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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.
*/
#include "modules/audio_coding/neteq/histogram.h"
#include <algorithm>
#include <cstdlib>
#include <numeric>
#include <optional>
#include "rtc_base/checks.h"
#include "rtc_base/numerics/safe_conversions.h"
namespace webrtc {
Histogram::Histogram(size_t num_buckets,
int forget_factor,
std::optional<double> start_forget_weight)
: buckets_(num_buckets, 0),
forget_factor_(0),
base_forget_factor_(forget_factor),
add_count_(0),
start_forget_weight_(start_forget_weight) {
RTC_DCHECK_LT(base_forget_factor_, 1 << 15);
}
Histogram::~Histogram() {}
// Each element in the vector is first multiplied by the forgetting factor
// `forget_factor_`. Then the vector element indicated by `iat_packets` is then
// increased (additive) by 1 - `forget_factor_`. This way, the probability of
// `value` is slightly increased, while the sum of the histogram remains
// constant (=1).
// Due to inaccuracies in the fixed-point arithmetic, the histogram may no
// longer sum up to 1 (in Q30) after the update. To correct this, a correction
// term is added or subtracted from the first element (or elements) of the
// vector.
// The forgetting factor `forget_factor_` is also updated. When the DelayManager
// is reset, the factor is set to 0 to facilitate rapid convergence in the
// beginning. With each update of the histogram, the factor is increased towards
// the steady-state value `base_forget_factor_`.
void Histogram::Add(int value) {
RTC_DCHECK(value >= 0);
RTC_DCHECK(value < static_cast<int>(buckets_.size()));
int vector_sum = 0; // Sum up the vector elements as they are processed.
// Multiply each element in `buckets_` with `forget_factor_`.
for (int& bucket : buckets_) {
bucket = (static_cast<int64_t>(bucket) * forget_factor_) >> 15;
vector_sum += bucket;
}
// Increase the probability for the currently observed inter-arrival time
// by 1 - `forget_factor_`. The factor is in Q15, `buckets_` in Q30.
// Thus, left-shift 15 steps to obtain result in Q30.
buckets_[value] += (32768 - forget_factor_) << 15;
vector_sum += (32768 - forget_factor_) << 15; // Add to vector sum.
// `buckets_` should sum up to 1 (in Q30), but it may not due to
// fixed-point rounding errors.
vector_sum -= 1 << 30; // Should be zero. Compensate if not.
if (vector_sum != 0) {
// Modify a few values early in `buckets_`.
int flip_sign = vector_sum > 0 ? -1 : 1;
for (int& bucket : buckets_) {
// Add/subtract 1/16 of the element, but not more than `vector_sum`.
int correction = flip_sign * std::min(std::abs(vector_sum), bucket >> 4);
bucket += correction;
vector_sum += correction;
if (std::abs(vector_sum) == 0) {
break;
}
}
}
RTC_DCHECK(vector_sum == 0); // Verify that the above is correct.
++add_count_;
// Update `forget_factor_` (changes only during the first seconds after a
// reset). The factor converges to `base_forget_factor_`.
if (start_forget_weight_) {
if (forget_factor_ != base_forget_factor_) {
int old_forget_factor = forget_factor_;
int forget_factor =
(1 << 15) * (1 - start_forget_weight_.value() / (add_count_ + 1));
forget_factor_ =
std::max(0, std::min(base_forget_factor_, forget_factor));
// The histogram is updated recursively by forgetting the old histogram
// with `forget_factor_` and adding a new sample multiplied by |1 -
// forget_factor_|. We need to make sure that the effective weight on the
// new sample is no smaller than those on the old samples, i.e., to
// satisfy the following DCHECK.
RTC_DCHECK_GE((1 << 15) - forget_factor_,
((1 << 15) - old_forget_factor) * forget_factor_ >> 15);
}
} else {
forget_factor_ += (base_forget_factor_ - forget_factor_ + 3) >> 2;
}
}
int Histogram::Quantile(int probability) {
// Find the bucket for which the probability of observing an
// inter-arrival time larger than or equal to `index` is larger than or
// equal to `probability`. The sought probability is estimated using
// the histogram as the reverse cumulant PDF, i.e., the sum of elements from
// the end up until `index`. Now, since the sum of all elements is 1
// (in Q30) by definition, and since the solution is often a low value for
// `iat_index`, it is more efficient to start with `sum` = 1 and subtract
// elements from the start of the histogram.
int inverse_probability = (1 << 30) - probability;
size_t index = 0; // Start from the beginning of `buckets_`.
int sum = 1 << 30; // Assign to 1 in Q30.
sum -= buckets_[index];
while ((sum > inverse_probability) && (index < buckets_.size() - 1)) {
// Subtract the probabilities one by one until the sum is no longer greater
// than `inverse_probability`.
++index;
sum -= buckets_[index];
}
return static_cast<int>(index);
}
// Set the histogram vector to an exponentially decaying distribution
// buckets_[i] = 0.5^(i+1), i = 0, 1, 2, ...
// buckets_ is in Q30.
void Histogram::Reset() {
// Set temp_prob to (slightly more than) 1 in Q14. This ensures that the sum
// of buckets_ is 1.
uint16_t temp_prob = 0x4002; // 16384 + 2 = 100000000000010 binary.
for (int& bucket : buckets_) {
temp_prob >>= 1;
bucket = temp_prob << 16;
}
forget_factor_ = 0; // Adapt the histogram faster for the first few packets.
add_count_ = 0;
}
int Histogram::NumBuckets() const {
return buckets_.size();
}
} // namespace webrtc