Integrating Data Layout Transformations with the Polyhedral Model

In the polyhedral model, classical loop transformations and statement reordering transformations have been unified and formalized as affine scheduling problems that can be applied to optimization goals such as locality and parallelism. More recently, data layout transformations have shown significant benefits in improving performance by contributing to improved efficiencies in spatial locality, multi-core parallelism and vector parallelism. However, integration of data layout transformations in the polyhedral model has received relatively little attention thus far. In this paper, we report on our work-in-progress on integrating data layout transformations in the polyhedral model, with a focus on affine representations of data layout transformations. We also demonstrate the potential benefit of performing loop and data layout transformations as an integrated optimization problem, compared to standard decoupled approaches which pick a specific phase order (e.g., data layout transformations before loop transformations) and can thereby miss opportunities to co-optimize both data layout transformations and loop transformations.