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457 lines
12 KiB
C
457 lines
12 KiB
C
/********************************************************************
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* *
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* THIS FILE IS PART OF THE OggVorbis SOFTWARE CODEC SOURCE CODE. *
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* USE, DISTRIBUTION AND REPRODUCTION OF THIS LIBRARY SOURCE IS *
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* GOVERNED BY A BSD-STYLE SOURCE LICENSE INCLUDED WITH THIS SOURCE *
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* IN 'COPYING'. PLEASE READ THESE TERMS BEFORE DISTRIBUTING. *
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* *
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* THE OggVorbis SOURCE CODE IS (C) COPYRIGHT 1994-2009 *
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* by the Xiph.Org Foundation http://www.xiph.org/ *
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* *
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********************************************************************
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function: LSP (also called LSF) conversion routines
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last mod: $Id: lsp.c 16227 2009-07-08 06:58:46Z xiphmont $
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The LSP generation code is taken (with minimal modification and a
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few bugfixes) from "On the Computation of the LSP Frequencies" by
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Joseph Rothweiler (see http://www.rothweiler.us for contact info).
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The paper is available at:
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http://www.myown1.com/joe/lsf
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********************************************************************/
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/* Note that the lpc-lsp conversion finds the roots of polynomial with
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an iterative root polisher (CACM algorithm 283). It *is* possible
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to confuse this algorithm into not converging; that should only
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happen with absurdly closely spaced roots (very sharp peaks in the
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LPC f response) which in turn should be impossible in our use of
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the code. If this *does* happen anyway, it's a bug in the floor
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finder; find the cause of the confusion (probably a single bin
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spike or accidental near-float-limit resolution problems) and
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correct it. */
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#include <math.h>
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#include <string.h>
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#include <stdlib.h>
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#include "lsp.h"
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#include "os.h"
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#include "misc.h"
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#include "lookup.h"
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#include "scales.h"
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/* three possible LSP to f curve functions; the exact computation
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(float), a lookup based float implementation, and an integer
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implementation. The float lookup is likely the optimal choice on
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any machine with an FPU. The integer implementation is *not* fixed
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point (due to the need for a large dynamic range and thus a
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seperately tracked exponent) and thus much more complex than the
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relatively simple float implementations. It's mostly for future
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work on a fully fixed point implementation for processors like the
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ARM family. */
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/* define either of these (preferably FLOAT_LOOKUP) to have faster
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but less precise implementation. */
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#undef FLOAT_LOOKUP
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#undef INT_LOOKUP
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#ifdef FLOAT_LOOKUP
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#include "vorbis_lookup.c" /* catch this in the build system; we #include for
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compilers (like gcc) that can't inline across
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modules */
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/* side effect: changes *lsp to cosines of lsp */
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void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
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float amp,float ampoffset){
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int i;
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float wdel=M_PI/ln;
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vorbis_fpu_control fpu;
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vorbis_fpu_setround(&fpu);
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for(i=0;i<m;i++)lsp[i]=vorbis_coslook(lsp[i]);
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i=0;
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while(i<n){
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int k=map[i];
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int qexp;
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float p=.7071067812f;
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float q=.7071067812f;
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float w=vorbis_coslook(wdel*k);
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float *ftmp=lsp;
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int c=m>>1;
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do{
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q*=ftmp[0]-w;
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p*=ftmp[1]-w;
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ftmp+=2;
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}while(--c);
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if(m&1){
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/* odd order filter; slightly assymetric */
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/* the last coefficient */
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q*=ftmp[0]-w;
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q*=q;
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p*=p*(1.f-w*w);
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}else{
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/* even order filter; still symmetric */
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q*=q*(1.f+w);
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p*=p*(1.f-w);
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}
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q=frexp(p+q,&qexp);
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q=vorbis_fromdBlook(amp*
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vorbis_invsqlook(q)*
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vorbis_invsq2explook(qexp+m)-
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ampoffset);
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do{
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curve[i++]*=q;
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}while(map[i]==k);
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}
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vorbis_fpu_restore(fpu);
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}
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#else
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#ifdef INT_LOOKUP
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#include "vorbis_lookup.c" /* catch this in the build system; we #include for
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compilers (like gcc) that can't inline across
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modules */
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static const int MLOOP_1[64]={
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0,10,11,11, 12,12,12,12, 13,13,13,13, 13,13,13,13,
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14,14,14,14, 14,14,14,14, 14,14,14,14, 14,14,14,14,
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15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15,
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15,15,15,15, 15,15,15,15, 15,15,15,15, 15,15,15,15,
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};
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static const int MLOOP_2[64]={
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0,4,5,5, 6,6,6,6, 7,7,7,7, 7,7,7,7,
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8,8,8,8, 8,8,8,8, 8,8,8,8, 8,8,8,8,
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9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9,
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9,9,9,9, 9,9,9,9, 9,9,9,9, 9,9,9,9,
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};
