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Static Analysis of the Numerical Stability of Loops

  • Matthieu Martel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2477)

Abstract

We introduce a relational static analysis to determine the stability of the numerical errors arising inside a loop in which floating-point computations are carried out. This analysis is based on a stability test for non-linear functions and on a precise semantics for floating-point numbers that computes the propagation of the errors made at each operation. A major advantage of this approach is that higher-order error terms are not neglected. We introduce two algorithms for the analysis. The first one, less complex, only determines the global stability of the loop. The second algorithm determines which particular operation makes a loop unstable. Both algorithms have been implemented and we present some experimental results.

Keywords

Abstract Interpretation Numerical Precision Relational Analysis Semantics of Floating-point Numbers 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Matthieu Martel
    • 1
  1. 1.CEA - Recherche TechnologiqueLIST-DTSI-SLAGif-Sur-YvetteFrance

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