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 Libav.
   8  *
   9  * Libav 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  * Libav 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 Libav; 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
  26  * FFT/IFFT transforms.
  27  */
  28
  29 #include <stdlib.h>
  30 #include <string.h>
  31 #include "libavutil/mathematics.h"
  32 #include "fft.h"
  33 #include "fft-internal.h"
  34
  35 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
  36 #if !CONFIG_HARDCODED_TABLES
  37 COSTABLE(16);
  38 COSTABLE(32);
  39 COSTABLE(64);
  40 COSTABLE(128);
  41 COSTABLE(256);
  42 COSTABLE(512);
  43 COSTABLE(1024);
  44 COSTABLE(2048);
  45 COSTABLE(4096);
  46 COSTABLE(8192);
  47 COSTABLE(16384);
  48 COSTABLE(32768);
  49 COSTABLE(65536);
  50 #endif
  51 COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
  52     NULL, NULL, NULL, NULL,
  53     FFT_NAME(ff_cos_16),
  54     FFT_NAME(ff_cos_32),
  55     FFT_NAME(ff_cos_64),
  56     FFT_NAME(ff_cos_128),
  57     FFT_NAME(ff_cos_256),
  58     FFT_NAME(ff_cos_512),
  59     FFT_NAME(ff_cos_1024),
  60     FFT_NAME(ff_cos_2048),
  61     FFT_NAME(ff_cos_4096),
  62     FFT_NAME(ff_cos_8192),
  63     FFT_NAME(ff_cos_16384),
  64     FFT_NAME(ff_cos_32768),
  65     FFT_NAME(ff_cos_65536),
  66 };
  67
  68 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z);
  69 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z);
  70
  71 static int split_radix_permutation(int i, int n, int inverse)
  72 {
  73     int m;
  74     if(n <= 2) return i&1;
  75     m = n >> 1;
  76     if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
  77     m >>= 1;
  78     if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
  79     else                  return split_radix_permutation(i, m, inverse)*4 - 1;
  80 }
  81
  82 av_cold void ff_init_ff_cos_tabs(int index)
  83 {
  84 #if !CONFIG_HARDCODED_TABLES
  85     int i;
  86     int m = 1<<index;
  87     double freq = 2*M_PI/m;
  88     FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
  89     for(i=0; i<=m/4; i++)
  90         tab[i] = FIX15(cos(i*freq));
  91     for(i=1; i<m/4; i++)
  92         tab[m/2-i] = tab[i];
  93 #endif
  94 }
  95
  96 static const int avx_tab[] = {
  97     0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
  98 };
  99
 100 static int is_second_half_of_fft32(int i, int n)
 101 {
 102     if (n <= 32)
 103         return i >= 16;
 104     else if (i < n/2)
 105         return is_second_half_of_fft32(i, n/2);
 106     else if (i < 3*n/4)
 107         return is_second_half_of_fft32(i - n/2, n/4);
 108     else
 109         return is_second_half_of_fft32(i - 3*n/4, n/4);
 110 }
 111
 112 static av_cold void fft_perm_avx(FFTContext *s)
 113 {
 114     int i;
 115     int n = 1 << s->nbits;
 116
 117     for (i = 0; i < n; i += 16) {
 118         int k;
 119         if (is_second_half_of_fft32(i, n)) {
 120             for (k = 0; k < 16; k++)
 121                 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =
 122                     i + avx_tab[k];
 123
 124         } else {
 125             for (k = 0; k < 16; k++) {
 126                 int j = i + k;
 127                 j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);
 128                 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;
 129             }
 130         }
 131     }
 132 }
 133
 134 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
 135 {
 136     int i, j, n;
 137
 138     if (nbits < 2 || nbits > 16)
 139         goto fail;
 140     s->nbits = nbits;
 141     n = 1 << nbits;
 142
 143     s->revtab = av_malloc(n * sizeof(uint16_t));
 144     if (!s->revtab)
 145         goto fail;
 146     s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
 147     if (!s->tmp_buf)
 148         goto fail;
 149     s->inverse = inverse;
 150     s->fft_permutation = FF_FFT_PERM_DEFAULT;
 151
 152     s->fft_permute = ff_fft_permute_c;
 153     s->fft_calc    = ff_fft_calc_c;
 154 #if CONFIG_MDCT
 155     s->imdct_calc  = ff_imdct_calc_c;
 156     s->imdct_half  = ff_imdct_half_c;
 157     s->mdct_calc   = ff_mdct_calc_c;
 158 #endif
 159
 160 #if CONFIG_FFT_FLOAT
 161     if (ARCH_ARM)     ff_fft_init_arm(s);
