| 1 | n/a | """Tests for Lib/fractions.py.""" |
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| 2 | n/a | |
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| 3 | n/a | from decimal import Decimal |
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| 4 | n/a | from test.support import requires_IEEE_754 |
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| 5 | n/a | import math |
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| 6 | n/a | import numbers |
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| 7 | n/a | import operator |
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| 8 | n/a | import fractions |
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| 9 | n/a | import sys |
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| 10 | n/a | import unittest |
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| 11 | n/a | import warnings |
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| 12 | n/a | from copy import copy, deepcopy |
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| 13 | n/a | from pickle import dumps, loads |
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| 14 | n/a | F = fractions.Fraction |
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| 15 | n/a | gcd = fractions.gcd |
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| 16 | n/a | |
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| 17 | n/a | class DummyFloat(object): |
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| 18 | n/a | """Dummy float class for testing comparisons with Fractions""" |
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| 19 | n/a | |
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| 20 | n/a | def __init__(self, value): |
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| 21 | n/a | if not isinstance(value, float): |
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| 22 | n/a | raise TypeError("DummyFloat can only be initialized from float") |
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| 23 | n/a | self.value = value |
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| 24 | n/a | |
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| 25 | n/a | def _richcmp(self, other, op): |
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| 26 | n/a | if isinstance(other, numbers.Rational): |
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| 27 | n/a | return op(F.from_float(self.value), other) |
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| 28 | n/a | elif isinstance(other, DummyFloat): |
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| 29 | n/a | return op(self.value, other.value) |
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| 30 | n/a | else: |
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| 31 | n/a | return NotImplemented |
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| 32 | n/a | |
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| 33 | n/a | def __eq__(self, other): return self._richcmp(other, operator.eq) |
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| 34 | n/a | def __le__(self, other): return self._richcmp(other, operator.le) |
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| 35 | n/a | def __lt__(self, other): return self._richcmp(other, operator.lt) |
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| 36 | n/a | def __ge__(self, other): return self._richcmp(other, operator.ge) |
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| 37 | n/a | def __gt__(self, other): return self._richcmp(other, operator.gt) |
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| 38 | n/a | |
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| 39 | n/a | # shouldn't be calling __float__ at all when doing comparisons |
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| 40 | n/a | def __float__(self): |
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| 41 | n/a | assert False, "__float__ should not be invoked for comparisons" |
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| 42 | n/a | |
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| 43 | n/a | # same goes for subtraction |
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| 44 | n/a | def __sub__(self, other): |
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| 45 | n/a | assert False, "__sub__ should not be invoked for comparisons" |
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| 46 | n/a | __rsub__ = __sub__ |
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| 47 | n/a | |
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| 48 | n/a | |
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| 49 | n/a | class DummyRational(object): |
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| 50 | n/a | """Test comparison of Fraction with a naive rational implementation.""" |
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| 51 | n/a | |
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| 52 | n/a | def __init__(self, num, den): |
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| 53 | n/a | g = math.gcd(num, den) |
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| 54 | n/a | self.num = num // g |
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| 55 | n/a | self.den = den // g |
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| 56 | n/a | |
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| 57 | n/a | def __eq__(self, other): |
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| 58 | n/a | if isinstance(other, fractions.Fraction): |
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| 59 | n/a | return (self.num == other._numerator and |
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| 60 | n/a | self.den == other._denominator) |
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| 61 | n/a | else: |
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| 62 | n/a | return NotImplemented |
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| 63 | n/a | |
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| 64 | n/a | def __lt__(self, other): |
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| 65 | n/a | return(self.num * other._denominator < self.den * other._numerator) |
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| 66 | n/a | |
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| 67 | n/a | def __gt__(self, other): |
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| 68 | n/a | return(self.num * other._denominator > self.den * other._numerator) |
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| 69 | n/a | |
