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1 /***********************************************************************
2 Copyright (c) 2006-2011, Skype Limited. All rights reserved.
3 Redistribution and use in source and binary forms, with or without
4 modification, are permitted provided that the following conditions
5 are met:
6 - Redistributions of source code must retain the above copyright notice,
7 this list of conditions and the following disclaimer.
8 - Redistributions in binary form must reproduce the above copyright
9 notice, this list of conditions and the following disclaimer in the
10 documentation and/or other materials provided with the distribution.
11 - Neither the name of Internet Society, IETF or IETF Trust, nor the
12 names of specific contributors, may be used to endorse or promote
13 products derived from this software without specific prior written
14 permission.
15 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
16 AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
19 LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
20 CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
21 SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
22 INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
23 CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
24 ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
25 POSSIBILITY OF SUCH DAMAGE.
26 ***********************************************************************/
27 
28 #ifdef HAVE_CONFIG_H
29 #include "config.h"
30 #endif
31 
32 #include "main_FIX.h"
33 #include "stack_alloc.h"
34 #include "tuning_parameters.h"
35 
36 /*****************************/
37 /* Internal function headers */
38 /*****************************/
39 
40 typedef struct {
41     opus_int32 Q36_part;
42     opus_int32 Q48_part;
43 } inv_D_t;
44 
45 /* Factorize square matrix A into LDL form */
46 static OPUS_INLINE void silk_LDL_factorize_FIX(
47     opus_int32          *A,         /* I/O Pointer to Symetric Square Matrix                            */
48     opus_int            M,          /* I   Size of Matrix                                               */
49     opus_int32          *L_Q16,     /* I/O Pointer to Square Upper triangular Matrix                    */
50     inv_D_t             *inv_D      /* I/O Pointer to vector holding inverted diagonal elements of D    */
51 );
52 
53 /* Solve Lx = b, when L is lower triangular and has ones on the diagonal */
54 static OPUS_INLINE void silk_LS_SolveFirst_FIX(
55     const opus_int32    *L_Q16,     /* I    Pointer to Lower Triangular Matrix                          */
56     opus_int            M,          /* I    Dim of Matrix equation                                      */
57     const opus_int32    *b,         /* I    b Vector                                                    */
58     opus_int32          *x_Q16      /* O    x Vector                                                    */
59 );
60 
61 /* Solve L^t*x = b, where L is lower triangular with ones on the diagonal */
62 static OPUS_INLINE void silk_LS_SolveLast_FIX(
63     const opus_int32    *L_Q16,     /* I    Pointer to Lower Triangular Matrix                          */
64     const opus_int      M,          /* I    Dim of Matrix equation                                      */
65     const opus_int32    *b,         /* I    b Vector                                                    */
66     opus_int32          *x_Q16      /* O    x Vector                                                    */
67 );
68 
69 static OPUS_INLINE void silk_LS_divide_Q16_FIX(
70     opus_int32          T[],        /* I/O  Numenator vector                                            */
71     inv_D_t             *inv_D,     /* I    1 / D vector                                                */
72     opus_int            M           /* I    dimension                                                   */
73 );
74 
75 /* Solves Ax = b, assuming A is symmetric */
silk_solve_LDL_FIX(opus_int32 * A,opus_int M,const opus_int32 * b,opus_int32 * x_Q16)76 void silk_solve_LDL_FIX(
77     opus_int32                      *A,                                     /* I    Pointer to symetric square matrix A                                         */
