1. CS 201 Compiler Construction
Code Optimizations:
Constant Propagation & Folding

2. Constant Propagation & Folding
1. Use of var replaced
by a constant value
- propagation.
2. Exp. is evaluated or
folded if all of its
operands are
constants.

3. Constant Propagation & Folding
Evaluation of branch
outcomes may be
enabled.
2. Can take advantage
of non-executable
paths.

4. Problem Characteristics
Not Partitionable
Values of variables are interdependent.
if Y > 0 then
X = 2
endif
Z = X + 1
Z depends upon
X and Y.
Not a bit-vector problem
The solution is not true/false  rather can be any constant value.

5. Data Flow Analysis
Constant Prop.
Lattice for a
Single variable.

6. Contd..
Meet Operator
for a Single
variable.

7. Contd.. Lattice for all variables (L,∧‘) VAR – set of variables
VAL – set of values (all constants, Τ, )
L = {β: β is a total function β: VARVAL}
i.e., set of all states of variables.
forall v ε VAR
β1 ∧’ β2(v) = β1 (v) ∧ β2 (v)

8. Contd.. Transfer Function S: A = B op C
fS(β) – transfer function of S.
fS(β) =

9. Contd.. Transfer Function S: A = c, constant assignment
S: A = B, copy statement
S: A < B, conditional

10. Example

11. Worklist Algorithm Each node is a single statement
IN and OUT contain the lattice values at node entry and exit
Algorithm will take advantage of resolved branches. How ?
Mark edges as executable or non-executable and propagate information only along executable edges
Branch (true) (false) (true or false) – mark edges executable accordingly

12. Algorithm: Initialization
Mark all edges as unexecutable
Worklist  { n0 } (start node in the CFG)
IN[n0] = β (none of the variables is a constant)
∨ n ε N – {n0}, IN[n] = OUT[n] = β (all undefined) Τ

13. Algorithm: Analysis p ε Pred(n) While Worklist ≠ Φ do
get n from Worklist
IN[n] = Λ’ OUT[p] st p  n is executable
if n is an assignment statement then
n: A = B op C or A = c or A = B
OUT[n] = fn ( IN[n] )
mark outgoing edges as executable
else – n is a predicate
evaluate condition: value is
true or false or not-a-constant
mark appropriate edges executable
true edge or false edge or both
endif
if OUT[n] changed then add Succ(n) to Worklist
endwhile
p ε Pred(n)