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+/*---------------------------------------------------------------------------*\
+Original copyright
+ FILE........: lsp.c
+ AUTHOR......: David Rowe
+ DATE CREATED: 24/2/93
+
+Heavily modified by Jean-Marc Valin (c) 2002-2006 (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.
+*/
+
+/*---------------------------------------------------------------------------*\
+
+ Introduction to Line Spectrum Pairs (LSPs)
+ ------------------------------------------
+
+ LSPs are used to encode the LPC filter coefficients {ak} for
+ transmission over the channel. LSPs have several properties (like
+ less sensitivity to quantisation noise) that make them superior to
+ direct quantisation of {ak}.
+
+ A(z) is a polynomial of order lpcrdr with {ak} as the coefficients.
+
+ A(z) is transformed to P(z) and Q(z) (using a substitution and some
+ algebra), to obtain something like:
+
+ A(z) = 0.5[P(z)(z+z^-1) + Q(z)(z-z^-1)] (1)
+
+ As you can imagine A(z) has complex zeros all over the z-plane. P(z)
+ and Q(z) have the very neat property of only having zeros _on_ the
+ unit circle. So to find them we take a test point z=exp(jw) and
+ evaluate P (exp(jw)) and Q(exp(jw)) using a grid of points between 0
+ and pi.
+
+ The zeros (roots) of P(z) also happen to alternate, which is why we
+ swap coefficients as we find roots. So the process of finding the
+ LSP frequencies is basically finding the roots of 5th order
+ polynomials.
+
+ The root so P(z) and Q(z) occur in symmetrical pairs at +/-w, hence
+ the name Line Spectrum Pairs (LSPs).
+
+ To convert back to ak we just evaluate (1), "clocking" an impulse
+ thru it lpcrdr times gives us the impulse response of A(z) which is
+ {ak}.
+
+\*---------------------------------------------------------------------------*/
+
+#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))
+
+#ifdef BFIN_ASM
+#include "lsp_bfin.h"
+#endif
+
+#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
+
+#ifndef OVERRIDE_CHEB_POLY_EVA
+static inline spx_word32_t cheb_poly_eva(
+ spx_word16_t *coef, /* P or Q coefs in Q13 format */
+ spx_word16_t x, /* cos of freq (-1.0 to 1.0) in Q14 format */
+ int m, /* LPC order/2 */
+ char *stack
+)
+{
+ int i;
+ spx_word16_t b0, b1;
+ spx_word32_t sum;
+
+ /*Prevents overflows*/
+ if (x>16383)
+ x = 16383;
+ if (x<-16383)
+ x = -16383;
+
+ /* Initialise values */
+ b1=16384;
+ b0=x;
+
+ /* Evaluate Chebyshev series formulation usin g iterative approach */
+ sum = ADD32(EXTEND32(coef[m]), EXTEND32(MULT16_16_P14(coef[m-1],x)));
+ for(i=2;i<=m;i++)
+ {
+ spx_word16_t tmp=b0;
+ b0 = SUB16(MULT16_16_Q13(x,b0), b1);
+ b1 = tmp;
+ sum = ADD32(sum, EXTEND32(MULT16_16_P14(coef[m-i],b0)));
+ }
+
+ return sum;
+}
+#endif
+
+#else
+
+static float cheb_poly_eva(spx_word32_t *coef, spx_word16_t x, int m, char *stack)
+{
+ int k;
+ float b0, b1, tmp;
+
+ /* Initial conditions */
+ b0=0; /* b_(m+1) */
+ b1=0; /* b_(m+2) */
+
+ x*=2;
+
+ /* Calculate the b_(k) */
+ for(k=m;k>0;k--)
+ {
+ tmp=b0; /* tmp holds the previous value of b0 */
+ b0=x*b0-b1+coef[m-k]; /* b0 holds its new value based on b0 and b1 */
+ b1=tmp; /* b1 holds the previous value of b0 */
+ }
+
+ return(-b1+.5*x*b0+coef[m]);
+}
+#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);
+ VARDECL(spx_word16_t *Q16); /* ptrs for memory allocation */
+ VARDECL(spx_word16_t *P16);
+ spx_word32_t *px; /* ptrs of respective P'(z) & Q'(z) */
+ spx_word32_t *qx;
+ spx_word32_t *p;
+ spx_word32_t *q;
+ spx_word16_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;
+
+ /* now that we have computed P and Q convert to 16 bits to
+ speed up cheb_poly_eval */
+
+ ALLOC(P16, m+1, spx_word16_t);
+ ALLOC(Q16, m+1, spx_word16_t);
+
+ for (i=0;i<m+1;i++)
+ {
+ P16[i] = P[i];
+ Q16[i] = Q[i];
+ }
+
+ /* 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 = Q16;
+ else
+ pt = P16;
+
+ psuml = cheb_poly_eva(pt,xl,m,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,m,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,m,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
+
+ 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,xin;
+ spx_word32_t mult, a;
+ VARDECL(spx_word16_t *freqn);
+ VARDECL(spx_word32_t **xp);
+ VARDECL(spx_word32_t *xpmem);
+ VARDECL(spx_word32_t **xq);
+ VARDECL(spx_word32_t *xqmem);
+ int m = lpcrdr>>1;
+
+ /*
+
+ Reconstruct P(z) and Q(z) by cascading second order polynomials
+ in form 1 - 2cos(w)z(-1) + z(-2), where w is the LSP frequency.
