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564 lines
15 KiB
C
564 lines
15 KiB
C
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/********************************************************************
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* *
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* THIS FILE IS PART OF THE OggVorbis SOFTWARE CODEC SOURCE CODE. *
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* USE, DISTRIBUTION AND REPRODUCTION OF THIS LIBRARY SOURCE IS *
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* GOVERNED BY A BSD-STYLE SOURCE LICENSE INCLUDED WITH THIS SOURCE *
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* IN 'COPYING'. PLEASE READ THESE TERMS BEFORE DISTRIBUTING. *
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* *
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* THE OggVorbis SOURCE CODE IS (C) COPYRIGHT 1994-2009 *
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* by the Xiph.Org Foundation http://www.xiph.org/ *
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* *
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********************************************************************
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function: normalized modified discrete cosine transform
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power of two length transform only [64 <= n ]
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last mod: $Id: mdct.c 16227 2009-07-08 06:58:46Z xiphmont $
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Original algorithm adapted long ago from _The use of multirate filter
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banks for coding of high quality digital audio_, by T. Sporer,
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K. Brandenburg and B. Edler, collection of the European Signal
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Processing Conference (EUSIPCO), Amsterdam, June 1992, Vol.1, pp
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211-214
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The below code implements an algorithm that no longer looks much like
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that presented in the paper, but the basic structure remains if you
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dig deep enough to see it.
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This module DOES NOT INCLUDE code to generate/apply the window
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function. Everybody has their own weird favorite including me... I
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happen to like the properties of y=sin(.5PI*sin^2(x)), but others may
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vehemently disagree.
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********************************************************************/
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/* this can also be run as an integer transform by uncommenting a
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define in mdct.h; the integerization is a first pass and although
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it's likely stable for Vorbis, the dynamic range is constrained and
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roundoff isn't done (so it's noisy). Consider it functional, but
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only a starting point. There's no point on a machine with an FPU */
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <math.h>
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#include "vorbis/codec.h"
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#include "mdct.h"
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#include "os.h"
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#include "misc.h"
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/* build lookups for trig functions; also pre-figure scaling and
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some window function algebra. */
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void mdct_init(mdct_lookup *lookup,int n){
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int *bitrev=_ogg_malloc(sizeof(*bitrev)*(n/4));
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DATA_TYPE *T=_ogg_malloc(sizeof(*T)*(n+n/4));
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int i;
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int n2=n>>1;
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int log2n=lookup->log2n=rint(log((float)n)/log(2.f));
