text: """Tests for Lib/fractions.py."""
  
  from decimal import Decimal
  from test.test_support import run_unittest
  import math
  import operator
  import fractions
  import unittest
  from copy import copy, deepcopy
  from cPickle import dumps, loads
  F = fractions.Fraction
  gcd = fractions.gcd
  
  
  class GcdTest(unittest.TestCase):
  
      def testMisc(self):
          self.assertEquals(0, gcd(0, 0))
          self.assertEquals(1, gcd(1, 0))
          self.assertEquals(-1, gcd(-1, 0))
          self.assertEquals(1, gcd(0, 1))
          self.assertEquals(-1, gcd(0, -1))
          self.assertEquals(1, gcd(7, 1))
          self.assertEquals(-1, gcd(7, -1))
          self.assertEquals(1, gcd(-23, 15))
          self.assertEquals(12, gcd(120, 84))
          self.assertEquals(-12, gcd(84, -120))
  
  
  def _components(r):
      return (r.numerator, r.denominator)
  
  
  class FractionTest(unittest.TestCase):
  
      def assertTypedEquals(self, expected, actual):
          """Asserts that both the types and values are the same."""
          self.assertEquals(type(expected), type(actual))
          self.assertEquals(expected, actual)
  
      def assertRaisesMessage(self, exc_type, message,
                              callable, *args, **kwargs):
          """Asserts that callable(*args, **kwargs) raises exc_type(message)."""
          try:
              callable(*args, **kwargs)
          except exc_type, e:
              self.assertEquals(message, str(e))
          else:
              self.fail("%s not raised" % exc_type.__name__)
  
      def testInit(self):
          self.assertEquals((0, 1), _components(F()))
          self.assertEquals((7, 1), _components(F(7)))
          self.assertEquals((7, 3), _components(F(F(7, 3))))
  
          self.assertEquals((-1, 1), _components(F(-1, 1)))
          self.assertEquals((-1, 1), _components(F(1, -1)))
          self.assertEquals((1, 1), _components(F(-2, -2)))
          self.assertEquals((1, 2), _components(F(5, 10)))
          self.assertEquals((7, 15), _components(F(7, 15)))
          self.assertEquals((10**23, 1), _components(F(10**23)))
  
          self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
                                   F, 12, 0)
          self.assertRaises(TypeError, F, 1.5)
          self.assertRaises(TypeError, F, 1.5 + 3j)
  
          self.assertRaises(TypeError, F, F(1, 2), 3)
          self.assertRaises(TypeError, F, "3/2", 3)
  
      def testFromString(self):
          self.assertEquals((5, 1), _components(F("5")))
          self.assertEquals((3, 2), _components(F("3/2")))
          self.assertEquals((3, 2), _components(F(" \n  +3/2")))
          self.assertEquals((-3, 2), _components(F("-3/2  ")))
          self.assertEquals((13, 2), _components(F("    013/02 \n  ")))
          self.assertEquals((13, 2), _components(F(u"    013/02 \n  ")))
  
          self.assertEquals((16, 5), _components(F(" 3.2 ")))
          self.assertEquals((-16, 5), _components(F(u" -3.2 ")))
          self.assertEquals((-3, 1), _components(F(u" -3. ")))
          self.assertEquals((3, 5), _components(F(u" .6 ")))
  
  
          self.assertRaisesMessage(
              ZeroDivisionError, "Fraction(3, 0)",
              F, "3/0")
          self.assertRaisesMessage(
              ValueError, "Invalid literal for Fraction: '3/'",
              F, "3/")
          self.assertRaisesMessage(
              ValueError, "Invalid literal for Fraction: '3 /2'",
              F, "3 /2")
          self.assertRaisesMessage(
              # Denominators don't need a sign.
              ValueError, "Invalid literal for Fraction: '3/+2'",
              F, "3/+2")
          self.assertRaisesMessage(
              # Imitate float's parsing.
              ValueError, "Invalid literal for Fraction: '+ 3/2'",
              F, "+ 3/2")
          self.assertRaisesMessage(
              # Avoid treating '.' as a regex special character.
              ValueError, "Invalid literal for Fraction: '3a2'",
              F, "3a2")
          self.assertRaisesMessage(
              # Only parse ordinary decimals, not scientific form.
              ValueError, "Invalid literal for Fraction: '3.2e4'",
              F, "3.2e4")
          self.assertRaisesMessage(
              # Don't accept combinations of decimals and fractions.
              ValueError, "Invalid literal for Fraction: '3/7.2'",
              F, "3/7.2")
          self.assertRaisesMessage(
              # Don't accept combinations of decimals and fractions.
              ValueError, "Invalid literal for Fraction: '3.2/7'",
              F, "3.2/7")
          self.assertRaisesMessage(
              # Allow 3. and .3, but not .
              ValueError, "Invalid literal for Fraction: '.'",
              F, ".")
  
