论文标题
一种抽象引导的方法，用于可扩展和严格的浮点误差分析
An Abstraction-guided Approach to Scalable and Rigorous Floating-Point Error Analysis
论文作者
论文摘要
在正式验证正确性和精确调整的领域中，用于严格浮点圆形错误分析的自动化技术很重要。现有的工具和技术在提供紧密的界限的同时，无法与数百多名运营商分析表达式，因此无法涵盖重要的实际问题。在这项工作中，我们展示了讽刺，这是一种新工具，阐明了如何通过增量分析，抽象以及对混凝土和符号评估的明智使用以及明智地使用的结合来实现的可伸缩性和界限。讽刺已处理超过200万运营商的问题。我们介绍了讽刺的潜在错误分析方法，信息理论的抽象启发式方法以及广泛的案例研究，评估涵盖了FFT，Lorenz方程系统和各种PDE模板类型。我们的结果表明，讽刺界限的紧密性，可接受的运行时以及提供的宝贵见解。
Automated techniques for rigorous floating-point round-off error analysis are important in areas including formal verification of correctness and precision tuning. Existing tools and techniques, while providing tight bounds, fail to analyze expressions with more than a few hundred operators, thus unable to cover important practical problems. In this work, we present Satire, a new tool that sheds light on how scalability and bound-tightness can be attained through a combination of incremental analysis, abstraction, and judicious use of concrete and symbolic evaluation. Satire has handled problems exceeding 200K operators. We present Satire's underlying error analysis approach, information-theoretic abstraction heuristics, and a wide range of case studies, with evaluation covering FFT, Lorenz system of equations, and various PDE stencil types. Our results demonstrate the tightness of Satire's bounds, its acceptable runtime, and valuable insights provided.
