3 Independent Partitioning of Loops. This section presents a precise ... 5.3 Loop with Linearly Dependent Distance Vectors. Consider the following ...

non-uniform dependence sets, these distances are linear functions of the loop indices. So we can write these dependence distance functions in a general form as.

However, we observe that the same location is written and read in each iteration of the k-loop. This means that there is a dependence between all k-instances of ...

Data Dependence in Loops. C i ht © S th G ld t i 2008. Lecture 6. 15-745 ... // P is an output variable, containing the set of partitions. // np is the ...

The set of inequalities and dependence distances of the loop in Example 2 is com- puted as follows: DCH1: (7) . DCH2: (8) . Fig. 3 DCHs and the unique head ...

By parallelizing anti dependence region using variable renaming, there remains only flow dependence in the loop. We then divide the iteration space into FDT ...

• Variables in loop indices are integers → Diophantine equations. • The ... • We get ∆I = 1 ⇒ Loop-carried dependence with distance vector (1) and ...

We can parallelize a loop that contains an antidependence by giving each iteration a private copy of the location and initializing the copy related to S1 with ...

Missing: Partitioning | Show results with:Partitioning

Our approach is based on the Convex Hull theory, and also based on minimum dependence distance tiling, the unique set oriented partitioning, and three region ...