Lib/test/test_complex.py

   1 import unittest
   2 from test import test_support
   3
   4 from random import random
   5 from math import atan2, isnan, copysign
   6
   7 INF = float("inf")
   8 NAN = float("nan")
   9 # These tests ensure that complex math does the right thing
  10
  11 class ComplexTest(unittest.TestCase):
  12
  13     def assertAlmostEqual(self, a, b):
  14         if isinstance(a, complex):
  15             if isinstance(b, complex):
  16                 unittest.TestCase.assertAlmostEqual(self, a.real, b.real)
  17                 unittest.TestCase.assertAlmostEqual(self, a.imag, b.imag)
  18             else:
  19                 unittest.TestCase.assertAlmostEqual(self, a.real, b)
  20                 unittest.TestCase.assertAlmostEqual(self, a.imag, 0.)
  21         else:
  22             if isinstance(b, complex):
  23                 unittest.TestCase.assertAlmostEqual(self, a, b.real)
  24                 unittest.TestCase.assertAlmostEqual(self, 0., b.imag)
  25             else:
  26                 unittest.TestCase.assertAlmostEqual(self, a, b)
  27
  28     def assertCloseAbs(self, x, y, eps=1e-9):
  29         """Return true iff floats x and y "are close\""""
  30         # put the one with larger magnitude second
  31         if abs(x) > abs(y):
  32             x, y = y, x
  33         if y == 0:
  34             return abs(x) < eps
  35         if x == 0:
  36             return abs(y) < eps
  37         # check that relative difference < eps
  38         self.assertTrue(abs((x-y)/y) < eps)
  39
  40     def assertFloatsAreIdentical(self, x, y):
  41         """assert that floats x and y are identical, in the sense that:
  42         (1) both x and y are nans, or
  43         (2) both x and y are infinities, with the same sign, or
  44         (3) both x and y are zeros, with the same sign, or
  45         (4) x and y are both finite and nonzero, and x == y
  46
  47         """
  48         msg = 'floats {!r} and {!r} are not identical'
  49
  50         if isnan(x) or isnan(y):
  51             if isnan(x) and isnan(y):
  52                 return
  53         elif x == y:
  54             if x != 0.0:
  55                 return
  56             # both zero; check that signs match
  57             elif copysign(1.0, x) == copysign(1.0, y):
  58                 return
  59             else:
  60                 msg += ': zeros have different signs'
  61         self.fail(msg.format(x, y))
  62
  63     def assertClose(self, x, y, eps=1e-9):
  64         """Return true iff complexes x and y "are close\""""
  65         self.assertCloseAbs(x.real, y.real, eps)
  66         self.assertCloseAbs(x.imag, y.imag, eps)
  67
  68     def check_div(self, x, y):
  69         """Compute complex z=x*y, and check that z/x==y and z/y==x."""
  70         z = x * y
  71         if x != 0:
  72             q = z / x
  73             self.assertClose(q, y)
  74             q = z.__div__(x)
  75             self.assertClose(q, y)
  76             q = z.__truediv__(x)
  77             self.assertClose(q, y)
  78         if y != 0:
  79             q = z / y
  80             self.assertClose(q, x)
  81             q = z.__div__(y)
  82             self.assertClose(q, x)
  83             q = z.__truediv__(y)
  84             self.assertClose(q, x)
  85
  86     def test_div(self):
  87         simple_real = [float(i) for i in xrange(-5, 6)]
  88         simple_complex = [complex(x, y) for x in simple_real for y in simple_real]
  89         for x in simple_complex:
  90             for y in simple_complex:
  91                 self.check_div(x, y)
  92
  93         # A naive complex division algorithm (such as in 2.0) is very prone to
  94         # nonsense errors for these (overflows and underflows).
  95         self.check_div(complex(1e200, 1e200), 1+0j)
  96         self.check_div(complex(1e-200, 1e-200), 1+0j)
  97
  98         # Just for fun.
