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import math
import unittest
class PowTest(unittest.TestCase):
def powtest(self, type):
if type != float:
for i in range(-1000, 1000):
self.assertEqual(pow(type(i), 0), 1)
self.assertEqual(pow(type(i), 1), type(i))
self.assertEqual(pow(type(0), 1), type(0))
self.assertEqual(pow(type(1), 1), type(1))
for i in range(-100, 100):
self.assertEqual(pow(type(i), 3), i*i*i)
pow2 = 1
for i in range(0, 31):
self.assertEqual(pow(2, i), pow2)
if i != 30 : pow2 = pow2*2
for i in list(range(-10, 0)) + list(range(1, 10)):
ii = type(i)
inv = pow(ii, -1) # inverse of ii
for jj in range(-10, 0):
self.assertAlmostEqual(pow(ii, jj), pow(inv, -jj))
for othertype in int, float:
for i in range(1, 100):
zero = type(0)
exp = -othertype(i/10.0)
if exp == 0:
continue
self.assertRaises(ZeroDivisionError, pow, zero, exp)
il, ih = -20, 20
jl, jh = -5, 5
kl, kh = -10, 10
asseq = self.assertEqual
if type == float:
il = 1
asseq = self.assertAlmostEqual
elif type == int:
jl = 0
elif type == int:
jl, jh = 0, 15
for i in range(il, ih+1):
for j in range(jl, jh+1):
for k in range(kl, kh+1):
if k != 0:
if type == float or j < 0:
self.assertRaises(TypeError, pow, type(i), j, k)
continue
asseq(
pow(type(i),j,k),
pow(type(i),j)% type(k)
)
def test_powint(self):
self.powtest(int)
def test_powfloat(self):
self.powtest(float)
def test_other(self):
# Other tests-- not very systematic
self.assertEqual(pow(3,3) % 8, pow(3,3,8))
self.assertEqual(pow(3,3) % -8, pow(3,3,-8))
self.assertEqual(pow(3,2) % -2, pow(3,2,-2))
self.assertEqual(pow(-3,3) % 8, pow(-3,3,8))
self.assertEqual(pow(-3,3) % -8, pow(-3,3,-8))
self.assertEqual(pow(5,2) % -8, pow(5,2,-8))
self.assertEqual(pow(3,3) % 8, pow(3,3,8))
self.assertEqual(pow(3,3) % -8, pow(3,3,-8))
self.assertEqual(pow(3,2) % -2, pow(3,2,-2))
self.assertEqual(pow(-3,3) % 8, pow(-3,3,8))
self.assertEqual(pow(-3,3) % -8, pow(-3,3,-8))
self.assertEqual(pow(5,2) % -8, pow(5,2,-8))
for i in range(-10, 11):
for j in range(0, 6):
for k in range(-7, 11):
if j >= 0 and k != 0:
self.assertEqual(
pow(i,j) % k,
pow(i,j,k)
)
if j >= 0 and k != 0:
self.assertEqual(
pow(int(i),j) % k,
pow(int(i),j,k)
)
def test_big_exp(self):
import random
self.assertEqual(pow(2, 50000), 1 << 50000)
# Randomized modular tests, checking the identities
# a**(b1 + b2) == a**b1 * a**b2
# a**(b1 * b2) == (a**b1)**b2
prime = 1000000000039 # for speed, relatively small prime modulus
for i in range(10):
a = random.randrange(1000, 1000000)
bpower = random.randrange(1000, 50000)
b = random.randrange(1 << (bpower - 1), 1 << bpower)
b1 = random.randrange(1, b)
b2 = b - b1
got1 = pow(a, b, prime)
got2 = pow(a, b1, prime) * pow(a, b2, prime) % prime
if got1 != got2:
self.fail(f"{a=:x} {b1=:x} {b2=:x} {got1=:x} {got2=:x}")
got3 = pow(a, b1 * b2, prime)
got4 = pow(pow(a, b1, prime), b2, prime)
if got3 != got4:
self.fail(f"{a=:x} {b1=:x} {b2=:x} {got3=:x} {got4=:x}")
def test_bug643260(self):
class TestRpow:
def __rpow__(self, other):
return None
None ** TestRpow() # Won't fail when __rpow__ invoked. SF bug #643260.
def test_bug705231(self):
# -1.0 raised to an integer should never blow up. It did if the
# platform pow() was buggy, and Python didn't worm around it.
eq = self.assertEqual
a = -1.0
# The next two tests can still fail if the platform floor()
# function doesn't treat all large inputs as integers
# test_math should also fail if that is happening
eq(pow(a, 1.23e167), 1.0)
eq(pow(a, -1.23e167), 1.0)
for b in range(-10, 11):
eq(pow(a, float(b)), b & 1 and -1.0 or 1.0)
for n in range(0, 100):
fiveto = float(5 ** n)
# For small n, fiveto will be odd. Eventually we run out of
# mantissa bits, though, and thereafer fiveto will be even.
expected = fiveto % 2.0 and -1.0 or 1.0
eq(pow(a, fiveto), expected)
eq(pow(a, -fiveto), expected)
eq(expected, 1.0) # else we didn't push fiveto to evenness
def test_negative_exponent(self):
for a in range(-50, 50):
for m in range(-50, 50):
with self.subTest(a=a, m=m):
if m != 0 and math.gcd(a, m) == 1:
# Exponent -1 should give an inverse, with the
# same sign as m.
inv = pow(a, -1, m)
self.assertEqual(inv, inv % m)
self.assertEqual((inv * a - 1) % m, 0)
# Larger exponents
self.assertEqual(pow(a, -2, m), pow(inv, 2, m))
self.assertEqual(pow(a, -3, m), pow(inv, 3, m))
self.assertEqual(pow(a, -1001, m), pow(inv, 1001, m))
else:
with self.assertRaises(ValueError):
pow(a, -1, m)
with self.assertRaises(ValueError):
pow(a, -2, m)
with self.assertRaises(ValueError):
pow(a, -1001, m)
if __name__ == "__main__":
unittest.main()
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