Mercurial > cpython-lru_cache-weakref
annotate Lib/test/test_float.py @ 48715:48dddfd2fbf3
RPC_WSTR is not available Visual Studio 2003 or earlier.
(Maybe I should have defined RPC_WSTR on old compiler,
but uuidcreate() is only place using it, so I simply replaced
with unsigned short *)
| author | Hirokazu Yamamoto <ocean-city@m2.ccsnet.ne.jp> |
|---|---|
| date | Sun, 17 Aug 2008 07:26:26 +0000 |
| parents | de0bf60f1245 |
| children | a77022dc3f61 |
| rev | line source |
|---|---|
| 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 from test import support |
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5 import math |
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6 from math import isinf, isnan, copysign, ldexp |
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7 import operator |
| 34972 | 8 |
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9 INF = float("inf") |
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10 NAN = float("nan") |
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11 |
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12 class GeneralFloatCases(unittest.TestCase): |
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13 |
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14 def test_float(self): |
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15 self.assertEqual(float(3.14), 3.14) |
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16 self.assertEqual(float(314), 314.0) |
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17 self.assertEqual(float(" 3.14 "), 3.14) |
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18 self.assertRaises(ValueError, float, " 0x3.1 ") |
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19 self.assertRaises(ValueError, float, " -0x3.p-1 ") |
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20 self.assertRaises(ValueError, float, " +0x3.p-1 ") |
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21 self.assertRaises(ValueError, float, "++3.14") |
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22 self.assertRaises(ValueError, float, "+-3.14") |
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23 self.assertRaises(ValueError, float, "-+3.14") |
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24 self.assertRaises(ValueError, float, "--3.14") |
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25 self.assertEqual(float(unicode(" 3.14 ")), 3.14) |
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26 self.assertEqual(float(unicode(" \u0663.\u0661\u0664 ",'raw-unicode-escape')), 3.14) |
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27 # Implementation limitation in PyFloat_FromString() |
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28 self.assertRaises(ValueError, float, unicode("1"*10000)) |
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29 |
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30 @support.run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE') |
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31 def test_float_with_comma(self): |
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32 # set locale to something that doesn't use '.' for the decimal point |
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33 # float must not accept the locale specific decimal point but |
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34 # it still has to accept the normal python syntac |
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35 import locale |
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36 if not locale.localeconv()['decimal_point'] == ',': |
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37 return |
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38 |
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39 self.assertEqual(float(" 3.14 "), 3.14) |
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40 self.assertEqual(float("+3.14 "), 3.14) |
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41 self.assertEqual(float("-3.14 "), -3.14) |
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42 self.assertEqual(float(".14 "), .14) |
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43 self.assertEqual(float("3. "), 3.0) |
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44 self.assertEqual(float("3.e3 "), 3000.0) |
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45 self.assertEqual(float("3.2e3 "), 3200.0) |
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46 self.assertEqual(float("2.5e-1 "), 0.25) |
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47 self.assertEqual(float("5e-1"), 0.5) |
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48 self.assertRaises(ValueError, float, " 3,14 ") |
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49 self.assertRaises(ValueError, float, " +3,14 ") |
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50 self.assertRaises(ValueError, float, " -3,14 ") |
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51 self.assertRaises(ValueError, float, " 0x3.1 ") |
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52 self.assertRaises(ValueError, float, " -0x3.p-1 ") |
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53 self.assertRaises(ValueError, float, " +0x3.p-1 ") |
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54 self.assertEqual(float(" 25.e-1 "), 2.5) |
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55 self.assertEqual(fcmp(float(" .25e-1 "), .025), 0) |
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56 |
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57 def test_floatconversion(self): |
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58 # Make sure that calls to __float__() work properly |
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59 class Foo0: |
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60 def __float__(self): |
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61 return 42. |
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62 |
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63 class Foo1(object): |
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64 def __float__(self): |
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65 return 42. |
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66 |
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67 class Foo2(float): |
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68 def __float__(self): |
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69 return 42. |
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70 |
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71 class Foo3(float): |
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72 def __new__(cls, value=0.): |
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73 return float.__new__(cls, 2*value) |
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75 def __float__(self): |
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76 return self |
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78 class Foo4(float): |
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79 def __float__(self): |
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80 return 42 |
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81 |
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82 self.assertAlmostEqual(float(Foo0()), 42.) |
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83 self.assertAlmostEqual(float(Foo1()), 42.) |
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84 self.assertAlmostEqual(float(Foo2()), 42.) |
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85 self.assertAlmostEqual(float(Foo3(21)), 42.) |
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86 self.assertRaises(TypeError, float, Foo4(42)) |
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87 |
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88 def test_floatasratio(self): |
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89 for f, ratio in [ |
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90 (0.875, (7, 8)), |
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91 (-0.875, (-7, 8)), |
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92 (0.0, (0, 1)), |
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93 (11.5, (23, 2)), |
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94 ]: |
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95 self.assertEqual(f.as_integer_ratio(), ratio) |
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96 |
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97 for i in range(10000): |
