The class which contains the interval arithmetic including trigonometric functions. More...

#include <Interval.h>

Inheritance diagram for carl::Interval< Number >:

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Collaboration diagram for carl::Interval< Number >:

Public Types
using	Policy = policies< Number, Interval< Number > >

using	BoostIntervalPolicies = boost::numeric::interval_lib::policies< typename Policy::roundingP, typename Policy::checkingP >

using	BoostInterval = boost::numeric::interval< Number, BoostIntervalPolicies >

using	evalintervalmap = std::map< Variable, Interval< Number > >

using	roundingP = carl::rounding< Number >

using	checkingP = carl::checking< Number >

Public Member Functions
	Interval ()
	Default constructor which constructs the empty interval at point 0. More...

	Interval (const Number &n)
	Constructor which constructs the pointinterval at n. More...

	Interval (const Number &lower, const Number &upper)
	Constructor which constructs the weak-bounded interval between lower and upper. More...

	Interval (const BoostInterval &content, BoundType lowerBoundType=BoundType::WEAK, BoundType upperBoundType=BoundType::WEAK)
	Constructor which constructs the interval according to the passed boost interval with the passed bound types. More...

	Interval (const Number &lower, BoundType lowerBoundType, const Number &upper, BoundType upperBoundType)
	Constructor which constructs the interval according to the passed bounds with the passed bound types. More...

	Interval (const Interval< Number > &o)
	Copy constructor. More...

template<typename Other , DisableIf< std::is_same< Number, Other >> = dummy>
	Interval (const Interval< Other > &o)

template<typename N = Number, DisableIf< std::is_same< N, double >> = dummy, DisableIf< is_rational_type< N >> = dummy>
	Interval (const double &n)
	Constructor which constructs a pointinterval from a passed double. More...

template<typename N = Number, DisableIf< std::is_same< N, double >> = dummy, DisableIf< is_rational_type< N >> = dummy>
	Interval (double lower, double upper)
	Constructor which constructs an interval from the passed double bounds. More...

template<typename N = Number, DisableIf< std::is_same< N, double >> = dummy, DisableIf< is_rational_type< N >> = dummy>
	Interval (double lower, BoundType lowerBoundType, double upper, BoundType upperBoundType)
	Constructor which constructs the interval according to the passed double bounds with the passed bound types. More...

template<typename N = Number, DisableIf< std::is_same< N, int >> = dummy>
	Interval (const int &n)
	Constructor which constructs a pointinterval from a passed int. More...

template<typename N = Number, DisableIf< std::is_same< N, int >> = dummy>
	Interval (int lower, int upper)
	Constructor which constructs an interval from the passed int bounds. More...

template<typename N = Number, DisableIf< std::is_same< N, int >> = dummy>
	Interval (int lower, BoundType lowerBoundType, int upper, BoundType upperBoundType)
	Constructor which constructs the interval according to the passed int bounds with the passed bound types. More...

template<typename N = Number, DisableIf< std::is_same< N, unsigned int >> = dummy>
	Interval (const unsigned int &n)
	Constructor which constructs a pointinterval from a passed unsigned int. More...

template<typename N = Number, DisableIf< std::is_same< N, unsigned int >> = dummy>
	Interval (unsigned int lower, unsigned int upper)
	Constructor which constructs an interval from the passed unsigned int bounds. More...

template<typename N = Number, DisableIf< std::is_same< N, unsigned int >> = dummy>
	Interval (unsigned int lower, BoundType lowerBoundType, unsigned int upper, BoundType upperBoundType)
	Constructor which constructs the interval according to the passed unsigned int bounds with the passed bound types. More...

template<typename Num = Number, typename Rational , EnableIf< std::is_floating_point< Num >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>
	Interval (Rational n)
	Constructor which constructs a pointinterval from a passed general rational number. More...

template<typename Num = Number, typename Rational , EnableIf< std::is_floating_point< Num >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>
	Interval (Rational lower, Rational upper)
	Constructor which constructs an interval from the passed general rational bounds. More...

template<typename Num = Number, typename Rational , EnableIf< std::is_floating_point< Num >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>
	Interval (Rational lower, BoundType lowerBoundType, Rational upper, BoundType upperBoundType)
	Constructor which constructs the interval according to the passed general rational bounds with the passed bound types. More...

template<typename Num = Number, typename Float , EnableIf< is_rational_type< Num >> = dummy, EnableIf< std::is_floating_point< Float >> = dummy, DisableIf< std::is_same< Num, Float >> = dummy>
	Interval (Float n)
	Constructor which constructs a pointinterval from a passed general float number (e.g. More...

template<typename Num = Number, typename Float , EnableIf< is_rational_type< Num >> = dummy, EnableIf< std::is_floating_point< Float >> = dummy, DisableIf< std::is_same< Num, Float >> = dummy>
	Interval (Float lower, Float upper)
	Constructor which constructs an interval from the passed general float bounds (e.g. More...

template<typename Num = Number, typename Float , EnableIf< is_rational_type< Num >> = dummy, EnableIf< std::is_floating_point< Float >> = dummy, DisableIf< std::is_same< Num, Float >> = dummy, DisableIf< std::is_floating_point< Num >> = dummy>
	Interval (Float lower, BoundType lowerBoundType, Float upper, BoundType upperBoundType)
	Constructor which constructs the interval according to the passed general float bounds (e.g. More...

template<typename Num = Number, typename Rational , EnableIf< is_rational_type< Num >> = dummy, EnableIf< is_rational_type< Rational >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>
	Interval (Rational n)
	Constructor which constructs a pointinterval from a passed general float number (e.g. More...

template<typename Num = Number, typename Rational , EnableIf< is_rational_type< Num >> = dummy, EnableIf< is_rational_type< Rational >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>
	Interval (Rational lower, Rational upper)
	Constructor which constructs an interval from the passed general float bounds (e.g. More...

template<typename Num = Number, typename Rational , EnableIf< is_rational_type< Num >> = dummy, EnableIf< is_rational_type< Rational >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>
	Interval (Rational lower, BoundType lowerBoundType, Rational upper, BoundType upperBoundType)
	Constructor which constructs the interval according to the passed general float bounds (e.g. More...

