release/src/router/libvorbis/lib/mdct.c

   1 /********************************************************************
   2  *                                                                  *
   3  * THIS FILE IS PART OF THE OggVorbis SOFTWARE CODEC SOURCE CODE.   *
   4  * USE, DISTRIBUTION AND REPRODUCTION OF THIS LIBRARY SOURCE IS     *
   5  * GOVERNED BY A BSD-STYLE SOURCE LICENSE INCLUDED WITH THIS SOURCE *
   6  * IN 'COPYING'. PLEASE READ THESE TERMS BEFORE DISTRIBUTING.       *
   7  *                                                                  *
   8  * THE OggVorbis SOURCE CODE IS (C) COPYRIGHT 1994-2009             *
   9  * by the Xiph.Org Foundation http://www.xiph.org/                  *
  10  *                                                                  *
  11  ********************************************************************
  12
  13  function: normalized modified discrete cosine transform
  14            power of two length transform only [64 <= n ]
  15  last mod: $Id: mdct.c 16227 2009-07-08 06:58:46Z xiphmont $
  16
  17  Original algorithm adapted long ago from _The use of multirate filter
  18  banks for coding of high quality digital audio_, by T. Sporer,
  19  K. Brandenburg and B. Edler, collection of the European Signal
  20  Processing Conference (EUSIPCO), Amsterdam, June 1992, Vol.1, pp
  21  211-214
  22
  23  The below code implements an algorithm that no longer looks much like
  24  that presented in the paper, but the basic structure remains if you
  25  dig deep enough to see it.
  26
  27  This module DOES NOT INCLUDE code to generate/apply the window
  28  function.  Everybody has their own weird favorite including me... I
  29  happen to like the properties of y=sin(.5PI*sin^2(x)), but others may
  30  vehemently disagree.
  31
  32  ********************************************************************/
  33
  34 /* this can also be run as an integer transform by uncommenting a
  35    define in mdct.h; the integerization is a first pass and although
  36    it's likely stable for Vorbis, the dynamic range is constrained and
  37    roundoff isn't done (so it's noisy).  Consider it functional, but
  38    only a starting point.  There's no point on a machine with an FPU */
  39
  40 #include <stdio.h>
  41 #include <stdlib.h>
  42 #include <string.h>
  43 #include <math.h>
  44 #include "vorbis/codec.h"
  45 #include "mdct.h"
  46 #include "os.h"
  47 #include "misc.h"
  48
  49 /* build lookups for trig functions; also pre-figure scaling and
  50    some window function algebra. */
  51
  52 void mdct_init(mdct_lookup *lookup,int n){
  53   int   *bitrev=_ogg_malloc(sizeof(*bitrev)*(n/4));
  54   DATA_TYPE *T=_ogg_malloc(sizeof(*T)*(n+n/4));
  55
  56   int i;
  57   int n2=n>>1;
  58   int log2n=lookup->log2n=rint(log((float)n)/log(2.f));
  59   lookup->n=n;
  60   lookup->trig=T;
  61   lookup->bitrev=bitrev;
  62
  63 /* trig lookups... */
  64
  65   for(i=0;i<n/4;i++){
  66     T[i*2]=FLOAT_CONV(cos((M_PI/n)*(4*i)));
