1 /********************************************************************
3 * THIS FILE IS PART OF THE Ogg Vorbis SOFTWARE CODEC SOURCE CODE. *
4 * USE, DISTRIBUTION AND REPRODUCTION OF THIS SOURCE IS GOVERNED BY *
5 * THE GNU PUBLIC LICENSE 2, WHICH IS INCLUDED WITH THIS SOURCE. *
6 * PLEASE READ THESE TERMS DISTRIBUTING. *
8 * THE OggSQUISH SOURCE CODE IS (C) COPYRIGHT 1994-1999 *
9 * by 1999 Monty <monty@xiph.org> and The XIPHOPHORUS Company *
10 * http://www.xiph.org/ *
12 ********************************************************************
14 function: modified discrete cosine transform
15 power of two length transform only [16 <= n ]
17 author: Monty <xiphmont@mit.edu>
18 modifications by: Monty
19 last modification date: Oct 10 1999
21 Algorithm adapted from _The use of multirate filter banks for coding
22 of high quality digital audio_, by T. Sporer, K. Brandenburg and
23 B. Edler, collection of the European Signal Processing Conference
24 (EUSIPCO), Amsterdam, June 1992, Vol.1, pp 211-214
26 Note that the below code won't make much sense without the paper;
27 The presented algorithm was already fairly polished, and the code
28 once followed it closely. The current code both corrects several
29 typos in the paper and goes beyond the presented optimizations
30 (steps 4 through 6 are, for example, entirely eliminated).
32 This module DOES NOT INCLUDE code to generate the window function.
33 Everybody has their own weird favorite including me... I happen to
34 like the properties of y=sin(2PI*sin^2(x)), but others may vehemently
37 ********************************************************************/
44 /* build lookups for trig functions; also pre-figure scaling and
45 some window function algebra. */
47 void mdct_init(mdct_lookup *lookup,int n){
48 int *bitrev=malloc(sizeof(int)*(n/4));
49 double *trig=malloc(sizeof(double)*(n+n/4));
61 int log2n=lookup->log2n=rint(log(n)/log(2));
64 lookup->bitrev=bitrev;
69 AE[i]=cos((M_PI/n)*(4*i));
70 AO[i]=-sin((M_PI/n)*(4*i));
71 BE[i]=cos((M_PI/(2*n))*(2*i+1));
72 BO[i]=sin((M_PI/(2*n))*(2*i+1));
75 CE[i]=cos((M_PI/n)*(4*i+2));
76 CO[i]=-sin((M_PI/n)*(4*i+2));
79 /* bitreverse lookup... */
82 int mask=(1<<(log2n-1))-1,i,j;
87 if((msb>>j)&i)acc|=1<<j;
88 bitA[i]=((~acc)&mask)*2;
94 void mdct_clear(mdct_lookup *l){
96 if(l->trig)free(l->trig);
97 if(l->bitrev)free(l->bitrev);
98 memset(l,0,sizeof(mdct_lookup));
102 static inline void _mdct_kernel(double *x,
103 int n, int n2, int n4, int n8,
105 double *w=x+1; /* interleaved access improves cache locality */
113 double *AE=init->trig+n4;
117 double x0=xA[i]-xB[i];
118 double x1=xA[i+2]-xB[i+2];
121 w[i] =x0 * *AE + x1 * *AO;
124 w[i] =x1 * *AE - x0 * *AO;
134 for(i=0;i<init->log2n-3;i++){
138 double *AE=init->trig;
142 for(r=0;r<(n4>>i);r+=4){
144 int w2=wbase-(k0>>1);
149 for(s=0;s<(2<<i);s++){
150 x[w1+2]=w[w1+2]+w[w2+2];
154 x[w2+2]=wA*AEv - wB*AOv;
155 x[w2] =wB*AEv + wA*AOv;
170 /* step 4, 5, 6, 7 */
172 double *CE=init->trig+n;
174 int *bitA=init->bitrev;
184 double wA=w[t1]-w[t2];
185 double wB=w[t3]+w[t4];
186 double wC=w[t1]+w[t2];
187 double wD=w[t3]-w[t4];
190 double wBCO=wB* *(CO++);
192 double wBCE=wB* *(CE++);
194 *x1 =( wC+wACO+wBCE)*.5;
195 *(x2-2)=( wC-wACO-wBCE)*.5;
196 *(x1+2)=( wD+wBCO-wACE)*.5;
197 *x2 =(-wD+wBCO-wACE)*.5;
204 void mdct_forward(mdct_lookup *init, double *in, double *out, double *window){
206 double *x=alloca(n*sizeof(double));
212 /* window + rotate + step 1 */
217 double *AE=init->trig+n4;
223 tempA= in[in1+2]*window[in1+2] + in[in2]*window[in2];
224 tempB= in[in1]*window[in1] + in[in2+2]*window[in2+2];
227 x[i]= tempB* *AO + tempA* *AE;
228 x[i+2]= tempB* *AE - tempA* *AO;
234 tempA= in[in1+2]*window[in1+2] - in[in2]*window[in2];
235 tempB= in[in1]*window[in1] - in[in2+2]*window[in2+2];
238 x[i]= tempB* *AO + tempA* *AE;
239 x[i+2]= tempB* *AE - tempA* *AO;
245 tempA= -in[in1+2]*window[in1+2] - in[in2]*window[in2];
246 tempB= -in[in1]*window[in1] - in[in2+2]*window[in2+2];
249 x[i]= tempB* *AO + tempA* *AE;
250 x[i+2]= tempB* *AE - tempA* *AO;
254 _mdct_kernel(x,n,n2,n4,n8,init);
259 double *BE=init->trig+n2;
264 out[i] =(x[0]* *BE+x[2]* *BO)*scale;
265 *(--out2)=(x[0]* *BO-x[2]* *BE)*scale;
273 void mdct_backward(mdct_lookup *init, double *in, double *out, double *window){
275 double *x=alloca(n*sizeof(double));
281 /* window + rotate + step 1 */
285 double *AE=init->trig+n4;
290 *xO=-*(inO+2)* *AO - *inO * *AE;
292 *xO= *inO * *AO - *(inO+2)* *AE;
301 *xO=*inO * *AO + *(inO+2) * *AE;
303 *xO=*inO * *AE - *(inO+2) * *AO;
310 _mdct_kernel(x,n,n2,n4,n8,init);
315 double *BE=init->trig+n2;
318 int o3=n4+n2,o4=o3-1;
321 double temp= (*x * *BO - *(x+2) * *BE);
322 out[o3]=out[o4]= -(*x * *BE + *(x+2) * *BO);
323 out[o1]=-temp*window[o1];
324 out[o2]=temp*window[o2];