A long note on Mulders' short product

Guillaume Hanrot 1 Paul Zimmermann 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The short product of two power series is the meaningful part of the product of these objects, i.e. $\sum_{i+j < n} a_ib_j x^{i+j}$. In \cite{Mulders00}, Mulders gives an algorithm to compute a short product faster than the full product in the case of Karatsuba's multiplication \cite{KaOf62}. This algorithm works by selecting a cutoff point $k$ and performing a full $k\times k$ product and two $(n-k)\times (n-k)$ short products recursively. Mulders also gives a heuristically optimal cutoff point $\beta n$. 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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Submitted on : Tuesday, September 26, 2006 - 10:13:52 AM
Last modification on : Thursday, January 11, 2018 - 6:20:00 AM

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Guillaume Hanrot, Paul Zimmermann. A long note on Mulders' short product. Journal of Symbolic Computation, Elsevier, 2004, 37 (3), pp.391--401. ⟨inria-00100069⟩

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