Fast Computations of the Exponential Function
- Timm AhrendtAffiliated withInstitut für Informatik II, Universität Bonn
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 .
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)  and Ω(ν(n)) , 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).
- Fast Computations of the Exponential Function
- Book Title
- STACS 99
- Book Subtitle
- 16th Annual Symposium on Theoretical Aspects of Computer Science Trier, Germany, March 4–6, 1999 Proceedings
- pp 302-312
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- Series Title
- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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