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 #if !CONFIG_HARDCODED_TABLES
  33 COSTABLE(16);
  34 COSTABLE(32);
  35 COSTABLE(64);
  36 COSTABLE(128);
  37 COSTABLE(256);
  38 COSTABLE(512);
  39 COSTABLE(1024);
  40 COSTABLE(2048);
  41 COSTABLE(4096);
  42 COSTABLE(8192);
  43 COSTABLE(16384);
  44 COSTABLE(32768);
  45 COSTABLE(65536);
  46 #endif
  47 COSTABLE_CONST FFTSample * const ff_cos_tabs[] = {
  48     ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
  49     ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
  50 };
  51
  52 static int split_radix_permutation(int i, int n, int inverse)
  53 {
  54     int m;
  55     if(n <= 2) return i&1;
  56     m = n >> 1;
  57     if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
  58     m >>= 1;
  59     if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
  60     else                  return split_radix_permutation(i, m, inverse)*4 - 1;
  61 }
  62
  63 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
  64 {
  65     int i, j, m, n;
  66     float alpha, c1, s1, s2;
  67     int av_unused has_vectors;
  68
  69     if (nbits < 2 || nbits > 16)
  70         goto fail;
  71     s->nbits = nbits;
  72     n = 1 << nbits;
  73
  74     s->tmp_buf = NULL;
  75     s->exptab  = av_malloc((n / 2) * sizeof(FFTComplex));
  76     if (!s->exptab)
  77         goto fail;
  78     s->revtab = av_malloc(n * sizeof(uint16_t));
  79     if (!s->revtab)
  80         goto fail;
  81     s->inverse = inverse;
  82
  83     s2 = inverse ? 1.0 : -1.0;
  84
  85     s->fft_permute = ff_fft_permute_c;
  86     s->fft_calc    = ff_fft_calc_c;
  87     s->imdct_calc  = ff_imdct_calc_c;
  88     s->imdct_half  = ff_imdct_half_c;
  89     s->mdct_calc   = ff_mdct_calc_c;
  90     s->exptab1     = NULL;
  91     s->split_radix = 1;
  92
  93     if (ARCH_ARM)     ff_fft_init_arm(s);
  94     if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
  95     if (HAVE_MMX)     ff_fft_init_mmx(s);
  96
  97     if (s->split_radix) {
  98 #if !CONFIG_HARDCODED_TABLES
  99         for(j=4; j<=nbits; j++) {
 100             int m = 1<<j;
 101             double freq = 2*M_PI/m;
 102             FFTSample *tab = ff_cos_tabs[j-4];
 103             for(i=0; i<=m/4; i++)
 104                 tab[i] = cos(i*freq);
 105             for(i=1; i<m/4; i++)
 106                 tab[m/2-i] = tab[i];
 107         }
 108 #endif
 109         for(i=0; i<n; i++)
 110             s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
 111         s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
 112     } else {
 113         int np, nblocks, np2, l;
 114         FFTComplex *q;
 115
 116         for(i=0; i<(n/2); i++) {
 117             alpha = 2 * M_PI * (float)i / (float)n;
 118             c1 = cos(alpha);
 119             s1 = sin(alpha) * s2;
 120             s->exptab[i].re = c1;
 121             s->exptab[i].im = s1;
 122         }
 123
 124         np = 1 << nbits;
 125         nblocks = np >> 3;
 126         np2 = np >> 1;
 127         s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
 128         if (!s->exptab1)
 129             goto fail;
 130         q = s->exptab1;
 131         do {
 132             for(l = 0; l < np2; l += 2 * nblocks) {
 133                 *q++ = s->exptab[l];
 134                 *q++ = s->exptab[l + nblocks];
 135
 136                 q->re = -s->exptab[l].im;
 137                 q->im = s->exptab[l].re;
 138                 q++;
 139                 q->re = -s->exptab[l + nblocks].im;
 140                 q->im = s->exptab[l + nblocks].re;
 141                 q++;
 142             }
 143             nblocks = nblocks >> 1;
 144         } while (nblocks != 0);
 145         av_freep(&s->exptab);
 146
 147         /* compute bit reverse table */
 148         for(i=0;i<n;i++) {
 149             m=0;
 150             for(j=0;j<nbits;j++) {
 151                 m |= ((i >> j) & 1) << (nbits-j-1);
 152             }
 153             s->revtab[i]=m;
 154         }
 155     }
 156
 157     return 0;
 158  fail:
 159     av_freep(&s->revtab);
 160     av_freep(&s->exptab);
 161     av_freep(&s->exptab1);
 162     av_freep(&s->tmp_buf);
 163     return -1;
 164 }
 165
 166 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
 167 {
 168     int j, k, np;
 169     FFTComplex tmp;
 170     const uint16_t *revtab = s->revtab;
 171     np = 1 << s->nbits;
 172
 173     if (s->tmp_buf) {
 174         /* TODO: handle split-radix permute in a more optimal way, probably in-place */
 175         for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
 176         memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
 177         return;
 178     }
 179
 180     /* reverse */
 181     for(j=0;j<np;j++) {
 182         k = revtab[j];
 183         if (k < j) {
 184             tmp = z[k];
 185             z[k] = z[j];
 186             z[j] = tmp;
 187         }
 188     }
 189 }
 190
 191 av_cold void ff_fft_end(FFTContext *s)
 192 {
 193     av_freep(&s->revtab);
 194     av_freep(&s->exptab);
 195     av_freep(&s->exptab1);
 196     av_freep(&s->tmp_buf);
 197 }
 198
 199 #define sqrthalf (float)M_SQRT1_2
 200
 201 #define BF(x,y,a,b) {\
 202     x = a - b;\
 203     y = a + b;\
 204 }
 205
 206 #define BUTTERFLIES(a0,a1,a2,a3) {\
 207     BF(t3, t5, t5, t1);\
 208     BF(a2.re, a0.re, a0.re, t5);\
 209     BF(a3.im, a1.im, a1.im, t3);\
 210     BF(t4, t6, t2, t6);\
 211     BF(a3.re, a1.re, a1.re, t4);\
 212     BF(a2.im, a0.im, a0.im, t6);\
 213 }
 214
 215 // force loading all the inputs before storing any.
