Corpus ID: 4857806

Fast integer multiplication using generalized Fermat primes

@article{Covanov2015FastIM,
  title={Fast integer multiplication using generalized Fermat primes},
  author={S. Covanov and Emmanuel Thom{\'e}},
  journal={arXiv: Symbolic Computation},
  year={2015}
}
For almost 35 years, Sch{\"o}nhage-Strassen's algorithm has been the fastest algorithm known for multiplying integers, with a time complexity O(n $\times$ log n $\times$ log log n) for multiplying n-bit inputs. In 2007, F{\"u}rer proved that there exists K > 1 and an algorithm performing this operation in O(n $\times$ log n $\times$ K log n). Recent work by Harvey, van der Hoeven, and Lecerf showed that this complexity estimate can be improved in order to get K = 8, and conjecturally K = 4… Expand

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