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)||3.43MiB|
Fri 18 Jan
|16:37 - 16:59|
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 File Attached
|16:59 - 17:21|
Krishnendu ChatterjeeIST Austria, Amir Kafshdar GoharshadyIST Austria, Nastaran OkatiFerdowsi University of Mashhad, Andreas PavlogiannisEPFL, SwitzerlandLink to publication DOI Pre-print File Attached
|17:21 - 17:43|
Valentin TouzeauUniv. Grenoble Alpes, Claire MaizaVerimag, France, David MonniauxCNRS, VERIMAG, Jan ReinekeSaarland UniversityLink to publication DOI File Attached