Interval arithmetics. More...

Classes
class	Interval
	Definition of template class Interval. More...

class	IntervalError
	Instation of the IntervalError class is throwed by the Interval class on error. More...

class	IntervalIOTraits

class	IntervalIOTraits< double >

class	IntervalIOTraits< float >

class	IntervalIOTraits< MpReal >

class	IntervalTraits

class	IntervalTraits< double >

class	IntervalTraits< float >

class	IntervalTraits< long double >

Typedefs
typedef capd::intervals::Interval< double, capd::rounding::DoubleRounding >	DoubleInterval

template<typename T >
using	IComplex = capd::fields::Complex< T >
	Definition for backward compatibility. More...

typedef capd::multiPrec::MpReal	MpReal

typedef capd::multiPrec::MpReal	MpfrClass

typedef Interval< MpReal, MpReal >	MpInterval

Functions
template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	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	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 >	mid (const Interval< T_Bound, T_Rnd > &A_iv)

template<typename T_Bound , typename T_Rnd >
bool	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 >	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	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	split (Interval< T_Bound, T_Rnd > &A_rIv, T_Bound &A_diam)

template<typename T_Bound , typename T_Rnd >
bool	isSingular (const Interval< T_Bound, T_Rnd > &A_x)

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	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 >	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 >	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 >	sin (const Interval< T_Bound, T_Rnd > &x)
	sinus of x More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	cos (const Interval< T_Bound, T_Rnd > &x)
	cosinus of x More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	tan (const Interval< T_Bound, T_Rnd > &x)
	tangens of x More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	cot (const Interval< T_Bound, T_Rnd > &x)
	cotangens of x More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	atan (const Interval< T_Bound, T_Rnd > &x)
	arctangens of x More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	asin (const Interval< T_Bound, T_Rnd > &x)

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	acos (const Interval< T_Bound, T_Rnd > &x)

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	sinh (const Interval< T_Bound, T_Rnd > &x)
	sinh More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	cosh (const Interval< T_Bound, T_Rnd > &x)
	cosh More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	tanh (const Interval< T_Bound, T_Rnd > &x)
	tanh More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	coth (const Interval< T_Bound, T_Rnd > &x)
	coth More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	exp (const Interval< T_Bound, T_Rnd > &x)
	returns exp(x) More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	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 >	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 >	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 >	sqr (const Interval< T_Bound, T_Rnd > &x)

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	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 >	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 >	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 >	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 >	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 >	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	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	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 >	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 >
T_Bound	positivePower (T_Bound value, unsigned exponent)
	a computation of value^{exponent} with current rounding settings (exponent has to be positive) More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	scaledSin2 (const Interval< T_Bound, T_Rnd > &x)
	a rigorous computation of sin(x) for 0 <= x <= pi More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	scaledSin1 (const Interval< T_Bound, T_Rnd > &x)
	the function computes sin(x) for $x \subset [0,\infty]$ More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	scaledAtan2 (const Interval< T_Bound, T_Rnd > &x)
	a rigorous computation of atan(x) for 0 <= x <= sqrt(2)-1 More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	scaledAtan1 (const Interval< T_Bound, T_Rnd > &x)
	a rigorous computation of atan(x) for 0 <= x More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	scaledAsin1 (const Interval< T_Bound, T_Rnd > &x)
	A rigorous computation of asin(x) far from -1 and 1 i.e. for -0.7 <= x <= 0.7. More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	scaledAsin2 (const Interval< T_Bound, T_Rnd > &x)
	A rigorous computation of asin(x) for 0.7 < x <=1. More...

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	pointAsin (const Interval< T_Bound, T_Rnd > &x)

template<typename T_Bound , typename T_Rnd >
Interval< T_Bound, T_Rnd >	scaledAcos (const Interval< T_Bound, T_Rnd > &x)
	A rigorous computation of acos(x) for point intervals. More...

template<typename T_Bound >
T_Bound	scaledExp (T_Bound x, int expTaylorOrder)
	returns exp(x) for x in [0,1] with actual rounding More...

template<typename T_Bound >
T_Bound	scaledLogUp (const T_Bound &x, int logTaylorOrder)
	computes upper bound for log(1+x) for $x \in [0,1/2]$ More...

template<typename T_Bound >
T_Bound	scaledLogDown (const T_Bound &x, int logTaylorOrder)
	computes lower bound for log(1+x) for $x \in [0,1/2]$ More...

