270 lines
11 KiB
C++
270 lines
11 KiB
C++
// Copyright Paul A. Bristow 2016, 2017, 2018.
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// Copyright John Maddock 2016.
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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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// test_lambert_w_integrals.cpp
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//! \brief quadrature tests that cover the whole range of the Lambert W0 function.
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#include <boost/config.hpp> // for BOOST_MSVC definition etc.
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#include <boost/version.hpp> // for BOOST_MSVC versions.
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// Boost macros
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#define BOOST_TEST_MAIN
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#define BOOST_LIB_DIAGNOSTIC "on" // Report library file details.
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#include <boost/test/included/unit_test.hpp> // Boost.Test
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// #include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/tools/floating_point_comparison.hpp>
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#include <boost/array.hpp>
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#include <boost/lexical_cast.hpp>
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#include <boost/type_traits/is_constructible.hpp>
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#include <boost/multiprecision/cpp_bin_float.hpp>
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using boost::multiprecision::cpp_bin_float_quad;
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#include <boost/math/special_functions/fpclassify.hpp> // isnan, ifinite.
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#include <boost/math/special_functions/next.hpp> // float_next, float_prior
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using boost::math::float_next;
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using boost::math::float_prior;
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#include <boost/math/special_functions/ulp.hpp> // ulp
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#include <boost/math/tools/test_value.hpp> // for create_test_value and macro BOOST_MATH_TEST_VALUE.
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#include <boost/math/policies/policy.hpp>
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using boost::math::policies::digits2;
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using boost::math::policies::digits10;
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#include <boost/math/special_functions/lambert_w.hpp> // For Lambert W lambert_w function.
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using boost::math::lambert_wm1;
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using boost::math::lambert_w0;
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#include <limits>
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#include <cmath>
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#include <typeinfo>
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#include <iostream>
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#include <type_traits>
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#include <exception>
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std::string show_versions(void);
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// Added code and test for Integral of the Lambert W function: by Nick Thompson.
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// https://en.wikipedia.org/wiki/Lambert_W_function#Definite_integrals
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#include <boost/math/constants/constants.hpp> // for integral tests.
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#include <boost/math/quadrature/tanh_sinh.hpp> // for integral tests.
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#include <boost/math/quadrature/exp_sinh.hpp> // for integral tests.
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using boost::math::policies::policy;
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using boost::math::policies::make_policy;
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// using statements needed for changing error handling policy.
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using boost::math::policies::evaluation_error;
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using boost::math::policies::domain_error;
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using boost::math::policies::overflow_error;
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using boost::math::policies::ignore_error;
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using boost::math::policies::throw_on_error;
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typedef policy<
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domain_error<throw_on_error>,
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overflow_error<ignore_error>
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> no_throw_policy;
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// Assumes that function has a throw policy, for example:
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// NOT lambert_w0<T>(1 / (x * x), no_throw_policy());
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// Error in function boost::math::quadrature::exp_sinh<double>::integrate:
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// The exp_sinh quadrature evaluated your function at a singular point and resulted in inf.
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// Please ensure your function evaluates to a finite number of its entire domain.
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template <typename T>
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T debug_integration_proc(T x)
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{
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T result; // warning C4701: potentially uninitialized local variable 'result' used
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// T result = 0 ; // But result may not be assigned below?
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try
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{
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// Assign function call to result in here...
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if (x <= sqrt(boost::math::tools::min_value<T>()) )
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{
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result = 0;
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}
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else
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{
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result = lambert_w0<T>(1 / (x * x));
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}
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// result = lambert_w0<T>(1 / (x * x), no_throw_policy()); // Bad idea, less helpful diagnostic message is:
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// Error in function boost::math::quadrature::exp_sinh<double>::integrate:
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// The exp_sinh quadrature evaluated your function at a singular point and resulted in inf.
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// Please ensure your function evaluates to a finite number of its entire domain.
