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Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 32: Iteration
The Lecture Contains:
Iteration Space
Iteration Vector
Normalized Iteration Vector
Dependence Distance
Direction Vector
Loop Carried Dependence Relations
Dependence Level
Iteration Vector - Triangular Space
Non Tightly Nested Loops
Code Sinking
Data Dependence With Conditionals
Conditionals in Loops
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 32: Iteration
Iteration Space
Concept associated with the loops Contains one point for each iteration of the loop If a statement in one iteration dependes on a statement in another iteration then dependence is represented by an edge from source to target (called iteration space dependence graph)
for i = 2 to 9 do x[i] =... =... x[i-1]... endfor
Space requirement too large Compiler can not always determine number of iterations
Iteration Vector
Each iteration is assigned a vector iv = ( I 1 , I 2 ,.. ., In ) Where I (^) k is the value of loop index variable of kth nested loop at that iteration.
for i = 3 to 7 do for j = 6 to 2 step -2 do a[i,j] = a[i,,j+2] + 1 endfor endfor
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 32: Iteration
For statements involving A[i,,j] distance vector (0,0) direction vector (=,=) dependence is loop independent For statements involving B[i,,j] distance vector (0,1) direction vector (=,<) dependence is carried by the inner loop For statements involving C[i,,j] distance vector (1,-1) direction vector (<,>) dependence is carried by the outer loop
Dependence Level
Loop nest level that carries the data dependence relation
Therefore, for C[i,,j] level is 1 for B[i,,j] level is 2 for A[i,,j] level is
Iteration Vector - Triangular Space
Advantages of normalized iteration vector:
Later iterations have larger iteration vector Adjacent iterations differ by only one However, neither of these require first iteration to have vector (0,0, · · ·, 0).
Consider following program:
for i = 1 to 7 do for j = i to 7 do A[i+1,,j] = A[i,,j]+ endfor endfor
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 32: Iteration
Dependence distance vector is (1, -1)
A more natural way to depict such a loop is to assign iteration vectors that give triangular space as:
Semi normalized iteration vector: when distance between successive iterations is 1 and the lower limit is not zero
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 32: Iteration
Code Sinking
Data Dependence With Conditionals
There must be a path from definition to use In case of conditionals, path cannot be determined at compile time Any path may be taken at runtime Data dependence cannot occur between statements in alternate paths
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 32: Iteration
1. X = 1
2. Y = 2
- if Y < T then
- X = 2
- else
- Y = X
- endif
- Z = X + Y
Find out data dependence for X.
Definition of X in 1 and 4 Use of X at 6 and 8
Therefore
Conditionals in Loops
Statements that can’t be executed on the same iteration cannot be involved in a loop- independent dependence Conditionals do not affect loop carried dependence
- for i = 2 to 9 do
- if a(i) > 0 then
- a(i) = b(i-1) + 1
- else
- b(i) = a(i) * 2
- endif
- endfor Note:
