pjmedia/src/pjmedia-codec/speex/lsp.c - pjproject - Gitiles

 /*---------------------------------------------------------------------------*\
 Original copyright
 	FILE........: AKSLSPD.C
 	TYPE........: Turbo C
 	COMPANY.....: Voicetronix
 	AUTHOR......: David Rowe
 	DATE CREATED: 24/2/93

 Heavily 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_POINT

 static 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;
 }
 #else
 static 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)
 #endif


 int 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 	*/
 	flag = 1;
 	while(flag && (xr >= -FREQ_SCALE)){
            spx_word16_t dd;
            /* Modified by JMV to provide smaller steps around x=+-1 */
 #ifdef FIXED_POINT
            dd = MULT16_16_Q15(delta,SUB16(FREQ_SCALE, MULT16_16_Q14(MULT16_16_Q14(xl,xl),14000)));
            if (psuml<512 && psuml>-512)
               dd = PSHR16(dd,1);
 #else
            dd=delta*(1-.9*xl*xl);
            if (fabs(psuml)<.2)
               dd *= .5;
 #endif
            xr = SUB16(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(SIGN_CHANGE(psumr,psuml))
             {
 		roots++;

 		psumm=psuml;
 		for(k=0;k<=nb;k++){
 #ifdef FIXED_POINT
 		    xm = ADD16(PSHR16(xl,1),PSHR16(xr,1));        	/* bisect the interval 	*/
 #else
                     xm = .5*(xl+xr);        	/* bisect the interval 	*/
 #endif
 		    psumm=cheb_poly_eva(pt,xm,lpcrdr,stack);
 		    /*if(psumm*psuml>0.)*/
 		    if(!SIGN_CHANGE(psumm,psuml))
                     {
 			psuml=psumm;
 			xl=xm;
 		    } else {
 			psumr=psumm;
 			xr=xm;
 		    }
 		}

 	       /* once zero is found, reset initial interval to xr 	*/
 	       freq[j] = X2ANGLE(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.

 \*---------------------------------------------------------------------------*/

 #ifdef FIXED_POINT

 void lsp_to_lpc(spx_lsp_t *freq,spx_coef_t *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;
     spx_word32_t xout1,xout2,xin1,xin2;
     VARDECL(spx_word32_t *Wp);
     spx_word32_t *pw,*n1,*n2,*n3,*n4=NULL;
     VARDECL(spx_word16_t *freqn);
     int m = lpcrdr>>1;

     ALLOC(freqn, lpcrdr, spx_word16_t);
     for (i=0;i<lpcrdr;i++)
        freqn[i] = ANGLE2X(freq[i]);

     ALLOC(Wp, 4*m+2, spx_word32_t);
     pw = Wp;


     /* initialise contents of array */

     for(i=0;i<=4*m+1;i++){       	/* set contents of buffer to 0 */
 	*pw++ = 0;
     }

     /* Set pointers up */

     pw = Wp;
     xin1 = 1048576;
     xin2 = 1048576;

     /* 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++){
        spx_word16_t *fr=freqn;
 	for(i=0;i<m;i++){
 	    n1 = pw+(i<<2);
 	    n2 = n1 + 1;
 	    n3 = n2 + 1;
 	    n4 = n3 + 1;
 	    xout1 = ADD32(SUB32(xin1, MULT16_32_Q14(*fr,*n1)), *n2);
             fr++;
             xout2 = ADD32(SUB32(xin2, MULT16_32_Q14(*fr,*n3)), *n4);
             fr++;
 	    *n2 = *n1;
 	    *n4 = *n3;
 	    *n1 = xin1;
 	    *n3 = xin2;
 	    xin1 = xout1;
 	    xin2 = xout2;
 	}
 	xout1 = xin1 + *(n4+1);
 	xout2 = xin2 - *(n4+2);
         /* FIXME: perhaps apply bandwidth expansion in case of overflow? */
 	if (j>0)
 	{
         if (xout1 + xout2>SHL32(EXTEND32(32766),8))
            ak[j-1] = 32767;
         else if (xout1 + xout2 < -SHL32(EXTEND32(32766),8))
            ak[j-1] = -32767;
         else
            ak[j-1] = EXTRACT16(PSHR32(ADD32(xout1,xout2),8));
 	} else {/*speex_warning_int("ak[0] = ", EXTRACT16(PSHR32(ADD32(xout1,xout2),8)));*/}
 	*(n4+1) = xin1;
 	*(n4+2) = xin2;

