An accurate elementary mathematical library for the IEEE floating point standard
ACM Transactions on Mathematical Software (TOMS)
Fast evaluation of elementary mathematical functions with correctly rounded last bit
ACM Transactions on Mathematical Software (TOMS)
Feasibility of “perfect” function evaluation
ACM SIGNUM Newsletter
Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
A Decimal Floating-Point Specification
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Worst Cases for Correct Rounding of the Elementary Functions in Double Precision
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Searching Worst Cases of a One-Variable Function Using Lattice Reduction
IEEE Transactions on Computers
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
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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驴 15ulp, and we give the worst ones. In particular, the worst case for |x| 驴 3 ×10驴 11is $\exp(9.407822313572878 \times 10^{-2}) = 1.098645682066338\,5\,0000000000000000\,278\ldots$. 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.