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| 70 | n/a | def __le__(self, other): |
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| 71 | n/a | return(self.num * other._denominator <= self.den * other._numerator) |
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| 72 | n/a | |
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| 73 | n/a | def __ge__(self, other): |
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| 74 | n/a | return(self.num * other._denominator >= self.den * other._numerator) |
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| 75 | n/a | |
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| 76 | n/a | # this class is for testing comparisons; conversion to float |
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| 77 | n/a | # should never be used for a comparison, since it loses accuracy |
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| 78 | n/a | def __float__(self): |
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| 79 | n/a | assert False, "__float__ should not be invoked" |
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| 80 | n/a | |
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| 81 | n/a | class DummyFraction(fractions.Fraction): |
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| 82 | n/a | """Dummy Fraction subclass for copy and deepcopy testing.""" |
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| 83 | n/a | |
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| 84 | n/a | class GcdTest(unittest.TestCase): |
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| 85 | n/a | |
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| 86 | n/a | def testMisc(self): |
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| 87 | n/a | # fractions.gcd() is deprecated |
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| 88 | n/a | with self.assertWarnsRegex(DeprecationWarning, r'fractions\.gcd'): |
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| 89 | n/a | gcd(1, 1) |
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| 90 | n/a | with warnings.catch_warnings(): |
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| 91 | n/a | warnings.filterwarnings('ignore', r'fractions\.gcd', |
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| 92 | n/a | DeprecationWarning) |
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| 93 | n/a | self.assertEqual(0, gcd(0, 0)) |
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| 94 | n/a | self.assertEqual(1, gcd(1, 0)) |
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| 95 | n/a | self.assertEqual(-1, gcd(-1, 0)) |
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| 96 | n/a | self.assertEqual(1, gcd(0, 1)) |
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| 97 | n/a | self.assertEqual(-1, gcd(0, -1)) |
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| 98 | n/a | self.assertEqual(1, gcd(7, 1)) |
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| 99 | n/a | self.assertEqual(-1, gcd(7, -1)) |
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| 100 | n/a | self.assertEqual(1, gcd(-23, 15)) |
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| 101 | n/a | self.assertEqual(12, gcd(120, 84)) |
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| 102 | n/a | self.assertEqual(-12, gcd(84, -120)) |
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| 103 | n/a | self.assertEqual(gcd(120.0, 84), 12.0) |
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| 104 | n/a | self.assertEqual(gcd(120, 84.0), 12.0) |
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| 105 | n/a | self.assertEqual(gcd(F(120), F(84)), F(12)) |
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| 106 | n/a | self.assertEqual(gcd(F(120, 77), F(84, 55)), F(12, 385)) |
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| 107 | n/a | |
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| 108 | n/a | |
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| 109 | n/a | def _components(r): |
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| 110 | n/a | return (r.numerator, r.denominator) |
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| 111 | n/a | |
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| 112 | n/a | |
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| 113 | n/a | class FractionTest(unittest.TestCase): |
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| 114 | n/a | |
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| 115 | n/a | def assertTypedEquals(self, expected, actual): |
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| 116 | n/a | """Asserts that both the types and values are the same.""" |
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| 117 | n/a | self.assertEqual(type(expected), type(actual)) |
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| 118 | n/a | self.assertEqual(expected, actual) |
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| 119 | n/a | |
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| 120 | n/a | def assertRaisesMessage(self, exc_type, message, |
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| 121 | n/a | callable, *args, **kwargs): |
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| 122 | n/a | """Asserts that callable(*args, **kwargs) raises exc_type(message).""" |
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| 123 | n/a | try: |
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| 124 | n/a | callable(*args, **kwargs) |
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| 125 | n/a | except exc_type as e: |
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| 126 | n/a | self.assertEqual(message, str(e)) |
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| 127 | n/a | else: |
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| 128 | n/a | self.fail("%s not raised" % exc_type.__name__) |
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| 129 | n/a | |
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| 130 | n/a | def testInit(self): |
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| 131 | n/a | self.assertEqual((0, 1), _components(F())) |
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| 132 | n/a | self.assertEqual((7, 1), _components(F(7))) |
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| 133 | n/a | self.assertEqual((7, 3), _components(F(F(7, 3)))) |
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| 134 | n/a | |
