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, n;
00084 
00085     if (nbits < 2 || nbits > 16)
00086         goto fail;
00087     s->nbits = nbits;
00088     n = 1 << nbits;
00089 
00090     s->revtab = av_malloc(n * sizeof(uint16_t));
00091     if (!s->revtab)
00092         goto fail;
00093     s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
00094     if (!s->tmp_buf)
00095         goto fail;
00096     s->inverse = inverse;
00097 
00098     s->fft_permute = ff_fft_permute_c;
00099     s->fft_calc    = ff_fft_calc_c;
00100 #if CONFIG_MDCT
00101     s->imdct_calc  = ff_imdct_calc_c;
00102     s->imdct_half  = ff_imdct_half_c;
00103     s->mdct_calc   = ff_mdct_calc_c;
00104 #endif
00105 
00106     if (ARCH_ARM)     ff_fft_init_arm(s);
00107     if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
00108     if (HAVE_MMX)     ff_fft_init_mmx(s);
00109 
00110     for(j=4; j<=nbits; j++) {
00111         ff_init_ff_cos_tabs(j);
00112     }
00113     for(i=0; i<n; i++)
00114         s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
00115 
00116     return 0;
00117  fail:
00118     av_freep(&s->revtab);
00119     av_freep(&s->tmp_buf);
00120     return -1;
00121 }
00122 
00123 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
00124 {
00125     int j, np;
00126     const uint16_t *revtab = s->revtab;
00127     np = 1 << s->nbits;
00128     /* TODO: handle split-radix permute in a more optimal way, probably in-place */
00129     for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
00130     memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
00131 }
00132 
00133 av_cold void ff_fft_end(FFTContext *s)
00134 {
00135     av_freep(&s->revtab);
00136     av_freep(&s->tmp_buf);
00137 }
00138 
00139 #define sqrthalf (float)M_SQRT1_2
00140 
00141 #define BF(x,y,a,b) {\
00142     x = a - b;\
00143     y = a + b;\
00144 }
00145 
00146 #define BUTTERFLIES(a0,a1,a2,a3) {\
00147     BF(t3, t5, t5, t1);\
00148     BF(a2.re, a0.re, a0.re, t5);\
00149     BF(a3.im, a1.im, a1.im, t3);\
00150     BF(t4, t6, t2, t6);\
00151     BF(a3.re, a1.re, a1.re, t4);\
00152     BF(a2.im, a0.im, a0.im, t6);\
00153 }
00154 
00155 // force loading all the inputs before storing any.
00156 // this is slightly slower for small data, but avoids store->load aliasing
00157 // for addresses separated by large powers of 2.
00158 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
00159     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
00160     BF(t3, t5, t5, t1);\
00161     BF(a2.re, a0.re, r0, t5);\
00162     BF(a3.im, a1.im, i1, t3);\
00163     BF(t4, t6, t2, t6);\
00164     BF(a3.re, a1.re, r1, t4);\
00165     BF(a2.im, a0.im, i0, t6);\
00166 }
00167 
00168 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
00169     t1 = a2.re * wre + a2.im * wim;\
00170     t2 = a2.im * wre - a2.re * wim;\
00171     t5 = a3.re * wre - a3.im * wim;\
00172     t6 = a3.im * wre + a3.re * wim;\
00173     BUTTERFLIES(a0,a1,a2,a3)\
00174 }
00175 
00176 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
00177     t1 = a2.re;\
00178     t2 = a2.im;\
00179     t5 = a3.re;\
00180     t6 = a3.im;\
00181     BUTTERFLIES(a0,a1,a2,a3)\
00182 }
00183 
00184 /* z[0...8n-1], w[1...2n-1] */
00185 #define PASS(name)\
00186 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
00187 {\
00188     FFTSample t1, t2, t3, t4, t5, t6;\
00189     int o1 = 2*n;\
00190     int o2 = 4*n;\
00191     int o3 = 6*n;\
00192     const FFTSample *wim = wre+o1;\
00193     n--;\
00194 \
00195     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
00196     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
00197     do {\
00198         z += 2;\
00199         wre += 2;\
00200         wim -= 2;\
00201         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
00202         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
00203     } while(--n);\
00204 }
00205 
00206 PASS(pass)
00207 #undef BUTTERFLIES
00208 #define BUTTERFLIES BUTTERFLIES_BIG
00209 PASS(pass_big)
00210 
00211 #define DECL_FFT(n,n2,n4)\
00212 static void fft##n(FFTComplex *z)\
00213 {\
00214     fft##n2(z);\
00215     fft##n4(z+n4*2);\
00216     fft##n4(z+n4*3);\
00217     pass(z,ff_cos_##n,n4/2);\
00218 }
00219 
00220 static void fft4(FFTComplex *z)
00221 {
00222     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
00223 
00224     BF(t3, t1, z[0].re, z[1].re);
00225     BF(t8, t6, z[3].re, z[2].re);
00226     BF(z[2].re, z[0].re, t1, t6);
00227     BF(t4, t2, z[0].im, z[1].im);
00228     BF(t7, t5, z[2].im, z[3].im);
00229     BF(z[3].im, z[1].im, t4, t8);
00230     BF(z[3].re, z[1].re, t3, t7);
00231     BF(z[2].im, z[0].im, t2, t5);
00232 }
00233 
00234 static void fft8(FFTComplex *z)
00235 {
00236     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
00237 
00238     fft4(z);
00239 
00240     BF(t1, z[5].re, z[4].re, -z[5].re);
00241     BF(t2, z[5].im, z[4].im, -z[5].im);
00242     BF(t3, z[7].re, z[6].re, -z[7].re);
00243     BF(t4, z[7].im, z[6].im, -z[7].im);
00244     BF(t8, t1, t3, t1);
00245     BF(t7, t2, t2, t4);
00246     BF(z[4].re, z[0].re, z[0].re, t1);
00247     BF(z[4].im, z[0].im, z[0].im, t2);
00248     BF(z[6].re, z[2].re, z[2].re, t7);
00249     BF(z[6].im, z[2].im, z[2].im, t8);
00250 
00251     TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
00252 }
00253 
00254 #if !CONFIG_SMALL
00255 static void fft16(FFTComplex *z)
00256 {
00257     FFTSample t1, t2, t3, t4, t5, t6;
00258 
00259     fft8(z);
00260     fft4(z+8);
00261     fft4(z+12);
00262 
00263     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
00264     TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
00265     TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
00266     TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
00267 }
00268 #else
00269 DECL_FFT(16,8,4)
00270 #endif
00271 DECL_FFT(32,16,8)
00272 DECL_FFT(64,32,16)
00273 DECL_FFT(128,64,32)
00274 DECL_FFT(256,128,64)
00275 DECL_FFT(512,256,128)
00276 #if !CONFIG_SMALL
00277 #define pass pass_big
00278 #endif
00279 DECL_FFT(1024,512,256)
00280 DECL_FFT(2048,1024,512)
00281 DECL_FFT(4096,2048,1024)
00282 DECL_FFT(8192,4096,2048)
00283 DECL_FFT(16384,8192,4096)
00284 DECL_FFT(32768,16384,8192)
00285 DECL_FFT(65536,32768,16384)
00286 
00287 static void (* const fft_dispatch[])(FFTComplex*) = {
00288     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
00289     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
00290 };
00291 
00292 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
00293 {
00294     fft_dispatch[s->nbits-2](z);
00295 }
00296