 	xin1 = 0;
 	xin2 = 0;
     }
 }
 #else

 void lsp_to_lpc(spx_lsp_t *freq,spx_coef_t *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;
     VARDECL(float *Wp);
     float *pw,*n1,*n2,*n3,*n4=NULL;
     VARDECL(float *x_freq);
     int m = lpcrdr>>1;

     ALLOC(Wp, 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;

     ALLOC(x_freq, lpcrdr, float);
     for (i=0;i<lpcrdr;i++)
        x_freq[i] = ANGLE2X(freq[i]);

     /* 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.f*x_freq[i2] * *n1 + *n2;
 	    xout2 = xin2 - 2.f*x_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);
 	if (j>0)
 	   ak[j-1] = (xout1 + xout2)*0.5f;
 	*(n4+1) = xin1;
 	*(n4+2) = xin2;

 	xin1 = 0.0;
 	xin2 = 0.0;
     }

 }
 #endif


 #ifdef FIXED_POINT

 /*Makes sure the LSPs are stable*/
 void lsp_enforce_margin(spx_lsp_t *lsp, int len, spx_word16_t margin)
 {
    int i;
    spx_word16_t m = margin;
    spx_word16_t m2 = 25736-margin;

    if (lsp[0]<m)
       lsp[0]=m;
    if (lsp[len-1]>m2)
       lsp[len-1]=m2;
    for (i=1;i<len-1;i++)
    {
       if (lsp[i]<lsp[i-1]+m)
          lsp[i]=lsp[i-1]+m;

       if (lsp[i]>lsp[i+1]-m)
          lsp[i]= SHR16(lsp[i],1) + SHR16(lsp[i+1]-m,1);
    }
 }


 void lsp_interpolate(spx_lsp_t *old_lsp, spx_lsp_t *new_lsp, spx_lsp_t *interp_lsp, int len, int subframe, int nb_subframes)
 {
    int i;
    spx_word16_t tmp = DIV32_16(SHL32(EXTEND32(1 + subframe),14),nb_subframes);
    spx_word16_t tmp2 = 16384-tmp;
    for (i=0;i<len;i++)
    {
       interp_lsp[i] = MULT16_16_P14(tmp2,old_lsp[i]) + MULT16_16_P14(tmp,new_lsp[i]);
    }
 }

 #else

 /*Makes sure the LSPs are stable*/
 void lsp_enforce_margin(spx_lsp_t *lsp, int len, spx_word16_t margin)
 {
    int i;
    if (lsp[0]<LSP_SCALING*margin)
       lsp[0]=LSP_SCALING*margin;
    if (lsp[len-1]>LSP_SCALING*(M_PI-margin))
       lsp[len-1]=LSP_SCALING*(M_PI-margin);
    for (i=1;i<len-1;i++)
    {
       if (lsp[i]<lsp[i-1]+LSP_SCALING*margin)
          lsp[i]=lsp[i-1]+LSP_SCALING*margin;

       if (lsp[i]>lsp[i+1]-LSP_SCALING*margin)
          lsp[i]= .5f* (lsp[i] + lsp[i+1]-LSP_SCALING*margin);
    }
 }


 void lsp_interpolate(spx_lsp_t *old_lsp, spx_lsp_t *new_lsp, spx_lsp_t *interp_lsp, int len, int subframe, int nb_subframes)
 {
    int i;
    float tmp = (1.0f + subframe)/nb_subframes;
    for (i=0;i<len;i++)
    {
       interp_lsp[i] = (1-tmp)*old_lsp[i] + tmp*new_lsp[i];
    }
 }

