Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60706,60708-60712,60714-60724 via svnmerge from

svn+ssh://pythondev@svn.python.org/python/trunk

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  r60701 | georg.brandl | 2008-02-09 22:36:15 +0100 (Sat, 09 Feb 2008) | 2 lines

  Needs only 2.4 now.
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  r60702 | georg.brandl | 2008-02-09 22:38:54 +0100 (Sat, 09 Feb 2008) | 2 lines

  Docs are rst now.
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  r60703 | georg.brandl | 2008-02-09 23:00:00 +0100 (Sat, 09 Feb 2008) | 2 lines

  Fix link.
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  r60704 | georg.brandl | 2008-02-10 00:09:25 +0100 (Sun, 10 Feb 2008) | 2 lines

  Fix for newest doctools.
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  r60709 | raymond.hettinger | 2008-02-10 08:21:09 +0100 (Sun, 10 Feb 2008) | 1 line

  Clarify that decimal also supports fixed-point arithmetic.
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  r60710 | nick.coghlan | 2008-02-10 08:32:52 +0100 (Sun, 10 Feb 2008) | 1 line

  Add missing NEWS entry for r60695
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  r60712 | mark.dickinson | 2008-02-10 15:58:38 +0100 (Sun, 10 Feb 2008) | 3 lines

  Turn classmethods into staticmethods, and avoid calling the constructor
  of subclasses of Rational.  (See discussion in issue #1682.)
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  r60715 | mark.dickinson | 2008-02-10 16:19:58 +0100 (Sun, 10 Feb 2008) | 2 lines

  Typos in decimal comment and documentation
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  r60716 | skip.montanaro | 2008-02-10 16:31:54 +0100 (Sun, 10 Feb 2008) | 2 lines

  Get the saying right. ;-)
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  r60717 | skip.montanaro | 2008-02-10 16:32:16 +0100 (Sun, 10 Feb 2008) | 2 lines

  whoops - revert
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  r60718 | mark.dickinson | 2008-02-10 20:23:36 +0100 (Sun, 10 Feb 2008) | 2 lines

  Remove reference to Rational
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  r60719 | raymond.hettinger | 2008-02-10 21:35:16 +0100 (Sun, 10 Feb 2008) | 1 line

  Complete an open todo on pickletools -- add a pickle optimizer.
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  r60721 | mark.dickinson | 2008-02-10 22:29:51 +0100 (Sun, 10 Feb 2008) | 3 lines

  Rename rational.Rational to fractions.Fraction, to avoid name clash
  with numbers.Rational.  See issue #1682 for related discussion.
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  r60722 | christian.heimes | 2008-02-11 03:26:22 +0100 (Mon, 11 Feb 2008) | 1 line

  The test requires the network resource
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  r60723 | mark.dickinson | 2008-02-11 04:11:55 +0100 (Mon, 11 Feb 2008) | 3 lines

  Put an extra space into the repr of a Fraction:
  Fraction(1, 2) instead of Fraction(1,2).
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1 files changed, 427 insertions, 0 deletions

diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
new file mode 100644
index 0000000..00fd549
--- /dev/null
+++ b/Lib/test/test_fractions.py
@@ -0,0 +1,427 @@
+"""Tests for Lib/fractions.py."""
+
+from decimal import Decimal
+from test.test_support import run_unittest, verbose
+import math
+import operator
+import fractions
+import unittest
+from copy import copy, deepcopy
+from pickle import dumps, loads
+R = 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 as e:
+            self.assertEquals(message, str(e))
+        else:
+            self.fail("%s not raised" % exc_type.__name__)
+
+    def testInit(self):
+        self.assertEquals((0, 1), _components(R()))
+        self.assertEquals((7, 1), _components(R(7)))
+        self.assertEquals((7, 3), _components(R(R(7, 3))))
+
+        self.assertEquals((-1, 1), _components(R(-1, 1)))
+        self.assertEquals((-1, 1), _components(R(1, -1)))
+        self.assertEquals((1, 1), _components(R(-2, -2)))
+        self.assertEquals((1, 2), _components(R(5, 10)))
+        self.assertEquals((7, 15), _components(R(7, 15)))
+        self.assertEquals((10**23, 1), _components(R(10**23)))
+
+        self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
+                                 R, 12, 0)
+        self.assertRaises(TypeError, R, 1.5)
+        self.assertRaises(TypeError, R, 1.5 + 3j)
+
+        self.assertRaises(TypeError, R, R(1, 2), 3)
+        self.assertRaises(TypeError, R, "3/2", 3)
+
+    def testFromString(self):
+        self.assertEquals((5, 1), _components(R("5")))
+        self.assertEquals((3, 2), _components(R("3/2")))
+        self.assertEquals((3, 2), _components(R(" \n  +3/2")))
+        self.assertEquals((-3, 2), _components(R("-3/2  ")))
+        self.assertEquals((3, 2), _components(R("    03/02 \n  ")))
+        self.assertEquals((3, 2), _components(R("    03/02 \n  ")))
+        self.assertEquals((16, 5), _components(R(" 3.2 ")))
+        self.assertEquals((-16, 5), _components(R(" -3.2 ")))
+        self.assertEquals((-3, 1), _components(R(" -3. ")))
+        self.assertEquals((3, 5), _components(R(" .6 ")))
+
+        self.assertRaisesMessage(
+            ZeroDivisionError, "Fraction(3, 0)",
+            R, "3/0")
+        self.assertRaisesMessage(
+            ValueError, "Invalid literal for Fraction: 3/",
+            R, "3/")
+        self.assertRaisesMessage(
+            ValueError, "Invalid literal for Fraction: 3 /2",
+            R, "3 /2")
+        self.assertRaisesMessage(
+            # Denominators don't need a sign.
+            ValueError, "Invalid literal for Fraction: 3/+2",
+            R, "3/+2")
+        self.assertRaisesMessage(
+            # Imitate float's parsing.
+            ValueError, "Invalid literal for Fraction: + 3/2",
+            R, "+ 3/2")
+        self.assertRaisesMessage(
+            # Avoid treating '.' as a regex special character.
+            ValueError, "Invalid literal for Fraction: 3a2",
+            R, "3a2")
+        self.assertRaisesMessage(
+            # Only parse ordinary decimals, not scientific form.
+            ValueError, "Invalid literal for Fraction: 3.2e4",
+            R, "3.2e4")
+        self.assertRaisesMessage(
+            # Don't accept combinations of decimals and rationals.
+            ValueError, "Invalid literal for Fraction: 3/7.2",
+            R, "3/7.2")
+        self.assertRaisesMessage(
+            # Don't accept combinations of decimals and rationals.
+            ValueError, "Invalid literal for Fraction: 3.2/7",
+            R, "3.2/7")
+        self.assertRaisesMessage(
+            # Allow 3. and .3, but not .
+            ValueError, "Invalid literal for Fraction: .",
+            R, ".")
+
+    def testImmutable(self):
+        r = R(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(R(4, 2), r)
+
+    def testFromFloat(self):
+        self.assertRaisesMessage(
+            TypeError, "Fraction.from_float() only takes floats, not 3 (int)",