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} // try
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catch (const std::exception& e)
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{
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std::cout << "Exception " << e.what() << std::endl;
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// set breakpoint here:
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std::cout << "Unexpected exception thrown in integration code at abscissa (x): " << x << "." << std::endl;
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if (!std::isfinite(result))
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{
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// set breakpoint here:
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std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl;
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}
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if (std::isnan(result))
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{
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// set breakpoint here:
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std::cout << "Unexpected non-finite result in integration code at abscissa (x): " << x << "." << std::endl;
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}
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} // catch
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return result;
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} // T debug_integration_proc(T x)
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template<class Real>
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void test_integrals()
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{
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// Integral of the Lambert W function:
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// https://en.wikipedia.org/wiki/Lambert_W_function
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using boost::math::quadrature::tanh_sinh;
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using boost::math::quadrature::exp_sinh;
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// file:///I:/modular-boost/libs/math/doc/html/math_toolkit/quadrature/double_exponential/de_tanh_sinh.html
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using std::sqrt;
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std::cout << "Integration of type " << typeid(Real).name() << std::endl;
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Real tol = std::numeric_limits<Real>::epsilon();
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{ // // Integrate for function lambert_W0(z);
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tanh_sinh<Real> ts;
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Real a = 0;
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Real b = boost::math::constants::e<Real>();
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auto f = [](Real z)->Real
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{
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return lambert_w0<Real>(z);
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};
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Real z = ts.integrate(f, a, b); // OK without any decltype(f)
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BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::e<Real>() - 1, tol);
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}
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{
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// Integrate for function lambert_W0(z/(z sqrt(z)).
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exp_sinh<Real> es;
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auto f = [](Real z)->Real
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{
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return lambert_w0<Real>(z)/(z * sqrt(z));
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};
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Real z = es.integrate(f); // OK
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BOOST_CHECK_CLOSE_FRACTION(z, 2 * boost::math::constants::root_two_pi<Real>(), tol);
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}
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{
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// Integrate for function lambert_W0(1/z^2).
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exp_sinh<Real> es;
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//const Real sqrt_min = sqrt(boost::math::tools::min_value<Real>()); // 1.08420217e-19 fo 32-bit float.
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// error C3493: 'sqrt_min' cannot be implicitly captured because no default capture mode has been specified
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auto f = [](Real z)->Real
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{
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if (z <= sqrt(boost::math::tools::min_value<Real>()) )
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{ // Too small would underflow z * z and divide by zero to overflow 1/z^2 for lambert_w0 z parameter.
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return static_cast<Real>(0);
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}
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else
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{
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return lambert_w0<Real>(1 / (z * z)); // warning C4756: overflow in constant arithmetic, even though cannot happen.
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}
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};
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Real z = es.integrate(f);
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BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::root_two_pi<Real>(), tol);
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}
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} // template<class Real> void test_integrals()
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BOOST_AUTO_TEST_CASE( integrals )
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{
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std::cout << "Macro BOOST_MATH_LAMBERT_W0_INTEGRALS is defined." << std::endl;
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BOOST_TEST_MESSAGE("\nTest Lambert W0 integrals.");
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try
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{
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// using statements needed to change precision policy.
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using boost::math::policies::policy;
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using boost::math::policies::make_policy;
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using boost::math::policies::precision;
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using boost::math::policies::digits2;
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using boost::math::policies::digits10;
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// using statements needed for changing error handling policy.
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using boost::math::policies::evaluation_error;
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using boost::math::policies::domain_error;
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using boost::math::policies::overflow_error;
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using boost::math::policies::ignore_error;
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using boost::math::policies::throw_on_error;
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/*
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typedef policy<
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domain_error<throw_on_error>,
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overflow_error<ignore_error>
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> no_throw_policy;
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// Experiment with better diagnostics.
