Mercurial > cpython-lru_cache-weakref

annotate Lib/test/test_fractions.py @ 54294:dba767bc3155 legacy-trunk

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remove mention of old ctypes version
author Benjamin Peterson <benjamin@python.org>
date Sat, 23 May 2009 20:59:09 +0000
parents 114059c26794
children 9dc5aa62be72
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 """Tests for Lib/fractions.py."""
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2
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3 from decimal import Decimal
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4 from test.test_support import run_unittest
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5 import math
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6 import operator
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7 import fractions
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8 import unittest
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9 from copy import copy, deepcopy
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10 from cPickle import dumps, loads
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11 F = fractions.Fraction
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12 gcd = fractions.gcd
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13
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14
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15 class GcdTest(unittest.TestCase):
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16
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17 def testMisc(self):
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18 self.assertEquals(0, gcd(0, 0))
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19 self.assertEquals(1, gcd(1, 0))
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20 self.assertEquals(-1, gcd(-1, 0))
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21 self.assertEquals(1, gcd(0, 1))
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22 self.assertEquals(-1, gcd(0, -1))
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23 self.assertEquals(1, gcd(7, 1))
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24 self.assertEquals(-1, gcd(7, -1))
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25 self.assertEquals(1, gcd(-23, 15))
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26 self.assertEquals(12, gcd(120, 84))
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27 self.assertEquals(-12, gcd(84, -120))
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28
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29
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30 def _components(r):
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31 return (r.numerator, r.denominator)
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32
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33
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34 class FractionTest(unittest.TestCase):
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35
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36 def assertTypedEquals(self, expected, actual):
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37 """Asserts that both the types and values are the same."""
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38 self.assertEquals(type(expected), type(actual))
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39 self.assertEquals(expected, actual)
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40
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41 def assertRaisesMessage(self, exc_type, message,
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42 callable, *args, **kwargs):
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43 """Asserts that callable(*args, **kwargs) raises exc_type(message)."""
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44 try:
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45 callable(*args, **kwargs)
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46 except exc_type, e:
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47 self.assertEquals(message, str(e))
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48 else:
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49 self.fail("%s not raised" % exc_type.__name__)
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50
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51 def testInit(self):
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52 self.assertEquals((0, 1), _components(F()))
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53 self.assertEquals((7, 1), _components(F(7)))
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54 self.assertEquals((7, 3), _components(F(F(7, 3))))
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55
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56 self.assertEquals((-1, 1), _components(F(-1, 1)))
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57 self.assertEquals((-1, 1), _components(F(1, -1)))
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58 self.assertEquals((1, 1), _components(F(-2, -2)))
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59 self.assertEquals((1, 2), _components(F(5, 10)))
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60 self.assertEquals((7, 15), _components(F(7, 15)))
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61 self.assertEquals((10**23, 1), _components(F(10**23)))
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62
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63 self.assertEquals((3, 77), _components(F(F(3, 7), 11)))
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64 self.assertEquals((-9, 5), _components(F(2, F(-10, 9))))
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65 self.assertEquals((2486, 2485), _components(F(F(22, 7), F(355, 113))))
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66
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67 self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
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68 F, 12, 0)
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69 self.assertRaises(TypeError, F, 1.5)
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70 self.assertRaises(TypeError, F, 1.5 + 3j)
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71
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72 self.assertRaises(TypeError, F, "3/2", 3)
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73 self.assertRaises(TypeError, F, 3, 0j)
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74 self.assertRaises(TypeError, F, 3, 1j)
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75
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76
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77 def testFromString(self):
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78 self.assertEquals((5, 1), _components(F("5")))
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79 self.assertEquals((3, 2), _components(F("3/2")))
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80 self.assertEquals((3, 2), _components(F(" \n +3/2")))
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81 self.assertEquals((-3, 2), _components(F("-3/2 ")))
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82 self.assertEquals((13, 2), _components(F(" 013/02 \n ")))
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83 self.assertEquals((13, 2), _components(F(u" 013/02 \n ")))
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84
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85 self.assertEquals((16, 5), _components(F(" 3.2 ")))
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86 self.assertEquals((-16, 5), _components(F(u" -3.2 ")))
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87 self.assertEquals((-3, 1), _components(F(u" -3. ")))
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88 self.assertEquals((3, 5), _components(F(u" .6 ")))
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89 self.assertEquals((1, 3125), _components(F("32.e-5")))
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90 self.assertEquals((1000000, 1), _components(F("1E+06")))
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91 self.assertEquals((-12300, 1), _components(F("-1.23e4")))
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92 self.assertEquals((0, 1), _components(F(" .0e+0\t")))
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93 self.assertEquals((0, 1), _components(F("-0.000e0")))
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94
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95
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96 self.assertRaisesMessage(
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97 ZeroDivisionError, "Fraction(3, 0)",
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98 F, "3/0")
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99 self.assertRaisesMessage(
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100 ValueError, "Invalid literal for Fraction: '3/'",
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101 F, "3/")
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102 self.assertRaisesMessage(
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103 ValueError, "Invalid literal for Fraction: '/2'",
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104 F, "/2")
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105 self.assertRaisesMessage(
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106 ValueError, "Invalid literal for Fraction: '3 /2'",
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107 F, "3 /2")
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108 self.assertRaisesMessage(
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109 # Denominators don't need a sign.
