While GPUs play an increasingly important role in today's
high-performance computers, optimizing GPU performance continues to
impose large burdens upon programmers. A major challenge in
optimizing codes for GPUs stems from the two levels of hardware
parallelism, blocks and threads; each of these levels has
significantly different characteristics, requiring different
optimization strategies.

In this paper, we propose a novel compiler optimization algorithm for
GPU parallelism. Our approach is based on the polyhedral model, which
has enabled significant advances in program analysis and
transformation compared to traditional AST-based frameworks. We
extend polyhedral schedules to enable two-level parallelization
through the idea of superposition, which integrates separate
schedules for block-level and thread-level parallelism. Our
experimental results demonstrate that our proposed compiler
optimization framework can deliver 1.8$\times$ and 2.1$\times$
geometric mean improvements on NVIDIA Tesla M2050 and K80 GPUs,
compared to a state-of-the-art polyhedral parallel code generator
(PPCG) for GPGPUs.