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 Libav. 8 * 9 * Libav 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 * Libav 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 Libav; 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 26 * FFT/IFFT transforms. 27 */ 28 29#include <stdlib.h> 30#include <string.h> 31#include "libavutil/mathematics.h" 32#include "fft.h" 33#include "fft-internal.h" 34 35/* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */ 36#if !CONFIG_HARDCODED_TABLES 37COSTABLE(16); 38COSTABLE(32); 39COSTABLE(64); 40COSTABLE(128); 41COSTABLE(256); 42COSTABLE(512); 43COSTABLE(1024); 44COSTABLE(2048); 45COSTABLE(4096); 46COSTABLE(8192); 47COSTABLE(16384); 48COSTABLE(32768); 49COSTABLE(65536); 50#endif 51COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = { 52 NULL, NULL, NULL, NULL, 53 FFT_NAME(ff_cos_16), 54 FFT_NAME(ff_cos_32), 55 FFT_NAME(ff_cos_64), 56 FFT_NAME(ff_cos_128), 57 FFT_NAME(ff_cos_256), 58 FFT_NAME(ff_cos_512), 59 FFT_NAME(ff_cos_1024), 60 FFT_NAME(ff_cos_2048), 61 FFT_NAME(ff_cos_4096), 62 FFT_NAME(ff_cos_8192), 63 FFT_NAME(ff_cos_16384), 64 FFT_NAME(ff_cos_32768), 65 FFT_NAME(ff_cos_65536), 66}; 67 68static void ff_fft_permute_c(FFTContext *s, FFTComplex *z); 69static void ff_fft_calc_c(FFTContext *s, FFTComplex *z); 70 71static int split_radix_permutation(int i, int n, int inverse) 72{ 73 int m; 74 if(n <= 2) return i&1; 75 m = n >> 1; 76 if(!(i&m)) return split_radix_permutation(i, m, inverse)*2; 77 m >>= 1; 78 if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1; 79 else return split_radix_permutation(i, m, inverse)*4 - 1; 80} 81 82av_cold void ff_init_ff_cos_tabs(int index) 83{ 84#if !CONFIG_HARDCODED_TABLES 85 int i; 86 int m = 1<<index; 87 double freq = 2*M_PI/m; 88 FFTSample *tab = FFT_NAME(ff_cos_tabs)[index]; 89 for(i=0; i<=m/4; i++) 90 tab[i] = FIX15(cos(i*freq)); 91 for(i=1; i<m/4; i++) 92 tab[m/2-i] = tab[i]; 93#endif 94} 95 96static const int avx_tab[] = { 97 0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15 98}; 99 100static int is_second_half_of_fft32(int i, int n) 101{ 102 if (n <= 32) 103 return i >= 16; 104 else if (i < n/2) 105 return is_second_half_of_fft32(i, n/2); 106 else if (i < 3*n/4) 107 return is_second_half_of_fft32(i - n/2, n/4); 108 else 109 return is_second_half_of_fft32(i - 3*n/4, n/4); 110} 111 112static av_cold void fft_perm_avx(FFTContext *s) 113{ 114 int i; 115 int n = 1 << s->nbits; 116 117 for (i = 0; i < n; i += 16) { 118 int k; 119 if (is_second_half_of_fft32(i, n)) { 120 for (k = 0; k < 16; k++) 121 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = 122 i + avx_tab[k]; 123 124 } else { 125 for (k = 0; k < 16; k++) { 126 int j = i + k; 127 j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4); 128 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j; 129 } 130 } 131 } 132} 133 134av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse) 135{ 136 int i, j, n; 137 138 if (nbits < 2 || nbits > 16) 139 goto fail; 140 s->nbits = nbits; 141 n = 1 << nbits; 142 143 s->revtab = av_malloc(n * sizeof(uint16_t)); 144 if (!s->revtab) 145 goto fail; 146 s->tmp_buf = av_malloc(n * sizeof(FFTComplex)); 147 if (!s->tmp_buf) 148 goto fail; 149 s->inverse = inverse; 150 s->fft_permutation = FF_FFT_PERM_DEFAULT; 151 152 s->fft_permute = ff_fft_permute_c; 153 s->fft_calc = ff_fft_calc_c; 154#if CONFIG_MDCT 155 s->imdct_calc = ff_imdct_calc_c; 156 s->imdct_half = ff_imdct_half_c; 157 s->mdct_calc = ff_mdct_calc_c; 158#endif 159 160#if CONFIG_FFT_FLOAT 161 if (ARCH_ARM) ff_fft_init_arm(s); 162 if (HAVE_ALTIVEC) ff_fft_init_altivec(s); 163 if (HAVE_MMX) ff_fft_init_mmx(s); 164 if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc; 165#else 166 if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c; 167 if (ARCH_ARM) ff_fft_fixed_init_arm(s); 168#endif 169 170 for(j=4; j<=nbits; j++) { 171 ff_init_ff_cos_tabs(j); 172 } 173 174 if (s->fft_permutation == FF_FFT_PERM_AVX) { 175 fft_perm_avx(s); 176 } else { 177 for(i=0; i<n; i++) { 178 int j = i; 179 if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS) 180 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2); 181 s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j; 182 } 183 } 184 185 return 0; 186 fail: 187 av_freep(&s->revtab); 188 av_freep(&s->tmp_buf); 189 return -1; 190} 191 192static