This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (January 2024) (Learn how and when to remove this template message)

Control dependency is a situation in which a program instruction executes if the previous instruction evaluates in a way that allows its execution.

An instruction B has a control dependency on a preceding instruction A if the outcome of A determines whether B should be executed or not. In the following example, the instruction has a control dependency on instruction . However, does not depend on because is always executed irrespective of the outcome of .

S1.         if (a == b)
S2.             a = a + b
S3.         b = a + b

Intuitively, there is control dependence between two statements A and B if

A typical example is that there are control dependences between the condition part of an if statement and the statements in its true/false bodies.

A formal definition of control dependence can be presented as follows:

A statement is said to be control dependent on another statement iff

Expressed with the help of (post-)dominance the two conditions are equivalent to

Construction of control dependences

Control dependences are essentially the dominance frontier in the reverse graph of the control-flow graph (CFG).[1] Thus, one way of constructing them, would be to construct the post-dominance frontier of the CFG, and then reversing it to obtain a control dependence graph.

The following is a pseudo-code for constructing the post-dominance frontier:

for each X in a bottom-up traversal of the post-dominator tree do:
    PostDominanceFrontier(X) ← ∅
    for each Y ∈ Predecessors(X) do:
        if immediatePostDominator(Y) ≠ X:
            then PostDominanceFrontier(X) ← PostDominanceFrontier(X) ∪ {Y}
    done
    for each Z ∈ Children(X) do:
        for each Y ∈ PostDominanceFrontier(Z) do:
            if immediatePostDominator(Y) ≠ X:
                then PostDominanceFrontier(X) ← PostDominanceFrontier(X) ∪ {Y}
        done
    done
done

Here, Children(X) is the set of nodes in the CFG that are immediately post-dominated by X, and Predecessors(X) are the set of nodes in the CFG that directly precede X in the CFG. Note that node X shall be processed only after all its Children have been processed. Once the post-dominance frontier map is computed, reversing it will result in a map from the nodes in the CFG to the nodes that have a control dependence on them.

See also

References

  1. ^ Cytron, R.; Ferrante, J.; Rosen, B. K.; Wegman, M. N.; Zadeck, F. K. (1989-01-01). "An efficient method of computing static single assignment form". Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '89. New York, NY, USA: ACM. pp. 25–35. doi:10.1145/75277.75280. ISBN 0897912942. S2CID 8301431.