New Results on the Distance between a Segment and Z ² . Application to the Exact Rounding

This paper presents extensions to Lefevre´s algorithm that computes a lower bound on the distance between a segment and a regular grid Zopf². This algorithm and, in particular, the extensions are useful in the search for worst cases for the exact rounding of unary elementary functions or base-conversion functions. The proof that is presented is simpler and less technical than the original proof. This paper also gives benchmark results with various optimization parameters, explanations of these results, and an application to base conversion