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Fast recursive division

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Burnikel,  Christoph
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Ziegler,  Joachim
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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1998-1-022
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Burnikel, C., & Ziegler, J.(1998). Fast recursive division (MPI-I-1998-1-022). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-7B75-8
Abstract
We present a new recursive method for division with remainder of integers. Its running time is $2K(n)+O(n \log n)$ for division of a $2n$-digit number by an $n$-digit number where $K(n)$ is the Karatsuba multiplication time. It pays in p ractice for numbers with 860 bits or more. Then we show how we can lower this bo und to $3/2 K(n)+O(n\log n)$ if we are not interested in the remainder. As an application of division with remainder we show how to speedup modular multiplication. We also give practical results of an implementation that allow u s to say that we have the fastest integer division on a SPARC architecture compa red to all other integer packages we know of.