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GO Classes DPP | COMPILER|LIVE VARIABLE ANALYSIS

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Consider the following basic block of Three-Address Code:

1. a = 1
2. b = a + 1
3. c = a + b
4. a = c + b
5. return a

A variable is live at a point if its current value will be used in the future before being redefined. Assuming only the variable $\mathrm{a}$ is live at the exit of this block, which variables are live immediately after statement $2$ has executed?

  1. $\{\mathrm{a, b}\}$
     
  2. $\{\mathrm{b, c}\}$
     
  3. $\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$
     
  4. $\{\mathrm{a, c}\}$

1 Answer

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After 5: $\{\mathrm{a}\}$ is live (given).

After 4: To compute $\mathrm{a=c+b}$, we need $\mathrm{c}$ and $\mathrm{b}$. So $\{\mathrm{c}, \mathrm{b}\}$ are live.

After 3: To compute $\mathrm{c}=\mathrm{a}+\mathrm{b}$, we need $\mathrm{a}$ and $\mathrm{b}$. However, $\mathrm{b}$ is also needed for the later instruction (line 4). So $\{\mathrm{a}, \mathrm{b}\}$ are live.

Immediately after statement 2, we need both $\mathrm{a}$ and $\mathrm{b}$ to satisfy the requirements of statements 3 and 4 .

The live set is $\{\mathrm{a}, \mathrm{b}\}$.
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