text: /***********************************************************************
  Copyright (c) 2006-2012 IETF Trust and Skype Limited. All rights reserved.
  
  This file is extracted from RFC6716. Please see that RFC for additional
  information.
  
  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 Internet Society, IETF or IETF Trust, nor the
  names of specific 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 COPYRIGHT OWNER 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 "SigProc_FIX.h"
  #include "define.h"
  #include "tuning_parameters.h"
  
  #define MAX_FRAME_SIZE              384             /* subfr_length * nb_subfr = ( 0.005 * 16000 + 16 ) * 4 = 384 */
  
  #define QA                          25
  #define N_BITS_HEAD_ROOM            2
  #define MIN_RSHIFTS                 -16
  #define MAX_RSHIFTS                 (32 - QA)
  
  /* Compute reflection coefficients from input signal */
  void silk_burg_modified(
      opus_int32                  *res_nrg,           /* O    Residual energy                                             */
      opus_int                    *res_nrg_Q,         /* O    Residual energy Q value                                     */
      opus_int32                  A_Q16[],            /* O    Prediction coefficients (length order)                      */
      const opus_int16            x[],                /* I    Input signal, length: nb_subfr * ( D + subfr_length )       */
      const opus_int32            minInvGain_Q30,     /* I    Inverse of max prediction gain                              */
      const opus_int              subfr_length,       /* I    Input signal subframe length (incl. D preceeding samples)   */
      const opus_int              nb_subfr,           /* I    Number of subframes stacked in x                            */
      const opus_int              D                   /* I    Order                                                       */
  )
  {
      opus_int         k, n, s, lz, rshifts, rshifts_extra, reached_max_gain;
      opus_int32       C0, num, nrg, rc_Q31, invGain_Q30, Atmp_QA, Atmp1, tmp1, tmp2, x1, x2;
      const opus_int16 *x_ptr;
      opus_int32       C_first_row[ SILK_MAX_ORDER_LPC ];
      opus_int32       C_last_row[  SILK_MAX_ORDER_LPC ];
      opus_int32       Af_QA[       SILK_MAX_ORDER_LPC ];
      opus_int32       CAf[ SILK_MAX_ORDER_LPC + 1 ];
      opus_int32       CAb[ SILK_MAX_ORDER_LPC + 1 ];
  
      silk_assert( subfr_length * nb_subfr <= MAX_FRAME_SIZE );
  
      /* Compute autocorrelations, added over subframes */
      silk_sum_sqr_shift( &C0, &rshifts, x, nb_subfr * subfr_length );
      if( rshifts > MAX_RSHIFTS ) {
          C0 = silk_LSHIFT32( C0, rshifts - MAX_RSHIFTS );
          silk_assert( C0 > 0 );
          rshifts = MAX_RSHIFTS;
      } else {
          lz = silk_CLZ32( C0 ) - 1;
          rshifts_extra = N_BITS_HEAD_ROOM - lz;
          if( rshifts_extra > 0 ) {
              rshifts_extra = silk_min( rshifts_extra, MAX_RSHIFTS - rshifts );
              C0 = silk_RSHIFT32( C0, rshifts_extra );
          } else {
              rshifts_extra = silk_max( rshifts_extra, MIN_RSHIFTS - rshifts );
              C0 = silk_LSHIFT32( C0, -rshifts_extra );
          }
          rshifts += rshifts_extra;
      }
      CAb[ 0 ] = CAf[ 0 ] = C0 + silk_SMMUL( SILK_FIX_CONST( FIND_LPC_COND_FAC, 32 ), C0 ) + 1;                                /* Q(-rshifts) */
      silk_memset( C_first_row, 0, SILK_MAX_ORDER_LPC * sizeof( opus_int32 ) );
      if( rshifts > 0 ) {
          for( s = 0; s < nb_subfr; s++ ) {
              x_ptr = x + s * subfr_length;
              for( n = 1; n < D + 1; n++ ) {
                  C_first_row[ n - 1 ] += (opus_int32)silk_RSHIFT64(
                      silk_inner_prod16_aligned_64( x_ptr, x_ptr + n, subfr_length - n ), rshifts );
              }
          }
      } else {
          for( s = 0; s < nb_subfr; s++ ) {
              x_ptr = x + s * subfr_length;
              for( n = 1; n < D + 1; n++ ) {
                  C_first_row[ n - 1 ] += silk_LSHIFT32(
                      silk_inner_prod_aligned( x_ptr, x_ptr + n, subfr_length - n ), -rshifts );
              }
          }
      }
      silk_memcpy( C_last_row, C_first_row, SILK_MAX_ORDER_LPC * sizeof( opus_int32 ) );
  