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static const int MLOOP_3[8]={0,1,2,2,3,3,3,3};
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/* side effect: changes *lsp to cosines of lsp */
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void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
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float amp,float ampoffset){
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/* 0 <= m < 256 */
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/* set up for using all int later */
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int i;
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int ampoffseti=rint(ampoffset*4096.f);
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int ampi=rint(amp*16.f);
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long *ilsp=alloca(m*sizeof(*ilsp));
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for(i=0;i<m;i++)ilsp[i]=vorbis_coslook_i(lsp[i]/M_PI*65536.f+.5f);
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i=0;
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while(i<n){
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int j,k=map[i];
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unsigned long pi=46341; /* 2**-.5 in 0.16 */
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unsigned long qi=46341;
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int qexp=0,shift;
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long wi=vorbis_coslook_i(k*65536/ln);
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qi*=labs(ilsp[0]-wi);
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pi*=labs(ilsp[1]-wi);
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for(j=3;j<m;j+=2){
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if(!(shift=MLOOP_1[(pi|qi)>>25]))
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if(!(shift=MLOOP_2[(pi|qi)>>19]))
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shift=MLOOP_3[(pi|qi)>>16];
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qi=(qi>>shift)*labs(ilsp[j-1]-wi);
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pi=(pi>>shift)*labs(ilsp[j]-wi);
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qexp+=shift;
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}
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if(!(shift=MLOOP_1[(pi|qi)>>25]))
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if(!(shift=MLOOP_2[(pi|qi)>>19]))
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shift=MLOOP_3[(pi|qi)>>16];
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/* pi,qi normalized collectively, both tracked using qexp */
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if(m&1){
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/* odd order filter; slightly assymetric */
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/* the last coefficient */
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qi=(qi>>shift)*labs(ilsp[j-1]-wi);
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pi=(pi>>shift)<<14;
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qexp+=shift;
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if(!(shift=MLOOP_1[(pi|qi)>>25]))
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if(!(shift=MLOOP_2[(pi|qi)>>19]))
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shift=MLOOP_3[(pi|qi)>>16];
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pi>>=shift;
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qi>>=shift;
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qexp+=shift-14*((m+1)>>1);
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pi=((pi*pi)>>16);
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qi=((qi*qi)>>16);
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qexp=qexp*2+m;
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pi*=(1<<14)-((wi*wi)>>14);
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qi+=pi>>14;
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}else{
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/* even order filter; still symmetric */
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/* p*=p(1-w), q*=q(1+w), let normalization drift because it isn't
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worth tracking step by step */
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pi>>=shift;
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qi>>=shift;
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qexp+=shift-7*m;
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pi=((pi*pi)>>16);
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qi=((qi*qi)>>16);
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qexp=qexp*2+m;
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pi*=(1<<14)-wi;
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qi*=(1<<14)+wi;
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qi=(qi+pi)>>14;
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}
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/* we've let the normalization drift because it wasn't important;
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however, for the lookup, things must be normalized again. We
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need at most one right shift or a number of left shifts */
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if(qi&0xffff0000){ /* checks for 1.xxxxxxxxxxxxxxxx */
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qi>>=1; qexp++;
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}else
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while(qi && !(qi&0x8000)){ /* checks for 0.0xxxxxxxxxxxxxxx or less*/
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qi<<=1; qexp--;
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}
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amp=vorbis_fromdBlook_i(ampi* /* n.4 */
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vorbis_invsqlook_i(qi,qexp)-
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/* m.8, m+n<=8 */
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ampoffseti); /* 8.12[0] */
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curve[i]*=amp;
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while(map[++i]==k)curve[i]*=amp;
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}
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}
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#else
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/* old, nonoptimized but simple version for any poor sap who needs to
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figure out what the hell this code does, or wants the other
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fraction of a dB precision */
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/* side effect: changes *lsp to cosines of lsp */
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void vorbis_lsp_to_curve(float *curve,int *map,int n,int ln,float *lsp,int m,
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float amp,float ampoffset){
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int i;
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float wdel=M_PI/ln;
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for(i=0;i<m;i++)lsp[i]=2.f*cos(lsp[i]);
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i=0;
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while(i<n){
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int j,k=map[i];
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float p=.5f;
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float q=.5f;
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float w=2.f*cos(wdel*k);
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for(j=1;j<m;j+=2){
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q *= w-lsp[j-1];
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p *= w-lsp[j];
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}
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if(j==m){
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/* odd order filter; slightly assymetric */
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/* the last coefficient */
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q*=w-lsp[j-1];
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p*=p*(4.f-w*w);
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q*=q;
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}else{
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/* even order filter; still symmetric */
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p*=p*(2.f-w);
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q*=q*(2.f+w);
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}
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q=fromdB(amp/sqrt(p+q)-ampoffset);
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curve[i]*=q;
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while(map[++i]==k)curve[i]*=q;
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}
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}
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#endif
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#endif
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static void cheby(float *g, int ord) {
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int i, j;
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g[0] *= .5f;
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for(i=2; i<= ord; i++) {
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for(j=ord; j >= i; j--) {
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g[j-2] -= g[j];
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g[j] += g[j];
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}
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}
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}
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static int comp(const void *a,const void *b){
