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 operator
   7 import fractions
   8 import unittest
   9 from copy import copy, deepcopy
  10 from cPickle import dumps, loads
  11 F = fractions.Fraction
  12 gcd = fractions.gcd
  13
  14
  15 class GcdTest(unittest.TestCase):
  16
  17     def testMisc(self):
  18         self.assertEquals(0, gcd(0, 0))
  19         self.assertEquals(1, gcd(1, 0))
  20         self.assertEquals(-1, gcd(-1, 0))
  21         self.assertEquals(1, gcd(0, 1))
  22         self.assertEquals(-1, gcd(0, -1))
  23         self.assertEquals(1, gcd(7, 1))
  24         self.assertEquals(-1, gcd(7, -1))
  25         self.assertEquals(1, gcd(-23, 15))
  26         self.assertEquals(12, gcd(120, 84))
  27         self.assertEquals(-12, gcd(84, -120))
  28
  29
  30 def _components(r):
  31     return (r.numerator, r.denominator)
  32
  33
  34 class FractionTest(unittest.TestCase):
  35
  36     def assertTypedEquals(self, expected, actual):
  37         """Asserts that both the types and values are the same."""
  38         self.assertEquals(type(expected), type(actual))
  39         self.assertEquals(expected, actual)
  40
  41     def assertRaisesMessage(self, exc_type, message,
  42                             callable, *args, **kwargs):
  43         """Asserts that callable(*args, **kwargs) raises exc_type(message)."""
  44         try:
  45             callable(*args, **kwargs)
  46         except exc_type, e:
  47             self.assertEquals(message, str(e))
  48         else:
  49             self.fail("%s not raised" % exc_type.__name__)
  50
  51     def testInit(self):
  52         self.assertEquals((0, 1), _components(F()))
  53         self.assertEquals((7, 1), _components(F(7)))
  54         self.assertEquals((7, 3), _components(F(F(7, 3))))
  55
  56         self.assertEquals((-1, 1), _components(F(-1, 1)))
  57         self.assertEquals((-1, 1), _components(F(1, -1)))
  58         self.assertEquals((1, 1), _components(F(-2, -2)))
  59         self.assertEquals((1, 2), _components(F(5, 10)))
  60         self.assertEquals((7, 15), _components(F(7, 15)))
  61         self.assertEquals((10**23, 1), _components(F(10**23)))
  62
  63         self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
  64                                  F, 12, 0)
  65         self.assertRaises(TypeError, F, 1.5)
  66         self.assertRaises(TypeError, F, 1.5 + 3j)
  67
  68         self.assertRaises(TypeError, F, F(1, 2), 3)
  69         self.assertRaises(TypeError, F, "3/2", 3)
  70
  71     def testFromString(self):
  72         self.assertEquals((5, 1), _components(F("5")))
  73         self.assertEquals((3, 2), _components(F("3/2")))
  74         self.assertEquals((3, 2), _components(F(" \n  +3/2")))
  75         self.assertEquals((-3, 2), _components(F("-3/2  ")))
  76         self.assertEquals((13, 2), _components(F("    013/02 \n  ")))
  77         self.assertEquals((13, 2), _components(F(u"    013/02 \n  ")))
  78
  79         self.assertEquals((16, 5), _components(F(" 3.2 ")))
  80         self.assertEquals((-16, 5), _components(F(u" -3.2 ")))
  81         self.assertEquals((-3, 1), _components(F(u" -3. ")))
  82         self.assertEquals((3, 5), _components(F(u" .6 ")))
  83
  84
  85         self.assertRaisesMessage(
  86             ZeroDivisionError, "Fraction(3, 0)",
  87             F, "3/0")
  88         self.assertRaisesMessage(
  89             ValueError, "Invalid literal for Fraction: '3/'",
  90             F, "3/")
  91         self.assertRaisesMessage(
  92             ValueError, "Invalid literal for Fraction: '3 /2'",
  93             F, "3 /2")
  94         self.assertRaisesMessage(
  95             # Denominators don't need a sign.
