Mercurial > cpython-lru_cache-weakref

annotate Lib/test/test_cmath.py @ 79691:05c8928362ee

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Merge __next__ method link fixes with 3.3.
author Ezio Melotti <ezio.melotti@gmail.com>
date Fri, 12 Oct 2012 13:46:37 +0300
parents 08418369da7b
children 4d62a62ba44d
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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f2a4ade36a1e Issue #10624: Use support.requires_IEEE_754 in all appropriate tests.
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1 from test.support import run_unittest, requires_IEEE_754
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2 from test.test_math import parse_testfile, test_file
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3 import unittest
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11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
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4 import cmath, math
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5 from cmath import phase, polar, rect, pi
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6 import sysconfig
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7
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8 INF = float('inf')
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9 NAN = float('nan')
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10
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11 complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]]
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12 complex_infinities = [complex(x, y) for x, y in [
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13 (INF, 0.0), # 1st quadrant
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14 (INF, 2.3),
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15 (INF, INF),
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16 (2.3, INF),
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17 (0.0, INF),
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18 (-0.0, INF), # 2nd quadrant
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19 (-2.3, INF),
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20 (-INF, INF),
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21 (-INF, 2.3),
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22 (-INF, 0.0),
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23 (-INF, -0.0), # 3rd quadrant
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24 (-INF, -2.3),
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25 (-INF, -INF),
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26 (-2.3, -INF),
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27 (-0.0, -INF),
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28 (0.0, -INF), # 4th quadrant
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29 (2.3, -INF),
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30 (INF, -INF),
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31 (INF, -2.3),
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32 (INF, -0.0)
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33 ]]
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34 complex_nans = [complex(x, y) for x, y in [
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35 (NAN, -INF),
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36 (NAN, -2.3),
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37 (NAN, -0.0),
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38 (NAN, 0.0),
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39 (NAN, 2.3),
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40 (NAN, INF),
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41 (-INF, NAN),
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42 (-2.3, NAN),
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43 (-0.0, NAN),
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44 (0.0, NAN),
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45 (2.3, NAN),
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46 (INF, NAN)
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47 ]]
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48
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49 class CMathTests(unittest.TestCase):
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50 # list of all functions in cmath
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51 test_functions = [getattr(cmath, fname) for fname in [
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52 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
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53 'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',
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54 'sqrt', 'tan', 'tanh']]
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55 # test first and second arguments independently for 2-argument log
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56 test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
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57 test_functions.append(lambda x : cmath.log(14.-27j, x))
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58
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59 def setUp(self):
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60 self.test_values = open(test_file)
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61
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62 def tearDown(self):
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63 self.test_values.close()
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64
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65 def assertFloatIdentical(self, x, y):
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66 """Fail unless floats x and y are identical, in the sense that:
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67 (1) both x and y are nans, or
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68 (2) both x and y are infinities, with the same sign, or
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69 (3) both x and y are zeros, with the same sign, or
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70 (4) x and y are both finite and nonzero, and x == y
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71
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72 """
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73 msg = 'floats {!r} and {!r} are not identical'
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74
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75 if math.isnan(x) or math.isnan(y):
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76 if math.isnan(x) and math.isnan(y):
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77 return
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78 elif x == y:
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79 if x != 0.0:
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80 return
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81 # both zero; check that signs match
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82 elif math.copysign(1.0, x) == math.copysign(1.0, y):
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83 return
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84 else:
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85 msg += ': zeros have different signs'
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86 self.fail(msg.format(x, y))
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87
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88 def assertComplexIdentical(self, x, y):
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89 """Fail unless complex numbers x and y have equal values and signs.
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90
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91 In particular, if x and y both have real (or imaginary) part
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92 zero, but the zeros have different signs, this test will fail.
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93
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94 """
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95 self.assertFloatIdentical(x.real, y.real)
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96 self.assertFloatIdentical(x.imag, y.imag)
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97
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98 def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323,
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99 msg=None):
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100 """Fail if the two floating-point numbers are not almost equal.
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101
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102 Determine whether floating-point values a and b are equal to within
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103 a (small) rounding error. The default values for rel_err and
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104 abs_err are chosen to be suitable for platforms where a float is
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105 represented by an IEEE 754 double. They allow an error of between
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106 9 and 19 ulps.
