1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
|
import unittest, os
from test import test_support
from random import random
# These tests ensure that complex math does the right thing
class ComplexTest(unittest.TestCase):
def assertAlmostEqual(self, a, b):
if isinstance(a, complex):
if isinstance(b, complex):
unittest.TestCase.assertAlmostEqual(self, a.real, b.real)
unittest.TestCase.assertAlmostEqual(self, a.imag, b.imag)
else:
unittest.TestCase.assertAlmostEqual(self, a.real, b)
unittest.TestCase.assertAlmostEqual(self, a.imag, 0.)
else:
if isinstance(b, complex):
unittest.TestCase.assertAlmostEqual(self, a, b.real)
unittest.TestCase.assertAlmostEqual(self, 0., b.imag)
else:
unittest.TestCase.assertAlmostEqual(self, a, b)
def assertCloseAbs(self, x, y, eps=1e-9):
"""Return true iff floats x and y "are close\""""
# put the one with larger magnitude second
if abs(x) > abs(y):
x, y = y, x
if y == 0:
return abs(x) < eps
if x == 0:
return abs(y) < eps
# check that relative difference < eps
self.assert_(abs((x-y)/y) < eps)
def assertClose(self, x, y, eps=1e-9):
"""Return true iff complexes x and y "are close\""""
self.assertCloseAbs(x.real, y.real, eps)
self.assertCloseAbs(x.imag, y.imag, eps)
def assertIs(self, a, b):
self.assert_(a is b)
def check_div(self, x, y):
"""Compute complex z=x*y, and check that z/x==y and z/y==x."""
z = x * y
if x != 0:
q = z / x
self.assertClose(q, y)
q = z.__truediv__(x)
self.assertClose(q, y)
if y != 0:
q = z / y
self.assertClose(q, x)
q = z.__truediv__(y)
self.assertClose(q, x)
def test_truediv(self):
simple_real = [float(i) for i in range(-5, 6)]
simple_complex = [complex(x, y) for x in simple_real for y in simple_real]
for x in simple_complex:
for y in simple_complex:
self.check_div(x, y)
# A naive complex division algorithm (such as in 2.0) is very prone to
# nonsense errors for these (overflows and underflows).
self.check_div(complex(1e200, 1e200), 1+0j)
self.check_div(complex(1e-200, 1e-200), 1+0j)
# Just for fun.
for i in range(100):
self.check_div(complex(random(), random()),
complex(random(), random()))
self.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j)
# FIXME: The following currently crashes on Alpha
# self.assertRaises(OverflowError, pow, 1e200+1j, 1e200+1j)
def test_truediv(self):
self.assertAlmostEqual(complex.__truediv__(2+0j, 1+1j), 1-1j)
self.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j)
def test_floordiv(self):
self.assertRaises(TypeError, complex.__floordiv__, 3+0j, 1.5+0j)
self.assertRaises(TypeError, complex.__floordiv__, 3+0j, 0+0j)
def test_richcompare(self):
self.assertRaises(OverflowError, complex.__eq__, 1+1j, 1<<10000)
self.assertEqual(complex.__lt__(1+1j, None), NotImplemented)
self.assertIs(complex.__eq__(1+1j, 1+1j), True)
self.assertIs(complex.__eq__(1+1j, 2+2j), False)
self.assertIs(complex.__ne__(1+1j, 1+1j), False)
self.assertIs(complex.__ne__(1+1j, 2+2j), True)
self.assertRaises(TypeError, complex.__lt__, 1+1j, 2+2j)
self.assertRaises(TypeError, complex.__le__, 1+1j, 2+2j)
self.assertRaises(TypeError, complex.__gt__, 1+1j, 2+2j)
self.assertRaises(TypeError, complex.__ge__, 1+1j, 2+2j)
def test_mod(self):
# % is no longer supported on complex numbers
self.assertRaises(TypeError, (1+1j).__mod__, 0+0j)
self.assertRaises(TypeError, lambda: (3.33+4.43j) % 0)
self.assertRaises(TypeError, (1+1j).__mod__, 4.3j)
def test_divmod(self):
self.assertRaises(TypeError, divmod, 1+1j, 1+0j)
self.assertRaises(TypeError, divmod, 1+1j, 0+0j)
def test_pow(self):
self.assertAlmostEqual(pow(1+1j, 0+0j), 1.0)
