Optimal and Near–Optimal Solutions for Hard Compilation Problems

Abstract

An optimizing compiler typically uses multiple program representations at different levels of program and performance abstractions in order to be able to perform transformations that – at least in the majority of cases – will lead to an overall improvement in program performance. The complexities of the program and performance abstractions used to formulate compiler optimization problems have to match the complexities of the high–level programming model and of the underlying target system. Scalable parallel systems typically have multi–level memory hierarchies and able to exploit coarse–grain and fine–grain parallelism. Most likely, future systems will have even deeper memory hierarchies and more granularities of parallelism. As a result, future compiler optimizations will have to use more and more complex, multi–level computation and performance models in order to keep up with the complexities of their future target systems. Most of the optimization problems encountered in highly optimizing compilers are already NP–hard, and there is little hope that most newly encountered optimization formulations will not be at least NP–hard as well. To face this "complexity crisis", new methods are needed to evaluate the benefits of a compiler optimization formulation. A crucial step in this evaluation process is to compute the optimal solution of the formulation. Using ad–hoc methods to compute optimal solutions to NP–complete problems may be prohibitively expensive. Recent improvements in mixed integer and 0–1 integer programming suggest that this technology may provide the key to efficient, optimal and near–optimal solutions to NP–complete compiler optimization problems. In fact, early results indicate that integer programming formulations may be efficient enough to be included in not only evaluation prototypes, but in production programming environments or even production compilers. This paper discusses the potential benefits of integer programming as a tool to deal with NP–complete compiler optimization formulations in compilers and programming environments.