	Interval (const LowerBound< Number > &lb, const UpperBound< Number > &ub)

	Interval (const LowerBound< Number > &lb, const LowerBound< Number > &ub)

	Interval (const UpperBound< Number > &lb, const UpperBound< Number > &ub)

	~Interval ()=default
	Destructor. More...

const Number &	lower () const
	The getter for the lower boundary of the interval. More...

const Number &	upper () const
	The getter for the upper boundary of the interval. More...

auto	lower_bound () const

auto	upper_bound () const

const BoostInterval &	content () const
	Returns a reference to the included boost interval. More...

BoostInterval &	content ()
	Returns a reference to the included boost interval. More...

BoundType	lower_bound_type () const
	The getter for the lower bound type of the interval. More...

BoundType	upper_bound_type () const
	The getter for the upper bound type of the interval. More...

void	set_lower (const Number &n)
	The setter for the lower boundary of the interval. More...

void	set_upper (const Number &n)
	The setter for the upper boundary of the interval. More...

void	set_lower_bound (const Number &n, BoundType b)
	The setter for the lower boundary of the interval. More...

void	set_upper_bound (const Number &n, BoundType b)
	The setter for the upper boundary of the interval. More...

void	set_lower_bound_type (BoundType b)
	The setter for the lower bound type of the interval. More...

void	set_upper_bound_type (BoundType b)
	The setter for the upper bound type of the interval. More...

Interval< Number > &	operator= (const Interval< Number > &rhs)
	The assignment operator. More...

void	set (const BoostInterval &content)
	Advanced setter to modify both boundaries at once. More...

void	set (const Number &lower, const Number &upper)
	Advanced setter to modify both boundaries at once by passing a boost interval. More...

bool	is_infinite () const
	Function which determines, if the interval is (-oo,oo). More...

bool	is_unbounded () const
	Function which determines, if the interval is unbounded. More...

bool	is_half_bounded () const
	Function which determines, if the interval is half-bounded. More...

bool	is_empty () const
	Function which determines, if the interval is empty. More...

bool	is_point_interval () const
	Function which determines, if the interval is a pointinterval. More...

bool	is_open_interval () const
	Function which determines, if the interval is open. More...

bool	is_closed_interval () const
	Function which determines, if the interval is closed. More...

bool	is_zero () const
	Function which determines, if the interval is the zero interval. More...

bool	is_one () const
	Function which determines, if the interval is the one interval. More...

bool	is_positive () const

bool	is_negative () const

bool	is_semi_positive () const

bool	is_semi_negative () const

Sign	sgn () const
	Determine whether the interval lays entirely left of 0 (NEGATIVE_SIGN), right of 0 (POSITIVE_SIGN) or contains 0 (ZERO_SIGN). More...

Interval< Number >	integral_part () const
	Computes the integral part of the given interval. More...

void	integralPart_assign ()
	Computes and assigns the integral part of the given interval. More...

bool	contains_integer () const
	Checks if the interval contains at least one integer value. More...

Number	diameter () const
	Returns the diameter of the interval. More...

void	diameter_assign ()
	Computes and assigns the diameter of the interval. More...

Number	diameter_ratio (const Interval< Number > &rhs) const
	Returns the ratio of the diameters of the given intervals. More...

void	diameter_ratio_assign (const Interval< Number > &rhs)
	Computes and assigns the ratio of the diameters of the given intervals. More...

Number	magnitude () const
	Returns the magnitude of the interval. More...

void	magnitude_assign ()
	Computes and assigns the magnitude of the interval. More...

void	center_assign ()
	Computes and assigns the center point of the interval. More...

bool	contains (const Number &val) const
	Checks if the interval contains the given value. More...

template<typename Num = Number, DisableIf< std::is_same< Num, int >> = dummy>
bool	contains (int val) const

bool	contains (const Interval< Number > &rhs) const
	Checks if the interval contains the given interval. More...

bool	meets (const Number &n) const
	Checks if the interval meets the given value, that is if the given value is contained in the closed interval defined by the bounds. More...

void	bloat_by (const Number &width)
	Bloats the interval by the given value. More...

void	bloat_times (const Number &factor)
	Bloats the interval times the factor (multiplies the overall width). More...

void	shrink_by (const Number &width)
	Shrinks the interval by the given value. More...

void	shrink_times (const Number &factor)
	Shrinks the interval by a multiple of its width. More...

std::pair< Interval< Number >, Interval< Number > >	split () const
	Splits the interval into 2 equally sized parts (strict-weak-cut). More...

std::list< Interval< Number > >	split (unsigned n) const
	Splits the interval into n equally sized parts (strict-weak-cut). More...

std::string	toString () const
	Creates a string representation of the interval. More...

Interval< Number >	add (const Interval< Number > &rhs) const
	Adds two intervals according to natural interval arithmetic. More...

void	add_assign (const Interval< Number > &rhs)

Interval< Number >	sub (const Interval< Number > &rhs) const
	Subtracts two intervals according to natural interval arithmetic. More...

void	sub_assign (const Interval< Number > &rhs)

Interval< Number >	mul (const Interval< Number > &rhs) const
	Multiplies two intervals according to natural interval arithmetic. More...

void	mul_assign (const Interval< Number > &rhs)

Interval< Number >	div (const Interval< Number > &rhs) const
	Divides two intervals according to natural interval arithmetic. More...

void	div_assign (const Interval< Number > &rhs)

bool	div_ext (const Interval< Number > &rhs, Interval< Number > &a, Interval< Number > &b) const
	Implements extended interval division with intervals containting zero. More...

Interval< Number >	inverse () const
	Calculates the additive inverse of an interval with respect to natural interval arithmetic. More...

