1 /*
2  * Copyright (c) 2019 Lynne <dev@lynne.ee>
3  * Power of two FFT:
4  * Copyright (c) 2008 Loren Merritt
5  * Copyright (c) 2002 Fabrice Bellard
6  * Partly based on libdjbfft by D. J. Bernstein
7  *
8  * This file is part of FFmpeg.
9  *
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.
14  *
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.
19  *
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
23  */
24 
25 /* All costabs for a type are defined here */
26 COSTABLE(16);
27 COSTABLE(32);
28 COSTABLE(64);
29 COSTABLE(128);
30 COSTABLE(256);
31 COSTABLE(512);
32 COSTABLE(1024);
33 COSTABLE(2048);
34 COSTABLE(4096);
35 COSTABLE(8192);
36 COSTABLE(16384);
37 COSTABLE(32768);
38 COSTABLE(65536);
39 COSTABLE(131072);
40 DECLARE_ALIGNED(32, FFTComplex, TX_NAME(ff_cos_53))[4];
41 
42 static FFTSample * const cos_tabs[18] = {
43     NULL,
44     NULL,
45     NULL,
46     NULL,
47     TX_NAME(ff_cos_16),
48     TX_NAME(ff_cos_32),
49     TX_NAME(ff_cos_64),
50     TX_NAME(ff_cos_128),
51     TX_NAME(ff_cos_256),
52     TX_NAME(ff_cos_512),
53     TX_NAME(ff_cos_1024),
54     TX_NAME(ff_cos_2048),
55     TX_NAME(ff_cos_4096),
56     TX_NAME(ff_cos_8192),
57     TX_NAME(ff_cos_16384),
58     TX_NAME(ff_cos_32768),
59     TX_NAME(ff_cos_65536),
60     TX_NAME(ff_cos_131072),
61 };
62 
init_cos_tabs_idx(int index)63 static av_always_inline void init_cos_tabs_idx(int index)
64 {
65     int m = 1 << 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];
72 }
73 
74 #define INIT_FF_COS_TABS_FUNC(index, size)                                     \
75 static av_cold void init_cos_tabs_ ## size (void)                              \
76 {                                                                              \
77     init_cos_tabs_idx(index);                                                  \
78 }
79 
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)
94 
ff_init_53_tabs(void)95 static av_cold void ff_init_53_tabs(void)
96 {
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)) };
101 }
102 
103 static CosTabsInitOnce cos_tabs_init_once[] = {
104     { ff_init_53_tabs, AV_ONCE_INIT },
105     { NULL },
106     { NULL },
107     { NULL },
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 },
122 };
123 
init_cos_tabs(int index)124 static av_cold void init_cos_tabs(int index)
125 {
126     ff_thread_once(&cos_tabs_init_once[index].control,
127                     cos_tabs_init_once[index].func);
128 }
129 
fft3(FFTComplex * out,FFTComplex * in,ptrdiff_t stride)130 static av_always_inline void fft3(FFTComplex *out, FFTComplex *in,
131                                   ptrdiff_t stride)
132 {
133     FFTComplex tmp[2];
134 #ifdef TX_INT32
135     int64_t mtmp[4];
136 #endif
137 
138     BF(tmp[0].re, tmp[1].im, in[1].im, in[2].im);
139     BF(tmp[0].im, tmp[1].re, in[1].re, in[2].re);
140 
141     out[0*stride].re = in[0].re + tmp[1].re;
142     out[0*stride].im = in[0].im + tmp[1].im;
143 
144 #ifdef TX_INT32
145     mtmp[0] = (int64_t)TX_NAME(ff_cos_53)[0].re * tmp[0].re;
146     mtmp[1] = (int64_t)TX_NAME(ff_cos_53)[0].im * tmp[0].im;
147     mtmp[2] = (int64_t)TX_NAME(ff_cos_53)[1].re * tmp[1].re;
148     mtmp[3] = (int64_t)TX_NAME(ff_cos_53)[1].re * tmp[1].im;
149     out[1*stride].re = in[0].re - (mtmp[2] + mtmp[0] + 0x40000000 >> 31);
150     out[1*stride].im = in[0].im - (mtmp[3] - mtmp[1] + 0x40000000 >> 31);
151     out[2*stride].re = in[0].re - (mtmp[2] - mtmp[0] + 0x40000000 >> 31);
152     out[2*stride].im = in[0].im - (mtmp[3] + mtmp[1] + 0x40000000 >> 31);
153 #else
154     tmp[0].re = TX_NAME(ff_cos_53)[0].re * tmp[0].re;
155     tmp[0].im = TX_NAME(ff_cos_53)[0].im * tmp[0].im;
156     tmp[1].re = TX_NAME(ff_cos_53)[1].re * tmp[1].re;
157     tmp[1].im = TX_NAME(ff_cos_53)[1].re * tmp[1].im;
158     out[1*stride].re = in[0].re - tmp[1].re + tmp[0].re;
159     out[1*stride].im = in[0].im - tmp[1].im - tmp[0].im;
160     out[2*stride].re = in[0].re - tmp[1].re - tmp[0].re;
161     out[2*stride].im = in[0].im - tmp[1].im + tmp[0].im;
162 #endif
163 }
164 
