CAPD interface for fast interval library filib. More...

#include <capd/filib/Interval.h>

Public Types
typedef ::filib::interval< T, R, M >	BaseInterval

typedef BaseInterval::value_type	BoundType

typedef ::filib::fp_traits< T, R >	RoundingPolicy

typedef capd::intervals::IntervalError< BoundType >	IntervalError

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 BaseInterval &interval)

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

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

BaseInterval &	getBaseInterval ()
	returns reference to base (filib) interval More...

const BaseInterval &	getBaseInterval () const
	returns const reference to base (filib) interval More...

const BoundType &	leftBound () const
	< returns the left end of the interval More...

const BoundType &	rightBound () const
	< returns the right end of the interval More...

const BoundType &	inf () const
	< returns the left end of the interval More...

const BoundType &	sup () const
	< returns the right end of the interval More...

void	setLeftBound (const BoundType &A_left)

void	setRightBound (const BoundType &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 More...

Interval	abs () const
	<Returns the interval of absolute values of this interval, i.e. More...

void	split (Interval &A_rMid, Interval &A_rRemainder) const
	Splits interval into the form mid + remainder, where mid - is middle point. More...

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 void	setup ()
	sets up floting point unit. More...

static void	reset ()
	resets default rounding mode (to the nearest) More...

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

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

Static Public Attributes
static const IntervalMode	mode = M

Protected Attributes
BaseInterval	m_interval

Friends
const BoundType &	leftBound (const Interval &x)

const BoundType &	rightBound (const Interval &x)

const BoundType &	inf (const Interval &x)

const BoundType &	sup (const Interval &x)

Interval	left (const Interval &x)

Interval	right (const Interval &x)

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)

bool	operator== (const Interval &A_iVal1, const BoundType &A_Val2)
	operator == (interval, scalar) More...

bool	operator== (const BoundType &A_Val1, const Interval &A_iVal2)
	operator == (scalar, interval) More...

bool	operator!= (const Interval &A_iVal1, const BoundType &A_Val2)
	operator != (interval, scalar) More...

bool	operator!= (const BoundType &A_Val1, const Interval &A_iVal2)
	operator != (scalar, interval) More...

bool	operator> (const Interval &A_iVal1, const BoundType &A_Val2)
	operator > (interval, scalar) More...

bool	operator> (const BoundType &A_Val1, const Interval &A_iVal2)
	operator > (scalar, interval) More...

bool	operator>= (const Interval &A_iVal1, const BoundType &A_Val2)
	operator >= (interval, scalar) More...

bool	operator>= (const BoundType &A_Val1, const Interval &A_iVal2)
	operator >= (scalar, interval) More...

bool	operator< (const Interval &A_iVal1, const BoundType &A_Val2)
	operator < (interval, scalar) More...

bool	operator< (const BoundType &A_Val1, const Interval &A_iVal2)
	operator < (scalar, interval) More...

bool	operator<= (const Interval &A_iVal1, const BoundType &A_Val2)
	operator <= (interval, scalar) More...

bool	operator<= (const BoundType &A_Val1, const Interval &A_iVal2)
	operator <= (scalar, interval) More...

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)

template<class E >
Interval	operator^ (const Interval &x, E)
	DW: this template is defined to prevent implicit conversion of exponent type In the previous implementation interval^double was converted to interval^int. More...

Interval	operator^ (const Interval &x, unsigned int n)

Interval	operator^ (const Interval &x, int n)

Interval	operator^ (const Interval &x, Interval::BoundType b)

Interval	operator^ (const Interval &a, const Interval &b)

Interval	operator+ (const Interval &A_iVal, const BoundType &A_x)
	operator + (interval, scalar) More...

Interval	operator+ (const BoundType &A_x, const Interval &A_iVal)
	operator + (scalar, interval) More...

Interval	operator- (const Interval &A_iVal, const BoundType &A_x)
	operator - (interval, scalar) More...

Interval	operator- (const BoundType &A_x, const Interval &A_iVal)
	operator - (scalar, interval) More...

Interval	operator* (const Interval &A_iVal, const BoundType &A_x)
	operator * (interval, scalar) More...

Interval	operator* (const BoundType &A_x, const Interval &A_iVal)
	operator * (scalar, interval) More...

Interval	operator/ (const Interval &A_iVal, const BoundType &A_x)
	operator / (scalar, interval) More...

