A Mechanically Checked Proof of the AMD5K86TM Floating-Point Division Program
IEEE Transactions on Computers
Approximating Elementary Functions with Symmetric Bipartite Tables
IEEE Transactions on Computers
Implementation of the Exponential Function in a Floating-Point Unit
Journal of VLSI Signal Processing Systems
The Symmetric Table Addition Method for Accurate Function Approximation
Journal of VLSI Signal Processing Systems
Developing the AMD-K5 Architecture
IEEE Micro
Analysis and applications of Priest's distillation
ACM Transactions on Mathematical Software (TOMS)
Automating custom-precision function evaluation for embedded processors
Proceedings of the 2005 international conference on Compilers, architectures and synthesis for embedded systems
The pitfalls of verifying floating-point computations
ACM Transactions on Programming Languages and Systems (TOPLAS)
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This paper describes the development of the transcendental instructions for the K5, AMD's recently completed x86 compatible superscalar microprocessor. A multi-level development cycle, with testing between levels, facilitated the early detection of errors and limited their effect on the design schedule. The algorithms for the transcendental functions use table-driven reductions followed by polynomial approximations. Multiprecision arithmetic operations are used when necessary to maintain sufficient accuracy and to ensure that the transcendental functions have a maximum error of one unit in the last place.