Definition of template class Interval. More...

#include <capd/intervals/minmax_interval.h>

Public Types
typedef T_Bound	BoundType

typedef T_Rnd	RoundingPolicy

typedef IntervalTraits< BoundType >::BoundContainer	BoundContainer

typedef IntervalTraits< BoundType >::BoundReturnType	BoundReturnType

Public Member Functions
	Interval ()

	Interval (const Interval &A_iv)
	copying constructor More...

	Interval (const BoundType &A_scalar)
	constructor from any class that can be coverted to BoundType More...

	Interval (const BoundType &A_left, const BoundType &A_right)
	constructor from any class that can be coverted to BoundType More...

	Interval (const char left[], const char right[])

	Interval (const std::string &left, const std::string &right)

BoundReturnType	leftBound () const
	returns the left end of the interval More...

BoundReturnType	rightBound () const
	returns the right end of the interval More...

void	setLeftBound (const T_Bound &A_left)

void	setRightBound (const T_Bound &A_right)

Interval	left () const
	returns interval containing left end More...

Interval	right () const
	returns interval containing right end More...

template<typename T_Scalar >
bool	contains (const T_Scalar &A_X) const
	checks if interval contains given point X More...

bool	contains (const Interval &A_iv) const
	checks if interval contains given interval iv More...

template<typename T_Scalar >
bool	containsInInterior (const T_Scalar &A_X) const
	checks if interval contains in interior given point X More...

bool	containsInInterior (const Interval &A_iv) const
	checks if interval contains in interior given interval iv More...

bool	subset (const Interval &A_iv) const
	checks if interval is subset of iv More...

bool	subsetInterior (const Interval &A_iv) const
	checks if interval is subset of interior of iv More...

Interval	mid () const
	returns middle point of interval Splits interval into the form mid + remainder, where mid - is middle point More...

void	split (Interval &A_rMid, Interval &A_rRemainder) const

void	split (BoundType &A_rMid, Interval &A_rRemainder) const

void	split (Interval &r)

Interval &	operator= (const Interval &A_iv)

Interval &	operator= (const BoundType &A_x)

Interval &	operator+= (const Interval &A_iv)

Interval &	operator-= (const Interval &A_iv)

Interval &	operator*= (const Interval &A_iv)

Interval &	operator/= (const Interval &A_iv)

Static Public Member Functions
static Interval	pi ()
	returns pi constant More...

static Interval	euler ()
	returns euler constant More...

static T_Bound	computeExpError ()
	an estimation for the remainder term during computation of "exp" More...

static T_Bound	computeSinError ()
	An estimation of the remainder term for "sin". More...

static T_Bound	computeAtanError ()
	An estimation of the remainder term for "atan" for \|x\|<(sqrt(2)-1) More...

Static Public Attributes
static const int	S_nExpTaylorOrder = 20
	Taylor series length used in the EXP function. More...

static const int	S_nLogTaylorOrder = 40
	Taylor series length used in the LOG function, it MUST be an EVEN value. More...

static const int	S_nSinTaylorOrder = 11
	Taylor series length used in the SIN function, it MUST be an ODD value. More...

static const int	S_nAtanTaylorOrder = 21
	Taylor series length used in the ATAN function, it MUST be an ODD value. More...

Protected Attributes
BoundContainer	m_left
	left end of an interval More...

BoundContainer	m_right
	right end of an interval More...

Friends
bool	subset (const Interval &A_iv1, const Interval &A_iv2)

bool	subsetInterior (const Interval &A_iv1, const Interval &A_iv2)

bool	operator== (const Interval &A_iv1, const Interval &A_iv2)

bool	operator<= (const Interval &A_iv1, const Interval &A_iv2)

bool	operator>= (const Interval &A_iv1, const Interval &A_iv2)

bool	operator< (const Interval &A_iv1, const Interval &A_iv2)

bool	operator> (const Interval &A_iv1, const Interval &A_iv2)

bool	operator!= (const Interval &A_iv1, const Interval &A_iv2)

