Additional Interval Orderings

In addition to the standard orderings operator < and rleated > <= >= that you will find in the librarie's function synopsis, intervals implement some additional orderings that can be useful.

T	discrete _interval	continuous _interval	right_open _interval	left_open _interval	closed _interval	open _interval
Interval bounds	dynamic	dynamic	static	static	static	static
Form			asymmetric	asymmetric	symmetric	symmetric
Orderings
`bool exclusive_less(const T&, const T&)`	1	1	1	1	1	1
bool lower_less(const T&, const T&) bool lower_equal(const T&, const T&) bool lower_less_equal(const T&, const T&)	1	1	1	1	1	1
bool upper_less(const T&, const T&) bool upper_equal(const T&, const T&) bool upper_less_equal(const T&, const T&)	1	1	1	1	1	1

A central role for the icl plays the exclusive_less ordering, which is used in all interval containers. The other orderings can be useful to simplify comparison of intervals specifically for dynamically bounded ones.

Orderings	Description
`bool exclusive_less(const T&, const T&)`	`exclusive_less(x1, x2)` is true if every element of interval `x1` is less than every element of interval `x2` w.r.t. the the intervals `Compare` ordering
bool lower_less(const T&, const T&) bool lower_equal(const T&, const T&) bool lower_less_equal(const T&, const T&)	Compares the beginnings of intervals. lower_less(x,y) == true; // x begins before y lower_equal(x,y) == true; // x and y begin at the same element lower_less_equal(x,y) == lower_less(x,y) \|\| lower_equal(x,y);
bool upper_less(const T&, const T&) bool upper_equal(const T&, const T&) bool upper_less_equal(const T&, const T&)	Compares the endings of intervals. upper_less(x,y) == true; // x ends before y upper_equal(x,y) == true; // x and y end at the same element upper_less_equal(x,y) == upper_less(x,y) \|\| upper_equal(x,y);

Orderings

Description

bool exclusive_less(const T&, const T&)

exclusive_less(x1, x2) is true if every element of interval x1 is less than every element of interval x2 w.r.t. the the intervals Compare ordering

bool lower_less(const T&, const T&)
bool lower_equal(const T&, const T&)
bool lower_less_equal(const T&, const T&)

Compares the beginnings of intervals.

lower_less(x,y)  == true; // x begins before y
lower_equal(x,y) == true; // x and y begin at the same element
lower_less_equal(x,y) == lower_less(x,y) || lower_equal(x,y);

bool upper_less(const T&, const T&)
bool upper_equal(const T&, const T&)
bool upper_less_equal(const T&, const T&)

Compares the endings of intervals.

upper_less(x,y)  == true; // x ends before y
upper_equal(x,y) == true; // x and y end at the same element
upper_less_equal(x,y) == upper_less(x,y) || upper_equal(x,y);

See also . . .

Equivalences and Orderings

Back to section . . .

Additional interval functions
Function Synopsis
Interface

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Additional Interval Orderings