1 /*
2 * Copyright (c) 2011 The WebRTC project authors. All Rights Reserved.
3 *
4 * Use of this source code is governed by a BSD-style license
5 * that can be found in the LICENSE file in the root of the source
6 * tree. An additional intellectual property rights grant can be found
7 * in the file PATENTS. All contributing project authors may
8 * be found in the AUTHORS file in the root of the source tree.
9 */
10
11
12 /*
13 * This file contains the function WebRtcSpl_LevinsonDurbin().
14 * The description header can be found in signal_processing_library.h
15 *
16 */
17
18 #include "common_audio/signal_processing/include/signal_processing_library.h"
19 #include "rtc_base/sanitizer.h"
20
21 #define SPL_LEVINSON_MAXORDER 20
22
23 int16_t RTC_NO_SANITIZE("signed-integer-overflow") // bugs.webrtc.org/5486
WebRtcSpl_LevinsonDurbin(const int32_t * R,int16_t * A,int16_t * K,size_t order)24 WebRtcSpl_LevinsonDurbin(const int32_t* R, int16_t* A, int16_t* K,
25 size_t order)
26 {
27 size_t i, j;
28 // Auto-correlation coefficients in high precision
29 int16_t R_hi[SPL_LEVINSON_MAXORDER + 1], R_low[SPL_LEVINSON_MAXORDER + 1];
30 // LPC coefficients in high precision
31 int16_t A_hi[SPL_LEVINSON_MAXORDER + 1], A_low[SPL_LEVINSON_MAXORDER + 1];
32 // LPC coefficients for next iteration
33 int16_t A_upd_hi[SPL_LEVINSON_MAXORDER + 1], A_upd_low[SPL_LEVINSON_MAXORDER + 1];
34 // Reflection coefficient in high precision
35 int16_t K_hi, K_low;
36 // Prediction gain Alpha in high precision and with scale factor
37 int16_t Alpha_hi, Alpha_low, Alpha_exp;
38 int16_t tmp_hi, tmp_low;
39 int32_t temp1W32, temp2W32, temp3W32;
40 int16_t norm;
41
42 // Normalize the autocorrelation R[0]...R[order+1]
43
44 norm = WebRtcSpl_NormW32(R[0]);
45
46 for (i = 0; i <= order; ++i)
47 {
48 temp1W32 = R[i] * (1 << norm);
49 // UBSan: 12 * 268435456 cannot be represented in type 'int'
50
51 // Put R in hi and low format
52 R_hi[i] = (int16_t)(temp1W32 >> 16);
53 R_low[i] = (int16_t)((temp1W32 - ((int32_t)R_hi[i] * 65536)) >> 1);
54 }
55
56 // K = A[1] = -R[1] / R[0]
57
58 temp2W32 = R[1] * (1 << norm); // R[1] in Q31
59 temp3W32 = WEBRTC_SPL_ABS_W32(temp2W32); // abs R[1]
60 temp1W32 = WebRtcSpl_DivW32HiLow(temp3W32, R_hi[0], R_low[0]); // abs(R[1])/R[0] in Q31
61 // Put back the sign on R[1]
62 if (temp2W32 > 0)
63 {
64 temp1W32 = -temp1W32;
65 }
66
67 // Put K in hi and low format
68 K_hi = (int16_t)(temp1W32 >> 16);
69 K_low = (int16_t)((temp1W32 - ((int32_t)K_hi * 65536)) >> 1);
70
71 // Store first reflection coefficient
72 K[0] = K_hi;
73
74 temp1W32 >>= 4; // A[1] in Q27.
75
76 // Put A[1] in hi and low format
77 A_hi[1] = (int16_t)(temp1W32 >> 16);
78 A_low[1] = (int16_t)((temp1W32 - ((int32_t)A_hi[1] * 65536)) >> 1);
79
80 // Alpha = R[0] * (1-K^2)
81
82 temp1W32 = ((K_hi * K_low >> 14) + K_hi * K_hi) * 2; // = k^2 in Q31
83
84 temp1W32 = WEBRTC_SPL_ABS_W32(temp1W32); // Guard against <0
85 temp1W32 = (int32_t)0x7fffffffL - temp1W32; // temp1W32 = (1 - K[0]*K[0]) in Q31
86
87 // Store temp1W32 = 1 - K[0]*K[0] on hi and low format
88 tmp_hi = (int16_t)(temp1W32 >> 16);
89 tmp_low = (int16_t)((temp1W32 - ((int32_t)tmp_hi << 16)) >> 1);
90
91 // Calculate Alpha in Q31
92 temp1W32 = (R_hi[0] * tmp_hi + (R_hi[0] * tmp_low >> 15) +
93 (R_low[0] * tmp_hi >> 15)) << 1;
94
95 // Normalize Alpha and put it in hi and low format
96
97 Alpha_exp = WebRtcSpl_NormW32(temp1W32);
98 temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, Alpha_exp);
99 Alpha_hi = (int16_t)(temp1W32 >> 16);
100 Alpha_low = (int16_t)((temp1W32 - ((int32_t)Alpha_hi << 16)) >> 1);
101
102 // Perform the iterative calculations in the Levinson-Durbin algorithm
103
104 for (i = 2; i <= order; i++)
105 {
106 /* ----
107 temp1W32 = R[i] + > R[j]*A[i-j]
108 /
109 ----