  67     T[i*2+1]=FLOAT_CONV(-sin((M_PI/n)*(4*i)));
  68     T[n2+i*2]=FLOAT_CONV(cos((M_PI/(2*n))*(2*i+1)));
  69     T[n2+i*2+1]=FLOAT_CONV(sin((M_PI/(2*n))*(2*i+1)));
  70   }
  71   for(i=0;i<n/8;i++){
  72     T[n+i*2]=FLOAT_CONV(cos((M_PI/n)*(4*i+2))*.5);
  73     T[n+i*2+1]=FLOAT_CONV(-sin((M_PI/n)*(4*i+2))*.5);
  74   }
  75
  76   /* bitreverse lookup... */
  77
  78   {
  79     int mask=(1<<(log2n-1))-1,i,j;
  80     int msb=1<<(log2n-2);
  81     for(i=0;i<n/8;i++){
  82       int acc=0;
  83       for(j=0;msb>>j;j++)
  84         if((msb>>j)&i)acc|=1<<j;
  85       bitrev[i*2]=((~acc)&mask)-1;
  86       bitrev[i*2+1]=acc;
  87
  88     }
  89   }
  90   lookup->scale=FLOAT_CONV(4.f/n);
  91 }
  92
  93 /* 8 point butterfly (in place, 4 register) */
  94 STIN void mdct_butterfly_8(DATA_TYPE *x){
  95   REG_TYPE r0   = x[6] + x[2];
  96   REG_TYPE r1   = x[6] - x[2];
  97   REG_TYPE r2   = x[4] + x[0];
  98   REG_TYPE r3   = x[4] - x[0];
  99
 100            x[6] = r0   + r2;
 101            x[4] = r0   - r2;
 102
 103            r0   = x[5] - x[1];
 104            r2   = x[7] - x[3];
 105            x[0] = r1   + r0;
 106            x[2] = r1   - r0;
 107
 108            r0   = x[5] + x[1];
 109            r1   = x[7] + x[3];
 110            x[3] = r2   + r3;
 111            x[1] = r2   - r3;
 112            x[7] = r1   + r0;
 113            x[5] = r1   - r0;
 114
 115 }
 116
 117 /* 16 point butterfly (in place, 4 register) */
 118 STIN void mdct_butterfly_16(DATA_TYPE *x){
 119   REG_TYPE r0     = x[1]  - x[9];
 120   REG_TYPE r1     = x[0]  - x[8];
 121
 122            x[8]  += x[0];
 123            x[9]  += x[1];
 124            x[0]   = MULT_NORM((r0   + r1) * cPI2_8);
 125            x[1]   = MULT_NORM((r0   - r1) * cPI2_8);
 126
 127            r0     = x[3]  - x[11];
 128            r1     = x[10] - x[2];
 129            x[10] += x[2];
 130            x[11] += x[3];
 131            x[2]   = r0;
 132            x[3]   = r1;
 133
 134            r0     = x[12] - x[4];
 135            r1     = x[13] - x[5];
 136            x[12] += x[4];
 137            x[13] += x[5];
 138            x[4]   = MULT_NORM((r0   - r1) * cPI2_8);
 139            x[5]   = MULT_NORM((r0   + r1) * cPI2_8);
 140
 141            r0     = x[14] - x[6];
 142            r1     = x[15] - x[7];
 143            x[14] += x[6];
 144            x[15] += x[7];
 145            x[6]  = r0;
 146            x[7]  = r1;
 147
 148            mdct_butterfly_8(x);
 149            mdct_butterfly_8(x+8);
 150 }
 151
 152 /* 32 point butterfly (in place, 4 register) */
 153 STIN void mdct_butterfly_32(DATA_TYPE *x){
 154   REG_TYPE r0     = x[30] - x[14];
 155   REG_TYPE r1     = x[31] - x[15];
 156
 157            x[30] +=         x[14];
 158            x[31] +=         x[15];
 159            x[14]  =         r0;
 160            x[15]  =         r1;
 161
 162            r0     = x[28] - x[12];
 163            r1     = x[29] - x[13];
 164            x[28] +=         x[12];
 165            x[29] +=         x[13];
 166            x[12]  = MULT_NORM( r0 * cPI1_8  -  r1 * cPI3_8 );
