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Re: Question about the structure of a program dependence graph

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Yes, a quadratic number of edges is possible, if you consider "switch".
You just have to desugar it into "if" for your simple language.

// initialize N variables x0..xN with zero
x0_0 = 0;
x1_0 = 0;
x2_0 = 0;
...
xN_0 = 0;
// switch over n cases, each set xn = 1
switch(rand) {
   case 0: x0_1 = 1; break;
   case 1: x1_1 = 1; break;
   case 2: x2_1 = 1; break;
   ...
   case N: xN_1 = 1; break;
}
// print all x
x0_2 = phi(x0_1, x0_0, x0_0, ..., x0_0);
x1_2 = phi(x1_0, x1_1, x1_0, ..., x1_0);
x2_2 = phi(x2_0, x2_0, x2_1, ..., x2_0);
...
xN_2 = phi(xN_0, xN_0, xN_0, ..., xN_1);
print(x0_2);
print(x1_2);
print(x2_2);
...
print(xN_2);

This program has N*3 variables (+1 for "rand") and each phi instruction
introduces N dependencies, because there is one for each control flow
predecessor. For example, the dependees of xi_2 are all xi_0, except one
xi_1. This means N edges for each of the N variables. QED

--
Andreas Zwinkau

  Karlsruhe Institute of Technology (KIT)
  Institut fuer Programmstrukturen und Datenorganisation (IPD)
  Lehrstuhl Prof. Snelting
  Adenauerring 20a
  76131 Karlsruhe

  Phone:  +49 721 608 48351
  Fax:    +49 721 608 48457
  Email:  zwinkau@kit.edu
  Web:    http://pp.info.uni-karlsruhe.de/person.php?id=107

  KIT b University of the State of Baden-Wuerttemberg and
  National Research Center of the Helmholtz Association

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Thread

Question about the structure of a program dependence graph Douglas do Couto Teixeira <douglasdocouto@gmail.com> - 2011-05-31 13:09 -0700
  Re: Question about the structure of a program dependence graph Andreas Zwinkau <zwinkau@kit.edu> - 2011-06-03 11:29 +0200
    Re: Question about the structure of a program dependence graph Douglas do Couto Teixeira <douglasdocouto@gmail.com> - 2011-06-05 11:22 -0300
      Re: Question about the structure of a program dependence graph Andreas Zwinkau <zwinkau@kit.edu> - 2011-06-06 10:37 +0200
  Re: Question about the structure of a program dependence graph George Neuner <gneuner2@comcast.net> - 2011-06-03 18:56 -0400

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