/*  Copyright 1992, 1993, 1994 by Jutta Degener and Carsten Bormann,  Technische Universitaet Berlin  Any use of this software is permitted provided that this notice is not  removed and that neither the authors nor the Technische Universitaet Berlin  are deemed to have made any representations as to the suitability of this  software for any purpose nor are held responsible for any defects of  this software.  THERE IS ABSOLUTELY NO WARRANTY FOR THIS SOFTWARE.  As a matter of courtesy, the authors request to be informed about uses  this software has found, about bugs in this software, and about any  improvements that may be of general interest.  Berlin, 28.11.1994  Jutta Degener  Carsten Bormann   Code slightly modified by Jean-Marc Valin   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.*//* LPC- and Reflection Coefficients * * The next two functions calculate linear prediction coefficients * and/or the related reflection coefficients from the first P_MAX+1 * values of the autocorrelation function. *//* Invented by N. Levinson in 1947, modified by J. Durbin in 1959. */#include "lpc.h"float                      /* returns minimum mean square error    */wld(    float       * lpc, /*      [0...p-1] LPC coefficients      */    const float * ac,  /*  in: [0...p] autocorrelation values  */    float       * ref, /* out: [0...p-1] reflection coef's     */    int p    ){   int i, j;  float r, error = ac[0];   if (ac[0] == 0) {      for (i = 0; i < p; i++) ref[i] = 0; return 0; }   for (i = 0; i < p; i++) {      /* Sum up this iteration's reflection coefficient.       */      r = -ac[i + 1];      for (j = 0; j < i; j++) r -= lpc[j] * ac[i - j];      ref[i] = r /= error;      /*  Update LPC coefficients and total error.       */      lpc[i] = r;      for (j = 0; j < i/2; j++) {         float tmp  = lpc[j];         lpc[j]     += r * lpc[i-1-j];         lpc[i-1-j] += r * tmp;      }      if (i % 2) lpc[j] += lpc[j] * r;      error *= 1.0 - r * r;   }   return error;}/* Compute the autocorrelation *                      ,--, *              ac(i) = >  x(n) * x(n-i)  for all n *                      `--' * for lags between 0 and lag-1, and x == 0 outside 0...n-1 */void _spx_autocorr(              const float * x,   /*  in: [0...n-1] samples x   */              float *ac,   /* out: [0...lag-1] ac values */              int lag, int   n){   float d; int i;   while (lag--) {      for (i = lag, d = 0; i < n; i++) d += x[i] * x[i-lag];      ac[lag] = d;   }}