Fixing init time error in smoothing filter.

webrtc/common_audio/smoothing_filter.cc

Index: webrtc/common_audio/smoothing_filter.cc
diff --git a/webrtc/common_audio/smoothing_filter.cc b/webrtc/common_audio/smoothing_filter.cc
index d2dde9d8542751d644157bd34e4c671cee177cad..2ab25981f1e3af4b4777026f212591094f75a78c 100644
--- a/webrtc/common_audio/smoothing_filter.cc
+++ b/webrtc/common_audio/smoothing_filter.cc
@@ -14,17 +14,20 @@
 
 namespace webrtc {
 
-SmoothingFilterImpl::SmoothingFilterImpl(int init_time_ms_, const Clock* clock)
-    : init_time_ms_(init_time_ms_),
+SmoothingFilterImpl::SmoothingFilterImpl(int init_time_ms, const Clock* clock)
+    : init_time_ms_(init_time_ms),
       // Duing the initalization time, we use an increasing alpha. Specifically,
-      //   alpha(n) = exp(pow(init_factor_, n)),
+      //   alpha(n) = exp(-powf(init_factor_, n)),
       // where |init_factor_| is chosen such that
       //   alpha(init_time_ms_) = exp(-1.0f / init_time_ms_),
-      init_factor_(pow(init_time_ms_, 1.0f / init_time_ms_)),
+      init_factor_(init_time_ms_ == 0 ? 0.0f : powf(init_time_ms_,
+                                                    -1.0f / init_time_ms_)),
       // |init_const_| is to a factor to help the calculation during
       // initialization phase.
-      init_const_(1.0f / (init_time_ms_ -
-                          pow(init_time_ms_, 1.0f - 1.0f / init_time_ms_))),
+      init_const_(init_time_ms_ == 0
+                      ? 0.0f
+                      : init_time_ms_ -
+                            powf(init_time_ms_, 1.0f - 1.0f / init_time_ms_)),
       clock_(clock) {
   UpdateAlpha(init_time_ms_);
 }
@@ -34,11 +37,11 @@ SmoothingFilterImpl::~SmoothingFilterImpl() = default;
 void SmoothingFilterImpl::AddSample(float sample) {
   const int64_t now_ms = clock_->TimeInMilliseconds();
 
-  if (!first_sample_time_ms_) {
+  if (!init_end_time_ms_) {
     // This is equivalent to assuming the filter has been receiving the same
     // value as the first sample since time -infinity.
     state_ = last_sample_ = sample;
-    first_sample_time_ms_ = rtc::Optional<int64_t>(now_ms);
+    init_end_time_ms_ = rtc::Optional<int64_t>(now_ms + init_time_ms_);
     last_state_time_ms_ = now_ms;
     return;
   }
@@ -48,15 +51,16 @@ void SmoothingFilterImpl::AddSample(float sample) {
 }
 
 rtc::Optional<float> SmoothingFilterImpl::GetAverage() {
-  if (!first_sample_time_ms_)
+  if (!init_end_time_ms_) {
+    // |init_end_time_ms_| undefined since we have not received any sample.
     return rtc::Optional<float>();
+  }
   ExtrapolateLastSample(clock_->TimeInMilliseconds());
   return rtc::Optional<float>(state_);
 }
 
 bool SmoothingFilterImpl::SetTimeConstantMs(int time_constant_ms) {
-  if (!first_sample_time_ms_ ||
-      last_state_time_ms_ < *first_sample_time_ms_ + init_time_ms_) {
+  if (!init_end_time_ms_ || last_state_time_ms_ < *init_end_time_ms_) {
     return false;
   }
   UpdateAlpha(time_constant_ms);
@@ -64,34 +68,43 @@ bool SmoothingFilterImpl::SetTimeConstantMs(int time_constant_ms) {
 }
 
 void SmoothingFilterImpl::UpdateAlpha(int time_constant_ms) {
-  alpha_ = exp(-1.0f / time_constant_ms);
+  alpha_ = time_constant_ms == 0 ? 0.0f : exp(-1.0f / time_constant_ms);
 }
 
 void SmoothingFilterImpl::ExtrapolateLastSample(int64_t time_ms) {
   RTC_DCHECK_GE(time_ms, last_state_time_ms_);
-  RTC_DCHECK(first_sample_time_ms_);
+  RTC_DCHECK(init_end_time_ms_);
 
