/* * FFT/IFFT transforms * Copyright (c) 2008 Loren Merritt * Copyright (c) 2002 Fabrice Bellard * Partly based on libdjbfft by D. J. Bernstein * * This file is part of Libav. * * Libav is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation; either * version 2.1 of the License, or (at your option) any later version. * * Libav is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with Libav; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ /** * @file * FFT/IFFT transforms. */ #include <stdlib.h> #include <string.h> #include "libavutil/mathematics.h" #include "fft.h" #include "fft-internal.h" /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */ #if !CONFIG_HARDCODED_TABLES COSTABLE(16); COSTABLE(32); COSTABLE(64); COSTABLE(128); COSTABLE(256); COSTABLE(512); COSTABLE(1024); COSTABLE(2048); COSTABLE(4096); COSTABLE(8192); COSTABLE(16384); COSTABLE(32768); COSTABLE(65536); #endif COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = { NULL, NULL, NULL, NULL, FFT_NAME(ff_cos_16), FFT_NAME(ff_cos_32), FFT_NAME(ff_cos_64), FFT_NAME(ff_cos_128), FFT_NAME(ff_cos_256), FFT_NAME(ff_cos_512), FFT_NAME(ff_cos_1024), FFT_NAME(ff_cos_2048), FFT_NAME(ff_cos_4096), FFT_NAME(ff_cos_8192), FFT_NAME(ff_cos_16384), FFT_NAME(ff_cos_32768), FFT_NAME(ff_cos_65536), }; static void ff_fft_permute_c(FFTContext *s, FFTComplex *z); static void ff_fft_calc_c(FFTContext *s, FFTComplex *z); static int split_radix_permutation(int i, int n, int inverse) { int m; if(n <= 2) return i&1; m = n >> 1; if(!(i&m)) return split_radix_permutation(i, m, inverse)*2; m >>= 1; if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1; else return split_radix_permutation(i, m, inverse)*4 - 1; } av_cold void ff_init_ff_cos_tabs(int index) { #if !CONFIG_HARDCODED_TABLES int i; int m = 1<<index; double freq = 2*M_PI/m; FFTSample *tab = FFT_NAME(ff_cos_tabs)[index]; for(i=0; i<=m/4; i++) tab[i] = FIX15(cos(i*freq)); for(i=1; i<m/4; i++) tab[m/2-i] = tab[i]; #endif } static const int avx_tab[] = { 0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15 }; static int is_second_half_of_fft32(int i, int n) { if (n <= 32) return i >= 16; else if (i < n/2) return is_second_half_of_fft32(i, n/2); else if (i < 3*n/4) return is_second_half_of_fft32(i - n/2, n/4); else return is_second_half_of_fft32(i - 3*n/4, n/4); } static av_cold void fft_perm_avx(FFTContext *s) { int i; int n = 1 << s->nbits; for (i = 0; i < n; i += 16) { int k; if (is_second_half_of_fft32(i, n)) { for (k = 0; k < 16; k++) s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = i + avx_tab[k]; } else { for (k = 0; k < 16; k++) { int j = i + k; j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4); s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j; } } } } av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse) { int i, j, n; if (nbits < 2 || nbits > 16) goto fail; s->nbits = nbits; n = 1 << nbits; s->revtab = av_malloc(n * sizeof(uint16_t)); if (!s->revtab) goto fail; s->tmp_buf = av_malloc(n * sizeof(FFTComplex)); if (!s->tmp_buf) goto fail; s->inverse = inverse; s->fft_permutation = FF_FFT_PERM_DEFAULT; s->fft_permute = ff_fft_permute_c; s->fft_calc = ff_fft_calc_c; #if CONFIG_MDCT s->imdct_calc = ff_imdct_calc_c; s->imdct_half = ff_imdct_half_c; s->mdct_calc = ff_mdct_calc_c; #endif #if CONFIG_FFT_FLOAT if (ARCH_ARM) ff_fft_init_arm(s); if (HAVE_ALTIVEC) ff_fft_init_altivec(s); if (HAVE_MMX) ff_fft_init_mmx(s); if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc; #else if (CONFIG_MDCT) s->mdct_calcw = ff_mdct_calcw_c; if (ARCH_ARM) ff_fft_fixed_init_arm(s); #endif for(j=4; j<=nbits; j++) { ff_init_ff_cos_tabs(j); } if (s->fft_permutation == FF_FFT_PERM_AVX) { fft_perm_avx(s); } else { for(i=0; i<n; i++) { int j = i; if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS) j = (j&~3) | ((j>>1)&1) | ((j<<1)&2); s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j; } } return 