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