  99         for i in xrange(100):
 100             self.check_div(complex(random(), random()),
 101                            complex(random(), random()))
 102
 103         self.assertRaises(ZeroDivisionError, complex.__div__, 1+1j, 0+0j)
 104         # FIXME: The following currently crashes on Alpha
 105         # self.assertRaises(OverflowError, pow, 1e200+1j, 1e200+1j)
 106
 107     def test_truediv(self):
 108         self.assertAlmostEqual(complex.__truediv__(2+0j, 1+1j), 1-1j)
 109         self.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j)
 110
 111     def test_floordiv(self):
 112         self.assertAlmostEqual(complex.__floordiv__(3+0j, 1.5+0j), 2)
 113         self.assertRaises(ZeroDivisionError, complex.__floordiv__, 3+0j, 0+0j)
 114
 115     def test_coerce(self):
 116         self.assertRaises(OverflowError, complex.__coerce__, 1+1j, 1L<<10000)
 117
 118     def test_no_implicit_coerce(self):
 119         # Python 2.7 removed implicit coercion from the complex type
 120         class A(object):
 121             def __coerce__(self, other):
 122                 raise RuntimeError
 123             __hash__ = None
 124             def __cmp__(self, other):
 125                 return -1
 126
 127         a = A()
 128         self.assertRaises(TypeError, lambda: a + 2.0j)
 129         self.assertTrue(a < 2.0j)
 130
 131     def test_richcompare(self):
 132         self.assertEqual(complex.__eq__(1+1j, 1L<<10000), False)
 133         self.assertEqual(complex.__lt__(1+1j, None), NotImplemented)
 134         self.assertIs(complex.__eq__(1+1j, 1+1j), True)
 135         self.assertIs(complex.__eq__(1+1j, 2+2j), False)
 136         self.assertIs(complex.__ne__(1+1j, 1+1j), False)
 137         self.assertIs(complex.__ne__(1+1j, 2+2j), True)
 138         self.assertRaises(TypeError, complex.__lt__, 1+1j, 2+2j)
 139         self.assertRaises(TypeError, complex.__le__, 1+1j, 2+2j)
 140         self.assertRaises(TypeError, complex.__gt__, 1+1j, 2+2j)
 141         self.assertRaises(TypeError, complex.__ge__, 1+1j, 2+2j)
 142
 143     def test_richcompare_boundaries(self):
 144         def check(n, deltas, is_equal, imag = 0.0):
 145             for delta in deltas:
 146                 i = n + delta
 147                 z = complex(i, imag)
 148                 self.assertIs(complex.__eq__(z, i), is_equal(delta))
 149                 self.assertIs(complex.__ne__(z, i), not is_equal(delta))
 150         # For IEEE-754 doubles the following should hold:
 151         #    x in [2 ** (52 + i), 2 ** (53 + i + 1)] -> x mod 2 ** i == 0
 152         # where the interval is representable, of course.
 153         for i in range(1, 10):
 154             pow = 52 + i
 155             mult = 2 ** i
 156             check(2 ** pow, range(1, 101), lambda delta: delta % mult == 0)
 157             check(2 ** pow, range(1, 101), lambda delta: False, float(i))
 158         check(2 ** 53, range(-100, 0), lambda delta: True)
 159
 160     def test_mod(self):
 161         self.assertRaises(ZeroDivisionError, (1+1j).__mod__, 0+0j)
 162
 163         a = 3.33+4.43j
 164         try:
 165             a % 0
 166         except ZeroDivisionError:
 167             pass
 168         else:
 169             self.fail("modulo parama can't be 0")
 170
 171     def test_divmod(self):
 172         self.assertRaises(ZeroDivisionError, divmod, 1+1j, 0+0j)
 173
 174     def test_pow(self):
 175         self.assertAlmostEqual(pow(1+1j, 0+0j), 1.0)
 176         self.assertAlmostEqual(pow(0+0j, 2+0j), 0.0)
 177         self.assertRaises(ZeroDivisionError, pow, 0+0j, 1j)
 178         self.assertAlmostEqual(pow(1j, -1), 1/1j)
 179         self.assertAlmostEqual(pow(1j, 200), 1)
 180         self.assertRaises(ValueError, pow, 1+1j, 1+1j, 1+1j)
 181
 182         a = 3.33+4.43j
 183         self.assertEqual(a ** 0j, 1)
 184         self.assertEqual(a ** 0.+0.j, 1)
 185
 186         self.assertEqual(3j ** 0j, 1)
