third_party/WebKit/PerformanceTests/resources/statistics.js

   1 /*
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   3  *
   4  * Redistribution and use in source and binary forms, with or without
   5  * modification, are permitted provided that the following conditions
   6  * are met:
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   8  *    notice, this list of conditions and the following disclaimer.
   9  * 2. Redistributions in binary form must reproduce the above copyright
  10  *    notice, this list of conditions and the following disclaimer in the
  11  *    documentation and/or other materials provided with the distribution.
  12  *
  13  * THIS SOFTWARE IS PROVIDED BY APPLE INC. AND ITS CONTRIBUTORS ``AS IS''
  14  * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
  15  * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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  22  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
  23  * THE POSSIBILITY OF SUCH DAMAGE.
  24  */
  25
  26 var Statistics = new (function () {
  27
  28     this.max = function (values) {
  29         var maxVal = values[0];
  30         for (var i = 1; i < values.length; i++) {
  31             maxVal = Math.max(maxVal, values[i]);
  32         }
  33         return maxVal;
  34     }
  35
  36     this.min = function (values) {
  37         var minVal = values[0];
  38         for (var i = 1; i < values.length; i++) {
  39             minVal = Math.min(minVal, values[i]);
  40         }
  41         return minVal;
  42     }
  43
  44     this.sum = function (values) {
  45         return values.reduce(function (a, b) { return a + b; }, 0);
  46     }
  47
  48     this.squareSum = function (values) {
  49         return values.reduce(function (sum, value) { return sum + value * value;}, 0);
  50     }
  51
  52     // With sum and sum of squares, we can compute the sample standard deviation in O(1).
  53     // See https://rniwa.com/2012-11-10/sample-standard-deviation-in-terms-of-sum-and-square-sum-of-samples/
  54     this.sampleStandardDeviation = function (numberOfSamples, sum, squareSum) {
  55         if (numberOfSamples < 2)
  56             return 0;
  57         return Math.sqrt(squareSum / (numberOfSamples - 1)
  58             - sum * sum / (numberOfSamples - 1) / numberOfSamples);
  59     }
  60
  61     this.supportedConfidenceLevels = function () {
  62         var supportedLevels = [];
  63         for (var quantile in tDistributionInverseCDF)
  64             supportedLevels.push((1 - (1 - quantile) * 2).toFixed(2));
  65         return supportedLevels;
  66     }
  67
  68     // Computes the delta d s.t. (mean - d, mean + d) is the confidence interval with the specified confidence level in O(1).
  69     this.confidenceIntervalDelta = function (confidenceLevel, numberOfSamples, sum, squareSum) {
  70         var probability = (1 - (1 - confidenceLevel) / 2);
  71         if (!(probability in tDistributionInverseCDF)) {
  72             console.warn('We only support ' + this.supportedConfidenceLevels().map(
  73                 function (level) { return level * 100 + '%'; } ).join(', ') + ' confidence intervals.');
  74             return NaN;
  75         }
  76         if (numberOfSamples < 2)
  77             return Number.POSITIVE_INFINITY;
  78
  79         var cdfForProbability = tDistributionInverseCDF[probability];
  80         var degreesOfFreedom = numberOfSamples - 1;
  81
  82         // tDistributionQuantile(degreesOfFreedom, confidenceLevel) * sampleStandardDeviation / sqrt(numberOfSamples) * S/sqrt(numberOfSamples)
  83         if (degreesOfFreedom <= 100)
  84           var quantile = cdfForProbability[degreesOfFreedom - 1]; // The first entry is for the one degree of freedom.
  85         else if (degreesOfFreedom <= 300)
  86           var quantile = cdfForProbability[Math.round(degreesOfFreedom / 10) + 100 - 10 - 1];
  87         else if (degreesOfFreedom <= 1300)
  88           var quantile = cdfForProbability[Math.round(degreesOfFreedom / 100) + 120 - 3 - 1];
  89         else
  90           var quantile = cdfForProbability[cdfForProbability.length - 1];
  91         return quantile * this.sampleStandardDeviation(numberOfSamples, sum, squareSum) / Math.sqrt(numberOfSamples);
  92     }
  93
  94     this.confidenceInterval = function (values, probability) {
  95         var sum = this.sum(values);
  96         var mean = sum / values.length;
  97         var delta = this.confidenceIntervalDelta(probability || 0.95, values.length, sum, this.squareSum(values));
  98         return [mean - delta, mean + delta];
  99     }
 100
 101     // See http://en.wikipedia.org/wiki/Student's_t-distribution#Table_of_selected_values
 102     // This table contains one sided (a.k.a. tail) values.