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98 f = random.random() |
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99 f *= 10 ** random.randint(-100, 100) |
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100 n, d = f.as_integer_ratio() |
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101 self.assertEqual(float(n).__truediv__(d), f) |
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102 |
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103 R = fractions.Fraction |
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104 self.assertEqual(R(0, 1), |
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105 R(*float(0.0).as_integer_ratio())) |
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106 self.assertEqual(R(5, 2), |
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107 R(*float(2.5).as_integer_ratio())) |
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108 self.assertEqual(R(1, 2), |
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109 R(*float(0.5).as_integer_ratio())) |
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110 self.assertEqual(R(4728779608739021, 2251799813685248), |
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111 R(*float(2.1).as_integer_ratio())) |
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112 self.assertEqual(R(-4728779608739021, 2251799813685248), |
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113 R(*float(-2.1).as_integer_ratio())) |
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114 self.assertEqual(R(-2100, 1), |
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115 R(*float(-2100.0).as_integer_ratio())) |
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116 |
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117 self.assertRaises(OverflowError, float('inf').as_integer_ratio) |
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118 self.assertRaises(OverflowError, float('-inf').as_integer_ratio) |
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119 self.assertRaises(ValueError, float('nan').as_integer_ratio) |
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120 |
| 34972 | 121 class FormatFunctionsTestCase(unittest.TestCase): |
| 122 | |
| 123 def setUp(self): | |
| 124 self.save_formats = {'double':float.__getformat__('double'), | |
| 125 'float':float.__getformat__('float')} | |
| 126 | |
| 127 def tearDown(self): | |
| 128 float.__setformat__('double', self.save_formats['double']) | |
| 129 float.__setformat__('float', self.save_formats['float']) | |
| 130 | |
| 131 def test_getformat(self): | |
| 132 self.assert_(float.__getformat__('double') in | |
| 133 ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) | |
| 134 self.assert_(float.__getformat__('float') in | |
| 135 ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) | |
| 136 self.assertRaises(ValueError, float.__getformat__, 'chicken') | |
| 137 self.assertRaises(TypeError, float.__getformat__, 1) | |
| 138 | |
| 139 def test_setformat(self): | |
| 140 for t in 'double', 'float': | |
| 141 float.__setformat__(t, 'unknown') | |
| 142 if self.save_formats[t] == 'IEEE, big-endian': | |
| 143 self.assertRaises(ValueError, float.__setformat__, | |
| 144 t, 'IEEE, little-endian') | |
| 145 elif self.save_formats[t] == 'IEEE, little-endian': | |
| 146 self.assertRaises(ValueError, float.__setformat__, | |
| 147 t, 'IEEE, big-endian') | |
| 148 else: | |
| 149 self.assertRaises(ValueError, float.__setformat__, | |
| 150 t, 'IEEE, big-endian') | |
| 151 self.assertRaises(ValueError, float.__setformat__, | |
| 152 t, 'IEEE, little-endian') | |
| 153 self.assertRaises(ValueError, float.__setformat__, | |
| 154 t, 'chicken') | |
| 155 self.assertRaises(ValueError, float.__setformat__, | |
| 156 'chicken', 'unknown') | |
| 157 | |
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158 BE_DOUBLE_INF = b'\x7f\xf0\x00\x00\x00\x00\x00\x00' |
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159 LE_DOUBLE_INF = bytes(reversed(BE_DOUBLE_INF)) |
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160 BE_DOUBLE_NAN = b'\x7f\xf8\x00\x00\x00\x00\x00\x00' |
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161 LE_DOUBLE_NAN = bytes(reversed(BE_DOUBLE_NAN)) |
| 34972 | 162 |
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163 BE_FLOAT_INF = b'\x7f\x80\x00\x00' |
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164 LE_FLOAT_INF = bytes(reversed(BE_FLOAT_INF)) |
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165 BE_FLOAT_NAN = b'\x7f\xc0\x00\x00' |
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166 LE_FLOAT_NAN = bytes(reversed(BE_FLOAT_NAN)) |
| 34972 | 167 |
| 168 # on non-IEEE platforms, attempting to unpack a bit pattern | |
| 169 # representing an infinity or a NaN should raise an exception. | |
| 170 | |
| 171 class UnknownFormatTestCase(unittest.TestCase): | |
| 172 def setUp(self): | |
| 173 self.save_formats = {'double':float.__getformat__('double'), | |
| 174 'float':float.__getformat__('float')} | |
| 175 float.__setformat__('double', 'unknown') | |
| 176 float.__setformat__('float', 'unknown') | |
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177 |
| 34972 | 178 def tearDown(self): |
| 179 float.__setformat__('double', self.save_formats['double']) | |
| 180 float.__setformat__('float', self.save_formats['float']) | |
| 181 | |
| 182 def test_double_specials_dont_unpack(self): | |
| 183 for fmt, data in [('>d', BE_DOUBLE_INF), | |
| 184 ('>d', BE_DOUBLE_NAN), | |
| 185 ('<d', LE_DOUBLE_INF), | |
| 186 ('<d', LE_DOUBLE_NAN)]: | |
| 187 self.assertRaises(ValueError, struct.unpack, fmt, data) | |
| 188 | |
| 189 def test_float_specials_dont_unpack(self): | |
| 190 for fmt, data in [('>f', BE_FLOAT_INF), | |
| 191 ('>f', BE_FLOAT_NAN), | |
| 192 ('<f', LE_FLOAT_INF), | |
| 193 ('<f', LE_FLOAT_NAN)]: | |
| 194 self.assertRaises(ValueError, struct.unpack, fmt, data) | |
| 195 | |
| 196 | |
| 197 # on an IEEE platform, all we guarantee is that bit patterns | |
| 198 # representing infinities or NaNs do not raise an exception; all else | |
| 199 # is accident (today). | |
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200 # let's also try to guarantee that -0.0 and 0.0 don't get confused. |
| 34972 | 201 |
| 202 class IEEEFormatTestCase(unittest.TestCase): | |
| 203 if float.__getformat__("double").startswith("IEEE"): | |
| 204 def test_double_specials_do_unpack(self): | |
| 205 for fmt, data in [('>d', BE_DOUBLE_INF), | |
| 206 ('>d', BE_DOUBLE_NAN), | |
| 207 ('<d', LE_DOUBLE_INF), | |
| 208 ('<d', LE_DOUBLE_NAN)]: | |
| 209 struct.unpack(fmt, data) | |
| 210 | |
| 211 if float.__getformat__("float").startswith("IEEE"): | |
| 212 def test_float_specials_do_unpack(self): | |
| 213 for fmt, data in [('>f', BE_FLOAT_INF), | |
| 214 ('>f', BE_FLOAT_NAN), | |
| 215 ('<f', LE_FLOAT_INF), | |
| 216 ('<f', LE_FLOAT_NAN)]: | |
| 217 struct.unpack(fmt, data) | |
| 218 | |
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219 if float.__getformat__("double").startswith("IEEE"): |
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220 def test_negative_zero(self): |
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221 import math |
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222 def pos_pos(): |
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223 return 0.0, math.atan2(0.0, -1) |
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224 def pos_neg(): |
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225 return 0.0, math.atan2(-0.0, -1) |
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226 def neg_pos(): |
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227 return -0.0, math.atan2(0.0, -1) |
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228 def neg_neg(): |
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229 return -0.0, math.atan2(-0.0, -1) |
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230 self.assertEquals(pos_pos(), neg_pos()) |
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231 self.assertEquals(pos_neg(), neg_neg()) |
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232 |
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233 class FormatTestCase(unittest.TestCase): |
| 43111 | 234 def test_format(self): |
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235 # these should be rewritten to use both format(x, spec) and |
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236 # x.__format__(spec) |
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237 |
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238 self.assertEqual(format(0.0, 'f'), '0.000000') |