+            R.from_float, 3)
+
+        self.assertEquals((0, 1), _components(R.from_float(-0.0)))
+        self.assertEquals((10, 1), _components(R.from_float(10.0)))
+        self.assertEquals((-5, 2), _components(R.from_float(-2.5)))
+        self.assertEquals((99999999999999991611392, 1),
+                          _components(R.from_float(1e23)))
+        self.assertEquals(float(10**23), float(R.from_float(1e23)))
+        self.assertEquals((3602879701896397, 1125899906842624),
+                          _components(R.from_float(3.2)))
+        self.assertEquals(3.2, float(R.from_float(3.2)))
+
+        inf = 1e1000
+        nan = inf - inf
+        self.assertRaisesMessage(
+            TypeError, "Cannot convert inf to Fraction.",
+            R.from_float, inf)
+        self.assertRaisesMessage(
+            TypeError, "Cannot convert -inf to Fraction.",
+            R.from_float, -inf)
+        self.assertRaisesMessage(
+            TypeError, "Cannot convert nan to Fraction.",
+            R.from_float, nan)
+
+    def testFromDecimal(self):
+        self.assertRaisesMessage(
+            TypeError,
+            "Fraction.from_decimal() only takes Decimals, not 3 (int)",
+            R.from_decimal, 3)
+        self.assertEquals(R(0), R.from_decimal(Decimal("-0")))
+        self.assertEquals(R(5, 10), R.from_decimal(Decimal("0.5")))
+        self.assertEquals(R(5, 1000), R.from_decimal(Decimal("5e-3")))
+        self.assertEquals(R(5000), R.from_decimal(Decimal("5e3")))
+        self.assertEquals(1 - R(1, 10**30),
+                          R.from_decimal(Decimal("0." + "9" * 30)))
+
+        self.assertRaisesMessage(
+            TypeError, "Cannot convert Infinity to Fraction.",
+            R.from_decimal, Decimal("inf"))
+        self.assertRaisesMessage(
+            TypeError, "Cannot convert -Infinity to Fraction.",
+            R.from_decimal, Decimal("-inf"))
+        self.assertRaisesMessage(
+            TypeError, "Cannot convert NaN to Fraction.",
+            R.from_decimal, Decimal("nan"))
+        self.assertRaisesMessage(
+            TypeError, "Cannot convert sNaN to Fraction.",
+            R.from_decimal, Decimal("snan"))
+
+    def testFromContinuedFraction(self):
+        self.assertRaises(TypeError, R.from_continued_fraction, None)
+        phi = R.from_continued_fraction([1]*100)
+        self.assertEquals(round(phi - (1 + 5 ** 0.5) / 2, 10), 0.0)
+
+        minusphi = R.from_continued_fraction([-1]*100)
+        self.assertEquals(round(minusphi + (1 + 5 ** 0.5) / 2, 10), 0.0)
+
+        self.assertEquals(R.from_continued_fraction([0]), R(0))
+        self.assertEquals(R.from_continued_fraction([]), R(0))
+
+    def testAsContinuedFraction(self):
+        self.assertEqual(R.from_float(math.pi).as_continued_fraction()[:15],
+                         [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 3, 3])
+        self.assertEqual(R.from_float(-math.pi).as_continued_fraction()[:16],
+                         [-4, 1, 6, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 3, 3])
+        self.assertEqual(R(0).as_continued_fraction(), [0])
+
+    def testApproximateFrom(self):
+        self.assertEqual(R.from_float(math.pi).approximate(10000), R(355, 113))
+        self.assertEqual(R.from_float(-math.pi).approximate(10000), R(-355, 113))
+        self.assertEqual(R.from_float(0.0).approximate(10000), R(0))
+
+    def testConversions(self):
+        self.assertTypedEquals(-1, math.trunc(R(-11, 10)))
+        self.assertTypedEquals(-2, math.floor(R(-11, 10)))
+        self.assertTypedEquals(-1, math.ceil(R(-11, 10)))
+        self.assertTypedEquals(-1, math.ceil(R(-10, 10)))
+        self.assertTypedEquals(-1, int(R(-11, 10)))
+
+        self.assertTypedEquals(0, round(R(-1, 10)))
+        self.assertTypedEquals(0, round(R(-5, 10)))
+        self.assertTypedEquals(-2, round(R(-15, 10)))
+        self.assertTypedEquals(-1, round(R(-7, 10)))
+
+        self.assertEquals(False, bool(R(0, 1)))
