Computing a Correct and Tight Rounding Error Bound Using Rounding-to-Nearest

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10152)

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 \(\varepsilon |x|\) or \(\varepsilon |{\circ }(x)|\). 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.

Keywords

Proof Assistant Processor Function Machine Epsilon Directed Rounding Small Normal Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Inria, Université Paris-SaclayPalaiseauFrance
  2. 2.LRI, CNRS & Univ. Paris-SudOrsayFrance

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