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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      */

/* functions are accurate inverses of each other                */

#ifdef HAVE_CONFIG_H

#include "config.h"

#endif

#include "SigProc_FIX.h"

#include "tables.h"

/* Number of binary divisions, when not in low complexity mode */

#define BIN_DIV_STEPS_A2NLSF_FIX      3 /* must be no higher than 16 - log2( LSF_COS_TAB_SZ_FIX ) */

#define MAX_ITERATIONS_A2NLSF_FIX    16

/* Helper function for A2NLSF(..)                    */

/* Transforms polynomials from cos(n*f) to cos(f)^n  */

static OPUS_INLINE void silk_A2NLSF_trans_poly(

    opus_int32          *p,                     /* I/O    Polynomial                                */

    const opus_int      dd                      /* I      Polynomial order (= filter order / 2 )    */

)

{

    opus_int k, n;

    for( k = 2; k <= dd; k++ ) {

        for( n = dd; n > k; n-- ) {

            p[ n - 2 ] -= p[ n ];

        }

        p[ k - 2 ] -= silk_LSHIFT( p[ k ], 1 );

    }

}

/* Helper function for A2NLSF(..) */

/* Polynomial evaluation          */

static OPUS_INLINE opus_int32 silk_A2NLSF_eval_poly( /* return the polynomial evaluation, in Q16     */

    opus_int32          *p,                     /* I    Polynomial, Q16                         */

    const opus_int32    x,                      /* I    Evaluation point, Q12                   */

    const opus_int      dd                      /* I    Order                                   */

)

{

    opus_int   n;

    opus_int32 x_Q16, y32;

    y32 = p[ dd ];                                  /* Q16 */

    x_Q16 = silk_LSHIFT( x, 4 );

    if ( opus_likely( 8 == dd ) )

    {

        y32 = silk_SMLAWW( p[ 7 ], y32, x_Q16 );

        y32 = silk_SMLAWW( p[ 6 ], y32, x_Q16 );

        y32 = silk_SMLAWW( p[ 5 ], y32, x_Q16 );

        y32 = silk_SMLAWW( p[ 4 ], y32, x_Q16 );

        y32 = silk_SMLAWW( p[ 3 ], y32, x_Q16 );

        y32 = silk_SMLAWW( p[ 2 ], y32, x_Q16 );

        y32 = silk_SMLAWW( p[ 1 ], y32, x_Q16 );

        y32 = silk_SMLAWW( p[ 0 ], y32, x_Q16 );

    }

    else

    {

        for( n = dd - 1; n >= 0; n-- ) {

            y32 = silk_SMLAWW( p[ n ], y32, x_Q16 );    /* Q16 */

        }

    }

    return y32;

}

static OPUS_INLINE void silk_A2NLSF_init(

     const opus_int32    *a_Q16,

     opus_int32          *P,

     opus_int32          *Q,

     const opus_int      dd

)

{

    opus_int k;

    /* Convert filter coefs to even and odd polynomials */

    P[dd] = silk_LSHIFT( 1, 16 );

    Q[dd] = silk_LSHIFT( 1, 16 );

    for( k = 0; k < dd; k++ ) {

        P[ k ] = -a_Q16[ dd - k - 1 ] - a_Q16[ dd + k ];    /* Q16 */

        Q[ k ] = -a_Q16[ dd - k - 1 ] + a_Q16[ dd + k ];    /* Q16 */

    }

    /* 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 */

    silk_A2NLSF_trans_poly( P, dd );

    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 silk_A2NLSF(

    opus_int16                  *NLSF,              /* O    Normalized Line Spectral Frequencies in Q15 (0..2^15-1) [d] */

    opus_int32                  *a_Q16,             /* I/O  Monic whitening filter coefficients in Q16 [d]              */

    const opus_int              d                   /* I    Filter order (must be even)                                 */

)

{

    opus_int   i, k, m, dd, root_ix, ffrac;

    opus_int32 xlo, xhi, xmid;

    opus_int32 ylo, yhi, ymid, thr;

    opus_int32 nom, den;

    opus_int32 P[ SILK_MAX_ORDER_LPC / 2 + 1 ];

    opus_int32 Q[ SILK_MAX_ORDER_LPC / 2 + 1 ];

    opus_int32 *PQ[ 2 ];

    opus_int32 *p;

