplex *z) = fft_dispatch[av_log2(m) - 2]; \
351 for (int i = 0; i < m; i++) { \
352 for (int j = 0; j < N; j++) \
353 fft##N##in[j] = in[in_map[i*N + j]]; \
354 fft##N(s->tmp + s->revtab[i], fft##N##in, m); \
357 for (int i = 0; i < N; i++) \
358 fftp(s->tmp + m*i); \
360 for (int i = 0; i < N*m; i++) \
361 out[i] = s->tmp[out_map[i]]; \
368 static void monolithic_fft(AVTXContext *s, void *_out, void *_in,
371 FFTComplex *in = _in;
372 FFTComplex *out = _out;
373 int m = s->m, mb = av_log2(m) - 2;
374 for (int i = 0; i < m; i++)
375 out[s->revtab[i]] = in[i];
376 fft_dispatch[mb](out);
379 #define DECL_COMP_IMDCT(N) \
380 static void compound_imdct_##N##xM(AVTXContext *s, void *_dst, void *_src, \
383 FFTComplex fft##N##in[N]; \
384 FFTComplex *z = _dst, *exp = s->exptab; \
385 const int m = s->m, len8 = N*m >> 1; \
386 const int *in_map = s->pfatab, *out_map = in_map + N*m; \
387 const FFTSample *src = _src, *in1, *in2; \
388 void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2]; \
390 stride /= sizeof(*src); /* To convert it from bytes */ \
392 in2 = src + ((N*m*2) - 1) * stride; \
394 for (int i = 0; i < m; i++) { \
395 for (int j = 0; j < N; j++) { \
396 const int k = in_map[i*N + j]; \
397 FFTComplex tmp = { in2[-k*stride], in1[k*stride] }; \
398 CMUL3(fft##N##in[j], tmp, exp[k >> 1]); \
400 fft##N(s->tmp + s->revtab[i], fft##N##in, m); \
403 for (int i = 0; i < N; i++) \
404 fftp(s->tmp + m*i); \
406 for (int i = 0; i < len8; i++) { \
407 const int i0 = len8 + i, i1 = len8 - i - 1; \
408 const int s0 = out_map[i0], s1 = out_map[i1]; \
409 FFTComplex src1 = { s->tmp[s1].im, s->tmp[s1].re }; \
410 FFTComplex src0 = { s->tmp[s0].im, s->tmp[s0].re }; \
412 CMUL(z[i1].re, z[i0].im, src1.re, src1.im, exp[i1].im, exp[i1].re); \
413 CMUL(z[i0].re, z[i1].im, src0.re, src0.im, exp[i0].im, exp[i0].re); \
421 #define DECL_COMP_MDCT(N) \
422 static void compound_mdct_##N##xM(AVTXContext *s, void *_dst, void *_src, \
425 FFTSample *src = _src, *dst = _dst; \
426 FFTComplex *exp = s->exptab, tmp, fft##N##in[N]; \
427 const int m = s->m, len4 = N*m, len3 = len4 * 3, len8 = len4 >> 1; \
428 const int *in_map = s->pfatab, *out_map = in_map + N*m; \
429 void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2]; \
431 stride /= sizeof(*dst); \
433 for (int i = 0; i < m; i++) { /* Folding and pre-reindexing */ \
434 for (int j = 0; j < N; j++) { \
435 const int k = in_map[i*N + j]; \
437 tmp.re = FOLD(-src[ len4 + k], src[1*len4 - 1 - k]); \
438 tmp.im = FOLD(-src[ len3 + k], -src[1*len3 - 1 - k]); \
440 tmp.re = FOLD(-src[ len4 + k], -src[5*len4 - 1 - k]); \
441 tmp.im = FOLD( src[-len4 + k], -src[1*len3 - 1 - k]); \
443 CMUL(fft##N##in[j].im, fft##N##in[j].re, tmp.re, tmp.im, \
444 exp[k >> 1].re, exp[k >> 1].im); \
446 fft##N(s->tmp + s->revtab[i], fft##N##in, m); \
449 for (int i = 0; i < N; i++) \
450 fftp(s->tmp + m*i); \
452 for (int i = 0; i < len8; i++) { \
453 const int i0 = len8 + i, i1 = len8 - i - 1; \
454 const int s0 = out_map[i0], s1 = out_map[i1]; \
455 FFTComplex src1 = { s->tmp[s1].re, s->tmp[s1].im }; \
456 FFTComplex src0 = { s->tmp[s0].re, s->tmp[s0].im }; \
458 CMUL(dst[2*i1*stride + stride], dst[2*i0*stride], src0.re, src0.im, \
459 exp[i0].im, exp[i0].re); \
460 CMUL(dst[2*i0*stride + stride], dst[2*i1*stride], src1.re, src1.im, \
461 exp[i1].im, exp[i1].re); \
469 static void monolithic_imdct(AVTXContext *s, void *_dst, void *_src,
472 FFTComplex *z = _dst, *exp = s->exptab;
473 const int m = s->m, len8 = m >> 1;
474 const FFTSample *src = _src, *in1, *in2;
