Abstract
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| ≥ 3 ×10− 11 is \(\exp(9.407822313572878 \times 10^{-2}) = 1.098645682066338\,5\,0000000000000000\,278\ldots\). 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.
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Lefèvre, V., Stehlé, D., Zimmermann, P. (2008). Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format. In: Hertling, P., Hoffmann, C.M., Luther, W., Revol, N. (eds) Reliable Implementation of Real Number Algorithms: Theory and Practice. Lecture Notes in Computer Science, vol 5045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85521-7_7
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DOI: https://doi.org/10.1007/978-3-540-85521-7_7
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