Space- and time-efficient polynomial multiplication

Daniel S. Roche
2009 Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09  
Countless algorithms have been developed for the multiplication of univariate polynomials and multi-precision integers, but all those with sub-quadratic time complexity currently require at least Ω(n) extra space for the computation. A new routine based on the Karatsuba/Ofman algorithm is presented with the same time complexity of O(n 1.59 ) but only O(log n) extra space. A second routine based on the method of Schönhage/Strassen achieves the same pseudolinear time and O(1) extra space, but
more » ... under certain conditions. A preliminary implementation over Fp[x], where p fits into a single machine word, is presented and compared with existing software.
doi:10.1145/1576702.1576743 dblp:conf/issac/Roche09 fatcat:bnh3ya5wanfyjbbidlg7g7bo4m