Interval< Number >	abs () const
	Calculates the absolute value of the interval. More...

void	abs_assign ()
	Calculates and assigns the absolute value of the interval. More...

void	inverse_assign ()
	Calculates and assigns the additive inverse of an interval with respect to natural interval arithmetic. More...

bool	reciprocal (Interval< Number > &a, Interval< Number > &b) const
	Calculates the multiplicative inverse of an interval with respect to natural interval arithmetic. More...

template<typename Num = Number, EnableIf< std::is_floating_point< Num >> = dummy>
Interval< Number >	root (int deg) const
	Calculates the nth root of the interval with respect to natural interval arithmetic. More...

template<typename Num = Number, EnableIf< std::is_floating_point< Num >> = dummy>
void	root_assign (unsigned deg)
	Calculates and assigns the nth root of the interval with respect to natural interval arithmetic. More...

bool	is_consistent () const
	A quick check for the bound values. More...

Number	distance (const Interval< Number > &intervalA)
	Calculates the distance between two Intervals. More...

Interval< Number >	convex_hull (const Interval< Number > &interval) const

Static Public Member Functions
static Interval< Number >	unbounded_interval ()
	Method which returns the unbounded interval rooted at 0. More...

static Interval< Number >	empty_interval ()
	Method which returns the empty interval rooted at 0. More...

static Interval< Number >	zero_interval ()
	Method which returns the pointinterval rooted at 0. More...

static void	sanitize (Interval< Number > &)

Protected Attributes
BoostInterval	mContent

BoundType	mLowerBoundType = BoundType::STRICT

BoundType	mUpperBoundType = BoundType::STRICT

Friends
std::ostream &	operator<< (std::ostream &str, const Interval< Number > &i)
	Operator which passes a string representation of this to the given ostream. More...

Detailed Description

template<typename Number>
class carl::Interval< Number >

The class which contains the interval arithmetic including trigonometric functions.

The template parameter contains the number type used for the boundaries. It is necessary to implement the rounding and checking policies for any non-primitive type such that the desired inclusion property can be maintained.

Requirements for the NumberType:

Operators +,-,*,/ with the expected functionality
Operators +=,-=,*=,/= with the expected functionality
Operators <,>,<=,>=,==,!= with the expected functionality
Operations abs, min, max, log, exp, power, sqrt
Trigonometric functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh, atanh (these functions are needed for the specialization of the rounding modes.
Operator <<

Definition at line 133 of file Interval.h.

Member Typedef Documentation

◆ BoostInterval

template<typename Number >

using carl::Interval< Number >::BoostInterval = boost::numeric::interval< Number, BoostIntervalPolicies >

Definition at line 143 of file Interval.h.

◆ BoostIntervalPolicies

template<typename Number >

using carl::Interval< Number >::BoostIntervalPolicies = boost::numeric::interval_lib::policies< typename Policy::roundingP, typename Policy::checkingP >

Definition at line 142 of file Interval.h.

◆ checkingP

using carl::policies< Number, Interval< Number > >::checkingP = carl::checking<Number>

inherited

Definition at line 70 of file Interval.h.

◆ evalintervalmap

template<typename Number >

using carl::Interval< Number >::evalintervalmap = std::map<Variable, Interval<Number> >

Definition at line 144 of file Interval.h.

◆ Policy

template<typename Number >

using carl::Interval< Number >::Policy = policies<Number, Interval<Number> >

Definition at line 136 of file Interval.h.

◆ roundingP

using carl::policies< Number, Interval< Number > >::roundingP = carl::rounding<Number>

inherited

Definition at line 69 of file Interval.h.

Constructor & Destructor Documentation

◆ Interval() [1/28]

template<typename Number >

carl::Interval< Number >::Interval ( )

inline

Default constructor which constructs the empty interval at point 0.

Definition at line 176 of file Interval.h.

◆ Interval() [2/28]

template<typename Number >

carl::Interval< Number >::Interval ( const Number & n )

inlineexplicit

Constructor which constructs the pointinterval at n.

Parameters

n	Location of the pointinterval.

Definition at line 184 of file Interval.h.

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template<typename Number >

carl::Interval< Number >::Interval	(	const Number &	lower,
		const Number &	upper
	)

inlineexplicit

Constructor which constructs the weak-bounded interval between lower and upper.

If the bounds are invalid an empty interval at point 0 is constructed.

Parameters

lower	The desired lower bound.
upper	The desired upper bound.

Definition at line 199 of file Interval.h.

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◆ Interval() [4/28]

template<typename Number >

carl::Interval< Number >::Interval	(	const BoostInterval< Number > &	content,
		BoundType	lowerBoundType = `BoundType::WEAK`,
		BoundType	upperBoundType = `BoundType::WEAK`
	)

inlineexplicit

Constructor which constructs the interval according to the passed boost interval with the passed bound types.

Note that if the interval is a pointinterval with both strict bounds or the content is invalid the empty interval is constructed and if both bounds are infty the unbounded interval is constructed.

Parameters

content	The passed boost interval.
lowerBoundType	The desired lower bound type, defaults to WEAK.
upperBoundType	The desired upper bound type, defaults to WEAK.

Definition at line 227 of file Interval.h.

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◆ Interval() [5/28]

template<typename Number >

carl::Interval< Number >::Interval	(	const Number &	lower,
		BoundType	lowerBoundType,
		const Number &	upper,
		BoundType	upperBoundType
	)

inline

Constructor which constructs the interval according to the passed bounds with the passed bound types.

Note that if the interval is a pointinterval with both strict bounds or the content is invalid the empty interval is constru

Parameters

lower	The desired lower bound.
lowerBoundType	The desired lower bound type.
upper	The desired upper bound.
upperBoundType	The desired upper bound type.

Definition at line 277 of file Interval.h.

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◆ Interval() [6/28]

template<typename Number >

carl::Interval< Number >::Interval ( const Interval< Number > & o )

inline

Copy constructor.

Parameters

o	The original interval.

Definition at line 320 of file Interval.h.

◆ Interval() [7/28]

template<typename Number >

template<typename Other , DisableIf< std::is_same< Number, Other >> = dummy>

carl::Interval< Number >::Interval ( const Interval< Other > & o )

inlineexplicit

Definition at line 326 of file Interval.h.