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| 135 | n/a | self.assertEqual((-1, 1), _components(F(-1, 1))) |
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| 136 | n/a | self.assertEqual((-1, 1), _components(F(1, -1))) |
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| 137 | n/a | self.assertEqual((1, 1), _components(F(-2, -2))) |
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| 138 | n/a | self.assertEqual((1, 2), _components(F(5, 10))) |
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| 139 | n/a | self.assertEqual((7, 15), _components(F(7, 15))) |
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| 140 | n/a | self.assertEqual((10**23, 1), _components(F(10**23))) |
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| 141 | n/a | |
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| 142 | n/a | self.assertEqual((3, 77), _components(F(F(3, 7), 11))) |
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| 143 | n/a | self.assertEqual((-9, 5), _components(F(2, F(-10, 9)))) |
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| 144 | n/a | self.assertEqual((2486, 2485), _components(F(F(22, 7), F(355, 113)))) |
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| 145 | n/a | |
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| 146 | n/a | self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)", |
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| 147 | n/a | F, 12, 0) |
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| 148 | n/a | self.assertRaises(TypeError, F, 1.5 + 3j) |
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| 149 | n/a | |
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| 150 | n/a | self.assertRaises(TypeError, F, "3/2", 3) |
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| 151 | n/a | self.assertRaises(TypeError, F, 3, 0j) |
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| 152 | n/a | self.assertRaises(TypeError, F, 3, 1j) |
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| 153 | n/a | self.assertRaises(TypeError, F, 1, 2, 3) |
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| 154 | n/a | |
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| 155 | n/a | @requires_IEEE_754 |
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| 156 | n/a | def testInitFromFloat(self): |
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| 157 | n/a | self.assertEqual((5, 2), _components(F(2.5))) |
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| 158 | n/a | self.assertEqual((0, 1), _components(F(-0.0))) |
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| 159 | n/a | self.assertEqual((3602879701896397, 36028797018963968), |
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| 160 | n/a | _components(F(0.1))) |
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| 161 | n/a | # bug 16469: error types should be consistent with float -> int |
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| 162 | n/a | self.assertRaises(ValueError, F, float('nan')) |
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| 163 | n/a | self.assertRaises(OverflowError, F, float('inf')) |
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| 164 | n/a | self.assertRaises(OverflowError, F, float('-inf')) |
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| 165 | n/a | |
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| 166 | n/a | def testInitFromDecimal(self): |
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| 167 | n/a | self.assertEqual((11, 10), |
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| 168 | n/a | _components(F(Decimal('1.1')))) |
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| 169 | n/a | self.assertEqual((7, 200), |
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| 170 | n/a | _components(F(Decimal('3.5e-2')))) |
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| 171 | n/a | self.assertEqual((0, 1), |
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| 172 | n/a | _components(F(Decimal('.000e20')))) |
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| 173 | n/a | # bug 16469: error types should be consistent with decimal -> int |
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| 174 | n/a | self.assertRaises(ValueError, F, Decimal('nan')) |
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| 175 | n/a | self.assertRaises(ValueError, F, Decimal('snan')) |
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| 176 | n/a | self.assertRaises(OverflowError, F, Decimal('inf')) |
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| 177 | n/a | self.assertRaises(OverflowError, F, Decimal('-inf')) |
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| 178 | n/a | |
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| 179 | n/a | def testFromString(self): |
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| 180 | n/a | self.assertEqual((5, 1), _components(F("5"))) |
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| 181 | n/a | self.assertEqual((3, 2), _components(F("3/2"))) |
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| 182 | n/a | self.assertEqual((3, 2), _components(F(" \n +3/2"))) |
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| 183 | n/a | self.assertEqual((-3, 2), _components(F("-3/2 "))) |
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| 184 | n/a | self.assertEqual((13, 2), _components(F(" 013/02 \n "))) |
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| 185 | n/a | self.assertEqual((16, 5), _components(F(" 3.2 "))) |
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| 186 | n/a | self.assertEqual((-16, 5), _components(F(" -3.2 "))) |
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| 187 | n/a | self.assertEqual((-3, 1), _components(F(" -3. "))) |
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| 188 | n/a | self.assertEqual((3, 5), _components(F(" .6 "))) |
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| 189 | n/a | self.assertEqual((1, 3125), _components(F("32.e-5"))) |
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| 190 | n/a | self.assertEqual((1000000, 1), _components(F("1E+06"))) |
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| 191 | n/a | self.assertEqual((-12300, 1), _components(F("-1.23e4"))) |
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| 192 | n/a | self.assertEqual((0, 1), _components(F(" .0e+0\t"))) |
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| 193 | n/a | self.assertEqual((0, 1), _components(F("-0.000e0"))) |
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| 194 | n/a | |
