Mercurial > cpython-lru_cache-weakref
annotate Lib/test/test_float.py @ 62799:dcc2e8bf64cf
Fix: Issue9091 Minor documentation clarification.
| author | Senthil Kumaran <orsenthil@gmail.com> |
|---|---|
| date | Mon, 05 Jul 2010 11:41:42 +0000 |
| parents | f271e1d0e9c4 |
| children | eafe07d40eb7 |
| rev | line source |
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| 34972 | 1 |
| 2 import unittest, struct | |
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Issue #1580: New free format floating point representation based on "Floating-Point Printer Sample Code", by Robert G. Burger. For example repr(11./5) now returns '2.2' instead of '2.2000000000000002'.
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3 import os |
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4 import sys |
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5 from test import support |
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6 import math |
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7 from math import isinf, isnan, copysign, ldexp |
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8 import operator |
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9 import random, fractions |
| 34972 | 10 |
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11 INF = float("inf") |
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12 NAN = float("nan") |
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13 |
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14 have_getformat = hasattr(float, "__getformat__") |
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15 requires_getformat = unittest.skipUnless(have_getformat, |
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16 "requires __getformat__") |
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17 requires_setformat = unittest.skipUnless(hasattr(float, "__setformat__"), |
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18 "requires __setformat__") |
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19 # decorator for skipping tests on non-IEEE 754 platforms |
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20 requires_IEEE_754 = unittest.skipUnless(have_getformat and |
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21 float.__getformat__("double").startswith("IEEE"), |
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22 "test requires IEEE 754 doubles") |
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23 |
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24 #locate file with float format test values |
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25 test_dir = os.path.dirname(__file__) or os.curdir |
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26 format_testfile = os.path.join(test_dir, 'formatfloat_testcases.txt') |
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27 |
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28 class GeneralFloatCases(unittest.TestCase): |
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29 |
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30 def test_float(self): |
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31 self.assertEqual(float(3.14), 3.14) |
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32 self.assertEqual(float(314), 314.0) |
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33 self.assertEqual(float(" 3.14 "), 3.14) |
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34 self.assertEqual(float(b" 3.14 "), 3.14) |
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35 self.assertRaises(ValueError, float, " 0x3.1 ") |
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36 self.assertRaises(ValueError, float, " -0x3.p-1 ") |
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37 self.assertRaises(ValueError, float, " +0x3.p-1 ") |
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38 self.assertRaises(ValueError, float, "++3.14") |
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39 self.assertRaises(ValueError, float, "+-3.14") |
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40 self.assertRaises(ValueError, float, "-+3.14") |
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41 self.assertRaises(ValueError, float, "--3.14") |
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42 self.assertRaises(ValueError, float, ".nan") |
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43 self.assertRaises(ValueError, float, "+.inf") |
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44 self.assertRaises(ValueError, float, ".") |
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45 self.assertRaises(ValueError, float, "-.") |
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46 # check that we don't accept alternate exponent markers |
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47 self.assertRaises(ValueError, float, "-1.7d29") |
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48 self.assertRaises(ValueError, float, "3D-14") |
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49 self.assertEqual(float(b" \u0663.\u0661\u0664 ".decode('raw-unicode-escape')), 3.14) |
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50 # extra long strings should not be a problem |
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51 float(b'.' + b'1'*1000) |
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52 float('.' + '1'*1000) |
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53 |
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54 @support.run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE') |
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55 def test_float_with_comma(self): |
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56 # set locale to something that doesn't use '.' for the decimal point |
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57 # float must not accept the locale specific decimal point but |
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58 # it still has to accept the normal python syntac |
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59 import locale |
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60 if not locale.localeconv()['decimal_point'] == ',': |
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61 return |
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63 self.assertEqual(float(" 3.14 "), 3.14) |
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64 self.assertEqual(float("+3.14 "), 3.14) |
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65 self.assertEqual(float("-3.14 "), -3.14) |
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66 self.assertEqual(float(".14 "), .14) |
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67 self.assertEqual(float("3. "), 3.0) |
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68 self.assertEqual(float("3.e3 "), 3000.0) |
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69 self.assertEqual(float("3.2e3 "), 3200.0) |
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70 self.assertEqual(float("2.5e-1 "), 0.25) |
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71 self.assertEqual(float("5e-1"), 0.5) |
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72 self.assertRaises(ValueError, float, " 3,14 ") |
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73 self.assertRaises(ValueError, float, " +3,14 ") |
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74 self.assertRaises(ValueError, float, " -3,14 ") |
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75 self.assertRaises(ValueError, float, " 0x3.1 ") |
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76 self.assertRaises(ValueError, float, " -0x3.p-1 ") |
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77 self.assertRaises(ValueError, float, " +0x3.p-1 ") |
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78 self.assertEqual(float(" 25.e-1 "), 2.5) |
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79 self.assertEqual(support.fcmp(float(" .25e-1 "), .025), 0) |
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80 |
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81 def test_floatconversion(self): |
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82 # Make sure that calls to __float__() work properly |
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83 class Foo0: |
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84 def __float__(self): |
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85 return 42. |
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86 |
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87 class Foo1(object): |
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88 def __float__(self): |
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89 return 42. |
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90 |
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91 class Foo2(float): |
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92 def __float__(self): |
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93 return 42. |
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95 class Foo3(float): |
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96 def __new__(cls, value=0.): |
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97 return float.__new__(cls, 2*value) |
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99 def __float__(self): |
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100 return self |
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101 |
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102 class Foo4(float): |
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103 def __float__(self): |
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104 return 42 |
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106 # Issue 5759: __float__ not called on str subclasses (though it is on |
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107 # unicode subclasses). |
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108 class FooStr(str): |
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109 def __float__(self): |
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110 return float(str(self)) + 1 |
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111 |
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112 self.assertAlmostEqual(float(Foo0()), 42.) |
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113 self.assertAlmostEqual(float(Foo1()), 42.) |
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114 self.assertAlmostEqual(float(Foo2()), 42.) |
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115 self.assertAlmostEqual(float(Foo3(21)), 42.) |
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116 self.assertRaises(TypeError, float, Foo4(42)) |
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117 self.assertAlmostEqual(float(FooStr('8')), 9.) |
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118 |
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119 def test_floatasratio(self): |
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120 for f, ratio in [ |
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121 (0.875, (7, 8)), |
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122 (-0.875, (-7, 8)), |
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123 (0.0, (0, 1)), |
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124 (11.5, (23, 2)), |
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125 ]: |
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126 self.assertEqual(f.as_integer_ratio(), ratio) |
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128 for i in range(10000): |
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129 f = random.random() |
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130 f *= 10 ** random.randint(-100, 100) |
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131 n, d = f.as_integer_ratio() |
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132 self.assertEqual(float(n).__truediv__(d), f) |
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134 R = fractions.Fraction |
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135 self.assertEqual(R(0, 1), |
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136 R(*float(0.0).as_integer_ratio())) |
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137 self.assertEqual(R(5, 2), |
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138 R(*float(2.5).as_integer_ratio())) |
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139 self.assertEqual(R(1, 2), |
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140 R(*float(0.5).as_integer_ratio())) |
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141 self.assertEqual(R(4728779608739021, 2251799813685248), |
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142 R(*float(2.1).as_integer_ratio())) |
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143 self.assertEqual(R(-4728779608739021, 2251799813685248), |
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144 R(*float(-2.1).as_integer_ratio())) |
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145 self.assertEqual(R(-2100, 1), |
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146 R(*float(-2100.0).as_integer_ratio())) |
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148 self.assertRaises(OverflowError, float('inf').as_integer_ratio) |
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149 self.assertRaises(OverflowError, float('-inf').as_integer_ratio) |
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150 self.assertRaises(ValueError, float('nan').as_integer_ratio) |
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152 def test_float_containment(self): |
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153 floats = (INF, -INF, 0.0, 1.0, NAN) |
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154 for f in floats: |
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155 self.assertIn(f, [f]) |
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156 self.assertIn(f, (f,)) |
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157 self.assertIn(f, {f}) |
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158 self.assertIn(f, {f: None}) |
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159 self.assertEqual([f].count(f), 1, "[].count('%r') != 1" % f) |
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160 self.assertIn(f, floats) |
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161 |
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162 for f in floats: |