 187         self.assertEqual(3j ** 0, 1)
 188
 189         try:
 190             0j ** a
 191         except ZeroDivisionError:
 192             pass
 193         else:
 194             self.fail("should fail 0.0 to negative or complex power")
 195
 196         try:
 197             0j ** (3-2j)
 198         except ZeroDivisionError:
 199             pass
 200         else:
 201             self.fail("should fail 0.0 to negative or complex power")
 202
 203         # The following is used to exercise certain code paths
 204         self.assertEqual(a ** 105, a ** 105)
 205         self.assertEqual(a ** -105, a ** -105)
 206         self.assertEqual(a ** -30, a ** -30)
 207
 208         self.assertEqual(0.0j ** 0, 1)
 209
 210         b = 5.1+2.3j
 211         self.assertRaises(ValueError, pow, a, b, 0)
 212
 213     def test_boolcontext(self):
 214         for i in xrange(100):
 215             self.assertTrue(complex(random() + 1e-6, random() + 1e-6))
 216         self.assertTrue(not complex(0.0, 0.0))
 217
 218     def test_conjugate(self):
 219         self.assertClose(complex(5.3, 9.8).conjugate(), 5.3-9.8j)
 220
 221     def test_constructor(self):
 222         class OS:
 223             def __init__(self, value): self.value = value
 224             def __complex__(self): return self.value
 225         class NS(object):
 226             def __init__(self, value): self.value = value
 227             def __complex__(self): return self.value
 228         self.assertEqual(complex(OS(1+10j)), 1+10j)
 229         self.assertEqual(complex(NS(1+10j)), 1+10j)
 230         self.assertRaises(TypeError, complex, OS(None))
 231         self.assertRaises(TypeError, complex, NS(None))
 232
 233         self.assertAlmostEqual(complex("1+10j"), 1+10j)
 234         self.assertAlmostEqual(complex(10), 10+0j)
 235         self.assertAlmostEqual(complex(10.0), 10+0j)
 236         self.assertAlmostEqual(complex(10L), 10+0j)
 237         self.assertAlmostEqual(complex(10+0j), 10+0j)
 238         self.assertAlmostEqual(complex(1,10), 1+10j)
 239         self.assertAlmostEqual(complex(1,10L), 1+10j)
 240         self.assertAlmostEqual(complex(1,10.0), 1+10j)
 241         self.assertAlmostEqual(complex(1L,10), 1+10j)
 242         self.assertAlmostEqual(complex(1L,10L), 1+10j)
 243         self.assertAlmostEqual(complex(1L,10.0), 1+10j)
 244         self.assertAlmostEqual(complex(1.0,10), 1+10j)
 245         self.assertAlmostEqual(complex(1.0,10L), 1+10j)
 246         self.assertAlmostEqual(complex(1.0,10.0), 1+10j)
 247         self.assertAlmostEqual(complex(3.14+0j), 3.14+0j)
 248         self.assertAlmostEqual(complex(3.14), 3.14+0j)
 249         self.assertAlmostEqual(complex(314), 314.0+0j)
 250         self.assertAlmostEqual(complex(314L), 314.0+0j)
 251         self.assertAlmostEqual(complex(3.14+0j, 0j), 3.14+0j)
 252         self.assertAlmostEqual(complex(3.14, 0.0), 3.14+0j)
 253         self.assertAlmostEqual(complex(314, 0), 314.0+0j)
 254         self.assertAlmostEqual(complex(314L, 0L), 314.0+0j)
 255         self.assertAlmostEqual(complex(0j, 3.14j), -3.14+0j)
 256         self.assertAlmostEqual(complex(0.0, 3.14j), -3.14+0j)
 257         self.assertAlmostEqual(complex(0j, 3.14), 3.14j)
 258         self.assertAlmostEqual(complex(0.0, 3.14), 3.14j)
 259         self.assertAlmostEqual(complex("1"), 1+0j)
 260         self.assertAlmostEqual(complex("1j"), 1j)
 261         self.assertAlmostEqual(complex(),  0)
 262         self.assertAlmostEqual(complex("-1"), -1)
 263         self.assertAlmostEqual(complex("+1"), +1)
 264         self.assertAlmostEqual(complex("(1+2j)"), 1+2j)
 265         self.assertAlmostEqual(complex("(1.3+2.2j)"), 1.3+2.2j)
 266         self.assertAlmostEqual(complex("3.14+1J"), 3.14+1j)
 267         self.assertAlmostEqual(complex(" ( +3.14-6J )"), 3.14-6j)
 268         self.assertAlmostEqual(complex(" ( +3.14-J )"), 3.14-1j)
 269         self.assertAlmostEqual(complex(" ( +3.14+j )"), 3.14+1j)
