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计算机工程 ›› 2012, Vol. 38 ›› Issue (15): 31-34. doi: 10.3969/j.issn.1000-3428.2012.15.009

• 软件技术与数据库 • 上一篇    下一篇

一种改进的超越函数通用算法

郭绍忠,许瑾晨,陈建勋   

  1. (解放军信息工程大学信息工程学院,郑州 450002)
  • 收稿日期:2011-09-19 出版日期:2012-08-05 发布日期:2012-08-05
  • 作者简介:郭绍忠(1964-),女,副教授、硕士,主研方向:高性能计算,分布式系统;许瑾晨、陈建勋,硕士研究生
  • 基金资助:
    国家“863”计划基金资助重点项目(2009AA012201);上海市科委重大科技攻关计划基金资助项目(08dz501600)

Improved Transcendental Function General Algorithm

GUO Shao-zhong, XU Jin-chen, CHEN Jian-xun   

  1. (Institute of Information Engineering, PLA Information Engineering University, Zhengzhou 450002, China)
  • Received:2011-09-19 Online:2012-08-05 Published:2012-08-05

摘要: 提出一种适用于高性能计算的基础数学库超越函数通用算法。基于转换、近似、重建等技术,对级数法和迭代法进行改进,运用函数收敛性最好的一段区间进行函数算法设计,通过减少运算次数来降低因多次运算导致的累积误差,保证函数算法的精度。利用查表法构造辅助表参与运算,减少算法开销。测试结果表明,与GNU数学库函数相比,基于该算法的数学库函数运行效率平均提升50.91%。

关键词: 基础数学库, 超越函数, 算法转换, 级数法, 迭代法, 查表法

Abstract: This paper proposes an improved general algorithm for the transcendental functions, which is appropriate for the high-performance computing. Based on various technologies, such as conversion, approximation and reconstruction, it advances the progression algorithm and iteration algorithm, designs the functions with the aid of the interval with best astringency. Additionally, the cumulative error caused by repeated operations is also reduced by minimizing the operation frequencies, so as to guarantee the function accuracies. At the same time, algorithm overheads are well reduced by constructing auxiliary tables with the look-up table algorithm. Experimental results show that the performance of the mathematic library functions based on this paper can be promoted by 50.91% compared with those of the GNU mathematic library.

Key words: basic mathematic library, transcendental function, algorithm conversion, series algorithm, iteration algorithm, look-up table algorithm

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