641 lines
24 KiB
Python
641 lines
24 KiB
Python
from test.support import requires_IEEE_754, cpython_only
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from test.test_math import parse_testfile, test_file
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import test.test_math as test_math
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import unittest
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import cmath, math
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from cmath import phase, polar, rect, pi
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import platform
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import sys
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INF = float('inf')
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NAN = float('nan')
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complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]]
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complex_infinities = [complex(x, y) for x, y in [
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(INF, 0.0), # 1st quadrant
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(INF, 2.3),
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(INF, INF),
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(2.3, INF),
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(0.0, INF),
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(-0.0, INF), # 2nd quadrant
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(-2.3, INF),
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(-INF, INF),
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(-INF, 2.3),
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(-INF, 0.0),
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(-INF, -0.0), # 3rd quadrant
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(-INF, -2.3),
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(-INF, -INF),
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(-2.3, -INF),
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(-0.0, -INF),
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(0.0, -INF), # 4th quadrant
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(2.3, -INF),
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(INF, -INF),
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(INF, -2.3),
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(INF, -0.0)
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]]
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complex_nans = [complex(x, y) for x, y in [
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(NAN, -INF),
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(NAN, -2.3),
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(NAN, -0.0),
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(NAN, 0.0),
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(NAN, 2.3),
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(NAN, INF),
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(-INF, NAN),
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(-2.3, NAN),
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(-0.0, NAN),
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(0.0, NAN),
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(2.3, NAN),
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(INF, NAN)
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]]
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class CMathTests(unittest.TestCase):
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# list of all functions in cmath
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test_functions = [getattr(cmath, fname) for fname in [
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'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
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'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',
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'sqrt', 'tan', 'tanh']]
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# test first and second arguments independently for 2-argument log
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test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
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test_functions.append(lambda x : cmath.log(14.-27j, x))
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def setUp(self):
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self.test_values = open(test_file)
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def tearDown(self):
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self.test_values.close()
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def assertFloatIdentical(self, x, y):
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"""Fail unless floats x and y are identical, in the sense that:
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(1) both x and y are nans, or
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(2) both x and y are infinities, with the same sign, or
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(3) both x and y are zeros, with the same sign, or
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(4) x and y are both finite and nonzero, and x == y
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"""
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msg = 'floats {!r} and {!r} are not identical'
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if math.isnan(x) or math.isnan(y):
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if math.isnan(x) and math.isnan(y):
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return
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elif x == y:
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if x != 0.0:
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return
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# both zero; check that signs match
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elif math.copysign(1.0, x) == math.copysign(1.0, y):
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return
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else:
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msg += ': zeros have different signs'
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self.fail(msg.format(x, y))
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def assertComplexIdentical(self, x, y):
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"""Fail unless complex numbers x and y have equal values and signs.
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In particular, if x and y both have real (or imaginary) part
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zero, but the zeros have different signs, this test will fail.
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"""
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self.assertFloatIdentical(x.real, y.real)
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self.assertFloatIdentical(x.imag, y.imag)
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def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323,
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msg=None):
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"""Fail if the two floating-point numbers are not almost equal.
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Determine whether floating-point values a and b are equal to within
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a (small) rounding error. The default values for rel_err and
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abs_err are chosen to be suitable for platforms where a float is
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represented by an IEEE 754 double. They allow an error of between
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9 and 19 ulps.
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"""
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# special values testing
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if math.isnan(a):
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if math.isnan(b):
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return
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self.fail(msg or '{!r} should be nan'.format(b))
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if math.isinf(a):
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if a == b:
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return
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self.fail(msg or 'finite result where infinity expected: '
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'expected {!r}, got {!r}'.format(a, b))
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# if both a and b are zero, check whether they have the same sign
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# (in theory there are examples where it would be legitimate for a
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# and b to have opposite signs; in practice these hardly ever
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# occur).
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if not a and not b:
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if math.copysign(1., a) != math.copysign(1., b):
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self.fail(msg or 'zero has wrong sign: expected {!r}, '
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'got {!r}'.format(a, b))
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# if a-b overflows, or b is infinite, return False. Again, in
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# theory there are examples where a is within a few ulps of the
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# max representable float, and then b could legitimately be
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# infinite. In practice these examples are rare.
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try:
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absolute_error = abs(b-a)
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except OverflowError:
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pass
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else:
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# test passes if either the absolute error or the relative
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# error is sufficiently small. The defaults amount to an
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# error of between 9 ulps and 19 ulps on an IEEE-754 compliant
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# machine.
