一句话：提出在 FPTaylor 的 Taylor 展开上应用集中不等式的概率浮点舍入分析方法，可高效生成概率阈值。
本文研究数值程序中普遍存在且可能导致灾难性故障的浮点舍入误差。确定性舍入阈值往往需覆盖小概率大误差，因而过于保守。作者提出概率化舍入分析：在 FPTaylor 的 Taylor 展开上应用集中不等式，推导“舍入误差超过阈值概率低于给定置信度”的概率阈值。主要困难在于 Taylor 展开含绝对值，使一阶偏导项期望难以计算。作者先给出多项式表达式中去除绝对值的可靠过近似，再将分式表达式转化为多项式情形，并用区间划分改进精度。该方法可扩展，关键计算是多变量独立多项式的期望，可利用期望的线性性与独立性高效完成。实验表明，与当前先进方法相比，该方法时间效率提升数个数量级，同时阈值精度相当。
Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one must derive guaranteed round-off thresholds to ensure the correctness of these programs. However, deterministic round-off thresholds tend to be too conservative to be usable in practice, since they often involve large round-off errors that occur with small probability. Probabilistic thresholds relax deterministic ones by specifying that the probability of the round-off error exceeding a threshold is below a given confidence. In this work, we propose a novel approach to probabilistic round-off analysis, by applying concentration inequalities over the Taylor expansion from FPTaylor (TOPLAS 2018). A major obstacle in applying concentration inequalities is that the Taylor expansion involves absolute value operators that make the calculation of the expected values of the first order partial differential terms difficult. Our first step to overcome this obstacle is a sound over-approximation that removes the absolute value operators in polynomial expressions. Then, we show how to handle fractional expressions by a transformation into polynomial case. Finally, we show how to improve our approach with range partitioning. Our approach is scalable since the key computational part is the calculation of expected values of polynomial expressions with independent variables, for which the linear and independence properties of expectation boost the computation. Experimental results show that our approach is orders of magnitude more time efficient, while producing thresholds with comparable precision against the state of the art.
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@article{abs-2605-04232,
title = {Probabilistic Floating-Point Round-Off Analysis via Concentration Inequalities},
author = {Yichen Tao and Hongfei Fu and Jiawei Chen and Jean-Baptiste Jeannin},
journal = {Proceedings of the ACM on Programming Languages},
volume = {10},
number = {OOPSLA2},
year = {2026},
doi = {10.1145/3839447}
}