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+// 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 */
+
+
+