Data-types optimization for floating-point formats by program transformation

Abstract

In floating-point arithmetic, a desirable property of computations is to be accurate, since in many industrial context small or large perturbations due to round-off errors may cause considerable damages. To cope with this matter of fact, we have developed a tool which corrects these errors by automatically transforming programs in a source to source manner. Our transformation, relying on static analysis by abstract abstraction, concerns pieces of code with assignments, conditionals and loops. By transforming programs, we can significantly optimize the numerical accuracy of computations by minimizing the error relatively to the exact result. An interesting side-effect of our technique is that more accurate computations may make it possible to use smaller data-types. In this article, we show that our transformed programs, executed in single precision, may compete with not transformed codes executed in double precision.