FFmpeg: libavcodec/fft.c Source File

00001 /*
00002  * FFT/IFFT transforms
00003  * Copyright (c) 2008 Loren Merritt
00004  * Copyright (c) 2002 Fabrice Bellard
00005  * Partly based on libdjbfft by D. J. Bernstein
00006  *
00007  * This file is part of FFmpeg.
00008  *
00009  * FFmpeg is free software; you can redistribute it and/or
00010  * modify it under the terms of the GNU Lesser General Public
00011  * License as published by the Free Software Foundation; either
00012  * version 2.1 of the License, or (at your option) any later version.
00013  *
00014  * FFmpeg is distributed in the hope that it will be useful,
00015  * but WITHOUT ANY WARRANTY; without even the implied warranty of
00016  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00017  * Lesser General Public License for more details.
00018  *
00019  * You should have received a copy of the GNU Lesser General Public
00020  * License along with FFmpeg; if not, write to the Free Software
00021  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
00022  */
00023 
00029 #include <stdlib.h>
00030 #include <string.h>
00031 #include "libavutil/mathematics.h"
00032 #include "fft.h"
00033 
00034 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
00035 #if !CONFIG_HARDCODED_TABLES
00036 COSTABLE(16);
00037 COSTABLE(32);
00038 COSTABLE(64);
00039 COSTABLE(128);
00040 COSTABLE(256);
00041 COSTABLE(512);
00042 COSTABLE(1024);
00043 COSTABLE(2048);
00044 COSTABLE(4096);
00045 COSTABLE(8192);
00046 COSTABLE(16384);
00047 COSTABLE(32768);
00048 COSTABLE(65536);
00049 #endif
00050 COSTABLE_CONST FFTSample * const ff_cos_tabs[] = {
00051     NULL, NULL, NULL, NULL,
00052     ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
00053     ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
00054 };
00055 
00056 static int split_radix_permutation(int i, int n, int inverse)
00057 {
00058     int m;
00059     if(n <= 2) return i&1;
00060     m = n >> 1;
00061     if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
00062     m >>= 1;
00063     if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
00064     else                  return split_radix_permutation(i, m, inverse)*4 - 1;
00065 }
00066 
00067 av_cold void ff_init_ff_cos_tabs(int index)
00068 {
00069 #if !CONFIG_HARDCODED_TABLES
00070     int i;
00071     int m = 1<<index;
00072     double freq = 2*M_PI/m;
00073     FFTSample *tab = ff_cos_tabs[index];
00074     for(i=0; i<=m/4; i++)
00075         tab[i] = cos(i*freq);
00076     for(i=1; i<m/4; i++)
00077         tab[m/2-i] = tab[i];
00078 #endif
00079 }
00080 
00081 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
00082 {
00083     int i, j, m, n;
00084     float alpha, c1, s1, s2;
00085     int av_unused has_vectors;
00086 
00087     if (nbits < 2 || nbits > 16)
00088         goto fail;
00089     s->nbits = nbits;
00090     n = 1 << nbits;
00091 
00092     s->tmp_buf = NULL;
00093     s->exptab  = av_malloc((n / 2) * sizeof(FFTComplex));
00094     if (!s->exptab)
00095         goto fail;
00096     s->revtab = av_malloc(n * sizeof(uint16_t));
00097     if (!s->revtab)
00098         goto fail;
00099     s->inverse = inverse;
00100 
00101     s2 = inverse ? 1.0 : -1.0;
00102 
00103     s->fft_permute = ff_fft_permute_c;
00104     s->fft_calc    = ff_fft_calc_c;
00105 #if CONFIG_MDCT
00106     s->imdct_calc  = ff_imdct_calc_c;
00107     s->imdct_half  = ff_imdct_half_c;
00108     s->mdct_calc   = ff_mdct_calc_c;
00109 #endif
00110     s->exptab1     = NULL;
00111     s->split_radix = 1;
00112 
00113     if (ARCH_ARM)     ff_fft_init_arm(s);
00114     if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
