ref: 89c5fd161bcf529e5e51add61c908d4cc4135b3b
dir: /libcelt/mdct.c/
/* (C) 2008 Jean-Marc Valin, CSIRO
*/
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*/
/* This is a simple MDCT implementation that uses a N/4 complex FFT
to do most of the work. It should be relatively straightforward to
plug in pretty much and FFT here.
This replaces the Vorbis FFT (and uses the exact same API), which
was a bit too messy and that was ending up duplicating code
(might as well use the same FFT everywhere).
The algorithm is similar to (and inspired from) Fabrice Bellard's
MDCT implementation in FFMPEG, but has differences in signs, ordering
and scaling in many places.
*/
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "mdct.h"
#include "kfft_double.h"
#include <math.h>
#include "os_support.h"
#include "mathops.h"
#include "stack_alloc.h"
#ifndef M_PI
#define M_PI 3.141592653
#endif
void mdct_init(mdct_lookup *l,int N)
{
int i;
int N2;
l->n = N;
N2 = N>>1;
l->kfft = cpx32_fft_alloc(N>>2);
l->trig = (kiss_twiddle_scalar*)celt_alloc(N2*sizeof(kiss_twiddle_scalar));
/* We have enough points that sine isn't necessary */
#if defined(FIXED_POINT)
#if defined(DOUBLE_PRECISION) & !defined(MIXED_PRECISION)
for (i=0;i<N2;i++)
l->trig[i] = SAMP_MAX*cos(2*M_PI*(i+1./8.)/N);
#else
for (i=0;i<N2;i++)
l->trig[i] = TRIG_UPSCALE*celt_cos_norm(DIV32(ADD32(SHL32(EXTEND32(i),17),16386),N));
#endif
#else
for (i=0;i<N2;i++)
l->trig[i] = cos(2*M_PI*(i+1./8.)/N);
#endif
}
void mdct_clear(mdct_lookup *l)
{
cpx32_fft_free(l->kfft);
celt_free(l->trig);
}
void mdct_forward(const mdct_lookup *l, kiss_fft_scalar *in, kiss_fft_scalar * restrict out)
{
int i;
int N, N2, N4;
VARDECL(kiss_fft_scalar, f);
SAVE_STACK;
N = l->n;
N2 = N>>1;
N4 = N>>2;
ALLOC(f, N2, kiss_fft_scalar);
/* Consider the input to be compused of four blocks: [a, b, c, d] */
/* Shuffle, fold, pre-rotate (part 1) */
for(i=0;i<N/8;i++)
{
kiss_fft_scalar re, im;
/* Real part arranged as -d-cR, Imag part arranged as -b+aR*/
re = -HALF32(in[N2+N4+2*i] + in[N2+N4-2*i-1]);
im = -HALF32(in[N4+2*i] - in[N4-2*i-1]);
/* We could remove the HALF32 above and just use MULT16_32_Q16 below
(MIXED_PRECISION only) */
out[2*i] = S_MUL(re,l->trig[i]) - S_MUL(im,l->trig[i+N4]);
out[2*i+1] = S_MUL(im,l->trig[i]) + S_MUL(re,l->trig[i+N4]);
}
for(;i<N4;i++)
{
kiss_fft_scalar re, im;
/* Real part arranged as a-bR, Imag part arranged as -c-dR */
re = HALF32(in[2*i-N4] - in[N2+N4-2*i-1]);
im = -HALF32(in[N4+2*i] + in[N+N4-2*i-1]);
/* We could remove the HALF32 above and just use MULT16_32_Q16 below
(MIXED_PRECISION only) */
out[2*i] = S_MUL(re,l->trig[i]) - S_MUL(im,l->trig[i+N4]);
out[2*i+1] = S_MUL(im,l->trig[i]) + S_MUL(re,l->trig[i+N4]);
}
/* N/4 complex FFT, which should normally down-scale by 4/N (but doesn't now) */
cpx32_fft(l->kfft, out, f, N4);
/* Post-rotate and apply the scaling if the FFT doesn't to it itself */
for(i=0;i<N4;i++)
{
out[2*i] = -S_MUL(f[2*i+1],l->trig[i+N4]) + S_MUL(f[2*i] ,l->trig[i]);
out[N2-1-2*i] = -S_MUL(f[2*i] ,l->trig[i+N4]) - S_MUL(f[2*i+1],l->trig[i]);
}
RESTORE_STACK;
}
void mdct_backward(const mdct_lookup *l, kiss_fft_scalar *in, kiss_fft_scalar * restrict out)
{
int i;
int N, N2, N4;
VARDECL(kiss_fft_scalar, f);
SAVE_STACK;
N = l->n;
N2 = N>>1;
N4 = N>>2;
ALLOC(f, N2, kiss_fft_scalar);
/* Pre-rotate */
for(i=0;i<N4;i++)
{
out[2*i] = -S_MUL(in[N2-2*i-1], l->trig[i]) - S_MUL(in[2*i],l->trig[i+N4]);
out[2*i+1] = S_MUL(in[N2-2*i-1], l->trig[i+N4]) - S_MUL(in[2*i],l->trig[i]);
}
/* Inverse N/4 complex FFT. This one should *not* downscale even in fixed-point */
cpx32_ifft(l->kfft, out, f, N4);
/* Post-rotate */
for(i=0;i<N4;i++)
{
kiss_fft_scalar re, im;
re = f[2*i];
im = f[2*i+1];
/* We'd scale up by 2 here, but instead it's done when mixing the windows */
f[2*i] = S_MUL(re,l->trig[i]) + S_MUL(im,l->trig[i+N4]);
f[2*i+1] = S_MUL(im,l->trig[i]) - S_MUL(re,l->trig[i+N4]);
}
/* De-shuffle the components for the middle of the window only */
for(i = 0; i < N4; i++)
{
out[N4+2*i] =-f[2*i];
out[N4+2*i+1] = f[N2-2*i-1];
}
/* Mirror on both sides for TDAC */
for(i = 0; i < N4; i++)
{
out[i] =-out[N2-i-1];
out[N-i-1] = out[N2+i];
}
RESTORE_STACK;
}