1 import unittest 2 from test import support 3 from test.test_grammar import (VALID_UNDERSCORE_LITERALS, 4 INVALID_UNDERSCORE_LITERALS) 5 6 from random import random 7 from math import atan2, isnan, copysign 8 import operator 9 10 INF = float("inf") 11 NAN = float("nan") 12 # These tests ensure that complex math does the right thing 13 14 class ComplexTest(unittest.TestCase): 15 16 def assertAlmostEqual(self, a, b): 17 if isinstance(a, complex): 18 if isinstance(b, complex): 19 unittest.TestCase.assertAlmostEqual(self, a.real, b.real) 20 unittest.TestCase.assertAlmostEqual(self, a.imag, b.imag) 21 else: 22 unittest.TestCase.assertAlmostEqual(self, a.real, b) 23 unittest.TestCase.assertAlmostEqual(self, a.imag, 0.) 24 else: 25 if isinstance(b, complex): 26 unittest.TestCase.assertAlmostEqual(self, a, b.real) 27 unittest.TestCase.assertAlmostEqual(self, 0., b.imag) 28 else: 29 unittest.TestCase.assertAlmostEqual(self, a, b) 30 31 def assertCloseAbs(self, x, y, eps=1e-9): 32 """Return true iff floats x and y "are close".""" 33 # put the one with larger magnitude second 34 if abs(x) > abs(y): 35 x, y = y, x 36 if y == 0: 37 return abs(x) < eps 38 if x == 0: 39 return abs(y) < eps 40 # check that relative difference < eps 41 self.assertTrue(abs((x-y)/y) < eps) 42 43 def assertFloatsAreIdentical(self, x, y): 44 """assert that floats x and y are identical, in the sense that: 45 (1) both x and y are nans, or 46 (2) both x and y are infinities, with the same sign, or 47 (3) both x and y are zeros, with the same sign, or 48 (4) x and y are both finite and nonzero, and x == y 49 50 """ 51 msg = 'floats {!r} and {!r} are not identical' 52 53 if isnan(x) or isnan(y): 54 if isnan(x) and isnan(y): 55 return 56 elif x == y: 57 if x != 0.0: 58 return 59 # both zero; check that signs match 60 elif copysign(1.0, x) == copysign(1.0, y): 61 return 62 else: 63 msg += ': zeros have different signs' 64 self.fail(msg.format(x, y)) 65 66 def assertClose(self, x, y, eps=1e-9): 67 """Return true iff complexes x and y "are close".""" 68 self.assertCloseAbs(x.real, y.real, eps) 69 self.assertCloseAbs(x.imag, y.imag, eps) 70 71 def check_div(self, x, y): 72 """Compute complex z=x*y, and check that z/x==y and z/y==x.""" 73 z = x * y 74 if x != 0: 75 q = z / x 76 self.assertClose(q, y) 77 q = z.__truediv__(x) 78 self.assertClose(q, y) 79 if y != 0: 80 q = z / y 81 self.assertClose(q, x) 82 q = z.__truediv__(y) 83 self.assertClose(q, x) 84 85 def test_truediv(self): 86 simple_real = [float(i) for i in range(-5, 6)] 87 simple_complex = [complex(x, y) for x in simple_real for y in simple_real] 88 for x in simple_complex: 89 for y in simple_complex: 90 self.check_div(x, y) 91 92 # A naive complex division algorithm (such as in 2.0) is very prone to 93 # nonsense errors for these (overflows and underflows). 94 self.check_div(complex(1e200, 1e200), 1+0j) 95 self.check_div(complex(1e-200, 1e-200), 1+0j) 96 97 # Just for fun. 98 for i in range(100): 99 self.check_div(complex(random(), random()), 100 complex(random(), random())) 101 102 self.