Interval	operator- (const Interval &A_iv)

Interval	operator+ (const Interval &A_iv1, const Interval &A_iv2)

Interval	operator- (const Interval &A_iv1, const Interval &A_iv2)

Interval	operator* (const Interval &A_iv1, const Interval &A_iv2)

Interval	operator/ (const Interval &A_iv1, const Interval &A_iv2)

Interval	operator^ (const Interval &A_iv1, int i)

std::ostream &	operator<< (std::ostream &s, const Interval &A_iv)

std::istream &	operator>> (std::istream &s, Interval &A_iv)

std::ostream &	bitWrite (std::ostream &out, const Interval &iv)

std::istream &	bitRead (std::istream &in, Interval &iv)

std::ostream &	hexWrite (std::ostream &out, const Interval &iv)

std::istream &	hexRead (std::istream &in, Interval &iv)

std::ostream &	binWrite (std::ostream &out, const Interval &iv)

std::istream &	binRead (std::istream &in, Interval &iv)

Detailed Description

template<typename T_Bound, typename T_Rnd>
class capd::intervals::Interval< T_Bound, T_Rnd >

Definition of template class Interval.

Template has two parameters:

T_Bound - type of interval ends,
T_Rnd - class that switches rounding (by default it is equal to T_Bound) .

T_Rnd has to provide methods that switch rounding mode:

roundUp,
roundDown,
roundNearest.

To provide full functionality of the class Interval and related functions class T_Bound has to provide methods:

constructors: from double, int.
relations == != < <= > >=
operators + - * / -(unary)
operator =
input, output operators << >>
log, sqrt.
capd::max, capd::min, capd::abs (to distinguish from standard template function)

Remarks: We do not assume that elementary function such sin, cos, tan, exp,... for BoundType are computed correctly and therefore we do not use them in interval version. If you have type of endpoint which guarantee correctness of up and down rounding you can write your own specialization of elementary functions e.g. taking advantage of monocity.

Author: Tomasz Kapela

Date: 11-01-2006

Member Typedef Documentation

◆ BoundContainer

template<typename T_Bound , typename T_Rnd >

typedef IntervalTraits<BoundType>::BoundContainer capd::intervals::Interval< T_Bound, T_Rnd >::BoundContainer

◆ BoundReturnType

template<typename T_Bound , typename T_Rnd >

typedef IntervalTraits<BoundType>::BoundReturnType capd::intervals::Interval< T_Bound, T_Rnd >::BoundReturnType

◆ BoundType

template<typename T_Bound , typename T_Rnd >

typedef T_Bound capd::intervals::Interval< T_Bound, T_Rnd >::BoundType

◆ RoundingPolicy

template<typename T_Bound , typename T_Rnd >

typedef T_Rnd capd::intervals::Interval< T_Bound, T_Rnd >::RoundingPolicy

Constructor & Destructor Documentation

◆ Interval() [1/6]

template<typename T_Bound , typename T_Rnd >

capd::intervals::Interval< T_Bound, T_Rnd >::Interval

inline

◆ Interval() [2/6]

template<typename T_Bound , typename T_Rnd >

capd::intervals::Interval< T_Bound, T_Rnd >::Interval ( const Interval< T_Bound, T_Rnd > & A_iv )

inline

copying constructor

◆ Interval() [3/6]

template<typename T_Bound , typename T_Rnd >

capd::intervals::Interval< T_Bound, T_Rnd >::Interval ( const BoundType & A_scalar )

inline

constructor from any class that can be coverted to BoundType

◆ Interval() [4/6]

template<typename T_Bound , typename T_Rnd >

capd::intervals::Interval< T_Bound, T_Rnd >::Interval	(	const BoundType &	A_left,
		const BoundType &	A_right
	)

constructor from any class that can be coverted to BoundType

◆ Interval() [5/6]

template<typename T_Bound , typename T_Rnd >

capd::intervals::Interval< T_Bound, T_Rnd >::Interval	(	const char	left[],
		const char	right[]
	)

inline

◆ Interval() [6/6]

template<typename T_Bound , typename T_Rnd >

capd::intervals::Interval< T_Bound, T_Rnd >::Interval	(	const std::string &	left,
		const std::string &	right
	)

inline

Member Function Documentation

◆ computeAtanError()

template<typename T_Bound , typename T_Rnd >

T_Bound capd::intervals::Interval< T_Bound, T_Rnd >::computeAtanError

static

An estimation of the remainder term for "atan" for |x|<(sqrt(2)-1)

