/*---------------------------------------------------------------------------*\
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
#ifdef _MSC_VER
#include "winpoop.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 C1 8192
#define C2 -4096
#define C3 340
#define C4 -10
static spx_word16_t spx_cos(spx_word16_t x)
{
spx_word16_t x2;
if (x<12868)
{
x2 = MULT16_16_P13(x,x);
return ADD32(C1, MULT16_16_P13(x2, ADD32(C2, MULT16_16_P13(x2, ADD32(C3, MULT16_16_P13(C4, x2))))));
} else {
x = SUB16(25736,x);
x2 = MULT16_16_P13(x,x);
return SUB32(-C1, MULT16_16_P13(x2, ADD32(C2, MULT16_16_P13(x2, ADD32(C3, MULT16_16_P13(C4, x2))))));
/*return SUB32(-C1, MULT16_16_Q13(x2, ADD32(C2, MULT16_16_Q13(C3, x2))));*/
}
}
#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 C1 0.9999932946f
#define C2 -0.4999124376f
#define C3 0.0414877472f
#define C4 -0.0012712095f
#define SPX_PI_2 1.5707963268
static inline spx_word16_t spx_cos(spx_word16_t x)
{
if (x<SPX_PI_2)
{
x *= x;
return C1 + x*(C2+x*(C3+C4*x));
} else {
x = M_PI-x;
x *= x;
return NEG16(C1 + x*(C2+x*(C3+C4*x)));
}
}
#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(coefn[m2], 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, 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=1;i<=m;i++){
*px++ = SUB32(ADD32(EXTEND32(a[i]),EXTEND32(a[lpcrdr+1-i])), *p++);
*qx++ = ADD32(SUB32(EXTEND32(a[i]),EXTEND32(a[lpcrdr+1-i])), *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=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++;
}
#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? */
/*FIXME: Is it OK to have a long constant? */
if (xout1 + xout2>SHL(32766,8))
ak[j] = 32767;
else if (xout1 + xout2 < -SHL(32766,8))
ak[j] = -32767;
else
ak[j] = 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);
ak[j] = (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(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