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