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110 ValueError, "Invalid literal for Fraction: '3/+2'",
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111 F, "3/+2")
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112 self.assertRaisesMessage(
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113 # Imitate float's parsing.
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114 ValueError, "Invalid literal for Fraction: '+ 3/2'",
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115 F, "+ 3/2")
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116 self.assertRaisesMessage(
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117 # Avoid treating '.' as a regex special character.
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118 ValueError, "Invalid literal for Fraction: '3a2'",
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119 F, "3a2")
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120 self.assertRaisesMessage(
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121 # Don't accept combinations of decimals and fractions.
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122 ValueError, "Invalid literal for Fraction: '3/7.2'",
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123 F, "3/7.2")
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124 self.assertRaisesMessage(
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125 # Don't accept combinations of decimals and fractions.
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126 ValueError, "Invalid literal for Fraction: '3.2/7'",
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127 F, "3.2/7")
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128 self.assertRaisesMessage(
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129 # Allow 3. and .3, but not .
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130 ValueError, "Invalid literal for Fraction: '.'",
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131 F, ".")
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132
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133 def testImmutable(self):
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134 r = F(7, 3)
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135 r.__init__(2, 15)
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136 self.assertEquals((7, 3), _components(r))
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137
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138 self.assertRaises(AttributeError, setattr, r, 'numerator', 12)
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139 self.assertRaises(AttributeError, setattr, r, 'denominator', 6)
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140 self.assertEquals((7, 3), _components(r))
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141
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142 # But if you _really_ need to:
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143 r._numerator = 4
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144 r._denominator = 2
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145 self.assertEquals((4, 2), _components(r))
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146 # Which breaks some important operations:
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147 self.assertNotEquals(F(4, 2), r)
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148
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149 def testFromFloat(self):
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150 self.assertRaises(TypeError, F.from_float, 3+4j)
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151 self.assertEquals((10, 1), _components(F.from_float(10)))
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152 bigint = 1234567890123456789
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153 self.assertEquals((bigint, 1), _components(F.from_float(bigint)))
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154 self.assertEquals((0, 1), _components(F.from_float(-0.0)))
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155 self.assertEquals((10, 1), _components(F.from_float(10.0)))
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156 self.assertEquals((-5, 2), _components(F.from_float(-2.5)))
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157 self.assertEquals((99999999999999991611392, 1),
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158 _components(F.from_float(1e23)))
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159 self.assertEquals(float(10**23), float(F.from_float(1e23)))
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160 self.assertEquals((3602879701896397, 1125899906842624),
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161 _components(F.from_float(3.2)))
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162 self.assertEquals(3.2, float(F.from_float(3.2)))
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163
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164 inf = 1e1000
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165 nan = inf - inf
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166 self.assertRaisesMessage(
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167 TypeError, "Cannot convert inf to Fraction.",
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168 F.from_float, inf)
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169 self.assertRaisesMessage(
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170 TypeError, "Cannot convert -inf to Fraction.",
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171 F.from_float, -inf)
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172 self.assertRaisesMessage(
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173 TypeError, "Cannot convert nan to Fraction.",
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174 F.from_float, nan)
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175
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176 def testFromDecimal(self):
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177 self.assertRaises(TypeError, F.from_decimal, 3+4j)
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178 self.assertEquals(F(10, 1), F.from_decimal(10))
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179 self.assertEquals(F(0), F.from_decimal(Decimal("-0")))
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180 self.assertEquals(F(5, 10), F.from_decimal(Decimal("0.5")))
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181 self.assertEquals(F(5, 1000), F.from_decimal(Decimal("5e-3")))
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182 self.assertEquals(F(5000), F.from_decimal(Decimal("5e3")))
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183 self.assertEquals(1 - F(1, 10**30),
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184 F.from_decimal(Decimal("0." + "9" * 30)))
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185
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186 self.assertRaisesMessage(
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187 TypeError, "Cannot convert Infinity to Fraction.",