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163 # nonidentical containers, same type, same contents |
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164 self.assertTrue([f] == [f], "[%r] != [%r]" % (f, f)) |
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165 self.assertTrue((f,) == (f,), "(%r,) != (%r,)" % (f, f)) |
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166 self.assertTrue({f} == {f}, "{%r} != {%r}" % (f, f)) |
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167 self.assertTrue({f : None} == {f: None}, "{%r : None} != " |
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168 "{%r : None}" % (f, f)) |
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169 |
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170 # identical containers |
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171 l, t, s, d = [f], (f,), {f}, {f: None} |
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172 self.assertTrue(l == l, "[%r] not equal to itself" % f) |
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173 self.assertTrue(t == t, "(%r,) not equal to itself" % f) |
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174 self.assertTrue(s == s, "{%r} not equal to itself" % f) |
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175 self.assertTrue(d == d, "{%r : None} not equal to itself" % f) |
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177 def assertEqualAndEqualSign(self, a, b): |
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178 # fail unless a == b and a and b have the same sign bit; |
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179 # the only difference from assertEqual is that this test |
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180 # distingishes -0.0 and 0.0. |
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181 self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b))) |
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182 |
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183 @requires_IEEE_754 |
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184 def test_float_pow(self): |
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185 # test builtin pow and ** operator for IEEE 754 special cases. |
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186 # Special cases taken from section F.9.4.4 of the C99 specification |
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187 |
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188 for pow_op in pow, operator.pow: |
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189 # x**NAN is NAN for any x except 1 |
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190 self.assertTrue(isnan(pow_op(-INF, NAN))) |
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191 self.assertTrue(isnan(pow_op(-2.0, NAN))) |
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192 self.assertTrue(isnan(pow_op(-1.0, NAN))) |
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193 self.assertTrue(isnan(pow_op(-0.5, NAN))) |
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194 self.assertTrue(isnan(pow_op(-0.0, NAN))) |
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195 self.assertTrue(isnan(pow_op(0.0, NAN))) |
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196 self.assertTrue(isnan(pow_op(0.5, NAN))) |
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197 self.assertTrue(isnan(pow_op(2.0, NAN))) |
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198 self.assertTrue(isnan(pow_op(INF, NAN))) |
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199 self.assertTrue(isnan(pow_op(NAN, NAN))) |
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200 |
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201 # NAN**y is NAN for any y except +-0 |
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202 self.assertTrue(isnan(pow_op(NAN, -INF))) |
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203 self.assertTrue(isnan(pow_op(NAN, -2.0))) |
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204 self.assertTrue(isnan(pow_op(NAN, -1.0))) |
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205 self.assertTrue(isnan(pow_op(NAN, -0.5))) |
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206 self.assertTrue(isnan(pow_op(NAN, 0.5))) |
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207 self.assertTrue(isnan(pow_op(NAN, 1.0))) |
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208 self.assertTrue(isnan(pow_op(NAN, 2.0))) |
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209 self.assertTrue(isnan(pow_op(NAN, INF))) |
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210 |
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211 # (+-0)**y raises ZeroDivisionError for y a negative odd integer |
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212 self.assertRaises(ZeroDivisionError, pow_op, -0.0, -1.0) |
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213 self.assertRaises(ZeroDivisionError, pow_op, 0.0, -1.0) |
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214 |
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215 # (+-0)**y raises ZeroDivisionError for y finite and negative |
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216 # but not an odd integer |
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217 self.assertRaises(ZeroDivisionError, pow_op, -0.0, -2.0) |
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218 self.assertRaises(ZeroDivisionError, pow_op, -0.0, -0.5) |
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219 self.assertRaises(ZeroDivisionError, pow_op, 0.0, -2.0) |
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220 self.assertRaises(ZeroDivisionError, pow_op, 0.0, -0.5) |
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221 |
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222 # (+-0)**y is +-0 for y a positive odd integer |
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223 self.assertEqualAndEqualSign(pow_op(-0.0, 1.0), -0.0) |
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224 self.assertEqualAndEqualSign(pow_op(0.0, 1.0), 0.0) |
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225 |
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226 # (+-0)**y is 0 for y finite and positive but not an odd integer |
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227 self.assertEqualAndEqualSign(pow_op(-0.0, 0.5), 0.0) |
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228 self.assertEqualAndEqualSign(pow_op(-0.0, 2.0), 0.0) |
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229 self.assertEqualAndEqualSign(pow_op(0.0, 0.5), 0.0) |
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230 self.assertEqualAndEqualSign(pow_op(0.0, 2.0), 0.0) |
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231 |
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232 # (-1)**+-inf is 1 |
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233 self.assertEqualAndEqualSign(pow_op(-1.0, -INF), 1.0) |
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234 self.assertEqualAndEqualSign(pow_op(-1.0, INF), 1.0) |
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235 |
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236 # 1**y is 1 for any y, even if y is an infinity or nan |
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237 self.assertEqualAndEqualSign(pow_op(1.0, -INF), 1.0) |
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238 self.assertEqualAndEqualSign(pow_op(1.0, -2.0), 1.0) |
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239 self.assertEqualAndEqualSign(pow_op(1.0, -1.0), 1.0) |
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240 self.assertEqualAndEqualSign(pow_op(1.0, -0.5), 1.0) |
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241 self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0) |
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242 self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0) |
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243 self.assertEqualAndEqualSign(pow_op(1.0, 0.5), 1.0) |
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244 self.assertEqualAndEqualSign(pow_op(1.0, 1.0), 1.0) |
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245 self.assertEqualAndEqualSign(pow_op(1.0, 2.0), 1.0) |
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246 self.assertEqualAndEqualSign(pow_op(1.0, INF), 1.0) |
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247 self.assertEqualAndEqualSign(pow_op(1.0, NAN), 1.0) |
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248 |
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249 # x**+-0 is 1 for any x, even if x is a zero, infinity, or nan |
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250 self.assertEqualAndEqualSign(pow_op(-INF, 0.0), 1.0) |
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251 self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0) |
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252 self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0) |
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253 self.assertEqualAndEqualSign(pow_op(-0.5, 0.0), 1.0) |
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254 self.assertEqualAndEqualSign(pow_op(-0.0, 0.0), 1.0) |
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255 self.assertEqualAndEqualSign(pow_op(0.0, 0.0), 1.0) |
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256 self.assertEqualAndEqualSign(pow_op(0.5, 0.0), 1.0) |
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257 self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0) |
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258 self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0) |
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259 self.assertEqualAndEqualSign(pow_op(INF, 0.0), 1.0) |
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260 self.assertEqualAndEqualSign(pow_op(NAN, 0.0), 1.0) |
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261 self.assertEqualAndEqualSign(pow_op(-INF, -0.0), 1.0) |
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262 self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0) |
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263 self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0) |
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264 self.assertEqualAndEqualSign(pow_op(-0.5, -0.0), 1.0) |
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265 self.assertEqualAndEqualSign(pow_op(-0.0, -0.0), 1.0) |
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266 self.assertEqualAndEqualSign(pow_op(0.0, -0.0), 1.0) |
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267 self.assertEqualAndEqualSign(pow_op(0.5, -0.0), 1.0) |
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268 self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0) |
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269 self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0) |
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270 self.assertEqualAndEqualSign(pow_op(INF, -0.0), 1.0) |
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271 self.assertEqualAndEqualSign(pow_op(NAN, -0.0), 1.0) |
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272 |
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273 # x**y defers to complex pow for finite negative x and |
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274 # non-integral y. |
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275 self.assertEqual(type(pow_op(-2.0, -0.5)), complex) |
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276 self.assertEqual(type(pow_op(-2.0, 0.5)), complex) |
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277 self.assertEqual(type(pow_op(-1.0, -0.5)), complex) |
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278 self.assertEqual(type(pow_op(-1.0, 0.5)), complex) |
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279 self.assertEqual(type(pow_op(-0.5, -0.5)), complex) |
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280 self.assertEqual(type(pow_op(-0.5, 0.5)), complex) |
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281 |
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282 # x**-INF is INF for abs(x) < 1 |
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283 self.assertEqualAndEqualSign(pow_op(-0.5, -INF), INF) |
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284 self.assertEqualAndEqualSign(pow_op(-0.0, -INF), INF) |
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285 self.assertEqualAndEqualSign(pow_op(0.0, -INF), INF) |
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286 self.assertEqualAndEqualSign(pow_op(0.5, -INF), INF) |
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287 |
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288 # x**-INF is 0 for abs(x) > 1 |
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289 self.assertEqualAndEqualSign(pow_op(-INF, -INF), 0.0) |
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290 self.assertEqualAndEqualSign(pow_op(-2.0, -INF), 0.0) |
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291 self.assertEqualAndEqualSign(pow_op(2.0, -INF), 0.0) |
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292 self.assertEqualAndEqualSign(pow_op(INF, -INF), 0.0) |
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293 |
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294 # x**INF is 0 for abs(x) < 1 |
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295 self.assertEqualAndEqualSign(pow_op(-0.5, INF), 0.0) |
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296 self.assertEqualAndEqualSign(pow_op(-0.0, INF), 0.0) |
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297 self.assertEqualAndEqualSign(pow_op(0.0, INF), 0.0) |
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298 self.assertEqualAndEqualSign(pow_op(0.5, INF), 0.0) |
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299 |
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300 # x**INF is INF for abs(x) > 1 |
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301 self.assertEqualAndEqualSign(pow_op(-INF, INF), INF) |
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302 self.assertEqualAndEqualSign(pow_op(-2.0, INF), INF) |
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303 self.assertEqualAndEqualSign(pow_op(2.0, INF), INF) |
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304 self.assertEqualAndEqualSign(pow_op(INF, INF), INF) |
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305 |