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◆ Interval() [8/28]

template<typename Number >

template<typename N = Number, DisableIf< std::is_same< N, double >> = dummy, DisableIf< is_rational_type< N >> = dummy>

carl::Interval< Number >::Interval ( const double & n )

inlineexplicit

Constructor which constructs a pointinterval from a passed double.

Parameters

n	The passed double.

Definition at line 336 of file Interval.h.

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template<typename Number >

template<typename N = Number, DisableIf< std::is_same< N, double >> = dummy, DisableIf< is_rational_type< N >> = dummy>

carl::Interval< Number >::Interval	(	double	lower,
		double	upper
	)

inlineexplicit

Constructor which constructs an interval from the passed double bounds.

Parameters

lower	The desired lower bound.
upper	The desired upper bound.

Definition at line 349 of file Interval.h.

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◆ Interval() [10/28]

template<typename Number >

template<typename N = Number, DisableIf< std::is_same< N, double >> = dummy, DisableIf< is_rational_type< N >> = dummy>

carl::Interval< Number >::Interval	(	double	lower,
		BoundType	lowerBoundType,
		double	upper,
		BoundType	upperBoundType
	)

inline

Constructor which constructs the interval according to the passed double bounds with the passed bound types.

Note that if the interval is a pointinterval with both strict bounds or the content is invalid the empty interval is constru

Parameters

lower	The desired double lower bound.
lowerBoundType	The desired lower bound type.
upper	The desired double upper bound.
upperBoundType	The desired upper bound type.

Definition at line 377 of file Interval.h.

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◆ Interval() [11/28]

template<typename Number >

template<typename N = Number, DisableIf< std::is_same< N, int >> = dummy>

carl::Interval< Number >::Interval ( const int & n )

inlineexplicit

Constructor which constructs a pointinterval from a passed int.

Parameters

n	The passed double.

Definition at line 420 of file Interval.h.

◆ Interval() [12/28]

template<typename Number >

template<typename N = Number, DisableIf< std::is_same< N, int >> = dummy>

carl::Interval< Number >::Interval	(	int	lower,
		int	upper
	)

inlineexplicit

Constructor which constructs an interval from the passed int bounds.

Parameters

lower	The desired lower bound.
upper	The desired upper bound.

Definition at line 431 of file Interval.h.

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◆ Interval() [13/28]

template<typename Number >

template<typename N = Number, DisableIf< std::is_same< N, int >> = dummy>

carl::Interval< Number >::Interval	(	int	lower,
		BoundType	lowerBoundType,
		int	upper,
		BoundType	upperBoundType
	)

inline

Constructor which constructs the interval according to the passed int bounds with the passed bound types.

Note that if the interval is a pointinterval with both strict bounds or the content is invalid the empty interval is constru

Parameters

lower	The desired lower bound.
lowerBoundType	The desired lower bound type.
upper	The desired upper bound.
upperBoundType	The desired upper bound type.

Definition at line 458 of file Interval.h.

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◆ Interval() [14/28]

template<typename Number >

template<typename N = Number, DisableIf< std::is_same< N, unsigned int >> = dummy>

carl::Interval< Number >::Interval ( const unsigned int & n )

inlineexplicit

Constructor which constructs a pointinterval from a passed unsigned int.

Parameters

n	The passed double.

Definition at line 500 of file Interval.h.

◆ Interval() [15/28]

template<typename Number >

template<typename N = Number, DisableIf< std::is_same< N, unsigned int >> = dummy>

carl::Interval< Number >::Interval	(	unsigned int	lower,
		unsigned int	upper
	)

inlineexplicit

Constructor which constructs an interval from the passed unsigned int bounds.

Parameters

lower	The desired lower bound.
upper	The desired upper bound.

Definition at line 511 of file Interval.h.

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◆ Interval() [16/28]

template<typename Number >

template<typename N = Number, DisableIf< std::is_same< N, unsigned int >> = dummy>

carl::Interval< Number >::Interval	(	unsigned int	lower,
		BoundType	lowerBoundType,
		unsigned int	upper,
		BoundType	upperBoundType
	)

inline

Constructor which constructs the interval according to the passed unsigned int bounds with the passed bound types.

Note that if the interval is a pointinterval with both strict bounds or the content is invalid the empty interval is constru

Parameters

lower	The desired lower bound.
lowerBoundType	The desired lower bound type.
upper	The desired upper bound.
upperBoundType	The desired upper bound type.

Definition at line 538 of file Interval.h.

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◆ Interval() [17/28]

template<typename Number >

template<typename Num = Number, typename Rational , EnableIf< std::is_floating_point< Num >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>

carl::Interval< Number >::Interval ( Rational n )

inlineexplicit

Constructor which constructs a pointinterval from a passed general rational number.

Parameters

n	The passed double.

Definition at line 581 of file Interval.h.

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◆ Interval() [18/28]

template<typename Number >

template<typename Num = Number, typename Rational , EnableIf< std::is_floating_point< Num >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>

carl::Interval< Number >::Interval	(	Rational	lower,
		Rational	upper
	)

inlineexplicit

Constructor which constructs an interval from the passed general rational bounds.

Parameters

lower	The desired lower bound.
upper	The desired upper bound.

Definition at line 595 of file Interval.h.

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◆ Interval() [19/28]

template<typename Number >

template<typename Num = Number, typename Rational , EnableIf< std::is_floating_point< Num >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>

carl::Interval< Number >::Interval	(	Rational	lower,
		BoundType	lowerBoundType,
		Rational	upper,
		BoundType	upperBoundType
	)

inline

Constructor which constructs the interval according to the passed general rational bounds with the passed bound types.

Note that if the interval is a pointinterval with both strict bounds or the content is invalid the empty interval is constru

Parameters

lower	The desired lower bound.
lowerBoundType	The desired lower bound type.
upper	The desired upper bound.
upperBoundType	The desired upper bound type.

Definition at line 613 of file Interval.h.

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◆ Interval() [20/28]

template<typename Number >

template<typename Num = Number, typename Float , EnableIf< is_rational_type< Num >> = dummy, EnableIf< std::is_floating_point< Float >> = dummy, DisableIf< std::is_same< Num, Float >> = dummy>

carl::Interval< Number >::Interval ( Float n )

inlineexplicit

Constructor which constructs a pointinterval from a passed general float number (e.g.