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

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

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

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

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

template<typename T_Bound , typename T_Rnd >
__INLINE__ std::istream &	operator>> (std::istream &inp, Interval< T_Bound, T_Rnd > &i)

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

template<typename T_Bound , typename T_Rnd >
std::istream &	bitRead (std::istream &inp, Interval< T_Bound, T_Rnd > &iv)

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

template<typename T_Bound , typename T_Rnd >
std::istream &	hexRead (std::istream &inp, Interval< T_Bound, T_Rnd > &iv)

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

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

template<typename T_Bound , typename T_Rnd >
__INLINE__ Interval< T_Bound, T_Rnd >	add (const Interval< T_Bound, T_Rnd > &A_iv, const T_Bound &A_x)

template<typename T_Bound , typename T_Rnd >
__INLINE__ Interval< T_Bound, T_Rnd >	substract (const Interval< T_Bound, T_Rnd > &A_iv, const T_Bound &A_x)

template<typename T_Bound , typename T_Rnd >
__INLINE__ Interval< T_Bound, T_Rnd >	substract (const T_Bound &A_x, const Interval< T_Bound, T_Rnd > &A_iv)

template<typename T_Bound , typename T_Rnd >
__INLINE__ Interval< T_Bound, T_Rnd >	multiply (const Interval< T_Bound, T_Rnd > &A_iv, const T_Bound &A_x)

template<typename T_Bound , typename T_Rnd >
__INLINE__ Interval< T_Bound, T_Rnd >	divide (const Interval< T_Bound, T_Rnd > &A_iv, const T_Bound &A_x)

template<typename T_Bound , typename T_Rnd >
__INLINE__ Interval< T_Bound, T_Rnd >	divide (const T_Bound &A_x, const Interval< T_Bound, T_Rnd > &A_iv)

template<class T >
void	ignore_unused (T &)
	Function for a debugging purposes. Function checkInterval helps to get rid of many "ifdef's". If DEBUGGING options is set it checks if ends of the interval are in the right order. Otherwise it does nothing. More...

template<typename T_Bound >
void	checkInterval (const char *A_msg, const T_Bound &A_left, const T_Bound &A_right)

void	testNaN (const MpInterval &x)

template<>
MpInterval	sin (const MpInterval &x)

template<>
MpInterval	cos (const MpInterval &x)

template<>
MpInterval	tan (const MpInterval &x)

template<>
MpInterval	log (const MpInterval &x)

template<>
MpInterval	exp (const MpInterval &x)

template<>
MpInterval	sqrt (const MpInterval &z)

template<>
MpInterval	power (const MpInterval &a, const MpInterval &b)

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

Interval< MpReal >::BoundType	quadrant (const Interval< MpReal >::BoundType &x)

int	modulo4 (MpReal x)

template double	width< double, DoubleRounding > (const DoubleInterval &)

template DoubleInterval	diam< double, DoubleRounding > (const DoubleInterval &)

template bool	intersection< double, DoubleRounding > (DoubleInterval A_iv1, DoubleInterval A_iv2, DoubleInterval &A_rIntersection)

template DoubleInterval	intervalHull< double, DoubleRounding > (const DoubleInterval &A_iv1, const DoubleInterval &A_iv2)

template void	split< double, DoubleRounding > (DoubleInterval &A_iv, DoubleInterval &A_rMid, double &A_diam)

template DoubleInterval	power< double, DoubleRounding > (const DoubleInterval &x, int n)

template DoubleInterval	power< double, DoubleRounding > (const DoubleInterval &a, const DoubleInterval &b)

template DoubleInterval	sqrt< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	sin< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	cos< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	tan< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	cot< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	atan< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	asin< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	acos< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	sinh< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	cosh< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	tanh< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	coth< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	exp< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	log< double, DoubleRounding > (const DoubleInterval &x)

template DoubleInterval	solveAffineInclusion< double, DoubleRounding > (const DoubleInterval &a, const DoubleInterval &p, const DoubleInterval &c)

template DoubleInterval	solveAffineInclusion< double, DoubleRounding > (const DoubleInterval &a, const DoubleInterval &p, const DoubleInterval &c, int &dir)

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

Detailed Description

Interval arithmetics.