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306 # (-INF)**y is -0.0 for y a negative odd integer |
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307 self.assertEqualAndEqualSign(pow_op(-INF, -1.0), -0.0) |
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308 |
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309 # (-INF)**y is 0.0 for y negative but not an odd integer |
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310 self.assertEqualAndEqualSign(pow_op(-INF, -0.5), 0.0) |
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311 self.assertEqualAndEqualSign(pow_op(-INF, -2.0), 0.0) |
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312 |
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313 # (-INF)**y is -INF for y a positive odd integer |
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314 self.assertEqualAndEqualSign(pow_op(-INF, 1.0), -INF) |
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315 |
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316 # (-INF)**y is INF for y positive but not an odd integer |
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317 self.assertEqualAndEqualSign(pow_op(-INF, 0.5), INF) |
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318 self.assertEqualAndEqualSign(pow_op(-INF, 2.0), INF) |
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319 |
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320 # INF**y is INF for y positive |
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321 self.assertEqualAndEqualSign(pow_op(INF, 0.5), INF) |
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322 self.assertEqualAndEqualSign(pow_op(INF, 1.0), INF) |
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323 self.assertEqualAndEqualSign(pow_op(INF, 2.0), INF) |
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324 |
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325 # INF**y is 0.0 for y negative |
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326 self.assertEqualAndEqualSign(pow_op(INF, -2.0), 0.0) |
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327 self.assertEqualAndEqualSign(pow_op(INF, -1.0), 0.0) |
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328 self.assertEqualAndEqualSign(pow_op(INF, -0.5), 0.0) |
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329 |
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330 # basic checks not covered by the special cases above |
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331 self.assertEqualAndEqualSign(pow_op(-2.0, -2.0), 0.25) |
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332 self.assertEqualAndEqualSign(pow_op(-2.0, -1.0), -0.5) |
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333 self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0) |
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334 self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0) |
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335 self.assertEqualAndEqualSign(pow_op(-2.0, 1.0), -2.0) |
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336 self.assertEqualAndEqualSign(pow_op(-2.0, 2.0), 4.0) |
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337 self.assertEqualAndEqualSign(pow_op(-1.0, -2.0), 1.0) |
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338 self.assertEqualAndEqualSign(pow_op(-1.0, -1.0), -1.0) |
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339 self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0) |
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340 self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0) |
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341 self.assertEqualAndEqualSign(pow_op(-1.0, 1.0), -1.0) |
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342 self.assertEqualAndEqualSign(pow_op(-1.0, 2.0), 1.0) |
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343 self.assertEqualAndEqualSign(pow_op(2.0, -2.0), 0.25) |
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344 self.assertEqualAndEqualSign(pow_op(2.0, -1.0), 0.5) |
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345 self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0) |
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346 self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0) |
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347 self.assertEqualAndEqualSign(pow_op(2.0, 1.0), 2.0) |
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348 self.assertEqualAndEqualSign(pow_op(2.0, 2.0), 4.0) |
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349 |
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350 # 1 ** large and -1 ** large; some libms apparently |
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351 # have problems with these |
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352 self.assertEqualAndEqualSign(pow_op(1.0, -1e100), 1.0) |
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353 self.assertEqualAndEqualSign(pow_op(1.0, 1e100), 1.0) |
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354 self.assertEqualAndEqualSign(pow_op(-1.0, -1e100), 1.0) |
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355 self.assertEqualAndEqualSign(pow_op(-1.0, 1e100), 1.0) |
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356 |
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357 # check sign for results that underflow to 0 |
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358 self.assertEqualAndEqualSign(pow_op(-2.0, -2000.0), 0.0) |
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359 self.assertEqual(type(pow_op(-2.0, -2000.5)), complex) |
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360 self.assertEqualAndEqualSign(pow_op(-2.0, -2001.0), -0.0) |
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361 self.assertEqualAndEqualSign(pow_op(2.0, -2000.0), 0.0) |
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362 self.assertEqualAndEqualSign(pow_op(2.0, -2000.5), 0.0) |
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363 self.assertEqualAndEqualSign(pow_op(2.0, -2001.0), 0.0) |
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364 self.assertEqualAndEqualSign(pow_op(-0.5, 2000.0), 0.0) |
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365 self.assertEqual(type(pow_op(-0.5, 2000.5)), complex) |
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366 self.assertEqualAndEqualSign(pow_op(-0.5, 2001.0), -0.0) |
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367 self.assertEqualAndEqualSign(pow_op(0.5, 2000.0), 0.0) |
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368 self.assertEqualAndEqualSign(pow_op(0.5, 2000.5), 0.0) |
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369 self.assertEqualAndEqualSign(pow_op(0.5, 2001.0), 0.0) |
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370 |
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371 # check we don't raise an exception for subnormal results, |
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372 # and validate signs. Tests currently disabled, since |
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373 # they fail on systems where a subnormal result from pow |
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374 # is flushed to zero (e.g. Debian/ia64.) |
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375 #self.assertTrue(0.0 < pow_op(0.5, 1048) < 1e-315) |
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376 #self.assertTrue(0.0 < pow_op(-0.5, 1048) < 1e-315) |
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377 #self.assertTrue(0.0 < pow_op(0.5, 1047) < 1e-315) |
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378 #self.assertTrue(0.0 > pow_op(-0.5, 1047) > -1e-315) |
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379 #self.assertTrue(0.0 < pow_op(2.0, -1048) < 1e-315) |
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380 #self.assertTrue(0.0 < pow_op(-2.0, -1048) < 1e-315) |
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381 #self.assertTrue(0.0 < pow_op(2.0, -1047) < 1e-315) |
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382 #self.assertTrue(0.0 > pow_op(-2.0, -1047) > -1e-315) |
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384 |
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385 @requires_setformat |
| 34972 | 386 class FormatFunctionsTestCase(unittest.TestCase): |
| 387 | |
| 388 def setUp(self): | |
| 389 self.save_formats = {'double':float.__getformat__('double'), | |
| 390 'float':float.__getformat__('float')} | |
| 391 | |
| 392 def tearDown(self): | |
| 393 float.__setformat__('double', self.save_formats['double']) | |
| 394 float.__setformat__('float', self.save_formats['float']) | |
| 395 | |
| 396 def test_getformat(self): | |
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397 self.assertIn(float.__getformat__('double'), |
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398 ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) |
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399 self.assertIn(float.__getformat__('float'), |
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400 ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) |
| 34972 | 401 self.assertRaises(ValueError, float.__getformat__, 'chicken') |
| 402 self.assertRaises(TypeError, float.__getformat__, 1) | |
| 403 | |
| 404 def test_setformat(self): | |
| 405 for t in 'double', 'float': | |
| 406 float.__setformat__(t, 'unknown') | |
| 407 if self.save_formats[t] == 'IEEE, big-endian': | |
| 408 self.assertRaises(ValueError, float.__setformat__, | |
| 409 t, 'IEEE, little-endian') | |
| 410 elif self.save_formats[t] == 'IEEE, little-endian': | |
| 411 self.assertRaises(ValueError, float.__setformat__, | |
| 412 t, 'IEEE, big-endian') | |
| 413 else: | |
| 414 self.assertRaises(ValueError, float.__setformat__, | |
| 415 t, 'IEEE, big-endian') | |
| 416 self.assertRaises(ValueError, float.__setformat__, | |
| 417 t, 'IEEE, little-endian') | |
| 418 self.assertRaises(ValueError, float.__setformat__, | |
| 419 t, 'chicken') | |
| 420 self.assertRaises(ValueError, float.__setformat__, | |
| 421 'chicken', 'unknown') | |
| 422 | |
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423 BE_DOUBLE_INF = b'\x7f\xf0\x00\x00\x00\x00\x00\x00' |
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424 LE_DOUBLE_INF = bytes(reversed(BE_DOUBLE_INF)) |
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425 BE_DOUBLE_NAN = b'\x7f\xf8\x00\x00\x00\x00\x00\x00' |
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426 LE_DOUBLE_NAN = bytes(reversed(BE_DOUBLE_NAN)) |
| 34972 | 427 |
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428 BE_FLOAT_INF = b'\x7f\x80\x00\x00' |
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429 LE_FLOAT_INF = bytes(reversed(BE_FLOAT_INF)) |
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430 BE_FLOAT_NAN = b'\x7f\xc0\x00\x00' |
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431 LE_FLOAT_NAN = bytes(reversed(BE_FLOAT_NAN)) |
| 34972 | 432 |
| 433 # on non-IEEE platforms, attempting to unpack a bit pattern | |
| 434 # representing an infinity or a NaN should raise an exception. | |
| 435 | |
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436 @requires_setformat |
| 34972 | 437 class UnknownFormatTestCase(unittest.TestCase): |
| 438 def setUp(self): | |
| 439 self.save_formats = {'double':float.__getformat__('double'), | |
| 440 'float':float.__getformat__('float')} | |
| 441 float.__setformat__('double', 'unknown') | |
| 442 float.__setformat__('float', 'unknown') | |
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443 |
| 34972 | 444 def tearDown(self): |
| 445 float.__setformat__('double', self.save_formats['double']) | |
| 446 float.__setformat__('float', self.save_formats['float']) | |
| 447 | |
| 448 def test_double_specials_dont_unpack(self): | |
| 449 for fmt, data in [('>d', BE_DOUBLE_INF), | |
| 450 ('>d', BE_DOUBLE_NAN), | |
| 451 ('<d', LE_DOUBLE_INF), | |
| 452 ('<d', LE_DOUBLE_NAN)]: | |
| 453 self.assertRaises(ValueError, struct.unpack, fmt, data) | |
| 454 | |
| 455 def test_float_specials_dont_unpack(self): | |
| 456 for fmt, data in [('>f', BE_FLOAT_INF), | |
| 457 ('>f', BE_FLOAT_NAN), | |
| 458 ('<f', LE_FLOAT_INF), | |
| 459 ('<f', LE_FLOAT_NAN)]: | |
| 460 self.assertRaises(ValueError, struct.unpack, fmt, data) | |
| 461 | |
| 462 | |
| 463 # on an IEEE platform, all we guarantee is that bit patterns | |
| 464 # representing infinities or NaNs do not raise an exception; all else | |
| 465 # is accident (today). | |
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466 # let's also try to guarantee that -0.0 and 0.0 don't get confused. |
| 34972 | 467 |
| 468 class IEEEFormatTestCase(unittest.TestCase): | |
| 469 | |
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470 @requires_IEEE_754 |
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471 def test_double_specials_do_unpack(self): |
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472 for fmt, data in [('>d', BE_DOUBLE_INF), |
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473 ('>d', BE_DOUBLE_NAN), |
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474 ('<d', LE_DOUBLE_INF), |
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475 ('<d', LE_DOUBLE_NAN)]: |
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476 struct.unpack(fmt, data) |
| 34972 | 477 |
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478 @requires_IEEE_754 |
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479 def test_float_specials_do_unpack(self): |
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480 for fmt, data in [('>f', BE_FLOAT_INF), |
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481 ('>f', BE_FLOAT_NAN), |
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482 ('<f', LE_FLOAT_INF), |
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483 ('<f', LE_FLOAT_NAN)]: |
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484 struct.unpack(fmt, data) |
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485 |
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486 class FormatTestCase(unittest.TestCase): |
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487 |
| 43111 | 488 def test_format(self): |
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489 # these should be rewritten to use both format(x, spec) and |
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490 # x.__format__(spec) |
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491 |
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492 self.assertEqual(format(0.0, 'f'), '0.000000') |
