Schnelle Multiplikation großer Zahlen

@article{Schnhage2005SchnelleMG,
  title={Schnelle Multiplikation gro{\ss}er Zahlen},
  author={Arnold Sch{\"o}nhage and Volker Strassen},
  journal={Computing},
  year={2005},
  volume={7},
  pages={281-292}
}
ZusammenfassungEs wird ein Algorithmus zur Berechnung des Produktes von zweiN-stelligen Dualzahlen angegeben. Zwei Arten der Realisierung werden betrachtet: Turingmaschinen mit mehreren Bändern und logische Netze (aus zweistelligen logischen Elementen aufgebaut).SummaryAn algorithm is given for computing the product of twoN-digit binary numbers byO (N lgN lg lgN) steps. Two ways of implementing the algorithm are considered: multitape Turing machines and logical nets (with step=binary logical… 
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708 Citations

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An improved implementation of Schönhage-Strassen's algorithm, based on the one distributed within the GMP library is presented, with improvements to faster arithmetic modulo 2n + 1, improved cache locality and tuning.
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An alternative algorithm, which relies on arithmetic modulo generalized Fermat primes, is used to obtain conjecturally the same result K = 4 via a careful complexity analysis in the deterministic multitape Turing model.
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