 162     if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
 163     if (ARCH_X86)     ff_fft_init_x86(s);
 164     if (CONFIG_MDCT)  s->mdct_calcw = s->mdct_calc;
 165 #else
 166     if (CONFIG_MDCT)  s->mdct_calcw = ff_mdct_calcw_c;
 167     if (ARCH_ARM)     ff_fft_fixed_init_arm(s);
 168 #endif
 169
 170     for(j=4; j<=nbits; j++) {
 171         ff_init_ff_cos_tabs(j);
 172     }
 173
 174     if (s->fft_permutation == FF_FFT_PERM_AVX) {
 175         fft_perm_avx(s);
 176     } else {
 177         for(i=0; i<n; i++) {
 178             int j = i;
 179             if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
 180                 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
 181             s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
 182         }
 183     }
 184
 185     return 0;
 186  fail:
 187     av_freep(&s->revtab);
 188     av_freep(&s->tmp_buf);
 189     return -1;
 190 }
 191
 192 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
 193 {
 194     int j, np;
 195     const uint16_t *revtab = s->revtab;
 196     np = 1 << s->nbits;
 197     /* TODO: handle split-radix permute in a more optimal way, probably in-place */
 198     for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
 199     memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
 200 }
 201
 202 av_cold void ff_fft_end(FFTContext *s)
 203 {
 204     av_freep(&s->revtab);
 205     av_freep(&s->tmp_buf);
 206 }
 207
 208 #define BUTTERFLIES(a0,a1,a2,a3) {\
 209     BF(t3, t5, t5, t1);\
 210     BF(a2.re, a0.re, a0.re, t5);\
 211     BF(a3.im, a1.im, a1.im, t3);\
 212     BF(t4, t6, t2, t6);\
 213     BF(a3.re, a1.re, a1.re, t4);\
 214     BF(a2.im, a0.im, a0.im, t6);\
 215 }
 216
 217 // force loading all the inputs before storing any.
 218 // this is slightly slower for small data, but avoids store->load aliasing
 219 // for addresses separated by large powers of 2.
 220 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 221     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 222     BF(t3, t5, t5, t1);\
 223     BF(a2.re, a0.re, r0, t5);\
 224     BF(a3.im, a1.im, i1, t3);\
 225     BF(t4, t6, t2, t6);\
 226     BF(a3.re, a1.re, r1, t4);\
 227     BF(a2.im, a0.im, i0, t6);\
 228 }
 229
 230 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 231     CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
 232     CMUL(t5, t6, a3.re, a3.im, wre,  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     FFTDouble 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,FFT_NAME(ff_cos_##n),n4/2);\
 278 }
 279
 280 static void fft4(FFTComplex *z)
 281 {
 282     FFTDouble 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     FFTDouble t1, t2, t3, t4, t5, t6;
 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(t5, z[7].re, z[6].re, -z[7].re);
 303     BF(t6, z[7].im, z[6].im, -z[7].im);
 304
 305     BUTTERFLIES(z[0],z[2],z[4],z[6]);
 306     TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
 307 }
 308
 309 #if !CONFIG_SMALL
 310 static void fft16(FFTComplex *z)
 311 {
 312     FFTDouble t1, t2, t3, t4, t5, t6;
 313     FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
 314     FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
 315
 316     fft8(z);
 317     fft4(z+8);
 318     fft4(z+12);
 319
 320     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
 321     TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
 322     TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
 323     TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
 324 }
 325 #else
 326 DECL_FFT(16,8,4)
 327 #endif
 328 DECL_FFT(32,16,8)
 329 DECL_FFT(64,32,16)
 330 DECL_FFT(128,64,32)
 331 DECL_FFT(256,128,64)
 332 DECL_FFT(512,256,128)
 333 #if !CONFIG_SMALL
 334 #define pass pass_big
 335 #endif
 336 DECL_FFT(1024,512,256)
 337 DECL_FFT(2048,1024,512)
 338 DECL_FFT(4096,2048,1024)
 339 DECL_FFT(8192,4096,2048)
 340 DECL_FFT(16384,8192,4096)
 341 DECL_FFT(32768,16384,8192)
 342 DECL_FFT(65536,32768,16384)
 343
 344 static void (* const fft_dispatch[])(FFTComplex*) = {
 345     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 346     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 347 };
 348
 349 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
 350 {
 351     fft_dispatch[s->nbits-2](z);
 352 }