      def testImmutable(self):
          r = F(7, 3)
          r.__init__(2, 15)
          self.assertEquals((7, 3), _components(r))
  
          self.assertRaises(AttributeError, setattr, r, 'numerator', 12)
          self.assertRaises(AttributeError, setattr, r, 'denominator', 6)
          self.assertEquals((7, 3), _components(r))
  
          # But if you _really_ need to:
          r._numerator = 4
          r._denominator = 2
          self.assertEquals((4, 2), _components(r))
          # Which breaks some important operations:
          self.assertNotEquals(F(4, 2), r)
  
      def testFromFloat(self):
          self.assertRaises(TypeError, F.from_float, 3+4j)
          self.assertEquals((10, 1), _components(F.from_float(10)))
          bigint = 1234567890123456789
          self.assertEquals((bigint, 1), _components(F.from_float(bigint)))
          self.assertEquals((0, 1), _components(F.from_float(-0.0)))
          self.assertEquals((10, 1), _components(F.from_float(10.0)))
          self.assertEquals((-5, 2), _components(F.from_float(-2.5)))
          self.assertEquals((99999999999999991611392, 1),
                            _components(F.from_float(1e23)))
          self.assertEquals(float(10**23), float(F.from_float(1e23)))
          self.assertEquals((3602879701896397, 1125899906842624),
                            _components(F.from_float(3.2)))
          self.assertEquals(3.2, float(F.from_float(3.2)))
  
          inf = 1e1000
          nan = inf - inf
          self.assertRaisesMessage(
              TypeError, "Cannot convert inf to Fraction.",
              F.from_float, inf)
          self.assertRaisesMessage(
              TypeError, "Cannot convert -inf to Fraction.",
              F.from_float, -inf)
          self.assertRaisesMessage(
              TypeError, "Cannot convert nan to Fraction.",
              F.from_float, nan)
  
      def testFromDecimal(self):
          self.assertRaises(TypeError, F.from_decimal, 3+4j)
          self.assertEquals(F(10, 1), F.from_decimal(10))
          self.assertEquals(F(0), F.from_decimal(Decimal("-0")))
          self.assertEquals(F(5, 10), F.from_decimal(Decimal("0.5")))
          self.assertEquals(F(5, 1000), F.from_decimal(Decimal("5e-3")))
          self.assertEquals(F(5000), F.from_decimal(Decimal("5e3")))
          self.assertEquals(1 - F(1, 10**30),
                            F.from_decimal(Decimal("0." + "9" * 30)))
  
          self.assertRaisesMessage(
              TypeError, "Cannot convert Infinity to Fraction.",
              F.from_decimal, Decimal("inf"))
          self.assertRaisesMessage(
              TypeError, "Cannot convert -Infinity to Fraction.",
              F.from_decimal, Decimal("-inf"))
          self.assertRaisesMessage(
              TypeError, "Cannot convert NaN to Fraction.",
              F.from_decimal, Decimal("nan"))
          self.assertRaisesMessage(
              TypeError, "Cannot convert sNaN to Fraction.",
              F.from_decimal, Decimal("snan"))
  
      def testLimitDenominator(self):
          rpi = F('3.1415926535897932')
          self.assertEqual(rpi.limit_denominator(10000), F(355, 113))
          self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113))
          self.assertEqual(rpi.limit_denominator(113), F(355, 113))
          self.assertEqual(rpi.limit_denominator(112), F(333, 106))
          self.assertEqual(F(201, 200).limit_denominator(100), F(1))
          self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101))
          self.assertEqual(F(0).limit_denominator(10000), F(0))
  
      def testConversions(self):
          self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
          self.assertTypedEquals(-1, int(F(-11, 10)))
  
          self.assertEquals(False, bool(F(0, 1)))
          self.assertEquals(True, bool(F(3, 2)))
          self.assertTypedEquals(0.1, float(F(1, 10)))
  