self.assertAlmostEqual(pow(0+0j, 2+0j), 0.0)
self.assertRaises(ZeroDivisionError, pow, 0+0j, 1j)
self.assertAlmostEqual(pow(1j, -1), 1/1j)
self.assertAlmostEqual(pow(1j, 200), 1)
self.assertRaises(ValueError, pow, 1+1j, 1+1j, 1+1j)
a = 3.33+4.43j
self.assertEqual(a ** 0j, 1)
self.assertEqual(a ** 0.+0.j, 1)
self.assertEqual(3j ** 0j, 1)
self.assertEqual(3j ** 0, 1)
try:
0j ** a
except ZeroDivisionError:
pass
else:
self.fail("should fail 0.0 to negative or complex power")
try:
0j ** (3-2j)
except ZeroDivisionError:
pass
else:
self.fail("should fail 0.0 to negative or complex power")
# The following is used to exercise certain code paths
self.assertEqual(a ** 105, a ** 105)
self.assertEqual(a ** -105, a ** -105)
self.assertEqual(a ** -30, a ** -30)
self.assertEqual(0.0j ** 0, 1)
b = 5.1+2.3j
self.assertRaises(ValueError, pow, a, b, 0)
def test_boolcontext(self):
for i in range(100):
self.assert_(complex(random() + 1e-6, random() + 1e-6))
self.assert_(not complex(0.0, 0.0))
def test_conjugate(self):
self.assertClose(complex(5.3, 9.8).conjugate(), 5.3-9.8j)
def test_constructor(self):
class OS:
def __init__(self, value): self.value = value
def __complex__(self): return self.value
class NS(object):
def __init__(self, value): self.value = value
def __complex__(self): return self.value
self.assertEqual(complex(OS(1+10j)), 1+10j)
self.assertEqual(complex(NS(1+10j)), 1+10j)
self.assertRaises(TypeError, complex, OS(None))
self.assertRaises(TypeError, complex, NS(None))
self.assertAlmostEqual(complex("1+10j"), 1+10j)
self.assertAlmostEqual(complex(10), 10+0j)
self.assertAlmostEqual(complex(10.0), 10+0j)
self.assertAlmostEqual(complex(10), 10+0j)
self.assertAlmostEqual(complex(10+0j), 10+0j)
self.assertAlmostEqual(complex(1,10), 1+10j)
self.assertAlmostEqual(complex(1,10), 1+10j)
self.assertAlmostEqual(complex(1,10.0), 1+10j)
self.assertAlmostEqual(complex(1,10), 1+10j)
self.assertAlmostEqual(complex(1,10), 1+10j)
self.assertAlmostEqual(complex(1,10.0), 1+10j)
self.assertAlmostEqual(complex(1.0,10), 1+10j)
self.assertAlmostEqual(complex(1.0,10), 1+10j)
self.assertAlmostEqual(complex(1.0,10.0), 1+10j)
self.assertAlmostEqual(complex(3.14+0j), 3.14+0j)
self.assertAlmostEqual(complex(3.14), 3.14+0j)
self.assertAlmostEqual(complex(314), 314.0+0j)
self.assertAlmostEqual(complex(314), 314.0+0j)
self.assertAlmostEqual(complex(3.14+0j, 0j), 3.14+0j)
self.assertAlmostEqual(complex(3.14, 0.0), 3.14+0j)
self.assertAlmostEqual(complex(314, 0), 314.0+0j)
self.assertAlmostEqual(complex(314, 0), 314.0+0j)
self.assertAlmostEqual(complex(0j, 3.14j), -3.14+0j)
self.assertAlmostEqual(complex(0.0, 3.14j), -3.14+0j)
self.assertAlmostEqual(complex(0j, 3.14), 3.14j)
self.assertAlmostEqual(complex(0.0, 3.14), 3.14j)
self.assertAlmostEqual(complex("1"), 1+0j)
self.assertAlmostEqual(complex("1j"), 1j)
self.assertAlmostEqual(complex(), 0)
self.assertAlmostEqual(complex("-1"), -1)
self.assertAlmostEqual(complex("+1"), +1)
self.assertAlmostEqual(complex("(1+2j)"), 1+2j)
self.assertAlmostEqual(complex("(1.3+2.2j)"), 1.3+2.2j)
class complex2(complex): pass
self.assertAlmostEqual(complex(complex2(1+1j)), 1+1j)
self.assertAlmostEqual(complex(real=17, imag=23), 17+23j)
self.assertAlmostEqual(complex(real=17+23j), 17+23j)
self.assertAlmostEqual(complex(real=17+23j, imag=23), 17+46j)
self.assertAlmostEqual(complex(real=1+2j, imag=3+4j), -3+5j)
c = 3.14 + 1j
self.assert_(complex(c) is c)
del c
self.assertRaises(TypeError, complex, "1", "1")
self.assertRaises(TypeError, complex, 1, "1")
self.assertEqual(complex(" 3.14+J "), 3.14+1j)
