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#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

/* conversion between prediction filter coefficients and LSFs   */
/* order should be even                                         */
/* a piecewise linear approximation maps LSF <-> cos(LSF)       */
/* therefore the result is not accurate LSFs, but the two       */
/* functions are accurate inverses of each other                */

#include "SigProc_FIX.h"
#include "tables.h"

#define QA      16

/* helper function for NLSF2A(..) */
static OPUS_INLINE void silk_NLSF2A_find_poly(
    opus_int32          *out,      /* O    intermediate polynomial, QA [dd+1]        */
    const opus_int32    *cLSF,     /* I    vector of interleaved 2*cos(LSFs), QA [d] */
    opus_int            dd         /* I    polynomial order (= 1/2 * filter order)   */
)
{
    opus_int   k, n;
    opus_int32 ftmp;

    out[0] = silk_LSHIFT( 1, QA );
    out[1] = -cLSF[0];
    for( k = 1; k < dd; k++ ) {
        ftmp = cLSF[2*k];            /* QA*/
        out[k+1] = silk_LSHIFT( out[k-1], 1 ) - (opus_int32)silk_RSHIFT_ROUND64( silk_SMULL( ftmp, out[k] ), QA );
        for( n = k; n > 1; n-- ) {
            out[n] += out[n-2] - (opus_int32)silk_RSHIFT_ROUND64( silk_SMULL( ftmp, out[n-1] ), QA );
        }
        out[1] -= ftmp;
    }
}

/* compute whitening filter coefficients from normalized line spectral frequencies */
void silk_NLSF2A(
    opus_int16                  *a_Q12,             /* O    monic whitening filter coefficients in Q12,  [ d ]          */
    const opus_int16            *NLSF,              /* I    normalized line spectral frequencies in Q15, [ d ]          */
    const opus_int              d                   /* I    filter order (should be even)                               */
)
{
    /* This ordering was found to maximize quality. It improves numerical accuracy of
       silk_NLSF2A_find_poly() compared to "standard" ordering. */
    static const unsigned char ordering16[16] = {
      0, 15, 8, 7, 4, 11, 12, 3, 2, 13, 10, 5, 6, 9, 14, 1
    };
    static const unsigned char ordering10[10] = {
      0, 9, 6, 3, 4, 5, 8, 1, 2, 7
    };
    const unsigned char *ordering;
    opus_int   k, i, dd;
    opus_int32 cos_LSF_QA[ SILK_MAX_ORDER_LPC ];
    opus_int32 P[ SILK_MAX_ORDER_LPC / 2 + 1 ], Q[ SILK_MAX_ORDER_LPC / 2 + 1 ];
    opus_int32 Ptmp, Qtmp, f_int, f_frac, cos_val, delta;
    opus_int32 a32_QA1[ SILK_MAX_ORDER_LPC ];
    opus_int32 maxabs, absval, idx=0, sc_Q16;

    silk_assert( LSF_COS_TAB_SZ_FIX == 128 );
    silk_assert( d==10||d==16 );

    /* convert LSFs to 2*cos(LSF), using piecewise linear curve from table */
    ordering = d == 16 ? ordering16 : ordering10;
    for( k = 0; k < d; k++ ) {
        silk_assert(NLSF[k] >= 0 );

        /* f_int on a scale 0-127 (rounded down) */
        f_int = silk_RSHIFT( NLSF[k], 15 - 7 );

        /* f_frac, range: 0..255 */
        f_frac = NLSF[k] - silk_LSHIFT( f_int, 15 - 7 );

        silk_assert(f_int >= 0);
        silk_assert(f_int < LSF_COS_TAB_SZ_FIX );

        /* Read start and end value from table */
        cos_val = silk_LSFCosTab_FIX_Q12[ f_int ];                /* Q12 */
        delta   = silk_LSFCosTab_FIX_Q12[ f_int + 1 ] - cos_val;  /* Q12, with a range of 0..200 */

