/usr/include/boost/math/special_functions
Edit: /usr/include/boost/math/special_functions/acosh.hpp (3693B)
// boost asinh.hpp header file
// (C) Copyright Eric Ford 2001.
// (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_ACOSH_HPP
#define BOOST_ACOSH_HPP
#ifdef _MSC_VER
#pragma once
#endif
#include
#include
#include
#include
#include
#include
#include
// This is the inverse of the hyperbolic cosine function.
namespace boost
{
namespace math
{
namespace detail
{
template
inline T acosh_imp(const T x, const Policy& pol)
{
BOOST_MATH_STD_USING
if((x < 1) || (boost::math::isnan)(x))
{
return policies::raise_domain_error(
"boost::math::acosh<%1%>(%1%)",
"acosh requires x >= 1, but got x = %1%.", x, pol);
}
else if ((x - 1) >= tools::root_epsilon())
{
if (x > 1 / tools::root_epsilon())
{
// 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) + constants::ln_two();
}
else if(x < 1.5f)
{
// This is just a rearrangement of the standard form below
// devised to minimise 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
inline typename tools::promote_args::type acosh(T x, const Policy&)
{
typedef typename tools::promote_args::type result_type;
typedef typename policies::evaluation::type value_type;
typedef typename policies::normalise<
Policy,
policies::promote_float,
policies::promote_double,
policies::discrete_quantile<>,
policies::assert_undefined<> >::type forwarding_policy;
return policies::checked_narrowing_cast(
detail::acosh_imp(static_cast(x), forwarding_policy()),
"boost::math::acosh<%1%>(%1%)");
}
template
inline typename tools::promote_args::type acosh(T x)
{
return boost::math::acosh(x, policies::policy<>());
}
}
}
#endif /* BOOST_ACOSH_HPP */