Typedef Documentation

◆ DoubleInterval

typedef capd::intervals::Interval<double, capd::rounding::DoubleRounding> capd::intervals::DoubleInterval

◆ IComplex

template<typename T >

using capd::intervals::IComplex = typedef capd::fields::Complex<T>

Definition for backward compatibility.

◆ MpfrClass

typedef capd::multiPrec::MpReal capd::intervals::MpfrClass

◆ MpInterval

typedef Interval<MpReal, MpReal> capd::intervals::MpInterval

◆ MpReal

typedef capd::multiPrec::MpReal capd::intervals::MpReal

Function Documentation

◆ acos< double, DoubleRounding >()

template DoubleInterval capd::intervals::acos< double, DoubleRounding > ( const DoubleInterval & x )

◆ add()

template<typename T_Bound , typename T_Rnd >

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

◆ asin< double, DoubleRounding >()

template DoubleInterval capd::intervals::asin< double, DoubleRounding > ( const DoubleInterval & x )

◆ atan< double, DoubleRounding >()

template DoubleInterval capd::intervals::atan< double, DoubleRounding > ( const DoubleInterval & x )

◆ binRead()

template<typename T_Bound , typename T_Rnd >

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

◆ binWrite()

template<typename T_Bound , typename T_Rnd >

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

◆ bitRead()

template<typename T_Bound , typename T_Rnd >

std::istream& capd::intervals::bitRead	(	std::istream &	inp,
		Interval< T_Bound, T_Rnd > &	iv
	)

◆ bitWrite()

template<typename T_Bound , typename T_Rnd >

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

◆ checkInterval()

template<typename T_Bound >

void capd::intervals::checkInterval	(	const char *	A_msg,
		const T_Bound &	A_left,
		const T_Bound &	A_right
	)

inline

◆ cos< double, DoubleRounding >()

template DoubleInterval capd::intervals::cos< double, DoubleRounding > ( const DoubleInterval & x )

◆ cosh< double, DoubleRounding >()

template DoubleInterval capd::intervals::cosh< double, DoubleRounding > ( const DoubleInterval & x )

◆ cot< double, DoubleRounding >()

template DoubleInterval capd::intervals::cot< double, DoubleRounding > ( const DoubleInterval & x )

◆ coth< double, DoubleRounding >()

template DoubleInterval capd::intervals::coth< double, DoubleRounding > ( const DoubleInterval & x )

◆ diam< double, DoubleRounding >()

template DoubleInterval capd::intervals::diam< double, DoubleRounding > ( const DoubleInterval & )

◆ divide() [1/2]

template<typename T_Bound , typename T_Rnd >

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

◆ divide() [2/2]

template<typename T_Bound , typename T_Rnd >

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

◆ exp< double, DoubleRounding >()

template DoubleInterval capd::intervals::exp< double, DoubleRounding > ( const DoubleInterval & x )

◆ hexRead()

template<typename T_Bound , typename T_Rnd >

std::istream& capd::intervals::hexRead	(	std::istream &	inp,
		Interval< T_Bound, T_Rnd > &	iv
	)

◆ hexWrite()

template<typename T_Bound , typename T_Rnd >

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

◆ ignore_unused()

template<class T >

void capd::intervals::ignore_unused ( T & )

Function for a debugging purposes. Function checkInterval helps to get rid of many "ifdef's". If DEBUGGING options is set it checks if ends of the interval are in the right order. Otherwise it does nothing.

Author: Tomasz Kapela

Date: 11-01-2006

◆ intersection< double, DoubleRounding >()

template bool capd::intervals::intersection< double, DoubleRounding >	(	DoubleInterval	A_iv1,
		DoubleInterval	A_iv2,
		DoubleInterval &	A_rIntersection
	)

◆ intervalHull< double, DoubleRounding >()

template DoubleInterval capd::intervals::intervalHull< double, DoubleRounding >	(	const DoubleInterval &	A_iv1,
		const DoubleInterval &	A_iv2
	)

◆ log< double, DoubleRounding >()

template DoubleInterval capd::intervals::log< double, DoubleRounding > ( const DoubleInterval & x )

◆ multiply()

template<typename T_Bound , typename T_Rnd >

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

◆ operator*()

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd> capd::intervals::operator*	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

