Correctly rounded evaluation of a function: why, how, and at what cost?

Abstract

The two accompanying files are: - The SageMath code computing upper bounds for the hardness to round of exp, trigonometric and hyperbolic functions over the firstfew binades surrounding 1;- the LACoR library that implements the BH algorithm for computing upper bounds on the hardness to roundInternational audienceThe goal of this article is to give a survey on the various computational and mathematical issues and progress related to the problem of providing efficient correctly rounded elementary functions in floating-point arithmetic. We also aim at convincing the reader that a future standard for floating-point arithmetic should require the availability of a correctly rounded version of a well-chosen core set of elementary functions. We discuss the interest and feasibility of this requirement