1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
|
/* Copyright 2012 10gen Inc.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License, version 3,
* as published by the Free Software Foundation.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* As a special exception, the copyright holders give permission to link the
* code of portions of this program with the OpenSSL library under certain
* conditions as described in each individual source file and distribute
* linked combinations including the program with the OpenSSL library. You
* must comply with the GNU Affero General Public License in all respects
* for all of the code used other than as permitted herein. If you modify
* file(s) with this exception, you may extend this exception to your
* version of the file(s), but you are not obligated to do so. If you do not
* wish to do so, delete this exception statement from your version. If you
* delete this exception statement from all source files in the program,
* then also delete it in the license file.
*
* 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
|