 167            x[13]  = MULT_NORM( r0 * cPI3_8  +  r1 * cPI1_8 );
 168
 169            r0     = x[26] - x[10];
 170            r1     = x[27] - x[11];
 171            x[26] +=         x[10];
 172            x[27] +=         x[11];
 173            x[10]  = MULT_NORM(( r0  - r1 ) * cPI2_8);
 174            x[11]  = MULT_NORM(( r0  + r1 ) * cPI2_8);
 175
 176            r0     = x[24] - x[8];
 177            r1     = x[25] - x[9];
 178            x[24] += x[8];
 179            x[25] += x[9];
 180            x[8]   = MULT_NORM( r0 * cPI3_8  -  r1 * cPI1_8 );
 181            x[9]   = MULT_NORM( r1 * cPI3_8  +  r0 * cPI1_8 );
 182
 183            r0     = x[22] - x[6];
 184            r1     = x[7]  - x[23];
 185            x[22] += x[6];
 186            x[23] += x[7];
 187            x[6]   = r1;
 188            x[7]   = r0;
 189
 190            r0     = x[4]  - x[20];
 191            r1     = x[5]  - x[21];
 192            x[20] += x[4];
 193            x[21] += x[5];
 194            x[4]   = MULT_NORM( r1 * cPI1_8  +  r0 * cPI3_8 );
 195            x[5]   = MULT_NORM( r1 * cPI3_8  -  r0 * cPI1_8 );
 196
 197            r0     = x[2]  - x[18];
 198            r1     = x[3]  - x[19];
 199            x[18] += x[2];
 200            x[19] += x[3];
 201            x[2]   = MULT_NORM(( r1  + r0 ) * cPI2_8);
 202            x[3]   = MULT_NORM(( r1  - r0 ) * cPI2_8);
 203
 204            r0     = x[0]  - x[16];
 205            r1     = x[1]  - x[17];
 206            x[16] += x[0];
 207            x[17] += x[1];
 208            x[0]   = MULT_NORM( r1 * cPI3_8  +  r0 * cPI1_8 );
 209            x[1]   = MULT_NORM( r1 * cPI1_8  -  r0 * cPI3_8 );
 210
 211            mdct_butterfly_16(x);
 212            mdct_butterfly_16(x+16);
 213
 214 }
 215
 216 /* N point first stage butterfly (in place, 2 register) */
 217 STIN void mdct_butterfly_first(DATA_TYPE *T,
 218                                         DATA_TYPE *x,
 219                                         int points){
 220
 221   DATA_TYPE *x1        = x          + points      - 8;
 222   DATA_TYPE *x2        = x          + (points>>1) - 8;
 223   REG_TYPE   r0;
 224   REG_TYPE   r1;
 225
 226   do{
 227
 228                r0      = x1[6]      -  x2[6];
 229                r1      = x1[7]      -  x2[7];
 230                x1[6]  += x2[6];
 231                x1[7]  += x2[7];
 232                x2[6]   = MULT_NORM(r1 * T[1]  +  r0 * T[0]);
 233                x2[7]   = MULT_NORM(r1 * T[0]  -  r0 * T[1]);
 234
 235                r0      = x1[4]      -  x2[4];
 236                r1      = x1[5]      -  x2[5];
 237                x1[4]  += x2[4];
 238                x1[5]  += x2[5];
 239                x2[4]   = MULT_NORM(r1 * T[5]  +  r0 * T[4]);
 240                x2[5]   = MULT_NORM(r1 * T[4]  -  r0 * T[5]);
 241
 242                r0      = x1[2]      -  x2[2];
 243                r1      = x1[3]      -  x2[3];
 244                x1[2]  += x2[2];
 245                x1[3]  += x2[3];
