High-performance bidiagonal reduction using tile algorithms on homogeneous multicore architectures

Handle URI:
http://hdl.handle.net/10754/575572
Title:
High-performance bidiagonal reduction using tile algorithms on homogeneous multicore architectures
Authors:
Ltaief, Hatem ( 0000-0002-6897-1095 ) ; Luszczek, Piotr R.; Dongarra, Jack
Abstract:
This article presents a new high-performance bidiagonal reduction (BRD) for homogeneous multicore architectures. This article is an extension of the high-performance tridiagonal reduction implemented by the same authors [Luszczek et al., IPDPS 2011] to the BRD case. The BRD is the first step toward computing the singular value decomposition of a matrix, which is one of the most important algorithms in numerical linear algebra due to its broad impact in computational science. The high performance of the BRD described in this article comes from the combination of four important features: (1) tile algorithms with tile data layout, which provide an efficient data representation in main memory; (2) a two-stage reduction approach that allows to cast most of the computation during the first stage (reduction to band form) into calls to Level 3 BLAS and reduces the memory traffic during the second stage (reduction from band to bidiagonal form) by using high-performance kernels optimized for cache reuse; (3) a data dependence translation layer that maps the general algorithm with column-major data layout into the tile data layout; and (4) a dynamic runtime system that efficiently schedules the newly implemented kernels across the processing units and ensures that the data dependencies are not violated. A detailed analysis is provided to understand the critical impact of the tile size on the total execution time, which also corresponds to the matrix bandwidth size after the reduction of the first stage. The performance results show a significant improvement over currently established alternatives. The new high-performance BRD achieves up to a 30-fold speedup on a 16-core Intel Xeon machine with a 12000×12000 matrix size against the state-of-the-art open source and commercial numerical software packages, namely LAPACK, compiled with optimized and multithreaded BLAS from MKL as well as Intel MKL version 10.2. © 2013 ACM.
KAUST Department:
KAUST Supercomputing Laboratory (KSL); Extreme Computing Research Center
Publisher:
Association for Computing Machinery (ACM)
Journal:
ACM Transactions on Mathematical Software
Issue Date:
1-Apr-2013
DOI:
10.1145/2450153.2450154
Type:
Article
ISSN:
00983500
Sponsors:
This research reported here was supported in part by the National Science Foundation, the Department of Energy, and Microsoft Research.
Appears in Collections:
Articles; KAUST Supercomputing Laboratory (KSL); Extreme Computing Research Center

Full metadata record

DC FieldValue Language
dc.contributor.authorLtaief, Hatemen
dc.contributor.authorLuszczek, Piotr R.en
dc.contributor.authorDongarra, Jacken
dc.date.accessioned2015-08-24T08:33:13Zen
dc.date.available2015-08-24T08:33:13Zen
dc.date.issued2013-04-01en
dc.identifier.issn00983500en
dc.identifier.doi10.1145/2450153.2450154en
dc.identifier.urihttp://hdl.handle.net/10754/575572en
dc.description.abstractThis article presents a new high-performance bidiagonal reduction (BRD) for homogeneous multicore architectures. This article is an extension of the high-performance tridiagonal reduction implemented by the same authors [Luszczek et al., IPDPS 2011] to the BRD case. The BRD is the first step toward computing the singular value decomposition of a matrix, which is one of the most important algorithms in numerical linear algebra due to its broad impact in computational science. The high performance of the BRD described in this article comes from the combination of four important features: (1) tile algorithms with tile data layout, which provide an efficient data representation in main memory; (2) a two-stage reduction approach that allows to cast most of the computation during the first stage (reduction to band form) into calls to Level 3 BLAS and reduces the memory traffic during the second stage (reduction from band to bidiagonal form) by using high-performance kernels optimized for cache reuse; (3) a data dependence translation layer that maps the general algorithm with column-major data layout into the tile data layout; and (4) a dynamic runtime system that efficiently schedules the newly implemented kernels across the processing units and ensures that the data dependencies are not violated. A detailed analysis is provided to understand the critical impact of the tile size on the total execution time, which also corresponds to the matrix bandwidth size after the reduction of the first stage. The performance results show a significant improvement over currently established alternatives. The new high-performance BRD achieves up to a 30-fold speedup on a 16-core Intel Xeon machine with a 12000×12000 matrix size against the state-of-the-art open source and commercial numerical software packages, namely LAPACK, compiled with optimized and multithreaded BLAS from MKL as well as Intel MKL version 10.2. © 2013 ACM.en
dc.description.sponsorshipThis research reported here was supported in part by the National Science Foundation, the Department of Energy, and Microsoft Research.en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.subjectBidiagional reductionen
dc.subjectBulge chasingen
dc.subjectData translation layeren
dc.subjectDynamic schedulingen
dc.subjectHigh performance kernelsen
dc.subjectTile algorithmsen
dc.subjectTwo-stage approachen
dc.titleHigh-performance bidiagonal reduction using tile algorithms on homogeneous multicore architecturesen
dc.typeArticleen
dc.contributor.departmentKAUST Supercomputing Laboratory (KSL)en
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalACM Transactions on Mathematical Softwareen
dc.contributor.institutionInnovative Computing Laboratory, Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN 37996, United Statesen
dc.contributor.institutionUniversity of Tennessee, Oak Ridge National Laboratory, United Statesen
dc.contributor.institutionUniversity of Manchester, United Statesen
kaust.authorLtaief, Hatemen
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