yading@10: /*
yading@10:  * FFT/IFFT transforms
yading@10:  * Copyright (c) 2008 Loren Merritt
yading@10:  * Copyright (c) 2002 Fabrice Bellard
yading@10:  * Partly based on libdjbfft by D. J. Bernstein
yading@10:  *
yading@10:  * This file is part of FFmpeg.
yading@10:  *
yading@10:  * FFmpeg is free software; you can redistribute it and/or
yading@10:  * modify it under the terms of the GNU Lesser General Public
yading@10:  * License as published by the Free Software Foundation; either
yading@10:  * version 2.1 of the License, or (at your option) any later version.
yading@10:  *
yading@10:  * FFmpeg is distributed in the hope that it will be useful,
yading@10:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
yading@10:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
yading@10:  * Lesser General Public License for more details.
yading@10:  *
yading@10:  * You should have received a copy of the GNU Lesser General Public
yading@10:  * License along with FFmpeg; if not, write to the Free Software
yading@10:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
yading@10:  */
yading@10: 
yading@10: /**
yading@10:  * @file
yading@10:  * FFT/IFFT transforms.
yading@10:  */
yading@10: 
yading@10: #include <stdlib.h>
yading@10: #include <string.h>
yading@10: #include "libavutil/mathematics.h"
yading@10: #include "fft.h"
yading@10: #include "fft-internal.h"
yading@10: 
yading@10: /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
yading@10: #if !CONFIG_HARDCODED_TABLES
yading@10: COSTABLE(16);
yading@10: COSTABLE(32);
yading@10: COSTABLE(64);
yading@10: COSTABLE(128);
yading@10: COSTABLE(256);
yading@10: COSTABLE(512);
yading@10: COSTABLE(1024);
yading@10: COSTABLE(2048);
yading@10: COSTABLE(4096);
yading@10: COSTABLE(8192);
yading@10: COSTABLE(16384);
yading@10: COSTABLE(32768);
yading@10: COSTABLE(65536);
yading@10: #endif
yading@10: COSTABLE_CONST FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
yading@10:     NULL, NULL, NULL, NULL,
yading@10:     FFT_NAME(ff_cos_16),
yading@10:     FFT_NAME(ff_cos_32),
yading@10:     FFT_NAME(ff_cos_64),
yading@10:     FFT_NAME(ff_cos_128),
yading@10:     FFT_NAME(ff_cos_256),
yading@10:     FFT_NAME(ff_cos_512),
yading@10:     FFT_NAME(ff_cos_1024),
yading@10:     FFT_NAME(ff_cos_2048),
yading@10:     FFT_NAME(ff_cos_4096),
yading@10:     FFT_NAME(ff_cos_8192),
yading@10:     FFT_NAME(ff_cos_16384),
yading@10:     FFT_NAME(ff_cos_32768),
yading@10:     FFT_NAME(ff_cos_65536),
yading@10: };
yading@10: 
yading@10: static void ff_fft_permute_c(FFTContext *s, FFTComplex *z);
yading@10: static void ff_fft_calc_c(FFTContext *s, FFTComplex *z);
yading@10: 
yading@10: static int split_radix_permutation(int i, int n, int inverse)
yading@10: {
yading@10:     int m;
yading@10:     if(n <= 2) return i&1;
yading@10:     m = n >> 1;
yading@10:     if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
yading@10:     m >>= 1;
yading@10:     if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
yading@10:     else                  return split_radix_permutation(i, m, inverse)*4 - 1;
yading@10: }
yading@10: 
yading@10: av_cold void ff_init_ff_cos_tabs(int index)
yading@10: {
yading@10: #if !CONFIG_HARDCODED_TABLES
yading@10:     int i;
yading@10:     int m = 1<<index;
yading@10:     double freq = 2*M_PI/m;
yading@10:     FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
yading@10:     for(i=0; i<=m/4; i++)
yading@10:         tab[i] = FIX15(cos(i*freq));
yading@10:     for(i=1; i<m/4; i++)
yading@10:         tab[m/2-i] = tab[i];
yading@10: #endif
yading@10: }
yading@10: 
yading@10: static const int avx_tab[] = {
yading@10:     0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15
yading@10: };
yading@10: 
yading@10: static int is_second_half_of_fft32(int i, int n)
yading@10: {
yading@10:     if (n <= 32)
yading@10:         return i >= 16;
yading@10:     else if (i < n/2)
yading@10:         return is_second_half_of_fft32(i, n/2);
yading@10:     else if (i < 3*n/4)
yading@10:         return is_second_half_of_fft32(i - n/2, n/4);
yading@10:     else
yading@10:         return is_second_half_of_fft32(i - 3*n/4, n/4);
yading@10: }
yading@10: 