00115     if (HAVE_MMX)     ff_fft_init_mmx(s);
00116 
00117     if (s->split_radix) {
00118         for(j=4; j<=nbits; j++) {
00119             ff_init_ff_cos_tabs(j);
00120         }
00121         for(i=0; i<n; i++)
00122             s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
00123         s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
00124     } else {
00125         int np, nblocks, np2, l;
00126         FFTComplex *q;
00127 
00128         for(i=0; i<(n/2); i++) {
00129             alpha = 2 * M_PI * (float)i / (float)n;
00130             c1 = cos(alpha);
00131             s1 = sin(alpha) * s2;
00132             s->exptab[i].re = c1;
00133             s->exptab[i].im = s1;
00134         }
00135 
00136         np = 1 << nbits;
00137         nblocks = np >> 3;
00138         np2 = np >> 1;
00139         s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
00140         if (!s->exptab1)
00141             goto fail;
00142         q = s->exptab1;
00143         do {
00144             for(l = 0; l < np2; l += 2 * nblocks) {
00145                 *q++ = s->exptab[l];
00146                 *q++ = s->exptab[l + nblocks];
00147 
00148                 q->re = -s->exptab[l].im;
00149                 q->im = s->exptab[l].re;
00150                 q++;
00151                 q->re = -s->exptab[l + nblocks].im;
00152                 q->im = s->exptab[l + nblocks].re;
00153                 q++;
00154             }
00155             nblocks = nblocks >> 1;
00156         } while (nblocks != 0);
00157         av_freep(&s->exptab);
00158 
00159         /* compute bit reverse table */
00160         for(i=0;i<n;i++) {
00161             m=0;
00162             for(j=0;j<nbits;j++) {
00163                 m |= ((i >> j) & 1) << (nbits-j-1);
00164             }
00165             s->revtab[i]=m;
00166         }
00167     }
00168 
00169     return 0;
00170  fail:
00171     av_freep(&s->revtab);
00172     av_freep(&s->exptab);
00173     av_freep(&s->exptab1);
00174     av_freep(&s->tmp_buf);
00175     return -1;
00176 }
00177 
00178 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
00179 {
00180     int j, k, np;
00181     FFTComplex tmp;
00182     const uint16_t *revtab = s->revtab;
00183     np = 1 << s->nbits;
00184 
00185     if (s->tmp_buf) {
00186         /* TODO: handle split-radix permute in a more optimal way, probably in-place */
00187         for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
00188         memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
00189         return;
00190     }
00191 
00192     /* reverse */
00193     for(j=0;j<np;j++) {
00194         k = revtab[j];
00195         if (k < j) {
00196             tmp = z[k];
00197             z[k] = z[j];
00198             z[j] = tmp;
00199         }
00200     }
00201 }
00202 
00203 av_cold void ff_fft_end(FFTContext *s)
00204 {
00205     av_freep(&s->revtab);
00206     av_freep(&s->exptab);
00207     av_freep(&s->exptab1);
00208     av_freep(&s->tmp_buf);
00209 }
00210 
00211 #define sqrthalf (float)M_SQRT1_2
00212 
00213 #define BF(x,y,a,b) {\
00214     x = a - b;\
00215     y = a + b;\
00216 }
00217 
00218 #define BUTTERFLIES(a0,a1,a2,a3) {\
00219     BF(t3, t5, t5, t1);\
00220     BF(a2.re, a0.re, a0.re, t5);\
00221     BF(a3.im, a1.im, a1.im, t3);\
00222     BF(t4, t6, t2, t6);\
00223     BF(a3.re, a1.re, a1.re, t4);\
00224     BF(a2.im, a0.im, a0.im, t6);\
00225 }
00226 
00227 // force loading all the inputs before storing any.
00228 // this is slightly slower for small data, but avoids store->load aliasing
00229 // for addresses separated by large powers of 2.
