New scalar and vector elementary functions for the IBM system/370
IBM Journal of Research and Development
Computer Approximations
Computing Elementary Functions: A New Approach for Achieving High Accuracy and Good Performance
Proceedings of the Symposium on Accurate Scientific Computations
Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics)
Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics)
Accurate and efficient testing of the exponential and logarithm functions
ACM Transactions on Mathematical Software (TOMS)
Table-driven implementation of the logarithm function in IEEE floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
A portable generic elementary function package in Ada and an accurate test suite
ACM SIGAda Ada Letters - Special issue on Ada numerics standardization and testing
Table-driven implementation of the Expm1 function in IEEE floating-point arithmetic
ACM Transactions on Mathematical Software (TOMS)
The design of floating-point data types
ACM Letters on Programming Languages and Systems (LOPLAS)
Floating Point Verification in HOL Light: The Exponential Function
Formal Methods in System Design
A Priori Worst Case Error Bounds for Floating-Point Computations
IEEE Transactions on Computers
Enabling Hardware Verification through Design Changes
ICFEM '02 Proceedings of the 4th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
An Exponentiation Unit for an OpenGL Lighting Engine
IEEE Transactions on Computers
Near Optimality of Chebyshev Interpolation for Elementary Function Computations
IEEE Transactions on Computers
Computing machine-efficient polynomial approximations
ACM Transactions on Mathematical Software (TOMS)
Certification of bounds on expressions involving rounded operators
ACM Transactions on Mathematical Software (TOMS)
Unified Tables for Exponential and Logarithm Families
ACM Transactions on Mathematical Software (TOMS)
A special-purpose compiler for look-up table and code generation for function evaluation
Proceedings of the Conference on Design, Automation and Test in Europe
Floating-Point Exponentiation Units for Reconfigurable Computing
ACM Transactions on Reconfigurable Technology and Systems (TRETS)
Tool support for software lookup table optimization
Scientific Programming
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Algorithms and implementation details for the exponential function in both single- and double-precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.54 ulp as long as the final result does not underflow. When the final result suffers gradual underflow, the error is still no worse than 0.77 ulp.