15-745 Project report: An integer programming approach to optimal code scheduling on clustered architectures

This report describes what we believe to be the first attempt to apply integer programming to code scheduling for a clustered architecture. We give an integer linear program (ILP) for instruction scheduling on the Texas Instruments TMS C6X CPU family, which has constraints on the communication between its two clusters. Using CPLEX to solve the ILP, we show that our approach finds shorter schedules than a standard list scheduling approach in a reasonable amount of time. Introduction Code scheduling is the problem of scheduling machine-level instructions in a basic block so as to produce shorter schedules (and consequently shorter run times). Register allocation is the problem of assigning variables to registers in such a way so as to minimize the amount of non-register memory accesses required by the program. Both of these problems are NP-hard, and the literature is full of different approaches that have been tried. There is increasing interest in tackling both of these problems simultaneously to avoid phase-ordering problems. Of course the NP-hardness holds for the combined problem. Integer programming, in which a linear objective is optimized subject to linear constraints and integrality constraints on some of the variables, is a widely used approach for modeling difficult optimization problems [3]. Optimizing an integer program is in itself NP-hard, but recent research and development has led to the development of commercial software1 that is able to solve large, difficult integer programming instances with modest computational requirements. In many fields, researchers have been able to develop integer programming-based approaches for tackling a wide range of computationally intractable problems. The Texas Instruments TMS C6X CPU family, with its clustered architecture and predicated instruction support, provides unique opportunites and challenges to the compiler writer. In particular, the instruction-level parallelism that it offers can be exploited to greatly improve running times via better scheduling. However, because of the clustered architecture and the constraints under which different clusters can communicate with the register file of the opposite cluster, the scheduling depends heavily on the register allocation. Thus, for this architecture especially, a combined approach to the register allocation and code scheduling problems could have the greatest impact. In this project, we propose using an integer programming-based approach for solving the code scheduling and register allocation problems simultaneously. Our target platform will be the C6X processor. In solving integer programs, there are many different techniques that may be tried. Branching strategies, cutting planes, and problem formulation are all different techniques that can be specialized to a specific family of integer programs to improve performance. By utilizing some of these techniques, we plan to investigate (1) how well an integer programming approach can scale when both register allocation and code scheduling is considered, and (2) how well an integer programming approach can approximate an optimal solution when faced with limited computational resources. 1The most popular piece of commercial software for integer programming is CPLEX, produced by ILOG. This is the software we will use in our research.