Computer Science ›› 2015, Vol. 42 ›› Issue (4): 25-30.doi: 10.11896/j.issn.1002-137X.2015.04.003

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Validated Evaluation and Error Analysis of Elementary Functions

LIU Jian, TANG Min, ZENG Xia and ZENG Zhen-bing   

  • Online:2018-11-14 Published:2018-11-14

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.

Key words: Elementary functions,Error analysis,Interval arithmetic,Validated evaluation

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