 103     // Use TINV((1 - probability) * 2, df) in your favorite spreadsheet software to compute these.
 104     // The spacing of the values with df greater than 100 maintains error less than 0.8%.
 105     var tDistributionInverseCDF = {
 106         0.9: [
 107             // 1 - 100 step 1
 108             3.077684, 1.885618, 1.637744, 1.533206, 1.475884, 1.439756, 1.414924, 1.396815, 1.383029, 1.372184,
 109             1.363430, 1.356217, 1.350171, 1.345030, 1.340606, 1.336757, 1.333379, 1.330391, 1.327728, 1.325341,
 110             1.323188, 1.321237, 1.319460, 1.317836, 1.316345, 1.314972, 1.313703, 1.312527, 1.311434, 1.310415,
 111             1.309464, 1.308573, 1.307737, 1.306952, 1.306212, 1.305514, 1.304854, 1.304230, 1.303639, 1.303077,
 112             1.302543, 1.302035, 1.301552, 1.301090, 1.300649, 1.300228, 1.299825, 1.299439, 1.299069, 1.298714,
 113             1.298373, 1.298045, 1.297730, 1.297426, 1.297134, 1.296853, 1.296581, 1.296319, 1.296066, 1.295821,
 114             1.295585, 1.295356, 1.295134, 1.294920, 1.294712, 1.294511, 1.294315, 1.294126, 1.293942, 1.293763,
 115             1.293589, 1.293421, 1.293256, 1.293097, 1.292941, 1.292790, 1.292643, 1.292500, 1.292360, 1.292224,
 116             1.292091, 1.291961, 1.291835, 1.291711, 1.291591, 1.291473, 1.291358, 1.291246, 1.291136, 1.291029,
 117             1.290924, 1.290821, 1.290721, 1.290623, 1.290527, 1.290432, 1.290340, 1.290250, 1.290161, 1.290075,
 118             // 110 - 300 step 10
 119             1.289295, 1.288646, 1.288098, 1.287628, 1.287221, 1.286865, 1.286551, 1.286272, 1.286023, 1.285799,
 120             1.285596, 1.285411, 1.285243, 1.285089, 1.284947, 1.284816, 1.284695, 1.284582, 1.284478, 1.284380,
 121             // 400 - 1300 step 100
 122             1.283672, 1.283247, 1.282964, 1.282762, 1.282611, 1.282493, 1.282399, 1.282322, 1.282257, 1.282203,
 123             // Infinity
 124             1.281548],
 125         0.95: [
 126             // 1 - 100 step 1
 127             6.313752, 2.919986, 2.353363, 2.131847, 2.015048, 1.943180, 1.894579, 1.859548, 1.833113, 1.812461,
 128             1.795885, 1.782288, 1.770933, 1.761310, 1.753050, 1.745884, 1.739607, 1.734064, 1.729133, 1.724718,
 129             1.720743, 1.717144, 1.713872, 1.710882, 1.708141, 1.705618, 1.703288, 1.701131, 1.699127, 1.697261,
 130             1.695519, 1.693889, 1.692360, 1.690924, 1.689572, 1.688298, 1.687094, 1.685954, 1.684875, 1.683851,
 131             1.682878, 1.681952, 1.681071, 1.680230, 1.679427, 1.678660, 1.677927, 1.677224, 1.676551, 1.675905,
 132             1.675285, 1.674689, 1.674116, 1.673565, 1.673034, 1.672522, 1.672029, 1.671553, 1.671093, 1.670649,
 133             1.670219, 1.669804, 1.669402, 1.669013, 1.668636, 1.668271, 1.667916, 1.667572, 1.667239, 1.666914,
 134             1.666600, 1.666294, 1.665996, 1.665707, 1.665425, 1.665151, 1.664885, 1.664625, 1.664371, 1.664125,
 135             1.663884, 1.663649, 1.663420, 1.663197, 1.662978, 1.662765, 1.662557, 1.662354, 1.662155, 1.661961,
 136             1.661771, 1.661585, 1.661404, 1.661226, 1.661052, 1.660881, 1.660715, 1.660551, 1.660391, 1.660234,
 137             // 110 - 300 step 10
 138             1.658824, 1.657651, 1.656659, 1.655811, 1.655076, 1.654433, 1.653866, 1.653363, 1.652913, 1.652508,
 139             1.652142, 1.651809, 1.651506, 1.651227, 1.650971, 1.650735, 1.650517, 1.650314, 1.650125, 1.649949,
 140             // 400 - 1300 step 100
 141             1.648672, 1.647907, 1.647397, 1.647033, 1.646761, 1.646548, 1.646379, 1.646240, 1.646124, 1.646027,
 142             // Infinity
