/*---------------------------------------------------------------------------*\Original copyright	FILE........: AKSLSPD.C	TYPE........: Turbo C	COMPANY.....: Voicetronix	AUTHOR......: David Rowe	DATE CREATED: 24/2/93Modified by Jean-Marc Valin   This file contains functions for converting Linear Prediction   Coefficients (LPC) to Line Spectral Pair (LSP) and back. Note that the   LSP coefficients are not in radians format but in the x domain of the   unit circle.   Speex License:   Redistribution and use in source and binary forms, with or without   modification, are permitted provided that the following conditions   are met:      - Redistributions of source code must retain the above copyright   notice, this list of conditions and the following disclaimer.      - Redistributions in binary form must reproduce the above copyright   notice, this list of conditions and the following disclaimer in the   documentation and/or other materials provided with the distribution.      - Neither the name of the Xiph.org Foundation nor the names of its   contributors may be used to endorse or promote products derived from   this software without specific prior written permission.      THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS   ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR   A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR   CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.*/#include <math.h>#include "lsp.h"#include "stack_alloc.h"#ifndef M_PI#define M_PI           3.14159265358979323846  /* pi */#endif#ifndef NULL#define NULL 0#endif/*---------------------------------------------------------------------------*\	FUNCTION....: cheb_poly_eva()	AUTHOR......: David Rowe	DATE CREATED: 24/2/93    This function evaluates a series of Chebyshev polynomials\*---------------------------------------------------------------------------*/static float cheb_poly_eva(float *coef,float x,int m,char *stack)/*  float coef[]  	coefficients of the polynomial to be evaluated 	*//*  float x   		the point where polynomial is to be evaluated 	*//*  int m 		order of the polynomial 			*/{    int i;    float *T,sum;    int m2=m>>1;    /* Allocate memory for Chebyshev series formulation */    T=PUSH(stack, m2+1, float);    /* Initialise values */    T[0]=1;    T[1]=x;    /* Evaluate Chebyshev series formulation using iterative approach  */    /* Evaluate polynomial and return value also free memory space */    sum = coef[m2] + coef[m2-1]*x;    x *= 2;    for(i=2;i<=m2;i++)    {       T[i] = x*T[i-1] - T[i-2];       sum += coef[m2-i] * T[i];    }        return sum;}/*---------------------------------------------------------------------------*\	FUNCTION....: lpc_to_lsp()	AUTHOR......: David Rowe	DATE CREATED: 24/2/93    This function converts LPC coefficients to LSP    coefficients.\*---------------------------------------------------------------------------*/int lpc_to_lsp (float *a,int lpcrdr,float *freq,int nb,float delta, char *stack)/*  float *a 		     	lpc coefficients			*//*  int lpcrdr			order of LPC coefficients (10) 		*//*  float *freq 	      	LSP frequencies in the x domain       	*//*  int nb			number of sub-intervals (4) 		*//*  float delta			grid spacing interval (0.02) 		*/{    float psuml,psumr,psumm,temp_xr,xl,xr,xm=0;    float temp_psumr/*,temp_qsumr*/;    int i,j,m,flag,k;    float *Q;                 	/* ptrs for memory allocation 		*/    float *P;    float *px;                	/* ptrs of respective P'(z) & Q'(z)	*/    float *qx;    float *p;    float *q;    float *pt;                	/* ptr used for cheb_poly_eval()				whether P' or Q' 			*/    int roots=0;              	/* DR 8/2/94: number of roots found 	*/    flag = 1;                	/*  program is searching for a root when,				1 else has found one 			*/    m = lpcrdr/2;            	/* order of P'(z) & Q'(z) polynomials 	*/    /* Allocate memory space for polynomials */    Q = PUSH(stack, (m+1), float);    P = PUSH(stack, (m+1), float);    /* determine P'(z)'s and Q'(z)'s coefficients where      P'(z) = P(z)/(1 + z^(-1)) and Q'(z) = Q(z)/(1-z^(-1)) */    px = P;                      /* initialise ptrs 			*/    qx = Q;    p = px;    q = qx;    *px++ = 1.0;    *qx++ = 1.0;    for(i=1;i<=m;i++){	*px++ = a[i]+a[lpcrdr+1-i]-*p++;	*qx++ = a[i]-a[lpcrdr+1-i]+*q++;    }    px = P;    qx = Q;    for(i=0;i<m;i++){	*px = 2**px;	*qx = 2**qx;	 px++;	 qx++;    }    px = P;             	/* re-initialise ptrs 			*/    qx = Q;    /* Search for a zero in P'(z) polynomial first and then alternate to Q'(z).    