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