Stefan K Muller

Motivated by the increasing importance of general-purpose Graphic Processing Units (GPGPU) programming, exemplified by NVIDIA’s CUDA framework, as well as the difficulty, especially for novice programmers, of reasoning about performance in GPGPU kernels, we introduce a novel quantitative program logic for CUDA kernels. The logic allows programmers to reason about both functional correctness and resource usage of CUDA kernels, paying particular attention to a set of common but CUDA-specific performance bottlenecks: warp divergences, uncoalesced memory accesses, and bank conflicts. The logic is proved sound with respect to a novel operational cost semantics for CUDA kernels. The semantics, logic, and soundness proofs are formalized in Coq. An inference algorithm based on LP solving automatically synthesizes symbolic resource bounds by generating derivations in the logic. This algorithm is the basis of RaCUDA, an end-to-end resource-analysis tool for kernels, which has been implemented using an existing resource-analysis tool for imperative programs. An experimental evaluation on a suite of benchmarks shows that the analysis is effective in aiding the detection of performance bugs in CUDA kernels.