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/*
* Created by Martin on 15/06/2019.
* Adapted from donated nonius code.
*
* Distributed under the Boost Software License, Version 1.0. (See accompanying
* file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
*/
// Statistical analysis tools
#if defined(CATCH_CONFIG_ENABLE_BENCHMARKING)
#include "catch_stats.hpp"
#include "../../catch_compiler_capabilities.h"
#include <cassert>
#include <random>
#if defined(CATCH_CONFIG_USE_ASYNC)
#include <future>
#endif
namespace {
double erf_inv(double x) {
// Code accompanying the article "Approximating the erfinv function" in GPU Computing Gems, Volume 2
double w, p;
w = -log((1.0 - x) * (1.0 + x));
if (w < 6.250000) {
w = w - 3.125000;
p = -3.6444120640178196996e-21;
p = -1.685059138182016589e-19 + p * w;
p = 1.2858480715256400167e-18 + p * w;
p = 1.115787767802518096e-17 + p * w;
p = -1.333171662854620906e-16 + p * w;
p = 2.0972767875968561637e-17 + p * w;
p = 6.6376381343583238325e-15 + p * w;
p = -4.0545662729752068639e-14 + p * w;
p = -8.1519341976054721522e-14 + p * w;
p = 2.6335093153082322977e-12 + p * w;
p = -1.2975133253453532498e-11 + p * w;
p = -5.4154120542946279317e-11 + p * w;
p = 1.051212273321532285e-09 + p * w;
p = -4.1126339803469836976e-09 + p * w;
p = -2.9070369957882005086e-08 + p * w;
p = 4.2347877827932403518e-07 + p * w;
p = -1.3654692000834678645e-06 + p * w;
p = -1.3882523362786468719e-05 + p * w;
p = 0.0001867342080340571352 + p * w;
p = -0.00074070253416626697512 + p * w;
p = -0.0060336708714301490533 + p * w;
p = 0.24015818242558961693 + p * w;
p = 1.6536545626831027356 + p * w;
} else if (w < 16.000000) {
w = sqrt(w) - 3.250000;
p = 2.2137376921775787049e-09;
p = 9.0756561938885390979e-08 + p * w;
p = -2.7517406297064545428e-07 + p * w;
p = 1.8239629214389227755e-08 + p * w;
p = 1.5027403968909827627e-06 + p * w;
p = -4.013867526981545969e-06 + p * w;
p = 2.9234449089955446044e-06 + p * w;
p = 1.2475304481671778723e-05 + p * w;
p = -4.7318229009055733981e-05 + p * w;
p = 6.8284851459573175448e-05 + p * w;
p = 2.4031110387097893999e-05 + p * w;
p = -0.0003550375203628474796 + p * w;
p = 0.00095328937973738049703 + p * w;
p = -0.0016882755560235047313 + p * w;
p = 0.0024914420961078508066 + p * w;
p = -0.0037512085075692412107 + p * w;
p = 0.005370914553590063617 + p * w;
p = 1.0052589676941592334 + p * w;
p = 3.0838856104922207635 + p * w;
} else {
w = sqrt(w) - 5.000000;
p = -2.7109920616438573243e-11;
p = -2.5556418169965252055e-10 + p * w;
p = 1.5076572693500548083e-09 + p * w;
p = -3.7894654401267369937e-09 + p * w;
p = 7.6157012080783393804e-09 + p * w;
p = -1.4960026627149240478e-08 + p * w;
p = 2.9147953450901080826e-08 + p * w;
p = -6.7711997758452339498e-08 + p * w;
p = 2.2900482228026654717e-07 + p * w;
p = -9.9298272942317002539e-07 + p * w;
p = 4.5260625972231537039e-06 + p * w;
p = -1.9681778105531670567e-05 + p * w;
p = 7.5995277030017761139e-05 + p * w;
p = -0.00021503011930044477347 + p * w;
p = -0.00013871931833623122026 + p * w;
p = 1.0103004648645343977 + p * w;
p = 4.8499064014085844221 + p * w;
}
return p * x;
}
double standard_deviation(std::vector<double>::iterator first, std::vector<double>::iterator last) {
auto m = Catch::Benchmark::Detail::mean(first, last);
double variance = std::accumulate(first, last, 0., [m](double a, double b) {
double diff = b - m;