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239 |
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240 # the default is 'g', except for empty format spec |
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241 self.assertEqual(format(0.0, ''), '0.0') |
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242 self.assertEqual(format(0.01, ''), '0.01') |
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243 self.assertEqual(format(0.01, 'g'), '0.01') |
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244 |
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245 |
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246 self.assertEqual(format(1.0, 'f'), '1.000000') |
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247 |
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248 self.assertEqual(format(-1.0, 'f'), '-1.000000') |
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249 |
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250 self.assertEqual(format( 1.0, ' f'), ' 1.000000') |
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251 self.assertEqual(format(-1.0, ' f'), '-1.000000') |
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252 self.assertEqual(format( 1.0, '+f'), '+1.000000') |
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253 self.assertEqual(format(-1.0, '+f'), '-1.000000') |
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254 |
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255 # % formatting |
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256 self.assertEqual(format(-1.0, '%'), '-100.000000%') |
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257 |
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258 # conversion to string should fail |
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259 self.assertRaises(ValueError, format, 3.0, "s") |
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260 |
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261 # other format specifiers shouldn't work on floats, |
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262 # in particular int specifiers |
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263 for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] + |
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264 [chr(x) for x in range(ord('A'), ord('Z')+1)]): |
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265 if not format_spec in 'eEfFgGn%': |
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266 self.assertRaises(ValueError, format, 0.0, format_spec) |
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267 self.assertRaises(ValueError, format, 1.0, format_spec) |
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268 self.assertRaises(ValueError, format, -1.0, format_spec) |
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269 self.assertRaises(ValueError, format, 1e100, format_spec) |
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270 self.assertRaises(ValueError, format, -1e100, format_spec) |
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271 self.assertRaises(ValueError, format, 1e-100, format_spec) |
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272 self.assertRaises(ValueError, format, -1e-100, format_spec) |
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274 class ReprTestCase(unittest.TestCase): |
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275 def test_repr(self): |
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276 floats_file = open(os.path.join(os.path.split(__file__)[0], |
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277 'floating_points.txt')) |
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278 for line in floats_file: |
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279 line = line.strip() |
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280 if not line or line.startswith('#'): |
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281 continue |
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282 v = eval(line) |
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283 self.assertEqual(v, eval(repr(v))) |
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284 floats_file.close() |
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285 |
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286 # Beginning with Python 2.6 float has cross platform compatible |
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287 # ways to create and represent inf and nan |
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288 class InfNanTest(unittest.TestCase): |
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289 def test_inf_from_str(self): |
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290 self.assert_(isinf(float("inf"))) |
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291 self.assert_(isinf(float("+inf"))) |
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292 self.assert_(isinf(float("-inf"))) |
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293 self.assert_(isinf(float("infinity"))) |
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294 self.assert_(isinf(float("+infinity"))) |
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295 self.assert_(isinf(float("-infinity"))) |
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296 |
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297 self.assertEqual(repr(float("inf")), "inf") |
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298 self.assertEqual(repr(float("+inf")), "inf") |
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299 self.assertEqual(repr(float("-inf")), "-inf") |
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300 self.assertEqual(repr(float("infinity")), "inf") |
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301 self.assertEqual(repr(float("+infinity")), "inf") |
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302 self.assertEqual(repr(float("-infinity")), "-inf") |
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303 |
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304 self.assertEqual(repr(float("INF")), "inf") |
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305 self.assertEqual(repr(float("+Inf")), "inf") |
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306 self.assertEqual(repr(float("-iNF")), "-inf") |
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307 self.assertEqual(repr(float("Infinity")), "inf") |
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308 self.assertEqual(repr(float("+iNfInItY")), "inf") |
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309 self.assertEqual(repr(float("-INFINITY")), "-inf") |
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310 |
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311 self.assertEqual(str(float("inf")), "inf") |
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312 self.assertEqual(str(float("+inf")), "inf") |
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313 self.assertEqual(str(float("-inf")), "-inf") |
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314 self.assertEqual(str(float("infinity")), "inf") |
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315 self.assertEqual(str(float("+infinity")), "inf") |
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316 self.assertEqual(str(float("-infinity")), "-inf") |
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317 |
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318 self.assertRaises(ValueError, float, "info") |
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319 self.assertRaises(ValueError, float, "+info") |
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320 self.assertRaises(ValueError, float, "-info") |
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321 self.assertRaises(ValueError, float, "in") |
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322 self.assertRaises(ValueError, float, "+in") |
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323 self.assertRaises(ValueError, float, "-in") |
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324 self.assertRaises(ValueError, float, "infinit") |
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325 self.assertRaises(ValueError, float, "+Infin") |
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326 self.assertRaises(ValueError, float, "-INFI") |
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327 self.assertRaises(ValueError, float, "infinitys") |
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328 |
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329 def test_inf_as_str(self): |
