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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
75 if ( opus_likely( 8 == dd ) )
76 {
77 y32 = silk_SMLAWW( p[ 7 ], y32, x_Q16 );
78 y32 = silk_SMLAWW( p[ 6 ], y32, x_Q16 );
79 y32 = silk_SMLAWW( p[ 5 ], y32, x_Q16 );
80 y32 = silk_SMLAWW( p[ 4 ], y32, x_Q16 );
81 y32 = silk_SMLAWW( p[ 3 ], y32, x_Q16 );
82 y32 = silk_SMLAWW( p[ 2 ], y32, x_Q16 );
83 y32 = silk_SMLAWW( p[ 1 ], y32, x_Q16 );
84 y32 = silk_SMLAWW( p[ 0 ], y32, x_Q16 );
85 }
86 else
87 {
88 for( n = dd - 1; n >= 0; n-- ) {
89 y32 = silk_SMLAWW( p[ n ], y32, x_Q16 ); /* Q16 */
90 }
91 }
92 return y32;
93 }
94
silk_A2NLSF_init(const opus_int32 * a_Q16,opus_int32 * P,opus_int32 * Q,const opus_int dd)95 static OPUS_INLINE void silk_A2NLSF_init(
96 const opus_int32 *a_Q16,
97 opus_int32 *P,
98 opus_int32 *Q,
99 const opus_int dd
100 )
101 {
102 opus_int k;
103
104 /* Convert filter coefs to even and odd polynomials */
105 P[dd] = silk_LSHIFT( 1, 16 );
106 Q[dd] = silk_LSHIFT( 1, 16 );
107 for( k = 0; k < dd; k++ ) {
108 P[ k ] = -a_Q16[ dd - k - 1 ] - a_Q16[ dd + k ]; /* Q16 */
109 Q[ k ] = -a_Q16[ dd - k - 1 ] + a_Q16[ dd + k ]; /* Q16 */
110 }
111
112 /* Divide out zeros as we have that for even filter orders, */
113 /* z = 1 is always a root in Q, and */
114 /* z = -1 is always a root in P */
115 for( k = dd; k > 0; k-- ) {
116 P[ k - 1 ] -= P[ k ];
117 Q[ k - 1 ] += Q[ k ];
118 }
119
120 /* Transform polynomials from cos(n*f) to cos(f)^n */
121 silk_A2NLSF_trans_poly( P, dd );
122 silk_A2NLSF_trans_poly( Q, dd );
123 }
124
125 /* Compute Normalized Line Spectral Frequencies (NLSFs) from whitening filter coefficients */
126 /* 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)127 void silk_A2NLSF(
128 opus_int16 *NLSF, /* O Normalized Line Spectral Frequencies in Q15 (0..2^15-1) [d] */
129 opus_int32 *a_Q16, /* I/O Monic whitening filter coefficients in Q16 [d] */
130 const opus_int d /* I Filter order (must be even) */
131 )
132 {
133 opus_int i, k, m, dd, root_ix, ffrac;
134 opus_int32 xlo, xhi, xmid;
135 opus_int32 ylo, yhi, ymid, thr;
136 opus_int32 nom, den;
137 opus_int32 P[ SILK_MAX_ORDER_LPC / 2 + 1 ];
138 opus_int32 Q[ SILK_MAX_ORDER_LPC / 2 + 1 ];
139 opus_int32 *PQ[ 2 ];
140 opus_int32 *p;
141
142 /* Store pointers to array */
143 PQ[ 0 ] = P;
144 PQ[ 1 ] = Q;
145
146 dd = silk_RSHIFT( d, 1 );
147
148 silk_A2NLSF_init( a_Q16, P, Q, dd );
149
150 /* Find roots, alternating between P and Q */
151 p = P; /* Pointer to polynomial */
152
153 xlo = silk_LSFCosTab_FIX_Q12[ 0 ]; /* Q12*/
154 ylo = silk_A2NLSF_eval_poly( p, xlo, dd );
155
156 if( ylo < 0 ) {
157 /* Set the first NLSF to zero and move on to the next */
158 NLSF[ 0 ] = 0;
159 p = Q; /* Pointer to polynomial */
160 ylo = silk_A2NLSF_eval_poly( p, xlo, dd );
161 root_ix = 1; /* Index of current root */
162 } else {
163 root_ix = 0; /* Index of current root */
164 }
165 k = 1; /* Loop counter */
166 i = 0; /* Counter for bandwidth expansions applied */
