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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2011, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program 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 2 of the *
* License, or (at your option) any later version. *
* *
* This program 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. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
/*! \file maths/approx.h
* \brief Provides facilities for working around rounding errors when
* dealing with real numbers.
*/
#ifndef __APPROX_H
#ifndef __DOXYGEN
#define __APPROX_H
#endif
#include "regina-core.h"
namespace regina {
/**
* \weakgroup maths
* @{
*/
/**
* A very small positive real designed to accommodate for rounding error.
* Any two numbers within \a epsilon of each other are considered to be
* equal by the generic zero-testing and sign-testing routines defined in
* this file (isZero(), isPositive(), isNonNegative() and so on).
*/
REGINA_API extern const double epsilon;
/**
* Determines whether the given real number is zero.
* Any number within \a regina::epsilon of zero is considered to be zero.
*
* \pre R must be of a floating point real type.
*
* \ifacespython Not present.
*
* @param x the number to examine.
* @return \c true if and only if the given number is approximately zero.
*/
template <class R>
inline bool isZero(R x) {
return (x > -epsilon && x < epsilon);
}
/**
* Determines whether the given real number is non-zero.
* Any number within \a regina::epsilon of zero is considered to be zero.
*
* \pre R must be of a floating point real type.
*
* \ifacespython Not present.
*
* @param x the number to examine.
* @return \c true if and only if the given number is approximately non-zero.
*/
template <class R>
inline bool isNonZero(R x) {
return (x < -epsilon || x > epsilon);
}
/**
* Determines whether the given real number is strictly positive.
* Any number within \a regina::epsilon of zero is considered to be zero.
*
* \pre R must be of a floating point real type.
*
* \ifacespython Not present.
*
* @param x the number to examine.
* @return \c true if and only if the given number is strictly positive.
*/
template <class R>
inline bool isPositive(R x) {
return (x > epsilon);
}
/**
* Determines whether the given real number is strictly negative.
* Any number within \a regina::epsilon of zero is considered to be zero.
*
* \pre R must be of a floating point real type.
*
* \ifacespython Not present.
*
* @param x the number to examine.
* @return \c true if and only if the given number is strictly negative.
*/
template <class R>
inline bool isNegative(R x) {
return (x < -epsilon);
}
/**
* Determines whether the given real number is non-negative.
* Any number within \a regina::epsilon of zero is considered to be zero.
*
* \pre R must be of a floating point real type.
*
* \ifacespython Not present.
*
* @param x the number to examine.
* @return \c true if and only if the given number is non-negative.
*/
template <class R>
inline bool isNonNegative(R x) {
return (x > -epsilon);
}
/**
* Determines whether the given real number is non-positive.
* Any number within \a regina::epsilon of zero is considered to be zero.
*
* \pre R must be of a floating point real type.
*
* \ifacespython Not present.
*
* @param x the number to examine.
* @return \c true if and only if the given number is non-positive.
*/
template <class R>
inline bool isNonPositive(R x) {
return (x < epsilon);
}
/*@}*/
} // namespace regina
#endif
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