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- // lambert_w_test_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 J:\Cpp\Misc\lambert_w_1000_test_values\lambert_w_mp_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.
- // 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;
- #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>
- #include <algorithm>
- using std::transform;
- const char* prefix = "static "; // "static const" or "static constexpr" or just "const "" or "" even?
- // But problems with VS2017 and GCC not accepting same format mean only static at present.
- const long double eps = std::numeric_limits<long double>::epsilon();
- /*
- // Sample test values from Wolfram.
- template <typename RealType>
- static RealType zs[noof_tests];
- template <typename RealType>
- void init_zs()
- {
- zs<RealType>[0] = BOOST_MATH_TEST_VALUE(RealType, -0.35);
- zs<RealType>[1] = BOOST_MATH_TEST_VALUE(RealType, -0.3);
- zs<RealType>[2] = BOOST_MATH_TEST_VALUE(RealType, -0.01);
- zs<RealType>[3] = BOOST_MATH_TEST_VALUE(RealType, +0.01);
- zs<RealType>[4] = BOOST_MATH_TEST_VALUE(RealType, 0.1);
- zs<RealType>[5] = BOOST_MATH_TEST_VALUE(RealType, 0.5);
- zs<RealType>[6] = BOOST_MATH_TEST_VALUE(RealType, 1.);
- zs<RealType>[7] = BOOST_MATH_TEST_VALUE(RealType, 2.);
- zs<RealType>[8] = BOOST_MATH_TEST_VALUE(RealType, 5.);
- zs<RealType>[9] = BOOST_MATH_TEST_VALUE(RealType, 10.);
- zs<RealType>[10] = BOOST_MATH_TEST_VALUE(RealType, 100.);
- zs<RealType>[11] = BOOST_MATH_TEST_VALUE(RealType, 1e+6);
- };
- // 'Known good' Lambert w values using N[productlog(-0.3), 50]
- // evaluated to full precision of RealType (up to 50 decimal digits).
- template <typename RealType>
- static RealType ws[noof_tests];
- template <typename RealType>
- void init_ws()
- {
- ws<RealType>[0] = BOOST_MATH_TEST_VALUE(RealType, -0.7166388164560738505881698000038650406110575701385055261614344530078353170171071547711151137001759321);
- ws<RealType>[1] = BOOST_MATH_TEST_VALUE(RealType, -0.4894022271802149690362312519962933689234100060163590345114659679736814083816206187318524147462752111);
- ws<RealType>[2] = BOOST_MATH_TEST_VALUE(RealType, -0.01010152719853875327292018767138623973670903993475235877290726369225412969738704722202330440072213641);
- ws<RealType>[3] = BOOST_MATH_TEST_VALUE(RealType, 0.009901473843595011885336326816570107953627746494917415482611387085655068978243229360100010886171970918);
- ws<RealType>[4] = BOOST_MATH_TEST_VALUE(RealType, 0.09127652716086226429989572142317956865311922405147203264830839460717224625441755165020664592995606710);
- ws<RealType>[5] = BOOST_MATH_TEST_VALUE(RealType, 0.3517337112491958260249093009299510651714642155171118040466438461099606107203387108968323038321915693);
- ws<RealType>[6] = BOOST_MATH_TEST_VALUE(RealType, 0.5671432904097838729999686622103555497538157871865125081351310792230457930866845666932194469617522946); // Output from https://www.wolframalpha.com/input/?i=lambert_w0(1)
- ws<RealType>[7] = BOOST_MATH_TEST_VALUE(RealType, 0.8526055020137254913464724146953174668984533001514035087721073946525150656742630448965773783502494847);
- ws<RealType>[8] = BOOST_MATH_TEST_VALUE(RealType, 1.326724665242200223635099297758079660128793554638047479789290393025342679920536226774469916608426789); // https://www.wolframalpha.com/input/?i=N%5Bproductlog(5),+100%5D
- ws<RealType>[9] = BOOST_MATH_TEST_VALUE(RealType, 1.745528002740699383074301264875389911535288129080941331322206048555557259941551704989523510778883075);
- ws<RealType>[10] = BOOST_MATH_TEST_VALUE(RealType, 3.385630140290050184888244364529726867491694170157806680386174654885206544913039277686735236213650781);
- ws<RealType>[11] = BOOST_MATH_TEST_VALUE(RealType, 11.38335808614005262200015678158500428903377470601886512143238610626898610768018867797709315493717650);
- ////W(1e35) = 76.256377207295812974093508663841808129811690961764 too big for float.
