| 1 | #include <stdio.h>
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| 2 | #include <string.h>
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| 3 | #ifdef _CIVL
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| 4 | #include <civlc.cvh>
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| 5 | #pragma CIVL ACSL
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| 6 | #endif
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| 7 |
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| 8 | #ifdef _CIVL
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| 9 | $input int ni,nj;
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| 10 | $assume(ni > 1);
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| 11 | $assume(nj > 1);
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| 12 | $input double uin[ni][nj];
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| 13 | #endif
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| 14 |
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| 15 | int main(int argc, char** argv) {
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| 16 | int i,j,ir,jr;
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| 17 | double u1[ni][nj];
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| 18 | double u2[ni][nj];
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| 19 |
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| 20 | $havoc(&i); $havoc(&j);
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| 21 | $assume($forall (int i : 0 .. ni-1)
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| 22 | ($forall (int j : 0 .. nj-1) u1[i][j] == 0 && u2[i][j] == 0)
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| 23 | );
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| 24 |
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| 25 | double tmp1[ni][nj];
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| 26 |
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| 27 | $assume($forall (int i : 1 .. ni-2)
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| 28 | ($forall (int j : 1 .. nj-2) tmp1[i][j] == uin[i][j] * uin[i][j])
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| 29 | );
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| 30 | $assume($forall (int i, j | i == 0 || i == ni-1 || j == 0 || j == nj-1) tmp1[i][j] == 0);
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| 31 | memcpy(u1, tmp1, sizeof(double) * ni * nj);
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| 32 |
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| 33 | double tmp2[ni][nj];
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| 34 |
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| 35 | $assume($forall (int i | 1 <= i && i < ni - 2 && i % 2 != 0)
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| 36 | ($forall (int j | 1 <= j && j < nj - 2 && j % 2 != 0)
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| 37 | tmp2[i][j] == uin[i][j]*uin[i][j] &&
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| 38 | tmp2[i+1][j] == uin[i+1][j]*uin[i+1][j] &&
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| 39 | tmp2[i][j+1] == uin[i][j+1]*uin[i][j+1] &&
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| 40 | tmp2[i+1][j+1] == uin[i+1][j+1]*uin[i+1][j+1])
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| 41 | );
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| 42 | $assume($forall (int i, j | i == 0 || i == ni-1 || j == 0 || j == nj-1) tmp2[i][j] == 0);
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| 43 | memcpy(u2, tmp2, sizeof(double) * ni * nj);
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| 44 | // remainder
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| 45 | if(i==ni-2) {
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| 46 | /*@ loop invariant 1 <= jr && jr <= nj-1;
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| 47 | @ loop invariant \forall int t; 1 <= t && t < jr ==>
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| 48 | @ u2[i][t] == uin[i][t]*uin[i][t];
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| 49 | @ loop assigns jr, u2[i][1 .. nj-2];
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| 50 | @*/
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| 51 | for(jr=1;jr<nj-1;jr++) {
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| 52 | u2[i][jr] = uin[i][jr]*uin[i][jr];
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| 53 | }
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| 54 | }
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| 55 | if(j==nj-2) {
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| 56 | /*@ loop invariant 1 <= ir && ir <= ni-1;
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| 57 | @ loop invariant \forall int t; 1 <= t && t < ir ==>
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| 58 | @ u2[t][j] == uin[t][j]*uin[t][j];
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| 59 | @ loop assigns ir, u2[1 .. ni-2][j];
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| 60 | @*/
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| 61 | for(ir=1;ir<ni-1;ir++) {
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| 62 | u2[ir][j] = uin[ir][j]*uin[ir][j];
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| 63 | }
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| 64 | }
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| 65 | if(i==ni-2 && j==nj-2) u2[i][j] = uin[i][j]*uin[i][j];
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| 66 |
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| 67 | $assert($forall (int i: 0 .. ni-1)
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| 68 | ($forall (int j: 0 .. nj-1) u1[i][j] == u2[i][j])
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| 69 | );
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| 70 | }
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