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     11 - Neither the name of Internet Society, IETF or IETF Trust, nor the
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     13 products derived from this software without specific prior written
     14 permission.
     15 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS
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     24 ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
     25 POSSIBILITY OF SUCH DAMAGE.
     26 ***********************************************************************/
     27 
     28 #ifdef HAVE_CONFIG_H
     29 #include "config.h"
     30 #endif
     31 
     32 /* conversion between prediction filter coefficients and LSFs   */
     33 /* order should be even                                         */
     34 /* a piecewise linear approximation maps LSF <-> cos(LSF)       */
     35 /* therefore the result is not accurate LSFs, but the two       */
     36 /* functions are accurate inverses of each other                */
     37 
     38 #include "SigProc_FIX.h"
     39 #include "tables.h"
     40 
     41 #define QA      16
     42 
     43 /* helper function for NLSF2A(..) */
     44 static inline void silk_NLSF2A_find_poly(
     45     opus_int32          *out,      /* O    intermediate polynomial, QA [dd+1]        */
     46     const opus_int32    *cLSF,     /* I    vector of interleaved 2*cos(LSFs), QA [d] */
     47     opus_int            dd         /* I    polynomial order (= 1/2 * filter order)   */
     48 )
     49 {
     50     opus_int   k, n;
     51     opus_int32 ftmp;
     52 
     53     out[0] = silk_LSHIFT( 1, QA );
     54     out[1] = -cLSF[0];
     55     for( k = 1; k < dd; k++ ) {
     56         ftmp = cLSF[2*k];            /* QA*/
     57         out[k+1] = silk_LSHIFT( out[k-1], 1 ) - (opus_int32)silk_RSHIFT_ROUND64( silk_SMULL( ftmp, out[k] ), QA );
     58         for( n = k; n > 1; n-- ) {
     59             out[n] += out[n-2] - (opus_int32)silk_RSHIFT_ROUND64( silk_SMULL( ftmp, out[n-1] ), QA );
     60         }
     61         out[1] -= ftmp;
     62     }
     63 }
     64 
     65 /* compute whitening filter coefficients from normalized line spectral frequencies */
     66 void silk_NLSF2A(
     67     opus_int16                  *a_Q12,             /* O    monic whitening filter coefficients in Q12,  [ d ]          */
     68     const opus_int16            *NLSF,              /* I    normalized line spectral frequencies in Q15, [ d ]          */
     69     const opus_int              d                   /* I    filter order (should be even)                               */
     70 )
     71 {
     72     /* This ordering was found to maximize quality. It improves numerical accuracy of
     73        silk_NLSF2A_find_poly() compared to "standard" ordering. */
     74     static const unsigned char ordering16[16] = {
     75       0, 15, 8, 7, 4, 11, 12, 3, 2, 13, 10, 5, 6, 9, 14, 1
     76     };
     77     static const unsigned char ordering10[10] = {
     78       0, 9, 6, 3, 4, 5, 8, 1, 2, 7
     79     };
     80     const unsigned char *ordering;
     81     opus_int   k, i, dd;
     82     opus_int32 cos_LSF_QA[ SILK_MAX_ORDER_LPC ];
     83     opus_int32 P[ SILK_MAX_ORDER_LPC / 2 + 1 ], Q[ SILK_MAX_ORDER_LPC / 2 + 1 ];
     84     opus_int32 Ptmp, Qtmp, f_int, f_frac, cos_val, delta;
     85     opus_int32 a32_QA1[ SILK_MAX_ORDER_LPC ];
     86     opus_int32 maxabs, absval, idx=0, sc_Q16;
     87 
     88     silk_assert( LSF_COS_TAB_SZ_FIX == 128 );
     89     silk_assert( d==10||d==16 );
     90 
     91     /* convert LSFs to 2*cos(LSF), using piecewise linear curve from table */
     92     ordering = d == 16 ? ordering16 : ordering10;
     93     for( k = 0; k < d; k++ ) {
     94         silk_assert(NLSF[k] >= 0 );
     95 
     96         /* f_int on a scale 0-127 (rounded down) */
     97         f_int = silk_RSHIFT( NLSF[k], 15 - 7 );
     98 
