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/* Conversion between prediction filter coefficients and NLSFs  */
/* Requires the order to be an even number                      */
/* A piecewise linear approximation maps LSF <-> cos(LSF)       */
/* Therefore the result is not accurate NLSFs, but the two      */
/* function are accurate inverses of each other                 */

#include "SKP_Silk_SigProc_FIX.h"

/* Number of binary divisions, when not in low complexity mode */
#define BIN_DIV_STEPS_A2NLSF_FIX      2 /* must be no higher than 16 - log2( LSF_COS_TAB_SZ_FIX ) */
#define QPoly                        16
#define MAX_ITERATIONS_A2NLSF_FIX    50

/* Flag for using 2x as many cosine sampling points, reduces the risk of missing a root */
#define OVERSAMPLE_COSINE_TABLE       0

/* Helper function for A2NLSF(..)                    */
/* Transforms polynomials from cos(n*f) to cos(f)^n  */
SKP_INLINE void SKP_Silk_A2NLSF_trans_poly(
    SKP_int32        *p,    /* I/O    Polynomial                                */
    const SKP_int    dd     /* I      Polynomial order (= filter order / 2 )    */
)
{
    SKP_int k, n;
    
    for( k = 2; k <= dd; k++ ) {
        for( n = dd; n > k; n-- ) {
            p[ n - 2 ] -= p[ n ];
        }
        p[ k - 2 ] -= SKP_LSHIFT( p[ k ], 1 );
    }
}    

/* Helper function for A2NLSF(..)                    */
/* Polynomial evaluation                             */
SKP_INLINE SKP_int32 SKP_Silk_A2NLSF_eval_poly(    /* return the polynomial evaluation, in QPoly */
    SKP_int32        *p,    /* I    Polynomial, QPoly        */
    const SKP_int32    x,   /* I    Evaluation point, Q12    */
    const SKP_int    dd     /* I    Order                    */
)
{
    SKP_int   n;
    SKP_int32 x_Q16, y32;

    y32 = p[ dd ];                                    /* QPoly */
    x_Q16 = SKP_LSHIFT( x, 4 );
    for( n = dd - 1; n >= 0; n-- ) {
        y32 = SKP_SMLAWW( p[ n ], y32, x_Q16 );       /* QPoly */
    }
    return y32;
}

SKP_INLINE void SKP_Silk_A2NLSF_init(
     const SKP_int32    *a_Q16,
     SKP_int32            *P, 
     SKP_int32            *Q, 
     const SKP_int        dd
) 
{
    SKP_int k;

    /* Convert filter coefs to even and odd polynomials */
    P[dd] = SKP_LSHIFT( 1, QPoly );
    Q[dd] = SKP_LSHIFT( 1, QPoly );
    for( k = 0; k < dd; k++ ) {
#if( QPoly < 16 )
        P[ k ] = SKP_RSHIFT_ROUND( -a_Q16[ dd - k - 1 ] - a_Q16[ dd + k ], 16 - QPoly ); /* QPoly */
        Q[ k ] = SKP_RSHIFT_ROUND( -a_Q16[ dd - k - 1 ] + a_Q16[ dd + k ], 16 - QPoly ); /* QPoly */
#elif( Qpoly == 16 )
        P[ k ] = -a_Q16[ dd - k - 1 ] - a_Q16[ dd + k ]; // QPoly
        Q[ k ] = -a_Q16[ dd - k - 1 ] + a_Q16[ dd + k ]; // QPoly
#else
        P[ k ] = SKP_LSHIFT( -a_Q16[ dd - k - 1 ] - a_Q16[ dd + k ], QPoly - 16 ); /* QPoly */
        Q[ k ] = SKP_LSHIFT( -a_Q16[ dd - k - 1 ] + a_Q16[ dd + k ], QPoly - 16 ); /* QPoly */
#endif
    }

    /* Divide out zeros as we have that for even filter orders, */
    /* z =  1 is always a root in Q, and                        */
    /* z = -1 is always a root in P                             */
    for( k = dd; k > 0; k-- ) {
        P[ k - 1 ] -= P[ k ]; 
        Q[ k - 1 ] += Q[ k ]; 
    }

