Collective loop fusion for array contraction

Abstract

In this paper we propose a loop fusion algorithm specifically designed to increase opportunities for array contraction. Array contraction is an optimization that transforms array variables into scalar variables within a loop nest. In contrast to array elements, scalar variables have better cache behavior and can be allocated to registers. In past work we investigated loop interchange and loop reversal as optimizations that increase opportunities for array contraction [13]. This paper extends this work by including the loop fusion optimization. The fusion method discussed in this paper uses the maxflow-mincut algorithm to do loop clustering. Our collective loop fusion algorithm is efficient, and we demonstrate its usefulness for array contraction with a simple example.