NDLI: A sound and complete abstraction for reasoning about parallel prefix sums

Content Provider	ACM Digital Library
Author	Donaldson, Alastair F. Ketema, Jeroen Chong, Nathan
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 parallel 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 soundness and completeness result showing that a generic sequential prefix 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 input and result require O(n lg(n)) space. This improves upon an existing result by Sheeran where the input requires O(n lg(n)) space and the result $O(n^{2}$ \lg(n)) space, and is more feasible for large n than a method by Voigtlaender that uses O(n) space for the input and result but requires running $O(n^{2})$ tests. We then extend our abstraction and results to the context of data-parallel programs, developing an automated verification method for GPU implementations of prefix sums. Our method uses static verification to prove that a generic prefix sum implementation is data race-free, after which functional correctness of the implementation can be determined by running a single test case under the interval of summations abstraction. We present an experimental evaluation using four different prefix sum algorithms, showing that our method is highly automatic, scales to large thread counts, and significantly outperforms Voigtlaender's method when applied to large arrays.
Starting Page	397
Ending Page	409
Page Count	13
File Format	PDF MP4
ISSN	03621340 15581160
DOI	10.1145/2578855.2535882
Journal	ACM SIGPLAN Notices (SIGP)
Volume Number	49
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1983-05-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Gpus Abstraction Parallel prefix sum computation Formal verification
Content Type	Audio Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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