R. Johnson, D. Pearson, and K. Pingali. Finding regions fast: Single entry single exit and control regions in linear time. In Proc. Sigplan'94 PLDI, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....assignment version. 14 4.2 Minimal and pruned SSA forms. 16 5.1 A comparison of SSA and SSI forms. 17 5.2 Minimal and pruned SSI forms. 22 5. 3 Transformation from directed to undirected graph (from [18]) 25 5.4 Datatypes and operations for the cycle equivalency algorithm. 26 5.5 Control flow graph and cycle equivalent edges. 28 5.6 Datatypes and operations used in construction of the PST. 30 5.7 SESE regions and PST for the CFG of Figure 5.5 (from [19] 32 5.8 An flowgraph where ....

....7.7 Event driven transition rules for SSI . 83 List of Tables 6.1 Meet and binary operation rules on the SCC value lattice. 56 6.2 Class hierarchy statistics for several large O O projects. 62 List of Algorithms 5. 1 The cycle equivalency algorithm (corrected from [18]) 27 5.2 Computing nested SESE regions and the PST. 31 5.3 Placing OE and oe functions. 33 5.4 SSI renaming algorithm. 38 5.5 SSI renaming algorithm, cont. 39 5.6 ....

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R. Johnson, D. Pearson, and K. Pingali. Finding regions fast: Single entry single exit and control regions in linear time. Technical Report TR 93-1365, Cornell University, Ithaca, NY 14853-7501, July 1993.

....blocks and graph rewriting We concentrate on the notion of single entry single exit regions as our objects of rewriting. For convenience we will refer to these regions as graph blocks. The term hammocks is sometimes used for this, but the use of this terminology is inconsistent, as pointed out in [21]. Often analysis in compilers is in terms of basic blocks, these are also graph blocks but tend to be speci ed as not containing cycles and maximal with respect to this property. We do not put this restriction on graph blocks since we need a ner granularity to specify transformations. Any single ....

R. Johnson, D. Pearson, and K. Pingali. Finding regions fast: Single entry single exit and control regions in linear time, 1993.

....single basic block nor the composition of other SESE regions. A node d is a SESE bottom if, for some node c, c and d enclose a SESE region. Finally, for each CFG node a, let bottom(a) be the postdominator of the smallest SESE region containing a; bottom(a) can be found for all nodes in O(E) time [JPP93] A join is symptomatic of looping or unstructured control iff it is not a SESE bottom. End analysis associates with each branch (join) node a branch end (join end) The analysis depends on whether the node is a SESE bottom or not. If a branch is a SESE bottom node, the branch end is that ....

Richard Johnson, David Pearson, and Keshav Pingali. Finding regions fast: Single entry single exit and control regions in linear time. Technical Report CTC93TR141, Cornell University, July 1993.

....the same time bounds. Cycle Equivalence: Two edges e 1 and e 2 of an undirected graph are cycle equivalent iff the set of cycles that contain e 1 is exactly the same as the set of cycles that contain e 2 . Finding the cycle equivalence classes is central to several compilation problems. See [12, 20, 6] for some applications of cycle equivalence. As mentioned in [8] dynamic algorithms for this problem can speed up incremental compilers. No special purpose incremental or backtracking algorithms are known for this problem. The only dynamic algorithms known for handling an incremental or a ....

Richard Johnson, David Pearson, and Keshav Pingali. Finding regions fast: Single entry single exit and control regions in linear time. In Proceedings of ACM SIGPLAN '94 Conference on Programming Language Design and Implementation, pages 171--185, 1994.

....chains in the postdominator tree that are the reverse of chains in the dominator tree. When examining a child w of vertex v in the postdominator tree (line [7] the algorithm checks if w is the parent of v in the dominator tree (line [8] If so, then v and w are in the same weak region (lines [9 10]) If not, then vertices v and w cannot occupy the same weak region (lines [11 14] A new weak region is created and w is the tail of this region (the depth first search builds weak regions in reverse order) 4. STRONG REGIONS Vertices v and w are in the same strong region of a control flow graph ....

