Detailed Description

an interval of two double values.

Contains methods for intersection, union, and more.

This is one of the most-used basic classes in free-space and reachability algorithms.

It is up to the user of an interval object, whether the interval is interpreted as a closed, open or semi-open interval. (e.g. when constructing a free-space diagram, intervals are usually meant to be closed). The Interval class just manages two interval borders, without imposing an interpretation.

Invalid intervals are indicated by NAN values.

Empty intervals have lower bound == upper bound. Those intervals can be interpreted as empty, or as containing exactly one point.

Empty intervals with lower bound > upper are valid to, but are usually to be avoided.

Since Interval objects are small (two words) it is perfectly alright to pass them by value.

Author: Peter Schäfer

Definition at line 31 of file interval.h.

#include <interval.h>

Inherited by frechet::k::MappedInterval, and frechet::reach::BoundarySegment.

Public Member Functions
	Interval ()
	Default constructor. Creates an invalid Interval. More...

	Interval (double lower, double upper)
	Constructor from boundary values. More...

	Interval (const Interval &that)
	Copy constructor. More...

	Interval (const Interval &that, double shift)
	Copy constructor with shift offset. More...

double	size () const
	size of the interval (upper - lower). More...

bool	valid () const
	validity test More...

bool	empty () const
	empty test More...

	operator bool () const

bool	operator! () const

double	lower () const

double	upper () const

double &	lower ()

double &	upper ()

Interval &	setLower (double value)
	update lower bound More...

Interval &	setUpper (double value)
	update upper bound More...

double	mid () const

Interval &	operator= (const Interval &that)
	assignment operator More...

bool	operator== (const Interval &that) const
	equality comparator More...

bool	equals (const Interval &that, double precision) const
	equalality comparator with tolerance More...

bool	operator!= (const Interval &that) const
	non-equality comparator More...

Interval	normalized () const
	normalized More...

Interval &	normalize ()
	make sure that lower <= upper, swapping bounds, if necessary More...

Interval &	clear ()
	make this an invalid interval More...

bool	contains (double x) const
	containment test (assumes closed interval, bounds inclusive) More...

bool	contains (double x, double precision) const
	containment test with tolerance (assumes closed interval, bounds inclusive) More...

bool	contains (const Interval &that) const
	containment test (closed interval, bounds inclusive) More...

bool	intersects (const Interval &that) const
	intersection test (closed interval, bounds inclusive) More...

bool	intersects_proper (const Interval &that) const
	intersection test (open interval, bounds exclusive) More...

bool	bordersTo (const Interval &that) const
	adjacency test More...

double	mapToUnitInterval (double x) const
	re-map a value from this interval to the unit interval More...

double	mapFromUnitInterval (double x) const
	re-map a value from the unit interval to this interval More...

double	mapTo (double x, const Interval &other) const
	re-map a value to another interval More...

double	mapFrom (double x, const Interval &other) const
	re-map a value from another interval to this interval More...

Interval	operator+ (double offset) const
	shift the interval by a fixed offset More...

Interval &	operator+= (double offset)
	shift the interval by a fixed offset More...

Interval	operator- (double offset) const
	shift the interval by a fixed offset More...

Interval &	operator-= (double offset)
	shift the interval by a fixed offset More...

Interval	operator * (double factor) const
	multiply by a factor More...

Interval &	operator *= (double factor)
	multiply by a factor More...

Interval	operator/ (double factor) const
	divide by a factor More...

Interval &	operator/= (double factor)
	multiply by a factor More...

Interval	operator+ (const Interval &that) const
	union operator More...

Interval &	operator+= (const Interval &that)
	union operator More...

Interval	operator- (const Interval &that) const
	difference operator More...

Interval	operator-= (const Interval &that)
	difference operator More...

Interval	operator & (const Interval &that) const
	intersection operator More...

Interval &	operator&= (const Interval &that)
	intersection operator More...

Interval &	union_lf (const Interval &that)
	lock-free union operator; not used and not tested More...

Static Public Member Functions
static bool	equals (double a, double b)
	equality comparator More...

Static Public Attributes
static const Interval	UNIT
	the unit interval [0,1] More...

static const Interval	INVALID = Interval ()
	an invalid interval (contains NAN values) More...

Private Member Functions
Interval &	assign (double lower, double upper)
	assign new bounds More...

Static Private Member Functions
static void	assign_min_lf (volatile double *value, double update_value)
	lock-free assigment; not used and not tested More...

static void	assign_max_lf (volatile double *value, double update_value)
	lock-free assigment; not used and not tested More...

static int64_t	compare_and_swap (volatile int64_t *value, int64_t old_value, int64_t update_value)
	lock-free compare-and-swap; not used and not tested More...

