Multithreaded Transposition of Square Matrices with Common Code for Intel Xeon Processors and Intel Xeon Phi Coprocessors

by Andrey Vladimirov 12. August 2013 11:44

Complete Paper: PDF logo Colfax_Transposition-7110P.pdf (513 kb)

In-place matrix transposition, a standard operation in linear algebra, is a memory bandwidth-bound operation. The theoretical maximum performance of transposition is the memory copy bandwidth. However, due to non-contiguous memory access in the transposition operation, practical performance is usually lower. The ratio of the transposition rate to the memory copy bandwidth is a measure of the transposition algorithm efficiency.

This paper demonstrates and discusses an efficient C language implementation of parallel in-place square matrix transposition. For large matrices, it achieves a transposition rate of 49 GB/s (82% efficiency) on Intel Xeon CPUs and 113 GB/s (67% efficiency) on Intel Xeon Phi coprocessors. The code is tuned with pragma-based compiler hints and compiler arguments. Thread parallelism in the code is handled by OpenMP, and vectorization is automatically implemented by the Intel compiler. This approach allows to use the same C code for a CPU and for a MIC architecture executable, both demonstrating high efficiency. For benchmarks, an Intel Xeon Phi 7110P coprocessor is used.

Complete Paper: PDF logo Colfax_Transposition-7110P.pdf (513 kb)

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Colfax International provides an arsenal of novel computational tools, which need to be leveraged in order to harness their full power. We are collaborating with researchers in science and industry, including our customers, to produce case studies, white papers, and develop a wide knowledge base of the applications of current and future computational technologies.

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Andrey Vladimirov, PhD, is the Head of HPC Research at Colfax International. His primary research interest is the application of modern computing technologies to computationally demanding scientific problems. Prior to joining Colfax, Andrey was involved in theoretical astrophysics research at the Ioffe Institute (Russia), North Carolina State University, and Stanford University (USA), where he studied cosmic rays, collisionless plasmas and the interstellar medium using computer simulations. 

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Vadim Karpusenko, PhD, is a Principal HPC Research Engineer at Colfax International. His research interests are in the area of physical modeling with HPC clusters, highly parallel architectures, and code optimization. Vadim holds a PhD in Physics from North Carolina State University for his computational research of the free energy and stability of helical secondary structures of proteins.

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