FLOAT_T).

Parameters

n	The passed double.

Definition at line 652 of file Interval.h.

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◆ Interval() [21/28]

template<typename Number >

template<typename Num = Number, typename Float , EnableIf< is_rational_type< Num >> = dummy, EnableIf< std::is_floating_point< Float >> = dummy, DisableIf< std::is_same< Num, Float >> = dummy>

carl::Interval< Number >::Interval	(	Float	lower,
		Float	upper
	)

inlineexplicit

Constructor which constructs an interval from the passed general float bounds (e.g.

FLOAT_T).

Parameters

lower	The desired lower bound.
upper	The desired upper bound.

Definition at line 666 of file Interval.h.

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◆ Interval() [22/28]

template<typename Number >

template<typename Num = Number, typename Float , EnableIf< is_rational_type< Num >> = dummy, EnableIf< std::is_floating_point< Float >> = dummy, DisableIf< std::is_same< Num, Float >> = dummy, DisableIf< std::is_floating_point< Num >> = dummy>

carl::Interval< Number >::Interval	(	Float	lower,
		BoundType	lowerBoundType,
		Float	upper,
		BoundType	upperBoundType
	)

inline

Constructor which constructs the interval according to the passed general float bounds (e.g.

FLOAT_T) with the passed bound types. Note that if the interval is a pointinterval with both strict bounds or the content is invalid the empty interval is constru

Parameters

lower	The desired lower bound.
lowerBoundType	The desired lower bound type.
upper	The desired upper bound.
upperBoundType	The desired upper bound type.

Definition at line 684 of file Interval.h.

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◆ Interval() [23/28]

template<typename Number >

template<typename Num = Number, typename Rational , EnableIf< is_rational_type< Num >> = dummy, EnableIf< is_rational_type< Rational >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>

carl::Interval< Number >::Interval ( Rational n )

inlineexplicit

Constructor which constructs a pointinterval from a passed general float number (e.g.

FLOAT_T).

Parameters

n	The passed double.

Definition at line 722 of file Interval.h.

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◆ Interval() [24/28]

template<typename Number >

template<typename Num = Number, typename Rational , EnableIf< is_rational_type< Num >> = dummy, EnableIf< is_rational_type< Rational >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>

carl::Interval< Number >::Interval	(	Rational	lower,
		Rational	upper
	)

inlineexplicit

Constructor which constructs an interval from the passed general float bounds (e.g.

FLOAT_T).

Parameters

lower	The desired lower bound.
upper	The desired upper bound.

Definition at line 736 of file Interval.h.

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◆ Interval() [25/28]

template<typename Number >

template<typename Num = Number, typename Rational , EnableIf< is_rational_type< Num >> = dummy, EnableIf< is_rational_type< Rational >> = dummy, DisableIf< std::is_same< Num, Rational >> = dummy>

carl::Interval< Number >::Interval	(	Rational	lower,
		BoundType	lowerBoundType,
		Rational	upper,
		BoundType	upperBoundType
	)

inline

Constructor which constructs the interval according to the passed general float bounds (e.g.

FLOAT_T) with the passed bound types. Note that if the interval is a pointinterval with both strict bounds or the content is invalid the empty interval is constru

Parameters

lower	The desired lower bound.
lowerBoundType	The desired lower bound type.
upper	The desired upper bound.
upperBoundType	The desired upper bound type.

Definition at line 754 of file Interval.h.

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◆ Interval() [26/28]

template<typename Number >

carl::Interval< Number >::Interval	(	const LowerBound< Number > &	lb,
		const UpperBound< Number > &	ub
	)

inline

Definition at line 785 of file Interval.h.

◆ Interval() [27/28]

template<typename Number >

carl::Interval< Number >::Interval	(	const LowerBound< Number > &	lb,
		const LowerBound< Number > &	ub
	)

inline

Definition at line 790 of file Interval.h.

◆ Interval() [28/28]

template<typename Number >

carl::Interval< Number >::Interval	(	const UpperBound< Number > &	lb,
		const UpperBound< Number > &	ub
	)

inline

Definition at line 795 of file Interval.h.

◆ ~Interval()

template<typename Number >

carl::Interval< Number >::~Interval ( )

default

Destructor.

Member Function Documentation

◆ abs()

template<typename Number >

Interval<Number> carl::Interval< Number >::abs ( ) const

Calculates the absolute value of the interval.

Returns: Interval.

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◆ abs_assign()

template<typename Number >

void carl::Interval< Number >::abs_assign ( )

Calculates and assigns the absolute value of the interval.

◆ add()

template<typename Number >

Interval<Number> carl::Interval< Number >::add ( const Interval< Number > & rhs ) const

Adds two intervals according to natural interval arithmetic.

Parameters

rhs Interval.

Returns: Result.

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◆ add_assign()

template<typename Number >

void carl::Interval< Number >::add_assign ( const Interval< Number > & rhs )

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◆ bloat_by()

template<typename Number >

void carl::Interval< Number >::bloat_by ( const Number & width )

Bloats the interval by the given value.

Parameters

width Width.

◆ bloat_times()

template<typename Number >

void carl::Interval< Number >::bloat_times ( const Number & factor )

Bloats the interval times the factor (multiplies the overall width).

Parameters

factor Factor.

◆ center_assign()

template<typename Number >

void carl::Interval< Number >::center_assign ( )

Computes and assigns the center point of the interval.

◆ contains() [1/3]

template<typename Number >

bool carl::Interval< Number >::contains ( const Interval< Number > & rhs ) const

Checks if the interval contains the given interval.

Parameters

rhs	Interval to be checked.

Returns: True if rhs is contained in this.

◆ contains() [2/3]

template<typename Number >

bool carl::Interval< Number >::contains ( const Number & val ) const

Checks if the interval contains the given value.

Parameters

val	Value to be checked.

Returns: True if the value is contained in this.

