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Fast Computations of the Exponential Function

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STACS 99 (STACS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1563))

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Abstract

In this paper we present an algorithm which shows that the exponential function has algebraic complexity O(log2 n), i.e., can be evaluated with relative error O(2-n) using O(log2 n) infinite-precision additions, subtractions, multiplications and divisions. This solves a question of J. M. Borwein and P. B. Borwein [9].

The best known lower bound for the algebraic complexity of the exponential function is Ω(log n).

The best known upper and lower bounds for the bit complexity of the exponential function are O(μ(n) log n) [10] and Ω(ν(n)) [4], respectively, where μ(n) denotes an upper bound and ν(n) denotes a lower bound for the bit complexity of n-bit integer multiplication.

The presented algorithm has bit complexity O(μ(n) log n).

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Author information

Authors and Affiliations

  1. Institut für Informatik II, Universität Bonn, Römerstr. 164, D - 53117, Bonn, Germany

    Timm Ahrendt

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  1. Timm Ahrendt
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Editor information

Editors and Affiliations

  1. FB IV - Informatik, Universität Trier, D-54286, Trier, Germany

    Christoph Meinel

  2. LIFL, Université de Lille I, Bătiment 3, F-59655, Villeneuve d’Ascq Cedex, France

    Sophie Tison

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© 1999 Springer-Verlag Berlin Heidelberg

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Ahrendt, T. (1999). Fast Computations of the Exponential Function. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_28

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  • DOI: https://doi.org/10.1007/3-540-49116-3_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65691-3

  • Online ISBN: 978-3-540-49116-3

  • eBook Packages: Springer Book Archive

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