Approximate rational arithmetic systems: Analysis of recovery of simple fractions during expression evaluation

  • David W. Matula
  • Peter Kornerup
9. Symbolic-Numeric Interface
Part of the Lecture Notes in Computer Science book series (LNCS, volume 72)


Closed approximate rational arithmetic systems are described and their number theoretic foundations are surveyed. The arithmetic is shown to implicitly contain an adaptive single-to-double precision natural rounding behavior that acts to recover true simple fractional results. The probability of such recovery is investigated and shown to be quite favorable.

Key Words

Rational arithmetic gcd-algorithm continued fractions fixed- and floating-slash number systems adaptive variable precision recovery of exactness symbolic/numberic interface 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • David W. Matula
    • 1
    • 2
  • Peter Kornerup
    • 1
    • 2
  1. 1.Department of Computer Science and EngineeringSouthern Methodist UniversityDallas
  2. 2.Computer Science DepartmentAarhus UniversityAarhusDenmark

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