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+// boost asinh.hpp header file
+
+// (C) Copyright Eric Ford 2001 & Hubert Holin.
+// (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_ACOSH_HPP
+#define BOOST_ACOSH_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 cosine 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
+
+ template<typename T, typename Policy>
+ inline T acosh_imp(const T x, const Policy& pol)
+ {
+ BOOST_MATH_STD_USING
+
+ if(x < 1)
+ {
+ return policies::raise_domain_error<T>(
+ "boost::math::acosh<%1%>(%1%)",
+ "acosh requires x >= 1, but got x = %1%.", x, pol);
+ }
+ else if ((x - 1) >= tools::root_epsilon<T>())
+ {
+ if (x > 1 / tools::root_epsilon<T>())
+ {
+ // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/
+ // approximation by laurent series in 1/x at 0+ order from -1 to 0
+ return( log( x * 2) );
+ }
+ else if(x < 1.5f)
+ {
+ // This is just a rearrangement of the standard form below
+ // devised to minimse loss of precision when x ~ 1:
+ T y = x - 1;
+ return boost::math::log1p(y + sqrt(y * y + 2 * y), pol);
+ }
+ else
+ {
+ // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
+ return( log( x + sqrt(x * x - 1) ) );
+ }
+ }
+ else
+ {
+ // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
+ T y = x - 1;
+
+ // approximation by taylor series in y at 0 up to order 2
+ T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160);
+ return result;
+ }
+ }
+ }
+
+ template<typename T, typename Policy>
+ inline typename tools::promote_args<T>::type acosh(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::acosh_imp(static_cast<value_type>(x), forwarding_policy()),
+ "boost::math::acosh<%1%>(%1%)");
+ }
+ template<typename T>
+ inline typename tools::promote_args<T>::type acosh(T x)
+ {
+ return boost::math::acosh(x, policies::policy<>());
+ }
+
+ }
+}
+
+#endif /* BOOST_ACOSH_HPP */
+
+