Loops in flow
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This document discusses loops in flow graphs. It defines dominators and uses them to define natural loops and inner loops. It explains how to build a dominator tree and find natural loops given a back edge. Reducible flow graphs are introduced as graphs that can be partitioned into forward and back edges such that the forward edges form an acyclic subgraph, allowing certain loop transformations. Examples of natural inner and outer loops are provided. Pre-headers, which are added to loops to facilitate transformations, are also discussed.
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Loops in flow
- 1. LOOPS IN FLOW GRAPHS BP150511 R. RAMYA
- 2. LOOPS IN FLOW GRAPHS We shall use the notion of a node “Dominating” another to define “Natural Loop” and the important special class of “Reducible” of flow graphs. An algorithm for finding dominators and checking reducibility of flow graphs.
- 3. i. Dominators ii. Natural loops iii. Inner loops iv. Pre-Headers v. Reducible flow graphs
- 4. DOMINATORS d dom n – Node d of a CFG dominates node n if every path from the initial node of the CFG to n goes through d– The loop entry dominates all nodes in the loop The immediate dominator m of a node n is the last dominator on the path from the initial node to n – If d ≠ n and d dom n then d dom m
- 6. Build a dominator tree as follows: – Root is CFG entry node n0 – m is child of node n iff n=Idom (m)
- 7. NATURAL LOOPS A back edge is is an edge a → b whose head b dominates its tail a Given a back edge n → d 1. The natural loop consists of d plus the nodes that can reach n without going through d 2. The loop header is node d • Unless two loops have the same header, they are disjoint or one is nested within the other – A nested loop is an inner loop if it contains no other loops
- 9. NATURAL INNER LOOPS EXAMPLE
- 10. NATURAL OUTER LOOPS EXAMPLE
- 11. PRE-HEADERS To facilitate loop transformations, a compiler often adds a pre-header to a loop • Code motion, strength reduction, and other loop transformations populate the pre-header
- 13. REDUCIBLE FLOW GRAPHS Reducible graph = disjoint partition in forward and back edges such that the forward edges form an acyclic (sub)graph.
- 15. VIDEO video1
- 16. THANKYOU