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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/cstdint.hpp>
- #include <boost/exception/exception.hpp> // boost::exception
- #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::domain_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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