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107 """
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108
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109 # special values testing
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110 if math.isnan(a):
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111 if math.isnan(b):
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112 return
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113 self.fail(msg or '{!r} should be nan'.format(b))
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114
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115 if math.isinf(a):
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116 if a == b:
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117 return
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118 self.fail(msg or 'finite result where infinity expected: '
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119 'expected {!r}, got {!r}'.format(a, b))
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120
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121 # if both a and b are zero, check whether they have the same sign
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122 # (in theory there are examples where it would be legitimate for a
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123 # and b to have opposite signs; in practice these hardly ever
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124 # occur).
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125 if not a and not b:
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126 if math.copysign(1., a) != math.copysign(1., b):
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127 self.fail(msg or 'zero has wrong sign: expected {!r}, '
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128 'got {!r}'.format(a, b))
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129
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130 # if a-b overflows, or b is infinite, return False. Again, in
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131 # theory there are examples where a is within a few ulps of the
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132 # max representable float, and then b could legitimately be
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133 # infinite. In practice these examples are rare.
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134 try:
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135 absolute_error = abs(b-a)
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136 except OverflowError:
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137 pass
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138 else:
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139 # test passes if either the absolute error or the relative
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140 # error is sufficiently small. The defaults amount to an
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141 # error of between 9 ulps and 19 ulps on an IEEE-754 compliant
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142 # machine.
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143 if absolute_error <= max(abs_err, rel_err * abs(a)):
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144 return
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145 self.fail(msg or
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146 '{!r} and {!r} are not sufficiently close'.format(a, b))
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147
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148 def test_constants(self):
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149 e_expected = 2.71828182845904523536
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150 pi_expected = 3.14159265358979323846
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151 self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
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152 msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
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153 self.assertAlmostEqual(cmath.e, e_expected, places=9,
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154 msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
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155
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156 def test_user_object(self):
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157 # Test automatic calling of __complex__ and __float__ by cmath
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158 # functions
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159
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160 # some random values to use as test values; we avoid values
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161 # for which any of the functions in cmath is undefined
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162 # (i.e. 0., 1., -1., 1j, -1j) or would cause overflow
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163 cx_arg = 4.419414439 + 1.497100113j
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164 flt_arg = -6.131677725
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165
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166 # a variety of non-complex numbers, used to check that
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167 # non-complex return values from __complex__ give an error
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168 non_complexes = ["not complex", 1, 5, 2., None,
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169 object(), NotImplemented]
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170
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171 # Now we introduce a variety of classes whose instances might
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172 # end up being passed to the cmath functions
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173
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174 # usual case: new-style class implementing __complex__
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175 class MyComplex(object):
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176 def __init__(self, value):
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177 self.value = value
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178 def __complex__(self):
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179 return self.value
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180
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181 # old-style class implementing __complex__
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182 class MyComplexOS:
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183 def __init__(self, value):
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184 self.value = value
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185 def __complex__(self):
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186 return self.value
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187
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188 # classes for which __complex__ raises an exception
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189 class SomeException(Exception):
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190 pass
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191 class MyComplexException(object):
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192 def __complex__(self):
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193 raise SomeException
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194 class MyComplexExceptionOS:
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195 def __complex__(self):
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196 raise SomeException
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197
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198 # some classes not providing __float__ or __complex__
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199 class NeitherComplexNorFloat(object):
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200 pass
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201 class NeitherComplexNorFloatOS:
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202 pass
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203 class MyInt(object):
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204 def __int__(self): return 2
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205 def __index__(self): return 2
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206 class MyIntOS:
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207 def __int__(self): return 2
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208 def __index__(self): return 2
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209
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210 # other possible combinations of __float__ and __complex__
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211 # that should work
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212 class FloatAndComplex(object):
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213 def __float__(self):
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214 return flt_arg
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215 def __complex__(self):
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216 return cx_arg
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217 class FloatAndComplexOS:
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218 def __float__(self):
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219 return flt_arg
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220 def __complex__(self):
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221 return cx_arg
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222 class JustFloat(object):
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223 def __float__(self):
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224 return flt_arg
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225 class JustFloatOS:
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226 def __float__(self):
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227 return flt_arg
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228
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229 for f in self.test_functions:
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230 # usual usage
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231 self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
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232 self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg))
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233 # other combinations of __float__ and __complex__
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234 self.assertEqual(f(FloatAndComplex()), f(cx_arg))
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235 self.assertEqual(f(FloatAndComplexOS()), f(cx_arg))
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236 self.assertEqual(f(JustFloat()), f(flt_arg))
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237 self.assertEqual(f(JustFloatOS()), f(flt_arg))
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238 # TypeError should be raised for classes not providing
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239 # either __complex__ or __float__, even if they provide
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240 # __int__ or __index__. An old-style class
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241 # currently raises AttributeError instead of a TypeError;
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242 # this could be considered a bug.
