Re: Question about the structure of a program dependence graph

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


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    Fax: +49 721 608 48457
    Email: zwinkau@kit.edu
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    KIT b University of the State of Baden-Wuerttemberg and
    National Research Center of the Helmholtz Association

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