◆ computeExpError()

template<typename T_Bound , typename T_Rnd >

T_Bound capd::intervals::Interval< T_Bound, T_Rnd >::computeExpError

static

an estimation for the remainder term during computation of "exp"

◆ computeSinError()

template<typename T_Bound , typename T_Rnd >

T_Bound capd::intervals::Interval< T_Bound, T_Rnd >::computeSinError

static

An estimation of the remainder term for "sin".

◆ contains() [1/2]

template<typename T_Bound , typename T_Rnd >

bool capd::intervals::Interval< T_Bound, T_Rnd >::contains ( const Interval< T_Bound, T_Rnd > & A_iv ) const

inline

checks if interval contains given interval iv

◆ contains() [2/2]

template<typename T_Bound , typename T_Rnd >

template<typename T_Scalar >

bool capd::intervals::Interval< T_Bound, T_Rnd >::contains ( const T_Scalar & A_X ) const

inline

checks if interval contains given point X

◆ containsInInterior() [1/2]

template<typename T_Bound , typename T_Rnd >

bool capd::intervals::Interval< T_Bound, T_Rnd >::containsInInterior ( const Interval< T_Bound, T_Rnd > & A_iv ) const

inline

checks if interval contains in interior given interval iv

◆ containsInInterior() [2/2]

template<typename T_Bound , typename T_Rnd >

template<typename T_Scalar >

bool capd::intervals::Interval< T_Bound, T_Rnd >::containsInInterior ( const T_Scalar & A_X ) const

inline

checks if interval contains in interior given point X

◆ euler()

MpInterval capd::intervals::MpInterval::euler

inlinestatic

returns euler constant

◆ left()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd > capd::intervals::Interval< T_Bound, T_Rnd >::left

inline

returns interval containing left end

◆ leftBound()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd >::BoundReturnType capd::intervals::Interval< T_Bound, T_Rnd >::leftBound

inline

returns the left end of the interval

◆ mid()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd > capd::intervals::Interval< T_Bound, T_Rnd >::mid

inline

returns middle point of interval Splits interval into the form mid + remainder, where mid - is middle point

◆ operator*=()

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd > & capd::intervals::Interval< T_Bound, T_Rnd >::operator*= ( const Interval< T_Bound, T_Rnd > & A_iv )

◆ operator+=()

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd > & capd::intervals::Interval< T_Bound, T_Rnd >::operator+= ( const Interval< T_Bound, T_Rnd > & A_iv )

◆ operator-=()

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd > & capd::intervals::Interval< T_Bound, T_Rnd >::operator-= ( const Interval< T_Bound, T_Rnd > & A_iv )

◆ operator/=()

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd > & capd::intervals::Interval< T_Bound, T_Rnd >::operator/= ( const Interval< T_Bound, T_Rnd > & A_iv )

(A_iv.m_left<=0 && A_iv.m_right>=0)

◆ operator=() [1/2]

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd > & capd::intervals::Interval< T_Bound, T_Rnd >::operator= ( const BoundType & A_x )

◆ operator=() [2/2]

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd > & capd::intervals::Interval< T_Bound, T_Rnd >::operator= ( const Interval< T_Bound, T_Rnd > & A_iv )

◆ pi()