Private Attributes
double	_lower
	lower and upper border of the interval More...

double	_upper

Constructor & Destructor Documentation

◆ Interval() [1/4]

frechet::data::Interval::Interval ( )

inline

Default constructor. Creates an invalid Interval.

Definition at line 44 of file interval.h.

◆ Interval() [2/4]

frechet::data::Interval::Interval	(	double	lower,
		double	upper
	)

inline

Constructor from boundary values.

Parameters

lower	lower bound
upper	upper bound

Definition at line 50 of file interval.h.

◆ Interval() [3/4]

frechet::data::Interval::Interval ( const Interval & that )

inline

Copy constructor.

Parameters

that	object to copy from

Definition at line 55 of file interval.h.

◆ Interval() [4/4]

frechet::data::Interval::Interval	(	const Interval &	that,
		double	shift
	)

inline

Copy constructor with shift offset.

Parameters

that	object to copy from
shift	offset resulting interval by this value

Definition at line 61 of file interval.h.

Member Function Documentation

◆ assign()

Interval& frechet::data::Interval::assign	(	double	lower,
		double	upper
	)

inlineprivate

assign new bounds

Parameters

lower	new lower bound
upper	new upper bound

Returns: this interval, with new bounds

Definition at line 434 of file interval.h.

◆ assign_max_lf()

void Interval::assign_max_lf	(	volatile double *	value,
		double	update_value
	)

staticprivate

lock-free assigment; not used and not tested

Definition at line 46 of file interval.cpp.

◆ assign_min_lf()

void Interval::assign_min_lf	(	volatile double *	value,
		double	update_value
	)

staticprivate

lock-free assigment; not used and not tested

Definition at line 28 of file interval.cpp.

◆ bordersTo()

bool frechet::data::Interval::bordersTo ( const Interval & that ) const

inline

adjacency test

Parameters

that	interval to compare to

Returns: true, if both intervals are adjacent

Definition at line 252 of file interval.h.

◆ clear()

Interval& frechet::data::Interval::clear ( )

inline

make this an invalid interval

Returns: this interval, now invalid

Definition at line 197 of file interval.h.

◆ compare_and_swap()

int64_t Interval::compare_and_swap	(	volatile int64_t *	value,
		int64_t	old_value,
		int64_t	update_value
	)

staticprivate

lock-free compare-and-swap; not used and not tested

Definition at line 64 of file interval.cpp.

◆ contains() [1/3]

bool frechet::data::Interval::contains ( double x ) const

inline

containment test (assumes closed interval, bounds inclusive)

Parameters

x a value

Returns: true, if x >= lower and x <= upper.

Definition at line 206 of file interval.h.

◆ contains() [2/3]

bool frechet::data::Interval::contains	(	double	x,
		double	precision
	)		const

inline

containment test with tolerance (assumes closed interval, bounds inclusive)

Parameters

x	a value
precision	tolerance

Returns: true, if x >= lower-precision and x <= upper+precision.

Definition at line 216 of file interval.h.

◆ contains() [3/3]

bool frechet::data::Interval::contains ( const Interval & that ) const

inline

containment test (closed interval, bounds inclusive)

Parameters

that	interval to test for

Returns: true if that subseteq this

Definition at line 225 of file interval.h.

◆ empty()

bool frechet::data::Interval::empty ( ) const

inline

empty test

Returns: true, if lower > upper

Definition at line 79 of file interval.h.

◆ equals() [1/2]

static bool frechet::data::Interval::equals	(	double	a,
		double	b
	)

inlinestatic

equality comparator

Returns: true, if a == b, or if both values are NAN

Definition at line 137 of file interval.h.

◆ equals() [2/2]

bool frechet::data::Interval::equals	(	const Interval &	that,
		double	precision
	)		const

inline

equalality comparator with tolerance

Parameters

that	interval to compare to
precision	tolerance

Returns: true, if both intervals are equal with regard to the given tolerance.

Definition at line 159 of file interval.h.

◆ intersects()

bool frechet::data::Interval::intersects ( const Interval & that ) const

inline

intersection test (closed interval, bounds inclusive)

Parameters

that	interval to test for

Returns: true if that intersected with this is not empty

Definition at line 234 of file interval.h.

◆ intersects_proper()

bool frechet::data::Interval::intersects_proper ( const Interval & that ) const

inline

intersection test (open interval, bounds exclusive)

Parameters

that	interval to test for

Returns: true if that intersected with this is not empty

Definition at line 243 of file interval.h.