      /* Initialize */
      CAb[ 0 ] = CAf[ 0 ] = C0 + silk_SMMUL( SILK_FIX_CONST( FIND_LPC_COND_FAC, 32 ), C0 ) + 1;                                /* Q(-rshifts) */
  
      invGain_Q30 = 1 << 30;
      reached_max_gain = 0;
      for( n = 0; n < D; n++ ) {
          /* Update first row of correlation matrix (without first element) */
          /* Update last row of correlation matrix (without last element, stored in reversed order) */
          /* Update C * Af */
          /* Update C * flipud(Af) (stored in reversed order) */
          if( rshifts > -2 ) {
              for( s = 0; s < nb_subfr; s++ ) {
                  x_ptr = x + s * subfr_length;
                  x1  = -silk_LSHIFT32( (opus_int32)x_ptr[ n ],                    16 - rshifts );        /* Q(16-rshifts) */
                  x2  = -silk_LSHIFT32( (opus_int32)x_ptr[ subfr_length - n - 1 ], 16 - rshifts );        /* Q(16-rshifts) */
                  tmp1 = silk_LSHIFT32( (opus_int32)x_ptr[ n ],                    QA - 16 );             /* Q(QA-16) */
                  tmp2 = silk_LSHIFT32( (opus_int32)x_ptr[ subfr_length - n - 1 ], QA - 16 );             /* Q(QA-16) */
                  for( k = 0; k < n; k++ ) {
                      C_first_row[ k ] = silk_SMLAWB( C_first_row[ k ], x1, x_ptr[ n - k - 1 ]            ); /* Q( -rshifts ) */
                      C_last_row[ k ]  = silk_SMLAWB( C_last_row[ k ],  x2, x_ptr[ subfr_length - n + k ] ); /* Q( -rshifts ) */
                      Atmp_QA = Af_QA[ k ];
                      tmp1 = silk_SMLAWB( tmp1, Atmp_QA, x_ptr[ n - k - 1 ]            );                 /* Q(QA-16) */
                      tmp2 = silk_SMLAWB( tmp2, Atmp_QA, x_ptr[ subfr_length - n + k ] );                 /* Q(QA-16) */
                  }
                  tmp1 = silk_LSHIFT32( -tmp1, 32 - QA - rshifts );                                       /* Q(16-rshifts) */
                  tmp2 = silk_LSHIFT32( -tmp2, 32 - QA - rshifts );                                       /* Q(16-rshifts) */
                  for( k = 0; k <= n; k++ ) {
                      CAf[ k ] = silk_SMLAWB( CAf[ k ], tmp1, x_ptr[ n - k ]                    );        /* Q( -rshift ) */
                      CAb[ k ] = silk_SMLAWB( CAb[ k ], tmp2, x_ptr[ subfr_length - n + k - 1 ] );        /* Q( -rshift ) */
                  }
              }
          } else {
              for( s = 0; s < nb_subfr; s++ ) {
                  x_ptr = x + s * subfr_length;
                  x1  = -silk_LSHIFT32( (opus_int32)x_ptr[ n ],                    -rshifts );            /* Q( -rshifts ) */
                  x2  = -silk_LSHIFT32( (opus_int32)x_ptr[ subfr_length - n - 1 ], -rshifts );            /* Q( -rshifts ) */
                  tmp1 = silk_LSHIFT32( (opus_int32)x_ptr[ n ],                    17 );                  /* Q17 */
                  tmp2 = silk_LSHIFT32( (opus_int32)x_ptr[ subfr_length - n - 1 ], 17 );                  /* Q17 */
                  for( k = 0; k < n; k++ ) {
                      C_first_row[ k ] = silk_MLA( C_first_row[ k ], x1, x_ptr[ n - k - 1 ]            ); /* Q( -rshifts ) */
                      C_last_row[ k ]  = silk_MLA( C_last_row[ k ],  x2, x_ptr[ subfr_length - n + k ] ); /* Q( -rshifts ) */
                      Atmp1 = silk_RSHIFT_ROUND( Af_QA[ k ], QA - 17 );                                   /* Q17 */
                      tmp1 = silk_MLA( tmp1, x_ptr[ n - k - 1 ],            Atmp1 );                      /* Q17 */
                      tmp2 = silk_MLA( tmp2, x_ptr[ subfr_length - n + k ], Atmp1 );                      /* Q17 */
                  }
                  tmp1 = -tmp1;                                                                           /* Q17 */
                  tmp2 = -tmp2;                                                                           /* Q17 */
                  for( k = 0; k <= n; k++ ) {
                      CAf[ k ] = silk_SMLAWW( CAf[ k ], tmp1,
                          silk_LSHIFT32( (opus_int32)x_ptr[ n - k ], -rshifts - 1 ) );                    /* Q( -rshift ) */
                      CAb[ k ] = silk_SMLAWW( CAb[ k ], tmp2,
                          silk_LSHIFT32( (opus_int32)x_ptr[ subfr_length - n + k - 1 ], -rshifts - 1 ) ); /* Q( -rshift ) */
                  }
              }
          }
  
