IrGEMM: An Input-Aware Tuning Framework for Irregular GEMM on ARM and X86 CPUs

The matrix multiplication algorithm is a fundamental numerical technique in linear algebra and plays a crucial role in many scientific computing applications. Despite the high performance of mainstream basic linear algebra libraries for large-scale dense matrix multiplications, they exhibit poor performance when applied to matrix multiplication with irregular input. This paper proposes an input-aware tuning framework that accounts for application scenarios and computer architectures to provide high-performance irregular matrix multiplication on ARMv8 and X86 CPUs. The framework comprises two stages: the install-time stage and the run-time stage. The install-time stage utilizes our proposed computational template to generate high-performance kernels for general data layout and SIMD-friendly data layout. The run-time stage utilizes a tiling algorithm suitable for irregular GEMM to select the optimal kernel and link as an execution plan. Additionally, load-balanced multi-threaded optimization algorithms are defined to exploit the multi-threading capability of modern processors. Experiments demonstrate that the proposed IrGEMM framework can achieve significant performance improvements for irregular GEMM on both ARMv8 and X86 CPUs compared to other mainstream BLAS libraries.