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◆ contains() [3/3]

template<typename Number >

template<typename Num = Number, DisableIf< std::is_same< Num, int >> = dummy>

bool carl::Interval< Number >::contains ( int val ) const

inline

Definition at line 1237 of file Interval.h.

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◆ contains_integer()

template<typename Number >

bool carl::Interval< Number >::contains_integer ( ) const

Checks if the interval contains at least one integer value.

Returns: true, if the interval contains an integer.

◆ content() [1/2]

template<typename Number >

BoostInterval& carl::Interval< Number >::content ( )

inline

Returns a reference to the included boost interval.

Returns: Boost interval reference.

Definition at line 874 of file Interval.h.

◆ content() [2/2]

template<typename Number >

const BoostInterval& carl::Interval< Number >::content ( ) const

inline

Returns a reference to the included boost interval.

Returns: Boost interval reference.

Definition at line 865 of file Interval.h.

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◆ convex_hull()

template<typename Number >

Interval<Number> carl::Interval< Number >::convex_hull ( const Interval< Number > & interval ) const

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◆ diameter()

template<typename Number >

Number carl::Interval< Number >::diameter ( ) const

Returns the diameter of the interval.

Returns: Diameter.

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◆ diameter_assign()

template<typename Number >

void carl::Interval< Number >::diameter_assign ( )

Computes and assigns the diameter of the interval.

◆ diameter_ratio()

template<typename Number >

Number carl::Interval< Number >::diameter_ratio ( const Interval< Number > & rhs ) const

Returns the ratio of the diameters of the given intervals.

Parameters

rhs	Other interval.

Returns: Ratio.

◆ diameter_ratio_assign()

template<typename Number >

void carl::Interval< Number >::diameter_ratio_assign ( const Interval< Number > & rhs )

Computes and assigns the ratio of the diameters of the given intervals.

Parameters

rhs	Other interval.

◆ distance()

template<typename Number >

Number carl::Interval< Number >::distance ( const Interval< Number > & intervalA )

Calculates the distance between two Intervals.

Parameters

intervalA Interval to wich we want to know the distance.

Returns: distance to intervalA

◆ div()

template<typename Number >

Interval<Number> carl::Interval< Number >::div ( const Interval< Number > & rhs ) const

Divides two intervals according to natural interval arithmetic.

Parameters

rhs Interval.

Returns: Result.

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◆ div_assign()

template<typename Number >

void carl::Interval< Number >::div_assign ( const Interval< Number > & rhs )

◆ div_ext()

template<typename Number >

bool carl::Interval< Number >::div_ext	(	const Interval< Number > &	rhs,
		Interval< Number > &	a,
		Interval< Number > &	b
	)		const

Implements extended interval division with intervals containting zero.

Parameters

rhs	Interval.
a	Result a.
b	Result b.

Returns: True if split occurred.

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◆ empty_interval()

template<typename Number >

static Interval<Number> carl::Interval< Number >::empty_interval ( )

inlinestatic

Method which returns the empty interval rooted at 0.

Returns: Empty interval.

Definition at line 813 of file Interval.h.

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◆ integral_part()

template<typename Number >

Interval<Number> carl::Interval< Number >::integral_part ( ) const

Computes the integral part of the given interval.

Returns: Interval.

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◆ integralPart_assign()

template<typename Number >

void carl::Interval< Number >::integralPart_assign ( )

Computes and assigns the integral part of the given interval.

Returns: Interval.

◆ inverse()

template<typename Number >

Interval<Number> carl::Interval< Number >::inverse ( ) const

Calculates the additive inverse of an interval with respect to natural interval arithmetic.

Returns: Interval.

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◆ inverse_assign()

template<typename Number >

void carl::Interval< Number >::inverse_assign ( )

Calculates and assigns the additive inverse of an interval with respect to natural interval arithmetic.

◆ is_closed_interval()

template<typename Number >

bool carl::Interval< Number >::is_closed_interval ( ) const

inline

Function which determines, if the interval is closed.

Returns: True if both bounds are WEAK.

Definition at line 1091 of file Interval.h.

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◆ is_consistent()

template<typename Number >

bool carl::Interval< Number >::is_consistent ( ) const

inline

A quick check for the bound values.

Returns: True if the lower bound is less or equal to the upper bound.

Definition at line 1426 of file Interval.h.

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◆ is_empty()

template<typename Number >

bool carl::Interval< Number >::is_empty ( ) const

inline

Function which determines, if the interval is empty.

Returns: True if the interval is empty.

Definition at line 1056 of file Interval.h.

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◆ is_half_bounded()

template<typename Number >

bool carl::Interval< Number >::is_half_bounded ( ) const

inline

Function which determines, if the interval is half-bounded.

Returns: True if exactly one bound is INFTY.

Definition at line 1046 of file Interval.h.

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◆ is_infinite()

template<typename Number >

bool carl::Interval< Number >::is_infinite ( ) const

inline

Function which determines, if the interval is (-oo,oo).

Returns: True if both bounds are INFTY.

Definition at line 1026 of file Interval.h.

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◆ is_negative()

template<typename Number >

bool carl::Interval< Number >::is_negative ( ) const

inline

Returns: true, if it this interval contains only negative values.

Definition at line 1133 of file Interval.h.

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◆ is_one()

template<typename Number >

bool carl::Interval< Number >::is_one ( ) const

inline

Function which determines, if the interval is the one interval.

Returns: True if it is a pointinterval rooted at 1.

Definition at line 1111 of file Interval.h.

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◆ is_open_interval()

template<typename Number >

bool carl::Interval< Number >::is_open_interval ( ) const

inline

Function which determines, if the interval is open.

Returns: True if both bounds are STRICT.

Definition at line 1081 of file Interval.h.

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◆ is_point_interval()

template<typename Number >

bool carl::Interval< Number >::is_point_interval ( ) const

inline

Function which determines, if the interval is a pointinterval.

Returns: True if this is a pointinterval.

Definition at line 1071 of file Interval.h.

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◆ is_positive()

template<typename Number >

bool carl::Interval< Number >::is_positive ( ) const

inline

Returns: true, if it this interval contains only positive values.

Definition at line 1120 of file Interval.h.