165 #define DECL_FFT5(NAME, D0, D1, D2, D3, D4)                                                       \
166 static av_always_inline void NAME(FFTComplex *out, FFTComplex *in,                                \
167                                   ptrdiff_t stride)                                               \
168 {                                                                                                 \
169     FFTComplex z0[4], t[6];                                                                       \
170                                                                                                   \
171     BF(t[1].im, t[0].re, in[1].re, in[4].re);                                                     \
172     BF(t[1].re, t[0].im, in[1].im, in[4].im);                                                     \
173     BF(t[3].im, t[2].re, in[2].re, in[3].re);                                                     \
174     BF(t[3].re, t[2].im, in[2].im, in[3].im);                                                     \
175                                                                                                   \
176     out[D0*stride].re = in[0].re + t[0].re + t[2].re;                                             \
177     out[D0*stride].im = in[0].im + t[0].im + t[2].im;                                             \
178                                                                                                   \
179     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); \
180     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); \
181     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); \
182     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); \
183                                                                                                   \
184     BF(z0[0].re, z0[3].re, t[0].re, t[1].re);                                                     \
185     BF(z0[0].im, z0[3].im, t[0].im, t[1].im);                                                     \
186     BF(z0[2].re, z0[1].re, t[4].re, t[5].re);                                                     \
187     BF(z0[2].im, z0[1].im, t[4].im, t[5].im);                                                     \
188                                                                                                   \
189     out[D1*stride].re = in[0].re + z0[3].re;                                                      \
190     out[D1*stride].im = in[0].im + z0[0].im;                                                      \
191     out[D2*stride].re = in[0].re + z0[2].re;                                                      \
192     out[D2*stride].im = in[0].im + z0[1].im;                                                      \
193     out[D3*stride].re = in[0].re + z0[1].re;                                                      \
194     out[D3*stride].im = in[0].im + z0[2].im;                                                      \
195     out[D4*stride].re = in[0].re + z0[0].re;                                                      \
196     out[D4*stride].im = in[0].im + z0[3].im;                                                      \
197 }
198 
199 DECL_FFT5(fft5,     0,  1,  2,  3,  4)
200 DECL_FFT5(fft5_m1,  0,  6, 12,  3,  9)
201 DECL_FFT5(fft5_m2, 10,  1,  7, 13,  4)
202 DECL_FFT5(fft5_m3,  5, 11,  2,  8, 14)
203 
fft15(FFTComplex * out,FFTComplex * in,ptrdiff_t stride)204 static av_always_inline void fft15(FFTComplex *out, FFTComplex *in,
205                                    ptrdiff_t stride)
206 {
207     FFTComplex tmp[15];
208 
209     for (int i = 0; i < 5; i++)
210         fft3(tmp + i, in + i*3, 5);
211 
212     fft5_m1(out, tmp +  0, stride);
213     fft5_m2(out, tmp +  5, stride);
214     fft5_m3(out, tmp + 10, stride);
215 }
216 
217 #define BUTTERFLIES(a0,a1,a2,a3) {\
218     BF(t3, t5, t5, t1);\
219     BF(a2.re, a0.re, a0.re, t5);\
220     BF(a3.im, a1.im, a1.im, t3);\
221     BF(t4, t6, t2, t6);\
222     BF(a3.re, a1.re, a1.re, t4);\
223     BF(a2.im, a0.im, a0.im, t6);\
224 }
225 
226 // force loading all the inputs before storing any.
