A long note on Mulders' short product

G. Hanrot, P. Zimmermann
2004 Journal of symbolic computation  
The short product of two power series is the meaningful part of the product of these objects, i.e., i+ j <n a i b j x i+ j . Mulders (AAECC 11 (2000) 69) gives an algorithm to compute a short product faster than the full product in the case of Karatsuba's multiplication (Karatsuba and Ofman, Dokl. Akad. Nauk SSSR 145 (1962) 293 ). This algorithm works by selecting a cutoff point k and performing a full k × k product and two (n − k) × (n − k) short products recursively. Mulders also gives a
more » ... stically optimal cutoff point βn. In this paper, we determine the optimal cutoff point in Mulders' algorithm. We also give a slightly more general description of Mulders' method.
doi:10.1016/j.jsc.2003.03.001 fatcat:rjkerdngsnfnnoyd2owk6rtdtq