Possible comparison

Stable Numerics Subroutine Library
Programming Reference Manual
Version 1.0 DD-00006-010

5.5.3 Possible comparison

bool peq(const interval<T>&, const interval<T>&);
bool pne(const interval<T>&, const interval<T>&);
bool ple(const interval<T>&, const interval<T>&);
bool pge(const interval<T>&, const interval<T>&);
bool plt(const interval<T>&, const interval<T>&);
bool pgt(const interval<T>&, const interval<T>&);

Possible comparison operators compare two intervals without checking for overlap between the intervals, that is possible comparison operators only check the appropriate extremas for matching and don’t consider whether they overlap. As follows for a logical comparison operator $□∈ {=,̸=,<,≤,>,≥}$ for $X,Y ∈ IR$ possible comparison operators are defined as:

X□Y ≡(X,Y ̸=∅) ∧(∃a∈X, ∃b∈Y :a□b)

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