# Boost C++ Libraries

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### boost/math/special_functions/sinhc.hpp

```//  boost sinhc.hpp header file

//  (C) Copyright Hubert Holin 2001.
//  accompanying file LICENSE_1_0.txt or copy at

// 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 <boost/math/tools/precision.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <limits>
#include <string>
#include <stdexcept>
#include <cmath>

// These are the the "Hyperbolic Sinus Cardinal" functions.

namespace boost
{
namespace math
{
namespace detail
{
// This is the "Hyperbolic Sinus Cardinal" of index Pi.

template<typename T>
inline T    sinhc_pi_imp(const T x)
{
using    ::std::abs;
using    ::std::sinh;
using    ::std::sqrt;

static T const    taylor_0_bound = tools::epsilon<T>();
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<T>(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<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);
}
}

} // namespace detail

template <class T>
inline typename tools::promote_args<T>::type sinhc_pi(T x)
{
typedef typename tools::promote_args<T>::type result_type;
return detail::sinhc_pi_imp(static_cast<result_type>(x));
}

template <class T, class Policy>
inline typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&)
{
return boost::math::sinhc_pi(x);
}

template<typename T, template<typename> class U>
inline U<T>    sinhc_pi(const U<T> x)
{
using std::abs;
using std::sinh;
using std::sqrt;

using    ::std::numeric_limits;

static T const    taylor_0_bound = tools::epsilon<T>();
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<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);
}
}
}
}

#endif /* BOOST_SINHC_HPP */

```