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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: LSP (also called LSF) conversion routines
+
+ The LSP generation code is taken (with minimal modification and a
+ few bugfixes) from "On the Computation of the LSP Frequencies" by
+ Joseph Rothweiler (see http://www.rothweiler.us for contact info).
+ The paper is available at:
+
+ http://www.myown1.com/joe/lsf
+
+ ********************************************************************/
+
+/* Note that the lpc-lsp conversion finds the roots of polynomial with
+ an iterative root polisher (CACM algorithm 283). It *is* possible
+ to confuse this algorithm into not converging; that should only
+ happen with absurdly closely spaced roots (very sharp peaks in the
+ LPC f response) which in turn should be impossible in our use of
+ the code. If this *does* happen anyway, it's a bug in the floor
+ finder; find the cause of the confusion (probably a single bin
+ spike or accidental near-float-limit resolution problems) and
+ correct it. */
+
+#include <math.h>
+#include <string.h>
+#include <stdlib.h>
+#include "lsp.h"
+#include "os.h"
+#include "misc.h"
+#include "lookup.h"
+#include "scales.h"
+
+/* three possible LSP to f curve functions; the exact computation
+ (float), a lookup based float implementation, and an integer
+ implementation. The float lookup is likely the optimal choice on
+ any machine with an FPU. The integer implementation is *not* fixed
+ point (due to the need for a large dynamic range and thus a
+ separately tracked exponent) and thus much more complex than the
+ relatively simple float implementations. It's mostly for future
+ work on a fully fixed point implementation for processors like the
+ ARM family. */
+
+/* define either of these (preferably FLOAT_LOOKUP) to have faster
+ but less precise implementation. */
+#undef FLOAT_LOOKUP
+#undef INT_LOOKUP
+
+#ifdef FLOAT_LOOKUP
+#include "lookup.c" /* catch this in the build system; we #include for
+ compilers (like gcc) that can't inline across
+ modules */
+
+/* side effect: changes *lsp to cosines of lsp */
+void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
+ float amp,float ampoffset){
+ int i;
+ float wdel=M_PI/ln;
+ vorbis_fpu_control fpu;
+
+ vorbis_fpu_setround(&fpu);
+ for(i=0;i<m;i++)lsp[i]=vorbis_coslook(lsp[i]);
+
+ i=0;
+ while(i<n){
+ int k=map[i];
+ int qexp;
+ float p=.7071067812f;
+ float q=.7071067812f;
+ float w=vorbis_coslook(wdel*k);
+ float *ftmp=lsp;
+ int c=m>>1;
+
+ while(c--){
+ q*=ftmp[0]-w;
+ p*=ftmp[1]-w;
+ ftmp+=2;
+ }
+
+ if(m&1){
+ /* odd order filter; slightly assymetric */
+ /* the last coefficient */
+ q*=ftmp[0]-w;
+ q*=q;
+ p*=p*(1.f-w*w);
+ }else{
+ /* even order filter; still symmetric */
+ q*=q*(1.f+w);
+ p*=p*(1.f-w);
+ }
+
+ q=frexp(p+q,&qexp);
+ q=vorbis_fromdBlook(amp*
+ vorbis_invsqlook(q)*
+ vorbis_invsq2explook(qexp+m)-
+ ampoffset);
+
+ do{
+ curve[i++]*=q;
+ }while(map[i]==k);
+ }
+ vorbis_fpu_restore(fpu);
+}
+
+#else
+
+#ifdef INT_LOOKUP
+#include "lookup.c" /* catch this in the build system; we #include for
+ compilers (like gcc) that can't inline across
+ modules */
+
+static const int MLOOP_1[64]={
+ 0,10,11,11, 12,12,12,12, 13,13,13,13, 13,13,13,13,
+ 14,14,14,14, 14,14,14,14, 14,14,14,14, 14,14,14,14,
+ 15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15,
+ 15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15,
+};
+
+static const int MLOOP_2[64]={
+ 0,4,5,5, 6,6,6,6, 7,7,7,7, 7,7,7,7,
+ 8,8,8,8, 8,8,8,8, 8,8,8,8, 8,8,8,8,
+ 9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9,
+ 9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9,
+};
+
