def test_coorespondance(self):
'''
Check if the bounded hyperop matches with the regular
version for small values of a,b.
'''
bound = hyperop(4)(3, 3)
vals = range(1, 4)
for N in range(0, 5):
H = hyperop(N, primitive=True)
Hb = bounded_hyperop(N, bound=bound, primitive=True)
for a, b in itertools.product(vals, repeat=2):
assert H(a, b) == Hb(a, b)
def test_coorespondance(self):
'''
Check if the bounded hyperop matches with the regular
version for small values of a,b.
'''
bound = hyperop(4)(3, 3)
vals = range(1, 4)
for N in range(0, 5):
H = hyperop(N, primitive=True)
Hb = bounded_hyperop(N, bound=bound, primitive=True)
for a, b in itertools.product(vals, repeat=2):
assert H(a, b) == Hb(a, b)
def calculateNthRightHyperoperatorOperator(a, b, c):
if a == 0:
return c + 1
if b == 0:
if c == 1:
return 0
return 1
if c == 0:
return 1
if a > 1 and b == 1:
return 1
if a > 1 and c == 1:
return b
if b == 2 and c == 2:
if a == 0:
return 3
return 4
if a > 4 and c > 2:
raise ValueError('overflow')
if a > 4 and b > 5:
raise ValueError('overflow')
return hyperop(a)(b, c)
def test_non_integral_H5(self):
H = hyperop(5)
with self.assertRaises(ValueError):
H(1.1, 2)
with self.assertRaises(ValueError):
H(2, 1.1)
def test_non_integral_H5(self):
H = hyperop(5)
with self.assertRaises(ValueError):
H(1.1, 2)
with self.assertRaises(ValueError):
H(2, 1.1)
def test_H5(self):
H = hyperop(5)
# Small fixed values, a=2
assert H(2, 1) == 2
assert H(2, 2) == 4
assert H(2, 3) == 65536
# Small fixed values, a=3
assert H(3, 1) == 3
assert H(3, 2) == 7625597484987
def test_H5(self):
H = hyperop(5)
# Small fixed values, a=2
assert H(2, 1) == 2
assert H(2, 2) == 4
assert H(2, 3) == 65536
# Small fixed values, a=3
assert H(3, 1) == 3
assert H(3, 2) == 7625597484987
def test_special_case_b0(self):
H0 = dict([(n, hyperop(n)) for n in range(15)])
Hb = dict([(n, bounded_hyperop(n)) for n in range(15)])
for H in [H0, Hb]:
for a in testing_values:
assert H[0](a, 0) == 1
assert H[1](a, 0) == a
assert H[2](a, 0) == 0
for n in range(3, 15):
assert H[n](a, 0) == 1
def test_special_case_b0(self):
H0 = dict([(n, hyperop(n)) for n in range(15)])
Hb = dict([(n, bounded_hyperop(n)) for n in range(15)])
for H in [H0, Hb]:
for a in testing_values:
assert H[0](a, 0) == 1
assert H[1](a, 0) == a
assert H[2](a, 0) == 0
for n in range(3, 15):
assert H[n](a, 0) == 1
def test_special_case_a0(self):
H0 = dict([(n, hyperop(n)) for n in range(15)])
Hb = dict([(n, bounded_hyperop(n)) for n in range(15)])
for H in [H0, Hb]:
for b in testing_values:
assert H[0](0, b) == b + 1
assert H[1](0, b) == b
assert H[2](0, b) == 0
assert H[3](0, b) == 0
for n in range(4, 15):
assert H[n](0, b) == (b % 2 == 0)
def test_special_case_a0(self):
H0 = dict([(n, hyperop(n)) for n in range(15)])
Hb = dict([(n, bounded_hyperop(n)) for n in range(15)])
for H in [H0, Hb]:
for b in testing_values:
assert H[0](0, b) == b + 1
assert H[1](0, b) == b
assert H[2](0, b) == 0
assert H[3](0, b) == 0
for n in range(4, 15):
assert H[n](0, b) == (b % 2 == 0)
def test_H4(self):
H = hyperop(4)
# Small fixed values, a=2
assert H(2, 1) == 2
assert H(2, 2) == 4
assert H(2, 3) == 16
assert H(2, 4) == 65536
# Small fixed values, a=3
assert H(3, 1) == 3
assert H(3, 2) == 27
assert H(3, 3) == 7625597484987
# Log of large value should be related to smaller one
a2_5 = round(math.log(H(2, 5), 2))
assert a2_5 == H(2, 4)
def test_H4(self):
H = hyperop(4)
# Small fixed values, a=2
assert H(2, 1) == 2
assert H(2, 2) == 4
assert H(2, 3) == 16
assert H(2, 4) == 65536
# Small fixed values, a=3
assert H(3, 1) == 3
assert H(3, 2) == 27
assert H(3, 3) == 7625597484987
# Log of large value should be related to smaller one
a2_5 = round(math.log(H(2, 5), 2))
assert a2_5 == H(2, 4)
def test_primitive_H1(self):
check_range(hyperop(1, primitive=True), operator.add)
def test_H3(self):
check_range(hyperop(3), operator.pow)
def test_H2(self):
check_range(hyperop(2), operator.mul)
def test_H1(self):
check_range(hyperop(1), operator.add)
def test_H0(self):
def successor(_, b):
return 1 + b
check_range(hyperop(0), successor)
def test_non_negative_n(self):
with self.assertRaises(ValueError):
hyperop(-1)
def test_primitive_H3(self):
check_range(hyperop(3, primitive=True), operator.pow)
def test_primitive_H2(self):
check_range(hyperop(2, primitive=True), operator.mul)
def test_H0(self):
def successor(_, b):
return 1 + b
check_range(hyperop(0), successor)
def test_primitive_H1(self):
check_range(hyperop(1, primitive=True), operator.add)
def test_non_negative_n(self):
with self.assertRaises(ValueError):
hyperop(-1)
def test_non_integral_n(self):
with self.assertRaises(ValueError):
hyperop(1.2)
def test_H1(self):
check_range(hyperop(1), operator.add)
def test_non_integral_H4(self):
H = hyperop(4)
with self.assertRaises(ValueError):
H(2, 0.5)
def test_H2(self):
check_range(hyperop(2), operator.mul)
def test_non_integral_H4(self):
H = hyperop(4)
with self.assertRaises(ValueError):
H(2, 0.5)
def test_primitive_H2(self):
check_range(hyperop(2, primitive=True), operator.mul)
def test_non_integral_n(self):
with self.assertRaises(ValueError):
hyperop(1.2)
def test_primitive_H3(self):
check_range(hyperop(3, primitive=True), operator.pow)
def calculateNthRightHyperoperator( a, b, c ):
return hyperop( a )( b, c )
def test_H3(self):
check_range(hyperop(3), operator.pow)
