git.sesse.net Git - ffmpeg/blob - libavutil/tx_template.c

   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
  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] = 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
  95 static av_cold void ff_init_53_tabs(void)
  96 {
  97     TX_NAME(ff_cos_53)[0] = (FFTComplex){ cos(2 * M_PI / 12), cos(2 * M_PI / 12) };
  98     TX_NAME(ff_cos_53)[1] = (FFTComplex){ 0.5, 0.5 };
  99     TX_NAME(ff_cos_53)[2] = (FFTComplex){ cos(2 * M_PI /  5), sin(2 * M_PI /  5) };
 100     TX_NAME(ff_cos_53)[3] = (FFTComplex){ cos(2 * M_PI / 10), 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
 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
 130 static av_always_inline void fft3(FFTComplex *out, FFTComplex *in,
 131                                   ptrdiff_t stride)
 132 {
 133     FFTComplex tmp[2];
 134
 135     tmp[0].re = in[1].im - in[2].im;
 136     tmp[0].im = in[1].re - in[2].re;
 137     tmp[1].re = in[1].re + in[2].re;
 138     tmp[1].im = in[1].im + in[2].im;
 139
 140     out[0*stride].re = in[0].re + tmp[1].re;
 141     out[0*stride].im = in[0].im + tmp[1].im;
 142
 143     tmp[0].re *= TX_NAME(ff_cos_53)[0].re;
 144     tmp[0].im *= TX_NAME(ff_cos_53)[0].im;
 145     tmp[1].re *= TX_NAME(ff_cos_53)[1].re;
 146     tmp[1].im *= TX_NAME(ff_cos_53)[1].re;
 147
 148     out[1*stride].re = in[0].re - tmp[1].re + tmp[0].re;
 149     out[1*stride].im = in[0].im - tmp[1].im - tmp[0].im;
 150     out[2*stride].re = in[0].re - tmp[1].re - tmp[0].re;
 151     out[2*stride].im = in[0].im - tmp[1].im + tmp[0].im;
 152 }
 153
 154 #define DECL_FFT5(NAME, D0, D1, D2, D3, D4)                                    \
 155 static av_always_inline void NAME(FFTComplex *out, FFTComplex *in,             \
 156                                   ptrdiff_t stride)                            \
 157 {                                                                              \
 158     FFTComplex z0[4], t[6];                                                    \
 159                                                                                \
 160     t[0].re = in[1].re + in[4].re;                                             \
 161     t[0].im = in[1].im + in[4].im;                                             \
 162     t[1].im = in[1].re - in[4].re;                                             \
 163     t[1].re = in[1].im - in[4].im;                                             \
 164     t[2].re = in[2].re + in[3].re;                                             \
 165     t[2].im = in[2].im + in[3].im;                                             \
 166     t[3].im = in[2].re - in[3].re;                                             \
 167     t[3].re = in[2].im - in[3].im;                                             \
 168                                                                                \
 169     out[D0*stride].re = in[0].re + in[1].re + in[2].re +                       \
 170                         in[3].re + in[4].re;                                   \
 171     out[D0*stride].im = in[0].im + in[1].im + in[2].im +                       \
 172                         in[3].im + in[4].im;                                   \
 173                                                                                \
 174     t[4].re  = TX_NAME(ff_cos_53)[2].re * t[2].re;                             \
 175     t[4].im  = TX_NAME(ff_cos_53)[2].re * t[2].im;                             \
 176     t[4].re -= TX_NAME(ff_cos_53)[3].re * t[0].re;                             \
 177     t[4].im -= TX_NAME(ff_cos_53)[3].re * t[0].im;                             \
