Work-Efficient Parallel Algorithms for Accurate Floating-Point Prefix Sums

Abstract

Existing work-efficient parallel algorithms for floating-point prefix sums exhibit either good performance or good numerical accuracy, but not both. Consequently, prefix-sum algorithms cannot easily be used in scientific-computing applications that require both high performance and accuracy. We have designed and implemented two new algorithms, called CAST _BLK and PAIR_BLK, whose accuracy is significantly higher than that of the high-performing prefix-sum algorithm from the Problem Based Benchmark Suite, while running with comparable performance on modern multicore machines. Specifically, the root mean squared error of the PBBS code on a large array of uniformly distributed 64-bit floating-point numbers is 8 times higher than that of CAST _BLK and 5.8 times higher than that of PAIR_BLK. These two codes employ the PBBS three-stage strategy for performance, but they are designed to achieve high accuracy, both theoretically and in practice. A vectorization enhancement to these two scalar codes trades off a small amount of accuracy to match or outperform the PBBS code while still maintaining lower error.