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lookup->n=n;
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lookup->trig=T;
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lookup->bitrev=bitrev;
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/* trig lookups... */
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for(i=0;i<n/4;i++){
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T[i*2]=FLOAT_CONV(cos((M_PI/n)*(4*i)));
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T[i*2+1]=FLOAT_CONV(-sin((M_PI/n)*(4*i)));
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T[n2+i*2]=FLOAT_CONV(cos((M_PI/(2*n))*(2*i+1)));
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T[n2+i*2+1]=FLOAT_CONV(sin((M_PI/(2*n))*(2*i+1)));
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}
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for(i=0;i<n/8;i++){
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T[n+i*2]=FLOAT_CONV(cos((M_PI/n)*(4*i+2))*.5);
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T[n+i*2+1]=FLOAT_CONV(-sin((M_PI/n)*(4*i+2))*.5);
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}
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/* bitreverse lookup... */
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{
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int mask=(1<<(log2n-1))-1,i,j;
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int msb=1<<(log2n-2);
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for(i=0;i<n/8;i++){
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int acc=0;
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for(j=0;msb>>j;j++)
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if((msb>>j)&i)acc|=1<<j;
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bitrev[i*2]=((~acc)&mask)-1;
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bitrev[i*2+1]=acc;
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}
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}
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lookup->scale=FLOAT_CONV(4.f/n);
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}
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/* 8 point butterfly (in place, 4 register) */
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STIN void mdct_butterfly_8(DATA_TYPE *x){
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REG_TYPE r0 = x[6] + x[2];
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REG_TYPE r1 = x[6] - x[2];
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REG_TYPE r2 = x[4] + x[0];
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REG_TYPE r3 = x[4] - x[0];
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x[6] = r0 + r2;
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x[4] = r0 - r2;
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r0 = x[5] - x[1];
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r2 = x[7] - x[3];
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x[0] = r1 + r0;
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x[2] = r1 - r0;
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r0 = x[5] + x[1];
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r1 = x[7] + x[3];
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x[3] = r2 + r3;
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x[1] = r2 - r3;
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x[7] = r1 + r0;
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x[5] = r1 - r0;
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}
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/* 16 point butterfly (in place, 4 register) */
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STIN void mdct_butterfly_16(DATA_TYPE *x){
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REG_TYPE r0 = x[1] - x[9];
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REG_TYPE r1 = x[0] - x[8];
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x[8] += x[0];
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x[9] += x[1];
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x[0] = MULT_NORM((r0 + r1) * cPI2_8);
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x[1] = MULT_NORM((r0 - r1) * cPI2_8);
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r0 = x[3] - x[11];
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r1 = x[10] - x[2];
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x[10] += x[2];
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x[11] += x[3];
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x[2] = r0;
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x[3] = r1;