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330 self.assertEqual(repr(1e300 * 1e300), "inf") |
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331 self.assertEqual(repr(-1e300 * 1e300), "-inf") |
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332 |
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333 self.assertEqual(str(1e300 * 1e300), "inf") |
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334 self.assertEqual(str(-1e300 * 1e300), "-inf") |
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335 |
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336 def test_nan_from_str(self): |
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337 self.assert_(isnan(float("nan"))) |
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338 self.assert_(isnan(float("+nan"))) |
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339 self.assert_(isnan(float("-nan"))) |
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340 |
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341 self.assertEqual(repr(float("nan")), "nan") |
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342 self.assertEqual(repr(float("+nan")), "nan") |
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343 self.assertEqual(repr(float("-nan")), "nan") |
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344 |
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345 self.assertEqual(repr(float("NAN")), "nan") |
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346 self.assertEqual(repr(float("+NAn")), "nan") |
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347 self.assertEqual(repr(float("-NaN")), "nan") |
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348 |
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349 self.assertEqual(str(float("nan")), "nan") |
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350 self.assertEqual(str(float("+nan")), "nan") |
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351 self.assertEqual(str(float("-nan")), "nan") |
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352 |
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353 self.assertRaises(ValueError, float, "nana") |
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354 self.assertRaises(ValueError, float, "+nana") |
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355 self.assertRaises(ValueError, float, "-nana") |
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356 self.assertRaises(ValueError, float, "na") |
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357 self.assertRaises(ValueError, float, "+na") |
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358 self.assertRaises(ValueError, float, "-na") |
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359 |
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360 def test_nan_as_str(self): |
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361 self.assertEqual(repr(1e300 * 1e300 * 0), "nan") |
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362 self.assertEqual(repr(-1e300 * 1e300 * 0), "nan") |
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363 |
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364 self.assertEqual(str(1e300 * 1e300 * 0), "nan") |
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365 self.assertEqual(str(-1e300 * 1e300 * 0), "nan") |
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366 |
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367 def notest_float_nan(self): |
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368 self.assert_(NAN.is_nan()) |
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369 self.failIf(INF.is_nan()) |
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370 self.failIf((0.).is_nan()) |
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371 |
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372 def notest_float_inf(self): |
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373 self.assert_(INF.is_inf()) |
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374 self.failIf(NAN.is_inf()) |
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375 self.failIf((0.).is_inf()) |
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376 |
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377 fromHex = float.fromhex |
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378 toHex = float.hex |
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379 class HexFloatTestCase(unittest.TestCase): |
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380 MAX = fromHex('0x.fffffffffffff8p+1024') # max normal |
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381 MIN = fromHex('0x1p-1022') # min normal |
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382 TINY = fromHex('0x0.0000000000001p-1022') # min subnormal |
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383 EPS = fromHex('0x0.0000000000001p0') # diff between 1.0 and next float up |
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384 |
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385 def identical(self, x, y): |
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386 # check that floats x and y are identical, or that both |
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387 # are NaNs |
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388 if isnan(x) or isnan(y): |
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389 if isnan(x) == isnan(y): |
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390 return |
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391 elif x == y and (x != 0.0 or copysign(1.0, x) == copysign(1.0, y)): |
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392 return |
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393 self.fail('%r not identical to %r' % (x, y)) |
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394 |
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395 def test_ends(self): |
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396 self.identical(self.MIN, ldexp(1.0, -1022)) |
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397 self.identical(self.TINY, ldexp(1.0, -1074)) |
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398 self.identical(self.EPS, ldexp(1.0, -52)) |
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399 self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970))) |
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400 |
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401 def test_invalid_inputs(self): |
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402 invalid_inputs = [ |
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403 'infi', # misspelt infinities and nans |
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404 '-Infinit', |
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405 '++inf', |
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406 '-+Inf', |
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407 '--nan', |
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408 '+-NaN', |
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409 'snan', |
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410 'NaNs', |
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411 'nna', |
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412 '0xnan', |
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413 '', |
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414 ' ', |
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415 'x1.0p0', |
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416 '0xX1.0p0', |
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417 '+ 0x1.0p0', # internal whitespace |
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418 '- 0x1.0p0', |
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419 '0 x1.0p0', |
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420 '0x 1.0p0', |
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421 '0x1 2.0p0', |
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422 '+0x1 .0p0', |
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423 '0x1. 0p0', |
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424 '-0x1.0 1p0', |
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425 '-0x1.0 p0', |
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426 '+0x1.0p +0', |
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427 '0x1.0p -0', |
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428 '0x1.0p 0', |
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429 '+0x1.0p+ 0', |
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430 '-0x1.0p- 0', |