          /* Calculate nominator and denominator for the next order reflection (parcor) coefficient */
          tmp1 = C_first_row[ n ];                                                                        /* Q( -rshifts ) */
          tmp2 = C_last_row[ n ];                                                                         /* Q( -rshifts ) */
          num  = 0;                                                                                       /* Q( -rshifts ) */
          nrg  = silk_ADD32( CAb[ 0 ], CAf[ 0 ] );                                                        /* Q( 1-rshifts ) */
          for( k = 0; k < n; k++ ) {
              Atmp_QA = Af_QA[ k ];
              lz = silk_CLZ32( silk_abs( Atmp_QA ) ) - 1;
              lz = silk_min( 32 - QA, lz );
              Atmp1 = silk_LSHIFT32( Atmp_QA, lz );                                                       /* Q( QA + lz ) */
  
              tmp1 = silk_ADD_LSHIFT32( tmp1, silk_SMMUL( C_last_row[  n - k - 1 ], Atmp1 ), 32 - QA - lz );  /* Q( -rshifts ) */
              tmp2 = silk_ADD_LSHIFT32( tmp2, silk_SMMUL( C_first_row[ n - k - 1 ], Atmp1 ), 32 - QA - lz );  /* Q( -rshifts ) */
              num  = silk_ADD_LSHIFT32( num,  silk_SMMUL( CAb[ n - k ],             Atmp1 ), 32 - QA - lz );  /* Q( -rshifts ) */
              nrg  = silk_ADD_LSHIFT32( nrg,  silk_SMMUL( silk_ADD32( CAb[ k + 1 ], CAf[ k + 1 ] ),
                                                                                  Atmp1 ), 32 - QA - lz );    /* Q( 1-rshifts ) */
          }
          CAf[ n + 1 ] = tmp1;                                                                            /* Q( -rshifts ) */
          CAb[ n + 1 ] = tmp2;                                                                            /* Q( -rshifts ) */
          num = silk_ADD32( num, tmp2 );                                                                  /* Q( -rshifts ) */
          num = silk_LSHIFT32( -num, 1 );                                                                 /* Q( 1-rshifts ) */
  
          /* Calculate the next order reflection (parcor) coefficient */
          if( silk_abs( num ) < nrg ) {
              rc_Q31 = silk_DIV32_varQ( num, nrg, 31 );
          } else {
              rc_Q31 = ( num > 0 ) ? silk_int32_MAX : silk_int32_MIN;
          }
  
          /* Update inverse prediction gain */
          tmp1 = ( (opus_int32)1 << 30 ) - silk_SMMUL( rc_Q31, rc_Q31 );
          tmp1 = silk_LSHIFT( silk_SMMUL( invGain_Q30, tmp1 ), 2 );
          if( tmp1 <= minInvGain_Q30 ) {
              /* Max prediction gain exceeded; set reflection coefficient such that max prediction gain is exactly hit */
              tmp2 = ( 1 << 30 ) - silk_DIV32_varQ( minInvGain_Q30, invGain_Q30, 30 );            /* Q30 */
              rc_Q31 = silk_SQRT_APPROX( tmp2 );                                                  /* Q15 */
              /* Newton-Raphson iteration */
              rc_Q31 = silk_RSHIFT32( rc_Q31 + silk_DIV32( tmp2, rc_Q31 ), 1 );                   /* Q15 */
              rc_Q31 = silk_LSHIFT32( rc_Q31, 16 );                                               /* Q31 */
              if( num < 0 ) {
                  /* Ensure adjusted reflection coefficients has the original sign */
                  rc_Q31 = -rc_Q31;
              }
              invGain_Q30 = minInvGain_Q30;
              reached_max_gain = 1;
          } else {
              invGain_Q30 = tmp1;
          }
  