227 // this is slightly slower for small data, but avoids store->load aliasing
228 // for addresses separated by large powers of 2.
229 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
230     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
231     BF(t3, t5, t5, t1);\
232     BF(a2.re, a0.re, r0, t5);\
233     BF(a3.im, a1.im, i1, t3);\
234     BF(t4, t6, t2, t6);\
235     BF(a3.re, a1.re, r1, t4);\
236     BF(a2.im, a0.im, i0, t6);\
237 }
238 
239 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
240     CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
241     CMUL(t5, t6, a3.re, a3.im, wre,  wim);\
242     BUTTERFLIES(a0,a1,a2,a3)\
243 }
244 
245 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
246     t1 = a2.re;\
247     t2 = a2.im;\
248     t5 = a3.re;\
249     t6 = a3.im;\
250     BUTTERFLIES(a0,a1,a2,a3)\
251 }
252 
253 /* z[0...8n-1], w[1...2n-1] */
254 #define PASS(name)\
255 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
256 {\
257     FFTSample t1, t2, t3, t4, t5, t6;\
258     int o1 = 2*n;\
259     int o2 = 4*n;\
260     int o3 = 6*n;\
261     const FFTSample *wim = wre+o1;\
262     n--;\
263 \
264     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
265     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
266     do {\
267         z += 2;\
268         wre += 2;\
269         wim -= 2;\
270         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
271         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
272     } while(--n);\
273 }
274 
275 PASS(pass)
276 #undef BUTTERFLIES
277 #define BUTTERFLIES BUTTERFLIES_BIG
PASS(pass_big)278 PASS(pass_big)
279 
280 #define DECL_FFT(n,n2,n4)\
281 static void fft##n(FFTComplex *z)\
282 {\
283     fft##n2(z);\
284     fft##n4(z+n4*2);\
285     fft##n4(z+n4*3);\
286     pass(z,TX_NAME(ff_cos_##n),n4/2);\
287 }
288 
289 static void fft2(FFTComplex *z)
290 {
291     FFTComplex tmp;
292     BF(tmp.re, z[0].re, z[0].re, z[1].re);
293     BF(tmp.im, z[0].im, z[0].im, z[1].im);
294     z[1] = tmp;
295 }
296 
fft4(FFTComplex * z)297 static void fft4(FFTComplex *z)
298 {
299     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
300 
301     BF(t3, t1, z[0].re, z[1].re);
302     BF(t8, t6, z[3].re, z[2].re);
303     BF(z[2].re, z[0].re, t1, t6);
304     BF(t4, t2, z[0].im, z[1].im);
305     BF(t7, t5, z[2].im, z[3].im);
306     BF(z[3].im, z[1].im, t4, t8);
307     BF(z[3].re, z[1].re, t3, t7);
308     BF(z[2].im, z[0].im, t2, t5);
309 }
310 
fft8(FFTComplex * z)311 static void fft8(FFTComplex *z)
312 {
313     FFTSample t1, t2, t3, t4, t5, t6;
314 
315     fft4(z);
316 
317     BF(t1, z[5].re, z[4].re, -z[5].re);
318     BF(t2, z[5].im, z[4].im, -z[5].im);
319     BF(t5, z[7].re, z[6].re, -z[7].re);
320     BF(t6, z[7].im, z[6].im, -z[7].im);
321 
322     BUTTERFLIES(z[0],z[2],z[4],z[6]);
323     TRANSFORM(z[1],z[3],z[5],z[7],RESCALE(M_SQRT1_2),RESCALE(M_SQRT1_2));
324 }
325 
fft16(FFTComplex * z)326 static void fft16(FFTComplex *z)
327 {
328     FFTSample t1, t2, t3, t4, t5, t6;
329     FFTSample cos_16_1 = TX_NAME(ff_cos_16)[1];
330     FFTSample cos_16_3 = TX_NAME(ff_cos_16)[3];
331 
332     fft8(z);
333     fft4(z+8);
334     fft4(z+12);
335 
336     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
337     TRANSFORM(z[2],z[6],z[10],z[14],RESCALE(M_SQRT1_2),RESCALE(M_SQRT1_2));
338     TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
339     TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
340 }
341 
342 DECL_FFT(32,16,8)
343 DECL_FFT(64,32,16)
344 DECL_FFT(128,64,32)
345 DECL_FFT(256,128,64)
346 DECL_FFT(512,256,128)
347 #define pass pass_big
348 DECL_FFT(1024,512,256)
349 DECL_FFT(2048,1024,512)
350 DECL_FFT(4096,2048,1024)
351 DECL_FFT(8192,4096,2048)
352 DECL_FFT(16384,8192,4096)
353 DECL_FFT(32768,16384,8192)
354 DECL_FFT(65536,32768,16384)
355 DECL_FFT(131072,65536,32768)
