A data locality optimizing algorithm

Abstract

This paper proposes an algorithm that improves the locality of a loop nest by transforming the code via interchange, reversal, skewing and tiling. The loop transformation algorithm is based on two concepts: a mathematical formulation of reuse and locality, and a loop transformation theory that unifies the various transforms as unimodular matrix transformations.The algorithm has been implemented in the SUIF (Stanford University Intermediate Format) compiler, and is successful in optimizing codes such as matrix multiplication, successive over-relaxation (SOR), LU decomposition without pivoting, and Givens QR factorization. Performance evaluation indicates that locality optimization is especially crucial for scaling up the performance of parallel code.