1 /********************************************************************
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. *
8 * THE OggVorbis SOURCE CODE IS (C) COPYRIGHT 1994-2009 *
9 * by the Xiph.Org Foundation http://www.xiph.org/ *
11 ********************************************************************
13 function: LSP (also called LSF) conversion routines
14 last mod: $Id: lsp.c 17538 2010-10-15 02:52:29Z tterribe $
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:
21 http://www.myown1.com/joe/lsf
23 ********************************************************************/
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
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 separately 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
54 /* define either of these (preferably FLOAT_LOOKUP) to have faster
55 but less precise implementation. */
60 #include "lookup.c" /* catch this in the build system; we #include for
61 compilers (like gcc) that can't inline across
64 /* side effect: changes *lsp to cosines of lsp */
65 void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
66 float amp,float ampoffset){
69 vorbis_fpu_control fpu;
71 vorbis_fpu_setround(&fpu);
72 for(i=0;i<m;i++)lsp[i]=vorbis_coslook(lsp[i]);
80 float w=vorbis_coslook(wdel*k);
91 /* odd order filter; slightly assymetric */
92 /* the last coefficient */
97 /* even order filter; still symmetric */
103 q=vorbis_fromdBlook(amp*
105 vorbis_invsq2explook(qexp+m)-
112 vorbis_fpu_restore(fpu);
118 #include "lookup.c" /* catch this in the build system; we #include for
119 compilers (like gcc) that can't inline across
122 static const int MLOOP_1[64]={
123 0,10,11,11, 12,12,12,12, 13,13,13,13, 13,13,13,13,
124 14,14,14,14, 14,14,14,14, 14,14,14,14, 14,14,14,14,
125 15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15,
126 15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15,
129 static const int MLOOP_2[64]={
130 0,4,5,5, 6,6,6,6, 7,7,7,7, 7,7,7,7,
131 8,8,8,8, 8,8,8,8, 8,8,8,8, 8,8,8,8,
132 9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9,
133 9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9,
136 static const int MLOOP_3[8]={0,1,2,2,3,3,3,3};
139 /* side effect: changes *lsp to cosines of lsp */
140 void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
141 float amp,float ampoffset){
145 /* set up for using all int later */
147 int ampoffseti=rint(ampoffset*4096.f);
148 int ampi=rint(amp*16.f);
149 long *ilsp=alloca(m*sizeof(*ilsp));
150 for(i=0;i<m;i++)ilsp[i]=vorbis_coslook_i(lsp[i]/M_PI*65536.f+.5f);
155 unsigned long pi=46341; /* 2**-.5 in 0.16 */
156 unsigned long qi=46341;
158 long wi=vorbis_coslook_i(k*65536/ln);
160 qi*=labs(ilsp[0]-wi);
161 pi*=labs(ilsp[1]-wi);
164 if(!(shift=MLOOP_1[(pi|qi)>>25]))
165 if(!(shift=MLOOP_2[(pi|qi)>>19]))
166 shift=MLOOP_3[(pi|qi)>>16];
167 qi=(qi>>shift)*labs(ilsp[j-1]-wi);
168 pi=(pi>>shift)*labs(ilsp[j]-wi);
171 if(!(shift=MLOOP_1[(pi|qi)>>25]))
172 if(!(shift=MLOOP_2[(pi|qi)>>19]))
173 shift=MLOOP_3[(pi|qi)>>16];
175 /* pi,qi normalized collectively, both tracked using qexp */
178 /* odd order filter; slightly assymetric */
179 /* the last coefficient */
180 qi=(qi>>shift)*labs(ilsp[j-1]-wi);
184 if(!(shift=MLOOP_1[(pi|qi)>>25]))
185 if(!(shift=MLOOP_2[(pi|qi)>>19]))
186 shift=MLOOP_3[(pi|qi)>>16];
190 qexp+=shift-14*((m+1)>>1);
196 pi*=(1<<14)-((wi*wi)>>14);
200 /* even order filter; still symmetric */
202 /* p*=p(1-w), q*=q(1+w), let normalization drift because it isn't
203 worth tracking step by step */
220 /* we've let the normalization drift because it wasn't important;
221 however, for the lookup, things must be normalized again. We
222 need at most one right shift or a number of left shifts */
224 if(qi&0xffff0000){ /* checks for 1.xxxxxxxxxxxxxxxx */
227 while(qi && !(qi&0x8000)){ /* checks for 0.0xxxxxxxxxxxxxxx or less*/
231 amp=vorbis_fromdBlook_i(ampi* /* n.4 */
232 vorbis_invsqlook_i(qi,qexp)-
234 ampoffseti); /* 8.12[0] */