   float multiplier = 0.0f;
-  if (time_ms <= *first_sample_time_ms_ + init_time_ms_) {
+
+  if (time_ms <= *init_end_time_ms_) {
     // Current update is to be made during initialization phase.
     // We update the state as if the |alpha| has been increased according
-    //   alpha(n) = exp(pow(init_factor_, n)),
+    //   alpha(n) = exp(-powf(init_factor_, n)),
     // where n is the time (in millisecond) since the first sample received.
     // With algebraic derivation as shown in the Appendix, we can find that the
     // state can be updated in a similar manner as if alpha is a constant,
     // except for a different multiplier.
-    multiplier = exp(-init_const_ *
-        (pow(init_factor_,
-             *first_sample_time_ms_ + init_time_ms_ - last_state_time_ms_) -
-         pow(init_factor_, *first_sample_time_ms_ + init_time_ms_ - time_ms)));
+    if (init_time_ms_ == 0) {
+      // This means |init_factor_| = 0.
+      multiplier = 0.0f;
+    } else if (init_time_ms_ == 1) {
+      // This means |init_factor_| = 1.
+      multiplier = exp(last_state_time_ms_ - time_ms);
+    } else {
+      multiplier =
+          exp(-(powf(init_factor_, last_state_time_ms_ - *init_end_time_ms_) -
+                powf(init_factor_, time_ms - *init_end_time_ms_)) /
+              init_const_);
+    }
   } else {
-    if (last_state_time_ms_ < *first_sample_time_ms_ + init_time_ms_) {
+    if (last_state_time_ms_ < *init_end_time_ms_) {
       // The latest state update was made during initialization phase.
       // We first extrapolate to the initialization time.
-      ExtrapolateLastSample(*first_sample_time_ms_ + init_time_ms_);
+      ExtrapolateLastSample(*init_end_time_ms_);
       // Then extrapolate the rest by the following.
     }
-    multiplier = pow(alpha_, time_ms - last_state_time_ms_);
+    multiplier = powf(alpha_, time_ms - last_state_time_ms_);
   }
 
   state_ = multiplier * state_ + (1.0f - multiplier) * last_sample_;
@@ -108,17 +121,21 @@ void SmoothingFilterImpl::ExtrapolateLastSample(int64_t time_ms) {
 //          &= \left(\prod_{i=m}^{n-1} \alpha_i\right) y(m) +
 //             \left(1 - \prod_{i=m}^{n-1} \alpha_i \right) x(m)
 //   \end{align}
-// Taking $\alpha_{n} = \exp{\gamma^n}$, $\gamma$ denotes init\_factor\_, the
+// Taking $\alpha_{n} = \exp(-\gamma^n)$, $\gamma$ denotes init\_factor\_, the
 // multiplier becomes
 //   \begin{align}
 //     \prod_{i=m}^{n-1} \alpha_i
-//     &= \exp\left(\prod_{i=m}^{n-1} \gamma^i \right) \\*
-//     &= \exp\left(\frac{\gamma^m - \gamma^n}{1 - \gamma} \right)
+//     &= \exp\left(-\sum_{i=m}^{n-1} \gamma^i \right) \\*
+//     &= \begin{cases}
+//          \exp\left(-\frac{\gamma^m - \gamma^n}{1 - \gamma} \right)
+//          & \gamma \neq 1 \\*
+//          m-n & \gamma = 1
+//        \end{cases}
 //   \end{align}
-// We know $\gamma = T^\frac{1}{T}$, where $T$ denotes init\_time\_ms\_. Then
+// We know $\gamma = T^{-\frac{1}{T}}$, where $T$ denotes init\_time\_ms\_. Then
 // $1 - \gamma$ approaches zero when $T$ increases. This can cause numerical
-// difficulties. We multiply $T$ to both numerator and denominator in the
-// fraction. See.
+// difficulties. We multiply $T$ (if $T > 0$) to both numerator and denominator
+// in the fraction. See.
 //   \begin{align}
 //     \frac{\gamma^m - \gamma^n}{1 - \gamma}
 //     &= \frac{T^\frac{T-m}{T} - T^\frac{T-n}{T}}{T - T^{1-\frac{1}{T}}}