Chapter

Computer Algebra in Scientific Computing

Volume 7442 of the series Lecture Notes in Computer Science pp 34-46

A New Algorithm for Long Integer Cube Computation with Some Insight into Higher Powers

  • Marco BodratoAffiliated withmambaSoft
  • , Alberto ZanoniAffiliated withDipartimento di Scienze Statistiche, Università “Sapienza”

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Abstract

A new approach for the computation of long integer cube (third power) based on a splitting-in-two divide et impera approach and on a modified Toom-Cook-3 unbalanced method is presented, showing that the “classical” square-and-multiply algorithm is not (always) optimal. The new algorithm is used as a new basic tool to improve long integer exponentiation: different techniques combining binary and ternary exponent expansion are shown. Effective implementations by using the GMP library are tested, and performance comparisons are presented.

AMS Subject Classification

11N64 11A25 13B25

Keywords and phrases

Toom-Cook cube third power long integers