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math/test/test_lambert_w.cpp
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// Copyright Paul A. Bristow 2016, 2017.
// Copyright John Maddock 2016.
// 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)
// test_lambert_w.cpp
//! \brief Basic sanity tests for Lambert W function plog productlog
//! or lambert_w using algorithm informed by Thomas Luu, Veberic and Tosio Fukushima.
#include <boost/config.hpp> // for BOOST_MSVC definition.
#include <boost/version.hpp> // for BOOST_MSVC versions.
#include <boost/math/concepts/real_concept.hpp> // for real_concept
// Boost macros
#define BOOST_TEST_MAIN
#define BOOST_LIB_DIAGNOSTIC "on" // Report library file details.
#include <boost/test/unit_test.hpp> // Boost.Test
#include <boost/test/floating_point_comparison.hpp>
#include <boost/array.hpp>
#include <boost/lexical_cast.hpp>
#include <boost/type_traits/is_constructible.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp> // boost::multiprecision::cpp_dec_float_50
using boost::multiprecision::cpp_dec_float_50;
#include <boost/multiprecision/cpp_bin_float.hpp>
using boost::multiprecision::cpp_bin_float_quad;
//#include <boost/fixed_point/fixed_point.hpp> // If available.
#include <boost/math/special_functions/fpclassify.hpp> // isnan, ifinite.
#include <boost/math/special_functions/next.hpp> // float_next, float_prior
using boost::math::float_next;
using boost::math::float_prior;
#include <boost/math/tools/test_value.hpp> // for create_test_value and macro BOOST_MATH_TEST_VALUE.
#include <boost/math/policies/policy.hpp>
using boost::math::policies::digits2;
#include <boost/math/special_functions/lambert_w.hpp> // For Lambert W lambert_w function.
using boost::math::lambert_wm1;
using boost::math::lambert_w0; // Use jm version instead.
#define BOOST_MATH_LAMBERT_W_INTEGRALS
#ifdef BOOST_MATH_LAMBERT_W_INTEGRALS
// Added code and test for Integral of the Lambert W function: by Nick Thompson.
// https://en.wikipedia.org/wiki/Lambert_W_function#Definite_integrals
#include <boost/math/constants/constants.hpp> // for integral tests
#include <boost/math/quadrature/tanh_sinh.hpp> // for integral tests
#include <boost/math/quadrature/exp_sinh.hpp> // for integral tests
template<class Real>
void test_integrals()
{
// Integral of the Lambert W function:
// https://en.wikipedia.org/wiki/Lambert_W_function
using boost::math::quadrature::tanh_sinh;
using boost::math::quadrature::exp_sinh;
// file:///I:/modular-boost/libs/math/doc/html/math_toolkit/quadrature/double_exponential/de_tanh_sinh.html
using std::sqrt;
Real tol = std::numeric_limits<Real>::epsilon();
{ // // Integrate for function lambert_W0(z);
tanh_sinh<Real> ts;
Real a = 0;
Real b = boost::math::constants::e<Real>();
auto f = [](Real z)->Real
{
return lambert_w0<Real>(z);
};
Real z = ts.integrate(f, a, b); // OK without any decltype(f)
BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::e<Real>() - 1, tol);
}
{
// Integrate for function lambert_W0(z/(z sqrt(z)).
exp_sinh<Real> es;
auto f = [](Real z)->Real
{
return lambert_w0<Real>(z)/(z * sqrt(z));
};
Real z = es.integrate(f); // OK
BOOST_CHECK_CLOSE_FRACTION(z, 2 * boost::math::constants::root_two_pi<Real>(), tol);
}
{
// Integrate for function lambert_W0(1/z^2).
exp_sinh<Real> es;
auto f = [](Real z)->Real
{
return lambert_w0<Real>(1 / (z * z));
};
Real z = es.integrate(f);
BOOST_CHECK_CLOSE_FRACTION(z, boost::math::constants::root_two_pi<Real>(), tol);
}
} // template<class Real> void test_integrals()
#endif // BOOST_MATH_LAMBERT_W_INTEGRALS
#include <limits>
#include <cmath>
#include <typeinfo>
#include <iostream>
#include <type_traits>
#include <exception>
//! Build a message of information about build, architecture, address model, platform, ...
std::string show_versions()
{
// Some of this information can also be obtained from running with a Custom Post-build step
// adding the option --build_info=yes
// "$(TargetDir)$(TargetName).exe" --build_info=yes
std::ostringstream message;
message << "Program: " << __FILE__ << "\n";
#ifdef __TIMESTAMP__
message << __TIMESTAMP__;
#endif
message << "\nBuildInfo:\n" " Platform " << BOOST_PLATFORM;
// http://stackoverflow.com/questions/1505582/determining-32-vs-64-bit-in-c
#if defined(__LP64__) || defined(_WIN64) || (defined(__x86_64__) && !defined(__ILP32__) ) || defined(_M_X64) || defined(__ia64) || defined (_M_IA64) || defined(__aarch64__) || defined(__powerpc64__)
#define IS64BIT 1
message << ", 64-bit.";
#else
#define IS32BIT 1
message << ", 32-bit.";
#endif
message << "\n Compiler " BOOST_COMPILER;
#ifdef BOOST_MSC_VER
#ifdef _MSC_FULL_VER
message << "\n MSVC version " << BOOST_STRINGIZE(_MSC_FULL_VER) << ".";
#endif
#ifdef __WIN64
mess age << "\n WIN64" << std::endl;
#endif // __WIN64
#ifdef _WIN32
message << "\n WIN32" << std::endl;
#endif // __WIN32
#endif
#ifdef __GNUC__
//PRINT_MACRO(__GNUC__);
//PRINT_MACRO(__GNUC_MINOR__);
//PRINT_MACRO(__GNUC_PATCH__);
std::cout << "GCC " << __VERSION__ << std::endl;
//PRINT_MACRO(LONG_MAX);
#endif // __GNUC__
#ifdef __MINGW64__
std::cout << "MINGW64 " << __MINGW32_MAJOR_VERSION << __MINGW32_MINOR_VERSION << std::endl;
//
// << __MINGW64_MAJOR_VERSION << __MINGW64_MINOR_VERSION << std::endl; not declared in this scope???
