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.

中文翻译：

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一种可扩展且严格的浮点误差分析的抽象引导方法

用于严格浮点舍入误差分析的自动化技术在正确性的形式验证和精度调整等领域非常重要。现有的工具和技术虽然提供了严格的界限，但无法分析具有数百个以上运算符的表达式，因此无法涵盖重要的实际问题。在这项工作中，我们展示了 Satire，一种新工具，它阐明了如何通过增量分析、抽象以及明智地使用具体和符号评估的组合来实现可扩展性和约束性。Satire 已经处理了超过 200K 运营商的问题。我们展示了 Satire 的基本错误分析方法、信息理论抽象启发式方法和广泛的案例研究，评估涵盖 FFT、洛伦兹方程组和各种 PDE 模板类型。