Waypoint: Analytically Modeling GEMM for CPUs

arXiv:2610.34914v1 Announce Type: new Abstract: High-performance General Matrix Multiplication (GEMM) implementations rely on breaking down GEMM into carefully selected tiles to achieve peak performance. We present Waypoint, a new analytical model to automatically identify the optimal tile size for a given hardware and input matrix shape. Waypoint estimates the achievable performance for a given tile choice by capturing all the architectural effects including interactions with memory hierarchy, instruction-level parallelism, and multi-threading. Using the estimates as a proxy, we search through the space of possible tile sizes to identify the one that maximizes performance. Additionally, Waypoint helps hardware designers estimate realistic performance on experimental hardware optimizations