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.
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