 270         self.assertAlmostEqual(complex("J"), 1j)
 271         self.assertAlmostEqual(complex("( j )"), 1j)
 272         self.assertAlmostEqual(complex("+J"), 1j)
 273         self.assertAlmostEqual(complex("( -j)"), -1j)
 274         self.assertAlmostEqual(complex('1e-500'), 0.0 + 0.0j)
 275         self.assertAlmostEqual(complex('-1e-500j'), 0.0 - 0.0j)
 276         self.assertAlmostEqual(complex('-1e-500+1e-500j'), -0.0 + 0.0j)
 277
 278         class complex2(complex): pass
 279         self.assertAlmostEqual(complex(complex2(1+1j)), 1+1j)
 280         self.assertAlmostEqual(complex(real=17, imag=23), 17+23j)
 281         self.assertAlmostEqual(complex(real=17+23j), 17+23j)
 282         self.assertAlmostEqual(complex(real=17+23j, imag=23), 17+46j)
 283         self.assertAlmostEqual(complex(real=1+2j, imag=3+4j), -3+5j)
 284
 285         # check that the sign of a zero in the real or imaginary part
 286         # is preserved when constructing from two floats.  (These checks
 287         # are harmless on systems without support for signed zeros.)
 288         def split_zeros(x):
 289             """Function that produces different results for 0. and -0."""
 290             return atan2(x, -1.)
 291
 292         self.assertEqual(split_zeros(complex(1., 0.).imag), split_zeros(0.))
 293         self.assertEqual(split_zeros(complex(1., -0.).imag), split_zeros(-0.))
 294         self.assertEqual(split_zeros(complex(0., 1.).real), split_zeros(0.))
 295         self.assertEqual(split_zeros(complex(-0., 1.).real), split_zeros(-0.))
 296
 297         c = 3.14 + 1j
 298         self.assertTrue(complex(c) is c)
 299         del c
 300
 301         self.assertRaises(TypeError, complex, "1", "1")
 302         self.assertRaises(TypeError, complex, 1, "1")
 303
 304         if test_support.have_unicode:
 305             self.assertEqual(complex(unicode("  3.14+J  ")), 3.14+1j)
 306
 307         # SF bug 543840:  complex(string) accepts strings with \0
 308         # Fixed in 2.3.
 309         self.assertRaises(ValueError, complex, '1+1j\0j')
 310
 311         self.assertRaises(TypeError, int, 5+3j)
 312         self.assertRaises(TypeError, long, 5+3j)
 313         self.assertRaises(TypeError, float, 5+3j)
 314         self.assertRaises(ValueError, complex, "")
 315         self.assertRaises(TypeError, complex, None)
 316         self.assertRaises(ValueError, complex, "\0")
 317         self.assertRaises(ValueError, complex, "3\09")
 318         self.assertRaises(TypeError, complex, "1", "2")
 319         self.assertRaises(TypeError, complex, "1", 42)
 320         self.assertRaises(TypeError, complex, 1, "2")
 321         self.assertRaises(ValueError, complex, "1+")
 322         self.assertRaises(ValueError, complex, "1+1j+1j")
 323         self.assertRaises(ValueError, complex, "--")
 324         self.assertRaises(ValueError, complex, "(1+2j")
 325         self.assertRaises(ValueError, complex, "1+2j)")
 326         self.assertRaises(ValueError, complex, "1+(2j)")
 327         self.assertRaises(ValueError, complex, "(1+2j)123")
 328         if test_support.have_unicode:
 329             self.assertRaises(ValueError, complex, unicode("x"))
 330         self.assertRaises(ValueError, complex, "1j+2")
 331         self.assertRaises(ValueError, complex, "1e1ej")
 332         self.assertRaises(ValueError, complex, "1e++1ej")
 333         self.assertRaises(ValueError, complex, ")1+2j(")
 334         # the following three are accepted by Python 2.6
 335         self.assertRaises(ValueError, complex, "1..1j")
 336         self.assertRaises(ValueError, complex, "1.11.1j")
 337         self.assertRaises(ValueError, complex, "1e1.1j")
 338
 339         if test_support.have_unicode:
 340             # check that complex accepts long unicode strings
 341             self.assertEqual(type(complex(unicode("1"*500))), complex)
 342
 343         class EvilExc(Exception):
