大整数的快速乘法：DKSS算法的实现与分析
Fast Multiplication of Large Integers: Implementation and Analysis of the DKSS Algorithm
摘要：
Schönhage-Strassen算法（SSA）是大整数乘法的事实标准。对于$N$位数，它的时间界限为$O(N \cdot \log N \cdot \log \log N)$。De，Kurur，Saha和Saptharishi（DKSS）提出了一种渐近快速的算法，该算法具有更好的时间界$N \cdot \log N \cdot 2^{O(\log^* N)}$。在这篇毕业论文中，DKSS乘法的实现结果：运行时间比SSA大30倍，而内存需求比SSA高3.75倍。一个可能的交叉点估计是遥不可及的，即使我们利用整个宇宙的计算机内存。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
