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catch2/src/catch2/benchmark/detail/catch_stats.cpp

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// Copyright Catch2 Authors
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.txt or copy at
// https://www.boost.org/LICENSE_1_0.txt)
// SPDX-License-Identifier: BSL-1.0
// Adapted from donated nonius code.
#include <catch2/benchmark/detail/catch_stats.hpp>
#include <catch2/internal/catch_compiler_capabilities.hpp>
#include <catch2/internal/catch_floating_point_helpers.hpp>
#include <catch2/internal/catch_random_number_generator.hpp>
#include <catch2/internal/catch_uniform_integer_distribution.hpp>
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstddef>
#include <numeric>
#include <random>
#if defined(CATCH_CONFIG_USE_ASYNC)
#include <future>
#endif
namespace Catch {
namespace Benchmark {
namespace Detail {
namespace {
template <typename URng, typename Estimator>
static sample
resample( URng& rng,
unsigned int resamples,
double const* first,
double const* last,
Estimator& estimator ) {
auto n = static_cast<size_t>( last - first );
Catch::uniform_integer_distribution<size_t> dist( 0, n - 1 );
sample out;
out.reserve( resamples );
std::vector<double> resampled;
resampled.reserve( n );
for ( size_t i = 0; i < resamples; ++i ) {
resampled.clear();
for ( size_t s = 0; s < n; ++s ) {
resampled.push_back( first[dist( rng )] );
}
const auto estimate =
estimator( resampled.data(), resampled.data() + resampled.size() );
out.push_back( estimate );
}
std::sort( out.begin(), out.end() );
return out;
}
static 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 static_cast<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;
}
static 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;
}
static double
standard_deviation( double const* first, double const* 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 );
}
static sample jackknife( double ( *estimator )( double const*,
double const* ),
double* first,
double* last ) {
const auto second = first + 1;
sample results;
results.reserve( static_cast<size_t>( last - first ) );
for ( auto it = first; it != last; ++it ) {
std::iter_swap( it, first );
results.push_back( estimator( second, last ) );
}
return results;
}
} // namespace
} // namespace Detail
} // namespace Benchmark
} // namespace Catch
namespace Catch {
namespace Benchmark {
namespace Detail {
double weighted_average_quantile( int k,
int q,
double* first,
double* 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 ( Catch::Detail::directCompare( g, 0 ) ) {
return xj;
}
auto xj1 = *std::min_element(first + (j + 1), last);
return xj + g * (xj1 - xj);
}
OutlierClassification
classify_outliers( double const* first, double const* last ) {
std::vector<double> copy( first, last );
auto q1 = weighted_average_quantile( 1, 4, copy.data(), copy.data() + copy.size() );
auto q3 = weighted_average_quantile( 3, 4, copy.data(), copy.data() + copy.size() );
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 ) {
const double 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;
}
double mean( double const* first, double const* last ) {
auto count = last - first;
double sum = 0.;
while (first != last) {
sum += *first;
++first;
}
return sum / static_cast<double>(count);
}
double normal_cdf( double x ) {
return std::erfc( -x / std::sqrt( 2.0 ) ) / 2.0;
}
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;
}
Estimate<double>
bootstrap( double confidence_level,
double* first,
double* last,
sample const& resample,
double ( *estimator )( double const*, double const* ) ) {
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.data(), jack.data() + jack.size() );
double sum_squares = 0, sum_cubes = 0;
for ( double x : jack ) {
auto difference = jack_mean - x;
auto square = difference * difference;
auto cube = square * difference;
sum_squares += square;
sum_cubes += cube;
}
double accel = sum_cubes / ( 6 * std::pow( sum_squares, 1.5 ) );
long n = static_cast<long>( resample.size() );
double prob_n =
std::count_if( resample.begin(),
resample.end(),
[point]( double x ) { return x < point; } ) /
static_cast<double>( n );
// degenerate case with uniform samples
if ( Catch::Detail::directCompare( 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 ) -> long {
return std::lround( normal_cdf( x ) *
static_cast<double>( 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 = static_cast<size_t>( (std::max)( cumn( a1 ), 0l ) );
auto hi =
static_cast<size_t>( (std::min)( cumn( a2 ), n - 1 ) );
return { point, resample[lo], resample[hi], confidence_level };
}
bootstrap_analysis analyse_samples(double confidence_level,
unsigned int n_resamples,
double* first,
double* last) {
auto mean = &Detail::mean;
auto stddev = &standard_deviation;
#if defined(CATCH_CONFIG_USE_ASYNC)
auto Estimate = [=](double(*f)(double const*, double const*)) {
std::random_device rd;
auto seed = rd();
return std::async(std::launch::async, [=] {
SimplePcg32 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)(double const* , double const*)) {
std::random_device rd;
auto seed = rd();
SimplePcg32 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
auto n = static_cast<int>(last - first); // seriously, one can't use integral types without hell in C++
double outlier_variance = Detail::outlier_variance(mean_estimate, stddev_estimate, n);
return { mean_estimate, stddev_estimate, outlier_variance };
}
} // namespace Detail
} // namespace Benchmark
} // namespace Catch
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