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j) 103 # FIXME: The following currently crashes on Alpha 104 # self.assertRaises(OverflowError, pow, 1e200+1j, 1e200+1j) 105 106 self.assertAlmostEqual(complex.__truediv__(2+0j, 1+1j), 1-1j) 107 self.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j) 108 109 for denom_real, denom_imag in [(0, NAN), (NAN, 0), (NAN, NAN)]: 110 z = complex(0, 0) / complex(denom_real, denom_imag) 111 self.assertTrue(isnan(z.real)) 112 self.assertTrue(isnan(z.imag)) 113 114 def test_floordiv(self): 115 self.assertRaises(TypeError, complex.__floordiv__, 3+0j, 1.5+0j) 116 self.assertRaises(TypeError, complex.__floordiv__, 3+0j, 0+0j) 117 118 def test_richcompare(self): 119 self.assertIs(complex.__eq__(1+1j, 1<<10000), False) 120 self.assertIs(complex.__lt__(1+1j, None), NotImplemented) 121 self.assertIs(complex.__eq__(1+1j, 1+1j), True) 122 self.assertIs(complex.__eq__(1+1j, 2+2j), False) 123 self.assertIs(complex.__ne__(1+1j, 1+1j), False) 124 self.assertIs(complex.__ne__(1+1j, 2+2j), True) 125 for i in range(1, 100): 126 f = i / 100.0 127 self.assertIs(complex.__eq__(f+0j, f), True) 128 self.assertIs(complex.__ne__(f+0j, f), False) 129 self.assertIs(complex.__eq__(complex(f, f), f), False) 130 self.assertIs(complex.__ne__(complex(f, f), f), True) 131 self.assertIs(complex.__lt__(1+1j, 2+2j), NotImplemented) 132 self.assertIs(complex.__le__(1+1j, 2+2j), NotImplemented) 133 self.assertIs(complex.__gt__(1+1j, 2+2j), NotImplemented) 134 self.assertIs(complex.__ge__(1+1j, 2+2j), NotImplemented) 135 self.assertRaises(TypeError, operator.lt, 1+1j, 2+2j) 136 self.assertRaises(TypeError, operator.le, 1+1j, 2+2j) 137 self.assertRaises(TypeError, operator.gt, 1+1j, 2+2j) 138 self.assertRaises(TypeError, operator.ge, 1+1j, 2+2j) 139 self.assertIs(operator.eq(1+1j, 1+1j), True) 140 self.assertIs(operator.eq(1+1j, 2+2j), False) 141 self.assertIs(operator.ne(1+1j, 1+1j), False) 142 self.assertIs(operator.ne(1+1j, 2+2j), True) 143 144 def test_richcompare_boundaries(self): 145 def check(n, deltas, is_equal, imag = 0.0): 146 for delta in deltas: 147 i = n + delta 148 z = complex(i, imag) 149 self.assertIs(complex.__eq__(z, i), is_equal(delta)) 150 self.assertIs(complex.__ne__(z, i), not is_equal(delta)) 151 # For IEEE-754 doubles the following should hold: 152 # x in [2 ** (52 + i), 2 ** (53 + i + 1)] -> x mod 2 ** i == 0 153 # where the interval is representable, of course. 154 for i in range(1, 10): 155 pow = 52 + i 156 mult = 2 ** i 157 check(2 ** pow, range(1, 101), lambda delta: delta % mult == 0) 158 check(2 ** pow, range(1, 101), lambda delta: False, float(i)) 159 check(2 ** 53, range(-100, 0), lambda delta: True) 160 161 def test_mod(self): 162 # % is no longer supported on complex numbers 163 self.assertRaises(TypeError, (1+1j).__mod__, 0+0j) 164 self.assertRaises(TypeError, lambda: (3.33+4.43j) % 0) 165 self.assertRaises(TypeError, (1+1j).