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