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Home > Archive>Volume 31, Issue 12, 2020 >3685-3699. DOI:10.13328/j.cnki.jos.005883
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Reliable Algorithm for Computing Cyclic Iterative Program
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National Key Research and Development Program of China (2017YFB1001800); National Natural Science Foundation of China (61772203, 61972150, 61876034)

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    Abstract:

    As a basic component of software, the correct running of cyclic iteration program is of great significance. However, sometimes (e.g., when its NID is greater than 0) the rounding error (or representation error) in the calculation can lead to unstable results of the cyclic iteration. Based on the computing technology of “automatic dynamic adjustment of intermediate calculation accuracy”, a reliable calculation algorithm for cyclic iteration is presented in this paper. By using this algorithm, the value of arbitrary precision of cyclic iteration can be obtained. At present, the algorithm has been programmed and implemented in ISReal through C++ language.

    Reference
    [1] Muller JM. Arithmétique des Ordinateurs. Paris:Masson, 1989(in French).
    [2] Muller JM, Brisebarre N, Dinechin FD, et al. Handbook of Floating-point Arithmetic. Boston:Birkhauser Boston, 2010. 8-10.
    [3] Kahan W. How futile are mindless assessments of roundoff in floating-point computation? 2006. http://www.cs.berkeley.edu/~wkahan/Mindless.pdf
    [4] Benz F, Hildebrandt A, Hack S. A Dynamic program analysis to find floating-point accuracy problems. In:Proc. of the 2012 ACM SIGPLAN Conf. on Programming Language Design and Implementation. 2012. 453-462.
    [5] Zhao SZ. Reasons of miscalculation in floating point arithmetic. Sciencepaper Online. 2017(in Chinese with English abstract). http://www.paper.edu.cn/releasepaper/content/201707-86
    [6] Zhao SZ. CuoShu of six binary basic elementary operations and functions. Sciencepaper Online. 2019. (in Chinese with English abstract) http://www.paper.edu.cn/releasepaper/content/201910-3
    [7] Zhao SZ. A reliable computing algorithm and its software ISReal for arithmetic expressions. Scientia Sinica Informationis, 2016, 46(6):698-713(in Chinese with English abstract).
    [8] Zhao SZ, Liu XF, Song F. Error-Controlled computation of expressions. In:Proc. of the 18th Int'l Symp. on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations. 2018. 172-173.
    附中文参考文献:
    [5] 赵世忠.浮点运算错误计算原因.中国科技论文在线.2017. http://www.paper.edu.cn/releasepaper/content/201707-86
    [6] 赵世忠.二元运算的错数.中国科技论文在线.2019. http://www.paper.edu.cn/releasepaper/content/201910-3
    [7] 赵世忠.算术表达式的一种可信计算算法及其软件ISReal.中国科学:信息科学,2016,46(6):698-713.
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赵世忠,陈冬火,刘静.循环迭代程序的一种可信计算算法.软件学报,2020,31(12):3685-3699

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History
  • Received:April 17,2019
  • Revised:July 21,2019
  • Online: December 03,2020
  • Published: December 06,2020
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