yading@10: static av_cold void fft_perm_avx(FFTContext *s)
yading@10: {
yading@10:     int i;
yading@10:     int n = 1 << s->nbits;
yading@10: 
yading@10:     for (i = 0; i < n; i += 16) {
yading@10:         int k;
yading@10:         if (is_second_half_of_fft32(i, n)) {
yading@10:             for (k = 0; k < 16; k++)
yading@10:                 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] =
yading@10:                     i + avx_tab[k];
yading@10: 
yading@10:         } else {
yading@10:             for (k = 0; k < 16; k++) {
yading@10:                 int j = i + k;
yading@10:                 j = (j & ~7) | ((j >> 1) & 3) | ((j << 2) & 4);
yading@10:                 s->revtab[-split_radix_permutation(i + k, n, s->inverse) & (n - 1)] = j;
yading@10:             }
yading@10:         }
yading@10:     }
yading@10: }
yading@10: 
yading@10: av_cold int ff_fft_init(FFTContext *s, int nbits, int inverse)
yading@10: {
yading@10:     int i, j, n;
yading@10: 
yading@10:     if (nbits < 2 || nbits > 16)
yading@10:         goto fail;
yading@10:     s->nbits = nbits;
yading@10:     n = 1 << nbits;
yading@10: 
yading@10:     s->revtab = av_malloc(n * sizeof(uint16_t));
yading@10:     if (!s->revtab)
yading@10:         goto fail;
yading@10:     s->tmp_buf = av_malloc(n * sizeof(FFTComplex));
yading@10:     if (!s->tmp_buf)
yading@10:         goto fail;
yading@10:     s->inverse = inverse;
yading@10:     s->fft_permutation = FF_FFT_PERM_DEFAULT;
yading@10: 
yading@10:     s->fft_permute = ff_fft_permute_c;
yading@10:     s->fft_calc    = ff_fft_calc_c;
yading@10: #if CONFIG_MDCT
yading@10:     s->imdct_calc  = ff_imdct_calc_c;
yading@10:     s->imdct_half  = ff_imdct_half_c;
yading@10:     s->mdct_calc   = ff_mdct_calc_c;
yading@10: #endif
yading@10: 
yading@10: #if CONFIG_FFT_FLOAT
yading@10:     if (ARCH_ARM)     ff_fft_init_arm(s);
yading@10:     if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
yading@10:     if (ARCH_X86)     ff_fft_init_x86(s);
yading@10:     if (CONFIG_MDCT)  s->mdct_calcw = s->mdct_calc;
yading@10:     if (HAVE_MIPSFPU) ff_fft_init_mips(s);
yading@10: #else
yading@10:     if (CONFIG_MDCT)  s->mdct_calcw = ff_mdct_calcw_c;
yading@10:     if (ARCH_ARM)     ff_fft_fixed_init_arm(s);
yading@10: #endif
yading@10: 
yading@10:     for(j=4; j<=nbits; j++) {
yading@10:         ff_init_ff_cos_tabs(j);
yading@10:     }
yading@10: 
yading@10:     if (s->fft_permutation == FF_FFT_PERM_AVX) {
yading@10:         fft_perm_avx(s);
yading@10:     } else {
yading@10:         for(i=0; i<n; i++) {
yading@10:             int j = i;
yading@10:             if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
yading@10:                 j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
yading@10:             s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = j;
yading@10:         }
yading@10:     }
yading@10: 
yading@10:     return 0;
yading@10:  fail:
yading@10:     av_freep(&s->revtab);
yading@10:     av_freep(&s->tmp_buf);
yading@10:     return -1;
yading@10: }
yading@10: 
yading@10: static void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
yading@10: {
yading@10:     int j, np;
yading@10:     const uint16_t *revtab = s->revtab;
yading@10:     np = 1 << s->nbits;
yading@10:     /* TODO: handle split-radix permute in a more optimal way, probably in-place */
yading@10:     for(j=0;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
yading@10:     memcpy(z, s->tmp_buf, np * sizeof(FFTComplex));
yading@10: }
yading@10: 
yading@10: av_cold void ff_fft_end(FFTContext *s)
yading@10: {
yading@10:     av_freep(&s->revtab);
yading@10:     av_freep(&s->tmp_buf);
yading@10: }
yading@10: 
yading@10: #define BUTTERFLIES(a0,a1,a2,a3) {\
yading@10:     BF(t3, t5, t5, t1);\
yading@10:     BF(a2.re, a0.re, a0.re, t5);\
yading@10:     BF(a3.im, a1.im, a1.im, t3);\
yading@10:     BF(t4, t6, t2, t6);\
yading@10:     BF(a3.re, a1.re, a1.re, t4);\
yading@10:     BF(a2.im, a0.im, a0.im, t6);\
yading@10: }
yading@10: 
yading@10: // force loading all the inputs before storing any.
yading@10: // this is slightly slower for small data, but avoids store->load aliasing
yading@10: // for addresses separated by large powers of 2.
