How fast can we multiply large integers on an actual computer?

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    8 Scopus citations

    Abstract

    We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity of a task like multiplication of long integers. The Turing machine is more useful here, but fails to take into account the multiplication instruction for short integers, which is available on physical computing devices. An interesting outcome is that the proposed refined complexity measures do not rank the well known multiplication algorithms the same way as the Turing machine model.

    Original languageEnglish (US)
    Title of host publicationLATIN 2014
    Subtitle of host publicationTheoretical Informatics - 11th Latin American Symposium, Proceedings
    PublisherSpringer Verlag
    Pages660-670
    Number of pages11
    ISBN (Print)9783642544224
    DOIs
    StatePublished - Jan 1 2014
    Event11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay
    Duration: Mar 31 2014Apr 4 2014

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume8392 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other11th Latin American Theoretical Informatics Symposium, LATIN 2014
    CountryUruguay
    CityMontevideo
    Period3/31/144/4/14

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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  • Cite this

    Fürer, M. (2014). How fast can we multiply large integers on an actual computer? In LATIN 2014: Theoretical Informatics - 11th Latin American Symposium, Proceedings (pp. 660-670). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-54423-1_57