#endif // __MINGW64__
#ifdef __MINGW32__
std::cout << "MINGW64 " << __MINGW32_MAJOR_VERSION << __MINGW32_MINOR_VERSION << std::endl;
#endif // __MINGW32__
message << "\n STL " << BOOST_STDLIB;
message << "\n Boost version " << BOOST_VERSION / 100000 << "." << BOOST_VERSION / 100 % 1000 << "." << BOOST_VERSION % 100;
#ifdef BOOST_HAS_FLOAT128
message << ", BOOST_HAS_FLOAT128" << std::endl;
#endif
message << std::endl;
return message.str();
} // std::string versions()
template <class RealType>
void test_spots(RealType)
{
// (Unused Parameter value, arbitrarily zero, only communicates the floating point type).
// test_spots(0.F); test_spots(0.); test_spots(0.L);
using boost::math::lambert_w0;
using boost::math::lambert_wm1;
using boost::math::constants::exp_minus_one;
using boost::math::constants::e;
using boost::math::policies::policy;
/* Example of an exception-free 'ignore_all' policy (possibly ill-advised?).
*/
typedef policy <
boost::math::policies::domain_error<boost::math::policies::ignore_error>,
boost::math::policies::overflow_error<boost::math::policies::ignore_error>,
boost::math::policies::underflow_error<boost::math::policies::ignore_error>,
boost::math::policies::denorm_error<boost::math::policies::ignore_error>,
boost::math::policies::pole_error<boost::math::policies::ignore_error>,
boost::math::policies::evaluation_error<boost::math::policies::ignore_error>
> ignore_all_policy;
// Test some bad parameters to the function, with default policy and also with ignore_all policy.
#ifndef BOOST_NO_EXCEPTIONS
BOOST_CHECK_THROW(lambert_w0<RealType>(-1.), std::domain_error);
BOOST_CHECK_THROW(lambert_wm1<RealType>(-1.), std::domain_error);
BOOST_CHECK_THROW(lambert_w0<RealType>(std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // Would be NaN.
//BOOST_CHECK_EQUAL(lambert_w0<RealType>(std::numeric_limits<RealType>::quiet_NaN(), ignore_all_policy()), std::numeric_limits<RealType>::quiet_NaN()); // Should be NaN.
// Fails as NaN != NaN by definition.
BOOST_CHECK(boost::math::isnan(lambert_w0<RealType>(std::numeric_limits<RealType>::quiet_NaN(), ignore_all_policy())));
//BOOST_MATH_CHECK_EQUAL(boost::math::lambert_w0<RealType>(std::numeric_limits<RealType>::infinity(), ignore_all_policy()), std::numeric_limits<RealType::infinity()); // infinity.
// BOOST_CHECK_THROW(lambert_w0<RealType>(std::numeric_limits<RealType>::infinity()), std::domain_error); // Was if infinity should throw, now infinity.
BOOST_CHECK_THROW(lambert_w0<RealType>(-static_cast<RealType>(0.4)), std::domain_error); // Would be complex.
#else // No exceptions, so set policy to ignore and check result is NaN.
BOOST_MATH_CHECK_EQUAL(boost::math::lambert_w0<RealType>(std::numeric_limits<RealType>::quiet_NaN(), ignore_all_policy()), std::numeric_limits<RealType::quiet_NaN()); // NaN.
BOOST_MATH_CHECK_EQUAL(boost::math::lambert_w0<RealType>(std::numeric_limits<RealType>::infinity(), ignore_all_policy()), std::numeric_limits<RealType::infinity()); // infinity.
BOOST_MATH_CHECK_EQUAL(boost::math::lambert_w0<RealType>(std::numeric_limits<RealType>::infinity(), ignore_all_policy()), std::numeric_limits<RealType::infinity()); // infinity.
#endif
std::cout << "\nTesting type " << typeid(RealType).name() << std::endl;
int epsilons = 1;
if (std::numeric_limits<RealType>::digits > 53)
{ // Multiprecision types.
epsilons *= 8; // (Perhaps needed because need slightly longer (55) reference values?).
}
RealType tolerance = boost::math::tools::epsilon<RealType>() * epsilons; // 2 eps as a fraction.
std::cout << "Tolerance " << epsilons << " * epsilon == " << tolerance << std::endl;
std::cout << "Precision " << std::numeric_limits<RealType>::digits10 << " decimal digits." << std::endl;
// std::cout.precision(std::numeric_limits<RealType>::digits10);
std::cout.precision(std::numeric_limits <RealType>::max_digits10);
std::cout.setf(std::ios_base::showpoint); // show trailing significant zeros.
std::cout << "-exp(-1) = " << -exp_minus_one<RealType>() << std::endl;
// Test at singularity.
//RealType test_value = BOOST_MATH_TEST_VALUE(RealType, -0.36787944117144232159552377016146086744581113103176783450783680169746149574489980335714727434591964374662732527);
RealType singular_value = -exp_minus_one<RealType>();
// -exp(-1) = -0.36787944117144232159552377016146086744581113103176783450783680169746149574489980335714727434591964374662732527
// lambert_w0[-0.367879441171442321595523770161460867445811131031767834] == -1
// -0.36787945032119751
RealType minus_one_value = BOOST_MATH_TEST_VALUE(RealType, -1.);
//std::cout << "singular_value " << singular_value << ", expected Lambert W = " << minus_one_value << std::endl;
BOOST_CHECK_CLOSE_FRACTION( // Check -exp(-1) = -0.367879450 = -1max
lambert_w0(singular_value),
minus_one_value,
tolerance); // OK
BOOST_CHECK_CLOSE_FRACTION( // Check -exp(-1) ~= -0.367879450 == -1
lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.36787944117144232159552377016146086744581113103176783450783680169746149574489980335714727434591964374662732527)),
BOOST_MATH_TEST_VALUE(RealType, -1.),
tolerance);
BOOST_CHECK_CLOSE_FRACTION( // Check -exp(-1) ~= -0.367879450 == -1
lambert_w0<RealType>(-exp_minus_one<RealType>()),
BOOST_MATH_TEST_VALUE(RealType, -1.),
tolerance);
// Tests with some spot values computed using
// https://www.wolframalpha.com/input
// For example: N[lambert_w[1], 50] outputs:
// 0.56714329040978387299996866221035554975381578718651
// At branch junction singularity.
