/*---------------------------------------------------------------------------*\Original copyright	FILE........: AKSLSPD.C	TYPE........: Turbo C	COMPANY.....: Voicetronix	AUTHOR......: David Rowe	DATE CREATED: 24/2/93Heavily modified by Jean-Marc Valin (fixed-point, optimizations,                                      additional functions, ...)   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.*/#ifdef HAVE_CONFIG_H#include "config.h"#endif#include <math.h>#include "lsp.h"#include "stack_alloc.h"#include "math_approx.h"#ifndef M_PI#define M_PI           3.14159265358979323846  /* pi */#endif#ifndef NULL#define NULL 0#endif#ifdef FIXED_POINT#define FREQ_SCALE 16384/*#define ANGLE2X(a) (32768*cos(((a)/8192.)))*/#define ANGLE2X(a) (SHL16(spx_cos(a),2))/*#define X2ANGLE(x) (acos(.00006103515625*(x))*LSP_SCALING)*/#define X2ANGLE(x) (spx_acos(x))#else/*#define C1 0.99940307#define C2 -0.49558072#define C3 0.03679168*/#define FREQ_SCALE 1.#define ANGLE2X(a) (spx_cos(a))#define X2ANGLE(x) (acos(x))#endif/*---------------------------------------------------------------------------*\	FUNCTION....: cheb_poly_eva()	AUTHOR......: David Rowe	DATE CREATED: 24/2/93    This function evaluates a series of Chebyshev polynomials\*---------------------------------------------------------------------------*/#ifdef FIXED_POINTstatic inline spx_word32_t cheb_poly_eva(spx_word32_t *coef,spx_word16_t 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;    VARDECL(spx_word16_t *T);    spx_word32_t sum;    int m2=m>>1;    VARDECL(spx_word16_t *coefn);    /*Prevents overflows*/    if (x>16383)       x = 16383;    if (x<-16383)       x = -16383;    /* Allocate memory for Chebyshev series formulation */    ALLOC(T, m2+1, spx_word16_t);    ALLOC(coefn, m2+1, spx_word16_t);    for (i=0;i<m2+1;i++)    {       coefn[i] = coef[i];       /*printf ("%f ", coef[i]);*/    }    /*printf ("\n");*/    /* Initialise values */    T[0]=16384;    T[1]=x;    /* Evaluate Chebyshev series formulation using iterative approach  */    /* Evaluate polynomial and return value also free memory space */    sum = ADD32(EXTEND32(coefn[m2]), EXTEND32(MULT16_16_P14(coefn[m2-1],x)));    /*x *= 2;*/    for(i=2;i<=m2;i++)    {       T[i] = SUB16(MULT16_16_Q13(x,T[i-1]), T[i-2]);       sum = ADD32(sum, EXTEND32(MULT16_16_P14(coefn[m2-i],T[i])));       /*printf ("%f ", sum);*/    }        /*printf ("\n");*/    return sum;}#elsestatic float cheb_poly_eva(spx_word32_t *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;    VARDECL(float *T);    float sum;    int m2=m>>1;    /* Allocate memory for Chebyshev series formulation */    ALLOC(T, 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;}#endif/*---------------------------------------------------------------------------*\	FUNCTION....: lpc_to_lsp()	AUTHOR......: David Rowe	DATE CREATED: 24/2/93    This function converts LPC coefficients to LSP    coefficients.\*---------------------------------------------------------------------------*/#ifdef FIXED_POINT#define SIGN_CHANGE(a,b) (((a)&0x70000000)^((b)&0x70000000)||(b==0))#else#define SIGN_CHANGE(a,b) (((a)*(b))<0.0)#endifint lpc_to_lsp (spx_coef_t *a,int lpcrdr,spx_lsp_t *freq,int nb,spx_word16_t 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) 		*/{    spx_word16_t temp_xr,xl,xr,xm=0;    spx_word32_t psuml,psumr,psumm,temp_psumr/*,temp_qsumr*/;    int i,j,m,flag,k;    VARDECL(spx_word32_t *Q);                 	/* ptrs for memory allocation 		*/    VARDECL(spx_word32_t *P);    spx_word32_t *px;                	/* ptrs of respective P'(z) & Q'(z)	*/    spx_word32_t *qx;    spx_word32_t *p;    spx_word32_t *q;    spx_word32_t *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 */    ALLOC(Q, (m+1), spx_word32_t);    ALLOC(P, (m+1), spx_word32_t);    /* 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;#ifdef FIXED_POINT    *px++ = LPC_SCALING;    *qx++ = LPC_SCALING;    for(i=0;i<m;i++){       *px++ = SUB32(ADD32(EXTEND32(a[i]),EXTEND32(a[lpcrdr-i-1])), *p++);       *qx++ = ADD32(SUB32(EXTEND32(a[i]),EXTEND32(a[lpcrdr-i-1])), *q++);    }    px = P;    qx = Q;    for(i=0;i<m;i++)    {       /*if (fabs(*px)>=32768)          speex_warning_int("px", *px);       if (fabs(*qx)>=32768)       speex_warning_int("qx", *qx);*/       *px = PSHR32(*px,2);       *qx = PSHR32(*qx,2);       px++;       qx++;    }    /* The reason for this lies in the way cheb_poly_eva() is implemented for fixed-point */    P[m] = PSHR32(P[m],3);    Q[m] = PSHR32(Q[m],3);#else    *px++ = LPC_SCALING;    *qx++ = LPC_SCALING;    for(i=0;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++;    }#endif    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 = FREQ_SCALE;               	/* start at point xl = 1 		*/    for(j=0;j<lpcrdr;j++){	if(j&1)            	/* determines whether P' or Q' is eval. */	    pt = qx;	else	    pt = px;	psuml = cheb_poly_eva(pt,xl,lpcrdr,stack);	/* evals poly. at xl 	*/