+ In the time domain this is:
+
+ y(n) = x(n) - 2cos(w)x(n-1) + x(n-2)
+
+ This is what the ALLOCS below are trying to do:
+
+ int xp[m+1][lpcrdr+1+2]; // P matrix in QIMP
+ int xq[m+1][lpcrdr+1+2]; // Q matrix in QIMP
+
+ These matrices store the output of each stage on each row. The
+ final (m-th) row has the output of the final (m-th) cascaded
+ 2nd order filter. The first row is the impulse input to the
+ system (not written as it is known).
+
+ The version below takes advantage of the fact that a lot of the
+ outputs are zero or known, for example if we put an inpulse
+ into the first section the "clock" it 10 times only the first 3
+ outputs samples are non-zero (it's an FIR filter).
+ */
+
+ ALLOC(xp, (m+1), spx_word32_t*);
+ ALLOC(xpmem, (m+1)*(lpcrdr+1+2), spx_word32_t);
+
+ ALLOC(xq, (m+1), spx_word32_t*);
+ ALLOC(xqmem, (m+1)*(lpcrdr+1+2), spx_word32_t);
+
+ for(i=0; i<=m; i++) {
+ xp[i] = xpmem + i*(lpcrdr+1+2);
+ xq[i] = xqmem + i*(lpcrdr+1+2);
+ }
+
+ /* work out 2cos terms in Q14 */
+
+ ALLOC(freqn, lpcrdr, spx_word16_t);
+ for (i=0;i<lpcrdr;i++)
+ freqn[i] = ANGLE2X(freq[i]);
+
+ #define QIMP 21 /* scaling for impulse */
+
+ xin = SHL32(EXTEND32(1), (QIMP-1)); /* 0.5 in QIMP format */
+
+ /* first col and last non-zero values of each row are trivial */
+
+ for(i=0;i<=m;i++) {
+ xp[i][1] = 0;
+ xp[i][2] = xin;
+ xp[i][2+2*i] = xin;
+ xq[i][1] = 0;
+ xq[i][2] = xin;
+ xq[i][2+2*i] = xin;
+ }
+
+ /* 2nd row (first output row) is trivial */
+
+ xp[1][3] = -MULT16_32_Q14(freqn[0],xp[0][2]);
+ xq[1][3] = -MULT16_32_Q14(freqn[1],xq[0][2]);
+
+ xout1 = xout2 = 0;
+
+ /* now generate remaining rows */
+
+ for(i=1;i<m;i++) {
+
+ for(j=1;j<2*(i+1)-1;j++) {
+ mult = MULT16_32_Q14(freqn[2*i],xp[i][j+1]);
+ xp[i+1][j+2] = ADD32(SUB32(xp[i][j+2], mult), xp[i][j]);
+ mult = MULT16_32_Q14(freqn[2*i+1],xq[i][j+1]);
+ xq[i+1][j+2] = ADD32(SUB32(xq[i][j+2], mult), xq[i][j]);
+ }
+
+ /* for last col xp[i][j+2] = xq[i][j+2] = 0 */
+
+ mult = MULT16_32_Q14(freqn[2*i],xp[i][j+1]);
+ xp[i+1][j+2] = SUB32(xp[i][j], mult);
+ mult = MULT16_32_Q14(freqn[2*i+1],xq[i][j+1]);
+ xq[i+1][j+2] = SUB32(xq[i][j], mult);
+ }
+
+ /* process last row to extra a{k} */
+
+ for(j=1;j<=lpcrdr;j++) {
+ int shift = QIMP-13;
+
+ /* final filter sections */
+ a = PSHR32(xp[m][j+2] + xout1 + xq[m][j+2] - xout2, shift);
+ xout1 = xp[m][j+2];
+ xout2 = xq[m][j+2];
+
+ /* hard limit ak's to +/- 32767 */
+
+ if (a < -32767) a = -32767;
+ if (a > 32767) a = 32767;
+ ak[j-1] = (short)a;
+
+ }
+
+}
+
+#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