Re: Number of Phi-functions in SSA graph

Diego Novillo <dnovillo@redhat.com>
25 Mar 2005 21:54:19 -0500

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From: Diego Novillo <dnovillo@redhat.com>
Newsgroups: comp.compilers
Date: 25 Mar 2005 21:54:19 -0500
Organization: Red Hat Canada
References: 04-07-030 04-07-041 05-03-086
Keywords: SSA, analysis

On Thu, Mar 24, 2005 at 09:15:05PM -0500, Bageshri Sathe wrote:


> I was wondering what is the upper bound on number of phi-functions in a
> minimal SSA graph. Does it depend upon number of program variables or join
> nodes in the CFG or both?


I assume that you mean minimal in the original sense (i.e., PHI nodes
are always added to the iterated dominance frontier of definition
sites). The pruned and semi-pruned forms will actually yield a
smaller number of PHI nodes, as the IDFs are pruned with live-in
information.


The main factor is the size of the iterated dominance frontier of each
definition site, and, of course, the number of definition sites.


For instance, if you have a very convoluted graph but all the
definitions are in the entry block, there will be exactly 0 PHI nodes
(the example is extreme and is only meant as an illustration). At the
other extreme, you may have just 1 definition site that is very "deep"
inside the CFG and has a huge IDF. Each block in that IDF will need a
PHI node.


> Any literature that discusses this?


The various papers that describe techniques for PHI placement should
help, but I'm not aware of anything that discusses this particular
topic in detail.


Diego.



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