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