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// Math extensions -*- 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 ext/math_util.h
* This file is a GNU extension to the Standard C++ Library.
*/
#ifndef _EXT_MATH_UTIL_H
#define _EXT_MATH_UTIL_H 1
#pragma GCC system_header
#if __cplusplus < 201103L
# include <bits/c++0x_warning.h>
#else
namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
/**
* A function to reliably compare two floating point numbers.
*
* @param __a The left hand side
* @param __b The right hand side
* @param __mul The multiplier for numeric epsilon for comparison
* @return @c true if a and b are equal to zero
* or differ only by @f$ max(a,b) * mul * epsilon @f$
*/
template<typename _Tp>
inline bool
__fpequal(_Tp __a, _Tp __b, _Tp __mul = _Tp{5})
{
const auto _S_eps = std::numeric_limits<_Tp>::epsilon();
const auto _S_tol = __mul * _S_eps;
bool __retval = true;
if ((__a != _Tp{0}) || (__b != _Tp{0}))
// Looks mean, but is necessary that the next line has sense.
__retval = (std::abs(__a - __b) < std::max(std::abs(__a),
std::abs(__b)) * _S_tol);
return __retval;
}
/**
* A function to reliably detect if a floating point number is an integer.
*
* @param __a The floating point number
* @return @c true if a is an integer within mul * epsilon.
*/
template<typename _Tp>
inline bool
__fpinteger(_Tp __a, _Tp __mul = _Tp{5})
{
auto __n = std::nearbyint(__a);
return __fpequal(__a, _Tp(__n), __mul);
}
/**
* A function to reliably detect if a floating point number is a half-integer.
*
* @param __a The floating point number
* @return @c true if 2*a is an integer within mul * epsilon.
*/
template<typename _Tp>
inline bool
__fp_half_integer(_Tp __a, _Tp __mul = _Tp{5})
{
auto __n = std::nearbyint(_Tp(2) * __a);
return __fpequal(_Tp(2) * __a, _Tp(__n), __mul);
}
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace __gnu_cxx
#endif // C++11
#endif // _EXT_MATH_UTIL_H
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