    /* Transform polynomials from cos(n*f) to cos(f)^n */
    SKP_Silk_A2NLSF_trans_poly( P, dd );
    SKP_Silk_A2NLSF_trans_poly( Q, dd );
}

/* Compute Normalized Line Spectral Frequencies (NLSFs) from whitening filter coefficients        */
/* If not all roots are found, the a_Q16 coefficients are bandwidth expanded until convergence.    */
void SKP_Silk_A2NLSF(
    SKP_int          *NLSF,                 /* O    Normalized Line Spectral Frequencies, Q15 (0 - (2^15-1)), [d]    */
    SKP_int32        *a_Q16,                /* I/O  Monic whitening filter coefficients in Q16 [d]                   */
    const SKP_int    d                      /* I    Filter order (must be even)                                      */
)
{
    SKP_int      i, k, m, dd, root_ix, ffrac;
    SKP_int32 xlo, xhi, xmid;
    SKP_int32 ylo, yhi, ymid;
    SKP_int32 nom, den;
    SKP_int32 P[ SigProc_MAX_ORDER_LPC / 2 + 1 ];
    SKP_int32 Q[ SigProc_MAX_ORDER_LPC / 2 + 1 ];
    SKP_int32 *PQ[ 2 ];
    SKP_int32 *p;

    /* Store pointers to array */
    PQ[ 0 ] = P;
    PQ[ 1 ] = Q;

    dd = SKP_RSHIFT( d, 1 );

    SKP_Silk_A2NLSF_init( a_Q16, P, Q, dd );

    /* Find roots, alternating between P and Q */
    p = P;    /* Pointer to polynomial */
    
    xlo = SKP_Silk_LSFCosTab_FIX_Q12[ 0 ]; // Q12
    ylo = SKP_Silk_A2NLSF_eval_poly( p, xlo, dd );

    if( ylo < 0 ) {
        /* Set the first NLSF to zero and move on to the next */
        NLSF[ 0 ] = 0;
        p = Q;                      /* Pointer to polynomial */
        ylo = SKP_Silk_A2NLSF_eval_poly( p, xlo, dd );
        root_ix = 1;                /* Index of current root */
    } else {
        root_ix = 0;                /* Index of current root */
    }
    k = 1;                          /* Loop counter */
    i = 0;                          /* Counter for bandwidth expansions applied */
    while( 1 ) {
        /* Evaluate polynomial */
#if OVERSAMPLE_COSINE_TABLE
        xhi = SKP_Silk_LSFCosTab_FIX_Q12[   k       >> 1 ] +
          ( ( SKP_Silk_LSFCosTab_FIX_Q12[ ( k + 1 ) >> 1 ] - 
              SKP_Silk_LSFCosTab_FIX_Q12[   k       >> 1 ] ) >> 1 );    /* Q12 */
#else
        xhi = SKP_Silk_LSFCosTab_FIX_Q12[ k ]; /* Q12 */
#endif
        yhi = SKP_Silk_A2NLSF_eval_poly( p, xhi, dd );
        
        /* Detect zero crossing */
        if( ( ylo <= 0 && yhi >= 0 ) || ( ylo >= 0 && yhi <= 0 ) ) {
            /* Binary division */
#if OVERSAMPLE_COSINE_TABLE
            ffrac = -128;
#else
            ffrac = -256;
#endif
            for( m = 0; m < BIN_DIV_STEPS_A2NLSF_FIX; m++ ) {
                /* Evaluate polynomial */
                xmid = SKP_RSHIFT_ROUND( xlo + xhi, 1 );
                ymid = SKP_Silk_A2NLSF_eval_poly( p, xmid, dd );

                /* Detect zero crossing */
                if( ( ylo <= 0 && ymid >= 0 ) || ( ylo >= 0 && ymid <= 0 ) ) {
                    /* Reduce frequency */
                    xhi = xmid;
                    yhi = ymid;
                } else {
                    /* Increase frequency */
                    xlo = xmid;
                    ylo = ymid;
#if OVERSAMPLE_COSINE_TABLE
                    ffrac = SKP_ADD_RSHIFT( ffrac,  64, m );
#else
                    ffrac = SKP_ADD_RSHIFT( ffrac, 128, m );
#endif
                }
            }
            
