Static Analysis of Numerical Algorithms

  • Eric Goubault
  • Sylvie Putot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4134)


We present a new numerical abstract domain for static analysis of the errors introduced by the approximation by floating-point arithmetic of real numbers computation, by abstract interpretation [3]. This work extends a former domain [4,8], with an implicitly relational domain for the approximation of the floating-point values of variables, based on affine arithmetic [2]. It allows us to analyze non trivial numerical computations, that no other abstract domain we know of can analyze with such precise results, such as linear recursive filters of different orders, Newton methods for solving non-linear equations, polynomial iterations, conjugate gradient algorithms.


Arithmetic Operation Interval Arithmetic Abstract Interpretation Relational Domain Abstract Domain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Eric Goubault
    • 1
  • Sylvie Putot
    • 1
  1. 1.CEA SaclayGif-sur-YvetteFrance

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