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| 195 | n/a | self.assertRaisesMessage( |
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| 196 | n/a | ZeroDivisionError, "Fraction(3, 0)", |
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| 197 | n/a | F, "3/0") |
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| 198 | n/a | self.assertRaisesMessage( |
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| 199 | n/a | ValueError, "Invalid literal for Fraction: '3/'", |
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| 200 | n/a | F, "3/") |
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| 201 | n/a | self.assertRaisesMessage( |
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| 202 | n/a | ValueError, "Invalid literal for Fraction: '/2'", |
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| 203 | n/a | F, "/2") |
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| 204 | n/a | self.assertRaisesMessage( |
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| 205 | n/a | ValueError, "Invalid literal for Fraction: '3 /2'", |
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| 206 | n/a | F, "3 /2") |
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| 207 | n/a | self.assertRaisesMessage( |
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| 208 | n/a | # Denominators don't need a sign. |
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| 209 | n/a | ValueError, "Invalid literal for Fraction: '3/+2'", |
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| 210 | n/a | F, "3/+2") |
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| 211 | n/a | self.assertRaisesMessage( |
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| 212 | n/a | # Imitate float's parsing. |
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| 213 | n/a | ValueError, "Invalid literal for Fraction: '+ 3/2'", |
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| 214 | n/a | F, "+ 3/2") |
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| 215 | n/a | self.assertRaisesMessage( |
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| 216 | n/a | # Avoid treating '.' as a regex special character. |
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| 217 | n/a | ValueError, "Invalid literal for Fraction: '3a2'", |
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| 218 | n/a | F, "3a2") |
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| 219 | n/a | self.assertRaisesMessage( |
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| 220 | n/a | # Don't accept combinations of decimals and rationals. |
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| 221 | n/a | ValueError, "Invalid literal for Fraction: '3/7.2'", |
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| 222 | n/a | F, "3/7.2") |
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| 223 | n/a | self.assertRaisesMessage( |
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| 224 | n/a | # Don't accept combinations of decimals and rationals. |
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| 225 | n/a | ValueError, "Invalid literal for Fraction: '3.2/7'", |
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| 226 | n/a | F, "3.2/7") |
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| 227 | n/a | self.assertRaisesMessage( |
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| 228 | n/a | # Allow 3. and .3, but not . |
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| 229 | n/a | ValueError, "Invalid literal for Fraction: '.'", |
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| 230 | n/a | F, ".") |
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| 231 | n/a | |
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| 232 | n/a | def testImmutable(self): |
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| 233 | n/a | r = F(7, 3) |
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| 234 | n/a | r.__init__(2, 15) |
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| 235 | n/a | self.assertEqual((7, 3), _components(r)) |
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| 236 | n/a | |
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| 237 | n/a | self.assertRaises(AttributeError, setattr, r, 'numerator', 12) |
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| 238 | n/a | self.assertRaises(AttributeError, setattr, r, 'denominator', 6) |
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| 239 | n/a | self.assertEqual((7, 3), _components(r)) |
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| 240 | n/a | |
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| 241 | n/a | # But if you _really_ need to: |
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| 242 | n/a | r._numerator = 4 |
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| 243 | n/a | r._denominator = 2 |
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| 244 | n/a | self.assertEqual((4, 2), _components(r)) |
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| 245 | n/a | # Which breaks some important operations: |
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| 246 | n/a | self.assertNotEqual(F(4, 2), r) |
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| 247 | n/a | |
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| 248 | n/a | def testFromFloat(self): |
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| 249 | n/a | self.assertRaises(TypeError, F.from_float, 3+4j) |
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| 250 | n/a | self.assertEqual((10, 1), _components(F.from_float(10))) |
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| 251 | n/a | bigint = 1234567890123456789 |
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| 252 | n/a | self.assertEqual((bigint, 1), _components(F.from_float(bigint))) |
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| 253 | n/a | self.assertEqual((0, 1), _components(F.from_float(-0.0))) |
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| 254 | n/a | self.assertEqual((10, 1), _components(F.from_float(10.0))) |
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| 255 | n/a | self.assertEqual((-5, 2), _components(F.from_float(-2.5))) |
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| 256 | n/a | self.assertEqual((99999999999999991611392, 1), |
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| 257 | n/a | _components(F.from_float(1e23))) |
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| 258 | n/a | self.assertEqual(float(10**23), float(F.from_float(1e23))) |
