| // Copyright John Maddock 2006 |
| // Copyright Paul A. Bristow 2007 |
| // 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) |
| |
| #include <pch.hpp> |
| |
| #ifdef _MSC_VER |
| # pragma warning(disable : 4267) // conversion from 'size_t' to 'const unsigned int', possible loss of data |
| # pragma warning(disable : 4180) // qualifier applied to function type has no meaning; ignored |
| # pragma warning(disable : 4224) // nonstandard extension used : formal parameter 'function_ptr' was previously defined as a type |
| # pragma warning(disable : 4100) // unreferenced formal parameter (in ublas/functional) |
| #endif |
| |
| #include <boost/math/tools/remez.hpp> |
| #include <boost/test/test_exec_monitor.hpp> |
| #include <boost/test/floating_point_comparison.hpp> |
| #include <boost/math/special_functions/expm1.hpp> |
| |
| |
| void test_polynomial() |
| { |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| double (*f)(double) = boost::math::expm1<double>; |
| #else |
| double (*f)(double) = boost::math::expm1; |
| #endif |
| std::cout << "Testing expm1 approximation, pinned to origin, abolute error, 6 term polynomial\n"; |
| boost::math::tools::remez_minimax<double> approx1(f, 6, 0, -1, 1, true, false); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx1.iterate(); |
| std::cout << approx1.error_term() << " " << approx1.max_error() << " " << approx1.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| std::cout << "Testing expm1 approximation, pinned to origin, relative error, 6 term polynomial\n"; |
| boost::math::tools::remez_minimax<double> approx2(f, 6, 0, -1, 1, true, true); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx2.iterate(); |
| std::cout << approx2.error_term() << " " << approx2.max_error() << " " << approx2.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| |
| f = std::exp; |
| std::cout << "Testing exp approximation, not pinned to origin, abolute error, 6 term polynomial\n"; |
| boost::math::tools::remez_minimax<double> approx3(f, 6, 0, -1, 1, false, false); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx3.iterate(); |
| std::cout << approx3.error_term() << " " << approx3.max_error() << " " << approx3.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| std::cout << "Testing exp approximation, not pinned to origin, relative error, 6 term polynomial\n"; |
| boost::math::tools::remez_minimax<double> approx4(f, 6, 0, -1, 1, false, true); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx4.iterate(); |
| std::cout << approx4.error_term() << " " << approx4.max_error() << " " << approx4.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| |
| f = std::cos; |
| std::cout << "Testing cos approximation, not pinned to origin, abolute error, 5 term polynomial\n"; |
| boost::math::tools::remez_minimax<double> approx5(f, 5, 0, -1, 1, false, false); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx5.iterate(); |
| std::cout << approx5.error_term() << " " << approx5.max_error() << " " << approx5.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| std::cout << "Testing cos approximation, not pinned to origin, relative error, 5 term polynomial\n"; |
| boost::math::tools::remez_minimax<double> approx6(f, 5, 0, -1, 1, false, true); |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx6.iterate(); |
| std::cout << approx6.error_term() << " " << approx6.max_error() << " " << approx6.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| |
| f = std::sin; |
| std::cout << "Testing sin approximation, pinned to origin, abolute error, 4 term polynomial\n"; |
| boost::math::tools::remez_minimax<double> approx7(f, 4, 0, 0, 1, true, false); |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx7.iterate(); |
| std::cout << approx7.error_term() << " " << approx7.max_error() << " " << approx7.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| std::cout << "Testing sin approximation, pinned to origin, relative error, 4 term polynomial\n"; |
| boost::math::tools::remez_minimax<double> approx8(f, 4, 0, 0, 1, true, true); |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx8.iterate(); |
| std::cout << approx8.error_term() << " " << approx8.max_error() << " " << approx8.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| } |
| |
| void test_rational() |
| { |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| double (*f)(double) = boost::math::expm1<double>; |
| #else |
| double (*f)(double) = boost::math::expm1; |
| #endif |
| std::cout << "Testing expm1 approximation, pinned to origin, abolute error, 3+3 term rational\n"; |
| boost::math::tools::remez_minimax<double> approx1(f, 3, 3, -1, 1, true, false); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx1.iterate(); |
| std::cout << approx1.error_term() << " " << approx1.max_error() << " " << approx1.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| #if 0 |
| // |
| // This one causes UBLAS to fail on some systems, so disabled for now. |
| // |
| std::cout << "Testing expm1 approximation, pinned to origin, relative error, 3+3 term rational\n"; |
| boost::math::tools::remez_minimax<double> approx2(f, 3, 3, -1, 1, true, true); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx2.iterate(); |
| std::cout << approx2.error_term() << " " << approx2.max_error() << " " << approx2.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| #endif |
| f = std::exp; |
| std::cout << "Testing exp approximation, not pinned to origin, abolute error, 3+3 term rational\n"; |
| boost::math::tools::remez_minimax<double> approx3(f, 3, 3, -1, 1, false, false); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx3.iterate(); |
| std::cout << approx3.error_term() << " " << approx3.max_error() << " " << approx3.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| std::cout << "Testing exp approximation, not pinned to origin, relative error, 3+3 term rational\n"; |
| boost::math::tools::remez_minimax<double> approx4(f, 3, 3, -1, 1, false, true); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx4.iterate(); |
| std::cout << approx4.error_term() << " " << approx4.max_error() << " " << approx4.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| |
| f = std::cos; |
| std::cout << "Testing cos approximation, not pinned to origin, abolute error, 2+2 term rational\n"; |
| boost::math::tools::remez_minimax<double> approx5(f, 2, 2, 0, 1, false, false); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx5.iterate(); |
| std::cout << approx5.error_term() << " " << approx5.max_error() << " " << approx5.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| std::cout << "Testing cos approximation, not pinned to origin, relative error, 2+2 term rational\n"; |
| boost::math::tools::remez_minimax<double> approx6(f, 2, 2, 0, 1, false, true); |
| std::cout << "Interpolation Error: " << approx1.max_error() << std::endl; |
| for(unsigned i = 0; i < 7; ++i) |
| { |
| approx6.iterate(); |
| std::cout << approx6.error_term() << " " << approx6.max_error() << " " << approx6.max_change() << std::endl; |
| } |
| std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl; |
| } |
| |
| int test_main(int, char* []) |
| { |
| test_polynomial(); |
| test_rational(); |
| return 0; |
| } |
| |
| |