Capturing the Expert: Generating Fast Matrix-Multiply Kernels with Spiral

Matrix-Matrix Multiplication (MMM) is a fundamental operation in scientific computing. Achieving the floating point peak with this operation requires expert knowledge of linear algebra and computer architecture to craft a tuned implementation, for a given microarchitecture. The expert follows a mechanical process for implementing MMM, by deriving the algorithm models from the literature. Then, by hand, applying optimizations which are well suited for that architecture. Lastly, the experts codes that implementation at the assembly level. In this paper, we argue that this process is mechanical and can be captured in an autotuning and program generation system such as Spiral. We then show that given this machinery, Spiral can produce code for large size MMM implementations that are competitive with hand tuned code.