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 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 ${\displaystyle S1\ \delta ^{c}\ S2}${\displaystyle 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 ${\displaystyle S1\in PDF(S2)}${\displaystyle S1\in PDF(S2)} where ${\displaystyle PDF(S)}${\displaystyle PDF(S)} is the post dominance frontier of statement ${\displaystyle S}${\displaystyle 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.

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

A statement S2 is flow dependent on S1 (written ${\displaystyle S1\ \delta ^{f}\ S2}${\displaystyle 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

A statement S2 is antidependent on S1 (written ${\displaystyle S1\ \delta ^{a}\ S2}${\displaystyle 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.

A statement S2 is output dependent on S1 (written ${\displaystyle S1\ \delta ^{o}\ S2}${\displaystyle 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.

A statement S2 is input dependent on S1 (written ${\displaystyle S1\ \delta ^{i}\ S2}${\displaystyle 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.

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.

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

• 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.

• Static program analysis