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libavcodec/fft.c

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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 "dsputil.h"
00030 
00031 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
00032 DECLARE_ALIGNED_16(FFTSample, ff_cos_16[8]);
00033 DECLARE_ALIGNED_16(FFTSample, ff_cos_32[16]);
00034 DECLARE_ALIGNED_16(FFTSample, ff_cos_64[32]);
00035 DECLARE_ALIGNED_16(FFTSample, ff_cos_128[64]);
00036 DECLARE_ALIGNED_16(FFTSample, ff_cos_256[128]);
00037 DECLARE_ALIGNED_16(FFTSample, ff_cos_512[256]);
00038 DECLARE_ALIGNED_16(FFTSample, ff_cos_1024[512]);
00039 DECLARE_ALIGNED_16(FFTSample, ff_cos_2048[1024]);
00040 DECLARE_ALIGNED_16(FFTSample, ff_cos_4096[2048]);
00041 DECLARE_ALIGNED_16(FFTSample, ff_cos_8192[4096]);
00042 DECLARE_ALIGNED_16(FFTSample, ff_cos_16384[8192]);
00043 DECLARE_ALIGNED_16(FFTSample, ff_cos_32768[16384]);
00044 DECLARE_ALIGNED_16(FFTSample, ff_cos_65536[32768]);
00045 FFTSample *ff_cos_tabs[] = {
00046     ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
00047     ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
00048 };
00049 
00050 static int split_radix_permutation(int i, int n, int inverse)
00051 {
00052     int m;
00053     if(n <= 2) return i&1;
00054     m = n >> 1;
00055     if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
00056     m >>= 1;
00057     if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
00058     else                  return split_radix_permutation(i, m, inverse)*4 - 1;
00059 }
00060 
00061 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
00062 {
00063     int i, j, m, n;
00064     float alpha, c1, s1, s2;
00065     int split_radix = 1;
00066     int av_unused has_vectors;
00067     int revtab_shift = 0;
00068 
00069     if (nbits < 2 || nbits > 16)
00070         goto fail;
00071     s->nbits = nbits;
00072     n = 1 << nbits;
00073 
00074     s->tmp_buf = NULL;
00075     s->exptab  = av_malloc((n / 2) * sizeof(FFTComplex));
00076     if (!s->exptab)
00077         goto fail;
00078     s->revtab = av_malloc(n * sizeof(uint16_t));
00079     if (!s->revtab)
00080         goto fail;
00081     s->inverse = inverse;
00082 
00083     s2 = inverse ? 1.0 : -1.0;
00084 
00085     s->fft_permute = ff_fft_permute_c;
00086     s->fft_calc    = ff_fft_calc_c;
00087     s->imdct_calc  = ff_imdct_calc_c;
00088     s->imdct_half  = ff_imdct_half_c;
00089     s->mdct_calc   = ff_mdct_calc_c;
00090     s->exptab1     = NULL;
00091 
00092 #if HAVE_MMX && HAVE_YASM
00093     has_vectors = mm_support();
00094     if (has_vectors & FF_MM_SSE && HAVE_SSE) {
00095         /* SSE for P3/P4/K8 */
00096         s->imdct_calc  = ff_imdct_calc_sse;
00097         s->imdct_half  = ff_imdct_half_sse;
00098         s->fft_permute = ff_fft_permute_sse;
00099         s->fft_calc    = ff_fft_calc_sse;
00100     } else if (has_vectors & FF_MM_3DNOWEXT && HAVE_AMD3DNOWEXT) {
00101         /* 3DNowEx for K7 */
00102         s->imdct_calc = ff_imdct_calc_3dn2;
00103         s->imdct_half = ff_imdct_half_3dn2;
00104         s->fft_calc   = ff_fft_calc_3dn2;
00105     } else if (has_vectors & FF_MM_3DNOW && HAVE_AMD3DNOW) {
00106         /* 3DNow! for K6-2/3 */
00107         s->imdct_calc = ff_imdct_calc_3dn;
00108         s->imdct_half = ff_imdct_half_3dn;
00109         s->fft_calc   = ff_fft_calc_3dn;
00110     }
00111 #elif HAVE_ALTIVEC && !defined ALTIVEC_USE_REFERENCE_C_CODE
00112     has_vectors = mm_support();
00113     if (has_vectors & FF_MM_ALTIVEC) {
00114         s->fft_calc = ff_fft_calc_altivec;
00115         split_radix = 0;
00116     }
00117 #elif HAVE_NEON
00118     s->fft_permute = ff_fft_permute_neon;
00119     s->fft_calc    = ff_fft_calc_neon;
00120     s->imdct_calc  = ff_imdct_calc_neon;
00121     s->imdct_half  = ff_imdct_half_neon;
00122     s->mdct_calc   = ff_mdct_calc_neon;
