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| A Numerical-based Parametric Error Analysis Method for Goldschmidt Floating Point Division | |
| 2023-04-14 | |
| 状态 | 已发表 |
| 摘要 | This paper proposes a parametric error analysis method for Goldschmidt floating point division, which reveals how the errors of the intermediate results accumulate and propagate during the Goldschmidt iterations. The analysis is developed by separating the error terms with and without convergence to zero, which are the key parts of the iterative approximate value. The proposed method leads to a state-of-the-art wordlength reduction for intermediate results during the Goldschmidt iterative computation. It enables at least half of the calculation precision reduction for the iterative factor to implement the rectangular multiplier in the divider through flexible numerical method, which can also be applied in the analysis of Goldschmidt iteration with iterative factors assigned under other ways for faster convergence. Based on the proposed method, two proof-of-concept divider models with different configurations are developed, which are verified by more than 100 billion random test vectors to show the correctness and tightness of the proposed error analysis. |
| 关键词 | Floating point division Goldschmidt Error Analysis Parametric Numerical |
| 语种 | 英语 |
| DOI | arXiv:2305.03728 |
| 相关网址 | 查看原文 |
| 出处 | Arxiv |
| 收录类别 | PPRN.PPRN |
| WOS记录号 | PPRN:68522421 |
| WOS类目 | Computer Science, Interdisciplinary Applications ; Mathematics |
| 文献类型 | 预印本 |
| 条目标识符 | https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/483978 |
| 专题 | 信息科学与技术学院 信息科学与技术学院_PI研究组_娄鑫组 信息科学与技术学院_硕士生 信息科学与技术学院_本科生 |
| 通讯作者 | Yuan, Binzhe |
| 作者单位 | Shanghai Tech Univ, Sch Informat Sci & Technol, Shanghai 201210, Peoples R China |
| 推荐引用方式 GB/T 7714 | Yuan, Binzhe,Dai, Liangtao,Lou, Xin. A Numerical-based Parametric Error Analysis Method for Goldschmidt Floating Point Division. 2023. |
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