Periodic register saturation in innermost loops

This article treats register constraints in high performance codes and embedded VLIW computing, aiming to decouple register constraints from instruction scheduling. It extends the register saturation (RS) concept to periodic instruction schedules, i.e., software pipelining (SWP). We formally study an approach which consists in computing the exact upper-bound of the register need for all the valid SWP schedules of an innermost loop (without overestimation), independently of the functional unit constraints. We call this upper-limit the periodic register saturation (PRS) of the data dependence graph (DDG). PRS is well adapted to situations where spilling is not a favourite solution for reducing register pressure compared to ILP scheduling: spill operations request memory data with a higher energy consumption. Also, spill code introduces unpredictable cache effects and makes Worst-Case-Execution-Time (WCET) estimation less accurate. PRS is a computer science concept that has many possible applications. First, it provides compiler designers new ways to generate better codes regarding register optimisation by avoiding useless spilling. Second, its computation can help architectural designers to decide about the most suitable number of available registers inside an embedded VLIW processor; such architectural decision can be done with full respect to instruction level parallelism extraction, independently of the chosen functional units configuration. Third, it can be used to verify prior to instruction scheduling that a code does not require spilling. In this paper, we write an appropriate mathematical formalism for the problem of PRS computation and reduction in the case of loops where data dependence graphs may be cyclic. We prove that PRS reduction is NP-hard and we provide optimal and approximate methods. We have implemented our methods, and our experimental results demonstrate the practical usefulness and efficiency of the PRS approach.