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| 259 | n/a | self.assertEqual((3602879701896397, 1125899906842624), |
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| 260 | n/a | _components(F.from_float(3.2))) |
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| 261 | n/a | self.assertEqual(3.2, float(F.from_float(3.2))) |
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| 262 | n/a | |
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| 263 | n/a | inf = 1e1000 |
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| 264 | n/a | nan = inf - inf |
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| 265 | n/a | # bug 16469: error types should be consistent with float -> int |
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| 266 | n/a | self.assertRaisesMessage( |
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| 267 | n/a | OverflowError, "cannot convert Infinity to integer ratio", |
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| 268 | n/a | F.from_float, inf) |
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| 269 | n/a | self.assertRaisesMessage( |
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| 270 | n/a | OverflowError, "cannot convert Infinity to integer ratio", |
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| 271 | n/a | F.from_float, -inf) |
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| 272 | n/a | self.assertRaisesMessage( |
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| 273 | n/a | ValueError, "cannot convert NaN to integer ratio", |
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| 274 | n/a | F.from_float, nan) |
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| 275 | n/a | |
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| 276 | n/a | def testFromDecimal(self): |
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| 277 | n/a | self.assertRaises(TypeError, F.from_decimal, 3+4j) |
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| 278 | n/a | self.assertEqual(F(10, 1), F.from_decimal(10)) |
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| 279 | n/a | self.assertEqual(F(0), F.from_decimal(Decimal("-0"))) |
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| 280 | n/a | self.assertEqual(F(5, 10), F.from_decimal(Decimal("0.5"))) |
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| 281 | n/a | self.assertEqual(F(5, 1000), F.from_decimal(Decimal("5e-3"))) |
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| 282 | n/a | self.assertEqual(F(5000), F.from_decimal(Decimal("5e3"))) |
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| 283 | n/a | self.assertEqual(1 - F(1, 10**30), |
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| 284 | n/a | F.from_decimal(Decimal("0." + "9" * 30))) |
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| 285 | n/a | |
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| 286 | n/a | # bug 16469: error types should be consistent with decimal -> int |
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| 287 | n/a | self.assertRaisesMessage( |
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| 288 | n/a | OverflowError, "cannot convert Infinity to integer ratio", |
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| 289 | n/a | F.from_decimal, Decimal("inf")) |
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| 290 | n/a | self.assertRaisesMessage( |
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| 291 | n/a | OverflowError, "cannot convert Infinity to integer ratio", |
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| 292 | n/a | F.from_decimal, Decimal("-inf")) |
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| 293 | n/a | self.assertRaisesMessage( |
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| 294 | n/a | ValueError, "cannot convert NaN to integer ratio", |
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| 295 | n/a | F.from_decimal, Decimal("nan")) |
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| 296 | n/a | self.assertRaisesMessage( |
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| 297 | n/a | ValueError, "cannot convert NaN to integer ratio", |
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| 298 | n/a | F.from_decimal, Decimal("snan")) |
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| 299 | n/a | |
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| 300 | n/a | def testLimitDenominator(self): |
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| 301 | n/a | rpi = F('3.1415926535897932') |
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| 302 | n/a | self.assertEqual(rpi.limit_denominator(10000), F(355, 113)) |
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| 303 | n/a | self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113)) |
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| 304 | n/a | self.assertEqual(rpi.limit_denominator(113), F(355, 113)) |
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| 305 | n/a | self.assertEqual(rpi.limit_denominator(112), F(333, 106)) |
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| 306 | n/a | self.assertEqual(F(201, 200).limit_denominator(100), F(1)) |
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| 307 | n/a | self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101)) |
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| 308 | n/a | self.assertEqual(F(0).limit_denominator(10000), F(0)) |
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| 309 | n/a | for i in (0, -1): |
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| 310 | n/a | self.assertRaisesMessage( |
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| 311 | n/a | ValueError, "max_denominator should be at least 1", |
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| 312 | n/a | F(1).limit_denominator, i) |
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| 313 | n/a | |
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| 314 | n/a | def testConversions(self): |
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| 315 | n/a | self.assertTypedEquals(-1, math.trunc(F(-11, 10))) |
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| 316 | n/a | self.assertTypedEquals(1, math.trunc(F(11, 10))) |
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| 317 | n/a | self.assertTypedEquals(-2, math.floor(F(-11, 10))) |
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| 318 | n/a | self.assertTypedEquals(-1, math.ceil(F(-11, 10))) |
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| 319 | n/a | self.assertTypedEquals(-1, math.ceil(F(-10, 10))) |
