Mr Marc Gouicem (Université Paris 6)
The IEEE 754-2008 standard recommends correctly rounding elementary functions. However, these functions are transcendental and their results can only be approximated with error epsilon >0. If o_p is a rounding function at precision p , there may exist some arguments x, called (p,epsilon) hard-to-round arguments, such that o_p(f(x)−epsilon) be distinct of o_p(f(x)+epsilon), inducing an uncertainty on the rounding of f(x). Finding an error epsilon such that there are no (p,epsilon) hard-to-round arguments is known as the Table Maker’s Dilemma (TMD).