__mod__, 4.3j) 166 167 def test_divmod(self): 168 self.assertRaises(TypeError, divmod, 1+1j, 1+0j) 169 self.assertRaises(TypeError, divmod, 1+1j, 0+0j) 170 171 def test_pow(self): 172 self.assertAlmostEqual(pow(1+1j, 0+0j), 1.0) 173 self.assertAlmostEqual(pow(0+0j, 2+0j), 0.0) 174 self.assertRaises(ZeroDivisionError, pow, 0+0j, 1j) 175 self.assertAlmostEqual(pow(1j, -1), 1/1j) 176 self.assertAlmostEqual(pow(1j, 200), 1) 177 self.assertRaises(ValueError, pow, 1+1j, 1+1j, 1+1j) 178 179 a = 3.33+4.43j 180 self.assertEqual(a ** 0j, 1) 181 self.assertEqual(a ** 0.+0.j, 1) 182 183 self.assertEqual(3j ** 0j, 1) 184 self.assertEqual(3j ** 0, 1) 185 186 try: 187 0j ** a 188 except ZeroDivisionError: 189 pass 190 else: 191 self.fail("should fail 0.0 to negative or complex power") 192 193 try: 194 0j ** (3-2j) 195 except ZeroDivisionError: 196 pass 197 else: 198 self.fail("should fail 0.0 to negative or complex power") 199 200 # The following is used to exercise certain code paths 201 self.assertEqual(a ** 105, a ** 105) 202 self.assertEqual(a ** -105, a ** -105) 203 self.assertEqual(a ** -30, a ** -30) 204 205 self.assertEqual(0.0j ** 0, 1) 206 207 b = 5.1+2.3j 208 self.assertRaises(ValueError, pow, a, b, 0) 209 210 def test_boolcontext(self): 211 for i in range(100): 212 self.assertTrue(complex(random() + 1e-6, random() + 1e-6)) 213 self.assertTrue(not complex(0.0, 0.0)) 214 215 def test_conjugate(self): 216 self.assertClose(complex(5.3, 9.8).conjugate(), 5.3-9.8j) 217 218 def test_constructor(self): 219 class OS: 220 def __init__(self, value): self.value = value 221 def __complex__(self): return self.value 222 class NS(object): 223 def __init__(self, value): self.value = value 224 def __complex__(self): return self.value 225 self.assertEqual(complex(OS(1+10j)), 1+10j) 226 self.assertEqual(complex(NS(1+10j)), 1+10j) 227 self.assertRaises(TypeError, complex, OS(None)) 228 self.assertRaises(TypeError, complex, NS(None)) 229 self.assertRaises(TypeError, complex, {}) 230 self.assertRaises(TypeError, complex, NS(1.5)) 231 self.assertRaises(TypeError, complex, NS(1)) 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(10), 10+0j) 237 self.assertAlmostEqual(complex(10+0j), 10+0j) 238 self.assertAlmostEqual(complex(1,10), 1+10j) 239 self.assertAlmostEqual(complex(1,10), 1+10j) 240 self.assertAlmostEqual(complex(1,10.0), 1+10j) 241 self.assertAlmostEqual(complex(1,10), 1+10j) 242 self.assertAlmostEqual(complex(1,10), 1+10j) 243 self.assertAlmostEqual(complex(1,10.0), 1+10j) 244 self.assertAlmostEqual(complex(1.0,10), 1+10j) 245 self.assertAlmostEqual(complex(1.0,10), 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(314), 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(314, 0), 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 # SF bug 543840: complex(string) accepts strings with \0 305 # Fixed in 2.3. 