A gmp-based implementation of schönhage-strassen's large integer multiplication algorithm

Abstract

Schönhage-Strassen's algorithm is one of the best known algorithms for multiplying large integers. Implementing it ef?ciently is of utmost importance, since many other algorithms rely on it as a subroutine. We present here an improved implementation, based on the one distributed within the GMP library. The following ideas and techniques were used or tried: faster arithmetic modulo 2n + 1, improved cache locality, Mersenne transforms, Chinese Remainder Reconstruction, the √2 trick, Harley's and Granlund's tricks, improved tuning.