void abort() { }; extern int __VERIFIER_nondet_int(); void assume_abort_if_not(int cond) { if(!cond) {abort();} } /*@ requires ((1 <= \old(cond))) && (cond != 0); ensures ((1 <= \old(cond))) && (1); @*/ void __VERIFIER_assert(int cond) { if (!(cond)) { ERROR: {/*@ assert(0); */;} } return; } int main() { int A, R; long long u, v, r; A = __VERIFIER_nondet_int(); R = __VERIFIER_nondet_int(); //assume_abort_if_not(A >= 1); assume_abort_if_not(((long long) R - 1) * ((long long) R - 1) < A); //assume_abort_if_not(A <= R * R); assume_abort_if_not(A % 2 == 1); u = ((long long) 2 * R) + 1; v = 1; r = ((long long) R * R) - A; /*@ loop invariant (((((__int128) v * 2) + ((__int128) u * u)) == (((((__int128) v * v) + ((__int128) u * 2)) + ((long long) A * 4)) + ((__int128) r * 4)))); @*/ while (1) { __VERIFIER_assert(4*(A+r) == u*u - v*v - 2*u + 2*v); if (!(r != 0)) break; if (r > 0) { r = r - v; v = v + 2; } else { r = r + u; u = u + 2; } } //return (u - v) / 2; __VERIFIER_assert(((long long) 4*A) == u*u - v*v - 2*u + 2*v); return 0; }