 344             pass
 345
 346         class evilcomplex:
 347             def __complex__(self):
 348                 raise EvilExc
 349
 350         self.assertRaises(EvilExc, complex, evilcomplex())
 351
 352         class float2:
 353             def __init__(self, value):
 354                 self.value = value
 355             def __float__(self):
 356                 return self.value
 357
 358         self.assertAlmostEqual(complex(float2(42.)), 42)
 359         self.assertAlmostEqual(complex(real=float2(17.), imag=float2(23.)), 17+23j)
 360         self.assertRaises(TypeError, complex, float2(None))
 361
 362         class complex0(complex):
 363             """Test usage of __complex__() when inheriting from 'complex'"""
 364             def __complex__(self):
 365                 return 42j
 366
 367         class complex1(complex):
 368             """Test usage of __complex__() with a __new__() method"""
 369             def __new__(self, value=0j):
 370                 return complex.__new__(self, 2*value)
 371             def __complex__(self):
 372                 return self
 373
 374         class complex2(complex):
 375             """Make sure that __complex__() calls fail if anything other than a
 376             complex is returned"""
 377             def __complex__(self):
 378                 return None
 379
 380         self.assertAlmostEqual(complex(complex0(1j)), 42j)
 381         self.assertAlmostEqual(complex(complex1(1j)), 2j)
 382         self.assertRaises(TypeError, complex, complex2(1j))
 383
 384     def test_subclass(self):
 385         class xcomplex(complex):
 386             def __add__(self,other):
 387                 return xcomplex(complex(self) + other)
 388             __radd__ = __add__
 389
 390             def __sub__(self,other):
 391                 return xcomplex(complex(self) + other)
 392             __rsub__ = __sub__
 393
 394             def __mul__(self,other):
 395                 return xcomplex(complex(self) * other)
 396             __rmul__ = __mul__
 397
 398             def __div__(self,other):
 399                 return xcomplex(complex(self) / other)
 400
 401             def __rdiv__(self,other):
 402                 return xcomplex(other / complex(self))
 403
 404             __truediv__ = __div__
 405             __rtruediv__ = __rdiv__
 406
 407             def __floordiv__(self,other):
 408                 return xcomplex(complex(self) // other)
 409
 410             def __rfloordiv__(self,other):
 411                 return xcomplex(other // complex(self))
 412
 413             def __pow__(self,other):
 414                 return xcomplex(complex(self) ** other)
 415
 416             def __rpow__(self,other):
 417                 return xcomplex(other ** complex(self) )
 418
 419             def __mod__(self,other):
 420                 return xcomplex(complex(self) % other)
 421
 422             def __rmod__(self,other):
 423                 return xcomplex(other % complex(self))
 424
 425         infix_binops = ('+', '-', '*', '**', '%', '//', '/')
 426         xcomplex_values = (xcomplex(1), xcomplex(123.0),
 427                            xcomplex(-10+2j), xcomplex(3+187j),
 428                            xcomplex(3-78j))
 429         test_values = (1, 123.0, 10-19j, xcomplex(1+2j),
 430                        xcomplex(1+87j), xcomplex(10+90j))
 431
 432         for op in infix_binops:
 433             for x in xcomplex_values:
 434                 for y in test_values:
 435                     a = 'x %s y' % op
 436                     b = 'y %s x' % op
 437                     self.assertTrue(type(eval(a)) is type(eval(b)) is xcomplex)
 438
 439     def test_hash(self):
 440         for x in xrange(-30, 30):
 441             self.assertEqual(hash(x), hash(complex(x, 0)))
 442             x /= 3.0    # now check against floating point
 443             self.assertEqual(hash(x), hash(complex(x, 0.)))
