lsp.c (12341B)
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 1994-2002 * 9 * by the XIPHOPHORUS Company http://www.xiph.org/ * 10 * * 11 ******************************************************************** 12 13 function: LSP (also called LSF) conversion routines 14 last mod: $Id: lsp.c 1919 2005-07-24 14:18:04Z baford $ 15 16 The LSP generation code is taken (with minimal modification and a 17 few bugfixes) from "On the Computation of the LSP Frequencies" by 18 Joseph Rothweiler (see http://www.rothweiler.us for contact info). 19 The paper is available at: 20 21 http://www.myown1.com/joe/lsf 22 23 ********************************************************************/ 24 25 /* Note that the lpc-lsp conversion finds the roots of polynomial with 26 an iterative root polisher (CACM algorithm 283). It *is* possible 27 to confuse this algorithm into not converging; that should only 28 happen with absurdly closely spaced roots (very sharp peaks in the 29 LPC f response) which in turn should be impossible in our use of 30 the code. If this *does* happen anyway, it's a bug in the floor 31 finder; find the cause of the confusion (probably a single bin 32 spike or accidental near-float-limit resolution problems) and 33 correct it. */ 34 35 #include <math.h> 36 #include <string.h> 37 #include <stdlib.h> 38 #include "lsp.h" 39 #include "os.h" 40 #include "misc.h" 41 #include "lookup.h" 42 #include "scales.h" 43 44 /* three possible LSP to f curve functions; the exact computation 45 (float), a lookup based float implementation, and an integer 46 implementation. The float lookup is likely the optimal choice on 47 any machine with an FPU. The integer implementation is *not* fixed 48 point (due to the need for a large dynamic range and thus a 49 seperately tracked exponent) and thus much more complex than the 50 relatively simple float implementations. It's mostly for future 51 work on a fully fixed point implementation for processors like the 52 ARM family. */ 53 54 /* undefine both for the 'old' but more precise implementation */ 55 #define FLOAT_LOOKUP 56 #undef INT_LOOKUP 57 58 #ifdef FLOAT_LOOKUP 59 #include "lookup.c" /* catch this in the build system; we #include for 60 compilers (like gcc) that can't inline across 61 modules */ 62 63 /* side effect: changes *lsp to cosines of lsp */ 64 void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m, 65 float amp,float ampoffset){ 66 int i; 67 float wdel=M_PI/ln; 68 vorbis_fpu_control fpu; 69 70 vorbis_fpu_setround(&fpu); 71 for(i=0;i<m;i++)lsp[i]=vorbis_coslook(lsp[i]); 72 73 i=0; 74 while(i<n){ 75 int k=map[i]; 76 int qexp; 77 float p=.7071067812f; 78 float q=.7071067812f; 79 float w=vorbis_coslook(wdel*k); 80 float *ftmp=lsp; 81 int c=m>>1; 82 83 do{ 84 q*=ftmp[0]-w; 85 p*=ftmp[1]-w; 86 ftmp+=2; 87 }while(--c); 88 89 if(m&1){ 90 /* odd order filter; slightly assymetric */ 91 /* the last coefficient */ 92 q*=ftmp[0]-w; 93 q*=q; 94 p*=p*(1.f-w*w); 95 }else{ 96 /* even order filter; still symmetric */ 