return a + diff * diff;
}) / (last - first);
return std::sqrt(variance);
}
}
namespace Catch {
namespace Benchmark {
namespace Detail {
double weighted_average_quantile(int k, int q, std::vector<double>::iterator first, std::vector<double>::iterator last) {
auto count = last - first;
double idx = (count - 1) * k / static_cast<double>(q);
int j = static_cast<int>(idx);
double g = idx - j;
std::nth_element(first, first + j, last);
auto xj = first[j];
if (g == 0) return xj;
auto xj1 = *std::min_element(first + (j + 1), last);
return xj + g * (xj1 - xj);
}
double erfc_inv(double x) {
return erf_inv(1.0 - x);
}
double normal_quantile(double p) {
static const double ROOT_TWO = std::sqrt(2.0);
double result = 0.0;
assert(p >= 0 && p <= 1);
if (p < 0 || p > 1) {
return result;
}
result = -erfc_inv(2.0 * p);
// result *= normal distribution standard deviation (1.0) * sqrt(2)
result *= /*sd * */ ROOT_TWO;
// result += normal disttribution mean (0)
return result;
}
double outlier_variance(Estimate<double> mean, Estimate<double> stddev, int n) {
double sb = stddev.point;
double mn = mean.point / n;
double mg_min = mn / 2.;
double sg = (std::min)(mg_min / 4., sb / std::sqrt(n));
double sg2 = sg * sg;
double sb2 = sb * sb;
auto c_max = [n, mn, sb2, sg2](double x) -> double {
double k = mn - x;
double d = k * k;
double nd = n * d;
double k0 = -n * nd;
double k1 = sb2 - n * sg2 + nd;
double det = k1 * k1 - 4 * sg2 * k0;
return (int)(-2. * k0 / (k1 + std::sqrt(det)));
};
auto var_out = [n, sb2, sg2](double c) {
double nc = n - c;
return (nc / n) * (sb2 - nc * sg2);
};
return (std::min)(var_out(1), var_out((std::min)(c_max(0.), c_max(mg_min)))) / sb2;
}
bootstrap_analysis analyse_samples(double confidence_level, int n_resamples, std::vector<double>::iterator first, std::vector<double>::iterator last) {
CATCH_INTERNAL_START_WARNINGS_SUPPRESSION
CATCH_INTERNAL_SUPPRESS_GLOBALS_WARNINGS
static std::random_device entropy;
CATCH_INTERNAL_STOP_WARNINGS_SUPPRESSION
auto n = static_cast<int>(last - first); // seriously, one can't use integral types without hell in C++
auto mean = &Detail::mean<std::vector<double>::iterator>;
auto stddev = &standard_deviation;
#if defined(CATCH_CONFIG_USE_ASYNC)
auto Estimate = [=](double(*f)(std::vector<double>::iterator, std::vector<double>::iterator)) {
auto seed = entropy();
return std::async(std::launch::async, [=] {
std::mt19937 rng(seed);
auto resampled = resample(rng, n_resamples, first, last, f);
return bootstrap(confidence_level, first, last, resampled, f);
});
};
auto mean_future = Estimate(mean);
auto stddev_future = Estimate(stddev);
auto mean_estimate = mean_future.get();
auto stddev_estimate = stddev_future.get();
#else
auto Estimate = [=](double(*f)(std::vector<double>::iterator, std::vector<double>::iterator)) {
auto seed = entropy();
std::mt19937 rng(seed);
auto resampled = resample(rng, n_resamples, first, last, f);
return bootstrap(confidence_level, first, last, resampled, f);
};
auto mean_estimate = Estimate(mean);
auto stddev_estimate = Estimate(stddev);
#endif // CATCH_USE_ASYNC
double outlier_variance = Detail::outlier_variance(mean_estimate, stddev_estimate, n);
return { mean_estimate, stddev_estimate, outlier_variance };
}
} // namespace Detail
} // namespace Benchmark
} // namespace Catch
#endif // CATCH_CONFIG_ENABLE_BENCHMARKING
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