Interval.h File Reference

Interval Arithmetics Interface. More...

#include <iostream>
#include "capd/basicalg/minmax.h"
#include "capd/intervals/IntervalSettings.h"
#include "capd/intervals/IntervalError.h"
#include "capd/basicalg/TypeTraits.h"
#include "capd/rounding/RoundingTraits.h"
#include "capd/intervals/IntervalTraits.h"
#include "capd/basicalg/doubleFun.h"
#include "capd/intervals/Interval_Friend.h"
#include "capd/intervals/Interval_FriendInternal.h"
#include "capd/intervals/Interval_Base.h"
#include "capd/intervals/Interval_Deprecated.h"
#include "capd/intervals/Interval_Op.hpp"

Classes
class	capd::intervals::Interval< T_Bound, T_Rnd >
	Definition of template class Interval. More...
class	capd::TypeTraits< ::capd::intervals::Interval< T, RT > >
	Specialization of TypeTraits for intervals. More...

Namespaces
	capd
	capd::intervals
	Interval arithmetics.

Functions
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::diam (const Interval< T_Bound, T_Rnd > &A_iVal)
	upper bound for a diameter of an interval More...
template<typename T_Bound , typename T_Rnd >
T_Bound	capd::intervals::width (const Interval< T_Bound, T_Rnd > &A_iVal)
	non-rigorous diameter of an interval More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::mid (const Interval< T_Bound, T_Rnd > &A_iv)
template<typename T_Bound , typename T_Rnd >
bool	capd::intervals::intersection (Interval< T_Bound, T_Rnd > A_iv1, Interval< T_Bound, T_Rnd > A_iv2, Interval< T_Bound, T_Rnd > &A_rInter)
	Intersection of two intervals. More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::intervalHull (const Interval< T_Bound, T_Rnd > &A_iv1, const Interval< T_Bound, T_Rnd > &A_iv2)
	returns an interval containing A_iv1 and A_iv2 More...
template<typename T_Bound , typename T_Rnd >
void	capd::intervals::split (Interval< T_Bound, T_Rnd > &A_iv, Interval< T_Bound, T_Rnd > &A_rMid, T_Bound &A_diam)
	On output: . More...
template<typename T_Bound , typename T_Rnd >
void	capd::intervals::split (Interval< T_Bound, T_Rnd > &A_rIv, T_Bound &A_diam)
template<typename T_Bound , typename T_Rnd >
bool	capd::intervals::isSingular (const Interval< T_Bound, T_Rnd > &A_x)
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::power (const Interval< T_Bound, T_Rnd > &base, int exponent)
	a computation of base^{exponent} More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::power (const Interval< T_Bound, T_Rnd > &a, const Interval< T_Bound, T_Rnd > &b)
	a computation of a^b More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::sqrt (const Interval< T_Bound, T_Rnd > &x)
	square root of x More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::sin (const Interval< T_Bound, T_Rnd > &x)
	sinus of x More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::cos (const Interval< T_Bound, T_Rnd > &x)
	cosinus of x More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::tan (const Interval< T_Bound, T_Rnd > &x)
	tangens of x More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::cot (const Interval< T_Bound, T_Rnd > &x)
	cotangens of x More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::atan (const Interval< T_Bound, T_Rnd > &x)
	arctangens of x More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::asin (const Interval< T_Bound, T_Rnd > &x)
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::acos (const Interval< T_Bound, T_Rnd > &x)
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::sinh (const Interval< T_Bound, T_Rnd > &x)
	sinh More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::cosh (const Interval< T_Bound, T_Rnd > &x)
	cosh More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::tanh (const Interval< T_Bound, T_Rnd > &x)
	tanh More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::coth (const Interval< T_Bound, T_Rnd > &x)
	coth More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::exp (const Interval< T_Bound, T_Rnd > &x)
	returns exp(x) More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::log (const Interval< T_Bound, T_Rnd > &x)
	computes natural logarithm of x, x>0 More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::solveAffineInclusion (const Interval< T_Bound, T_Rnd > &a, const Interval< T_Bound, T_Rnd > &p, const Interval< T_Bound, T_Rnd > &c)
	solves inclusion More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::solveAffineInclusion (const Interval< T_Bound, T_Rnd > &a, const Interval< T_Bound, T_Rnd > &p, const Interval< T_Bound, T_Rnd > &c, int &dir)
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::sqr (const Interval< T_Bound, T_Rnd > &x)
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::nonnegativePart (const Interval< T_Bound, T_Rnd > &iv)
	returns nonnegative part of interval More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::ball (const Interval< T_Bound, T_Rnd > &iv, const Interval< T_Bound, T_Rnd > &r)
	Ball with center iv and radius r. More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::ball (const Interval< T_Bound, T_Rnd > &iv, const T_Bound &r)
	Ball with center iv and radius r. More...
template<typename T_Bound , typename T_Rnd >
intervals::Interval< T_Bound, T_Rnd >	capd::intervals::iabs (const intervals::Interval< T_Bound, T_Rnd > &A_inter)
	an absolute value More...
template<typename T_Bound , typename T_Rnd >
intervals::Interval< T_Bound, T_Rnd >	capd::intervals::imax (const intervals::Interval< T_Bound, T_Rnd > &A_iv1, const intervals::Interval< T_Bound, T_Rnd > &A_iv2)
	maximum More...
template<typename T_Bound , typename T_Rnd >
intervals::Interval< T_Bound, T_Rnd >	capd::intervals::imin (const intervals::Interval< T_Bound, T_Rnd > &A_iv1, const intervals::Interval< T_Bound, T_Rnd > &A_iv2)
	minimum More...
template<typename T_Bound , typename T_Rnd >
bool	capd::intervals::isinf (const Interval< T_Bound, T_Rnd > &r)
	returns true if any of endpoints is infinite More...
template<typename T_Bound , typename T_Rnd >
bool	capd::intervals::isnan (const capd::intervals::Interval< T_Bound, T_Rnd > &r)
	returns true if any of endpoints is a NaN More...
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	capd::intervals::copysign (const Interval< T_Bound, T_Rnd > &x, const Interval< T_Bound, T_Rnd > &y)
	returns interval containing copysign(a, b) for each a in x and b in y More...
template<typename T_Bound , typename T_Rnd >
bool	isInf (const capd::intervals::Interval< T_Bound, T_Rnd > &r)

Detailed Description

Interval Arithmetics Interface.

Remarks

include this file if you link your program with capd library

Author

Tomasz Kapela

Date

11-01-2006

Function Documentation

isInf()

template<typename T_Bound , typename T_Rnd >

bool isInf ( const capd::intervals::Interval< T_Bound, T_Rnd > &  r )

inline