◆ lower() [1/2]

double frechet::data::Interval::lower ( ) const

inline

Returns: the lower bound of the interval

Definition at line 92 of file interval.h.

◆ lower() [2/2]

double& frechet::data::Interval::lower ( )

inline

Returns: an updatable reference to the lower bound

Definition at line 101 of file interval.h.

◆ mapFrom()

double frechet::data::Interval::mapFrom	(	double	x,
		const Interval &	other
	)		const

inline

re-map a value from another interval to this interval

Parameters

x	a value (possibly contained in this interval)
other	another interval

Returns: x remapped to this interval

Definition at line 293 of file interval.h.

◆ mapFromUnitInterval()

double frechet::data::Interval::mapFromUnitInterval ( double x ) const

inline

re-map a value from the unit interval to this interval

Parameters

x	a value (possibly contained in this interval)

Returns: x remapped to the this interval

Definition at line 273 of file interval.h.

◆ mapTo()

double frechet::data::Interval::mapTo	(	double	x,
		const Interval &	other
	)		const

inline

re-map a value to another interval

Parameters

x	a value (possibly contained in this interval)
other	another interval

Returns: x remapped to the otehr interval

Definition at line 283 of file interval.h.

◆ mapToUnitInterval()

double frechet::data::Interval::mapToUnitInterval ( double x ) const

inline

re-map a value from this interval to the unit interval

Parameters

x	a value (possibly contained in this interval)

Returns: x remapped to the unit interval

Definition at line 260 of file interval.h.

◆ mid()

double frechet::data::Interval::mid ( ) const

inline

Returns: the middle of the interval, (lower+upper)/2

Definition at line 121 of file interval.h.

◆ normalize()

Interval& frechet::data::Interval::normalize ( )

inline

make sure that lower <= upper, swapping bounds, if necessary

Returns: this interval, possibly after swapping bounds

Definition at line 187 of file interval.h.

◆ normalized()

Interval frechet::data::Interval::normalized ( ) const

inline

normalized

Returns

Definition at line 177 of file interval.h.

◆ operator &()

Interval frechet::data::Interval::operator & ( const Interval & that ) const

inline

intersection operator

Parameters

that	another interval

Returns: the intersection of both intervals

Definition at line 405 of file interval.h.

◆ operator *()

Interval frechet::data::Interval::operator * ( double factor ) const

inline

multiply by a factor

Returns: copy of this interval, with bounds multiplied

Definition at line 330 of file interval.h.

◆ operator *=()

Interval& frechet::data::Interval::operator *= ( double factor )

inline

multiply by a factor

Returns: this interval, after bounds multiplied

Definition at line 337 of file interval.h.

◆ operator bool()

frechet::data::Interval::operator bool ( ) const

inline

Returns: true, if valid and not empty

Definition at line 83 of file interval.h.

◆ operator!()

bool frechet::data::Interval::operator! ( ) const

inline

Returns: true, if not valid or empty

Definition at line 87 of file interval.h.

◆ operator!=()

bool frechet::data::Interval::operator!= ( const Interval & that ) const

inline

non-equality comparator

Parameters

that	interval to compare to

Returns: true, if both intervals are not equal

Definition at line 167 of file interval.h.

◆ operator&=()

Interval& frechet::data::Interval::operator&= ( const Interval & that )

inline

intersection operator

Parameters

that	another interval

Returns: this interval, containng the intersection of both intervals

Definition at line 416 of file interval.h.

◆ operator+() [1/2]

Interval frechet::data::Interval::operator+ ( double offset ) const

inline

shift the interval by a fixed offset

Returns: copy of this interval, shifted by offset

Definition at line 301 of file interval.h.

◆ operator+() [2/2]

Interval frechet::data::Interval::operator+ ( const Interval & that ) const

inline

union operator

Parameters

that	another interval

Returns: the union of both intervals

Definition at line 361 of file interval.h.

◆ operator+=() [1/2]

Interval& frechet::data::Interval::operator+= ( double offset )

inline

shift the interval by a fixed offset

Returns: this interval, after being shifted by offset

Definition at line 308 of file interval.h.

◆ operator+=() [2/2]

Interval& frechet::data::Interval::operator+= ( const Interval & that )

inline

union operator

Parameters

that	another interval

Returns: this interval, containing the union of both intervals

Definition at line 372 of file interval.h.

◆ operator-() [1/2]

Interval frechet::data::Interval::operator- ( double offset ) const

inline

shift the interval by a fixed offset

Returns: copy of this interval, shifted by offset

Definition at line 316 of file interval.h.

