Papers › Fast Multiplication of Large Integers: Implementation and Analysis of the DKSS Algorithm
Fast Multiplication of Large Integers: Implementation and Analysis of the DKSS Algorithm
Christoph Lüders
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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 ·logN ·loglogN). De, Kurur, Saha and Saptharishi (DKSS) presented an asymptotically faster algorithm with a better time bound of N ·logN ·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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