Yay, odd coefficient LSP filters work now. Haven't added the changes

to the lookup-based versions (committing now as I don't want to lose
it all.  Took 7 bloody hours to figure it out).

Monty

svn path=/branches/monty_branch_20001226/vorbis/; revision=1149

1 files changed, 399 insertions, 0 deletions

diff --git a/lib/lsp.c b/lib/lsp.c
new file mode 100644
index 00000000..ec69c398
--- /dev/null
+++ b/lib/lsp.c
@@ -0,0 +1,399 @@
+/********************************************************************
+ *                                                                  *
+ * THIS FILE IS PART OF THE OggVorbis SOFTWARE CODEC SOURCE CODE.   *
+ * USE, DISTRIBUTION AND REPRODUCTION OF THIS SOURCE IS GOVERNED BY *
+ * THE GNU LESSER/LIBRARY PUBLIC LICENSE, WHICH IS INCLUDED WITH    *
+ * THIS SOURCE. PLEASE READ THESE TERMS BEFORE DISTRIBUTING.        *
+ *                                                                  *
+ * THE OggVorbis SOURCE CODE IS (C) COPYRIGHT 1994-2000             *
+ * by Monty <monty@xiph.org> and the XIPHOPHORUS Company            *
+ * http://www.xiph.org/                                             *
+ *                                                                  *
+ ********************************************************************
+
+  function: LSP (also called LSF) conversion routines
+  last mod: $Id: lsp.c,v 1.13.2.1 2001/01/04 04:05:08 xiphmont Exp $
+
+  The LSP generation code is taken (with minimal modification) from
+  "On the Computation of the LSP Frequencies" by Joseph Rothweiler
+  <rothwlr@altavista.net>, available at:
+  
+  http://www2.xtdl.com/~rothwlr/lsfpaper/lsfpage.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
+   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 */
+#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;
+
+    do{
+      p*=ftmp[0]-w;
+      q*=ftmp[1]-w;
+      ftmp+=2;
+    }while(--c);
+
+    q=frexp(p*p*(1.f+w)+q*q*(1.f-w),&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);
+  long *ilsp=alloca(m*sizeof(long));
+  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);
+
+    pi*=labs(ilsp[0]-wi);
+    qi*=labs(ilsp[1]-wi);
+
+    for(j=2;j<m;j+=2){
+      if(!(shift=MLOOP_1[(pi|qi)>>25]))
+	if(!(shift=MLOOP_2[(pi|qi)>>19]))
+	  shift=MLOOP_3[(pi|qi)>>16];
+      pi=(pi>>shift)*labs(ilsp[j]-wi);
+      qi=(qi>>shift)*labs(ilsp[j+1]-wi);
+      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-7*m;
+
+    /* pi,qi normalized collectively, both tracked using qexp */
+
+    /* p*=p(1-w), q*=q(1+w), let normalization drift because it isn't
+       worth tracking step by step */
+
+    pi=((pi*pi)>>16);
+    qi=((qi*qi)>>16);
+    qexp=qexp*2+m;
+
+    qi*=(1<<14)-wi;
+    pi*=(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 */
+
+#include <stdio.h>
+/* 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]);
+
+  fprintf(stderr,"m=%d ",m);
+
+  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){
+  if(*(float *)a<*(float *)b)
+    return(1);
+  else
+    return(-1);
+}
+
+/* This is one of those 'mathemeticians should not write code' kind of
+   cases.  Newton's method of polishing roots is straightforward
+   enough... except in those cases where it just fails in the real
+   world.  In our case below, we're worried about a local mini/maxima
+   shooting a root estimation off to infinity, or the new estimation
+   chaotically oscillating about convergence (shouldn't actually be a
+   problem in our usage.
+
+   Maehly's modification (zero suppression, to prevent two tenative
+   roots from collapsing to the same actual root) similarly can
+   temporarily shoot a root off toward infinity.  It would come
+   back... if it were not for the fact that machine representation has
+   limited dynamic range and resolution.  This too is guarded by
+   limiting delta.
+
+   Last problem is convergence criteria; we don't know what a 'double'
+   is on our hardware/compiler, and the convergence limit is bounded
+   by roundoff noise.  So, we hack convergence:
+
+   Require at most 1e-6 mean squared error for all zeroes.  When
+   converging, start the clock ticking at 1e-6; limit our polishing to
+   as many more iterations as took us to get this far, 100 max.
+
+   Past max iters, quit when MSE is no longer decreasing *or* we go
+   below ~1e-20 MSE, whichever happens first. */
+
+static void Newton_Raphson_Maehly(float *a,int ord,float *r){
+  int i, k, count=0, maxiter=0;
+  double error=1.,besterror=1.;
+  double *root=alloca(ord*sizeof(double));
+
+  for(i=0; i<ord;i++) root[i] = 2.0 * (i+0.5) / ord - 1.0;
+  
+  while(error>1e-20){
+    error=0;
+    
+    for(i=0; i<ord; i++) { /* Update each point. */
+      double ac=0.,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];
+	if (k != i) ac += 1./(rooti - root[k]);
+      }
+      ac=p*ac;
+
+      delta = p/(pp-ac);
+
+      /* don't allow the correction to scream off into infinity if we
+         happened to polish right at a local mini/maximum */
+
+      if(delta<-3.)delta=-3.;
+      if(delta>3.)delta=3.; /* 3 is not a random choice; it's large
+                               enough to make sure the first pass
+                               can't accidentally limit two poles to
+                               the same value in a fatal nonelastic
+                               collision.  */
+
+      root[i] -= delta;
+      error += delta*delta;
+    }
+    
+    if(maxiter && count>maxiter && error>=besterror)break;
+
+    /* anything to help out the polisher; converge using doubles */
+    if(!count || error<besterror){
+      for(i=0; i<ord; i++) r[i]=root[i]; 
+      besterror=error;
+      if(error<1e-6){ /* rough minimum criteria */
+	maxiter=count*2+10;
+	if(maxiter>100)maxiter=100;
+      }
+    }
+
+    count++;
+  }
+
+  /* Replaced the original bubble sort with a real sort.  With your
+     help, we can eliminate the bubble sort in our lifetime. --Monty */
+  
+  qsort(r,ord,sizeof(float),comp);
+
+}
+
+/* Convert lpc coefficients to lsp coefficients */
+void vorbis_lpc_to_lsp(float *lpc,float *lsp,int m){
+  int order2=(m+1)>>1;
+  int g1_order,g2_order;
+  float *g1=alloca(sizeof(float)*(order2+1));
+  float *g2=alloca(sizeof(float)*(order2+1));
+  float *g1r=alloca(sizeof(float)*(order2+1));
+  float *g2r=alloca(sizeof(float)*(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.*/
+  
+  Newton_Raphson_Maehly(g1,g1_order,g1r);
+  Newton_Raphson_Maehly(g2,g2_order,g2r);
+
+  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]);
+  
+}