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 or not it is safe to reorder or parallelize statements.

Control dependencies

Control dependence is a situation in which a program’s 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. 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 is not a dependence in the same line as the others, as it does not prohibit reordering instructions. Some compiler optimizations still find this definition useful, however.

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.

See also

• Program analysis (computer science)
• Automatic parallelization
• Vectorization (parallel computing)
• Loop dependence analysis
• Frameworks supporting the polyhedral model

Further reading

• Cooper, Keith D.; & Torczon, Linda. (2005). Engineering a Compiler. Morgan Kaufmann. ISBN 1-55860-698-X. 
• Kennedy, Ken; & Allen, Randy. (2001). Optimizing Compilers for Modern Architectures: A Dependence-based Approach. Morgan Kaufmann. ISBN 1-55860-286-0. 
• Muchnick, Steven S. (1997). Advanced Compiler Design and Implementation. Morgan Kaufmann. ISBN 1-55860-320-4.