306 self.assertRaises(ValueError, complex, '1+1j\0j') 307 308 self.assertRaises(TypeError, int, 5+3j) 309 self.assertRaises(TypeError, int, 5+3j) 310 self.assertRaises(TypeError, float, 5+3j) 311 self.assertRaises(ValueError, complex, "") 312 self.assertRaises(TypeError, complex, None) 313 self.assertRaisesRegex(TypeError, "not 'NoneType'", complex, None) 314 self.assertRaises(ValueError, complex, "\0") 315 self.assertRaises(ValueError, complex, "3\09") 316 self.assertRaises(TypeError, complex, "1", "2") 317 self.assertRaises(TypeError, complex, "1", 42) 318 self.assertRaises(TypeError, complex, 1, "2") 319 self.assertRaises(ValueError, complex, "1+") 320 self.assertRaises(ValueError, complex, "1+1j+1j") 321 self.assertRaises(ValueError, complex, "--") 322 self.assertRaises(ValueError, complex, "(1+2j") 323 self.assertRaises(ValueError, complex, "1+2j)") 324 self.assertRaises(ValueError, complex, "1+(2j)") 325 self.assertRaises(ValueError, complex, "(1+2j)123") 326 self.assertRaises(ValueError, complex, "x") 327 self.assertRaises(ValueError, complex, "1j+2") 328 self.assertRaises(ValueError, complex, "1e1ej") 329 self.assertRaises(ValueError, complex, "1e++1ej") 330 self.assertRaises(ValueError, complex, ")1+2j(") 331 self.assertRaisesRegex( 332 TypeError, 333 "first argument must be a string or a number, not 'dict'", 334 complex, {1:2}, 1) 335 self.assertRaisesRegex( 336 TypeError, 337 "second argument must be a number, not 'dict'", 338 complex, 1, {1:2}) 339 # the following three are accepted by Python 2.6 340 self.assertRaises(ValueError, complex, "1..1j") 341 self.assertRaises(ValueError, complex, "1.11.1j") 342 self.assertRaises(ValueError, complex, "1e1.1j") 343 344 # check that complex accepts long unicode strings 345 self.assertEqual(type(complex("1"*500)), complex) 346 # check whitespace processing 347 self.assertEqual(complex('\N{EM SPACE}(\N{EN SPACE}1+1j ) '), 1+1j) 348 349 class EvilExc(Exception): 350 pass 351 352 class evilcomplex: 353 def __complex__(self): 354 raise EvilExc 355 356 self.assertRaises(EvilExc, complex, evilcomplex()) 357 358 class float2: 359 def __init__(self, value): 360 self.value = value 361 def __float__(self): 362 return self.value 363 364 self.assertAlmostEqual(complex(float2(42.)), 42) 365 self.assertAlmostEqual(complex(real=float2(17.), imag=float2(23.)), 17+23j) 366 self.assertRaises(TypeError, complex, float2(None)) 367 368 class complex0(complex): 369 """Test usage of __complex__() when inheriting from 'complex'""" 370 def __complex__(self): 371 return 42j 372 373 class complex1(complex): 374 """Test usage of __complex__() with a __new__() method""" 375 def __new__(self, value=0j): 376 return complex.__new__(self, 2*value) 377 def __complex__(self): 378 return self 379 380 class complex2(complex): 381 """Make sure that __complex__() calls fail if anything other than a 382 complex is returned""" 383 def __complex__(self): 384 return None 385 386 self.assertAlmostEqual(complex(complex0(1j)), 42j) 387 self.assertAlmostEqual(complex(complex1(1j)), 2j) 388 self.assertRaises(TypeError, complex, complex2(1j)) 389 390 @support.requires_IEEE_754 391 def test_constructor_special_numbers(self): 392 class complex2(complex): 393 pass 394 for x in 0.0, -0.0, INF, -INF, NAN: 395 for y in 0.0, -0.0, INF, -INF, NAN: 396 with self.subTest(x=x, y=y): 397 