Libav 0.7.1
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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 Libav. 00008 * 00009 * Libav 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 * Libav 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 Libav; 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 #include "fft-internal.h" 00034 00035 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */ 00036 #if !CONFIG_HARDCODED_TABLES 00037 COSTABLE(16); 00038 COSTABLE(32); 00039 COSTABLE(64); 00040 COSTABLE(128); 00041 COSTABLE(256); 00042 COSTABLE(512); 00043 COSTABLE(1024); 00044 COSTABLE(2048); 00045 COSTABLE(4096); 00046 COSTABLE(8192); 00047 COSTABLE(16384); 00048 COSTABLE(32768); 00049 COSTABLE(65536); 00050 #endif 00051 COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = { 00052 NULL, NULL, NULL, NULL, 00053 FFT_NAME(ff_cos_16), 00054 FFT_NAME(ff_cos_32), 00055 FFT_NAME(ff_cos_64), 00056 FFT_NAME(ff_cos_128), 00057 FFT_NAME(ff_cos_256), 00058 FFT_NAME(ff_cos_512), 00059 FFT_NAME(ff_cos_1024), 00060 FFT_NAME(ff_cos_2048), 00061 FFT_NAME(ff_cos_4096), 00062 FFT_NAME(ff_cos_8192), 00063 FFT_NAME(ff_cos_16384), 00064 FFT_NAME(ff_cos_32768), 00065 FFT_NAME(ff_cos_65536), 00066 }; 00067 00068 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z); 00069 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z); 00070 00071 static int split_radix_permutation(int i, int n, int inverse) 00072 { 00073 int m; 00074 if(n <= 2) return i&1; 00075 m = n >> 1; 00076 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2; 00077 m >>= 1; 00078 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1; 00079 else return split_radix_permutation(i, m, inverse)*4 - 1; 00080 } 00081 00082 av_cold void ff_init_ff_cos_tabs(int index) 00083 { 00084 #if !CONFIG_HARDCODED_TABLES 00085 int i; 00086 int m = 1<<index; 00087 double freq = 2*M_PI/m; 00088 FFTSample *tab = FFT_NAME(ff_cos_tabs)[index]; 00089 for(i=0; i<=m/4; i++) 00090 tab[i] = FIX15(cos(i*freq)); 00091 for(i=1; i<m/4; i++) 00092 tab[m/2-i] = tab[i]; 00093 #endif 00094 } 00095 00096 static const int avx_tab[] = { 00097 0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15 00098 }; 00099 00100 static int is_second_half_of_fft32(int i, int n) 00101 { 00102 if (n <= 32) 00103 return i >= 16; 00104 else if (i < n/2) 00105 return is_second_half_of_fft32(i, n/2); 00106 else if (i < 3*n/4) 00107 return is_second_half_of_fft32(i - n/2, n/4); 00108 else 00109 return is_second_half_of_fft32(i - 3*n/4, n/4); 00110 } 00111 00112 static av_cold void fft_perm_avx(FFTContext *s) 00113 { 00114 int i; 00115 int n = 1 << s->nbits; 00116 00117 for (i = 0; i < n; i += 16) { 00118 int k; 00119 if (is_second_half_of_fft32(i, n)) { 00120 for (k = 0; k < 16; k++) 00121 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = 00122 i + avx_tab[k]; 00123 00124 } else { 00125 for (k = 0; k < 16; k++) { 00126 int j = i + k; 00127 j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4); 00128 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j; 00129 } 00130 } 00131 } 00132 } 00133 00134 av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse) 00135 { 00136 int i, j, n; 00137 00138 if (nbits < 2 || nbits > 16) 00139 goto fail; 00140 s->nbits = nbits; 00141 n = 1 << nbits; 00142 00143 s->revtab = av_malloc(n * sizeof(uint16_t)); 00144 if (!s->revtab) 00145 goto fail; 00146 s->tmp_buf = av_malloc(n * sizeof(FFTComplex)); 00147 if (!s->tmp_buf) 00148 goto fail; 00149 s->inverse = inverse; 00150 s->fft_permutation = FF_FFT_PERM_DEFAULT; 00151 00152 s->fft_permute = ff_fft_permute_c; 00153 s->fft_calc = ff_fft_calc_c; 00154 #if CONFIG_MDCT 00155 s->imdct_calc = ff_imdct_calc_c; 00156 s->imdct_half = ff_imdct_half_c; 00157 s->mdct_calc = ff_mdct_calc_c; 00158 #endif 00159 00160 #if CONFIG_FFT_FLOAT 00161 if (ARCH_ARM) ff_fft_init_arm(s); 00162 if (HAVE_ALTIVEC) ff_fft_init_altivec(s); 00163 if (HAVE_MMX) ff_fft_init_mmx(s); 00164 if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc; 00165 #else 00166 if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c; 00167 if (ARCH_ARM) ff_fft_fixed_init_arm(s); 00168 #endif 00169 00170 for(j=4; j<=nbits; j++) { 00171 ff_init_ff_cos_tabs(j); 00172 } 00173 00174 if (s->fft_permutation == FF_FFT_PERM_AVX) { 00175 fft_perm_avx(s); 00176 } else { 00177 for(i=0; i<n; i++) { 00178 int j = i; 00179 if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS) 00180 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2); 00181 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j; 00182 } 00183 } 00184 00185 return 0; 00186 fail: 00187 av_freep(&s->revtab); 00188 av_freep(&s->tmp_buf); 00189 return -1; 00190 } 00191 00192 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z) 