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if absolute_error <= max(abs_err, rel_err * abs(a)):
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return
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self.fail(msg or
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'{!r} and {!r} are not sufficiently close'.format(a, b))
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def test_constants(self):
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e_expected = 2.71828182845904523536
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pi_expected = 3.14159265358979323846
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self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
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msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
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self.assertAlmostEqual(cmath.e, e_expected, places=9,
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msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
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def test_infinity_and_nan_constants(self):
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self.assertEqual(cmath.inf.real, math.inf)
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self.assertEqual(cmath.inf.imag, 0.0)
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self.assertEqual(cmath.infj.real, 0.0)
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self.assertEqual(cmath.infj.imag, math.inf)
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self.assertTrue(math.isnan(cmath.nan.real))
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self.assertEqual(cmath.nan.imag, 0.0)
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self.assertEqual(cmath.nanj.real, 0.0)
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self.assertTrue(math.isnan(cmath.nanj.imag))
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# Check consistency with reprs.
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self.assertEqual(repr(cmath.inf), "inf")
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self.assertEqual(repr(cmath.infj), "infj")
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self.assertEqual(repr(cmath.nan), "nan")
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self.assertEqual(repr(cmath.nanj), "nanj")
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def test_user_object(self):
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# Test automatic calling of __complex__ and __float__ by cmath
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# functions
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# some random values to use as test values; we avoid values
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# for which any of the functions in cmath is undefined
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# (i.e. 0., 1., -1., 1j, -1j) or would cause overflow
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cx_arg = 4.419414439 + 1.497100113j
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flt_arg = -6.131677725
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# a variety of non-complex numbers, used to check that
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# non-complex return values from __complex__ give an error
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non_complexes = ["not complex", 1, 5, 2., None,
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object(), NotImplemented]
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# Now we introduce a variety of classes whose instances might
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# end up being passed to the cmath functions
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# usual case: new-style class implementing __complex__
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class MyComplex(object):
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def __init__(self, value):
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self.value = value
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def __complex__(self):
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return self.value
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# old-style class implementing __complex__
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class MyComplexOS:
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def __init__(self, value):
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self.value = value
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def __complex__(self):
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return self.value
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# classes for which __complex__ raises an exception
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class SomeException(Exception):
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pass
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class MyComplexException(object):
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def __complex__(self):
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raise SomeException
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class MyComplexExceptionOS:
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def __complex__(self):
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raise SomeException
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# some classes not providing __float__ or __complex__
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class NeitherComplexNorFloat(object):
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pass
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class NeitherComplexNorFloatOS:
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pass
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class Index:
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def __int__(self): return 2
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def __index__(self): return 2
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class MyInt:
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def __int__(self): return 2
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# other possible combinations of __float__ and __complex__
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# that should work
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class FloatAndComplex(object):
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def __float__(self):
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return flt_arg
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def __complex__(self):
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return cx_arg
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class FloatAndComplexOS:
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def __float__(self):
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return flt_arg
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def __complex__(self):
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return cx_arg
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class JustFloat(object):
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def __float__(self):
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return flt_arg
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class JustFloatOS:
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def __float__(self):
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return flt_arg
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for f in self.test_functions:
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# usual usage
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self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
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self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg))
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# other combinations of __float__ and __complex__
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self.assertEqual(f(FloatAndComplex()), f(cx_arg))
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self.assertEqual(f(FloatAndComplexOS()), f(cx_arg))
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self.assertEqual(f(JustFloat()), f(flt_arg))
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self.assertEqual(f(JustFloatOS()), f(flt_arg))
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self.assertEqual(f(Index()), f(int(Index())))
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# TypeError should be raised for classes not providing
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# either __complex__ or __float__, even if they provide
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# __int__ or __index__. An old-style class
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# currently raises AttributeError instead of a TypeError;
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# this could be considered a bug.
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self.assertRaises(TypeError, f, NeitherComplexNorFloat())
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self.assertRaises(TypeError, f, MyInt())
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self.assertRaises(Exception, f, NeitherComplexNorFloatOS())
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# non-complex return value from __complex__ -> TypeError
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for bad_complex in non_complexes:
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self.assertRaises(TypeError, f, MyComplex(bad_complex))
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self.assertRaises(TypeError, f, MyComplexOS(bad_complex))
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# exceptions in __complex__ should be propagated correctly
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self.assertRaises(SomeException, f, MyComplexException())
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self.assertRaises(SomeException, f, MyComplexExceptionOS())
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def test_input_type(self):
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# ints should be acceptable inputs to all cmath
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# functions, by virtue of providing a __float__ method
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for f in self.test_functions:
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for arg in [2, 2.]:
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self.assertEqual(f(arg), f(arg.__float__()))
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# but strings should give a TypeError
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for f in self.test_functions:
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for arg in ["a", "long_string", "0", "1j", ""]:
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self.assertRaises(TypeError, f, arg)
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def test_cmath_matches_math(self):
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# check that corresponding cmath and math functions are equal
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# for floats in the appropriate range
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# test_values in (0, 1)
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test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
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# test_values for functions defined on [-1., 1.]
