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/* 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       */
/* function are accurate inverses of each other                 */

#include "SKP_Silk_SigProc_FIX.h"

/* helper function for NLSF2A(..) */
SKP_INLINE void SKP_Silk_NLSF2A_find_poly(
    SKP_int32        *out,        /* o    intermediate polynomial, Q20            */
    const SKP_int32    *cLSF,     /* i    vector of interleaved 2*cos(LSFs), Q20  */
    SKP_int            dd         /* i    polynomial order (= 1/2 * filter order) */
)
{
    SKP_int        k, n;
    SKP_int32    ftmp;

    out[0] = SKP_LSHIFT( 1, 20 );
    out[1] = -cLSF[0];
    for( k = 1; k < dd; k++ ) {
        ftmp = cLSF[2*k];            // Q20
        out[k+1] = SKP_LSHIFT( out[k-1], 1 ) - (SKP_int32)SKP_RSHIFT_ROUND64( SKP_SMULL( ftmp, out[k] ), 20 );
        for( n = k; n > 1; n-- ) {
            out[n] += out[n-2] - (SKP_int32)SKP_RSHIFT_ROUND64( SKP_SMULL( ftmp, out[n-1] ), 20 );
        }
        out[1] -= ftmp;
    }
}

/* compute whitening filter coefficients from normalized line spectral frequencies */
void SKP_Silk_NLSF2A(
    SKP_int16       *a,               /* o    monic whitening filter coefficients in Q12,  [d]    */
    const SKP_int    *NLSF,           /* i    normalized line spectral frequencies in Q15, [d]    */
    const SKP_int    d                /* i    filter order (should be even)                       */
)
{
    SKP_int k, i, dd;
    SKP_int32 cos_LSF_Q20[SKP_Silk_MAX_ORDER_LPC];
    SKP_int32 P[SKP_Silk_MAX_ORDER_LPC/2+1], Q[SKP_Silk_MAX_ORDER_LPC/2+1];
    SKP_int32 Ptmp, Qtmp;
    SKP_int32 f_int;
    SKP_int32 f_frac;
    SKP_int32 cos_val, delta;
    SKP_int32 a_int32[SKP_Silk_MAX_ORDER_LPC];
    SKP_int32 maxabs, absval, idx=0, sc_Q16; 

    SKP_assert(LSF_COS_TAB_SZ_FIX == 128);

    /* convert LSFs to 2*cos(LSF(i)), using piecewise linear curve from table */
    for( k = 0; k < d; k++ ) {
        SKP_assert(NLSF[k] >= 0 );
        SKP_assert(NLSF[k] <= 32767 );

        /* f_int on a scale 0-127 (rounded down) */
        f_int = SKP_RSHIFT( NLSF[k], 15 - 7 ); 
        
        /* f_frac, range: 0..255 */
        f_frac = NLSF[k] - SKP_LSHIFT( f_int, 15 - 7 ); 

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

        /* Read start and end value from table */
        cos_val = SKP_Silk_LSFCosTab_FIX_Q12[ f_int ];                /* Q12 */
        delta   = SKP_Silk_LSFCosTab_FIX_Q12[ f_int + 1 ] - cos_val;  /* Q12, with a range of 0..200 */

        /* Linear interpolation */
        cos_LSF_Q20[k] = SKP_LSHIFT( cos_val, 8 ) + SKP_MUL( delta, f_frac ); /* Q20 */
    }
    
    dd = SKP_RSHIFT( d, 1 );

    /* generate even and odd polynomials using convolution */
    SKP_Silk_NLSF2A_find_poly( P, &cos_LSF_Q20[0], dd );
    SKP_Silk_NLSF2A_find_poly( Q, &cos_LSF_Q20[1], dd );

    /* convert even and odd polynomials to SKP_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 */

        a_int32[k]     = -SKP_RSHIFT_ROUND( Ptmp + Qtmp, 9 ); /* Q20 -> Q12 */
        a_int32[d-k-1] =  SKP_RSHIFT_ROUND( Qtmp - Ptmp, 9 ); /* Q20 -> Q12 */
    }

    /* Limit the maximum absolute value of the prediction coefficients */
    for( i = 0; i < 10; i++ ) {
        /* Find maximum absolute value and its index */
        maxabs = 0;
        for( k = 0; k < d; k++ ) {
            absval = SKP_abs( a_int32[k] );
            if( absval > maxabs ) {
                maxabs = absval;
                idx       = k;
            }    
        }
    
        if( maxabs > SKP_int16_MAX ) {    
            /* Reduce magnitude of prediction coefficients */
            maxabs = SKP_min( maxabs, 98369 ); // ( SKP_int32_MAX / ( 65470 >> 2 ) ) + SKP_int16_MAX = 98369 
            sc_Q16 = 65470 - SKP_DIV32( SKP_MUL( 65470 >> 2, maxabs - SKP_int16_MAX ), 
                                        SKP_RSHIFT32( SKP_MUL( maxabs, idx + 1), 2 ) );
            SKP_Silk_bwexpander_32( a_int32, d, sc_Q16 );
        } else {
            break;
        }
    }    

    /* Reached the last iteration */
    if( i == 10 ) {
        SKP_assert(0);
        for( k = 0; k < d; k++ ) {
            a_int32[k] = SKP_SAT16( a_int32[k] ); 
        }
    }

    /* Return as SKP_int16 Q12 coefficients */
    for( k = 0; k < d; k++ ) {
        a[k] = (SKP_int16)a_int32[k];
    }
}