110 j=1..i-1
111 */
112
113 temp1W32 = 0;
114
115 for (j = 1; j < i; j++)
116 {
117 // temp1W32 is in Q31
118 temp1W32 += (R_hi[j] * A_hi[i - j] * 2) +
119 (((R_hi[j] * A_low[i - j] >> 15) +
120 (R_low[j] * A_hi[i - j] >> 15)) * 2);
121 }
122
123 temp1W32 = temp1W32 * 16;
124 temp1W32 += ((int32_t)R_hi[i] * 65536)
125 + WEBRTC_SPL_LSHIFT_W32((int32_t)R_low[i], 1);
126
127 // K = -temp1W32 / Alpha
128 temp2W32 = WEBRTC_SPL_ABS_W32(temp1W32); // abs(temp1W32)
129 temp3W32 = WebRtcSpl_DivW32HiLow(temp2W32, Alpha_hi, Alpha_low); // abs(temp1W32)/Alpha
130
131 // Put the sign of temp1W32 back again
132 if (temp1W32 > 0)
133 {
134 temp3W32 = -temp3W32;
135 }
136
137 // Use the Alpha shifts from earlier to de-normalize
138 norm = WebRtcSpl_NormW32(temp3W32);
139 if ((Alpha_exp <= norm) || (temp3W32 == 0))
140 {
141 temp3W32 = temp3W32 * (1 << Alpha_exp);
142 } else
143 {
144 if (temp3W32 > 0)
145 {
146 temp3W32 = (int32_t)0x7fffffffL;
147 } else
148 {
149 temp3W32 = (int32_t)0x80000000L;
150 }
151 }
152
153 // Put K on hi and low format
154 K_hi = (int16_t)(temp3W32 >> 16);
155 K_low = (int16_t)((temp3W32 - ((int32_t)K_hi * 65536)) >> 1);
156
157 // Store Reflection coefficient in Q15
158 K[i - 1] = K_hi;
159
160 // Test for unstable filter.
161 // If unstable return 0 and let the user decide what to do in that case
162
163 if ((int32_t)WEBRTC_SPL_ABS_W16(K_hi) > (int32_t)32750)
164 {
165 return 0; // Unstable filter
166 }
167
168 /*
169 Compute updated LPC coefficient: Anew[i]
170 Anew[j]= A[j] + K*A[i-j] for j=1..i-1
171 Anew[i]= K
172 */
173
174 for (j = 1; j < i; j++)
175 {
176 // temp1W32 = A[j] in Q27
177 temp1W32 = (int32_t)A_hi[j] * 65536
178 + WEBRTC_SPL_LSHIFT_W32((int32_t)A_low[j],1);
179
180 // temp1W32 += K*A[i-j] in Q27
181 temp1W32 += (K_hi * A_hi[i - j] + (K_hi * A_low[i - j] >> 15) +
182 (K_low * A_hi[i - j] >> 15)) * 2;
183
184 // Put Anew in hi and low format
185 A_upd_hi[j] = (int16_t)(temp1W32 >> 16);
186 A_upd_low[j] = (int16_t)(
187 (temp1W32 - ((int32_t)A_upd_hi[j] * 65536)) >> 1);
188 }
189
190 // temp3W32 = K in Q27 (Convert from Q31 to Q27)
191 temp3W32 >>= 4;
192
193 // Store Anew in hi and low format
194 A_upd_hi[i] = (int16_t)(temp3W32 >> 16);
195 A_upd_low[i] = (int16_t)(
196 (temp3W32 - ((int32_t)A_upd_hi[i] * 65536)) >> 1);
197
198 // Alpha = Alpha * (1-K^2)
199
200 temp1W32 = ((K_hi * K_low >> 14) + K_hi * K_hi) * 2; // K*K in Q31
201
202 temp1W32 = WEBRTC_SPL_ABS_W32(temp1W32); // Guard against <0
203 temp1W32 = (int32_t)0x7fffffffL - temp1W32; // 1 - K*K in Q31
204
205 // Convert 1- K^2 in hi and low format
206 tmp_hi = (int16_t)(temp1W32 >> 16);
207 tmp_low = (int16_t)((temp1W32 - ((int32_t)tmp_hi << 16)) >> 1);
208
209 // Calculate Alpha = Alpha * (1-K^2) in Q31
210 temp1W32 = (Alpha_hi * tmp_hi + (Alpha_hi * tmp_low >> 15) +
211 (Alpha_low * tmp_hi >> 15)) << 1;
212
213 // Normalize Alpha and store it on hi and low format
214
215 norm = WebRtcSpl_NormW32(temp1W32);
216 temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, norm);
217
218 Alpha_hi = (int16_t)(temp1W32 >> 16);
219 Alpha_low = (int16_t)((temp1W32 - ((int32_t)Alpha_hi << 16)) >> 1);
220
221 // Update the total normalization of Alpha
222 Alpha_exp = Alpha_exp + norm;
223
224 // Update A[]
225
226 for (j = 1; j <= i; j++)
227 {
228 A_hi[j] = A_upd_hi[j];
229 A_low[j] = A_upd_low[j];
230 }
231 }
232
233 /*
234 Set A[0] to 1.0 and store the A[i] i=1...order in Q12
235 (Convert from Q27 and use rounding)
236 */
237
238 A[0] = 4096;
239
240 for (i = 1; i <= order; i++)
241 {
242 // temp1W32 in Q27
243 temp1W32 = (int32_t)A_hi[i] * 65536
244 + WEBRTC_SPL_LSHIFT_W32((int32_t)A_low[i], 1);
245 // Round and store upper word
246 A[i] = (int16_t)(((temp1W32 * 2) + 32768) >> 16);
247 }
248 return 1; // Stable filters
249 }
250