Certain comparison

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

5.5.4 Certain comparison

bool ceq(const interval<T>&, const interval<T>&);
bool cne(const interval<T>&, const interval<T>&);
bool cle(const interval<T>&, const interval<T>&);
bool cge(const interval<T>&, const interval<T>&);
bool clt(const interval<T>&, const interval<T>&);
bool cgt(const interval<T>&, const interval<T>&);

Certain comparison operators check that the intervals do not overlap for their respective comparison operation. As follows for a logical comparison operator $□ ∈{=,̸=,<,≤,>,≥}$ for $X,Y ∈ IR$ certain comparison operators are defined as:

X□Y ≡ (X,Y ̸=∅)∧ (∀a∈X, ∀b∈ Y :a□b)

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