  96             ValueError, "Invalid literal for Fraction: '3/+2'",
  97             F, "3/+2")
  98         self.assertRaisesMessage(
  99             # Imitate float's parsing.
 100             ValueError, "Invalid literal for Fraction: '+ 3/2'",
 101             F, "+ 3/2")
 102         self.assertRaisesMessage(
 103             # Avoid treating '.' as a regex special character.
 104             ValueError, "Invalid literal for Fraction: '3a2'",
 105             F, "3a2")
 106         self.assertRaisesMessage(
 107             # Only parse ordinary decimals, not scientific form.
 108             ValueError, "Invalid literal for Fraction: '3.2e4'",
 109             F, "3.2e4")
 110         self.assertRaisesMessage(
 111             # Don't accept combinations of decimals and fractions.
 112             ValueError, "Invalid literal for Fraction: '3/7.2'",
 113             F, "3/7.2")
 114         self.assertRaisesMessage(
 115             # Don't accept combinations of decimals and fractions.
 116             ValueError, "Invalid literal for Fraction: '3.2/7'",
 117             F, "3.2/7")
 118         self.assertRaisesMessage(
 119             # Allow 3. and .3, but not .
 120             ValueError, "Invalid literal for Fraction: '.'",
 121             F, ".")
 122
 123     def testImmutable(self):
 124         r = F(7, 3)
 125         r.__init__(2, 15)
 126         self.assertEquals((7, 3), _components(r))
 127
 128         self.assertRaises(AttributeError, setattr, r, 'numerator', 12)
 129         self.assertRaises(AttributeError, setattr, r, 'denominator', 6)
 130         self.assertEquals((7, 3), _components(r))
 131
 132         # But if you _really_ need to:
 133         r._numerator = 4
 134         r._denominator = 2
 135         self.assertEquals((4, 2), _components(r))
 136         # Which breaks some important operations:
 137         self.assertNotEquals(F(4, 2), r)
 138
 139     def testFromFloat(self):
 140         self.assertRaises(TypeError, F.from_float, 3+4j)
 141         self.assertEquals((10, 1), _components(F.from_float(10)))
 142         self.assertEquals((0, 1), _components(F.from_float(-0.0)))
 143         self.assertEquals((10, 1), _components(F.from_float(10.0)))
 144         self.assertEquals((-5, 2), _components(F.from_float(-2.5)))
 145         self.assertEquals((99999999999999991611392, 1),
 146                           _components(F.from_float(1e23)))
 147         self.assertEquals(float(10**23), float(F.from_float(1e23)))
 148         self.assertEquals((3602879701896397, 1125899906842624),
 149                           _components(F.from_float(3.2)))
 150         self.assertEquals(3.2, float(F.from_float(3.2)))
 151
 152         inf = 1e1000
 153         nan = inf - inf
 154         self.assertRaisesMessage(
 155             TypeError, "Cannot convert inf to Fraction.",
 156             F.from_float, inf)
 157         self.assertRaisesMessage(
 158             TypeError, "Cannot convert -inf to Fraction.",
 159             F.from_float, -inf)
 160         self.assertRaisesMessage(
 161             TypeError, "Cannot convert nan to Fraction.",
 162             F.from_float, nan)
 163
 164     def testFromDecimal(self):
 165         self.assertRaises(TypeError, F.from_decimal, 3+4j)
 166         self.assertEquals(F(10, 1), F.from_decimal(10))
 167         self.assertEquals(F(0), F.from_decimal(Decimal("-0")))
 168         self.assertEquals(F(5, 10), F.from_decimal(Decimal("0.5")))
 169         self.assertEquals(F(5, 1000), F.from_decimal(Decimal("5e-3")))
 170         self.assertEquals(F(5000), F.from_decimal(Decimal("5e3")))
 171         self.assertEquals(1 - F(1, 10**30),
 172                           F.from_decimal(Decimal("0." + "9" * 30)))
 173
