// boost atanh.hpp header file | |
// (C) Copyright Hubert Holin 2001. | |
// (C) Copyright John Maddock 2008. | |
// 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) | |
// See http://www.boost.org for updates, documentation, and revision history. | |
#ifndef BOOST_ATANH_HPP | |
#define BOOST_ATANH_HPP | |
#ifdef _MSC_VER | |
#pragma once | |
#endif | |
#include <boost/config/no_tr1/cmath.hpp> | |
#include <boost/config.hpp> | |
#include <boost/math/tools/precision.hpp> | |
#include <boost/math/policies/error_handling.hpp> | |
#include <boost/math/special_functions/math_fwd.hpp> | |
#include <boost/math/special_functions/log1p.hpp> | |
// This is the inverse of the hyperbolic tangent function. | |
namespace boost | |
{ | |
namespace math | |
{ | |
namespace detail | |
{ | |
#if defined(__GNUC__) && (__GNUC__ < 3) | |
// gcc 2.x ignores function scope using declarations, | |
// put them in the scope of the enclosing namespace instead: | |
using ::std::abs; | |
using ::std::sqrt; | |
using ::std::log; | |
using ::std::numeric_limits; | |
#endif | |
// This is the main fare | |
template<typename T, typename Policy> | |
inline T atanh_imp(const T x, const Policy& pol) | |
{ | |
BOOST_MATH_STD_USING | |
static const char* function = "boost::math::atanh<%1%>(%1%)"; | |
if(x < -1) | |
{ | |
return policies::raise_domain_error<T>( | |
function, | |
"atanh requires x >= -1, but got x = %1%.", x, pol); | |
} | |
else if(x < -1 + tools::epsilon<T>()) | |
{ | |
// -Infinity: | |
return -policies::raise_overflow_error<T>(function, 0, pol); | |
} | |
else if(x > 1 - tools::epsilon<T>()) | |
{ | |
// Infinity: | |
return -policies::raise_overflow_error<T>(function, 0, pol); | |
} | |
else if(x > 1) | |
{ | |
return policies::raise_domain_error<T>( | |
function, | |
"atanh requires x <= 1, but got x = %1%.", x, pol); | |
} | |
else if(abs(x) >= tools::forth_root_epsilon<T>()) | |
{ | |
// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/ | |
if(abs(x) < 0.5f) | |
return (boost::math::log1p(x, pol) - boost::math::log1p(-x, pol)) / 2; | |
return(log( (1 + x) / (1 - x) ) / 2); | |
} | |
else | |
{ | |
// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/ | |
// approximation by taylor series in x at 0 up to order 2 | |
T result = x; | |
if (abs(x) >= tools::root_epsilon<T>()) | |
{ | |
T x3 = x*x*x; | |
// approximation by taylor series in x at 0 up to order 4 | |
result += x3/static_cast<T>(3); | |
} | |
return(result); | |
} | |
} | |
} | |
template<typename T, typename Policy> | |
inline typename tools::promote_args<T>::type atanh(T x, const Policy&) | |
{ | |
typedef typename tools::promote_args<T>::type result_type; | |
typedef typename policies::evaluation<result_type, Policy>::type value_type; | |
typedef typename policies::normalise< | |
Policy, | |
policies::promote_float<false>, | |
policies::promote_double<false>, | |
policies::discrete_quantile<>, | |
policies::assert_undefined<> >::type forwarding_policy; | |
return policies::checked_narrowing_cast<result_type, forwarding_policy>( | |
detail::atanh_imp(static_cast<value_type>(x), forwarding_policy()), | |
"boost::math::atanh<%1%>(%1%)"); | |
} | |
template<typename T> | |
inline typename tools::promote_args<T>::type atanh(T x) | |
{ | |
return boost::math::atanh(x, policies::policy<>()); | |
} | |
} | |
} | |
#endif /* BOOST_ATANH_HPP */ | |