◆ operator+()

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd> capd::intervals::operator+	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

◆ operator-()

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd> capd::intervals::operator-	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

◆ operator/()

template<typename T_Bound , typename T_Rnd >

__INLINE__ Interval< T_Bound, T_Rnd> capd::intervals::operator/	(	const Interval< T_Bound, T_Rnd > &	A_iv1,
		const Interval< T_Bound, T_Rnd > &	A_iv2
	)

◆ operator<<()

template<typename T_Bound , typename T_Rnd >

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

◆ operator>>()

template<typename T_Bound , typename T_Rnd >

__INLINE__ std::istream& capd::intervals::operator>>	(	std::istream &	inp,
		Interval< T_Bound, T_Rnd > &	i
	)

◆ pointAsin()

template<typename T_Bound , typename T_Rnd >

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

◆ positivePower()

template<typename T_Bound >

T_Bound capd::intervals::positivePower	(	T_Bound	value,
		unsigned	exponent
	)

a computation of value^{exponent} with current rounding settings (exponent has to be positive)

◆ power()

template<>

MpInterval capd::intervals::power	(	const MpInterval &	a,
		const MpInterval &	b
	)

inline

◆ power< double, DoubleRounding >() [1/2]

template DoubleInterval capd::intervals::power< double, DoubleRounding >	(	const DoubleInterval &	a,
		const DoubleInterval &	b
	)

◆ power< double, DoubleRounding >() [2/2]

template DoubleInterval capd::intervals::power< double, DoubleRounding >	(	const DoubleInterval &	x,
		int	n
	)

◆ quadrant()

Interval<MpReal>::BoundType capd::intervals::quadrant ( const Interval< MpReal >::BoundType & x )

◆ scaledAcos()

template<typename T_Bound , typename T_Rnd >

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

A rigorous computation of acos(x) for point intervals.

Remarks: we expect x to be a point interval

◆ scaledAsin1()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd> capd::intervals::scaledAsin1 ( const Interval< T_Bound, T_Rnd > & x )

inline

A rigorous computation of asin(x) far from -1 and 1 i.e. for -0.7 <= x <= 0.7.

Remarks: we expect x to be a point interval

◆ scaledAsin2()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd> capd::intervals::scaledAsin2 ( const Interval< T_Bound, T_Rnd > & x )

inline

A rigorous computation of asin(x) for 0.7 < x <=1.

we use: asin(x) = pi/2 - atan(sqrt(1-x^2) / x)

Remarks: we expect x to be a point interval

◆ scaledAtan1()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd> capd::intervals::scaledAtan1 ( const Interval< T_Bound, T_Rnd > & x )

a rigorous computation of atan(x) for 0 <= x

Remarks: if x<0 , then we compute sin(x=0); we expect x to be a point interval

◆ scaledAtan2()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd> capd::intervals::scaledAtan2 ( const Interval< T_Bound, T_Rnd > & x )

a rigorous computation of atan(x) for 0 <= x <= sqrt(2)-1

Remarks: if x<0 , then we compute sin(x=0); we expect x to be a point interval

◆ scaledExp()

template<typename T_Bound >

T_Bound capd::intervals::scaledExp	(	T_Bound	x,
		int	expTaylorOrder
	)

returns exp(x) for x in [0,1] with actual rounding

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

◆ scaledLogDown()

template<typename T_Bound >

T_Bound capd::intervals::scaledLogDown	(	const T_Bound &	x,
		int	logTaylorOrder
	)

computes lower bound for log(1+x) for $x \in [0,1/2]$

Remarks: the constant S_LogTaylorOrder must be even round down mode needs to be set

◆ scaledLogUp()

template<typename T_Bound >

T_Bound capd::intervals::scaledLogUp	(	const T_Bound &	x,
		int	logTaylorOrder
	)

computes upper bound for log(1+x) for $x \in [0,1/2]$

Remarks: the constant S_LogTaylorOrder must be even round UP mode needs to be set

◆ scaledSin1()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd> capd::intervals::scaledSin1 ( const Interval< T_Bound, T_Rnd > & x )

the function computes sin(x) for $x \subset [0,\infty]$

◆ scaledSin2()

template<typename T_Bound , typename T_Rnd >

Interval< T_Bound, T_Rnd> capd::intervals::scaledSin2 ( const Interval< T_Bound, T_Rnd > & x )

a rigorous computation of sin(x) for 0 <= x <= pi

Remarks: if x<0 , then we compute sin(x=0); we expect x to be a point interval

◆ sin< double, DoubleRounding >()

template DoubleInterval capd::intervals::sin< double, DoubleRounding > ( const DoubleInterval & x )