 178     t[0].re  = TX_NAME(ff_cos_53)[2].re * t[0].re;                             \
 179     t[0].im  = TX_NAME(ff_cos_53)[2].re * t[0].im;                             \
 180     t[0].re -= TX_NAME(ff_cos_53)[3].re * t[2].re;                             \
 181     t[0].im -= TX_NAME(ff_cos_53)[3].re * t[2].im;                             \
 182     t[5].re  = TX_NAME(ff_cos_53)[2].im * t[3].re;                             \
 183     t[5].im  = TX_NAME(ff_cos_53)[2].im * t[3].im;                             \
 184     t[5].re -= TX_NAME(ff_cos_53)[3].im * t[1].re;                             \
 185     t[5].im -= TX_NAME(ff_cos_53)[3].im * t[1].im;                             \
 186     t[1].re  = TX_NAME(ff_cos_53)[2].im * t[1].re;                             \
 187     t[1].im  = TX_NAME(ff_cos_53)[2].im * t[1].im;                             \
 188     t[1].re += TX_NAME(ff_cos_53)[3].im * t[3].re;                             \
 189     t[1].im += TX_NAME(ff_cos_53)[3].im * t[3].im;                             \
 190                                                                                \
 191     z0[0].re = t[0].re - t[1].re;                                              \
 192     z0[0].im = t[0].im - t[1].im;                                              \
 193     z0[1].re = t[4].re + t[5].re;                                              \
 194     z0[1].im = t[4].im + t[5].im;                                              \
 195                                                                                \
 196     z0[2].re = t[4].re - t[5].re;                                              \
 197     z0[2].im = t[4].im - t[5].im;                                              \
 198     z0[3].re = t[0].re + t[1].re;                                              \
 199     z0[3].im = t[0].im + t[1].im;                                              \
 200                                                                                \
 201     out[D1*stride].re = in[0].re + z0[3].re;                                   \
 202     out[D1*stride].im = in[0].im + z0[0].im;                                   \
 203     out[D2*stride].re = in[0].re + z0[2].re;                                   \
 204     out[D2*stride].im = in[0].im + z0[1].im;                                   \
 205     out[D3*stride].re = in[0].re + z0[1].re;                                   \
 206     out[D3*stride].im = in[0].im + z0[2].im;                                   \
 207     out[D4*stride].re = in[0].re + z0[0].re;                                   \
 208     out[D4*stride].im = in[0].im + z0[3].im;                                   \
 209 }
 210
 211 DECL_FFT5(fft5,     0,  1,  2,  3,  4)
 212 DECL_FFT5(fft5_m1,  0,  6, 12,  3,  9)
 213 DECL_FFT5(fft5_m2, 10,  1,  7, 13,  4)
 214 DECL_FFT5(fft5_m3,  5, 11,  2,  8, 14)
 215
 216 static av_always_inline void fft15(FFTComplex *out, FFTComplex *in,
 217                                    ptrdiff_t stride)
 218 {
 219     FFTComplex tmp[15];
 220
 221     for (int i = 0; i < 5; i++)
 222         fft3(tmp + i, in + i*3, 5);
 223
 224     fft5_m1(out, tmp +  0, stride);
 225     fft5_m2(out, tmp +  5, stride);
 226     fft5_m3(out, tmp + 10, stride);
 227 }
 228
 229 #define BUTTERFLIES(a0,a1,a2,a3) {\
 230     BF(t3, t5, t5, t1);\
 231     BF(a2.re, a0.re, a0.re, t5);\
 232     BF(a3.im, a1.im, a1.im, t3);\
 233     BF(t4, t6, t2, t6);\
 234     BF(a3.re, a1.re, a1.re, t4);\
 235     BF(a2.im, a0.im, a0.im, t6);\
 236 }
 237
 238 // force loading all the inputs before storing any.
 239 // this is slightly slower for small data, but avoids store->load aliasing
 240 // for addresses separated by large powers of 2.
