Correct rounding of algebraic functions

Correct rounding of algebraic functions

We explicit the link between the computer arithmetic problem of providing correctly rounded algebraic functions and some diophantine approximation issues. This allows to get bounds on the accuracy with which intermediate calculations must be performed to correctly round these functions. Mathematics Subject Classification. 11J68, 65D20, 65G.

Rounding errors in algebraic processes

Worst Cases for Correct Rounding of the Elementary Functions in Double Precision

We give the results of our search for the worst cases for correct rounding of themajor elementary functions in double precision floating-point arithmetic. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to ...

Fast correct rounding of elementary functions in double precision using double-extended arithmetic

This article shows that IEEE-754 double-precision correct rounding of the most common elementary functions (exp/log, trigonometric and hyperbolic) is achievable on current processors using only double-double-extended arithmetic. This allows to improve by several orders of magnitude the worst case performance of a correctly-rounded mathematical library, compared to the current state of the art. ...

Integration of algebraic functions

We show how the \rational" approach for integrating algebraic functions can be extended to handle elementary functions. The resulting algorithm is a practical decision procedure for determining whether a given elementary function has an elementary antiderivative, and for computing it if it exists.