Interval	operator/ (const BoundType &A_x, const Interval &A_iVal)
	operator / (interval, scalar) More...

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)

Interval	diam (const Interval &ix)

Interval	mid (const Interval &A_iv)

bool	intersection (const Interval &A_iv1, const Interval &A_iv2, Interval &A_rIntersection)
	Intersection of two intervals. More...

Interval	intervalHull (const Interval &ix, const Interval &iy)
	returns an interval containing ix and iy More...

void	split (Interval &A_iv, Interval &A_rMid, BoundType &A_diam)

void	split (Interval &A_rIv, BoundType &A_diam)

bool	isSingular (const Interval &A_x)

template<class E >
Interval	power (const Interval &x, E n)

Interval	sqrt (const Interval &x)

Interval	sin (const Interval &x)

Interval	cos (const Interval &x)

Interval	tan (const Interval &x)

Interval	cot (const Interval &x)

Interval	atan (const Interval &x)

Interval	asin (const Interval &x)

Interval	acos (const Interval &x)

Interval	sinh (const Interval &x)

Interval	cosh (const Interval &x)

Interval	tanh (const Interval &x)

Interval	coth (const Interval &x)

Interval	exp (const Interval &x)

Interval	log (const Interval &x)

Interval	sqr (const Interval &x)

bool	isinf (const Interval &r)
	returns true if any of endpoints is infinite More...

bool	isnan (const Interval &r)
	returns true if any of endpoints is a NaN More...

Interval	copysign (const Interval &x, const Interval &y)
	returns interval containing copysign(a, b) for each a in x and b in y More...

Interval	nonnegativePart (const Interval &iv)
	returns nonnegative part of interval More...

Interval	ball (const Interval &iv, const Interval &r)
	Ball with center iv and radius r. More...

Interval	ball (const Interval &iv, const BoundType &r)
	Ball with center iv and radius r. More...

Interval	solveAffineInclusion (const Interval &a, const Interval &p, const Interval &c)
	solves inclusion a+[0,t]*p\subset c for t More...

Interval	solveAffineInclusion (const Interval &a, const Interval &p, const Interval &c, int &dir)
	solves inclusion a+[0,t]*p\subset c for t More...

Detailed Description

template<typename T, RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>
class capd::filib::Interval< T, R, M >

CAPD interface for fast interval library filib.

This template class has three parameters

T - type of endpoints,
R - rounding policy (
See also
RoundingStrategy for possible values),
M - interval mode (
See also
IntervalMode for possible values). It works as an adapter for the other CAPD routines. It has exactly the same interface as native CAPD interval and it just calls the corresponding functions from the filib.
Most common used intervals (they can be used as T parameter of a Interval template)
- Interval<double, ::filib::native_directed > - intervals with double endpoints that switch rounding and do not restore rounding after each operation,
- Interval<double, ::filib::native_switched > - intervals with double endpoints that switch rounding and restore rounding 'to nearest' after each operation,
- Interval<double, ::filib::native_switched, filib::i_mode_extended > - extended. exception free intervals with double endpoints that can handle empty intervals, unbounded intervals.

To prevent misusing and enable easy interchange of a different interval implementation the filib interval T is not a base class of the Interval class and can be accesed only by getBaseInterval() method.

Member Typedef Documentation

◆ BaseInterval

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

typedef ::filib::interval<T, R, M > capd::filib::Interval< T, R, M >::BaseInterval

◆ BoundType

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

typedef BaseInterval::value_type capd::filib::Interval< T, R, M >::BoundType

◆ IntervalError

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

typedef capd::intervals::IntervalError<BoundType> capd::filib::Interval< T, R, M >::IntervalError

◆ RoundingPolicy

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

typedef ::filib::fp_traits<T, R> capd::filib::Interval< T, R, M >::RoundingPolicy