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243 self.assertRaises(TypeError, f, NeitherComplexNorFloat())
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244 self.assertRaises(TypeError, f, MyInt())
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245 self.assertRaises(Exception, f, NeitherComplexNorFloatOS())
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246 self.assertRaises(Exception, f, MyIntOS())
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247 # non-complex return value from __complex__ -> TypeError
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248 for bad_complex in non_complexes:
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249 self.assertRaises(TypeError, f, MyComplex(bad_complex))
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250 self.assertRaises(TypeError, f, MyComplexOS(bad_complex))
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251 # exceptions in __complex__ should be propagated correctly
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252 self.assertRaises(SomeException, f, MyComplexException())
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253 self.assertRaises(SomeException, f, MyComplexExceptionOS())
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254
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255 def test_input_type(self):
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256 # ints and longs should be acceptable inputs to all cmath
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257 # functions, by virtue of providing a __float__ method
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258 for f in self.test_functions:
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259 for arg in [2, 2.]:
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260 self.assertEqual(f(arg), f(arg.__float__()))
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261
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262 # but strings should give a TypeError
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263 for f in self.test_functions:
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264 for arg in ["a", "long_string", "0", "1j", ""]:
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265 self.assertRaises(TypeError, f, arg)
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266
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267 def test_cmath_matches_math(self):
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268 # check that corresponding cmath and math functions are equal
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269 # for floats in the appropriate range
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270
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271 # test_values in (0, 1)
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272 test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
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273
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274 # test_values for functions defined on [-1., 1.]
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275 unit_interval = test_values + [-x for x in test_values] + \
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276 [0., 1., -1.]
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277
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278 # test_values for log, log10, sqrt
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279 positive = test_values + [1.] + [1./x for x in test_values]
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280 nonnegative = [0.] + positive
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281
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282 # test_values for functions defined on the whole real line
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283 real_line = [0.] + positive + [-x for x in positive]
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284
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285 test_functions = {
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286 'acos' : unit_interval,
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287 'asin' : unit_interval,
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288 'atan' : real_line,
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289 'cos' : real_line,
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290 'cosh' : real_line,
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291 'exp' : real_line,
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292 'log' : positive,
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293 'log10' : positive,
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294 'sin' : real_line,
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295 'sinh' : real_line,
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296 'sqrt' : nonnegative,
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297 'tan' : real_line,
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298 'tanh' : real_line}
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299
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300 for fn, values in test_functions.items():
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301 float_fn = getattr(math, fn)
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302 complex_fn = getattr(cmath, fn)
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303 for v in values:
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304 z = complex_fn(v)
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305 self.rAssertAlmostEqual(float_fn(v), z.real)
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306 self.assertEqual(0., z.imag)
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307
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308 # test two-argument version of log with various bases
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309 for base in [0.5, 2., 10.]:
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310 for v in positive:
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311 z = cmath.log(v, base)
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312 self.rAssertAlmostEqual(math.log(v, base), z.real)
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313 self.assertEqual(0., z.imag)
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314
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315 @requires_IEEE_754
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316 def test_specific_values(self):
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317 def rect_complex(z):
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318 """Wrapped version of rect that accepts a complex number instead of
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319 two float arguments."""
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320 return cmath.rect(z.real, z.imag)
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321
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322 def polar_complex(z):
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323 """Wrapped version of polar that returns a complex number instead of
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324 two floats."""