z = complex(x, y) 398 self.assertFloatsAreIdentical(z.real, x) 399 self.assertFloatsAreIdentical(z.imag, y) 400 z = complex2(x, y) 401 self.assertIs(type(z), complex2) 402 self.assertFloatsAreIdentical(z.real, x) 403 self.assertFloatsAreIdentical(z.imag, y) 404 z = complex(complex2(x, y)) 405 self.assertIs(type(z), complex) 406 self.assertFloatsAreIdentical(z.real, x) 407 self.assertFloatsAreIdentical(z.imag, y) 408 z = complex2(complex(x, y)) 409 self.assertIs(type(z), complex2) 410 self.assertFloatsAreIdentical(z.real, x) 411 self.assertFloatsAreIdentical(z.imag, y) 412 413 def test_underscores(self): 414 # check underscores 415 for lit in VALID_UNDERSCORE_LITERALS: 416 if not any(ch in lit for ch in 'xXoObB'): 417 self.assertEqual(complex(lit), eval(lit)) 418 self.assertEqual(complex(lit), complex(lit.replace('_', ''))) 419 for lit in INVALID_UNDERSCORE_LITERALS: 420 if lit in ('0_7', '09_99'): # octals are not recognized here 421 continue 422 if not any(ch in lit for ch in 'xXoObB'): 423 self.assertRaises(ValueError, complex, lit) 424 425 def test_hash(self): 426 for x in range(-30, 30): 427 self.assertEqual(hash(x), hash(complex(x, 0))) 428 x /= 3.0 # now check against floating point 429 self.assertEqual(hash(x), hash(complex(x, 0.))) 430 431 def test_abs(self): 432 nums = [complex(x/3., y/7.) for x in range(-9,9) for y in range(-9,9)] 433 for num in nums: 434 self.assertAlmostEqual((num.real**2 + num.imag**2) ** 0.5, abs(num)) 435 436 def test_repr_str(self): 437 def test(v, expected, test_fn=self.assertEqual): 438 test_fn(repr(v), expected) 439 test_fn(str(v), expected) 440 441 test(1+6j, '(1+6j)') 442 test(1-6j, '(1-6j)') 443 444 test(-(1+0j), '(-1+-0j)', test_fn=self.assertNotEqual) 445 446 test(complex(1., INF), "(1+infj)") 447 test(complex(1., -INF), "(1-infj)") 448 test(complex(INF, 1), "(inf+1j)") 449 test(complex(-INF, INF), "(-inf+infj)") 450 test(complex(NAN, 1), "(nan+1j)") 451 test(complex(1, NAN), "(1+nanj)") 452 test(complex(NAN, NAN), "(nan+nanj)") 453 454 test(complex(0, INF), "infj") 455 test(complex(0, -INF), "-infj") 456 test(complex(0, NAN), "nanj") 457 458 self.assertEqual(1-6j,complex(repr(1-6j))) 459 self.assertEqual(1+6j,complex(repr(1+6j))) 460 self.assertEqual(-6j,complex(repr(-6j))) 461 self.assertEqual(6j,complex(repr(6j))) 462 463 @support.requires_IEEE_754 464 def test_negative_zero_repr_str(self): 465 def test(v, expected, test_fn=self.assertEqual): 466 test_fn(repr(v), expected) 467 test_fn(str(v), expected) 468 469 test(complex(0., 1.), "1j") 470 test(complex(-0., 1.), "(-0+1j)") 471 test(complex(0., -1.), "-1j") 472 test(complex(-0., -1.), "(-0-1j)") 473 474 test(complex(0., 0.), "0j") 475 test(complex(0., -0.), "-0j") 476 test(complex(-0., 0.), "(-0+0j)") 477 test(complex(-0., -0.), "(-0-0j)") 478 479 def test_neg(self): 480 self.assertEqual(-(1+6j), -1-6j) 481 482 def test_file(self): 483 a = 3.33+4.43j 484 b = 5.1+2.3j 485 486 fo = None 487 try: 488 fo = open(support.TESTFN, "w") 489 print(a, b, file=fo) 490 fo.close() 491 fo = open(support.TESTFN, "r") 492 self.assertEqual(fo.read(), ("%s %s\n" % (a, b))) 493 finally: 494 if (fo is not None) and (not fo.closed): 495 fo.close() 496 support.unlink(support.TESTFN) 497 498 def test_getnewargs(self): 499 self.assertEqual((1+2j).