Lib/test/test_fractions.py

   1 """Tests for Lib/fractions.py."""
   2
   3 from decimal import Decimal
   4 from test.test_support import run_unittest
   5 import math
   6 import numbers
   7 import operator
   8 import fractions
   9 import unittest
  10 from copy import copy, deepcopy
  11 from cPickle import dumps, loads
  12 F = fractions.Fraction
  13 gcd = fractions.gcd
  14
  15 class DummyFloat(object):
  16     """Dummy float class for testing comparisons with Fractions"""
  17
  18     def __init__(self, value):
  19         if not isinstance(value, float):
  20             raise TypeError("DummyFloat can only be initialized from float")
  21         self.value = value
  22
  23     def _richcmp(self, other, op):
  24         if isinstance(other, numbers.Rational):
  25             return op(F.from_float(self.value), other)
  26         elif isinstance(other, DummyFloat):
  27             return op(self.value, other.value)
  28         else:
  29             return NotImplemented
  30
  31     def __eq__(self, other): return self._richcmp(other, operator.eq)
  32     def __le__(self, other): return self._richcmp(other, operator.le)
  33     def __lt__(self, other): return self._richcmp(other, operator.lt)
  34     def __ge__(self, other): return self._richcmp(other, operator.ge)
  35     def __gt__(self, other): return self._richcmp(other, operator.gt)
  36
  37     # shouldn't be calling __float__ at all when doing comparisons
  38     def __float__(self):
  39         assert False, "__float__ should not be invoked for comparisons"
  40
  41     # same goes for subtraction
  42     def __sub__(self, other):
  43         assert False, "__sub__ should not be invoked for comparisons"
  44     __rsub__ = __sub__
  45
  46
  47 class DummyRational(object):
  48     """Test comparison of Fraction with a naive rational implementation."""
  49
  50     def __init__(self, num, den):
  51         g = gcd(num, den)
  52         self.num = num // g
  53         self.den = den // g
  54
  55     def __eq__(self, other):
  56         if isinstance(other, fractions.Fraction):
  57             return (self.num == other._numerator and
  58                     self.den == other._denominator)
  59         else:
  60             return NotImplemented
  61
  62     def __lt__(self, other):
  63         return(self.num * other._denominator < self.den * other._numerator)
  64
  65     def __gt__(self, other):
  66         return(self.num * other._denominator > self.den * other._numerator)
  67
  68     def __le__(self, other):
  69         return(self.num * other._denominator <= self.den * other._numerator)
  70
  71     def __ge__(self, other):
  72         return(self.num * other._denominator >= self.den * other._numerator)
  73
  74     # this class is for testing comparisons; conversion to float
  75     # should never be used for a comparison, since it loses accuracy
  76     def __float__(self):
  77         assert False, "__float__ should not be invoked"
  78
  79 class GcdTest(unittest.TestCase):
  80
  81     def testMisc(self):
  82         self.assertEquals(0, gcd(0, 0))
  83         self.assertEquals(1, gcd(1, 0))
  84         self.assertEquals(-1, gcd(-1, 0))
  85         self.assertEquals(1, gcd(0, 1))
  86         self.assertEquals(-1, gcd(0, -1))
  87         self.assertEquals(1, gcd(7, 1))
  88         self.assertEquals(-1, gcd(7, -1))
  89         self.assertEquals(1, gcd(-23, 15))
  90         self.assertEquals(12, gcd(120, 84))
  91         self.assertEquals(-12, gcd(84, -120))
  92
  93
  94 def _components(r):
  95     return (r.numerator, r.denominator)
  96
  97
  98 class FractionTest(unittest.TestCase):
  99
 100     def assertTypedEquals(self, expected, actual):
 101         """Asserts that both the types and values are the same."""
 102         self.assertEquals(type(expected), type(actual))
 103         self.assertEquals(expected, actual)
 104
 105     def assertRaisesMessage(self, exc_type, message,
 106                             callable, *args, **kwargs):
 107         """Asserts that callable(*args, **kwargs) raises exc_type(message)."""
