计算机科学

计算机科学 ›› 2026, Vol. 53 ›› Issue (6): 408-415.doi: 10.11896/jsjkx.250600214

• 计算机软件 • 上一篇    下一篇

浮点误差的特征分析

段孟瑶, 许瑾晨, 杨鸿儒, 张嘉宁, 张涛, 李飞, 周蓓   

  1. 信息工程大学网络空间安全学院 郑州 450001
  • 收稿日期:2025-06-27 修回日期:2025-10-24 出版日期:2026-06-15 发布日期:2026-06-09
  • 通讯作者: 周蓓(beibei_0812@126.com)
  • 作者简介:(dmy200102@163.com)

Characterizing Floating-point Errors

DUAN Mengyao, XU Jinchen, YANG Hongru, ZHANG Jianing, ZHANG Tao, LI Fei, ZHOU Bei   

  1. School of Cyberspace Security,University of Information Engineering,Zhengzhou 450001,China
  • Received:2025-06-27 Revised:2025-10-24 Published:2026-06-15 Online:2026-06-09
  • About author:DUAN Mengyao,born in 2001,postgraduate.Her main research interest is high-performance computing.
    ZHOU Bei,born in 1977,Ph.D,associate professor.Her main research interest is high-performance computing.

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摘要： 浮点误差是计算机科学中不可避免的问题,特别是在科学计算、金融分析等对精度要求较高的领域,误差可能会带来严重后果。该研究对浮点误差特征进行了分析,选取了4个具有代表性的测试集,构成了109个测试程序,主要研究了浮点数精度、指数和表达式类型对误差的影响,探讨了浮点误差是否存在规律。研究结果表明,浮点误差的分布存在一定的规律性,其中包括:1)对于浮点表达式,有98.46%的表达式单精度和双精度的误差分布趋势相同;2)在双参数表达式中,当两个参数之间存在乘除关系时,有86.67%的显著误差集中在两个参数的指数位呈线性关系时;3)90.91%的分式型表达式的最大误差集中在使分母趋近于零的临界点领域。通过对浮点误差特征进行研究,揭示了浮点误差的规律性,并为改进误差检测工具、优化数值计算算法以及制定更严谨的误差控制策略提供了依据。

关键词: 浮点误差, 浮点表达式, 误差特征, 浮点算术, 误差检测

Abstract: Floating-point errors represent an inherent challenge in computer science,particularly in precision-sensitive domains such as scientific computing and financial analysis where such errors may lead to severe consequences.This study conducts a systematic analysis of floating-point error characteristics using four representative test suites comprising 109 benchmark programs,with particular focus on investigating the impact of floating-point precision,exponents and expression types to identify potential error regularities.Experimental results demonstrate statistically significant patterns in error distributions:1)98.46% of floating-point expressions exhibit identical error distribution trends between single-precision(FP32) and double-precision(FP64) formats;2)For dual-parameter expressions with multiplicative/divisive relationships,86.67% of significant errors occur when the exponents of both parameters demonstrate linear dependence;3)90.91% of rational expressions manifest maximum errors within critical neighborhoods where denominators approach zero.These empirical regularities in floating-point error behavior not only advance fundamental understanding of numerical inaccuracies but also provide actionable insights for enhancing error detection tools,optimizing numerical algorithms,and formulating rigorous error control strategies.

Key words: Floating-point errors, Floating-point expressions, Error characteristics, Floating-point arithmetic, Error detection

中图分类号: 

  • TP314
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