Analysis of the subtractive algorithm for greatest common divisors

@article{Yao1975AnalysisOT,
  title={Analysis of the subtractive algorithm for greatest common divisors},
  author={Andrew Chi-Chih Yao and Donald E. Knuth},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1975},
  volume={72 12},
  pages={4720-2}
}
The sum of all partial quotients in the regular continued fraction expansions of m/n, for 1 ≤m≤n, is shown to be 6Π<sup>-2</sup> n(ln n)<sup>2</sup>+ O(n log n(log log n)<sup>2</sup>). This result is applied to the analysis of what is perhaps the oldest nontrivial algorithm for number-theoretic computations. 

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