Using the parallel karatsuba algorithm for long integer multiplication and division

Abstract

We experiment with the sequential and parallel Karatsuba algorithm under the paclib system on a Sequent Symmetry shared-memory architecture, obtaining efficiency 88% on 9 processors for the controlled-depth version, and 71% on 18 processors for the scalable version. Moreover, we use the Karatsuba algorithm within long integer division, by a recent divide-and-conquer technique. The parallel version exhibits modest speed-ups (2.3 on 3 processors and 3.4 on 9 processors), however the combined speed-up over the classical sequential method is more than 10 at 500 words.