Constructor & Destructor Documentation

◆ Interval() [1/7]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

capd::filib::Interval< T, R, M >::Interval ( )

inline

◆ Interval() [2/7]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

capd::filib::Interval< T, R, M >::Interval ( const Interval< T, R, M > & A_iv )

inline

copying constructor

◆ Interval() [3/7]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

capd::filib::Interval< T, R, M >::Interval ( const BoundType & A_scalar )

inline

constructor from any class that can be coverted to BoundType

◆ Interval() [4/7]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

capd::filib::Interval< T, R, M >::Interval	(	const BoundType &	A_left,
		const BoundType &	A_right
	)

inline

constructor from any class that can be coverted to BoundType

◆ Interval() [5/7]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

capd::filib::Interval< T, R, M >::Interval ( const BaseInterval< T, R, M > & interval )

inline

◆ Interval() [6/7]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

capd::filib::Interval< T, R, M >::Interval	(	const char	left[],
		const char	right[]
	)

inline

◆ Interval() [7/7]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

capd::filib::Interval< T, R, M >::Interval	(	const std::string &	left,
		const std::string &	right
	)

inline

Member Function Documentation

◆ abs()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval capd::filib::Interval< T, R, M >::abs ( ) const

inline

<Returns the interval of absolute values of this interval, i.e.

◆ contains() [1/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool capd::filib::Interval< T, R, M >::contains ( const Interval< T, R, M > & A_iv ) const

inline

< checks if interval contains given interval iv

◆ contains() [2/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

template<typename T_Scalar >

bool capd::filib::Interval< T, R, M >::contains ( const T_Scalar & A_X ) const

inline

< checks if interval contains given point X

◆ containsInInterior() [1/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool capd::filib::Interval< T, R, M >::containsInInterior ( const Interval< T, R, M > & A_iv ) const

inline

< checks if interval contains in interior given interval iv

◆ containsInInterior() [2/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

template<typename T_Scalar >

bool capd::filib::Interval< T, R, M >::containsInInterior ( const T_Scalar & A_X ) const

inline

< checks if interval contains in interior given point X

◆ euler()

template<typename T , RoundingStrategy R, IntervalMode M>

Interval< T, R, M > capd::filib::Interval< T, R, M >::euler

inlinestatic

returns euler constant

◆ getBaseInterval() [1/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

BaseInterval & capd::filib::Interval< T, R, M >::getBaseInterval ( )

inline

returns reference to base (filib) interval

◆ getBaseInterval() [2/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const BaseInterval & capd::filib::Interval< T, R, M >::getBaseInterval ( ) const

inline

returns const reference to base (filib) interval

◆ inf()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const BoundType & capd::filib::Interval< T, R, M >::inf ( ) const

inline

< returns the left end of the interval

◆ left()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval capd::filib::Interval< T, R, M >::left ( ) const

inline

< returns interval containing left end

◆ leftBound()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const BoundType & capd::filib::Interval< T, R, M >::leftBound ( ) const

inline

< returns the left end of the interval

◆ mid()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval capd::filib::Interval< T, R, M >::mid ( ) const

inline

< returns middle point of interval

◆ operator*=()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval & capd::filib::Interval< T, R, M >::operator*= ( const Interval< T, R, M > & A_iv )

inline

◆ operator+=()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval & capd::filib::Interval< T, R, M >::operator+= ( const Interval< T, R, M > & A_iv )

inline

◆ operator-=()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval & capd::filib::Interval< T, R, M >::operator-= ( const Interval< T, R, M > & A_iv )

inline

◆ operator/=()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval & capd::filib::Interval< T, R, M >::operator/= ( const Interval< T, R, M > & A_iv )

inline

◆ operator=() [1/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval & capd::filib::Interval< T, R, M >::operator= ( const BoundType & A_x )

inline

◆ operator=() [2/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval & capd::filib::Interval< T, R, M >::operator= ( const Interval< T, R, M > & A_iv )

inline

◆ pi()

template<typename T , RoundingStrategy R, IntervalMode M>

Interval< T, R, M > capd::filib::Interval< T, R, M >::pi

inlinestatic

returns pi constant

◆ reset()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

static void capd::filib::Interval< T, R, M >::reset ( )

inlinestatic

resets default rounding mode (to the nearest)

◆ right()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval capd::filib::Interval< T, R, M >::right ( ) const

inline

< returns interval containing right end

◆ rightBound()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const BoundType & capd::filib::Interval< T, R, M >::rightBound ( ) const

inline

< returns the right end of the interval

◆ setLeftBound()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

void capd::filib::Interval< T, R, M >::setLeftBound ( const BoundType & A_left )

inline

◆ setRightBound()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

void capd::filib::Interval< T, R, M >::setRightBound ( const BoundType & A_right )

inline

◆ setup()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

static void capd::filib::Interval< T, R, M >::setup ( )

inlinestatic

sets up floting point unit.

