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// boost atanh.hpp header file
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// (C) Copyright Hubert Holin 2001.
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// See http://www.boost.org for updates, documentation, and revision history.
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#ifndef BOOST_ATANH_HPP
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#define BOOST_ATANH_HPP
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#include <cmath>
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#include <limits>
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#include <string>
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#include <stdexcept>
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#include <boost/config.hpp>
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// This is the inverse of the hyperbolic tangent function.
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namespace boost
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{
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namespace math
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{
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#if defined(__GNUC__) && (__GNUC__ < 3)
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// gcc 2.x ignores function scope using declarations,
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// put them in the scope of the enclosing namespace instead:
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using ::std::abs;
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using ::std::sqrt;
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using ::std::log;
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using ::std::numeric_limits;
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#endif
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#if defined(BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION)
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// This is the main fare
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template<typename T>
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inline T atanh(const T x)
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{
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using ::std::abs;
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using ::std::sqrt;
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using ::std::log;
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using ::std::numeric_limits;
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T const one = static_cast<T>(1);
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T const two = static_cast<T>(2);
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static T const taylor_2_bound = sqrt(numeric_limits<T>::epsilon());
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static T const taylor_n_bound = sqrt(taylor_2_bound);
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if (x < -one)
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{
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if (numeric_limits<T>::has_quiet_NaN)
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{
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return(numeric_limits<T>::quiet_NaN());
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}
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else
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{
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::std::string error_reporting("Argument to atanh is strictly greater than +1 or strictly smaller than -1!");
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::std::domain_error bad_argument(error_reporting);
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throw(bad_argument);
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}
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}
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else if (x < -one+numeric_limits<T>::epsilon())
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{
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if (numeric_limits<T>::has_infinity)
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{
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return(-numeric_limits<T>::infinity());
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}
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else
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{
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::std::string error_reporting("Argument to atanh is -1 (result: -Infinity)!");
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::std::out_of_range bad_argument(error_reporting);
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throw(bad_argument);
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}
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}
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else if (x > +one-numeric_limits<T>::epsilon())
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{
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if (numeric_limits<T>::has_infinity)
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{
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return(+numeric_limits<T>::infinity());
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}
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else
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{
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::std::string error_reporting("Argument to atanh is +1 (result: +Infinity)!");
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::std::out_of_range bad_argument(error_reporting);
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throw(bad_argument);
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}
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}
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else if (x > +one)
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{
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if (numeric_limits<T>::has_quiet_NaN)
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{
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return(numeric_limits<T>::quiet_NaN());
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}
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else
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{
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::std::string error_reporting("Argument to atanh is strictly greater than +1 or strictly smaller than -1!");
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::std::domain_error bad_argument(error_reporting);
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throw(bad_argument);
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}
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}
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else if (abs(x) >= taylor_n_bound)
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{
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return(log( (one + x) / (one - x) ) / two);
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}
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else
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{
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// approximation by taylor series in x at 0 up to order 2
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T result = x;
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if (abs(x) >= taylor_2_bound)
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{
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T x3 = x*x*x;
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// approximation by taylor series in x at 0 up to order 4
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result += x3/static_cast<T>(3);
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}
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return(result);
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}
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}
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#else
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// These are implementation details (for main fare see below)
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namespace detail
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{
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template <
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typename T,
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bool InfinitySupported
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>
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struct atanh_helper1_t
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{
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static T get_pos_infinity()
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{
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return(+::std::numeric_limits<T>::infinity());
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}
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static T get_neg_infinity()
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{
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return(-::std::numeric_limits<T>::infinity());
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}
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}; // boost::math::detail::atanh_helper1_t
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template<typename T>
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struct atanh_helper1_t<T, false>
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{
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static T get_pos_infinity()
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{
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::std::string error_reporting("Argument to atanh is +1 (result: +Infinity)!");
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::std::out_of_range bad_argument(error_reporting);
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throw(bad_argument);
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}
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static T get_neg_infinity()
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{
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::std::string error_reporting("Argument to atanh is -1 (result: -Infinity)!");
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::std::out_of_range bad_argument(error_reporting);
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throw(bad_argument);
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}
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}; // boost::math::detail::atanh_helper1_t
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template <
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typename T,
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bool QuietNanSupported
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>
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struct atanh_helper2_t
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{
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static T get_NaN()
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{
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return(::std::numeric_limits<T>::quiet_NaN());
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}
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}; // boost::detail::atanh_helper2_t
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template<typename T>
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struct atanh_helper2_t<T, false>
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{
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static T get_NaN()
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{
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::std::string error_reporting("Argument to atanh is strictly greater than +1 or strictly smaller than -1!");
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::std::domain_error bad_argument(error_reporting);
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throw(bad_argument);
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}
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}; // boost::detail::atanh_helper2_t
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} // boost::detail
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// This is the main fare
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template<typename T>
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inline T atanh(const T x)
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{
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using ::std::abs;
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using ::std::sqrt;
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using ::std::log;
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using ::std::numeric_limits;
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typedef detail::atanh_helper1_t<T, ::std::numeric_limits<T>::has_infinity> helper1_type;
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typedef detail::atanh_helper2_t<T, ::std::numeric_limits<T>::has_quiet_NaN> helper2_type;
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T const one = static_cast<T>(1);
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T const two = static_cast<T>(2);
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static T const taylor_2_bound = sqrt(numeric_limits<T>::epsilon());
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static T const taylor_n_bound = sqrt(taylor_2_bound);
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if (x < -one)
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{
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return(helper2_type::get_NaN());
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}
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else if (x < -one+numeric_limits<T>::epsilon())
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{
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return(helper1_type::get_neg_infinity());
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}
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else if (x > +one-numeric_limits<T>::epsilon())
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{
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return(helper1_type::get_pos_infinity());
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}
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else if (x > +one)
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{
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return(helper2_type::get_NaN());
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}
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else if (abs(x) >= taylor_n_bound)
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{
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return(log( (one + x) / (one - x) ) / two);
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}
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else
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{
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// approximation by taylor series in x at 0 up to order 2
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T result = x;
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if (abs(x) >= taylor_2_bound)
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{
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T x3 = x*x*x;
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// approximation by taylor series in x at 0 up to order 4
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result += x3/static_cast<T>(3);
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}
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return(result);
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}
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}
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#endif /* defined(BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION) */
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}
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}
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#endif /* BOOST_ATANH_HPP */
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