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Kahan's algorithm for a correct discriminant computation at last formally proven

Sylvie Boldo 1, 2
1 PROVAL - Proof of Programs
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : This article tackles Kahan's algorithm to compute accurately the discriminant whatever the inputs. This is a known difficult problem and this algorithm leads to an error bounded by 2 ulps of the result. The proofs involved are long and tricky and even trickier than expected as the test involved may give an unexpected result. We give here the total demonstration of the validity of this algorithm and we provide sufficient conditions to guarantee neither Overflow, nor Underflow will jeopardize the result. The program was annotated using the Caduceus tool and the proof obligations were done using the Coq automatic proof checker.
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Submitted on : Tuesday, November 24, 2009 - 11:00:56 AM
Last modification on : Wednesday, February 9, 2022 - 5:26:06 PM
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Sylvie Boldo. Kahan's algorithm for a correct discriminant computation at last formally proven. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2009, 58 (2), pp.220-225. ⟨10.1109/TC.2008.200⟩. ⟨inria-00171497v2⟩



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