Iterative Toom-Cook methods for very unbalanced long integer multiplication

Authors:
Alberto Zanoni
Affiliations:
Università degli Studi di Roma "Tor Vergata", Via Columbia, Roma, (Italy)
Venue:
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Year:
2010

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Abstract

We consider the multiplication of long integers when one factor is much larger than the other one. We describe an iterative approach using Toom-Cook unbalanced methods, which results in the evaluation of the smaller integer only once. The particular case of Toom-2.5 is considered in full detail. A further optimization depending on the parity of the shortest operand evaluation in 1 is also described. A comparison with GMP library is also presented.