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431 '++0x1.0p-0', # double signs |
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432 '--0x1.0p0', |
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433 '+-0x1.0p+0', |
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434 '-+0x1.0p0', |
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435 '0x1.0p++0', |
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436 '+0x1.0p+-0', |
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437 '-0x1.0p-+0', |
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438 '0x1.0p--0', |
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439 '0x1.0.p0', |
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440 '0x.p0', # no hex digits before or after point |
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441 '0x1,p0', # wrong decimal point character |
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442 '0x1pa', |
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443 '0x1p\uff10', # fullwidth Unicode digits |
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444 '\uff10x1p0', |
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445 '0x\uff11p0', |
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446 '0x1.\uff10p0', |
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447 '0x1p0 \n 0x2p0', |
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448 '0x1p0\0 0x1p0', # embedded null byte is not end of string |
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449 ] |
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450 for x in invalid_inputs: |
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451 self.assertRaises(ValueError, fromHex, x) |
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452 |
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453 |
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454 def test_from_hex(self): |
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455 MIN = self.MIN; |
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456 MAX = self.MAX; |
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457 TINY = self.TINY; |
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458 EPS = self.EPS; |
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459 |
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460 # two spellings of infinity, with optional signs; case-insensitive |
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461 self.identical(fromHex('inf'), INF) |
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462 self.identical(fromHex('+Inf'), INF) |
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463 self.identical(fromHex('-INF'), -INF) |
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464 self.identical(fromHex('iNf'), INF) |
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465 self.identical(fromHex('Infinity'), INF) |
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466 self.identical(fromHex('+INFINITY'), INF) |
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467 self.identical(fromHex('-infinity'), -INF) |
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468 self.identical(fromHex('-iNFiNitY'), -INF) |
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469 |
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470 # nans with optional sign; case insensitive |
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471 self.identical(fromHex('nan'), NAN) |
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472 self.identical(fromHex('+NaN'), NAN) |
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473 self.identical(fromHex('-NaN'), NAN) |
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474 self.identical(fromHex('-nAN'), NAN) |
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475 |
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476 # variations in input format |
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477 self.identical(fromHex('1'), 1.0) |
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478 self.identical(fromHex('+1'), 1.0) |
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479 self.identical(fromHex('1.'), 1.0) |
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480 self.identical(fromHex('1.0'), 1.0) |
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481 self.identical(fromHex('1.0p0'), 1.0) |
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482 self.identical(fromHex('01'), 1.0) |
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483 self.identical(fromHex('01.'), 1.0) |
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484 self.identical(fromHex('0x1'), 1.0) |
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485 self.identical(fromHex('0x1.'), 1.0) |
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486 self.identical(fromHex('0x1.0'), 1.0) |
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487 self.identical(fromHex('+0x1.0'), 1.0) |
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488 self.identical(fromHex('0x1p0'), 1.0) |
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489 self.identical(fromHex('0X1p0'), 1.0) |
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490 self.identical(fromHex('0X1P0'), 1.0) |
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491 self.identical(fromHex('0x1P0'), 1.0) |
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492 self.identical(fromHex('0x1.p0'), 1.0) |
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493 self.identical(fromHex('0x1.0p0'), 1.0) |
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494 self.identical(fromHex('0x.1p4'), 1.0) |
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495 self.identical(fromHex('0x.1p04'), 1.0) |
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496 self.identical(fromHex('0x.1p004'), 1.0) |
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497 self.identical(fromHex('0x1p+0'), 1.0) |
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498 self.identical(fromHex('0x1P-0'), 1.0) |
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499 self.identical(fromHex('+0x1p0'), 1.0) |
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500 self.identical(fromHex('0x01p0'), 1.0) |
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501 self.identical(fromHex('0x1p00'), 1.0) |
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502 self.identical(fromHex(' 0x1p0 '), 1.0) |
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503 self.identical(fromHex('\n 0x1p0'), 1.0) |
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504 self.identical(fromHex('0x1p0 \t'), 1.0) |
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505 self.identical(fromHex('0xap0'), 10.0) |
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506 self.identical(fromHex('0xAp0'), 10.0) |
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507 self.identical(fromHex('0xaP0'), 10.0) |
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508 self.identical(fromHex('0xAP0'), 10.0) |
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509 self.identical(fromHex('0xbep0'), 190.0) |
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510 self.identical(fromHex('0xBep0'), 190.0) |
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511 self.identical(fromHex('0xbEp0'), 190.0) |
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512 self.identical(fromHex('0XBE0P-4'), 190.0) |
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513 self.identical(fromHex('0xBEp0'), 190.0) |
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514 self.identical(fromHex('0xB.Ep4'), 190.0) |
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515 self.identical(fromHex('0x.BEp8'), 190.0) |
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516 self.identical(fromHex('0x.0BEp12'), 190.0) |
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517 |
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518 # moving the point around |
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519 pi = fromHex('0x1.921fb54442d18p1') |
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520 self.identical(fromHex('0x.006487ed5110b46p11'), pi) |
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521 self.identical(fromHex('0x.00c90fdaa22168cp10'), pi) |
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522 self.identical(fromHex('0x.01921fb54442d18p9'), pi) |
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523 self.identical(fromHex('0x.03243f6a8885a3p8'), pi) |
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524 self.identical(fromHex('0x.06487ed5110b46p7'), pi) |