__getnewargs__(), (1.0, 2.0)) 500 self.assertEqual((1-2j).__getnewargs__(), (1.0, -2.0)) 501 self.assertEqual((2j).__getnewargs__(), (0.0, 2.0)) 502 self.assertEqual((-0j).__getnewargs__(), (0.0, -0.0)) 503 self.assertEqual(complex(0, INF).__getnewargs__(), (0.0, INF)) 504 self.assertEqual(complex(INF, 0).__getnewargs__(), (INF, 0.0)) 505 506 @support.requires_IEEE_754 507 def test_plus_minus_0j(self): 508 # test that -0j and 0j literals are not identified 509 z1, z2 = 0j, -0j 510 self.assertEqual(atan2(z1.imag, -1.), atan2(0., -1.)) 511 self.assertEqual(atan2(z2.imag, -1.), atan2(-0., -1.)) 512 513 @support.requires_IEEE_754 514 def test_negated_imaginary_literal(self): 515 z0 = -0j 516 z1 = -7j 517 z2 = -1e1000j 518 # Note: In versions of Python < 3.2, a negated imaginary literal 519 # accidentally ended up with real part 0.0 instead of -0.0, thanks to a 520 # modification during CST -> AST translation (see issue #9011). That's 521 # fixed in Python 3.2. 522 self.assertFloatsAreIdentical(z0.real, -0.0) 523 self.assertFloatsAreIdentical(z0.imag, -0.0) 524 self.assertFloatsAreIdentical(z1.real, -0.0) 525 self.assertFloatsAreIdentical(z1.imag, -7.0) 526 self.assertFloatsAreIdentical(z2.real, -0.0) 527 self.assertFloatsAreIdentical(z2.imag, -INF) 528 529 @support.requires_IEEE_754 530 def test_overflow(self): 531 self.assertEqual(complex("1e500"), complex(INF, 0.0)) 532 self.assertEqual(complex("-1e500j"), complex(0.0, -INF)) 533 self.assertEqual(complex("-1e500+1.8e308j"), complex(-INF, INF)) 534 535 @support.requires_IEEE_754 536 def test_repr_roundtrip(self): 537 vals = [0.0, 1e-500, 1e-315, 1e-200, 0.0123, 3.1415, 1e50, INF, NAN] 538 vals += [-v for v in vals] 539 540 # complex(repr(z)) should recover z exactly, even for complex 541 # numbers involving an infinity, nan, or negative zero 542 for x in vals: 543 for y in vals: 544 z = complex(x, y) 545 roundtrip = complex(repr(z)) 546 self.assertFloatsAreIdentical(z.real, roundtrip.real) 547 self.assertFloatsAreIdentical(z.imag, roundtrip.imag) 548 549 # if we predefine some constants, then eval(repr(z)) should 550 # also work, except that it might change the sign of zeros 551 inf, nan = float('inf'), float('nan') 552 infj, nanj = complex(0.0, inf), complex(0.0, nan) 553 for x in vals: 554 for y in vals: 555 z = complex(x, y) 556 roundtrip = eval(repr(z)) 557 # adding 0.0 has no effect beside changing -0.0 to 0.0 558 self.assertFloatsAreIdentical(0.0 + z.real, 559 0.0 + roundtrip.real) 560 self.assertFloatsAreIdentical(0.0 + z.imag, 561 0.0 + roundtrip.imag) 562 563 def test_format(self): 564 # empty format string is same as str() 565 self.assertEqual(format(1+3j, ''), str(1+3j)) 566 self.assertEqual(format(1.5+3.5j, ''), str(1.5+3.5j)) 567 self.assertEqual(format(3j, ''), str(3j)) 568 self.assertEqual(format(3.2j, ''), str(3.2j)) 569 self.assertEqual(format(3+0j, ''), str(3+0j)) 570 self.assertEqual(format(3.2+0j, ''), str(3.2+0j)) 571 572 # empty presentation type should still be analogous to str, 573 # even when format string is nonempty (issue #5920). 