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math/reporting/performance/ellint_performance.cpp
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// (C) Copyright John Maddock 2022.
// Use, modification and distribution are subject to 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)
//
// The purpose of this performance test is to probe the performance
// the of polynomial approximation to Elliptic integrals K and E.
//
// In the original paper:
// "Fast computation of complete elliptic integrals and Jacobian elliptic functions",
// Celestial Mechanics and Dynamical Astronomy, April 2012.
// they claim performance comparable to std::log, so we add comparison to log here
// as a reference "known good".
//
// We also measure the effect of disabling overflow errors, and of a "bare-bones"
// implementation which lacks a lot of our usual boilerplate.
//
// Note in the performance test routines, we had to sum the results of the function calls
// otherwise some msvc results were unrealistically fast, despite the use of
// benchmark::DoNotOptimize.
//
// Some sample results from msvc, and taking log(double) as a score of 1:
//
// ellint_1_performance<double> 1.7
// ellint_1_performance_no_overflow_check<double> 1.6
// ellint_2_performance<double> 1.8
// ellint_2_performance_no_overflow_check<double> 1.6
// basic_ellint_rational_performance<double> 1.6
//
// We can in fact get basic_ellint_rational_performance to much the same performance as log
// ONLY if we remove all error handling for cases with m > 0.9. In particular the code appears
// to be ultra-sensitive to the presence of "if" statements which significantly hamper optimisation.
//
// Performance with gcc-cygwin appears to be broadly similar.
//
#include <vector>
#include <benchmark/benchmark.h>
#include <boost/math/special_functions/ellint_1.hpp>
#include <boost/math/special_functions/ellint_2.hpp>
#include <boost/math/tools/random_vector.hpp>
using boost::math::generate_random_uniform_vector;
template <typename Real>
const std::vector<Real>& get_test_data()
{
static const std::vector<Real> data = generate_random_uniform_vector<Real>(1024, 12345, 0.0, 0.9);
return data;
}
template <typename Real>
Real& get_result_data()
{
static Real data = 0;
return data;
}
template <class T>
BOOST_FORCEINLINE T basic_ellint_rational(T k)
{
using namespace boost::math::tools;
static const char* function = "boost::math::ellint_k<%1%>(%1%)";
T m = k * k;
switch (static_cast<int>(m * 20))
{
case 0:
case 1:
//if (m < 0.1)
{
constexpr T coef[] =
{
1.591003453790792180,
0.416000743991786912,
0.245791514264103415,
0.179481482914906162,
0.144556057087555150,
0.123200993312427711,
0.108938811574293531,
0.098853409871592910,
0.091439629201749751,
0.085842591595413900,
0.081541118718303215,
0.078199656811256481910
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.05);
}
case 2:
case 3:
//else if (m < 0.2)
{
constexpr T coef[] =
{
1.635256732264579992,
0.471190626148732291,
0.309728410831499587,
0.252208311773135699,
0.226725623219684650,
0.215774446729585976,
0.213108771877348910,
0.216029124605188282,
0.223255831633057896,
0.234180501294209925,
0.248557682972264071,
0.266363809892617521
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.15);
}
case 4:
case 5:
//else if (m < 0.3)
{
constexpr T coef[] =
{
1.685750354812596043,
0.541731848613280329,
0.401524438390690257,
0.369642473420889090,
0.376060715354583645,
0.405235887085125919,
0.453294381753999079,
0.520518947651184205,
0.609426039204995055,
0.724263522282908870,
0.871013847709812357,
1.057652872753547036
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.25);
}
case 6:
case 7:
//else if (m < 0.4)
{
