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A Sound and Complete Abstraction for Reasoning about Parallel Prefix Sums ∗
| Citations: | 5 - 3 self |
BibTeX
@MISC{Chong_asound,
author = {Nathan Chong and Alastair F. Donaldson and Jeroen Ketema},
title = {A Sound and Complete Abstraction for Reasoning about Parallel Prefix Sums ∗},
year = {}
}
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Abstract
Prefix sums are key building blocks in the implementation of many concurrent software applications, and recently much work has gone into efficiently implementing prefix sums to run on massively par-allel graphics processing units (GPUs). Because they lie at the heart of many GPU-accelerated applications, the correctness of prefix sum implementations is of prime importance. We introduce a novel abstraction, the interval of summations, that allows scalable reasoning about implementations of prefix sums. We present this abstraction as a monoid, and prove a sound-ness and completeness result showing that a generic sequential pre-fix sum implementation is correct for an array of length n if and only if it computes the correct result for a specific test case when instantiated with the interval of summations monoid. This allows correctness to be established by running a single test where the in-
Keyphrases
prefix sum parallel prefix sum complete abstraction many gpu-accelerated application prefix sum implementation completeness result single test many concurrent software application novel abstraction par-allel graphic much work specific test case generic sequential pre-fix sum implementation prime importance correct result