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493 |
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494 # the default is 'g', except for empty format spec |
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495 self.assertEqual(format(0.0, ''), '0.0') |
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496 self.assertEqual(format(0.01, ''), '0.01') |
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497 self.assertEqual(format(0.01, 'g'), '0.01') |
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498 |
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499 # empty presentation type should format in the same way as str |
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500 # (issue 5920) |
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501 x = 100/7. |
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502 self.assertEqual(format(x, ''), str(x)) |
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503 self.assertEqual(format(x, '-'), str(x)) |
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504 self.assertEqual(format(x, '>'), str(x)) |
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505 self.assertEqual(format(x, '2'), str(x)) |
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506 |
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507 self.assertEqual(format(1.0, 'f'), '1.000000') |
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508 |
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509 self.assertEqual(format(-1.0, 'f'), '-1.000000') |
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510 |
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511 self.assertEqual(format( 1.0, ' f'), ' 1.000000') |
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512 self.assertEqual(format(-1.0, ' f'), '-1.000000') |
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513 self.assertEqual(format( 1.0, '+f'), '+1.000000') |
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514 self.assertEqual(format(-1.0, '+f'), '-1.000000') |
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515 |
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516 # % formatting |
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517 self.assertEqual(format(-1.0, '%'), '-100.000000%') |
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518 |
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519 # conversion to string should fail |
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520 self.assertRaises(ValueError, format, 3.0, "s") |
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521 |
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522 # other format specifiers shouldn't work on floats, |
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523 # in particular int specifiers |
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524 for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] + |
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525 [chr(x) for x in range(ord('A'), ord('Z')+1)]): |
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526 if not format_spec in 'eEfFgGn%': |
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527 self.assertRaises(ValueError, format, 0.0, format_spec) |
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528 self.assertRaises(ValueError, format, 1.0, format_spec) |
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529 self.assertRaises(ValueError, format, -1.0, format_spec) |
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530 self.assertRaises(ValueError, format, 1e100, format_spec) |
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531 self.assertRaises(ValueError, format, -1e100, format_spec) |
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532 self.assertRaises(ValueError, format, 1e-100, format_spec) |
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533 self.assertRaises(ValueError, format, -1e-100, format_spec) |
| 34972 | 534 |
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535 # issue 3382 |
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536 self.assertEqual(format(NAN, 'f'), 'nan') |
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537 self.assertEqual(format(NAN, 'F'), 'NAN') |
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538 self.assertEqual(format(INF, 'f'), 'inf') |
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539 self.assertEqual(format(INF, 'F'), 'INF') |
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540 |
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541 @requires_IEEE_754 |
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542 def test_format_testfile(self): |
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543 for line in open(format_testfile): |
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544 if line.startswith('--'): |
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545 continue |
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546 line = line.strip() |
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547 if not line: |
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548 continue |
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549 |
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550 lhs, rhs = map(str.strip, line.split('->')) |
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551 fmt, arg = lhs.split() |
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552 self.assertEqual(fmt % float(arg), rhs) |
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553 self.assertEqual(fmt % -float(arg), '-' + rhs) |
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554 |
|
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555 def test_issue5864(self): |
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556 self.assertEquals(format(123.456, '.4'), '123.5') |
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557 self.assertEquals(format(1234.56, '.4'), '1.235e+03') |
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558 self.assertEquals(format(12345.6, '.4'), '1.235e+04') |
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559 |
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560 class ReprTestCase(unittest.TestCase): |
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561 def test_repr(self): |
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562 floats_file = open(os.path.join(os.path.split(__file__)[0], |
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563 'floating_points.txt')) |
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564 for line in floats_file: |
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565 line = line.strip() |
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566 if not line or line.startswith('#'): |
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567 continue |
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568 v = eval(line) |
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569 self.assertEqual(v, eval(repr(v))) |
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570 floats_file.close() |
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571 |
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572 @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', |
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573 "applies only when using short float repr style") |
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574 def test_short_repr(self): |
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575 # test short float repr introduced in Python 3.1. One aspect |
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576 # of this repr is that we get some degree of str -> float -> |
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577 # str roundtripping. In particular, for any numeric string |
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578 # containing 15 or fewer significant digits, those exact same |
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579 # digits (modulo trailing zeros) should appear in the output. |
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580 # No more repr(0.03) -> "0.029999999999999999"! |
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581 |
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582 test_strings = [ |
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583 # output always includes *either* a decimal point and at |
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584 # least one digit after that point, or an exponent. |
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585 '0.0', |
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586 '1.0', |
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587 '0.01', |
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588 '0.02', |
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589 '0.03', |
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590 '0.04', |
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591 '0.05', |
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592 '1.23456789', |
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593 '10.0', |
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594 '100.0', |
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595 # values >= 1e16 get an exponent... |
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596 '1000000000000000.0', |
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597 '9999999999999990.0', |
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598 '1e+16', |
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599 '1e+17', |
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600 # ... and so do values < 1e-4 |
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601 '0.001', |
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602 '0.001001', |
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603 '0.00010000000000001', |
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604 '0.0001', |
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605 '9.999999999999e-05', |
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606 '1e-05', |
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607 # values designed to provoke failure if the FPU rounding |
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608 # precision isn't set correctly |
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609 '8.72293771110361e+25', |
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610 '7.47005307342313e+26', |
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611 '2.86438000439698e+28', |
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612 '8.89142905246179e+28', |
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613 '3.08578087079232e+35', |
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614 ] |
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615 |
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616 for s in test_strings: |
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617 negs = '-'+s |
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618 self.assertEqual(s, repr(float(s))) |
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619 self.assertEqual(negs, repr(float(negs))) |
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620 |
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621 |
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622 @requires_IEEE_754 |
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623 class RoundTestCase(unittest.TestCase): |
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624 |
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625 def test_inf_nan(self): |
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626 self.assertRaises(OverflowError, round, INF) |
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627 self.assertRaises(OverflowError, round, -INF) |
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628 self.assertRaises(ValueError, round, NAN) |
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629 self.assertRaises(TypeError, round, INF, 0.0) |
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630 self.assertRaises(TypeError, round, -INF, 1.0) |
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631 self.assertRaises(TypeError, round, NAN, "ceci n'est pas un integer") |
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632 self.assertRaises(TypeError, round, -0.0, 1j) |
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633 |
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634 def test_large_n(self): |
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635 for n in [324, 325, 400, 2**31-1, 2**31, 2**32, 2**100]: |
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636 self.assertEqual(round(123.456, n), 123.456) |
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637 self.assertEqual(round(-123.456, n), -123.456) |
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638 self.assertEqual(round(1e300, n), 1e300) |
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639 self.assertEqual(round(1e-320, n), 1e-320) |
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640 self.assertEqual(round(1e150, 300), 1e150) |
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641 self.assertEqual(round(1e300, 307), 1e300) |
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642 self.assertEqual(round(-3.1415, 308), -3.1415) |
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643 self.assertEqual(round(1e150, 309), 1e150) |
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644 self.assertEqual(round(1.4e-315, 315), 1e-315) |
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645 |
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646 def test_small_n(self): |
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647 for n in [-308, -309, -400, 1-2**31, -2**31, -2**31-1, -2**100]: |
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648 self.assertEqual(round(123.456, n), 0.0) |
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649 self.assertEqual(round(-123.456, n), -0.0) |
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650 self.assertEqual(round(1e300, n), 0.0) |
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651 self.assertEqual(round(1e-320, n), 0.0) |
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652 |
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653 def test_overflow(self): |
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654 self.assertRaises(OverflowError, round, 1.6e308, -308) |
