Static and Dynamic Locality Optimizations Using Integer Linear Programming

The delivered performance on modern processors that employ deep memory hierarchies is closely related to the performance of the memory subsystem. Compiler optimizations aimed at improving cache locality are critical in realizing the performance potential of powerful processors. For scientific applications, several loop transformations have been shown to be useful in improving both temporal and spatial locality. Recently, there has been some work in the area of data layout optimizations, i.e., changing the memory layouts of multidimensional arrays from the language-defined default such as column-major storage in Fortran. The effect of such memory layout decisions is on the spatial locality characteristics of loop nests. While data layout transformations are not constrained by data dependences, they have no effect on temporal locality. On the other hand, loop transformations are not readily applicable to imperfect loop nests and are constrained by data dependences. More importantly, loop transformations affect the memory access patterns of all the arrays accessed in a loop nest and, as a result, the locality characteristics of some of the arrays may worsen. This paper presents a technique based on integer linear programming (ILP) that attempts to derive the best combination of loop and data layout transformations. Prior attempts to unify loop and data layout transformations for programs consisting of a sequence of loop nests have been based on heuristics not only for transformations for a single loop nest but also for the sequence in which loop nests will be considered. The ILP formulation presented here obviates the need for such heuristics and gives us a bar against which the heuristic algorithms can be compared. More importantly, our approach is able to transform memory layouts dynamically during program execution. This is particularly useful in applications whose disjoint code segments demand different layouts for a given array. In addition, we show how this formulation can be extended to address the false sharing problem in a multiprocessor environment. The key data structure we introduce is the memory layout graph (MLG) that allows us to formulate the problems as path problems. The paper discusses the relationship of this ILP approach based on the memory layout graphs to other work in the area including our previous work. Experimental results on a MIPS R10000-based system demonstrate the benefits of this approach and show that the use of the ILP formulation does not increase the compilation time significantly.