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r0 = x[12] - x[4];
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r1 = x[13] - x[5];
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x[12] += x[4];
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x[13] += x[5];
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x[4] = MULT_NORM((r0 - r1) * cPI2_8);
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x[5] = MULT_NORM((r0 + r1) * cPI2_8);
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r0 = x[14] - x[6];
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r1 = x[15] - x[7];
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x[14] += x[6];
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x[15] += x[7];
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x[6] = r0;
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x[7] = r1;
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mdct_butterfly_8(x);
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mdct_butterfly_8(x+8);
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}
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/* 32 point butterfly (in place, 4 register) */
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STIN void mdct_butterfly_32(DATA_TYPE *x){
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REG_TYPE r0 = x[30] - x[14];
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REG_TYPE r1 = x[31] - x[15];
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x[30] += x[14];
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x[31] += x[15];
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x[14] = r0;
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x[15] = r1;
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r0 = x[28] - x[12];
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r1 = x[29] - x[13];
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x[28] += x[12];
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x[29] += x[13];
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x[12] = MULT_NORM( r0 * cPI1_8 - r1 * cPI3_8 );
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x[13] = MULT_NORM( r0 * cPI3_8 + r1 * cPI1_8 );
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r0 = x[26] - x[10];
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r1 = x[27] - x[11];
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x[26] += x[10];
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x[27] += x[11];
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x[10] = MULT_NORM(( r0 - r1 ) * cPI2_8);
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x[11] = MULT_NORM(( r0 + r1 ) * cPI2_8);
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r0 = x[24] - x[8];
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r1 = x[25] - x[9];
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x[24] += x[8];
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x[25] += x[9];
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x[8] = MULT_NORM( r0 * cPI3_8 - r1 * cPI1_8 );
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x[9] = MULT_NORM( r1 * cPI3_8 + r0 * cPI1_8 );
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r0 = x[22] - x[6];
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r1 = x[7] - x[23];
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x[22] += x[6];
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x[23] += x[7];
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x[6] = r1;
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x[7] = r0;
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r0 = x[4] - x[20];
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r1 = x[5] - x[21];
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x[20] += x[4];
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x[21] += x[5];
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x[4] = MULT_NORM( r1 * cPI1_8 + r0 * cPI3_8 );
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x[5] = MULT_NORM( r1 * cPI3_8 - r0 * cPI1_8 );
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r0 = x[2] - x[18];
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r1 = x[3] - x[19];
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x[18] += x[2];
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x[19] += x[3];
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x[2] = MULT_NORM(( r1 + r0 ) * cPI2_8);
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x[3] = MULT_NORM(( r1 - r0 ) * cPI2_8);
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r0 = x[0] - x[16];