# SF bug 543840: complex(string) accepts strings with \0
# Fixed in 2.3.
self.assertRaises(ValueError, complex, '1+1j\0j')
self.assertRaises(TypeError, int, 5+3j)
self.assertRaises(TypeError, int, 5+3j)
self.assertRaises(TypeError, float, 5+3j)
self.assertRaises(ValueError, complex, "")
self.assertRaises(TypeError, complex, None)
self.assertRaises(ValueError, complex, "\0")
self.assertRaises(ValueError, complex, "3\09")
self.assertRaises(TypeError, complex, "1", "2")
self.assertRaises(TypeError, complex, "1", 42)
self.assertRaises(TypeError, complex, 1, "2")
self.assertRaises(ValueError, complex, "1+")
self.assertRaises(ValueError, complex, "1+1j+1j")
self.assertRaises(ValueError, complex, "--")
self.assertRaises(ValueError, complex, "(1+2j")
self.assertRaises(ValueError, complex, "1+2j)")
self.assertRaises(ValueError, complex, "1+(2j)")
self.assertRaises(ValueError, complex, "(1+2j)123")
self.assertRaises(ValueError, complex, "1"*500)
self.assertRaises(ValueError, complex, "x")
class EvilExc(Exception):
pass
class evilcomplex:
def __complex__(self):
raise EvilExc
self.assertRaises(EvilExc, complex, evilcomplex())
class float2:
def __init__(self, value):
self.value = value
def __float__(self):
return self.value
self.assertAlmostEqual(complex(float2(42.)), 42)
self.assertAlmostEqual(complex(real=float2(17.), imag=float2(23.)), 17+23j)
self.assertRaises(TypeError, complex, float2(None))
class complex0(complex):
"""Test usage of __complex__() when inheriting from 'complex'"""
def __complex__(self):
return 42j
class complex1(complex):
"""Test usage of __complex__() with a __new__() method"""
def __new__(self, value=0j):
return complex.__new__(self, 2*value)
def __complex__(self):
return self
class complex2(complex):
"""Make sure that __complex__() calls fail if anything other than a
complex is returned"""
def __complex__(self):
return None
self.assertAlmostEqual(complex(complex0(1j)), 42j)
self.assertAlmostEqual(complex(complex1(1j)), 2j)
self.assertRaises(TypeError, complex, complex2(1j))
def test_hash(self):
for x in range(-30, 30):
self.assertEqual(hash(x), hash(complex(x, 0)))
x /= 3.0 # now check against floating point
self.assertEqual(hash(x), hash(complex(x, 0.)))
def test_abs(self):
nums = [complex(x/3., y/7.) for x in range(-9,9) for y in range(-9,9)]
for num in nums:
self.assertAlmostEqual((num.real**2 + num.imag**2) ** 0.5, abs(num))
def test_repr(self):
self.assertEqual(repr(1+6j), '(1+6j)')
self.assertEqual(repr(1-6j), '(1-6j)')
self.assertNotEqual(repr(-(1+0j)), '(-1+-0j)')
self.assertEqual(1-6j,complex(repr(1-6j)))
self.assertEqual(1+6j,complex(repr(1+6j)))
self.assertEqual(-6j,complex(repr(-6j)))
self.assertEqual(6j,complex(repr(6j)))
def test_neg(self):
self.assertEqual(-(1+6j), -1-6j)
def test_file(self):
a = 3.33+4.43j
b = 5.1+2.3j
fo = None
try:
fo = open(test_support.TESTFN, "w")
print(a, b, file=fo)
fo.close()
fo = open(test_support.TESTFN, "r")
self.assertEqual(fo.read(), ("%s %s\n" % (a, b)))
finally:
if (fo is not None) and (not fo.closed):
fo.close()
try:
os.remove(test_support.TESTFN)
except (OSError, IOError):
pass
def test_main():
test_support.run_unittest(ComplexTest)
if __name__ == "__main__":
test_main()
|
