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Journal Articles Journal of Symbolic Computation Year : 2004

## A long note on Mulders' short product

(1) , (1)
1
Guillaume Hanrot
• Function : Author
• PersonId : 831392
Paul Zimmermann

#### 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.

#### Domains

Computer Science [cs] Other [cs.OH]

### Dates and versions

inria-00100069 , version 1 (26-09-2006)

### Identifiers

• HAL Id : inria-00100069 , version 1

### Cite

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

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