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A Mechanically Checked Proof of IEEE Compliance of the Floating Point Multiplication, Division and Square Root Algorithms of the AMD-K7™ Processor

Published online by Cambridge University Press:  01 February 2010

David M. Russinoff
David M. Russinoff
Affiliation:
Advanced Micro Devices, Inc., 5900 E. Ben White Blvd, MS 625, Austin, TX 78741, U.S.A., david.russinoff@amd.com

Abstract

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We describe a mechanically verified proof of correctness of the floating point multiplication, division, and square root instructions of the AMD-K7 microprocessor. The instructions are implemented in hardware and represented here by register-transfer level specifications, the primitives of which are logical operations on bit vectors. On the other hand, the statements of correctness, derived from IEEE Standard 754, are arithmetic in nature and considerably more abstract. Therefore, we begin by developing a theory of bit vectors and their role in floating point representations and rounding. We then present the hardware model and a rigorous proof of its correctness. All of our definitions, lemmas and theorems have been formally encoded in the ACL2 logic, and every step in the proof has been mechanically checked with the ACL2 prover.

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 1 , 1998 , pp. 148 - 200
Copyright
Copyright © London Mathematical Society 1998

References

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Supplementary material: File

Russinoff Appendix

Appendix

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