◆ operator-() [2/2]

Interval frechet::data::Interval::operator- ( const Interval & that ) const

inline

difference operator

Parameters

that	another interval

Returns: the difference (this-that)

Definition at line 383 of file interval.h.

◆ operator-=() [1/2]

Interval& frechet::data::Interval::operator-= ( double offset )

inline

shift the interval by a fixed offset

Returns: this interval, after being shifted by offset

Definition at line 323 of file interval.h.

◆ operator-=() [2/2]

Interval frechet::data::Interval::operator-= ( const Interval & that )

inline

difference operator

Parameters

that	another interval

Returns: this interval, containing the difference (this-that)

Definition at line 394 of file interval.h.

◆ operator/()

Interval frechet::data::Interval::operator/ ( double factor ) const

inline

divide by a factor

Returns: copy of this interval, with bounds updated

Definition at line 345 of file interval.h.

◆ operator/=()

Interval& frechet::data::Interval::operator/= ( double factor )

inline

multiply by a factor

Returns: this interval, after bounds updated

Definition at line 352 of file interval.h.

◆ operator=()

Interval& frechet::data::Interval::operator= ( const Interval & that )

inline

assignment operator

Parameters

that	interval to copy from

Returns: this interval, after being updated

Definition at line 130 of file interval.h.

◆ operator==()

bool frechet::data::Interval::operator== ( const Interval & that ) const

inline

equality comparator

Parameters

that	interval to compare to

Returns: true, if both intervals are equal

Definition at line 149 of file interval.h.

◆ setLower()

Interval& frechet::data::Interval::setLower ( double value )

inline

update lower bound

Parameters

value new value for lower bound

Returns: this object, after being updated

Definition at line 111 of file interval.h.

◆ setUpper()

Interval& frechet::data::Interval::setUpper ( double value )

inline

update upper bound

Parameters

value new value for upper bound

Returns: this object, after being updated

Definition at line 117 of file interval.h.

◆ size()

double frechet::data::Interval::size ( ) const

inline

size of the interval (upper - lower).

Returns: upper - lower

Definition at line 67 of file interval.h.

◆ union_lf()

Interval & Interval::union_lf ( const Interval & that )

lock-free union operator; not used and not tested

Sketch for a lock-free union operator

Definition at line 19 of file interval.cpp.

◆ upper() [1/2]

double frechet::data::Interval::upper ( ) const

inline

Returns: the upper bound of the interval

Definition at line 96 of file interval.h.

◆ upper() [2/2]

double& frechet::data::Interval::upper ( )

inline

Returns: an updatable reference to the upper bound

Definition at line 105 of file interval.h.

◆ valid()

bool frechet::data::Interval::valid ( ) const

inline

validity test

Returns: true if both values are valid (!= NAN)

Deprecated:: use operator bool instead

Definition at line 74 of file interval.h.

Member Data Documentation

◆ _lower

double frechet::data::Interval::_lower

private

lower and upper border of the interval

Definition at line 34 of file interval.h.

◆ _upper

double frechet::data::Interval::_upper

private

Definition at line 34 of file interval.h.

◆ INVALID

const Interval Interval::INVALID = Interval ()

static

an invalid interval (contains NAN values)

Definition at line 39 of file interval.h.

◆ UNIT

const Interval Interval::UNIT

static

the unit interval [0,1]

Definition at line 37 of file interval.h.

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

include/data/interval.h
src/data/interval.cpp

Detailed Description

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Member Functions

Static Private Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ Interval() [1/4]

◆ Interval() [2/4]

◆ Interval() [3/4]

◆ Interval() [4/4]

Member Function Documentation

◆ assign()

◆ assign_max_lf()

◆ assign_min_lf()

◆ bordersTo()

◆ clear()

◆ compare_and_swap()

◆ contains() [1/3]

◆ contains() [2/3]

◆ contains() [3/3]

◆ empty()

◆ equals() [1/2]

◆ equals() [2/2]

◆ intersects()

◆ intersects_proper()

◆ lower() [1/2]

◆ lower() [2/2]

◆ mapFrom()

◆ mapFromUnitInterval()

◆ mapTo()

◆ mapToUnitInterval()

◆ mid()

◆ normalize()

◆ normalized()

◆ operator &()

◆ operator *()

◆ operator *=()

◆ operator bool()

◆ operator!()

◆ operator!=()

◆ operator&=()

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==()

◆ setLower()

◆ setUpper()

◆ size()

◆ union_lf()

◆ upper() [1/2]

◆ upper() [2/2]

◆ valid()

Member Data Documentation

◆ _lower

◆ _upper

◆ INVALID

◆ UNIT