     99         /* f_frac, range: 0..255 */
    100         f_frac = NLSF[k] - silk_LSHIFT( f_int, 15 - 7 );
    101 
    102         silk_assert(f_int >= 0);
    103         silk_assert(f_int < LSF_COS_TAB_SZ_FIX );
    104 
    105         /* Read start and end value from table */
    106         cos_val = silk_LSFCosTab_FIX_Q12[ f_int ];                /* Q12 */
    107         delta   = silk_LSFCosTab_FIX_Q12[ f_int + 1 ] - cos_val;  /* Q12, with a range of 0..200 */
    108 
    109         /* Linear interpolation */
    110         cos_LSF_QA[ordering[k]] = silk_RSHIFT_ROUND( silk_LSHIFT( cos_val, 8 ) + silk_MUL( delta, f_frac ), 20 - QA ); /* QA */
    111     }
    112 
    113     dd = silk_RSHIFT( d, 1 );
    114 
    115     /* generate even and odd polynomials using convolution */
    116     silk_NLSF2A_find_poly( P, &cos_LSF_QA[ 0 ], dd );
    117     silk_NLSF2A_find_poly( Q, &cos_LSF_QA[ 1 ], dd );
    118 
    119     /* convert even and odd polynomials to opus_int32 Q12 filter coefs */
    120     for( k = 0; k < dd; k++ ) {
    121         Ptmp = P[ k+1 ] + P[ k ];
    122         Qtmp = Q[ k+1 ] - Q[ k ];
    123 
    124         /* the Ptmp and Qtmp values at this stage need to fit in int32 */
    125         a32_QA1[ k ]     = -Qtmp - Ptmp;        /* QA+1 */
    126         a32_QA1[ d-k-1 ] =  Qtmp - Ptmp;        /* QA+1 */
    127     }
    128 
    129     /* Limit the maximum absolute value of the prediction coefficients, so that they'll fit in int16 */
    130     for( i = 0; i < 10; i++ ) {
    131         /* Find maximum absolute value and its index */
    132         maxabs = 0;
    133         for( k = 0; k < d; k++ ) {
    134             absval = silk_abs( a32_QA1[k] );
    135             if( absval > maxabs ) {
    136                 maxabs = absval;
    137                 idx    = k;
    138             }
    139         }
    140         maxabs = silk_RSHIFT_ROUND( maxabs, QA + 1 - 12 );                                          /* QA+1 -> Q12 */
    141 
    142         if( maxabs > silk_int16_MAX ) {
    143             /* Reduce magnitude of prediction coefficients */
    144             maxabs = silk_min( maxabs, 163838 );  /* ( silk_int32_MAX >> 14 ) + silk_int16_MAX = 163838 */
    145             sc_Q16 = SILK_FIX_CONST( 0.999, 16 ) - silk_DIV32( silk_LSHIFT( maxabs - silk_int16_MAX, 14 ),
    146                                         silk_RSHIFT32( silk_MUL( maxabs, idx + 1), 2 ) );
    147             silk_bwexpander_32( a32_QA1, d, sc_Q16 );
    148         } else {
    149             break;
    150         }
    151     }
    152 
    153     if( i == 10 ) {
    154         /* Reached the last iteration, clip the coefficients */
    155         for( k = 0; k < d; k++ ) {
    156             a_Q12[ k ] = (opus_int16)silk_SAT16( silk_RSHIFT_ROUND( a32_QA1[ k ], QA + 1 - 12 ) );  /* QA+1 -> Q12 */
    157             a32_QA1[ k ] = silk_LSHIFT( (opus_int32)a_Q12[ k ], QA + 1 - 12 );
    158         }
    159     } else {
    160         for( k = 0; k < d; k++ ) {
    161             a_Q12[ k ] = (opus_int16)silk_RSHIFT_ROUND( a32_QA1[ k ], QA + 1 - 12 );                /* QA+1 -> Q12 */
    162         }
    163     }
    164 
    165     for( i = 0; i < MAX_LPC_STABILIZE_ITERATIONS; i++ ) {
    166         if( silk_LPC_inverse_pred_gain( a_Q12, d ) < SILK_FIX_CONST( 1.0 / MAX_PREDICTION_POWER_GAIN, 30 ) ) {
    167             /* Prediction coefficients are (too close to) unstable; apply bandwidth expansion   */
    168             /* on the unscaled coefficients, convert to Q12 and measure again                   */
    169             silk_bwexpander_32( a32_QA1, d, 65536 - silk_LSHIFT( 2, i ) );
    170             for( k = 0; k < d; k++ ) {
    171                 a_Q12[ k ] = (opus_int16)silk_RSHIFT_ROUND( a32_QA1[ k ], QA + 1 - 12 );            /* QA+1 -> Q12 */
    172             }
    173         } else {
    174             break;
    175         }
    176     }
    177 }
    178 
    179