New Results on the Distance Between a Segment and Z². Application to the Exact Rounding

Vincent Lefèvre (1)

1 SPACES - Solving problems through algebraic computation and efficient software

This paper presents extensions to Lefèvre's algorithm that computes a lower bound on the distance between a segment and a regular grid Z². 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 here 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.

Mots clés: computer arithmetic; correct rounding; exact rounding; table maker's dilemma; base conversion

Domaines: Algorithme et structure de données [cs.DS]

Vincent Lefèvre. New Results on the Distance Between a Segment and Z². Application to the Exact Rounding. 17th IEEE Symposium on Computer Arithmetic - Arith'17, Jun 2005, Cape Cod, MA, United States. pp.68-75, ⟨10.1109/ARITH.2005.4⟩. ⟨inria-00000025⟩