Path: csiph.com!x330-a1.tempe.blueboxinc.net!usenet.pasdenom.info!selfless.tophat.at!news.glorb.com!news.ripco.com!rahul.net!wasp.rahul.net!rahul.net!news.misty.com!news.iecc.com!nerds-end From: George Neuner Newsgroups: comp.compilers Subject: Re: Question about the structure of a program dependence graph Date: Fri, 03 Jun 2011 18:56:11 -0400 Organization: A noiseless patient Spider Lines: 38 Sender: news@iecc.com Approved: comp.compilers@iecc.com Message-ID: <11-06-004@comp.compilers> References: <11-06-002@comp.compilers> NNTP-Posting-Host: news.iecc.com X-Trace: gal.iecc.com 1307281526 34428 64.57.183.58 (5 Jun 2011 13:45:26 GMT) X-Complaints-To: abuse@iecc.com NNTP-Posting-Date: Sun, 5 Jun 2011 13:45:26 +0000 (UTC) Keywords: analysis Posted-Date: 05 Jun 2011 09:45:26 EDT X-submission-address: compilers@iecc.com X-moderator-address: compilers-request@iecc.com X-FAQ-and-archives: http://compilers.iecc.com Xref: x330-a1.tempe.blueboxinc.net comp.compilers:130 On Tue, 31 May 2011 13:09:58 -0700 (PDT), Douglas do Couto Teixeira wrote: > Given a program P in SSA form, let its dependence graph G = (V, E) >be a graph with a vertex nv for each variable v in P, and an edge >(na->nb) if b is defined by an instruction that uses a. > > If P is a general program with GOTOs, then it is possible to have a >graph G that is dense, i.e., has O(N^2) edges, where N is the number >of variables in P. Not exactly. Recall that a GOTO has a single target label. There is no more edge fan-out with GOTO than with a conditional or loop construct. > However, if P contains only IF and WHILE, then it seems that the >number of edges in P will be O(N). Could you tell me if that is the >case? Otherwise, could you provide me a counter example? It will be between O(N) and O(N^2). Remember that multiple loops may have the same entry or exit, multiple conditionals may converge, and as Andreas already has mentioned, case/switch constructs have at least as many edges as they have cases (remember the default case may not be explicit and may not change the value). Additionally, if the language includes pointers to non-local data, then there will be edges associated with manipulations of both the pointer and the value. > If I add a break with a label, or exceptions, like in Java, then I >am tempted to believe that the number of edges in the dependence graph >is still O(N). Could you tell me if this assumption is wrong? Break is the same as GOTO. For exceptions the answer depends on the particular implementation. George