Analysis of fast versions of the euclid algorithm
Résumé
There exist fast variants of the gcd algorithm which are all based on principles due to Knuth and Sch¨onhage. 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).
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