constexpr T coef[] =
{
1.744350597225613243,
0.634864275371935304,
0.539842564164445538,
0.571892705193787391,
0.670295136265406100,
0.832586590010977199,
1.073857448247933265,
1.422091460675497751,
1.920387183402304829,
2.632552548331654201,
3.652109747319039160,
5.115867135558865806,
7.224080007363877411
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.35);
}
case 8:
case 9:
//else if (m < 0.5)
{
constexpr T coef[] =
{
1.813883936816982644,
0.763163245700557246,
0.761928605321595831,
0.951074653668427927,
1.315180671703161215,
1.928560693477410941,
2.937509342531378755,
4.594894405442878062,
7.330071221881720772,
11.87151259742530180,
19.45851374822937738,
32.20638657246426863,
53.73749198700554656,
90.27388602940998849
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.45);
}
case 10:
case 11:
//else if (m < 0.6)
{
constexpr T coef[] =
{
1.898924910271553526,
0.950521794618244435,
1.151077589959015808,
1.750239106986300540,
2.952676812636875180,
5.285800396121450889,
9.832485716659979747,
18.78714868327559562,
36.61468615273698145,
72.45292395127771801,
145.1079577347069102,
293.4786396308497026,
598.3851815055010179,
1228.420013075863451,
2536.529755382764488
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.55);
}
case 12:
case 13:
//else if (m < 0.7)
{
constexpr T coef[] =
{
2.007598398424376302,
1.248457231212347337,
1.926234657076479729,
3.751289640087587680,
8.119944554932045802,
18.66572130873555361,
44.60392484291437063,
109.5092054309498377,
274.2779548232413480,
697.5598008606326163,
1795.716014500247129,
4668.381716790389910,
12235.76246813664335,
32290.17809718320818,
85713.07608195964685,
228672.1890493117096,
612757.2711915852774
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.65);
}
case 14:
case 15:
//else if (m < 0.8)
{
constexpr T coef[] =
{
2.156515647499643235,
1.791805641849463243,
3.826751287465713147,
10.38672468363797208,
31.40331405468070290,
100.9237039498695416,
337.3268282632272897,
1158.707930567827917,
4060.990742193632092,
14454.00184034344795,
52076.66107599404803,
189493.6591462156887,
695184.5762413896145,
2567994.048255284686,
9541921.966748386322,
35634927.44218076174,
133669298.4612040871,
503352186.6866284541,
1901975729.538660119,
7208915015.330103756
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.75);
}
case 16:
//else if (m < 0.85)
{
constexpr T coef[] =
{
2.318122621712510589,
2.616920150291232841,
7.897935075731355823,
30.50239715446672327,
131.4869365523528456,
602.9847637356491617,
2877.024617809972641,
14110.51991915180325,
70621.44088156540229,
358977.2665825309926,
1847238.263723971684,
9600515.416049214109,
50307677.08502366879,
265444188.6527127967,
1408862325.028702687,
7515687935.373774627
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.825);
}
case 17:
//else if (m < 0.90)
{
constexpr T coef[] =
{
2.473596173751343912,
3.727624244118099310,
15.60739303554930496,
84.12850842805887747,
506.9818197040613935,
3252.277058145123644,
21713.24241957434256,
149037.0451890932766,
1043999.331089990839,
7427974.817042038995,
53503839.67558661151,
389249886.9948708474,
2855288351.100810619,
21090077038.76684053,
156699833947.7902014,
1170222242422.439893,
8777948323668.937971,
66101242752484.95041,
499488053713388.7989,
37859743397240299.20
};
return boost::math::tools::evaluate_polynomial(coef, m - 0.875);
}
case 18:
case 19:
return boost::math::detail::ellint_k_imp(k, boost::math::policies::policy<>(), std::integral_constant<int, 2>());
default:
if (m == 1)
{
return boost::math::policies::raise_overflow_error<T>(function, nullptr, boost::math::policies::policy<>());
}
else
return boost::math::policies::raise_domain_error<T>(function,
