Co-Design of the Dense Linear AlgebravSoftware Stack for Multicore Processors

This paper advocates for an intertwined design of the dense linear algebra software stack that breaks down the strict barriers between the high-level, blocked algorithms in LAPACK (Linear Algebra PACKage) and the low-level, architecture-dependent kernels in BLAS (Basic Linear Algebra Subprograms). Specifically, we propose customizing the GEMM (general matrix multiplication) kernel, which is invoked from the blocked algorithms for relevant matrix factorizations in LAPACK, to improve performance on modern multicore processors with hierarchical cache memories. To achieve this, we leverage an analytical model to dynamically adapt the cache configuration parameters of the GEMM to the shape of the matrix operands. Additionally, we accommodate a flexible development of architecture-specific micro-kernels that allow us to further improve the utilization of the cache hierarchy. Our experiments on two platforms, equipped with ARM (NVIDIA Carmel, Neon) and x86 (AMD EPYC, AVX2) multi-core processors, demonstrate the benefits of this approach in terms of better cache utilization and, in general, higher performance. However, they also reveal the delicate balance between optimizing for multi-threaded parallelism versus cache usage.