  The extent of parallelization of a loop is largely determined by the
dependences between its statements. While dependence free loops are fully
parallelizable, those with loop carried dependences are not. Dependence
distance is a measure of absolute difference between a pair of dependent
iterations. Loops with constant distance data dependence, because of uniform
distance between the dependent iterations, lead to easy partitioning of the
iteration space and hence they have been successfully dealt with.
  Parallelization of loops with variable distance data dependences is a
considerably difficult problem. It is our belief that partitioning the
iteration space in such loops cannot be done without examining solutions of the
corresponding Linear Diophantine Equations. Focus of this work is to study
variable distance data dependences and examine the relation between dependent
iterations. Our analysis based on parametric solution leads to a mathematical
formulation capturing dependence between iterations. Our approach shows the
existence of reasonable exploitable parallelism in variable distance data
dependences loops with multiple LDEs.
