Towards Supporting Semiring in MLIR-Based COMET Compiler.

Semirings are widely used in large-scale scientific applications of high-dimensional data and graph analytics for linear algebra computations. In this work, we propose a semiring compiler for today's high-performance computing (HPC) systems, often armed with heterogeneous devices, as an alternative to library-based approaches. In particular, we extend a domain-specific language (DSL) and compiler framework to automatically generate kernel code for semiring operations within the COMpiler for Extreme Targets (COMET) based on the Multi-Level Intermediate Representation (MLIR) framework. We provide a high-level programming abstraction representing various semiring operations with the familiar Einstein notation. We also build a semiring dialect and efficient code generation based on MLIR's extensible framework that can process a variety of semiring operators. By leveraging high-level semantics information and progressive lowering in code generation, we achieved better performance with up to 3.8x speedup compared with operations in the LAGraph library.