◆ sinh< double, DoubleRounding >()

template DoubleInterval capd::intervals::sinh< double, DoubleRounding > ( const DoubleInterval & x )

◆ solveAffineInclusion< double, DoubleRounding >() [1/2]

template DoubleInterval capd::intervals::solveAffineInclusion< double, DoubleRounding >	(	const DoubleInterval &	a,
		const DoubleInterval &	p,
		const DoubleInterval &	c
	)

◆ solveAffineInclusion< double, DoubleRounding >() [2/2]

template DoubleInterval capd::intervals::solveAffineInclusion< double, DoubleRounding >	(	const DoubleInterval &	a,
		const DoubleInterval &	p,
		const DoubleInterval &	c,
		int &	dir
	)

◆ split< double, DoubleRounding >()

template void capd::intervals::split< double, DoubleRounding >	(	DoubleInterval &	A_iv,
		DoubleInterval &	A_rMid,
		double &	A_diam
	)

◆ sqrt< double, DoubleRounding >()

template DoubleInterval capd::intervals::sqrt< double, DoubleRounding > ( const DoubleInterval & x )

◆ substract() [1/2]

template<typename T_Bound , typename T_Rnd >

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

◆ substract() [2/2]

template<typename T_Bound , typename T_Rnd >

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

◆ tan< double, DoubleRounding >()

template DoubleInterval capd::intervals::tan< double, DoubleRounding > ( const DoubleInterval & x )

◆ tanh< double, DoubleRounding >()

template DoubleInterval capd::intervals::tanh< double, DoubleRounding > ( const DoubleInterval & x )

◆ testNaN()

void capd::intervals::testNaN ( const MpInterval & x )

inline

◆ width< double, DoubleRounding >()

template double capd::intervals::width< double, DoubleRounding > ( const DoubleInterval & )

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ DoubleInterval

◆ IComplex

◆ MpfrClass

◆ MpInterval

◆ MpReal

Function Documentation

◆ acos< double, DoubleRounding >()

◆ add()

◆ asin< double, DoubleRounding >()

◆ atan< double, DoubleRounding >()

◆ binRead()

◆ binWrite()

◆ bitRead()

◆ bitWrite()

◆ checkInterval()

◆ cos< double, DoubleRounding >()

◆ cosh< double, DoubleRounding >()

◆ cot< double, DoubleRounding >()

◆ coth< double, DoubleRounding >()

◆ diam< double, DoubleRounding >()

◆ divide() [1/2]

◆ divide() [2/2]

◆ exp< double, DoubleRounding >()

◆ hexRead()

◆ hexWrite()

◆ ignore_unused()

◆ intersection< double, DoubleRounding >()

◆ intervalHull< double, DoubleRounding >()

◆ log< double, DoubleRounding >()

◆ multiply()

◆ operator*()

◆ operator+()

◆ operator-()

◆ operator/()

◆ operator<<()

◆ operator>>()

◆ pointAsin()

◆ positivePower()

◆ power()

◆ power< double, DoubleRounding >() [1/2]

◆ power< double, DoubleRounding >() [2/2]

◆ quadrant()

◆ scaledAcos()

◆ scaledAsin1()

◆ scaledAsin2()

◆ scaledAtan1()

◆ scaledAtan2()

◆ scaledExp()

◆ scaledLogDown()

◆ scaledLogUp()

◆ scaledSin1()

◆ scaledSin2()

◆ sin< double, DoubleRounding >()

◆ sinh< double, DoubleRounding >()

◆ solveAffineInclusion< double, DoubleRounding >() [1/2]

◆ solveAffineInclusion< double, DoubleRounding >() [2/2]

◆ split< double, DoubleRounding >()

◆ sqrt< double, DoubleRounding >()

◆ substract() [1/2]

◆ substract() [2/2]

◆ tan< double, DoubleRounding >()

◆ tanh< double, DoubleRounding >()

◆ testNaN()

◆ width< double, DoubleRounding >()