1import math
2import unittest
3
4class PowTest(unittest.TestCase):
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 TestRpow:
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
169if __name__ == "__main__":
170    unittest.main()
171