Common Subexpression Elimination Johnathon Jamison CS 265 S
Common Subexpression Elimination Johnathon Jamison CS 265 S. Graham
Outline • • • Titanium Def/Use analysis (used by CSE) Common Subexpression Elimination Implementation Examples
Titanium • Titanium is an extension of Java • The Titanium compiler compiles Titanium code to C • The C code is then compiled by the system compiler, e. g. gcc
Def/Use • Given: a=… … …a… • We want to link the use of a to the definition of a above.
Def/Use • Every use of a variable has a list of all possible definitions associated with it • Every definition of a variable has a list of all possible uses associated with it • Method calls and pointer indirection are included in this analysis
Def/Use • The Titanium compile has def/use information available • It seems this could be leveraged for CSE
CSE • Given: a=f*i … b=f*i • We want to compute f * i only once
CSE • We could do: a=f*i temp = a … b = temp • But only if the value of f * i has not changed
Finding CSEs 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 – Leverage our def/use analysis! • But checking for that could be onerous
Finding CSEs • 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
Finding CSEs 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
Handing Global CSEs • This is fine and dandy for straight line code, but what if you have: a=f*i b=f*i … … c=f*i
Handing Global CSEs • 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 definition introduced by this analysis? • If not, then an elimination can occur
Simultaneous CSEs • The def/use analysis is expensive – You can not run the def use analysis for every potential CSE • Thus all CSEs should be analyzed simultaneously • So, extra assignments are placed everywhere in the code a CSE could be
Simultaneous CSEs • When tracing definitions, those introduced definitions must be explicitly ignored • Trace back from a use • If it is a definition associated with a CSE we are cool • If it is an introduced one, pass through • If it is neither, we can not use this
Altogether Now… • Insert the extra assignments • For every similar expression – At every site, try to eliminate this expression • Delete the assignments, so as not to interfere with anything else
Interaction with Copy Propagation • Any temps introduced are placed after the calculation, so that copy propagation can remove them a=f*i temp_1 = a … … b=f*i b = temp_1 temp_2 = b … … c=f*i c = temp_2
CSE Tidbits • Compiler temps are placed at top level, as the live range of CSEs are unknown • Associativity is accounted for • Only binary and unary operations are done – Can be extended
Examples
Timings – Preliminary Results • CSE alone seems to have negligable effect • Global copy propagation gives a few percent increase • CSE on top of global copy propagation gives a couple percent more
Local CSE • Used Muchnick’s algorithm (described in class) • Used defs to find what was killed • Fully implemented – Except method calls • Since we are using defs already, why not so something more substantial?
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