/usr/include/boost/math/special_functions
Edit: /usr/include/boost/math/special_functions/sinhc.hpp (4643B)
// boost sinhc.hpp header file
// (C) Copyright Hubert Holin 2001.
// 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_SINHC_HPP
#define BOOST_SINHC_HPP
#ifdef _MSC_VER
#pragma once
#endif
#include
#include
#include
#include
#include
#include
#include
#include
// These are the the "Hyperbolic Sinus Cardinal" functions.
namespace boost
{
namespace math
{
namespace detail
{
// This is the "Hyperbolic Sinus Cardinal" of index Pi.
template
inline T sinhc_pi_imp(const T x)
{
#if defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC)
using ::abs;
using ::sinh;
using ::sqrt;
#else /* BOOST_NO_STDC_NAMESPACE */
using ::std::abs;
using ::std::sinh;
using ::std::sqrt;
#endif /* BOOST_NO_STDC_NAMESPACE */
static T const taylor_0_bound = tools::epsilon();
static T const taylor_2_bound = sqrt(taylor_0_bound);
static T const taylor_n_bound = sqrt(taylor_2_bound);
if (abs(x) >= taylor_n_bound)
{
return(sinh(x)/x);
}
else
{
// approximation by taylor series in x at 0 up to order 0
T result = static_cast(1);
if (abs(x) >= taylor_0_bound)
{
T x2 = x*x;
// approximation by taylor series in x at 0 up to order 2
result += x2/static_cast(6);
if (abs(x) >= taylor_2_bound)
{
// approximation by taylor series in x at 0 up to order 4
result += (x2*x2)/static_cast(120);
}
}
return(result);
}
}
} // namespace detail
template
inline typename tools::promote_args::type sinhc_pi(T x)
{
typedef typename tools::promote_args::type result_type;
return detail::sinhc_pi_imp(static_cast(x));
}
template
inline typename tools::promote_args::type sinhc_pi(T x, const Policy&)
{
return boost::math::sinhc_pi(x);
}
#ifdef BOOST_NO_TEMPLATE_TEMPLATES
#else /* BOOST_NO_TEMPLATE_TEMPLATES */
template class U>
inline U sinhc_pi(const U x)
{
#if defined(BOOST_FUNCTION_SCOPE_USING_DECLARATION_BREAKS_ADL) || defined(__GNUC__)
using namespace std;
#elif defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC)
using ::abs;
using ::sinh;
using ::sqrt;
#else /* BOOST_NO_STDC_NAMESPACE */
using ::std::abs;
using ::std::sinh;
using ::std::sqrt;
#endif /* BOOST_NO_STDC_NAMESPACE */
using ::std::numeric_limits;
static T const taylor_0_bound = tools::epsilon();
static T const taylor_2_bound = sqrt(taylor_0_bound);
static T const taylor_n_bound = sqrt(taylor_2_bound);
if (abs(x) >= taylor_n_bound)
{
return(sinh(x)/x);
}
else
{
// approximation by taylor series in x at 0 up to order 0
#ifdef __MWERKS__
U result = static_cast >(1);
#else
U result = U(1);
#endif
if (abs(x) >= taylor_0_bound)
{
U x2 = x*x;
// approximation by taylor series in x at 0 up to order 2
result += x2/static_cast(6);
if (abs(x) >= taylor_2_bound)
{
// approximation by taylor series in x at 0 up to order 4
result += (x2*x2)/static_cast(120);
}
}
return(result);
}
}
#endif /* BOOST_NO_TEMPLATE_TEMPLATES */
}
}
#endif /* BOOST_SINHC_HPP */