        /* Linear interpolation */
        cos_LSF_QA[ordering[k]] = silk_RSHIFT_ROUND( silk_LSHIFT( cos_val, 8 ) + silk_MUL( delta, f_frac ), 20 - QA ); /* QA */
    }

    dd = silk_RSHIFT( d, 1 );

    /* generate even and odd polynomials using convolution */
    silk_NLSF2A_find_poly( P, &cos_LSF_QA[ 0 ], dd );
    silk_NLSF2A_find_poly( Q, &cos_LSF_QA[ 1 ], dd );

    /* convert even and odd polynomials to opus_int32 Q12 filter coefs */
    for( k = 0; k < dd; k++ ) {
        Ptmp = P[ k+1 ] + P[ k ];
        Qtmp = Q[ k+1 ] - Q[ k ];

        /* the Ptmp and Qtmp values at this stage need to fit in int32 */
        a32_QA1[ k ]     = -Qtmp - Ptmp;        /* QA+1 */
        a32_QA1[ d-k-1 ] =  Qtmp - Ptmp;        /* QA+1 */
    }

    /* Limit the maximum absolute value of the prediction coefficients, so that they'll fit in int16 */
    for( i = 0; i < 10; i++ ) {
        /* Find maximum absolute value and its index */
        maxabs = 0;
        for( k = 0; k < d; k++ ) {
            absval = silk_abs( a32_QA1[k] );
            if( absval > maxabs ) {
                maxabs = absval;
                idx    = k;
            }
        }
        maxabs = silk_RSHIFT_ROUND( maxabs, QA + 1 - 12 );                                          /* QA+1 -> Q12 */

        if( maxabs > silk_int16_MAX ) {
            /* Reduce magnitude of prediction coefficients */
            maxabs = silk_min( maxabs, 163838 );  /* ( silk_int32_MAX >> 14 ) + silk_int16_MAX = 163838 */
            sc_Q16 = SILK_FIX_CONST( 0.999, 16 ) - silk_DIV32( silk_LSHIFT( maxabs - silk_int16_MAX, 14 ),
                                        silk_RSHIFT32( silk_MUL( maxabs, idx + 1), 2 ) );
            silk_bwexpander_32( a32_QA1, d, sc_Q16 );
        } else {
            break;
        }
    }

    if( i == 10 ) {
        /* Reached the last iteration, clip the coefficients */
        for( k = 0; k < d; k++ ) {
            a_Q12[ k ] = (opus_int16)silk_SAT16( silk_RSHIFT_ROUND( a32_QA1[ k ], QA + 1 - 12 ) );  /* QA+1 -> Q12 */
            a32_QA1[ k ] = silk_LSHIFT( (opus_int32)a_Q12[ k ], QA + 1 - 12 );
        }
    } else {
        for( k = 0; k < d; k++ ) {
            a_Q12[ k ] = (opus_int16)silk_RSHIFT_ROUND( a32_QA1[ k ], QA + 1 - 12 );                /* QA+1 -> Q12 */
        }
    }

    for( i = 0; i < MAX_LPC_STABILIZE_ITERATIONS; i++ ) {
        if( silk_LPC_inverse_pred_gain( a_Q12, d ) < SILK_FIX_CONST( 1.0 / MAX_PREDICTION_POWER_GAIN, 30 ) ) {
            /* Prediction coefficients are (too close to) unstable; apply bandwidth expansion   */
            /* on the unscaled coefficients, convert to Q12 and measure again                   */
            silk_bwexpander_32( a32_QA1, d, 65536 - silk_LSHIFT( 2, i ) );
            for( k = 0; k < d; k++ ) {
                a_Q12[ k ] = (opus_int16)silk_RSHIFT_ROUND( a32_QA1[ k ], QA + 1 - 12 );            /* QA+1 -> Q12 */
            }
        } else {
            break;
        }
    }
}