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| 320 | n/a | self.assertTypedEquals(-1, int(F(-11, 10))) |
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| 321 | n/a | self.assertTypedEquals(0, round(F(-1, 10))) |
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| 322 | n/a | self.assertTypedEquals(0, round(F(-5, 10))) |
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| 323 | n/a | self.assertTypedEquals(-2, round(F(-15, 10))) |
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| 324 | n/a | self.assertTypedEquals(-1, round(F(-7, 10))) |
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| 325 | n/a | |
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| 326 | n/a | self.assertEqual(False, bool(F(0, 1))) |
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| 327 | n/a | self.assertEqual(True, bool(F(3, 2))) |
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| 328 | n/a | self.assertTypedEquals(0.1, float(F(1, 10))) |
|---|
| 329 | n/a | |
|---|
| 330 | n/a | # Check that __float__ isn't implemented by converting the |
|---|
| 331 | n/a | # numerator and denominator to float before dividing. |
|---|
| 332 | n/a | self.assertRaises(OverflowError, float, int('2'*400+'7')) |
|---|
| 333 | n/a | self.assertAlmostEqual(2.0/3, |
|---|
| 334 | n/a | float(F(int('2'*400+'7'), int('3'*400+'1')))) |
|---|
| 335 | n/a | |
|---|
| 336 | n/a | self.assertTypedEquals(0.1+0j, complex(F(1,10))) |
|---|
| 337 | n/a | |
|---|
| 338 | n/a | def testRound(self): |
|---|
| 339 | n/a | self.assertTypedEquals(F(-200), round(F(-150), -2)) |
|---|
| 340 | n/a | self.assertTypedEquals(F(-200), round(F(-250), -2)) |
|---|
| 341 | n/a | self.assertTypedEquals(F(30), round(F(26), -1)) |
|---|
| 342 | n/a | self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1)) |
|---|
| 343 | n/a | self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1)) |
|---|
| 344 | n/a | |
|---|
| 345 | n/a | def testArithmetic(self): |
|---|
| 346 | n/a | self.assertEqual(F(1, 2), F(1, 10) + F(2, 5)) |
|---|
| 347 | n/a | self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5)) |
|---|
| 348 | n/a | self.assertEqual(F(1, 25), F(1, 10) * F(2, 5)) |
|---|
| 349 | n/a | self.assertEqual(F(1, 4), F(1, 10) / F(2, 5)) |
|---|
| 350 | n/a | self.assertTypedEquals(2, F(9, 10) // F(2, 5)) |
|---|
| 351 | n/a | self.assertTypedEquals(10**23, F(10**23, 1) // F(1)) |
|---|
| 352 | n/a | self.assertEqual(F(2, 3), F(-7, 3) % F(3, 2)) |
|---|
| 353 | n/a | self.assertEqual(F(8, 27), F(2, 3) ** F(3)) |
|---|
| 354 | n/a | self.assertEqual(F(27, 8), F(2, 3) ** F(-3)) |
|---|
| 355 | n/a | self.assertTypedEquals(2.0, F(4) ** F(1, 2)) |
|---|
| 356 | n/a | self.assertEqual(F(1, 1), +F(1, 1)) |
|---|
| 357 | n/a | z = pow(F(-1), F(1, 2)) |
|---|
| 358 | n/a | self.assertAlmostEqual(z.real, 0) |
|---|
| 359 | n/a | self.assertEqual(z.imag, 1) |
|---|
| 360 | n/a | # Regression test for #27539. |
|---|
| 361 | n/a | p = F(-1, 2) ** 0 |
|---|
| 362 | n/a | self.assertEqual(p, F(1, 1)) |
|---|
| 363 | n/a | self.assertEqual(p.numerator, 1) |
|---|
| 364 | n/a | self.assertEqual(p.denominator, 1) |
|---|
| 365 | n/a | p = F(-1, 2) ** -1 |
|---|
| 366 | n/a | self.assertEqual(p, F(-2, 1)) |
|---|
| 367 | n/a | self.assertEqual(p.numerator, -2) |
|---|
| 368 | n/a | self.assertEqual(p.denominator, 1) |
|---|
| 369 | n/a | p = F(-1, 2) ** -2 |
|---|
| 370 | n/a | self.assertEqual(p, F(4, 1)) |
|---|
| 371 | n/a | self.assertEqual(p.numerator, 4) |
|---|
| 372 | n/a | self.assertEqual(p.denominator, 1) |
|---|
| 373 | n/a | |
|---|
| 374 | n/a | def testMixedArithmetic(self): |
|---|
| 375 | n/a | self.assertTypedEquals(F(11, 10), F(1, 10) + 1) |
|---|
| 376 | n/a | self.assertTypedEquals(1.1, F(1, 10) + 1.0) |
|---|
| 377 | n/a | self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j)) |
|---|
| 378 | n/a | self.assertTypedEquals(F(11, 10), 1 + F(1, 10)) |
|---|
| 379 | n/a | self.assertTypedEquals(1.1, 1.0 + F(1, 10)) |
|---|
| 380 | n/a | self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10)) |
|---|
| 381 | n/a | |
|---|
| 382 | n/a | self.assertTypedEquals(F(-9, 10), F(1, 10) - 1) |
|---|
| 383 | n/a | self.assertTypedEquals(-0.9, F(1, 10) - 1.0) |
|---|
| 384 | n/a | self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j)) |
|---|
| 385 | n/a | self.assertTypedEquals(F(9, 10), 1 - F(1, 10)) |
|---|
| 386 | n/a | self.assertTypedEquals(0.9, 1.0 - F(1, 10)) |
|---|
| 387 | n/a | self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10)) |
|---|
| 388 | n/a | |
|---|
| 389 | n/a | self.assertTypedEquals(F(1, 10), F(1, 10) * 1) |
|---|
| 390 | n/a | self.assertTypedEquals(0.1, F(1, 10) * 1.0) |
|---|
| 391 | n/a | self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j)) |
|---|
| 392 | n/a | self.assertTypedEquals(F(1, 10), 1 * F(1, 10)) |
|---|
| 393 | n/a | self.assertTypedEquals(0.1, 1.0 * F(1, 10)) |
|---|
| 394 | n/a | self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10)) |
|---|
| 395 | n/a | |
|---|
| 396 | n/a | self.assertTypedEquals(F(1, 10), F(1, 10) / 1) |
|---|
| 397 | n/a | self.assertTypedEquals(0.1, F(1, 10) / 1.0) |
|---|
| 398 | n/a | self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j)) |
|---|
| 399 | n/a | self.assertTypedEquals(F(10, 1), 1 / F(1, 10)) |
|---|
| 400 | n/a | self.assertTypedEquals(10.0, 1.0 / F(1, 10)) |
|---|
| 401 | n/a | self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10)) |
|---|
| 402 | n/a | |
|---|
| 403 | n/a | self.assertTypedEquals(0, F(1, 10) // 1) |
|---|
| 404 | n/a | self.assertTypedEquals(0, F(1, 10) // 1.0) |
|---|
| 405 | n/a | self.assertTypedEquals(10, 1 // F(1, 10)) |
|---|
| 406 | n/a | self.assertTypedEquals(10**23, 10**22 // F(1, 10)) |
|---|
| 407 | n/a | self.assertTypedEquals(10, 1.0 // F(1, 10)) |
|---|
| 408 | n/a | |
|---|
| 409 | n/a | self.assertTypedEquals(F(1, 10), F(1, 10) % 1) |
|---|
| 410 | n/a | self.assertTypedEquals(0.1, F(1, 10) % 1.0) |
|---|
| 411 | n/a | self.assertTypedEquals(F(0, 1), 1 % F(1, 10)) |
|---|
| 412 | n/a | self.assertTypedEquals(0.0, 1.0 % F(1, 10)) |
|---|
| 413 | n/a | |
|---|
| 414 | n/a | # No need for divmod since we don't override it. |
|---|
| 415 | n/a | |
|---|
| 416 | n/a | # ** has more interesting conversion rules. |
|---|
| 417 | n/a | self.assertTypedEquals(F(100, 1), F(1, 10) ** -2) |
|---|
| 418 | n/a | self.assertTypedEquals(F(100, 1), F(10, 1) ** 2) |
|---|
| 419 | n/a | self.assertTypedEquals(0.1, F(1, 10) ** 1.0) |
|---|
