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| 1 | <?php |
| 2 | /** |
| 3 | * This program is free software; you can redistribute it and/or modify |
| 4 | * it under the terms of the GNU General Public License as published by |
| 5 | * the Free Software Foundation; either version 2 of the License, or |
| 6 | * (at your option) any later version. |
| 7 | * |
| 8 | * This program is distributed in the hope that it will be useful, |
| 9 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 10 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 11 | * GNU General Public License for more details. |
| 12 | * |
| 13 | * You should have received a copy of the GNU General Public License along |
| 14 | * with this program; if not, write to the Free Software Foundation, Inc., |
| 15 | * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. |
| 16 | * http://www.gnu.org/copyleft/gpl.html |
| 17 | * |
| 18 | * @file |
| 19 | * @author Ori Livneh <ori@wikimedia.org> |
| 20 | */ |
| 21 | |
| 22 | namespace Wikimedia; |
| 23 | |
| 24 | /** |
| 25 | * Represents a running, online estimate of a p-quantile for a series |
| 26 | * of observations using the P-squared algorithm. |
| 27 | * |
| 28 | * The algorithm is from "The P-Square Algorithm for Dynamic Calculation of |
| 29 | * Percentiles and Histograms without Storing Observations," Communications of |
| 30 | * the ACM, October 1985 by R. Jain and I. Chlamtac. |
| 31 | */ |
| 32 | class PSquare { |
| 33 | /** |
| 34 | * Percentile to estimate. |
| 35 | * @var float $p |
| 36 | */ |
| 37 | private $p; |
| 38 | |
| 39 | /** |
| 40 | * Position of each marker. |
| 41 | * @var int[] $positions |
| 42 | */ |
| 43 | private $positions; |
| 44 | |
| 45 | /** |
| 46 | * Desired position of each marker. |
| 47 | * @var float[] $desired |
| 48 | */ |
| 49 | private $desired; |
| 50 | |
| 51 | /** @var float[] $increments */ |
| 52 | private $increments; |
| 53 | |
| 54 | /** |
| 55 | * Number of observations. |
| 56 | * @var int $numObservations |
| 57 | */ |
| 58 | private $numObservations = 0; |
| 59 | |
| 60 | /** |
| 61 | * Height of each marker. |
| 62 | * @var float[] $heights |
| 63 | */ |
| 64 | private $heights = []; |
| 65 | |
| 66 | /** |
| 67 | * @param float $p the percentile (defaults to 0.5, or median). |
| 68 | */ |
| 69 | public function __construct( $p = 0.5 ) { |
| 70 | $this->p = $p; |
| 71 | $this->positions = [ 0, 1, 2, 3, 4 ]; |
| 72 | $this->desired = [ 0, ( 2 * $p ), ( 4 * $p ), 2 + ( 2 * $p ), 4 ]; |
| 73 | $this->increments = [ 0, ( $p / 2 ), $p, ( ( 1 + $p ) / 2 ), 1 ]; |
| 74 | } |
| 75 | |
| 76 | /** |
| 77 | * Export state, e.g. for serializing and caching. |
| 78 | * |
| 79 | * @return array |
| 80 | */ |
| 81 | public function __serialize(): array { |
| 82 | return [ |
| 83 | 'percentile' => $this->p, |
| 84 | 'positions' => $this->positions, |
| 85 | 'desired' => $this->desired, |
| 86 | 'increments' => $this->increments, |
| 87 | 'numObservations' => $this->numObservations, |
| 88 | 'heights' => $this->heights, |
| 89 | ]; |
| 90 | } |
| 91 | |
| 92 | /** |
| 93 | * @param array $data |
| 94 | */ |
| 95 | public function __unserialize( array $data ): void { |
| 96 | $this->p = $data['percentile']; |
| 97 | $this->positions = $data['positions']; |
| 98 | $this->desired = $data['desired']; |
| 99 | $this->increments = $data['increments']; |
| 100 | $this->numObservations = $data['numObservations']; |
| 101 | $this->heights = $data['heights']; |
| 102 | } |
| 103 | |
| 104 | /** |
| 105 | * Get the total number of accumulated observations. |
| 106 | * |
| 107 | * @return int |
| 108 | */ |
| 109 | public function getCount() { |
| 110 | return $this->numObservations; |
| 111 | } |
| 112 | |
| 113 | /** |
| 114 | * Add an observation. |
| 115 | * |
