Re: Question about the structure of a program dependence graph

Dear Andreas,


Thanks for your answer. I built a small program in C to reproduce your
suggestion. And after converted to SSA form it seems produce a
quadratic number of edges. The program is:


#include <stdio.h>


int main(int argc, char** argv) {
    int x0 = 0, x1 = 0, x2 = 0, x3 = 0;


    switch(argc) {
        case 0: x0 = 2; break;
        case 1: x1 = 44; break;
        case 2: x2 = 42; break;
        case 3: x3 = 67; break;
        default:
              x0 = x1 = x2 = x3 = -1; break;
    }


    printf("%d %d %d %d\n", x0, x1, x2, x3);


    return 0;
}




Thanks again,


Douglas




On Fri, Jun 3, 2011 at 6:29 AM, Andreas Zwinkau <zwinkau@kit.edu> wrote:
> 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
>

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