Scalarization Using Loop Alignment and Loop Skewing

Abstract

Array syntax, which is supported in many technical programming languages, adds expressive power by allowing operations on and assignments to whole arrays and array sections. To compile an array assignment statement to a uniprocessor, the language processor must convert the statement into a loop that has the same meaning. This process is called scalarization.

Scalarization presents a significant technical problem because an array assignment needs to be implemented as if all inputs are fetched before any outputs are stored. Since a loop intermixes loads and stores, the compiler typically allocates a temporary array to hold the intermediate result. Because these extra temporary arrays can cause performance problems in cache, many techniques have been developed to avoid their use or minimize their size.

In this paper, we present a novel application of two compiler strategies—loop alignment and loop skewing—to address this problem. We show that these strategies can achieve the asymptotically minimal memory allocation for stencil computations. Our experiments with loop alignment and loop skewing demonstrate that it is extremely effective in improving memory hierarchy performance of Fortran 90 array code on standard uniprocessors. The result should be applicable to other array languages, such as MATLAB.