.... we show how to compute strong regions (regions arising from full control dependence) Since our algorithm was originally developed, Johnson, Pearson, and Pingali have developed an algorithm for finding strong regions for which they claim linear time performance on arbitrary control flow graphs [9]. They use a characterization of strong regions that is nearly identical to ours. However, their algorithm does not require construction of either the dominator or postdominator relation. 14 7. CONCLUSIONS Regions of control dependence have a variety of uses in optimizing and parallelizing ....

Johnson, R., Pearson, D., and Pingali, K. Finding regions fast: single entry single exit and control regions in linear time. Technical Report 93-1365, Department of Computer Science, Cornell University (July 1993).

....as in Figure 3. FIGURE 3. Abstract Syntax to CDG transforms for language L 0 ) Predicates in a conditional give rise to one or two regions depending on the number of sides the predicate controls. This notion of associating a direction with control dependence is very useful in constructing CDGs [9]. Loops give rise to two regions, one that controls the execution of the loop predicate (P.hdr) of the loop and one that controls the execution of the loop body (P.bdy) Regions thus explicate the control conditions that cause the controlled statements to execute. The algorithm to perform the ....

R. Johnson, D. Pearson and K. Pingali, "Finding Regions Fast: Single Entry Single Exit and Control Regions in Linear Time", Technical Report #CTC93TR141, Cornell University, July 1993.

.... version of the control flow graph [12] In particular, code optimization algorithms, such as static singleassignment form construction, and data flow analysis, such as determining the subexpression availability, can be sped up if the cycle equivalence classes of the control flow graph are known [13]. A third application of the control dependence equivalence relation is in global scheduling of instructions for pipelined machines [11] In [13] a static algorithm is used that computes the cycle equivalence relation in linear time. Then the question is posed if the cycle equivalence relation ....

.... analysis, such as determining the subexpression availability, can be sped up if the cycle equivalence classes of the control flow graph are known [13] A third application of the control dependence equivalence relation is in global scheduling of instructions for pipelined machines [11] In [13], a static algorithm is used that computes the cycle equivalence relation in linear time. Then the question is posed if the cycle equivalence relation can be maintained efficiently during modifications of the control flow graph. This problem is of practical significance, because it can speed up ....

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R. Johnson, D. Pearson, and K. Pingali, "Finding Regions Fast: Single Entry Single Exit and Control Regions in Linear Time." To appear in Proc. Sigplan'94 PLDI.

....to a control flow graph G . Nodes a and b in G have the same set of control dependences iff a and b are cycle equivalent in S. We leave it to the reader to verify this theorem for the example shown in Figure 1(a) The proof of this theorem is straightforward, if tedious, and can be found in [JPP93] Unlike the edge cycle equivalence relation, node cycle equivalence is not preserved when edge directions are removed from a graph. Fortunately, a simple construction lets us reduce the problem of finding node cycle equivalence in directed graphs to the problem of edge cycle equivalence in a ....

....more complex, but the savings in space and time over working with the explicitly transformed graph are significant. In a related technical report, we have shown that this algorithm runs faster than dominator computation, which is just the first step in all previous algorithms for this problem [JPP93] 6 Applications of the PST The Program Structure Tree is a tool for enhancing the performance of program analysis algorithms by providing a simple framework for exploiting global structure, local structure, and sparsity. The intuitive idea is the following. Global structure: The PST is a tree ....

Richard Johnson, David Pearson, and Keshav Pingali. Finding regions fast: Single entry single exit and control regions in linear time. Technical Report 93-1365, Department of Computer Science, Cornell University, July 1993.

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R. Johnson, D. Pearson, and K. Pingali. Finding regions fast: Single entry single exit and control regions in linear time. In Proc. Sigplan'94 PLDI, 1994.

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R. Johnson, D. Pearson, and K. Pingali. Finding regions fast: Single entry single exit and control regions in linear time. Technical Report TR 93-1365, Cornell University, Ithaca, NY 14853-7501, July 1993.

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