 108         try:
 109             callable(*args, **kwargs)
 110         except exc_type, e:
 111             self.assertEquals(message, str(e))
 112         else:
 113             self.fail("%s not raised" % exc_type.__name__)
 114
 115     def testInit(self):
 116         self.assertEquals((0, 1), _components(F()))
 117         self.assertEquals((7, 1), _components(F(7)))
 118         self.assertEquals((7, 3), _components(F(F(7, 3))))
 119
 120         self.assertEquals((-1, 1), _components(F(-1, 1)))
 121         self.assertEquals((-1, 1), _components(F(1, -1)))
 122         self.assertEquals((1, 1), _components(F(-2, -2)))
 123         self.assertEquals((1, 2), _components(F(5, 10)))
 124         self.assertEquals((7, 15), _components(F(7, 15)))
 125         self.assertEquals((10**23, 1), _components(F(10**23)))
 126
 127         self.assertEquals((3, 77), _components(F(F(3, 7), 11)))
 128         self.assertEquals((-9, 5), _components(F(2, F(-10, 9))))
 129         self.assertEquals((2486, 2485), _components(F(F(22, 7), F(355, 113))))
 130
 131         self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
 132                                  F, 12, 0)
 133         self.assertRaises(TypeError, F, 1.5)
 134         self.assertRaises(TypeError, F, 1.5 + 3j)
 135
 136         self.assertRaises(TypeError, F, "3/2", 3)
 137         self.assertRaises(TypeError, F, 3, 0j)
 138         self.assertRaises(TypeError, F, 3, 1j)
 139
 140
 141     def testFromString(self):
 142         self.assertEquals((5, 1), _components(F("5")))
 143         self.assertEquals((3, 2), _components(F("3/2")))
 144         self.assertEquals((3, 2), _components(F(" \n  +3/2")))
 145         self.assertEquals((-3, 2), _components(F("-3/2  ")))
 146         self.assertEquals((13, 2), _components(F("    013/02 \n  ")))
 147         self.assertEquals((13, 2), _components(F(u"    013/02 \n  ")))
 148
 149         self.assertEquals((16, 5), _components(F(" 3.2 ")))
 150         self.assertEquals((-16, 5), _components(F(u" -3.2 ")))
 151         self.assertEquals((-3, 1), _components(F(u" -3. ")))
 152         self.assertEquals((3, 5), _components(F(u" .6 ")))
 153         self.assertEquals((1, 3125), _components(F("32.e-5")))
 154         self.assertEquals((1000000, 1), _components(F("1E+06")))
 155         self.assertEquals((-12300, 1), _components(F("-1.23e4")))
 156         self.assertEquals((0, 1), _components(F(" .0e+0\t")))
 157         self.assertEquals((0, 1), _components(F("-0.000e0")))
 158
 159
 160         self.assertRaisesMessage(
 161             ZeroDivisionError, "Fraction(3, 0)",
 162             F, "3/0")
 163         self.assertRaisesMessage(
 164             ValueError, "Invalid literal for Fraction: '3/'",
 165             F, "3/")
 166         self.assertRaisesMessage(
 167             ValueError, "Invalid literal for Fraction: '/2'",
 168             F, "/2")
 169         self.assertRaisesMessage(
 170             ValueError, "Invalid literal for Fraction: '3 /2'",
 171             F, "3 /2")
 172         self.assertRaisesMessage(
 173             # Denominators don't need a sign.
 174             ValueError, "Invalid literal for Fraction: '3/+2'",
 175             F, "3/+2")
 176         self.assertRaisesMessage(
 177             # Imitate float's parsing.
 178             ValueError, "Invalid literal for Fraction: '+ 3/2'",
 179             F, "+ 3/2")
 180         self.assertRaisesMessage(
 181             # Avoid treating '.' as a regex special character.
 182             ValueError, "Invalid literal for Fraction: '3a2'",
 183             F, "3a2")
 184         self.assertRaisesMessage(
 185             # Don't accept combinations of decimals and fractions.
 186             ValueError, "Invalid literal for Fraction: '3/7.2'",
 187             F, "3/7.2")
 188         self.assertRaisesMessage(
 189             # Don't accept combinations of decimals and fractions.
 190             ValueError, "Invalid literal for Fraction: '3.2/7'",
 191             F, "3.2/7")
 192         self.assertRaisesMessage(
 193             # Allow 3. and .3, but not .