 444
 445     def test_abs(self):
 446         nums = [complex(x/3., y/7.) for x in xrange(-9,9) for y in xrange(-9,9)]
 447         for num in nums:
 448             self.assertAlmostEqual((num.real**2 + num.imag**2)  ** 0.5, abs(num))
 449
 450     def test_repr(self):
 451         self.assertEqual(repr(1+6j), '(1+6j)')
 452         self.assertEqual(repr(1-6j), '(1-6j)')
 453
 454         self.assertNotEqual(repr(-(1+0j)), '(-1+-0j)')
 455
 456         self.assertEqual(1-6j,complex(repr(1-6j)))
 457         self.assertEqual(1+6j,complex(repr(1+6j)))
 458         self.assertEqual(-6j,complex(repr(-6j)))
 459         self.assertEqual(6j,complex(repr(6j)))
 460
 461         self.assertEqual(repr(complex(1., INF)), "(1+infj)")
 462         self.assertEqual(repr(complex(1., -INF)), "(1-infj)")
 463         self.assertEqual(repr(complex(INF, 1)), "(inf+1j)")
 464         self.assertEqual(repr(complex(-INF, INF)), "(-inf+infj)")
 465         self.assertEqual(repr(complex(NAN, 1)), "(nan+1j)")
 466         self.assertEqual(repr(complex(1, NAN)), "(1+nanj)")
 467         self.assertEqual(repr(complex(NAN, NAN)), "(nan+nanj)")
 468
 469         self.assertEqual(repr(complex(0, INF)), "infj")
 470         self.assertEqual(repr(complex(0, -INF)), "-infj")
 471         self.assertEqual(repr(complex(0, NAN)), "nanj")
 472
 473     def test_neg(self):
 474         self.assertEqual(-(1+6j), -1-6j)
 475
 476     def test_file(self):
 477         a = 3.33+4.43j
 478         b = 5.1+2.3j
 479
 480         fo = None
 481         try:
 482             fo = open(test_support.TESTFN, "wb")
 483             print >>fo, a, b
 484             fo.close()
 485             fo = open(test_support.TESTFN, "rb")
 486             self.assertEqual(fo.read(), "%s %s\n" % (a, b))
 487         finally:
 488             if (fo is not None) and (not fo.closed):
 489                 fo.close()
 490             test_support.unlink(test_support.TESTFN)
 491
 492     def test_getnewargs(self):
 493         self.assertEqual((1+2j).__getnewargs__(), (1.0, 2.0))
 494         self.assertEqual((1-2j).__getnewargs__(), (1.0, -2.0))
 495         self.assertEqual((2j).__getnewargs__(), (0.0, 2.0))
 496         self.assertEqual((-0j).__getnewargs__(), (0.0, -0.0))
 497         self.assertEqual(complex(0, INF).__getnewargs__(), (0.0, INF))
 498         self.assertEqual(complex(INF, 0).__getnewargs__(), (INF, 0.0))
 499
 500     if float.__getformat__("double").startswith("IEEE"):
 501         def test_plus_minus_0j(self):
 502             # test that -0j and 0j literals are not identified
 503             z1, z2 = 0j, -0j
 504             self.assertEquals(atan2(z1.imag, -1.), atan2(0., -1.))
 505             self.assertEquals(atan2(z2.imag, -1.), atan2(-0., -1.))
