Optimal Live Range Merge for Address Register Allocation in Embedded Programs

Abstract

Abstract. The increasing demand for wireless devices running mobile applications has renewed the interest on the research of high performance low power processors that can be programmed using very compact code. One way to achieve this goal is to design specialized processors with short instruction formats and shallow pipelines. Given that it enables such architectural features, indirect addressing is the most used addressing mode in embedded programs. This paper analyzes the problem of allocating address registers to array references in loops using auto-increment addressing mode. It leverages on previous work, which is based on a heuristic that merges address register live ranges. We prove, for the first time, that the merge operation is NP-hard in general, and show the existence of an optimal linear-time algorithm, based on dynamic programming, for a special case of the problem.

Address register allocation for arrays in loops of embedded programs

“…This paper extends previous work [13,27] on Global Array Reference Allocation (GARA), which is the problem of allocating address registers to array references in loops running on embedded processors. As an example, consider the Control-Flow Graph (CFG) from Fig.…”

“…A heuristic was used to decide which pair of live ranges should be merged. The problem of finding the minimal number of update instructions when merging pairs of live ranges has been proved to be NP-complete in general [27]. The difficulty of the problem lies in choosing the best (minimum cardinality) set of update instructions among a combinatorial number of possible sets.…”

“…The large number of sets results from the need to keep correct, on every possible execution path, the value of the address register for the array references on the merged live range. Ottoni et al [27] proves the existence of an optimal dynamic programming algorithm to find the minimal set of update instructions, for a special case of live range topology. Preliminary experimental results in Ref.…”

“…Preliminary experimental results in Ref. [27] speculated that this particular topology would be very common in practice, although not enough benchmark data was presented to support that. The experimental results from Section 6 confirm this hypothesis to be true for the MediaBench programs.…”

“…Section 3 describes, for the first time, the Extended Single Reference Form (ESRF), which is required to guarantee the optimality of the dynamic programming algorithm proposed in Ref. [27]. Two heuristics for GARA are summarized in Sections 4 and 5 proposes a method to compute its exact solution.…”