 174         self.assertRaisesMessage(
 175             TypeError, "Cannot convert Infinity to Fraction.",
 176             F.from_decimal, Decimal("inf"))
 177         self.assertRaisesMessage(
 178             TypeError, "Cannot convert -Infinity to Fraction.",
 179             F.from_decimal, Decimal("-inf"))
 180         self.assertRaisesMessage(
 181             TypeError, "Cannot convert NaN to Fraction.",
 182             F.from_decimal, Decimal("nan"))
 183         self.assertRaisesMessage(
 184             TypeError, "Cannot convert sNaN to Fraction.",
 185             F.from_decimal, Decimal("snan"))
 186
 187     def testLimitDenominator(self):
 188         rpi = F('3.1415926535897932')
 189         self.assertEqual(rpi.limit_denominator(10000), F(355, 113))
 190         self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113))
 191         self.assertEqual(rpi.limit_denominator(113), F(355, 113))
 192         self.assertEqual(rpi.limit_denominator(112), F(333, 106))
 193         self.assertEqual(F(201, 200).limit_denominator(100), F(1))
 194         self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101))
 195         self.assertEqual(F(0).limit_denominator(10000), F(0))
 196
 197     def testConversions(self):
 198         self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
 199         self.assertTypedEquals(-1, int(F(-11, 10)))
 200
 201         self.assertEquals(False, bool(F(0, 1)))
 202         self.assertEquals(True, bool(F(3, 2)))
 203         self.assertTypedEquals(0.1, float(F(1, 10)))
 204
 205         # Check that __float__ isn't implemented by converting the
 206         # numerator and denominator to float before dividing.
 207         self.assertRaises(OverflowError, float, long('2'*400+'7'))
 208         self.assertAlmostEquals(2.0/3,
 209                                 float(F(long('2'*400+'7'), long('3'*400+'1'))))
 210
 211         self.assertTypedEquals(0.1+0j, complex(F(1,10)))
 212
 213
 214     def testArithmetic(self):
 215         self.assertEquals(F(1, 2), F(1, 10) + F(2, 5))
 216         self.assertEquals(F(-3, 10), F(1, 10) - F(2, 5))
 217         self.assertEquals(F(1, 25), F(1, 10) * F(2, 5))
 218         self.assertEquals(F(1, 4), F(1, 10) / F(2, 5))
 219         self.assertTypedEquals(2, F(9, 10) // F(2, 5))
 220         self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
 221         self.assertEquals(F(2, 3), F(-7, 3) % F(3, 2))
 222         self.assertEquals(F(8, 27), F(2, 3) ** F(3))
 223         self.assertEquals(F(27, 8), F(2, 3) ** F(-3))
 224         self.assertTypedEquals(2.0, F(4) ** F(1, 2))
 225         # Will return 1j in 3.0:
 226         self.assertRaises(ValueError, pow, F(-1), F(1, 2))
 227
 228     def testMixedArithmetic(self):
 229         self.assertTypedEquals(F(11, 10), F(1, 10) + 1)
 230         self.assertTypedEquals(1.1, F(1, 10) + 1.0)
 231         self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j))
 232         self.assertTypedEquals(F(11, 10), 1 + F(1, 10))
 233         self.assertTypedEquals(1.1, 1.0 + F(1, 10))
 234         self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10))
 235
 236         self.assertTypedEquals(F(-9, 10), F(1, 10) - 1)
 237         self.assertTypedEquals(-0.9, F(1, 10) - 1.0)
 238         self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j))
 239         self.assertTypedEquals(F(9, 10), 1 - F(1, 10))
 240         self.assertTypedEquals(0.9, 1.0 - F(1, 10))
 241         self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10))
 242
 243         self.assertTypedEquals(F(1, 10), F(1, 10) * 1)
 244         self.assertTypedEquals(0.1, F(1, 10) * 1.0)
 245         self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j))
 246         self.assertTypedEquals(F(1, 10), 1 * F(1, 10))