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◆ is_semi_negative()

template<typename Number >

bool carl::Interval< Number >::is_semi_negative ( ) const

inline

Returns: true, if it this interval contains only negative values or 0.

Definition at line 1157 of file Interval.h.

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◆ is_semi_positive()

template<typename Number >

bool carl::Interval< Number >::is_semi_positive ( ) const

inline

Returns: true, if it this interval contains only positive values or 0.

Definition at line 1146 of file Interval.h.

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◆ is_unbounded()

template<typename Number >

bool carl::Interval< Number >::is_unbounded ( ) const

inline

Function which determines, if the interval is unbounded.

Returns: True if at least one bound is INFTY.

Definition at line 1036 of file Interval.h.

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◆ is_zero()

template<typename Number >

bool carl::Interval< Number >::is_zero ( ) const

inline

Function which determines, if the interval is the zero interval.

Returns: True if it is a pointinterval rooted at 0.

Definition at line 1101 of file Interval.h.

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◆ lower()

template<typename Number >

const Number& carl::Interval< Number >::lower ( ) const

inline

The getter for the lower boundary of the interval.

Returns: Lower interval boundary.

Definition at line 840 of file Interval.h.

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◆ lower_bound()

template<typename Number >

auto carl::Interval< Number >::lower_bound ( ) const

inline

Definition at line 854 of file Interval.h.

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◆ lower_bound_type()

template<typename Number >

BoundType carl::Interval< Number >::lower_bound_type ( ) const

inline

The getter for the lower bound type of the interval.

Returns: Lower bound type.

Definition at line 883 of file Interval.h.

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◆ magnitude()

template<typename Number >

Number carl::Interval< Number >::magnitude ( ) const

Returns the magnitude of the interval.

Returns: Magnitude.

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◆ magnitude_assign()

template<typename Number >

void carl::Interval< Number >::magnitude_assign ( )

Computes and assigns the magnitude of the interval.

◆ meets()

template<typename Number >

bool carl::Interval< Number >::meets ( const Number & n ) const

Checks if the interval meets the given value, that is if the given value is contained in the closed interval defined by the bounds.

Parameters

val	Value to be checked.

Returns: True if val is fully contained in this.

◆ mul()

template<typename Number >

Interval<Number> carl::Interval< Number >::mul ( const Interval< Number > & rhs ) const

Multiplies two intervals according to natural interval arithmetic.

Parameters

rhs Interval.

Returns: Result.

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◆ mul_assign()

template<typename Number >

void carl::Interval< Number >::mul_assign ( const Interval< Number > & rhs )

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◆ operator=()

template<typename Number >

Interval<Number>& carl::Interval< Number >::operator= ( const Interval< Number > & rhs )

inline

The assignment operator.

Parameters

rhs	Source interval.

Returns

Definition at line 990 of file Interval.h.

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◆ reciprocal()

template<typename Number >

bool carl::Interval< Number >::reciprocal	(	Interval< Number > &	a,
		Interval< Number > &	b
	)		const

Calculates the multiplicative inverse of an interval with respect to natural interval arithmetic.

Parameters

a	Result a.
b	Result b.

Returns: True, if split occured.

◆ root()

template<typename Number >

template<typename Num = Number, EnableIf< std::is_floating_point< Num >> = dummy>

Interval<Number> carl::Interval< Number >::root ( int deg ) const

Calculates the nth root of the interval with respect to natural interval arithmetic.

Parameters

deg Degree.

Returns: Result.

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◆ root_assign()

template<typename Number >

template<typename Num = Number, EnableIf< std::is_floating_point< Num >> = dummy>

void carl::Interval< Number >::root_assign ( unsigned deg )

Calculates and assigns the nth root of the interval with respect to natural interval arithmetic.

Parameters

deg Degree.

◆ sanitize()

static void carl::policies< Number, Interval< Number > >::sanitize ( Interval< Number > & )

inlinestaticinherited

Definition at line 71 of file Interval.h.

◆ set() [1/2]

template<typename Number >

void carl::Interval< Number >::set ( const BoostInterval< Number > & content )

inline

Advanced setter to modify both boundaries at once.

Parameters

lower	Lower boundary.
upper	Upper boundary.

Definition at line 1007 of file Interval.h.

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◆ set() [2/2]

template<typename Number >

void carl::Interval< Number >::set	(	const Number &	lower,
		const Number &	upper
	)

inline

Advanced setter to modify both boundaries at once by passing a boost interval.

Parameters

content Boost interval.

Definition at line 1017 of file Interval.h.

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◆ set_lower()

template<typename Number >

void carl::Interval< Number >::set_lower ( const Number & n )

inline

The setter for the lower boundary of the interval.

Parameters

n	Lower boundary.

Definition at line 901 of file Interval.h.

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◆ set_lower_bound()

template<typename Number >

void carl::Interval< Number >::set_lower_bound	(	const Number &	n,
		BoundType	b
	)

inline

The setter for the lower boundary of the interval.

Parameters

n	Lower boundary.

TODO: Fix this.

Definition at line 919 of file Interval.h.

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◆ set_lower_bound_type()

template<typename Number >

void carl::Interval< Number >::set_lower_bound_type ( BoundType b )

inline

The setter for the lower bound type of the interval.

Parameters

b	Lower bound type.

Definition at line 963 of file Interval.h.

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◆ set_upper()

template<typename Number >

void carl::Interval< Number >::set_upper ( const Number & n )

inline

The setter for the upper boundary of the interval.

Parameters

n	Upper boundary.

Definition at line 910 of file Interval.h.

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◆ set_upper_bound()

template<typename Number >

void carl::Interval< Number >::set_upper_bound	(	const Number &	n,
		BoundType	b
	)

inline

The setter for the upper boundary of the interval.

Parameters

n	Upper boundary.

TODO: Fix this.

Definition at line 941 of file Interval.h.

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◆ set_upper_bound_type()

template<typename Number >

void carl::Interval< Number >::set_upper_bound_type ( BoundType b )

inline

The setter for the upper bound type of the interval.

Parameters

b	Upper bound type.