 194             ValueError, "Invalid literal for Fraction: '.'",
 195             F, ".")
 196
 197     def testImmutable(self):
 198         r = F(7, 3)
 199         r.__init__(2, 15)
 200         self.assertEquals((7, 3), _components(r))
 201
 202         self.assertRaises(AttributeError, setattr, r, 'numerator', 12)
 203         self.assertRaises(AttributeError, setattr, r, 'denominator', 6)
 204         self.assertEquals((7, 3), _components(r))
 205
 206         # But if you _really_ need to:
 207         r._numerator = 4
 208         r._denominator = 2
 209         self.assertEquals((4, 2), _components(r))
 210         # Which breaks some important operations:
 211         self.assertNotEquals(F(4, 2), r)
 212
 213     def testFromFloat(self):
 214         self.assertRaises(TypeError, F.from_float, 3+4j)
 215         self.assertEquals((10, 1), _components(F.from_float(10)))
 216         bigint = 1234567890123456789
 217         self.assertEquals((bigint, 1), _components(F.from_float(bigint)))
 218         self.assertEquals((0, 1), _components(F.from_float(-0.0)))
 219         self.assertEquals((10, 1), _components(F.from_float(10.0)))
 220         self.assertEquals((-5, 2), _components(F.from_float(-2.5)))
 221         self.assertEquals((99999999999999991611392, 1),
 222                           _components(F.from_float(1e23)))
 223         self.assertEquals(float(10**23), float(F.from_float(1e23)))
 224         self.assertEquals((3602879701896397, 1125899906842624),
 225                           _components(F.from_float(3.2)))
 226         self.assertEquals(3.2, float(F.from_float(3.2)))
 227
 228         inf = 1e1000
 229         nan = inf - inf
 230         self.assertRaisesMessage(
 231             TypeError, "Cannot convert inf to Fraction.",
 232             F.from_float, inf)
 233         self.assertRaisesMessage(
 234             TypeError, "Cannot convert -inf to Fraction.",
 235             F.from_float, -inf)
 236         self.assertRaisesMessage(
 237             TypeError, "Cannot convert nan to Fraction.",
 238             F.from_float, nan)
 239
 240     def testFromDecimal(self):
 241         self.assertRaises(TypeError, F.from_decimal, 3+4j)
 242         self.assertEquals(F(10, 1), F.from_decimal(10))
 243         self.assertEquals(F(0), F.from_decimal(Decimal("-0")))
 244         self.assertEquals(F(5, 10), F.from_decimal(Decimal("0.5")))
 245         self.assertEquals(F(5, 1000), F.from_decimal(Decimal("5e-3")))
 246         self.assertEquals(F(5000), F.from_decimal(Decimal("5e3")))
 247         self.assertEquals(1 - F(1, 10**30),
 248                           F.from_decimal(Decimal("0." + "9" * 30)))
 249
 250         self.assertRaisesMessage(
 251             TypeError, "Cannot convert Infinity to Fraction.",
 252             F.from_decimal, Decimal("inf"))
 253         self.assertRaisesMessage(
 254             TypeError, "Cannot convert -Infinity to Fraction.",
 255             F.from_decimal, Decimal("-inf"))
 256         self.assertRaisesMessage(
 257             TypeError, "Cannot convert NaN to Fraction.",
 258             F.from_decimal, Decimal("nan"))
 259         self.assertRaisesMessage(
 260             TypeError, "Cannot convert sNaN to Fraction.",
 261             F.from_decimal, Decimal("snan"))
 262
 263     def testLimitDenominator(self):
 264         rpi = F('3.1415926535897932')
 265         self.assertEqual(rpi.limit_denominator(10000), F(355, 113))
 266         self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113))
 267         self.assertEqual(rpi.limit_denominator(113), F(355, 113))
 268         self.assertEqual(rpi.limit_denominator(112), F(333, 106))
 269         self.assertEqual(F(201, 200).limit_denominator(100), F(1))
 270         self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101))
 271         self.assertEqual(F(0).limit_denominator(10000), F(0))
 272
 273     def testConversions(self):
 274         self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
 275         self.assertTypedEquals(-1, int(F(-11, 10)))
 276
 277         self.assertEquals(False, bool(F(0, 1)))
 278         self.assertEquals(True, bool(F(3, 2)))
 279         self.assertTypedEquals(0.1, float(F(1, 10)))
 280
 281         # Check that __float__ isn't implemented by converting the
 282         # numerator and denominator to float before dividing.
