1 import math
2 import unittest
3
4 class ESC[4;38;5;81mPowTest(ESC[4;38;5;149munittestESC[4;38;5;149m.ESC[4;38;5;149mTestCase):
5
6 def powtest(self, type):
7 if type != float:
8 for i in range(-1000, 1000):
9 self.assertEqual(pow(type(i), 0), 1)
10 self.assertEqual(pow(type(i), 1), type(i))
11 self.assertEqual(pow(type(0), 1), type(0))
12 self.assertEqual(pow(type(1), 1), type(1))
13
14 for i in range(-100, 100):
15 self.assertEqual(pow(type(i), 3), i*i*i)
16
17 pow2 = 1
18 for i in range(0, 31):
19 self.assertEqual(pow(2, i), pow2)
20 if i != 30 : pow2 = pow2*2
21
22 for i in list(range(-10, 0)) + list(range(1, 10)):
23 ii = type(i)
24 inv = pow(ii, -1) # inverse of ii
25 for jj in range(-10, 0):
26 self.assertAlmostEqual(pow(ii, jj), pow(inv, -jj))
27
28 for othertype in int, float:
29 for i in range(1, 100):
30 zero = type(0)
31 exp = -othertype(i/10.0)
32 if exp == 0:
33 continue
34 self.assertRaises(ZeroDivisionError, pow, zero, exp)
35
36 il, ih = -20, 20
37 jl, jh = -5, 5
38 kl, kh = -10, 10
39 asseq = self.assertEqual
40 if type == float:
41 il = 1
42 asseq = self.assertAlmostEqual
43 elif type == int:
44 jl = 0
45 elif type == int:
46 jl, jh = 0, 15
47 for i in range(il, ih+1):
48 for j in range(jl, jh+1):
49 for k in range(kl, kh+1):
50 if k != 0:
51 if type == float or j < 0:
52 self.assertRaises(TypeError, pow, type(i), j, k)
53 continue
54 asseq(
55 pow(type(i),j,k),
56 pow(type(i),j)% type(k)
57 )
58
59 def test_powint(self):
60 self.powtest(int)
61
62 def test_powfloat(self):
63 self.powtest(float)
64
65 def test_other(self):
66 # Other tests-- not very systematic
67 self.assertEqual(pow(3,3) % 8, pow(3,3,8))
68 self.assertEqual(pow(3,3) % -8, pow(3,3,-8))
69 self.assertEqual(pow(3,2) % -2, pow(3,2,-2))
70 self.assertEqual(pow(-3,3) % 8, pow(-3,3,8))
71 self.assertEqual(pow(-3,3) % -8, pow(-3,3,-8))
72 self.assertEqual(pow(5,2) % -8, pow(5,2,-8))
73
74 self.assertEqual(pow(3,3) % 8, pow(3,3,8))
75 self.assertEqual(pow(3,3) % -8, pow(3,3,-8))
76 self.assertEqual(pow(3,2) % -2, pow(3,2,-2))
77 self.assertEqual(pow(-3,3) % 8, pow(-3,3,8))
78 self.assertEqual(pow(-3,3) % -8, pow(-3,3,-8))
79 self.assertEqual(pow(5,2) % -8, pow(5,2,-8))
80
81 for i in range(-10, 11):
82 for j in range(0, 6):
83 for k in range(-7, 11):
84 if j >= 0 and k != 0:
85 self.assertEqual(
86 pow(i,j) % k,
87 pow(i,j,k)
88 )
89 if j >= 0 and k != 0:
90 self.assertEqual(
91 pow(int(i),j) % k,
92 pow(int(i),j,k)
93 )
94
95 def test_big_exp(self):
96 import random
97 self.assertEqual(pow(2, 50000), 1 << 50000)
98 # Randomized modular tests, checking the identities
99 # a**(b1 + b2) == a**b1 * a**b2
100 # a**(b1 * b2) == (a**b1)**b2
101 prime = 1000000000039 # for speed, relatively small prime modulus
102 for i in range(10):
103 a = random.randrange(1000, 1000000)
104 bpower = random.randrange(1000, 50000)
105 b = random.randrange(1 << (bpower - 1), 1 << bpower)
106 b1 = random.randrange(1, b)
107 b2 = b - b1
108 got1 = pow(a, b, prime)
109 got2 = pow(a, b1, prime) * pow(a, b2, prime) % prime
110 if got1 != got2:
111 self.fail(f"{a=:x} {b1=:x} {b2=:x} {got1=:x} {got2=:x}")
112 got3 = pow(a, b1 * b2, prime)
113 got4 = pow(pow(a, b1, prime), b2, prime)
114 if got3 != got4:
115 self.fail(f"{a=:x} {b1=:x} {b2=:x} {got3=:x} {got4=:x}")
116
117 def test_bug643260(self):
118 class ESC[4;38;5;81mTestRpow:
119 def __rpow__(self, other):
120 return None
121 None ** TestRpow() # Won't fail when __rpow__ invoked. SF bug #643260.
122
123 def test_bug705231(self):
124 # -1.0 raised to an integer should never blow up. It did if the
125 # platform pow() was buggy, and Python didn't worm around it.
126 eq = self.assertEqual
127 a = -1.0
128 # The next two tests can still fail if the platform floor()
129 # function doesn't treat all large inputs as integers
130 # test_math should also fail if that is happening
131 eq(pow(a, 1.23e167), 1.0)
132 eq(pow(a, -1.23e167), 1.0)
133 for b in range(-10, 11):
134 eq(pow(a, float(b)), b & 1 and -1.0 or 1.0)
135 for n in range(0, 100):
136 fiveto = float(5 ** n)
137 # For small n, fiveto will be odd. Eventually we run out of
138 # mantissa bits, though, and thereafer fiveto will be even.
139 expected = fiveto % 2.0 and -1.0 or 1.0
140 eq(pow(a, fiveto), expected)
141 eq(pow(a, -fiveto), expected)
142 eq(expected, 1.0) # else we didn't push fiveto to evenness
143
144 def test_negative_exponent(self):
145 for a in range(-50, 50):
146 for m in range(-50, 50):
147 with self.subTest(a=a, m=m):
148 if m != 0 and math.gcd(a, m) == 1:
149 # Exponent -1 should give an inverse, with the
150 # same sign as m.
151 inv = pow(a, -1, m)
152 self.assertEqual(inv, inv % m)
153 self.assertEqual((inv * a - 1) % m, 0)
154
155 # Larger exponents
156 self.assertEqual(pow(a, -2, m), pow(inv, 2, m))
157 self.assertEqual(pow(a, -3, m), pow(inv, 3, m))
158 self.assertEqual(pow(a, -1001, m), pow(inv, 1001, m))
159
160 else:
161 with self.assertRaises(ValueError):
162 pow(a, -1, m)
163 with self.assertRaises(ValueError):
164 pow(a, -2, m)
165 with self.assertRaises(ValueError):
166 pow(a, -1001, m)
167
168
169 if __name__ == "__main__":
170 unittest.main()