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// boost sinc.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_SINC_HPP
#define BOOST_SINC_HPP
#ifdef _MSC_VER
#pragma once
#endif
#include <boost/math/tools/config.hpp>
#include <boost/math/tools/precision.hpp>
#include <boost/math/policies/policy.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/config/no_tr1/cmath.hpp>
#include <boost/limits.hpp>
#include <string>
#include <stdexcept>
#include <boost/config.hpp>
// These are the the "Sinus Cardinal" functions.
namespace boost
{
namespace math
{
namespace detail
{
// This is the "Sinus Cardinal" of index Pi.
template<typename T>
inline T sinc_pi_imp(const T x)
{
BOOST_MATH_STD_USING
if (abs(x) >= 3.3 * tools::forth_root_epsilon<T>())
{
return(sin(x)/x);
}
else
{
// |x| < (eps*120)^(1/4)
return 1 - x * x / 6;
}
}
} // namespace detail
template <class T>
inline typename tools::promote_args<T>::type sinc_pi(T x)
{
typedef typename tools::promote_args<T>::type result_type;
return detail::sinc_pi_imp(static_cast<result_type>(x));
}
template <class T, class Policy>
inline typename tools::promote_args<T>::type sinc_pi(T x, const Policy&)
{
typedef typename tools::promote_args<T>::type result_type;
return detail::sinc_pi_imp(static_cast<result_type>(x));
}
#ifndef BOOST_NO_TEMPLATE_TEMPLATES
template<typename T, template<typename> class U>
inline U<T> sinc_pi(const U<T> x)
{
BOOST_MATH_STD_USING
using ::std::numeric_limits;
T const taylor_0_bound = tools::epsilon<T>();
T const taylor_2_bound = tools::root_epsilon<T>();
T const taylor_n_bound = tools::forth_root_epsilon<T>();
if (abs(x) >= taylor_n_bound)
{
return(sin(x)/x);
}
else
{
// approximation by taylor series in x at 0 up to order 0
#ifdef __MWERKS__
U<T> result = static_cast<U<T> >(1);
#else
U<T> result = U<T>(1);
#endif
if (abs(x) >= taylor_0_bound)
{
U<T> x2 = x*x;
// approximation by taylor series in x at 0 up to order 2
result -= x2/static_cast<T>(6);
if (abs(x) >= taylor_2_bound)
{
// approximation by taylor series in x at 0 up to order 4
result += (x2*x2)/static_cast<T>(120);
}
}
return(result);
}
}
template<typename T, template<typename> class U, class Policy>
inline U<T> sinc_pi(const U<T> x, const Policy&)
{
return sinc_pi(x);
}
#endif /* BOOST_NO_TEMPLATE_TEMPLATES */
}
}
#endif /* BOOST_SINC_HPP */
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