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Formal Verification of a Floating-Point Expansion Renormalization Algorithm

Abstract : Many numerical problems require a higher computing precision than the one offered by standard floating-point formats. A common way of extending the precision is to use floating-point expansions. As the problems may be critical and as the algorithms used have very complex proofs (many sub-cases), a formal guarantee of correctness is a wish that can now be fulfilled, using interactive theorem proving. In this article we give a formal proof in Coq for one of the algorithms used as a basic brick when computing with floating-point expansions, the renormaliza-tion, which is usually applied after each operation. It is a critical step needed to ensure that the resulted expansion has the same property as the input one, and is more " compressed ". The formal proof uncovered several gaps in the pen-and-paper proof and gives the algorithm a very high level of guarantee.
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Submitted on : Sunday, April 23, 2017 - 12:52:53 AM
Last modification on : Saturday, September 11, 2021 - 3:18:34 AM
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  • HAL Id : hal-01512417, version 1


Sylvie Boldo, Mioara Joldes, Jean-Michel Muller, Valentina Popescu. Formal Verification of a Floating-Point Expansion Renormalization Algorithm. 8th International Conference on Interactive Theorem Proving (ITP'2017), Sep 2017, Brasilia, Brazil. ⟨hal-01512417⟩



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