Discussion
Consider the control flow graph given below.
Which one of the following options is the set of live variables at the exit point of each basic block?
Answer: A
The live variables at block exits are B1:{a, b, c, e, f}, B2:{d, e}, B3:{b, c, e, f}, B4:∅.
Liveness flows backwards: OUT(B) is the union of IN over B's successors, and IN(B) = USE(B) ∪ (OUT(B) - DEF(B)). The edges are B1 → B2, B1 → B3, B3 → B1 and B2 → B4.
- B4 (g = d + e) leads to EXIT, and g is never used: OUT(B4) = ∅, IN(B4) = {d, e}.
- B2 (d = a + e): OUT(B2) = IN(B4) = {d, e}; IN(B2) = {a, e}.
- B1 (a = b + c) and B3 (e = a + f) form a loop. Iterating to a fixed point: IN(B1) = {b, c, e, f} and IN(B3) = {a, b, c, f}.
- OUT(B1) = IN(B2) ∪ IN(B3) = {a, b, c, e, f}; OUT(B3) = IN(B1) = {b, c, e, f}.
The options with B1:∅ ignore that a is used in both successors of B1. The option with B3:{c, e, f} drops b, which is live because B1, reached from B3, uses it.
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