356 
357 static void (* const fft_dispatch[])(FFTComplex*) = {
358     NULL, fft2, fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512,
359     fft1024, fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, fft131072
360 };
361 
362 #define DECL_COMP_FFT(N)                                                       \
363 static void compound_fft_##N##xM(AVTXContext *s, void *_out,                   \
364                                  void *_in, ptrdiff_t stride)                  \
365 {                                                                              \
366     const int m = s->m, *in_map = s->pfatab, *out_map = in_map + N*m;          \
367     FFTComplex *in = _in;                                                      \
368     FFTComplex *out = _out;                                                    \
369     FFTComplex fft##N##in[N];                                                  \
370     void (*fftp)(FFTComplex *z) = fft_dispatch[av_log2(m)];                    \
371                                                                                \
372     for (int i = 0; i < m; i++) {                                              \
373         for (int j = 0; j < N; j++)                                            \
374             fft##N##in[j] = in[in_map[i*N + j]];                               \
375         fft##N(s->tmp + s->revtab[i], fft##N##in, m);                          \
376     }                                                                          \
377                                                                                \
378     for (int i = 0; i < N; i++)                                                \
379         fftp(s->tmp + m*i);                                                    \
380                                                                                \
381     for (int i = 0; i < N*m; i++)                                              \
382         out[i] = s->tmp[out_map[i]];                                           \
383 }
384 
385 DECL_COMP_FFT(3)
386 DECL_COMP_FFT(5)
387 DECL_COMP_FFT(15)
388 
monolithic_fft(AVTXContext * s,void * _out,void * _in,ptrdiff_t stride)389 static void monolithic_fft(AVTXContext *s, void *_out, void *_in,
390                            ptrdiff_t stride)
391 {
392     FFTComplex *in = _in;
393     FFTComplex *out = _out;
394     int m = s->m, mb = av_log2(m);
395 
396     if (s->flags & AV_TX_INPLACE) {
397         FFTComplex tmp;
398         int src, dst, *inplace_idx = s->inplace_idx;
399 
400         src = *inplace_idx++;
401 
402         do {
403             tmp = out[src];
404             dst = s->revtab[src];
405             do {
406                 FFSWAP(FFTComplex, tmp, out[dst]);
407                 dst = s->revtab[dst];
408             } while (dst != src); /* Can be > as well, but is less predictable */
409             out[dst] = tmp;
410         } while ((src = *inplace_idx++));
411     } else {
412         for (int i = 0; i < m; i++)
413             out[i] = in[s->revtab[i]];
414     }
415 
416     fft_dispatch[mb](out);
417 }
418 
naive_fft(AVTXContext * s,void * _out,void * _in,ptrdiff_t stride)419 static void naive_fft(AVTXContext *s, void *_out, void *_in,
420                       ptrdiff_t stride)
421 {
422     FFTComplex *in = _in;
423     FFTComplex *out = _out;
424     const int n = s->n;
425     double phase = s->inv ? 2.0*M_PI/n : -2.0*M_PI/n;
426 
427     for(int i = 0; i < n; i++) {
428         FFTComplex tmp = { 0 };
429         for(int j = 0; j < n; j++) {
430             const double factor = phase*i*j;
431             const FFTComplex mult = {
432                 RESCALE(cos(factor)),
433                 RESCALE(sin(factor)),
434             };
435             FFTComplex res;
436             CMUL3(res, in[j], mult);
437             tmp.re += res.re;
