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Fast recursive division

Burnikel, Christoph and Ziegler, Joachim

October 1998, 29 pages.

Status: available - back from printing

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.

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  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},