          /* Update the AR coefficients */
          for( k = 0; k < (n + 1) >> 1; k++ ) {
              tmp1 = Af_QA[ k ];                                                                  /* QA */
              tmp2 = Af_QA[ n - k - 1 ];                                                          /* QA */
              Af_QA[ k ]         = silk_ADD_LSHIFT32( tmp1, silk_SMMUL( tmp2, rc_Q31 ), 1 );      /* QA */
              Af_QA[ n - k - 1 ] = silk_ADD_LSHIFT32( tmp2, silk_SMMUL( tmp1, rc_Q31 ), 1 );      /* QA */
          }
          Af_QA[ n ] = silk_RSHIFT32( rc_Q31, 31 - QA );                                          /* QA */
  
          if( reached_max_gain ) {
              /* Reached max prediction gain; set remaining coefficients to zero and exit loop */
              for( k = n + 1; k < D; k++ ) {
                  Af_QA[ k ] = 0;
              }
              break;
          }
  
          /* Update C * Af and C * Ab */
          for( k = 0; k <= n + 1; k++ ) {
              tmp1 = CAf[ k ];                                                                    /* Q( -rshifts ) */
              tmp2 = CAb[ n - k + 1 ];                                                            /* Q( -rshifts ) */
              CAf[ k ]         = silk_ADD_LSHIFT32( tmp1, silk_SMMUL( tmp2, rc_Q31 ), 1 );        /* Q( -rshifts ) */
              CAb[ n - k + 1 ] = silk_ADD_LSHIFT32( tmp2, silk_SMMUL( tmp1, rc_Q31 ), 1 );        /* Q( -rshifts ) */
          }
      }
  
      if( reached_max_gain ) {
          for( k = 0; k < D; k++ ) {
              /* Scale coefficients */
              A_Q16[ k ] = -silk_RSHIFT_ROUND( Af_QA[ k ], QA - 16 );
          }
          /* Subtract energy of preceeding samples from C0 */
          if( rshifts > 0 ) {
              for( s = 0; s < nb_subfr; s++ ) {
                  x_ptr = x + s * subfr_length;
                  C0 -= (opus_int32)silk_RSHIFT64( silk_inner_prod16_aligned_64( x_ptr, x_ptr, D ), rshifts );
              }
          } else {
              for( s = 0; s < nb_subfr; s++ ) {
                  x_ptr = x + s * subfr_length;
                  C0 -= silk_LSHIFT32( silk_inner_prod_aligned( x_ptr, x_ptr, D ), -rshifts );
              }
          }
          /* Approximate residual energy */
          *res_nrg = silk_LSHIFT( silk_SMMUL( invGain_Q30, C0 ), 2 );
          *res_nrg_Q = -rshifts;
      } else {
          /* Return residual energy */
          nrg  = CAf[ 0 ];                                                                            /* Q( -rshifts ) */
          tmp1 = 1 << 16;                                                                             /* Q16 */
          for( k = 0; k < D; k++ ) {
              Atmp1 = silk_RSHIFT_ROUND( Af_QA[ k ], QA - 16 );                                       /* Q16 */
              nrg  = silk_SMLAWW( nrg, CAf[ k + 1 ], Atmp1 );                                         /* Q( -rshifts ) */
              tmp1 = silk_SMLAWW( tmp1, Atmp1, Atmp1 );                                               /* Q16 */
              A_Q16[ k ] = -Atmp1;
          }
          *res_nrg = silk_SMLAWW( nrg, silk_SMMUL( FIND_LPC_COND_FAC, C0 ), -tmp1 );                  /* Q( -rshifts ) */
          *res_nrg_Q = -rshifts;
      }
  }
  