438             tmp.im += res.im;
439         }
440         out[i] = tmp;
441     }
442 }
443 
444 #define DECL_COMP_IMDCT(N)                                                     \
445 static void compound_imdct_##N##xM(AVTXContext *s, void *_dst, void *_src,     \
446                                    ptrdiff_t stride)                           \
447 {                                                                              \
448     FFTComplex fft##N##in[N];                                                  \
449     FFTComplex *z = _dst, *exp = s->exptab;                                    \
450     const int m = s->m, len8 = N*m >> 1;                                       \
451     const int *in_map = s->pfatab, *out_map = in_map + N*m;                    \
452     const FFTSample *src = _src, *in1, *in2;                                   \
453     void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m)];                     \
454                                                                                \
455     stride /= sizeof(*src); /* To convert it from bytes */                     \
456     in1 = src;                                                                 \
457     in2 = src + ((N*m*2) - 1) * stride;                                        \
458                                                                                \
459     for (int i = 0; i < m; i++) {                                              \
460         for (int j = 0; j < N; j++) {                                          \
461             const int k = in_map[i*N + j];                                     \
462             FFTComplex tmp = { in2[-k*stride], in1[k*stride] };                \
463             CMUL3(fft##N##in[j], tmp, exp[k >> 1]);                            \
464         }                                                                      \
465         fft##N(s->tmp + s->revtab[i], fft##N##in, m);                          \
466     }                                                                          \
467                                                                                \
468     for (int i = 0; i < N; i++)                                                \
469         fftp(s->tmp + m*i);                                                    \
470                                                                                \
471     for (int i = 0; i < len8; i++) {                                           \
472         const int i0 = len8 + i, i1 = len8 - i - 1;                            \
473         const int s0 = out_map[i0], s1 = out_map[i1];                          \
474         FFTComplex src1 = { s->tmp[s1].im, s->tmp[s1].re };                    \
475         FFTComplex src0 = { s->tmp[s0].im, s->tmp[s0].re };                    \
476                                                                                \
477         CMUL(z[i1].re, z[i0].im, src1.re, src1.im, exp[i1].im, exp[i1].re);    \
478         CMUL(z[i0].re, z[i1].im, src0.re, src0.im, exp[i0].im, exp[i0].re);    \
479     }                                                                          \
480 }
481 
482 DECL_COMP_IMDCT(3)
483 DECL_COMP_IMDCT(5)
484 DECL_COMP_IMDCT(15)
485 
486 #define DECL_COMP_MDCT(N)                                                      \
487 static void compound_mdct_##N##xM(AVTXContext *s, void *_dst, void *_src,      \
488                                   ptrdiff_t stride)                            \
489 {                                                                              \
490     FFTSample *src = _src, *dst = _dst;                                        \
491     FFTComplex *exp = s->exptab, tmp, fft##N##in[N];                           \
492     const int m = s->m, len4 = N*m, len3 = len4 * 3, len8 = len4 >> 1;         \
