lsp.c

/********************************************************************
 *                                                                  *
 * 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 https://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:

  https://web.archive.org/web/20110810174000/http://home.myfairpoint.net/vzenxj75/myown1/joe/lsf/index.html

 ********************************************************************/

/* 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);
}