00230 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
00231     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
00232     BF(t3, t5, t5, t1);\
00233     BF(a2.re, a0.re, r0, t5);\
00234     BF(a3.im, a1.im, i1, t3);\
00235     BF(t4, t6, t2, t6);\
00236     BF(a3.re, a1.re, r1, t4);\
00237     BF(a2.im, a0.im, i0, t6);\
00238 }
00239 
00240 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
00241     t1 = a2.re * wre + a2.im * wim;\
00242     t2 = a2.im * wre - a2.re * wim;\
00243     t5 = a3.re * wre - a3.im * wim;\
00244     t6 = a3.im * wre + a3.re * wim;\
00245     BUTTERFLIES(a0,a1,a2,a3)\
00246 }
00247 
00248 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
00249     t1 = a2.re;\
00250     t2 = a2.im;\
00251     t5 = a3.re;\
00252     t6 = a3.im;\
00253     BUTTERFLIES(a0,a1,a2,a3)\
00254 }
00255 
00256 /* z[0...8n-1], w[1...2n-1] */
00257 #define PASS(name)\
00258 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
00259 {\
00260     FFTSample t1, t2, t3, t4, t5, t6;\
00261     int o1 = 2*n;\
00262     int o2 = 4*n;\
00263     int o3 = 6*n;\
00264     const FFTSample *wim = wre+o1;\
00265     n--;\
00266 \
00267     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
00268     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
00269     do {\
00270         z += 2;\
00271         wre += 2;\
00272         wim -= 2;\
00273         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
00274         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
00275     } while(--n);\
00276 }
00277 
00278 PASS(pass)
00279 #undef BUTTERFLIES
00280 #define BUTTERFLIES BUTTERFLIES_BIG
00281 PASS(pass_big)
00282 
00283 #define DECL_FFT(n,n2,n4)\
00284 static void fft##n(FFTComplex *z)\
00285 {\
00286     fft##n2(z);\
00287     fft##n4(z+n4*2);\
00288     fft##n4(z+n4*3);\
00289     pass(z,ff_cos_##n,n4/2);\
00290 }
00291 
00292 static void fft4(FFTComplex *z)
00293 {
00294     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
00295 
00296     BF(t3, t1, z[0].re, z[1].re);
00297     BF(t8, t6, z[3].re, z[2].re);
00298     BF(z[2].re, z[0].re, t1, t6);
00299     BF(t4, t2, z[0].im, z[1].im);
00300     BF(t7, t5, z[2].im, z[3].im);
00301     BF(z[3].im, z[1].im, t4, t8);
00302     BF(z[3].re, z[1].re, t3, t7);
00303     BF(z[2].im, z[0].im, t2, t5);
00304 }
00305 
00306 static void fft8(FFTComplex *z)
00307 {
00308     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
00309 
00310     fft4(z);
00311 
00312     BF(t1, z[5].re, z[4].re, -z[5].re);
00313     BF(t2, z[5].im, z[4].im, -z[5].im);
00314     BF(t3, z[7].re, z[6].re, -z[7].re);
00315     BF(t4, z[7].im, z[6].im, -z[7].im);
00316     BF(t8, t1, t3, t1);
00317     BF(t7, t2, t2, t4);
00318     BF(z[4].re, z[0].re, z[0].re, t1);
00319     BF(z[4].im, z[0].im, z[0].im, t2);
00320     BF(z[6].re, z[2].re, z[2].re, t7);
00321     BF(z[6].im, z[2].im, z[2].im, t8);
00322 
00323     TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
00324 }
00325 
00326 #if !CONFIG_SMALL
00327 static void fft16(FFTComplex *z)
00328 {
00329     FFTSample t1, t2, t3, t4, t5, t6;
00330 
00331     fft8(z);
00332     fft4(z+8);
00333     fft4(z+12);
00334 
00335     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
00336     TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
00337     TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
00338     TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
00339 }
00340 #else
00341 DECL_FFT(16,8,4)
00342 #endif
00343 DECL_FFT(32,16,8)
00344 DECL_FFT(64,32,16)
00345 DECL_FFT(128,64,32)
00346 DECL_FFT(256,128,64)
00347 DECL_FFT(512,256,128)
00348 #if !CONFIG_SMALL
00349 #define pass pass_big
00350 #endif
00351 DECL_FFT(1024,512,256)
00352 DECL_FFT(2048,1024,512)
00353 DECL_FFT(4096,2048,1024)
00354 DECL_FFT(8192,4096,2048)
00355 DECL_FFT(16384,8192,4096)
00356 DECL_FFT(32768,16384,8192)
00357 DECL_FFT(65536,32768,16384)
00358 
00359 static void (* const fft_dispatch[])(FFTComplex*) = {
00360     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
00361     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
00362 };
00363 
00364 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
00365 {
00366     fft_dispatch[s->nbits-2](z);
00367 }
00368