FFmpeg: libavcodec/fft.c Source File

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fft.c

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1 /*

2 * FFT/IFFT transforms

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 */

24 /**

25 * @file

26 * FFT/IFFT transforms.

27 */

29 #include <stdlib.h>

30 #include <string.h>

31 #include "libavutil/mathematics.h"

32 #include "fft.h"

33 #include "fft-internal.h"

35 #if CONFIG_FFT_FIXED_32

36 #include "fft_table.h"

37 #else /* CONFIG_FFT_FIXED_32 */

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 };

72 #endif /* CONFIG_FFT_FIXED_32 */

74 static void fft_permute_c(FFTContext *s, FFTComplex *z);

75 static void fft_calc_c(FFTContext *s, FFTComplex *z);

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 }

88 av_cold void ff_init_ff_cos_tabs(int index)

89 {

90 #if (!CONFIG_HARDCODED_TABLES) && (!CONFIG_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

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

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

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 CONFIG_FFT_FIXED_32

167 {

168 int n=0;

169 ff_fft_lut_init(fft_offsets_lut, 0, 1 << 16, &n);

170 }

171 #else /* CONFIG_FFT_FIXED_32 */

172 #if CONFIG_FFT_FLOAT

173 if (ARCH_ARM) ff_fft_init_arm(s);

174 if (ARCH_PPC) ff_fft_init_ppc(s);

175 if (ARCH_X86) ff_fft_init_x86(s);

176 if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc;

177 if (HAVE_MIPSFPU) ff_fft_init_mips(s);

178 #else

179 if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c;

180 if (ARCH_ARM) ff_fft_fixed_init_arm(s);

181 #endif

182 for(j=4; j<=nbits; j++) {

183 ff_init_ff_cos_tabs(j);

184 }

185 #endif /* CONFIG_FFT_FIXED_32 */

186

187

188 if (s->fft_permutation == FF_FFT_PERM_AVX) {

189 fft_perm_avx(s);

190 } else {

191 for(i=0; i<n; i++) {

192 j = i;

193 if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)

194 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);

195 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;

196 }

197 }

198

199 return 0;

200 fail:

201 av_freep(&s->revtab);

202 av_freep(&s->tmp_buf);

203 return -1;

204 }

205

206 static void fft_permute_c(FFTContext *s, FFTComplex *z)

207 {

208 int j, np;

209 const uint16_t *revtab = s->revtab;

210 np = 1 << s->nbits;

211 /* TODO: handle split-radix permute in a more optimal way, probably in-place */

212 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];

213 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));

214 }

215

216 av_cold void ff_fft_end(FFTContext *s)

217 {

218 av_freep(&s->revtab);

219 av_freep(&s->tmp_buf);

220 }

221

222 #if CONFIG_FFT_FIXED_32

223

224 static void fft_calc_c(FFTContext *s, FFTComplex *z) {

225

226 int nbits, i, n, num_transforms, offset, step;

227 int n4, n2, n34;

228 FFTSample tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8;

229 FFTComplex *tmpz;

230 FFTSample w_re, w_im;

231 FFTSample *w_re_ptr, *w_im_ptr;

232 const int fft_size = (1 << s->nbits);

233 int64_t accu;

234

235 num_transforms = (0x2aab >> (16 - s->nbits)) | 1;

236

237 for (n=0; n<num_transforms; n++){

238 offset = fft_offsets_lut[n] << 2;

239 tmpz = z + offset;

240

241 tmp1 = tmpz[0].re + tmpz[1].re;

242 tmp5 = tmpz[2].re + tmpz[3].re;

243 tmp2 = tmpz[0].im + tmpz[1].im;

244 tmp6 = tmpz[2].im + tmpz[3].im;

245 tmp3 = tmpz[0].re - tmpz[1].re;

246 tmp8 = tmpz[2].im - tmpz[3].im;

247 tmp4 = tmpz[0].im - tmpz[1].im;

248 tmp7 = tmpz[2].re - tmpz[3].re;

249

250 tmpz[0].re = tmp1 + tmp5;

251 tmpz[2].re = tmp1 - tmp5;

252 tmpz[0].im = tmp2 + tmp6;

253 tmpz[2].im = tmp2 - tmp6;

