The Scalar Type interval. More...

#include <interval.hpp>

Collaboration diagram for cxsc::interval:

Public Member Functions
	interval ()
	Constructor of class interval.

	interval (const dotprecision &) noexcept
	Constructor of class interval.

	interval (const dotprecision &, const dotprecision &)
	Constructor of class interval.

	interval (const idotprecision &) noexcept
	Constructor of class interval.

	interval (const imatrix &m) noexcept
	Constructor of class interval.

	interval (const imatrix_slice &m) noexcept
	Constructor of class interval.

	interval (const ivector &) noexcept
	Constructor of class interval.

	interval (const ivector_slice &) noexcept
	Constructor of class interval.

	interval (const l_interval &) noexcept
	Constructor of class interval.

	interval (const l_real &) noexcept
	Constructor of class interval.

	interval (const l_real &, const l_real &)
	Constructor of class interval.

	interval (const real &, const real &)
	Constructor of class interval.

	interval (const real &r) noexcept
	Typecast for converting a real value in an interval.

interval &	operator= (const dotprecision &) noexcept
	Implementation of standard assigning operator.

interval &	operator= (const idotprecision &) noexcept
	Implementation of standard assigning operator.

interval &	operator= (const l_interval &) noexcept
	Implementation of standard assigning operator.

interval &	operator= (const l_real &) noexcept
	Implementation of standard assigning operator.

interval &	operator= (const lx_interval &) noexcept
	Implementation of standard assigning operator.

interval &	operator= (const real &a)
	Implementation of standard assigning operator.

Friends
interval	_interval (const imatrix &m) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

interval	_interval (const imatrix_slice &m) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

interval	_interval (const ivector &) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

interval	_interval (const ivector_slice &) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

interval	_interval (const l_interval &a) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

interval	_interval (const l_real &a) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

interval	_interval (const l_real &a, const l_real &b)
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

interval	_unchecked_interval (const real &, const real &)
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

interval	abs (const interval &) noexcept
	Returns the absolute value of the interval.

real	diam (const interval &) noexcept
	Returns the rounded diameter of the interval.

const real &	Inf (const interval &) noexcept
	Returns the infimum of an interval.

real &	Inf (interval &) noexcept
	Returns the infimum of an interval.

bool	IsEmpty (const interval &) noexcept
	Returns true if the interval is empty.

real	mid (const interval &) noexcept
	Returns the rounded middle of the interval.

bool	operator! (const interval &) noexcept
	Implementation of standard negation operation.

bool	operator!= (const dotprecision &, const interval &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const double &, const interval &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const int &, const interval &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const interval &, const dotprecision &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const interval &, const double &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const interval &, const int &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const interval &, const interval &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const interval &, const long &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const interval &, const real &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const long &, const interval &) noexcept
	Implementation of standard negated equality operation.

bool	operator!= (const real &, const interval &) noexcept
	Implementation of standard negated equality operation.

idotprecision	operator& (const idotprecision &, const interval &)
	Returns the intersection of the arguments.

idotprecision	operator& (const interval &, const idotprecision &)
	Returns the intersection of the arguments.

interval	operator& (const interval &, const interval &)
	Returns the intersection of the arguments.

interval	operator& (const interval &, const real &)
	Returns the intersection of the arguments.

interval	operator& (const real &, const interval &)
	Returns the intersection of the arguments.

interval &	operator&= (interval &, const interval &)
	Allocates the intersection of the arguments to the first argument.

interval &	operator&= (interval &, const real &)
	Allocates the intersection of the arguments to the first argument.

interval	operator* (const interval &, const interval &) noexcept
	Implementation of standard algebraic multiplication operation.

interval	operator* (const interval &, const real &) noexcept
	Implementation of standard algebraic multiplication operation.

interval	operator* (const real &, const interval &) noexcept
	Implementation of standard algebraic multiplication operation.

interval &	*operator=** (interval &, const interval &) noexcept
	Implementation of standard algebraic multiplication and allocation operation.

interval &	*operator=** (interval &, const real &) noexcept
	Implementation of standard algebraic multiplication and allocation operation.

idotprecision	operator+ (const idotprecision &, const interval &) noexcept
	Implementation of standard algebraic addition operation.