| 116 | * @param int|float $x Value to add |
| 117 | */ |
| 118 | public function addObservation( $x ) { |
| 119 | $this->numObservations++; |
| 120 | |
| 121 | if ( $this->numObservations <= 5 ) { |
| 122 | $this->heights[] = $x; |
| 123 | if ( $this->numObservations === 5 ) { |
| 124 | sort( $this->heights ); |
| 125 | } |
| 126 | return; |
| 127 | } |
| 128 | |
| 129 | if ( $x < $this->heights[0] ) { |
| 130 | $this->heights[0] = $x; |
| 131 | $k = 0; |
| 132 | } elseif ( $x >= $this->heights[4] ) { |
| 133 | $this->heights[4] = $x; |
| 134 | $k = 3; |
| 135 | } else { |
| 136 | for ( $i = 1; $i < 5; $i++ ) { |
| 137 | if ( $x < $this->heights[$i] ) { |
| 138 | $k = $i - 1; |
| 139 | break; |
| 140 | } |
| 141 | } |
| 142 | } |
| 143 | |
| 144 | // @phan-suppress-next-line PhanPossiblyUndeclaredVariable |
| 145 | for ( $i = $k + 1; $i < 5; $i++ ) { |
| 146 | $this->positions[$i]++; |
| 147 | } |
| 148 | |
| 149 | for ( $i = 0; $i < 5; $i++ ) { |
| 150 | $this->desired[$i] += $this->increments[$i]; |
| 151 | } |
| 152 | |
| 153 | for ( $i = 1; $i < 4; $i++ ) { |
| 154 | $n = $this->positions[$i]; |
| 155 | $nPrev = $this->positions[$i - 1]; |
| 156 | $nNext = $this->positions[$i + 1]; |
| 157 | |
| 158 | $d = $this->desired[$i] - $n; |
| 159 | |
| 160 | if ( ( $d >= 1 && $nNext - $n > 1 ) || ( $d <= -1 && $nPrev - $n < -1 ) ) { |
| 161 | $d = ( $d < 0 ) ? -1 : 1; |
| 162 | |
| 163 | $q = $this->computeParabolic( $i, $d ); |
| 164 | $qPrev = $this->heights[$i - 1]; |
| 165 | $qNext = $this->heights[$i + 1]; |
| 166 | |
| 167 | if ( $qPrev < $q && $q < $qNext ) { |
| 168 | $this->heights[$i] = $q; |
| 169 | } else { |
| 170 | $this->heights[$i] = $this->computeLinear( $i, $d ); |
| 171 | } |
| 172 | |
| 173 | $this->positions[$i] += $d; |
| 174 | } |
| 175 | } |
| 176 | } |
| 177 | |
| 178 | /** |
| 179 | * Use piecewise parabolic prediction to predict the ideal |
| 180 | * height of a marker. |
| 181 | * |
| 182 | * @param int $i index of marker to adjust |
| 183 | * @param int $d always -1 or 1 |
| 184 | * @return float ideal height of marker |
| 185 | */ |
| 186 | private function computeParabolic( $i, $d ) { |
| 187 | $q = $this->heights[$i]; |
| 188 | $qPrev = $this->heights[$i - 1]; |
| 189 | $qNext = $this->heights[$i + 1]; |
| 190 | |
| 191 | $n = $this->positions[$i]; |
| 192 | $nPrev = $this->positions[$i - 1]; |
| 193 | $nNext = $this->positions[$i + 1]; |
| 194 | |
| 195 | return ( $q + |
| 196 | $d / ( $nNext - $nPrev ) * |
| 197 | ( |
| 198 | ( $n - $nPrev + $d ) * ( $qNext - $q ) / ( $nNext - $n ) + |
| 199 | ( $nNext - $n - $d ) * ( $q - $qPrev ) / ( $n - $nPrev ) |
| 200 | ) |
| 201 | ); |
| 202 | } |
| 203 | |
| 204 | /** |
| 205 | * Linear formula to predict ideal position of a marker. |
| 206 | * |
| 207 | * @param int $i index of marker to adjust |
| 208 | * @param int $d always -1 or 1 |
| 209 | * @return float ideal height of marker |
| 210 | */ |
| 211 | private function computeLinear( $i, $d ) { |
| 212 | $q = $this->heights[$i]; |
| 213 | $n = $this->positions[$i]; |
| 214 | return ( $q + $d * |
| 215 | ( $this->heights[$i + $d] - $q ) / |
| 216 | ( $this->positions[$i + $d] - $n ) |
| 217 | ); |
| 218 | } |
| 219 | |
| 220 | /** |
| 221 | * Get the estimated p-quantile value. |
| 222 | * |
| 223 | * @return float |
| 224 | */ |
| 225 | public function getValue() { |
| 226 | // If we have five samples or fewer, fall back to a naive method. |
| 227 | if ( $this->getCount() <= 5 ) { |
| 228 | sort( $this->heights ); |
| 229 | $i = $this->p * count( $this->heights ); |
| 230 | if ( $i === floor( $i ) ) { |
| 231 | return ( $this->heights[$i - 1] + $this->heights[$i] ) / 2; |
| 232 | } else { |
| 233 | return $this->heights[floor( $i )]; |
| 234 | } |
| 235 | } |
| 236 | |
| 237 | return $this->heights[2]; |
| 238 | } |
| 239 | } |