BOOST_CHECK_CLOSE_FRACTION( // Check -exp(-1) ~= -0.367879450 == -1
lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.36787944117144232159552377016146086744581113103176783450783680169746149574489980335714727434591964374662732527)),
BOOST_MATH_TEST_VALUE(RealType, -1.),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.1)),
BOOST_MATH_TEST_VALUE(RealType, 0.091276527160862264299895721423179568653119224051472),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(0.2)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.2)),
BOOST_MATH_TEST_VALUE(RealType, 0.16891597349910956511647490370581839872844691351073),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(0.2)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.5)),
BOOST_MATH_TEST_VALUE(RealType, 0.351733711249195826024909300929951065171464215517111804046),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(0.5)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1.)),
BOOST_MATH_TEST_VALUE(RealType, 0.56714329040978387299996866221035554975381578718651),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(1)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 2.)),
BOOST_MATH_TEST_VALUE(RealType, 0.852605502013725491346472414695317466898453300151403508772),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(2.)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 3.)),
BOOST_MATH_TEST_VALUE(RealType, 1.049908894964039959988697070552897904589466943706341452932),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(3.)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 5.)),
BOOST_MATH_TEST_VALUE(RealType, 1.326724665242200223635099297758079660128793554638047479789),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(0.5)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 6.)),
BOOST_MATH_TEST_VALUE(RealType, 1.432404775898300311234078007212058694786434608804302025655),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(6)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 100.)),
BOOST_MATH_TEST_VALUE(RealType, 3.3856301402900501848882443645297268674916941701578),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(100)
tolerance);
if (std::numeric_limits<RealType>::has_infinity)
{
BOOST_CHECK_THROW(lambert_w0(std::numeric_limits<RealType>::infinity()), std::overflow_error); // If should throw exception.
//BOOST_CHECK_EQUAL(lambert_w0(std::numeric_limits<RealType>::infinity()), +std::numeric_limits<RealType>::infinity()); // message is:
// Error in "test_types": class boost::exception_detail::clone_impl<struct boost::exception_detail::error_info_injector<class std::overflow_error> > :
// Error in function boost::math::lambert_w0<RealType>(<RealType>) : Argument z is infinite!
//BOOST_CHECK_EQUAL(lambert_w0(std::numeric_limits<RealType>::infinity()), +std::numeric_limits<RealType>::infinity()); // If infinity allowed.
BOOST_CHECK_THROW(lambert_wm1(std::numeric_limits<RealType>::infinity()), std::domain_error); // Infinity NOT allowed.
}
if (std::numeric_limits<RealType>::has_quiet_NaN)
{ // Argument Z == NaN is always an throwable error for both branches.
// BOOST_CHECK_EQUAL(lambert_w0(std::numeric_limits<RealType>::quiet_NaN()), +std::numeric_limits<RealType>::infinity()); // message is:
// Error in function boost::math::lambert_w0<RealType>(<RealType>): Argument z is NaN!
BOOST_CHECK_THROW(lambert_w0(std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
BOOST_CHECK_THROW(lambert_wm1(std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
}
// denorm - but might be == min or zero?
if (std::numeric_limits<RealType>::has_denorm == true)
{ // Might also return infinity like z == 0?
BOOST_CHECK_THROW(lambert_wm1(std::numeric_limits<RealType>::denorm_min()), std::overflow_error);
}
// Tests of Lambert W-1 branch.
BOOST_CHECK_CLOSE_FRACTION( // Check -exp(-1) ~= -0.367879450 == -1 at the singularity branch point.
lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.36787944117144232159552377016146086744581113103176783450783680169746149574489980335714727434591964374662732527)),
BOOST_MATH_TEST_VALUE(RealType, -1.),
tolerance);
// Near singularity and using series approximation.
// N[productlog(-1, -0.36), 50] = -1.2227701339785059531429380734238623131735264411311
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.36)),
BOOST_MATH_TEST_VALUE(RealType, -1.2227701339785059531429380734238623131735264411311),
10 * tolerance); // tolerance OK for quad
// -1.2227701339785059531429380734238623131735264411311
// -1.222770133978505953142938073423862313173526441131033
// Just using series approximation (switch at -0.35).
// N[productlog(-0.351), 50] = -0.72398644140937651483634596143951001600417138085814
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.351)),
BOOST_MATH_TEST_VALUE(RealType, -0.72398644140937651483634596143951001600417138085814),
// 2 * tolerance); // Note 2 * tolerance for PB fukushima
// got -0.723986441409376931150560229265736446 without Halley
// exp -0.72398644140937651483634596143951001
// got -0.72398644140937651483634596143951029 with Halley
10 * tolerance); // expect -0.72398644140937651 float -0.723987103 needs 10 * tolerance
// 2 * tolerance is fine for double and up.
// Float is OK
// Same for W-1 branch
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.351)),
BOOST_MATH_TEST_VALUE(RealType, -1.3385736984773431852492145715526995809854973408320),
10 * tolerance); // 2 tolerance OK for quad
// Near singularity and NOT using series approximation (switch at -0.35)
// N[productlog(-1, -0.34), 50]
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.34)),
BOOST_MATH_TEST_VALUE(RealType, -1.4512014851325470735077533710339268100722032730024),
10 * tolerance); // tolerance OK for quad
//
// Decreasing z until near zero (small z) .