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655 self.assertRaises(OverflowError, round, -1.7e308, -308) |
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656 |
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657 @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', |
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658 "applies only when using short float repr style") |
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659 def test_previous_round_bugs(self): |
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660 # particular cases that have occurred in bug reports |
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661 self.assertEqual(round(562949953421312.5, 1), |
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662 562949953421312.5) |
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663 self.assertEqual(round(56294995342131.5, 3), |
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664 56294995342131.5) |
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665 # round-half-even |
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666 self.assertEqual(round(25.0, -1), 20.0) |
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667 self.assertEqual(round(35.0, -1), 40.0) |
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668 self.assertEqual(round(45.0, -1), 40.0) |
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669 self.assertEqual(round(55.0, -1), 60.0) |
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670 self.assertEqual(round(65.0, -1), 60.0) |
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671 self.assertEqual(round(75.0, -1), 80.0) |
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672 self.assertEqual(round(85.0, -1), 80.0) |
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673 self.assertEqual(round(95.0, -1), 100.0) |
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674 |
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675 @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', |
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676 "applies only when using short float repr style") |
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677 def test_matches_float_format(self): |
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678 # round should give the same results as float formatting |
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679 for i in range(500): |
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680 x = i/1000. |
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681 self.assertEqual(float(format(x, '.0f')), round(x, 0)) |
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682 self.assertEqual(float(format(x, '.1f')), round(x, 1)) |
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683 self.assertEqual(float(format(x, '.2f')), round(x, 2)) |
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684 self.assertEqual(float(format(x, '.3f')), round(x, 3)) |
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685 |
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686 for i in range(5, 5000, 10): |
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687 x = i/1000. |
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688 self.assertEqual(float(format(x, '.0f')), round(x, 0)) |
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689 self.assertEqual(float(format(x, '.1f')), round(x, 1)) |
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690 self.assertEqual(float(format(x, '.2f')), round(x, 2)) |
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691 self.assertEqual(float(format(x, '.3f')), round(x, 3)) |
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692 |
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693 for i in range(500): |
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694 x = random.random() |
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695 self.assertEqual(float(format(x, '.0f')), round(x, 0)) |
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696 self.assertEqual(float(format(x, '.1f')), round(x, 1)) |
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697 self.assertEqual(float(format(x, '.2f')), round(x, 2)) |
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698 self.assertEqual(float(format(x, '.3f')), round(x, 3)) |
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699 |
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700 def test_format_specials(self): |
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701 # Test formatting of nans and infs. |
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702 |
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703 def test(fmt, value, expected): |
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704 # Test with both % and format(). |
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705 self.assertEqual(fmt % value, expected, fmt) |
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706 if not '#' in fmt: |
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707 # Until issue 7094 is implemented, format() for floats doesn't |
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708 # support '#' formatting |
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709 fmt = fmt[1:] # strip off the % |
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710 self.assertEqual(format(value, fmt), expected, fmt) |
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711 |
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712 for fmt in ['%e', '%f', '%g', '%.0e', '%.6f', '%.20g', |
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713 '%#e', '%#f', '%#g', '%#.20e', '%#.15f', '%#.3g']: |
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714 pfmt = '%+' + fmt[1:] |
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715 sfmt = '% ' + fmt[1:] |
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716 test(fmt, INF, 'inf') |
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717 test(fmt, -INF, '-inf') |
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718 test(fmt, NAN, 'nan') |
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719 test(fmt, -NAN, 'nan') |
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720 # When asking for a sign, it's always provided. nans are |
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721 # always positive. |
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722 test(pfmt, INF, '+inf') |
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723 test(pfmt, -INF, '-inf') |
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724 test(pfmt, NAN, '+nan') |
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725 test(pfmt, -NAN, '+nan') |
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726 # When using ' ' for a sign code, only infs can be negative. |
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727 # Others have a space. |
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728 test(sfmt, INF, ' inf') |
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729 test(sfmt, -INF, '-inf') |
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730 test(sfmt, NAN, ' nan') |
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731 test(sfmt, -NAN, ' nan') |
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732 |
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733 |
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734 # Beginning with Python 2.6 float has cross platform compatible |
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735 # ways to create and represent inf and nan |
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736 class InfNanTest(unittest.TestCase): |
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737 def test_inf_from_str(self): |
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738 self.assertTrue(isinf(float("inf"))) |
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739 self.assertTrue(isinf(float("+inf"))) |
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740 self.assertTrue(isinf(float("-inf"))) |
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741 self.assertTrue(isinf(float("infinity"))) |
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742 self.assertTrue(isinf(float("+infinity"))) |
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743 self.assertTrue(isinf(float("-infinity"))) |
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745 self.assertEqual(repr(float("inf")), "inf") |
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746 self.assertEqual(repr(float("+inf")), "inf") |
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747 self.assertEqual(repr(float("-inf")), "-inf") |
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748 self.assertEqual(repr(float("infinity")), "inf") |
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749 self.assertEqual(repr(float("+infinity")), "inf") |
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750 self.assertEqual(repr(float("-infinity")), "-inf") |
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752 self.assertEqual(repr(float("INF")), "inf") |
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753 self.assertEqual(repr(float("+Inf")), "inf") |
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754 self.assertEqual(repr(float("-iNF")), "-inf") |
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755 self.assertEqual(repr(float("Infinity")), "inf") |
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756 self.assertEqual(repr(float("+iNfInItY")), "inf") |
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757 self.assertEqual(repr(float("-INFINITY")), "-inf") |
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759 self.assertEqual(str(float("inf")), "inf") |
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760 self.assertEqual(str(float("+inf")), "inf") |
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761 self.assertEqual(str(float("-inf")), "-inf") |
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762 self.assertEqual(str(float("infinity")), "inf") |
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763 self.assertEqual(str(float("+infinity")), "inf") |
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764 self.assertEqual(str(float("-infinity")), "-inf") |
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765 |
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766 self.assertRaises(ValueError, float, "info") |
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767 self.assertRaises(ValueError, float, "+info") |
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768 self.assertRaises(ValueError, float, "-info") |
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769 self.assertRaises(ValueError, float, "in") |
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770 self.assertRaises(ValueError, float, "+in") |
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771 self.assertRaises(ValueError, float, "-in") |
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772 self.assertRaises(ValueError, float, "infinit") |
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773 self.assertRaises(ValueError, float, "+Infin") |
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774 self.assertRaises(ValueError, float, "-INFI") |
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775 self.assertRaises(ValueError, float, "infinitys") |
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776 |
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777 self.assertRaises(ValueError, float, "++Inf") |
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778 self.assertRaises(ValueError, float, "-+inf") |
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779 self.assertRaises(ValueError, float, "+-infinity") |
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780 self.assertRaises(ValueError, float, "--Infinity") |
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781 |
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782 def test_inf_as_str(self): |
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783 self.assertEqual(repr(1e300 * 1e300), "inf") |
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784 self.assertEqual(repr(-1e300 * 1e300), "-inf") |
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785 |
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786 self.assertEqual(str(1e300 * 1e300), "inf") |
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787 self.assertEqual(str(-1e300 * 1e300), "-inf") |
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788 |
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789 def test_nan_from_str(self): |
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790 self.assertTrue(isnan(float("nan"))) |
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791 self.assertTrue(isnan(float("+nan"))) |
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792 self.assertTrue(isnan(float("-nan"))) |
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793 |
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794 self.assertEqual(repr(float("nan")), "nan") |
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795 self.assertEqual(repr(float("+nan")), "nan") |
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796 self.assertEqual(repr(float("-nan")), "nan") |
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798 self.assertEqual(repr(float("NAN")), "nan") |
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799 self.assertEqual(repr(float("+NAn")), "nan") |
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800 self.assertEqual(repr(float("-NaN")), "nan") |
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802 self.assertEqual(str(float("nan")), "nan") |
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803 self.assertEqual(str(float("+nan")), "nan") |
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804 self.assertEqual(str(float("-nan")), "nan") |
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805 |
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806 self.assertRaises(ValueError, float, "nana") |
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807 self.assertRaises(ValueError, float, "+nana") |
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808 self.assertRaises(ValueError, float, "-nana") |
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809 self.assertRaises(ValueError, float, "na") |
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810 self.assertRaises(ValueError, float, "+na") |
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811 self.assertRaises(ValueError, float, "-na") |
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812 |