          # Check that __float__ isn't implemented by converting the
          # numerator and denominator to float before dividing.
          self.assertRaises(OverflowError, float, long('2'*400+'7'))
          self.assertAlmostEquals(2.0/3,
                                  float(F(long('2'*400+'7'), long('3'*400+'1'))))
  
          self.assertTypedEquals(0.1+0j, complex(F(1,10)))
  
  
      def testArithmetic(self):
          self.assertEquals(F(1, 2), F(1, 10) + F(2, 5))
          self.assertEquals(F(-3, 10), F(1, 10) - F(2, 5))
          self.assertEquals(F(1, 25), F(1, 10) * F(2, 5))
          self.assertEquals(F(1, 4), F(1, 10) / F(2, 5))
          self.assertTypedEquals(2, F(9, 10) // F(2, 5))
          self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
          self.assertEquals(F(2, 3), F(-7, 3) % F(3, 2))
          self.assertEquals(F(8, 27), F(2, 3) ** F(3))
          self.assertEquals(F(27, 8), F(2, 3) ** F(-3))
          self.assertTypedEquals(2.0, F(4) ** F(1, 2))
          # Will return 1j in 3.0:
          self.assertRaises(ValueError, pow, F(-1), F(1, 2))
  
      def testMixedArithmetic(self):
          self.assertTypedEquals(F(11, 10), F(1, 10) + 1)
          self.assertTypedEquals(1.1, F(1, 10) + 1.0)
          self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j))
          self.assertTypedEquals(F(11, 10), 1 + F(1, 10))
          self.assertTypedEquals(1.1, 1.0 + F(1, 10))
          self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10))
  
          self.assertTypedEquals(F(-9, 10), F(1, 10) - 1)
          self.assertTypedEquals(-0.9, F(1, 10) - 1.0)
          self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j))
          self.assertTypedEquals(F(9, 10), 1 - F(1, 10))
          self.assertTypedEquals(0.9, 1.0 - F(1, 10))
          self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10))
  
          self.assertTypedEquals(F(1, 10), F(1, 10) * 1)
          self.assertTypedEquals(0.1, F(1, 10) * 1.0)
          self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j))
          self.assertTypedEquals(F(1, 10), 1 * F(1, 10))
          self.assertTypedEquals(0.1, 1.0 * F(1, 10))
          self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10))
  
          self.assertTypedEquals(F(1, 10), F(1, 10) / 1)
          self.assertTypedEquals(0.1, F(1, 10) / 1.0)
          self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j))
          self.assertTypedEquals(F(10, 1), 1 / F(1, 10))
          self.assertTypedEquals(10.0, 1.0 / F(1, 10))
          self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10))
  
          self.assertTypedEquals(0, F(1, 10) // 1)
          self.assertTypedEquals(0.0, F(1, 10) // 1.0)
          self.assertTypedEquals(10, 1 // F(1, 10))
          self.assertTypedEquals(10**23, 10**22 // F(1, 10))
          self.assertTypedEquals(10.0, 1.0 // F(1, 10))
  
          self.assertTypedEquals(F(1, 10), F(1, 10) % 1)
          self.assertTypedEquals(0.1, F(1, 10) % 1.0)
          self.assertTypedEquals(F(0, 1), 1 % F(1, 10))
          self.assertTypedEquals(0.0, 1.0 % F(1, 10))
  
          # No need for divmod since we don't override it.
  
          # ** has more interesting conversion rules.
          self.assertTypedEquals(F(100, 1), F(1, 10) ** -2)
          self.assertTypedEquals(F(100, 1), F(10, 1) ** 2)
          self.assertTypedEquals(0.1, F(1, 10) ** 1.0)
          self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j))
          self.assertTypedEquals(4 , 2 ** F(2, 1))
          # Will return 1j in 3.0:
          self.assertRaises(ValueError, pow, (-1), F(1, 2))
          self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1))
          self.assertTypedEquals(2.0 , 4 ** F(1, 2))
          self.assertTypedEquals(0.25, 2.0 ** F(-2, 1))
          self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10))
  
      def testMixingWithDecimal(self):
          # Decimal refuses mixed comparisons.
          self.assertRaisesMessage(
              TypeError,
              "unsupported operand type(s) for +: 'Fraction' and 'Decimal'",
              operator.add, F(3,11), Decimal('3.1415926'))
          self.assertNotEquals(F(5, 2), Decimal('2.5'))
  
      def testComparisons(self):
          self.assertTrue(F(1, 2) < F(2, 3))
          self.assertFalse(F(1, 2) < F(1, 2))
          self.assertTrue(F(1, 2) <= F(2, 3))
          self.assertTrue(F(1, 2) <= F(1, 2))
          self.assertFalse(F(2, 3) <= F(1, 2))
          self.assertTrue(F(1, 2) == F(1, 2))
          self.assertFalse(F(1, 2) == F(1, 3))
          self.assertFalse(F(1, 2) != F(1, 2))
          self.assertTrue(F(1, 2) != F(1, 3))
  
