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// 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>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/special_functions/expm1.hpp>
#include <iostream>
#include <iomanip>
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, absolute 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, absolute 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, absolute 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, absolute 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, absolute 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, absolute 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, absolute 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;
}
BOOST_AUTO_TEST_CASE( test_main )
{
test_polynomial();
test_rational();
}
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