97 q*=q*(1.f+w); 98 p*=p*(1.f-w); 99 } 100 101 q=frexp(p+q,&qexp); 102 q=vorbis_fromdBlook(amp* 103 vorbis_invsqlook(q)* 104 vorbis_invsq2explook(qexp+m)- 105 ampoffset); 106 107 do{ 108 curve[i++]*=q; 109 }while(map[i]==k); 110 } 111 vorbis_fpu_restore(fpu); 112 } 113 114 #else 115 116 #ifdef INT_LOOKUP 117 #include "lookup.c" /* catch this in the build system; we #include for 118 compilers (like gcc) that can't inline across 119 modules */ 120 121 static int MLOOP_1[64]={ 122 0,10,11,11, 12,12,12,12, 13,13,13,13, 13,13,13,13, 123 14,14,14,14, 14,14,14,14, 14,14,14,14, 14,14,14,14, 124 15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15, 125 15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15, 126 }; 127 128 static int MLOOP_2[64]={ 129 0,4,5,5, 6,6,6,6, 7,7,7,7, 7,7,7,7, 130 8,8,8,8, 8,8,8,8, 8,8,8,8, 8,8,8,8, 131 9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9, 132 9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9, 133 }; 134 135 static int MLOOP_3[8]={0,1,2,2,3,3,3,3}; 136 137 138 /* side effect: changes *lsp to cosines of lsp */ 139 void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m, 140 float amp,float ampoffset){ 141 142 /* 0 <= m < 256 */ 143 144 /* set up for using all int later */ 145 int i; 146 int ampoffseti=rint(ampoffset*4096.f); 147 int ampi=rint(amp*16.f); 148 long *ilsp=alloca(m*sizeof(*ilsp)); 149 for(i=0;i<m;i++)ilsp[i]=vorbis_coslook_i(lsp[i]/M_PI*65536.f+.5f); 150 151 i=0; 152 while(i<n){ 153 int j,k=map[i]; 154 unsigned long pi=46341; /* 2**-.5 in 0.16 */ 155 unsigned long qi=46341; 156 int qexp=0,shift; 157 long wi=vorbis_coslook_i(k*65536/ln); 158 159 qi*=labs(ilsp[0]-wi); 160 pi*=labs(ilsp[1]-wi); 161 162 for(j=3;j<m;j+=2){ 163 if(!(shift=MLOOP_1[(pi|qi)>>25])) 164 if(!(shift=MLOOP_2[(pi|qi)>>19])) 165 shift=MLOOP_3[(pi|qi)>>16]; 166 qi=(qi>>shift)*labs(ilsp[j-1]-wi); 167 pi=(pi>>shift)*labs(ilsp[j]-wi); 168 qexp+=shift; 169 } 170 if(!(shift=MLOOP_1[(pi|qi)>>25])) 171 if(!(shift=MLOOP_2[(pi|qi)>>19])) 172 shift=MLOOP_3[(pi|qi)>>16]; 173 174 /* pi,qi normalized collectively, both tracked using qexp */ 175 176 if(m&1){ 177 /* odd order filter; slightly assymetric */ 178 /* the last coefficient */ 179 qi=(qi>>shift)*labs(ilsp[j-1]-wi); 180 pi=(pi>>shift)<<14; 181 qexp+=shift; 182 183 if(!(shift=MLOOP_1[(pi|qi)>>25])) 184 if(!(shift=MLOOP_2[(pi|qi)>>19])) 185 shift=MLOOP_3[(pi|qi)>>16]; 186 187 pi>>=shift; 188 qi>>=shift; 189 qexp+=shift-14*((m+1)>>1); 190 191 pi=((pi*pi)>>16); 192 qi=((qi*qi)>>16); 193 qexp=qexp*2+m; 194 195 pi*=(1<<14)-((wi*wi)>>14); 196 qi+=pi>>14; 197 198 }else{ 199 /* even order filter; still symmetric */ 200 201 /* p*=p(1-w), q*=q(1+w), let normalization drift because it isn't 202 worth tracking step by step */ 203 204 pi>>=shift; 205 qi>>=shift; 206 qexp+=shift-7*m; 207 208 pi=((pi*pi)>>16); 209 qi=((qi*qi)>>16); 210 qexp=qexp*2+m; 211 212 pi*=(1<<14)-wi; 213 qi*=(1<<14)+wi; 214 qi=(qi+pi)>>14; 215 216 } 217 218 219 /* we've let the normalization drift because it wasn't important; 220 however, for the lookup, things must be normalized again. We 221 need at most one right shift or a number of left shifts */ 222 223 if(qi&0xffff0000){ /* checks for 1.xxxxxxxxxxxxxxxx */ 224 qi>>=1; qexp++; 225 }else 226 while(qi && !