      def testMixedLess(self):
          self.assertTrue(2 < F(5, 2))
          self.assertFalse(2 < F(4, 2))
          self.assertTrue(F(5, 2) < 3)
          self.assertFalse(F(4, 2) < 2)
  
          self.assertTrue(F(1, 2) < 0.6)
          self.assertFalse(F(1, 2) < 0.4)
          self.assertTrue(0.4 < F(1, 2))
          self.assertFalse(0.5 < F(1, 2))
  
      def testMixedLessEqual(self):
          self.assertTrue(0.5 <= F(1, 2))
          self.assertFalse(0.6 <= F(1, 2))
          self.assertTrue(F(1, 2) <= 0.5)
          self.assertFalse(F(1, 2) <= 0.4)
          self.assertTrue(2 <= F(4, 2))
          self.assertFalse(2 <= F(3, 2))
          self.assertTrue(F(4, 2) <= 2)
          self.assertFalse(F(5, 2) <= 2)
  
      def testBigFloatComparisons(self):
          # Because 10**23 can't be represented exactly as a float:
          self.assertFalse(F(10**23) == float(10**23))
          # The first test demonstrates why these are important.
          self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1)))
          self.assertTrue(1e23 < F(math.trunc(1e23) + 1))
          self.assertFalse(1e23 <= F(math.trunc(1e23) - 1))
          self.assertTrue(1e23 > F(math.trunc(1e23) - 1))
          self.assertFalse(1e23 >= F(math.trunc(1e23) + 1))
  
      def testBigComplexComparisons(self):
          self.assertFalse(F(10**23) == complex(10**23))
          self.assertTrue(F(10**23) > complex(10**23))
          self.assertFalse(F(10**23) <= complex(10**23))
  
      def testMixedEqual(self):
          self.assertTrue(0.5 == F(1, 2))
          self.assertFalse(0.6 == F(1, 2))
          self.assertTrue(F(1, 2) == 0.5)
          self.assertFalse(F(1, 2) == 0.4)
          self.assertTrue(2 == F(4, 2))
          self.assertFalse(2 == F(3, 2))
          self.assertTrue(F(4, 2) == 2)
          self.assertFalse(F(5, 2) == 2)
  
      def testStringification(self):
          self.assertEquals("Fraction(7, 3)", repr(F(7, 3)))
          self.assertEquals("Fraction(6283185307, 2000000000)",
                            repr(F('3.1415926535')))
          self.assertEquals("Fraction(-1, 100000000000000000000)",
                            repr(F(1, -10**20)))
          self.assertEquals("7/3", str(F(7, 3)))
          self.assertEquals("7", str(F(7, 1)))
  
      def testHash(self):
          self.assertEquals(hash(2.5), hash(F(5, 2)))
          self.assertEquals(hash(10**50), hash(F(10**50)))
          self.assertNotEquals(hash(float(10**23)), hash(F(10**23)))
  
      def testApproximatePi(self):
          # Algorithm borrowed from
          # http://docs.python.org/lib/decimal-recipes.html
          three = F(3)
          lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
          while abs(s - lasts) > F(1, 10**9):
              lasts = s
              n, na = n+na, na+8
              d, da = d+da, da+32
              t = (t * n) / d
              s += t
          self.assertAlmostEquals(math.pi, s)
  
      def testApproximateCos1(self):
          # Algorithm borrowed from
          # http://docs.python.org/lib/decimal-recipes.html
          x = F(1)
          i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1
          while abs(s - lasts) > F(1, 10**9):
              lasts = s
              i += 2
              fact *= i * (i-1)
              num *= x * x
              sign *= -1
              s += num / fact * sign
          self.assertAlmostEquals(math.cos(1), s)
  
      def test_copy_deepcopy_pickle(self):
          r = F(13, 7)
          self.assertEqual(r, loads(dumps(r)))
          self.assertEqual(id(r), id(copy(r)))
          self.assertEqual(id(r), id(deepcopy(r)))
  
      def test_slots(self):
          # Issue 4998
          r = F(13, 7)
          self.assertRaises(AttributeError, setattr, r, 'a', 10)
  
  def test_main():
      run_unittest(FractionTest, GcdTest)
  
  if __name__ == '__main__':
      test_main()
  