/********************************************************************
* *
* 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 1994-2002 *
* by the XIPHOPHORUS Company http://www.xiph.org/ *
* *
********************************************************************
function: LSP (also called LSF) conversion routines
last mod: $Id: lsp.c 7187 2004-07-20 07:24:27Z xiphmont $
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
seperately 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. */
/* undefine both for the 'old' but more precise implementation */
#define 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;
do{
q*=ftmp[0]-w;
p*=ftmp[1]-w;
ftmp+=2;
}while(--c);
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 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 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 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);
#ifdef Plan9
long *ilsp=malloc(m*sizeof(*ilsp));
#else
long *ilsp=alloca(m*sizeof(*ilsp));
#endif
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;
}
#ifdef Plan9
free(ilsp);
#endif
}
#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 lastdelta=0.f;
#ifdef Plan9
double *defl=malloc(sizeof(*defl)*(ord+1));
#else
double *defl=alloca(sizeof(*defl)*(ord+1));
#endif
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);
#ifdef Plan9
if(denom<0){
free(defl);
return(-1);
}
#else
if(denom<0)
return(-1); /* complex root! The LPC generator handed us a bad filter */
#endif
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;
lastdelta=delta;
}
r[m-1]=new;
/* forward deflation */
for(i=m;i>0;i--)
defl[i-1]+=new*defl[i];
defl++;
}
#ifdef Plan9
free(defl);
#endif
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;
#ifdef Plan9
double *root=malloc(ord*sizeof(*root));
#else
double *root=alloca(ord*sizeof(*root));
#endif
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;
}
#ifdef Plan9
if(count>40){
free(root);
return(-1);
}
#else
if(count>40)return(-1);
#endif
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];
#ifdef Plan9
free(root);
#endif
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;
#ifdef Plan9
float *g1=malloc(sizeof(*g1)*(order2+1));
float *g2=malloc(sizeof(*g2)*(order2+1));
float *g1r=malloc(sizeof(*g1r)*(order2+1));
float *g2r=malloc(sizeof(*g2r)*(order2+1));
#else
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));
#endif
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.*/
#ifdef Plan9
if(Laguerre_With_Deflation(g1,g1_order,g1r) ||
Laguerre_With_Deflation(g2,g2_order,g2r)){
free(g1);
free(g2);
free(g1r);
free(g2r);
return(-1);
}
#else
if(Laguerre_With_Deflation(g1,g1_order,g1r) ||
Laguerre_With_Deflation(g2,g2_order,g2r))
return(-1);
#endif
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]);
#ifdef Plan9
free(g1);
free(g2);
free(g1r);
free(g2r);
#endif
return(0);
}
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