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r1 = x[1] - x[17];
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x[16] += x[0];
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x[17] += x[1];
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x[0] = MULT_NORM( r1 * cPI3_8 + r0 * cPI1_8 );
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x[1] = MULT_NORM( r1 * cPI1_8 - r0 * cPI3_8 );
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mdct_butterfly_16(x);
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mdct_butterfly_16(x+16);
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}
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/* N point first stage butterfly (in place, 2 register) */
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STIN void mdct_butterfly_first(DATA_TYPE *T,
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DATA_TYPE *x,
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int points){
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DATA_TYPE *x1 = x + points - 8;
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DATA_TYPE *x2 = x + (points>>1) - 8;
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REG_TYPE r0;
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REG_TYPE r1;
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do{
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r0 = x1[6] - x2[6];
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r1 = x1[7] - x2[7];
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x1[6] += x2[6];
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x1[7] += x2[7];
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x2[6] = MULT_NORM(r1 * T[1] + r0 * T[0]);
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x2[7] = MULT_NORM(r1 * T[0] - r0 * T[1]);
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r0 = x1[4] - x2[4];
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r1 = x1[5] - x2[5];
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x1[4] += x2[4];
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x1[5] += x2[5];
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x2[4] = MULT_NORM(r1 * T[5] + r0 * T[4]);
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x2[5] = MULT_NORM(r1 * T[4] - r0 * T[5]);
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r0 = x1[2] - x2[2];
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r1 = x1[3] - x2[3];
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x1[2] += x2[2];
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x1[3] += x2[3];
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x2[2] = MULT_NORM(r1 * T[9] + r0 * T[8]);
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x2[3] = MULT_NORM(r1 * T[8] - r0 * T[9]);
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r0 = x1[0] - x2[0];
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r1 = x1[1] - x2[1];
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x1[0] += x2[0];
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x1[1] += x2[1];
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x2[0] = MULT_NORM(r1 * T[13] + r0 * T[12]);
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x2[1] = MULT_NORM(r1 * T[12] - r0 * T[13]);
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x1-=8;
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x2-=8;
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T+=16;
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}while(x2>=x);
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}
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/* N/stage point generic N stage butterfly (in place, 2 register) */
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STIN void mdct_butterfly_generic(DATA_TYPE *T,
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DATA_TYPE *x,
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int points,
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int trigint){
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DATA_TYPE *x1 = x + points - 8;
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DATA_TYPE *x2 = x + (points>>1) - 8;
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REG_TYPE r0;
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REG_TYPE r1;
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do{
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r0 = x1[6] - x2[6];
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r1 = x1[7] - x2[7];
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x1[6] += x2[6];
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x1[7] += x2[7];