 246                x2[2]   = MULT_NORM(r1 * T[9]  +  r0 * T[8]);
 247                x2[3]   = MULT_NORM(r1 * T[8]  -  r0 * T[9]);
 248
 249                r0      = x1[0]      -  x2[0];
 250                r1      = x1[1]      -  x2[1];
 251                x1[0]  += x2[0];
 252                x1[1]  += x2[1];
 253                x2[0]   = MULT_NORM(r1 * T[13] +  r0 * T[12]);
 254                x2[1]   = MULT_NORM(r1 * T[12] -  r0 * T[13]);
 255
 256     x1-=8;
 257     x2-=8;
 258     T+=16;
 259
 260   }while(x2>=x);
 261 }
 262
 263 /* N/stage point generic N stage butterfly (in place, 2 register) */
 264 STIN void mdct_butterfly_generic(DATA_TYPE *T,
 265                                           DATA_TYPE *x,
 266                                           int points,
 267                                           int trigint){
 268
 269   DATA_TYPE *x1        = x          + points      - 8;
 270   DATA_TYPE *x2        = x          + (points>>1) - 8;
 271   REG_TYPE   r0;
 272   REG_TYPE   r1;
 273
 274   do{
 275
 276                r0      = x1[6]      -  x2[6];
 277                r1      = x1[7]      -  x2[7];
 278                x1[6]  += x2[6];
 279                x1[7]  += x2[7];
 280                x2[6]   = MULT_NORM(r1 * T[1]  +  r0 * T[0]);
 281                x2[7]   = MULT_NORM(r1 * T[0]  -  r0 * T[1]);
 282
 283                T+=trigint;
 284
 285                r0      = x1[4]      -  x2[4];
 286                r1      = x1[5]      -  x2[5];
 287                x1[4]  += x2[4];
 288                x1[5]  += x2[5];
 289                x2[4]   = MULT_NORM(r1 * T[1]  +  r0 * T[0]);
 290                x2[5]   = MULT_NORM(r1 * T[0]  -  r0 * T[1]);
 291
 292                T+=trigint;
 293
 294                r0      = x1[2]      -  x2[2];
 295                r1      = x1[3]      -  x2[3];
 296                x1[2]  += x2[2];
 297                x1[3]  += x2[3];
 298                x2[2]   = MULT_NORM(r1 * T[1]  +  r0 * T[0]);
 299                x2[3]   = MULT_NORM(r1 * T[0]  -  r0 * T[1]);
 300
 301                T+=trigint;
 302
 303                r0      = x1[0]      -  x2[0];
 304                r1      = x1[1]      -  x2[1];
 305                x1[0]  += x2[0];
 306                x1[1]  += x2[1];
 307                x2[0]   = MULT_NORM(r1 * T[1]  +  r0 * T[0]);
 308                x2[1]   = MULT_NORM(r1 * T[0]  -  r0 * T[1]);
 309
 310                T+=trigint;
 311     x1-=8;
 312     x2-=8;
 313
 314   }while(x2>=x);
 315 }
 316
 317 STIN void mdct_butterflies(mdct_lookup *init,
 318                              DATA_TYPE *x,
 319                              int points){
 320
 321   DATA_TYPE *T=init->trig;
 322   int stages=init->log2n-5;
 323   int i,j;
 324
 325   if(--stages>0){
 326     mdct_butterfly_first(T,x,points);
 327   }
 328
 329   for(i=1;--stages>0;i++){
 330     for(j=0;j<(1<<i);j++)
 331       mdct_butterfly_generic(T,x+(points>>i)*j,points>>i,4<<i);
 332   }
 333
 334   for(j=0;j<points;j+=32)
 335     mdct_butterfly_32(x+j);
 336
 337 }
 338
 339 void mdct_clear(mdct_lookup *l){
