Fast Computations of the Exponential Function

  • Timm Ahrendt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1563)


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).


Exponential Function Root Extraction Fast Computation Newton Iteration Nest Iteration 
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 1999

Authors and Affiliations

  • Timm Ahrendt
    • 1
  1. 1.Institut für Informatik IIUniversität BonnBonnGermany

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