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27
28 /* Conversion between prediction filter coefficients and NLSFs */
29 /* Requires the order to be an even number */
30 /* A piecewise linear approximation maps LSF <-> cos(LSF) */
31 /* Therefore the result is not accurate NLSFs, but the two */
32 /* functions are accurate inverses of each other */
33
34 #ifdef HAVE_CONFIG_H
35 #include "config.h"
36 #endif
37
38 #include "SigProc_FIX.h"
39 #include "tables.h"
40
41 /* Number of binary divisions, when not in low complexity mode */
42 #define BIN_DIV_STEPS_A2NLSF_FIX 3 /* must be no higher than 16 - log2( LSF_COS_TAB_SZ_FIX ) */
43 #define MAX_ITERATIONS_A2NLSF_FIX 30
44
45 /* Helper function for A2NLSF(..) */
46 /* Transforms polynomials from cos(n*f) to cos(f)^n */
silk_A2NLSF_trans_poly(opus_int32 * p,const opus_int dd)47 static OPUS_INLINE void silk_A2NLSF_trans_poly(
48 opus_int32 *p, /* I/O Polynomial */
49 const opus_int dd /* I Polynomial order (= filter order / 2 ) */
50 )
51 {
52 opus_int k, n;
53
54 for( k = 2; k <= dd; k++ ) {
55 for( n = dd; n > k; n-- ) {
56 p[ n - 2 ] -= p[ n ];
57 }
58 p[ k - 2 ] -= silk_LSHIFT( p[ k ], 1 );
59 }
60 }
61 /* Helper function for A2NLSF(..) */
62 /* Polynomial evaluation */
silk_A2NLSF_eval_poly(opus_int32 * p,const opus_int32 x,const opus_int dd)63 static OPUS_INLINE opus_int32 silk_A2NLSF_eval_poly( /* return the polynomial evaluation, in Q16 */
64 opus_int32 *p, /* I Polynomial, Q16 */
65 const opus_int32 x, /* I Evaluation point, Q12 */
66 const opus_int dd /* I Order */
67 )
68 {
69 opus_int n;
70 opus_int32 x_Q16, y32;
71
72 y32 = p[ dd ]; /* Q16 */
73 x_Q16 = silk_LSHIFT( x, 4 );
74 for( n = dd - 1; n >= 0; n-- ) {
75 y32 = silk_SMLAWW( p[ n ], y32, x_Q16 ); /* Q16 */
76 }
77 return y32;
78 }
79
silk_A2NLSF_init(const opus_int32 * a_Q16,opus_int32 * P,opus_int32 * Q,const opus_int dd)80 static OPUS_INLINE void silk_A2NLSF_init(
81 const opus_int32 *a_Q16,
82 opus_int32 *P,
83 opus_int32 *Q,
84 const opus_int dd
85 )
86 {
87 opus_int k;
88
89 /* Convert filter coefs to even and odd polynomials */
90 P[dd] = silk_LSHIFT( 1, 16 );
91 Q[dd] = silk_LSHIFT( 1, 16 );
92 for( k = 0; k < dd; k++ ) {
93 P[ k ] = -a_Q16[ dd - k - 1 ] - a_Q16[ dd + k ]; /* Q16 */
94 Q[ k ] = -a_Q16[ dd - k - 1 ] + a_Q16[ dd + k ]; /* Q16 */
95 }
96
97 /* Divide out zeros as we have that for even filter orders, */
98 /* z = 1 is always a root in Q, and */
99 /* z = -1 is always a root in P */
100 for( k = dd; k > 0; k-- ) {
101 P[ k - 1 ] -= P[ k ];
102 Q[ k - 1 ] += Q[ k ];
103 }
104
105 /* Transform polynomials from cos(n*f) to cos(f)^n */
106 silk_A2NLSF_trans_poly( P, dd );
107 silk_A2NLSF_trans_poly( Q, dd );
108 }
109
110 /* Compute Normalized Line Spectral Frequencies (NLSFs) from whitening filter coefficients */
111 /* If not all roots are found, the a_Q16 coefficients are bandwidth expanded until convergence. */
silk_A2NLSF(opus_int16 * NLSF,opus_int32 * a_Q16,const opus_int d)112 void silk_A2NLSF(
113 opus_int16 *NLSF, /* O Normalized Line Spectral Frequencies in Q15 (0..2^15-1) [d] */
114 opus_int32 *a_Q16, /* I/O Monic whitening filter coefficients in Q16 [d] */
115 const opus_int d /* I Filter order (must be even) */
116 )
117 {
118 opus_int i, k, m, dd, root_ix, ffrac;
119 opus_int32 xlo, xhi, xmid;
120 opus_int32 ylo, yhi, ymid, thr;
121 opus_int32 nom, den;
122 opus_int32 P[ SILK_MAX_ORDER_LPC / 2 + 1 ];
123 opus_int32 Q[ SILK_MAX_ORDER_LPC / 2 + 1 ];
124 opus_int32 *PQ[ 2 ];
125 opus_int32 *p;
126
127 /* Store pointers to array */
128 PQ[ 0 ] = P;
129 PQ[ 1 ] = Q;
130
131 dd = silk_RSHIFT( d, 1 );
132