00123     revtab_shift = 3;
00124 #endif
00125 
00126     if (split_radix) {
00127         for(j=4; j<=nbits; j++) {
00128             int m = 1<<j;
00129             double freq = 2*M_PI/m;
00130             FFTSample *tab = ff_cos_tabs[j-4];
00131             for(i=0; i<=m/4; i++)
00132                 tab[i] = cos(i*freq);
00133             for(i=1; i<m/4; i++)
00134                 tab[m/2-i] = tab[i];
00135         }
00136         for(i=0; i<n; i++)
00137             s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] =
00138                 i << revtab_shift;
00139         s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
00140     } else {
00141         int np, nblocks, np2, l;
00142         FFTComplex *q;
00143 
00144         for(i=0; i<(n/2); i++) {
00145             alpha = 2 * M_PI * (float)i / (float)n;
00146             c1 = cos(alpha);
00147             s1 = sin(alpha) * s2;
00148             s->exptab[i].re = c1;
00149             s->exptab[i].im = s1;
00150         }
00151 
00152         np = 1 << nbits;
00153         nblocks = np >> 3;
00154         np2 = np >> 1;
00155         s->exptab1 = av_malloc(np * 2 * sizeof(FFTComplex));
00156         if (!s->exptab1)
00157             goto fail;
00158         q = s->exptab1;
00159         do {
00160             for(l = 0; l < np2; l += 2 * nblocks) {
00161                 *q++ = s->exptab[l];
00162                 *q++ = s->exptab[l + nblocks];
00163 
00164                 q->re = -s->exptab[l].im;
00165                 q->im = s->exptab[l].re;
00166                 q++;
00167                 q->re = -s->exptab[l + nblocks].im;
00168                 q->im = s->exptab[l + nblocks].re;
00169                 q++;
00170             }
00171             nblocks = nblocks >> 1;
00172         } while (nblocks != 0);
00173         av_freep(&s->exptab);
00174 
00175         /* compute bit reverse table */
00176         for(i=0;i<n;i++) {
00177             m=0;
00178             for(j=0;j<nbits;j++) {
00179                 m |= ((i >> j) & 1) << (nbits-j-1);
00180             }
00181             s->revtab[i]=m;
00182         }
00183     }
00184 
00185     return 0;
00186  fail:
00187     av_freep(&s->revtab);
00188     av_freep(&s->exptab);
00189     av_freep(&s->exptab1);
00190     av_freep(&s->tmp_buf);
00191     return -1;
00192 }
00193 
00194 void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
00195 {
00196     int j, k, np;
00197     FFTComplex tmp;
00198     const uint16_t *revtab = s->revtab;
00199     np = 1 << s->nbits;
00200 
00201     if (s->tmp_buf) {
00202         /* TODO: handle split-radix permute in a more optimal way, probably in-place */
00203         for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
00204         memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
00205         return;
00206     }
00207 
00208     /* reverse */
00209     for(j=0;j<np;j++) {
00210         k = revtab[j];
00211         if (k < j) {
00212             tmp = z[k];
00213             z[k] = z[j];
00214             z[j] = tmp;
00215         }
00216     }
00217 }
00218 
00219 av_cold void ff_fft_end(FFTContext *s)
00220 {
00221     av_freep(&s->revtab);
00222     av_freep(&s->exptab);
00223     av_freep(&s->exptab1);
00224     av_freep(&s->tmp_buf);
00225 }
00226 
00227 #define sqrthalf (float)M_SQRT1_2
00228 
00229 #define BF(x,y,a,b) {\
00230     x = a - b;\
00231     y = a + b;\
00232 }
00233 
00234 #define BUTTERFLIES(a0,a1,a2,a3) {\
00235     BF(t3, t5, t5, t1);\
00236     BF(a2.re, a0.re, a0.re, t5);\
00237     BF(a3.im, a1.im, a1.im, t3);\
00238     BF(t4, t6, t2, t6);\
00239     BF(a3.re, a1.re, a1.re, t4);\
00240     BF(a2.im, a0.im, a0.im, t6);\
00241 }
00242 
00243 // force loading all the inputs before storing any.
00244 // this is slightly slower for small data, but avoids store->load aliasing
00245 // for addresses separated by large powers of 2.
