Generalisation of Recursive Doubling for AllReduce

Abstract

The performance of AllReduce is crucial at scale. The recursive doubling with pairwise exchange algorithm theoretically achieves O(log2 N) scaling for short messages with N peers, but is limited by improvements in network latency. A multi-way exchange can be implemented using message pipelining, which is easier to improve than latency. Using our method, recursive multiplying, we show reductions in execution time of between 8% and 40% of AllReduce on a Cray XC30 over recursive doubling.