Performance portable GPU code generation for matrix multiplication

Parallel accelerators such as GPUs are notoriously hard to program; exploiting their full performance potential is a job best left for ninja programmers. High-level programming languages coupled with optimizing compilers have been proposed to attempt to address this issue. However, they rely on device-specific heuristics or hard-coded library implementations to achieve good performance resulting in non-portable solutions that need to be re-optimized for every new device. Achieving performance portability is the holy grail of high-performance computing and has so far remained an open problem even for well studied applications like matrix multiplication. We argue that what is needed is a way to describe applications at a high-level without committing to particular implementations. To this end, we developed in a previous paper a functional data-parallel language which allows applications to be expressed in a device neutral way. We use a set of well-defined rewrite rules to automatically transform programs into semantically equivalent device-specific forms, from which OpenCL code is generated. In this paper, we demonstrate how this approach produces high-performance OpenCL code for GPUs with a well-studied, well-understood application: matrix multiplication. Starting from a single high-level program, our compiler automatically generate highly optimized and specialized implementations. We group simple rewrite rules into more complex macro-rules, each describing a well-known optimization like tiling and register blocking in a composable way. Using an exploration strategy our compiler automatically generates 50,000 OpenCL kernels, each providing a differently optimized -- but provably correct -- implementation of matrix multiplication. The automatically generated code offers competitive performance compared to the manually tuned MAGMA library implementations of matrix multiplication on Nvidia and even outperforms AMD's clBLAS library.