"Got k = %1%, function requires |k| <= 1", k, boost::math::policies::policy<>());
}
}
template <typename Real>
void basic_ellint_rational_performance(benchmark::State& state)
{
std::vector<Real>const& test_set = get_test_data<Real>();
Real& r = get_result_data<Real>();
for(auto _ : state)
{
for(unsigned i = 0; i < test_set.size(); ++i)
benchmark::DoNotOptimize(r += basic_ellint_rational(test_set[i]));
}
}
template <typename Real>
void basic_ellint_rational_performance_no_error_check(benchmark::State& state)
{
std::vector<Real>const& test_set = get_test_data<Real>();
Real& r = get_result_data<Real>();
for(auto _ : state)
{
for(unsigned i = 0; i < test_set.size(); ++i)
benchmark::DoNotOptimize(r += basic_ellint_rational_no_error_checks(test_set[i]));
}
}
template <typename Real>
void ellint_1_performance(benchmark::State& state)
{
std::vector<Real>const& test_set = get_test_data<Real>();
Real& r = get_result_data<Real>();
for(auto _ : state)
{
for(unsigned i = 0; i < test_set.size(); ++i)
benchmark::DoNotOptimize(r += boost::math::ellint_1(test_set[i]));
}
}
template <typename Real>
void ellint_1_performance_no_overflow_check(benchmark::State& state)
{
std::vector<Real>const& test_set = get_test_data<Real>();
Real& r = get_result_data<Real>();
for(auto _ : state)
{
for(unsigned i = 0; i < test_set.size(); ++i)
benchmark::DoNotOptimize(r += boost::math::ellint_1(test_set[i], boost::math::policies::make_policy(boost::math::policies::overflow_error<boost::math::policies::ignore_error>())));
}
}
template <typename Real>
void ellint_2_performance(benchmark::State& state)
{
std::vector<Real>const& test_set = get_test_data<Real>();
Real& r = get_result_data<Real>();
for(auto _ : state)
{
for(unsigned i = 0; i < test_set.size(); ++i)
benchmark::DoNotOptimize(r += boost::math::ellint_2(test_set[i]));
}
}
template <typename Real>
void ellint_2_performance_no_overflow_check(benchmark::State& state)
{
std::vector<Real>const& test_set = get_test_data<Real>();
Real& r = get_result_data<Real>();
for(auto _ : state)
{
for(unsigned i = 0; i < test_set.size(); ++i)
benchmark::DoNotOptimize(r += boost::math::ellint_2(test_set[i], boost::math::policies::make_policy(boost::math::policies::overflow_error<boost::math::policies::ignore_error>())));
}
}
template <typename Real>
void log_performance(benchmark::State& state)
{
std::vector<Real>const& test_set = get_test_data<Real>();
Real& r = get_result_data<Real>();
for(auto _ : state)
{
for(unsigned i = 0; i < test_set.size(); ++i)
benchmark::DoNotOptimize(r += log(test_set[i]));
}
}
BENCHMARK_TEMPLATE(ellint_1_performance, float);
BENCHMARK_TEMPLATE(ellint_1_performance, double);
BENCHMARK_TEMPLATE(ellint_1_performance, long double);
BENCHMARK_TEMPLATE(ellint_1_performance_no_overflow_check, float);
BENCHMARK_TEMPLATE(ellint_1_performance_no_overflow_check, double);
BENCHMARK_TEMPLATE(ellint_1_performance_no_overflow_check, long double);
BENCHMARK_TEMPLATE(ellint_2_performance, float);
BENCHMARK_TEMPLATE(ellint_2_performance, double);
BENCHMARK_TEMPLATE(ellint_2_performance, long double);
BENCHMARK_TEMPLATE(ellint_2_performance_no_overflow_check, float);
BENCHMARK_TEMPLATE(ellint_2_performance_no_overflow_check, double);
BENCHMARK_TEMPLATE(ellint_2_performance_no_overflow_check, long double);
BENCHMARK_TEMPLATE(log_performance, float);
BENCHMARK_TEMPLATE(log_performance, double);
BENCHMARK_TEMPLATE(log_performance, long double);
BENCHMARK_TEMPLATE(basic_ellint_rational_performance, float);
BENCHMARK_TEMPLATE(basic_ellint_rational_performance, double);
BENCHMARK_TEMPLATE(basic_ellint_rational_performance, long double);
BENCHMARK_MAIN();
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