 247         self.assertTypedEquals(0.1, 1.0 * F(1, 10))
 248         self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10))
 249
 250         self.assertTypedEquals(F(1, 10), F(1, 10) / 1)
 251         self.assertTypedEquals(0.1, F(1, 10) / 1.0)
 252         self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j))
 253         self.assertTypedEquals(F(10, 1), 1 / F(1, 10))
 254         self.assertTypedEquals(10.0, 1.0 / F(1, 10))
 255         self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10))
 256
 257         self.assertTypedEquals(0, F(1, 10) // 1)
 258         self.assertTypedEquals(0.0, F(1, 10) // 1.0)
 259         self.assertTypedEquals(10, 1 // F(1, 10))
 260         self.assertTypedEquals(10**23, 10**22 // F(1, 10))
 261         self.assertTypedEquals(10.0, 1.0 // F(1, 10))
 262
 263         self.assertTypedEquals(F(1, 10), F(1, 10) % 1)
 264         self.assertTypedEquals(0.1, F(1, 10) % 1.0)
 265         self.assertTypedEquals(F(0, 1), 1 % F(1, 10))
 266         self.assertTypedEquals(0.0, 1.0 % F(1, 10))
 267
 268         # No need for divmod since we don't override it.
 269
 270         # ** has more interesting conversion rules.
 271         self.assertTypedEquals(F(100, 1), F(1, 10) ** -2)
 272         self.assertTypedEquals(F(100, 1), F(10, 1) ** 2)
 273         self.assertTypedEquals(0.1, F(1, 10) ** 1.0)
 274         self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j))
 275         self.assertTypedEquals(4 , 2 ** F(2, 1))
 276         # Will return 1j in 3.0:
 277         self.assertRaises(ValueError, pow, (-1), F(1, 2))
 278         self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1))
 279         self.assertTypedEquals(2.0 , 4 ** F(1, 2))
 280         self.assertTypedEquals(0.25, 2.0 ** F(-2, 1))
 281         self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10))
 282
 283     def testMixingWithDecimal(self):
 284         # Decimal refuses mixed comparisons.
 285         self.assertRaisesMessage(
 286             TypeError,
 287             "unsupported operand type(s) for +: 'Fraction' and 'Decimal'",
 288             operator.add, F(3,11), Decimal('3.1415926'))
 289         self.assertNotEquals(F(5, 2), Decimal('2.5'))
 290
 291     def testComparisons(self):
 292         self.assertTrue(F(1, 2) < F(2, 3))
 293         self.assertFalse(F(1, 2) < F(1, 2))
 294         self.assertTrue(F(1, 2) <= F(2, 3))
 295         self.assertTrue(F(1, 2) <= F(1, 2))
 296         self.assertFalse(F(2, 3) <= F(1, 2))
 297         self.assertTrue(F(1, 2) == F(1, 2))
 298         self.assertFalse(F(1, 2) == F(1, 3))
 299         self.assertFalse(F(1, 2) != F(1, 2))
 300         self.assertTrue(F(1, 2) != F(1, 3))
 301
 302     def testMixedLess(self):
 303         self.assertTrue(2 < F(5, 2))
 304         self.assertFalse(2 < F(4, 2))
 305         self.assertTrue(F(5, 2) < 3)
 306         self.assertFalse(F(4, 2) < 2)
 307
 308         self.assertTrue(F(1, 2) < 0.6)
 309         self.assertFalse(F(1, 2) < 0.4)
 310         self.assertTrue(0.4 < F(1, 2))
 311         self.assertFalse(0.5 < F(1, 2))
 312
 313     def testMixedLessEqual(self):
 314         self.assertTrue(0.5 <= F(1, 2))
 315         self.assertFalse(0.6 <= F(1, 2))
 316         self.assertTrue(F(1, 2) <= 0.5)
 317         self.assertFalse(F(1, 2) <= 0.4)
 318         self.assertTrue(2 <= F(4, 2))
 319         self.assertFalse(2 <= F(3, 2))
 320         self.assertTrue(F(4, 2) <= 2)
 321         self.assertFalse(F(5, 2) <= 2)
 322
 323     def testBigFloatComparisons(self):
 324         # Because 10**23 can't be represented exactly as a float:
 325         self.assertFalse(F(10**23) == float(10**23))
 326         # The first test demonstrates why these are important.
