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#include "webrtc/common_audio/vad/vad_gmm.h"
12
13#include "webrtc/common_audio/signal_processing/include/signal_processing_library.h"
14#include "webrtc/typedefs.h"
15
16static const int32_t kCompVar = 22005;
17static const int16_t kLog2Exp = 5909;  // log2(exp(1)) in Q12.
18
19// For a normal distribution, the probability of |input| is calculated and
20// returned (in Q20). The formula for normal distributed probability is
21//
22// 1 / s * exp(-(x - m)^2 / (2 * s^2))
23//
24// where the parameters are given in the following Q domains:
25// m = |mean| (Q7)
26// s = |std| (Q7)
27// x = |input| (Q4)
28// in addition to the probability we output |delta| (in Q11) used when updating
29// the noise/speech model.
30int32_t WebRtcVad_GaussianProbability(int16_t input,
31                                      int16_t mean,
32                                      int16_t std,
33                                      int16_t* delta) {
34  int16_t tmp16, inv_std, inv_std2, exp_value = 0;
35  int32_t tmp32;
36
37  // Calculate |inv_std| = 1 / s, in Q10.
38  // 131072 = 1 in Q17, and (|std| >> 1) is for rounding instead of truncation.
39  // Q-domain: Q17 / Q7 = Q10.
40  tmp32 = (int32_t) 131072 + (int32_t) (std >> 1);
41  inv_std = (int16_t) WebRtcSpl_DivW32W16(tmp32, std);
42
43  // Calculate |inv_std2| = 1 / s^2, in Q14.
44  tmp16 = (inv_std >> 2);  // Q10 -> Q8.
45  // Q-domain: (Q8 * Q8) >> 2 = Q14.
46  inv_std2 = (int16_t)((tmp16 * tmp16) >> 2);
47  // TODO(bjornv): Investigate if changing to
48  // inv_std2 = (int16_t)((inv_std * inv_std) >> 6);
49  // gives better accuracy.
50
51  tmp16 = (input << 3);  // Q4 -> Q7
52  tmp16 = tmp16 - mean;  // Q7 - Q7 = Q7
53
54  // To be used later, when updating noise/speech model.
55  // |delta| = (x - m) / s^2, in Q11.
56  // Q-domain: (Q14 * Q7) >> 10 = Q11.
57  *delta = (int16_t)((inv_std2 * tmp16) >> 10);
58
59  // Calculate the exponent |tmp32| = (x - m)^2 / (2 * s^2), in Q10. Replacing
60  // division by two with one shift.
61  // Q-domain: (Q11 * Q7) >> 8 = Q10.
62  tmp32 = (*delta * tmp16) >> 9;
63
64  // If the exponent is small enough to give a non-zero probability we calculate
65  // |exp_value| ~= exp(-(x - m)^2 / (2 * s^2))
66  //             ~= exp2(-log2(exp(1)) * |tmp32|).
67  if (tmp32 < kCompVar) {
68    // Calculate |tmp16| = log2(exp(1)) * |tmp32|, in Q10.
69    // Q-domain: (Q12 * Q10) >> 12 = Q10.
70    tmp16 = (int16_t)((kLog2Exp * tmp32) >> 12);
71    tmp16 = -tmp16;
72    exp_value = (0x0400 | (tmp16 & 0x03FF));
73    tmp16 ^= 0xFFFF;
74    tmp16 >>= 10;
75    tmp16 += 1;
76    // Get |exp_value| = exp(-|tmp32|) in Q10.
77    exp_value >>= tmp16;
78  }
79
80  // Calculate and return (1 / s) * exp(-(x - m)^2 / (2 * s^2)), in Q20.
81  // Q-domain: Q10 * Q10 = Q20.
82  return inv_std * exp_value;
83}
84