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.
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© 1993 Springer-Verlag Berlin Heidelberg
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Kulisch, U., Hammer, R., Ratz, D., Hocks, M. (1993). Evaluation of Arithmetic Expressions. In: Numerical Toolbox for Verified Computing I. Springer Series in Computational Mathematics, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78423-1_8
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DOI: https://doi.org/10.1007/978-3-642-78423-1_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78425-5
Online ISBN: 978-3-642-78423-1
eBook Packages: Springer Book Archive