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Evaluation of Arithmetic Expressions

  • Ulrich Kulisch
  • Rolf Hammer
  • Matthias Hocks
  • Dietmar Ratz

Abstract

The evaluation of arithmetic expressions using floating-point arithmetic may lead to unpredictable results due to an accumulation of roundoff errors. As an example, the evaluation of x + 1 − x for x > 1020 using the standard floating-point format on almost every digital computer yields the wrong result 0. Since the evaluation of arithmetic expressions is a basic task in digital computing, we should have a method to evaluate a given expression to an arbitrary accuracy. We will develop such a method for real expressions composed of the operations +, −, ·, and ↑, where ↑ denotes exponentiation by an integer. The method is based on the principle of iterative refinement as discussed in Section 3.8.

Keywords

Intermediate Result Error Code Iterative Refinement Stagger Representation Error Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Ulrich Kulisch
    • 1
  • Rolf Hammer
    • 1
  • Matthias Hocks
    • 1
  • Dietmar Ratz
    • 1
  1. 1.Institut für Angewandte MathematikUniversität KarlsruheKarlsruheGermany

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