            /* Interpolate */
            if( SKP_abs( ylo ) < 65536 ) {
                /* Avoid dividing by zero */
                den = ylo - yhi;
                nom = SKP_LSHIFT( ylo, 8 - BIN_DIV_STEPS_A2NLSF_FIX ) + SKP_RSHIFT( den, 1 );
                if( den != 0 ) {
                    ffrac += SKP_DIV32( nom, den );
                }
            } else {
                /* No risk of dividing by zero because abs(ylo - yhi) >= abs(ylo) >= 65536 */
                ffrac += SKP_DIV32( ylo, SKP_RSHIFT( ylo - yhi, 8 - BIN_DIV_STEPS_A2NLSF_FIX ) );
            }
#if OVERSAMPLE_COSINE_TABLE
            NLSF[ root_ix ] = (SKP_int)SKP_min_32( SKP_LSHIFT( (SKP_int32)k, 7 ) + ffrac, SKP_int16_MAX ); 
#else
            NLSF[ root_ix ] = (SKP_int)SKP_min_32( SKP_LSHIFT( (SKP_int32)k, 8 ) + ffrac, SKP_int16_MAX ); 
#endif

            SKP_assert( NLSF[ root_ix ] >=     0 );
            SKP_assert( NLSF[ root_ix ] <= 32767 );

            root_ix++;        /* Next root */
            if( root_ix >= d ) {
                /* Found all roots */
                break;
            }
            /* Alternate pointer to polynomial */
            p = PQ[ root_ix & 1 ];
            
            /* Evaluate polynomial */
#if OVERSAMPLE_COSINE_TABLE
            xlo = SKP_Silk_LSFCosTab_FIX_Q12[ ( k - 1 ) >> 1 ] +
              ( ( SKP_Silk_LSFCosTab_FIX_Q12[   k       >> 1 ] - 
                  SKP_Silk_LSFCosTab_FIX_Q12[ ( k - 1 ) >> 1 ] ) >> 1 ); // Q12
#else
            xlo = SKP_Silk_LSFCosTab_FIX_Q12[ k - 1 ]; // Q12
#endif
            ylo = SKP_LSHIFT( 1 - ( root_ix & 2 ), 12 );
        } else {
            /* Increment loop counter */
            k++;
            xlo    = xhi;
            ylo    = yhi;
            
#if OVERSAMPLE_COSINE_TABLE
            if( k > 2 * LSF_COS_TAB_SZ_FIX ) {
#else
            if( k > LSF_COS_TAB_SZ_FIX ) {
#endif
                i++;
                if( i > MAX_ITERATIONS_A2NLSF_FIX ) {
                    /* Set NLSFs to white spectrum and exit */
                    NLSF[ 0 ] = SKP_DIV32_16( 1 << 15, d + 1 );
                    for( k = 1; k < d; k++ ) {
                        NLSF[ k ] = SKP_SMULBB( k + 1, NLSF[ 0 ] );
                    }
                    return;
                }

                /* Error: Apply progressively more bandwidth expansion and run again */
                SKP_Silk_bwexpander_32( a_Q16, d, 65536 - SKP_SMULBB( 66, i ) ); // 66_Q16 = 0.001

                SKP_Silk_A2NLSF_init( a_Q16, P, Q, dd );
                p = P;                            /* Pointer to polynomial */
                xlo = SKP_Silk_LSFCosTab_FIX_Q12[ 0 ]; // Q12
                ylo = SKP_Silk_A2NLSF_eval_poly( p, xlo, dd );
                if( ylo < 0 ) {
                    /* Set the first NLSF to zero and move on to the next */
                    NLSF[ 0 ] = 0;
                    p = Q;                        /* Pointer to polynomial */
                    ylo = SKP_Silk_A2NLSF_eval_poly( p, xlo, dd );
                    root_ix = 1;                /* Index of current root */
                } else {
                    root_ix = 0;                /* Index of current root */
                }
                k = 1;                            /* Reset loop counter */
            }
        }
    }
}
