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SCIENTIA SINICA Informationis, Volume 46 , Issue 6 : 698-713(2016) https://doi.org/10.1360/N112015-00061

A reliable computing algorithm and its software application ISReal for arithmetic expressions

More info
  • ReceivedJul 22, 2015
  • AcceptedOct 15, 2015
  • PublishedMay 27, 2016

Abstract


Funded by

国家自然科学基金(61321064)

上海市高可信计算重点实验室开放课题(07dz22304201405)

国家自然科学基金(614025 37)

国家自然科学基金(61572195)

国家自然科学基金(11371143)


References

[1] Lorenz E N. Deterministic nonperiodic flow. J Atmos Sci, 1963, 20: 130-141 CrossRef Google Scholar

[2] Quinn K. Even had problems rounding off figures? This stock exchange has. Wall Street J, 1983, 202: 37. Google Scholar

[3] Stroud R. Rounding error costs DHSS 100 million pounds. Risks Digest, 1987, 5. Google Scholar

[4] Robert S. Roundoff error and the patriot missile. SIAM News, 1992, 25 : 11. Google Scholar

[5] Jakobsen B, Rosendahl F. The Sleipner platform accident. Struct Eng Int, 1994, 4: 190-193 CrossRef Google Scholar

[6] Selby R G, Vecchio F J, Collins M P. The failure of an offshore platform. Concrete Int, 1997, 19 : 28-35. Google Scholar

[7] McCullough B D, Vinod H D. The numerical reliability of econometric software. J Economic Literature, 1999, 37: 633-665 CrossRef Google Scholar

[8] Yang L, Zhou C C, Zhan N J, et al. Recent advances in program verification through computer algebra. Front Comput Sci China, 2010, 4: 1-16 CrossRef Google Scholar

[9] Tang E Y, Barr E, Su Z D, et al. Program instability detection based on systematically optimized numerical perturbation. Sci Sin Inform, 2014, 44 : 1445-1466 [汤恩义, BARR Earl, 苏振东, 等. 程序数值误差的扰动检测与优化. 中国科学: 信息科学, 2014, 44 : 1445-1466 ]. Google Scholar

[10] Zou D, Wang R, Xiong Y F, et al. A genetic algorithm for detecting significant floating-point inaccuracies. In: Proceedings of the 37th IEEE International Conference on Software Engineering. California: IEEE Computer Society, 2015. 529-539. Google Scholar

[11] Zhang J Z, Feng Y. Obtaining accurate values by approximate calculation. Sci China Math, 2007, 37: 809-816 [张景中, 冯勇. 采用近似计算获得准确值. 中国科学: 数学, 2007, 37 : 809-816]. Google Scholar

[12] Cuyt A, Verdonk B, Becuwe S, et al. A remarkable example of catastrophic cancellation unraveled. Computing, 2001, 66: 309-320 CrossRef Google Scholar

[13] Li Q Y, Wang N C, Yi D Y. Numerical Analysis. 5th ed. Beijing: Tsinghua University Press, 2008. 18 [李庆扬, 王能超, 易大义. 数值分析. 第5版. 北京: 清华大学出版社, 2008. 18]. Google Scholar

[14] Zimmermann P. Reliable computing with GNU MPFR. In: Mathematical Software-ICMS 2010. Berlin: Springer, 2010. 42-45. Google Scholar

[15] Rump S. Algorithms for verified inclusion: theory and practice. In: Reliability in Computing: the Role of Interval Methods in Scientific Computing. Boston: Academic Press, 1988. 109-126. Google Scholar

[16] Muller J M, Brisebarre N, Dinechin F D, et al. Handbook of Floating-Point Arithmetic. Boston: Birkhauser Boston, 2010. 12. Google Scholar

[17] Loh E, Walster G W. Rump's example revisited. Reliable Comput, 2002, 8: 245-248 CrossRef Google Scholar

[18] Higham N J. Accuracy and Stability of Numerical Algorithms. 2nd ed. Philadelphia: SIAM, 2002. 17. Google Scholar

[19] Inverse trigonometric functions. Wikipedia. http://en.wikipedia.org/wiki/Inverse\_trigonometric\_function. Google Scholar

[20] John Machin. Wikipedia. https://en.wikipedia.org/wiki/John\_Machin. Google Scholar

[21] Zhen X F. Applied Numerical Method. Beijing: Tsinghua University Press, 2006. 53-80 [甄西丰. 实用数值计算方法. 北京: 清华大学出版社, 2006. 53-80]. Google Scholar