It has to be called before first use of intervals

◆ split() [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

void capd::filib::Interval< T, R, M >::split	(	BoundType &	A_rMid,
		Interval< T, R, M > &	A_rRemainder
	)		const

inline

◆ split() [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

void capd::filib::Interval< T, R, M >::split	(	Interval< T, R, M > &	A_rMid,
		Interval< T, R, M > &	A_rRemainder
	)		const

inline

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

◆ split() [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

void capd::filib::Interval< T, R, M >::split ( Interval< T, R, M > & r )

inline

◆ subset()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool capd::filib::Interval< T, R, M >::subset ( const Interval< T, R, M > & A_iv ) const

inline

< checks if interval is subset of iv

◆ subsetInterior()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool capd::filib::Interval< T, R, M >::subsetInterior ( const Interval< T, R, M > & A_iv ) const

inline

< checks if interval is subset of interior of iv

◆ sup()

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const BoundType & capd::filib::Interval< T, R, M >::sup ( ) const

inline

< returns the right end of the interval

Friends And Related Function Documentation

◆ acos

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval acos ( const Interval< T, R, M > & x )

friend

◆ asin

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval asin ( const Interval< T, R, M > & x )

friend

◆ atan

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval atan ( const Interval< T, R, M > & x )

friend

◆ ball [1/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval ball	(	const Interval< T, R, M > &	iv,
		const BoundType &	r
	)

friend

Ball with center iv and radius r.

◆ ball [2/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval ball	(	const Interval< T, R, M > &	iv,
		const Interval< T, R, M > &	r
	)

friend

Ball with center iv and radius r.

◆ binRead

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

std::istream & binRead	(	std::istream &	in,
		Interval< T, R, M > &	iv
	)

friend

◆ binWrite

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

std::ostream & binWrite	(	std::ostream &	out,
		const Interval< T, R, M > &	iv
	)

friend

◆ bitRead

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

std::istream & bitRead	(	std::istream &	in,
		Interval< T, R, M > &	iv
	)

friend

◆ bitWrite

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

std::ostream & bitWrite	(	std::ostream &	out,
		const Interval< T, R, M > &	iv
	)

friend

◆ copysign

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval copysign	(	const Interval< T, R, M > &	x,
		const Interval< T, R, M > &	y
	)

friend

returns interval containing copysign(a, b) for each a in x and b in y

◆ cos

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval cos ( const Interval< T, R, M > & x )

friend

◆ cosh

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval cosh ( const Interval< T, R, M > & x )

friend

◆ cot

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval cot ( const Interval< T, R, M > & x )

friend

◆ coth

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval coth ( const Interval< T, R, M > & x )

friend

◆ diam

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval diam ( const Interval< T, R, M > & ix )

friend

◆ exp

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval exp ( const Interval< T, R, M > & x )

friend

◆ hexRead

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

std::istream & hexRead	(	std::istream &	in,
		Interval< T, R, M > &	iv
	)

friend

◆ hexWrite

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

std::ostream & hexWrite	(	std::ostream &	out,
		const Interval< T, R, M > &	iv
	)

friend

◆ inf

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const BoundType & inf ( const Interval< T, R, M > & x )

friend

Parameters

x	returns the left end of the interval

◆ intersection

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool intersection	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2,
		Interval< T, R, M > &	A_rIntersection
	)

friend

Intersection of two intervals.

◆ intervalHull

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval intervalHull	(	const Interval< T, R, M > &	ix,
		const Interval< T, R, M > &	iy
	)

friend

returns an interval containing ix and iy

◆ isinf

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool isinf ( const Interval< T, R, M > & r )

friend

returns true if any of endpoints is infinite

◆ isnan

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool isnan ( const Interval< T, R, M > & r )

friend

returns true if any of endpoints is a NaN

◆ isSingular

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool isSingular ( const Interval< T, R, M > & A_x )

friend

◆ left

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval left ( const Interval< T, R, M > & x )

friend

Parameters

x	returns interval containing left end

◆ leftBound

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const BoundType & leftBound ( const Interval< T, R, M > & x )

friend

Parameters

x	returns the left end of the interval

◆ log

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval log ( const Interval< T, R, M > & x )

friend

◆ mid

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval mid ( const Interval< T, R, M > & A_iv )

friend

◆ nonnegativePart

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval nonnegativePart ( const Interval< T, R, M > & iv )

friend

returns nonnegative part of interval

Remarks: if nonnegative part is empty throws exception

◆ operator!= [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator!=	(	const BoundType &	A_Val1,
		const Interval< T, R, M > &	A_iVal2
	)

friend

operator != (scalar, interval)

