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Improving the numerical accuracy of programs by automatic transformation

  • Nasrine DamoucheEmail author
  • Matthieu Martel
  • Alexandre Chapoutot
FMICS 2015/2016

Abstract

The dangers of programs performing floating-point computations are well known. This is due to the sensitivity of the results to the way formulæ are written. These last years, several techniques have been proposed concerning the transformation of arithmetic expressions in order to improve their numerical accuracy and, in this article, we go one step further by automatically transforming larger pieces of code containing assignments and control structures. We define a set of transformation rules allowing the generation, under certain conditions and in polynomial time, of larger expressions by performing limited formal computations, possibly among several iterations of a loop. These larger expressions are better suited to improve, by reparsing, the numerical accuracy of the program results. We use abstract interpretation-based static analysis techniques to over-approximate the round-off errors in programs and during the transformation of expressions. A tool has been implemented and experimental results are presented concerning classical numerical algorithms and algorithms for embedded systems.

Keywords

Program transformation Floating-point numbers Static analysis IEEE754 standard Numerical accuracy 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Nasrine Damouche
    • 1
    Email author
  • Matthieu Martel
    • 1
  • Alexandre Chapoutot
    • 2
  1. 1.LAMPS LaboratoryUniversity of Perpignan Via DomitiaPerpignanFrance
  2. 2.U2IS, ENSTA ParisTech, Université Paris-SaclayPalaiseau cedexFrance

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