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return (*(float *)a<*(float *)b)-(*(float *)a>*(float *)b);
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}
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/* Newton-Raphson-Maehly actually functioned as a decent root finder,
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but there are root sets for which it gets into limit cycles
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(exacerbated by zero suppression) and fails. We can't afford to
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fail, even if the failure is 1 in 100,000,000, so we now use
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Laguerre and later polish with Newton-Raphson (which can then
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afford to fail) */
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#define EPSILON 10e-7
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static int Laguerre_With_Deflation(float *a,int ord,float *r){
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int i,m;
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double lastdelta=0.f;
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double *defl=alloca(sizeof(*defl)*(ord+1));
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for(i=0;i<=ord;i++)defl[i]=a[i];
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for(m=ord;m>0;m--){
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double new=0.f,delta;
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/* iterate a root */
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while(1){
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double p=defl[m],pp=0.f,ppp=0.f,denom;
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/* eval the polynomial and its first two derivatives */
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for(i=m;i>0;i--){
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ppp = new*ppp + pp;
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pp = new*pp + p;
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p = new*p + defl[i-1];
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}
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/* Laguerre's method */
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denom=(m-1) * ((m-1)*pp*pp - m*p*ppp);
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if(denom<0)
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return(-1); /* complex root! The LPC generator handed us a bad filter */
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if(pp>0){
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denom = pp + sqrt(denom);
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if(denom<EPSILON)denom=EPSILON;
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}else{
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denom = pp - sqrt(denom);
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if(denom>-(EPSILON))denom=-(EPSILON);
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}
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delta = m*p/denom;
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new -= delta;
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if(delta<0.f)delta*=-1;
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if(fabs(delta/new)<10e-12)break;
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lastdelta=delta;
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}
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r[m-1]=new;
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/* forward deflation */
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for(i=m;i>0;i--)
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defl[i-1]+=new*defl[i];
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defl++;
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}
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return(0);
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}
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/* for spit-and-polish only */
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static int Newton_Raphson(float *a,int ord,float *r){
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int i, k, count=0;
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double error=1.f;
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double *root=alloca(ord*sizeof(*root));
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for(i=0; i<ord;i++) root[i] = r[i];
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while(error>1e-20){
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error=0;
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for(i=0; i<ord; i++) { /* Update each point. */
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double pp=0.,delta;
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double rooti=root[i];
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double p=a[ord];
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for(k=ord-1; k>= 0; k--) {
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pp= pp* rooti + p;
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p = p * rooti + a[k];
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}
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delta = p/pp;
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root[i] -= delta;
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error+= delta*delta;
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}
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if(count>40)return(-1);
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count++;
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}
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/* Replaced the original bubble sort with a real sort. With your
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help, we can eliminate the bubble sort in our lifetime. --Monty */
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for(i=0; i<ord;i++) r[i] = root[i];
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return(0);
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}
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/* Convert lpc coefficients to lsp coefficients */
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int vorbis_lpc_to_lsp(float *lpc,float *lsp,int m){
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int order2=(m+1)>>1;
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int g1_order,g2_order;
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float *g1=alloca(sizeof(*g1)*(order2+1));
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float *g2=alloca(sizeof(*g2)*(order2+1));
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float *g1r=alloca(sizeof(*g1r)*(order2+1));
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float *g2r=alloca(sizeof(*g2r)*(order2+1));
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int i;
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/* even and odd are slightly different base cases */
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g1_order=(m+1)>>1;
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g2_order=(m) >>1;
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/* Compute the lengths of the x polynomials. */
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/* Compute the first half of K & R F1 & F2 polynomials. */
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/* Compute half of the symmetric and antisymmetric polynomials. */
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/* Remove the roots at +1 and -1. */
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g1[g1_order] = 1.f;
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for(i=1;i<=g1_order;i++) g1[g1_order-i] = lpc[i-1]+lpc[m-i];
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g2[g2_order] = 1.f;
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for(i=1;i<=g2_order;i++) g2[g2_order-i] = lpc[i-1]-lpc[m-i];
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if(g1_order>g2_order){
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for(i=2; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+2];
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}else{
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for(i=1; i<=g1_order;i++) g1[g1_order-i] -= g1[g1_order-i+1];
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for(i=1; i<=g2_order;i++) g2[g2_order-i] += g2[g2_order-i+1];
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}
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/* Convert into polynomials in cos(alpha) */
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cheby(g1,g1_order);
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cheby(g2,g2_order);
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/* Find the roots of the 2 even polynomials.*/
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if(Laguerre_With_Deflation(g1,g1_order,g1r) ||
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Laguerre_With_Deflation(g2,g2_order,g2r))
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return(-1);
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Newton_Raphson(g1,g1_order,g1r); /* if it fails, it leaves g1r alone */
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Newton_Raphson(g2,g2_order,g2r); /* if it fails, it leaves g2r alone */
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qsort(g1r,g1_order,sizeof(*g1r),comp);
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qsort(g2r,g2_order,sizeof(*g2r),comp);
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for(i=0;i<g1_order;i++)
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lsp[i*2] = acos(g1r[i]);
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for(i=0;i<g2_order;i++)
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lsp[i*2+1] = acos(g2r[i]);
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return(0);
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}
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