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325 return complex(*polar(z))
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326
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327 for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
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328 arg = complex(ar, ai)
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329 expected = complex(er, ei)
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330 if fn == 'rect':
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331 function = rect_complex
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332 elif fn == 'polar':
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333 function = polar_complex
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334 else:
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335 function = getattr(cmath, fn)
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336 if 'divide-by-zero' in flags or 'invalid' in flags:
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337 try:
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338 actual = function(arg)
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339 except ValueError:
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340 continue
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341 else:
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342 self.fail('ValueError not raised in test '
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343 '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
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344
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345 if 'overflow' in flags:
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346 try:
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347 actual = function(arg)
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348 except OverflowError:
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349 continue
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350 else:
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351 self.fail('OverflowError not raised in test '
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352 '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
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353
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354 actual = function(arg)
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355
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356 if 'ignore-real-sign' in flags:
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357 actual = complex(abs(actual.real), actual.imag)
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358 expected = complex(abs(expected.real), expected.imag)
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359 if 'ignore-imag-sign' in flags:
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360 actual = complex(actual.real, abs(actual.imag))
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361 expected = complex(expected.real, abs(expected.imag))
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362
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363 # for the real part of the log function, we allow an
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364 # absolute error of up to 2e-15.
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365 if fn in ('log', 'log10'):
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366 real_abs_err = 2e-15
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367 else:
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368 real_abs_err = 5e-323
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369
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370 error_message = (
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371 '{}: {}(complex({!r}, {!r}))\n'
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372 'Expected: complex({!r}, {!r})\n'
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373 'Received: complex({!r}, {!r})\n'
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374 'Received value insufficiently close to expected value.'
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375 ).format(id, fn, ar, ai,
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376 expected.real, expected.imag,
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377 actual.real, actual.imag)
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378 self.rAssertAlmostEqual(expected.real, actual.real,
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379 abs_err=real_abs_err,
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380 msg=error_message)
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381 self.rAssertAlmostEqual(expected.imag, actual.imag,
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382 msg=error_message)
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383
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384 def assertCISEqual(self, a, b):
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385 eps = 1E-7
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386 if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps:
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387 self.fail((a ,b))
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388
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389 def test_polar(self):
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390 self.assertCISEqual(polar(0), (0., 0.))
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391 self.assertCISEqual(polar(1.), (1., 0.))
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392 self.assertCISEqual(polar(-1.), (1., pi))
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393 self.assertCISEqual(polar(1j), (1., pi/2))
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394 self.assertCISEqual(polar(-1j), (1., -pi/2))
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395
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396 def test_phase(self):
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397 self.assertAlmostEqual(phase(0), 0.)
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398 self.assertAlmostEqual(phase(1.), 0.)
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399 self.assertAlmostEqual(phase(-1.), pi)
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400 self.assertAlmostEqual(phase(-1.+1E-300j), pi)
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401 self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
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402 self.assertAlmostEqual(phase(1j), pi/2)
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403 self.assertAlmostEqual(phase(-1j), -pi/2)
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404
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405 # zeros
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406 self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
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407 self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
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408 self.assertEqual(phase(complex(-0.0, 0.0)), pi)
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409 self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
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410
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411 # infinities
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412 self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
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413 self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
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414 self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
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415 self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
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416 self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
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417 self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
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418 self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
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419 self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
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420 self.assertEqual(phase(complex(INF, -2.3)), -0.0)
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421 self.assertEqual(phase(complex(INF, -0.0)), -0.0)
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422 self.assertEqual(phase(complex(INF, 0.0)), 0.0)
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423 self.assertEqual(phase(complex(INF, 2.3)), 0.0)
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424 self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
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425 self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
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426 self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
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427 self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
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428 self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
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429 self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
