Numerical Accuracy Improvement by Interprocedural Program Transformation

Abstract

Floating-point numbers are used to approximate the exact real numbers in a wide range of domains like numerical simulations, embedded software, etc. However, floating-point numbers are a finite approximation of real numbers. In practice, this approximation may introduce round-off errors and this can lead to catastrophic results. To cope with this issue, we have developed a tool which corrects partly these round-off errors and which consequently improves the numerical accuracy of computations by automatically transforming programs in a source to source manner. Our transformation, relies on static analysis by abstract interpretation and operates on pieces of code with assignments, conditionals and loops. In former work, we have focused on the intraprocedural transformation of programs and, in this article, we introduce the interprocedural transformation to improve accuracy.