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Efficient automated repair of high floating-point errors in numerical libraries 有效地自动修复数值库中的高浮点数错误

Proc. ACM Program. Lang. Pub Date : 2019-01-02 DOI: 10.1145/3290369

Xin Yi, Liqian Chen, Xiaoguang Mao, Tao Ji

{"title":"Efficient automated repair of high floating-point errors in numerical libraries","authors":"Xin Yi, Liqian Chen, Xiaoguang Mao, Tao Ji","doi":"10.1145/3290369","DOIUrl":"https://doi.org/10.1145/3290369","url":null,"abstract":"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. \u0000 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.","PeriodicalId":143298,"journal":{"name":"Proc. ACM Program. Lang.","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125433998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 35

Hefty Algebras: Modular Elaboration of Higher-Order Algebraic Effects 沉重的代数:高阶代数效应的模块化阐述

Proc. ACM Program. Lang. Pub Date : 1900-01-01 DOI: 10.1145/3571255

Casper Bach Poulsen, Cas van der Rest

{"title":"Hefty Algebras: Modular Elaboration of Higher-Order Algebraic Effects","authors":"Casper Bach Poulsen, Cas van der Rest","doi":"10.1145/3571255","DOIUrl":"https://doi.org/10.1145/3571255","url":null,"abstract":"Algebraic effects and handlers is an increasingly popular approach to programming with effects. An attraction of the approach is its modularity: effectful programs are written against an interface of declared operations, which allows the implementation of these operations to be defined and refined without changing or recompiling programs written against the interface. However, higher-order operations (i.e., operations that take computations as arguments) break this modularity. While it is possible to encode higher-order operations by elaborating them into more primitive algebraic effects and handlers, such elaborations are typically not modular. In particular, operations defined by elaboration are typically not a part of any effect interface, so we cannot define and refine their implementation without changing or recompiling programs. To resolve this problem, a recent line of research focuses on developing new and improved effect handlers. In this paper we present a (surprisingly) simple alternative solution to the modularity problem with higher-order operations: we modularize the previously non-modular elaborations commonly used to encode higher-order operations. Our solution is as expressive as the state of the art in effects and handlers.","PeriodicalId":143298,"journal":{"name":"Proc. ACM Program. Lang.","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121247185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1