ref: 5e9f7fc31db7336ce8c5946a4e3edaf4392af097
dir: /silk/silk_A2NLSF.c/
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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 */
#include "silk_SigProc_FIX.h"
#include "silk_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 QPoly 16
#define MAX_ITERATIONS_A2NLSF_FIX 30
/* 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 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 ] -= SKP_LSHIFT( p[ k ], 1 );
}
}
/* Helper function for A2NLSF(..) */
/* Polynomial evaluation */
SKP_INLINE opus_int32 silk_A2NLSF_eval_poly( /* return the polynomial evaluation, in QPoly */
opus_int32 *p, /* I Polynomial, QPoly */
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 ]; /* 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 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] = 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 */
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, 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;
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 = SKP_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 */
while( 1 ) {
/* Evaluate polynomial */
#if OVERSAMPLE_COSINE_TABLE
xhi = silk_LSFCosTab_FIX_Q12[ k >> 1 ] +
( ( silk_LSFCosTab_FIX_Q12[ ( k + 1 ) >> 1 ] -
silk_LSFCosTab_FIX_Q12[ k >> 1 ] ) >> 1 ); /* Q12 */
#else
xhi = silk_LSFCosTab_FIX_Q12[ k ]; /* Q12 */
#endif
yhi = 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 = 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 ] = (opus_int16)SKP_min_32( SKP_LSHIFT( (opus_int32)k, 7 ) + ffrac, SKP_int16_MAX );
#else
NLSF[ root_ix ] = (opus_int16)SKP_min_32( SKP_LSHIFT( (opus_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 = silk_LSFCosTab_FIX_Q12[ ( k - 1 ) >> 1 ] +
( ( silk_LSFCosTab_FIX_Q12[ k >> 1 ] -
silk_LSFCosTab_FIX_Q12[ ( k - 1 ) >> 1 ] ) >> 1 ); // Q12
#else
xlo = 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 ] = (opus_int16)SKP_DIV32_16( 1 << 15, d + 1 );
for( k = 1; k < d; k++ ) {
NLSF[ k ] = (opus_int16)SKP_SMULBB( k + 1, NLSF[ 0 ] );
}
return;
}
/* Error: Apply progressively more bandwidth expansion and run again */
silk_bwexpander_32( a_Q16, d, 65536 - SKP_SMULBB( 10 + i, i ) ); // 10_Q16 = 0.00015
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 */
}
}
}
}