You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and dots ('.'), can be up to 35 characters long. Letters must be lowercase.
128 lines
4.1 KiB
128 lines
4.1 KiB
// 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 */ |
|
|
|
|
|
|
|
|