Title: New results on the Table Maker's Dilemma
Authors: Vincent Lefevre and Jean-Michel Muller, LIP, projet ARENAIRE,
Ecole Normale Superieure de Lyon, 46 Allee d'Italie, 69364 Lyon Cedex
07, France

Abstract: The Table Maker's Dilemma (TMD) is the problem of always
return a correctly rounded result (e.g., the exact value rounded to the
nearest) when evaluating a transcendental function in floating-point
arithmetic. The functions that are at stake are: sine, cosine,
exponential and logarithm (radices 2 and e) and arc-tangent. We show
that the TMD can be solved at a "reasonnable" cost (at least for
double-precision arithmetic). This will allow a complete specification
of all numerical primitives (arithmetic operations and elementary
functions) of most computer languages, which may improve the reliability
and portability of numerical software. The techniques used for solving
the TMD are a mix-up of numerical and computer algebra methods.
--
Jean-Michel Muller, CNRS-LIP, projet CNRS/INRIA/ENSL ARENAIRE
Ecole Normale Sup. de Lyon, 46 Allee d'Italie, 69364 Lyon Cedex 07
FRANCE
Tel. (+33) 4 72728229 Secr. (+33) 4 72728037  Fax. (+33) 4 72728080
Email: Jean-Michel.Muller@ens-lyon.fr, j.muller@computer.org
http://www.ens-lyon.fr/~jmmuller