libavcodec/fft.c

   1 /*
   2  * FFT/IFFT transforms
   3  * Copyright (c) 2008 Loren Merritt
   4  * Copyright (c) 2002 Fabrice Bellard.
   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  */
  23
  24 /**
  25  * @file fft.c
  26  * FFT/IFFT transforms.
  27  */
  28
  29 #include "dsputil.h"
  30
  31 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
  32 DECLARE_ALIGNED_16(FFTSample, ff_cos_16[8]);
  33 DECLARE_ALIGNED_16(FFTSample, ff_cos_32[16]);
  34 DECLARE_ALIGNED_16(FFTSample, ff_cos_64[32]);
  35 DECLARE_ALIGNED_16(FFTSample, ff_cos_128[64]);
  36 DECLARE_ALIGNED_16(FFTSample, ff_cos_256[128]);
  37 DECLARE_ALIGNED_16(FFTSample, ff_cos_512[256]);
  38 DECLARE_ALIGNED_16(FFTSample, ff_cos_1024[512]);
  39 DECLARE_ALIGNED_16(FFTSample, ff_cos_2048[1024]);
  40 DECLARE_ALIGNED_16(FFTSample, ff_cos_4096[2048]);
  41 DECLARE_ALIGNED_16(FFTSample, ff_cos_8192[4096]);
  42 DECLARE_ALIGNED_16(FFTSample, ff_cos_16384[8192]);
  43 DECLARE_ALIGNED_16(FFTSample, ff_cos_32768[16384]);
  44 DECLARE_ALIGNED_16(FFTSample, ff_cos_65536[32768]);
  45 static FFTSample *ff_cos_tabs[] = {
  46     ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
  47     ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
  48 };
  49
  50 static int split_radix_permutation(int i, int n, int inverse)
  51 {
  52     int m;
  53     if(n <= 2) return i&1;
  54     m = n >> 1;
  55     if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
  56     m >>= 1;
  57     if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
  58     else                  return split_radix_permutation(i, m, inverse)*4 - 1;
  59 }
  60
  61 /**
  62  * The size of the FFT is 2^nbits. If inverse is TRUE, inverse FFT is
  63  * done
  64  */
  65 int ff_fft_init(FFTContext *s, int nbits, int inverse)
  66 {
  67     int i, j, m, n;
  68     float alpha, c1, s1, s2;
  69     int split_radix = 1;
  70     int av_unused has_vectors;
  71
  72     if (nbits < 2 || nbits > 16)
  73         goto fail;
  74     s->nbits = nbits;
  75     n = 1 << nbits;
  76
  77     s->tmp_buf = NULL;
  78     s->exptab = av_malloc((n / 2) * sizeof(FFTComplex));
  79     if (!s->exptab)
  80         goto fail;
  81     s->revtab = av_malloc(n * sizeof(uint16_t));
  82     if (!s->revtab)
  83         goto fail;
  84     s->inverse = inverse;
  85
  86     s2 = inverse ? 1.0 : -1.0;
  87
  88     s->fft_permute = ff_fft_permute_c;
  89     s->fft_calc = ff_fft_calc_c;
  90     s->imdct_calc = ff_imdct_calc_c;
  91     s->imdct_half = ff_imdct_half_c;
  92     s->exptab1 = NULL;
  93
  94 #if defined HAVE_MMX && defined HAVE_YASM
  95     has_vectors = mm_support();
  96     if (has_vectors & FF_MM_SSE) {
  97         /* SSE for P3/P4/K8 */
  98         s->imdct_calc = ff_imdct_calc_sse;
  99         s->imdct_half = ff_imdct_half_sse;
 100         s->fft_permute = ff_fft_permute_sse;
 101         s->fft_calc = ff_fft_calc_sse;
 102     } else if (has_vectors & FF_MM_3DNOWEXT) {
 103         /* 3DNowEx for K7 */
 104         s->imdct_calc = ff_imdct_calc_3dn2;
 105         s->imdct_half = ff_imdct_half_3dn2;
 106         s->fft_calc = ff_fft_calc_3dn2;
 107     } else if (has_vectors & FF_MM_3DNOW) {
 108         /* 3DNow! for K6-2/3 */
 109         s->imdct_calc = ff_imdct_calc_3dn;
 110         s->imdct_half = ff_imdct_half_3dn;
 111         s->fft_calc = ff_fft_calc_3dn;
 112     }
 113 #elif defined HAVE_ALTIVEC && !defined ALTIVEC_USE_REFERENCE_C_CODE
 114     has_vectors = mm_support();
 115     if (has_vectors & FF_MM_ALTIVEC) {
 116         s->fft_calc = ff_fft_calc_altivec;
 117         split_radix = 0;
 118     }
 119 #endif
 120
 121     if (split_radix) {
 122         for(j=4; j<=nbits; j++) {