574 self.assertEqual(format(3.2+0j, '-'), str(3.2+0j)) 575 self.assertEqual(format(3.2+0j, '<'), str(3.2+0j)) 576 z = 4/7. - 100j/7. 577 self.assertEqual(format(z, ''), str(z)) 578 self.assertEqual(format(z, '-'), str(z)) 579 self.assertEqual(format(z, '<'), str(z)) 580 self.assertEqual(format(z, '10'), str(z)) 581 z = complex(0.0, 3.0) 582 self.assertEqual(format(z, ''), str(z)) 583 self.assertEqual(format(z, '-'), str(z)) 584 self.assertEqual(format(z, '<'), str(z)) 585 self.assertEqual(format(z, '2'), str(z)) 586 z = complex(-0.0, 2.0) 587 self.assertEqual(format(z, ''), str(z)) 588 self.assertEqual(format(z, '-'), str(z)) 589 self.assertEqual(format(z, '<'), str(z)) 590 self.assertEqual(format(z, '3'), str(z)) 591 592 self.assertEqual(format(1+3j, 'g'), '1+3j') 593 self.assertEqual(format(3j, 'g'), '0+3j') 594 self.assertEqual(format(1.5+3.5j, 'g'), '1.5+3.5j') 595 596 self.assertEqual(format(1.5+3.5j, '+g'), '+1.5+3.5j') 597 self.assertEqual(format(1.5-3.5j, '+g'), '+1.5-3.5j') 598 self.assertEqual(format(1.5-3.5j, '-g'), '1.5-3.5j') 599 self.assertEqual(format(1.5+3.5j, ' g'), ' 1.5+3.5j') 600 self.assertEqual(format(1.5-3.5j, ' g'), ' 1.5-3.5j') 601 self.assertEqual(format(-1.5+3.5j, ' g'), '-1.5+3.5j') 602 self.assertEqual(format(-1.5-3.5j, ' g'), '-1.5-3.5j') 603 604 self.assertEqual(format(-1.5-3.5e-20j, 'g'), '-1.5-3.5e-20j') 605 self.assertEqual(format(-1.5-3.5j, 'f'), '-1.500000-3.500000j') 606 self.assertEqual(format(-1.5-3.5j, 'F'), '-1.500000-3.500000j') 607 self.assertEqual(format(-1.5-3.5j, 'e'), '-1.500000e+00-3.500000e+00j') 608 self.assertEqual(format(-1.5-3.5j, '.2e'), '-1.50e+00-3.50e+00j') 609 self.assertEqual(format(-1.5-3.5j, '.2E'), '-1.50E+00-3.50E+00j') 610 self.assertEqual(format(-1.5e10-3.5e5j, '.2G'), '-1.5E+10-3.5E+05j') 611 612 self.assertEqual(format(1.5+3j, '<20g'), '1.5+3j ') 613 self.assertEqual(format(1.5+3j, '*<20g'), '1.5+3j**************') 614 self.assertEqual(format(1.5+3j, '>20g'), ' 1.5+3j') 615 self.assertEqual(format(1.5+3j, '^20g'), ' 1.5+3j ') 616 self.assertEqual(format(1.5+3j, '<20'), '(1.5+3j) ') 617 self.assertEqual(format(1.5+3j, '>20'), ' (1.5+3j)') 618 self.assertEqual(format(1.5+3j, '^20'), ' (1.5+3j) ') 619 self.assertEqual(format(1.123-3.123j, '^20.2'), ' (1.1-3.1j) ') 620 621 self.assertEqual(format(1.5+3j, '20.2f'), ' 1.50+3.00j') 622 self.assertEqual(format(1.5+3j, '>20.2f'), ' 1.50+3.00j') 623 self.assertEqual(format(1.5+3j, '<20.2f'), '1.50+3.00j ') 624 self.assertEqual(format(1.5e20+3j, '<20.2f'), '150000000000000000000.00+3.00j') 625 self.assertEqual(format(1.5e20+3j, '>40.2f'), ' 150000000000000000000.00+3.00j') 626 self.assertEqual(format(1.5e20+3j, '^40,.2f'), ' 150,000,000,000,000,000,000.00+3.00j ') 627 self.assertEqual(format(1.5e21+3j, '^40,.2f'), ' 1,500,000,000,000,000,000,000.00+3.00j ') 628 self.assertEqual(format(1.5e21+3000j, ',.2f'), '1,500,000,000,000,000,000,000.00+3,000.00j') 629 630 # Issue 7094: Alternate formatting (specified by #) 631 self.assertEqual(format(1+1j, '.0e'), '1e+00+1e+00j') 632 self.assertEqual(format(1+1j, '#.0e'), '1.e+00+1.e+00j') 633 self.assertEqual(format(1+1j, '.0f'), '1+1j') 634 self.assertEqual(format(1+1j, '#.0f'), '1.