1. Common Subexpression Elimination
Johnathon Jamison
CS265
S. Graham

2. Titanium
Titanium is a compiler

3. CSE
Given:
a = f * i …
b = f * i
We want to compute f * i only once

4. CSE We could do: a = f * i temp = a … b = temp
But only if the value of f * i has not changed

5. Def/Use Given: a = … … …a…
We want to link the use of a to the definition of a above.

6. Def/Use The link should be of every possible definition of a
Thus method calls or pointer indirection could define a

7. Def/Use Titanium has def/use information available
Every use of a variable has a list of all possible definitions associated with it
It seems this could be leveraged for CSE

8. CSE Revisited a = f * i … b = f * i
The second f * i can be eliminated if the definitions of f and i that are used are exactly the same as the first
But checking for that could be onerous

9. CSE Revisited
So, lets create some fake definitions of f and i immediately before the first f * i
Then, there is one explicit definition that can be traced to for checking the previously mentioned condition

10. CSE Revisited f = f i = i a = f * i … b = f * i
Thus, if f and i have the same definitions in both places, then the second f * i can be eliminated

11. CSE Revisited
This is fine and dandy for straight line code, but what if you have:
a = f * i b = f * i
… … V
c = f * i

12. CSE Revisited
So, you need to see if f and i have the same definitions in all pairs of places where the common subexpression exists.
I.E., does f or i have any definition that is not associated with a fake def introduced by this analysis?
If not, then an elimination can occur

13. CSE Revisited
This is complicated by the fact that all CSEs are done simultaneously
So, extra assignments are placed everywhere in the code a CSE could be
Therefore, when tracing defs, those introduced defs must be explicitly ignored

14. CSE Tidbits
After completion, these assignments are deleted, so as not to interfere with anything else
Any temps introduced are placed after the calculation, so that copy propagation can remove them
Compiler temps are placed at top level, as the live range of CSEs are unknown
Associatively is accounted for
Only binary and unary operations are done

15. CSE Examples

16. Timings

17. Local CSE Used the standard Muchnik (sp?) algorithm
Used defs to find what was killed
Fully implemented
Except method calls