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525 self.identical(fromHex('0x.0c90fdaa22168cp6'), pi) |
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526 self.identical(fromHex('0x.1921fb54442d18p5'), pi) |
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527 self.identical(fromHex('0x.3243f6a8885a3p4'), pi) |
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528 self.identical(fromHex('0x.6487ed5110b46p3'), pi) |
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529 self.identical(fromHex('0x.c90fdaa22168cp2'), pi) |
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530 self.identical(fromHex('0x1.921fb54442d18p1'), pi) |
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531 self.identical(fromHex('0x3.243f6a8885a3p0'), pi) |
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532 self.identical(fromHex('0x6.487ed5110b46p-1'), pi) |
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533 self.identical(fromHex('0xc.90fdaa22168cp-2'), pi) |
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534 self.identical(fromHex('0x19.21fb54442d18p-3'), pi) |
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535 self.identical(fromHex('0x32.43f6a8885a3p-4'), pi) |
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536 self.identical(fromHex('0x64.87ed5110b46p-5'), pi) |
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537 self.identical(fromHex('0xc9.0fdaa22168cp-6'), pi) |
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538 self.identical(fromHex('0x192.1fb54442d18p-7'), pi) |
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539 self.identical(fromHex('0x324.3f6a8885a3p-8'), pi) |
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540 self.identical(fromHex('0x648.7ed5110b46p-9'), pi) |
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541 self.identical(fromHex('0xc90.fdaa22168cp-10'), pi) |
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542 self.identical(fromHex('0x1921.fb54442d18p-11'), pi) |
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543 # ... |
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544 self.identical(fromHex('0x1921fb54442d1.8p-47'), pi) |
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545 self.identical(fromHex('0x3243f6a8885a3p-48'), pi) |
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546 self.identical(fromHex('0x6487ed5110b46p-49'), pi) |
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547 self.identical(fromHex('0xc90fdaa22168cp-50'), pi) |
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548 self.identical(fromHex('0x1921fb54442d18p-51'), pi) |
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549 self.identical(fromHex('0x3243f6a8885a30p-52'), pi) |
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550 self.identical(fromHex('0x6487ed5110b460p-53'), pi) |
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551 self.identical(fromHex('0xc90fdaa22168c0p-54'), pi) |
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552 self.identical(fromHex('0x1921fb54442d180p-55'), pi) |
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553 |
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554 |
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555 # results that should overflow... |
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556 self.assertRaises(OverflowError, fromHex, '-0x1p1024') |
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557 self.assertRaises(OverflowError, fromHex, '0x1p+1025') |
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558 self.assertRaises(OverflowError, fromHex, '+0X1p1030') |
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559 self.assertRaises(OverflowError, fromHex, '-0x1p+1100') |
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560 self.assertRaises(OverflowError, fromHex, '0X1p123456789123456789') |
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561 self.assertRaises(OverflowError, fromHex, '+0X.8p+1025') |
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562 self.assertRaises(OverflowError, fromHex, '+0x0.8p1025') |
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563 self.assertRaises(OverflowError, fromHex, '-0x0.4p1026') |
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564 self.assertRaises(OverflowError, fromHex, '0X2p+1023') |
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565 self.assertRaises(OverflowError, fromHex, '0x2.p1023') |
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566 self.assertRaises(OverflowError, fromHex, '-0x2.0p+1023') |
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567 self.assertRaises(OverflowError, fromHex, '+0X4p+1022') |
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568 self.assertRaises(OverflowError, fromHex, '0x1.ffffffffffffffp+1023') |
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569 self.assertRaises(OverflowError, fromHex, '-0X1.fffffffffffff9p1023') |
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570 self.assertRaises(OverflowError, fromHex, '0X1.fffffffffffff8p1023') |
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571 self.assertRaises(OverflowError, fromHex, '+0x3.fffffffffffffp1022') |
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572 self.assertRaises(OverflowError, fromHex, '0x3fffffffffffffp+970') |
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573 self.assertRaises(OverflowError, fromHex, '0x10000000000000000p960') |
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574 self.assertRaises(OverflowError, fromHex, '-0Xffffffffffffffffp960') |
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575 |
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576 # ...and those that round to +-max float |
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577 self.identical(fromHex('+0x1.fffffffffffffp+1023'), MAX) |
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578 self.identical(fromHex('-0X1.fffffffffffff7p1023'), -MAX) |
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579 self.identical(fromHex('0X1.fffffffffffff7fffffffffffffp1023'), MAX) |
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580 |
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581 # zeros |
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582 self.identical(fromHex('0x0p0'), 0.0) |
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583 self.identical(fromHex('0x0p1000'), 0.0) |
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584 self.identical(fromHex('-0x0p1023'), -0.0) |
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585 self.identical(fromHex('0X0p1024'), 0.0) |
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586 self.identical(fromHex('-0x0p1025'), -0.0) |
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587 self.identical(fromHex('0X0p2000'), 0.0) |
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588 self.identical(fromHex('0x0p123456789123456789'), 0.0) |
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589 self.identical(fromHex('-0X0p-0'), -0.0) |
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590 self.identical(fromHex('-0X0p-1000'), -0.0) |
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591 self.identical(fromHex('0x0p-1023'), 0.0) |
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592 self.identical(fromHex('-0X0p-1024'), -0.0) |
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593 self.identical(fromHex('-0x0p-1025'), -0.0) |
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594 self.identical(fromHex('-0x0p-1072'), -0.0) |
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595 self.identical(fromHex('0X0p-1073'), 0.0) |
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596 self.identical(fromHex('-0x0p-1074'), -0.0) |
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597 self.identical(fromHex('0x0p-1075'), 0.0) |
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598 self.identical(fromHex('0X0p-1076'), 0.0) |
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599 self.identical(fromHex('-0X0p-2000'), -0.0) |
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600 self.identical(fromHex('-0x0p-123456789123456789'), -0.0) |
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601 |
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602 # values that should underflow to 0 |
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603 self.identical(fromHex('0X1p-1075'), 0.0) |
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604 self.identical(fromHex('-0X1p-1075'), -0.0) |
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605 self.identical(fromHex('-0x1p-123456789123456789'), -0.0) |