 123             int m = 1<<j;
 124             double freq = 2*M_PI/m;
 125             FFTSample *tab = ff_cos_tabs[j-4];
 126             for(i=0; i<=m/4; i++)
 127                 tab[i] = cos(i*freq);
 128             for(i=1; i<m/4; i++)
 129                 tab[m/2-i] = tab[i];
 130         }
 131         for(i=0; i<n; i++)
 132             s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
 133         s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
 134     } else {
 135         int np, nblocks, np2, l;
 136         FFTComplex *q;
 137
 138         for(i=0; i<(n/2); i++) {
 139             alpha = 2 * M_PI * (float)i / (float)n;
 140             c1 = cos(alpha);
 141             s1 = sin(alpha) * s2;
 142             s->exptab[i].re = c1;
 143             s->exptab[i].im = s1;
 144         }
 145
 146         np = 1 << nbits;
 147         nblocks = np >> 3;
 148         np2 = np >> 1;
 149         s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
 150         if (!s->exptab1)
 151             goto fail;
 152         q = s->exptab1;
 153         do {
 154             for(l = 0; l < np2; l += 2 * nblocks) {
 155                 *q++ = s->exptab[l];
 156                 *q++ = s->exptab[l + nblocks];
 157
 158                 q->re = -s->exptab[l].im;
 159                 q->im = s->exptab[l].re;
 160                 q++;
 161                 q->re = -s->exptab[l + nblocks].im;
 162                 q->im = s->exptab[l + nblocks].re;
 163                 q++;
 164             }
 165             nblocks = nblocks >> 1;
 166         } while (nblocks != 0);
 167         av_freep(&s->exptab);
 168
 169         /* compute bit reverse table */
 170         for(i=0;i<n;i++) {
 171             m=0;
 172             for(j=0;j<nbits;j++) {
 173                 m |= ((i >> j) & 1) << (nbits-j-1);
 174             }
 175             s->revtab[i]=m;
 176         }
 177     }
 178
 179     return 0;
 180  fail:
 181     av_freep(&s->revtab);
 182     av_freep(&s->exptab);
 183     av_freep(&s->exptab1);
 184     av_freep(&s->tmp_buf);
 185     return -1;
 186 }
 187
 188 /**
 189  * Do the permutation needed BEFORE calling ff_fft_calc()
 190  */
 191 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
 192 {
 193     int j, k, np;
 194     FFTComplex tmp;
 195     const uint16_t *revtab = s->revtab;
 196     np = 1 << s->nbits;
 197
 198     if (s->tmp_buf) {
 199         /* TODO: handle split-radix permute in a more optimal way, probably in-place */
 200         for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
 201         memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
 202         return;
 203     }
 204
 205     /* reverse */
 206     for(j=0;j<np;j++) {
 207         k = revtab[j];
 208         if (k < j) {
 209             tmp = z[k];
 210             z[k] = z[j];
 211             z[j] = tmp;
 212         }
 213     }
 214 }
 215
 216 void ff_fft_end(FFTContext *s)
 217 {
 218     av_freep(&s->revtab);
 219     av_freep(&s->exptab);
 220     av_freep(&s->exptab1);
 221     av_freep(&s->tmp_buf);
 222 }
 223
 224 #define sqrthalf (float)M_SQRT1_2
 225
 226 #define BF(x,y,a,b) {\
 227     x = a - b;\
 228     y = a + b;\
 229 }
 230
 231 #define BUTTERFLIES(a0,a1,a2,a3) {\
 232     BF(t3, t5, t5, t1);\
 233     BF(a2.re, a0.re, a0.re, t5);\
 234     BF(a3.im, a1.im, a1.im, t3);\
 235     BF(t4, t6, t2, t6);\
 236     BF(a3.re, a1.re, a1.re, t4);\
 237     BF(a2.im, a0.im, a0.im, t6);\
 238 }
 239
 240 // force loading all the inputs before storing any.
 241 // this is slightly slower for small data, but avoids store->load aliasing
 242 // for addresses separated by large powers of 2.
