Analysis
Important Dependence for Optimization
Instruction scheduling Data-cache optimization
Software engineering
Program understanding Reverse engineering Debugging
Various kinds of dependences Data related Control related
Data-Dependence Graph
A data-dependence graph has one node for every variable (basic block) and one edge representing the flow of data between the two nodes Different types of data dependence
Flow: def to use Anti: use to def Output: def to def Input: use to use B2
X = 1 Z > 2 entry
Z > 1 B1 X = 2 B4
Further classifiable as
Loop-carried: requires iterations Loop-independent: occurs anyway
B3
Y = X + 1
B5
Z = X 3 X = 4
B6
exit
Z = X + 7
1
Data-Dependence Graph
entry entry
Z > 1 B1 X = 1 Z > 2 X = 2 B4 X = 1 Z > 2
Z > 1 B1 X = 2 B4
B2
B2
Z = X 3 X = 4
B3
Y = X + 1
B5
B3
Y = X + 1
B5
Z = X 3 X = 4
B6
exit
Z = X + 7
B6
exit
Z = X + 7
Data-Dependence Graph
entry entry
Z > 1 B1 X = 1 Z > 2 X = 2 B4 X = 1 Z > 2
Z > 1 B1 X = 2 B4
B2
X
X B5
Z = X 3 X = 4
B2
X B3
Y = X + 1
B3
Y = X + 1
B5
Z = X 3 X = 4
X B6
exit Z = X + 7
B6
exit
Z = X + 7
2
Data-Dependence Graph
entry entry
Z Z
Z > 1 B1 Z > 1 B1 X = 2 B4 X = 1 Z > 2 X = 2 B4
B2
X = 1 Z > 2
Z X
Y
X B5
Z = X 3 X = 4
B2
X B3
X
Y = X + 1
B3
Y = X + 1
B5
Z = X 3 X = 4
X Y B6
exit
X B6
exit Z = X + 7
Z = X + 7
Z
Control-Dependence Analysis
Intuition
A statement S1 is control dependent on a statement S2 if the outcome of S2 directly determines whether S1 may not be reached What are the control dependences for each statement in the CFG on the right? entry Z > 1 B1
T
X = 1
F
X = 2 B4
B2 Z > 2 T B3 Y = X + 1
F
Z = X 3
B5 X = 4 B6 Z = X + 7
exit
3
Control-Dependence Analysis
Intuition
A statement S1 is control dependent on a statement S2 if the outcome of S2 directly determines whether S1 may not be reached What are the control dependences for each statement in the CFG on the right?
entry, B1, exit entering code B2 B1T B3 B2T B4 B1F B5 B2F, B1F B6 B2F, B1F
entry Z > 1 B1
T
X = 1
F
X = 2 B4
B2 Z > 2 T B3 Y = X + 1
F
Z = X 3
B5 X = 4 B6 Z = X + 7
exit
Control-Dependence Analysis
Definition Let G be a CFG, with X and Y nodes in G. Y is controldependent on X iff
1. There exists a path P from X to Y with any Z in P (excluding X and Y) postdominated by Y and 2. X is not postdominated by Y (there are two edges out of X; traversing one edges always leads to Y, the other may not lead to Y) entry Z > 1 B1
T
X = 1
F
X = 2 B4
B2 Z > 2 T B3 Y = X + 1
F
Z = X 3
B5 X = 4 B6 Z = X + 7
exit
4
Computing CD Using FOW
1. Construct basic CDG 2. Add region nodes
Computing CD Using FOW
Augment the CFG by adding a node Start with edge (Start, entry) labeled "T" and edge (Start, exit) labeled "F"; call this AugCFG
AugCFG T
En
T
2
1
F
4
Start
T
3
F
F
5
6 Ex
5
Computing CD Using FOW
Construct the postdominator tree for AugCFG
AugCFG T
En
T
2
1
F
4
Start
T
3
F
F
5
6 Ex
Computing CD Using FOW
Construct the postdominator tree for AugCFG
Pdom Tree
Start 2 Ex
3
6
1
5
En
4
6
Computing CD Using FOW
Consider set S of edges (m, n) in AugCFG such that n does not postdominate m For AugCFG S consists of:
AugCFG T
En
T
2
1
F
4
Pdom Tree
Start 2
Ex
Start
6 1
T
3
F
3
F
5
5
En Ex
6
4
Computing CD Using FOW
Consider set S of edges (m, n) in AugCFG such that n does not postdominate m For AugCFG S consists of: (Start, En) (1,2) (1,4) (2,3) (2,5)
AugCFG T
En
T
2
1
F
4
Start
T
3
F
F
5
6 Ex
7
Computing CD Using FOW
Consider, for each edge (A,B) in S, those nodes in the Pdom tree from to B least common ancestor L of A and B
Including L if L is A Excluding L if L is not A Pdom Tree
Start 2 Ex
3
6
1
5
En
4
Computing CD Using FOW
Consider, for each edge (A,B) in S, those nodes in the Pdom tree from B to least common ancestor L of A and B
Including L if L is A Excluding L if L is not A Pdom Tree
Start 2 Ex
3
6
1
5
En
Edge
Start, En 1, 2 1, 4 2, 3 2, 5
L
Nodes
4
8
Computing CD Using FOW
Consider, for each edge (A,B) in S, those nodes in the Pdom tree from B to least common ancestor L of A and B
Including L if L is A Excluding L if L is not A Pdom Tree
Start 2 Ex
3
6
1
5
En
Edge
Start, En 1, 2 1, 4 2, 3 2, 5
L
Ex Ex Ex Ex Ex
Nodes
En, 1 2 4, 5, 6 3 5, 6 4
All identified nodes are control dependent on A
Computing CD Using FOW
Consider, for each edge (A,B) in S, those nodes in the Pdom tree from B to least common ancestor L of A and B
Including L if L is A Excluding L if L is not A Pdom Tree
Start 2 Ex
3
6
1
5
En
Edge
Start, En 1, 2 1, 4 2, 3 2, 5
L
Ex Ex Ex Ex Ex
Nodes
En, 1 2 4, 5, 6 3 5, 6
CD on
Start, T 1, T 1, F 2, T 2, F 4
All identified nodes are control dependent on A
9
Computing CD Using FOW
Given (A,B), how can you find the set of nodes control dependent on A easily? Why is the set we obtain correct?
Pdom Tree
Start 2 Ex
3
6
1
5
En
Edge
Start, En 1, 2 1, 4 2, 3 2, 5
L
Ex Ex Ex Ex Ex
Nodes
En, 1 2 4, 5, 6 3 5, 6
CD on
Start, T 1, T 1, F 2, T 2, F 4
Computing CD Using FOW
Edge
Start, En 1, 2 1, 4 2, 3 2, 5
L
Ex Ex Ex Ex Ex
Nodes
En, 1 2 4, 5, 6 3 5, 6
CD on
Start, T
Create CDG
T
Start
T T
T
1, T 1, F 2, T 2, F
En 2
1
F F F F F
3
6
5
4
10
Computing CD Using FOW
1. Construct basic CDG 2. Add region nodes
Computing CD Using FOW
Why adding regions? Group nodes with same set of control conditions Only two successors for predicate nodes (=> hierarchical organization)
11
Computing CD Using FOW
Method for adding regions: Consider set CD of control dependence predecessors of each non-region node with more than one unlabeled controldependence predecessor Create region node R for each CD and move edges accordingly
Nodes with control dependence CD connected to R R connected to CD
Computing CD Using FOW
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