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188 F.from_decimal, Decimal("inf"))
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189 self.assertRaisesMessage(
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190 TypeError, "Cannot convert -Infinity to Fraction.",
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191 F.from_decimal, Decimal("-inf"))
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192 self.assertRaisesMessage(
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193 TypeError, "Cannot convert NaN to Fraction.",
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194 F.from_decimal, Decimal("nan"))
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195 self.assertRaisesMessage(
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196 TypeError, "Cannot convert sNaN to Fraction.",
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197 F.from_decimal, Decimal("snan"))
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198
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199 def testLimitDenominator(self):
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200 rpi = F('3.1415926535897932')
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201 self.assertEqual(rpi.limit_denominator(10000), F(355, 113))
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202 self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113))
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203 self.assertEqual(rpi.limit_denominator(113), F(355, 113))
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204 self.assertEqual(rpi.limit_denominator(112), F(333, 106))
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205 self.assertEqual(F(201, 200).limit_denominator(100), F(1))
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206 self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101))
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207 self.assertEqual(F(0).limit_denominator(10000), F(0))
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208
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209 def testConversions(self):
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210 self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
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211 self.assertTypedEquals(-1, int(F(-11, 10)))
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212
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213 self.assertEquals(False, bool(F(0, 1)))
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214 self.assertEquals(True, bool(F(3, 2)))
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215 self.assertTypedEquals(0.1, float(F(1, 10)))
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216
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217 # Check that __float__ isn't implemented by converting the
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218 # numerator and denominator to float before dividing.
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219 self.assertRaises(OverflowError, float, long('2'*400+'7'))
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220 self.assertAlmostEquals(2.0/3,
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221 float(F(long('2'*400+'7'), long('3'*400+'1'))))
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222
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223 self.assertTypedEquals(0.1+0j, complex(F(1,10)))
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224
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225
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226 def testArithmetic(self):
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227 self.assertEquals(F(1, 2), F(1, 10) + F(2, 5))
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228 self.assertEquals(F(-3, 10), F(1, 10) - F(2, 5))
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229 self.assertEquals(F(1, 25), F(1, 10) * F(2, 5))
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230 self.assertEquals(F(1, 4), F(1, 10) / F(2, 5))
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231 self.assertTypedEquals(2, F(9, 10) // F(2, 5))
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232 self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
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233 self.assertEquals(F(2, 3), F(-7, 3) % F(3, 2))
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234 self.assertEquals(F(8, 27), F(2, 3) ** F(3))
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235 self.assertEquals(F(27, 8), F(2, 3) ** F(-3))
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236 self.assertTypedEquals(2.0, F(4) ** F(1, 2))
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237 # Will return 1j in 3.0:
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238 self.assertRaises(ValueError, pow, F(-1), F(1, 2))
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239
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240 def testMixedArithmetic(self):
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241 self.assertTypedEquals(F(11, 10), F(1, 10) + 1)
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242 self.assertTypedEquals(1.1, F(1, 10) + 1.0)
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243 self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j))
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244 self.assertTypedEquals(F(11, 10), 1 + F(1, 10))
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245 self.assertTypedEquals(1.1, 1.0 + F(1, 10))
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246 self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10))
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247
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248 self.assertTypedEquals(F(-9, 10), F(1, 10) - 1)
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249 self.assertTypedEquals(-0.9, F(1, 10) - 1.0)
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250 self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j))
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251 self.assertTypedEquals(F(9, 10), 1 - F(1, 10))
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252 self.assertTypedEquals(0.9, 1.0 - F(1, 10))
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253 self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10))
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254
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255 self.assertTypedEquals(F(1, 10), F(1, 10) * 1)
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256 self.assertTypedEquals(0.1, F(1, 10) * 1.0)
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257 self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j))
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258 self.assertTypedEquals(F(1, 10), 1 * F(1, 10))
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259 self.assertTypedEquals(0.1, 1.0 * F(1, 10))
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260 self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10))