void ff_fft_permute_c(FFTContext *s, FFTComplex *z) 193{ 194 int j, np; 195 const uint16_t *revtab = s->revtab; 196 np = 1 << s->nbits; 197 /* TODO: handle split-radix permute in a more optimal way, probably in-place */ 198 for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j]; 199 memcpy(z, s->tmp_buf, np * sizeof(FFTComplex)); 200} 201 202av_cold void ff_fft_end(FFTContext *s) 203{ 204 av_freep(&s->revtab); 205 av_freep(&s->tmp_buf); 206} 207 208#define BUTTERFLIES(a0,a1,a2,a3) {\ 209 BF(t3, t5, t5, t1);\ 210 BF(a2.re, a0.re, a0.re, t5);\ 211 BF(a3.im, a1.im, a1.im, t3);\ 212 BF(t4, t6, t2, t6);\ 213 BF(a3.re, a1.re, a1.re, t4);\ 214 BF(a2.im, a0.im, a0.im, t6);\ 215} 216 217// force loading all the inputs before storing any. 218// this is slightly slower for small data, but avoids store->load aliasing 219// for addresses separated by large powers of 2. 220#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\ 221 FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\ 222 BF(t3, t5, t5, t1);\ 223 BF(a2.re, a0.re, r0, t5);\ 224 BF(a3.im, a1.im, i1, t3);\ 225 BF(t4, t6, t2, t6);\ 226 BF(a3.re, a1.re, r1, t4);\ 227 BF(a2.im, a0.im, i0, t6);\ 228} 229 230#define TRANSFORM(a0,a1,a2,a3,wre,wim) {\ 231 CMUL(t1, t2, a2.re, a2.im, wre, -wim);\ 232 CMUL(t5, t6, a3.re, a3.im, wre, wim);\ 233 BUTTERFLIES(a0,a1,a2,a3)\ 234} 235 236#define TRANSFORM_ZERO(a0,a1,a2,a3) {\ 237 t1 = a2.re;\ 238 t2 = a2.im;\ 239 t5 = a3.re;\ 240 t6 = a3.im;\ 241 BUTTERFLIES(a0,a1,a2,a3)\ 242} 243 244/* z[0...8n-1], w[1...2n-1] */ 245#define PASS(name)\ 246static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\ 247{\ 248 FFTDouble t1, t2, t3, t4, t5, t6;\ 249 int o1 = 2*n;\ 250 int o2 = 4*n;\ 251 int o3 = 6*n;\ 252 const FFTSample *wim = wre+o1;\ 253 n--;\ 254\ 255 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\ 256 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\ 257 do {\ 258 z += 2;\ 259 wre += 2;\ 260 wim -= 2;\ 261 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\ 262 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\ 263 } while(--n);\ 264} 265 266PASS(pass) 267#undef BUTTERFLIES 268#define BUTTERFLIES BUTTERFLIES_BIG 269PASS(pass_big) 270 271#define DECL_FFT(n,n2,n4)\ 272static void fft##n(FFTComplex *z)\ 273{\ 274 fft##n2(z);\ 275 fft##n4(z+n4*2);\ 276 fft##n4(z+n4*3);\ 277 pass(z,FFT_NAME(ff_cos_##n),n4/2);\ 278} 279 280static void fft4(FFTComplex *z) 281{ 282 FFTDouble t1, t2, t3, t4, t5, t6, t7, t8; 283 284 BF(t3, t1, z[0].re, z[1].re); 285 BF(t8, t6, z[3].re, z[2].re); 286 BF(z[2].re, z[0].re, t1, t6); 287 BF(t4, t2, z[0].im, z[1].im); 288 BF(t7, t5, z[2].im, z[3].im); 289 BF(z[3].im, z[1].im, t4, t8); 290 BF(z[3].re, z[1].re, t3, t7); 291 BF(z[2].im, z[0].im, t2, t5); 292} 293 294static void fft8(FFTComplex *z) 295{ 296 FFTDouble t1, t2, t3, t4, t5, t6; 297 298 fft4(z); 299 300 BF(t1, z[5].re, z[4].re, -z[5].re); 301 BF(t2, z[5].im, z[4].im, -z[5].im); 302 BF(t5, z[7].re, z[6].re, -z[7].re); 303 BF(t6, z[7].im, z[6].im, -z[7].im); 304 305 BUTTERFLIES(z[0],z[2],z[4],z[6]); 306 TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf); 307} 308 309#if !CONFIG_SMALL 310static void fft16(FFTComplex *z) 311{ 312 FFTDouble t1, t2, t3, t4, t5, t6; 313 FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1]; 314 FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3]; 315 316 fft8(z); 317 fft4(z+8); 318 fft4(z+12); 319 320 TRANSFORM_ZERO(z[0],z[4],z[8],z[12]); 321 TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf); 322 TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3); 323 TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1); 324} 325#else 326DECL_FFT(16,8,4) 327#endif 328DECL_FFT(32,16,8) 329DECL_FFT(64,32,16) 330DECL_FFT(128,64,32) 331DECL_FFT(256,128,64) 332DECL_FFT(512,256,128) 333#if !CONFIG_SMALL 334#define pass pass_big 335#endif 336DECL_FFT(1024,512,256) 337DECL_FFT(2048,1024,512) 338DECL_FFT(4096,2048,1024) 339DECL_FFT(8192,4096,2048) 340DECL_FFT(16384,8192,4096) 341DECL_FFT(32768,16384,8192) 342DECL_FFT(65536,32768,16384) 343 344static void (* const fft_dispatch[])(FFTComplex*) = { 345 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024, 346 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, 347}; 348 349static void ff_fft_calc_c(FFTContext *s, FFTComplex *z) 350{ 351 fft_dispatch[s->nbits-2](z); 352} 353 354