 241 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 242     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 243     BF(t3, t5, t5, t1);\
 244     BF(a2.re, a0.re, r0, t5);\
 245     BF(a3.im, a1.im, i1, t3);\
 246     BF(t4, t6, t2, t6);\
 247     BF(a3.re, a1.re, r1, t4);\
 248     BF(a2.im, a0.im, i0, t6);\
 249 }
 250
 251 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 252     CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
 253     CMUL(t5, t6, a3.re, a3.im, wre,  wim);\
 254     BUTTERFLIES(a0,a1,a2,a3)\
 255 }
 256
 257 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
 258     t1 = a2.re;\
 259     t2 = a2.im;\
 260     t5 = a3.re;\
 261     t6 = a3.im;\
 262     BUTTERFLIES(a0,a1,a2,a3)\
 263 }
 264
 265 /* z[0...8n-1], w[1...2n-1] */
 266 #define PASS(name)\
 267 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
 268 {\
 269     FFTSample t1, t2, t3, t4, t5, t6;\
 270     int o1 = 2*n;\
 271     int o2 = 4*n;\
 272     int o3 = 6*n;\
 273     const FFTSample *wim = wre+o1;\
 274     n--;\
 275 \
 276     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
 277     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 278     do {\
 279         z += 2;\
 280         wre += 2;\
 281         wim -= 2;\
 282         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
 283         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 284     } while(--n);\
 285 }
 286
 287 PASS(pass)
 288 #undef BUTTERFLIES
 289 #define BUTTERFLIES BUTTERFLIES_BIG
 290 PASS(pass_big)
 291
 292 #define DECL_FFT(n,n2,n4)\
 293 static void fft##n(FFTComplex *z)\
 294 {\
 295     fft##n2(z);\
 296     fft##n4(z+n4*2);\
 297     fft##n4(z+n4*3);\
 298     pass(z,TX_NAME(ff_cos_##n),n4/2);\
 299 }
 300
 301 static void fft4(FFTComplex *z)
 302 {
 303     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
 304
 305     BF(t3, t1, z[0].re, z[1].re);
 306     BF(t8, t6, z[3].re, z[2].re);
 307     BF(z[2].re, z[0].re, t1, t6);
 308     BF(t4, t2, z[0].im, z[1].im);
 309     BF(t7, t5, z[2].im, z[3].im);
 310     BF(z[3].im, z[1].im, t4, t8);
 311     BF(z[3].re, z[1].re, t3, t7);
 312     BF(z[2].im, z[0].im, t2, t5);
 313 }
 314
 315 static void fft8(FFTComplex *z)
 316 {
 317     FFTSample t1, t2, t3, t4, t5, t6;
 318
 319     fft4(z);
 320
 321     BF(t1, z[5].re, z[4].re, -z[5].re);
 322     BF(t2, z[5].im, z[4].im, -z[5].im);
 323     BF(t5, z[7].re, z[6].re, -z[7].re);
 324     BF(t6, z[7].im, z[6].im, -z[7].im);
 325
 326     BUTTERFLIES(z[0],z[2],z[4],z[6]);
 327     TRANSFORM(z[1],z[3],z[5],z[7],M_SQRT1_2,M_SQRT1_2);
 328 }
 329
 330 static void fft16(FFTComplex *z)
 331 {
 332     FFTSample t1, t2, t3, t4, t5, t6;
 333     FFTSample cos_16_1 = TX_NAME(ff_cos_16)[1];
 334     FFTSample cos_16_3 = TX_NAME(ff_cos_16)[3];
 335
 336     fft8(z);
 337     fft4(z+8);
 338     fft4(z+12);
 339
 340     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
 341     TRANSFORM(z[2],z[6],z[10],z[14],M_SQRT1_2,M_SQRT1_2);
 342     TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
 343     TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
 344 }
 345
 346 DECL_FFT(32,16,8)
 347 DECL_FFT(64,32,16)
 348 DECL_FFT(128,64,32)
 349 DECL_FFT(256,128,64)
 350 DECL_FFT(512,256,128)
 351 #define pass pass_big
 352 DECL_FFT(1024,512,256)
 353 DECL_FFT(2048,1024,512)
 354 DECL_FFT(4096,2048,1024)
 355 DECL_FFT(8192,4096,2048)
 356 DECL_FFT(16384,8192,4096)
 357 DECL_FFT(32768,16384,8192)
 358 DECL_FFT(65536,32768,16384)
 359 DECL_FFT(131072,65536,32768)
 360
 361 static void (* const fft_dispatch[])(FFTComplex*) = {
 362     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 363     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, fft131072
 364 };
 365
 366 #define DECL_COMP_FFT(N)                                                       \
 367 static void compound_fft_##N##xM(AVTXContext *s, void *_out,                   \
 368                                  void *_in, ptrdiff_t stride)                  \
 369 {                                                                              \
 370     const int m = s->m, *in_map = s->pfatab, *out_map = in_map + N*m;          \
 371     FFTComplex *in = _in;                                                      \
 372     FFTComplex *out = _out;                                                    \
 373     FFTComplex fft##N##in[N];                                                  \
 374     void (*fftp)(FFTComplex *z) = fft_dispatch[av_log2(m) - 2];                \
 375                                                                                \
 376     for (int i = 0; i < m; i++) {                                              \