Definition at line 976 of file Interval.h.

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◆ sgn()

template<typename Number >

Sign carl::Interval< Number >::sgn ( ) const

inline

Determine whether the interval lays entirely left of 0 (NEGATIVE_SIGN), right of 0 (POSITIVE_SIGN) or contains 0 (ZERO_SIGN).

Returns: NEGATIVE_SIGN, if the interval lays entirely left of 0; POSITIVE_SIGN, if right of 0; or ZERO_SIGN, if contains 0.

◆ shrink_by()

template<typename Number >

void carl::Interval< Number >::shrink_by ( const Number & width )

Shrinks the interval by the given value.

Parameters

width Width.

◆ shrink_times()

template<typename Number >

void carl::Interval< Number >::shrink_times ( const Number & factor )

Shrinks the interval by a multiple of its width.

Parameters

factor Factor.

◆ split() [1/2]

template<typename Number >

std::pair<Interval<Number>, Interval<Number > > carl::Interval< Number >::split ( ) const

Splits the interval into 2 equally sized parts (strict-weak-cut).

Returns: pair<interval, interval>.

◆ split() [2/2]

template<typename Number >

std::list<Interval<Number > > carl::Interval< Number >::split ( unsigned n ) const

Splits the interval into n equally sized parts (strict-weak-cut).

Returns: list<interval>.

◆ sub()

template<typename Number >

Interval<Number> carl::Interval< Number >::sub ( const Interval< Number > & rhs ) const

Subtracts two intervals according to natural interval arithmetic.

Parameters

rhs Interval.

Returns: Result.

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◆ sub_assign()

template<typename Number >

void carl::Interval< Number >::sub_assign ( const Interval< Number > & rhs )

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◆ toString()

template<typename Number >

std::string carl::Interval< Number >::toString ( ) const

Creates a string representation of the interval.

Returns: String representation of this.

◆ unbounded_interval()

template<typename Number >

static Interval<Number> carl::Interval< Number >::unbounded_interval ( )

inlinestatic

Method which returns the unbounded interval rooted at 0.

Returns: Unbounded interval.

Definition at line 804 of file Interval.h.

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◆ upper()

template<typename Number >

const Number& carl::Interval< Number >::upper ( ) const

inline

The getter for the upper boundary of the interval.

Returns: Upper interval boundary.

Definition at line 849 of file Interval.h.

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◆ upper_bound()

template<typename Number >

auto carl::Interval< Number >::upper_bound ( ) const

inline

Definition at line 857 of file Interval.h.

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◆ upper_bound_type()

template<typename Number >

BoundType carl::Interval< Number >::upper_bound_type ( ) const

inline

The getter for the upper bound type of the interval.

Returns: Upper bound type.

Definition at line 892 of file Interval.h.

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◆ zero_interval()

template<typename Number >

static Interval<Number> carl::Interval< Number >::zero_interval ( )

inlinestatic

Method which returns the pointinterval rooted at 0.

Returns: Pointinterval(0).

Definition at line 822 of file Interval.h.

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Friends And Related Function Documentation

◆ operator<<

template<typename Number >

std::ostream& operator<<	(	std::ostream &	str,
		const Interval< Number > &	i
	)

friend

Operator which passes a string representation of this to the given ostream.

Parameters

str	The ostream.
i	The interval.

Returns: A reference to ostream.

Definition at line 1304 of file Interval.h.

Field Documentation

◆ mContent

template<typename Number >

BoostInterval carl::Interval< Number >::mContent

protected

Definition at line 163 of file Interval.h.

◆ mLowerBoundType

template<typename Number >

BoundType carl::Interval< Number >::mLowerBoundType = BoundType::STRICT

protected

Definition at line 164 of file Interval.h.

◆ mUpperBoundType

template<typename Number >

BoundType carl::Interval< Number >::mUpperBoundType = BoundType::STRICT

protected

Definition at line 165 of file Interval.h.

The documentation for this class was generated from the following file:

carl-arith/interval/Interval.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

template<typename Number> class carl::Interval< Number >

Member Typedef Documentation

◆ BoostInterval

◆ BoostIntervalPolicies

◆ checkingP

◆ evalintervalmap

◆ Policy

◆ roundingP

Constructor & Destructor Documentation

◆ Interval() [1/28]

◆ Interval() [2/28]

◆ Interval() [3/28]

◆ Interval() [4/28]

◆ Interval() [5/28]

◆ Interval() [6/28]

◆ Interval() [7/28]

◆ Interval() [8/28]

◆ Interval() [9/28]

◆ Interval() [10/28]

◆ Interval() [11/28]

◆ Interval() [12/28]

◆ Interval() [13/28]

◆ Interval() [14/28]

◆ Interval() [15/28]

◆ Interval() [16/28]

◆ Interval() [17/28]

◆ Interval() [18/28]

◆ Interval() [19/28]

◆ Interval() [20/28]

◆ Interval() [21/28]

◆ Interval() [22/28]

◆ Interval() [23/28]

◆ Interval() [24/28]

◆ Interval() [25/28]

◆ Interval() [26/28]

◆ Interval() [27/28]

◆ Interval() [28/28]

◆ ~Interval()

Member Function Documentation

◆ abs()

◆ abs_assign()

◆ add()

◆ add_assign()

◆ bloat_by()

◆ bloat_times()

◆ center_assign()

◆ contains() [1/3]

◆ contains() [2/3]

◆ contains() [3/3]

◆ contains_integer()

◆ content() [1/2]

◆ content() [2/2]

◆ convex_hull()

◆ diameter()

◆ diameter_assign()

◆ diameter_ratio()

◆ diameter_ratio_assign()

◆ distance()

◆ div()

◆ div_assign()

◆ div_ext()

◆ empty_interval()

◆ integral_part()

◆ integralPart_assign()

◆ inverse()

◆ inverse_assign()

◆ is_closed_interval()

◆ is_consistent()

◆ is_empty()

◆ is_half_bounded()

◆ is_infinite()

◆ is_negative()

◆ is_one()

◆ is_open_interval()

template<typename Number>
class carl::Interval< Number >