Restarted the production of the app

libs/Catch2/include/internal/benchmark/detail/catch_stats.hpp

@@ -0,0 +1,160 @@
+/*
+ *  Created by Joachim on 16/04/2019.
+ *  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
+
+#ifndef TWOBLUECUBES_CATCH_DETAIL_ANALYSIS_HPP_INCLUDED
+#define TWOBLUECUBES_CATCH_DETAIL_ANALYSIS_HPP_INCLUDED
+
+#include "../catch_clock.hpp"
+#include "../catch_estimate.hpp"
+#include "../catch_outlier_classification.hpp"
+
+#include <algorithm>
+#include <functional>
+#include <vector>
+#include <iterator>
+#include <numeric>
+#include <tuple>
+#include <cmath>
+#include <utility>
+#include <cstddef>
+#include <random>
+
+namespace Catch {
+    namespace Benchmark {
+        namespace Detail {
+            using sample = std::vector<double>;
+
+            double weighted_average_quantile(int k, int q, std::vector<double>::iterator first, std::vector<double>::iterator last);
+
+            template <typename Iterator>
+            OutlierClassification classify_outliers(Iterator first, Iterator last) {
+                std::vector<double> copy(first, last);
+
+                auto q1 = weighted_average_quantile(1, 4, copy.begin(), copy.end());
+                auto q3 = weighted_average_quantile(3, 4, copy.begin(), copy.end());
+                auto iqr = q3 - q1;
+                auto los = q1 - (iqr * 3.);
+                auto lom = q1 - (iqr * 1.5);
+                auto him = q3 + (iqr * 1.5);
+                auto his = q3 + (iqr * 3.);
+
+                OutlierClassification o;
+                for (; first != last; ++first) {
+                    auto&& t = *first;
+                    if (t < los) ++o.low_severe;
+                    else if (t < lom) ++o.low_mild;
+                    else if (t > his) ++o.high_severe;
+                    else if (t > him) ++o.high_mild;
+                    ++o.samples_seen;
+                }
+                return o;
+            }
+
+            template <typename Iterator>
+            double mean(Iterator first, Iterator last) {
+                auto count = last - first;
+                double sum = std::accumulate(first, last, 0.);
+                return sum / count;
+            }
+
+            template <typename URng, typename Iterator, typename Estimator>
+            sample resample(URng& rng, int resamples, Iterator first, Iterator last, Estimator& estimator) {
+                auto n = last - first;
+                std::uniform_int_distribution<decltype(n)> dist(0, n - 1);
+
+                sample out;
+                out.reserve(resamples);
+                std::generate_n(std::back_inserter(out), resamples, [n, first, &estimator, &dist, &rng] {
+                    std::vector<double> resampled;
+                    resampled.reserve(n);
+                    std::generate_n(std::back_inserter(resampled), n, [first, &dist, &rng] { return first[dist(rng)]; });
+                    return estimator(resampled.begin(), resampled.end());
+                });
+                std::sort(out.begin(), out.end());
+                return out;
+            }
+
+            template <typename Estimator, typename Iterator>
+            sample jackknife(Estimator&& estimator, Iterator first, Iterator last) {
+                auto n = last - first;
+                auto second = std::next(first);
+                sample results;
+                results.reserve(n);
+
+                for (auto it = first; it != last; ++it) {
+                    std::iter_swap(it, first);
+                    results.push_back(estimator(second, last));
+                }
+
+                return results;
+            }
+
+            inline double normal_cdf(double x) {
+                return std::erfc(-x / std::sqrt(2.0)) / 2.0;
+            }
+
+            double erfc_inv(double x);
+
+            double normal_quantile(double p);
+
+            template <typename Iterator, typename Estimator>
+            Estimate<double> bootstrap(double confidence_level, Iterator first, Iterator last, sample const& resample, Estimator&& estimator) {
+                auto n_samples = last - first;
+
+                double point = estimator(first, last);
+                // Degenerate case with a single sample
+                if (n_samples == 1) return { point, point, point, confidence_level };
+
+                sample jack = jackknife(estimator, first, last);
+                double jack_mean = mean(jack.begin(), jack.end());
+                double sum_squares, sum_cubes;
+                std::tie(sum_squares, sum_cubes) = std::accumulate(jack.begin(), jack.end(), std::make_pair(0., 0.), [jack_mean](std::pair<double, double> sqcb, double x) -> std::pair<double, double> {
+                    auto d = jack_mean - x;
+                    auto d2 = d * d;
+                    auto d3 = d2 * d;
+                    return { sqcb.first + d2, sqcb.second + d3 };
+                });
+
+                double accel = sum_cubes / (6 * std::pow(sum_squares, 1.5));
+                int n = static_cast<int>(resample.size());
+                double prob_n = std::count_if(resample.begin(), resample.end(), [point](double x) { return x < point; }) / (double)n;
+                // degenerate case with uniform samples
+                if (prob_n == 0) return { point, point, point, confidence_level };
+
+                double bias = normal_quantile(prob_n);
+                double z1 = normal_quantile((1. - confidence_level) / 2.);
+
+                auto cumn = [n](double x) -> int {
+                    return std::lround(normal_cdf(x) * n); };
+                auto a = [bias, accel](double b) { return bias + b / (1. - accel * b); };
+                double b1 = bias + z1;
+                double b2 = bias - z1;
+                double a1 = a(b1);
+                double a2 = a(b2);
+                auto lo = (std::max)(cumn(a1), 0);
+                auto hi = (std::min)(cumn(a2), n - 1);
+
+                return { point, resample[lo], resample[hi], confidence_level };
+            }
+
+            double outlier_variance(Estimate<double> mean, Estimate<double> stddev, int n);
+
+            struct bootstrap_analysis {
+                Estimate<double> mean;
+                Estimate<double> standard_deviation;
+                double outlier_variance;
+            };
+
+            bootstrap_analysis analyse_samples(double confidence_level, int n_resamples, std::vector<double>::iterator first, std::vector<double>::iterator last);
+        } // namespace Detail
+    } // namespace Benchmark
+} // namespace Catch
+
+#endif // TWOBLUECUBES_CATCH_DETAIL_ANALYSIS_HPP_INCLUDED