 283         self.assertRaises(OverflowError, float, long('2'*400+'7'))
 284         self.assertAlmostEquals(2.0/3,
 285                                 float(F(long('2'*400+'7'), long('3'*400+'1'))))
 286
 287         self.assertTypedEquals(0.1+0j, complex(F(1,10)))
 288
 289
 290     def testArithmetic(self):
 291         self.assertEquals(F(1, 2), F(1, 10) + F(2, 5))
 292         self.assertEquals(F(-3, 10), F(1, 10) - F(2, 5))
 293         self.assertEquals(F(1, 25), F(1, 10) * F(2, 5))
 294         self.assertEquals(F(1, 4), F(1, 10) / F(2, 5))
 295         self.assertTypedEquals(2, F(9, 10) // F(2, 5))
 296         self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
 297         self.assertEquals(F(2, 3), F(-7, 3) % F(3, 2))
 298         self.assertEquals(F(8, 27), F(2, 3) ** F(3))
 299         self.assertEquals(F(27, 8), F(2, 3) ** F(-3))
 300         self.assertTypedEquals(2.0, F(4) ** F(1, 2))
 301         # Will return 1j in 3.0:
 302         self.assertRaises(ValueError, pow, F(-1), F(1, 2))
 303
 304     def testMixedArithmetic(self):
 305         self.assertTypedEquals(F(11, 10), F(1, 10) + 1)
 306         self.assertTypedEquals(1.1, F(1, 10) + 1.0)
 307         self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j))
 308         self.assertTypedEquals(F(11, 10), 1 + F(1, 10))
 309         self.assertTypedEquals(1.1, 1.0 + F(1, 10))
 310         self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10))
 311
 312         self.assertTypedEquals(F(-9, 10), F(1, 10) - 1)
 313         self.assertTypedEquals(-0.9, F(1, 10) - 1.0)
 314         self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j))
 315         self.assertTypedEquals(F(9, 10), 1 - F(1, 10))
 316         self.assertTypedEquals(0.9, 1.0 - F(1, 10))
 317         self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10))
 318
 319         self.assertTypedEquals(F(1, 10), F(1, 10) * 1)
 320         self.assertTypedEquals(0.1, F(1, 10) * 1.0)
 321         self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j))
 322         self.assertTypedEquals(F(1, 10), 1 * F(1, 10))
 323         self.assertTypedEquals(0.1, 1.0 * F(1, 10))
 324         self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10))
 325
 326         self.assertTypedEquals(F(1, 10), F(1, 10) / 1)
 327         self.assertTypedEquals(0.1, F(1, 10) / 1.0)
 328         self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j))
 329         self.assertTypedEquals(F(10, 1), 1 / F(1, 10))
 330         self.assertTypedEquals(10.0, 1.0 / F(1, 10))
 331         self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10))
 332
 333         self.assertTypedEquals(0, F(1, 10) // 1)
 334         self.assertTypedEquals(0.0, F(1, 10) // 1.0)
 335         self.assertTypedEquals(10, 1 // F(1, 10))
 336         self.assertTypedEquals(10**23, 10**22 // F(1, 10))
 337         self.assertTypedEquals(10.0, 1.0 // F(1, 10))
 338
 339         self.assertTypedEquals(F(1, 10), F(1, 10) % 1)
 340         self.assertTypedEquals(0.1, F(1, 10) % 1.0)
 341         self.assertTypedEquals(F(0, 1), 1 % F(1, 10))
 342         self.assertTypedEquals(0.0, 1.0 % F(1, 10))
 343
 344         # No need for divmod since we don't override it.
 345
 346         # ** has more interesting conversion rules.
 347         self.assertTypedEquals(F(100, 1), F(1, 10) ** -2)
 348         self.assertTypedEquals(F(100, 1), F(10, 1) ** 2)
 349         self.assertTypedEquals(0.1, F(1, 10) ** 1.0)
 350         self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j))
 351         self.assertTypedEquals(4 , 2 ** F(2, 1))
 352         # Will return 1j in 3.0:
 353         self.assertRaises(ValueError, pow, (-1), F(1, 2))
 354         self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1))
 355         self.assertTypedEquals(2.0 , 4 ** F(1, 2))
 356         self.assertTypedEquals(0.25, 2.0 ** F(-2, 1))
 357         self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10))
 358
 359     def testMixingWithDecimal(self):
 360         # Decimal refuses mixed comparisons.