237 while(map[++i]==k)curve[i]*=amp;
243 /* old, nonoptimized but simple version for any poor sap who needs to
244 figure out what the hell this code does, or wants the other
245 fraction of a dB precision */
247 /* side effect: changes *lsp to cosines of lsp */
248 void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
249 float amp,float ampoffset){
252 for(i=0;i<m;i++)lsp[i]=2.f*cos(lsp[i]);
259 float w=2.f*cos(wdel*k);
265 /* odd order filter; slightly assymetric */
266 /* the last coefficient */
271 /* even order filter; still symmetric */
276 q=fromdB(amp/sqrt(p+q)-ampoffset);
279 while(map[++i]==k)curve[i]*=q;
286 static void cheby(float *g, int ord) {
290 for(i=2; i<= ord; i++) {
291 for(j=ord; j >= i; j--) {
298 static int comp(const void *a,const void *b){
299 return (*(float *)a<*(float *)b)-(*(float *)a>*(float *)b);
302 /* Newton-Raphson-Maehly actually functioned as a decent root finder,
303 but there are root sets for which it gets into limit cycles
304 (exacerbated by zero suppression) and fails. We can't afford to
305 fail, even if the failure is 1 in 100,000,000, so we now use
306 Laguerre and later polish with Newton-Raphson (which can then
309 #define EPSILON 10e-7
310 static int Laguerre_With_Deflation(float *a,int ord,float *r){
312 double *defl=alloca(sizeof(*defl)*(ord+1));
313 for(i=0;i<=ord;i++)defl[i]=a[i];
316 double new=0.f,delta;
320 double p=defl[m],pp=0.f,ppp=0.f,denom;
322 /* eval the polynomial and its first two derivatives */
326 p = new*p + defl[i-1];
329 /* Laguerre's method */
330 denom=(m-1) * ((m-1)*pp*pp - m*p*ppp);
332 return(-1); /* complex root! The LPC generator handed us a bad filter */
335 denom = pp + sqrt(denom);
336 if(denom<EPSILON)denom=EPSILON;
338 denom = pp - sqrt(denom);
339 if(denom>-(EPSILON))denom=-(EPSILON);
345 if(delta<0.f)delta*=-1;
347 if(fabs(delta/new)<10e-12)break;
352 /* forward deflation */
355 defl[i-1]+=new*defl[i];
363 /* for spit-and-polish only */
364 static int Newton_Raphson(float *a,int ord,float *r){
367 double *root=alloca(ord*sizeof(*root));
369 for(i=0; i<ord;i++) root[i] = r[i];
374 for(i=0; i<ord; i++) { /* Update each point. */
376 double rooti=root[i];
378 for(k=ord-1; k>= 0; k--) {
381 p = p * rooti + a[k];
389 if(count>40)return(-1);
394 /* Replaced the original bubble sort with a real sort. With your
395 help, we can eliminate the bubble sort in our lifetime. --Monty */
397 for(i=0; i<ord;i++) r[i] = root[i];
402 /* Convert lpc coefficients to lsp coefficients */
403 int vorbis_lpc_to_lsp(float *lpc,float *lsp,int m){
405 int g1_order,g2_order;
406 float *g1=alloca(sizeof(*g1)*(order2+1));
407 float *g2=alloca(sizeof(*g2)*(order2+1));
408 float *g1r=alloca(sizeof(*g1r)*(order2+1));
409 float *g2r=alloca(sizeof(*g2r)*(order2+1));
412 /* even and odd are slightly different base cases */
416 /* Compute the lengths of the x polynomials. */
417 /* Compute the first half of K & R F1 & F2 polynomials. */
418 /* Compute half of the symmetric and antisymmetric polynomials. */
419 /* Remove the roots at +1 and -1. */
422 for(i=1;i<=g1_order;i++) g1[g1_order-i] = lpc[i-1]+lpc[m-i];
424 for(i=1;i<=g2_order;i++) g2[g2_order-i] = lpc[i-1]-lpc[m-i];
426 if(g1_order>g2_order){
427 for(i=2; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+2];
429 for(i=1; i<=g1_order;i++) g1[g1_order-i] -= g1[g1_order-i+1];
430 for(i=1; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+1];
433 /* Convert into polynomials in cos(alpha) */
437 /* Find the roots of the 2 even polynomials.*/
438 if(Laguerre_With_Deflation(g1,g1_order,g1r) ||
439 Laguerre_With_Deflation(g2,g2_order,g2r))
442 Newton_Raphson(g1,g1_order,g1r); /* if it fails, it leaves g1r alone */
443 Newton_Raphson(g2,g2_order,g2r); /* if it fails, it leaves g2r alone */
445 qsort(g1r,g1_order,sizeof(*g1r),comp);
446 qsort(g2r,g2_order,sizeof(*g2r),comp);
448 for(i=0;i<g1_order;i++)
449 lsp[i*2] = acos(g1r[i]);
451 for(i=0;i<g2_order;i++)
452 lsp[i*2+1] = acos(g2r[i]);