Implementation of the DKSS Algorithm for Multiplication of Large Numbers — ISSAC’15

My paper “Implementation of the DKSS Algorithm for Multiplication of Large Numbers” was accepted for ISSAC’15 Conference to be held on 6-9 July 2015 at the University of Bath, U.K. !

Abstract: The Schönhage-Strassen algorithm (SSA) is the de-facto standard for multiplication of large integers. For \(N\)-bit numbers it has a time bound of \(O(N \cdot \log N \cdot \log \log N)\). De, Kurur, Saha and Saptharishi (DKSS) presented an asymptotically faster algorithm with a better time bound of \(N \cdot \log N \cdot 2^{O(\log^∗ N)}\). For this paper, a simplified DKSS multiplication was implemented. Assuming a sensible upper limit on the input size, some required constants could be precomputed. This allowed to simplify the algorithm to save some complexity and run-time. Still, run-time is about 30 times larger than SSA, while memory requirements are about 2.3 times higher than SSA. A possible crossover point is estimated to be out of reach even if we utilized the whole universe for computer memory.

This is an improved version of what I wrote about in my diploma thesis.

My source code that was used for the tests is available here and is licensed under LGPL.

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