Value comparison

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

5.5.2 Value comparison

bool veq(const interval<T>&, const interval<T>&);
bool vne(const interval<T>&, const interval<T>&);
bool vle(const interval<T>&, const interval<T>&);
bool vge(const interval<T>&, const interval<T>&);
bool vlt(const interval<T>&, const interval<T>&);
bool vgt(const interval<T>&, const interval<T>&);

Value comparison operators treat the given intervals as if they were a single number. Empty intervals of $∅$ are explicitly considered valid. That is for $X,Y ∈IR$ and $□∈ {=,<,≤,>,≥}$ :

X□Y ≡ (∀a∈ X,∃b∈ Y :a□b)

A special case is for inequality $̸=$ which is the same as above but using a disjunction instead of a conjunction, that is:

X ̸= Y ≡ (∀a∈ X,∃b∈ Y :a ̸=b)

[next] [prev] [prev-tail] [front] [up]