def test_diophantine_overflow():
# Smoke test integer overflow detection
max_intp = np.iinfo(np.intp).max
max_int64 = np.iinfo(np.int64).max
if max_int64 <= max_intp:
# Check that the algorithm works internally in 128-bit;
# solving this problem requires large intermediate numbers
A = (max_int64//2, max_int64//2 - 10)
U = (max_int64//2, max_int64//2 - 10)
b = 2*(max_int64//2) - 10
assert_equal(solve_diophantine(A, U, b), (1, 1))
def test_diophantine_overflow():
# Smoke test integer overflow detection
max_intp = np.iinfo(np.intp).max
max_int64 = np.iinfo(np.int64).max
if max_int64 <= max_intp:
# Check that the algorithm works internally in 128-bit;
# solving this problem requires large intermediate numbers
A = (max_int64 // 2, max_int64 // 2 - 10)
U = (max_int64 // 2, max_int64 // 2 - 10)
b = 2 * (max_int64 // 2) - 10
assert_equal(solve_diophantine(A, U, b), (1, 1))
def check(A, U, exists=None):
X = solve_diophantine(A, U, 0, require_ub_nontrivial=1)
if exists is None:
exists = (X is not None)
if X is not None:
assert_(sum(a*x for a, x in zip(A, X)) == sum(a*u//2 for a, u in zip(A, U)))
assert_(all(0 <= x <= u for x, u in zip(X, U)))
assert_(any(x != u//2 for x, u in zip(X, U)))
if exists:
assert_(X is not None, repr(X))
else:
assert_(X is None, repr(X))
def check(A, U, exists=None):
X = solve_diophantine(A, U, 0, require_ub_nontrivial=1)
if exists is None:
exists = (X is not None)
if X is not None:
assert_(sum(a*x for a, x in zip(A, X)) == sum(a*u//2 for a, u in zip(A, U)))
assert_(all(0 <= x <= u for x, u in zip(X, U)))
assert_(any(x != u//2 for x, u in zip(X, U)))
if exists:
assert_(X is not None, repr(X))
else:
assert_(X is None, repr(X))
def test_diophantine_fuzz():
# Fuzz test the diophantine solver
rng = np.random.RandomState(1234)
max_int = np.iinfo(np.intp).max
for ndim in range(10):
feasible_count = 0
infeasible_count = 0
min_count = 500//(ndim + 1)
numbers = []
while min(feasible_count, infeasible_count) < min_count:
# Ensure big and small integer problems
A_max = 1 + rng.randint(0, 11, dtype=np.intp)**6
U_max = rng.randint(0, 11, dtype=np.intp)**6
A_max = min(max_int, A_max)
U_max = min(max_int-1, U_max)
A = tuple(rng.randint(1, A_max+1, dtype=np.intp)
for j in range(ndim))
U = tuple(rng.randint(0, U_max+2, dtype=np.intp)
for j in range(ndim))
b_ub = min(max_int-2, sum(a*ub for a, ub in zip(A, U)))
b = rng.randint(-1, b_ub+2, dtype=np.intp)
if ndim == 0 and feasible_count < min_count:
b = 0
X = solve_diophantine(A, U, b)
if X is None:
# Check the simplified decision problem agrees
X_simplified = solve_diophantine(A, U, b, simplify=1)
assert_(X_simplified is None, (A, U, b, X_simplified))
# Check no solution exists (provided the problem is
# small enough so that brute force checking doesn't
# take too long)
try:
ranges = tuple(xrange(0, a*ub+1, a) for a, ub in zip(A, U))
except OverflowError:
# xrange on 32-bit Python 2 may overflow
continue
size = 1
for r in ranges:
size *= len(r)
if size < 100000:
assert_(not any(sum(w) == b for w in itertools.product(*ranges)))
infeasible_count += 1
else:
# Check the simplified decision problem agrees
X_simplified = solve_diophantine(A, U, b, simplify=1)
assert_(X_simplified is not None, (A, U, b, X_simplified))
# Check validity
assert_(sum(a*x for a, x in zip(A, X)) == b)
assert_(all(0 <= x <= ub for x, ub in zip(X, U)))
feasible_count += 1
def test_diophantine_fuzz():
# Fuzz test the diophantine solver
rng = np.random.RandomState(1234)
max_int = np.iinfo(np.intp).max
for ndim in range(10):
feasible_count = 0
infeasible_count = 0
min_count = 500 // (ndim + 1)
numbers = []
while min(feasible_count, infeasible_count) < min_count:
# Ensure big and small integer problems
A_max = 1 + rng.randint(0, 11)**6
U_max = rng.randint(0, 11)**6
A_max = min(max_int, A_max)
U_max = min(max_int - 1, U_max)
A = tuple(rng.randint(1, A_max + 1) for j in range(ndim))
U = tuple(rng.randint(0, U_max + 2) for j in range(ndim))
b_ub = min(max_int - 2, sum(a * ub for a, ub in zip(A, U)))
b = rng.randint(-1, b_ub + 2)
if ndim == 0 and feasible_count < min_count:
b = 0
X = solve_diophantine(A, U, b)
if X is None:
# Check the simplified decision problem agrees
X_simplified = solve_diophantine(A, U, b, simplify=1)
assert_(X_simplified is None, (A, U, b, X_simplified))
# Check no solution exists (provided the problem is
# small enough so that brute force checking doesn't
# take too long)
try:
ranges = tuple(
xrange(0, a * ub + 1, a) for a, ub in zip(A, U))
except OverflowError:
# xrange on 32-bit Python 2 may overflow
continue
size = 1
for r in ranges:
size *= len(r)
if size < 100000:
assert_(not any(
sum(w) == b for w in itertools.product(*ranges)))
infeasible_count += 1
else:
# Check the simplified decision problem agrees
X_simplified = solve_diophantine(A, U, b, simplify=1)
assert_(X_simplified is not None, (A, U, b, X_simplified))
# Check validity
assert_(sum(a * x for a, x in zip(A, X)) == b)
assert_(all(0 <= x <= ub for x, ub in zip(X, U)))
feasible_count += 1