Algorithm XXX: Automatic Generators for a Family of Matrix Multiplication Routines with Apache TVM

Abstract

We explore the utilization of the Apache TVM open source framework to automatically generate a family of algorithms that follow the approach taken by popular linear algebra libraries, such as GotoBLAS2, BLIS and OpenBLAS, in order to obtain high-performance blocked formulations of the general matrix multiplication (gemm). In addition, we fully automatize the generation process, by also leveraging the Apache TVM framework to derive a complete variety of the processor-specific micro-kernels for gemm. This is in contrast with the convention in high performance libraries, which hand-encode a single micro-kernel per architecture using Assembly code. In global, the combination of our TVM-generated blocked algorithms and micro-kernels for gemm 1) improves portability, maintainability and, globally, streamlines the software life cycle; 2) provides high flexibility to easily tailor and optimize the solution to different data types, processor architectures, and matrix operand shapes, yielding performance on a par (or even superior for specific matrix shapes) with that of hand-tuned libraries; and 3) features a small memory footprint.