| N. Megiddo and V. Sarkar. Optimal weighted loop fusion for parallel programs. In Proceedings of the 9th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 282--291, Newport, Rhode Island, June 22--25, 1997. 2.1.1 |
....loop fusion for array contraction, developing a heuristic based on a maxflow mincut algorithm. Then, several authors (see the Related Work section) contributed to loop fusion optimizations, but with slightly di#erent objectives, focusing on loop fusion for locality [17] weighted loop fusion [19], maximal fusion (number of loops) 4] loop fusion for memory reduction [25, 15] etc. All these approaches keep in mind array contraction but they do not optimize directly for it. They target variants of data locality (for example, number of fused dependences) and, in favorable cases (but not ....
....in Section 6. 2 Program Model and Objectives To simplify the discussion, we consider a sequence of simple (i.e. not nested) loops, with unitary loop steps, each loop containing one or several simple statements (assignments to an array or scalar variable) Following the terminology in [7, 19], we assume that all loops are conformable (or of same type [11] i.e. regardless of dependences, they could be fused without code generation or semantics problems (similar headers, same control dependences, etc. Figure 1 shows a sample program fragment (this is a modified version of the ....
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Nimrod Megiddo and Vivek Sarkar. Optimal weighted loop fusion for parallel programs. In 9th annual ACM symposium on parallel algorithms and architectures (SPAA'97), pages 282--291, Newport, Rhode Island, 1997.
....The rst group is in the form as ## 10 # =1###1, while the second group is in the form of ## 10 # = ##1# #1. Because loop fusion can be regarded as a special case of multiple loop partition when the partition size is 1, The problem to group loop nests is the same as the fusible loop problem [5] in essence. 6. ....
N. Megiddo and V. Sarkar. Optimal weighted loop fusion for parallel programs. In Proceedings of 9th ACM symposium on Parallel algorithms and architectures, pages 282-291, Newport, RI, June 1997.
....with small code portions: in this case, more accurate performance models can then be used for picking the right solution. For example, exponential (in the worse case) algorithms based on branch and bound or integer linear programming can also be useful as it has been shown by Megiddo and Sarkar in [12]. However, when a compiler has to perform such an optimization on larger codes, or even frequently on small portions, then heuristics have to be used: a reasonable one seems to be 17 the ordered typed fusion if code compaction is the rst goal. McKinley and Kennedy also proposed a very simple ....
Nimrod Megiddo and Vivek Sarkar. Optimal weighted loop fusion for parallel programs. In 9th annual ACM symposium on parallel algorithms and architectures (SPAA'97), pages 282291, Newport, Rhode Island, 1997.
....the closeness of one node to another. The problem is to break the graph into clusters so that the nodes that are close are grouped together in the same cluster. A heuristic for clustering has been successfully used by Sih and Lee for multiprocessor scheduling [14] Previous fusion approaches [1, 15, 16, 17] considered the fusion problem in isolation. Kennedy and McKinley considered the two objectives of maximizing parallelism and increasing data locality separately which may not give optimal results [15, 18] Also, they restricted their attention to fusing only conformable loop nests. In many ....
....they require all loops to be conformable (having exactly same header) and because they do not allow reordering of loop nests. Also, they do not try to optimize both for uniprocessors and multiprocessors. Megiddo and Sarkar give an integer programming solution for the weighted fusion problem [17] which produces optimal solutions but does not model parallelism or register constraints, neither is it parameterizable. Manjikian and Abdelrahman consider fusion for parallelism and locality but not together [20, 21] Moreover, they do not get an optimal solution. They utilize loop shifting and ....
Megiddo, N. and Sarkar, V. (1997 June) Optimal Weighted Loop Fusion for Parallel Programs. In Proceedings of the Ninth Annual ACM Symposium on Parallel Algorithms and Architectures. Newport, Rhode Island.
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N. Megiddo and V. Sarkar. Optimal weighted loop fusion for parallel programs. In Proceedings of the 9th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 282--291, Newport, Rhode Island, June 22--25, 1997. 2.1.1
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N. Megiddo and V. Sarkar. Optimal weighted loop fusion for parallel programs. In Proceedings of the 9th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 282--291, Newport, Rhode Island, June 22--25, 1997. 2.1.1
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Nimrod Megiddo and Vivek Sarkar. Optimal weighted loop fusion for parallel programs. In 9th annual ACM symposium on parallel algorithms and architectures (SPAA'97), pages 282--291, Newport, Rhode Island, 1997.
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