SIMDizing pairwise sums: a summation algorithm balancing accuracy with throughput

Abstract

Implementing summation when accuracy and throughput need to be balanced is a challenging endevour. We present experimental results that provide a sense when to start worrying and the expense of the various solutions that exist. We also present a new algorithm based on pairwise summation that achieves 89% of the throughput of the fastest summation algorithms when the data is not resident in L1 cache while eclipsing the accuracy of signifigantly slower compensated sums like Kahan summation and Kahan-Babuska that are typically used when accuracy is important.