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- // \modular-boost\libs\math\test\lambert_w_high_reference_values.cpp
- // Copyright Paul A. Bristow 2017.
- // 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)
- // Write a C++ file \lambert_w_mp_hi_values.ipp
- // containing arrays of z arguments and 100 decimal digit precision lambert_w0(z) reference values.
- // These can be used in tests of precision of less-precise types like
- // built-in float, double, long double and quad and cpp_dec_float_50.
- // These cover the range from 0.5 to (std::numeric_limits<>::max)();
- // The Fukushima algorithm changes from a series function for all z > 0.5.
- // Multiprecision types:
- //#include <boost/multiprecision/cpp_bin_float.hpp>
- #include <boost/multiprecision/cpp_dec_float.hpp> // boost::multiprecision::cpp_dec_float_100
- using boost::multiprecision::cpp_dec_float_100;
- #include <boost/math/special_functions/lambert_w.hpp> //
- using boost::math::lambert_w0;
- using boost::math::lambert_wm1;
- #include <iostream>
- // using std::cout; using std::std::endl; using std::ios; using std::std::cerr;
- #include <iomanip>
- using std::setprecision;
- using std::showpoint;
- #include <fstream>
- using std::ofstream;
- #include <cassert>
- #include <cfloat> // for DBL_EPS etc
- #include <limits> // for numeric limits.
- //#include <ctype>
- #include <string>
- const long double eps = std::numeric_limits<long double>::epsilon();
- // Creates if no file exists, & uses default overwrite/ ios::replace.
- const char filename[] = "lambert_w_high_reference_values.ipp"; //
- std::ofstream fout(filename, std::ios::out);
- typedef cpp_dec_float_100 RealType; // 100 decimal digits for the value fed to macro BOOST_MATH_TEST_VALUE.
- // Could also use cpp_dec_float_50 or cpp_bin_float types.
- const int no_of_tests = 450; // 500 overflows float.
- static const float min_z = 0.5F; // for element[0]
- int main()
- { // Make C++ file containing Lambert W test values.
- std::cout << filename << " ";
- std::cout << std::endl;
- std::cout << "Lambert W0 decimal digit precision values for high z argument values." << std::endl;
- if (!fout.is_open())
- { // File failed to open OK.
- std::cerr << "Open file " << filename << " failed!" << std::endl;
- std::cerr << "errno " << errno << std::endl;
- return -1;
- }
- try
- {
- int output_precision = std::numeric_limits<RealType>::digits10;
- // cpp_dec_float_100 is ample precision and
- // has several extra bits internally so max_digits10 are not needed.
- fout.precision(output_precision);
- fout << std::showpoint << std::endl; // Do show trailing zeros.
- // Intro for RealType values.
- std::cout << "Lambert W test values written to file " << filename << std::endl;
- fout <<
- "\n"
- "// A collection of big Lambert W test values computed using "
- << output_precision << " decimal digits precision.\n"
- "// C++ floating-point type is " << "RealType." "\n"
- "\n"
- "// Written by " << __FILE__ << " " << __TIMESTAMP__ << "\n"
- "\n"
- "// Copyright Paul A. Bristow 2017." "\n"
- "// Distributed under the Boost Software License, Version 1.0." "\n"
- "// (See accompanying file LICENSE_1_0.txt" "\n"
- "// or copy at http://www.boost.org/LICENSE_1_0.txt)" "\n"
- << std::endl;
- fout << "// Size of arrays of arguments z and Lambert W" << std::endl;
- fout << "static const unsigned int noof_tests = " << no_of_tests << ";" << std::endl;
- // Declare arrays of z and Lambert W.
- fout << "\n// Declare arrays of arguments z and Lambert W(z)" << std::endl;
- fout <<
- "\n"
- "template <typename RealType>""\n"
- "static RealType zs[" << no_of_tests << "];"
- << std::endl;
- fout <<
- "\n"
- "template <typename RealType>""\n"
- "static RealType ws[" << no_of_tests << "];"
- << std::endl;
- fout << "// The values are defined using the macro BOOST_MATH_TEST_VALUE to ensure\n"
- "// that both built-in and multiprecision types are correctly initialiased with full precision.\n"
- "// built-in types like float, double require a floating-point literal like 3.14,\n"
- "// but multiprecision types require a decimal digit string like \"3.14\".\n"
- "// Numerical values are chosen to avoid exactly representable values."
- << std::endl;
- static const RealType min_z = 0.6; // for element[0]
- const RealType max_z = (std::numeric_limits<float>::max)() / 10; // (std::numeric_limits<float>::max)() to make sure is OK for all floating-point types.
- // Less a bit as lambert_w0(max) may be inaccurate.
- const RealType step_size = 0.5F; // Increment step size.
- const RealType step_factor = 2.f; // Multiple factor, typically 2, 5 or 10.
- const int step_modulo = 5;
- RealType z = min_z;
- // Output function to initialize array of arguments z and Lambert W.
- fout <<
- "\n"
- << "template <typename RealType>\n"
- "void init_zws()\n"
- "{\n";
- for (size_t index = 0; (index != no_of_tests); index++)
- {
- fout
- << " zs<RealType>[" << index << "] = BOOST_MATH_TEST_VALUE(RealType, "
- << z // Since start with converting a float may get lots of usefully random digits.
- << ");"
- << std::endl;
- fout
- << " ws<RealType>[" << index << "] = BOOST_MATH_TEST_VALUE(RealType, "
- << lambert_w0(z)
- << ");"
- << std::endl;
- if ((index % step_modulo) == 0)
- {
- z *= step_factor; //
- }
- z += step_size;
- if (z >= max_z)
- { // Don't go over max for float.
- std::cout << "too big z" << std::endl;
- break;
- }
- } // for index
- fout << "};" << std::endl;
- fout << "// End of lambert_w_mp_high_values.ipp " << std::endl;
- }
- catch (std::exception& ex)
- {
- std::cout << "Exception " << ex.what() << std::endl;
- }
- fout.close();
- std::cout << no_of_tests << " Lambert_w0 values written to files " << __TIMESTAMP__ << std::endl;
- return 0;
- } // main
- /*
- A few spot checks again Wolfram:
- zs<RealType>[1] = BOOST_MATH_TEST_VALUE(RealType, 1.6999999999999999555910790149937383830547332763671875);
- ws<RealType>[1] = BOOST_MATH_TEST_VALUE(RealType, 0.7796011225311008662356536916883580556792500749037209859530390902424444585607630246126725241921761054);
- Wolfram 0.7796011225311008662356536916883580556792500749037209859530390902424444585607630246126725241921761054
- zs<RealType>[99] = BOOST_MATH_TEST_VALUE(RealType, 3250582.599999999976716935634613037109375);
- ws<RealType>[99] = BOOST_MATH_TEST_VALUE(RealType, 12.47094339016839065212822905567651460418204106065566910956134121802725695306834966790193342511971825);
- Wolfram 12.47094339016839065212822905567651460418204106065566910956134121802725695306834966790193342511971825
- */
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