 377         for (int j = 0; j < N; j++)                                            \
 378             fft##N##in[j] = in[in_map[i*N + j]];                               \
 379         fft##N(s->tmp + s->revtab[i], fft##N##in, m);                          \
 380     }                                                                          \
 381                                                                                \
 382     for (int i = 0; i < N; i++)                                                \
 383         fftp(s->tmp + m*i);                                                    \
 384                                                                                \
 385     for (int i = 0; i < N*m; i++)                                              \
 386         out[i] = s->tmp[out_map[i]];                                           \
 387 }
 388
 389 DECL_COMP_FFT(3)
 390 DECL_COMP_FFT(5)
 391 DECL_COMP_FFT(15)
 392
 393 static void monolithic_fft(AVTXContext *s, void *_out, void *_in,
 394                            ptrdiff_t stride)
 395 {
 396     FFTComplex *in = _in;
 397     FFTComplex *out = _out;
 398     int m = s->m, mb = av_log2(m) - 2;
 399     for (int i = 0; i < m; i++)
 400         out[s->revtab[i]] = in[i];
 401     fft_dispatch[mb](out);
 402 }
 403
 404 #define DECL_COMP_IMDCT(N)                                                     \
 405 static void compound_imdct_##N##xM(AVTXContext *s, void *_dst, void *_src,     \
 406                                    ptrdiff_t stride)                           \
 407 {                                                                              \
 408     FFTComplex fft##N##in[N];                                                  \
 409     FFTComplex *z = _dst, *exp = s->exptab;                                    \
 410     const int m = s->m, len8 = N*m >> 1;                                       \
 411     const int *in_map = s->pfatab, *out_map = in_map + N*m;                    \
 412     const FFTSample *src = _src, *in1, *in2;                                   \
 413     void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];                 \
 414                                                                                \
 415     stride /= sizeof(*src); /* To convert it from bytes */                     \
 416     in1 = src;                                                                 \
 417     in2 = src + ((N*m*2) - 1) * stride;                                        \
 418                                                                                \
 419     for (int i = 0; i < m; i++) {                                              \
 420         for (int j = 0; j < N; j++) {                                          \
 421             const int k = in_map[i*N + j];                                     \
 422             FFTComplex tmp = { in2[-k*stride], in1[k*stride] };                \
 423             CMUL3(fft##N##in[j], tmp, exp[k >> 1]);                            \
 424         }                                                                      \
 425         fft##N(s->tmp + s->revtab[i], fft##N##in, m);                          \
 426     }                                                                          \
 427                                                                                \
 428     for (int i = 0; i < N; i++)                                                \
 429         fftp(s->tmp + m*i);                                                    \
 430                                                                                \
 431     for (int i = 0; i < len8; i++) {                                           \
 432         const int i0 = len8 + i, i1 = len8 - i - 1;                            \
 433         const int s0 = out_map[i0], s1 = out_map[i1];                          \
 434         FFTComplex src1 = { s->tmp[s1].im, s->tmp[s1].re };                    \
 435         FFTComplex src0 = { s->tmp[s0].im, s->tmp[s0].re };                    \
 436                                                                                \
 437         CMUL(z[i1].re, z[i0].im, src1.re, src1.im, exp[i1].im, exp[i1].re);    \
 438         CMUL(z[i0].re, z[i1].im, src0.re, src0.im, exp[i0].im, exp[i0].re);    \
 439     }                                                                          \
 440 }
 441
 442 DECL_COMP_IMDCT(3)
 443 DECL_COMP_IMDCT(5)
 444 DECL_COMP_IMDCT(15)
 445
 446 #define DECL_COMP_MDCT(N)                                                      \
 447 static void compound_mdct_##N##xM(AVTXContext *s, void *_dst, void *_src,      \
