ref: fe5fe9e14b0abcc32178c0c65f98b1a44ef8eb23
dir: /silk/fixed/solve_LS_FIX.c/
/***********************************************************************
Copyright (c) 2006-2011, Skype Limited. All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, (subject to the limitations in the disclaimer below)
are permitted provided that the following conditions are met:
- Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
- Neither the name of Skype Limited, nor the names of specific
contributors, may be used to endorse or promote products derived from
this software without specific prior written permission.
NO EXPRESS OR IMPLIED LICENSES TO ANY PARTY'S PATENT RIGHTS ARE GRANTED
BY THIS LICENSE. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
CONTRIBUTORS ''AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
***********************************************************************/
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "main_FIX.h"
#include "tuning_parameters.h"
/*****************************/
/* Internal function headers */
/*****************************/
typedef struct {
opus_int32 Q36_part;
opus_int32 Q48_part;
} inv_D_t;
/* Factorize square matrix A into LDL form */
static inline void silk_LDL_factorize_FIX(
opus_int32 *A, /* I/O Pointer to Symetric Square Matrix */
opus_int M, /* I Size of Matrix */
opus_int32 *L_Q16, /* I/O Pointer to Square Upper triangular Matrix */
inv_D_t *inv_D /* I/O Pointer to vector holding inverted diagonal elements of D */
);
/* Solve Lx = b, when L is lower triangular and has ones on the diagonal */
static inline void silk_LS_SolveFirst_FIX(
const opus_int32 *L_Q16, /* I Pointer to Lower Triangular Matrix */
opus_int M, /* I Dim of Matrix equation */
const opus_int32 *b, /* I b Vector */
opus_int32 *x_Q16 /* O x Vector */
);
/* Solve L^t*x = b, where L is lower triangular with ones on the diagonal */
static inline void silk_LS_SolveLast_FIX(
const opus_int32 *L_Q16, /* I Pointer to Lower Triangular Matrix */
const opus_int M, /* I Dim of Matrix equation */
const opus_int32 *b, /* I b Vector */
opus_int32 *x_Q16 /* O x Vector */
);
static inline void silk_LS_divide_Q16_FIX(
opus_int32 T[], /* I/O Numenator vector */
inv_D_t *inv_D, /* I 1 / D vector */
opus_int M /* I dimension */
);
/* Solves Ax = b, assuming A is symmetric */
void silk_solve_LDL_FIX(
opus_int32 *A, /* I Pointer to symetric square matrix A */
opus_int M, /* I Size of matrix */
const opus_int32 *b, /* I Pointer to b vector */
opus_int32 *x_Q16 /* O Pointer to x solution vector */
)
{
opus_int32 L_Q16[ MAX_MATRIX_SIZE * MAX_MATRIX_SIZE ];
opus_int32 Y[ MAX_MATRIX_SIZE ];
inv_D_t inv_D[ MAX_MATRIX_SIZE ];
silk_assert( M <= MAX_MATRIX_SIZE );
/***************************************************
Factorize A by LDL such that A = L*D*L',
where L is lower triangular with ones on diagonal
****************************************************/
silk_LDL_factorize_FIX( A, M, L_Q16, inv_D );
/****************************************************
* substitute D*L'*x = Y. ie:
L*D*L'*x = b => L*Y = b <=> Y = inv(L)*b
******************************************************/
silk_LS_SolveFirst_FIX( L_Q16, M, b, Y );
/****************************************************
D*L'*x = Y <=> L'*x = inv(D)*Y, because D is
diagonal just multiply with 1/d_i
****************************************************/
silk_LS_divide_Q16_FIX( Y, inv_D, M );
/****************************************************
x = inv(L') * inv(D) * Y
*****************************************************/
silk_LS_SolveLast_FIX( L_Q16, M, Y, x_Q16 );
}
static inline void silk_LDL_factorize_FIX(
opus_int32 *A, /* I/O Pointer to Symetric Square Matrix */
opus_int M, /* I Size of Matrix */
opus_int32 *L_Q16, /* I/O Pointer to Square Upper triangular Matrix */
inv_D_t *inv_D /* I/O Pointer to vector holding inverted diagonal elements of D */