Keep alternating between the two polynomials as each zero is found 	*/    xr = 0;             	/* initialise xr to zero 		*/    xl = 1.0;               	/* start at point xl = 1 		*/    for(j=0;j<lpcrdr;j++){	if(j%2)            	/* determines whether P' or Q' is eval. */	    pt = qx;	else	    pt = px;	psuml = cheb_poly_eva(pt,xl,lpcrdr,stack);	/* evals poly. at xl 	*/	flag = 1;	while(flag && (xr >= -1.0)){           float dd;           /* Modified by JMV to provide smaller steps around x=+-1 */           dd=(delta*(1-.9*xl*xl));           if (fabs(psuml)<.2)              dd *= .5;           xr = xl - dd;                        	/* interval spacing 	*/	    psumr = cheb_poly_eva(pt,xr,lpcrdr,stack);/* poly(xl-delta_x) 	*/	    temp_psumr = psumr;	    temp_xr = xr;    /* if no sign change increment xr and re-evaluate poly(xr). Repeat til    sign change.    if a sign change has occurred the interval is bisected and then    checked again for a sign change which determines in which    interval the zero lies in.    If there is no sign change between poly(xm) and poly(xl) set interval    between xm and xr else set interval between xl and xr and repeat till    root is located within the specified limits 			*/	    if((psumr*psuml)<0.0){		roots++;		psumm=psuml;		for(k=0;k<=nb;k++){		    xm = (xl+xr)/2;        	/* bisect the interval 	*/		    psumm=cheb_poly_eva(pt,xm,lpcrdr,stack);		    if(psumm*psuml>0.){			psuml=psumm;			xl=xm;		    }		    else{			psumr=psumm;			xr=xm;		    }		}	       /* once zero is found, reset initial interval to xr 	*/	       freq[j] = (xm);	       xl = xm;	       flag = 0;       		/* reset flag for next search 	*/	    }	    else{		psuml=temp_psumr;		xl=temp_xr;	    }	}    }    return(roots);}/*---------------------------------------------------------------------------*\	FUNCTION....: lsp_to_lpc()	AUTHOR......: David Rowe	DATE CREATED: 24/2/93    lsp_to_lpc: This function converts LSP coefficients to LPC    coefficients.\*---------------------------------------------------------------------------*/void lsp_to_lpc(float *freq,float *ak,int lpcrdr, char *stack)/*  float *freq 	array of LSP frequencies in the x domain	*//*  float *ak 		array of LPC coefficients 			*//*  int lpcrdr  	order of LPC coefficients 			*/{    int i,j;    float xout1,xout2,xin1,xin2;    float *Wp;    float *pw,*n1,*n2,*n3,*n4=NULL;    int m = lpcrdr/2;    Wp = PUSH(stack, 4*m+2, float);    pw = Wp;    /* initialise contents of array */    for(i=0;i<=4*m+1;i++){       	/* set contents of buffer to 0 */	*pw++ = 0.0;    }    /* Set pointers up */    pw = Wp;    xin1 = 1.0;    xin2 = 1.0;    /* reconstruct P(z) and Q(z) by  cascading second order      polynomials in form 1 - 2xz(-1) +z(-2), where x is the      LSP coefficient */    for(j=0;j<=lpcrdr;j++){       int i2=0;	for(i=0;i<m;i++,i2+=2){	    n1 = pw+(i*4);	    n2 = n1 + 1;	    n3 = n2 + 1;	    n4 = n3 + 1;	    xout1 = xin1 - 2*(freq[i2]) * *n1 + *n2;	    xout2 = xin2 - 2*(freq[i2+1]) * *n3 + *n4;	    *n2 = *n1;	    *n4 = *n3;	    *n1 = xin1;	    *n3 = xin2;	    xin1 = xout1;	    xin2 = xout2;	}	xout1 = xin1 + *(n4+1);	xout2 = xin2 - *(n4+2);	ak[j] = (xout1 + xout2)*0.5;	*(n4+1) = xin1;	*(n4+2) = xin2;	xin1 = 0.0;	xin2 = 0.0;    }}/*Added by JMV  Makes sure the LSPs are stable*/void lsp_enforce_margin(float *lsp, int len, float margin){   int i;   if (lsp[0]<margin)      lsp[0]=margin;   if (lsp[len-1]>M_PI-margin)      lsp[len-1]=M_PI-margin;   for (i=1;i<len-1;i++)   {      if (lsp[i]<lsp[i-1]+margin)         lsp[i]=lsp[i-1]+margin;      if (lsp[i]>lsp[i+1]-margin)         lsp[i]= .5* (lsp[i] + lsp[i+1]-margin);   }}