◆ operator!= [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator!=	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator!= [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator!=	(	const Interval< T, R, M > &	A_iVal1,
		const BoundType &	A_Val2
	)

friend

operator != (interval, scalar)

◆ operator* [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator*	(	const BoundType &	A_x,
		const Interval< T, R, M > &	A_iVal
	)

friend

operator * (scalar, interval)

◆ operator* [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator*	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator* [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator*	(	const Interval< T, R, M > &	A_iVal,
		const BoundType &	A_x
	)

friend

operator * (interval, scalar)

◆ operator+ [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator+	(	const BoundType &	A_x,
		const Interval< T, R, M > &	A_iVal
	)

friend

operator + (scalar, interval)

◆ operator+ [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator+	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator+ [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator+	(	const Interval< T, R, M > &	A_iVal,
		const BoundType &	A_x
	)

friend

operator + (interval, scalar)

◆ operator- [1/4]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator-	(	const BoundType &	A_x,
		const Interval< T, R, M > &	A_iVal
	)

friend

operator - (scalar, interval)

◆ operator- [2/4]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator- ( const Interval< T, R, M > & A_iv )

friend

◆ operator- [3/4]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator-	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator- [4/4]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator-	(	const Interval< T, R, M > &	A_iVal,
		const BoundType &	A_x
	)

friend

operator - (interval, scalar)

◆ operator/ [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator/	(	const BoundType &	A_x,
		const Interval< T, R, M > &	A_iVal
	)

friend

operator / (interval, scalar)

◆ operator/ [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator/	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator/ [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator/	(	const Interval< T, R, M > &	A_iVal,
		const BoundType &	A_x
	)

friend

operator / (scalar, interval)

◆ operator< [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator<	(	const BoundType &	A_Val1,
		const Interval< T, R, M > &	A_iVal2
	)

friend

operator < (scalar, interval)

◆ operator< [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator<	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator< [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator<	(	const Interval< T, R, M > &	A_iVal1,
		const BoundType &	A_Val2
	)

friend

operator < (interval, scalar)

◆ operator<<

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

std::ostream & operator<<	(	std::ostream &	s,
		const Interval< T, R, M > &	A_iv
	)

friend

◆ operator<= [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator<=	(	const BoundType &	A_Val1,
		const Interval< T, R, M > &	A_iVal2
	)

friend

operator <= (scalar, interval)

◆ operator<= [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator<=	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator<= [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator<=	(	const Interval< T, R, M > &	A_iVal1,
		const BoundType &	A_Val2
	)

friend

operator <= (interval, scalar)

◆ operator== [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator==	(	const BoundType &	A_Val1,
		const Interval< T, R, M > &	A_iVal2
	)

friend

operator == (scalar, interval)

◆ operator== [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator==	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator== [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator==	(	const Interval< T, R, M > &	A_iVal1,
		const BoundType &	A_Val2
	)

friend

operator == (interval, scalar)

◆ operator> [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator>	(	const BoundType &	A_Val1,
		const Interval< T, R, M > &	A_iVal2
	)

friend

operator > (scalar, interval)

◆ operator> [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator>	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator> [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator>	(	const Interval< T, R, M > &	A_iVal1,
		const BoundType &	A_Val2
	)

friend

operator > (interval, scalar)

◆ operator>= [1/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator>=	(	const BoundType &	A_Val1,
		const Interval< T, R, M > &	A_iVal2
	)

friend

operator >= (scalar, interval)

◆ operator>= [2/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator>=	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ operator>= [3/3]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool operator>=	(	const Interval< T, R, M > &	A_iVal1,
		const BoundType &	A_Val2
	)

friend

operator >= (interval, scalar)

◆ operator>>

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

std::istream & operator>>	(	std::istream &	s,
		Interval< T, R, M > &	A_iv
	)

friend

◆ operator^ [1/5]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator^	(	const Interval< T, R, M > &	a,
		const Interval< T, R, M > &	b
	)

friend

◆ operator^ [2/5]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

template<class E >

Interval operator^	(	const Interval< T, R, M > &	x,
		E
	)

friend

DW: this template is defined to prevent implicit conversion of exponent type In the previous implementation interval^double was converted to interval^int.

