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/*
* (I)RDFT transforms
* Copyright (c) 2009 Alex Converse <alex dot converse at gmail dot com>
*
* This file is part of Libav.
*
* Libav 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.
*
* Libav 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 Libav; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include <stdlib.h>
#include <math.h>
#include "libavutil/mathematics.h"
#include "rdft.h"
/**
* @file
* (Inverse) Real Discrete Fourier Transforms.
*/
/* sin(2*pi*x/n) for 0<=x<n/4, followed by n/2<=x<3n/4 */
#if !CONFIG_HARDCODED_TABLES
SINTABLE(16);
SINTABLE(32);
SINTABLE(64);
SINTABLE(128);
SINTABLE(256);
SINTABLE(512);
SINTABLE(1024);
SINTABLE(2048);
SINTABLE(4096);
SINTABLE(8192);
SINTABLE(16384);
SINTABLE(32768);
SINTABLE(65536);
#endif
static SINTABLE_CONST FFTSample * const ff_sin_tabs[] = {
NULL, NULL, NULL, NULL,
ff_sin_16, ff_sin_32, ff_sin_64, ff_sin_128, ff_sin_256, ff_sin_512, ff_sin_1024,
ff_sin_2048, ff_sin_4096, ff_sin_8192, ff_sin_16384, ff_sin_32768, ff_sin_65536,
};
/** Map one real FFT into two parallel real even and odd FFTs. Then interleave
* the two real FFTs into one complex FFT. Unmangle the results.
* ref: http://www.engineeringproductivitytools.com/stuff/T0001/PT10.HTM
*/
static void ff_rdft_calc_c(RDFTContext* s, FFTSample* data)
{
int i, i1, i2;
FFTComplex ev, od;
const int n = 1 << s->nbits;
const float k1 = 0.5;
const float k2 = 0.5 - s->inverse;
const FFTSample *tcos = s->tcos;
const FFTSample *tsin = s->tsin;
if (!s->inverse) {
s->fft.fft_permute(&s->fft, (FFTComplex*)data);
s->fft.fft_calc(&s->fft, (FFTComplex*)data);
}
/* i=0 is a special case because of packing, the DC term is real, so we
are going to throw the N/2 term (also real) in with it. */
ev.re = data[0];
data[0] = ev.re+data[1];
data[1] = ev.re-data[1];
for (i = 1; i < (n>>2); i++) {
i1 = 2*i;
i2 = n-i1;
/* Separate even and odd FFTs */
ev.re = k1*(data[i1 ]+data[i2 ]);
od.im = -k2*(data[i1 ]-data[i2 ]);
ev.im = k1*(data[i1+1]-data[i2+1]);
od.re = k2*(data[i1+1]+data[i2+1]);
/* Apply twiddle factors to the odd FFT and add to the even FFT */
data[i1 ] = ev.re + od.re*tcos[i] - od.im*tsin[i];
data[i1+1] = ev.im + od.im*tcos[i] + od.re*tsin[i];
data[i2 ] = ev.re - od.re*tcos[i] + od.im*tsin[i];
data[i2+1] = -ev.im + od.im*tcos[i] + od.re*tsin[i];
}
data[2*i+1]=s->sign_convention*data[2*i+1];
if (s->inverse) {
data[0] *= k1;
data[1] *= k1;
s->fft.fft_permute(&s->fft, (FFTComplex*)data);
s->fft.fft_calc(&s->fft, (FFTComplex*)data);
}
}
av_cold int ff_rdft_init(RDFTContext *s, int nbits, enum RDFTransformType trans)
{
int n = 1 << nbits;
int i;
const double theta = (trans == DFT_R2C || trans == DFT_C2R ? -1 : 1)*2*M_PI/n;
s->nbits = nbits;
s->inverse = trans == IDFT_C2R || trans == DFT_C2R;
s->sign_convention = trans == IDFT_R2C || trans == DFT_C2R ? 1 : -1;
if (nbits < 4 || nbits > 16)
return -1;
if (ff_fft_init(&s->fft, nbits-1, trans == IDFT_C2R || trans == IDFT_R2C) < 0)
return -1;
ff_init_ff_cos_tabs(nbits);
s->tcos = ff_cos_tabs[nbits];
s->tsin = ff_sin_tabs[nbits]+(trans == DFT_R2C || trans == DFT_C2R)*(n>>2);
#if !CONFIG_HARDCODED_TABLES
for (i = 0; i < (n>>2); i++) {
s->tsin[i] = sin(i*theta);
}
#endif
s->rdft_calc = ff_rdft_calc_c;
if (ARCH_ARM) ff_rdft_init_arm(s);
return 0;
}
av_cold void ff_rdft_end(RDFTContext *s)
{
ff_fft_end(&s->fft);
}