Multi-dimensional Interval Test

摘要

In this paper, we propose a sophisticated technique of data dependence analysis for distributed memory parallel environments that is used for converting sequential code into a parallel form targeted for a particular architecture. Two-dimensional arrays with subscripts formed by induction variable in real programs appear quite frequently. We test if there are integer-valued solutions for two-dimensional arrays with subscripts formed by induction variable. It is demonstrated that without direction vectors there are integer-valued solutions for two-dimensional arrays with subscripts formed by induction variable. Furthermore, it is also shown that under a specific direction vector θ = (=_1, …, =_d ) there are integer-valued solutions for two-dimensional arrays with subscripts formed by induction variable. Finally, we point out that for other direction vectors there are no integer-valued solutions for two-dimensional arrays with subscripts formed by induction variable.