//N[productlog(-1, -0.3), 50] = -1.7813370234216276119741702815127452608215583564545
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.3)),
BOOST_MATH_TEST_VALUE(RealType, -1.7813370234216276119741702815127452608215583564545),
2 * tolerance);
// -1.78133702342162761197417028151274526082155835645446
//N[productlog(-1, -0.2), 50] = -2.5426413577735264242938061566618482901614749075294
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.2)),
BOOST_MATH_TEST_VALUE(RealType, -2.5426413577735264242938061566618482901614749075294),
2 * tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.1)),
BOOST_MATH_TEST_VALUE(RealType, -3.577152063957297218409391963511994880401796257793),
tolerance);
//N[productlog(-1, -0.01), 50] = -6.4727751243940046947410578927244880371043455902257
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.01)),
BOOST_MATH_TEST_VALUE(RealType, -6.4727751243940046947410578927244880371043455902257),
tolerance);
// N[productlog(-1, -0.001), 50] = -9.1180064704027401212583371820468142742704349737639
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.001)),
BOOST_MATH_TEST_VALUE(RealType, -9.1180064704027401212583371820468142742704349737639),
tolerance);
// N[productlog(-1, -0.000001), 50] = -16.626508901372473387706432163984684996461726803805
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.000001)),
BOOST_MATH_TEST_VALUE(RealType, -16.626508901372473387706432163984684996461726803805),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1e-12)),
BOOST_MATH_TEST_VALUE(RealType, -31.067172842017230842039496250208586707880448763222),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1e-25)),
BOOST_MATH_TEST_VALUE(RealType, -61.686695602074505366866968627049381352503620377944),
tolerance);
// z nearly too small.
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -2e-26)),
BOOST_MATH_TEST_VALUE(RealType, -63.322302839923597803393585145387854867226970485197),
tolerance* 2);
// z very nearly too small. G(k=64) g[63] = -1.0264389699511303e-26 to using 1.027e-26
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1.027e-26)),
BOOST_MATH_TEST_VALUE(RealType, -63.999444896732265186957073549916026532499356695343),
tolerance);
// So -64 is the most negative value that can be determined using lookup.
// N[productlog(-1, -1.0264389699511303 * 10^-26 ), 50] -63.999999999999997947255011093606206983577811736472 == -64
// G[k=64] = g[63] = -1.0264389699511303e-26
// z too small for G(k=64) g[63] = -1.0264389699511303e-26 to using 1.027e-26
// N[productlog(-1, -10 ^ -26), 50] = -31.067172842017230842039496250208586707880448763222
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1e-26)),
BOOST_MATH_TEST_VALUE(RealType, -64.026509628385889681156090340691637712441162092868),
tolerance); // -64.0265121
if (std::numeric_limits<RealType>::has_infinity)
{
BOOST_CHECK_EQUAL(lambert_wm1(0), -std::numeric_limits<RealType>::infinity());
}
if (std::numeric_limits<RealType>::has_quiet_NaN)
{
// BOOST_CHECK_EQUAL(lambert_w0(std::numeric_limits<RealType>::quiet_NaN()), +std::numeric_limits<RealType>::infinity()); // message is:
// Error in function boost::math::lambert_w0<RealType>(<RealType>): Argument z is NaN!
BOOST_CHECK_THROW(lambert_wm1(std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
}
// W0 Tests for too big and too small to use lookup table.
// Exactly W = 64, not enough to be OK for lookup.
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 3.9904954117194348050619127737142206366920907815909119e+29)),
BOOST_MATH_TEST_VALUE(RealType, 64.0),
tolerance);
// Just below z for F[64]
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 3.99045411719434e+29)),
BOOST_MATH_TEST_VALUE(RealType, 63.999989810930513468726486827408823607175844852495), tolerance);
// Fails for quad_float -1.22277013397850595265
// -1.22277013397850595319
// Just too big, so using log approx and Halley refinement.
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 4e+29)),
BOOST_MATH_TEST_VALUE(RealType, 64.002342375637950350970694519073803643686041499677),
tolerance);
// Check at reduced precision.
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 4e+29), policy<digits2<11> >()),
BOOST_MATH_TEST_VALUE(RealType, 64.002342375637950350970694519073803643686041499677),
0.00002); // 0.00001 fails.
// Tests to ensure that all JM rational polynomials are being checked.
// 1st polynomal if (z < 0.5) // 0.05 < z < 0.5
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.49)),
BOOST_MATH_TEST_VALUE(RealType, 0.3465058086974944293540338951489158955895910665452626949),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.051)),
BOOST_MATH_TEST_VALUE(RealType, 0.04858156174600359264950777241723801201748517590507517888),
tolerance);
// 2st polynomal if 0.5 < z < 2
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.51)),
BOOST_MATH_TEST_VALUE(RealType, 0.3569144916935871518694242462560450385494399307379277704),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1.9)),
BOOST_MATH_TEST_VALUE(RealType, 0.8291763302658400337004358009672187071638421282477162293),
tolerance);
// 3rd polynomials 2 < z < 6
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 2.1)),
BOOST_MATH_TEST_VALUE(RealType, 0.8752187586805470099843211502166029752154384079916131962),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 5.9)),
BOOST_MATH_TEST_VALUE(RealType, 1.422521411785098213935338853943459424120416844150520831),
tolerance);
// 4th polynomials 6 < z < 18
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 6.1)),
BOOST_MATH_TEST_VALUE(RealType, 1.442152194116056579987235881273412088690824214100254315),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 17.9)),
BOOST_MATH_TEST_VALUE(RealType, 2.129100923757568114366514708174691237123820852409339147),
tolerance);
// 5th polynomials if (z < 9897.12905874) // 2.8 < log(z) < 9.2
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 18.1)),
BOOST_MATH_TEST_VALUE(RealType, 2.136665501382339778305178680563584563343639180897328666),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 9897.)),
BOOST_MATH_TEST_VALUE(RealType, 7.222751047988674263127929506116648714752441161828893633),
tolerance);
// 6th polynomials if (z < 7.896296e+13) // 9.2 < log(z) <= 32
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 9999.)),
BOOST_MATH_TEST_VALUE(RealType, 7.231758181708737258902175236106030961433080976032516996),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 7.7e+13)),
BOOST_MATH_TEST_VALUE(RealType, 28.62069643025822480911439831021393125282095606713326376),
tolerance);
// 7th polynomial // 32 < log(z) < 100
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 8.0e+18)),
BOOST_MATH_TEST_VALUE(RealType, 39.84107480517853176296156400093560722439428484537515586),
tolerance);
// Largest 32-bit float. (Larger values for other types tested using max())
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1.e38)),
BOOST_MATH_TEST_VALUE(RealType, 83.07844821316409592720410446942538465411465113447713574),
tolerance);
// Small z < 0.05 if (z < -0.051) -0.27 < z < -0.051
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.28)),
BOOST_MATH_TEST_VALUE(RealType, -0.4307588745271127579165306568413721388196459822705155385),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.05)),
BOOST_MATH_TEST_VALUE(RealType, -0.05270598355154634795995650617915721289427674396592395160),
tolerance);
// Using z small series function < 0.05
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.049)),
BOOST_MATH_TEST_VALUE(RealType, 0.04676143671340832342497289393737051868103596756298863555),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.049)),
BOOST_MATH_TEST_VALUE(RealType, -0.05159448479219405354564920228913331280713177046648170658),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1e-6)),
BOOST_MATH_TEST_VALUE(RealType, 9.999990000014999973333385416558666900096702096424344715e-7),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -1e-6)),
BOOST_MATH_TEST_VALUE(RealType, -1.000001000001500002666671875010800023343107568372593753e-6),
tolerance);
// Near Smallest float.
