BLAS GEMM Benchmarks

In a scientific application I develop we make extensive use of matrix-matrix multiplications. It is therefore important that these operations are performant. Highly tuned multiplication kernels are a core component of the basic linear algebra subprograms (BLAS) API. There exist a wide variety of BLAS implementations—both open source and proprietary—for almost all HPC platforms.

What follows are a series of benchmarks for the matrix sizes that arise in our application for a variety of BLAS libraries. It is hoped that these benchmarks will help users to make informed decisions when deciding on a specific BLAS.

The dimensions of the matrices, with the exception of the final test-case (M = N = K = 2048), are all real-world examples taken from my solver.

Methodology

When conducting the benchmarks the following procedures were employed:

• all BLAS libraries were compiled/run in serial with all operations running on a single CPU core;
• each benchmark was repeated 5000 times;
• the benchmarking process was pinned to the first core on the system;
• FLOPS were computed using 5000×(2×M×N×K)/Δt where N, M, and K are the relevant dimensions of the matrices and Δt is the wall clock time;
• all matrices were stored row major order;
• all matrices were initialised with random values with a consistent seed being used throughout;
• the GEMM parameters α and β were taken as 1.0 and 0.0 respectively;
• the transpose parameters were both set to CblasNoTrans;
• all numbers are quoted in gigaflops.

Core i7 3770K

The following comparison is between ATLAS 3.11.11 and the current Git Head of OpenBLAS. Both were compiled using GCC 4.7.2 on a Gentoo Linux system. The CPU was a 3.5Ghz Intel Core i7 3770K with turbo-boost (to 3.9Ghz) enabled. Peak is ~62.7 gigaflops single precision and ~31.4 gigaflops double precision.

We note here that ATLAS tends to outperform OpenBLAS when working at single precision until M = 24. At this point OpenBLAS pulls away; often delivering 20% more FLOPS than ATLAS.