| 420 | n/a | self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j)) |
|---|
| 421 | n/a | self.assertTypedEquals(4 , 2 ** F(2, 1)) |
|---|
| 422 | n/a | z = pow(-1, F(1, 2)) |
|---|
| 423 | n/a | self.assertAlmostEqual(0, z.real) |
|---|
| 424 | n/a | self.assertEqual(1, z.imag) |
|---|
| 425 | n/a | self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1)) |
|---|
| 426 | n/a | self.assertTypedEquals(2.0 , 4 ** F(1, 2)) |
|---|
| 427 | n/a | self.assertTypedEquals(0.25, 2.0 ** F(-2, 1)) |
|---|
| 428 | n/a | self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10)) |
|---|
| 429 | n/a | self.assertRaises(ZeroDivisionError, operator.pow, |
|---|
| 430 | n/a | F(0, 1), -2) |
|---|
| 431 | n/a | |
|---|
| 432 | n/a | def testMixingWithDecimal(self): |
|---|
| 433 | n/a | # Decimal refuses mixed arithmetic (but not mixed comparisons) |
|---|
| 434 | n/a | self.assertRaises(TypeError, operator.add, |
|---|
| 435 | n/a | F(3,11), Decimal('3.1415926')) |
|---|
| 436 | n/a | self.assertRaises(TypeError, operator.add, |
|---|
| 437 | n/a | Decimal('3.1415926'), F(3,11)) |
|---|
| 438 | n/a | |
|---|
| 439 | n/a | def testComparisons(self): |
|---|
| 440 | n/a | self.assertTrue(F(1, 2) < F(2, 3)) |
|---|
| 441 | n/a | self.assertFalse(F(1, 2) < F(1, 2)) |
|---|
| 442 | n/a | self.assertTrue(F(1, 2) <= F(2, 3)) |
|---|
| 443 | n/a | self.assertTrue(F(1, 2) <= F(1, 2)) |
|---|
| 444 | n/a | self.assertFalse(F(2, 3) <= F(1, 2)) |
|---|
| 445 | n/a | self.assertTrue(F(1, 2) == F(1, 2)) |
|---|
| 446 | n/a | self.assertFalse(F(1, 2) == F(1, 3)) |
|---|
| 447 | n/a | self.assertFalse(F(1, 2) != F(1, 2)) |
|---|
| 448 | n/a | self.assertTrue(F(1, 2) != F(1, 3)) |
|---|
| 449 | n/a | |
|---|
| 450 | n/a | def testComparisonsDummyRational(self): |
|---|
| 451 | n/a | self.assertTrue(F(1, 2) == DummyRational(1, 2)) |
|---|
| 452 | n/a | self.assertTrue(DummyRational(1, 2) == F(1, 2)) |
|---|
| 453 | n/a | self.assertFalse(F(1, 2) == DummyRational(3, 4)) |
|---|
| 454 | n/a | self.assertFalse(DummyRational(3, 4) == F(1, 2)) |
|---|
| 455 | n/a | |
|---|
| 456 | n/a | self.assertTrue(F(1, 2) < DummyRational(3, 4)) |
|---|
| 457 | n/a | self.assertFalse(F(1, 2) < DummyRational(1, 2)) |
|---|
| 458 | n/a | self.assertFalse(F(1, 2) < DummyRational(1, 7)) |
|---|
| 459 | n/a | self.assertFalse(F(1, 2) > DummyRational(3, 4)) |
|---|
| 460 | n/a | self.assertFalse(F(1, 2) > DummyRational(1, 2)) |
|---|
| 461 | n/a | self.assertTrue(F(1, 2) > DummyRational(1, 7)) |
|---|
| 462 | n/a | self.assertTrue(F(1, 2) <= DummyRational(3, 4)) |
|---|
| 463 | n/a | self.assertTrue(F(1, 2) <= DummyRational(1, 2)) |
|---|
| 464 | n/a | self.assertFalse(F(1, 2) <= DummyRational(1, 7)) |
|---|
| 465 | n/a | self.assertFalse(F(1, 2) >= DummyRational(3, 4)) |
|---|
| 466 | n/a | self.assertTrue(F(1, 2) >= DummyRational(1, 2)) |
|---|
| 467 | n/a | self.assertTrue(F(1, 2) >= DummyRational(1, 7)) |
|---|
| 468 | n/a | |
|---|
| 469 | n/a | self.assertTrue(DummyRational(1, 2) < F(3, 4)) |
|---|
| 470 | n/a | self.assertFalse(DummyRational(1, 2) < F(1, 2)) |
|---|
| 471 | n/a | self.assertFalse(DummyRational(1, 2) < F(1, 7)) |
|---|
| 472 | n/a | self.assertFalse(DummyRational(1, 2) > F(3, 4)) |
|---|
| 473 | n/a | self.assertFalse(DummyRational(1, 2) > F(1, 2)) |
|---|
| 474 | n/a | self.assertTrue(DummyRational(1, 2) > F(1, 7)) |
|---|
| 475 | n/a | self.assertTrue(DummyRational(1, 2) <= F(3, 4)) |
|---|
| 476 | n/a | self.assertTrue(DummyRational(1, 2) <= F(1, 2)) |
|---|
| 477 | n/a | self.assertFalse(DummyRational(1, 2) <= F(1, 7)) |
|---|
| 478 | n/a | self.assertFalse(DummyRational(1, 2) >= F(3, 4)) |
|---|
| 479 | n/a | self.assertTrue(DummyRational(1, 2) >= F(1, 2)) |
|---|
| 480 | n/a | self.assertTrue(DummyRational(1, 2) >= F(1, 7)) |
|---|
| 481 | n/a | |
|---|
| 482 | n/a | def testComparisonsDummyFloat(self): |
|---|
| 483 | n/a | x = DummyFloat(1./3.) |
|---|
| 484 | n/a | y = F(1, 3) |
|---|
| 485 | n/a | self.assertTrue(x != y) |
|---|
| 486 | n/a | self.assertTrue(x < y or x > y) |
|---|
| 487 | n/a | self.assertFalse(x == y) |
|---|
| 488 | n/a | self.assertFalse(x <= y and x >= y) |
|---|
| 489 | n/a | self.assertTrue(y != x) |
|---|
| 490 | n/a | self.assertTrue(y < x or y > x) |
|---|
| 491 | n/a | self.assertFalse(y == x) |
|---|
| 492 | n/a | self.assertFalse(y <= x and y >= x) |
|---|
| 493 | n/a | |
|---|
| 494 | n/a | def testMixedLess(self): |
|---|
| 495 | n/a | self.assertTrue(2 < F(5, 2)) |
|---|
| 496 | n/a | self.assertFalse(2 < F(4, 2)) |
|---|
| 497 | n/a | self.assertTrue(F(5, 2) < 3) |
|---|
| 498 | n/a | self.assertFalse(F(4, 2) < 2) |
|---|
| 499 | n/a | |
|---|
| 500 | n/a | self.assertTrue(F(1, 2) < 0.6) |
|---|
| 501 | n/a | self.assertFalse(F(1, 2) < 0.4) |
|---|
| 502 | n/a | self.assertTrue(0.4 < F(1, 2)) |
|---|
| 503 | n/a | self.assertFalse(0.5 < F(1, 2)) |
|---|
| 504 | n/a | |
|---|
| 505 | n/a | self.assertFalse(float('inf') < F(1, 2)) |
|---|
| 506 | n/a | self.assertTrue(float('-inf') < F(0, 10)) |
|---|
| 507 | n/a | self.assertFalse(float('nan') < F(-3, 7)) |
|---|
| 508 | n/a | self.assertTrue(F(1, 2) < float('inf')) |
|---|
| 509 | n/a | self.assertFalse(F(17, 12) < float('-inf')) |
|---|
| 510 | n/a | self.assertFalse(F(144, -89) < float('nan')) |
|---|
| 511 | n/a | |
|---|
| 512 | n/a | def testMixedLessEqual(self): |
|---|
| 513 | n/a | self.assertTrue(0.5 <= F(1, 2)) |
|---|
| 514 | n/a | self.assertFalse(0.6 <= F(1, 2)) |
|---|
| 515 | n/a | self.assertTrue(F(1, 2) <= 0.5) |
|---|
| 516 | n/a | self.assertFalse(F(1, 2) <= 0.4) |
|---|
| 517 | n/a | self.assertTrue(2 <= F(4, 2)) |
|---|
| 518 | n/a | self.assertFalse(2 <= F(3, 2)) |
|---|
| 519 | n/a | self.assertTrue(F(4, 2) <= 2) |
|---|
| 520 | n/a | self.assertFalse(F(5, 2) <= 2) |
|---|
| 521 | n/a | |
|---|
| 522 | n/a | self.assertFalse(float('inf') <= F(1, 2)) |
|---|
| 523 | n/a | self.assertTrue(float('-inf') <= F(0, 10)) |
|---|
| 524 | n/a | self.assertFalse(float('nan') <= F(-3, 7)) |
|---|
| 525 | n/a | self.assertTrue(F(1, 2) <= float('inf')) |
|---|
| 526 | n/a | self.assertFalse(F(17, 12) <= float('-inf')) |
|---|
| 527 | n/a | self.assertFalse(F(144, -89) <= float('nan')) |
|---|
| 528 | n/a | |
|---|
| 529 | n/a | def testBigFloatComparisons(self): |
|---|
| 530 | n/a | # Because 10**23 can't be represented exactly as a float: |
|---|
| 531 | n/a | self.assertFalse(F(10**23) == float(10**23)) |
|---|
| 532 | n/a | # The first test demonstrates why these are important. |
|---|
| 533 | n/a | self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1))) |