+1.j') 635 self.assertEqual(format(1.1+1.1j, 'g'), '1.1+1.1j') 636 self.assertEqual(format(1.1+1.1j, '#g'), '1.10000+1.10000j') 637 638 # Alternate doesn't make a difference for these, they format the same with or without it 639 self.assertEqual(format(1+1j, '.1e'), '1.0e+00+1.0e+00j') 640 self.assertEqual(format(1+1j, '#.1e'), '1.0e+00+1.0e+00j') 641 self.assertEqual(format(1+1j, '.1f'), '1.0+1.0j') 642 self.assertEqual(format(1+1j, '#.1f'), '1.0+1.0j') 643 644 # Misc. other alternate tests 645 self.assertEqual(format((-1.5+0.5j), '#f'), '-1.500000+0.500000j') 646 self.assertEqual(format((-1.5+0.5j), '#.0f'), '-2.+0.j') 647 self.assertEqual(format((-1.5+0.5j), '#e'), '-1.500000e+00+5.000000e-01j') 648 self.assertEqual(format((-1.5+0.5j), '#.0e'), '-2.e+00+5.e-01j') 649 self.assertEqual(format((-1.5+0.5j), '#g'), '-1.50000+0.500000j') 650 self.assertEqual(format((-1.5+0.5j), '.0g'), '-2+0.5j') 651 self.assertEqual(format((-1.5+0.5j), '#.0g'), '-2.+0.5j') 652 653 # zero padding is invalid 654 self.assertRaises(ValueError, (1.5+0.5j).__format__, '010f') 655 656 # '=' alignment is invalid 657 self.assertRaises(ValueError, (1.5+3j).__format__, '=20') 658 659 # integer presentation types are an error 660 for t in 'bcdoxX': 661 self.assertRaises(ValueError, (1.5+0.5j).__format__, t) 662 663 # make sure everything works in ''.format() 664 self.assertEqual('*{0:.3f}*'.format(3.14159+2.71828j), '*3.142+2.718j*') 665 666 # issue 3382 667 self.assertEqual(format(complex(NAN, NAN), 'f'), 'nan+nanj') 668 self.assertEqual(format(complex(1, NAN), 'f'), '1.000000+nanj') 669 self.assertEqual(format(complex(NAN, 1), 'f'), 'nan+1.000000j') 670 self.assertEqual(format(complex(NAN, -1), 'f'), 'nan-1.000000j') 671 self.assertEqual(format(complex(NAN, NAN), 'F'), 'NAN+NANj') 672 self.assertEqual(format(complex(1, NAN), 'F'), '1.000000+NANj') 673 self.assertEqual(format(complex(NAN, 1), 'F'), 'NAN+1.000000j') 674 self.assertEqual(format(complex(NAN, -1), 'F'), 'NAN-1.000000j') 675 self.assertEqual(format(complex(INF, INF), 'f'), 'inf+infj') 676 self.assertEqual(format(complex(1, INF), 'f'), '1.000000+infj') 677 self.assertEqual(format(complex(INF, 1), 'f'), 'inf+1.000000j') 678 self.assertEqual(format(complex(INF, -1), 'f'), 'inf-1.000000j') 679 self.assertEqual(format(complex(INF, INF), 'F'), 'INF+INFj') 680 self.assertEqual(format(complex(1, INF), 'F'), '1.000000+INFj') 681 self.assertEqual(format(complex(INF, 1), 'F'), 'INF+1.000000j') 682 self.assertEqual(format(complex(INF, -1), 'F'), 'INF-1.000000j') 683 684 def test_main(): 685 support.run_unittest(ComplexTest) 686 687 if __name__ == "__main__": 688 test_main() 689