0; fail: av_freep(&s->revtab); av_freep(&s->tmp_buf); return -1; } static void ff_fft_permute_c(FFTContext *s, FFTComplex *z) { int j, np; const uint16_t *revtab = s->revtab; np = 1 << s->nbits; /* TODO: handle split-radix permute in a more optimal way, probably in-place */ for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j]; memcpy(z, s->tmp_buf, np * sizeof(FFTComplex)); } av_cold void ff_fft_end(FFTContext *s) { av_freep(&s->revtab); av_freep(&s->tmp_buf); } #define BUTTERFLIES(a0,a1,a2,a3) {\ BF(t3, t5, t5, t1);\ BF(a2.re, a0.re, a0.re, t5);\ BF(a3.im, a1.im, a1.im, t3);\ BF(t4, t6, t2, t6);\ BF(a3.re, a1.re, a1.re, t4);\ BF(a2.im, a0.im, a0.im, t6);\ } // force loading all the inputs before storing any. // this is slightly slower for small data, but avoids store->load aliasing // for addresses separated by large powers of 2. #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\ FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\ BF(t3, t5, t5, t1);\ BF(a2.re, a0.re, r0, t5);\ BF(a3.im, a1.im, i1, t3);\ BF(t4, t6, t2, t6);\ BF(a3.re, a1.re, r1, t4);\ BF(a2.im, a0.im, i0, t6);\ } #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\ CMUL(t1, t2, a2.re, a2.im, wre, -wim);\ CMUL(t5, t6, a3.re, a3.im, wre, wim);\ BUTTERFLIES(a0,a1,a2,a3)\ } #define TRANSFORM_ZERO(a0,a1,a2,a3) {\ t1 = a2.re;\ t2 = a2.im;\ t5 = a3.re;\ t6 = a3.im;\ BUTTERFLIES(a0,a1,a2,a3)\ } /* z[0...8n-1], w[1...2n-1] */ #define PASS(name)\ static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\ {\ FFTDouble t1, t2, t3, t4, t5, t6;\ int o1 = 2*n;\ int o2 = 4*n;\ int o3 = 6*n;\ const FFTSample *wim = wre+o1;\ n--;\ \ TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\ TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\ do {\ z += 2;\ wre += 2;\ wim -= 2;\ TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\ TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\ } while(--n);\ } PASS(pass) #undef BUTTERFLIES #define BUTTERFLIES BUTTERFLIES_BIG PASS(pass_big) #define DECL_FFT(n,n2,n4)\ static void fft##n(FFTComplex *z)\ {\ fft##n2(z);\ fft##n4(z+n4*2);\ fft##n4(z+n4*3);\ pass(z,FFT_NAME(ff_cos_##n),n4/2);\ } static void fft4(FFTComplex *z) { FFTDouble t1, t2, t3, t4, t5, t6, t7, t8; BF(t3, t1, z[0].re, z[1].re); BF(t8, t6, z[3].re, z[2].re); BF(z[2].re, z[0].re, t1, t6); BF(t4, t2, z[0].im, z[1].im); BF(t7, t5, z[2].im, z[3].im); BF(z[3].im, z[1].im, t4, t8); BF(z[3].re, z[1].re, t3, t7); BF(z[2].im, z[0].im, t2, t5); } static void fft8(FFTComplex *z) { FFTDouble t1, t2, t3, t4, t5, t6; fft4(z); BF(t1, z[5].re, z[4].re, -z[5].re); BF(t2, z[5].im, z[4].im, -z[5].im); BF(t5, z[7].re, z[6].re, -z[7].re); BF(t6, z[7].im, z[6].im, -z[7].im); BUTTERFLIES(z[0],z[2],z[4],z[6]); TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf); } #if !CONFIG_SMALL static void fft16(FFTComplex *z) { FFTDouble t1, t2, t3, t4, t5, t6; FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1]; FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3]; fft8(z); fft4(z+8); fft4(z+12); TRANSFORM_ZERO(z[0],z[4],z[8],z[12]); TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf); TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3); TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1); } #else DECL_FFT(16,8,4) #endif DECL_FFT(32,16,8) DECL_FFT(64,32,16) DECL_FFT(128,64,32) DECL_FFT(256,128,64) DECL_FFT(512,256,128) #if !CONFIG_SMALL #define pass pass_big #endif DECL_FFT(1024,512,256) DECL_FFT(2048,1024,512) DECL_FFT(4096,2048,1024) DECL_FFT(8192,4096,2048) DECL_FFT(16384,8192,4096) DECL_FFT(32768,16384,8192) DECL_FFT(65536,32768,16384) static void (* const fft_dispatch[])(FFTComplex*) = { fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024, fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, }; static void ff_fft_calc_c(FFTContext *s, FFTComplex *z) { fft_dispatch[s->nbits-2](z); }