671 CS Graduate Seminar Challenge Problem 1 Local Common Subexpression Elimination
In lecture 2, we talked about the DAG construction algorithm for local common subexpression elimination. Show the DAG for the following piece of code 1. 2. 3. 4. 5. a z x z b = = = = = y x y b y + + + + + 2 w 2 c 2
a, x, b z + 2 x + w b + c z
y
DAG edges
Use basic algorithm as discussed in lecture 2, and in ASU p. 548. The problem here is that the naive code generation does not enforce any ordering on the independent expression DAGS. Describe an algorithm that generates correct code from such DAG. a Here is one possible approach: Introduce dependence edges between internal operation nodes. Code generation process uses rPOSTORDER to generate code for the subtrees. Depth-rst search starts at nodes that do not have any incoming dependence edges.
b:anti
a, x, b
+ 2
x:anti
z + x
z:output
z + b c
y
w
Dependence edges DAG edges
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