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Reports (Research Report) Year : 2002

A long note on Mulders' short product


The short product of two power series is the meaningful part of the product of these objects, i.e., _i+j < n a_ib_j x^i+j. In , Mulders gives an algorithm to compute a short product faster than the full product in the case of Karatsuba's multiplication . This algorithm work by selecting a cutoff point k and performing a full kk product and two (n-k)(n-k) short products recursively. Mulders also gives an heuristically optimal cutoff point n. In this paper, we determine the optimal cutoff point in Mulders' algorithm. We also give a slightly more general description of Mulders' method.


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Dates and versions

inria-00071931 , version 1 (23-05-2006)


  • HAL Id : inria-00071931 , version 1


Guillaume Hanrot, Paul Zimmermann. A long note on Mulders' short product. [Research Report] RR-4654, INRIA. 2002. ⟨inria-00071931⟩
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