157 lines
6.3 KiB
C++
157 lines
6.3 KiB
C++
// Copyright 2017 John Maddock
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <boost/math/special_functions/bessel.hpp>
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#include <boost/math/special_functions/relative_difference.hpp>
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#include <boost/multiprecision/cpp_bin_float.hpp>
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#include <boost/random.hpp>
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#include <boost/svg_plot/svg_2d_plot.hpp>
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#include <sstream>
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#ifdef BOOST_HAS_FLOAT128
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#include <boost/multiprecision/float128.hpp>
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#endif
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typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<256, boost::multiprecision::backends::digit_base_2>, boost::multiprecision::et_on> mp_type;
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template <class T>
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void test_type(const char* name)
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{
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typedef boost::math::policies::policy<
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boost::math::policies::promote_double<false>,
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boost::math::policies::promote_float<false>,
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boost::math::policies::overflow_error<boost::math::policies::ignore_error>
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> policy_type;
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boost::random::mt19937 dist;
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boost::random::uniform_real_distribution<T> ur(0, 7.75);
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boost::random::uniform_real_distribution<T> ur2(0, 1 / 7.75);
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float max_err = 0;
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std::map<double, double> small, medium, large;
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for(unsigned i = 0; i < 1000; ++i)
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{
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T input = ur(dist);
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mp_type input2(input);
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T result = boost::math::cyl_bessel_i(1, input, policy_type());
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mp_type result2 = boost::math::cyl_bessel_i(1, input2);
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mp_type err = boost::math::relative_difference(result2, mp_type(result)) / mp_type(std::numeric_limits<T>::epsilon());
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if(result2 < mp_type(result))
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err = -err;
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if(fabs(err) > max_err)
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{
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/*
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std::cout << std::setprecision(34) << input << std::endl;
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std::cout << std::setprecision(34) << input2 << std::endl;
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std::cout << std::setprecision(34) << result << std::endl;
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std::cout << std::setprecision(34) << result2 << std::endl;
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std::cout << "New max error at x = " << input << " expected " << result2 << " got " << result << " error " << err << std::endl;
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*/
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max_err = static_cast<float>(fabs(err));
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}
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if(fabs(err) <= 1)
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small[static_cast<double>(input)] = static_cast<double>(err);
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else if(fabs(err) <= 2)
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medium[static_cast<double>(input)] = static_cast<double>(err);
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else
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large[static_cast<double>(input)] = static_cast<double>(err);
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}
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int y_interval = static_cast<int>(ceil(max_err / 5));
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std::stringstream ss;
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ss << "cyl_bessel_i<" << name << ">(1, x) over [0, 7.75]\n(max error = " << std::setprecision(2) << max_err << ")" << std::endl;
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boost::svg::svg_2d_plot my_plot;
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// Size of SVG image and X and Y range settings.
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my_plot.x_range(0, 7.75).image_x_size(700).legend_border_color(boost::svg::lightgray).plot_border_color(boost::svg::lightgray).background_border_color(boost::svg::lightgray)
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.y_range(-(int)ceil(max_err), (int)ceil(max_err)).x_label("x").title(ss.str()).y_major_interval(y_interval).x_major_interval(1.0).legend_on(true).plot_window_on(true);
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my_plot.plot(small, "< 1eps").stroke_color(boost::svg::green).fill_color(boost::svg::green).size(2);
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if(max_err > 1)
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{
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my_plot.plot(medium, "< 2eps").stroke_color(boost::svg::orange).fill_color(boost::svg::orange).size(2);
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if(max_err > 2)
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my_plot.plot(large, "> 2eps").stroke_color(boost::svg::red).fill_color(boost::svg::red).size(2);
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}
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std::string filename("bessel_i1_0_7_");
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filename += name;
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filename += ".svg";
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my_plot.write(filename);
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std::cout << "Maximum error for type " << name << " was: " << max_err << std::endl;
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max_err = 0;
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for(unsigned i = 0; i < 1000; ++i)
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{
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T input = 1 / ur2(dist);
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mp_type input2(input);
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T result = boost::math::cyl_bessel_i(1, input, policy_type());
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mp_type result2 = boost::math::cyl_bessel_i(1, input2);
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mp_type err = boost::math::relative_difference(result2, mp_type(result)) / mp_type(std::numeric_limits<T>::epsilon());
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if(boost::math::isinf(result))
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{
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if(result2 > mp_type((std::numeric_limits<T>::max)()))
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err = 0;
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else
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std::cout << "Bad result at x = " << input << " result = " << result << " true result = " << result2 << std::endl;
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}
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if(result2 < mp_type(result))
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err = -err;
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if(fabs(err) > max_err)
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{
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max_err = static_cast<float>(fabs(err));
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}
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if(fabs(err) <= 1)
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small[1 / static_cast<double>(input)] = static_cast<double>(err);
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else if(fabs(err) <= 2)
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medium[1 / static_cast<double>(input)] = static_cast<double>(err);
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else
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large[1 / static_cast<double>(input)] = static_cast<double>(err);
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}
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y_interval = static_cast<int>(ceil(max_err / 5));
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ss.str("");
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ss << "cyl_bessel_i<" << name << ">(1, x) over [0, 7.75]\n(max error = " << std::setprecision(2) << max_err << ")" << std::endl;
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boost::svg::svg_2d_plot my_plot2;
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// Size of SVG image and X and Y range settings.
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my_plot2.x_range(0, 1 / 7.75).image_x_size(700).legend_border_color(boost::svg::lightgray).plot_border_color(boost::svg::lightgray).background_border_color(boost::svg::lightgray)
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.y_range(-(int)ceil(max_err), (int)ceil(max_err)).x_label("1 / x").title(ss.str()).y_major_interval(y_interval).x_major_interval(0.01).legend_on(true).plot_window_on(true);
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my_plot2.plot(small, "< 1eps").stroke_color(boost::svg::green).fill_color(boost::svg::green).size(2);
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if(max_err > 1)
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{
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my_plot2.plot(medium, "< 2eps").stroke_color(boost::svg::orange).fill_color(boost::svg::orange).size(2);
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if(max_err > 2)
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my_plot2.plot(large, "> 2eps").stroke_color(boost::svg::red).fill_color(boost::svg::red).size(2);
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}
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filename = "bessel_i1_7_inf_";
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filename += name;
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filename += ".svg";
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my_plot2.write(filename);
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std::cout << "Maximum error for type " << name << " was: " << max_err << std::endl;
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}
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int main()
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{
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test_type<float>("float");
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test_type<double>("double");
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#if LDBL_MANT_DIG == 64
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test_type<long double>("long double");
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#else
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test_type<boost::multiprecision::cpp_bin_float_double_extended>("double-extended");
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#endif
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#ifdef BOOST_HAS_FLOAT128
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test_type<boost::multiprecision::float128>("float128");
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#else
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test_type<boost::multiprecision::cpp_bin_float_quad>("quad");
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#endif
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return 0;
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}
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