133 silk_A2NLSF_init( a_Q16, P, Q, dd );
134
135 /* Find roots, alternating between P and Q */
136 p = P; /* Pointer to polynomial */
137
138 xlo = silk_LSFCosTab_FIX_Q12[ 0 ]; /* Q12*/
139 ylo = silk_A2NLSF_eval_poly( p, xlo, dd );
140
141 if( ylo < 0 ) {
142 /* Set the first NLSF to zero and move on to the next */
143 NLSF[ 0 ] = 0;
144 p = Q; /* Pointer to polynomial */
145 ylo = silk_A2NLSF_eval_poly( p, xlo, dd );
146 root_ix = 1; /* Index of current root */
147 } else {
148 root_ix = 0; /* Index of current root */
149 }
150 k = 1; /* Loop counter */
151 i = 0; /* Counter for bandwidth expansions applied */
152 thr = 0;
153 while( 1 ) {
154 /* Evaluate polynomial */
155 xhi = silk_LSFCosTab_FIX_Q12[ k ]; /* Q12 */
156 yhi = silk_A2NLSF_eval_poly( p, xhi, dd );
157
158 /* Detect zero crossing */
159 if( ( ylo <= 0 && yhi >= thr ) || ( ylo >= 0 && yhi <= -thr ) ) {
160 if( yhi == 0 ) {
161 /* If the root lies exactly at the end of the current */
162 /* interval, look for the next root in the next interval */
163 thr = 1;
164 } else {
165 thr = 0;
166 }
167 /* Binary division */
168 ffrac = -256;
169 for( m = 0; m < BIN_DIV_STEPS_A2NLSF_FIX; m++ ) {
170 /* Evaluate polynomial */
171 xmid = silk_RSHIFT_ROUND( xlo + xhi, 1 );
172 ymid = silk_A2NLSF_eval_poly( p, xmid, dd );
173
174 /* Detect zero crossing */
175 if( ( ylo <= 0 && ymid >= 0 ) || ( ylo >= 0 && ymid <= 0 ) ) {
176 /* Reduce frequency */
177 xhi = xmid;
178 yhi = ymid;
179 } else {
180 /* Increase frequency */
181 xlo = xmid;
182 ylo = ymid;
183 ffrac = silk_ADD_RSHIFT( ffrac, 128, m );
184 }
185 }
186
187 /* Interpolate */
188 if( silk_abs( ylo ) < 65536 ) {
189 /* Avoid dividing by zero */
190 den = ylo - yhi;
191 nom = silk_LSHIFT( ylo, 8 - BIN_DIV_STEPS_A2NLSF_FIX ) + silk_RSHIFT( den, 1 );
192 if( den != 0 ) {
193 ffrac += silk_DIV32( nom, den );
194 }
195 } else {
196 /* No risk of dividing by zero because abs(ylo - yhi) >= abs(ylo) >= 65536 */
197 ffrac += silk_DIV32( ylo, silk_RSHIFT( ylo - yhi, 8 - BIN_DIV_STEPS_A2NLSF_FIX ) );
198 }
199 NLSF[ root_ix ] = (opus_int16)silk_min_32( silk_LSHIFT( (opus_int32)k, 8 ) + ffrac, silk_int16_MAX );
200
201 silk_assert( NLSF[ root_ix ] >= 0 );
202
203 root_ix++; /* Next root */
204 if( root_ix >= d ) {
205 /* Found all roots */
206 break;
207 }
208 /* Alternate pointer to polynomial */
209 p = PQ[ root_ix & 1 ];
210
211 /* Evaluate polynomial */
212 xlo = silk_LSFCosTab_FIX_Q12[ k - 1 ]; /* Q12*/
213 ylo = silk_LSHIFT( 1 - ( root_ix & 2 ), 12 );
214 } else {
215 /* Increment loop counter */
216 k++;
217 xlo = xhi;
218 ylo = yhi;
219 thr = 0;
220
221 if( k > LSF_COS_TAB_SZ_FIX ) {
222 i++;
223 if( i > MAX_ITERATIONS_A2NLSF_FIX ) {
224 /* Set NLSFs to white spectrum and exit */
225 NLSF[ 0 ] = (opus_int16)silk_DIV32_16( 1 << 15, d + 1 );
226 for( k = 1; k < d; k++ ) {
227 NLSF[ k ] = (opus_int16)silk_SMULBB( k + 1, NLSF[ 0 ] );
228 }
229 return;
230 }
231
232 /* Error: Apply progressively more bandwidth expansion and run again */
233 silk_bwexpander_32( a_Q16, d, 65536 - silk_SMULBB( 10 + i, i ) ); /* 10_Q16 = 0.00015*/
234
235 silk_A2NLSF_init( a_Q16, P, Q, dd );
236 p = P; /* Pointer to polynomial */
237 xlo = silk_LSFCosTab_FIX_Q12[ 0 ]; /* Q12*/
238 ylo = silk_A2NLSF_eval_poly( p, xlo, dd );
239 if( ylo < 0 ) {
240 /* Set the first NLSF to zero and move on to the next */
241 NLSF[ 0 ] = 0;
242 p = Q; /* Pointer to polynomial */
243 ylo = silk_A2NLSF_eval_poly( p, xlo, dd );
244 root_ix = 1; /* Index of current root */
245 } else {
246 root_ix = 0; /* Index of current root */
247 }
248 k = 1; /* Reset loop counter */
249 }
250 }
251 }
252 }
253