Live-variable analysis: Difference between revisions

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a = f(b * c)

The set of live variables between lines two2 and three3 is {<code>b</code>, <code>c</code>} because both are used in the multiplication on line 3. But the set of live variables after line {{code|L1}}1 is only {<code>b</code>}, since variable <code>c</code> is updated later, inon {{code|L2}}line 2. The value of variable <code>a</code> is not used in this code.

Note that <code>f</code>the mayassignment have side effects (printingto <code>b * ca</code>, perhaps),may sobe theeliminated assignment toas <code>a</code> mayis benot eliminatedused later, but there is insufficient information to justify removing all of line 3 as <code>L3f</code> may have [[Side effect (computer science)|side effects]] (printing <code>b * c</code>, perhaps).

== Expression in terms of dataflow equations ==

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Liveness analysis is a "backwards may" analysis. The analysis is done in a [[Data-flow_analysis#Backward_Analysis|backwards]] order, and the dataflow [[confluence operator]] is [[set union]]. In other words, if applying liveness analysis to a function with a particular number of logical branches within it, the analysis is performed starting from the end of the function working towards the beginning (hence "backwards"), and a variable is considered live if any of the branches moving forward within the function might potentially (hence "may") need the variable's current value. This is in contrast to a "backwards must" analysis which would instead enforce this condition on all branches moving forward.

The dataflow equations used for a given basic block ''<math>s''</math> and exiting block ''f''<math>\mathit{final}</math> in live variable analysis are the following:

:<math>

{\mbox{GEN}}[s] </math>: The set of variables that are used in s before any assignment in the same basic block.

:<math>

{\mbox{KILL}}[s] </math>: The set of variables that are assigned a value in s (in many books{{Clarify|date=May 2015}}that discuss compiler design, KILL (s) is also defined as the set of variables assigned a value in s ''before any use'', but this does not change the solution of the dataflow equation):

:<math>

{\mbox{LIVE}}_{\mathrm{in}}[s] = {\mbox{GEN}}[s] \cup ({\mbox{LIVE}}_{\mathrm{out}}[s] - {\mbox{KILL}}[s])

</math>

:<math>

{\mbox{LIVE}}_{\mathrm{out}}[\mathit{final}] = {\emptyset}

</math>

:<math>

{\mbox{LIVE}}_{\mathrm{out}}[s] = \bigcup_{p \in \mathrm{succ}[Ss]} {\mbox{LIVE}}_{\mathrm{in}}[p]

</math>

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{|

|

// in: {}; predecessor blocks: none

b1: a = 3;

b = 5;

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// out: {a,b,d} //union of all (in) successors of b1 => b2: {a,b}, and b3:{b,d}

// in: {a,b}; predecessor blocks: b1

b2: c = a + b;

d = 2;

// out: {b,d}

// in: {b,d}; predecessor blocks: b1 and b2

b3: endif

c = 4;

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==References==

{{reflist|30em}}

{{cite book|last1=Aho|first1=Alfred|last2=Lam|first2=Monica|last3=Sethi|first3=Ravi|last4=Ullman|first4=Jeffrey|year=2007|edition=2|title=Compilers: Principles, Techniques, and Tools|page=608}}

{{Compiler optimizations}}

[[Category:Compiler optimizations]]