/* * 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 FFmpeg. * * FFmpeg 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. * * FFmpeg 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 FFmpeg; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ /** * @file * FFT/IFFT transforms. */ #include #include #include "libavutil/mathematics.h" #include "libavutil/thread.h" #include "fft.h" #include "fft-internal.h" #if FFT_FIXED_32 #include "fft_table.h" static void av_cold fft_lut_init(void) { int n = 0; ff_fft_lut_init(ff_fft_offsets_lut, 0, 1 << 17, &n); } #else /* FFT_FIXED_32 */ /* 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); COSTABLE(131072); static av_cold void init_ff_cos_tabs(int index) { int i; int m = 1<> 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) && (!FFT_FIXED_32) ff_thread_once(&cos_tabs_init_once[index].control, cos_tabs_init_once[index].func); #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; s->revtab = NULL; s->revtab32 = NULL; if (nbits < 2 || nbits > 17) goto fail; s->nbits = nbits; n = 1 << nbits; if (nbits <= 16) { s->revtab = av_malloc(n * sizeof(uint16_t)); if (!s->revtab) goto fail; } else { s->revtab32 = av_malloc(n * sizeof(uint32_t)); if (!s->revtab32) 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 = fft_permute_c; s->fft_calc = 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 FFT_FIXED_32 { static AVOnce control = AV_ONCE_INIT; ff_thread_once(&control, fft_lut_init); } #else /* FFT_FIXED_32 */ #if FFT_FLOAT if (ARCH_AARCH64) ff_fft_init_aarch64(s); if (ARCH_ARM) ff_fft_init_arm(s); if (ARCH_PPC) ff_fft_init_ppc(s); if (ARCH_X86) ff_fft_init_x86(s); if (CONFIG_MDCT) s->mdct_calcw = s->mdct_calc; if (HAVE_MIPSFPU) ff_fft_init_mips(s); #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); } #endif /* FFT_FIXED_32 */ if (s->fft_permutation == FF_FFT_PERM_AVX) { fft_perm_avx(s); } else { #define PROCESS_FFT_PERM_SWAP_LSBS(num) do {\ for(i = 0; i < n; i++) {\ int k;\ j = i;\ j = (j & ~3) | ((j >> 1) & 1) | ((j << 1) & 2);\ k = -split_radix_permutation(i, n, s->inverse) & (n - 1);\ s->revtab##num[k] = j;\ } \ } while(0); #define PROCESS_FFT_PERM_DEFAULT(num) do {\ for(i = 0; i < n; i++) {\ int k;\ j = i;\ k = -split_radix_permutation(i, n, s->inverse) & (n - 1);\ s->revtab##num[k] = j;\ } \ } while(0); #define SPLIT_RADIX_PERMUTATION(num) do { \ if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS) {\ PROCESS_FFT_PERM_SWAP_LSBS(num) \ } else {\ PROCESS_FFT_PERM_DEFAULT(num) \ }\ } while(0); if (s->revtab) SPLIT_RADIX_PERMUTATION() if (s->revtab32) SPLIT_RADIX_PERMUTATION(32) #undef PROCESS_FFT_PERM_DEFAULT #undef PROCESS_FFT_PERM_SWAP_LSBS #undef SPLIT_RADIX_PERMUTATION } return 0; fail: av_freep(&s->revtab); av_freep(&s->revtab32); av_freep(&s->tmp_buf); return -1; } static void fft_permute_c(FFTContext *s, FFTComplex *z) { int j, np; const uint16_t *revtab = s->revtab; const uint32_t *revtab32 = s->revtab32; np = 1 << s->nbits; /* TODO: handle split-radix permute in a more optimal way, probably in-place */ if (revtab) { for(j=0;jtmp_buf[revtab[j]] = z[j]; } else for(j=0;jtmp_buf[revtab32[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->revtab32); av_freep(&s->tmp_buf); } #if FFT_FIXED_32 static void fft_calc_c(FFTContext *s, FFTComplex *z) { int nbits, i, n, num_transforms, offset, step; int n4, n2, n34; unsigned tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8; FFTComplex *tmpz; const int fft_size = (1 << s->nbits); int64_t accu; num_transforms = (0x2aab >> (16 - s->nbits)) | 1; for (n=0; n> 1) | 1; for (n=0; n> 31); accu = (int64_t)Q31(M_SQRT1_2)*(int)(tmp3 - tmp4); tmp7 = (int32_t)((accu + 0x40000000) >> 31); accu = (int64_t)Q31(M_SQRT1_2)*(int)(tmp2 - tmp1); tmp6 = (int32_t)((accu + 0x40000000) >> 31); accu = (int64_t)Q31(M_SQRT1_2)*(int)(tmp3 + tmp4); tmp8 = (int32_t)((accu + 0x40000000) >> 31); tmp1 = tmp5 + tmp7; tmp3 = tmp5 - tmp7; tmp2 = tmp6 + tmp8; tmp4 = tmp6 - tmp8; tmpz[5].re = tmpz[1].re - tmp1; tmpz[1].re = tmpz[1].re + tmp1; tmpz[5].im = tmpz[1].im - tmp2; tmpz[1].im = tmpz[1].im + tmp2; tmpz[7].re = tmpz[3].re - tmp4; tmpz[3].re = tmpz[3].re + tmp4; tmpz[7].im = tmpz[3].im + tmp3; tmpz[3].im = tmpz[3].im - tmp3; } step = 1 << ((MAX_LOG2_NFFT-4) - 4); n4 = 4; for (nbits=4; nbits<=s->nbits; nbits++){ n2 = 2*n4; n34 = 3*n4; num_transforms = (num_transforms >> 1) | 1; for (n=0; n> 31); accu = (int64_t)w_re*tmpz[ n2+i].im; accu -= (int64_t)w_im*tmpz[ n2+i].re; tmp2 = (int32_t)((accu + 0x40000000) >> 31); accu = (int64_t)w_re*tmpz[n34+i].re; accu -= (int64_t)w_im*tmpz[n34+i].im; tmp3 = (int32_t)((accu + 0x40000000) >> 31); accu = (int64_t)w_re*tmpz[n34+i].im; accu += (int64_t)w_im*tmpz[n34+i].re; tmp4 = (int32_t)((accu + 0x40000000) >> 31); tmp5 = tmp1 + tmp3; tmp1 = tmp1 - tmp3; tmp6 = tmp2 + tmp4; tmp2 = tmp2 - tmp4; tmpz[ n2+i].re = tmpz[ i].re - tmp5; tmpz[ i].re = tmpz[ i].re + tmp5; tmpz[ n2+i].im = tmpz[ i].im - tmp6; tmpz[ i].im = tmpz[ i].im + tmp6; tmpz[n34+i].re = tmpz[n4+i].re - tmp2; tmpz[ n4+i].re = tmpz[n4+i].re + tmp2; tmpz[n34+i].im = tmpz[n4+i].im + tmp1; tmpz[ n4+i].im = tmpz[n4+i].im - tmp1; w_re_ptr += step; w_im_ptr -= step; } } step >>= 1; n4 <<= 1; } } #else /* FFT_FIXED_32 */ #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) #if !CONFIG_SMALL #undef BUTTERFLIES #define BUTTERFLIES BUTTERFLIES_BIG PASS(pass_big) #endif #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) DECL_FFT(131072,65536,32768) static void (* const fft_dispatch[])(FFTComplex*) = { fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024, fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, fft131072 }; static void fft_calc_c(FFTContext *s, FFTComplex *z) { fft_dispatch[s->nbits-2](z); } #endif /* FFT_FIXED_32 */