Dependence analysis

In compiler theory, dependence analysis produces execution-order constraints between statements/instructions. Broadly speaking, a statement S2 depends on S1 if S1 must be executed before S2. Broadly, there are two classes of dependencies--control dependencies and data dependencies.

Dependence analysis determines whether it is safe to reorder or parallelize statements.

Control dependencies

Control dependency is a situation in which a program instruction executes if the previous instruction evaluates in a way that allows its execution.

A statement S2 is control dependent on S1 (written $S1\ \delta ^{c}\ S2$ ) if and only if S2's execution is conditionally guarded by S1. S2 is control dependent on S1 if and only if $S1\in PDF(S2)$ where $PDF(S)$ is the post dominance frontier of statement $S$ . The following is an example of such a control dependence:

S1       if x > 2 goto L1
S2       y := 3   
S3   L1: z := y   1

Here, S2 only runs if the predicate in S1 is false.

Data dependencies

A data dependence arises from two statements which access or modify the same resource.

Flow(True) dependence

A statement S2 is flow dependent on S1 (written $S1\ \delta ^{f}\ S2$ ) if and only if S1 modifies a resource that S2 reads and S1 precedes S2 in execution. The following is an example of a flow dependence (RAW: Read After Write):

S1       x := 10
S2       y := x   c

Antidependence

A statement S2 is antidependent on S1 (written $S1\ \delta ^{a}\ S2$ ) if and only if S2 modifies a resource that S1 reads and S1 precedes S2 in execution. The following is an example of an antidependence (WAR: Write After Read):

S1       x := y   c
S2       y := 10

Here, S2 sets the value of y but S1 reads a prior value of y.

Output dependence

A statement S2 is output dependent on S1 (written $S1\ \delta ^{o}\ S2$ ) if and only if S1 and S2 modify the same resource and S1 precedes S2 in execution. The following is an example of an output dependence (WAW: Write After Write):

S1       x := 10
S2       x := 20

Here, S2 and S1 both set the variable x.

Input dependence

A statement S2 is input dependent on S1 (written $S1\ \delta ^{i}\ S2$ ) if and only if S1 and S2 read the same resource and S1 precedes S2 in execution. The following is an example of an input dependence (RAR: Read-After-Read):

S1       y := x   3
S2       z := x   5

Here, S2 and S1 both access the variable x. This dependence does not prohibit reordering.

Loop dependencies

The problem of computing dependencies within loops, which is a significant and nontrivial problem, is tackled by loop dependence analysis, which extends the dependence framework given here.