OFP-Repair: Repairing Floating-point Errors via Original-Precision Arithmetic

Abstract

Errors in floating-point programs can lead to severe consequences, particularly in critical domains such as military, aerospace, and financial systems, making their repair a crucial research problem. In practice, some errors can be fixed using original-precision arithmetic, while others require high-precision computation. Developers often avoid addressing the latter due to excessive computational resources required. However, they sometimes struggle to distinguish between these two types of errors, and existing repair tools fail to assist in this differentiation. Most current repair tools rely on high-precision implementations, which are time-consuming to develop and demand specialized expertise. Although a few tools do not require high-precision programs, they can only fix a limited subset of errors or produce suboptimal results. To address these challenges, we propose a novel method, named OFP-Repair.On ACESO's dataset, our patches achieve improvements of three, seven, three, and eight orders of magnitude across four accuracy metrics. In real-world cases, our method successfully detects all five original-precision-repairable errors and fixes three, whereas ACESO only repairs one. Notably, these results are based on verified data and do not fully capture the potential of OFP-Repair. To further validate our method, we deploy it on a decade-old open bug report from GNU Scientific Library (GSL), successfully repairing five out of 15 bugs. The developers have expressed interest in our method and are considering integrating our tool into their development workflow. We are currently working on applying our patches to GSL. The results are highly encouraging, demonstrating the practical applicability of our technique.