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Propagation of Roundoff Errors in Finite Precision Computations: A Semantics Approach

  • Matthieu Martel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2305)

Abstract

We introduce a concrete semantics for floating-point operations which describes the propagation of roundoff errors throughout a computation. This semantics is used to assert the correctness of an abstract interpretation which can be straightforwardly derived from it. In our model, every elementary operation introduces a new first order error term, which is later combined with other error terms, yielding higher order error terms. The semantics is parameterized by the maximal order of error to be examined and verifies whether higher order errors actually are negligible. We consider also coarser semantics computing the contribution, to the final error, of the errors due to some intermediate computations.

Keywords

Numerical Precision Abstract Interpretation Floating-point Arithmetic IEEE Standard 754 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Matthieu Martel
    • 1
  1. 1.CEA - Recherche Technologique LIST-DTSI-SLAGif-Sur-Yvette CedexFrance

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