Magazine

Overview

This collection of code samples accompany an article written for issue #34 of the magazine The Parallel Universe, an Intel publication. The articles focuses on Blaze-, Eigen-, and LIBXSMM-variants of Small Matrix Multiplications (SMMs). The set of sample codes now also includes a variant relying on BLAS and a variant that showcases LIBXSMM's explicit batch-interface.

The baseline requirements are libraries that can operate on column-major storage order, "zero copy" when using existing memory buffers, and an API that is powerful enough to describe leading dimensions. Typically a library-internal parallelization of matrix multiplication is desired. However, for the magazine sample collection there is no performance gain expected since the matrices are small, and nested parallelism may only add overhead. Hence library-internal parallelism is disabled (BLAZE_USE_SHARED_MEMORY_PARALLELIZATION=0, EIGEN_DONT_PARALLELIZE). LIBXSMM provides parallelization on a per-functions basis and no global toggle is needed.

The sample codes rely on the minimum programming language supported by the library in question (API): C++ in case of Blaze and Eigen, and C in case of LIBXSMM (both C++ and Fortran interfaces are available as well). For Blaze and Eigen, the build-system ensures to not map implementation into a BLAS library (normally desired but this would not test the library-native implementation).

Results

To reproduce or repeat the performance measurements on a system of choice, all matrix operands are streamed by default. The file magazine.h can be edited to reproduce the desired combination (STREAM_A, STREAM_B, and STREAM_C). Whether or not matrix operands are streamed is motivated in publication. To reduce dependency on the compiler's OpenMP implementation, the benchmarks run single-threaded by default (make OMP=1 can parallelize the batch of matrix multiplications). The outer/batch-level parallelization is also disabled to avoid accounting for proper first-touch memory population on multi-socket systems (NUMA). For the latter, the init-function (located in magazine.h) is not parallelized for simplicity.

cd libxsmm; make
cd samples/magazine; make

To run the benchmark kernels presented by the article:

./benchmark.sh

Please note that if multiple threads are enabled and used, an appropriate pin-strategy should be used (OMP_PLACES=threads, OMP_PROC_BIND=TRUE). To finally produce the benchmark charts:

./benchmark-plot.sh blaze
./benchmark-plot.sh eigen
./benchmark-plot.sh xsmm

The plot script relies at least on Gnuplot. ImageMagick (mogrify) can be also useful if PNGs are created, e.g., ./benchmark-plot.sh xsmm png 0 (the last argument disables single-file charts in contrast to multi-page PDFs created by default, the option also disables chart titles).

The set of kernels executed during the benchmark can be larger than the kernels presented by the plots: benchmark.set selects the kernels independent of the kernels executed (union).