Parallel Algorithms for Summing Floating-Point Numbers

TL;DR

This paper introduces efficient parallel algorithms across various models for accurately summing large sets of floating-point numbers, addressing the limitations of sequential methods and enabling scalable, faithful rounding in big data computations.

Contribution

It presents novel parallel algorithms for floating-point summation in PRAM, external-memory, and MapReduce models, with experimental validation for practical efficiency.

Findings

Algorithms produce faithfully rounded sums

Parallel algorithms scale to large datasets

Experimental results confirm efficiency

Abstract

The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point operations, this problem becomes very challenging. Moreover, all existing solutions rely on sequential algorithms which cannot scale to the huge datasets that need to be processed. In this paper, we provide several efficient parallel algorithms for summing n floating point numbers, so as to produce a faithfully rounded floating-point representation of the sum. We present algorithms in PRAM, external-memory, and MapReduce models, and we also provide an experimental analysis of our MapReduce algorithms, due to their simplicity and practical efficiency.