A domain-specific compiler for linear algebra operations

Abstract. We present a prototypical linear algebra compiler that automatically exploits domain-specific knowledge to generate high-performance algorithms. The input to the compiler is a target equation together with knowledge of both the structure of the problem and the properties of the operands. The output is a variety of high-performance algorithms, and the corresponding source code, to solve the target equa-tion. Our approach consists in the decomposition of the input equation into a sequence of library-supported kernels. Since in general such a de-composition is not unique, our compiler returns not one but a number of algorithms. The potential of the compiler is shown by means of its application to a challenging equation arising within the genome-wide association study. As a result, the compiler produces multiple “best” algorithms that outperform the best existing libraries.