107 lines
3.7 KiB
C++
107 lines
3.7 KiB
C++
// 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 (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 */
|
|
|