 340   if(l){
 341     if(l->trig)_ogg_free(l->trig);
 342     if(l->bitrev)_ogg_free(l->bitrev);
 343     memset(l,0,sizeof(*l));
 344   }
 345 }
 346
 347 STIN void mdct_bitreverse(mdct_lookup *init,
 348                             DATA_TYPE *x){
 349   int        n       = init->n;
 350   int       *bit     = init->bitrev;
 351   DATA_TYPE *w0      = x;
 352   DATA_TYPE *w1      = x = w0+(n>>1);
 353   DATA_TYPE *T       = init->trig+n;
 354
 355   do{
 356     DATA_TYPE *x0    = x+bit[0];
 357     DATA_TYPE *x1    = x+bit[1];
 358
 359     REG_TYPE  r0     = x0[1]  - x1[1];
 360     REG_TYPE  r1     = x0[0]  + x1[0];
 361     REG_TYPE  r2     = MULT_NORM(r1     * T[0]   + r0 * T[1]);
 362     REG_TYPE  r3     = MULT_NORM(r1     * T[1]   - r0 * T[0]);
 363
 364               w1    -= 4;
 365
 366               r0     = HALVE(x0[1] + x1[1]);
 367               r1     = HALVE(x0[0] - x1[0]);
 368
 369               w0[0]  = r0     + r2;
 370               w1[2]  = r0     - r2;
 371               w0[1]  = r1     + r3;
 372               w1[3]  = r3     - r1;
 373
 374               x0     = x+bit[2];
 375               x1     = x+bit[3];
 376
 377               r0     = x0[1]  - x1[1];
 378               r1     = x0[0]  + x1[0];
 379               r2     = MULT_NORM(r1     * T[2]   + r0 * T[3]);
 380               r3     = MULT_NORM(r1     * T[3]   - r0 * T[2]);
 381
 382               r0     = HALVE(x0[1] + x1[1]);
 383               r1     = HALVE(x0[0] - x1[0]);
 384
 385               w0[2]  = r0     + r2;
 386               w1[0]  = r0     - r2;
 387               w0[3]  = r1     + r3;
 388               w1[1]  = r3     - r1;
 389
 390               T     += 4;
 391               bit   += 4;
 392               w0    += 4;
 393
 394   }while(w0<w1);
 395 }
 396
 397 void mdct_backward(mdct_lookup *init, DATA_TYPE *in, DATA_TYPE *out){
 398   int n=init->n;
 399   int n2=n>>1;
 400   int n4=n>>2;
 401
 402   /* rotate */
 403
 404   DATA_TYPE *iX = in+n2-7;
 405   DATA_TYPE *oX = out+n2+n4;
 406   DATA_TYPE *T  = init->trig+n4;
 407
 408   do{
 409     oX         -= 4;
 410     oX[0]       = MULT_NORM(-iX[2] * T[3] - iX[0]  * T[2]);
 411     oX[1]       = MULT_NORM (iX[0] * T[3] - iX[2]  * T[2]);
 412     oX[2]       = MULT_NORM(-iX[6] * T[1] - iX[4]  * T[0]);
 413     oX[3]       = MULT_NORM (iX[4] * T[1] - iX[6]  * T[0]);
 414     iX         -= 8;
 415     T          += 4;
 416   }while(iX>=in);
 417
 418   iX            = in+n2-8;
 419   oX            = out+n2+n4;
 420   T             = init->trig+n4;
 421
 422   do{
 423     T          -= 4;
 424     oX[0]       =  MULT_NORM (iX[4] * T[3] + iX[6] * T[2]);
 425     oX[1]       =  MULT_NORM (iX[4] * T[2] - iX[6] * T[3]);
 426     oX[2]       =  MULT_NORM (iX[0] * T[1] + iX[2] * T[0]);
 427     oX[3]       =  MULT_NORM (iX[0] * T[0] - iX[2] * T[1]);
 428     iX         -= 8;
 429     oX         += 4;
 430   }while(iX>=in);
 431
 432   mdct_butterflies(init,out+n2,n2);
 433   mdct_bitreverse(init,out);
 434
 435   /* roatate + window */
