Polyhedral expression propagation

Polyhedral techniques have proven to be powerful for various optimizations, from automatic parallelization to accelerator programming. At their core, these techniques compute accurate dependences among statement instances in order to apply complex program transformations. Such transformations comprise memory layout or program order modifications by optimizing memory access functions or scheduling functions. However, these approaches treat statements as opaque entities and do not consider changing the structure of the contained expressions or the memory accesses involved. In this paper we present a technique that statically propagates expressions in order to avoid communicating their result via memory. While orthogonal to other polyhedral optimizations, this transformation can be used to enable them. Applied separately, expression propagation can increase parallelism, eliminate temporary arrays, create independent computations and improve cache utilization. It is especially useful for streaming codes that involve temporary arrays and scalar variables. For multiple image processing pipelines we achieve portable speedups of up to 21.3× as well as a significant memory reduction compared to a naive parallel implementation. In 6 out of 7 cases, expression propagation outperforms a state-of-the-art polyhedral optimization especially designed for this kind of programs by a factor of up to 2.03×.