    /* Store pointers to array */

    PQ[ 0 ] = P;

    PQ[ 1 ] = Q;

    dd = silk_RSHIFT( d, 1 );

    silk_A2NLSF_init( a_Q16, P, Q, dd );

    /* Find roots, alternating between P and Q */

    p = P;                          /* Pointer to polynomial */

    xlo = silk_LSFCosTab_FIX_Q12[ 0 ]; /* Q12*/

    ylo = 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 = 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 */

    thr = 0;

    while( 1 ) {

        /* Evaluate polynomial */

        xhi = silk_LSFCosTab_FIX_Q12[ k ]; /* Q12 */

        yhi = silk_A2NLSF_eval_poly( p, xhi, dd );

        /* Detect zero crossing */

        if( ( ylo <= 0 && yhi >= thr ) || ( ylo >= 0 && yhi <= -thr ) ) {

            if( yhi == 0 ) {

                /* If the root lies exactly at the end of the current       */

                /* interval, look for the next root in the next interval    */

                thr = 1;

            } else {

                thr = 0;

            }

            /* Binary division */

            ffrac = -256;

            for( m = 0; m < BIN_DIV_STEPS_A2NLSF_FIX; m++ ) {

                /* Evaluate polynomial */

                xmid = silk_RSHIFT_ROUND( xlo + xhi, 1 );

                ymid = 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;

                    ffrac = silk_ADD_RSHIFT( ffrac, 128, m );

                }

            }

            /* Interpolate */

            if( silk_abs( ylo ) < 65536 ) {

                /* Avoid dividing by zero */

                den = ylo - yhi;

                nom = silk_LSHIFT( ylo, 8 - BIN_DIV_STEPS_A2NLSF_FIX ) + silk_RSHIFT( den, 1 );

                if( den != 0 ) {

                    ffrac += silk_DIV32( nom, den );

                }

            } else {

                /* No risk of dividing by zero because abs(ylo - yhi) >= abs(ylo) >= 65536 */

                ffrac += silk_DIV32( ylo, silk_RSHIFT( ylo - yhi, 8 - BIN_DIV_STEPS_A2NLSF_FIX ) );

            }

            NLSF[ root_ix ] = (opus_int16)silk_min_32( silk_LSHIFT( (opus_int32)k, 8 ) + ffrac, silk_int16_MAX );

            silk_assert( NLSF[ root_ix ] >= 0 );

            root_ix++;        /* Next root */

            if( root_ix >= d ) {

                /* Found all roots */

                break;

            }

            /* Alternate pointer to polynomial */

            p = PQ[ root_ix & 1 ];

            /* Evaluate polynomial */

            xlo = silk_LSFCosTab_FIX_Q12[ k - 1 ]; /* Q12*/

            ylo = silk_LSHIFT( 1 - ( root_ix & 2 ), 12 );

        } else {

            /* Increment loop counter */

            k++;

            xlo = xhi;

            ylo = yhi;

            thr = 0;

            if( k > LSF_COS_TAB_SZ_FIX ) {

                i++;

                if( i > MAX_ITERATIONS_A2NLSF_FIX ) {

                    /* Set NLSFs to white spectrum and exit */

                    NLSF[ 0 ] = (opus_int16)silk_DIV32_16( 1 << 15, d + 1 );

                    for( k = 1; k < d; k++ ) {

                        NLSF[ k ] = (opus_int16)silk_ADD16( NLSF[ k-1 ], NLSF[ 0 ] );

                    }

                    return;

                }

                /* Error: Apply progressively more bandwidth expansion and run again */

                silk_bwexpander_32( a_Q16, d, 65536 - silk_LSHIFT( 1, i ) );

                silk_A2NLSF_init( a_Q16, P, Q, dd );

                p = P;                            /* Pointer to polynomial */

                xlo = silk_LSFCosTab_FIX_Q12[ 0 ]; /* Q12*/

                ylo = 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 = 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 */

            }

        }

    }

}