◆ operator^ [3/5]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator^	(	const Interval< T, R, M > &	x,
		int	n
	)

friend

◆ operator^ [4/5]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator^	(	const Interval< T, R, M > &	x,
		Interval< T, R, M >::BoundType	b
	)

friend

◆ operator^ [5/5]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval operator^	(	const Interval< T, R, M > &	x,
		unsigned int	n
	)

friend

◆ power

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

template<class E >

Interval power	(	const Interval< T, R, M > &	x,
		E	n
	)

friend

◆ right

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval right ( const Interval< T, R, M > & x )

friend

Parameters

x	returns interval containing right end

◆ rightBound

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const BoundType & rightBound ( const Interval< T, R, M > & x )

friend

Parameters

x	returns the right end of the interval

◆ sin

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval sin ( const Interval< T, R, M > & x )

friend

◆ sinh

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval sinh ( const Interval< T, R, M > & x )

friend

◆ solveAffineInclusion [1/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval solveAffineInclusion	(	const Interval< T, R, M > &	a,
		const Interval< T, R, M > &	p,
		const Interval< T, R, M > &	c
	)

friend

solves inclusion a+[0,t]*p\subset c for t

◆ solveAffineInclusion [2/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval solveAffineInclusion	(	const Interval< T, R, M > &	a,
		const Interval< T, R, M > &	p,
		const Interval< T, R, M > &	c,
		int &	dir
	)

friend

solves inclusion a+[0,t]*p\subset c for t

◆ split [1/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

void split	(	Interval< T, R, M > &	A_iv,
		Interval< T, R, M > &	A_rMid,
		BoundType &	A_diam
	)

friend

TODO : correct to not switch rounding

◆ split [2/2]

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

void split	(	Interval< T, R, M > &	A_rIv,
		BoundType &	A_diam
	)

friend

◆ sqr

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval sqr ( const Interval< T, R, M > & x )

friend

◆ sqrt

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval sqrt ( const Interval< T, R, M > & x )

friend

◆ subset

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool subset	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ subsetInterior

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

bool subsetInterior	(	const Interval< T, R, M > &	A_iv1,
		const Interval< T, R, M > &	A_iv2
	)

friend

◆ sup

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const BoundType & sup ( const Interval< T, R, M > & x )

friend

Parameters

x	returns the right end of the interval

◆ tan

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval tan ( const Interval< T, R, M > & x )

friend

◆ tanh

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

Interval tanh ( const Interval< T, R, M > & x )

friend

Member Data Documentation

◆ m_interval

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

BaseInterval capd::filib::Interval< T, R, M >::m_interval

protected

◆ mode

template<typename T , RoundingStrategy R = ::filib::native_directed, IntervalMode M = ::filib::i_mode_normal>

const IntervalMode capd::filib::Interval< T, R, M >::mode = M

static

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ BaseInterval

◆ BoundType

◆ IntervalError

◆ RoundingPolicy

Constructor & Destructor Documentation

◆ Interval() [1/7]

◆ Interval() [2/7]

◆ Interval() [3/7]

◆ Interval() [4/7]

◆ Interval() [5/7]

◆ Interval() [6/7]

◆ Interval() [7/7]

Member Function Documentation

◆ abs()

◆ contains() [1/2]

◆ contains() [2/2]

◆ containsInInterior() [1/2]

◆ containsInInterior() [2/2]

◆ euler()

◆ getBaseInterval() [1/2]

◆ getBaseInterval() [2/2]

◆ inf()

◆ left()

◆ leftBound()

◆ mid()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ pi()

◆ reset()

◆ right()

◆ rightBound()

◆ setLeftBound()

◆ setRightBound()

◆ setup()

◆ split() [1/3]

◆ split() [2/3]

◆ split() [3/3]

◆ subset()

◆ subsetInterior()

◆ sup()

Friends And Related Function Documentation

◆ acos

◆ asin

◆ atan

◆ ball [1/2]

◆ ball [2/2]

◆ binRead

◆ binWrite

◆ bitRead

◆ bitWrite

◆ copysign

◆ cos

◆ cosh

◆ cot

◆ coth

◆ diam

◆ exp

◆ hexRead

◆ hexWrite

◆ inf

◆ intersection

◆ intervalHull

◆ isinf

◆ isnan

◆ isSingular

◆ left

◆ leftBound

◆ log