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 [math]\displaystyle{ S1\ \delta^c\ S2 }[/math]) if and only if S2's execution is conditionally guarded by S1. S2 is control dependent on S1 if and only if [math]\displaystyle{ S1 \in PDF(S2) }[/math] where [math]\displaystyle{ PDF(S) }[/math] is the post dominance frontier of statement [math]\displaystyle{ S }[/math]. 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 [math]\displaystyle{ S1\ \delta^f\ S2 }[/math]) 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 [math]\displaystyle{ S1\ \delta^a\ S2 }[/math]) 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 [math]\displaystyle{ S1\ \delta^o\ S2 }[/math]) 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 [math]\displaystyle{ S1\ \delta^i\ S2 }[/math]) 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.

See also

• Program analysis (computer science)
• Automatic parallelization
• Automatic vectorization
• Loop dependence analysis
• Frameworks supporting the polyhedral model
• Hazard (computer architecture)
• Program slicing
• Dead code elimination

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. https://archive.org/details/advancedcompiler00much.