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))) |
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329 | n/a | |
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330 | n/a | # Check that __float__ isn't implemented by converting the |
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331 | n/a | # numerator and denominator to float before dividing. |
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332 | n/a | self.assertRaises(OverflowError, float, int('2'*400+'7')) |
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333 | n/a | self.assertAlmostEqual(2.0/3, |
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334 | n/a | float(F(int('2'*400+'7'), int('3'*400+'1')))) |
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335 | n/a | |
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336 | n/a | self.assertTypedEquals(0.1+0j, complex(F(1,10))) |
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337 | n/a | |
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338 | n/a | def testRound(self): |
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339 | n/a | self.assertTypedEquals(F(-200), round(F(-150), -2)) |
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340 | n/a | self.assertTypedEquals(F(-200), round(F(-250), -2)) |
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341 | n/a | self.assertTypedEquals(F(30), round(F(26), -1)) |
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342 | n/a | self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1)) |
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343 | n/a | self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1)) |
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344 | n/a | |
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345 | n/a | def testArithmetic(self): |
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346 | n/a | self.assertEqual(F(1, 2), F(1, 10) + F(2, 5)) |
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347 | n/a | self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5)) |
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348 | n/a | self.assertEqual(F(1, 25), F(1, 10) * F(2, 5)) |
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349 | n/a | self.assertEqual(F(1, 4), F(1, 10) / F(2, 5)) |
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350 | n/a | self.assertTypedEquals(2, F(9, 10) // F(2, 5)) |
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351 | n/a | self.assertTypedEquals(10**23, F(10**23, 1) // F(1)) |
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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) |
---|
613 | n/a | num *= x * x |
---|
614 | n/a | sign *= -1 |
---|
615 | n/a | s += num / fact * sign |
---|
616 | n/a | self.assertAlmostEqual(math.cos(1), s) |
---|
617 | n/a | |
---|
618 | n/a | def test_copy_deepcopy_pickle(self): |
---|
619 | n/a | r = F(13, 7) |
---|
620 | n/a | dr = DummyFraction(13, 7) |
---|
621 | n/a | self.assertEqual(r, loads(dumps(r))) |
---|
622 | n/a | self.assertEqual(id(r), id(copy(r))) |
---|
623 | n/a | self.assertEqual(id(r), id(deepcopy(r))) |
---|
624 | n/a | self.assertNotEqual(id(dr), id(copy(dr))) |
---|
625 | n/a | self.assertNotEqual(id(dr), id(deepcopy(dr))) |
---|
626 | n/a | self.assertTypedEquals(dr, copy(dr)) |
---|
627 | n/a | self.assertTypedEquals(dr, deepcopy(dr)) |
---|
628 | n/a | |
---|
629 | n/a | def test_slots(self): |
---|
630 | n/a | # Issue 4998 |
---|
631 | n/a | r = F(13, 7) |
---|
632 | n/a | self.assertRaises(AttributeError, setattr, r, 'a', 10) |
---|
633 | n/a | |
---|
634 | n/a | if __name__ == '__main__': |
---|
635 | n/a | unittest.main() |
---|