 #endif
	/---------------------------------------------------------------------------\
	Original copyright
	FILE........: AKSLSPD.C
	TYPE........: Turbo C
	COMPANY.....: Voicetronix
	AUTHOR......: David Rowe
	DATE CREATED: 24/2/93

	Heavily 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) (32768cos(((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_POINT

	static 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;
	}
	#else
	static 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)
	#endif


	int 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 */
	flag = 1;
	while(flag && (xr >= -FREQ_SCALE)){
	spx_word16_t dd;
	/* Modified by JMV to provide smaller steps around x=+-1 */
	#ifdef FIXED_POINT
	dd = MULT16_16_Q15(delta,SUB16(FREQ_SCALE, MULT16_16_Q14(MULT16_16_Q14(xl,xl),14000)));
	if (psuml<512 && psuml>-512)
	dd = PSHR16(dd,1);
	#else
	dd=delta(1-.9xl*xl);
	if (fabs(psuml)<.2)
	dd *= .5;
	#endif
	xr = SUB16(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(SIGN_CHANGE(psumr,psuml))
	{
	roots++;

	psumm=psuml;
	for(k=0;k<=nb;k++){
	#ifdef FIXED_POINT
	xm = ADD16(PSHR16(xl,1),PSHR16(xr,1)); /* bisect the interval */
	#else
	xm = .5(xl+xr); / bisect the interval */
	#endif
	psumm=cheb_poly_eva(pt,xm,lpcrdr,stack);
	/if(psummpsuml>0.)*/
	if(!SIGN_CHANGE(psumm,psuml))
	{
	psuml=psumm;
	xl=xm;
	} else {
	psumr=psumm;
	xr=xm;
	}
	}

	/* once zero is found, reset initial interval to xr */
	freq[j] = X2ANGLE(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.

	\---------------------------------------------------------------------------/

	#ifdef FIXED_POINT

	void lsp_to_lpc(spx_lsp_t freq,spx_coef_t 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;
	spx_word32_t xout1,xout2,xin1,xin2;
	VARDECL(spx_word32_t *Wp);
	spx_word32_t pw,n1,n2,n3,*n4=NULL;
	VARDECL(spx_word16_t *freqn);
	int m = lpcrdr>>1;

	ALLOC(freqn, lpcrdr, spx_word16_t);
	for (i=0;i<lpcrdr;i++)
	freqn[i] = ANGLE2X(freq[i]);

	ALLOC(Wp, 4*m+2, spx_word32_t);
	pw = Wp;


	/* initialise contents of array */

	for(i=0;i<=4m+1;i++){ / set contents of buffer to 0 */
	*pw++ = 0;
	}

	/* Set pointers up */

	pw = Wp;
	xin1 = 1048576;
	xin2 = 1048576;

	/* 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++){
	spx_word16_t *fr=freqn;
	for(i=0;i<m;i++){
	n1 = pw+(i<<2);
	n2 = n1 + 1;
	n3 = n2 + 1;
	n4 = n3 + 1;
	xout1 = ADD32(SUB32(xin1, MULT16_32_Q14(fr,n1)), *n2);
	fr++;
	xout2 = ADD32(SUB32(xin2, MULT16_32_Q14(fr,n3)), *n4);
	fr++;
	n2 = n1;
	n4 = n3;
	*n1 = xin1;
	*n3 = xin2;
	xin1 = xout1;
	xin2 = xout2;
	}
	xout1 = xin1 + *(n4+1);
	xout2 = xin2 - *(n4+2);
	/* FIXME: perhaps apply bandwidth expansion in case of overflow? */
	if (j>0)
	{
	if (xout1 + xout2>SHL32(EXTEND32(32766),8))
	ak[j-1] = 32767;
	else if (xout1 + xout2 < -SHL32(EXTEND32(32766),8))
	ak[j-1] = -32767;
	else
	ak[j-1] = EXTRACT16(PSHR32(ADD32(xout1,xout2),8));
	} else {/speex_warning_int("ak[0] = ", EXTRACT16(PSHR32(ADD32(xout1,xout2),8)));/}
	*(n4+1) = xin1;
	*(n4+2) = xin2;

	xin1 = 0;
	xin2 = 0;
	}
	}
	#else

	void lsp_to_lpc(spx_lsp_t freq,spx_coef_t 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;
	VARDECL(float *Wp);
	float pw,n1,n2,n3,*n4=NULL;
	VARDECL(float *x_freq);
	int m = lpcrdr>>1;