|---|
| 534 | n/a | self.assertTrue(1e23 < F(math.trunc(1e23) + 1)) |
|---|
| 535 | n/a | self.assertFalse(1e23 <= F(math.trunc(1e23) - 1)) |
|---|
| 536 | n/a | self.assertTrue(1e23 > F(math.trunc(1e23) - 1)) |
|---|
| 537 | n/a | self.assertFalse(1e23 >= F(math.trunc(1e23) + 1)) |
|---|
| 538 | n/a | |
|---|
| 539 | n/a | def testBigComplexComparisons(self): |
|---|
| 540 | n/a | self.assertFalse(F(10**23) == complex(10**23)) |
|---|
| 541 | n/a | self.assertRaises(TypeError, operator.gt, F(10**23), complex(10**23)) |
|---|
| 542 | n/a | self.assertRaises(TypeError, operator.le, F(10**23), complex(10**23)) |
|---|
| 543 | n/a | |
|---|
| 544 | n/a | x = F(3, 8) |
|---|
| 545 | n/a | z = complex(0.375, 0.0) |
|---|
| 546 | n/a | w = complex(0.375, 0.2) |
|---|
| 547 | n/a | self.assertTrue(x == z) |
|---|
| 548 | n/a | self.assertFalse(x != z) |
|---|
| 549 | n/a | self.assertFalse(x == w) |
|---|
| 550 | n/a | self.assertTrue(x != w) |
|---|
| 551 | n/a | for op in operator.lt, operator.le, operator.gt, operator.ge: |
|---|
| 552 | n/a | self.assertRaises(TypeError, op, x, z) |
|---|
| 553 | n/a | self.assertRaises(TypeError, op, z, x) |
|---|
| 554 | n/a | self.assertRaises(TypeError, op, x, w) |
|---|
| 555 | n/a | self.assertRaises(TypeError, op, w, x) |
|---|
| 556 | n/a | |
|---|
| 557 | n/a | def testMixedEqual(self): |
|---|
| 558 | n/a | self.assertTrue(0.5 == F(1, 2)) |
|---|
| 559 | n/a | self.assertFalse(0.6 == F(1, 2)) |
|---|
| 560 | n/a | self.assertTrue(F(1, 2) == 0.5) |
|---|
| 561 | n/a | self.assertFalse(F(1, 2) == 0.4) |
|---|
| 562 | n/a | self.assertTrue(2 == F(4, 2)) |
|---|
| 563 | n/a | self.assertFalse(2 == F(3, 2)) |
|---|
| 564 | n/a | self.assertTrue(F(4, 2) == 2) |
|---|
| 565 | n/a | self.assertFalse(F(5, 2) == 2) |
|---|
| 566 | n/a | self.assertFalse(F(5, 2) == float('nan')) |
|---|
| 567 | n/a | self.assertFalse(float('nan') == F(3, 7)) |
|---|
| 568 | n/a | self.assertFalse(F(5, 2) == float('inf')) |
|---|
| 569 | n/a | self.assertFalse(float('-inf') == F(2, 5)) |
|---|
| 570 | n/a | |
|---|
| 571 | n/a | def testStringification(self): |
|---|
| 572 | n/a | self.assertEqual("Fraction(7, 3)", repr(F(7, 3))) |
|---|
| 573 | n/a | self.assertEqual("Fraction(6283185307, 2000000000)", |
|---|
| 574 | n/a | repr(F('3.1415926535'))) |
|---|
| 575 | n/a | self.assertEqual("Fraction(-1, 100000000000000000000)", |
|---|
| 576 | n/a | repr(F(1, -10**20))) |
|---|
| 577 | n/a | self.assertEqual("7/3", str(F(7, 3))) |
|---|
| 578 | n/a | self.assertEqual("7", str(F(7, 1))) |
|---|
| 579 | n/a | |
|---|
| 580 | n/a | def testHash(self): |
|---|
| 581 | n/a | hmod = sys.hash_info.modulus |
|---|
| 582 | n/a | hinf = sys.hash_info.inf |
|---|
| 583 | n/a | self.assertEqual(hash(2.5), hash(F(5, 2))) |
|---|
| 584 | n/a | self.assertEqual(hash(10**50), hash(F(10**50))) |
|---|
| 585 | n/a | self.assertNotEqual(hash(float(10**23)), hash(F(10**23))) |
|---|
| 586 | n/a | self.assertEqual(hinf, hash(F(1, hmod))) |
|---|
| 587 | n/a | # Check that __hash__ produces the same value as hash(), for |
|---|
| 588 | n/a | # consistency with int and Decimal. (See issue #10356.) |
|---|
| 589 | n/a | self.assertEqual(hash(F(-1)), F(-1).__hash__()) |
|---|
| 590 | n/a | |
|---|
| 591 | n/a | def testApproximatePi(self): |
|---|
| 592 | n/a | # Algorithm borrowed from |
|---|
| 593 | n/a | # http://docs.python.org/lib/decimal-recipes.html |
|---|
| 594 | n/a | three = F(3) |
|---|
| 595 | n/a | lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24 |
|---|
| 596 | n/a | while abs(s - lasts) > F(1, 10**9): |
|---|
| 597 | n/a | lasts = s |
|---|
| 598 | n/a | n, na = n+na, na+8 |
|---|
| 599 | n/a | d, da = d+da, da+32 |
|---|
| 600 | n/a | t = (t * n) / d |
|---|
| 601 | n/a | s += t |
|---|
| 602 | n/a | self.assertAlmostEqual(math.pi, s) |
|---|
| 603 | n/a | |
|---|
| 604 | n/a | def testApproximateCos1(self): |
|---|
| 605 | n/a | # Algorithm borrowed from |
|---|
| 606 | n/a | # http://docs.python.org/lib/decimal-recipes.html |
|---|
| 607 | n/a | x = F(1) |
|---|
| 608 | n/a | i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1 |
|---|
| 609 | n/a | while abs(s - lasts) > F(1, 10**9): |
|---|
| 610 | n/a | lasts = s |
|---|
| 611 | n/a | i += 2 |
|---|
| 612 | n/a | fact *= i * (i-1) |
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| 613 | n/a | num *= x * x |
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| 614 | n/a | sign *= -1 |
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| 615 | n/a | s += num / fact * sign |
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| 616 | n/a | self.assertAlmostEqual(math.cos(1), s) |
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| 617 | n/a | |
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| 618 | n/a | def test_copy_deepcopy_pickle(self): |
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| 619 | n/a | r = F(13, 7) |
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| 620 | n/a | dr = DummyFraction(13, 7) |
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| 621 | n/a | self.assertEqual(r, loads(dumps(r))) |
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| 622 | n/a | self.assertEqual(id(r), id(copy(r))) |
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| 623 | n/a | self.assertEqual(id(r), id(deepcopy(r))) |
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| 624 | n/a | self.assertNotEqual(id(dr), id(copy(dr))) |
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| 625 | n/a | self.assertNotEqual(id(dr), id(deepcopy(dr))) |
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| 626 | n/a | self.assertTypedEquals(dr, copy(dr)) |
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| 627 | n/a | self.assertTypedEquals(dr, deepcopy(dr)) |
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| 628 | n/a | |
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| 629 | n/a | def test_slots(self): |
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| 630 | n/a | # Issue 4998 |
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| 631 | n/a | r = F(13, 7) |
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| 632 | n/a | self.assertRaises(AttributeError, setattr, r, 'a', 10) |
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| 633 | n/a | |
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| 634 | n/a | if __name__ == '__main__': |
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| 635 | n/a | unittest.main() |
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