Evaluation of loop grouping methods based on orthogonal projection spaces

This paper compares three similar loop-grouping methods. All methods are based on projecting the n-dimensional iteration space Jⁿ onto a k-dimensional one, called the projected space, using (n-k) linear independent vectors. The dimension k is selected differently in each method giving various results. The projected space is divided into discrete groups of related iterations, which are assigned to different processors. Two of the methods preserve optimal time completion, by scheduling loop iterations according to the hyperplane method. The theoretical analysis of the experimental results indicates the appropriate method, for specific iteration spaces and target architectures