78     opus_int                        M,                                      /* I    Size of matrix                                                              */
79     const opus_int32                *b,                                     /* I    Pointer to b vector                                                         */
80     opus_int32                      *x_Q16                                  /* O    Pointer to x solution vector                                                */
81 )
82 {
83     VARDECL( opus_int32, L_Q16 );
84     opus_int32 Y[      MAX_MATRIX_SIZE ];
85     inv_D_t   inv_D[  MAX_MATRIX_SIZE ];
86     SAVE_STACK;
87 
88     silk_assert( M <= MAX_MATRIX_SIZE );
89     ALLOC( L_Q16, M * M, opus_int32 );
90 
91     /***************************************************
92     Factorize A by LDL such that A = L*D*L',
93     where L is lower triangular with ones on diagonal
94     ****************************************************/
95     silk_LDL_factorize_FIX( A, M, L_Q16, inv_D );
96 
97     /****************************************************
98     * substitute D*L'*x = Y. ie:
99     L*D*L'*x = b => L*Y = b <=> Y = inv(L)*b
100     ******************************************************/
101     silk_LS_SolveFirst_FIX( L_Q16, M, b, Y );
102 
103     /****************************************************
104     D*L'*x = Y <=> L'*x = inv(D)*Y, because D is
105     diagonal just multiply with 1/d_i
106     ****************************************************/
107     silk_LS_divide_Q16_FIX( Y, inv_D, M );
108 
109     /****************************************************
110     x = inv(L') * inv(D) * Y
111     *****************************************************/
112     silk_LS_SolveLast_FIX( L_Q16, M, Y, x_Q16 );
113     RESTORE_STACK;
114 }
115 
silk_LDL_factorize_FIX(opus_int32 * A,opus_int M,opus_int32 * L_Q16,inv_D_t * inv_D)116 static OPUS_INLINE void silk_LDL_factorize_FIX(
117     opus_int32          *A,         /* I/O Pointer to Symetric Square Matrix                            */
118     opus_int            M,          /* I   Size of Matrix                                               */
119     opus_int32          *L_Q16,     /* I/O Pointer to Square Upper triangular Matrix                    */
120     inv_D_t             *inv_D      /* I/O Pointer to vector holding inverted diagonal elements of D    */
121 )
122 {
123     opus_int   i, j, k, status, loop_count;
124     const opus_int32 *ptr1, *ptr2;
125     opus_int32 diag_min_value, tmp_32, err;
126     opus_int32 v_Q0[ MAX_MATRIX_SIZE ], D_Q0[ MAX_MATRIX_SIZE ];
127     opus_int32 one_div_diag_Q36, one_div_diag_Q40, one_div_diag_Q48;
128 
129     silk_assert( M <= MAX_MATRIX_SIZE );
130 
131     status = 1;
132     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 );
133     for( loop_count = 0; loop_count < M && status == 1; loop_count++ ) {
134         status = 0;
135         for( j = 0; j < M; j++ ) {
136             ptr1 = matrix_adr( L_Q16, j, 0, M );
137             tmp_32 = 0;
138             for( i = 0; i < j; i++ ) {
139                 v_Q0[ i ] = silk_SMULWW(         D_Q0[ i ], ptr1[ i ] ); /* Q0 */
140                 tmp_32    = silk_SMLAWW( tmp_32, v_Q0[ i ], ptr1[ i ] ); /* Q0 */
141             }
142             tmp_32 = silk_SUB32( matrix_ptr( A, j, j, M ), tmp_32 );
143 
144             if( tmp_32 < diag_min_value ) {
145                 tmp_32 = silk_SUB32( silk_SMULBB( loop_count + 1, diag_min_value ), tmp_32 );
146                 /* Matrix not positive semi-definite, or ill conditioned */
147                 for( i = 0; i < M; i++ ) {
148                     matrix_ptr( A, i, i, M ) = silk_ADD32( matrix_ptr( A, i, i, M ), tmp_32 );
149                 }
150                 status = 1;
151                 break;
152             }
153             D_Q0[ j ] = tmp_32;                         /* always < max(Correlation) */
154 
155             /* two-step division */
156             one_div_diag_Q36 = silk_INVERSE32_varQ( tmp_32, 36 );                    /* Q36 */
157             one_div_diag_Q40 = silk_LSHIFT( one_div_diag_Q36, 4 );                   /* Q40 */
158             err = silk_SUB32( (opus_int32)1 << 24, silk_SMULWW( tmp_32, one_div_diag_Q40 ) );     /* Q24 */
