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

Vincent Lefèvre and Damien Stehlé and Paul Zimmermann

We searched for the worst cases for correct rounding of the exponential function in the IEEE 754r decimal64 format, and computed all the bad cases whose distance from a breakpoint (for all rounding modes) is less than 10-15 ulp, and we give the worst ones. In particular, the worst case for |x| >= 3E-11 is exp(9.407822313572878E-2) = 1.09864568206633850000000000000000278... 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.

Download: pdf.

Complete lists of worst cases for the exponential are available for the IEEE 754r decimal32 and decimal64 formats.