MpInterval capd::intervals::MpInterval::pi

inlinestatic

returns pi constant

◆ right()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd > capd::intervals::Interval< T_Bound, T_Rnd >::right

inline

returns interval containing right end

◆ rightBound()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd >::BoundReturnType capd::intervals::Interval< T_Bound, T_Rnd >::rightBound

inline

returns the right end of the interval

◆ setLeftBound()

template<typename T_Bound , typename T_Rnd >

void capd::intervals::Interval< T_Bound, T_Rnd >::setLeftBound ( const T_Bound & A_left )

inline

◆ setRightBound()

template<typename T_Bound , typename T_Rnd >

void capd::intervals::Interval< T_Bound, T_Rnd >::setRightBound ( const T_Bound & A_right )

inline

◆ split() [1/3]

template<typename T_Bound , typename T_Rnd >

void capd::intervals::Interval< T_Bound, T_Rnd >::split	(	BoundType &	A_rMid,
		Interval< T_Bound, T_Rnd > &	A_rRemainder
	)		const

inline

◆ split() [2/3]

template<typename T_Bound , typename T_Rnd >

void capd::intervals::Interval< T_Bound, T_Rnd >::split	(	Interval< T_Bound, T_Rnd > &	A_rMid,
		Interval< T_Bound, T_Rnd > &	A_rRemainder
	)		const

inline

◆ split() [3/3]

template<typename T_Bound , typename T_Rnd >

void capd::intervals::Interval< T_Bound, T_Rnd >::split ( Interval< T_Bound, T_Rnd > & r )

inline

◆ subset()

template<typename T_Bound , typename T_Rnd >

bool capd::intervals::Interval< T_Bound, T_Rnd >::subset ( const Interval< T_Bound, T_Rnd > & A_iv ) const

inline

checks if interval is subset of iv

◆ subsetInterior()

template<typename T_Bound , typename T_Rnd >

bool capd::intervals::Interval< T_Bound, T_Rnd >::subsetInterior ( const Interval< T_Bound, T_Rnd > & A_iv ) const

inline

checks if interval is subset of interior of iv

Friends And Related Function Documentation

◆ binRead

template<typename T_Bound , typename T_Rnd >

std::istream& binRead	(	std::istream &	in,
		Interval< T_Bound, T_Rnd > &	iv
	)

friend

◆ binWrite

template<typename T_Bound , typename T_Rnd >

std::ostream& binWrite	(	std::ostream &	out,
		const Interval< T_Bound, T_Rnd > &	iv
	)

friend

◆ bitRead

template<typename T_Bound , typename T_Rnd >

std::istream& bitRead	(	std::istream &	in,
		Interval< T_Bound, T_Rnd > &	iv
	)

friend

◆ bitWrite

template<typename T_Bound , typename T_Rnd >

std::ostream& bitWrite	(	std::ostream &	out,
		const Interval< T_Bound, T_Rnd > &	iv
	)

friend

◆ hexRead

template<typename T_Bound , typename T_Rnd >

std::istream& hexRead	(	std::istream &	in,
		Interval< T_Bound, T_Rnd > &	iv
	)

friend

◆ hexWrite

template<typename T_Bound , typename T_Rnd >

std::ostream& hexWrite	(	std::ostream &	out,
		const Interval< T_Bound, T_Rnd > &	iv
	)

friend

◆ operator!=

template<typename T_Bound , typename T_Rnd >

bool operator!=	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator*

template<typename T_Bound , typename T_Rnd >

Interval operator*	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator+

template<typename T_Bound , typename T_Rnd >

Interval operator+	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator- [1/2]

template<typename T_Bound , typename T_Rnd >

Interval operator- ( const Interval< T_Bound, T_Rnd > & A_iv )

friend

◆ operator- [2/2]

template<typename T_Bound , typename T_Rnd >

Interval operator-	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator/

template<typename T_Bound , typename T_Rnd >

Interval operator/	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator<

template<typename T_Bound , typename T_Rnd >

bool operator<	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator<<

template<typename T_Bound , typename T_Rnd >

std::ostream& operator<<	(	std::ostream &	s,
		const Interval< T_Bound, T_Rnd > &	A_iv
	)

