MPI-I-98-1-022

Fast recursive division

Burnikel, Christoph and Ziegler, Joachim

MPI-I-98-1-022. October 1998, 29 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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.

Acknowledgement:
References to related material:

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URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1998-1-022

BibTeX
@TECHREPORT{BurnikelZiegler98, AUTHOR = {Burnikel, Christoph and Ziegler, Joachim}, TITLE = {Fast recursive division}, TYPE = {Research Report}, INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik}, ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany}, NUMBER = {MPI-I-98-1-022}, MONTH = {October}, YEAR = {1998}, ISSN = {0946-011X},}