493     const int *in_map = s->pfatab, *out_map = in_map + N*m;                    \
494     void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m)];                     \
495                                                                                \
496     stride /= sizeof(*dst);                                                    \
497                                                                                \
498     for (int i = 0; i < m; i++) { /* Folding and pre-reindexing */             \
499         for (int j = 0; j < N; j++) {                                          \
500             const int k = in_map[i*N + j];                                     \
501             if (k < len4) {                                                    \
502                 tmp.re = FOLD(-src[ len4 + k],  src[1*len4 - 1 - k]);          \
503                 tmp.im = FOLD(-src[ len3 + k], -src[1*len3 - 1 - k]);          \
504             } else {                                                           \
505                 tmp.re = FOLD(-src[ len4 + k], -src[5*len4 - 1 - k]);          \
506                 tmp.im = FOLD( src[-len4 + k], -src[1*len3 - 1 - k]);          \
507             }                                                                  \
508             CMUL(fft##N##in[j].im, fft##N##in[j].re, tmp.re, tmp.im,           \
509                  exp[k >> 1].re, exp[k >> 1].im);                              \
510         }                                                                      \
511         fft##N(s->tmp + s->revtab[i], fft##N##in, m);                          \
512     }                                                                          \
513                                                                                \
514     for (int i = 0; i < N; i++)                                                \
515         fftp(s->tmp + m*i);                                                    \
516                                                                                \
517     for (int i = 0; i < len8; i++) {                                           \
518         const int i0 = len8 + i, i1 = len8 - i - 1;                            \
519         const int s0 = out_map[i0], s1 = out_map[i1];                          \
520         FFTComplex src1 = { s->tmp[s1].re, s->tmp[s1].im };                    \
521         FFTComplex src0 = { s->tmp[s0].re, s->tmp[s0].im };                    \
522                                                                                \
523         CMUL(dst[2*i1*stride + stride], dst[2*i0*stride], src0.re, src0.im,    \
524              exp[i0].im, exp[i0].re);                                          \
525         CMUL(dst[2*i0*stride + stride], dst[2*i1*stride], src1.re, src1.im,    \
526              exp[i1].im, exp[i1].re);                                          \
527     }                                                                          \
528 }
529 
530 DECL_COMP_MDCT(3)
531 DECL_COMP_MDCT(5)
532 DECL_COMP_MDCT(15)
533 
monolithic_imdct(AVTXContext * s,void * _dst,void * _src,ptrdiff_t stride)534 static void monolithic_imdct(AVTXContext *s, void *_dst, void *_src,
535                              ptrdiff_t stride)
536 {
537     FFTComplex *z = _dst, *exp = s->exptab;
538     const int m = s->m, len8 = m >> 1;
539     const FFTSample *src = _src, *in1, *in2;
540     void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m)];
541 
542     stride /= sizeof(*src);
543     in1 = src;
544     in2 = src + ((m*2) - 1) * stride;
545 
546     for (int i = 0; i < m; i++) {
547         FFTComplex tmp = { in2[-2*i*stride], in1[2*i*stride] };
548         CMUL3(z[s->revtab[i]], tmp, exp[i]);
549     }
550 
551     fftp(z);
552 
553     for (int i = 0; i < len8; i++) {
554         const int i0 = len8 + i, i1 = len8 - i - 1;