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unit_interval = test_values + [-x for x in test_values] + \
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[0., 1., -1.]
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# test_values for log, log10, sqrt
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positive = test_values + [1.] + [1./x for x in test_values]
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nonnegative = [0.] + positive
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# test_values for functions defined on the whole real line
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real_line = [0.] + positive + [-x for x in positive]
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test_functions = {
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'acos' : unit_interval,
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'asin' : unit_interval,
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'atan' : real_line,
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'cos' : real_line,
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'cosh' : real_line,
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'exp' : real_line,
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'log' : positive,
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'log10' : positive,
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'sin' : real_line,
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'sinh' : real_line,
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'sqrt' : nonnegative,
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'tan' : real_line,
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'tanh' : real_line}
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for fn, values in test_functions.items():
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float_fn = getattr(math, fn)
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complex_fn = getattr(cmath, fn)
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for v in values:
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z = complex_fn(v)
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self.rAssertAlmostEqual(float_fn(v), z.real)
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self.assertEqual(0., z.imag)
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# test two-argument version of log with various bases
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for base in [0.5, 2., 10.]:
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for v in positive:
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z = cmath.log(v, base)
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self.rAssertAlmostEqual(math.log(v, base), z.real)
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self.assertEqual(0., z.imag)
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@requires_IEEE_754
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def test_specific_values(self):
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# Some tests need to be skipped on ancient OS X versions.
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# See issue #27953.
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SKIP_ON_TIGER = {'tan0064'}
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osx_version = None
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if sys.platform == 'darwin':
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version_txt = platform.mac_ver()[0]
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try:
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osx_version = tuple(map(int, version_txt.split('.')))
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except ValueError:
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pass
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def rect_complex(z):
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"""Wrapped version of rect that accepts a complex number instead of
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two float arguments."""
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return cmath.rect(z.real, z.imag)
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def polar_complex(z):
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"""Wrapped version of polar that returns a complex number instead of
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two floats."""
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return complex(*polar(z))
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for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
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arg = complex(ar, ai)
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expected = complex(er, ei)
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# Skip certain tests on OS X 10.4.
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if osx_version is not None and osx_version < (10, 5):
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if id in SKIP_ON_TIGER:
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continue
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if fn == 'rect':
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function = rect_complex
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elif fn == 'polar':
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function = polar_complex
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else:
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function = getattr(cmath, fn)
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if 'divide-by-zero' in flags or 'invalid' in flags:
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try:
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actual = function(arg)
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except ValueError:
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continue
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else:
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self.fail('ValueError not raised in test '
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'{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
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if 'overflow' in flags:
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try:
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actual = function(arg)
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except OverflowError:
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continue
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else:
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self.fail('OverflowError not raised in test '
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'{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
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actual = function(arg)
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if 'ignore-real-sign' in flags:
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actual = complex(abs(actual.real), actual.imag)
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expected = complex(abs(expected.real), expected.imag)
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if 'ignore-imag-sign' in flags:
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actual = complex(actual.real, abs(actual.imag))
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expected = complex(expected.real, abs(expected.imag))
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# for the real part of the log function, we allow an
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# absolute error of up to 2e-15.
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if fn in ('log', 'log10'):
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real_abs_err = 2e-15
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else:
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real_abs_err = 5e-323
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error_message = (
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'{}: {}(complex({!r}, {!r}))\n'
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'Expected: complex({!r}, {!r})\n'
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'Received: complex({!r}, {!r})\n'
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'Received value insufficiently close to expected value.'
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).format(id, fn, ar, ai,
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expected.real, expected.imag,
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actual.real, actual.imag)
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self.rAssertAlmostEqual(expected.real, actual.real,
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abs_err=real_abs_err,
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msg=error_message)
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self.rAssertAlmostEqual(expected.imag, actual.imag,
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msg=error_message)
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def check_polar(self, func):
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def check(arg, expected):
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got = func(arg)
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for e, g in zip(expected, got):
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self.rAssertAlmostEqual(e, g)
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check(0, (0., 0.))
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check(1, (1., 0.))
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check(-1, (1., pi))
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check(1j, (1., pi / 2))
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check(-3j, (3., -pi / 2))
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inf = float('inf')
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check(complex(inf, 0), (inf, 0.))
