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Formal proof for delayed finite field arithmetic using floating point operators

Sylvie Boldo 1 Marc Daumas 2 Pascal Giorgi 3
1 PROVAL - Proof of Programs
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR
3 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed solution of a triangular system over a finite field mixes operations on integers and operations on floating point numbers. We focus in this report on verifying proof obligations that state that no round off error occurred on any of the floating point operations. We use a tool named Gappa that can be learned in a matter of minutes to generate proofs related to floating point arithmetic and hide technicalities of formal proof checkers. We found that three facilities are missing from existing tools. The first one is the ability to use in Gappa new lemmas that cannot be easily expressed as rewriting rules. We coined the second one ``variable interchange'' as it would be required to validate loop interchanges. The third facility handles massive loop unrolling and argument instantiation by generating traces of execution for a large number of cases. We hope that these facilities may sometime in the future be integrated into mainstream code validation.
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Contributor : Marc Daumas <>
Submitted on : Wednesday, May 14, 2008 - 3:05:42 PM
Last modification on : Tuesday, January 12, 2021 - 3:33:24 AM
Long-term archiving on: : Thursday, September 23, 2010 - 5:05:00 PM


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  • HAL Id : hal-00135090, version 3
  • ARXIV : cs/0703026



Sylvie Boldo, Marc Daumas, Pascal Giorgi. Formal proof for delayed finite field arithmetic using floating point operators. 8th Conference on Real Numbers and Computers, Jul 2008, Saint Jacques de Compostelle, Spain. pp.113-122. ⟨hal-00135090v3⟩



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