World Library  
Flag as Inappropriate
Email this Article

Live variable analysis

Article Id: WHEBN0004051356
Reproduction Date:

Title: Live variable analysis  
Author: World Heritage Encyclopedia
Language: English
Subject: Data-flow analysis, Dead code, Compiler construction
Publisher: World Heritage Encyclopedia

Live variable analysis

In compiler theory, live variable analysis (or simply liveness analysis) is a classic data-flow analysis performed by compilers to calculate for each program point the variables that may be potentially read before their next write, that is, the variables that are live at the exit from each program point.

Stated simply: a variable is live if it holds a value that may be needed in the future.

It is a "backwards may" analysis. The analysis is done in a backwards order, and the dataflow confluence operator is set union.

L1: b := 3;
L2: c := 5;
L3: a := f(b + c);
goto L1;

The set of live variables at line L3 is {b, c} because both are used in the addition, and thereby the call to f and assignment to a. But the set of live variables at line L1 is only {b} since variable c is updated in L2. The value of variable a is never used. Note that f may be stateful, so the never-live assignment to a can be eliminated, but there is insufficient information to rule on the entirety of L3.

The dataflow equations used for a given basic block s and exiting block f in live variable analysis are the following:

{\mbox{GEN}}[s] : The set of variables that are used in s before any assignment.
{\mbox{KILL}}[s] : The set of variables that are assigned a value in s (in many books, KILL (s) is also defined as the set of variables assigned a value in s before any use, but this doesn't change the solution of the dataflow equation):

{\mbox{LIVE}}_{in}[s] = {\mbox{GEN}}[s] \cup ({\mbox{LIVE}}_{out}[s] - {\mbox{KILL}}[s])
{\mbox{LIVE}}_{out}[final] = {\emptyset}
{\mbox{LIVE}}_{out}[s] = \bigcup_{p \in succ[S]} {\mbox{LIVE}}_{in}[p]
{\mbox{GEN}}[d : y \leftarrow f(x_1,\cdots,x_n)] = \{x_1,...,x_n\}
{\mbox{KILL}}[d : y \leftarrow f(x_1,\cdots,x_n)] = \{y\}

The in-state of a block is the set of variables that are live at the start of the block. Its out-state is the set of variables that are live at the end of it. The out-state is the union of the in-states of the block's successors. The transfer function of a statement is applied by making the variables that are written dead, then making the variables that are read live.

// in: {}
b1: a = 3; 
    b = 5;
    d = 4;
    x = 100; //x is never being used later thus not in the out set {a,b,d}
    if a > b then
// out: {a,b,d}    //union of all (in) successors of b1 => b2: {a,b}, and b3:{b,d}  

// in: {a,b}
b2: c = a + b;
    d = 2;
// out: {b,d}

// in: {b,d}
b3: endif
    c = 4;
    return b * d + c;
// out:{}

The in-state of b3 only contains b and d, since c has been written. The out-state of b1 is the union of the in-states of b2 and b3. The definition of c in b2 can be removed, since c is not live immediately after the statement.

Solving the data flow equations starts with initializing all in-states and out-states to the empty set. The work list is initialized by inserting the exit point (b3) in the work list (typical for backward flow). Its computed in-state differs from the previous one, so its predecessors b1 and b2 are inserted and the process continues. The progress is summarized in the table below.

processing out-state old in-state new in-state work list
b3 {} {} {b,d} (b1,b2)
b1 {b,d} {} {} (b2)
b2 {b,d} {} {a,b} (b1)
b1 {a,b,d} {} {} ()

Note that b1 was entered in the list before b2, which forced processing b1 twice (b1 was re-entered as predecessor of b2). Inserting b2 before b1 would have allowed earlier completion.

Initializing with the empty set is an optimistic initialization: all variables start out as dead. Note that the out-states cannot shrink from one iteration to the next, although the out-state can be smaller than the in-state. This can be seen from the fact that after the first iteration the out-state can only change by a change of the in-state. Since the in-state starts as the empty set, it can only grow in further iterations. Recently as of 2006, various program analyses such as live variable analysis have been solved using Datalog. The Datalog specifications for such analyses are generally an order of magnitude shorter than their imperative counterparts (e.g. iterative analysis), and are at least as efficient.[1]


  1. ^ Whaley (2004). Using Datalog with Binary Decision Diagrams for Program Analysis. 
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.