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// Copyright Paul A. Bristow 2016, 2018.
// 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).
//! Lambert W examples of controlling precision
// #define BOOST_MATH_INSTRUMENT_LAMBERT_W // #define only for (much) diagnostic output.
#include <boost/config.hpp> // for BOOST_PLATFORM, BOOST_COMPILER, BOOST_STDLIB ...
#include <boost/version.hpp> // for BOOST_MSVC versions.
#include <boost/math/constants/constants.hpp> // For exp_minus_one == 3.67879441171442321595523770161460867e-01.
#include <boost/math/policies/policy.hpp>
#include <boost/math/special_functions/next.hpp> // for float_distance.
#include <boost/math/special_functions/relative_difference.hpp> // for relative and epsilon difference.
// Built-in/fundamental GCC float128 or Intel Quad 128-bit type, if available.
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp> // Not available for MSVC.
// sets BOOST_MP_USE_FLOAT128 for GCC
using boost::multiprecision::float128;
#endif //# NOT _MSC_VER
#include <boost/multiprecision/cpp_dec_float.hpp> // boost::multiprecision::cpp_dec_float_50
using boost::multiprecision::cpp_dec_float_50; // 50 decimal digits type.
using boost::multiprecision::cpp_dec_float_100; // 100 decimal digits type.
#include <boost/multiprecision/cpp_bin_float.hpp>
using boost::multiprecision::cpp_bin_float_double_extended;
using boost::multiprecision::cpp_bin_float_double;
using boost::multiprecision::cpp_bin_float_quad;
// For lambert_w function.
#include <boost/math/special_functions/lambert_w.hpp>
// using boost::math::lambert_w0;
// using boost::math::lambert_wm1;
#include <iostream>
#include <exception>
#include <stdexcept>
#include <string>
#include <limits> // For std::numeric_limits.
int main()
{
try
{
std::cout << "Lambert W examples of precision control." << std::endl;
std::cout.precision(std::numeric_limits<double>::max_digits10);
std::cout << std::showpoint << std::endl; // Show any trailing zeros.
using boost::math::constants::exp_minus_one;
using boost::math::lambert_w0;
using boost::math::lambert_wm1;
// Error handling policy examples.
using namespace boost::math::policies;
using boost::math::policies::make_policy;
using boost::math::policies::policy;
using boost::math::policies::evaluation_error;
using boost::math::policies::domain_error;
using boost::math::policies::overflow_error;
using boost::math::policies::throw_on_error;
//[lambert_w_precision_reference_w
using boost::multiprecision::cpp_bin_float_50;
using boost::math::float_distance;
cpp_bin_float_50 z("10."); // Note use a decimal digit string, not a double 10.
cpp_bin_float_50 r;
std::cout.precision(std::numeric_limits<cpp_bin_float_50>::digits10);
r = lambert_w0(z); // Default policy.
std::cout << "lambert_w0(z) cpp_bin_float_50 = " << r << std::endl;
//lambert_w0(z) cpp_bin_float_50 = 1.7455280027406993830743012648753899115352881290809
// [N[productlog[10], 50]] == 1.7455280027406993830743012648753899115352881290809
std::cout.precision(std::numeric_limits<double>::max_digits10);
std::cout << "lambert_w0(z) static_cast from cpp_bin_float_50 = "
<< static_cast<double>(r) << std::endl;
// double lambert_w0(z) static_cast from cpp_bin_float_50 = 1.7455280027406994
// [N[productlog[10], 17]] == 1.7455280027406994
std::cout << "bits different from Wolfram = "
<< static_cast<int>(float_distance(static_cast<double>(r), 1.7455280027406994))
<< std::endl; // 0
//] [/lambert_w_precision_reference_w]
//[lambert_w_precision_0
std::cout.precision(std::numeric_limits<float>::max_digits10); // Show all potentially significant decimal digits,
std::cout << std::showpoint << std::endl; // and show any significant trailing zeros too.
float x = 10.;
std::cout << "Lambert W (" << x << ") = " << lambert_w0(x) << std::endl;
//] [/lambert_w_precision_0]
/*
//[lambert_w_precision_output_0
Lambert W (10.0000000) = 1.74552800
//] [/lambert_w_precision_output_0]
*/
{ // Lambert W0 Halley step example
//[lambert_w_precision_1
using boost::math::lambert_w_detail::lambert_w_halley_step;
using boost::math::epsilon_difference;
using boost::math::relative_difference;
std::cout << std::showpoint << std::endl; // and show any significant trailing zeros too.