interval	operator+ (const interval &) noexcept
	Implementation of standard algebraic positive sign operation.

idotprecision	operator+ (const interval &, const idotprecision &) noexcept
	Implementation of standard algebraic addition operation.

interval	operator+ (const interval &, const interval &) noexcept
	Implementation of standard algebraic addition operation.

interval	operator+ (const interval &, const real &) noexcept
	Implementation of standard algebraic addition operation.

interval	operator+ (const real &, const interval &) noexcept
	Implementation of standard algebraic addition operation.

interval &	operator+= (interval &, const interval &) noexcept
	Implementation of standard algebraic addition and allocation operation.

interval &	operator+= (interval &, const real &) noexcept
	Implementation of standard algebraic addition and allocation operation.

idotprecision	operator- (const idotprecision &, const interval &) noexcept
	Implementation of standard algebraic subtraction operation.

interval	operator- (const interval &) noexcept
	Implementation of standard algebraic negative sign operation.

idotprecision	operator- (const interval &, const idotprecision &) noexcept
	Implementation of standard algebraic subtraction operation.

interval	operator- (const interval &, const interval &) noexcept
	Implementation of standard algebraic subtraction operation.

interval	operator- (const interval &, const real &) noexcept
	Implementation of standard algebraic subtraction operation.

interval	operator- (const real &, const interval &) noexcept
	Implementation of standard algebraic subtraction operation.

interval &	operator-= (interval &, const interval &) noexcept
	Implementation of standard algebraic subtraction and allocation operation.

interval &	operator-= (interval &, const real &) noexcept
	Implementation of standard algebraic subtraction and allocation operation

interval	operator/ (const interval &, const interval &)
	Implementation of standard algebraic division operation.

interval	operator/ (const interval &, const real &) noexcept
	Implementation of standard algebraic division operation.

interval	operator/ (const real &, const interval &) noexcept
	Implementation of standard algebraic division operation.

interval &	operator/= (interval &, const interval &) noexcept
	Implementation of standard algebraic division and allocation operation.

interval &	operator/= (interval &, const real &) noexcept
	Implementation of standard algebraic division and allocation operation.

bool	operator< (const dotprecision &, const interval &) noexcept
	Implementation of standard less-than operation.

bool	operator< (const interval &, const dotprecision &) noexcept
	Implementation of standard less-than operation.

bool	operator< (const interval &, const interval &) noexcept
	Implementation of standard less-than operation.

bool	operator< (const interval &, const real &) noexcept
	Implementation of standard less-than operation.

bool	operator< (const real &, const interval &) noexcept
	Implementation of standard less-than operation.

std::ostream &	operator<< (std::ostream &, const interval &) noexcept
	Implementation of standard output method.

std::string &	operator<< (std::string &, const interval &) noexcept
	Implementation of standard output method.

bool	operator<= (const dotprecision &, const interval &) noexcept
	Implementation of standard less-or-equal-than operation.

bool	operator<= (const interval &, const dotprecision &) noexcept
	Implementation of standard less-or-equal-than operation.

bool	operator<= (const interval &, const interval &) noexcept
	Implementation of standard less-or-equal-than operation.

bool	operator<= (const interval &, const real &) noexcept
	Implementation of standard less-or-equal-than operation.

bool	operator<= (const real &, const interval &) noexcept
	Implementation of standard less-or-equal-than operation.

bool	operator== (const dotprecision &, const interval &) noexcept
	Implementation of standard equality operation.

bool	operator== (const double &, const interval &) noexcept
	Implementation of standard equality operation.

bool	operator== (const int &, const interval &) noexcept
	Implementation of standard equality operation.

bool	operator== (const interval &, const dotprecision &) noexcept
	Implementation of standard equality operation.

bool	operator== (const interval &, const double &) noexcept
	Implementation of standard equality operation.

bool	operator== (const interval &, const int &) noexcept
	Implementation of standard equality operation.

bool	operator== (const interval &, const interval &) noexcept
	Implementation of standard equality operation.

bool	operator== (const interval &, const long &) noexcept
	Implementation of standard equality operation.