 506
 507     @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
 508                          "test requires IEEE 754 doubles")
 509     def test_overflow(self):
 510         self.assertEqual(complex("1e500"), complex(INF, 0.0))
 511         self.assertEqual(complex("-1e500j"), complex(0.0, -INF))
 512         self.assertEqual(complex("-1e500+1.8e308j"), complex(-INF, INF))
 513
 514     @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
 515                          "test requires IEEE 754 doubles")
 516     def test_repr_roundtrip(self):
 517         vals = [0.0, 1e-500, 1e-315, 1e-200, 0.0123, 3.1415, 1e50, INF, NAN]
 518         vals += [-v for v in vals]
 519
 520         # complex(repr(z)) should recover z exactly, even for complex
 521         # numbers involving an infinity, nan, or negative zero
 522         for x in vals:
 523             for y in vals:
 524                 z = complex(x, y)
 525                 roundtrip = complex(repr(z))
 526                 self.assertFloatsAreIdentical(z.real, roundtrip.real)
 527                 self.assertFloatsAreIdentical(z.imag, roundtrip.imag)
 528
 529         # if we predefine some constants, then eval(repr(z)) should
 530         # also work, except that it might change the sign of zeros
 531         inf, nan = float('inf'), float('nan')
 532         infj, nanj = complex(0.0, inf), complex(0.0, nan)
 533         for x in vals:
 534             for y in vals:
 535                 z = complex(x, y)
 536                 roundtrip = eval(repr(z))
 537                 # adding 0.0 has no effect beside changing -0.0 to 0.0
 538                 self.assertFloatsAreIdentical(0.0 + z.real,
 539                                               0.0 + roundtrip.real)
 540                 self.assertFloatsAreIdentical(0.0 + z.imag,
 541                                               0.0 + roundtrip.imag)
 542
 543     def test_format(self):
 544         # empty format string is same as str()
 545         self.assertEqual(format(1+3j, ''), str(1+3j))
 546         self.assertEqual(format(1.5+3.5j, ''), str(1.5+3.5j))
 547         self.assertEqual(format(3j, ''), str(3j))
 548         self.assertEqual(format(3.2j, ''), str(3.2j))
 549         self.assertEqual(format(3+0j, ''), str(3+0j))
 550         self.assertEqual(format(3.2+0j, ''), str(3.2+0j))
 551
 552         # empty presentation type should still be analogous to str,
 553         # even when format string is nonempty (issue #5920).
 554         self.assertEqual(format(3.2+0j, '-'), str(3.2+0j))
 555         self.assertEqual(format(3.2+0j, '<'), str(3.2+0j))
 556         z = 4/7. - 100j/7.
 557         self.assertEqual(format(z, ''), str(z))
 558         self.assertEqual(format(z, '-'), str(z))
 559         self.assertEqual(format(z, '<'), str(z))
 560         self.assertEqual(format(z, '10'), str(z))
 561
 562         self.assertEqual(format(1+3j, 'g'), '1+3j')
 563         self.assertEqual(format(3j, 'g'), '0+3j')
 564         self.assertEqual(format(1.5+3.5j, 'g'), '1.5+3.5j')
 565
 566         self.assertEqual(format(1.5+3.5j, '+g'), '+1.5+3.5j')
 567         self.assertEqual(format(1.5-3.5j, '+g'), '+1.5-3.5j')
 568         self.assertEqual(format(1.5-3.5j, '-g'), '1.5-3.5j')
 569         self.assertEqual(format(1.5+3.5j, ' g'), ' 1.5+3.5j')
 570         self.assertEqual(format(1.5-3.5j, ' g'), ' 1.5-3.5j')
 571         self.assertEqual(format(-1.5+3.5j, ' g'), '-1.5+3.5j')
 572         self.assertEqual(format(-1.5-3.5j, ' g'), '-1.5-3.5j')
 573
 574         self.assertEqual(format(-1.5-3.5e-20j, 'g'), '-1.5-3.5e-20j')
 575         self.assertEqual(format(-1.5-3.5j, 'f'), '-1.500000-3.500000j')
 576         self.assertEqual(format(-1.5-3.5j, 'F'), '-1.500000-3.500000j')
 577         self.assertEqual(format(-1.5-3.5j, 'e'), '-1.500000e+00-3.500000e+00j')