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x2[6] = MULT_NORM(r1 * T[1] + r0 * T[0]);
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x2[7] = MULT_NORM(r1 * T[0] - r0 * T[1]);
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T+=trigint;
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r0 = x1[4] - x2[4];
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r1 = x1[5] - x2[5];
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x1[4] += x2[4];
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x1[5] += x2[5];
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x2[4] = MULT_NORM(r1 * T[1] + r0 * T[0]);
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x2[5] = MULT_NORM(r1 * T[0] - r0 * T[1]);
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T+=trigint;
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r0 = x1[2] - x2[2];
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r1 = x1[3] - x2[3];
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x1[2] += x2[2];
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x1[3] += x2[3];
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x2[2] = MULT_NORM(r1 * T[1] + r0 * T[0]);
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x2[3] = MULT_NORM(r1 * T[0] - r0 * T[1]);
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T+=trigint;
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r0 = x1[0] - x2[0];
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r1 = x1[1] - x2[1];
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x1[0] += x2[0];
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x1[1] += x2[1];
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x2[0] = MULT_NORM(r1 * T[1] + r0 * T[0]);
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x2[1] = MULT_NORM(r1 * T[0] - r0 * T[1]);
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T+=trigint;
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x1-=8;
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x2-=8;
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}while(x2>=x);
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}
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STIN void mdct_butterflies(mdct_lookup *init,
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DATA_TYPE *x,
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int points){
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DATA_TYPE *T=init->trig;
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int stages=init->log2n-5;
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int i,j;
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if(--stages>0){
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mdct_butterfly_first(T,x,points);
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}
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for(i=1;--stages>0;i++){
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for(j=0;j<(1<<i);j++)
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mdct_butterfly_generic(T,x+(points>>i)*j,points>>i,4<<i);
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}
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for(j=0;j<points;j+=32)
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mdct_butterfly_32(x+j);
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}
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void mdct_clear(mdct_lookup *l){
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if(l){
|
||
|
|
if(l->trig)_ogg_free(l->trig);
|
||
|
|
if(l->bitrev)_ogg_free(l->bitrev);
|
||
|
|
memset(l,0,sizeof(*l));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
STIN void mdct_bitreverse(mdct_lookup *init,
|
||
|
|
DATA_TYPE *x){
|
||
|
|
int n = init->n;
|
||
|
|
int *bit = init->bitrev;
|
||
|
|
DATA_TYPE *w0 = x;
|
||
|
|
DATA_TYPE *w1 = x = w0+(n>>1);
|
||
|
|
DATA_TYPE *T = init->trig+n;
|
||
|
|
|
||
|
|
do{
|
||
|
|
DATA_TYPE *x0 = x+bit[0];
|
||
|
|
DATA_TYPE *x1 = x+bit[1];
|
||
|
|
|
||
|
|
REG_TYPE r0 = x0[1] - x1[1];
|
||
|
|
REG_TYPE r1 = x0[0] + x1[0];
|
||
|
|
REG_TYPE r2 = MULT_NORM(r1 * T[0] + r0 * T[1]);
|
||
|
|
REG_TYPE r3 = MULT_NORM(r1 * T[1] - r0 * T[0]);
|
||
|
|
|
||
|
|
w1 -= 4;
|
||
|
|
|
||
|
|
r0 = HALVE(x0[1] + x1[1]);
|
||
|
|
r1 = HALVE(x0[0] - x1[0]);
|
||
|
|
|
||
|
|
w0[0] = r0 + r2;
|
||
|
|
w1[2] = r0 - r2;
|
||
|
|
w0[1] = r1 + r3;
|
||
|
|
w1[3] = r3 - r1;
|
||
|
|
|
||
|
|
x0 = x+bit[2];
|
||
|
|
x1 = x+bit[3];
|
||
|
|
|
||
|
|
r0 = x0[1] - x1[1];
|
||
|
|
r1 = x0[0] + x1[0];
|
||
|
|
r2 = MULT_NORM(r1 * T[2] + r0 * T[3]);
|
||
|
|
r3 = MULT_NORM(r1 * T[3] - r0 * T[2]);
|
||
|
|
|
||
|
|
r0 = HALVE(x0[1] + x1[1]);
|
