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#ifndef _PASSENGER_ALGORITHMS_EXP_MOVING_AVERAGE_H_
#define _PASSENGER_ALGORITHMS_EXP_MOVING_AVERAGE_H_
#include <oxt/macros.hpp>
#include <boost/config.hpp>
#include <algorithm>
#include <utility>
#include <cmath>
namespace Passenger {
using namespace std;
/**
* Implements discontiguous exponential moving averaging, as described by John C. Gunther
* 1998. Can be used to compute moving exponentially decaying averages and standard
* deviations. Unlike normal exponential moving average, this algorithm also works when
* the data has gaps, and it also avoids initial value bias and postgap bias. See
* http://www.drdobbs.com/tools/discontiguous-exponential-averaging/184410671
*
* ## Template parameters
*
* ### alpha
*
* Specifies by what factor data should decay. Its range is [0, 1000]. Higher values
* cause the current value to have more weight (and thus the previous average
* to decay more quickly), lower values have the opposite effect.
*
* ### alphaTimeUnit
*
* Specifies the time, in microseconds, after which the data should decay
* by a factor of exactly `alpha`. For example, if `alpha = 0.5` and `alphaTimeUnit = 2000000`,
* then data decays by 0.5 per 2 seconds.
*
* The default value is 1 second.
*
* ### maxAge
*
* Represents an educational guess as to how long (in microseconds) it takes
* for the sampled data sequence to change significantly. If you don't expect large random
* variations then you should set this to a large value. For a data sequence dominated by
* large random variations, setting this to 1000000 (1 second) might be appropriate.
*
* If the time interval between updates is `dt`, using a `maxAge` of `N * dt` will cause
* each update to fill in up to `N - 1` of any preceeding skipped updates with the current
* data value.
*/
template<
unsigned int alpha,
unsigned long long alphaTimeUnit = 1000000,
unsigned long long maxAge = 1000000
>
class DiscExpMovingAverage {
private:
template<unsigned int, unsigned long long, unsigned long long>
friend class DiscExpMovingAverageWithStddev;
double sumOfWeights, sumOfData;
unsigned long long prevTime;
static BOOST_CONSTEXPR double floatingAlpha() {
return alpha / 1000.0;
}
static BOOST_CONSTEXPR double newDataWeightUpperBound() {
return pow(floatingAlpha(), maxAge / (double) alphaTimeUnit);
}
pair<double, double> internalUpdate(double value, unsigned long long now) {
double weightReductionFactor = pow(1 - floatingAlpha(),
(now - prevTime) / (double) alphaTimeUnit);
double newDataWeight = std::min(1 - weightReductionFactor,
newDataWeightUpperBound());
sumOfWeights = weightReductionFactor * sumOfWeights + newDataWeight;
sumOfData = weightReductionFactor * sumOfData + newDataWeight * value;
prevTime = now;
return make_pair(weightReductionFactor, newDataWeight);
}
public:
DiscExpMovingAverage(unsigned long long _prevTime = 0)
: sumOfWeights(0),
sumOfData(0),
prevTime(_prevTime)
{ }
void update(double value, unsigned long long now) {
if (OXT_LIKELY(now > prevTime)) {
internalUpdate(value, now);
}
}
bool available() const {
return sumOfWeights > 0;
}
double completeness(unsigned long long now) const {
return pow(floatingAlpha(), now - prevTime) * sumOfWeights;
}
double average() const {
return sumOfData / sumOfWeights;
}
double average(unsigned long long now) const {
DiscExpMovingAverage<alpha, alphaTimeUnit, maxAge> copy(*this);
copy.update(0, now);
return copy.average();
}
};
/**
* Like DescExpMovingAverage, but also keeps track of the standard deviation.
*/
template<
unsigned int alpha,
unsigned long long alphaTimeUnit = 1000000,
unsigned long long maxAge = 1
>
class DiscExpMovingAverageWithStddev {
private:
DiscExpMovingAverage<alpha, alphaTimeUnit, maxAge> dema;
double sumOfSquaredData;
public:
DiscExpMovingAverageWithStddev(unsigned long long prevTime = 0)
: dema(prevTime),
sumOfSquaredData(0)
{ }
void update(double value, unsigned long long now) {
if (OXT_UNLIKELY(now <= dema.prevTime)) {
return;
}
pair<double, double> p = dema.internalUpdate(value, now);
double weightReductionFactor = p.first;
double newDataWeight = p.second;
sumOfSquaredData = weightReductionFactor * sumOfSquaredData
+ newDataWeight * pow(value, 2.0);
}
bool available() const {
return dema.available();
}
double completeness(unsigned long long now) const {
return dema.completeness(now);
}
double average() const {
return dema.average();
}
double average(unsigned long long now) const {
return dema.average(now);
}
double stddev() const {
return sqrt(sumOfSquaredData / dema.sumOfWeights - pow(average(), 2));
}
double stddev(unsigned long long now) const {
DiscExpMovingAverageWithStddev<alpha, alphaTimeUnit, maxAge> copy(*this);
copy.update(0, now);
return sqrt(copy.sumOfSquaredData / copy.sumOfWeights - pow(copy.average(), 2));
}
};
/**
* Calculates an exponential moving average. `alpha` determines how much weight the
* current value has compared to the previous average. Higher values of `alpha`
* cause the current value to have more weight (and thus the previous average
* to decay more quickly), lower values have the opposite effect.
*
* This algorithm is not timing sensitive: it doesn't take into account gaps in the
* data over time, and treats all values equally regardless of when the value was
* collected. See also DiscExpMovingAverage.
*
* You should initialize the the average value with a value equal to `nullValue`.
* If `prevAverage` equals `nullValue` then this function simply returns `currentValue`.
*/
inline double
expMovingAverage(double prevAverage, double currentValue, double alpha, double nullValue = -1) {
if (OXT_UNLIKELY(prevAverage == nullValue)) {
return currentValue;
} else {
return alpha * currentValue + (1 - alpha) * prevAverage;
}
}
} // namespace Passenger
#endif /* _PASSENGER_ALGORITHMS_EXP_MOVING_AVERAGE_H_ */
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