 578         self.assertEqual(format(-1.5-3.5j, '.2e'), '-1.50e+00-3.50e+00j')
 579         self.assertEqual(format(-1.5-3.5j, '.2E'), '-1.50E+00-3.50E+00j')
 580         self.assertEqual(format(-1.5e10-3.5e5j, '.2G'), '-1.5E+10-3.5E+05j')
 581
 582         self.assertEqual(format(1.5+3j, '<20g'),  '1.5+3j              ')
 583         self.assertEqual(format(1.5+3j, '*<20g'), '1.5+3j**************')
 584         self.assertEqual(format(1.5+3j, '>20g'),  '              1.5+3j')
 585         self.assertEqual(format(1.5+3j, '^20g'),  '       1.5+3j       ')
 586         self.assertEqual(format(1.5+3j, '<20'),   '(1.5+3j)            ')
 587         self.assertEqual(format(1.5+3j, '>20'),   '            (1.5+3j)')
 588         self.assertEqual(format(1.5+3j, '^20'),   '      (1.5+3j)      ')
 589         self.assertEqual(format(1.123-3.123j, '^20.2'), '     (1.1-3.1j)     ')
 590
 591         self.assertEqual(format(1.5+3j, '20.2f'), '          1.50+3.00j')
 592         self.assertEqual(format(1.5+3j, '>20.2f'), '          1.50+3.00j')
 593         self.assertEqual(format(1.5+3j, '<20.2f'), '1.50+3.00j          ')
 594         self.assertEqual(format(1.5e20+3j, '<20.2f'), '150000000000000000000.00+3.00j')
 595         self.assertEqual(format(1.5e20+3j, '>40.2f'), '          150000000000000000000.00+3.00j')
 596         self.assertEqual(format(1.5e20+3j, '^40,.2f'), '  150,000,000,000,000,000,000.00+3.00j  ')
 597         self.assertEqual(format(1.5e21+3j, '^40,.2f'), ' 1,500,000,000,000,000,000,000.00+3.00j ')
 598         self.assertEqual(format(1.5e21+3000j, ',.2f'), '1,500,000,000,000,000,000,000.00+3,000.00j')
 599
 600         # alternate is invalid
 601         self.assertRaises(ValueError, (1.5+0.5j).__format__, '#f')
 602
 603         # zero padding is invalid
 604         self.assertRaises(ValueError, (1.5+0.5j).__format__, '010f')
 605
 606         # '=' alignment is invalid
 607         self.assertRaises(ValueError, (1.5+3j).__format__, '=20')
 608
 609         # integer presentation types are an error
 610         for t in 'bcdoxX':
 611             self.assertRaises(ValueError, (1.5+0.5j).__format__, t)
 612
 613         # make sure everything works in ''.format()
 614         self.assertEqual('*{0:.3f}*'.format(3.14159+2.71828j), '*3.142+2.718j*')
 615
 616         # issue 3382: 'f' and 'F' with inf's and nan's
 617         self.assertEqual('{0:f}'.format(INF+0j), 'inf+0.000000j')
 618         self.assertEqual('{0:F}'.format(INF+0j), 'INF+0.000000j')
 619         self.assertEqual('{0:f}'.format(-INF+0j), '-inf+0.000000j')
 620         self.assertEqual('{0:F}'.format(-INF+0j), '-INF+0.000000j')
 621         self.assertEqual('{0:f}'.format(complex(INF, INF)), 'inf+infj')
 622         self.assertEqual('{0:F}'.format(complex(INF, INF)), 'INF+INFj')
 623         self.assertEqual('{0:f}'.format(complex(INF, -INF)), 'inf-infj')
 624         self.assertEqual('{0:F}'.format(complex(INF, -INF)), 'INF-INFj')
 625         self.assertEqual('{0:f}'.format(complex(-INF, INF)), '-inf+infj')
 626         self.assertEqual('{0:F}'.format(complex(-INF, INF)), '-INF+INFj')
 627         self.assertEqual('{0:f}'.format(complex(-INF, -INF)), '-inf-infj')
 628         self.assertEqual('{0:F}'.format(complex(-INF, -INF)), '-INF-INFj')
 629
 630         self.assertEqual('{0:f}'.format(complex(NAN, 0)), 'nan+0.000000j')
 631         self.assertEqual('{0:F}'.format(complex(NAN, 0)), 'NAN+0.000000j')
 632         self.assertEqual('{0:f}'.format(complex(NAN, NAN)), 'nan+nanj')
 633         self.assertEqual('{0:F}'.format(complex(NAN, NAN)), 'NAN+NANj')
 634
 635 def test_main():
 636     with test_support.check_warnings(("complex divmod.., // and % are "
 637                                       "deprecated", DeprecationWarning)):
 638         test_support.run_unittest(ComplexTest)
 639
 640 if __name__ == "__main__":
 641     test_main()