Software Practice & Experience, 4:110, 2001. Japanese / 日本語 Technically, an unreachable node is dominated by every node in the graph; we will avoid the pathologies this can cause by deleting unreachable nodes from the graph before calculating dominators and doing loop optimizations. idom(n) does not dominate any other dominator of n. Every node except s0 is dominated by at least one node other than itself (since s0 dominates every node), so every node except s0 has exactly one immediate dominator. 0000008365 00000 n Converting to and from other data formats. 0000018192 00000 n Search
The natural loop of a back edge n → h, where h dominates n, isthesetof nodes x such that h dominates x and there is a path from x to n not containing h. The header of this loop will be h. The natural loop of the back edge 10 → 5 from Figure 18.3a includes nodes 5, 8, 9, 10 and has the loop 8, 9 nested within it. Please note that DISQUS operates this forum.
Single-vertex dominators can be found in time linear in the number of vertices of the graph [7, 8, 9]. Serbian / srpski
Except for start, the immediate dominators are the parents of their corresponding nodes in the dominator tree..
0000022663 00000 n Section 19.2 describes a faster algorithm for computing dominators. This algorithm can be made more efficient by ordering the set assignments in quasi-topological order, that is, according to a depth-first search of the graph (Algorithm 17.5). Last updated on Oct 26, 2015.
0000040651 00000 n 0000006896 00000 n %%EOF That is, the immediate dominator of a node is not necessarily its predecessor in the flow graph. By definition, every node dominates itself.
Revision 231c853b. Chinese Simplified / 简体中文 The result will not necessarily be a natural loop. 0000002703 00000 n Examples >>> G = nx.
idom –
trailer << /Size 154 /Info 91 0 R /Root 97 0 R /Prev 165843 /ID[<1f18318189775455b74c8970a7d2a357><1f18318189775455b74c8970a7d2a357>] >> startxref 0 %%EOF 97 0 obj << /Type /Catalog /Pages 90 0 R /Metadata 92 0 R /PageLabels 89 0 R /FICL:Enfocus 93 0 R >> endobj 152 0 obj << /S 359 /T 536 /L 586 /Filter /FlateDecode /Length 153 0 R >> stream However, we usually want to optimize an inner loop first, because most of the program's execution time is expected to be in the inner loop. The leaves of the loop-nest tree are the innermost loops. But we need one more iteration to verify that nothing changes d 10 .
However, they are quite rare in circuits. When you sign in to comment, IBM will provide your email, first name and last name to DISQUS. 0000003643 00000 n
path, the immediate dominator of v, this variable is eliminated.
Enable JavaScript use, and try again. It is more common that a vertex is dominated by a set of vertices. A node h can be the header of more than one natural loop, if there is more than one back edge into h. In Figure 18.3a, the natural loop of 3 → 2 consists of the nodes 3, 2 and the natural loop of 4 → 2 consists of 4, 2. idom – A dict containing the immediate dominators of each node reachable from
0000019078 00000 n Dominator tree Let us draw a graph containing every node of the flow graph, and for every node n an edge from idom(n) to n. The resulting graph will be a tree, because each node has exactly one immediate dominator. A simple, fast dominance algorithm. 0000004566 00000 n 0000007479 00000 n A flow-graph edge from a node n to a node h that dominates n is called a back edge.
Before we optimize the loops, we must find them in the flow graph. A common way of solving this problem is to merge all the natural loops with the same header. French / Français If d dominates each one of the pi, then it must dominate n, because every path from s0 to n must go through one of the pi, but every path from s0 to a pi must go through d. Conversely, if d dominates n, it must dominate all the pi ; otherwise there would be a path from s0 to n going through the predecessor not dominated by d. Let D[n] be the set of nodes that dominate n. Then, The simultaneous equations can be solved, as usual, by iteration, treating each equation as an assignment statement.
Dominator tree Let us draw a graph containing every node of the flow graph, and for every node n an edge from idom(n) to n. The resulting graph will be a tree, because each node has exactly one immediate dominator. Notes. 0000001508 00000 n 0000004048 00000 n 0000033991 00000 n Then there is some path from s0 to e that does not go through d. Therefore any path from e to n must go through d;otherwise d would not dominate n. Conversely, any path from d to n must go through e. But this means that to get from e to n the path must infinitely loop from d to e to d …and never get to n. This theorem tells us that every node n has no more than one immediate dominator, idom.n), such that. Slovenian / Slovenščina German / Deutsch
0 Please upgrade to a maintained version and see the current NetworkX documentation. 0000070823 00000 n Examples. corresponding nodes in the dominator tree. Where should such statements be put? h�b```f``�f`e``�� Ȁ �,@Q� ���a�2�.���{�^�/� a| �[�����=L�+��(+t�-���[(p庝��e��8ږ���Ӥx�T�|�S�S��9�� %�:Attd%N0�utt0�����������u����0��D� \.%�R -��`�p�XfF#����,�/�x��g>�p�9�m���-�>a��. Consider a node n with predecessors p1,…, pk, and a node d (with d ≠ n). In computer science, in control flow graphs, a node d dominates a node n if every path from the entry node to n must go through d. Notationally, this is written as d dom n (or sometimes d $${\displaystyle \gg }$$ n). Project advice The bottom line for your project: • You don’t need to generate SSA form for your project • However, if you decide to do this, then it is advisable to simplify matters by generating SSA directly during translation . 0000001623 00000 n Proof : Since every path from source S to any vertex w in the graph always passes through the source vertex, hence the source … 0000009891 00000 n That information, along with your comments, will be governed by 0000008342 00000 n 0000004187 00000 n Except for start, the immediate dominators are the parents of their start.