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1e-38)),
BOOST_MATH_TEST_VALUE(RealType, 9.99999999999999999999999999999999999990000000000000000e-39),
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -1e-38)),
BOOST_MATH_TEST_VALUE(RealType, -1.000000000000000000000000000000000000010000000000000000e-38),
tolerance);
// Similar 'too near zero' tests for W-1 branch.
// lambert_wm1(-1.0264389699511283e-26) = -64.000000000000000
// Exactly z for W=-64
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1.026438969951128225904695701851094643838952857740385870e-26)),
BOOST_MATH_TEST_VALUE(RealType, -64.000000000000000000000000000000000000),
2 * tolerance);
// Just more negative than G[64 max] = wm1zs[63] so can't use lookup table.
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1.5e-27)),
BOOST_MATH_TEST_VALUE(RealType, -65.953279000145077719128800110134854577850889171784),
tolerance); // -65.9532776
// Just less negative than G[64 max] = wm1zs[63] so can use lookup table.
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1.1e-26)),
BOOST_MATH_TEST_VALUE(RealType, -63.929686062157630858625440758283127600360210072859),
tolerance);
// N[productlog(-1, -10 ^ -26), 50] = -31.067172842017230842039496250208586707880448763222
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1e-26)),
BOOST_MATH_TEST_VALUE(RealType, -64.026509628385889681156090340691637712441162092868),
tolerance);
// 1e-28 is too small
// N[productlog(-1, -10 ^ -28), 50] = -31.067172842017230842039496250208586707880448763222
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1e-28)),
BOOST_MATH_TEST_VALUE(RealType, -68.702163291525429160769761667024460023336801014578),
tolerance);
// Check for overflow when using a double (including when using for approximate value for refinement for higher precision).
// N[productlog(-1, -10 ^ -30), 50] = -73.373110313822976797067478758120874529181611813766
//BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1e30)),
// BOOST_MATH_TEST_VALUE(RealType, -73.373110313822976797067478758120874529181611813766),
// tolerance);
//unknown location : fatal error : in "test_types" :
//class boost::exception_detail::clone_impl<struct boost::exception_detail::error_info_injector<class std::domain_error> >
// : Error in function boost::math::lambert_wm1<RealType>(<RealType>) :
// Argument z = -1.00000002e+30 out of range(z < -exp(-1) = -3.6787944) for Lambert W - 1 branch!
BOOST_CHECK_THROW(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1e30)), std::domain_error);
// Too negative
BOOST_CHECK_THROW(lambert_wm1(-0.5), std::domain_error);
// This fails for fixed_point type used for other tests because out of range?
//BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1.0e6)),
//BOOST_MATH_TEST_VALUE(RealType, 11.383358086140052622000156781585004289033774706019),
//// Output from https://www.wolframalpha.com/input/?i=lambert_w0(1e6)
//// tolerance * 1000); // fails for fixed_point type exceeds 0.00015258789063
// // 15.258789063
// // 11.383346558
// tolerance * 100000);
// So need to use some spot tests for specific types, or use a bigger fixed_point type.
// Check zero.
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.0)),
BOOST_MATH_TEST_VALUE(RealType, 0.0),
tolerance);
// these fail for cpp_dec_float_50
// 'boost::multiprecision::detail::expression<boost::multiprecision::detail::negate,boost::multiprecision::number<boost::multiprecision::backends::cpp_dec_float<50,int32_t,void>,boost::multiprecision::et_on>,void,void,void>'
// : no appropriate default constructor available
// TODO ???????????
} //template <class RealType>void test_spots(RealType)
BOOST_AUTO_TEST_CASE(test_types)
{
BOOST_MATH_CONTROL_FP;
// BOOST_TEST_MESSAGE output only appears if command line has --log_level="message"
// or call set_threshold_level function:
boost::unit_test_framework::unit_test_log.set_threshold_level(boost::unit_test_framework::log_messages);
BOOST_TEST_MESSAGE("\nTest Lambert W function for several types.");
BOOST_TEST_MESSAGE(show_versions()); // Full version of Boost, STL and compiler info.
// Fundamental built-in types:
test_spots(0.0F); // float
test_spots(0.0); // double
if (sizeof(long double) > sizeof(double))
{ // Avoid pointless re-testing if double and long double are identical (for example, MSVC).
test_spots(0.0L); // long double
}
// Multiprecision types:
test_spots(static_cast<boost::multiprecision::cpp_bin_float_double_extended>(0));
test_spots(static_cast<boost::multiprecision::cpp_bin_float_quad>(0));
test_spots(static_cast<boost::multiprecision::cpp_bin_float_50>(0));
//test_spots(static_cast<boost::multiprecision::cpp_dec_float_50>(0));
// Fixed-point types:
// Some fail 0.1 to 1.0 ???
// test_spots(static_cast<boost::fixed_point::negatable<15,-16> >(0));
// fixed_point::negatable<15,-16> has range 1.52587891e-05 to 32768, epsilon 3.05175781e-05
//test_spots(boost::math::concepts::real_concept(0.1)); // "real_concept" - was OK.
