Skip to Main content Skip to Navigation

When double rounding is odd

Abstract : Double rounding consists in a first rounding in an intermediate extended precision and then a second rounding in the working precision. The natural question is then of the precision and correctness of the final result. Unfortunately, the used double rounding algorithms do not obtain a correct rounding of the initial value. We prove an efficient algorithm for the double rounding to give the correct rounding to the nearest value assuming the first rounding is to odd. As this rounding is unusual and this property is surprising, we formally proved this property using the Coq automatic proof checker.
Document type :
Complete list of metadata

Cited literature [6 references]  Display  Hide  Download
Contributor : Colette Orange Connect in order to contact the contributor
Submitted on : Wednesday, April 17, 2019 - 9:11:15 AM
Last modification on : Tuesday, November 23, 2021 - 1:40:11 PM


Files produced by the author(s)


  • HAL Id : hal-02101979, version 1



Sylvie Boldo, Guillaume Melquiond. When double rounding is odd. [Research Report] LIP RR-2004-48, Laboratoire de l'informatique du parallélisme. 2004, 2+7p. ⟨hal-02101979⟩



Les métriques sont temporairement indisponibles