 361         self.assertRaisesMessage(
 362             TypeError,
 363             "unsupported operand type(s) for +: 'Fraction' and 'Decimal'",
 364             operator.add, F(3,11), Decimal('3.1415926'))
 365         self.assertNotEquals(F(5, 2), Decimal('2.5'))
 366
 367     def testComparisons(self):
 368         self.assertTrue(F(1, 2) < F(2, 3))
 369         self.assertFalse(F(1, 2) < F(1, 2))
 370         self.assertTrue(F(1, 2) <= F(2, 3))
 371         self.assertTrue(F(1, 2) <= F(1, 2))
 372         self.assertFalse(F(2, 3) <= F(1, 2))
 373         self.assertTrue(F(1, 2) == F(1, 2))
 374         self.assertFalse(F(1, 2) == F(1, 3))
 375         self.assertFalse(F(1, 2) != F(1, 2))
 376         self.assertTrue(F(1, 2) != F(1, 3))
 377
 378     def testComparisonsDummyRational(self):
 379         self.assertTrue(F(1, 2) == DummyRational(1, 2))
 380         self.assertTrue(DummyRational(1, 2) == F(1, 2))
 381         self.assertFalse(F(1, 2) == DummyRational(3, 4))
 382         self.assertFalse(DummyRational(3, 4) == F(1, 2))
 383
 384         self.assertTrue(F(1, 2) < DummyRational(3, 4))
 385         self.assertFalse(F(1, 2) < DummyRational(1, 2))
 386         self.assertFalse(F(1, 2) < DummyRational(1, 7))
 387         self.assertFalse(F(1, 2) > DummyRational(3, 4))
 388         self.assertFalse(F(1, 2) > DummyRational(1, 2))
 389         self.assertTrue(F(1, 2) > DummyRational(1, 7))
 390         self.assertTrue(F(1, 2) <= DummyRational(3, 4))
 391         self.assertTrue(F(1, 2) <= DummyRational(1, 2))
 392         self.assertFalse(F(1, 2) <= DummyRational(1, 7))
 393         self.assertFalse(F(1, 2) >= DummyRational(3, 4))
 394         self.assertTrue(F(1, 2) >= DummyRational(1, 2))
 395         self.assertTrue(F(1, 2) >= DummyRational(1, 7))
 396
 397         self.assertTrue(DummyRational(1, 2) < F(3, 4))
 398         self.assertFalse(DummyRational(1, 2) < F(1, 2))
 399         self.assertFalse(DummyRational(1, 2) < F(1, 7))
 400         self.assertFalse(DummyRational(1, 2) > F(3, 4))
 401         self.assertFalse(DummyRational(1, 2) > F(1, 2))
 402         self.assertTrue(DummyRational(1, 2) > F(1, 7))
 403         self.assertTrue(DummyRational(1, 2) <= F(3, 4))
 404         self.assertTrue(DummyRational(1, 2) <= F(1, 2))
 405         self.assertFalse(DummyRational(1, 2) <= F(1, 7))
 406         self.assertFalse(DummyRational(1, 2) >= F(3, 4))
 407         self.assertTrue(DummyRational(1, 2) >= F(1, 2))
 408         self.assertTrue(DummyRational(1, 2) >= F(1, 7))
 409
 410     def testComparisonsDummyFloat(self):
 411         x = DummyFloat(1./3.)
 412         y = F(1, 3)
 413         self.assertTrue(x != y)
 414         self.assertTrue(x < y or x > y)
 415         self.assertFalse(x == y)
 416         self.assertFalse(x <= y and x >= y)
 417         self.assertTrue(y != x)
 418         self.assertTrue(y < x or y > x)
 419         self.assertFalse(y == x)
 420         self.assertFalse(y <= x and y >= x)
 421
 422     def testMixedLess(self):
 423         self.assertTrue(2 < F(5, 2))
 424         self.assertFalse(2 < F(4, 2))
 425         self.assertTrue(F(5, 2) < 3)
 426         self.assertFalse(F(4, 2) < 2)
 427
 428         self.assertTrue(F(1, 2) < 0.6)
 429         self.assertFalse(F(1, 2) < 0.4)
 430         self.assertTrue(0.4 < F(1, 2))
 431         self.assertFalse(0.5 < F(1, 2))
 432
 433         self.assertFalse(float('inf') < F(1, 2))
 434         self.assertTrue(float('-inf') < F(0, 10))
 435         self.assertFalse(float('nan') < F(-3, 7))
 436         self.assertTrue(F(1, 2) < float('inf'))
 437         self.assertFalse(F(17, 12) < float('-inf'))
 438         self.assertFalse(F(144, -89) < float('nan'))
 439
 440     def testMixedLessEqual(self):
 441         self.assertTrue(0.5 <= F(1, 2))
 442         self.assertFalse(0.6 <= F(1, 2))
 443         self.assertTrue(F(1, 2) <= 0.5)
 444         self.assertFalse(F(1, 2) <= 0.4)
 445         self.assertTrue(2 <= F(4, 2))
 446         self.assertFalse(2 <= F(3, 2))
 447         self.assertTrue(F(4, 2) <= 2)
 448         self.assertFalse(F(5, 2) <= 2)
 449
 450         self.assertFalse(float('inf') <= F(1, 2))
 451         self.assertTrue(float('-inf') <= F(0, 10))
 452         self.assertFalse(float('nan') <= F(-3, 7))
 453         self.assertTrue(F(1, 2) <= float('inf'))
 454         self.assertFalse(F(17, 12) <= float('-inf'))
 455         self.assertFalse(F(144, -89) <= float('nan'))
 456
 457     def testBigFloatComparisons(self):
 458         # Because 10**23 can't be represented exactly as a float:
 459         self.assertFalse(F(10**23) == float(10**23))
 460         # The first test demonstrates why these are important.
