Dependence analysis

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 S 1   δ c   S 2 ) 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 L1S2 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 S 1   δ f   S 2 ) 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 := 10S2 y := x + c

Antidependence

A statement S2 is antidependent on S1 (written S 1   δ a   S 2 ) 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 + cS2 y := 10

Here, S2 sets the value of y but S1 reads a prior value of y. The term 'antidependece' widely used in literature is a misnomer because 'anti' means opposite. The correct term should be 'ante' means before. Hence the correct word should be antedependence.

Output dependence

A statement S2 is output dependent on S1 (written S 1   δ o   S 2 ) 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 := 10S2 x := 20

Here, S2 and S1 both set the variable x.

Input dependence

A statement S2 is input dependent on S1 (written S 1   δ i   S 2 ) 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 + 3S2 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.