boost/math/special_functions/asinh.hpp
// boost asinh.hpp header file
// (C) Copyright Eric Ford & 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_ASINH_HPP
#define BOOST_ASINH_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/special_functions/math_fwd.hpp>
#include <boost/math/special_functions/sqrt1pm1.hpp>
#include <boost/math/special_functions/log1p.hpp>
#include <boost/math/constants/constants.hpp>
// This is the inverse of the hyperbolic sine function.
namespace boost
{
namespace math
{
namespace detail{
template<typename T, class Policy>
inline T asinh_imp(const T x, const Policy& pol)
{
BOOST_MATH_STD_USING
if((boost::math::isnan)(x))
{
return policies::raise_domain_error<T>(
"boost::math::asinh<%1%>(%1%)",
"asinh requires a finite argument, but got x = %1%.", x, pol);
}
if (x >= tools::forth_root_epsilon<T>())
{
if (x > 1 / tools::root_epsilon<T>())
{
// http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
// approximation by laurent series in 1/x at 0+ order from -1 to 1
return constants::ln_two<T>() + log(x) + 1/ (4 * x * x);
}
else if(x < 0.5f)
{
// As below, but rearranged to preserve digits:
return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);
}
else
{
// http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
return( log( x + sqrt(x*x+1) ) );
}
}
else if (x <= -tools::forth_root_epsilon<T>())
{
return(-asinh(-x, pol));
}
else
{
// http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
// 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>(6);
}
return(result);
}
}
}
template<typename T>
inline typename tools::promote_args<T>::type asinh(T x)
{
return boost::math::asinh(x, policies::policy<>());
}
template<typename T, typename Policy>
inline typename tools::promote_args<T>::type asinh(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::asinh_imp(static_cast<value_type>(x), forwarding_policy()),
"boost::math::asinh<%1%>(%1%)");
}
}
}
#endif /* BOOST_ASINH_HPP */