254 tmpz[1].re = tmp3 + tmp8;

255 tmpz[3].re = tmp3 - tmp8;

256 tmpz[1].im = tmp4 - tmp7;

257 tmpz[3].im = tmp4 + tmp7;

258 }

259

260 if (fft_size < 8)

261 return;

262

263 num_transforms = (num_transforms >> 1) | 1;

264

265 for (n=0; n<num_transforms; n++){

266 offset = fft_offsets_lut[n] << 3;

267 tmpz = z + offset;

268

269 tmp1 = tmpz[4].re + tmpz[5].re;

270 tmp3 = tmpz[6].re + tmpz[7].re;

271 tmp2 = tmpz[4].im + tmpz[5].im;

272 tmp4 = tmpz[6].im + tmpz[7].im;

273 tmp5 = tmp1 + tmp3;

274 tmp7 = tmp1 - tmp3;

275 tmp6 = tmp2 + tmp4;

276 tmp8 = tmp2 - tmp4;

277

278 tmp1 = tmpz[4].re - tmpz[5].re;

279 tmp2 = tmpz[4].im - tmpz[5].im;

280 tmp3 = tmpz[6].re - tmpz[7].re;

281 tmp4 = tmpz[6].im - tmpz[7].im;

282

283 tmpz[4].re = tmpz[0].re - tmp5;

284 tmpz[0].re = tmpz[0].re + tmp5;

285 tmpz[4].im = tmpz[0].im - tmp6;

286 tmpz[0].im = tmpz[0].im + tmp6;

287 tmpz[6].re = tmpz[2].re - tmp8;

288 tmpz[2].re = tmpz[2].re + tmp8;

289 tmpz[6].im = tmpz[2].im + tmp7;

290 tmpz[2].im = tmpz[2].im - tmp7;

291

292 accu = (int64_t)Q31(M_SQRT1_2)*(tmp1 + tmp2);

293 tmp5 = (int32_t)((accu + 0x40000000) >> 31);

294 accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 - tmp4);

295 tmp7 = (int32_t)((accu + 0x40000000) >> 31);

296 accu = (int64_t)Q31(M_SQRT1_2)*(tmp2 - tmp1);

297 tmp6 = (int32_t)((accu + 0x40000000) >> 31);

298 accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 + tmp4);

299 tmp8 = (int32_t)((accu + 0x40000000) >> 31);

300 tmp1 = tmp5 + tmp7;

301 tmp3 = tmp5 - tmp7;

302 tmp2 = tmp6 + tmp8;

303 tmp4 = tmp6 - tmp8;

304

305 tmpz[5].re = tmpz[1].re - tmp1;

306 tmpz[1].re = tmpz[1].re + tmp1;

307 tmpz[5].im = tmpz[1].im - tmp2;

308 tmpz[1].im = tmpz[1].im + tmp2;

309 tmpz[7].re = tmpz[3].re - tmp4;

310 tmpz[3].re = tmpz[3].re + tmp4;

311 tmpz[7].im = tmpz[3].im + tmp3;

312 tmpz[3].im = tmpz[3].im - tmp3;

313 }

314

315 step = 1 << ((MAX_LOG2_NFFT-4) - 4);

316 n4 = 4;

317

318 for (nbits=4; nbits<=s->nbits; nbits++){

319 n2 = 2*n4;

320 n34 = 3*n4;

321 num_transforms = (num_transforms >> 1) | 1;

322

323 for (n=0; n<num_transforms; n++){

324 offset = fft_offsets_lut[n] << nbits;

325 tmpz = z + offset;

326

327 tmp5 = tmpz[ n2].re + tmpz[n34].re;

328 tmp1 = tmpz[ n2].re - tmpz[n34].re;

329 tmp6 = tmpz[ n2].im + tmpz[n34].im;

330 tmp2 = tmpz[ n2].im - tmpz[n34].im;

331

332 tmpz[ n2].re = tmpz[ 0].re - tmp5;

333 tmpz[ 0].re = tmpz[ 0].re + tmp5;

334 tmpz[ n2].im = tmpz[ 0].im - tmp6;

335 tmpz[ 0].im = tmpz[ 0].im + tmp6;

336 tmpz[n34].re = tmpz[n4].re - tmp2;

