Array Programming via Multi-Dimensional Homomorphisms

Explore the innovative "Multi-Dimensional Homomorphisms (MDH)" approach to array programming in this 29-minute conference talk from ACM SIGPLAN's ARRAY'23. Dive into a formalism for expressing data-parallel computations on arrays, including linear algebra routines and stencil computations, using higher-order functions. Discover how MDH automatically generates optimized program code for various hardware platforms, such as CUDA for GPUs and OpenCL for CPUs. Learn about the three major contributions of MDH: a high-level program representation for hardware-agnostic array computations, a low-level program representation for optimization reasoning and code generation, and a fully automatic process for converting high-level MDH programs into hardware-optimized low-level representations through auto-tuning. Gain insights into preliminary experimental results showing MDH's superior performance on GPUs and CPUs compared to state-of-practice approaches, including hand-optimized vendor libraries from NVIDIA and Intel.