Dobinski's formula

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 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
• Vectorization (parallel computing)
• Loop dependence analysis
• Frameworks supporting the polyhedral model

Further reading

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534