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Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 31: Data Dependence Analysis
The Lecture Contains:
Interprocedural Dataflow Analysis
Alias Computation
Example
Data Flow Analysis in Presence of Procedure Calls
Data Dependence Analysis
Data Dependence
Data Dependence Graph
Basic Block Dependence
Data Dependence in Loops
Unroll the Loop
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 31: Data Dependence Analysis
We can relate in, out and transfer as follows
Consider following control flow graph
Suppose a is an array, c is and integer, and p and q are pointer. Initially
Out
In
out
In
out
in
in
out ={(P,a),(q,a),(q,c) in
out
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 31: Data Dependence Analysis
Data Flow Analysis in Presence of Procedure Calls
Change[p ] set of global variables and formal parameters of p that might be changed during an execution of p. Def[p ] set of formal parameters and global variables having explicit definition within p. A: { a | a is a global variable or formal of p, such that for some procedure q and integer i, p calls q with a as the ith actual parameter and ith formal of q is in change[q] } G: { g | g is a global in change[q] and p calls q }
Data Dependence Analysis
Used for instruction scheduling Used for data cache optimization Determines ordering relationship; a dependence between two statements constraints their execution order Control dependence: arises from control flow
S1: a = b+c S2: if a > 10 goto L S3: d = b*e S4: e = d+ S5: L1: d = e/
Data Dependence
Arises from flow of data between two statements Compiler must analyze programs to find constraints preventing the reordering of operations.
Consider: A = 0 B = A C = A + D D = 2
Moving (2) above (1):: Value of A in (2) changes Moving (4) above (3):: results in wrong value of D in (3)
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 31: Data Dependence Analysis
Three types of constraints:
Flow or True Dependence: When a variable is assigned or defined in one statement and used in subsequent statement Anti Dependence: When a variable is used in one statement and reassigned in subsequently executed statement Output Dependence: When a variable is assigned in one statement and reassigned in subsequent statement
Anti dependence and Output dependence arise from reuse of variable and are also called False dependence.
Flow dependence is inherent in computation and cannot be eliminated by renaming. Therefore it is also called True dependence.
Data Dependence Graph
Data structure used to depict dependency between statements.
Each statement represents a node in the graph Nodes are connected by directed edges
- When S2 is flow dependent on S1, it is denoted by S1 S2 or S1 S2 and represented by S1 → S
- When there is an anti-dependence from S1 to S2, it is denoted by S1 S2 or S1 S2 and represented by S1 → S
- When there is an output-dependence from S1 to S2, it is denoted by S1 S2 and represented by S1 → S
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 31: Data Dependence Analysis
Latency: delay required between initiation times of I 1 and I 2 minus execution time required for I (^1) before another instruction can start. For example, if two cycles must elapse between I 1 and I 2 then latency is 1. r2 ← r1 r3 ← r1+4 r4 ← r2 + r r5 ← r2 - 1
assume load has latency of 1; requires 2 cycles to finish.
Data Dependence in Loops
Each statement executed many times Dependence can flow from one statement to any other Dependence can flow to the same statement
for i = 2, 9 do x(i) = y(i) + z(i) S (^1) a(i) = x(i-1) + 1 S (^2) endfor S 1 → S (^2)
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 31: Data Dependence Analysis
do i = 1, N a(i) = b(i) c(i) = a(i) + b(i) e(i) = c(i+1) enddo
Unroll The Loop
do I = 1, N A = B(I) C(I) = A + B(I) E(I) = C(I+1) enddo
file:///D|/...ry,%20Dr.%20Sanjeev%20K%20Aggrwal%20&%20Dr.%20Rajat%20Moona/Multi-core_Architecture/lecture%2031/31_10.htm[6/14/2012 12:10:50 PM]
Module 16: Data Flow Analysis in Presence of Procedure Calls
Lecture 31: Data Dependence Analysis
Example:
do I = 1, 100 X( 2I+1 ) = .... ...... = X( 2I+4 ) enddo
S 1
S 2
Is there a dependence from S 1 to S 2? Coarse grain analysis: S 1 writes into X and S 2 reads from X. Therefore, S 1 → S 2 or S 1 S (^2) Fine grain analysis: Eqn: 2i 1 + 1 = 2i^2 + 4 has no integer solution Therefore, no dependence from S 1 to S (^2)
DO I = 1, 50
X(I) = ....
.... = X(I+50)
ENDDO
Fine grain analysis: Eqn. i 1 = i 2 + 50 has integer solution. However, no integer solution in the range 1 = i 1 = i 2 = 50 therefore, no dependence from S 1 to S (^2) If are general functions, then the problem is intractable. If are linear functions of loop index, then to test dependence we need to find values of two integers such that
which can be rewritten as
These are called Linear Diophantine Equations.
