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Conference Papers Year : 2016

Computing a correct and tight rounding error bound using rounding-to-nearest

Abstract

When a floating-point computation is done, it is most of the time incorrect. The rounding error can be bounded by folklore formulas, such as ε|x| or ε| o (x)|. This gets more complicated when underflow is taken into account as an absolute term must be considered. Now, let us compute this error bound in practice. A common method is to use a directed rounding in order to be sure to get an over-approximation of this error bound. This article describes an algorithm that computes a correct bound using only rounding to nearest, therefore without requiring a costly change of the rounding mode. This is formally proved using the Coq formal proof assistant to increase the trust in this algorithm.
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Dates and versions

hal-01377152 , version 1 (06-10-2016)

Identifiers

  • HAL Id : hal-01377152 , version 1

Cite

Sylvie Boldo. Computing a correct and tight rounding error bound using rounding-to-nearest. 9th International Workshop on Numerical Software Verification, Jul 2016, Toronto, Canada. ⟨hal-01377152⟩
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