Communication-Free Alignment for Array References with Linear Subscripts in Three Loop Index Variables or Quadratic Subscripts

Bau et al. proposed an efficient and precise data alignment method to ascertain whether there is communication-free alignment of array reference function with linear subscripts in one loop index variable. Chu et al. presented an efficient and precise data alignment method to determine whether there is communication-free alignment of array reference function with linear subscripts in two loop index variables or quadratic subscripts (ai2+bi+d). However, for array reference function with linear subscripts in three loop index variables or quadratic subscripts (ai2+bi+cj+d), their methods cannot be applied. In this paper, we propose two new alignment functions for loop iteration space and array elements. The new alignment functions can be applied towards checking whether there is communication-free alignment of array reference function with linear subscripts in three loop index variables or quadratic subscripts. Experiments with benchmarks taken from Parallel loop and Vector loop showed that among the 7 nested loops tested, three of them had their data alignment improved by the method proposed.