text: /*
   *  Copyright (c) 2011 The WebRTC project authors. All Rights Reserved.
   *
   *  Use of this source code is governed by a BSD-style license
   *  that can be found in the LICENSE file in the root of the source
   *  tree. An additional intellectual property rights grant can be found
   *  in the file PATENTS.  All contributing project authors may
   *  be found in the AUTHORS file in the root of the source tree.
   */
  
  #include "common_audio/vad/vad_gmm.h"
  
  #include "common_audio/signal_processing/include/signal_processing_library.h"
  #include "typedefs.h"  // NOLINT(build/include)
  
  static const int32_t kCompVar = 22005;
  static const int16_t kLog2Exp = 5909;  // log2(exp(1)) in Q12.
  
  // For a normal distribution, the probability of |input| is calculated and
  // returned (in Q20). The formula for normal distributed probability is
  //
  // 1 / s * exp(-(x - m)^2 / (2 * s^2))
  //
  // where the parameters are given in the following Q domains:
  // m = |mean| (Q7)
  // s = |std| (Q7)
  // x = |input| (Q4)
  // in addition to the probability we output |delta| (in Q11) used when updating
  // the noise/speech model.
  int32_t WebRtcVad_GaussianProbability(int16_t input,
                                        int16_t mean,
                                        int16_t std,
                                        int16_t* delta) {
    int16_t tmp16, inv_std, inv_std2, exp_value = 0;
    int32_t tmp32;
  
    // Calculate |inv_std| = 1 / s, in Q10.
    // 131072 = 1 in Q17, and (|std| >> 1) is for rounding instead of truncation.
    // Q-domain: Q17 / Q7 = Q10.
    tmp32 = (int32_t) 131072 + (int32_t) (std >> 1);
    inv_std = (int16_t) WebRtcSpl_DivW32W16(tmp32, std);
  
    // Calculate |inv_std2| = 1 / s^2, in Q14.
    tmp16 = (inv_std >> 2);  // Q10 -> Q8.
    // Q-domain: (Q8 * Q8) >> 2 = Q14.
    inv_std2 = (int16_t)((tmp16 * tmp16) >> 2);
    // TODO(bjornv): Investigate if changing to
    // inv_std2 = (int16_t)((inv_std * inv_std) >> 6);
    // gives better accuracy.
  
    tmp16 = (input << 3);  // Q4 -> Q7
    tmp16 = tmp16 - mean;  // Q7 - Q7 = Q7
  
    // To be used later, when updating noise/speech model.
    // |delta| = (x - m) / s^2, in Q11.
    // Q-domain: (Q14 * Q7) >> 10 = Q11.
    *delta = (int16_t)((inv_std2 * tmp16) >> 10);
  
    // Calculate the exponent |tmp32| = (x - m)^2 / (2 * s^2), in Q10. Replacing
    // division by two with one shift.
    // Q-domain: (Q11 * Q7) >> 8 = Q10.
    tmp32 = (*delta * tmp16) >> 9;
  
    // If the exponent is small enough to give a non-zero probability we calculate
    // |exp_value| ~= exp(-(x - m)^2 / (2 * s^2))
    //             ~= exp2(-log2(exp(1)) * |tmp32|).
    if (tmp32 < kCompVar) {
      // Calculate |tmp16| = log2(exp(1)) * |tmp32|, in Q10.
      // Q-domain: (Q12 * Q10) >> 12 = Q10.
      tmp16 = (int16_t)((kLog2Exp * tmp32) >> 12);
      tmp16 = -tmp16;
      exp_value = (0x0400 | (tmp16 & 0x03FF));
      tmp16 ^= 0xFFFF;
      tmp16 >>= 10;
      tmp16 += 1;
      // Get |exp_value| = exp(-|tmp32|) in Q10.
      exp_value >>= tmp16;
    }
  
    // Calculate and return (1 / s) * exp(-(x - m)^2 / (2 * s^2)), in Q20.
    // Q-domain: Q10 * Q10 = Q20.
    return inv_std * exp_value;
  }
  