Intra-procedural Optimization of the Numerical Accuracy of Programs

Nasrine Damouche (1, 2) , Matthieu Martel (1, 2) , Alexandre Chapoutot (3)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
2 DALI - Digits, Architectures et Logiciels Informatiques
3 SFL - Sûreté et Fiabilité des Logiciels

Numerical programs performing floating-point computations are very sensitive to the way formulas are written. These last years, several techniques have been proposed concerning the transformation of arithmetic expressions in order to improve their 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 the numerical accuracy of the target variable. We use abstract interpretation-based static analysis techniques to over-approximate the roundoff errors in programs and during the transformation of expressions. A prototype has been implemented and experimental results are presented concerning classical numerical algorithm analysis and algorithm for embedded systems.

Keywords: Floating-Point Numbers; Static Analysis; IEEE754 Standard; Program Transformation

Domains: Programming Languages [cs.PL]

Nasrine Damouche, Matthieu Martel, Alexandre Chapoutot. Intra-procedural Optimization of the Numerical Accuracy of Programs. FMICS: Formal Methods for Industrial Critical Systems, Jun 2015, Oslo, Norway. pp.31-46, ⟨10.1007/978-3-319-19458-5_3⟩. ⟨hal-01164340⟩