 216 // this is slightly slower for small data, but avoids store->load aliasing
 217 // for addresses separated by large powers of 2.
 218 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 219     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 220     BF(t3, t5, t5, t1);\
 221     BF(a2.re, a0.re, r0, t5);\
 222     BF(a3.im, a1.im, i1, t3);\
 223     BF(t4, t6, t2, t6);\
 224     BF(a3.re, a1.re, r1, t4);\
 225     BF(a2.im, a0.im, i0, t6);\
 226 }
 227
 228 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 229     t1 = a2.re * wre + a2.im * wim;\
 230     t2 = a2.im * wre - a2.re * wim;\
 231     t5 = a3.re * wre - a3.im * wim;\
 232     t6 = a3.im * wre + a3.re * wim;\
 233     BUTTERFLIES(a0,a1,a2,a3)\
 234 }
 235
 236 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
 237     t1 = a2.re;\
 238     t2 = a2.im;\
 239     t5 = a3.re;\
 240     t6 = a3.im;\
 241     BUTTERFLIES(a0,a1,a2,a3)\
 242 }
 243
 244 /* z[0...8n-1], w[1...2n-1] */
 245 #define PASS(name)\
 246 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
 247 {\
 248     FFTSample t1, t2, t3, t4, t5, t6;\
 249     int o1 = 2*n;\
 250     int o2 = 4*n;\
 251     int o3 = 6*n;\
 252     const FFTSample *wim = wre+o1;\
 253     n--;\
 254 \
 255     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
 256     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 257     do {\
 258         z += 2;\
 259         wre += 2;\
 260         wim -= 2;\
 261         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
 262         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 263     } while(--n);\
 264 }
 265
 266 PASS(pass)
 267 #undef BUTTERFLIES
 268 #define BUTTERFLIES BUTTERFLIES_BIG
 269 PASS(pass_big)
 270
 271 #define DECL_FFT(n,n2,n4)\
 272 static void fft##n(FFTComplex *z)\
 273 {\
 274     fft##n2(z);\
 275     fft##n4(z+n4*2);\
 276     fft##n4(z+n4*3);\
 277     pass(z,ff_cos_##n,n4/2);\
 278 }
 279
 280 static void fft4(FFTComplex *z)
 281 {
 282     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
 283
 284     BF(t3, t1, z[0].re, z[1].re);
 285     BF(t8, t6, z[3].re, z[2].re);
 286     BF(z[2].re, z[0].re, t1, t6);
 287     BF(t4, t2, z[0].im, z[1].im);
 288     BF(t7, t5, z[2].im, z[3].im);
 289     BF(z[3].im, z[1].im, t4, t8);
 290     BF(z[3].re, z[1].re, t3, t7);
 291     BF(z[2].im, z[0].im, t2, t5);
 292 }
 293
 294 static void fft8(FFTComplex *z)
 295 {
 296     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
 297
 298     fft4(z);
 299
 300     BF(t1, z[5].re, z[4].re, -z[5].re);
 301     BF(t2, z[5].im, z[4].im, -z[5].im);
 302     BF(t3, z[7].re, z[6].re, -z[7].re);
 303     BF(t4, z[7].im, z[6].im, -z[7].im);
 304     BF(t8, t1, t3, t1);
 305     BF(t7, t2, t2, t4);
 306     BF(z[4].re, z[0].re, z[0].re, t1);
 307     BF(z[4].im, z[0].im, z[0].im, t2);
 308     BF(z[6].re, z[2].re, z[2].re, t7);
 309     BF(z[6].im, z[2].im, z[2].im, t8);
 310
 311     TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
 312 }
 313
 314 #if !CONFIG_SMALL
 315 static void fft16(FFTComplex *z)
 316 {
 317     FFTSample t1, t2, t3, t4, t5, t6;
 318
 319     fft8(z);
 320     fft4(z+8);
 321     fft4(z+12);
 322
 323     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
 324     TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
 325     TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
 326     TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
 327 }
 328 #else
 329 DECL_FFT(16,8,4)
 330 #endif
 331 DECL_FFT(32,16,8)
 332 DECL_FFT(64,32,16)
 333 DECL_FFT(128,64,32)
 334 DECL_FFT(256,128,64)
 335 DECL_FFT(512,256,128)
 336 #if !CONFIG_SMALL
 337 #define pass pass_big
 338 #endif
 339 DECL_FFT(1024,512,256)
 340 DECL_FFT(2048,1024,512)
 341 DECL_FFT(4096,2048,1024)
 342 DECL_FFT(8192,4096,2048)
 343 DECL_FFT(16384,8192,4096)
 344 DECL_FFT(32768,16384,8192)
 345 DECL_FFT(65536,32768,16384)
 346
 347 static void (* const fft_dispatch[])(FFTComplex*) = {
 348     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 349     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 350 };
 351
 352 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
 353 {
 354     fft_dispatch[s->nbits-2](z);
 355 }
 356