article

The p-sized partitioning algorithm for fast computation of factorials of numbers

Authors:

Ahmet Ugur,

Henry ThompsonAuthors Info & Claims

The Journal of Supercomputing, Volume 38, Issue 1

Pages 73 - 82

https://doi.org/10.1007/s11227-006-7285-5

Published: 01 October 2006 Publication History

Abstract

Computing products of large numbers has always been a challenging task in the field of computing. One such example would be the factorial function. Several methods have been implemented to compute this function including naive product, recursive product, Boiten split, and prime factorization, and linear difference. The method presented here is unique in the sense that it exploits finite order differences to reduce the number of multiplications necessary to compute the factorial. The differences generated are regrouped into a new sequence of numbers, which have at most half as many elements of the original sequence. When the terms of this new sequence are multiplied together, the factorial value is obtained. The cardinality of the new sequence can further be reduced by partitioning. The sequence is computed by using several difference tables that assist in establishing the pattern that determines the sequence. An analysis of the algorithm is presented. The analysis shows that the execution time can be reduced significantly by the algorithm presented.

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Index Terms

The p-sized partitioning algorithm for fast computation of factorials of numbers
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Number-theoretic computations
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Scheduling algorithms
    2. Online algorithms
      1. Online learning algorithms
        Scheduling algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning
        Sequential decision making

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Reviews

Reviewer: Harvey Cohn

The authors present an algorithm for calculating n! in fewer than the (naive) n-1 multiplications. The idea is to partition the sequence {1, ... , n} into approximately n/p sections whose product is given by a polynomial of degree p. The values of each subproduct are given by a difference scheme (as determined by p2 steps). Thus, n! would involve only n/p + p2 steps (optimized when n=2p3), leading to the order of n(2/3) multiplications. Computations verify the economy of the algorithm.

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cover image The Journal of Supercomputing

The Journal of Supercomputing Volume 38, Issue 1

October 2006

103 pages

ISSN:0920-8542

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Kluwer Academic Publishers

United States

Publication History

Published: 01 October 2006

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Abstract

References

Index Terms

Recommendations

p-ary unified sequences: p-ary extended d-form sequences with the ideal autocorrelation property

A Fast Multiple Longest Common Subsequence (MLCS) Algorithm

Fast computation of a longest increasing subsequence and application

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