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arXiv · 1503.04955

Fast Multiplication of Large Integers: Implementation and Analysis of the DKSS Algorithm

Christoph Lüders
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Abstract

The Sch\"onhage-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 $N \cdot \log N \cdot 2^{O(\log^* N)}$. In this diploma thesis, results of an implementation of DKSS multiplication are presented: run-time is about 30 times larger than SSA, while memory requirements are about 3.75 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.

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Christoph Lüders. 2015-03-17. Fast Multiplication of Large Integers: Implementation and Analysis of the DKSS Algorithm. https://arxiv.org/abs/1503.04955

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