+static const int MLOOP_3[8]={0,1,2,2,3,3,3,3};
+
+
+/* side effect: changes *lsp to cosines of lsp */
+void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
+ float amp,float ampoffset){
+
+ /* 0 <= m < 256 */
+
+ /* set up for using all int later */
+ int i;
+ int ampoffseti=rint(ampoffset*4096.f);
+ int ampi=rint(amp*16.f);
+ long *ilsp=alloca(m*sizeof(*ilsp));
+ for(i=0;i<m;i++)ilsp[i]=vorbis_coslook_i(lsp[i]/M_PI*65536.f+.5f);
+
+ i=0;
+ while(i<n){
+ int j,k=map[i];
+ unsigned long pi=46341; /* 2**-.5 in 0.16 */
+ unsigned long qi=46341;
+ int qexp=0,shift;
+ long wi=vorbis_coslook_i(k*65536/ln);
+
+ qi*=labs(ilsp[0]-wi);
+ pi*=labs(ilsp[1]-wi);
+
+ for(j=3;j<m;j+=2){
+ if(!(shift=MLOOP_1[(pi|qi)>>25]))
+ if(!(shift=MLOOP_2[(pi|qi)>>19]))
+ shift=MLOOP_3[(pi|qi)>>16];
+ qi=(qi>>shift)*labs(ilsp[j-1]-wi);
+ pi=(pi>>shift)*labs(ilsp[j]-wi);
+ qexp+=shift;
+ }
+ if(!(shift=MLOOP_1[(pi|qi)>>25]))
+ if(!(shift=MLOOP_2[(pi|qi)>>19]))
+ shift=MLOOP_3[(pi|qi)>>16];
+
+ /* pi,qi normalized collectively, both tracked using qexp */
+
+ if(m&1){
+ /* odd order filter; slightly assymetric */
+ /* the last coefficient */
+ qi=(qi>>shift)*labs(ilsp[j-1]-wi);
+ pi=(pi>>shift)<<14;
+ qexp+=shift;
+
+ if(!(shift=MLOOP_1[(pi|qi)>>25]))
+ if(!(shift=MLOOP_2[(pi|qi)>>19]))
+ shift=MLOOP_3[(pi|qi)>>16];
+
+ pi>>=shift;
+ qi>>=shift;
+ qexp+=shift-14*((m+1)>>1);
+
+ pi=((pi*pi)>>16);
+ qi=((qi*qi)>>16);
+ qexp=qexp*2+m;
+
+ pi*=(1<<14)-((wi*wi)>>14);
+ qi+=pi>>14;
+
+ }else{
+ /* even order filter; still symmetric */
+
+ /* p*=p(1-w), q*=q(1+w), let normalization drift because it isn't
+ worth tracking step by step */
+
+ pi>>=shift;
+ qi>>=shift;
+ qexp+=shift-7*m;
+
+ pi=((pi*pi)>>16);
+ qi=((qi*qi)>>16);
+ qexp=qexp*2+m;
+
+ pi*=(1<<14)-wi;
+ qi*=(1<<14)+wi;
+ qi=(qi+pi)>>14;
+
+ }
+
+
+ /* we've let the normalization drift because it wasn't important;
+ however, for the lookup, things must be normalized again. We
+ need at most one right shift or a number of left shifts */
+
+ if(qi&0xffff0000){ /* checks for 1.xxxxxxxxxxxxxxxx */
+ qi>>=1; qexp++;
+ }else
+ while(qi && !(qi&0x8000)){ /* checks for 0.0xxxxxxxxxxxxxxx or less*/
+ qi<<=1; qexp--;
+ }
+
+ amp=vorbis_fromdBlook_i(ampi* /* n.4 */
+ vorbis_invsqlook_i(qi,qexp)-
+ /* m.8, m+n<=8 */
+ ampoffseti); /* 8.12[0] */
+
+ curve[i]*=amp;
+ while(map[++i]==k)curve[i]*=amp;
+ }
+}
+
+#else
+
+/* old, nonoptimized but simple version for any poor sap who needs to
+ figure out what the hell this code does, or wants the other
+ fraction of a dB precision */
+
+/* side effect: changes *lsp to cosines of lsp */
+void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
+ float amp,float ampoffset){
+ int i;
+ float wdel=M_PI/ln;
+ for(i=0;i<m;i++)lsp[i]=2.f*cos(lsp[i]);
+
+ i=0;
+ while(i<n){
+ int j,k=map[i];
+ float p=.5f;
+ float q=.5f;
+ float w=2.f*cos(wdel*k);
+ for(j=1;j<m;j+=2){
+ q *= w-lsp[j-1];
+ p *= w-lsp[j];
+ }
+ if(j==m){
+ /* odd order filter; slightly assymetric */
+ /* the last coefficient */
+ q*=w-lsp[j-1];
+ p*=p*(4.f-w*w);
+ q*=q;
+ }else{
+ /* even order filter; still symmetric */
+ p*=p*(2.f-w);
+ q*=q*(2.f+w);
+ }
+
+ q=fromdB(amp/sqrt(p+q)-ampoffset);
+
+ curve[i]*=q;
+ while(map[++i]==k)curve[i]*=q;
+ }
+}
+
+#endif
+#endif
+
+static void cheby(float *g, int ord) {
+ int i, j;
+
+ g[0] *= .5f;
+ for(i=2; i<= ord; i++) {
+ for(j=ord; j >= i; j--) {
+ g[j-2] -= g[j];
+ g[j] += g[j];
+ }
+ }
+}
+
+static int comp(const void *a,const void *b){
+ return (*(float *)a<*(float *)b)-(*(float *)a>*(float *)b);
+}
+
+/* Newton-Raphson-Maehly actually functioned as a decent root finder,
+ but there are root sets for which it gets into limit cycles
+ (exacerbated by zero suppression) and fails. We can't afford to
