可变精度超越函数算法设计

doi:10.11896/jsjkx.200200013

计算机科学 ›› 2020, Vol. 47 ›› Issue (8): 71-79.doi: 10.11896/jsjkx.200200013

所属专题：高性能计算

可变精度超越函数算法设计

郝江伟, 郭绍忠, 夏媛媛, 许瑾晨

数学工程与先进计算国家重点实验室(信息工程大学) 郑州 450000

出版日期:2020-08-15 发布日期:2020-08-10
通讯作者: 许瑾晨(atao728208@126.com)
作者简介:1903377641@qq.com
基金资助:
国家自然科学基金(61802434)

Algorithm Design of Variable Precision Transcendental Functions

HAO Jiang-wei, GUO Shao-zhong, XIA Yuan-yuan, XU Jin-chen

State Key Laboratory of Mathematical Engineering and Advanced Computing, PLA Information Engineering University, Zhengzhou 450000, China

Online:2020-08-15 Published:2020-08-10
About author:HAO Jiang-wei, born in 1995, postgra-duate, is a student member of China Computer Federation.His main research interests include high-performance computing and so on.
XU Jin-chen, born in 1987, Ph.D, lectu-rer, is a member of China Computer Fe-deration.His main research interests include high-performance computing.
Supported by:
This work was supported by the National Natural Science Foundation of China(61802434).

摘要/Abstract

摘要： 超越函数是基础数学函数库的主体部分, 其精度和性能决定着上层应用的精度和性能。针对超越函数的实现繁琐易错、应用精度需求各异等问题, 文中提出并实现兼顾通用性和函数数学特性的可变精度超越函数算法。依据超越函数的相似性, 构建“转换-归约-逼近-重建”算法模板, 实现常见的超越函数算法;并通过调整算法模板参数来控制误差, 生成不同精度版本的函数代码。实验验证, 所提算法能够生成常见超越函数的不同精度版本的函数代码, 且相对标准数学库超越函数具有性能优势。

关键词: 超越函数, 可变精度, 误差控制

Abstract: Transcendental functions are the main part of fundamental mathematical software library.Their accuracy and perfor-mance greatly determine those of the upper-layer applications.Aiming at the problems of tedious and error-prone implementation of transcendental functions as well as accuracy requirements of different applications, a variable precision transcendental function algorithm is proposed, which considers both generality and mathematical characteristics of functions.Based on the similarity of transcendental functions, a transformation-reduction-approximation-reconstruction algorithm template is constructed to unify common transcendental function algorithm implementations, and the algorithm template parameters are adjusted to handle errors to generate different precision versions of function codes.Experiment results show that the algorithm is able to generate function codes of different precision versions of common transcendental functions and has performance advantages over the corresponding functions in the standard mathematical software library.

Key words: Error control, Transcendental functions, Variable precision

中图分类号:

TP311

郝江伟, 郭绍忠, 夏媛媛, 许瑾晨. 可变精度超越函数算法设计[J]. 计算机科学, 2020, 47(8): 71-79. https://doi.org/10.11896/jsjkx.200200013

HAO Jiang-wei, GUO Shao-zhong, XIA Yuan-yuan, XU Jin-chen. Algorithm Design of Variable Precision Transcendental Functions[J]. Computer Science, 2020, 47(8): 71-79. https://doi.org/10.11896/jsjkx.200200013

参考文献

[1] RANF R T.Damage to bridges during the 2001 Nisqually earthquake[C]∥2001 Earthquake Engineering Symposium for Young Researchers.New York:MCEER, 2001:273-293.
[2] OLVER F W, LOZIER D W, BOISVERT R F, et al.NISTHandbook of Mathematical Functions[M].Cambridge:Cambridge University Press, 2010.
[3] VOLDER J.The CORDIC trigonometic computing technique[C]∥Western Joint Computer Conference.New York:ACM, 1959:257-261.
[4] WALTHER J S.A unified algorithm for elementary functions[C]∥Spring Joint Computer Conference.New York:ACM, 1971:379-385.
[5] TANG P T P.Table-driven implementation of the expm1 function in IEEE floating-point arithmetic[J].ACM Transactions on Mathematical Software(TOMS), 1992, 18(2):211-222.

[6] GUO S Z, XU J C, CHEN J X.Improved Transcendental Function General Algorithm[J].Computer Engineering, 2012, 38(15):31-34.
[7] CHEVILLARD S, MIOARA J, LAUTER C.Sollya:An Envi-ronment for the Development of Numerical Codes[C]∥3rd International Congress on Mathematical Software(ICMS 2010).Berlin:Springer, 2010:28-31.
[8] BRISEBARRE N, CHEVILLARD S.Efficient polynomial L∞-approximations[C]∥18th IEEE Symposium on Computer Arithmetic(ARITH’07).Piscataway:IEEE, 2007:169-176.
[9] BRUNIE N, DINECHIN F D, KUPRIIANOVA O, et al.CodeGenerators for Mathematical Functions[C]∥22nd IEEE Symposium on Computer Arithmetic(ARITH’15).Piscataway:IEEE, 2015:58-65.
[10]KUPRIIANOVA O, LAUTER C.A Domain Splitting Algo-rithm for the Mathematical Functions Code Generator[C]∥48th Asilomar Conference on Signals, Systems and Computers.Piscataway:IEEE, 2014:1271-1275.
[11]甄西丰.实用数值计算方法[M].北京:清华大学出版社, 2006.
[12]QI H Y, XU J X, GUO S Z.Detection of the maximum error ofmathematical functions[J].The Journal of Supercomputing, 2018, 74(11):6275-6290.
[13]MULLER J M.Elementary functions:algorithms and implemen-tation[M].Basel:Birkhüuser Basel, 2006.
[14]XU J C, HUANG Y Z, GUO S Z, et al.Testing Platform for Floating Mathematical Function Libraries[J].Journal of Software, 2015, 26(6):1306-1321.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

可变精度超越函数算法设计

Algorithm Design of Variable Precision Transcendental Functions

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 8

Metrics

本文评价

推荐阅读 0

[1]	刘聃, 郭绍忠, 郝江伟, 许瑾晨. 基于SIMD扩展部件的长向量超越函数实现方法 Implementation of Transcendental Functions on Vectors Based on SIMD Extensions 计算机科学, 2021, 48(6): 26-33. https://doi.org/10.11896/jsjkx.200400007
[2]	陈玉金,李续武,贾英杰,张鑫. 可变多重代价决策粗糙集模型 Variable Multi-cost Based Decision Theoretic Rough Sets 计算机科学, 2017, 44(6): 245-249. https://doi.org/10.11896/j.issn.1002-137X.2017.06.042
[3]	冯林,李天瑞,余志强. 连续值属性决策表中的可变精度粗糙集模型及属性约简 Attributes Reduction Based on the Variable Precision Rough Set in Decision Tables Containing Continuous-valued Attributes 计算机科学, 2010, 37(9): 205-208.
[4]	. 可变精度粗糙集β值的增量计算计算机科学, 2008, 35(3): 228-230.
[5]	. 数据驱动的可变精度粗糙集噪音阈值获取方法计算机科学, 2008, 35(11): 174-177.
[6]	王卫尹建峰孙正兴. 一种手绘草图的快速参数化方法计算机科学, 2006, 33(1): 264-268.
[7]	王加阳陈松乔罗安. 可变精度粗集模型约简异常分析计算机科学, 2005, 32(12): 175-177.
[8]	. 基于数据库系统的可变精度粗糙集模型计算机科学, 2005, 32(12): 172-174.