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// TR29124 math special functions -*- C++ -*-
// Copyright (C) 2016 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
// <http://www.gnu.org/licenses/>.
/** @file bits/sf_airy.tcc
* This is an internal header file, included by other library headers.
* You should not attempt to use it directly.
*/
#ifndef _GLIBCXX_BITS_SF_CARDINAL_TCC
#define _GLIBCXX_BITS_SF_CARDINAL_TCC 1
#pragma GCC system_header
#include <bits/complex_util.h>
namespace std _GLIBCXX_VISIBILITY(default)
{
// Implementation-space details.
namespace __detail
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
/**
* @brief Return the sinus cardinal function
* @f[
* sinc(x) = \frac{\sin(x)}{x}
* @f]
*/
template<typename _Tp>
__gnu_cxx::__promote_fp_t<_Tp>
__sinc(_Tp __x)
{
if (__isnan(__x))
return __gnu_cxx::__quiet_NaN<_Tp>();
else if (std::abs(__x) == __gnu_cxx::__infinity<_Tp>())
return _Tp{0};
else if (std::abs(__x) < __gnu_cxx::__sqrt_min<_Tp>())
return _Tp{1} - __x * __x / _Tp{6};
else
return std::sin(__x) / __x;
}
/**
* @brief Return the reperiodized sinus cardinal function
* @f[
* sinc_\pi(x) = \frac{\sin(\pi x)}{\pi x}
* @f]
*/
template<typename _Tp>
__gnu_cxx::__promote_fp_t<_Tp>
__sinc_pi(_Tp __x)
{
constexpr auto _S_pi = __gnu_cxx::__math_constants<_Tp>::__pi;
if (__isnan(__x))
return __gnu_cxx::__quiet_NaN<_Tp>();
else if (std::abs(__x) == __gnu_cxx::__infinity<_Tp>())
return _Tp{0};
else
{
auto __arg = _S_pi * __x;
if (std::abs(__arg) < _Tp{4} * __gnu_cxx::__sqrt_min<_Tp>())
return _Tp{1} - __arg * __arg / _Tp{6};
else
return __sin_pi(__x) / __arg;
}
}
/**
* @brief Return the hyperbolic sinus cardinal function
* @f[
* sinhc(x) = \frac{\sinh(x)}{x}
* @f]
*/
template<typename _Tp>
__gnu_cxx::__promote_fp_t<_Tp>
__sinhc(_Tp __x)
{
if (__isnan(__x))
return __gnu_cxx::__quiet_NaN<_Tp>();
else if (std::abs(__x) < _Tp{4} * __gnu_cxx::__sqrt_min<_Tp>())
return _Tp{1} + __x * __x / _Tp{6};
else
return std::sinh(__x) / __x;
}
/**
* @brief Return the reperiodized hyperbolic sinus cardinal function
* @f[
* sinhc_\pi(x) = \frac{\sinh(\pi x)}{\pi x}
* @f]
*/
template<typename _Tp>
__gnu_cxx::__promote_fp_t<_Tp>
__sinhc_pi(_Tp __x)
{
constexpr auto _S_pi = __gnu_cxx::__math_constants<_Tp>::__pi;
if (__isnan(__x))
return __gnu_cxx::__quiet_NaN<_Tp>();
else
{
auto __arg = _S_pi * __x;
if (std::abs(__arg) < _Tp{4} * __gnu_cxx::__sqrt_min<_Tp>())
return _Tp{1} + __arg * __arg / _Tp{6};
else
return __sinh_pi(__x) / __arg;
}
}
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace __detail
} // namespace std
#endif // _GLIBCXX_BITS_SF_CARDINAL_TCC
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