std::cout.precision(std::numeric_limits<double>::max_digits10); // 17 decimal digits for double.
cpp_bin_float_50 z50("1.23"); // Note: use a decimal digit string, not a double 1.23!
double z = static_cast<double>(z50);
cpp_bin_float_50 w50;
w50 = lambert_w0(z50);
std::cout.precision(std::numeric_limits<cpp_bin_float_50>::max_digits10); // 50 decimal digits.
std::cout << "Reference Lambert W (" << z << ") =\n "
<< w50 << std::endl;
std::cout.precision(std::numeric_limits<double>::max_digits10); // 17 decimal digits for double.
double wr = static_cast<double>(w50);
std::cout << "Reference Lambert W (" << z << ") = " << wr << std::endl;
double w = lambert_w0(z);
std::cout << "Rat/poly Lambert W (" << z << ") = " << lambert_w0(z) << std::endl;
// Add a Halley step to the value obtained from rational polynomial approximation.
double ww = lambert_w_halley_step(lambert_w0(z), z);
std::cout << "Halley Step Lambert W (" << z << ") = " << lambert_w_halley_step(lambert_w0(z), z) << std::endl;
std::cout << "absolute difference from Halley step = " << w - ww << std::endl;
std::cout << "relative difference from Halley step = " << relative_difference(w, ww) << std::endl;
std::cout << "epsilon difference from Halley step = " << epsilon_difference(w, ww) << std::endl;
std::cout << "epsilon for float = " << std::numeric_limits<double>::epsilon() << std::endl;
std::cout << "bits different from Halley step = " << static_cast<int>(float_distance(w, ww)) << std::endl;
//] [/lambert_w_precision_1]
/*
//[lambert_w_precision_output_1
Reference Lambert W (1.2299999999999999822364316059974953532218933105468750) =
0.64520356959320237759035605255334853830173300262666480
Reference Lambert W (1.2300000000000000) = 0.64520356959320235
Rat/poly Lambert W (1.2300000000000000) = 0.64520356959320224
Halley Step Lambert W (1.2300000000000000) = 0.64520356959320235
absolute difference from Halley step = -1.1102230246251565e-16
relative difference from Halley step = 1.7207329236029286e-16
epsilon difference from Halley step = 0.77494921535422934
epsilon for float = 2.2204460492503131e-16
bits different from Halley step = 1
//] [/lambert_w_precision_output_1]
*/
} // Lambert W0 Halley step example
{ // Lambert W-1 Halley step example
//[lambert_w_precision_2
using boost::math::lambert_w_detail::lambert_w_halley_step;
using boost::math::epsilon_difference;
using boost::math::relative_difference;
std::cout << std::showpoint << std::endl; // and show any significant trailing zeros too.
std::cout.precision(std::numeric_limits<double>::max_digits10); // 17 decimal digits for double.
cpp_bin_float_50 z50("-0.123"); // Note: use a decimal digit string, not a double -1.234!
double z = static_cast<double>(z50);
cpp_bin_float_50 wm1_50;
wm1_50 = lambert_wm1(z50);
std::cout.precision(std::numeric_limits<cpp_bin_float_50>::max_digits10); // 50 decimal digits.
std::cout << "Reference Lambert W-1 (" << z << ") =\n "
<< wm1_50 << std::endl;
std::cout.precision(std::numeric_limits<double>::max_digits10); // 17 decimal digits for double.
double wr = static_cast<double>(wm1_50);
std::cout << "Reference Lambert W-1 (" << z << ") = " << wr << std::endl;
double w = lambert_wm1(z);
std::cout << "Rat/poly Lambert W-1 (" << z << ") = " << lambert_wm1(z) << std::endl;
// Add a Halley step to the value obtained from rational polynomial approximation.
