On the Near-Optimality of List Scheduling Heuristics for
Local and Global Instruction Scheduling.
MMath thesis, University of Waterloo, School of Computer Science, 2006.
Modern architectures allow multiple instructions to be issued at once and have other complex features. To account for this, compilers perform instruction scheduling after generating the output code. The instruction scheduling problem is to find an optimal schedule given the limitations and capabilities of the architecture. While this can be done optimally, a greedy algorithm known as list scheduling is used in practice in most production compilers.
List scheduling is generally regarded as being near-optimal in practice, provided a good choice of heuristic is used. However, previous work comparing a list scheduler against an optimal scheduler either makes the assumption that an idealized architectural model is being used or uses too few test cases to strongly prove or disprove the assumed near-optimality of list scheduling. It remains an open question whether or not list scheduling performs well when scheduling for a realistic architectural model.
Using constraint programming, we developed an efficient optimal scheduler capable of scheduling even very large blocks within a popular benchmark suite in a reasonable amount of time. I improved the architectural model and optimal scheduler by allowing for an issue width not equal to the number of functional units, instructions that monopolize the processor for one cycle, and non-fully pipelined instructions. I then evaluate the performance of list scheduling for this more realistic architectural model.
I found that when scheduling for basic blocks when using a realistic architectural model, only 6\% or less of schedules produced by a list scheduler are non-optimal, but when scheduling for superblocks, at least 40\% of schedules produced by a list scheduler are non-optimal. Furthermore, when the list scheduler and optimal scheduler differed, the optimal scheduler was able to improve schedule cost by at least 5\% on average, realizing maximum improvements of 82\%. This suggests that list scheduling is only a viable solution in practice when scheduling basic blocks. When scheduling superblocks, the advantage of using a list scheduler is its speed, not the quality of schedules produced, and other alternatives to list scheduling should be considered.