+ fail, even if the failure is 1 in 100,000,000, so we now use
+ Laguerre and later polish with Newton-Raphson (which can then
+ afford to fail) */
+
+#define EPSILON 10e-7
+static int Laguerre_With_Deflation(float *a,int ord,float *r){
+ int i,m;
+ double *defl=alloca(sizeof(*defl)*(ord+1));
+ for(i=0;i<=ord;i++)defl[i]=a[i];
+
+ for(m=ord;m>0;m--){
+ double new=0.f,delta;
+
+ /* iterate a root */
+ while(1){
+ double p=defl[m],pp=0.f,ppp=0.f,denom;
+
+ /* eval the polynomial and its first two derivatives */
+ for(i=m;i>0;i--){
+ ppp = new*ppp + pp;
+ pp = new*pp + p;
+ p = new*p + defl[i-1];
+ }
+
+ /* Laguerre's method */
+ denom=(m-1) * ((m-1)*pp*pp - m*p*ppp);
+ if(denom<0)
+ return(-1); /* complex root! The LPC generator handed us a bad filter */
+
+ if(pp>0){
+ denom = pp + sqrt(denom);
+ if(denom<EPSILON)denom=EPSILON;
+ }else{
+ denom = pp - sqrt(denom);
+ if(denom>-(EPSILON))denom=-(EPSILON);
+ }
+
+ delta = m*p/denom;
+ new -= delta;
+
+ if(delta<0.f)delta*=-1;
+
+ if(fabs(delta/new)<10e-12)break;
+ }
+
+ r[m-1]=new;
+
+ /* forward deflation */
+
+ for(i=m;i>0;i--)
+ defl[i-1]+=new*defl[i];
+ defl++;
+
+ }
+ return(0);
+}
+
+
+/* for spit-and-polish only */
+static int Newton_Raphson(float *a,int ord,float *r){
+ int i, k, count=0;
+ double error=1.f;
+ double *root=alloca(ord*sizeof(*root));
+
+ for(i=0; i<ord;i++) root[i] = r[i];
+
+ while(error>1e-20){
+ error=0;
+
+ for(i=0; i<ord; i++) { /* Update each point. */
+ double pp=0.,delta;
+ double rooti=root[i];
+ double p=a[ord];
+ for(k=ord-1; k>= 0; k--) {
+
+ pp= pp* rooti + p;
+ p = p * rooti + a[k];
+ }
+
+ delta = p/pp;
+ root[i] -= delta;
+ error+= delta*delta;
+ }
+
+ if(count>40)return(-1);
+
+ count++;
+ }
+
+ /* Replaced the original bubble sort with a real sort. With your
+ help, we can eliminate the bubble sort in our lifetime. --Monty */
+
+ for(i=0; i<ord;i++) r[i] = root[i];
+ return(0);
+}
+
+
+/* Convert lpc coefficients to lsp coefficients */
+int vorbis_lpc_to_lsp(float *lpc,float *lsp,int m){
+ int order2=(m+1)>>1;
+ int g1_order,g2_order;
+ float *g1=alloca(sizeof(*g1)*(order2+1));
+ float *g2=alloca(sizeof(*g2)*(order2+1));
+ float *g1r=alloca(sizeof(*g1r)*(order2+1));
+ float *g2r=alloca(sizeof(*g2r)*(order2+1));
+ int i;
+
+ /* even and odd are slightly different base cases */
+ g1_order=(m+1)>>1;
+ g2_order=(m) >>1;
+
+ /* Compute the lengths of the x polynomials. */
+ /* Compute the first half of K & R F1 & F2 polynomials. */
+ /* Compute half of the symmetric and antisymmetric polynomials. */
+ /* Remove the roots at +1 and -1. */
+
+ g1[g1_order] = 1.f;
+ for(i=1;i<=g1_order;i++) g1[g1_order-i] = lpc[i-1]+lpc[m-i];
+ g2[g2_order] = 1.f;
+ for(i=1;i<=g2_order;i++) g2[g2_order-i] = lpc[i-1]-lpc[m-i];
+
+ if(g1_order>g2_order){
+ for(i=2; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+2];
+ }else{
+ for(i=1; i<=g1_order;i++) g1[g1_order-i] -= g1[g1_order-i+1];
+ for(i=1; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+1];
+ }
+
+ /* Convert into polynomials in cos(alpha) */
+ cheby(g1,g1_order);
+ cheby(g2,g2_order);
+
+ /* Find the roots of the 2 even polynomials.*/
+ if(Laguerre_With_Deflation(g1,g1_order,g1r) ||
+ Laguerre_With_Deflation(g2,g2_order,g2r))
+ return(-1);
+
+ Newton_Raphson(g1,g1_order,g1r); /* if it fails, it leaves g1r alone */
+ Newton_Raphson(g2,g2_order,g2r); /* if it fails, it leaves g2r alone */
+
+ qsort(g1r,g1_order,sizeof(*g1r),comp);
+ qsort(g2r,g2_order,sizeof(*g2r),comp);
+
+ for(i=0;i<g1_order;i++)
+ lsp[i*2] = acos(g1r[i]);
+
+ for(i=0;i<g2_order;i++)
+ lsp[i*2+1] = acos(g2r[i]);
+ return(0);
+}
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