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check(complex(-inf, 0), (inf, pi))
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check(complex(3, inf), (inf, pi / 2))
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check(complex(5, -inf), (inf, -pi / 2))
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check(complex(inf, inf), (inf, pi / 4))
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check(complex(inf, -inf), (inf, -pi / 4))
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check(complex(-inf, inf), (inf, 3 * pi / 4))
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check(complex(-inf, -inf), (inf, -3 * pi / 4))
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nan = float('nan')
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check(complex(nan, 0), (nan, nan))
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check(complex(0, nan), (nan, nan))
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check(complex(nan, nan), (nan, nan))
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check(complex(inf, nan), (inf, nan))
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check(complex(-inf, nan), (inf, nan))
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check(complex(nan, inf), (inf, nan))
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check(complex(nan, -inf), (inf, nan))
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def test_polar(self):
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self.check_polar(polar)
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@cpython_only
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def test_polar_errno(self):
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# Issue #24489: check a previously set C errno doesn't disturb polar()
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from _testcapi import set_errno
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def polar_with_errno_set(z):
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set_errno(11)
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try:
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return polar(z)
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finally:
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set_errno(0)
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self.check_polar(polar_with_errno_set)
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def test_phase(self):
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self.assertAlmostEqual(phase(0), 0.)
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self.assertAlmostEqual(phase(1.), 0.)
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self.assertAlmostEqual(phase(-1.), pi)
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self.assertAlmostEqual(phase(-1.+1E-300j), pi)
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self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
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self.assertAlmostEqual(phase(1j), pi/2)
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self.assertAlmostEqual(phase(-1j), -pi/2)
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# zeros
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self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
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self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
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self.assertEqual(phase(complex(-0.0, 0.0)), pi)
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self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
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# infinities
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self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
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self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
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self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
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self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
|
|
self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
|
|
self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
|
|
self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
|
|
self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
|
|
self.assertEqual(phase(complex(INF, -2.3)), -0.0)
|
|
self.assertEqual(phase(complex(INF, -0.0)), -0.0)
|
|
self.assertEqual(phase(complex(INF, 0.0)), 0.0)
|
|
self.assertEqual(phase(complex(INF, 2.3)), 0.0)
|
|
self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
|
|
self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
|
|
self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
|
|
self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
|
|
self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
|
|
self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
|
|
self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
|
|
self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
|
|
|
|
# real or imaginary part NaN
|
|
for z in complex_nans:
|
|
self.assertTrue(math.isnan(phase(z)))
|
|
|
|
def test_abs(self):
|
|
# zeros
|
|
for z in complex_zeros:
|
|
self.assertEqual(abs(z), 0.0)
|
|
|
|
# infinities
|
|
for z in complex_infinities:
|
|
self.assertEqual(abs(z), INF)
|
|
|
|
# real or imaginary part NaN
|
|
self.assertEqual(abs(complex(NAN, -INF)), INF)
|
|
self.assertTrue(math.isnan(abs(complex(NAN, -2.3))))
|
|
self.assertTrue(math.isnan(abs(complex(NAN, -0.0))))
|
|
self.assertTrue(math.isnan(abs(complex(NAN, 0.0))))
|
|
self.assertTrue(math.isnan(abs(complex(NAN, 2.3))))
|
|
self.assertEqual(abs(complex(NAN, INF)), INF)
|
|
self.assertEqual(abs(complex(-INF, NAN)), INF)
|
|
self.assertTrue(math.isnan(abs(complex(-2.3, NAN))))
|
|
self.assertTrue(math.isnan(abs(complex(-0.0, NAN))))
|
|
self.assertTrue(math.isnan(abs(complex(0.0, NAN))))
|
|
self.assertTrue(math.isnan(abs(complex(2.3, NAN))))
|
|
self.assertEqual(abs(complex(INF, NAN)), INF)
|
|
self.assertTrue(math.isnan(abs(complex(NAN, NAN))))
|
|
|
|
|
|
@requires_IEEE_754
|
|
def test_abs_overflows(self):
|
|
# result overflows
|
|
self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308))
|
|
|
|
def assertCEqual(self, a, b):
|
|
eps = 1E-7
|
|
if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:
|
|
self.fail((a ,b))
|
|
|
|
def test_rect(self):
|
|
self.assertCEqual(rect(0, 0), (0, 0))
|
|
self.assertCEqual(rect(1, 0), (1., 0))
|
|
self.assertCEqual(rect(1, -pi), (-1., 0))
|
|
self.assertCEqual(rect(1, pi/2), (0, 1.))
|
|
self.assertCEqual(rect(1, -pi/2), (0, -1.))