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261
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262 self.assertTypedEquals(F(1, 10), F(1, 10) / 1)
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263 self.assertTypedEquals(0.1, F(1, 10) / 1.0)
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264 self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j))
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265 self.assertTypedEquals(F(10, 1), 1 / F(1, 10))
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266 self.assertTypedEquals(10.0, 1.0 / F(1, 10))
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267 self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10))
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268
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269 self.assertTypedEquals(0, F(1, 10) // 1)
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270 self.assertTypedEquals(0.0, F(1, 10) // 1.0)
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271 self.assertTypedEquals(10, 1 // F(1, 10))
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272 self.assertTypedEquals(10**23, 10**22 // F(1, 10))
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273 self.assertTypedEquals(10.0, 1.0 // F(1, 10))
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274
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275 self.assertTypedEquals(F(1, 10), F(1, 10) % 1)
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276 self.assertTypedEquals(0.1, F(1, 10) % 1.0)
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277 self.assertTypedEquals(F(0, 1), 1 % F(1, 10))
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278 self.assertTypedEquals(0.0, 1.0 % F(1, 10))
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279
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280 # No need for divmod since we don't override it.
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281
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282 # ** has more interesting conversion rules.
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283 self.assertTypedEquals(F(100, 1), F(1, 10) ** -2)
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284 self.assertTypedEquals(F(100, 1), F(10, 1) ** 2)
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285 self.assertTypedEquals(0.1, F(1, 10) ** 1.0)
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286 self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j))
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287 self.assertTypedEquals(4 , 2 ** F(2, 1))
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288 # Will return 1j in 3.0:
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289 self.assertRaises(ValueError, pow, (-1), F(1, 2))
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290 self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1))
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291 self.assertTypedEquals(2.0 , 4 ** F(1, 2))
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292 self.assertTypedEquals(0.25, 2.0 ** F(-2, 1))
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293 self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10))
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294
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295 def testMixingWithDecimal(self):
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296 # Decimal refuses mixed comparisons.
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297 self.assertRaisesMessage(
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298 TypeError,
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299 "unsupported operand type(s) for +: 'Fraction' and 'Decimal'",
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300 operator.add, F(3,11), Decimal('3.1415926'))
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301 self.assertNotEquals(F(5, 2), Decimal('2.5'))
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302
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303 def testComparisons(self):
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304 self.assertTrue(F(1, 2) < F(2, 3))
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305 self.assertFalse(F(1, 2) < F(1, 2))
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306 self.assertTrue(F(1, 2) <= F(2, 3))
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307 self.assertTrue(F(1, 2) <= F(1, 2))
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308 self.assertFalse(F(2, 3) <= F(1, 2))
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309 self.assertTrue(F(1, 2) == F(1, 2))
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310 self.assertFalse(F(1, 2) == F(1, 3))
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311 self.assertFalse(F(1, 2) != F(1, 2))
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312 self.assertTrue(F(1, 2) != F(1, 3))
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313
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314 def testMixedLess(self):
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315 self.assertTrue(2 < F(5, 2))
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316 self.assertFalse(2 < F(4, 2))
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317 self.assertTrue(F(5, 2) < 3)
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318 self.assertFalse(F(4, 2) < 2)
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319
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320 self.assertTrue(F(1, 2) < 0.6)
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321 self.assertFalse(F(1, 2) < 0.4)
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322 self.assertTrue(0.4 < F(1, 2))
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323 self.assertFalse(0.5 < F(1, 2))
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324
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325 def testMixedLessEqual(self):
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326 self.assertTrue(0.5 <= F(1, 2))
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327 self.assertFalse(0.6 <= F(1, 2))
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328 self.assertTrue(F(1, 2) <= 0.5)
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329 self.assertFalse(F(1, 2) <= 0.4)
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330 self.assertTrue(2 <= F(4, 2))
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331 self.assertFalse(2 <= F(3, 2))
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332 self.assertTrue(F(4, 2) <= 2)
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333 self.assertFalse(F(5, 2) <= 2)
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334
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335 def testBigFloatComparisons(self):
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336 # Because 10**23 can't be represented exactly as a float:
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337 self.assertFalse(F(10**23) == float(10**23))
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338 # The first test demonstrates why these are important.
