Efficient Automated Repair of High Floating-Point Errors in Numerical Libraries
Floating point computation is by nature inexact, and numerical libraries that intensively involve floating-point computations may encounter high floating-point errors. Due to the wide use of numerical libraries, it is highly desired to reduce high floating-point errors in them. Using higher precision will degrade performance and may also introduce extra errors for certain precision-specific operations in numerical libraries. Using mathematical rewriting that mostly focuses on rearranging floating-point expressions or taking Taylor expansions may not fit for reducing high floating-point errors evoked by ill-conditioned problems that are in the nature of the mathematical feature of many numerical programs in numerical libraries.
In this paper, we propose a novel approach for efficient automated repair of high floating-point errors in numerical libraries. Our main idea is to make use of the mathematical feature of a numerical program for detecting and reducing high floating-point errors. The key components include a detecting method based on two algorithms for detecting high floating-point errors and a repair method for deriving an approximation of a mathematical function to generate patch to satisfy a given repair criterion. We implement our approach by constructing a new tool called AutoRNP. Our experiments are conducted on 20 numerical programs in GNU Scientific Library (GSL). Experimental results show that our approach can efficiently repair (with $100%$ accuracy over all randomly sampled points) high floating-point errors for 19 of the 20 numerical programs.
|Efficient Automated Repair of High Floating-Point Errors in Numerical Libraries (POPL2019-yx-slide-v1-0118.pdf)||3.44MiB|
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Xin YiNational University of Defense Technology, Liqian ChenNational University of Defense Technology, Xiaoguang MaoNational University of Defense Technology, Tao JiNational University of Defense TechnologyLink to publication DOI Media Attached File Attached
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Krishnendu ChatterjeeIST Austria, Amir Kafshdar GoharshadyIST Austria, Nastaran OkatiFerdowsi University of Mashhad, Andreas PavlogiannisEPFL, SwitzerlandLink to publication DOI Pre-print Media Attached File Attached
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Valentin TouzeauUniv. Grenoble Alpes, Claire MaizaVerimag, France, David MonniauxCNRS, VERIMAG, Jan ReinekeSaarland UniversityLink to publication DOI Media Attached File Attached