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Replace boost math functions. #85

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113 changes: 106 additions & 7 deletions include/nonius/detail/stats.h++
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Original file line number Diff line number Diff line change
Expand Up @@ -18,9 +18,8 @@
#include <nonius/estimate.h++>
#include <nonius/outlier_classification.h++>

#include <boost/math/distributions/normal.hpp>

#include <algorithm>
#include <cassert>
#include <functional>
#include <iterator>
#include <vector>
Expand Down Expand Up @@ -124,10 +123,109 @@ namespace nonius {
return results;
}

inline double normal_cdf(double x) {
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;
}

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;
}

template <typename Iterator, typename Estimator>
estimate<double> bootstrap(double confidence_level, Iterator first, Iterator last, sample const& resample, Estimator&& estimator) {
namespace bm = boost::math;

auto n_samples = last - first;

double point = estimator(first, last);
Expand All @@ -150,10 +248,11 @@ namespace nonius {
// degenerate case with uniform samples
if(prob_n == 0) return { point, point, point, confidence_level };

double bias = bm::quantile(bm::normal{}, prob_n);
double z1 = bm::quantile(bm::normal{}, (1. - confidence_level) / 2.);
double bias = normal_quantile(prob_n);
double z1 = normal_quantile((1. - confidence_level) / 2.);

auto cumn = [n](double x) -> int { return std::lround(bm::cdf(bm::normal{}, x) * n); };
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;
Expand Down
24 changes: 24 additions & 0 deletions test/stats.c++
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Original file line number Diff line number Diff line change
Expand Up @@ -17,6 +17,30 @@

#include <vector>

TEST_CASE("normal_cdf") {
using nonius::detail::normal_cdf;
CHECK(normal_cdf(0.000000) == Approx(0.50000000000000000));
CHECK(normal_cdf(1.000000) == Approx(0.84134474606854293));
CHECK(normal_cdf(-1.000000) == Approx(0.15865525393145705));
CHECK(normal_cdf(2.809729) == Approx(0.99752083845315409));
CHECK(normal_cdf(-1.352570) == Approx(0.08809652095066035));
}

TEST_CASE("erfc_inv") {
using nonius::detail::erfc_inv;
CHECK(erfc_inv(1.103560) == Approx(-0.09203687623843015));
CHECK(erfc_inv(1.067400) == Approx(-0.05980291115763361));
CHECK(erfc_inv(0.050000) == Approx(1.38590382434967796));
}

TEST_CASE("normal_quantile") {
using nonius::detail::normal_quantile;
CHECK(normal_quantile(0.551780) == Approx(0.13015979861484198));
CHECK(normal_quantile(0.533700) == Approx(0.08457408802851875));
CHECK(normal_quantile(0.025000) == Approx(-1.95996398454005449));
}


TEST_CASE("mean") {
std::vector<double> x { 10., 20., 14., 16., 30., 24. };

Expand Down