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813 self.assertRaises(ValueError, float, "++nan") |
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814 self.assertRaises(ValueError, float, "-+NAN") |
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815 self.assertRaises(ValueError, float, "+-NaN") |
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816 self.assertRaises(ValueError, float, "--nAn") |
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818 def test_nan_as_str(self): |
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819 self.assertEqual(repr(1e300 * 1e300 * 0), "nan") |
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820 self.assertEqual(repr(-1e300 * 1e300 * 0), "nan") |
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822 self.assertEqual(str(1e300 * 1e300 * 0), "nan") |
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823 self.assertEqual(str(-1e300 * 1e300 * 0), "nan") |
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825 def notest_float_nan(self): |
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826 self.assertTrue(NAN.is_nan()) |
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827 self.assertFalse(INF.is_nan()) |
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828 self.assertFalse((0.).is_nan()) |
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830 def notest_float_inf(self): |
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831 self.assertTrue(INF.is_inf()) |
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832 self.assertFalse(NAN.is_inf()) |
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833 self.assertFalse((0.).is_inf()) |
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834 |
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835 fromHex = float.fromhex |
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836 toHex = float.hex |
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837 class HexFloatTestCase(unittest.TestCase): |
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838 MAX = fromHex('0x.fffffffffffff8p+1024') # max normal |
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839 MIN = fromHex('0x1p-1022') # min normal |
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840 TINY = fromHex('0x0.0000000000001p-1022') # min subnormal |
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841 EPS = fromHex('0x0.0000000000001p0') # diff between 1.0 and next float up |
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842 |
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843 def identical(self, x, y): |
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844 # check that floats x and y are identical, or that both |
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845 # are NaNs |
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846 if isnan(x) or isnan(y): |
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847 if isnan(x) == isnan(y): |
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848 return |
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849 elif x == y and (x != 0.0 or copysign(1.0, x) == copysign(1.0, y)): |
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850 return |
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851 self.fail('%r not identical to %r' % (x, y)) |
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852 |
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853 def test_ends(self): |
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854 self.identical(self.MIN, ldexp(1.0, -1022)) |
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855 self.identical(self.TINY, ldexp(1.0, -1074)) |
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856 self.identical(self.EPS, ldexp(1.0, -52)) |
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857 self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970))) |
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858 |
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859 def test_invalid_inputs(self): |
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860 invalid_inputs = [ |
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861 'infi', # misspelt infinities and nans |
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862 '-Infinit', |
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863 '++inf', |
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864 '-+Inf', |
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865 '--nan', |
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866 '+-NaN', |
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867 'snan', |
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868 'NaNs', |
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869 'nna', |
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870 'an', |
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871 'nf', |
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872 'nfinity', |
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873 'inity', |
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874 'iinity', |
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875 '0xnan', |
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876 '', |
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877 ' ', |
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878 'x1.0p0', |
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879 '0xX1.0p0', |
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880 '+ 0x1.0p0', # internal whitespace |
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881 '- 0x1.0p0', |
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882 '0 x1.0p0', |
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883 '0x 1.0p0', |
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884 '0x1 2.0p0', |
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885 '+0x1 .0p0', |
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886 '0x1. 0p0', |
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887 '-0x1.0 1p0', |
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888 '-0x1.0 p0', |
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889 '+0x1.0p +0', |
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890 '0x1.0p -0', |
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891 '0x1.0p 0', |
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892 '+0x1.0p+ 0', |
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893 '-0x1.0p- 0', |
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894 '++0x1.0p-0', # double signs |
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895 '--0x1.0p0', |
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896 '+-0x1.0p+0', |
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897 '-+0x1.0p0', |
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898 '0x1.0p++0', |
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899 '+0x1.0p+-0', |
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900 '-0x1.0p-+0', |
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901 '0x1.0p--0', |
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902 '0x1.0.p0', |
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903 '0x.p0', # no hex digits before or after point |
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904 '0x1,p0', # wrong decimal point character |
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905 '0x1pa', |
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906 '0x1p\uff10', # fullwidth Unicode digits |
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907 '\uff10x1p0', |
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908 '0x\uff11p0', |
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909 '0x1.\uff10p0', |
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910 '0x1p0 \n 0x2p0', |
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911 '0x1p0\0 0x1p0', # embedded null byte is not end of string |
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912 ] |
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913 for x in invalid_inputs: |
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48817
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914 try: |
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915 result = fromHex(x) |
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916 except ValueError: |
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917 pass |
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918 else: |
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919 self.fail('Expected float.fromhex(%r) to raise ValueError; ' |
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920 'got %r instead' % (x, result)) |
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921 |
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922 |
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923 def test_whitespace(self): |
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924 value_pairs = [ |
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925 ('inf', INF), |
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926 ('-Infinity', -INF), |
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927 ('nan', NAN), |
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928 ('1.0', 1.0), |
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929 ('-0x.2', -0.125), |
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930 ('-0.0', -0.0) |
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931 ] |
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932 whitespace = [ |
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933 '', |
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934 ' ', |
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935 '\t', |
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936 '\n', |
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937 '\n \t', |
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938 '\f', |
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939 '\v', |
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940 '\r' |
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941 ] |
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942 for inp, expected in value_pairs: |
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943 for lead in whitespace: |
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944 for trail in whitespace: |
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945 got = fromHex(lead + inp + trail) |
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946 self.identical(got, expected) |
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947 |
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948 |
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48497
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949 def test_from_hex(self): |
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950 MIN = self.MIN; |
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951 MAX = self.MAX; |
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952 TINY = self.TINY; |
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953 EPS = self.EPS; |
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954 |
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955 # two spellings of infinity, with optional signs; case-insensitive |
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956 self.identical(fromHex('inf'), INF) |
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957 self.identical(fromHex('+Inf'), INF) |
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958 self.identical(fromHex('-INF'), -INF) |
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959 self.identical(fromHex('iNf'), INF) |
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960 self.identical(fromHex('Infinity'), INF) |
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961 self.identical(fromHex('+INFINITY'), INF) |
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962 self.identical(fromHex('-infinity'), -INF) |
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963 self.identical(fromHex('-iNFiNitY'), -INF) |
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|
964 |
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965 # nans with optional sign; case insensitive |
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966 self.identical(fromHex('nan'), NAN) |
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967 self.identical(fromHex('+NaN'), NAN) |
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968 self.identical(fromHex('-NaN'), NAN) |
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969 self.identical(fromHex('-nAN'), NAN) |
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|
970 |
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971 # variations in input format |
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972 self.identical(fromHex('1'), 1.0) |
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973 self.identical(fromHex('+1'), 1.0) |
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974 self.identical(fromHex('1.'), 1.0) |
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975 self.identical(fromHex('1.0'), 1.0) |
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976 self.identical(fromHex('1.0p0'), 1.0) |
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977 self.identical(fromHex('01'), 1.0) |
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978 self.identical(fromHex('01.'), 1.0) |
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979 self.identical(fromHex('0x1'), 1.0) |
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980 self.identical(fromHex('0x1.'), 1.0) |
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981 self.identical(fromHex('0x1.0'), 1.0) |
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982 self.identical(fromHex('+0x1.0'), 1.0) |
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983 self.identical(fromHex('0x1p0'), 1.0) |
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984 self.identical(fromHex('0X1p0'), 1.0) |
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985 self.identical(fromHex('0X1P0'), 1.0) |
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986 self.identical(fromHex('0x1P0'), 1.0) |
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987 self.identical(fromHex('0x1.p0'), 1.0) |
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988 self.identical(fromHex('0x1.0p0'), 1.0) |
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989 self.identical(fromHex('0x.1p4'), 1.0) |