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typedef float Real;
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Real inf = std::numeric_limits<Real>::infinity();
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Real max = (std::numeric_limits<Real>::max)();
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std::cout.precision(std::numeric_limits<Real>::max_digits10);
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//std::cout << "lambert_w0(inf) = " << lambert_w0(inf) << std::endl; // lambert_w0(inf) = 1.79769e+308
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std::cout << "lambert_w0(inf, throw_policy()) = " << lambert_w0(inf, no_throw_policy()) << std::endl; // inf
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std::cout << "lambert_w0(max) = " << lambert_w0(max) << std::endl; // lambert_w0(max) = 703.227
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//std::cout << lambert_w0(inf) << std::endl; // inf - will throw.
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std::cout << "lambert_w0(0) = " << lambert_w0(0.) << std::endl; // 0
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std::cout << "lambert_w0(std::numeric_limits<Real>::denorm_min()) = " << lambert_w0(std::numeric_limits<Real>::denorm_min()) << std::endl; // 4.94066e-324
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std::cout << "lambert_w0(std::numeric_limits<Real>::min()) = " << lambert_w0((std::numeric_limits<Real>::min)()) << std::endl; // 2.22507e-308
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// Approximate the largest lambert_w you can get for type T?
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float max_w_f = boost::math::lambert_w_detail::lambert_w0_approx((std::numeric_limits<float>::max)()); // Corless equation 4.19, page 349, and Chapeau-Blondeau equation 20, page 2162.
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std::cout << "w max_f " << max_w_f << std::endl; // 84.2879
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Real max_w = boost::math::lambert_w_detail::lambert_w0_approx((std::numeric_limits<Real>::max)()); // Corless equation 4.19, page 349, and Chapeau-Blondeau equation 20, page 2162.
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std::cout << "w max " << max_w << std::endl; // 703.227
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std::cout << "lambert_w0(7.2416706213544837e-163) = " << lambert_w0(7.2416706213544837e-163) << std::endl; //
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std::cout << "test integral 1/z^2" << std::endl;
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std::cout << "ULP = " << boost::math::ulp(1., policy<digits2<> >()) << std::endl; // ULP = 2.2204460492503131e-16
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std::cout << "ULP = " << boost::math::ulp(1e-10, policy<digits2<> >()) << std::endl; // ULP = 2.2204460492503131e-16
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std::cout << "ULP = " << boost::math::ulp(1., policy<digits2<11> >()) << std::endl; // ULP = 2.2204460492503131e-16
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std::cout << "epsilon = " << std::numeric_limits<Real>::epsilon() << std::endl; //
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std::cout << "sqrt(max) = " << sqrt(boost::math::tools::max_value<float>() ) << std::endl; // sqrt(max) = 1.8446742974197924e+19
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std::cout << "sqrt(min) = " << sqrt(boost::math::tools::min_value<float>() ) << std::endl; // sqrt(min) = 1.0842021724855044e-19
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// Demo debug version.
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Real tol = std::numeric_limits<Real>::epsilon();
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Real x;
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{
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using boost::math::quadrature::exp_sinh;
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exp_sinh<Real> es;
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// Function to be integrated, lambert_w0(1/z^2).
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//auto f = [](Real z)->Real
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//{ // Naive - no protection against underflow and subsequent divide by zero.
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// return lambert_w0<Real>(1 / (z * z));
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//};
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// Diagnostic is:
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// Error in function boost::math::lambert_w0<Real>: Expected a finite value but got inf
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auto f = [](Real z)->Real
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{ // Debug with diagnostics for underflow and subsequent divide by zero and other bad things.
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return debug_integration_proc(z);
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};
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// Exception Error in function boost::math::lambert_w0<double>: Expected a finite value but got inf.
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// Unexpected exception thrown in integration code at abscissa: 7.2416706213544837e-163.
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// Unexpected exception thrown in integration code at abscissa (x): 3.478765835953569e-23.
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x = es.integrate(f);
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std::cout << "es.integrate(f) = " << x << std::endl;
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BOOST_CHECK_CLOSE_FRACTION(x, boost::math::constants::root_two_pi<Real>(), tol);
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// root_two_pi<double = 2.506628274631000502
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}
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*/
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test_integrals<cpp_bin_float_quad>();
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}
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catch (std::exception& ex)
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{
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std::cout << ex.what() << std::endl;
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}
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}
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