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+/*
+ *  Copyright (c) 2019 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.
+ */
+
+#ifndef API_NUMERICS_RUNNING_STATISTICS_H_
+#define API_NUMERICS_RUNNING_STATISTICS_H_
+
+#include <algorithm>
+#include <cmath>
+#include <limits>
+
+#include "absl/types/optional.h"
+#include "rtc_base/checks.h"
+#include "rtc_base/numerics/math_utils.h"
+
+namespace webrtc {
+namespace webrtc_impl {
+
+// tl;dr: Robust and efficient online computation of statistics,
+//        using Welford's method for variance. [1]
+//
+// This should be your go-to class if you ever need to compute
+// min, max, mean, variance and standard deviation.
+// If you need to get percentiles, please use webrtc::SamplesStatsCounter.
+//
+// Please note RemoveSample() won't affect min and max.
+// If you want a full-fledged moving window over N last samples,
+// please use webrtc::RollingAccumulator.
+//
+// The measures return absl::nullopt if no samples were fed (Size() == 0),
+// otherwise the returned optional is guaranteed to contain a value.
+//
+// [1]
+// https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm
+
+// The type T is a scalar which must be convertible to double.
+// Rationale: we often need greater precision for measures
+//            than for the samples themselves.
+template <typename T>
+class RunningStatistics {
+ public:
+  // Update stats ////////////////////////////////////////////
+
+  // Add a value participating in the statistics in O(1) time.
+  void AddSample(T sample) {
+    max_ = std::max(max_, sample);
+    min_ = std::min(min_, sample);
+    ++size_;
+    // Welford's incremental update.
+    const double delta = sample - mean_;
+    mean_ += delta / size_;
+    const double delta2 = sample - mean_;
+    cumul_ += delta * delta2;
+  }
+
+  // Remove a previously added value in O(1) time.
+  // Nb: This doesn't affect min or max.
+  // Calling RemoveSample when Size()==0 is incorrect.
+  void RemoveSample(T sample) {
+    RTC_DCHECK_GT(Size(), 0);
+    // In production, just saturate at 0.
+    if (Size() == 0) {
+      return;
+    }
+    // Since samples order doesn't matter, this is the
+    // exact reciprocal of Welford's incremental update.
+    --size_;
+    const double delta = sample - mean_;
+    mean_ -= delta / size_;
+    const double delta2 = sample - mean_;
+    cumul_ -= delta * delta2;
+  }
+
+  // Merge other stats, as if samples were added one by one, but in O(1).
+  void MergeStatistics(const RunningStatistics<T>& other) {
+    if (other.size_ == 0) {
+      return;
+    }
+    max_ = std::max(max_, other.max_);
+    min_ = std::min(min_, other.min_);
+    const int64_t new_size = size_ + other.size_;
+    const double new_mean =
+        (mean_ * size_ + other.mean_ * other.size_) / new_size;
+    // Each cumulant must be corrected.
+    //   * from: sum((x_i - mean_)²)
+    //   * to:   sum((x_i - new_mean)²)
+    auto delta = [new_mean](const RunningStatistics<T>& stats) {
+      return stats.size_ * (new_mean * (new_mean - 2 * stats.mean_) +
+                            stats.mean_ * stats.mean_);
+    };
+    cumul_ = cumul_ + delta(*this) + other.cumul_ + delta(other);
+    mean_ = new_mean;
+    size_ = new_size;
+  }
+
+  // Get Measures ////////////////////////////////////////////
+
+  // Returns number of samples involved via AddSample() or MergeStatistics(),
+  // minus number of times RemoveSample() was called.
+  int64_t Size() const { return size_; }
+
+  // Returns minimum among all seen samples, in O(1) time.
+  // This isn't affected by RemoveSample().
+  absl::optional<T> GetMin() const {
+    if (size_ == 0) {
+      return absl::nullopt;
+    }
+    return min_;
+  }
+
+  // Returns maximum among all seen samples, in O(1) time.
+  // This isn't affected by RemoveSample().
+  absl::optional<T> GetMax() const {
+    if (size_ == 0) {
+      return absl::nullopt;
+    }
+    return max_;
+  }
+
+  // Returns mean in O(1) time.
+  absl::optional<double> GetMean() const {
+    if (size_ == 0) {
+      return absl::nullopt;
+    }
+    return mean_;
+  }
+
+  // Returns unbiased sample variance in O(1) time.
+  absl::optional<double> GetVariance() const {
+    if (size_ == 0) {
+      return absl::nullopt;
+    }
+    return cumul_ / size_;
+  }
+
+  // Returns unbiased standard deviation in O(1) time.
+  absl::optional<double> GetStandardDeviation() const {
+    if (size_ == 0) {
+      return absl::nullopt;
+    }
+    return std::sqrt(*GetVariance());
+  }
+
+ private:
+  int64_t size_ = 0;  // Samples seen.
+  T min_ = infinity_or_max<T>();
+  T max_ = minus_infinity_or_min<T>();
+  double mean_ = 0;
+  double cumul_ = 0;  // Variance * size_, sometimes noted m2.
+};
+
+}  // namespace webrtc_impl
+}  // namespace webrtc
+
+#endif  // API_NUMERICS_RUNNING_STATISTICS_H_