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/*
* 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"
/* 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 ff_cos_tabs[] = {
NULL, NULL, NULL, NULL,
ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256, ff_cos_512, ff_cos_1024,
ff_cos_2048, ff_cos_4096, ff_cos_8192, ff_cos_16384, ff_cos_32768, ff_cos_65536,
};
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 = ff_cos_tabs[index];
for(i=0; i<=m/4; i++)
tab[i] = cos(i*freq);
for(i=1; i<m/4; i++)
tab[m/2-i] = tab[i];
#endif
}
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_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 (ARCH_ARM) ff_fft_init_arm(s);
if (HAVE_ALTIVEC) ff_fft_init_altivec(s);
if (HAVE_MMX) ff_fft_init_mmx(s);
for(j=4; j<=nbits; j++) {
ff_init_ff_cos_tabs(j);
}
for(i=0; i<n; i++)
s->revtab[-split_radix_permutation(i, n, s->inverse) & (n-1)] = i;
return 0;
fail:
av_freep(&s->revtab);
av_freep(&s->tmp_buf);
return -1;
}
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 sqrthalf (float)M_SQRT1_2
#define BF(x,y,a,b) {\
x = a - b;\
y = a + b;\
}
#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) {\
t1 = a2.re * wre + a2.im * wim;\
t2 = a2.im * wre - a2.re * wim;\
t5 = a3.re * wre - a3.im * wim;\
t6 = a3.im * wre + a3.re * 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)\
{\
FFTSample 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,ff_cos_##n,n4/2);\
}
static void fft4(FFTComplex *z)
{
FFTSample 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)
{
FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
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(t3, z[7].re, z[6].re, -z[7].re);
BF(t4, z[7].im, z[6].im, -z[7].im);
BF(t8, t1, t3, t1);
BF(t7, t2, t2, t4);
BF(z[4].re, z[0].re, z[0].re, t1);
BF(z[4].im, z[0].im, z[0].im, t2);
BF(z[6].re, z[2].re, z[2].re, t7);
BF(z[6].im, z[2].im, z[2].im, t8);
TRANSFORM(z[1],z[3],z[5],z[7],sqrthalf,sqrthalf);
}
#if !CONFIG_SMALL
static void fft16(FFTComplex *z)
{
FFTSample t1, t2, t3, t4, t5, t6;
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],ff_cos_16[1],ff_cos_16[3]);
TRANSFORM(z[3],z[7],z[11],z[15],ff_cos_16[3],ff_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,
};
void ff_fft_calc_c(FFTContext *s, FFTComplex *z)
{
fft_dispatch[s->nbits-2](z);
}
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