 243 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 244     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 245     BF(t3, t5, t5, t1);\
 246     BF(a2.re, a0.re, r0, t5);\
 247     BF(a3.im, a1.im, i1, t3);\
 248     BF(t4, t6, t2, t6);\
 249     BF(a3.re, a1.re, r1, t4);\
 250     BF(a2.im, a0.im, i0, t6);\
 251 }
 252
 253 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 254     t1 = a2.re * wre + a2.im * wim;\
 255     t2 = a2.im * wre - a2.re * wim;\
 256     t5 = a3.re * wre - a3.im * wim;\
 257     t6 = a3.im * wre + a3.re * wim;\
 258     BUTTERFLIES(a0,a1,a2,a3)\
 259 }
 260
 261 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
 262     t1 = a2.re;\
 263     t2 = a2.im;\
 264     t5 = a3.re;\
 265     t6 = a3.im;\
 266     BUTTERFLIES(a0,a1,a2,a3)\
 267 }
 268
 269 /* z[0...8n-1], w[1...2n-1] */
 270 #define PASS(name)\
 271 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
 272 {\
 273     FFTSample t1, t2, t3, t4, t5, t6;\
 274     int o1 = 2*n;\
 275     int o2 = 4*n;\
 276     int o3 = 6*n;\
 277     const FFTSample *wim = wre+o1;\
 278     n--;\
 279 \
 280     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
 281     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 282     do {\
 283         z += 2;\
 284         wre += 2;\
 285         wim -= 2;\
 286         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
 287         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 288     } while(--n);\
 289 }
 290
 291 PASS(pass)
 292 #undef BUTTERFLIES
 293 #define BUTTERFLIES BUTTERFLIES_BIG
 294 PASS(pass_big)
 295
 296 #define DECL_FFT(n,n2,n4)\
 297 static void fft##n(FFTComplex *z)\
 298 {\
 299     fft##n2(z);\
 300     fft##n4(z+n4*2);\
 301     fft##n4(z+n4*3);\
 302     pass(z,ff_cos_##n,n4/2);\
 303 }
 304
 305 static void fft4(FFTComplex *z)
 306 {
 307     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
 308
 309     BF(t3, t1, z[0].re, z[1].re);
 310     BF(t8, t6, z[3].re, z[2].re);
 311     BF(z[2].re, z[0].re, t1, t6);
 312     BF(t4, t2, z[0].im, z[1].im);
 313     BF(t7, t5, z[2].im, z[3].im);
 314     BF(z[3].im, z[1].im, t4, t8);
 315     BF(z[3].re, z[1].re, t3, t7);
 316     BF(z[2].im, z[0].im, t2, t5);
 317 }
 318
 319 static void fft8(FFTComplex *z)
 320 {
 321     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
 322
 323     fft4(z);
 324
 325     BF(t1, z[5].re, z[4].re, -z[5].re);
 326     BF(t2, z[5].im, z[4].im, -z[5].im);
 327     BF(t3, z[7].re, z[6].re, -z[7].re);
 328     BF(t4, z[7].im, z[6].im, -z[7].im);
 329     BF(t8, t1, t3, t1);
 330     BF(t7, t2, t2, t4);
 331     BF(z[4].re, z[0].re, z[0].re, t1);
 332     BF(z[4].im, z[0].im, z[0].im, t2);
 333     BF(z[6].re, z[2].re, z[2].re, t7);
 334     BF(z[6].im, z[2].im, z[2].im, t8);
 335
 336     TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
 337 }
 338
 339 #ifndef CONFIG_SMALL
 340 static void fft16(FFTComplex *z)
 341 {
 342     FFTSample t1, t2, t3, t4, t5, t6;
 343
 344     fft8(z);
 345     fft4(z+8);
 346     fft4(z+12);
 347
 348     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
 349     TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
 350     TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
 351     TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
 352 }
 353 #else
 354 DECL_FFT(16,8,4)
 355 #endif
 356 DECL_FFT(32,16,8)
 357 DECL_FFT(64,32,16)
 358 DECL_FFT(128,64,32)
 359 DECL_FFT(256,128,64)
 360 DECL_FFT(512,256,128)
 361 #ifndef CONFIG_SMALL
 362 #define pass pass_big
 363 #endif
 364 DECL_FFT(1024,512,256)
 365 DECL_FFT(2048,1024,512)
 366 DECL_FFT(4096,2048,1024)
 367 DECL_FFT(8192,4096,2048)
 368 DECL_FFT(16384,8192,4096)
 369 DECL_FFT(32768,16384,8192)
 370 DECL_FFT(65536,32768,16384)
 371
 372 static void (*fft_dispatch[])(FFTComplex*) = {
 373     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 374     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 375 };
 376
 377 /**
 378  * Do a complex FFT with the parameters defined in ff_fft_init(). The
 379  * input data must be permuted before with s->revtab table. No
 380  * 1.0/sqrt(n) normalization is done.
 381  */
 382 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
 383 {
 384     fft_dispatch[s->nbits-2](z);
 385 }
 386