Move the async-using parts of benchmarking into a .cpp file

This keeps it out of the main include path when benchmarking is
enabled, somewhat reducing the compilation-time penalty.

Also moved some other functions into the .cpp file, especially
helpers that could be given internal linkage, and concretized some
iterator-templated code that only ever used
`std::vector<double>::iterator`.

2 files changed, 228 insertions, 189 deletions

diff --git a/include/internal/benchmark/detail/catch_stats.cpp b/include/internal/benchmark/detail/catch_stats.cpp
new file mode 100644
index 00000000..dd0b8ea2
--- /dev/null
+++ b/include/internal/benchmark/detail/catch_stats.cpp
@@ -0,0 +1,223 @@
+/*
+ *  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_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_SUPPRESS_GLOBALS_WARNINGS
+                static std::random_device entropy;
+                CATCH_INTERNAL_UNSUPPRESS_GLOBALS_WARNINGS
+
+                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;
+
+#ifdef CATCH_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
diff --git a/include/internal/benchmark/detail/catch_stats.hpp b/include/internal/benchmark/detail/catch_stats.hpp
index 25fb9640..e686c1aa 100644
--- a/include/internal/benchmark/detail/catch_stats.hpp
+++ b/include/internal/benchmark/detail/catch_stats.hpp
@@ -16,40 +16,20 @@
 #include "../catch_outlier_classification.hpp"
 
 #include <algorithm>
-#include <cassert>
 #include <functional>
-#include <iterator>
 #include <vector>
-#include <array>
-#include <random>
 #include <numeric>
 #include <tuple>
 #include <cmath>
 #include <utility>
 #include <cstddef>
 
-#ifdef CATCH_USE_ASYNC
-#include <future>
-#endif
-
 namespace Catch {
     namespace Benchmark {
         namespace Detail {
             using sample = std::vector<double>;
 
-            template <typename Iterator>
-            double weighted_average_quantile(int k, int q, Iterator first, 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 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) {
@@ -82,16 +62,6 @@ namespace Catch {
                 return sum / count;
             }
 
-            template <typename Iterator>
-            double standard_deviation(Iterator first, Iterator last) {
-                auto m = 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);
-            }
-
             template <typename URng, typename Iterator, typename Estimator>
             sample resample(URng& rng, int resamples, Iterator first, Iterator last, Estimator& estimator) {
                 auto n = last - first;
@@ -128,100 +98,9 @@ namespace Catch {
                 return std::erfc(-x / std::sqrt(2.0)) / 2.0;
             }
 
-            inline 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;
-            }
-
-            inline double erfc_inv(double x) {
-                return erf_inv(1.0 - x);
-            }
-
-            inline 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;
-                }
+            double erfc_inv(double x);
 
-                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 normal_quantile(double p);
 
             template <typename Iterator, typename Estimator>
             Estimate<double> bootstrap(double confidence_level, Iterator first, Iterator last, sample const& resample, Estimator&& estimator) {
@@ -263,31 +142,7 @@ namespace Catch {
                 return { point, resample[lo], resample[hi], confidence_level };
             }
 
-            inline 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;
-            }
+            double outlier_variance(Estimate<double> mean, Estimate<double> stddev, int n);
 
             struct bootstrap_analysis {
                 Estimate<double> mean;
@@ -295,46 +150,7 @@ namespace Catch {
                 double outlier_variance;
             };
 
-            template <typename Iterator>
-            bootstrap_analysis analyse_samples(double confidence_level, int n_resamples, Iterator first, Iterator last) {
-                static std::random_device entropy;
-
-                auto n = static_cast<int>(last - first); // seriously, one can't use integral types without hell in C++
-
-                auto mean = &Detail::mean<Iterator>;
-                auto stddev = &Detail::standard_deviation<Iterator>;
-
-#ifdef CATCH_USE_ASYNC
-                auto Estimate = [=](double(*f)(Iterator, 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)(Iterator, 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 };
-            }
+            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