00193 { 00194 int j, np; 00195 const uint16_t *revtab = s->revtab; 00196 np = 1 << s->nbits; 00197 /* TODO: handle split-radix permute in a more optimal way, probably in-place */ 00198 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j]; 00199 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex)); 00200 } 00201 00202 av_cold void ff_fft_end(FFTContext *s) 00203 { 00204 av_freep(&s->revtab); 00205 av_freep(&s->tmp_buf); 00206 } 00207 00208 #define BUTTERFLIES(a0,a1,a2,a3) {\ 00209 BF(t3, t5, t5, t1);\ 00210 BF(a2.re, a0.re, a0.re, t5);\ 00211 BF(a3.im, a1.im, a1.im, t3);\ 00212 BF(t4, t6, t2, t6);\ 00213 BF(a3.re, a1.re, a1.re, t4);\ 00214 BF(a2.im, a0.im, a0.im, t6);\ 00215 } 00216 00217 // force loading all the inputs before storing any. 00218 // this is slightly slower for small data, but avoids store->load aliasing 00219 // for addresses separated by large powers of 2. 00220 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\ 00221 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\ 00222 BF(t3, t5, t5, t1);\ 00223 BF(a2.re, a0.re, r0, t5);\ 00224 BF(a3.im, a1.im, i1, t3);\ 00225 BF(t4, t6, t2, t6);\ 00226 BF(a3.re, a1.re, r1, t4);\ 00227 BF(a2.im, a0.im, i0, t6);\ 00228 } 00229 00230 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\ 00231 CMUL(t1, t2, a2.re, a2.im, wre, -wim);\ 00232 CMUL(t5, t6, a3.re, a3.im, wre, wim);\ 00233 BUTTERFLIES(a0,a1,a2,a3)\ 00234 } 00235 00236 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\ 00237 t1 = a2.re;\ 00238 t2 = a2.im;\ 00239 t5 = a3.re;\ 00240 t6 = a3.im;\ 00241 BUTTERFLIES(a0,a1,a2,a3)\ 00242 } 00243 00244 /* z[0...8n-1], w[1...2n-1] */ 00245 #define PASS(name)\ 00246 static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\ 00247 {\ 00248 FFTDouble t1, t2, t3, t4, t5, t6;\ 00249 int o1 = 2*n;\ 00250 int o2 = 4*n;\ 00251 int o3 = 6*n;\ 00252 const FFTSample *wim = wre+o1;\ 00253 n--;\ 00254 \ 00255 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\ 00256 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\ 00257 do {\ 00258 z += 2;\ 00259 wre += 2;\ 00260 wim -= 2;\ 00261 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\ 00262 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\ 00263 } while(--n);\ 00264 } 00265 00266 PASS(pass) 00267 #undef BUTTERFLIES 00268 #define BUTTERFLIES BUTTERFLIES_BIG 00269 PASS(pass_big) 00270 00271 #define DECL_FFT(n,n2,n4)\ 00272 static void fft##n(FFTComplex *z)\ 00273 {\ 00274 fft##n2(z);\ 00275 fft##n4(z+n4*2);\ 00276 fft##n4(z+n4*3);\ 00277 pass(z,FFT_NAME(ff_cos_##n),n4/2);\ 00278 } 00279 00280 static void fft4(FFTComplex *z) 00281 { 00282 FFTDouble t1, t2, t3, t4, t5, t6, t7, t8; 00283 00284 BF(t3, t1, z[0].re, z[1].re); 00285 BF(t8, t6, z[3].re, z[2].re); 00286 BF(z[2].re, z[0].re, t1, t6); 00287 BF(t4, t2, z[0].im, z[1].im); 00288 BF(t7, t5, z[2].im, z[3].im); 00289 BF(z[3].im, z[1].im, t4, t8); 00290 BF(z[3].re, z[1].re, t3, t7); 00291 BF(z[2].im, z[0].im, t2, t5); 00292 } 00293 00294 static void fft8(FFTComplex *z) 00295 { 00296 FFTDouble t1, t2, t3, t4, t5, t6; 00297 00298 fft4(z); 00299 00300 BF(t1, z[5].re, z[4].re, -z[5].re); 00301 BF(t2, z[5].im, z[4].im, -z[5].im); 00302 BF(t5, z[7].re, z[6].re, -z[7].re); 00303 BF(t6, z[7].im, z[6].im, -z[7].im); 00304 00305 BUTTERFLIES(z[0],z[2],z[4],z[6]); 00306 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf); 00307 } 00308 00309 #if !CONFIG_SMALL 00310 static void fft16(FFTComplex *z) 00311 { 00312 FFTDouble t1, t2, t3, t4, t5, t6; 00313 FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1]; 00314 FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3]; 00315 00316 fft8(z); 00317 fft4(z+8); 00318 fft4(z+12); 00319 00320 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]); 00321 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf); 00322 TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3); 00323 TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1); 00324 } 00325 #else 00326 DECL_FFT(16,8,4) 00327 #endif 00328 DECL_FFT(32,16,8) 00329 DECL_FFT(64,32,16) 00330 DECL_FFT(128,64,32) 00331 DECL_FFT(256,128,64) 00332 DECL_FFT(512,256,128) 00333 #if !CONFIG_SMALL 00334 #define pass pass_big 00335 #endif 00336 DECL_FFT(1024,512,256) 00337 DECL_FFT(2048,1024,512) 00338 DECL_FFT(4096,2048,1024) 00339 DECL_FFT(8192,4096,2048) 00340 DECL_FFT(16384,8192,4096) 00341 DECL_FFT(32768,16384,8192) 00342 DECL_FFT(65536,32768,16384) 00343 00344 static void (* const fft_dispatch[])(FFTComplex*) = { 00345 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024, 00346 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, 00347 }; 00348 00349 static void ff_fft_calc_c(FFTContext *s, FFTComplex *z) 00350 { 00351 fft_dispatch[s->nbits-2](z); 00352 } 00353