+        self.assertEquals(True, bool(R(3, 2)))
+        self.assertTypedEquals(0.1, float(R(1, 10)))
+
+        # Check that __float__ isn't implemented by converting the
+        # numerator and denominator to float before dividing.
+        self.assertRaises(OverflowError, float, int('2'*400+'7'))
+        self.assertAlmostEquals(2.0/3,
+                                float(R(int('2'*400+'7'), int('3'*400+'1'))))
+
+        self.assertTypedEquals(0.1+0j, complex(R(1,10)))
+
+    def testRound(self):
+        self.assertTypedEquals(R(-200), round(R(-150), -2))
+        self.assertTypedEquals(R(-200), round(R(-250), -2))
+        self.assertTypedEquals(R(30), round(R(26), -1))
+        self.assertTypedEquals(R(-2, 10), round(R(-15, 100), 1))
+        self.assertTypedEquals(R(-2, 10), round(R(-25, 100), 1))
+
+
+    def testArithmetic(self):
+        self.assertEquals(R(1, 2), R(1, 10) + R(2, 5))
+        self.assertEquals(R(-3, 10), R(1, 10) - R(2, 5))
+        self.assertEquals(R(1, 25), R(1, 10) * R(2, 5))
+        self.assertEquals(R(1, 4), R(1, 10) / R(2, 5))
+        self.assertTypedEquals(2, R(9, 10) // R(2, 5))
+        self.assertTypedEquals(10**23, R(10**23, 1) // R(1))
+        self.assertEquals(R(2, 3), R(-7, 3) % R(3, 2))
+        self.assertEquals(R(8, 27), R(2, 3) ** R(3))
+        self.assertEquals(R(27, 8), R(2, 3) ** R(-3))
+        self.assertTypedEquals(2.0, R(4) ** R(1, 2))
+        z = pow(R(-1), R(1, 2))
+        self.assertAlmostEquals(z.real, 0)
+        self.assertEquals(z.imag, 1)
+
+    def testMixedArithmetic(self):
+        self.assertTypedEquals(R(11, 10), R(1, 10) + 1)
+        self.assertTypedEquals(1.1, R(1, 10) + 1.0)
+        self.assertTypedEquals(1.1 + 0j, R(1, 10) + (1.0 + 0j))
+        self.assertTypedEquals(R(11, 10), 1 + R(1, 10))
+        self.assertTypedEquals(1.1, 1.0 + R(1, 10))
+        self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + R(1, 10))
+
+        self.assertTypedEquals(R(-9, 10), R(1, 10) - 1)
+        self.assertTypedEquals(-0.9, R(1, 10) - 1.0)
+        self.assertTypedEquals(-0.9 + 0j, R(1, 10) - (1.0 + 0j))
+        self.assertTypedEquals(R(9, 10), 1 - R(1, 10))
+        self.assertTypedEquals(0.9, 1.0 - R(1, 10))
+        self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - R(1, 10))
+
+        self.assertTypedEquals(R(1, 10), R(1, 10) * 1)
+        self.assertTypedEquals(0.1, R(1, 10) * 1.0)
+        self.assertTypedEquals(0.1 + 0j, R(1, 10) * (1.0 + 0j))
+        self.assertTypedEquals(R(1, 10), 1 * R(1, 10))
+        self.assertTypedEquals(0.1, 1.0 * R(1, 10))
+        self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * R(1, 10))
+
+        self.assertTypedEquals(R(1, 10), R(1, 10) / 1)
+        self.assertTypedEquals(0.1, R(1, 10) / 1.0)
+        self.assertTypedEquals(0.1 + 0j, R(1, 10) / (1.0 + 0j))
+        self.assertTypedEquals(R(10, 1), 1 / R(1, 10))
+        self.assertTypedEquals(10.0, 1.0 / R(1, 10))
+        self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / R(1, 10))
+
+        self.assertTypedEquals(0, R(1, 10) // 1)
+        self.assertTypedEquals(0, R(1, 10) // 1.0)
+        self.assertTypedEquals(10, 1 // R(1, 10))
+        self.assertTypedEquals(10**23, 10**22 // R(1, 10))
+        self.assertTypedEquals(10, 1.0 // R(1, 10))
+
+        self.assertTypedEquals(R(1, 10), R(1, 10) % 1)
+        self.assertTypedEquals(0.1, R(1, 10) % 1.0)
+        self.assertTypedEquals(R(0, 1), 1 % R(1, 10))
+        self.assertTypedEquals(0.0, 1.0 % R(1, 10))
+
+        # No need for divmod since we don't override it.
+
+        # ** has more interesting conversion rules.
+        self.assertTypedEquals(R(100, 1), R(1, 10) ** -2)
+        self.assertTypedEquals(R(100, 1), R(10, 1) ** 2)
+        self.assertTypedEquals(0.1, R(1, 10) ** 1.0)
+        self.assertTypedEquals(0.1 + 0j, R(1, 10) ** (1.0 + 0j))
+        self.assertTypedEquals(4 , 2 ** R(2, 1))
+        z = pow(-1, R(1, 2))
+        self.assertAlmostEquals(0, z.real)
