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. To do this an expert follows a mechanical process for implementing MMM, by deriving an algorithm from models found in the literature. Then, the expert applies optimizations which are well suited for the target architecture. Lastly, the expert expresses that implementation in assembly code. In this paper, we argue that this process is mechanical and can be captured in a rule based 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.