An Irredundant Decomposition of Data Flow with Affine Dependences

Optimization pipelines targeting polyhedral programs try to maximize the compute throughput. Traditional approaches favor reuse and temporal locality; while the communicated volume can be low, failure to optimize spatial locality may cause a low I/O performance. Memory allocation schemes using data partitioning such as data tiling can improve the spatial locality, but they are domain-specific and rarely applied by compilers when an existing allocation is supplied. In this paper, we propose to derive a partitioned memory allocation for tiled polyhedral programs using their data flow information. We extend the existing MARS partitioning to handle affine dependences, and determine which dependences can lead to a regular, simple control flow for communications. While this paper consists in a theoretical study, previous work on data partitioning in inter-node scenarios has shown performance improvements due to better bandwidth utilization.