Catalan / Català n ≠ s0) must be initialized to hold all the nodes in the graph, because each assignment D[n]← {n}∪… makes D[n] smaller (or unchanged), not larger. 0000015553 00000 n 0000021043 00000 n Software Practice & Experience, 4:110, 2001. 0000017582 00000 n 0000018814 00000 n Greek / Ελληνικά Immediate dominators • Parent of node b in tree, if it exists, is called the immediate dominator of b –written as idom(b) –idom not defined for START • Intuitively, all dominators of b other than b itself dominate idom(b) –In our example, idom(c) = a 910 11 12 This is called the dominator tree. can keep track of the immediate dominator If so, it can also create the necessary Φ nodes during translation .
0000020550 00000 n Immediate dominator An object is described as an immediate dominator if it is the dominator that is closest to a target object. 0000072158 00000 n Polish / polski
This is called the dominator tree. The notion of dominators is useful for that purpose. 0000017870 00000 n Immediate Dominator : A node u is said to be an immediate dominator of a node w (denoted as idom(w)) if u dominates w and every other dominator of w dominates u. Theorem-1: Every vertex of the directed graph, except the source S,will have at-least one dominator. Notes. Figure 18.5a illustrates a problem: If we want to insert statement s into a basic block immediately before the loop, we need to put s at the end of blocks 2 and 3. English / English Except for start, the immediate dominators are the parents of their corresponding nodes in the dominator tree.
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Bosnian / Bosanski 0000019187 00000 n A dict containing the immediate dominators of each node reachable from 0000011215 00000 n t1�{vn�i ��``j� U� ` ��% endstream endobj 153 0 obj 479 endobj 98 0 obj << /Type /Page /Parent 90 0 R /Resources << /Font << /F1 104 0 R /F3 105 0 R /F5 121 0 R /F4 101 0 R /F6 127 0 R /F2 109 0 R /F19 131 0 R >> /ExtGState << /R17 141 0 R /R6 148 0 R /R19 151 0 R >> /XObject << /Im14 135 0 R >> /ProcSet [ /PDF /Text /ImageC ] >> /Contents [ 111 0 R 113 0 R 115 0 R 122 0 R 129 0 R 133 0 R 136 0 R 144 0 R ] /Thumb 73 0 R /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 /LastModified (D:20050125124851) >> endobj 99 0 obj << /Filter /FlateDecode /Length 569 /Subtype /Type1C >> stream Single-vertex dominators can be found in time linear in the number of vertices of the graph [7, 8, 9]. 0000016216 00000 n Just to have a place to put nodes not in any loop, we could say that the entire procedure body is a pseudo-loop that sits at the root of the loop-nest tree. Arabic / عربية 0000072235 00000 n 0000033968 00000 n The procedure is, for a flow graph G: Find all the natural loops, and thus all the loop-header nodes. Immediate dominator: idom(w) ... Iterative Algorithm: Example process 4 i 2 h 7 a 11 iteration = 3 b 12 g 4 e 8 DONE!
Danish / Dansk In order to have one place to put such statements, we insert a new, initially empty, preheader node p outside the loop, with an edge p → h. All edges x → h from nodes x inside the loop are left unchanged, but all existing edges y → h from nodes y outside the loop are redirected to point to p. Dominator tree This view is built from the object graph.
We say that loop B is nested within A, orthat B is the inner loop. 0000012589 00000 n 0000072462 00000 n Figure 18.3 shows a flow graph and its dominator tree. Spanish / Español It is more common that a vertex is dominated by a set of vertices. If we merge all the loops with header 2 in Figure 18.3a, we obtain the loop 2, 3, 4 - which is not a natural loop. Hungarian / Magyar
0000072185 00000 n
Kazakh / Қазақша called the immediate dominator of b written as idomb idom not defined for START from CS 380C at University of Texas H�D�KLa����� }Hq4���,���� ���7�`�X�@�[c��i@y��N�q!l�D�>7$�5.�*���^B"ij;��|�RRb �Rk���l{�Q_��{l'`��jK�Ö�B�/���m��U핃(=w�7t{t��f_H���MM Bˀ8��:zC}�@oH7A�{(�/�F넖`P��,F�8"��������a�$9M��S�L��l�3����k� ��B�B�|0�>�eijl�a8n�E�uB�h;T��yiJv�$����. 83 0 obj <>/Filter/FlateDecode/ID[<096ACAD2A276B7449509F935DF02D447>]/Index[62 34]/Info 61 0 R/Length 100/Prev 286787/Root 63 0 R/Size 96/Type/XRef/W[1 2 1]>>stream 0000040674 00000 n 0000005321 00000 n 0000002203 00000 n Thai / ภาษาไทย Each control-flow graph must have a start node s0 with no predecessors, where program (or procedure) execution is assumed to begin. We can construct a loop-nest tree of loops in a program. Portuguese/Portugal / Português/Portugal 0000006561 00000 n DISQUS terms of service.
IBM Knowledge Center uses JavaScript. Many loop optimizations will insert statements immediately before the loop executes. 62 0 obj <> endobj 95 0 obj <>stream %PDF-1.6 %����
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