Formal Methods Applied to a Floating-Point Number System
IEEE Transactions on Software Engineering
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
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ACM Transactions on Design Automation of Electronic Systems (TODAES)
Methods of evaluating polynomial approximations in function evaluation routines
Communications of the ACM
Design, implementation and testing of extended and mixed precision BLAS
ACM Transactions on Mathematical Software (TOMS)
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FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Formal Verification of Floating Point Trigonometric Functions
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
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TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
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Innovations in Systems and Software Engineering
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We provide sufficient conditions that formally guarantee that the floating-point computation of a polynomial evaluation is faithful. To this end, we develop a formalization of floating-point numbers and rounding modes in the Program Verification System (PVS). Our work is based on a well-known formalization of floating-point arithmetic in the proof assistant Coq, where polynomial evaluation has been already studied. However, thanks to the powerful proof automation provided by PVS, the sufficient conditions proposed in our work are more general than the original ones.