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()