Files
file	DoubleInterval.cpp

Namespaces
	capd::cxsc
	fast interval library

	capd::filib
	fast interval library

	capd

Classes
class	capd::intervals::Interval< T_Bound, T_Rnd >
	Definition of template class Interval. More...

class	capd::intervals::IntervalTraits< T_Bound >

class	capd::intervals::IntervalTraits< double >

class	capd::intervals::IntervalTraits< float >

class	capd::intervals::IntervalTraits< long double >

class	capd::intervals::IntervalIOTraits< T_Bound >

class	capd::intervals::IntervalIOTraits< double >

class	capd::intervals::IntervalIOTraits< float >

class	capd::filib::Interval< T, R, M >
	CAPD interface for fast interval library filib. More...

Typedefs
typedef capd::rounding::DoubleRounding	DoubleRounding

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: $iv \subset Mid + [-diam , diam]$ . 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 $a+[0,t]*p\subset c for t$ 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...

MpInterval::BoundType	capd::intervals::quadrant (const MpInterval::BoundType &x)
	returns the integer part of the division of x by Pi/2 the result is exact More...

int	capd::intervals::modulo4 (MpReal x)

template<>
MpInterval	capd::intervals::sin (const MpInterval &x)

template<>
MpInterval	capd::intervals::cos (const MpInterval &x)

template<>
MpInterval	capd::intervals::tan (const MpInterval &x)

template<>
MpInterval	capd::intervals::log (const MpInterval &x)

template<>
MpInterval	capd::intervals::exp (const MpInterval &x)

template<>
MpInterval	capd::intervals::sqrt (const MpInterval &z)

template<>
MpInterval	capd::intervals::power (const MpInterval &value, int exponent)

Detailed Description

Typedef Documentation

◆ DoubleRounding

typedef capd::rounding::DoubleRounding DoubleRounding

Function Documentation

◆ acos()

template<typename T_Bound , typename T_Rnd >

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

◆ asin()

template<typename T_Bound , typename T_Rnd >

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

◆ atan()

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

◆ ball() [1/2]

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
	)

inline

Ball with center iv and radius r.

◆ ball() [2/2]

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
	)

inline

Ball with center iv and radius r.

◆ copysign()

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
	)

inline

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

◆ cos() [1/2]

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

◆ cos() [2/2]

template<>

MpInterval capd::intervals::cos ( const MpInterval & x )

◆ cosh()

template<typename T_Bound , typename T_Rnd >

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

cosh

◆ cot()

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

◆ coth()

template<typename T_Bound , typename T_Rnd >

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

coth

◆ diam()

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

◆ exp() [1/2]

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)

Remarks: do not add taylor expansion errors to upper bounds.

◆ exp() [2/2]

template<>

MpInterval capd::intervals::exp ( const MpInterval & x )

◆ iabs()

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 )

inline

an absolute value

◆ imax()

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
	)

inline

maximum

◆ imin()

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
	)

inline

minimum

◆ intersection()

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.

Parameters

[in]	A_iv1,A_iv2	two intervals
[out]	A_rInter	intersection of A_iv1 and A_iv2 (if non empty)

Returns: if common part of iv1 and iv2 is nonempty then inter =intersection of iv1 and iv2 and true is returned otherwise false is returned and inter is untouched

◆ intervalHull()

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

◆ isinf()

template<typename T_Bound , typename T_Rnd >

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

inline

returns true if any of endpoints is infinite

◆ isnan()

template<typename T_Bound , typename T_Rnd >

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

inline

returns true if any of endpoints is a NaN

◆ isSingular()

template<typename T_Bound , typename T_Rnd >

bool capd::intervals::isSingular ( const Interval< T_Bound, T_Rnd > & A_x )

inline

◆ log() [1/2]

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

◆ log() [2/2]

template<>

MpInterval capd::intervals::log ( const MpInterval & x )

◆ mid()

template<typename T_Bound , typename T_Rnd >

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

inline

◆ modulo4()

int capd::intervals::modulo4 ( MpReal x )

◆ nonnegativePart()

template<typename T_Bound , typename T_Rnd >

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

inline

returns nonnegative part of interval

Remarks: if nonnegative part is empty throws exception

◆ power() [1/3]

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

◆ power() [2/3]

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}

◆ power() [3/3]

template<>

MpInterval capd::intervals::power	(	const MpInterval &	value,
		int	exponent
	)

◆ quadrant()

MpInterval::BoundType capd::intervals::quadrant ( const MpInterval::BoundType & x )

returns the integer part of the division of x by Pi/2 the result is exact

◆ sin() [1/2]

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

◆ sin() [2/2]

template<>

MpInterval capd::intervals::sin ( const MpInterval & x )

◆ sinh()

template<typename T_Bound , typename T_Rnd >

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

sinh

◆ solveAffineInclusion() [1/2]

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

◆ solveAffineInclusion() [2/2]

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
	)

◆ split() [1/2]

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: $iv \subset Mid + [-diam , diam]$ .

◆ split() [2/2]

template<typename T_Bound , typename T_Rnd >

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

inline

◆ sqr()

template<typename T_Bound , typename T_Rnd >

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

◆ sqrt() [1/2]

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

◆ sqrt() [2/2]

template<>

MpInterval capd::intervals::sqrt ( const MpInterval & z )

◆ tan() [1/2]

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

◆ tan() [2/2]

template<>

MpInterval capd::intervals::tan ( const MpInterval & x )

◆ tanh()

template<typename T_Bound , typename T_Rnd >

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

tanh

◆ width()

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

Files

Namespaces

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ DoubleRounding

Function Documentation

◆ acos()

◆ asin()

◆ atan()

◆ ball() [1/2]

◆ ball() [2/2]

◆ copysign()

◆ cos() [1/2]

◆ cos() [2/2]

◆ cosh()

◆ cot()

◆ coth()

◆ diam()

◆ exp() [1/2]

◆ exp() [2/2]

◆ iabs()

◆ imax()

◆ imin()

◆ intersection()

◆ intervalHull()

◆ isinf()

◆ isnan()

◆ isSingular()

◆ log() [1/2]

◆ log() [2/2]

◆ mid()

◆ modulo4()

◆ nonnegativePart()

◆ power() [1/3]

◆ power() [2/3]

◆ power() [3/3]

◆ quadrant()

◆ sin() [1/2]

◆ sin() [2/2]

◆ sinh()

◆ solveAffineInclusion() [1/2]

◆ solveAffineInclusion() [2/2]

◆ split() [1/2]

◆ split() [2/2]

◆ sqr()

◆ sqrt() [1/2]

◆ sqrt() [2/2]

◆ tan() [1/2]

◆ tan() [2/2]

◆ tanh()

◆ width()