Reference distance as a metric for data locality

We propose the reference distance as a metric for data locality. Reference distance is the number of referenced memory blocks between two successive references to the same memory block. The effectiveness of program transformations for data locality can be evaluated by using reference distance. Our claim is demonstrated by showing the change in data locality and speedup of matrix multiplication due to loop interchange, loop tiling, and loop unrolling. We also present a result of an experiment using loop distribution and unrolling with respect to two subroutines of Perfect benchmark programs. Reference distance would serve as a useful tool for developing a program transformation scheme for data locality optimization