(qi&0x8000)){ /* checks for 0.0xxxxxxxxxxxxxxx or less*/ 227 qi<<=1; qexp--; 228 } 229 230 amp=vorbis_fromdBlook_i(ampi* /* n.4 */ 231 vorbis_invsqlook_i(qi,qexp)- 232 /* m.8, m+n<=8 */ 233 ampoffseti); /* 8.12[0] */ 234 235 curve[i]*=amp; 236 while(map[++i]==k)curve[i]*=amp; 237 } 238 } 239 240 #else 241 242 /* old, nonoptimized but simple version for any poor sap who needs to 243 figure out what the hell this code does, or wants the other 244 fraction of a dB precision */ 245 246 /* side effect: changes *lsp to cosines of lsp */ 247 void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m, 248 float amp,float ampoffset){ 249 int i; 250 float wdel=M_PI/ln; 251 for(i=0;i<m;i++)lsp[i]=2.f*cos(lsp[i]); 252 253 i=0; 254 while(i<n){ 255 int j,k=map[i]; 256 float p=.5f; 257 float q=.5f; 258 float w=2.f*cos(wdel*k); 259 for(j=1;j<m;j+=2){ 260 q *= w-lsp[j-1]; 261 p *= w-lsp[j]; 262 } 263 if(j==m){ 264 /* odd order filter; slightly assymetric */ 265 /* the last coefficient */ 266 q*=w-lsp[j-1]; 267 p*=p*(4.f-w*w); 268 q*=q; 269 }else{ 270 /* even order filter; still symmetric */ 271 p*=p*(2.f-w); 272 q*=q*(2.f+w); 273 } 274 275 q=fromdB(amp/sqrt(p+q)-ampoffset); 276 277 curve[i]*=q; 278 while(map[++i]==k)curve[i]*=q; 279 } 280 } 281 282 #endif 283 #endif 284 285 static void cheby(float *g, int ord) { 286 int i, j; 287 288 g[0] *= .5f; 289 for(i=2; i<= ord; i++) { 290 for(j=ord; j >= i; j--) { 291 g[j-2] -= g[j]; 292 g[j] += g[j]; 293 } 294 } 295 } 296 297 static int comp(const void *a,const void *b){ 298 return (*(float *)a<*(float *)b)-(*(float *)a>*(float *)b); 299 } 300 301 /* Newton-Raphson-Maehly actually functioned as a decent root finder, 302 but there are root sets for which it gets into limit cycles 303 (exacerbated by zero suppression) and fails. We can't afford to 304 fail, even if the failure is 1 in 100,000,000, so we now use 305 Laguerre and later polish with Newton-Raphson (which can then 306 afford to fail) */ 307 308 #define EPSILON 10e-7 309 static int Laguerre_With_Deflation(float *a,int ord,float *r){ 310 int i,m; 311 double lastdelta=0.f; 312 double *defl=alloca(sizeof(*defl)*(ord+1)); 313 for(i=0;i<=ord;i++)defl[i]=a[i]; 314 315 for(m=ord;m>0;m--){ 316 double new=0.f,delta; 317 318 /* iterate a root */ 319 while(1){ 320 double p=defl[m],pp=0.f,ppp=0.f,denom; 321 322 /* eval the polynomial and its first two derivatives */ 323 for(i=m;i>0;i--){ 324 ppp = new*ppp + pp; 325 pp = new*pp + p; 326 p = new*p + defl[i-1]; 327 } 328 329 /* Laguerre's method */ 330 denom=(m-1) * ((m-1)*pp*pp - m*p*ppp); 331 if(denom<0) 332 return(-1); /* complex root! The LPC generator handed us a bad filter */ 333 334 if(pp>0){ 335 denom = pp + sqrt(denom); 336 if(denom<EPSILON)denom=EPSILON; 337 }else{ 338 