bool	operator== (const interval &, const real &) noexcept
	Implementation of standard equality operation.

bool	operator== (const long &, const interval &) noexcept
	Implementation of standard equality operation.

bool	operator== (const real &, const interval &) noexcept
	Implementation of standard equality operation.

bool	operator> (const dotprecision &, const interval &) noexcept
	Implementation of standard greater-than operation.

bool	operator> (const interval &, const dotprecision &) noexcept
	Implementation of standard greater-than operation.

bool	operator> (const interval &, const interval &) noexcept
	Implementation of standard greater-than operation.

bool	operator> (const interval &, const real &) noexcept
	Implementation of standard greater-than operation.

bool	operator> (const real &, const interval &) noexcept
	Implementation of standard greater-than operation.

bool	operator>= (const dotprecision &, const interval &) noexcept
	Implementation of standard greater-or-equal-than operation.

bool	operator>= (const interval &, const dotprecision &) noexcept
	Implementation of standard greater-or-equal-than operation.

bool	operator>= (const interval &, const interval &) noexcept
	Implementation of standard greater-or-equal-than operation.

bool	operator>= (const interval &, const real &) noexcept
	Implementation of standard greater-or-equal-than operation.

bool	operator>= (const real &, const interval &) noexcept
	Implementation of standard greater-or-equal-than operation.

void	operator>> (const char *, interval &) noexcept
	Implementation of standard input method.

void	operator>> (const std::string &, interval &) noexcept
	Implementation of standard input method.

std::istream &	operator>> (std::istream &, interval &) noexcept
	Implementation of standard input method.

std::string &	operator>> (std::string &, interval &) noexcept
	Implementation of standard input method.

idotprecision	operator\| (const idotprecision &, const interval &) noexcept
	Returns the convex hull of the arguments.

idotprecision	operator\| (const interval &, const idotprecision &) noexcept
	Returns the convex hull of the arguments.

interval	operator\| (const interval &, const interval &) noexcept
	Returns the convex hull of the arguments.

interval	operator\| (const interval &, const real &) noexcept
	Returns the convex hull of the arguments.

interval	operator\| (const real &, const interval &) noexcept
	Returns the convex hull of the arguments.

interval	operator\| (const real &, const real &) noexcept
	Returns the convex hull of the arguments.

interval &	operator\|= (interval &, const interval &) noexcept
	Allocates the convex hull of the arguments to the first argument.

interval &	operator\|= (interval &, const real &) noexcept
	Allocates the convex hull of the arguments to the first argument.

interval &	SetInf (interval &, const real &) noexcept
	Returns the interval with the new given infimum value.

interval &	SetSup (interval &, const real &) noexcept
	Returns the interval with the new given supremum value.

const real &	Sup (const interval &) noexcept
	Returns the supremum of an interval.

real &	Sup (interval &) noexcept
	Returns the supremum of an interval.

void	times2pown (interval &, const int &) noexcept
	Multiplication of interval with .

interval &	UncheckedSetInf (interval &, const real &) noexcept
	Returns the interval with the unchecked new given infimum value.

interval &	UncheckedSetSup (interval &, const real &) noexcept
	Returns the interval with the unchecked new given supremum value.

Detailed Description

The Scalar Type interval.

The data type interval is used to represent intervals over the real floating-point numbers:

$\left[ a \right] = \left[ \underline a , \overline a \right] := \left\{ x \in R | \underline a \le x \le \overline a \right\} \in R$

i.e. $\left[ a \right]$ represents the set of all real numbers enclosed within the bounds $\underline a , \overline a \in R$ .

The notation $\underline a$ denotes the lower bound (infimum), and $\overline a$ denotes the upper bound (supremum) of the interval $\left[ a \right]$ .

Definition at line 54 of file interval.hpp.

Friends And Related Function Documentation

◆ _unchecked_interval

interval _unchecked_interval	(	const real &	a,
		const real &	b
	)

friend

Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

Deprecated:: use standard contructors for typecasting

See also: cxsc::interval::interval(const real&, const real&)

Definition at line 66 of file interval.inl.

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

Public Member Functions

Friends

Detailed Description

Friends And Related Function Documentation

◆ _unchecked_interval