} // BOOST_AUTO_TEST_CASE( test_types)
BOOST_AUTO_TEST_CASE(test_range_of_double_values)
{
using boost::math::constants::exp_minus_one;
using boost::math::lambert_w0;
BOOST_TEST_MESSAGE("\nTest Lambert W function type double for range of values.");
// Want to test almost largest value.
// test_value = (std::numeric_limits<RealType>::max)() / 4;
// std::cout << std::setprecision(std::numeric_limits<RealType>::max_digits10) << "Max value = " << test_value << std::endl;
// Can't use a test like this for all types because max_value depends on RealType
// and thus the expected result of lambert_w0 does too.
//BOOST_CHECK_CLOSE_FRACTION(lambert_w0<RealType>(test_value),
// BOOST_MATH_TEST_VALUE(RealType, ???),
// tolerance);
// So this section just tests a single type, say IEEE 64-bit double, for a range of spot values.
typedef double RealType; // Some tests assume type is double.
int epsilons = 1;
RealType tolerance = boost::math::tools::epsilon<RealType>() * epsilons; // 2 eps as a fraction.
std::cout << "Tolerance " << epsilons << " * epsilon == " << tolerance << std::endl;
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1.0e-6)),
BOOST_MATH_TEST_VALUE(RealType, 9.9999900000149999733333854165586669000967020964243e-7),
// Output from https://www.wolframalpha.com/input/ N[lambert_w[1e-6],50])
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.0001)),
BOOST_MATH_TEST_VALUE(RealType, 0.000099990001499733385405869000452213835767629477903460),
// Output from https://www.wolframalpha.com/input/ N[lambert_w[0.001],50])
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.001)),
BOOST_MATH_TEST_VALUE(RealType, 0.00099900149733853088995782787410778559957065467928884),
// Output from https://www.wolframalpha.com/input/ N[lambert_w[0.001],50])
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.01)),
BOOST_MATH_TEST_VALUE(RealType, 0.0099014738435950118853363268165701079536277464949174),
// Output from https://www.wolframalpha.com/input/ N[lambert_w[0.01],50])
tolerance * 25); // <<< Needs a much bigger tolerance???
// 0.0099014738435951096 this test max_digits10
// 0.00990147384359511 digits10
// 0.0099014738435950118 wolfram
// 0.00990147384359501 wolfram digits10
// 0.0099014738435950119 N[lambert_w[0.01],17]
// 0.00990147384359501 N[lambert_w[0.01],15] which really is more different than expected.
// 0.00990728209160670 approx
// 0.00990147384359511 previous
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.05)),
BOOST_MATH_TEST_VALUE(RealType, 0.047672308600129374726388900514160870747062965933891),
// Output from https://www.wolframalpha.com/input/ N[lambert_w[0.01],50])
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 0.1)),
BOOST_MATH_TEST_VALUE(RealType, 0.091276527160862264299895721423179568653119224051472),
// Output from https://www.wolframalpha.com/input/ N[lambert_w[1],50])
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1.)),
BOOST_MATH_TEST_VALUE(RealType, 0.56714329040978387299996866221035554975381578718651),
// Output from https://www.wolframalpha.com/input/ N[lambert_w[1],50])
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 2.)),
BOOST_MATH_TEST_VALUE(RealType, 0.852605502013725491346472414695317466898453300151403508772),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(2.)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 3.)),
BOOST_MATH_TEST_VALUE(RealType, 1.049908894964039959988697070552897904589466943706341452932),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(3.)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 5.)),
BOOST_MATH_TEST_VALUE(RealType, 1.326724665242200223635099297758079660128793554638047479789),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(0.5)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 6.)),
BOOST_MATH_TEST_VALUE(RealType, 1.432404775898300311234078007212058694786434608804302025655),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(6)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 10.)),
BOOST_MATH_TEST_VALUE(RealType, 1.7455280027406993830743012648753899115352881290809),
// Output from https://www.wolframalpha.com/input/ N[lambert_w[10],50])
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 100.)),
BOOST_MATH_TEST_VALUE(RealType, 3.3856301402900501848882443645297268674916941701578),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(100)
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1000.)),
BOOST_MATH_TEST_VALUE(RealType, 5.2496028524015962271260563196973062825214723860596),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(1000)
tolerance);
// This fails for fixed_point type used for other tests because out of range of the type?
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, 1.0e6)),
BOOST_MATH_TEST_VALUE(RealType, 11.383358086140052622000156781585004289033774706019),
// Output from https://www.wolframalpha.com/input/?i=lambert_w0(1e6)
tolerance); //
// Tests for double only near the max and the singularity where Lambert_w estimates are less precise.
if (std::numeric_limits<RealType>::is_specialized)
{ // is_specialized means that can use numeric_limits for tests.
// Check near std::numeric_limits<>::max() for type.
//std::cout << std::setprecision(std::numeric_limits<RealType>::max_digits10)
// << (std::numeric_limits<double>::max)() // == 1.7976931348623157e+308
// << " " << (std::numeric_limits<double>::max)()/4 // == 4.4942328371557893e+307
// << std::endl;
// All these result in faulty error message
// unknown location : fatal error : in "test_range_of_values": class boost::exception_detail::clone_impl<struct boost::exception_detail::error_info_injector<class std::domain_error> >: Error in function boost::math::lambert_w0<RealType>(<RealType>): Argument z = %1 too large.