475 void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];
477 stride /= sizeof(*src);
479 in2 = src + ((m*2) - 1) * stride;
481 for (int i = 0; i < m; i++) {
482 FFTComplex tmp = { in2[-2*i*stride], in1[2*i*stride] };
483 CMUL3(z[s->revtab[i]], tmp, exp[i]);
488 for (int i = 0; i < len8; i++) {
489 const int i0 = len8 + i, i1 = len8 - i - 1;
490 FFTComplex src1 = { z[i1].im, z[i1].re };
491 FFTComplex src0 = { z[i0].im, z[i0].re };
493 CMUL(z[i1].re, z[i0].im, src1.re, src1.im, exp[i1].im, exp[i1].re);
494 CMUL(z[i0].re, z[i1].im, src0.re, src0.im, exp[i0].im, exp[i0].re);
498 static void monolithic_mdct(AVTXContext *s, void *_dst, void *_src,
501 FFTSample *src = _src, *dst = _dst;
502 FFTComplex *exp = s->exptab, tmp, *z = _dst;
503 const int m = s->m, len4 = m, len3 = len4 * 3, len8 = len4 >> 1;
504 void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];
506 stride /= sizeof(*dst);
508 for (int i = 0; i < m; i++) { /* Folding and pre-reindexing */
511 tmp.re = FOLD(-src[ len4 + k], src[1*len4 - 1 - k]);
512 tmp.im = FOLD(-src[ len3 + k], -src[1*len3 - 1 - k]);
514 tmp.re = FOLD(-src[ len4 + k], -src[5*len4 - 1 - k]);
515 tmp.im = FOLD( src[-len4 + k], -src[1*len3 - 1 - k]);
517 CMUL(z[s->revtab[i]].im, z[s->revtab[i]].re, tmp.re, tmp.im,
518 exp[i].re, exp[i].im);
523 for (int i = 0; i < len8; i++) {
524 const int i0 = len8 + i, i1 = len8 - i - 1;
525 FFTComplex src1 = { z[i1].re, z[i1].im };
526 FFTComplex src0 = { z[i0].re, z[i0].im };
528 CMUL(dst[2*i1*stride + stride], dst[2*i0*stride], src0.re, src0.im,
529 exp[i0].im, exp[i0].re);
530 CMUL(dst[2*i0*stride + stride], dst[2*i1*stride], src1.re, src1.im,
531 exp[i1].im, exp[i1].re);
535 static int gen_mdct_exptab(AVTXContext *s, int len4, double scale)
537 const double theta = (scale < 0 ? len4 : 0) + 1.0/8.0;
539 if (!(s->exptab = av_malloc_array(len4, sizeof(*s->exptab))))
540 return AVERROR(ENOMEM);
542 scale = sqrt(fabs(scale));
543 for (int i = 0; i < len4; i++) {
544 const double alpha = M_PI_2 * (i + theta) / len4;
545 s->exptab[i].re = RESCALE(cos(alpha) * scale);
546 s->exptab[i].im = RESCALE(sin(alpha) * scale);
552 int TX_NAME(ff_tx_init_mdct_fft)(AVTXContext *s, av_tx_fn *tx,
553 enum AVTXType type, int inv, int len,
554 const void *scale, uint64_t flags)
556 const int is_mdct = ff_tx_type_is_mdct(type);
557 int err, n = 1, m = 1, max_ptwo = 1 << (FF_ARRAY_ELEMS(fft_dispatch) + 1);
562 #define CHECK_FACTOR(DST, FACTOR, SRC) \
563 if (DST == 1 && !(SRC % FACTOR)) { \
567 CHECK_FACTOR(n, 15, len)
568 CHECK_FACTOR(n, 5, len)
569 CHECK_FACTOR(n, 3, len)
572 /* len must be a power of two now */
573 if (!(len & (len - 1)) && len >= 4 && len <= max_ptwo) {
583 /* Filter out direct 3, 5 and 15 transforms, too niche */
584 if (len > 1 || m == 1) {
585 av_log(NULL, AV_LOG_ERROR, "Unsupported transform size: n = %i, "
586 "m = %i, residual = %i!\n", n, m, len);
587 return AVERROR(EINVAL);
588 } else if (n > 1 && m > 1) { /* 2D transform case */
589 if ((err = ff_tx_gen_compound_mapping(s)))
591 if (!(s->tmp = av_malloc(n*m*sizeof(*s->tmp))))
592 return AVERROR(ENOMEM);
593 *tx = n == 3 ? compound_fft_3xM :
594 n == 5 ? compound_fft_5xM :
597 *tx = n == 3 ? inv ? compound_imdct_3xM : compound_mdct_3xM :
598 n == 5 ? inv ? compound_imdct_5xM : compound_mdct_5xM :
599 inv ? compound_imdct_15xM : compound_mdct_15xM;
600 } else { /* Direct transform case */
601 *tx = monolithic_fft;
603 *tx = inv ? monolithic_imdct : monolithic_mdct;
609 ff_tx_gen_ptwo_revtab(s);
610 for (int i = 4; i <= av_log2(m); i++)
615 return gen_mdct_exptab(s, n*m, *((SCALE_TYPE *)scale));