|
|
|
|
def test_isfinite(self):
|
|
real_vals = [float('-inf'), -2.3, -0.0,
|
|
0.0, 2.3, float('inf'), float('nan')]
|
|
for x in real_vals:
|
|
for y in real_vals:
|
|
z = complex(x, y)
|
|
self.assertEqual(cmath.isfinite(z),
|
|
math.isfinite(x) and math.isfinite(y))
|
|
|
|
def test_isnan(self):
|
|
self.assertFalse(cmath.isnan(1))
|
|
self.assertFalse(cmath.isnan(1j))
|
|
self.assertFalse(cmath.isnan(INF))
|
|
self.assertTrue(cmath.isnan(NAN))
|
|
self.assertTrue(cmath.isnan(complex(NAN, 0)))
|
|
self.assertTrue(cmath.isnan(complex(0, NAN)))
|
|
self.assertTrue(cmath.isnan(complex(NAN, NAN)))
|
|
self.assertTrue(cmath.isnan(complex(NAN, INF)))
|
|
self.assertTrue(cmath.isnan(complex(INF, NAN)))
|
|
|
|
def test_isinf(self):
|
|
self.assertFalse(cmath.isinf(1))
|
|
self.assertFalse(cmath.isinf(1j))
|
|
self.assertFalse(cmath.isinf(NAN))
|
|
self.assertTrue(cmath.isinf(INF))
|
|
self.assertTrue(cmath.isinf(complex(INF, 0)))
|
|
self.assertTrue(cmath.isinf(complex(0, INF)))
|
|
self.assertTrue(cmath.isinf(complex(INF, INF)))
|
|
self.assertTrue(cmath.isinf(complex(NAN, INF)))
|
|
self.assertTrue(cmath.isinf(complex(INF, NAN)))
|
|
|
|
@requires_IEEE_754
|
|
def testTanhSign(self):
|
|
for z in complex_zeros:
|
|
self.assertComplexIdentical(cmath.tanh(z), z)
|
|
|
|
# The algorithm used for atan and atanh makes use of the system
|
|
# log1p function; If that system function doesn't respect the sign
|
|
# of zero, then atan and atanh will also have difficulties with
|
|
# the sign of complex zeros.
|
|
@requires_IEEE_754
|
|
def testAtanSign(self):
|
|
for z in complex_zeros:
|
|
self.assertComplexIdentical(cmath.atan(z), z)
|
|
|
|
@requires_IEEE_754
|
|
def testAtanhSign(self):
|
|
for z in complex_zeros:
|
|
self.assertComplexIdentical(cmath.atanh(z), z)
|
|
|
|
|
|
class IsCloseTests(test_math.IsCloseTests):
|
|
isclose = cmath.isclose
|
|
|
|
def test_reject_complex_tolerances(self):
|
|
with self.assertRaises(TypeError):
|
|
self.isclose(1j, 1j, rel_tol=1j)
|
|
|
|
with self.assertRaises(TypeError):
|
|
self.isclose(1j, 1j, abs_tol=1j)
|
|
|
|
with self.assertRaises(TypeError):
|
|
self.isclose(1j, 1j, rel_tol=1j, abs_tol=1j)
|
|
|
|
def test_complex_values(self):
|
|
# test complex values that are close to within 12 decimal places
|
|
complex_examples = [(1.0+1.0j, 1.000000000001+1.0j),
|
|
(1.0+1.0j, 1.0+1.000000000001j),
|
|
(-1.0+1.0j, -1.000000000001+1.0j),
|
|
(1.0-1.0j, 1.0-0.999999999999j),
|
|
]
|
|
|
|
self.assertAllClose(complex_examples, rel_tol=1e-12)
|
|
self.assertAllNotClose(complex_examples, rel_tol=1e-13)
|
|
|
|
def test_complex_near_zero(self):
|
|
# test values near zero that are near to within three decimal places
|
|
near_zero_examples = [(0.001j, 0),
|
|
(0.001, 0),
|
|
(0.001+0.001j, 0),
|
|
(-0.001+0.001j, 0),
|
|
(0.001-0.001j, 0),
|
|
(-0.001-0.001j, 0),
|
|
]
|
|
|
|
self.assertAllClose(near_zero_examples, abs_tol=1.5e-03)
|
|
self.assertAllNotClose(near_zero_examples, abs_tol=0.5e-03)
|
|
|
|
self.assertIsClose(0.001-0.001j, 0.001+0.001j, abs_tol=2e-03)
|
|
self.assertIsNotClose(0.001-0.001j, 0.001+0.001j, abs_tol=1e-03)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
unittest.main()
|