1. Machine-Independent Optimizations Ⅳ CS308 Compiler Theory1

2. Loops in Flow Graphs Loops are important because programs spend most of their time executing them Optimizations that improve the performance of loops can have a significant impact. CS308 Compiler Theory2

3. Dominators Say node d of a flow graph dominates node n, written d dom n, if every path from the entry node of the flow graph to n goes through d. Every node dominates itself. Which nodes are dominated by each node? CS308 Compiler Theory3

4. Dominator Tree The entry node is the root Each node d dominates only its descendants in the tree. CS308 Compiler Theory4

5. Finding Dominators CS308 Compiler Theory5

6. Depth-First Ordering The route of the search in a depth-first search forms a depth-first spanning tree (DFST). CS308 Compiler Theory6

7. Depth-First Ordering CS308 Compiler Theory7

8. Edges in a Depth-First Spanning Tree Advancing edges: going from a node m to a proper descendant of m in the tree Retreating edges: going from a node m to an ancestor of m in the tree (possibly to m itself). Cross edges: edges m  n such that neither m nor n is an ancestor of the other in the DFST CS308 Compiler Theory8

9. Back Edges and Reducibility A back edge is an edge a  b whose head b dominates its tail a. For any flow graph, every back edge is retreating, but not every retreating edge is a back edge. A flow graph is said to be reducible if all its retreating edges in any depth-first spanning tree are also back edges. CS308 Compiler Theory9

10. Depth of a Flow Graph Given a depth-first spanning tree for the graph, the depth is the largest number of retreating edges on any cycle-free path. CS308 Compiler Theory10 10  7  4  3 Depth=3

11. Natural Loops A natural loop is defined by two essential properties. 1. It must have a single-entry node, called the header. This entry node dominates all nodes in the loop, or it would not be the sole entry to the loop. 2. There must be a back edge that enters the loop header. Otherwise, it is not possible for the flow of control to return to the header directly from the "loop" ; i.e., there really is no loop. CS308 Compiler Theory11

12. Finding Natural Loops CS308 Compiler Theory12

13. Finding Natural Loops CS308 Compiler Theory13

14. Test yourself Exercise 9.6.1 CS308 Compiler Theory14