 461         self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1)))
 462         self.assertTrue(1e23 < F(math.trunc(1e23) + 1))
 463         self.assertFalse(1e23 <= F(math.trunc(1e23) - 1))
 464         self.assertTrue(1e23 > F(math.trunc(1e23) - 1))
 465         self.assertFalse(1e23 >= F(math.trunc(1e23) + 1))
 466
 467     def testBigComplexComparisons(self):
 468         self.assertFalse(F(10**23) == complex(10**23))
 469         self.assertTrue(F(10**23) > complex(10**23))
 470         self.assertFalse(F(10**23) <= complex(10**23))
 471
 472     def testMixedEqual(self):
 473         self.assertTrue(0.5 == F(1, 2))
 474         self.assertFalse(0.6 == F(1, 2))
 475         self.assertTrue(F(1, 2) == 0.5)
 476         self.assertFalse(F(1, 2) == 0.4)
 477         self.assertTrue(2 == F(4, 2))
 478         self.assertFalse(2 == F(3, 2))
 479         self.assertTrue(F(4, 2) == 2)
 480         self.assertFalse(F(5, 2) == 2)
 481         self.assertFalse(F(5, 2) == float('nan'))
 482         self.assertFalse(float('nan') == F(3, 7))
 483         self.assertFalse(F(5, 2) == float('inf'))
 484         self.assertFalse(float('-inf') == F(2, 5))
 485
 486     def testStringification(self):
 487         self.assertEquals("Fraction(7, 3)", repr(F(7, 3)))
 488         self.assertEquals("Fraction(6283185307, 2000000000)",
 489                           repr(F('3.1415926535')))
 490         self.assertEquals("Fraction(-1, 100000000000000000000)",
 491                           repr(F(1, -10**20)))
 492         self.assertEquals("7/3", str(F(7, 3)))
 493         self.assertEquals("7", str(F(7, 1)))
 494
 495     def testHash(self):
 496         self.assertEquals(hash(2.5), hash(F(5, 2)))
 497         self.assertEquals(hash(10**50), hash(F(10**50)))
 498         self.assertNotEquals(hash(float(10**23)), hash(F(10**23)))
 499
 500     def testApproximatePi(self):
 501         # Algorithm borrowed from
 502         # http://docs.python.org/lib/decimal-recipes.html
 503         three = F(3)
 504         lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
 505         while abs(s - lasts) > F(1, 10**9):
 506             lasts = s
 507             n, na = n+na, na+8
 508             d, da = d+da, da+32
 509             t = (t * n) / d
 510             s += t
 511         self.assertAlmostEquals(math.pi, s)
 512
 513     def testApproximateCos1(self):
 514         # Algorithm borrowed from
 515         # http://docs.python.org/lib/decimal-recipes.html
 516         x = F(1)
 517         i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1
 518         while abs(s - lasts) > F(1, 10**9):
 519             lasts = s
 520             i += 2
 521             fact *= i * (i-1)
 522             num *= x * x
 523             sign *= -1
 524             s += num / fact * sign
 525         self.assertAlmostEquals(math.cos(1), s)
 526
 527     def test_copy_deepcopy_pickle(self):
 528         r = F(13, 7)
 529         self.assertEqual(r, loads(dumps(r)))
 530         self.assertEqual(id(r), id(copy(r)))
 531         self.assertEqual(id(r), id(deepcopy(r)))
 532
 533     def test_slots(self):
 534         # Issue 4998
 535         r = F(13, 7)
 536         self.assertRaises(AttributeError, setattr, r, 'a', 10)
 537
 538 def test_main():
 539     run_unittest(FractionTest, GcdTest)
 540
 541 if __name__ == '__main__':
 542     test_main()