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339 self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1)))
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340 self.assertTrue(1e23 < F(math.trunc(1e23) + 1))
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341 self.assertFalse(1e23 <= F(math.trunc(1e23) - 1))
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342 self.assertTrue(1e23 > F(math.trunc(1e23) - 1))
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343 self.assertFalse(1e23 >= F(math.trunc(1e23) + 1))
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344
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345 def testBigComplexComparisons(self):
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346 self.assertFalse(F(10**23) == complex(10**23))
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347 self.assertTrue(F(10**23) > complex(10**23))
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348 self.assertFalse(F(10**23) <= complex(10**23))
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349
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350 def testMixedEqual(self):
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351 self.assertTrue(0.5 == F(1, 2))
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352 self.assertFalse(0.6 == F(1, 2))
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353 self.assertTrue(F(1, 2) == 0.5)
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354 self.assertFalse(F(1, 2) == 0.4)
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355 self.assertTrue(2 == F(4, 2))
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356 self.assertFalse(2 == F(3, 2))
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357 self.assertTrue(F(4, 2) == 2)
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358 self.assertFalse(F(5, 2) == 2)
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359
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360 def testStringification(self):
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361 self.assertEquals("Fraction(7, 3)", repr(F(7, 3)))
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362 self.assertEquals("Fraction(6283185307, 2000000000)",
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363 repr(F('3.1415926535')))
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364 self.assertEquals("Fraction(-1, 100000000000000000000)",
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365 repr(F(1, -10**20)))
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366 self.assertEquals("7/3", str(F(7, 3)))
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367 self.assertEquals("7", str(F(7, 1)))
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368
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369 def testHash(self):
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370 self.assertEquals(hash(2.5), hash(F(5, 2)))
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371 self.assertEquals(hash(10**50), hash(F(10**50)))
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372 self.assertNotEquals(hash(float(10**23)), hash(F(10**23)))
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373
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374 def testApproximatePi(self):
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375 # Algorithm borrowed from
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376 # http://docs.python.org/lib/decimal-recipes.html
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377 three = F(3)
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378 lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
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379 while abs(s - lasts) > F(1, 10**9):
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380 lasts = s
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381 n, na = n+na, na+8
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382 d, da = d+da, da+32
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383 t = (t * n) / d
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384 s += t
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385 self.assertAlmostEquals(math.pi, s)
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386
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387 def testApproximateCos1(self):
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388 # Algorithm borrowed from
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389 # http://docs.python.org/lib/decimal-recipes.html
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390 x = F(1)
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391 i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1
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392 while abs(s - lasts) > F(1, 10**9):
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393 lasts = s
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394 i += 2
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395 fact *= i * (i-1)
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396 num *= x * x
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397 sign *= -1
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398 s += num / fact * sign
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399 self.assertAlmostEquals(math.cos(1), s)
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400
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401 def test_copy_deepcopy_pickle(self):
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402 r = F(13, 7)
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403 self.assertEqual(r, loads(dumps(r)))
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404 self.assertEqual(id(r), id(copy(r)))
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405 self.assertEqual(id(r), id(deepcopy(r)))
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406
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407 def test_slots(self):
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408 # Issue 4998
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409 r = F(13, 7)
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410 self.assertRaises(AttributeError, setattr, r, 'a', 10)
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411
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412 def test_main():
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413 run_unittest(FractionTest, GcdTest)
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414
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415 if __name__ == '__main__':
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416 test_main()