Additive Symmetric: the Non-Negative Case
Résumé
An additive symmetric b of a with respect to c satisfies c = (a+b)/2. Existence and uniqueness of such $b$ are basic properties in exact arithmetic that fail when a and b are floating point numbers and the computation of $c$ performed in IEEE-754 like arithmetic. We exhibit and prove conditions on the existence, the uniqueness and the exact correspondence of an additive symmetric when b and c have the same sign.