Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Control Flow Analysis: Identifying Loops and Dominators in Compiler Construction - Prof. R, Study notes of Computer Science

University of California-RiversideComputer Science
Prof. Rajiv Gupta

The concepts of control flow analysis, specifically identifying loops and dominators in compiler construction. It covers the definitions, properties, and algorithms for finding loops and dominators, as well as the characteristics of dominator information and the dominator tree. The document also explains how to compute dominator sets and construct natural loops.

Typology: Study notes

Pre 2010

Uploaded on 03/28/2010

koofers-user-c9b
koofers-user-c9b 🇺🇸

9 documents

1 / 10

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
3/30/09
1
1
CS 201
Compiler Construction
Lecture 2
Control Flow Analysis
2
What is a loop ?
A subgraph of CFG with the following properties:
– Strongly Connected: there is a path from any node in the
loop to any other node in the loop; and
– Single Entry: there is a single entry into the loop from
outside the loop. The entry node of the loop is called the
loop header.
Loop nodes: 2, 3, 5
Header node: 2
Loop back edge: 52
TailHead
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Control Flow Analysis: Identifying Loops and Dominators in Compiler Construction - Prof. R and more Study notes Computer Science in PDF only on Docsity!

1

CS 201

Compiler Construction

Lecture 2 Control Flow Analysis 2 What is a loop? A subgraph of CFG with the following properties:

  • Strongly Connected: there is a path from any node in the loop to any other node in the loop; and
  • Single Entry: there is a single entry into the loop from outside the loop. The entry node of the loop is called the loop header. Loop nodes: 2, 3, 5 Header node: 2 Loop back edge: 5 2 TailHead

3 Property Given two loops: they are either disjoint or one is completely nested within the other. Loops {1,2,4} and {5,6} are Disjoint. Loop {5,6} is nested within loop {2,4,5,6}. Loop {5,6} is nested within loop {2,3,4,5,6}. Identifying Loops

Definitions:

Dominates: node n dominates node m iff

all paths from start node to node m pass

through node n, i.e. to visit node m we must

first visit node n.

A Natural Loop has

  • A single entry  the entry node dominates all nodes in the loop; and
  • A back edge, and edge AB such that B dominates A. B is the head & A is the tail. 4

Dominators: Characteristics

  1. Dominator information can be represented by a Dominator Tree. Edges in the dominator tree represent immediate dominator relationships. 7 1 is the immediate dominator of 2, 3 & 4 CFG Dominator Tree

Computing Dominator Sets

Observation: node m donimates node n iff m dominates all predecessors of n. 8 Let D(n) = set of dominators of n Where Pred(n) is set of immediate predecessors of n in the CFG

Computing Dominator Sets 9 Initial Approximation: D(no) = {no} no is the start node. D(n) = N, for all n!=no N is set of all nodes. Iteratively Refine D(n)’s: Algorithm: Example: Computing Dom. Sets 10

D(1) = {1}

D(2) = {2} U D(1) = {1,2}

D(3) = {3} U D(1) = {1,3}

D(4) = {4} U (D(2) D(3) D(9)) = {1,4}

D(5) = {5} U (D(4) D(10)) = {1,4,5}

D(6) = {6} U (D(5) D(7)) = {1,4,5,6}

D(7) = {7} U D(5) = {1,4,5,7}

D(8) = {8} U (D(6) D(10)) = {1,4,5,6,8}

D( 9 ) = {9} U D(8) = {1, 4 ,5,6,8,9}

D( 10 )= {10} U D(8) = {1,4, 5 ,6, 8 ,10}

Back Edges: 94, 108, 10 5

Example

Back Edge 7 2

13 Loop = {2,7} + {6} + {4} + {5} + {3} Stack = 7 6 4 5 3

D

N

Examples 14

L2  B, S

L1  A,S1,B,S

L2 nested in L L1  S1,S2,S3,S L2  S2,S3,S L2 nested in L While A do S While B do S Endwhile Endwhile ?

Reducible Flow Graph

The edges of a reducible flow graph can be

partitioned into two disjoint sets:

  • Forward – from an acyclic graph in which

every node can be reached from the initial

node.

  • Back – edges whose heads (sink) dominate

tails (source).

Any flow graph that cannot be partitioned as

above is a non-reducible or irreducible.

15 Reducible Flow Graph

How to check reducibility?

  • Remove all back edges and see if the resulting graph is acyclic. Reducible^16 Irreducible 2 3 not a back edge 3 2 not a back edge graph is not acyclic Node Splitting Converts irreducible to reducible

Example 19

CFG DFST

Depth First Ordering Back edge Forward edge