friend

◆ operator<=

template<typename T_Bound , typename T_Rnd >

bool operator<=	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator==

template<typename T_Bound , typename T_Rnd >

bool operator==	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator>

template<typename T_Bound , typename T_Rnd >

bool operator>	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator>=

template<typename T_Bound , typename T_Rnd >

bool operator>=	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ operator>>

template<typename T_Bound , typename T_Rnd >

std::istream& operator>>	(	std::istream &	s,
		Interval< T_Bound, T_Rnd > &	A_iv
	)

friend

◆ operator^

template<typename T_Bound , typename T_Rnd >

Interval operator^	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		int	i
	)

friend

◆ subset

template<typename T_Bound , typename T_Rnd >

bool subset	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

◆ subsetInterior

template<typename T_Bound , typename T_Rnd >

bool subsetInterior	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

friend

Member Data Documentation

◆ m_left

template<typename T_Bound , typename T_Rnd >

BoundContainer capd::intervals::Interval< T_Bound, T_Rnd >::m_left

protected

left end of an interval

◆ m_right

template<typename T_Bound , typename T_Rnd >

BoundContainer capd::intervals::Interval< T_Bound, T_Rnd >::m_right

protected

right end of an interval

◆ S_nAtanTaylorOrder

template<typename T_Bound , typename T_Rnd >

const int capd::intervals::Interval< T_Bound, T_Rnd >::S_nAtanTaylorOrder = 21

static

Taylor series length used in the ATAN function, it MUST be an ODD value.

◆ S_nExpTaylorOrder

template<typename T_Bound , typename T_Rnd >

const int capd::intervals::Interval< T_Bound, T_Rnd >::S_nExpTaylorOrder = 20

static

Taylor series length used in the EXP function.

◆ S_nLogTaylorOrder

template<typename T_Bound , typename T_Rnd >

const int capd::intervals::Interval< T_Bound, T_Rnd >::S_nLogTaylorOrder = 40

static

Taylor series length used in the LOG function, it MUST be an EVEN value.

◆ S_nSinTaylorOrder

template<typename T_Bound , typename T_Rnd >

const int capd::intervals::Interval< T_Bound, T_Rnd >::S_nSinTaylorOrder = 11

static

Taylor series length used in the SIN function, it MUST be an ODD value.

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Detailed Description

template<typename T_Bound, typename T_Rnd> class capd::intervals::Interval< T_Bound, T_Rnd >

Member Typedef Documentation

◆ BoundContainer

◆ BoundReturnType

◆ BoundType

◆ RoundingPolicy

Constructor & Destructor Documentation

◆ Interval() [1/6]

◆ Interval() [2/6]

◆ Interval() [3/6]

◆ Interval() [4/6]

◆ Interval() [5/6]

◆ Interval() [6/6]

Member Function Documentation

◆ computeAtanError()

◆ computeExpError()

◆ computeSinError()

◆ contains() [1/2]

◆ contains() [2/2]

◆ containsInInterior() [1/2]

◆ containsInInterior() [2/2]

◆ euler()

◆ left()

◆ leftBound()

◆ mid()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ pi()

◆ right()

◆ rightBound()

◆ setLeftBound()

◆ setRightBound()

◆ split() [1/3]

◆ split() [2/3]

◆ split() [3/3]

◆ subset()

◆ subsetInterior()

Friends And Related Function Documentation

◆ binRead

◆ binWrite

◆ bitRead

◆ bitWrite

◆ hexRead

◆ hexWrite

◆ operator!=

◆ operator*

◆ operator+

◆ operator- [1/2]

◆ operator- [2/2]

◆ operator/

◆ operator<

◆ operator<<

◆ operator<=

◆ operator==

◆ operator>

◆ operator>=

◆ operator>>

◆ operator^

◆ subset

◆ subsetInterior

Member Data Documentation

◆ m_left

◆ m_right

◆ S_nAtanTaylorOrder

◆ S_nExpTaylorOrder

◆ S_nLogTaylorOrder

◆ S_nSinTaylorOrder

template<typename T_Bound, typename T_Rnd>
class capd::intervals::Interval< T_Bound, T_Rnd >