 436
 437   {
 438     DATA_TYPE *oX1=out+n2+n4;
 439     DATA_TYPE *oX2=out+n2+n4;
 440     DATA_TYPE *iX =out;
 441     T             =init->trig+n2;
 442
 443     do{
 444       oX1-=4;
 445
 446       oX1[3]  =  MULT_NORM (iX[0] * T[1] - iX[1] * T[0]);
 447       oX2[0]  = -MULT_NORM (iX[0] * T[0] + iX[1] * T[1]);
 448
 449       oX1[2]  =  MULT_NORM (iX[2] * T[3] - iX[3] * T[2]);
 450       oX2[1]  = -MULT_NORM (iX[2] * T[2] + iX[3] * T[3]);
 451
 452       oX1[1]  =  MULT_NORM (iX[4] * T[5] - iX[5] * T[4]);
 453       oX2[2]  = -MULT_NORM (iX[4] * T[4] + iX[5] * T[5]);
 454
 455       oX1[0]  =  MULT_NORM (iX[6] * T[7] - iX[7] * T[6]);
 456       oX2[3]  = -MULT_NORM (iX[6] * T[6] + iX[7] * T[7]);
 457
 458       oX2+=4;
 459       iX    +=   8;
 460       T     +=   8;
 461     }while(iX<oX1);
 462
 463     iX=out+n2+n4;
 464     oX1=out+n4;
 465     oX2=oX1;
 466
 467     do{
 468       oX1-=4;
 469       iX-=4;
 470
 471       oX2[0] = -(oX1[3] = iX[3]);
 472       oX2[1] = -(oX1[2] = iX[2]);
 473       oX2[2] = -(oX1[1] = iX[1]);
 474       oX2[3] = -(oX1[0] = iX[0]);
 475
 476       oX2+=4;
 477     }while(oX2<iX);
 478
 479     iX=out+n2+n4;
 480     oX1=out+n2+n4;
 481     oX2=out+n2;
 482     do{
 483       oX1-=4;
 484       oX1[0]= iX[3];
 485       oX1[1]= iX[2];
 486       oX1[2]= iX[1];
 487       oX1[3]= iX[0];
 488       iX+=4;
 489     }while(oX1>oX2);
 490   }
 491 }
 492
 493 void mdct_forward(mdct_lookup *init, DATA_TYPE *in, DATA_TYPE *out){
 494   int n=init->n;
 495   int n2=n>>1;
 496   int n4=n>>2;
 497   int n8=n>>3;
 498   DATA_TYPE *w=alloca(n*sizeof(*w)); /* forward needs working space */
 499   DATA_TYPE *w2=w+n2;
 500
 501   /* rotate */
 502
 503   /* window + rotate + step 1 */
 504
 505   REG_TYPE r0;
 506   REG_TYPE r1;
 507   DATA_TYPE *x0=in+n2+n4;
 508   DATA_TYPE *x1=x0+1;
 509   DATA_TYPE *T=init->trig+n2;
 510
 511   int i=0;
 512
 513   for(i=0;i<n8;i+=2){
 514     x0 -=4;
 515     T-=2;
 516     r0= x0[2] + x1[0];
 517     r1= x0[0] + x1[2];
 518     w2[i]=   MULT_NORM(r1*T[1] + r0*T[0]);
 519     w2[i+1]= MULT_NORM(r1*T[0] - r0*T[1]);
 520     x1 +=4;
 521   }
 522
 523   x1=in+1;
 524
 525   for(;i<n2-n8;i+=2){
 526     T-=2;
 527     x0 -=4;
 528     r0= x0[2] - x1[0];
 529     r1= x0[0] - x1[2];
 530     w2[i]=   MULT_NORM(r1*T[1] + r0*T[0]);
 531     w2[i+1]= MULT_NORM(r1*T[0] - r0*T[1]);
 532     x1 +=4;
 533   }
 534
 535   x0=in+n;
 536
 537   for(;i<n2;i+=2){
 538     T-=2;
 539     x0 -=4;
 540     r0= -x0[2] - x1[0];
 541     r1= -x0[0] - x1[2];
 542     w2[i]=   MULT_NORM(r1*T[1] + r0*T[0]);
 543     w2[i+1]= MULT_NORM(r1*T[0] - r0*T[1]);
 544     x1 +=4;
 545   }
 546
 547
 548   mdct_butterflies(init,w+n2,n2);
 549   mdct_bitreverse(init,w);
 550
 551   /* roatate + window */
 552
 553   T=init->trig+n2;
 554   x0=out+n2;
 555
 556   for(i=0;i<n4;i++){
 557     x0--;
 558     out[i] =MULT_NORM((w[0]*T[0]+w[1]*T[1])*init->scale);
 559     x0[0]  =MULT_NORM((w[0]*T[1]-w[1]*T[0])*init->scale);
 560     w+=2;
 561     T+=2;
 562   }
 563 }