array expansion
A common problem in restructuring programs for vector or parallel execution is the suppression of false dependencies which originate in the reuse of the same memory cell for unrelated values. The method is simple and well understood in the case of scalars. This paper gives the general solution for the case of arrays. The expansion is done in two steps: first, modify all definitions of the offending array in order to obtain the single assignment property. Then, reconstruct the original data flow by adapting all uses of the array. This is done with the help of a new algorithm for solving parametric integer programs. The technique is quite general and may be used for other purposes, including program checking, collecting array predicates, etc 
arrays program vectorization parallel dependencies reuse memorialized values method case paper general definition order assignment data flow adapt help algorithm parametric collect