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990 self.identical(fromHex('0x.1p04'), 1.0) |
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991 self.identical(fromHex('0x.1p004'), 1.0) |
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992 self.identical(fromHex('0x1p+0'), 1.0) |
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993 self.identical(fromHex('0x1P-0'), 1.0) |
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994 self.identical(fromHex('+0x1p0'), 1.0) |
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995 self.identical(fromHex('0x01p0'), 1.0) |
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996 self.identical(fromHex('0x1p00'), 1.0) |
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997 self.identical(fromHex(' 0x1p0 '), 1.0) |
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998 self.identical(fromHex('\n 0x1p0'), 1.0) |
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999 self.identical(fromHex('0x1p0 \t'), 1.0) |
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1000 self.identical(fromHex('0xap0'), 10.0) |
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1001 self.identical(fromHex('0xAp0'), 10.0) |
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1002 self.identical(fromHex('0xaP0'), 10.0) |
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1003 self.identical(fromHex('0xAP0'), 10.0) |
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1004 self.identical(fromHex('0xbep0'), 190.0) |
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1005 self.identical(fromHex('0xBep0'), 190.0) |
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1006 self.identical(fromHex('0xbEp0'), 190.0) |
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1007 self.identical(fromHex('0XBE0P-4'), 190.0) |
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1008 self.identical(fromHex('0xBEp0'), 190.0) |
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1009 self.identical(fromHex('0xB.Ep4'), 190.0) |
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1010 self.identical(fromHex('0x.BEp8'), 190.0) |
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1011 self.identical(fromHex('0x.0BEp12'), 190.0) |
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1012 |
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|
1013 # moving the point around |
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1014 pi = fromHex('0x1.921fb54442d18p1') |
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1015 self.identical(fromHex('0x.006487ed5110b46p11'), pi) |
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1016 self.identical(fromHex('0x.00c90fdaa22168cp10'), pi) |
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1017 self.identical(fromHex('0x.01921fb54442d18p9'), pi) |
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1018 self.identical(fromHex('0x.03243f6a8885a3p8'), pi) |
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1019 self.identical(fromHex('0x.06487ed5110b46p7'), pi) |
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1020 self.identical(fromHex('0x.0c90fdaa22168cp6'), pi) |
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1021 self.identical(fromHex('0x.1921fb54442d18p5'), pi) |
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1022 self.identical(fromHex('0x.3243f6a8885a3p4'), pi) |
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1023 self.identical(fromHex('0x.6487ed5110b46p3'), pi) |
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1024 self.identical(fromHex('0x.c90fdaa22168cp2'), pi) |
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1025 self.identical(fromHex('0x1.921fb54442d18p1'), pi) |
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1026 self.identical(fromHex('0x3.243f6a8885a3p0'), pi) |
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1027 self.identical(fromHex('0x6.487ed5110b46p-1'), pi) |
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1028 self.identical(fromHex('0xc.90fdaa22168cp-2'), pi) |
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1029 self.identical(fromHex('0x19.21fb54442d18p-3'), pi) |
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1030 self.identical(fromHex('0x32.43f6a8885a3p-4'), pi) |
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1031 self.identical(fromHex('0x64.87ed5110b46p-5'), pi) |
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1032 self.identical(fromHex('0xc9.0fdaa22168cp-6'), pi) |
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1033 self.identical(fromHex('0x192.1fb54442d18p-7'), pi) |
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1034 self.identical(fromHex('0x324.3f6a8885a3p-8'), pi) |
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1035 self.identical(fromHex('0x648.7ed5110b46p-9'), pi) |
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1036 self.identical(fromHex('0xc90.fdaa22168cp-10'), pi) |
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1037 self.identical(fromHex('0x1921.fb54442d18p-11'), pi) |
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1038 # ... |
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1039 self.identical(fromHex('0x1921fb54442d1.8p-47'), pi) |
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1040 self.identical(fromHex('0x3243f6a8885a3p-48'), pi) |
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1041 self.identical(fromHex('0x6487ed5110b46p-49'), pi) |
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1042 self.identical(fromHex('0xc90fdaa22168cp-50'), pi) |
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1043 self.identical(fromHex('0x1921fb54442d18p-51'), pi) |
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1044 self.identical(fromHex('0x3243f6a8885a30p-52'), pi) |
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1045 self.identical(fromHex('0x6487ed5110b460p-53'), pi) |
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1046 self.identical(fromHex('0xc90fdaa22168c0p-54'), pi) |
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1047 self.identical(fromHex('0x1921fb54442d180p-55'), pi) |
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1048 |
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1049 |
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|
1050 # results that should overflow... |
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1051 self.assertRaises(OverflowError, fromHex, '-0x1p1024') |
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1052 self.assertRaises(OverflowError, fromHex, '0x1p+1025') |
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1053 self.assertRaises(OverflowError, fromHex, '+0X1p1030') |
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1054 self.assertRaises(OverflowError, fromHex, '-0x1p+1100') |
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1055 self.assertRaises(OverflowError, fromHex, '0X1p123456789123456789') |
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1056 self.assertRaises(OverflowError, fromHex, '+0X.8p+1025') |
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1057 self.assertRaises(OverflowError, fromHex, '+0x0.8p1025') |
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1058 self.assertRaises(OverflowError, fromHex, '-0x0.4p1026') |
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1059 self.assertRaises(OverflowError, fromHex, '0X2p+1023') |
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1060 self.assertRaises(OverflowError, fromHex, '0x2.p1023') |
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1061 self.assertRaises(OverflowError, fromHex, '-0x2.0p+1023') |
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1062 self.assertRaises(OverflowError, fromHex, '+0X4p+1022') |
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1063 self.assertRaises(OverflowError, fromHex, '0x1.ffffffffffffffp+1023') |
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1064 self.assertRaises(OverflowError, fromHex, '-0X1.fffffffffffff9p1023') |
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1065 self.assertRaises(OverflowError, fromHex, '0X1.fffffffffffff8p1023') |
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1066 self.assertRaises(OverflowError, fromHex, '+0x3.fffffffffffffp1022') |
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1067 self.assertRaises(OverflowError, fromHex, '0x3fffffffffffffp+970') |
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1068 self.assertRaises(OverflowError, fromHex, '0x10000000000000000p960') |
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1069 self.assertRaises(OverflowError, fromHex, '-0Xffffffffffffffffp960') |
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1070 |
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1071 # ...and those that round to +-max float |
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1072 self.identical(fromHex('+0x1.fffffffffffffp+1023'), MAX) |
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1073 self.identical(fromHex('-0X1.fffffffffffff7p1023'), -MAX) |
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1074 self.identical(fromHex('0X1.fffffffffffff7fffffffffffffp1023'), MAX) |
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1075 |
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1076 # zeros |
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1077 self.identical(fromHex('0x0p0'), 0.0) |
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1078 self.identical(fromHex('0x0p1000'), 0.0) |
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1079 self.identical(fromHex('-0x0p1023'), -0.0) |
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1080 self.identical(fromHex('0X0p1024'), 0.0) |
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1081 self.identical(fromHex('-0x0p1025'), -0.0) |
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1082 self.identical(fromHex('0X0p2000'), 0.0) |
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1083 self.identical(fromHex('0x0p123456789123456789'), 0.0) |
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1084 self.identical(fromHex('-0X0p-0'), -0.0) |
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1085 self.identical(fromHex('-0X0p-1000'), -0.0) |
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1086 self.identical(fromHex('0x0p-1023'), 0.0) |
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1087 self.identical(fromHex('-0X0p-1024'), -0.0) |
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1088 self.identical(fromHex('-0x0p-1025'), -0.0) |
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1089 self.identical(fromHex('-0x0p-1072'), -0.0) |
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1090 self.identical(fromHex('0X0p-1073'), 0.0) |
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1091 self.identical(fromHex('-0x0p-1074'), -0.0) |
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1092 self.identical(fromHex('0x0p-1075'), 0.0) |
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1093 self.identical(fromHex('0X0p-1076'), 0.0) |
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1094 self.identical(fromHex('-0X0p-2000'), -0.0) |
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1095 self.identical(fromHex('-0x0p-123456789123456789'), -0.0) |
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1096 |
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1097 # values that should underflow to 0 |
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1098 self.identical(fromHex('0X1p-1075'), 0.0) |
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1099 self.identical(fromHex('-0X1p-1075'), -0.0) |
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1100 self.identical(fromHex('-0x1p-123456789123456789'), -0.0) |
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1101 self.identical(fromHex('0x1.00000000000000001p-1075'), TINY) |
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1102 self.identical(fromHex('-0x1.1p-1075'), -TINY) |
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1103 self.identical(fromHex('0x1.fffffffffffffffffp-1075'), TINY) |
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1104 |
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1105 # check round-half-even is working correctly near 0 ... |
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1106 self.identical(fromHex('0x1p-1076'), 0.0) |
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1107 self.identical(fromHex('0X2p-1076'), 0.0) |
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1108 self.identical(fromHex('0X3p-1076'), TINY) |
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1109 self.identical(fromHex('0x4p-1076'), TINY) |
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1110 self.identical(fromHex('0X5p-1076'), TINY) |
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1111 self.identical(fromHex('0X6p-1076'), 2*TINY) |
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1112 self.identical(fromHex('0x7p-1076'), 2*TINY) |
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1113 self.identical(fromHex('0X8p-1076'), 2*TINY) |
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1114 self.identical(fromHex('0X9p-1076'), 2*TINY) |
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1115 self.identical(fromHex('0xap-1076'), 2*TINY) |
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1116 self.identical(fromHex('0Xbp-1076'), 3*TINY) |
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1117 self.identical(fromHex('0xcp-1076'), 3*TINY) |
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1118 self.identical(fromHex('0Xdp-1076'), 3*TINY) |
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1119 self.identical(fromHex('0Xep-1076'), 4*TINY) |
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1120 self.identical(fromHex('0xfp-1076'), 4*TINY) |
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1121 self.identical(fromHex('0x10p-1076'), 4*TINY) |
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1122 self.identical(fromHex('-0x1p-1076'), -0.0) |
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1123 self.identical(fromHex('-0X2p-1076'), -0.0) |
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1124 self.identical(fromHex('-0x3p-1076'), -TINY) |
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1125 self.identical(fromHex('-0X4p-1076'), -TINY) |
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1126 self.identical(fromHex('-0x5p-1076'), -TINY) |
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1127 self.identical(fromHex('-0x6p-1076'), -2*TINY) |
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1128 self.identical(fromHex('-0X7p-1076'), -2*TINY) |