00246 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
00247     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
00248     BF(t3, t5, t5, t1);\
00249     BF(a2.re, a0.re, r0, t5);\
00250     BF(a3.im, a1.im, i1, t3);\
00251     BF(t4, t6, t2, t6);\
00252     BF(a3.re, a1.re, r1, t4);\
00253     BF(a2.im, a0.im, i0, t6);\
00254 }
00255 
00256 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
00257     t1 = a2.re * wre + a2.im * wim;\
00258     t2 = a2.im * wre - a2.re * wim;\
00259     t5 = a3.re * wre - a3.im * wim;\
00260     t6 = a3.im * wre + a3.re * wim;\
00261     BUTTERFLIES(a0,a1,a2,a3)\
00262 }
00263 
00264 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
00265     t1 = a2.re;\
00266     t2 = a2.im;\
00267     t5 = a3.re;\
00268     t6 = a3.im;\
00269     BUTTERFLIES(a0,a1,a2,a3)\
00270 }
00271 
00272 /* z[0...8n-1], w[1...2n-1] */
00273 #define PASS(name)\
00274 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
00275 {\
00276     FFTSample t1, t2, t3, t4, t5, t6;\
00277     int o1 = 2*n;\
00278     int o2 = 4*n;\
00279     int o3 = 6*n;\
00280     const FFTSample *wim = wre+o1;\
00281     n--;\
00282 \
00283     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
00284     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
00285     do {\
00286         z += 2;\
00287         wre += 2;\
00288         wim -= 2;\
00289         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
00290         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
00291     } while(--n);\
00292 }
00293 
00294 PASS(pass)
00295 #undef BUTTERFLIES
00296 #define BUTTERFLIES BUTTERFLIES_BIG
00297 PASS(pass_big)
00298 
00299 #define DECL_FFT(n,n2,n4)\
00300 static void fft##n(FFTComplex *z)\
00301 {\
00302     fft##n2(z);\
00303     fft##n4(z+n4*2);\
00304     fft##n4(z+n4*3);\
00305     pass(z,ff_cos_##n,n4/2);\
00306 }
00307 
00308 static void fft4(FFTComplex *z)
00309 {
00310     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
00311 
00312     BF(t3, t1, z[0].re, z[1].re);
00313     BF(t8, t6, z[3].re, z[2].re);
00314     BF(z[2].re, z[0].re, t1, t6);
00315     BF(t4, t2, z[0].im, z[1].im);
00316     BF(t7, t5, z[2].im, z[3].im);
00317     BF(z[3].im, z[1].im, t4, t8);
00318     BF(z[3].re, z[1].re, t3, t7);
00319     BF(z[2].im, z[0].im, t2, t5);
00320 }
00321 
00322 static void fft8(FFTComplex *z)
00323 {
00324     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
00325 
00326     fft4(z);
00327 
00328     BF(t1, z[5].re, z[4].re, -z[5].re);
00329     BF(t2, z[5].im, z[4].im, -z[5].im);
00330     BF(t3, z[7].re, z[6].re, -z[7].re);
00331     BF(t4, z[7].im, z[6].im, -z[7].im);
00332     BF(t8, t1, t3, t1);
00333     BF(t7, t2, t2, t4);
00334     BF(z[4].re, z[0].re, z[0].re, t1);
00335     BF(z[4].im, z[0].im, z[0].im, t2);
00336     BF(z[6].re, z[2].re, z[2].re, t7);
00337     BF(z[6].im, z[2].im, z[2].im, t8);
00338 
00339     TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
00340 }
00341 
00342 #if !CONFIG_SMALL
00343 static void fft16(FFTComplex *z)
00344 {
00345     FFTSample t1, t2, t3, t4, t5, t6;
00346 
00347     fft8(z);
00348     fft4(z+8);
00349     fft4(z+12);
00350 
00351     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
00352     TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
00353     TRANSFORM(z[1],z[5],z[9],z[13],ff_cos_16[1],ff_cos_16[3]);
00354     TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_cos_16[1]);
00355 }
00356 #else
00357 DECL_FFT(16,8,4)
00358 #endif
00359 DECL_FFT(32,16,8)
00360 DECL_FFT(64,32,16)
00361 DECL_FFT(128,64,32)
00362 DECL_FFT(256,128,64)
00363 DECL_FFT(512,256,128)
00364 #if !CONFIG_SMALL
00365 #define pass pass_big
00366 #endif
00367 DECL_FFT(1024,512,256)
00368 DECL_FFT(2048,1024,512)
00369 DECL_FFT(4096,2048,1024)
00370 DECL_FFT(8192,4096,2048)
00371 DECL_FFT(16384,8192,4096)
00372 DECL_FFT(32768,16384,8192)
00373 DECL_FFT(65536,32768,16384)
00374 
00375 static void (*fft_dispatch[])(FFTComplex*) = {
00376     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
00377     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
00378 };
00379 
00380 void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
00381 {
00382     fft_dispatch[s->nbits-2](z);
00383 }
00384 

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