Efficient Exact Arithmetic over Constructive Reals

  • Yong Li
  • Jun-Hai Yong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)


We describe a computing method of the computable (or constructive) real numbers based on analysis of expressions. This method take precision estimate into account in order to get a better algorithm than Ménissier-Morain’s method, which is also based on the representation of constructive reals. We solve two problems which appear in exact real arithmetic based on the representation of constructive reals. First, by balancing every item’s precision in the expression, we can avoid unnecessary precision growth. Second, by distributing different weights to different operations, we can make sure that complex operations do not waste much time when to compute the whole expression. In these ways, we finally get a more efficient and proper method than prior implementations.


Real Number Cauchy Sequence Error Range Original Algorithm Linear Fractional Transformation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yong Li
    • 1
  • Jun-Hai Yong
    • 1
  1. 1.School of Software, Tsinghua University, Beijing 100084P.R. China

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