### 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 language | English (US) |
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Title of host publication | LATIN 2014 |

Subtitle of host publication | Theoretical Informatics - 11th Latin American Symposium, Proceedings |

Publisher | Springer Verlag |

Pages | 660-670 |

Number of pages | 11 |

ISBN (Print) | 9783642544224 |

DOIs | |

State | Published - Jan 1 2014 |

Event | 11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay Duration: Mar 31 2014 → Apr 4 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8392 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 11th Latin American Theoretical Informatics Symposium, LATIN 2014 |
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Country | Uruguay |

City | Montevideo |

Period | 3/31/14 → 4/4/14 |

### 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