yading@10: #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
yading@10:     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
yading@10:     BF(t3, t5, t5, t1);\
yading@10:     BF(a2.re, a0.re, r0, t5);\
yading@10:     BF(a3.im, a1.im, i1, t3);\
yading@10:     BF(t4, t6, t2, t6);\
yading@10:     BF(a3.re, a1.re, r1, t4);\
yading@10:     BF(a2.im, a0.im, i0, t6);\
yading@10: }
yading@10: 
yading@10: #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
yading@10:     CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
yading@10:     CMUL(t5, t6, a3.re, a3.im, wre,  wim);\
yading@10:     BUTTERFLIES(a0,a1,a2,a3)\
yading@10: }
yading@10: 
yading@10: #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
yading@10:     t1 = a2.re;\
yading@10:     t2 = a2.im;\
yading@10:     t5 = a3.re;\
yading@10:     t6 = a3.im;\
yading@10:     BUTTERFLIES(a0,a1,a2,a3)\
yading@10: }
yading@10: 
yading@10: /* z[0...8n-1], w[1...2n-1] */
yading@10: #define PASS(name)\
yading@10: static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
yading@10: {\
yading@10:     FFTDouble t1, t2, t3, t4, t5, t6;\
yading@10:     int o1 = 2*n;\
yading@10:     int o2 = 4*n;\
yading@10:     int o3 = 6*n;\
yading@10:     const FFTSample *wim = wre+o1;\
yading@10:     n--;\
yading@10: \
yading@10:     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
yading@10:     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
yading@10:     do {\
yading@10:         z += 2;\
yading@10:         wre += 2;\
yading@10:         wim -= 2;\
yading@10:         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
yading@10:         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
yading@10:     } while(--n);\
yading@10: }
yading@10: 
yading@10: PASS(pass)
yading@10: #undef BUTTERFLIES
yading@10: #define BUTTERFLIES BUTTERFLIES_BIG
yading@10: PASS(pass_big)
yading@10: 
yading@10: #define DECL_FFT(n,n2,n4)\
yading@10: static void fft##n(FFTComplex *z)\
yading@10: {\
yading@10:     fft##n2(z);\
yading@10:     fft##n4(z+n4*2);\
yading@10:     fft##n4(z+n4*3);\
yading@10:     pass(z,FFT_NAME(ff_cos_##n),n4/2);\
yading@10: }
yading@10: 
yading@10: static void fft4(FFTComplex *z)
yading@10: {
yading@10:     FFTDouble t1, t2, t3, t4, t5, t6, t7, t8;
yading@10: 
yading@10:     BF(t3, t1, z[0].re, z[1].re);
yading@10:     BF(t8, t6, z[3].re, z[2].re);
yading@10:     BF(z[2].re, z[0].re, t1, t6);
yading@10:     BF(t4, t2, z[0].im, z[1].im);
yading@10:     BF(t7, t5, z[2].im, z[3].im);
yading@10:     BF(z[3].im, z[1].im, t4, t8);
yading@10:     BF(z[3].re, z[1].re, t3, t7);
yading@10:     BF(z[2].im, z[0].im, t2, t5);
yading@10: }
yading@10: 
yading@10: static void fft8(FFTComplex *z)
yading@10: {
yading@10:     FFTDouble t1, t2, t3, t4, t5, t6;
yading@10: 
yading@10:     fft4(z);
yading@10: 
yading@10:     BF(t1, z[5].re, z[4].re, -z[5].re);
yading@10:     BF(t2, z[5].im, z[4].im, -z[5].im);
yading@10:     BF(t5, z[7].re, z[6].re, -z[7].re);
yading@10:     BF(t6, z[7].im, z[6].im, -z[7].im);
yading@10: 
yading@10:     BUTTERFLIES(z[0],z[2],z[4],z[6]);
yading@10:     TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
yading@10: }
yading@10: 
yading@10: #if !CONFIG_SMALL
yading@10: static void fft16(FFTComplex *z)
yading@10: {
yading@10:     FFTDouble t1, t2, t3, t4, t5, t6;
yading@10:     FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
yading@10:     FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
yading@10: 
yading@10:     fft8(z);
yading@10:     fft4(z+8);
yading@10:     fft4(z+12);
yading@10: 
yading@10:     TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
yading@10:     TRANSFORM(z[2],z[6],z[10],z[14],sqrthalf,sqrthalf);
yading@10:     TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
yading@10:     TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
yading@10: }
yading@10: #else
yading@10: DECL_FFT(16,8,4)
yading@10: #endif
yading@10: DECL_FFT(32,16,8)
yading@10: DECL_FFT(64,32,16)
yading@10: DECL_FFT(128,64,32)
yading@10: DECL_FFT(256,128,64)
yading@10: DECL_FFT(512,256,128)
yading@10: #if !CONFIG_SMALL
yading@10: #define pass pass_big
yading@10: #endif
yading@10: DECL_FFT(1024,512,256)
yading@10: DECL_FFT(2048,1024,512)
yading@10: DECL_FFT(4096,2048,1024)
yading@10: DECL_FFT(8192,4096,2048)
yading@10: DECL_FFT(16384,8192,4096)
yading@10: DECL_FFT(32768,16384,8192)
yading@10: DECL_FFT(65536,32768,16384)
yading@10: 
yading@10: static void (* const fft_dispatch[])(FFTComplex*) = {
yading@10:     fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
yading@10:     fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
yading@10: };
yading@10: 
yading@10: static void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
yading@10: {
yading@10:     fft_dispatch[s->nbits-2](z);
yading@10: }