Parallel Region Execution of Loops with Irregular Dependencies

Zaafrani, A.; Ito, M.R.

doi:10.1109/icpp.1994.153

Cited by 21 publications

(17 citation statements)

References 12 publications

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“…As the example, we can obtain the following results using the improved tiling method proposed in this section. From the algorithm to compute a two-dimensional IDCH in [5], we can obtain the extreme points such as (1, 1), (1,22), and (18, 1) as shown in Fig. 3(a).…”

Section: Procedures Tiling_methodsmentioning

confidence: 99%

“…Some techniques, based on Convex Hull theory [7] that has been proven to have enough information to handle non-uniform dependences, are the minimum dependence distance tiling method [5], [6], the unique set oriented partitioning method [4], and the three region partitioning [1], [3]. This paper will focus on parallelizing perfectly nested loops with non-uniform and flow dependences.…”

Section: Introductionmentioning

confidence: 99%

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Parallelism for Nested Loops with Non-uniform and Flow Dependences

Jeong

2004

Computational Science - ICCS 2004

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Abstract. Many methods are proposed in order to parallelize loops with nonuniform dependence, but most of such approaches perform poorly due to irregular and complex dependence constraints. This paper proposes an efficient method of tiling and transforming nested loops with non-uniform and flow dependences for maximizing parallelism. Our approach is based on the Convex Hull theory that has adequate information to handle non-uniform dependences, and also based on minimum dependence distance tiling, the unique set oriented partitioning, and three region partitioning methods. We will first show how to find the incrementing minimum dependence distance. Next, we will propose how to tile the iteration space efficiently according to the incrementing minimum dependence distance. Finally, we will show how to achieve more parallelism by loop interchanging and how to transform it into parallel loops.Comparison with some other methods shows more parallelism than other existing methods.

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Section: Procedures Tiling_methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parallelism for Nested Loops with Non-uniform and Flow Dependences

Jeong

2004

Computational Science - ICCS 2004

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“…5, Algorithm Region_Partition, we can determine whether the intersection of FDT and FDH is empty by position of two given lines d i (i 1 , j 1 ) = 0 and d i (i 2 , j 2 ) = 0, and two real values q 1 and q 3 given in (7). If the intersection of FDT and FDH is not empty, we divide the iteration space into two parallel regions and one serial region by two appropriate lines as given in the three region partitioning method [2], [7]. If the intersection of FDT and FDH is empty, we divide the iteration space into two parallel regions by the line d i (i 1 , j 1 ) = 0 or d i (i 2 , j 2 …”

Section: Region Partitioning Methods By Two Given Equationsmentioning

confidence: 99%

“…= A(i+2j+1, i+j+1) enddo enddo Several works has been done for loops with non-uniform dependences, but show us poor performance. Some techniques, based on Convex Hull theory [5] that has been proven to have enough information to handle non-uniform dependences, are the minimum dependence distance tiling method [4], the unique set oriented partitioning method [3], and the three region partitioning method [2], [7]. Fig.…”

Section: Example Lmentioning

confidence: 99%

Improving Parallelism of Nested Loops with Non-uniform Dependences

Jeong¹,

Han²

2005

Lecture Notes in Computer Science

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Abstract. This paper defines the properties of FDT (Flow Dependence Tail set) and FDH (Flow Dependence Head set), and presents two partitioning methods for finding two parallel regions in two-dimensional solution space. One is the region partitioning method by intersection of FDT and FDH. Another is the region partitioning method by two given equations. Both methods show how to determine whether the intersection of FDT and FDH is empty or not. In the case that FDT does not overlap FDH, we will divide the iteration space into two parallel regions by a line. The iterations within each area can be fully executed in parallel. So, we can find two parallel regions for doubly nested loops with non-uniform dependences for maximizing parallelism.

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“…Most of these vector decomposition techniques consider nested loops with uniform dependences and they perform poorly in parallelizing nested loops with irregular dependences. Zaafrani and Ito [9] divide the iteration space of the loop into parallel and serial regions. All the iterations in the parallel region can be fully executed in parallel.…”

mentioning

confidence: 99%

Compile Time Partitioning of Nested Loop Iteration Spaces With Non-Uniform Dependences*

Punyamurtul

Chaudhary

et al. 1997

Parallel Algorithms and Applications

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In this paper we address the problem of partitioning nested loops with non-uniform (irregular) dependence vectors. Parallelizing and partitioning of nested loops requires efficient inter-iteration dependence analysis. Although many methods exist for nested loop partitioning, most of these perform poorly when parallelizing nested loops with irregular dependences. Unlike the case of nested loops with uniform dependences these will have a complicated dependence pattern which forms a non-uniform dependence vector set. We apply the results of classical convex theory and principles of linear programming to iteration spaces and show the correspondence between minimum dependence distance computation and iteration space tiling. Cross-iteration dependences are analyzed by forming an Integer DependenceConvex Hull (IDCH). Every integer point in this IDCH corresponds to a dependence vector in the iteration space of the nested loops. A simple way to compute minimum dependence distances from the dependence distance vectors of the extreme points of the IDCH is presented. Using these minimum dependence distances the iteration space can be tiled. Iterations within a tile can be executed in parallel and the different tiles can then be executed with proper synchronization. We demonstrate that our technique gives much better speedup and extracts more parallelism than the existing techniques.

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Parallel Region Execution of Loops with Irregular Dependencies

Cited by 21 publications

References 12 publications

Parallelism for Nested Loops with Non-uniform and Flow Dependences

Parallelism for Nested Loops with Non-uniform and Flow Dependences

Improving Parallelism of Nested Loops with Non-uniform Dependences

Compile Time Partitioning of Nested Loop Iteration Spaces With Non-Uniform Dependences*

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