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// unit test file atanh.hpp for the special functions test suite
// (C) Copyright Hubert Holin 2003.
// 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)
#include <functional>
#include <iomanip>
//#include <iostream>
#include <boost/math/special_functions/atanh.hpp>
#include <boost/test/unit_test.hpp>
#include <boost/test/test_case_template.hpp>
template<typename T>
T atanh_error_evaluator(T x)
{
using ::std::abs;
using ::std::tanh;
using ::std::cosh;
using ::std::numeric_limits;
using ::boost::math::atanh;
static T const epsilon = numeric_limits<float>::epsilon();
T y = tanh(x);
T z = atanh(y);
T absolute_error = abs(z-x);
T relative_error = absolute_error/(cosh(x)*cosh(x));
T scaled_error = relative_error/epsilon;
return(scaled_error);
}
BOOST_TEST_CASE_TEMPLATE_FUNCTION(atanh_test, T)
{
using ::std::abs;
using ::std::tanh;
using ::std::log;
using ::std::numeric_limits;
using ::boost::math::atanh;
BOOST_MESSAGE("Testing atanh in the real domain for "
<< string_type_name<T>::_() << ".");
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(atanh<T>(static_cast<T>(0))))
(numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(atanh<T>(static_cast<T>(3)/5) - log(static_cast<T>(2))))
(numeric_limits<T>::epsilon()));
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(abs(atanh<T>(static_cast<T>(-3)/5) + log(static_cast<T>(2))))
(numeric_limits<T>::epsilon()));
for (int i = 0; i <= 100; i++)
{
T x = static_cast<T>(i-50)/static_cast<T>(5);
T y = tanh(x);
if (
(abs(y-static_cast<T>(1)) >= numeric_limits<T>::epsilon())&&
(abs(y+static_cast<T>(1)) >= numeric_limits<T>::epsilon())
)
{
BOOST_CHECK_PREDICATE(::std::less_equal<T>(),
(atanh_error_evaluator(x))
(static_cast<T>(4)));
}
}
}
void atanh_manual_check()
{
using ::std::abs;
using ::std::tanh;
using ::std::numeric_limits;
BOOST_MESSAGE(" ");
BOOST_MESSAGE("atanh");
for (int i = 0; i <= 100; i++)
{
float xf = static_cast<float>(i-50)/static_cast<float>(5);
double xd = static_cast<double>(i-50)/static_cast<double>(5);
long double xl =
static_cast<long double>(i-50)/static_cast<long double>(5);
float yf = tanh(xf);
double yd = tanh(xd);
(void) &yd; // avoid "unused variable" warning
long double yl = tanh(xl);
(void) &yl; // avoid "unused variable" warning
if (
std::numeric_limits<float>::has_infinity &&
std::numeric_limits<double>::has_infinity &&
std::numeric_limits<long double>::has_infinity
)
{
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
BOOST_MESSAGE( ::std::setw(15)
<< atanh_error_evaluator(xf)
<< ::std::setw(15)
<< atanh_error_evaluator(xd)
<< ::std::setw(15)
<< atanh_error_evaluator(xl));
#else
BOOST_MESSAGE( ::std::setw(15)
<< atanh_error_evaluator(xf)
<< ::std::setw(15)
<< atanh_error_evaluator(xd));
#endif
}
else
{
if (
(abs(yf-static_cast<float>(1)) <
numeric_limits<float>::epsilon())||
(abs(yf+static_cast<float>(1)) <
numeric_limits<float>::epsilon())||
(abs(yf-static_cast<double>(1)) <
numeric_limits<double>::epsilon())||
(abs(yf+static_cast<double>(1)) <
numeric_limits<double>::epsilon())||
(abs(yf-static_cast<long double>(1)) <
numeric_limits<long double>::epsilon())||
(abs(yf+static_cast<long double>(1)) <
numeric_limits<long double>::epsilon())
)
{
BOOST_MESSAGE("Platform's numerics may lack precision.");
}
else
{
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
BOOST_MESSAGE( ::std::setw(15)
<< atanh_error_evaluator(xf)
<< ::std::setw(15)
<< atanh_error_evaluator(xd)
<< ::std::setw(15)
<< atanh_error_evaluator(xl));
#else
BOOST_MESSAGE( ::std::setw(15)
<< atanh_error_evaluator(xf)
<< ::std::setw(15)
<< atanh_error_evaluator(xd));
#endif
}
}
}
BOOST_MESSAGE(" ");
}
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