555         FFTComplex src1 = { z[i1].im, z[i1].re };
556         FFTComplex src0 = { z[i0].im, z[i0].re };
557 
558         CMUL(z[i1].re, z[i0].im, src1.re, src1.im, exp[i1].im, exp[i1].re);
559         CMUL(z[i0].re, z[i1].im, src0.re, src0.im, exp[i0].im, exp[i0].re);
560     }
561 }
562 
monolithic_mdct(AVTXContext * s,void * _dst,void * _src,ptrdiff_t stride)563 static void monolithic_mdct(AVTXContext *s, void *_dst, void *_src,
564                             ptrdiff_t stride)
565 {
566     FFTSample *src = _src, *dst = _dst;
567     FFTComplex *exp = s->exptab, tmp, *z = _dst;
568     const int m = s->m, len4 = m, len3 = len4 * 3, len8 = len4 >> 1;
569     void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m)];
570 
571     stride /= sizeof(*dst);
572 
573     for (int i = 0; i < m; i++) { /* Folding and pre-reindexing */
574         const int k = 2*i;
575         if (k < len4) {
576             tmp.re = FOLD(-src[ len4 + k],  src[1*len4 - 1 - k]);
577             tmp.im = FOLD(-src[ len3 + k], -src[1*len3 - 1 - k]);
578         } else {
579             tmp.re = FOLD(-src[ len4 + k], -src[5*len4 - 1 - k]);
580             tmp.im = FOLD( src[-len4 + k], -src[1*len3 - 1 - k]);
581         }
582         CMUL(z[s->revtab[i]].im, z[s->revtab[i]].re, tmp.re, tmp.im,
583              exp[i].re, exp[i].im);
584     }
585 
586     fftp(z);
587 
588     for (int i = 0; i < len8; i++) {
589         const int i0 = len8 + i, i1 = len8 - i - 1;
590         FFTComplex src1 = { z[i1].re, z[i1].im };
591         FFTComplex src0 = { z[i0].re, z[i0].im };
592 
593         CMUL(dst[2*i1*stride + stride], dst[2*i0*stride], src0.re, src0.im,
594              exp[i0].im, exp[i0].re);
595         CMUL(dst[2*i0*stride + stride], dst[2*i1*stride], src1.re, src1.im,
596              exp[i1].im, exp[i1].re);
597     }
598 }
599 
naive_imdct(AVTXContext * s,void * _dst,void * _src,ptrdiff_t stride)600 static void naive_imdct(AVTXContext *s, void *_dst, void *_src,
601                         ptrdiff_t stride)
602 {
603     int len = s->n;
604     int len2 = len*2;
605     FFTSample *src = _src;
606     FFTSample *dst = _dst;
607     double scale = s->scale;
608     const double phase = M_PI/(4.0*len2);
609 
610     stride /= sizeof(*src);
611 
612     for (int i = 0; i < len; i++) {
613         double sum_d = 0.0;
614         double sum_u = 0.0;
615         double i_d = phase * (4*len  - 2*i - 1);
616         double i_u = phase * (3*len2 + 2*i + 1);
617         for (int j = 0; j < len2; j++) {
618             double a = (2 * j + 1);
619             double a_d = cos(a * i_d);
620             double a_u = cos(a * i_u);
621             double val = UNSCALE(src[j*stride]);
622             sum_d += a_d * val;
623             sum_u += a_u * val;
624         }
625         dst[i +   0] = RESCALE( sum_d*scale);
626         dst[i + len] = RESCALE(-sum_u*scale);
627     }
628 }
629 
naive_mdct(AVTXContext * s,void * _dst,void * _src,ptrdiff_t stride)630 static void naive_mdct(AVTXContext *s, void *_dst, void *_src,
631                        ptrdiff_t stride)
632 {
633     int len = s->n*2;
634     FFTSample *src = _src;
635     FFTSample *dst = _dst;
636     double scale = s->scale;
637     const double phase = M_PI/(4.0*len);
638 
639     stride /= sizeof(*dst);
640 
641     for (int i = 0; i < len; i++) {
642         double sum = 0.0;
643         for (int j = 0; j < len*2; j++) {
644             int a = (2*j + 1 + len) * (2*i + 1);
645             sum += UNSCALE(src[j]) * cos(a * phase);
646         }
647         dst[i*stride] = RESCALE(sum*scale);
648     }
649 }
650 
gen_mdct_exptab(AVTXContext * s,int len4,double scale)651 static int gen_mdct_exptab(AVTXContext *s, int len4, double scale)
652 {
653     const double theta = (scale < 0 ? len4 : 0) + 1.0/8.0;
654 
