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/* Copyright 2012 10gen Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
* Based upon boost.accumulators (www.boost.org/libs/accumulators/),
* distributed under the Boost Software License, Version 1.0.
* See distrc/THIRD_PARTY_NOTICES for the full License Notice for Boost.
*
*/
#pragma once
#include <algorithm>
#include <limits>
#include "mongo/util/mongoutils/str.h"
namespace mongo {
template <class Sample>
BasicEstimators<Sample>::BasicEstimators() :
_count(0),
_sum(0),
_diff(0),
_min(std::numeric_limits<Sample>::max()),
_max(std::numeric_limits<Sample>::min()) {
}
template <class Sample>
BasicEstimators<Sample>& BasicEstimators<Sample>::operator <<(const Sample sample) {
const double oldMean = (_count > 0) ? _sum / _count : 0;
const double delta = oldMean - static_cast<double>(sample);
const double weight = static_cast<double>(_count) / (_count + 1);
_diff += delta * delta * weight;
_sum += static_cast<double>(sample);
_count++;
_min = std::min(sample, _min);
_max = std::max(sample, _max);
return *this;
}
template <class Sample>
void BasicEstimators<Sample>::appendBasicToBSONObjBuilder(BSONObjBuilder& b) const {
b << "count" << static_cast<long long>(count())
<< "mean" << mean()
<< "stddev" << stddev()
<< "min" << min()
<< "max" << max();
}
template <std::size_t NumQuantiles>
DistributionEstimators<NumQuantiles>::DistributionEstimators() :
_count(0) {
for(std::size_t i = 0; i < NumMarkers; i++) {
_actual_positions[i] = i + 1;
}
for(std::size_t i = 0; i < NumMarkers; i++) {
_desired_positions[i] = 1.0 + (2.0 * (NumQuantiles + 1.0) * _positions_increments(i));
}
}
/*
* The quantile estimation follows the extended_p_square implementation in boost.accumulators.
* It differs by removing the ability to request arbitrary quantiles and computing exactly
* 'NumQuantiles' equidistant quantiles (plus minimum and maximum) instead.
* See http://www.boost.org/doc/libs/1_51_0/doc/html/boost/accumulators/impl/extended_p_square_impl.html ,
* R. Jain and I. Chlamtac, The P^2 algorithmus for dynamic calculation of quantiles and histograms without storing observations, Communications of the ACM, Volume 28 (October), Number 10, 1985, p. 1076-1085. and
* K. E. E. Raatikainen, Simultaneous estimation of several quantiles, Simulation, Volume 49, Number 4 (October), 1986, p. 159-164.
*/
template <std::size_t NumQuantiles>
DistributionEstimators<NumQuantiles>&
DistributionEstimators<NumQuantiles>::operator <<(const double sample) {
// first accumulate num_markers samples
if (_count++ < NumMarkers) {
_heights[_count - 1] = sample;
if (_count == NumMarkers)
{
std::sort(_heights, _heights + NumMarkers);
}
}
else {
std::size_t sample_cell = 1;
// find cell k = sample_cell such that heights[k-1] <= sample < heights[k]
if(sample < _heights[0])
{
_heights[0] = sample;
sample_cell = 1;
}
else if (sample >= _heights[NumMarkers - 1])
{
_heights[NumMarkers - 1] = sample;
sample_cell = NumMarkers - 1;
}
else {
double* it = std::upper_bound(_heights,
_heights + NumMarkers,
sample);
sample_cell = std::distance(_heights, it);
}
// update actual positions of all markers above sample_cell index
for(std::size_t i = sample_cell; i < NumMarkers; i++) {
_actual_positions[i]++;
}
// update desired positions of all markers
for(std::size_t i = 0; i < NumMarkers; i++) {
_desired_positions[i] += _positions_increments(i);
}
// adjust heights and actual positions of markers 1 to num_markers-2 if necessary
for(std::size_t i = 1; i <= NumMarkers - 2; i++) {
// offset to desired position
double d = _desired_positions[i] - _actual_positions[i];
// offset to next position
double dp = _actual_positions[i + 1] - _actual_positions[i];
// offset to previous position
double dm = _actual_positions[i - 1] - _actual_positions[i];
// height ds
double hp = (_heights[i + 1] - _heights[i]) / dp;
double hm = (_heights[i - 1] - _heights[i]) / dm;
if((d >= 1 && dp > 1) || (d <= -1 && dm < -1))
{
short sign_d = static_cast<short>(d / std::abs(d));
double h = _heights[i] + sign_d / (dp - dm) * ((sign_d - dm)*hp
+ (dp - sign_d) * hm);
// try adjusting heights[i] using p-squared formula
if(_heights[i - 1] < h && h < _heights[i + 1])
{
_heights[i] = h;
}
else
{
// use linear formula
if(d > 0)
{
_heights[i] += hp;
}
if(d < 0)
{
_heights[i] -= hm;
}
}
_actual_positions[i] += sign_d;
}
}
}
return *this;
}
template <std::size_t NumQuantiles>
void DistributionEstimators<NumQuantiles>::appendQuantilesToBSONArrayBuilder(
BSONArrayBuilder& arr) const {
verify(quantilesReady());
for (std::size_t i = 0; i <= NumQuantiles + 1; i++) {
arr << quantile(i);
}
}
template <std::size_t NumQuantiles>
inline double DistributionEstimators<NumQuantiles>::_positions_increments(std::size_t i) const {
return static_cast<double>(i) / (2 * (NumQuantiles + 1));
}
template <class Sample, std::size_t NumQuantiles>
BSONObj SummaryEstimators<Sample, NumQuantiles>::statisticSummaryToBSONObj() const {
BSONObjBuilder b;
this->BasicEstimators<Sample>::appendBasicToBSONObjBuilder(b);
if (this->DistributionEstimators<NumQuantiles>::quantilesReady()) {
// Not using appendQuantiles to be explicit about which probability each quantile
// refers to. This way the user does not need to count the quantiles or know in
// advance how many quantiles were computed to figure out their meaning.
BSONObjBuilder quantilesBuilder(b.subobjStart("quantiles"));
for (size_t i = 1; i <= NumQuantiles; i++) {
const double probability =
this->DistributionEstimators<NumQuantiles>::probability(i);
const double quantile =
this->DistributionEstimators<NumQuantiles>::quantile(i);
quantilesBuilder.append(std::string(mongoutils::str::stream() << probability),
quantile);
}
quantilesBuilder.doneFast();
}
return b.obj();
}
} // namespace mongo
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