||
|
|
r1 = HALVE(x0[0] - x1[0]);
|
||
|
|
|
||
|
|
w0[2] = r0 + r2;
|
||
|
|
w1[0] = r0 - r2;
|
||
|
|
w0[3] = r1 + r3;
|
||
|
|
w1[1] = r3 - r1;
|
||
|
|
|
||
|
|
T += 4;
|
||
|
|
bit += 4;
|
||
|
|
w0 += 4;
|
||
|
|
|
||
|
|
}while(w0<w1);
|
||
|
|
}
|
||
|
|
|
||
|
|
void mdct_backward(mdct_lookup *init, DATA_TYPE *in, DATA_TYPE *out){
|
||
|
|
int n=init->n;
|
||
|
|
int n2=n>>1;
|
||
|
|
int n4=n>>2;
|
||
|
|
|
||
|
|
/* rotate */
|
||
|
|
|
||
|
|
DATA_TYPE *iX = in+n2-7;
|
||
|
|
DATA_TYPE *oX = out+n2+n4;
|
||
|
|
DATA_TYPE *T = init->trig+n4;
|
||
|
|
|
||
|
|
do{
|
||
|
|
oX -= 4;
|
||
|
|
oX[0] = MULT_NORM(-iX[2] * T[3] - iX[0] * T[2]);
|
||
|
|
oX[1] = MULT_NORM (iX[0] * T[3] - iX[2] * T[2]);
|
||
|
|
oX[2] = MULT_NORM(-iX[6] * T[1] - iX[4] * T[0]);
|
||
|
|
oX[3] = MULT_NORM (iX[4] * T[1] - iX[6] * T[0]);
|
||
|
|
iX -= 8;
|
||
|
|
T += 4;
|
||
|
|
}while(iX>=in);
|
||
|
|
|
||
|
|
iX = in+n2-8;
|
||
|
|
oX = out+n2+n4;
|
||
|
|
T = init->trig+n4;
|
||
|
|
|
||
|
|
do{
|
||
|
|
T -= 4;
|
||
|
|
oX[0] = MULT_NORM (iX[4] * T[3] + iX[6] * T[2]);
|
||
|
|
oX[1] = MULT_NORM (iX[4] * T[2] - iX[6] * T[3]);
|
||
|
|
oX[2] = MULT_NORM (iX[0] * T[1] + iX[2] * T[0]);
|
||
|
|
oX[3] = MULT_NORM (iX[0] * T[0] - iX[2] * T[1]);
|
||
|
|
iX -= 8;
|
||
|
|
oX += 4;
|
||
|
|
}while(iX>=in);
|
||
|
|
|
||
|
|
mdct_butterflies(init,out+n2,n2);
|
||
|
|
mdct_bitreverse(init,out);
|
||
|
|
|
||
|
|
/* roatate + window */
|
||
|
|
|
||
|
|
{
|
||
|
|
DATA_TYPE *oX1=out+n2+n4;
|
||
|
|
DATA_TYPE *oX2=out+n2+n4;
|
||
|
|
DATA_TYPE *iX =out;
|
||
|
|
T =init->trig+n2;
|
||
|
|
|
||
|
|
do{
|
||
|
|
oX1-=4;
|
||
|
|
|
||
|
|
oX1[3] = MULT_NORM (iX[0] * T[1] - iX[1] * T[0]);
|
||
|
|
oX2[0] = -MULT_NORM (iX[0] * T[0] + iX[1] * T[1]);
|
||
|
|
|
||
|
|
oX1[2] = MULT_NORM (iX[2] * T[3] - iX[3] * T[2]);
|
||
|
|
oX2[1] = -MULT_NORM (iX[2] * T[2] + iX[3] * T[3]);
|
||
|
|
|
||
|
|
oX1[1] = MULT_NORM (iX[4] * T[5] - iX[5] * T[4]);
|
||
|
|
oX2[2] = -MULT_NORM (iX[4] * T[4] + iX[5] * T[5]);
|
||
|
|
|
||
|
|
oX1[0] = MULT_NORM (iX[6] * T[7] - iX[7] * T[6]);
|
||
|
|
oX2[3] = -MULT_NORM (iX[6] * T[6] + iX[7] * T[7]);
|
||
|
|
|
||
|
|
oX2+=4;
|
||
|
|
iX += 8;
|
||
|
|
T += 8;
|
||
|
|
}while(iX<oX1);
|
||
|
|
|
||
|
|
iX=out+n2+n4;
|
||
|
|
oX1=out+n4;
|
||
|
|
oX2=oX1;
|
||
|
|
|
||
|
|
do{
|
||
|
|
oX1-=4;
|
||
|
|
iX-=4;
|
||
|
|
|
||
|
|
oX2[0] = -(oX1[3] = iX[3]);
|
||
|
|
oX2[1] = -(oX1[2] = iX[2]);
|
||
|
|
oX2[2] = -(oX1[1] = iX[1]);
|
||
|
|
oX2[3] = -(oX1[0] = iX[0]);
|
||
|
|
|
||
|
|
oX2+=4;
|
||
|
|
}while(oX2<iX);
|
||
|
|
|
||
|
|
iX=out+n2+n4;
|
||
|
|
oX1=out+n2+n4;
|
||
|
|
oX2=out+n2;
|
||
|
|
do{
|
||
|
|
oX1-=4;
|
||
|
|
oX1[0]= iX[3];
|
||
|
|
oX1[1]= iX[2];
|
||
|
|
oX1[2]= iX[1];
|
||
|
|
oX1[3]= iX[0];
|
||
|
|
iX+=4;
|
||
|
|
}while(oX1>oX2);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void mdct_forward(mdct_lookup *init, DATA_TYPE *in, DATA_TYPE *out){
|
||
|
|
int n=init->n;
|
||
|
|
int n2=n>>1;
|
||
|
|
int n4=n>>2;
|
||
|
|
int n8=n>>3;
|
||
|
|
DATA_TYPE *w=alloca(n*sizeof(*w)); /* forward needs working space */
|
||
|
|
DATA_TYPE *w2=w+n2;
|
||
|
|
|
||
|
|
/* rotate */
|
||
|
|
|
||
|
|
/* window + rotate + step 1 */
|
||
|
|
|
||
|
|
REG_TYPE r0;
|
||
|
|
REG_TYPE r1;
|
||
|
|
DATA_TYPE *x0=in+n2+n4;
|
||
|
|
DATA_TYPE *x1=x0+1;
|
||
|
|
DATA_TYPE *T=init->trig+n2;
|
||
|
|
|
||
|
|
int i=0;
|
||
|
|
|
||
|
|
for(i=0;i<n8;i+=2){
|
||
|
|
x0 -=4;
|
||
|
|
T-=2;
|
||
|
|
r0= x0[2] + x1[0];
|
||
|
|
r1= x0[0] + x1[2];
|
||
|
|
w2[i]= MULT_NORM(r1*T[1] + r0*T[0]);
|
||
|
|
w2[i+1]= MULT_NORM(r1*T[0] - r0*T[1]);
|
||
|
|
x1 +=4;
|
||
|
|
}
|
||
|
|
|
||
|
|
x1=in+1;
|
||
|
|
|
||
|
|
for(;i<n2-n8;i+=2){
|
||
|
|
T-=2;
|
||
|
|
x0 -=4;
|
||
|
|
r0= x0[2] - x1[0];
|
||
|
|
r1= x0[0] - x1[2];
|
||
|
|
w2[i]= MULT_NORM(r1*T[1] + r0*T[0]);
|
||
|
|
w2[i+1]= MULT_NORM(r1*T[0] - r0*T[1]);
|
||
|
|
x1 +=4;
|
||
|
|
}
|
||
|
|
|
||
|
|
x0=in+n;
|
||
|
|
|
||
|
|
for(;i<n2;i+=2){
|
||
|
|
T-=2;
|
||
|
|
x0 -=4;
|
||
|
|
r0= -x0[2] - x1[0];
|
||
|
|
r1= -x0[0] - x1[2];
|
||
|
|
w2[i]= MULT_NORM(r1*T[1] + r0*T[0]);
|
||
|
|
w2[i+1]= MULT_NORM(r1*T[0] - r0*T[1]);
|
||
|
|
x1 +=4;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
mdct_butterflies(init,w+n2,n2);
|
||
|
|
mdct_bitreverse(init,w);
|
||
|
|
|
||
|
|
/* roatate + window */
|
||
|
|
|
||
|
|
T=init->trig+n2;
|
||
|
|
x0=out+n2;
|
||
|
|
|
||
|
|
for(i=0;i<n4;i++){
|
||
|
|
x0--;
|
||
|
|
out[i] =MULT_NORM((w[0]*T[0]+w[1]*T[1])*init->scale);
|
||
|
|
x0[0] =MULT_NORM((w[0]*T[1]-w[1]*T[0])*init->scale);
|
||
|
|
w+=2;
|
||
|
|
T+=2;
|
||
|
|
}
|
||
|
|
}
|