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