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Worklist Algorithm - Advanced Compiler - Lecture Slides , Slides of Computer Science

University of AllahabadComputer Science

These are the Lecture Slides of Advanced Compiler which includes Partial Transfer Functions, Input Information, Output Information, Data-Based Context Sensitivity, Bottom-Up Example, Infinite Domains, Interprocedural Analysis etc. Key important points are: Worklist Algorithm, Remove Node, Issues with Worklist Algorithm, Algorithm Terminate, Original Nodes, Order of Nodes, Topological Order, Reverse Depth First Order, Structure of Domain

Typology: Slides

2012/2013

Uploaded on 03/19/2013

dharmaa
dharmaa 🇮🇳

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Worklist algorithm
•Initialize all di to the empty set
•Store all nodes onto a worklist
•while worklist is not empty:
–remove node n from worklist
–apply flow function for node n
–update the appropriate di, and add nodes whose
inputs have changed back onto worklist
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Download Worklist Algorithm - Advanced Compiler - Lecture Slides and more Slides Computer Science in PDF only on Docsity!

Worklist algorithm

  • Initialize all d (^) i to the empty set
  • Store all nodes onto a worklist
  • while worklist is not empty:
    • remove node n from worklist
    • apply flow function for node n
    • update the appropriate di, and add nodes whose inputs have changed back onto worklist

Worklist algorithm

let m: map from edge to computed value at edge let worklist: work list of nodes

for each edge e in CFG do m(e) := ;

for each node n do worklist.add(n)

while (worklist.empty.not) do let n := worklist.remove_any; let info_in := m(n.incoming_edges); let info_out := F(n, info_in); for i := 0 .. info_out.length-1 do if (m(n.outgoing_edges[i]) ≠ info_out[i]) m(n.outgoing_edges[i]) := info_out[i]; worklist.add(n.outgoing_edges[i].dst);

Two issues with worklist algorithm

  • Ordering
    • In what order should the original nodes be added to the worklist?
    • What order should nodes be removed from the worklist?
  • Does this algorithm terminate?

Order of nodes

  • Topological order assuming back-edges have

been removed

  • Reverse depth first order
  • Use an ordered worklist

Termination

  • Why is termination important?
  • Can we stop the algorithm in the middle and

just say we’re done...

  • No: we need to run it to completion,

otherwise the results are not safe...

Termination

  • Assuming we’re doing reaching defs, let’s try

to guarantee that the worklist loop

terminates, regardless of what the flow

function F does while (worklist.empty.not) do

let n := worklist.remove_any; let info_in := m(n.incoming_edges); let info_out := F(n, info_in); for i := 0 .. info_out.length-1 do if (m(n.outgoing_edges[i]) ≠ info_out[i]) m(n.outgoing_edges[i]) := info_out[i]; worklist.add(n.outgoing_edges[i].dst);

Structure of the domain

  • We’re using the structure of the domain

outside of the flow functions

  • In general, it’s useful to have a framework that

formalizes this structure

  • We will use lattices

Background material

Relations

  • A relation over a set S is a set R μ S £ S
    • We write a R b for (a,b) 2 R
  • A relation R is:
    • reflexive iff 8 a 2 S. a R a
    • transitive iff 8 a 2 S, b 2 S, c 2 S. a R b Æb R c ) a R c
    • symmetric iff 8 a, b 2 S. a R b ) b R a
    • anti-symmetric iff 8 a, b, 2 S. a R b ) : (b R a) 8 a, b, 2 S. a R b Æb R a ) a = b

Partial orders

  • An equivalence class is a relation that is:
  • A partial order is a relation that is:

Lub and glb

  • Given a poset (S, · ), and two elements a 2 S

and b 2 S, then the:

  • least upper bound (lub) is an element c such that a · c, b · c, and 8 d 2 S. (a · d Æb · d) ) c · d
  • greatest lower bound (glb) is an element c such that c · a, c · b, and 8 d 2 S. (d · a Æd · b) ) d · c

Lub and glb

  • Given a poset (S, · ), and two elements a 2 S

and b 2 S, then the:

  • least upper bound (lub) is an element c such that a · c, b · c, and 8 d 2 S. (a · d Æb · d) ) c · d
  • greatest lower bound (glb) is an element c such that c · a, c · b, and 8 d 2 S. (d · a Æd · b) ) d · c
  • lub and glb don’t always exists:

Lattices

  • A lattice is a tuple (S, v ,? , > , t , u) such that:
    • (S, v ) is a poset
    • 8 a 2 S.? v a
    • 8 a 2 S. a v >
    • Every two elements from S have a lub and a glb
    • t is the least upper bound operator, called a join
    • u is the greatest lower bound operator, called a meet

Examples of lattices

  • Powerset lattice