Analysis of Fast Versions of the Euclid Algorithm

@inproceedings{Cesaratto2007AnalysisOF,
  title={Analysis of Fast Versions of the Euclid Algorithm},
  author={Eda Cesaratto and Benoit Daireaux and Lo{\"i}ck Lhote and V{\'e}ronique Maume-Deschamps and Brigitte Vall{\'e}e},
  booktitle={ANALCO},
  year={2007}
}
There exist fast variants of the gcd algorithm which are all based on principles due to Knuth and Schonhage. On inputs of size n, these algorithms use a Divide and Conquer approach, perform FFT multiplications and stop the recursion at a depth slightly smaller than lg n. A rough estimate of the worst--case complexity of these fast versions provides the bound O(n(log n)2 log log n). However, this estimate is based on some heuristics and is not actually proven. Here, we provide a precise… 

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