Loop Dependence Analysis - Iteration Vectors

Iteration Vectors

A specific iteration through a normalized loop is referenced through an iteration vector, which encodes the state of each iteration variable.

For a loop, an iteration vector is a member of the Cartesian product of the bounds for the loop variables. In the normalized form given previously, this space is defined to be U1 × U2 × ... × Un. Specific instances of statements may be parametrized by these iteration vectors, and they are also the domain of the array subscript functions found in the body of the loop. Of particular relevance, these vectors form a lexicographic order which corresponds with the chronological execution order.