godot/thirdparty/opus/silk/fixed/solve_LS_FIX.c

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#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include "main_FIX.h"
#include "stack_alloc.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 OPUS_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 OPUS_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 OPUS_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 OPUS_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                                                */
)
{
    VARDECL( opus_int32, L_Q16 );
    opus_int32 Y[      MAX_MATRIX_SIZE ];
    inv_D_t   inv_D[  MAX_MATRIX_SIZE ];
    SAVE_STACK;

    silk_assert( M <= MAX_MATRIX_SIZE );
    ALLOC( L_Q16, M * M, opus_int32 );

    /***************************************************
    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 );
    RESTORE_STACK;
}

static OPUS_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( (opus_int32)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 OPUS_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 OPUS_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 OPUS_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 );
    }
}