// I:\modular - boost\libs\math\test\test_lambert_w.cpp(456) : last checkpoint
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(1.7976931348623157e+308 ), // max_value for IEEE 64-bit double.
static_cast<double>(703.2270331047701868711791887193075929608934699575820028L),
// N[productlog[0, 1.7976931348623157*10^308 /2],50] == 702.53487067487671916110655783739076368512998658347
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(1.7976931348623157e+308 / 2), // max_value/2 for IEEE 64-bit double.
static_cast<double>(702.53487067487671916110655783739076368512998658347L),
// N[productlog[0, 1.7976931348623157*10^308 /2],50] == 702.53487067487671916110655783739076368512998658347
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(1.7976931348623157e+308 /4), // near max_value/4 for IEEE 64-bit double.
static_cast<double>(701.8427092142920014223182853764045476L),
// N[productlog(0, 1.7976931348623157* 10^308 /4 ), 37] =701.8427092142920014223182853764045476
// N[productlog(0, 0.25 * 1.7976931348623157*10^307), 37]
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(4.4942328371557893e+307), // max_value/4 for IEEE 64-bit double.
static_cast<double>(701.84270921429200143342782556643059L),
// N[lambert_w[4.4942328371557893e+307], 35] == 701.8427092142920014334278255664305887
// as a double == 701.83341468208209
// Lambert computed 702.02379914670587
0.000003); // OK Much less precise at the max edge???
BOOST_CHECK_CLOSE_FRACTION(lambert_w0((std::numeric_limits<double>::max)()), // max_value for IEEE 64-bit double.
static_cast<double>(703.2270331047701868711791887193075930),
// N[productlog(0, 1.7976931348623157* 10^308), 37] = 703.2270331047701868711791887193075930
// 703.22700325995515 lambert W
// 703.22703310477016 Wolfram
tolerance * 2e8); // OK but much less accurate near max.
// Compare precisions very close to the singularity.
// This test value is one epsilon close to the singularity at -exp(-1) * z
// (below which the result has a non-zero imaginary part).
RealType test_value = -exp_minus_one<RealType>();
test_value += (std::numeric_limits<RealType>::epsilon() * 1);
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(test_value),
BOOST_MATH_TEST_VALUE(RealType, -0.99999996349975895),
tolerance * 1000000000);
// -0.99999996788201051
// -0.99999996349975895
// Would not expect to get a result closer than sqrt(epsilon)?
} // if (std::numeric_limits<RealType>::is_specialized)
// Can only compare float_next for specific type T = double.
// Comparison with Wolfram N[productlog(0,-0.36787944117144228 ), 17]
// Note big loss of precision and big tolerance needed to pass.
BOOST_CHECK_CLOSE_FRACTION( // Check float_next(-exp(-1) )
lambert_w0(BOOST_MATH_TEST_VALUE(double, -0.36787944117144228)),
BOOST_MATH_TEST_VALUE(RealType, -0.99999998496215738),
1e8 * tolerance); // diff 6.03558e-09 v 2.2204460492503131e-16
BOOST_CHECK_CLOSE_FRACTION( // Check float_next(float_next(-exp(-1) ))
lambert_w0(BOOST_MATH_TEST_VALUE(double, -0.36787944117144222)),
BOOST_MATH_TEST_VALUE(RealType, -0.99999997649828679),
5e7 * tolerance);// diff 2.30785e-09 v 2.2204460492503131e-16
// Compare with previous PB/FK computations at double precision.
BOOST_CHECK_CLOSE_FRACTION( // Check float_next(-exp(-1) )
lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.36787944117144228)),
BOOST_MATH_TEST_VALUE(RealType, -0.99999997892657588),
tolerance); // diff 6.03558e-09 v 2.2204460492503131e-16
BOOST_CHECK_CLOSE_FRACTION( // Check float_next(float_next(-exp(-1) ))
lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.36787944117144222)),
BOOST_MATH_TEST_VALUE(RealType, -0.99999997419043196),
tolerance);// diff 2.30785e-09 v 2.2204460492503131e-16
// Comparison with Wolfram N[productlog(0,-0.36787944117144228 ), 17]
// Using conversion from double to higher precision cpp_bin_float_quad
using boost::multiprecision::cpp_bin_float_quad;
BOOST_CHECK_CLOSE_FRACTION( // Check float_next(-exp(-1) )
lambert_w0(BOOST_MATH_TEST_VALUE(cpp_bin_float_quad, -0.36787944117144228)),
BOOST_MATH_TEST_VALUE(RealType, -0.99999998496215738),
tolerance); // OK
BOOST_CHECK_CLOSE_FRACTION( // Check float_next(float_next(-exp(-1) ))
lambert_w0(BOOST_MATH_TEST_VALUE(cpp_bin_float_quad, -0.36787944117144222)),
BOOST_MATH_TEST_VALUE(RealType, -0.99999997649828679),
tolerance);// OK
// z increasingly close to singularity.
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.36)),
BOOST_MATH_TEST_VALUE(RealType, -0.8060843159708177782855213616209920019974599683466713016),
2 * tolerance); // -0.806084335
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.365)),
BOOST_MATH_TEST_VALUE(RealType, -0.8798200914159538111724840007674053239388642469453350954),
5 * tolerance); // Note 5 * tolerance
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.3678)),
BOOST_MATH_TEST_VALUE(RealType, -0.9793607149578284774761844434886481686055949229547379368),
15 * tolerance); // Note 15 * tolerance when this close to singularity.
// Just using series approximation (Fukushima switch at -0.35, but JM at 0.01 of singularity < -0.3679).
// N[productlog(-0.351), 50] = -0.72398644140937651483634596143951001600417138085814
// N[productlog(-0.351), 55] = -0.7239864414093765148363459614395100160041713808581379727
BOOST_CHECK_CLOSE_FRACTION(lambert_w0(BOOST_MATH_TEST_VALUE(RealType, -0.351)),
BOOST_MATH_TEST_VALUE(RealType, -0.72398644140937651483634596143951001600417138085814),
10 * tolerance); // Note was 2 * tolerance
// Check value just not using near_singularity series approximation (and using rational polynomial instead).
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.3)),
BOOST_MATH_TEST_VALUE(RealType, -1.7813370234216276119741702815127452608215583564545),
// Output from https://www.wolframalpha.com/input/
//N[productlog(-1, -0.3), 50] = -1.7813370234216276119741702815127452608215583564545
tolerance);
// Using table lookup and schroeder with decreasing z to zero.
