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Linear algebra software for large-scale accelerated multicore computing*

Published online by Cambridge University Press:  23 May 2016

A. Abdelfattah ,
H. Anzt ,
J. Dongarra ,
M. Gates ,
A. Haidar ,
J. Kurzak ,
P. Luszczek ,
S. Tomov ,
I. Yamazaki  and
A. YarKhan
A. Abdelfattah
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
H. Anzt
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
J. Dongarra
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
M. Gates
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
A. Haidar
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
J. Kurzak
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
P. Luszczek
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
S. Tomov
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
I. Yamazaki
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
A. YarKhan
Affiliation:
Innovative Computing Laboratory, University of Tennessee, 1122 Volunteer BoulevardSuite 203 Claxton, Knoxville, TN 37996, USA E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
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Abstract

Many crucial scientific computing applications, ranging from national security to medical advances, rely on high-performance linear algebra algorithms and technologies, underscoring their importance and broad impact. Here we present the state-of-the-art design and implementation practices for the acceleration of the predominant linear algebra algorithms on large-scale accelerated multicore systems. Examples are given with fundamental dense linear algebra algorithms – from the LU, QR, Cholesky, and LDLT factorizations needed for solving linear systems of equations, to eigenvalue and singular value decomposition (SVD) problems. The implementations presented are readily available via the open-source PLASMA and MAGMA libraries, which represent the next generation modernization of the popular LAPACK library for accelerated multicore systems.

To generate the extreme level of parallelism needed for the efficient use of these systems, algorithms of interest are redesigned and then split into well-chosen computational tasks. The task execution is scheduled over the computational components of a hybrid system of multicore CPUs with GPU accelerators and/or Xeon Phi coprocessors, using either static scheduling or light-weight runtime systems. The use of light-weight runtime systems keeps scheduling overheads low, similar to static scheduling, while enabling the expression of parallelism through sequential-like code. This simplifies the development effort and allows exploration of the unique strengths of the various hardware components. Finally, we emphasize the development of innovative linear algebra algorithms using three technologies – mixed precision arithmetic, batched operations, and asynchronous iterations – that are currently of high interest for accelerated multicore systems.

Type
Research Article
Information
Acta Numerica , Volume 25 , 01 May 2016 , pp. 1 - 160
Copyright
© Cambridge University Press, 2016 

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