+        self.assertEquals(1, z.imag)
+        self.assertTypedEquals(R(1, 4) , 2 ** R(-2, 1))
+        self.assertTypedEquals(2.0 , 4 ** R(1, 2))
+        self.assertTypedEquals(0.25, 2.0 ** R(-2, 1))
+        self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** R(1, 10))
+
+    def testMixingWithDecimal(self):
+        # Decimal refuses mixed comparisons.
+        self.assertRaisesMessage(
+            TypeError,
+            "unsupported operand type(s) for +: 'Fraction' and 'Decimal'",
+            operator.add, R(3,11), Decimal('3.1415926'))
+        self.assertNotEquals(R(5, 2), Decimal('2.5'))
+
+    def testComparisons(self):
+        self.assertTrue(R(1, 2) < R(2, 3))
+        self.assertFalse(R(1, 2) < R(1, 2))
+        self.assertTrue(R(1, 2) <= R(2, 3))
+        self.assertTrue(R(1, 2) <= R(1, 2))
+        self.assertFalse(R(2, 3) <= R(1, 2))
+        self.assertTrue(R(1, 2) == R(1, 2))
+        self.assertFalse(R(1, 2) == R(1, 3))
+        self.assertFalse(R(1, 2) != R(1, 2))
+        self.assertTrue(R(1, 2) != R(1, 3))
+
+    def testMixedLess(self):
+        self.assertTrue(2 < R(5, 2))
+        self.assertFalse(2 < R(4, 2))
+        self.assertTrue(R(5, 2) < 3)
+        self.assertFalse(R(4, 2) < 2)
+
+        self.assertTrue(R(1, 2) < 0.6)
+        self.assertFalse(R(1, 2) < 0.4)
+        self.assertTrue(0.4 < R(1, 2))
+        self.assertFalse(0.5 < R(1, 2))
+
+    def testMixedLessEqual(self):
+        self.assertTrue(0.5 <= R(1, 2))
+        self.assertFalse(0.6 <= R(1, 2))
+        self.assertTrue(R(1, 2) <= 0.5)
+        self.assertFalse(R(1, 2) <= 0.4)
+        self.assertTrue(2 <= R(4, 2))
+        self.assertFalse(2 <= R(3, 2))
+        self.assertTrue(R(4, 2) <= 2)
+        self.assertFalse(R(5, 2) <= 2)
+
+    def testBigFloatComparisons(self):
+        # Because 10**23 can't be represented exactly as a float:
+        self.assertFalse(R(10**23) == float(10**23))
+        # The first test demonstrates why these are important.
+        self.assertFalse(1e23 < float(R(math.trunc(1e23) + 1)))
+        self.assertTrue(1e23 < R(math.trunc(1e23) + 1))
+        self.assertFalse(1e23 <= R(math.trunc(1e23) - 1))
+        self.assertTrue(1e23 > R(math.trunc(1e23) - 1))
+        self.assertFalse(1e23 >= R(math.trunc(1e23) + 1))
+
+    def testBigComplexComparisons(self):
+        self.assertFalse(R(10**23) == complex(10**23))
+        self.assertTrue(R(10**23) > complex(10**23))
+        self.assertFalse(R(10**23) <= complex(10**23))
+
+    def testMixedEqual(self):
+        self.assertTrue(0.5 == R(1, 2))
+        self.assertFalse(0.6 == R(1, 2))
+        self.assertTrue(R(1, 2) == 0.5)
+        self.assertFalse(R(1, 2) == 0.4)
+        self.assertTrue(2 == R(4, 2))
+        self.assertFalse(2 == R(3, 2))
+        self.assertTrue(R(4, 2) == 2)
+        self.assertFalse(R(5, 2) == 2)
+
+    def testStringification(self):
+        self.assertEquals("Fraction(7,3)", repr(R(7, 3)))
+        self.assertEquals("7/3", str(R(7, 3)))
+        self.assertEquals("7", str(R(7, 1)))
+
+    def testHash(self):
+        self.assertEquals(hash(2.5), hash(R(5, 2)))
+        self.assertEquals(hash(10**50), hash(R(10**50)))
+        self.assertNotEquals(hash(float(10**23)), hash(R(10**23)))
+
+    def testApproximatePi(self):
+        # Algorithm borrowed from
+        # http://docs.python.org/lib/decimal-recipes.html
+        three = R(3)
+        lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
+        while abs(s - lasts) > R(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 = R(1)
+        i, lasts, s, fact, num, sign = 0, 0, R(1), 1, 1, 1
+        while abs(s - lasts) > R(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 = R(13, 7)
+        self.assertEqual(r, loads(dumps(r)))
+        self.assertEqual(id(r), id(copy(r)))
+        self.assertEqual(id(r), id(deepcopy(r)))
+
+def test_main():
+    run_unittest(FractionTest, GcdTest)
+
+if __name__ == '__main__':
+    test_main()