0,0 → 1,530 |
/* |
* 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 <stdlib.h> |
#include <string.h> |
#include "libavutil/mathematics.h" |
#include "fft.h" |
#include "fft-internal.h" |
|
#if CONFIG_FFT_FIXED_32 |
#include "fft_table.h" |
#else /* CONFIG_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); |
#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), |
}; |
|
#endif /* CONFIG_FFT_FIXED_32 */ |
|
static void fft_permute_c(FFTContext *s, FFTComplex *z); |
static void 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) && (!CONFIG_FFT_FIXED_32) |
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 = 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 CONFIG_FFT_FIXED_32 |
{ |
int n=0; |
ff_fft_lut_init(fft_offsets_lut, 0, 1 << 16, &n); |
} |
#else /* CONFIG_FFT_FIXED_32 */ |
#if CONFIG_FFT_FLOAT |
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 /* CONFIG_FFT_FIXED_32 */ |
|
|
if (s->fft_permutation == FF_FFT_PERM_AVX) { |
fft_perm_avx(s); |
} else { |
for(i=0; i<n; i++) { |
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 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); |
} |
|
#if CONFIG_FFT_FIXED_32 |
|
static void fft_calc_c(FFTContext *s, FFTComplex *z) { |
|
int nbits, i, n, num_transforms, offset, step; |
int n4, n2, n34; |
FFTSample tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8; |
FFTComplex *tmpz; |
FFTSample w_re, w_im; |
FFTSample *w_re_ptr, *w_im_ptr; |
const int fft_size = (1 << s->nbits); |
int64_t accu; |
|
num_transforms = (0x2aab >> (16 - s->nbits)) | 1; |
|
for (n=0; n<num_transforms; n++){ |
offset = fft_offsets_lut[n] << 2; |
tmpz = z + offset; |
|
tmp1 = tmpz[0].re + tmpz[1].re; |
tmp5 = tmpz[2].re + tmpz[3].re; |
tmp2 = tmpz[0].im + tmpz[1].im; |
tmp6 = tmpz[2].im + tmpz[3].im; |
tmp3 = tmpz[0].re - tmpz[1].re; |
tmp8 = tmpz[2].im - tmpz[3].im; |
tmp4 = tmpz[0].im - tmpz[1].im; |
tmp7 = tmpz[2].re - tmpz[3].re; |
|
tmpz[0].re = tmp1 + tmp5; |
tmpz[2].re = tmp1 - tmp5; |
tmpz[0].im = tmp2 + tmp6; |
tmpz[2].im = tmp2 - tmp6; |
tmpz[1].re = tmp3 + tmp8; |
tmpz[3].re = tmp3 - tmp8; |
tmpz[1].im = tmp4 - tmp7; |
tmpz[3].im = tmp4 + tmp7; |
} |
|
if (fft_size < 8) |
return; |
|
num_transforms = (num_transforms >> 1) | 1; |
|
for (n=0; n<num_transforms; n++){ |
offset = fft_offsets_lut[n] << 3; |
tmpz = z + offset; |
|
tmp1 = tmpz[4].re + tmpz[5].re; |
tmp3 = tmpz[6].re + tmpz[7].re; |
tmp2 = tmpz[4].im + tmpz[5].im; |
tmp4 = tmpz[6].im + tmpz[7].im; |
tmp5 = tmp1 + tmp3; |
tmp7 = tmp1 - tmp3; |
tmp6 = tmp2 + tmp4; |
tmp8 = tmp2 - tmp4; |
|
tmp1 = tmpz[4].re - tmpz[5].re; |
tmp2 = tmpz[4].im - tmpz[5].im; |
tmp3 = tmpz[6].re - tmpz[7].re; |
tmp4 = tmpz[6].im - tmpz[7].im; |
|
tmpz[4].re = tmpz[0].re - tmp5; |
tmpz[0].re = tmpz[0].re + tmp5; |
tmpz[4].im = tmpz[0].im - tmp6; |
tmpz[0].im = tmpz[0].im + tmp6; |
tmpz[6].re = tmpz[2].re - tmp8; |
tmpz[2].re = tmpz[2].re + tmp8; |
tmpz[6].im = tmpz[2].im + tmp7; |
tmpz[2].im = tmpz[2].im - tmp7; |
|
accu = (int64_t)Q31(M_SQRT1_2)*(tmp1 + tmp2); |
tmp5 = (int32_t)((accu + 0x40000000) >> 31); |
accu = (int64_t)Q31(M_SQRT1_2)*(tmp3 - tmp4); |
tmp7 = (int32_t)((accu + 0x40000000) >> 31); |
accu = (int64_t)Q31(M_SQRT1_2)*(tmp2 - tmp1); |
tmp6 = (int32_t)((accu + 0x40000000) >> 31); |
accu = (int64_t)Q31(M_SQRT1_2)*(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<num_transforms; n++){ |
offset = fft_offsets_lut[n] << nbits; |
tmpz = z + offset; |
|
tmp5 = tmpz[ n2].re + tmpz[n34].re; |
tmp1 = tmpz[ n2].re - tmpz[n34].re; |
tmp6 = tmpz[ n2].im + tmpz[n34].im; |
tmp2 = tmpz[ n2].im - tmpz[n34].im; |
|
tmpz[ n2].re = tmpz[ 0].re - tmp5; |
tmpz[ 0].re = tmpz[ 0].re + tmp5; |
tmpz[ n2].im = tmpz[ 0].im - tmp6; |
tmpz[ 0].im = tmpz[ 0].im + tmp6; |
tmpz[n34].re = tmpz[n4].re - tmp2; |
tmpz[ n4].re = tmpz[n4].re + tmp2; |
tmpz[n34].im = tmpz[n4].im + tmp1; |
tmpz[ n4].im = tmpz[n4].im - tmp1; |
|
w_re_ptr = w_tab_sr + step; |
w_im_ptr = w_tab_sr + MAX_FFT_SIZE/(4*16) - step; |
|
for (i=1; i<n4; i++){ |
w_re = w_re_ptr[0]; |
w_im = w_im_ptr[0]; |
accu = (int64_t)w_re*tmpz[ n2+i].re; |
accu += (int64_t)w_im*tmpz[ n2+i].im; |
tmp1 = (int32_t)((accu + 0x40000000) >> 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 /* CONFIG_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) |
#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 fft_calc_c(FFTContext *s, FFTComplex *z) |
{ |
fft_dispatch[s->nbits-2](z); |
} |
#endif /* CONFIG_FFT_FIXED_32 */ |