denom = pp - sqrt(denom); 339 if(denom>-(EPSILON))denom=-(EPSILON); 340 } 341 342 delta = m*p/denom; 343 new -= delta; 344 345 if(delta<0.f)delta*=-1; 346 347 if(fabs(delta/new)<10e-12)break; 348 lastdelta=delta; 349 } 350 351 r[m-1]=new; 352 353 /* forward deflation */ 354 355 for(i=m;i>0;i--) 356 defl[i-1]+=new*defl[i]; 357 defl++; 358 359 } 360 return(0); 361 } 362 363 364 /* for spit-and-polish only */ 365 static int Newton_Raphson(float *a,int ord,float *r){ 366 int i, k, count=0; 367 double error=1.f; 368 double *root=alloca(ord*sizeof(*root)); 369 370 for(i=0; i<ord;i++) root[i] = r[i]; 371 372 while(error>1e-20){ 373 error=0; 374 375 for(i=0; i<ord; i++) { /* Update each point. */ 376 double pp=0.,delta; 377 double rooti=root[i]; 378 double p=a[ord]; 379 for(k=ord-1; k>= 0; k--) { 380 381 pp= pp* rooti + p; 382 p = p * rooti + a[k]; 383 } 384 385 delta = p/pp; 386 root[i] -= delta; 387 error+= delta*delta; 388 } 389 390 if(count>40)return(-1); 391 392 count++; 393 } 394 395 /* Replaced the original bubble sort with a real sort. With your 396 help, we can eliminate the bubble sort in our lifetime. --Monty */ 397 398 for(i=0; i<ord;i++) r[i] = root[i]; 399 return(0); 400 } 401 402 403 /* Convert lpc coefficients to lsp coefficients */ 404 int vorbis_lpc_to_lsp(float *lpc,float *lsp,int m){ 405 int order2=(m+1)>>1; 406 int g1_order,g2_order; 407 float *g1=alloca(sizeof(*g1)*(order2+1)); 408 float *g2=alloca(sizeof(*g2)*(order2+1)); 409 float *g1r=alloca(sizeof(*g1r)*(order2+1)); 410 float *g2r=alloca(sizeof(*g2r)*(order2+1)); 411 int i; 412 413 /* even and odd are slightly different base cases */ 414 g1_order=(m+1)>>1; 415 g2_order=(m) >>1; 416 417 /* Compute the lengths of the x polynomials. */ 418 /* Compute the first half of K & R F1 & F2 polynomials. */ 419 /* Compute half of the symmetric and antisymmetric polynomials. */ 420 /* Remove the roots at +1 and -1. */ 421 422 g1[g1_order] = 1.f; 423 for(i=1;i<=g1_order;i++) g1[g1_order-i] = lpc[i-1]+lpc[m-i]; 424 g2[g2_order] = 1.f; 425 for(i=1;i<=g2_order;i++) g2[g2_order-i] = lpc[i-1]-lpc[m-i]; 426 427 if(g1_order>g2_order){ 428 for(i=2; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+2]; 429 }else{ 430 for(i=1; i<=g1_order;i++) g1[g1_order-i] -= g1[g1_order-i+1]; 431 for(i=1; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+1]; 432 } 433 434 /* Convert into polynomials in cos(alpha) */ 435 cheby(g1,g1_order); 436 cheby(g2,g2_order); 437 438 /* Find the roots of the 2 even polynomials.*/ 439 if(Laguerre_With_Deflation(g1,g1_order,g1r) || 440 Laguerre_With_Deflation(g2,g2_order,g2r)) 441 return(-1); 442 443 Newton_Raphson(g1,g1_order,g1r); /* if it fails, it leaves g1r alone */ 444 Newton_Raphson(g2,g2_order,g2r); /* if it fails, it leaves g2r alone */ 445 446 qsort(g1r,g1_order,sizeof(*g1r),comp); 447 qsort(g2r,g2_order,sizeof(*g2r),comp); 448 449 for(i=0;i<g1_order;i++) 450 lsp[i*2] = acos(g1r[i]); 451 452 for(i=0;i<g2_order;i++) 453 lsp[i*2+1] = acos(g2r[i]); 454 return(0); 455 }