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Evaluation of Arithmetic Expressions

In: C++ Toolbox for Verified Computing I

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ulrich Kulisch & Rolf Hammer & Matthias Hocks & Dietmar Ratz, 1995. "Evaluation of Arithmetic Expressions," Springer Books, in: C++ Toolbox for Verified Computing I, chapter 0, pages 140-163, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-79651-7_8
    DOI: 10.1007/978-3-642-79651-7_8
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