double ww = lambert_w_halley_step(lambert_wm1(z), z);
std::cout << "Halley Step Lambert W (" << z << ") = " << lambert_w_halley_step(lambert_wm1(z), z) << std::endl;
std::cout << "absolute difference from Halley step = " << w - ww << std::endl;
std::cout << "relative difference from Halley step = " << relative_difference(w, ww) << std::endl;
std::cout << "epsilon difference from Halley step = " << epsilon_difference(w, ww) << std::endl;
std::cout << "epsilon for float = " << std::numeric_limits<double>::epsilon() << std::endl;
std::cout << "bits different from Halley step = " << static_cast<int>(float_distance(w, ww)) << std::endl;
//] [/lambert_w_precision_2]
}
/*
//[lambert_w_precision_output_2
Reference Lambert W-1 (-0.12299999999999999822364316059974953532218933105468750) =
-3.2849102557740360179084675531714935199110302996513384
Reference Lambert W-1 (-0.12300000000000000) = -3.2849102557740362
Rat/poly Lambert W-1 (-0.12300000000000000) = -3.2849102557740357
Halley Step Lambert W (-0.12300000000000000) = -3.2849102557740362
absolute difference from Halley step = 4.4408920985006262e-16
relative difference from Halley step = 1.3519066740696092e-16
epsilon difference from Halley step = 0.60884463935795785
epsilon for float = 2.2204460492503131e-16
bits different from Halley step = -1
//] [/lambert_w_precision_output_2]
*/
// Similar example using cpp_bin_float_quad (128-bit floating-point types).
cpp_bin_float_quad zq = 10.;
std::cout << "\nTest evaluation of cpp_bin_float_quad Lambert W(" << zq << ")"
<< std::endl;
std::cout << std::setprecision(3) << "std::numeric_limits<cpp_bin_float_quad>::digits = " << std::numeric_limits<cpp_bin_float_quad>::digits << std::endl;
std::cout << std::setprecision(3) << "std::numeric_limits<cpp_bin_float_quad>::epsilon() = " << std::numeric_limits<cpp_bin_float_quad>::epsilon() << std::endl;
std::cout << std::setprecision(3) << "std::numeric_limits<cpp_bin_float_quad>::max_digits10 = " << std::numeric_limits<cpp_bin_float_quad>::max_digits10 << std::endl;
std::cout << std::setprecision(3) << "std::numeric_limits<cpp_bin_float_quad>::digits10 = " << std::numeric_limits<cpp_bin_float_quad>::digits10 << std::endl;
std::cout.precision(std::numeric_limits<cpp_bin_float_quad>::max_digits10);
// All are same precision because double precision first approximation used before Halley.
/*
*/
{ // Reference value for lambert_w0(10)
cpp_dec_float_50 z("10");
cpp_dec_float_50 r;
std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
r = lambert_w0(z); // Default policy.
std::cout << "lambert_w0(z) cpp_dec_float_50 = " << r << std::endl; // 0.56714329040978387299996866221035554975381578718651
std::cout.precision(std::numeric_limits<cpp_bin_float_quad>::max_digits10);
std::cout << "lambert_w0(z) cpp_dec_float_50 cast to quad (max_digits10(" << std::numeric_limits<cpp_bin_float_quad>::max_digits10 <<
" ) = " << static_cast<cpp_bin_float_quad>(r) << std::endl; // 1.7455280027406993830743012648753899115352881290809
std::cout.precision(std::numeric_limits<cpp_bin_float_quad>::digits10); // 1.745528002740699383074301264875389837
std::cout << "lambert_w0(z) cpp_dec_float_50 cast to quad (digits10(" << std::numeric_limits<cpp_bin_float_quad>::digits10 <<
" ) = " << static_cast<cpp_bin_float_quad>(r) << std::endl; // 1.74552800274069938307430126487539
std::cout.precision(std::numeric_limits<cpp_bin_float_quad>::digits10 + 1); //
std::cout << "lambert_w0(z) cpp_dec_float_50 cast to quad (digits10(" << std::numeric_limits<cpp_bin_float_quad>::digits10 <<
" ) = " << static_cast<cpp_bin_float_quad>(r) << std::endl; // 1.74552800274069938307430126487539
// [N[productlog[10], 50]] == 1.7455280027406993830743012648753899115352881290809
// [N[productlog[10], 37]] == 1.745528002740699383074301264875389912
// [N[productlog[10], 34]] == 1.745528002740699383074301264875390
// [N[productlog[10], 33]] == 1.74552800274069938307430126487539
// lambert_w0(z) cpp_dec_float_50 cast to quad = 1.745528002740699383074301264875389837
// lambert_w0(z) cpp_dec_float_50 = 1.7455280027406993830743012648753899115352881290809
// lambert_w0(z) cpp_dec_float_50 cast to quad = 1.745528002740699383074301264875389837
// lambert_w0(z) cpp_dec_float_50 cast to quad = 1.74552800274069938307430126487539
}
}
catch (std::exception& ex)
{
std::cout << ex.what() << std::endl;
}
} // int main()
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