clMAGMA: High Performance Dense Linear Algebra with OpenCL∗

This paper presents the design and implementation of several fun-damental dense linear algebra (DLA) algorithms in OpenCL. In particular, these are linear system solvers and eigenvalue problem solvers. Further, we give an overview of the clMAGMA library, an open source, high performance OpenCL library that incorporates various optimizations, and in general provides the DLA functional-ity of the popular LAPACK library on heterogeneous architectures. The LAPACK-compliance and use of OpenCL simplify the use of clMAGMA in applications, while providing them with portable performance. High performance is obtained through the use of the high-performance OpenCL BLAS, hardware- and OpenCL-specific tuning, and a hybridization methodology, where we split the algo-rithm into computational tasks of various granularities. Execution of those tasks is efficiently scheduled over the heterogeneous hard-ware components by minimizing data movements and mapping algorithmic requirements to the architectural strengths of the various heterogeneous hardware components