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430 self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
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431 self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
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432
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433 # real or imaginary part NaN
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434 for z in complex_nans:
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435 self.assertTrue(math.isnan(phase(z)))
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436
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437 def test_abs(self):
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438 # zeros
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439 for z in complex_zeros:
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440 self.assertEqual(abs(z), 0.0)
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441
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442 # infinities
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443 for z in complex_infinities:
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444 self.assertEqual(abs(z), INF)
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445
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446 # real or imaginary part NaN
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447 self.assertEqual(abs(complex(NAN, -INF)), INF)
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448 self.assertTrue(math.isnan(abs(complex(NAN, -2.3))))
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449 self.assertTrue(math.isnan(abs(complex(NAN, -0.0))))
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450 self.assertTrue(math.isnan(abs(complex(NAN, 0.0))))
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451 self.assertTrue(math.isnan(abs(complex(NAN, 2.3))))
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452 self.assertEqual(abs(complex(NAN, INF)), INF)
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453 self.assertEqual(abs(complex(-INF, NAN)), INF)
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454 self.assertTrue(math.isnan(abs(complex(-2.3, NAN))))
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455 self.assertTrue(math.isnan(abs(complex(-0.0, NAN))))
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456 self.assertTrue(math.isnan(abs(complex(0.0, NAN))))
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457 self.assertTrue(math.isnan(abs(complex(2.3, NAN))))
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458 self.assertEqual(abs(complex(INF, NAN)), INF)
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459 self.assertTrue(math.isnan(abs(complex(NAN, NAN))))
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460
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461
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462 @requires_IEEE_754
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463 def test_abs_overflows(self):
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464 # result overflows
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465 self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308))
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466
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467 def assertCEqual(self, a, b):
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468 eps = 1E-7
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469 if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:
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470 self.fail((a ,b))
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471
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472 def test_rect(self):
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473 self.assertCEqual(rect(0, 0), (0, 0))
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474 self.assertCEqual(rect(1, 0), (1., 0))
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475 self.assertCEqual(rect(1, -pi), (-1., 0))
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476 self.assertCEqual(rect(1, pi/2), (0, 1.))
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477 self.assertCEqual(rect(1, -pi/2), (0, -1.))
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478
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479 def test_isfinite(self):
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480 real_vals = [float('-inf'), -2.3, -0.0,
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481 0.0, 2.3, float('inf'), float('nan')]
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482 for x in real_vals:
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483 for y in real_vals:
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484 z = complex(x, y)
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485 self.assertEqual(cmath.isfinite(z),
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486 math.isfinite(x) and math.isfinite(y))
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487
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488 def test_isnan(self):
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489 self.assertFalse(cmath.isnan(1))
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490 self.assertFalse(cmath.isnan(1j))
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491 self.assertFalse(cmath.isnan(INF))
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492 self.assertTrue(cmath.isnan(NAN))
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493 self.assertTrue(cmath.isnan(complex(NAN, 0)))
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494 self.assertTrue(cmath.isnan(complex(0, NAN)))
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495 self.assertTrue(cmath.isnan(complex(NAN, NAN)))
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496 self.assertTrue(cmath.isnan(complex(NAN, INF)))
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497 self.assertTrue(cmath.isnan(complex(INF, NAN)))
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498
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499 def test_isinf(self):
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500 self.assertFalse(cmath.isinf(1))
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501 self.assertFalse(cmath.isinf(1j))
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502 self.assertFalse(cmath.isinf(NAN))
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503 self.assertTrue(cmath.isinf(INF))
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504 self.assertTrue(cmath.isinf(complex(INF, 0)))
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505 self.assertTrue(cmath.isinf(complex(0, INF)))
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506 self.assertTrue(cmath.isinf(complex(INF, INF)))
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507 self.assertTrue(cmath.isinf(complex(NAN, INF)))
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508 self.assertTrue(cmath.isinf(complex(INF, NAN)))
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509
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510 @requires_IEEE_754
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511 @unittest.skipIf(sysconfig.get_config_var('TANH_PRESERVES_ZERO_SIGN') == 0,
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512 "system tanh() function doesn't copy the sign")
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513 def testTanhSign(self):
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514 for z in complex_zeros:
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515 self.assertComplexIdentical(cmath.tanh(z), z)
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516
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517 # The algorithm used for atan and atanh makes use of the system
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518 # log1p function; If that system function doesn't respect the sign
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519 # of zero, then atan and atanh will also have difficulties with
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520 # the sign of complex zeros.
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521 @requires_IEEE_754
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522 def testAtanSign(self):
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523 for z in complex_zeros:
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524 self.assertComplexIdentical(cmath.atan(z), z)
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525
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526 @requires_IEEE_754
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527 def testAtanhSign(self):
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528 for z in complex_zeros:
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529 self.assertComplexIdentical(cmath.atanh(z), z)
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530
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531
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532 def test_main():
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533 run_unittest(CMathTests)
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534
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535 if __name__ == "__main__":
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536 test_main()