| 初等函数可验证赋值及误差分析 |
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| 引用本文： | 刘 剑,唐 敏,曾 霞,曾振柄. 初等函数可验证赋值及误差分析[J]. 计算机科学, 2015, 42(4): 25-30 |
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| 作者姓名： | 刘 剑 唐 敏 曾 霞 曾振柄 |
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| 作者单位： | 1. 华东师范大学上海高可信计算重点实验室 上海200062
2. 华东师范大学上海高可信计算重点实验室 上海200062;桂林电子科技大学数学与计算机学院 桂林541004 |
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| 基金项目： | 本文受国家自然科学基金(91118007),上海市教育委员会创新基金(14ZZ046)资助 |
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| 摘 要： | 研究了GNU标准下初等函数的赋值原理及算法实现.基于IEEE 754-2008浮点标准,利用误差分析基本结论,对GNU下C语言标准数学函数库中的初等函数赋值程序进行理论误差分析.利用Boost库中提供的区间类,将以浮点数作为基本数据类型的程序重写成以区间作为基本类型的程序,使用区间算术对初等函数进行可验证赋值,从而得到一个包含真实值的区间包络,并由此给出GNU下初等函数的数值误差界.
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| 关 键 词： | 初等函数 误差分析 区间算术 可验证赋值 |
Validated Evaluation and Error Analysis of Elementary Functions |
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| LIU Jian,TANG Min,ZENG Xia and ZENG Zhen-bing. Validated Evaluation and Error Analysis of Elementary Functions[J]. Computer Science, 2015, 42(4): 25-30 |
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| Authors: | LIU Jian TANG Min ZENG Xia ZENG Zhen-bing |
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| Affiliation: | Shanghai Key Laboratory of Trustworthy Computing,East China Normal University,Shanghai 200062,China,Shanghai Key Laboratory of Trustworthy Computing,East China Normal University,Shanghai 200062,China;School of Mathematics & Computing Science,Guilin University of Electrical Technology,Guilin 541004,China,Shanghai Key Laboratory of Trustworthy Computing,East China Normal University,Shanghai 200062,China and Shanghai Key Laboratory of Trustworthy Computing,East China Normal University,Shanghai 200062,China |
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| Abstract: | This paper discussed evaluation principle and implementation of elementary functions according to the standard of GNU.Based on the IEEE 754-2008 standard,theoretical error on elementary functions program in C language standard library was analyzed by error analysis fundamental theory.Firstly,the floating-point C program was transferred to the corresponding interval computing one using interval class provided by Boost library.Secondly,validated evaluation was used on these elementary functions by interval arithmetic.Finally,the interval,including real numeric,was obtained.Based on the interval,numerical error bounds on these elementary functions were presented. |
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| Keywords: | Elementary functions Error analysis Interval arithmetic Validated evaluation |
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