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606 self.identical(fromHex('0x1.00000000000000001p-1075'), TINY) |
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607 self.identical(fromHex('-0x1.1p-1075'), -TINY) |
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608 self.identical(fromHex('0x1.fffffffffffffffffp-1075'), TINY) |
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609 |
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610 # check round-half-even is working correctly near 0 ... |
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611 self.identical(fromHex('0x1p-1076'), 0.0) |
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612 self.identical(fromHex('0X2p-1076'), 0.0) |
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613 self.identical(fromHex('0X3p-1076'), TINY) |
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614 self.identical(fromHex('0x4p-1076'), TINY) |
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615 self.identical(fromHex('0X5p-1076'), TINY) |
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616 self.identical(fromHex('0X6p-1076'), 2*TINY) |
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617 self.identical(fromHex('0x7p-1076'), 2*TINY) |
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618 self.identical(fromHex('0X8p-1076'), 2*TINY) |
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619 self.identical(fromHex('0X9p-1076'), 2*TINY) |
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620 self.identical(fromHex('0xap-1076'), 2*TINY) |
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621 self.identical(fromHex('0Xbp-1076'), 3*TINY) |
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622 self.identical(fromHex('0xcp-1076'), 3*TINY) |
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623 self.identical(fromHex('0Xdp-1076'), 3*TINY) |
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624 self.identical(fromHex('0Xep-1076'), 4*TINY) |
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625 self.identical(fromHex('0xfp-1076'), 4*TINY) |
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626 self.identical(fromHex('0x10p-1076'), 4*TINY) |
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627 self.identical(fromHex('-0x1p-1076'), -0.0) |
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628 self.identical(fromHex('-0X2p-1076'), -0.0) |
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629 self.identical(fromHex('-0x3p-1076'), -TINY) |
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630 self.identical(fromHex('-0X4p-1076'), -TINY) |
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631 self.identical(fromHex('-0x5p-1076'), -TINY) |
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632 self.identical(fromHex('-0x6p-1076'), -2*TINY) |
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633 self.identical(fromHex('-0X7p-1076'), -2*TINY) |
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634 self.identical(fromHex('-0X8p-1076'), -2*TINY) |
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635 self.identical(fromHex('-0X9p-1076'), -2*TINY) |
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636 self.identical(fromHex('-0Xap-1076'), -2*TINY) |
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637 self.identical(fromHex('-0xbp-1076'), -3*TINY) |
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638 self.identical(fromHex('-0xcp-1076'), -3*TINY) |
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639 self.identical(fromHex('-0Xdp-1076'), -3*TINY) |
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640 self.identical(fromHex('-0xep-1076'), -4*TINY) |
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641 self.identical(fromHex('-0Xfp-1076'), -4*TINY) |
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642 self.identical(fromHex('-0X10p-1076'), -4*TINY) |
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643 |
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644 # ... and near MIN ... |
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645 self.identical(fromHex('0x0.ffffffffffffd6p-1022'), MIN-3*TINY) |
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646 self.identical(fromHex('0x0.ffffffffffffd8p-1022'), MIN-2*TINY) |
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647 self.identical(fromHex('0x0.ffffffffffffdap-1022'), MIN-2*TINY) |
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648 self.identical(fromHex('0x0.ffffffffffffdcp-1022'), MIN-2*TINY) |
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649 self.identical(fromHex('0x0.ffffffffffffdep-1022'), MIN-2*TINY) |
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650 self.identical(fromHex('0x0.ffffffffffffe0p-1022'), MIN-2*TINY) |
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651 self.identical(fromHex('0x0.ffffffffffffe2p-1022'), MIN-2*TINY) |
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652 self.identical(fromHex('0x0.ffffffffffffe4p-1022'), MIN-2*TINY) |
|
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653 self.identical(fromHex('0x0.ffffffffffffe6p-1022'), MIN-2*TINY) |
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654 self.identical(fromHex('0x0.ffffffffffffe8p-1022'), MIN-2*TINY) |
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655 self.identical(fromHex('0x0.ffffffffffffeap-1022'), MIN-TINY) |
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656 self.identical(fromHex('0x0.ffffffffffffecp-1022'), MIN-TINY) |
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657 self.identical(fromHex('0x0.ffffffffffffeep-1022'), MIN-TINY) |
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658 self.identical(fromHex('0x0.fffffffffffff0p-1022'), MIN-TINY) |
|
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659 self.identical(fromHex('0x0.fffffffffffff2p-1022'), MIN-TINY) |
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660 self.identical(fromHex('0x0.fffffffffffff4p-1022'), MIN-TINY) |
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661 self.identical(fromHex('0x0.fffffffffffff6p-1022'), MIN-TINY) |
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662 self.identical(fromHex('0x0.fffffffffffff8p-1022'), MIN) |
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663 self.identical(fromHex('0x0.fffffffffffffap-1022'), MIN) |
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664 self.identical(fromHex('0x0.fffffffffffffcp-1022'), MIN) |
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665 self.identical(fromHex('0x0.fffffffffffffep-1022'), MIN) |
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666 self.identical(fromHex('0x1.00000000000000p-1022'), MIN) |
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667 self.identical(fromHex('0x1.00000000000002p-1022'), MIN) |
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668 self.identical(fromHex('0x1.00000000000004p-1022'), MIN) |
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669 self.identical(fromHex('0x1.00000000000006p-1022'), MIN) |
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670 self.identical(fromHex('0x1.00000000000008p-1022'), MIN) |
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671 self.identical(fromHex('0x1.0000000000000ap-1022'), MIN+TINY) |
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672 self.identical(fromHex('0x1.0000000000000cp-1022'), MIN+TINY) |
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673 self.identical(fromHex('0x1.0000000000000ep-1022'), MIN+TINY) |
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674 self.identical(fromHex('0x1.00000000000010p-1022'), MIN+TINY) |
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675 self.identical(fromHex('0x1.00000000000012p-1022'), MIN+TINY) |
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676 self.identical(fromHex('0x1.00000000000014p-1022'), MIN+TINY) |
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677 self.identical(fromHex('0x1.00000000000016p-1022'), MIN+TINY) |
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678 self.identical(fromHex('0x1.00000000000018p-1022'), MIN+2*TINY) |
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679 |
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680 # ... and near 1.0. |
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681 self.identical(fromHex('0x0.fffffffffffff0p0'), 1.0-EPS) |
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682 self.identical(fromHex('0x0.fffffffffffff1p0'), 1.0-EPS) |
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683 self.identical(fromHex('0X0.fffffffffffff2p0'), 1.0-EPS) |