 143             1.644847],
 144         0.975: [
 145             // 1 - 100 step 1
 146             12.706205, 4.302653, 3.182446, 2.776445, 2.570582, 2.446912, 2.364624, 2.306004, 2.262157, 2.228139,
 147             2.200985, 2.178813, 2.160369, 2.144787, 2.131450, 2.119905, 2.109816, 2.100922, 2.093024, 2.085963,
 148             2.079614, 2.073873, 2.068658, 2.063899, 2.059539, 2.055529, 2.051831, 2.048407, 2.045230, 2.042272,
 149             2.039513, 2.036933, 2.034515, 2.032245, 2.030108, 2.028094, 2.026192, 2.024394, 2.022691, 2.021075,
 150             2.019541, 2.018082, 2.016692, 2.015368, 2.014103, 2.012896, 2.011741, 2.010635, 2.009575, 2.008559,
 151             2.007584, 2.006647, 2.005746, 2.004879, 2.004045, 2.003241, 2.002465, 2.001717, 2.000995, 2.000298,
 152             1.999624, 1.998972, 1.998341, 1.997730, 1.997138, 1.996564, 1.996008, 1.995469, 1.994945, 1.994437,
 153             1.993943, 1.993464, 1.992997, 1.992543, 1.992102, 1.991673, 1.991254, 1.990847, 1.990450, 1.990063,
 154             1.989686, 1.989319, 1.988960, 1.988610, 1.988268, 1.987934, 1.987608, 1.987290, 1.986979, 1.986675,
 155             1.986377, 1.986086, 1.985802, 1.985523, 1.985251, 1.984984, 1.984723, 1.984467, 1.984217, 1.983972,
 156             // 110 - 300 step 10
 157             1.981765, 1.979930, 1.978380, 1.977054, 1.975905, 1.974902, 1.974017, 1.973231, 1.972528, 1.971896,
 158             1.971325, 1.970806, 1.970332, 1.969898, 1.969498, 1.969130, 1.968789, 1.968472, 1.968178, 1.967903,
 159             // 400 - 1300 step 100
 160             1.965912, 1.964720, 1.963926, 1.963359, 1.962934, 1.962603, 1.962339, 1.962123, 1.961943, 1.961790,
 161             // Infinity
 162             1.959964],
 163         0.99: [
 164             // 1 - 100 step 1
 165             31.820516, 6.964557, 4.540703, 3.746947, 3.364930, 3.142668, 2.997952, 2.896459, 2.821438, 2.763769,
 166             2.718079, 2.680998, 2.650309, 2.624494, 2.602480, 2.583487, 2.566934, 2.552380, 2.539483, 2.527977,
 167             2.517648, 2.508325, 2.499867, 2.492159, 2.485107, 2.478630, 2.472660, 2.467140, 2.462021, 2.457262,
 168             2.452824, 2.448678, 2.444794, 2.441150, 2.437723, 2.434494, 2.431447, 2.428568, 2.425841, 2.423257,
 169             2.420803, 2.418470, 2.416250, 2.414134, 2.412116, 2.410188, 2.408345, 2.406581, 2.404892, 2.403272,
 170             2.401718, 2.400225, 2.398790, 2.397410, 2.396081, 2.394801, 2.393568, 2.392377, 2.391229, 2.390119,
 171             2.389047, 2.388011, 2.387008, 2.386037, 2.385097, 2.384186, 2.383302, 2.382446, 2.381615, 2.380807,
 172             2.380024, 2.379262, 2.378522, 2.377802, 2.377102, 2.376420, 2.375757, 2.375111, 2.374482, 2.373868,
 173             2.373270, 2.372687, 2.372119, 2.371564, 2.371022, 2.370493, 2.369977, 2.369472, 2.368979, 2.368497,
 174             2.368026, 2.367566, 2.367115, 2.366674, 2.366243, 2.365821, 2.365407, 2.365002, 2.364606, 2.364217,
 175             // 110 - 300 step 10
 176             2.360726, 2.357825, 2.355375, 2.353278, 2.351465, 2.349880, 2.348483, 2.347243, 2.346134, 2.345137,
 177             2.344236, 2.343417, 2.342670, 2.341985, 2.341356, 2.340775, 2.340238, 2.339739, 2.339275, 2.338842,
 178             // 400 - 1300 step 100
 179             2.335706, 2.333829, 2.332579, 2.331687, 2.331018, 2.330498, 2.330083, 2.329743, 2.329459, 2.329220,
 180             // Infinity
 181             2.326348],
 182     };
 183
 184 })();
 185
 186 if (typeof module != 'undefined') {
 187     for (var key in Statistics)
 188         module.exports[key] = Statistics[key];
 189 }