TY - GEN
T1 - Worst cases for the exponential function in the IEEE 754r decimal64 format
AU - Lefevre, Vincent
AU - Stehlé, Damien
AU - Zimmermann, Paul
PY - 2008
Y1 - 2008
N2 - 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 × 10⁻²) = 1.098645682066338 5 0000000000000000 278 . . .. 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.
AB - 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 × 10⁻²) = 1.098645682066338 5 0000000000000000 278 . . .. 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.
UR - https://www.scopus.com/pages/publications/50949132881
U2 - 10.1007/978-3-540-85521-7_7
DO - 10.1007/978-3-540-85521-7_7
M3 - Conference proceeding contribution
SN - 9783540855200
T3 - Lecture notes in computer science
SP - 114
EP - 126
BT - Reliable implementation of real number algorithms
A2 - Hertling, Peter
A2 - Hoffmann, Christoph M.
A2 - Luther, Wolfram
A2 - Revol, Nathalie
PB - Springer, Springer Nature
CY - Berlin/Heidelberg, Germany
T2 - International seminar on reliable implementation of real number algorithms : theory and practice
Y2 - 8 January 2006 through 13 January 2006
ER -