 448                                   ptrdiff_t stride)                            \
 449 {                                                                              \
 450     FFTSample *src = _src, *dst = _dst;                                        \
 451     FFTComplex *exp = s->exptab, tmp, fft##N##in[N];                           \
 452     const int m = s->m, len4 = N*m, len3 = len4 * 3, len8 = len4 >> 1;         \
 453     const int *in_map = s->pfatab, *out_map = in_map + N*m;                    \
 454     void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];                 \
 455                                                                                \
 456     stride /= sizeof(*dst);                                                    \
 457                                                                                \
 458     for (int i = 0; i < m; i++) { /* Folding and pre-reindexing */             \
 459         for (int j = 0; j < N; j++) {                                          \
 460             const int k = in_map[i*N + j];                                     \
 461             if (k < len4) {                                                    \
 462                 tmp.re = -src[ len4 + k] + src[1*len4 - 1 - k];                \
 463                 tmp.im = -src[ len3 + k] - src[1*len3 - 1 - k];                \
 464             } else {                                                           \
 465                 tmp.re = -src[ len4 + k] - src[5*len4 - 1 - k];                \
 466                 tmp.im =  src[-len4 + k] - src[1*len3 - 1 - k];                \
 467             }                                                                  \
 468             CMUL(fft##N##in[j].im, fft##N##in[j].re, tmp.re, tmp.im,           \
 469                  exp[k >> 1].re, exp[k >> 1].im);                              \
 470         }                                                                      \
 471         fft##N(s->tmp + s->revtab[i], fft##N##in, m);                          \
 472     }                                                                          \
 473                                                                                \
 474     for (int i = 0; i < N; i++)                                                \
 475         fftp(s->tmp + m*i);                                                    \
 476                                                                                \
 477     for (int i = 0; i < len8; i++) {                                           \
 478         const int i0 = len8 + i, i1 = len8 - i - 1;                            \
 479         const int s0 = out_map[i0], s1 = out_map[i1];                          \
 480         FFTComplex src1 = { s->tmp[s1].re, s->tmp[s1].im };                    \
 481         FFTComplex src0 = { s->tmp[s0].re, s->tmp[s0].im };                    \
 482                                                                                \
 483         CMUL(dst[2*i1*stride + stride], dst[2*i0*stride], src0.re, src0.im,    \
 484              exp[i0].im, exp[i0].re);                                          \
 485         CMUL(dst[2*i0*stride + stride], dst[2*i1*stride], src1.re, src1.im,    \
 486              exp[i1].im, exp[i1].re);                                          \
 487     }                                                                          \
 488 }
 489
 490 DECL_COMP_MDCT(3)
 491 DECL_COMP_MDCT(5)
 492 DECL_COMP_MDCT(15)
 493
 494 static void monolithic_imdct(AVTXContext *s, void *_dst, void *_src,
 495                              ptrdiff_t stride)
 496 {
 497     FFTComplex *z = _dst, *exp = s->exptab;
 498     const int m = s->m, len8 = m >> 1;
 499     const FFTSample *src = _src, *in1, *in2;
 500     void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];
 501
 502     stride /= sizeof(*src);
 503     in1 = src;
 504     in2 = src + ((m*2) - 1) * stride;
 505
 506     for (int i = 0; i < m; i++) {
 507         FFTComplex tmp = { in2[-2*i*stride], in1[2*i*stride] };
 508         CMUL3(z[s->revtab[i]], tmp, exp[i]);
 509     }
 510
 511     fftp(z);
 512
 513     for (int i = 0; i < len8; i++) {
 514         const int i0 = len8 + i, i1 = len8 - i - 1;
 515         FFTComplex src1 = { z[i1].im, z[i1].re };
 516         FFTComplex src0 = { z[i0].im, z[i0].re };
 517
 518         CMUL(z[i1].re, z[i0].im, src1.re, src1.im, exp[i1].im, exp[i1].re);
 519         CMUL(z[i0].re, z[i1].im, src0.re, src0.im, exp[i0].im, exp[i0].re);
 520     }
 521 }
 522
 523 static void monolithic_mdct(AVTXContext *s, void *_dst, void *_src,