655     if (!(s->exptab = av_malloc_array(len4, sizeof(*s->exptab))))
656         return AVERROR(ENOMEM);
657 
658     scale = sqrt(fabs(scale));
659     for (int i = 0; i < len4; i++) {
660         const double alpha = M_PI_2 * (i + theta) / len4;
661         s->exptab[i].re = RESCALE(cos(alpha) * scale);
662         s->exptab[i].im = RESCALE(sin(alpha) * scale);
663     }
664 
665     return 0;
666 }
667 
TX_NAME(ff_tx_init_mdct_fft)668 int TX_NAME(ff_tx_init_mdct_fft)(AVTXContext *s, av_tx_fn *tx,
669                                  enum AVTXType type, int inv, int len,
670                                  const void *scale, uint64_t flags)
671 {
672     const int is_mdct = ff_tx_type_is_mdct(type);
673     int err, l, n = 1, m = 1, max_ptwo = 1 << (FF_ARRAY_ELEMS(fft_dispatch) - 1);
674 
675     if (is_mdct)
676         len >>= 1;
677 
678     l = len;
679 
680 #define CHECK_FACTOR(DST, FACTOR, SRC)                                         \
681     if (DST == 1 && !(SRC % FACTOR)) {                                         \
682         DST = FACTOR;                                                          \
683         SRC /= FACTOR;                                                         \
684     }
685     CHECK_FACTOR(n, 15, len)
686     CHECK_FACTOR(n,  5, len)
687     CHECK_FACTOR(n,  3, len)
688 #undef CHECK_FACTOR
689 
690     /* len must be a power of two now */
691     if (!(len & (len - 1)) && len >= 2 && len <= max_ptwo) {
692         m = len;
693         len = 1;
694     }
695 
696     s->n = n;
697     s->m = m;
698     s->inv = inv;
699     s->type = type;
700     s->flags = flags;
701 
702     /* If we weren't able to split the length into factors we can handle,
703      * resort to using the naive and slow FT. This also filters out
704      * direct 3, 5 and 15 transforms as they're too niche. */
705     if (len > 1 || m == 1) {
706         if (is_mdct && (l & 1)) /* Odd (i)MDCTs are not supported yet */
707             return AVERROR(ENOSYS);
708         if (flags & AV_TX_INPLACE) /* Neither are in-place naive transforms */
709             return AVERROR(ENOSYS);
710         s->n = l;
711         s->m = 1;
712         *tx = naive_fft;
713         if (is_mdct) {
714             s->scale = *((SCALE_TYPE *)scale);
715             *tx = inv ? naive_imdct : naive_mdct;
716         }
717         return 0;
718     }
719 
720     if (n > 1 && m > 1) { /* 2D transform case */
721         if ((err = ff_tx_gen_compound_mapping(s)))
722             return err;
723         if (!(s->tmp = av_malloc(n*m*sizeof(*s->tmp))))
724             return AVERROR(ENOMEM);
725         *tx = n == 3 ? compound_fft_3xM :
726               n == 5 ? compound_fft_5xM :
727                        compound_fft_15xM;
728         if (is_mdct)
729             *tx = n == 3 ? inv ? compound_imdct_3xM  : compound_mdct_3xM :
730                   n == 5 ? inv ? compound_imdct_5xM  : compound_mdct_5xM :
731                            inv ? compound_imdct_15xM : compound_mdct_15xM;
732     } else { /* Direct transform case */
733         *tx = monolithic_fft;
734         if (is_mdct)
735             *tx = inv ? monolithic_imdct : monolithic_mdct;
736     }
737 
738     if (n != 1)
739         init_cos_tabs(0);
740     if (m != 1) {
741         if ((err = ff_tx_gen_ptwo_revtab(s, n == 1 && !is_mdct && !(flags & AV_TX_INPLACE))))
742             return err;
743         if (flags & AV_TX_INPLACE) {
744             if (is_mdct) /* In-place MDCTs are not supported yet */
745                 return AVERROR(ENOSYS);
746             if ((err = ff_tx_gen_ptwo_inplace_revtab_idx(s)))
747                 return err;
748         }
749         for (int i = 4; i <= av_log2(m); i++)
750             init_cos_tabs(i);
751     }
752 
753     if (is_mdct)
754         return gen_mdct_exptab(s, n*m, *((SCALE_TYPE *)scale));
755 
756     return 0;
757 }
758