Evaluation of Arithmetic Expressions

Ulrich Kulisch, Rolf Hammer, Matthias Hocks and Dietmar Ratz
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Ulrich Kulisch: Universität Karlsruhe, Institut für Angewandte Mathematik
Rolf Hammer: Universität Karlsruhe, Institut für Angewandte Mathematik
Matthias Hocks: Universität Karlsruhe, Institut für Angewandte Mathematik
Dietmar Ratz: Universität Karlsruhe, Institut für Angewandte Mathematik

Chapter Chapter 8 in C++ Toolbox for Verified Computing I, 1995, pp 140-163 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-3-642-79651-7_8

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