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 libavcodec/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 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 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
  62 {
  63     int i, j, m, n;
  64     float alpha, c1, s1, s2;
  65     int split_radix = 1;
  66     int av_unused has_vectors;
  67
  68     if (nbits < 2 || nbits > 16)
  69         goto fail;
  70     s->nbits = nbits;
  71     n = 1 << nbits;
  72
  73     s->tmp_buf = NULL;
  74     s->exptab  = av_malloc((n / 2) * sizeof(FFTComplex));
  75     if (!s->exptab)
  76         goto fail;
  77     s->revtab = av_malloc(n * sizeof(uint16_t));
  78     if (!s->revtab)
  79         goto fail;
  80     s->inverse = inverse;
  81
  82     s2 = inverse ? 1.0 : -1.0;
  83
  84     s->fft_permute = ff_fft_permute_c;
  85     s->fft_calc    = ff_fft_calc_c;
  86     s->imdct_calc  = ff_imdct_calc_c;
  87     s->imdct_half  = ff_imdct_half_c;
  88     s->exptab1     = NULL;
  89
  90 #if HAVE_MMX && HAVE_YASM
  91     has_vectors = mm_support();
  92     if (has_vectors & FF_MM_SSE && HAVE_SSE) {
  93         /* SSE for P3/P4/K8 */
  94         s->imdct_calc  = ff_imdct_calc_sse;
  95         s->imdct_half  = ff_imdct_half_sse;
  96         s->fft_permute = ff_fft_permute_sse;
  97         s->fft_calc    = ff_fft_calc_sse;
  98     } else if (has_vectors & FF_MM_3DNOWEXT && HAVE_AMD3DNOWEXT) {
  99         /* 3DNowEx for K7 */
 100         s->imdct_calc = ff_imdct_calc_3dn2;
 101         s->imdct_half = ff_imdct_half_3dn2;
 102         s->fft_calc   = ff_fft_calc_3dn2;
 103     } else if (has_vectors & FF_MM_3DNOW && HAVE_AMD3DNOW) {
 104         /* 3DNow! for K6-2/3 */
 105         s->imdct_calc = ff_imdct_calc_3dn;
 106         s->imdct_half = ff_imdct_half_3dn;
 107         s->fft_calc   = ff_fft_calc_3dn;
 108     }
 109 #elif HAVE_ALTIVEC
 110     has_vectors = mm_support();
 111     if (has_vectors & FF_MM_ALTIVEC) {
 112         s->fft_calc = ff_fft_calc_altivec;
 113         split_radix = 0;
 114     }
 115 #endif
 116
 117     if (split_radix) {
 118         for(j=4; j<=nbits; j++) {
 119             int m = 1<<j;
 120             double freq = 2*M_PI/m;
 121             FFTSample *tab = ff_cos_tabs[j-4];
 122             for(i=0; i<=m/4; i++)
 123                 tab[i] = cos(i*freq);
 124             for(i=1; i<m/4; i++)
 125                 tab[m/2-i] = tab[i];
 126         }
 127         for(i=0; i<n; i++)
 128             s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
 129         s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
 130     } else {
 131         int np, nblocks, np2, l;
 132         FFTComplex *q;
 133
 134         for(i=0; i<(n/2); i++) {
 135             alpha = 2 * M_PI * (float)i / (float)n;
 136             c1 = cos(alpha);
 137             s1 = sin(alpha) * s2;
 138             s->exptab[i].re = c1;
 139             s->exptab[i].im = s1;
 140         }
 141
 142         np = 1 << nbits;
 143         nblocks = np >> 3;
 144         np2 = np >> 1;
 145         s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
 146         if (!s->exptab1)
 147             goto fail;
 148         q = s->exptab1;
 149         do {
 150             for(l = 0; l < np2; l += 2 * nblocks) {
 151                 *q++ = s->exptab[l];
 152                 *q++ = s->exptab[l + nblocks];
 153
 154                 q->re = -s->exptab[l].im;
 155                 q->im = s->exptab[l].re;
 156                 q++;
 157                 q->re = -s->exptab[l + nblocks].im;
 158                 q->im = s->exptab[l + nblocks].re;
 159                 q++;
 160             }
 161             nblocks = nblocks >> 1;
 162         } while (nblocks != 0);
 163         av_freep(&s->exptab);
 164
 165         /* compute bit reverse table */
 166         for(i=0;i<n;i++) {
 167             m=0;
 168             for(j=0;j<nbits;j++) {
 169                 m |= ((i >> j) & 1) << (nbits-j-1);
 170             }
 171             s->revtab[i]=m;
 172         }
 173     }
 174
 175     return 0;
 176  fail:
 177     av_freep(&s->revtab);
 178     av_freep(&s->exptab);
 179     av_freep(&s->exptab1);
 180     av_freep(&s->tmp_buf);
 181     return -1;
 182 }
 183
 184 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
 185 {
 186     int j, k, np;
 187     FFTComplex tmp;
 188     const uint16_t *revtab = s->revtab;
 189     np = 1 << s->nbits;
 190
 191     if (s->tmp_buf) {
 192         /* TODO: handle split-radix permute in a more optimal way, probably in-place */
 193         for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
 194         memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
 195         return;
 196     }
 197
 198     /* reverse */
 199     for(j=0;j<np;j++) {
 200         k = revtab[j];
 201         if (k < j) {
 202             tmp = z[k];
 203             z[k] = z[j];
 204             z[j] = tmp;
 205         }
 206     }
 207 }
 208
 209 av_cold void ff_fft_end(FFTContext *s)
 210 {
 211     av_freep(&s->revtab);
 212     av_freep(&s->exptab);
 213     av_freep(&s->exptab1);
 214     av_freep(&s->tmp_buf);
 215 }
 216
 217 #define sqrthalf (float)M_SQRT1_2
 218
 219 #define BF(x,y,a,b) {\
 220     x = a - b;\
 221     y = a + b;\
 222 }
 223
 224 #define BUTTERFLIES(a0,a1,a2,a3) {\
 225     BF(t3, t5, t5, t1);\
 226     BF(a2.re, a0.re, a0.re, t5);\
 227     BF(a3.im, a1.im, a1.im, t3);\
 228     BF(t4, t6, t2, t6);\
 229     BF(a3.re, a1.re, a1.re, t4);\
 230     BF(a2.im, a0.im, a0.im, t6);\
 231 }
 232
 233 // force loading all the inputs before storing any.
