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Module 15: Reaching Definition
Lecture 29: Reaching Definition
The Lecture Contains:
Reaching Definition
Taxonomy of Dataflow Problems
Techniques
Four Kinds of Dataflow Problems
A Lattice L Consists of
Properties of Lattices
Example
Flow Functions For The Flow–graph in The Example
Iterative (forward) Data-flow Analysis
Control Tree Based Data-Flow Analysis
If-then Construct
If-then-else Construct
While Loop
Improper Region
Module 15: Reaching Definition
Lecture 29: Reaching Definition
Reaching Definition
Definition: Assignment of a value to a variable A definition d of a variable reaches a point p if there is a path from d to p and value of a variable is same as assigned at d Use iterative forward bit vector problem A bit vector of a 8 bit can be used to represent all the definition Initial condition in(entry) = = 00000000 in(i) = = 00000000 for all nodes i If an instruction re-defines a variable then it is killed
Gen: Definitions generated in a basic block and not subsequently killed in it gen(B1) = 1, 2, 3 = 11100000 gen(B3) = 4 = 00010000 gen(B6) = 5, 6, 7, 8 = 00001111 gen(i) = = 00000000 for i 6= B1, B3, B
Out: Definitions which reach at the end of a basic block out(i) = = 00000000 for all i A definition reaches end of a basic block iff either
It is generated in the basic block OR It reaches in and is preserved
Module 15: Reaching Definition
Lecture 29: Reaching Definition
A Lattice L Consists of
A set of values ’Meet’ operator ’Join’ operator
Properties of Lattices
such that (closure)
(Commutative)
and (associate)
and (distributive)
It has two unique element top and bottom Such that
Forward Reaching Definition Analysis
Elements are bit vectors Meet is bitwise and Join is bitwise or Bottom is 0 n^ and top is 1 n BV n^ denotes lattice of n bits for example BV 3 is
Module 15: Reaching Definition
Lecture 29: Reaching Definition
Example
A function f mapping a lattice to itself f:L → L is monotonic if for all x, y
for example f : BV 3 → BV 3 defined as f : (x 1 , x 2 , x 3 ) → (x 1 , 1, x 3 ) is monotonic Height: it is the length of the longest ascending chain such that there exists x 1 , x 2 ,... , x (^) n such that
Monotonicity and finite height ensure that the data-flow algorithms implementing function f terminate flow function maps lattice to lattice. Flow function for B 1 is given as
Let F (^) B () be the flow function representing flow through block B and F (^) p represent the composition of the flow functions encountered in following path p then
Module 15: Reaching Definition
Lecture 29: Reaching Definition
First Pass
If we do not distinguish between and then
Second Pass
in(if) = in(if-then) in(then) = (in(if))
If we do not distinguish between the true and the false parts
in(if) = in(if-then) in(then) = (in(if))
If-then-else Construct
First Pass
-then –else = (F then ) (F else o )
Second Pass
in(if) = in(if-then-else) in(then) = (in(if)) in(else) = (in(if))
Module 15: Reaching Definition
Lecture 29: Reaching Definition
While Loop
First Pass
Second Pass
in(while) = (in(while-loop)) in(body) = (in(while))
If we do not distinguish between and^ then
In(while) = (in while- loop)) In(body) = (in (while))
file:///D|/...ry,%20Dr.%20Sanjeev%20K%20Aggrwal%20&%20Dr.%20Rajat%20Moona/Multi-core_Architecture/lecture%2029/29_10.htm[6/14/2012 12:09:58 PM]
Module 15: Reaching Definition
Lecture 29: Reaching Definition
Example
Consider the flow graph in an earlier slide and its structural flow analysis
First Pass
Second Pass
For entrya block
file:///D|/...ry,%20Dr.%20Sanjeev%20K%20Aggrwal%20&%20Dr.%20Rajat%20Moona/Multi-core_Architecture/lecture%2029/29_10.htm[6/14/2012 12:09:58 PM]
For if-then else block
