Searching Worst Cases of a One-Variable Function Using Lattice Reduction
IEEE Transactions on Computers
Standardization and testing of implementations of mathematical functions in floating point numbers
Programming and Computing Software
Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format
Reliable Implementation of Real Number Algorithms: Theory and Practice
Test Construction for Mathematical Functions
TestCom '08 / FATES '08 Proceedings of the 20th IFIP TC 6/WG 6.1 international conference on Testing of Software and Communicating Systems: 8th International Workshop
Computing correctly rounded integer powers in floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
Standardization and testing of mathematical functions
PSI'09 Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics
Rigorous polynomial approximation using taylor models in Coq
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
VLIW coprocessor for IEEE-754 quadruple-precision elementary functions
ACM Transactions on Architecture and Code Optimization (TACO)
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Abstract: We give the results of a four-year search for the worst cases for correct rounding of the major elementary functions in double precision. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to easily test libraries that are claimed to provide correctly rounded functions.