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1129 self.identical(fromHex('-0X8p-1076'), -2*TINY) |
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1130 self.identical(fromHex('-0X9p-1076'), -2*TINY) |
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1131 self.identical(fromHex('-0Xap-1076'), -2*TINY) |
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1132 self.identical(fromHex('-0xbp-1076'), -3*TINY) |
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1133 self.identical(fromHex('-0xcp-1076'), -3*TINY) |
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1134 self.identical(fromHex('-0Xdp-1076'), -3*TINY) |
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1135 self.identical(fromHex('-0xep-1076'), -4*TINY) |
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1136 self.identical(fromHex('-0Xfp-1076'), -4*TINY) |
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1137 self.identical(fromHex('-0X10p-1076'), -4*TINY) |
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1138 |
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1139 # ... and near MIN ... |
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1140 self.identical(fromHex('0x0.ffffffffffffd6p-1022'), MIN-3*TINY) |
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1141 self.identical(fromHex('0x0.ffffffffffffd8p-1022'), MIN-2*TINY) |
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1142 self.identical(fromHex('0x0.ffffffffffffdap-1022'), MIN-2*TINY) |
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1143 self.identical(fromHex('0x0.ffffffffffffdcp-1022'), MIN-2*TINY) |
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1144 self.identical(fromHex('0x0.ffffffffffffdep-1022'), MIN-2*TINY) |
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1145 self.identical(fromHex('0x0.ffffffffffffe0p-1022'), MIN-2*TINY) |
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1146 self.identical(fromHex('0x0.ffffffffffffe2p-1022'), MIN-2*TINY) |
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1147 self.identical(fromHex('0x0.ffffffffffffe4p-1022'), MIN-2*TINY) |
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1148 self.identical(fromHex('0x0.ffffffffffffe6p-1022'), MIN-2*TINY) |
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1149 self.identical(fromHex('0x0.ffffffffffffe8p-1022'), MIN-2*TINY) |
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1150 self.identical(fromHex('0x0.ffffffffffffeap-1022'), MIN-TINY) |
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1151 self.identical(fromHex('0x0.ffffffffffffecp-1022'), MIN-TINY) |
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1152 self.identical(fromHex('0x0.ffffffffffffeep-1022'), MIN-TINY) |
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1153 self.identical(fromHex('0x0.fffffffffffff0p-1022'), MIN-TINY) |
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1154 self.identical(fromHex('0x0.fffffffffffff2p-1022'), MIN-TINY) |
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1155 self.identical(fromHex('0x0.fffffffffffff4p-1022'), MIN-TINY) |
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1156 self.identical(fromHex('0x0.fffffffffffff6p-1022'), MIN-TINY) |
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1157 self.identical(fromHex('0x0.fffffffffffff8p-1022'), MIN) |
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1158 self.identical(fromHex('0x0.fffffffffffffap-1022'), MIN) |
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1159 self.identical(fromHex('0x0.fffffffffffffcp-1022'), MIN) |
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1160 self.identical(fromHex('0x0.fffffffffffffep-1022'), MIN) |
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1161 self.identical(fromHex('0x1.00000000000000p-1022'), MIN) |
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1162 self.identical(fromHex('0x1.00000000000002p-1022'), MIN) |
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1163 self.identical(fromHex('0x1.00000000000004p-1022'), MIN) |
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1164 self.identical(fromHex('0x1.00000000000006p-1022'), MIN) |
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1165 self.identical(fromHex('0x1.00000000000008p-1022'), MIN) |
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1166 self.identical(fromHex('0x1.0000000000000ap-1022'), MIN+TINY) |
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1167 self.identical(fromHex('0x1.0000000000000cp-1022'), MIN+TINY) |
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1168 self.identical(fromHex('0x1.0000000000000ep-1022'), MIN+TINY) |
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1169 self.identical(fromHex('0x1.00000000000010p-1022'), MIN+TINY) |
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1170 self.identical(fromHex('0x1.00000000000012p-1022'), MIN+TINY) |
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1171 self.identical(fromHex('0x1.00000000000014p-1022'), MIN+TINY) |
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1172 self.identical(fromHex('0x1.00000000000016p-1022'), MIN+TINY) |
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1173 self.identical(fromHex('0x1.00000000000018p-1022'), MIN+2*TINY) |
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1174 |
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1175 # ... and near 1.0. |
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1176 self.identical(fromHex('0x0.fffffffffffff0p0'), 1.0-EPS) |
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1177 self.identical(fromHex('0x0.fffffffffffff1p0'), 1.0-EPS) |
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1178 self.identical(fromHex('0X0.fffffffffffff2p0'), 1.0-EPS) |
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1179 self.identical(fromHex('0x0.fffffffffffff3p0'), 1.0-EPS) |
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1180 self.identical(fromHex('0X0.fffffffffffff4p0'), 1.0-EPS) |
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1181 self.identical(fromHex('0X0.fffffffffffff5p0'), 1.0-EPS/2) |
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1182 self.identical(fromHex('0X0.fffffffffffff6p0'), 1.0-EPS/2) |
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1183 self.identical(fromHex('0x0.fffffffffffff7p0'), 1.0-EPS/2) |
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1184 self.identical(fromHex('0x0.fffffffffffff8p0'), 1.0-EPS/2) |
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1185 self.identical(fromHex('0X0.fffffffffffff9p0'), 1.0-EPS/2) |
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1186 self.identical(fromHex('0X0.fffffffffffffap0'), 1.0-EPS/2) |
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1187 self.identical(fromHex('0x0.fffffffffffffbp0'), 1.0-EPS/2) |
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1188 self.identical(fromHex('0X0.fffffffffffffcp0'), 1.0) |
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1189 self.identical(fromHex('0x0.fffffffffffffdp0'), 1.0) |
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1190 self.identical(fromHex('0X0.fffffffffffffep0'), 1.0) |
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1191 self.identical(fromHex('0x0.ffffffffffffffp0'), 1.0) |
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1192 self.identical(fromHex('0X1.00000000000000p0'), 1.0) |
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1193 self.identical(fromHex('0X1.00000000000001p0'), 1.0) |
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1194 self.identical(fromHex('0x1.00000000000002p0'), 1.0) |
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1195 self.identical(fromHex('0X1.00000000000003p0'), 1.0) |
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1196 self.identical(fromHex('0x1.00000000000004p0'), 1.0) |
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1197 self.identical(fromHex('0X1.00000000000005p0'), 1.0) |
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1198 self.identical(fromHex('0X1.00000000000006p0'), 1.0) |
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1199 self.identical(fromHex('0X1.00000000000007p0'), 1.0) |
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1200 self.identical(fromHex('0x1.00000000000007ffffffffffffffffffffp0'), |
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1201 1.0) |
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1202 self.identical(fromHex('0x1.00000000000008p0'), 1.0) |
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1203 self.identical(fromHex('0x1.00000000000008000000000000000001p0'), |
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1204 1+EPS) |
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1205 self.identical(fromHex('0X1.00000000000009p0'), 1.0+EPS) |
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1206 self.identical(fromHex('0x1.0000000000000ap0'), 1.0+EPS) |
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1207 self.identical(fromHex('0x1.0000000000000bp0'), 1.0+EPS) |
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1208 self.identical(fromHex('0X1.0000000000000cp0'), 1.0+EPS) |
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1209 self.identical(fromHex('0x1.0000000000000dp0'), 1.0+EPS) |
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1210 self.identical(fromHex('0x1.0000000000000ep0'), 1.0+EPS) |
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1211 self.identical(fromHex('0X1.0000000000000fp0'), 1.0+EPS) |
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1212 self.identical(fromHex('0x1.00000000000010p0'), 1.0+EPS) |
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1213 self.identical(fromHex('0X1.00000000000011p0'), 1.0+EPS) |
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1214 self.identical(fromHex('0x1.00000000000012p0'), 1.0+EPS) |
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1215 self.identical(fromHex('0X1.00000000000013p0'), 1.0+EPS) |
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1216 self.identical(fromHex('0X1.00000000000014p0'), 1.0+EPS) |
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1217 self.identical(fromHex('0x1.00000000000015p0'), 1.0+EPS) |
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1218 self.identical(fromHex('0x1.00000000000016p0'), 1.0+EPS) |
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1219 self.identical(fromHex('0X1.00000000000017p0'), 1.0+EPS) |
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1220 self.identical(fromHex('0x1.00000000000017ffffffffffffffffffffp0'), |
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1221 1.0+EPS) |
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1222 self.identical(fromHex('0x1.00000000000018p0'), 1.0+2*EPS) |
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1223 self.identical(fromHex('0X1.00000000000018000000000000000001p0'), |
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1224 1.0+2*EPS) |
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1225 self.identical(fromHex('0x1.00000000000019p0'), 1.0+2*EPS) |
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1226 self.identical(fromHex('0X1.0000000000001ap0'), 1.0+2*EPS) |
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1227 self.identical(fromHex('0X1.0000000000001bp0'), 1.0+2*EPS) |
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1228 self.identical(fromHex('0x1.0000000000001cp0'), 1.0+2*EPS) |
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1229 self.identical(fromHex('0x1.0000000000001dp0'), 1.0+2*EPS) |
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1230 self.identical(fromHex('0x1.0000000000001ep0'), 1.0+2*EPS) |
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1231 self.identical(fromHex('0X1.0000000000001fp0'), 1.0+2*EPS) |
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1232 self.identical(fromHex('0x1.00000000000020p0'), 1.0+2*EPS) |
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1233 |
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1234 def test_roundtrip(self): |
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1235 def roundtrip(x): |
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1236 return fromHex(toHex(x)) |
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1237 |
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1238 for x in [NAN, INF, self.MAX, self.MIN, self.MIN-self.TINY, self.TINY, 0.0]: |
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1239 self.identical(x, roundtrip(x)) |
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1240 self.identical(-x, roundtrip(-x)) |
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1241 |
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1242 # fromHex(toHex(x)) should exactly recover x, for any non-NaN float x. |
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1243 import random |
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1244 for i in range(10000): |
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1245 e = random.randrange(-1200, 1200) |
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1246 m = random.random() |
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1247 s = random.choice([1.0, -1.0]) |
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1248 try: |
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1249 x = s*ldexp(m, e) |
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1250 except OverflowError: |
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1251 pass |
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1252 else: |
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1253 self.identical(x, fromHex(toHex(x))) |
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1254 |
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1257 support.run_unittest( |
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| 34972 | 1259 FormatFunctionsTestCase, |
| 1260 UnknownFormatTestCase, | |
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1261 IEEEFormatTestCase, |
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1262 FormatTestCase, |
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1263 ReprTestCase, |
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1264 RoundTestCase, |
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1265 InfNanTest, |
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1266 HexFloatTestCase, |
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1267 ) |
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| 1269 if __name__ == '__main__': | |
| 1270 test_main() |