 524                             ptrdiff_t stride)
 525 {
 526     FFTSample *src = _src, *dst = _dst;
 527     FFTComplex *exp = s->exptab, tmp, *z = _dst;
 528     const int m = s->m, len4 = m, len3 = len4 * 3, len8 = len4 >> 1;
 529     void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];
 530
 531     stride /= sizeof(*dst);
 532
 533     for (int i = 0; i < m; i++) { /* Folding and pre-reindexing */
 534         const int k = 2*i;
 535         if (k < len4) {
 536             tmp.re = -src[ len4 + k] + src[1*len4 - 1 - k];
 537             tmp.im = -src[ len3 + k] - src[1*len3 - 1 - k];
 538         } else {
 539             tmp.re = -src[ len4 + k] - src[5*len4 - 1 - k];
 540             tmp.im =  src[-len4 + k] - src[1*len3 - 1 - k];
 541         }
 542         CMUL(z[s->revtab[i]].im, z[s->revtab[i]].re, tmp.re, tmp.im,
 543              exp[i].re, exp[i].im);
 544     }
 545
 546     fftp(z);
 547
 548     for (int i = 0; i < len8; i++) {
 549         const int i0 = len8 + i, i1 = len8 - i - 1;
 550         FFTComplex src1 = { z[i1].re, z[i1].im };
 551         FFTComplex src0 = { z[i0].re, z[i0].im };
 552
 553         CMUL(dst[2*i1*stride + stride], dst[2*i0*stride], src0.re, src0.im,
 554              exp[i0].im, exp[i0].re);
 555         CMUL(dst[2*i0*stride + stride], dst[2*i1*stride], src1.re, src1.im,
 556              exp[i1].im, exp[i1].re);
 557     }
 558 }
 559
 560 static int gen_mdct_exptab(AVTXContext *s, int len4, double scale)
 561 {
 562     const double theta = (scale < 0 ? len4 : 0) + 1.0/8.0;
 563
 564     if (!(s->exptab = av_malloc_array(len4, sizeof(*s->exptab))))
 565         return AVERROR(ENOMEM);
 566
 567     scale = sqrt(fabs(scale));
 568     for (int i = 0; i < len4; i++) {
 569         const double alpha = M_PI_2 * (i + theta) / len4;
 570         s->exptab[i].re = cos(alpha) * scale;
 571         s->exptab[i].im = sin(alpha) * scale;
 572     }
 573
 574     return 0;
 575 }
 576
 577 int TX_NAME(ff_tx_init_mdct_fft)(AVTXContext *s, av_tx_fn *tx,
 578                                  enum AVTXType type, int inv, int len,
 579                                  const void *scale, uint64_t flags)
 580 {
 581     const int is_mdct = type == AV_TX_FLOAT_MDCT || type == AV_TX_DOUBLE_MDCT;
 582     int err, n = 1, m = 1, max_ptwo = 1 << (FF_ARRAY_ELEMS(fft_dispatch) + 1);
 583
 584     if (is_mdct)
 585         len >>= 1;
 586
 587 #define CHECK_FACTOR(DST, FACTOR, SRC)                                         \
 588     if (DST == 1 && !(SRC % FACTOR)) {                                         \
 589         DST = FACTOR;                                                          \
 590         SRC /= FACTOR;                                                         \
 591     }
 592     CHECK_FACTOR(n, 15, len)
 593     CHECK_FACTOR(n,  5, len)
 594     CHECK_FACTOR(n,  3, len)
 595 #undef CHECK_NPTWO_FACTOR
 596
 597     /* len must be a power of two now */
 598     if (!(len & (len - 1)) && len >= 4 && len <= max_ptwo) {
 599         m = len;
 600         len = 1;
 601     }
 602
 603     s->n = n;
 604     s->m = m;
 605     s->inv = inv;
 606     s->type = type;
 607
 608     /* Filter out direct 3, 5 and 15 transforms, too niche */
 609     if (len > 1 || m == 1) {
 610         av_log(NULL, AV_LOG_ERROR, "Unsupported transform size: n = %i, "
 611                "m = %i, residual = %i!\n", n, m, len);
 612         return AVERROR(EINVAL);
 613     } else if (n > 1 && m > 1) { /* 2D transform case */
 614         if ((err = ff_tx_gen_compound_mapping(s)))
 615             return err;
 616         if (!(s->tmp = av_malloc(n*m*sizeof(*s->tmp))))
 617             return AVERROR(ENOMEM);
 618         *tx = n == 3 ? compound_fft_3xM :
 619               n == 5 ? compound_fft_5xM :
 620                        compound_fft_15xM;
 621         if (is_mdct)
 622             *tx = n == 3 ? inv ? compound_imdct_3xM  : compound_mdct_3xM :
 623                   n == 5 ? inv ? compound_imdct_5xM  : compound_mdct_5xM :
 624                            inv ? compound_imdct_15xM : compound_mdct_15xM;
 625     } else { /* Direct transform case */
 626         *tx = monolithic_fft;
 627         if (is_mdct)
 628             *tx = inv ? monolithic_imdct : monolithic_mdct;
 629     }
 630
 631     if (n != 1)
 632         init_cos_tabs(0);
 633     if (m != 1) {
 634         ff_tx_gen_ptwo_revtab(s);
 635         for (int i = 4; i <= av_log2(m); i++)
 636             init_cos_tabs(i);
 637     }
 638
 639     if (is_mdct)
 640         return gen_mdct_exptab(s, n*m, *((FFTSample *)scale));
 641
 642     return 0;
 643 }