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| 1 | +/* Compute the floor of the square root, by Dijkstra */ |
| 2 | + |
| 3 | +extern void abort(void); |
| 4 | +extern void __assert_fail(const char *, const char *, unsigned int, const char *) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__)); |
| 5 | +void reach_error() { __assert_fail("0", "dijkstra-u.c", 5, "reach_error"); } |
| 6 | +extern unsigned int __VERIFIER_nondet_unsigned_int(void); |
| 7 | +extern void abort(void); |
| 8 | +void assume_abort_if_not(int cond) { |
| 9 | + if(!cond) {abort();} |
| 10 | +} |
| 11 | +void __VERIFIER_assert(int cond) { |
| 12 | + if (!(cond)) { |
| 13 | + ERROR: |
| 14 | + {reach_error();} |
| 15 | + } |
| 16 | + return; |
| 17 | +} |
| 18 | + |
| 19 | +int main() { |
| 20 | + unsigned int n, p, q, r, h; |
| 21 | + |
| 22 | + n = __VERIFIER_nondet_unsigned_int(); |
| 23 | + assume_abort_if_not(n < 4294967295 / 4); // Avoid non-terminating loop |
| 24 | + |
| 25 | + p = 0; |
| 26 | + q = 1; |
| 27 | + r = n; |
| 28 | + h = 0; |
| 29 | + while (1) { |
| 30 | + if (!(q <= n)) |
| 31 | + break; |
| 32 | + |
| 33 | + q = 4 * q; |
| 34 | + } |
| 35 | + //q == 4^n |
| 36 | + |
| 37 | + while (1) { |
| 38 | + __VERIFIER_assert(r < 2 * p + q); |
| 39 | + __VERIFIER_assert(p*p + r*q == n*q); |
| 40 | + __VERIFIER_assert(h * h * h - 12 * h * n * q + 16 * n * p * q - h * q * q - 4 * p * q * q + 12 * h * q * r - 16 * p * q * r == 0); |
| 41 | + __VERIFIER_assert(h * h * n - 4 * h * n * p + 4 * (n * n) * q - n * q * q - h * h * r + 4 * h * p * r - 8 * n * q * r + q * q * r + 4 * q * r * r == 0); |
| 42 | + __VERIFIER_assert(h * h * p - 4 * h * n * q + 4 * n * p * q - p * q * q + 4 * h * q * r - 4 * p * q * r == 0); |
| 43 | + __VERIFIER_assert(p * p - n * q + q * r == 0); |
| 44 | + |
| 45 | + if (!(q != 1)) |
| 46 | + break; |
| 47 | + |
| 48 | + q = q / 4; |
| 49 | + h = p + q; |
| 50 | + p = p / 2; |
| 51 | + if (r >= h) { |
| 52 | + p = p + q; |
| 53 | + r = r - h; |
| 54 | + } |
| 55 | + } |
| 56 | + __VERIFIER_assert(h*h*h - 12*h*n + 16*n*p + 12*h*r - 16*p*r - h - 4*p == 0); |
| 57 | + __VERIFIER_assert(p*p - n + r == 0); |
| 58 | + __VERIFIER_assert(h*h*p - 4*h*n + 4*n*p + 4*h*r - 4*p*r - p == 0); |
| 59 | + return 0; |
| 60 | +} |
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