- };
- */
- // Global so accessible from output_value.
- // Creates if no file exists, & uses default overwrite/ ios::replace.
- const char filename[] = "lambert_w_low_reference values.ipp"; //
- std::ofstream fout(filename, std::ios::out); ; //
- // 100 decimal digits for the value fed to macro BOOST_MATH_TEST_VALUE
- typedef cpp_dec_float_100 RealType;
- void output_value(size_t index, RealType value)
- {
- fout
- << " zs<RealType>[" << index << "] = BOOST_MATH_TEST_VALUE(RealType, "
- << value
- << ");"
- << std::endl;
- return;
- }
- void output_lambert_w0(size_t index, RealType value)
- {
- fout
- << " ws<RealType>[" << index << "] = BOOST_MATH_TEST_VALUE(RealType, "
- << lambert_w0(value)
- << ");"
- << std::endl;
- return;
- }
- int main()
- { // Make C++ file containing Lambert W test values.
- std::cout << filename << " ";
- #ifdef __TIMESTAMP__
- std::cout << __TIMESTAMP__;
- #endif
- std::cout << std::endl;
- std::cout << "Lambert W0 decimal digit precision values." << std::endl;
- // Note __FILE__ & __TIMESTAMP__ are ANSI standard C & thus Std C++?
- 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;
- }
- int output_precision = std::numeric_limits<cpp_dec_float_100>::digits10;
- // cpp_dec_float_100 is ample precision and
- // has several extra bits internally so max_digits10 are not needed.
- fout.precision(output_precision);
- int no_of_tests = 100;
- // Intro for RealType values.
- std::cout << "Lambert W test values written to file " << filename << std::endl;
- fout <<
- "\n"
- "// A collection of 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 << "// Declare arrays of arguments z and Lambert W(z)" << 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 double require a floating-point literal like 3.14,\n"
- "// but multiprecision types require a decimal digit string like \"3.14\".\n"
- << 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;
- RealType max_z("10");
- RealType min_z("-0.35");
- RealType step_size("0.01");
- size_t step_count = no_of_tests;
- // Output to initialize array of arguments z for Lambert W.
- fout <<
- "\n"
- << "template <typename RealType>\n"
- "void init_zs()\n"
- "{\n";
- RealType z = min_z;
- for (size_t i = 0; (i < no_of_tests); i++)
- {
- output_value(i, z);
- z += step_size;
- }
- fout << "};" << std::endl;
- // Output array of Lambert W values.
- fout <<
- "\n"
- << "template <typename RealType>\n"
- "void init_ws()\n"
- "{\n";
- z = min_z;
- for (size_t i = 0; (i < step_count); i++)
- {
- output_lambert_w0(i, z);
- z += step_size;
- }
- fout << "};" << std::endl;
- fout << "// End of lambert_w_mp_values.ipp " << std::endl;
- fout.close();
- std::cout << "Lambert_w0 values written to files " << __TIMESTAMP__ << std::endl;
- return 0;
- } // main
- /*
- start and finish checks again Wolfram Alpha:
- ws<RealType>[0] = BOOST_MATH_TEST_VALUE(RealType, -0.7166388164560738505881698000038650406110575701385055261614344530078353170171071547711151137001759321);
- Wolfram N[productlog(-0.35), 100] -0.7166388164560738505881698000038650406110575701385055261614344530078353170171071547711151137001759321
- ws<RealType>[19] = BOOST_MATH_TEST_VALUE(RealType, 0.7397278549447991214587608743391115983469848985053641692586810406118264600667862543570373167046626221);
- Wolfram N[productlog(1.55), 100] 0.7397278549447991214587608743391115983469848985053641692586810406118264600667862543570373167046626221
- */
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