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684 self.identical(fromHex('0x0.fffffffffffff3p0'), 1.0-EPS) |
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685 self.identical(fromHex('0X0.fffffffffffff4p0'), 1.0-EPS) |
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686 self.identical(fromHex('0X0.fffffffffffff5p0'), 1.0-EPS/2) |
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687 self.identical(fromHex('0X0.fffffffffffff6p0'), 1.0-EPS/2) |
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688 self.identical(fromHex('0x0.fffffffffffff7p0'), 1.0-EPS/2) |
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689 self.identical(fromHex('0x0.fffffffffffff8p0'), 1.0-EPS/2) |
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690 self.identical(fromHex('0X0.fffffffffffff9p0'), 1.0-EPS/2) |
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691 self.identical(fromHex('0X0.fffffffffffffap0'), 1.0-EPS/2) |
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692 self.identical(fromHex('0x0.fffffffffffffbp0'), 1.0-EPS/2) |
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693 self.identical(fromHex('0X0.fffffffffffffcp0'), 1.0) |
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694 self.identical(fromHex('0x0.fffffffffffffdp0'), 1.0) |
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695 self.identical(fromHex('0X0.fffffffffffffep0'), 1.0) |
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696 self.identical(fromHex('0x0.ffffffffffffffp0'), 1.0) |
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697 self.identical(fromHex('0X1.00000000000000p0'), 1.0) |
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698 self.identical(fromHex('0X1.00000000000001p0'), 1.0) |
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699 self.identical(fromHex('0x1.00000000000002p0'), 1.0) |
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700 self.identical(fromHex('0X1.00000000000003p0'), 1.0) |
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701 self.identical(fromHex('0x1.00000000000004p0'), 1.0) |
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702 self.identical(fromHex('0X1.00000000000005p0'), 1.0) |
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703 self.identical(fromHex('0X1.00000000000006p0'), 1.0) |
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704 self.identical(fromHex('0X1.00000000000007p0'), 1.0) |
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705 self.identical(fromHex('0x1.00000000000007ffffffffffffffffffffp0'), |
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706 1.0) |
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707 self.identical(fromHex('0x1.00000000000008p0'), 1.0) |
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708 self.identical(fromHex('0x1.00000000000008000000000000000001p0'), |
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709 1+EPS) |
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710 self.identical(fromHex('0X1.00000000000009p0'), 1.0+EPS) |
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711 self.identical(fromHex('0x1.0000000000000ap0'), 1.0+EPS) |
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712 self.identical(fromHex('0x1.0000000000000bp0'), 1.0+EPS) |
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713 self.identical(fromHex('0X1.0000000000000cp0'), 1.0+EPS) |
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714 self.identical(fromHex('0x1.0000000000000dp0'), 1.0+EPS) |
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715 self.identical(fromHex('0x1.0000000000000ep0'), 1.0+EPS) |
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716 self.identical(fromHex('0X1.0000000000000fp0'), 1.0+EPS) |
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717 self.identical(fromHex('0x1.00000000000010p0'), 1.0+EPS) |
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718 self.identical(fromHex('0X1.00000000000011p0'), 1.0+EPS) |
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719 self.identical(fromHex('0x1.00000000000012p0'), 1.0+EPS) |
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720 self.identical(fromHex('0X1.00000000000013p0'), 1.0+EPS) |
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721 self.identical(fromHex('0X1.00000000000014p0'), 1.0+EPS) |
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722 self.identical(fromHex('0x1.00000000000015p0'), 1.0+EPS) |
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723 self.identical(fromHex('0x1.00000000000016p0'), 1.0+EPS) |
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724 self.identical(fromHex('0X1.00000000000017p0'), 1.0+EPS) |
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725 self.identical(fromHex('0x1.00000000000017ffffffffffffffffffffp0'), |
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726 1.0+EPS) |
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727 self.identical(fromHex('0x1.00000000000018p0'), 1.0+2*EPS) |
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728 self.identical(fromHex('0X1.00000000000018000000000000000001p0'), |
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729 1.0+2*EPS) |
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730 self.identical(fromHex('0x1.00000000000019p0'), 1.0+2*EPS) |
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731 self.identical(fromHex('0X1.0000000000001ap0'), 1.0+2*EPS) |
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732 self.identical(fromHex('0X1.0000000000001bp0'), 1.0+2*EPS) |
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733 self.identical(fromHex('0x1.0000000000001cp0'), 1.0+2*EPS) |
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734 self.identical(fromHex('0x1.0000000000001dp0'), 1.0+2*EPS) |
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735 self.identical(fromHex('0x1.0000000000001ep0'), 1.0+2*EPS) |
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736 self.identical(fromHex('0X1.0000000000001fp0'), 1.0+2*EPS) |
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737 self.identical(fromHex('0x1.00000000000020p0'), 1.0+2*EPS) |
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738 |
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739 def test_roundtrip(self): |
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740 def roundtrip(x): |
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741 return fromHex(toHex(x)) |
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742 |
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743 for x in [NAN, INF, self.MAX, self.MIN, self.MIN-self.TINY, self.TINY, 0.0]: |
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744 self.identical(x, roundtrip(x)) |
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745 self.identical(-x, roundtrip(-x)) |
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746 |
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747 # fromHex(toHex(x)) should exactly recover x, for any non-NaN float x. |
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748 import random |
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749 for i in range(10000): |
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750 e = random.randrange(-1200, 1200) |
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751 m = random.random() |
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752 s = random.choice([1.0, -1.0]) |
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753 try: |
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754 x = s*ldexp(m, e) |
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755 except OverflowError: |
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756 pass |
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757 else: |
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758 self.identical(x, fromHex(toHex(x))) |
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759 |
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| 34972 | 761 def test_main(): |
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762 support.run_unittest( |
| 34972 | 763 FormatFunctionsTestCase, |
| 764 UnknownFormatTestCase, | |
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765 IEEEFormatTestCase, |
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766 FormatTestCase, |
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767 ReprTestCase, |
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768 InfNanTest, |
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769 HexFloatTestCase, |
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770 ) |
| 34972 | 771 |
| 772 if __name__ == '__main__': | |
| 773 test_main() |