)
{
opus_int i, j, k, status, loop_count;
const opus_int32 *ptr1, *ptr2;
opus_int32 diag_min_value, tmp_32, err;
opus_int32 v_Q0[ MAX_MATRIX_SIZE ], D_Q0[ MAX_MATRIX_SIZE ];
opus_int32 one_div_diag_Q36, one_div_diag_Q40, one_div_diag_Q48;
silk_assert( M <= MAX_MATRIX_SIZE );
status = 1;
diag_min_value = silk_max_32( silk_SMMUL( silk_ADD_SAT32( A[ 0 ], A[ silk_SMULBB( M, M ) - 1 ] ), SILK_FIX_CONST( FIND_LTP_COND_FAC, 31 ) ), 1 << 9 );
for( loop_count = 0; loop_count < M && status == 1; loop_count++ ) {
status = 0;
for( j = 0; j < M; j++ ) {
ptr1 = matrix_adr( L_Q16, j, 0, M );
tmp_32 = 0;
for( i = 0; i < j; i++ ) {
v_Q0[ i ] = silk_SMULWW( D_Q0[ i ], ptr1[ i ] ); /* Q0 */
tmp_32 = silk_SMLAWW( tmp_32, v_Q0[ i ], ptr1[ i ] ); /* Q0 */
}
tmp_32 = silk_SUB32( matrix_ptr( A, j, j, M ), tmp_32 );
if( tmp_32 < diag_min_value ) {
tmp_32 = silk_SUB32( silk_SMULBB( loop_count + 1, diag_min_value ), tmp_32 );
/* Matrix not positive semi-definite, or ill conditioned */
for( i = 0; i < M; i++ ) {
matrix_ptr( A, i, i, M ) = silk_ADD32( matrix_ptr( A, i, i, M ), tmp_32 );
}
status = 1;
break;
}
D_Q0[ j ] = tmp_32; /* always < max(Correlation) */
/* two-step division */
one_div_diag_Q36 = silk_INVERSE32_varQ( tmp_32, 36 ); /* Q36 */
one_div_diag_Q40 = silk_LSHIFT( one_div_diag_Q36, 4 ); /* Q40 */
err = silk_SUB32( 1 << 24, silk_SMULWW( tmp_32, one_div_diag_Q40 ) ); /* Q24 */
one_div_diag_Q48 = silk_SMULWW( err, one_div_diag_Q40 ); /* Q48 */
/* Save 1/Ds */
inv_D[ j ].Q36_part = one_div_diag_Q36;
inv_D[ j ].Q48_part = one_div_diag_Q48;
matrix_ptr( L_Q16, j, j, M ) = 65536; /* 1.0 in Q16 */
ptr1 = matrix_adr( A, j, 0, M );
ptr2 = matrix_adr( L_Q16, j + 1, 0, M );
for( i = j + 1; i < M; i++ ) {
tmp_32 = 0;
for( k = 0; k < j; k++ ) {
tmp_32 = silk_SMLAWW( tmp_32, v_Q0[ k ], ptr2[ k ] ); /* Q0 */
}
tmp_32 = silk_SUB32( ptr1[ i ], tmp_32 ); /* always < max(Correlation) */
/* tmp_32 / D_Q0[j] : Divide to Q16 */
matrix_ptr( L_Q16, i, j, M ) = silk_ADD32( silk_SMMUL( tmp_32, one_div_diag_Q48 ),
silk_RSHIFT( silk_SMULWW( tmp_32, one_div_diag_Q36 ), 4 ) );
/* go to next column */
ptr2 += M;
}
}
}
silk_assert( status == 0 );
}
static inline void silk_LS_divide_Q16_FIX(
opus_int32 T[], /* I/O Numenator vector */
inv_D_t *inv_D, /* I 1 / D vector */
opus_int M /* I dimension */
)
{
opus_int i;
opus_int32 tmp_32;
opus_int32 one_div_diag_Q36, one_div_diag_Q48;
for( i = 0; i < M; i++ ) {
one_div_diag_Q36 = inv_D[ i ].Q36_part;
one_div_diag_Q48 = inv_D[ i ].Q48_part;
tmp_32 = T[ i ];
T[ i ] = silk_ADD32( silk_SMMUL( tmp_32, one_div_diag_Q48 ), silk_RSHIFT( silk_SMULWW( tmp_32, one_div_diag_Q36 ), 4 ) );
}
}
/* Solve Lx = b, when L is lower triangular and has ones on the diagonal */
static inline void silk_LS_SolveFirst_FIX(
const opus_int32 *L_Q16, /* I Pointer to Lower Triangular Matrix */
opus_int M, /* I Dim of Matrix equation */
const opus_int32 *b, /* I b Vector */
opus_int32 *x_Q16 /* O x Vector */
)
{
opus_int i, j;
const opus_int32 *ptr32;
opus_int32 tmp_32;
for( i = 0; i < M; i++ ) {
ptr32 = matrix_adr( L_Q16, i, 0, M );
tmp_32 = 0;
for( j = 0; j < i; j++ ) {
tmp_32 = silk_SMLAWW( tmp_32, ptr32[ j ], x_Q16[ j ] );
}
x_Q16[ i ] = silk_SUB32( b[ i ], tmp_32 );
}
}
/* Solve L^t*x = b, where L is lower triangular with ones on the diagonal */
static inline void silk_LS_SolveLast_FIX(
const opus_int32 *L_Q16, /* I Pointer to Lower Triangular Matrix */
const opus_int M, /* I Dim of Matrix equation */
const opus_int32 *b, /* I b Vector */
opus_int32 *x_Q16 /* O x Vector */
)
{
opus_int i, j;
const opus_int32 *ptr32;
opus_int32 tmp_32;
for( i = M - 1; i >= 0; i-- ) {
ptr32 = matrix_adr( L_Q16, 0, i, M );
tmp_32 = 0;
for( j = M - 1; j > i; j-- ) {
tmp_32 = silk_SMLAWW( tmp_32, ptr32[ silk_SMULBB( j, M ) ], x_Q16[ j ] );
}
x_Q16[ i ] = silk_SUB32( b[ i ], tmp_32 );
}
}