 327         self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1)))
 328         self.assertTrue(1e23 < F(math.trunc(1e23) + 1))
 329         self.assertFalse(1e23 <= F(math.trunc(1e23) - 1))
 330         self.assertTrue(1e23 > F(math.trunc(1e23) - 1))
 331         self.assertFalse(1e23 >= F(math.trunc(1e23) + 1))
 332
 333     def testBigComplexComparisons(self):
 334         self.assertFalse(F(10**23) == complex(10**23))
 335         self.assertTrue(F(10**23) > complex(10**23))
 336         self.assertFalse(F(10**23) <= complex(10**23))
 337
 338     def testMixedEqual(self):
 339         self.assertTrue(0.5 == F(1, 2))
 340         self.assertFalse(0.6 == F(1, 2))
 341         self.assertTrue(F(1, 2) == 0.5)
 342         self.assertFalse(F(1, 2) == 0.4)
 343         self.assertTrue(2 == F(4, 2))
 344         self.assertFalse(2 == F(3, 2))
 345         self.assertTrue(F(4, 2) == 2)
 346         self.assertFalse(F(5, 2) == 2)
 347
 348     def testStringification(self):
 349         self.assertEquals("Fraction(7, 3)", repr(F(7, 3)))
 350         self.assertEquals("Fraction(6283185307, 2000000000)",
 351                           repr(F('3.1415926535')))
 352         self.assertEquals("Fraction(-1, 100000000000000000000)",
 353                           repr(F(1, -10**20)))
 354         self.assertEquals("7/3", str(F(7, 3)))
 355         self.assertEquals("7", str(F(7, 1)))
 356
 357     def testHash(self):
 358         self.assertEquals(hash(2.5), hash(F(5, 2)))
 359         self.assertEquals(hash(10**50), hash(F(10**50)))
 360         self.assertNotEquals(hash(float(10**23)), hash(F(10**23)))
 361
 362     def testApproximatePi(self):
 363         # Algorithm borrowed from
 364         # http://docs.python.org/lib/decimal-recipes.html
 365         three = F(3)
 366         lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
 367         while abs(s - lasts) > F(1, 10**9):
 368             lasts = s
 369             n, na = n+na, na+8
 370             d, da = d+da, da+32
 371             t = (t * n) / d
 372             s += t
 373         self.assertAlmostEquals(math.pi, s)
 374
 375     def testApproximateCos1(self):
 376         # Algorithm borrowed from
 377         # http://docs.python.org/lib/decimal-recipes.html
 378         x = F(1)
 379         i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1
 380         while abs(s - lasts) > F(1, 10**9):
 381             lasts = s
 382             i += 2
 383             fact *= i * (i-1)
 384             num *= x * x
 385             sign *= -1
 386             s += num / fact * sign
 387         self.assertAlmostEquals(math.cos(1), s)
 388
 389     def test_copy_deepcopy_pickle(self):
 390         r = F(13, 7)
 391         self.assertEqual(r, loads(dumps(r)))
 392         self.assertEqual(id(r), id(copy(r)))
 393         self.assertEqual(id(r), id(deepcopy(r)))
 394
 395 def test_main():
 396     run_unittest(FractionTest, GcdTest)
 397
 398 if __name__ == '__main__':
 399     test_main()