159             one_div_diag_Q48 = silk_SMULWW( err, one_div_diag_Q40 );                 /* Q48 */
160 
161             /* Save 1/Ds */
162             inv_D[ j ].Q36_part = one_div_diag_Q36;
163             inv_D[ j ].Q48_part = one_div_diag_Q48;
164 
165             matrix_ptr( L_Q16, j, j, M ) = 65536; /* 1.0 in Q16 */
166             ptr1 = matrix_adr( A, j, 0, M );
167             ptr2 = matrix_adr( L_Q16, j + 1, 0, M );
168             for( i = j + 1; i < M; i++ ) {
169                 tmp_32 = 0;
170                 for( k = 0; k < j; k++ ) {
171                     tmp_32 = silk_SMLAWW( tmp_32, v_Q0[ k ], ptr2[ k ] ); /* Q0 */
172                 }
173                 tmp_32 = silk_SUB32( ptr1[ i ], tmp_32 ); /* always < max(Correlation) */
174 
175                 /* tmp_32 / D_Q0[j] : Divide to Q16 */
176                 matrix_ptr( L_Q16, i, j, M ) = silk_ADD32( silk_SMMUL( tmp_32, one_div_diag_Q48 ),
177                     silk_RSHIFT( silk_SMULWW( tmp_32, one_div_diag_Q36 ), 4 ) );
178 
179                 /* go to next column */
180                 ptr2 += M;
181             }
182         }
183     }
184 
185     silk_assert( status == 0 );
186 }
187 
silk_LS_divide_Q16_FIX(opus_int32 T[],inv_D_t * inv_D,opus_int M)188 static OPUS_INLINE void silk_LS_divide_Q16_FIX(
189     opus_int32          T[],        /* I/O  Numenator vector                                            */
190     inv_D_t             *inv_D,     /* I    1 / D vector                                                */
191     opus_int            M           /* I    dimension                                                   */
192 )
193 {
194     opus_int   i;
195     opus_int32 tmp_32;
196     opus_int32 one_div_diag_Q36, one_div_diag_Q48;
197 
198     for( i = 0; i < M; i++ ) {
199         one_div_diag_Q36 = inv_D[ i ].Q36_part;
200         one_div_diag_Q48 = inv_D[ i ].Q48_part;
201 
202         tmp_32 = T[ i ];
203         T[ i ] = silk_ADD32( silk_SMMUL( tmp_32, one_div_diag_Q48 ), silk_RSHIFT( silk_SMULWW( tmp_32, one_div_diag_Q36 ), 4 ) );
204     }
205 }
206 
207 /* Solve Lx = b, when L is lower triangular and has ones on the diagonal */
silk_LS_SolveFirst_FIX(const opus_int32 * L_Q16,opus_int M,const opus_int32 * b,opus_int32 * x_Q16)208 static OPUS_INLINE void silk_LS_SolveFirst_FIX(
209     const opus_int32    *L_Q16,     /* I    Pointer to Lower Triangular Matrix                          */
210     opus_int            M,          /* I    Dim of Matrix equation                                      */
211     const opus_int32    *b,         /* I    b Vector                                                    */
212     opus_int32          *x_Q16      /* O    x Vector                                                    */
213 )
214 {
215     opus_int i, j;
216     const opus_int32 *ptr32;
217     opus_int32 tmp_32;
218 
219     for( i = 0; i < M; i++ ) {
220         ptr32 = matrix_adr( L_Q16, i, 0, M );
221         tmp_32 = 0;
222         for( j = 0; j < i; j++ ) {
223             tmp_32 = silk_SMLAWW( tmp_32, ptr32[ j ], x_Q16[ j ] );
224         }
225         x_Q16[ i ] = silk_SUB32( b[ i ], tmp_32 );
226     }
227 }
228 
229 /* Solve L^t*x = b, where L is lower triangular with ones on the diagonal */
silk_LS_SolveLast_FIX(const opus_int32 * L_Q16,const opus_int M,const opus_int32 * b,opus_int32 * x_Q16)230 static OPUS_INLINE void silk_LS_SolveLast_FIX(
231     const opus_int32    *L_Q16,     /* I    Pointer to Lower Triangular Matrix                          */
232     const opus_int      M,          /* I    Dim of Matrix equation                                      */
233     const opus_int32    *b,         /* I    b Vector                                                    */
234     opus_int32          *x_Q16      /* O    x Vector                                                    */
235 )
236 {
237     opus_int i, j;
238     const opus_int32 *ptr32;
239     opus_int32 tmp_32;
240 
241     for( i = M - 1; i >= 0; i-- ) {
242         ptr32 = matrix_adr( L_Q16, 0, i, M );
243         tmp_32 = 0;
244         for( j = M - 1; j > i; j-- ) {
245             tmp_32 = silk_SMLAWW( tmp_32, ptr32[ silk_SMULBB( j, M ) ], x_Q16[ j ] );
246         }
247         x_Q16[ i ] = silk_SUB32( b[ i ], tmp_32 );
248     }
249 }
250