	ALLOC(Wp, 4*m+2, float);
	pw = Wp;

	/* initialise contents of array */

	for(i=0;i<=4m+1;i++){ / set contents of buffer to 0 */
	*pw++ = 0.0;
	}

	/* Set pointers up */

	pw = Wp;
	xin1 = 1.0;
	xin2 = 1.0;

	ALLOC(x_freq, lpcrdr, float);
	for (i=0;i<lpcrdr;i++)
	x_freq[i] = ANGLE2X(freq[i]);

	/* 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.fx_freq[i2] n1 + n2;
	xout2 = xin2 - 2.fx_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);
	if (j>0)
	ak[j-1] = (xout1 + xout2)*0.5f;
	*(n4+1) = xin1;
	*(n4+2) = xin2;

	xin1 = 0.0;
	xin2 = 0.0;
	}

	}
	#endif


	#ifdef FIXED_POINT

	/Makes sure the LSPs are stable/
	void lsp_enforce_margin(spx_lsp_t *lsp, int len, spx_word16_t margin)
	{
	int i;
	spx_word16_t m = margin;
	spx_word16_t m2 = 25736-margin;

	if (lsp[0]<m)
	lsp[0]=m;
	if (lsp[len-1]>m2)
	lsp[len-1]=m2;
	for (i=1;i<len-1;i++)
	{
	if (lsp[i]<lsp[i-1]+m)
	lsp[i]=lsp[i-1]+m;

	if (lsp[i]>lsp[i+1]-m)
	lsp[i]= SHR16(lsp[i],1) + SHR16(lsp[i+1]-m,1);
	}
	}


	void lsp_interpolate(spx_lsp_t old_lsp, spx_lsp_t new_lsp, spx_lsp_t *interp_lsp, int len, int subframe, int nb_subframes)
	{
	int i;
	spx_word16_t tmp = DIV32_16(SHL32(EXTEND32(1 + subframe),14),nb_subframes);
	spx_word16_t tmp2 = 16384-tmp;
	for (i=0;i<len;i++)
	{
	interp_lsp[i] = MULT16_16_P14(tmp2,old_lsp[i]) + MULT16_16_P14(tmp,new_lsp[i]);
	}
	}

	#else

	/Makes sure the LSPs are stable/
	void lsp_enforce_margin(spx_lsp_t *lsp, int len, spx_word16_t margin)
	{
	int i;
	if (lsp[0]<LSP_SCALING*margin)
	lsp[0]=LSP_SCALING*margin;
	if (lsp[len-1]>LSP_SCALING*(M_PI-margin))
	lsp[len-1]=LSP_SCALING*(M_PI-margin);
	for (i=1;i<len-1;i++)
	{
	if (lsp[i]<lsp[i-1]+LSP_SCALING*margin)
	lsp[i]=lsp[i-1]+LSP_SCALING*margin;

	if (lsp[i]>lsp[i+1]-LSP_SCALING*margin)
	lsp[i]= .5f* (lsp[i] + lsp[i+1]-LSP_SCALING*margin);
	}
	}


	void lsp_interpolate(spx_lsp_t old_lsp, spx_lsp_t new_lsp, spx_lsp_t *interp_lsp, int len, int subframe, int nb_subframes)
	{
	int i;
	float tmp = (1.0f + subframe)/nb_subframes;
	for (i=0;i<len;i++)
	{
	interp_lsp[i] = (1-tmp)old_lsp[i] + tmpnew_lsp[i];
	}
	}

	#endif