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.2)),
BOOST_MATH_TEST_VALUE(RealType, -2.5426413577735264242938061566618482901614749075294),
// N[productlog[-1, -0.2],50] -2.5426413577735264242938061566618482901614749075294
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.1)),
BOOST_MATH_TEST_VALUE(RealType, -3.5771520639572972184093919635119948804017962577931),
//N[productlog(-1, -0.1), 50] = -3.5771520639572972184093919635119948804017962577931
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.001)),
BOOST_MATH_TEST_VALUE(RealType, -9.1180064704027401212583371820468142742704349737639),
// N[productlog(-1, -0.001), 50] = -9.1180064704027401212583371820468142742704349737639
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -0.000001)),
BOOST_MATH_TEST_VALUE(RealType, -16.626508901372473387706432163984684996461726803805),
// N[productlog(-1, -0.000001), 50] = -16.626508901372473387706432163984684996461726803805
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1e-6)),
BOOST_MATH_TEST_VALUE(RealType, -16.626508901372473387706432163984684996461726803805),
// N[productlog(-1, -10 ^ -6), 50] = -16.626508901372473387706432163984684996461726803805
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1.0e-26)),
BOOST_MATH_TEST_VALUE(RealType, -64.026509628385889681156090340691637712441162092868),
// Output from https://www.wolframalpha.com/input/
// N[productlog(-1, -1 * 10^-26 ), 50] = -64.026509628385889681156090340691637712441162092868
tolerance);
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -2e-26)),
BOOST_MATH_TEST_VALUE(RealType, -63.322302839923597803393585145387854867226970485197),
// N[productlog[-1, -2*10^-26],50] = -63.322302839923597803393585145387854867226970485197
tolerance *2);
// Smaller than lookup table, so must use approx and Halley refinements.
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -1e-30)),
BOOST_MATH_TEST_VALUE(RealType, -73.373110313822976797067478758120874529181611813766),
// N[productlog(-1, -10 ^ -30), 50] = -73.373110313822976797067478758120874529181611813766
tolerance);
// std::numeric_limits<RealType>::min
std::cout.precision(std::numeric_limits<RealType>::max_digits10);
std::cout << "(std::numeric_limits<RealType>::min)() " << (std::numeric_limits<RealType>::min)() << std::endl;
BOOST_CHECK_CLOSE_FRACTION(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, -2.2250738585072014e-308)),
BOOST_MATH_TEST_VALUE(RealType, -714.96865723796647086868547560654825435542227693935),
// N[productlog[-1, -2.2250738585072014e-308],50] = -714.96865723796647086868547560654825435542227693935
tolerance);
// For z = 0, W = -infinity
if (std::numeric_limits<RealType>::has_infinity)
{
BOOST_CHECK_EQUAL(lambert_wm1(BOOST_MATH_TEST_VALUE(RealType, 0.)),
-std::numeric_limits<RealType>::infinity());
}
} // BOOST_AUTO_TEST_CASE(test_range_of_double_values)
#ifdef BOOST_MATH_LAMBERT_W_INTEGRALS
BOOST_AUTO_TEST_CASE( integrals )
{
BOOST_TEST_MESSAGE("\nTest Lambert W integrals.");
try
{
// using statements needed to change precision policy.
using boost::math::policies::policy;
using boost::math::policies::make_policy;
using boost::math::policies::precision;
using boost::math::policies::digits2;
using boost::math::policies::digits10;
// using statements needed for changing error handling policy.
using boost::math::policies::evaluation_error;
using boost::math::policies::domain_error;
using boost::math::policies::overflow_error;
using boost::math::policies::ignore_error;
using boost::math::policies::throw_on_error;
typedef policy<
domain_error<throw_on_error>,
overflow_error<ignore_error>
> throw_policy;
double inf = std::numeric_limits<double>::infinity();
double max = (std::numeric_limits<double>::max)();
// With check in
std::cout << "lambert_w0(inf) = " << lambert_w0(inf) << std::endl; // lambert_w0(inf) = 1.79769e+308
std::cout << "lambert_w0(inf, throw_policy()) = " << lambert_w0(inf, throw_policy()) << std::endl; // inf
std::cout << "lambert_w0(max) = " << lambert_w0(max) << std::endl; // lambert_w0(max) = 703.227
//std::cout << lambert_w0(inf) << std::endl; // inf - will throw.
std::cout << "lambert_w0(0) = " << lambert_w0(0.) << std::endl; // 0
std::cout << "lambert_w0(std::numeric_limits<double>::denorm_min()) = " << lambert_w0(std::numeric_limits<double>::denorm_min()) << std::endl; // 4.94066e-324
std::cout << "lambert_w0(std::numeric_limits<double>::min()) = " << lambert_w0((std::numeric_limits<double>::min)()) << std::endl; // 2.22507e-308
// Approximate the largest lambert_w you can get for type T?
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.
std::cout << "w max_f " << max_w_f << std::endl; // 84.2879
double max_w = boost::math::lambert_w_detail::lambert_w0_approx((std::numeric_limits<double>::max)()); // Corless equation 4.19, page 349, and Chapeau-Blondeau equation 20, page 2162.
std::cout << "w max " << max_w << std::endl; // 703.227
std::cout << "test integral 1/z^2" << std::endl;
typedef double Real;
Real tol = std::numeric_limits<Real>::epsilon();
Real x;
{
using boost::math::quadrature::exp_sinh;
exp_sinh<Real> es;
auto f = [](Real z)->Real
{
Real zz = 1 / (z * z);
//if (zz >= boost::math::tools::max_value<Real>())
//{
// zz = boost::math::tools::max_value<Real>();
//}
return lambert_w0<Real>(zz); //
//return lambert_w0<Real>(zz, throw_policy()); // still fails because returns inf.
};
x = es.integrate(f);
std::cout << x << std::endl;
BOOST_CHECK_CLOSE_FRACTION(x, boost::math::constants::root_two_pi<Real>(), tol);
// root_two_pi<double = 2.506628274631000502
}
test_integrals<float>();
test_integrals<double>();
//test_integrals<long double>();
test_integrals<cpp_bin_float_quad>();
}
catch (std::exception& ex)
{
std::cout << ex.what() << std::endl;
}
}
#endif // BOOST_MATH_LAMBERT_W_INTEGRALS
/*
Output:
*/
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