167 thr = 0;
168 while( 1 ) {
169 /* Evaluate polynomial */
170 xhi = silk_LSFCosTab_FIX_Q12[ k ]; /* Q12 */
171 yhi = silk_A2NLSF_eval_poly( p, xhi, dd );
172
173 /* Detect zero crossing */
174 if( ( ylo <= 0 && yhi >= thr ) || ( ylo >= 0 && yhi <= -thr ) ) {
175 if( yhi == 0 ) {
176 /* If the root lies exactly at the end of the current */
177 /* interval, look for the next root in the next interval */
178 thr = 1;
179 } else {
180 thr = 0;
181 }
182 /* Binary division */
183 ffrac = -256;
184 for( m = 0; m < BIN_DIV_STEPS_A2NLSF_FIX; m++ ) {
185 /* Evaluate polynomial */
186 xmid = silk_RSHIFT_ROUND( xlo + xhi, 1 );
187 ymid = silk_A2NLSF_eval_poly( p, xmid, dd );
188
189 /* Detect zero crossing */
190 if( ( ylo <= 0 && ymid >= 0 ) || ( ylo >= 0 && ymid <= 0 ) ) {
191 /* Reduce frequency */
192 xhi = xmid;
193 yhi = ymid;
194 } else {
195 /* Increase frequency */
196 xlo = xmid;
197 ylo = ymid;
198 ffrac = silk_ADD_RSHIFT( ffrac, 128, m );
199 }
200 }
201
202 /* Interpolate */
203 if( silk_abs( ylo ) < 65536 ) {
204 /* Avoid dividing by zero */
205 den = ylo - yhi;
206 nom = silk_LSHIFT( ylo, 8 - BIN_DIV_STEPS_A2NLSF_FIX ) + silk_RSHIFT( den, 1 );
207 if( den != 0 ) {
208 ffrac += silk_DIV32( nom, den );
209 }
210 } else {
211 /* No risk of dividing by zero because abs(ylo - yhi) >= abs(ylo) >= 65536 */
212 ffrac += silk_DIV32( ylo, silk_RSHIFT( ylo - yhi, 8 - BIN_DIV_STEPS_A2NLSF_FIX ) );
213 }
214 NLSF[ root_ix ] = (opus_int16)silk_min_32( silk_LSHIFT( (opus_int32)k, 8 ) + ffrac, silk_int16_MAX );
215
216 silk_assert( NLSF[ root_ix ] >= 0 );
217
218 root_ix++; /* Next root */
219 if( root_ix >= d ) {
220 /* Found all roots */
221 break;
222 }
223 /* Alternate pointer to polynomial */
224 p = PQ[ root_ix & 1 ];
225
226 /* Evaluate polynomial */
227 xlo = silk_LSFCosTab_FIX_Q12[ k - 1 ]; /* Q12*/
228 ylo = silk_LSHIFT( 1 - ( root_ix & 2 ), 12 );
229 } else {
230 /* Increment loop counter */
231 k++;
232 xlo = xhi;
233 ylo = yhi;
234 thr = 0;
235
236 if( k > LSF_COS_TAB_SZ_FIX ) {
237 i++;
238 if( i > MAX_ITERATIONS_A2NLSF_FIX ) {
239 /* Set NLSFs to white spectrum and exit */
240 NLSF[ 0 ] = (opus_int16)silk_DIV32_16( 1 << 15, d + 1 );
241 for( k = 1; k < d; k++ ) {
242 NLSF[ k ] = (opus_int16)silk_SMULBB( k + 1, NLSF[ 0 ] );
243 }
244 return;
245 }
246
247 /* Error: Apply progressively more bandwidth expansion and run again */
248 silk_bwexpander_32( a_Q16, d, 65536 - silk_SMULBB( 10 + i, i ) ); /* 10_Q16 = 0.00015*/
249
250 silk_A2NLSF_init( a_Q16, P, Q, dd );
251 p = P; /* Pointer to polynomial */
252 xlo = silk_LSFCosTab_FIX_Q12[ 0 ]; /* Q12*/
253 ylo = silk_A2NLSF_eval_poly( p, xlo, dd );
254 if( ylo < 0 ) {
255 /* Set the first NLSF to zero and move on to the next */
256 NLSF[ 0 ] = 0;
257 p = Q; /* Pointer to polynomial */
258 ylo = silk_A2NLSF_eval_poly( p, xlo, dd );
259 root_ix = 1; /* Index of current root */
260 } else {
261 root_ix = 0; /* Index of current root */
262 }
263 k = 1; /* Reset loop counter */
264 }
265 }
266 }
267 }
268