Re: Question about the structure of a program dependence graph

Douglas do Couto Teixeira <douglasdocouto@gmail.com>Sun, 5 Jun 2011 11:22:51 -0300

From comp.compilers

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Question about the structure of a program dependence graph douglasdocouto@gmail.com (Douglas do Couto Teixeira) (2011-05-31)
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Re: Question about the structure of a program dependence graph douglasdocouto@gmail.com (Douglas do Couto Teixeira) (2011-06-05)
Re: Question about the structure of a program dependence graph zwinkau@kit.edu (Andreas Zwinkau) (2011-06-06)
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 From: Douglas do Couto Teixeira Newsgroups: comp.compilers Date: Sun, 5 Jun 2011 11:22:51 -0300 Organization: Compilers Central References: 11-06-002 11-06-003 Keywords: analysis Posted-Date: 06 Jun 2011 12:45:36 EDT

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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