/*
* 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 "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<<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];
}
typedef struct CosTabsInitOnce {
void (*func)(void);
AVOnce control;
} CosTabsInitOnce;
#define INIT_FF_COS_TABS_FUNC(index, size) \
static av_cold void init_ff_cos_tabs_ ## size (void)\
{ \
init_ff_cos_tabs(index); \
}
INIT_FF_COS_TABS_FUNC(4, 16)
INIT_FF_COS_TABS_FUNC(5, 32)
INIT_FF_COS_TABS_FUNC(6, 64)
INIT_FF_COS_TABS_FUNC(7, 128)
INIT_FF_COS_TABS_FUNC(8, 256)
INIT_FF_COS_TABS_FUNC(9, 512)
INIT_FF_COS_TABS_FUNC(10, 1024)
INIT_FF_COS_TABS_FUNC(11, 2048)
INIT_FF_COS_TABS_FUNC(12, 4096)
INIT_FF_COS_TABS_FUNC(13, 8192)
INIT_FF_COS_TABS_FUNC(14, 16384)
INIT_FF_COS_TABS_FUNC(15, 32768)
INIT_FF_COS_TABS_FUNC(16, 65536)
INIT_FF_COS_TABS_FUNC(17, 131072)
static CosTabsInitOnce cos_tabs_init_once[] = {
{ NULL },
{ NULL },
{ NULL },
{ NULL },
{ init_ff_cos_tabs_16, AV_ONCE_INIT },
{ init_ff_cos_tabs_32, AV_ONCE_INIT },
{ init_ff_cos_tabs_64, AV_ONCE_INIT },
{ init_ff_cos_tabs_128, AV_ONCE_INIT },
{ init_ff_cos_tabs_256, AV_ONCE_INIT },
{ init_ff_cos_tabs_512, AV_ONCE_INIT },
{ init_ff_cos_tabs_1024, AV_ONCE_INIT },
{ init_ff_cos_tabs_2048, AV_ONCE_INIT },
{ init_ff_cos_tabs_4096, AV_ONCE_INIT },
{ init_ff_cos_tabs_8192, AV_ONCE_INIT },
{ init_ff_cos_tabs_16384, AV_ONCE_INIT },
{ init_ff_cos_tabs_32768, AV_ONCE_INIT },
{ init_ff_cos_tabs_65536, AV_ONCE_INIT },
{ init_ff_cos_tabs_131072, AV_ONCE_INIT },
};
#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),
FFT_NAME(ff_cos_131072),
};
#endif /* 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) && (!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 {
for(i=0; i<n; i++) {
int k;
j = i;
if (s->fft_permutation == FF_FFT_PERM_SWAP_LSBS)
j = (j&~3) | ((j>>1)&1) | ((j<<1)&2);
k = -split_radix_permutation(i, n, s->inverse) & (n-1);
if (s->revtab)
s->revtab[k] = j;
if (s->revtab32)
s->revtab32[k] = j;
}
}
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;j<np;j++) s->tmp_buf[revtab[j]] = z[j];
} else
for(j=0;j<np;j++) s->tmp_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<num_transforms; n++){
offset = ff_fft_offsets_lut[n] << 2;
tmpz = z + offset;
tmp1 = tmpz[0].re + (unsigned)tmpz[1].re;
tmp5 = tmpz[2].re + (unsigned)tmpz[3].re;
tmp2 = tmpz[0].im + (unsigned)tmpz[1].im;
tmp6 = tmpz[2].im + (unsigned)tmpz[3].im;
tmp3 = tmpz[0].re - (unsigned)tmpz[1].re;
tmp8 = tmpz[2].im - (unsigned)tmpz[3].im;
tmp4 = tmpz[0].im - (unsigned)tmpz[1].im;
tmp7 = tmpz[2].re - (unsigned)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 = ff_fft_offsets_lut[n] << 3;
tmpz = z + offset;
tmp1 = tmpz[4].re + (unsigned)tmpz[5].re;
tmp3 = tmpz[6].re + (unsigned)tmpz[7].re;
tmp2 = tmpz[4].im + (unsigned)tmpz[5].im;
tmp4 = tmpz[6].im + (unsigned)tmpz[7].im;
tmp5 = tmp1 + tmp3;
tmp7 = tmp1 - tmp3;
tmp6 = tmp2 + tmp4;
tmp8 = tmp2 - tmp4;
tmp1 = tmpz[4].re - (unsigned)tmpz[5].re;
tmp2 = tmpz[4].im - (unsigned)tmpz[5].im;
tmp3 = tmpz[6].re - (unsigned)tmpz[7].re;
tmp4 = tmpz[6].im - (unsigned)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)*(int)(tmp1 + tmp2);
tmp5 = (int32_t)((accu + 0x40000000) >> 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<num_transforms; n++){
const FFTSample *w_re_ptr = ff_w_tab_sr + step;
const FFTSample *w_im_ptr = ff_w_tab_sr + MAX_FFT_SIZE/(4*16) - step;
offset = ff_fft_offsets_lut[n] << nbits;
tmpz = z + offset;
tmp5 = tmpz[ n2].re + (unsigned)tmpz[n34].re;
tmp1 = tmpz[ n2].re - (unsigned)tmpz[n34].re;
tmp6 = tmpz[ n2].im + (unsigned)tmpz[n34].im;
tmp2 = tmpz[ n2].im - (unsigned)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;
for (i=1; i<n4; i++){
FFTSample w_re = w_re_ptr[0];
FFTSample 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 /* 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)
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 */