 234 // this is slightly slower for small data, but avoids store->load aliasing
 235 // for addresses separated by large powers of 2.
 236 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 237     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 238     BF(t3, t5, t5, t1);\
 239     BF(a2.re, a0.re, r0, t5);\
 240     BF(a3.im, a1.im, i1, t3);\
 241     BF(t4, t6, t2, t6);\
 242     BF(a3.re, a1.re, r1, t4);\
 243     BF(a2.im, a0.im, i0, t6);\
 244 }
 245
 246 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 247     t1 = a2.re * wre + a2.im * wim;\
 248     t2 = a2.im * wre - a2.re * wim;\
 249     t5 = a3.re * wre - a3.im * wim;\
 250     t6 = a3.im * wre + a3.re * wim;\
 251     BUTTERFLIES(a0,a1,a2,a3)\
 252 }
 253
 254 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
 255     t1 = a2.re;\
 256     t2 = a2.im;\
 257     t5 = a3.re;\
 258     t6 = a3.im;\
 259     BUTTERFLIES(a0,a1,a2,a3)\
 260 }
 261
 262 /* z[0...8n-1], w[1...2n-1] */
 263 #define PASS(name)\
 264 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
 265 {\
 266     FFTSample t1, t2, t3, t4, t5, t6;\
 267     int o1 = 2*n;\
 268     int o2 = 4*n;\
 269     int o3 = 6*n;\
 270     const FFTSample *wim = wre+o1;\
 271     n--;\
 272 \
 273     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
 274     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 275     do {\
 276         z += 2;\
 277         wre += 2;\
 278         wim -= 2;\
 279         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
 280         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 281     } while(--n);\
 282 }
 283
 284 PASS(pass)
 285 #undef BUTTERFLIES
 286 #define BUTTERFLIES BUTTERFLIES_BIG
 287 PASS(pass_big)
 288
 289 #define DECL_FFT(n,n2,n4)\
 290 static void fft##n(FFTComplex *z)\
 291 {\
 292     fft##n2(z);\
 293     fft##n4(z+n4*2);\
 294     fft##n4(z+n4*3);\
 295     pass(z,ff_cos_##n,n4/2);\
 296 }
 297
 298 static void fft4(FFTComplex *z)
 299 {
 300     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
 301
 302     BF(t3, t1, z[0].re, z[1].re);
 303     BF(t8, t6, z[3].re, z[2].re);
 304     BF(z[2].re, z[0].re, t1, t6);
 305     BF(t4, t2, z[0].im, z[1].im);
 306     BF(t7, t5, z[2].im, z[3].im);
 307     BF(z[3].im, z[1].im, t4, t8);
 308     BF(z[3].re, z[1].re, t3, t7);
 309     BF(z[2].im, z[0].im, t2, t5);
 310 }
 311
 312 static void fft8(FFTComplex *z)
 313 {
 314     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
 315
 316     fft4(z);
 317
 318     BF(t1, z[5].re, z[4].re, -z[5].re);
 319     BF(t2, z[5].im, z[4].im, -z[5].im);
 320     BF(t3, z[7].re, z[6].re, -z[7].re);
 321     BF(t4, z[7].im, z[6].im, -z[7].im);
 322     BF(t8, t1, t3, t1);
 323     BF(t7, t2, t2, t4);
 324     BF(z[4].re, z[0].re, z[0].re, t1);
 325     BF(z[4].im, z[0].im, z[0].im, t2);
 326     BF(z[6].re, z[2].re, z[2].re, t7);
 327     BF(z[6].im, z[2].im, z[2].im, t8);
 328
 329     TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
 330 }
 331
 332 #if !CONFIG_SMALL
 333 static void fft16(FFTComplex *z)
 334 {
 335     FFTSample t1, t2, t3, t4, t5, t6;
 336
 337     fft8(z);
 338     fft4(z+8);
 339     fft4(z+12);
 340
 341     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
 342     TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
 343     TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
 344     TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
 345 }
 346 #else
 347 DECL_FFT(16,8,4)
 348 #endif
 349 DECL_FFT(32,16,8)
 350 DECL_FFT(64,32,16)
 351 DECL_FFT(128,64,32)
 352 DECL_FFT(256,128,64)
 353 DECL_FFT(512,256,128)
 354 #if !CONFIG_SMALL
 355 #define pass pass_big
 356 #endif
 357 DECL_FFT(1024,512,256)
 358 DECL_FFT(2048,1024,512)
 359 DECL_FFT(4096,2048,1024)
 360 DECL_FFT(8192,4096,2048)
 361 DECL_FFT(16384,8192,4096)
 362 DECL_FFT(32768,16384,8192)
 363 DECL_FFT(65536,32768,16384)
 364
 365 static void (*fft_dispatch[])(FFTComplex*) = {
 366     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 367     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 368 };
 369
 370 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
 371 {
 372     fft_dispatch[s->nbits-2](z);
 373 }
 374