Efficient search for inputs causing high floating-point errors

Wei-Fan Chiang, G. Gopalakrishnan, Zvonimir Rakamaric, A. Solovyev
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引用次数: 77

Abstract

Tools for floating-point error estimation are fundamental to program understanding and optimization. In this paper, we focus on tools for determining the input settings to a floating point routine that maximizes its result error. Such tools can help support activities such as precision allocation, performance optimization, and auto-tuning. We benchmark current abstraction-based precision analysis methods, and show that they often do not work at scale, or generate highly pessimistic error estimates, often caused by non-linear operators or complex input constraints that define the set of legal inputs. We show that while concrete-testing-based error estimation methods based on maintaining shadow values at higher precision can search out higher error-inducing inputs, suit able heuristic search guidance is key to finding higher errors. We develop a heuristic search algorithm called Binary Guided Random Testing (BGRT). In 45 of the 48 total benchmarks, including many real-world routines, BGRT returns higher guaranteed errors. We also evaluate BGRT against two other heuristic search methods called ILS and PSO, obtaining better results.
有效搜索导致高浮点错误的输入
浮点误差估计工具是程序理解和优化的基础。在本文中,我们将重点介绍用于确定浮点例程的输入设置的工具,以使其结果误差最大化。这些工具可以帮助支持精确分配、性能优化和自动调优等活动。我们对当前基于抽象的精度分析方法进行了基准测试,并表明它们通常不能大规模工作,或者产生高度悲观的误差估计,这通常是由非线性操作符或定义合法输入集的复杂输入约束引起的。研究表明,基于阴影值保持的基于混凝土测试的误差估计方法可以在较高精度下搜索出较高的误差诱导输入,而合适的启发式搜索引导是发现较高误差的关键。我们开发了一种启发式搜索算法,称为二进制引导随机测试(BGRT)。在总共48个基准测试中的45个(包括许多实际例程)中,BGRT返回更高的保证错误。我们还将BGRT与另外两种启发式搜索方法(ILS和PSO)进行了比较,获得了更好的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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