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

“Fast Multiplication of Large Integers: Implementation and Analysis of the DKSS Algorithm”, that is my diploma thesis. I just uploaded it to arXiv: http://arxiv.org/abs/1503.04955

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 \(N \cdot \log N \cdot 2^{O(\log^∗ N)}\). 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.

It contains not only what the title promises, but also a long presentation of my own endeavors regarding fast multiplication, from ordinary multiplication, Karatsuba, Toom-Cook 3-way and Schönhage-Strassen with theory and some code examples.

I’m happy for any commentary.