Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format

Vincent Lefèvre (1) , Damien Stehlé (1) , Paul Zimmermann (1)

1 SPACES - Solving problems through algebraic computation and efficient software

We show how one can search for the worst cases for correct rounding of the exponential function in the IEEE 754r 64-bit decimal format, and give such bad cases that have been found so far. This work can be extended to other elementary functions in the decimal64 format, and allows the design of reasonably fast routines that will evaluate these functions with correct rounding, at least in some domains.

Mots clés: floating-point arithmetic; decimal arithmetic; table maker's dilemma; correct rounding; elementary functions

Domaines: Algorithme et structure de données [cs.DS]; Analyse numérique [cs.NA]

Vincent Lefèvre, Damien Stehlé, Paul Zimmermann. Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format. Reliable Implementation of Real Number Algorithms: Theory and Practice, Jan 2006, Dagstuhl, Germany. pp.114-126, ⟨10.1007/978-3-540-85521-7_7⟩. ⟨inria-00068731v1⟩