337 tmpz[ n4].re = tmpz[n4].re + tmp2;

338 tmpz[n34].im = tmpz[n4].im + tmp1;

339 tmpz[ n4].im = tmpz[n4].im - tmp1;

340

341 w_re_ptr = w_tab_sr + step;

342 w_im_ptr = w_tab_sr + MAX_FFT_SIZE/(4*16) - step;

343

344 for (i=1; i<n4; i++){

345 w_re = w_re_ptr[0];

346 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);

359

360 tmp5 = tmp1 + tmp3;

361 tmp1 = tmp1 - tmp3;

362 tmp6 = tmp2 + tmp4;

363 tmp2 = tmp2 - tmp4;

364

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;

373

374 w_re_ptr += step;

375 w_im_ptr -= step;

376 }

377 }

378 step >>= 1;

379 n4 <<= 1;

380 }

381 }

382

383 #else /* CONFIG_FFT_FIXED_32 */

384

385 #define BUTTERFLIES(a0,a1,a2,a3) {\

386 BF(t3, t5, t5, t1);\

387 BF(a2.re, a0.re, a0.re, t5);\

388 BF(a3.im, a1.im, a1.im, t3);\

389 BF(t4, t6, t2, t6);\

390 BF(a3.re, a1.re, a1.re, t4);\

391 BF(a2.im, a0.im, a0.im, t6);\

392 }

393

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;\

399 BF(t3, t5, t5, t1);\

400 BF(a2.re, a0.re, r0, t5);\

401 BF(a3.im, a1.im, i1, t3);\

402 BF(t4, t6, t2, t6);\

403 BF(a3.re, a1.re, r1, t4);\

404 BF(a2.im, a0.im, i0, t6);\

405 }

406

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)\

411 }

412

413 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\

414 t1 = a2.re;\

415 t2 = a2.im;\

416 t5 = a3.re;\

417 t6 = a3.im;\

418 BUTTERFLIES(a0,a1,a2,a3)\

419 }

420

421 /* z[0...8n-1], w[1...2n-1] */

422 #define PASS(name)\

423 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\

424 {\

425 FFTDouble t1, t2, t3, t4, t5, t6;\

426 int o1 = 2*n;\

427 int o2 = 4*n;\

428 int o3 = 6*n;\

429 const FFTSample *wim = wre+o1;\

430 n--;\

431 \

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]);\

434 do {\

435 z += 2;\

436 wre += 2;\

437 wim -= 2;\

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]);\

440 } while(--n);\

441 }

442

443 PASS(pass)

444 #undef BUTTERFLIES

445 #define BUTTERFLIES BUTTERFLIES_BIG

446 PASS(pass_big)

447

448 #define DECL_FFT(n,n2,n4)\

449 static void fft##n(FFTComplex *z)\

450 {\

451 fft##n2(z);\

452 fft##n4(z+n4*2);\

453 fft##n4(z+n4*3);\

454 pass(z,FFT_NAME(ff_cos_##n),n4/2);\

455 }

456

457 static void fft4(FFTComplex *z)

458 {

459 FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;

460

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);

469 }

470

471 static void fft8(FFTComplex *z)

472 {

473 FFTDouble t1, t2, t3, t4, t5, t6;

474

475 fft4(z);

476

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);

481

482 BUTTERFLIES(z[0],z[2],z[4],z[6]);

483 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);

484 }

485

486 #if !CONFIG_SMALL

487 static void fft16(FFTComplex *z)

488 {

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];

492

493 fft8(z);

494 fft4(z+8);

495 fft4(z+12);

496

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);

501 }

502 #else

503 DECL_FFT(16,8,4)

504 #endif

505 DECL_FFT(32,16,8)

506 DECL_FFT(64,32,16)

507 DECL_FFT(128,64,32)

508 DECL_FFT(256,128,64)

509 DECL_FFT(512,256,128)

510 #if !CONFIG_SMALL

511 #define pass pass_big

512 #endif

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

521 static void (* const fft_dispatch[])(FFTComplex*) = {

522 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,

523 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,

524 };

525

526 static void fft_calc_c(FFTContext *s, FFTComplex *z)

527 {

528 fft_dispatch[s->nbits-2](z);

529 }

530 #endif /* CONFIG_FFT_FIXED_32 */

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