B. Creusillet, F. Irigoin, Exact vs. Approximate Array Region Analyses, Proceedings of 9th Workshop on Language and Compilers for Parallel Computing, Aug. 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....One of the rst such studies [17] was done at Illinois as part of the Cedar project, by a group of people of which the author was a member. Similar studies have been done at Stanford [21] Researchers at Stanford [22] and Minnesota [20] plus the PIPS group at Ecole des mines de Paris [13, 14] and the Parafrase 2 group at Illinois [31] have implemented compilers including the same basic transformations found to be important in the Cedar Project. The results have been similar enough to form a general consensus as to which analysis techniques are important to provide in a parallelizing ....

....optimized it so as to avoid exponential running times for the constraints derived from most practical program situations. It also eliminates the requirement that the linear constraints form a convex hull, avoiding one source of precision loss. The PIPS project at Ecole des mines de Paris [13, 14] has added an indicator of the accuracy of the representation to the representation itself. When linear system manipulations must approximate, sometimes it is appropriate to under approximate (MUST analysis) while at other times it is appropriate to over approximate (MAY analysis) But by making ....

B. Creusillet and F. Irigoin. Exact vs. Approximate Array Region Analyses. In Lecture Notes in Computer Science. Springer Verlag, New York, New York, August 1996.

....array access analysis, summarizing collections of array elements in some standard form is essential to allow the compiler to manipulate the array access information more efficiently. For this reason, many researchers have proposed various array region descriptors and techniques to manipulate them [9, 15, 35, 40]. The form used to represent array accesses is obviously of fundamental importance to the compiler techniques which use it. Yet, despite this importance, little attention has been paid to the influence of the representation on the effectiveness of compiler algorithms. Using an appropriate ....

....exponential complexity, the algorithms built in to the solver do not require exponential running times for most practical program situations. It also eliminates the requirement that the linear constraints form a convex hull, avoiding one source of potential precision loss. The SUIF [27] and PIPS [15] compilers use constraint based techniques to make the representation useful for analyses other than just dependence analysis, such as array privatization and locality analysis. They use a set of region operations for systems of linear inequalities and special algorithms needed to maintain convex ....

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B. Creusillet and F. Irigoin. Exact vs. Approximate Array Region Analyses. In Lecture Notes in Computer Science. Springer Verlag, NY, August 1996.

....with the triplet notation. The same notation was used in papers by Tseng [10] and Chatterjee, Gilbert and Long [11] for message generation. Blume and Eigenmann [5] excluded the stride from the triplet notation in their dependence test for simplicity, but at the expense of accuracy. Convex regions [14, 17] express the geometrical shape of array accesses. They can be used with Fourier Motzkin based dependence tests [21, 22] Balasundaram and Kennedy [15] simplified the convex region to detect task parallelism. Such representations are designed to strike a balance between the efficiency of using the ....

B. Creusillet, F. Irigoin, Exact vs. Approximate Array Region Analyses, Proceedings of 9th Workshop on Language and Compilers for Parallel Computing, Aug. 1996.

....and communication analysis, a parallelizing compiler must have an efficient and flexible way of representing and manipulating memory access patterns. We found that most existing representations, such as triplet notation (also called regular section descriptor) 14, 20, 68, 70] and convex regions [7, 26] sometimes must discard critical information. This prevents the detection of parallelism in certain loops as well as prevents efficient communication analysis for data copying. For this purpose, we have conducted an in depth study of access patterns in many scientific benchmark programs to develop ....

....work. The same notation was used by Tseng [68] and Chatterjee, and Gilbert and Long [20] for message generation. To gain simplicity, Blume and Eigenmann [14] excluded the stride from the triplet notation in their dependence test, but this was at the expense of accuracy. Convex regions [26] express the geometrical shape of array accesses. They can be used with Fourier Motzkin based dependence tests [60, 67] Balasundaram and Kennedy [7] proposed a simplified form of the convex region representation to detect task parallelism. Such representations are designed to balance their ....

B. Creusillet and F. Irigoin. Exact vs. Approximate Array Region Analyses. In Lecture Notes in Computer Science. Springer Verlag, New York, New York, August 1996.

.... Delta Delta Delta ; d) the RD for the access in Figure 1 is X(s1(i) s2 (i) Delta Delta Delta ; sm(i) subject to l k i k uk ; for k = 1; 2; Delta Delta Delta ; d. Next, the compiler would summarize all the RDs in the section and store their union in some standard representation [9, 15, 19]. Simple accesses can be summarized with simple representations without losing precision in access analysis. For example, in Figure 2, the region accessed by reference b(i1 ; i 2) can be represented by b(0:nb :1,0:nb:1) using the traditional triplet notation. In general, more powerful ....

....associated with the two references are aggregated to form a linear system and the feasibility of the system is tested using Fourier Motzkin elimination [11] techniques. The Omega Test [26] is an example of a dependence test built in this way. The PIPS project at Ecole des Mines de Paris [9] has added an indicator of the accuracy of the representation, referred to as MUST MAY, to the representation itself. The notion of MUST MAY approximations helps a compiler to determine when a result is accurate or inaccurate. Linear constraint based techniques are generally considered more ....

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B. Creusillet and F. Irigoin. Exact vs. Approximate Array Region Analyses. In Lecture Notes in Computer Science. Springer Verlag, New York, New York, August 1996.

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B. Creusillet, F. Irigoin, Exact vs. Approximate Array Region Analyses, Proceedings of 9th Workshop on Language and Compilers for Parallel Computing, Aug. 1996.

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B. Creusillet and F. Irigoin. Exact vs. Approximate Array Region Analyses. In Lecture Notes in Computer Science. Springer Verlag, New York, New York, August 1996.

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B. Creusillet, F. Irigoin, Exact vs. Approximate Array Region Analyses, Proceedings of 9th Workshop on Language and Compilers for Parallel Computing, Aug. 1996.

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B. Creusillet and F. Irigoin. Exact vs. Approximate Array Region Analyses. In Lecture Notes in Computer Science. Springer Verlag, New York, New York, August 1996.

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