mirror of https://github.com/python/cpython
946 lines
40 KiB
Python
946 lines
40 KiB
Python
import unittest
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import sys
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from test import support
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from test.support.testcase import ComplexesAreIdenticalMixin
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from test.test_grammar import (VALID_UNDERSCORE_LITERALS,
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INVALID_UNDERSCORE_LITERALS)
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from random import random
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from math import isnan, copysign
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import operator
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INF = float("inf")
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NAN = float("nan")
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DBL_MAX = sys.float_info.max
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# These tests ensure that complex math does the right thing
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ZERO_DIVISION = (
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(1+1j, 0+0j),
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(1+1j, 0.0),
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(1+1j, 0),
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(1.0, 0+0j),
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(1, 0+0j),
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)
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class WithIndex:
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def __init__(self, value):
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self.value = value
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def __index__(self):
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return self.value
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class WithFloat:
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def __init__(self, value):
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self.value = value
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def __float__(self):
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return self.value
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class ComplexSubclass(complex):
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pass
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class OtherComplexSubclass(complex):
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pass
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class MyInt:
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def __init__(self, value):
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self.value = value
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def __int__(self):
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return self.value
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class WithComplex:
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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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class ComplexTest(ComplexesAreIdenticalMixin, unittest.TestCase):
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def assertAlmostEqual(self, a, b):
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if isinstance(a, complex):
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if isinstance(b, complex):
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unittest.TestCase.assertAlmostEqual(self, a.real, b.real)
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unittest.TestCase.assertAlmostEqual(self, a.imag, b.imag)
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else:
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unittest.TestCase.assertAlmostEqual(self, a.real, b)
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unittest.TestCase.assertAlmostEqual(self, a.imag, 0.)
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else:
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if isinstance(b, complex):
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unittest.TestCase.assertAlmostEqual(self, a, b.real)
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unittest.TestCase.assertAlmostEqual(self, 0., b.imag)
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else:
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unittest.TestCase.assertAlmostEqual(self, a, b)
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def assertCloseAbs(self, x, y, eps=1e-9):
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"""Return true iff floats x and y "are close"."""
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# put the one with larger magnitude second
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if abs(x) > abs(y):
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x, y = y, x
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if y == 0:
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return abs(x) < eps
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if x == 0:
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return abs(y) < eps
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# check that relative difference < eps
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self.assertTrue(abs((x-y)/y) < eps)
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def assertClose(self, x, y, eps=1e-9):
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"""Return true iff complexes x and y "are close"."""
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self.assertCloseAbs(x.real, y.real, eps)
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self.assertCloseAbs(x.imag, y.imag, eps)
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def check_div(self, x, y):
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"""Compute complex z=x*y, and check that z/x==y and z/y==x."""
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z = x * y
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if x != 0:
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q = z / x
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self.assertClose(q, y)
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q = z.__truediv__(x)
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self.assertClose(q, y)
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if y != 0:
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q = z / y
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self.assertClose(q, x)
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q = z.__truediv__(y)
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self.assertClose(q, x)
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def test_truediv(self):
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simple_real = [float(i) for i in range(-5, 6)]
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simple_complex = [complex(x, y) for x in simple_real for y in simple_real]
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for x in simple_complex:
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for y in simple_complex:
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self.check_div(x, y)
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# A naive complex division algorithm (such as in 2.0) is very prone to
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# nonsense errors for these (overflows and underflows).
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self.check_div(complex(1e200, 1e200), 1+0j)
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self.check_div(complex(1e-200, 1e-200), 1+0j)
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# Just for fun.
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for i in range(100):
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self.check_div(complex(random(), random()),
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complex(random(), random()))
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self.assertAlmostEqual(complex.__truediv__(2+0j, 1+1j), 1-1j)
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self.assertRaises(TypeError, operator.truediv, 1j, None)
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self.assertRaises(TypeError, operator.truediv, None, 1j)
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for denom_real, denom_imag in [(0, NAN), (NAN, 0), (NAN, NAN)]:
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z = complex(0, 0) / complex(denom_real, denom_imag)
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self.assertTrue(isnan(z.real))
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self.assertTrue(isnan(z.imag))
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self.assertComplexesAreIdentical(complex(INF, 1)/(0.0+1j),
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complex(NAN, -INF))
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# test recover of infs if numerator has infs and denominator is finite
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self.assertComplexesAreIdentical(complex(INF, -INF)/(1+0j),
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complex(INF, -INF))
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self.assertComplexesAreIdentical(complex(INF, INF)/(0.0+1j),
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complex(INF, -INF))
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self.assertComplexesAreIdentical(complex(NAN, INF)/complex(2**1000, 2**-1000),
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complex(INF, INF))
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self.assertComplexesAreIdentical(complex(INF, NAN)/complex(2**1000, 2**-1000),
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complex(INF, -INF))
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# test recover of zeros if denominator is infinite
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self.assertComplexesAreIdentical((1+1j)/complex(INF, INF), (0.0+0j))
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self.assertComplexesAreIdentical((1+1j)/complex(INF, -INF), (0.0+0j))
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self.assertComplexesAreIdentical((1+1j)/complex(-INF, INF),
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complex(0.0, -0.0))
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self.assertComplexesAreIdentical((1+1j)/complex(-INF, -INF),
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complex(-0.0, 0))
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self.assertComplexesAreIdentical((INF+1j)/complex(INF, INF),
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complex(NAN, NAN))
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self.assertComplexesAreIdentical(complex(1, INF)/complex(INF, INF),
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complex(NAN, NAN))
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self.assertComplexesAreIdentical(complex(INF, 1)/complex(1, INF),
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complex(NAN, NAN))
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def test_truediv_zero_division(self):
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for a, b in ZERO_DIVISION:
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with self.assertRaises(ZeroDivisionError):
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a / b
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def test_floordiv(self):
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with self.assertRaises(TypeError):
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(1+1j) // (1+0j)
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with self.assertRaises(TypeError):
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(1+1j) // 1.0
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with self.assertRaises(TypeError):
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(1+1j) // 1
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with self.assertRaises(TypeError):
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1.0 // (1+0j)
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with self.assertRaises(TypeError):
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1 // (1+0j)
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def test_floordiv_zero_division(self):
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for a, b in ZERO_DIVISION:
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with self.assertRaises(TypeError):
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a // b
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def test_richcompare(self):
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self.assertIs(complex.__eq__(1+1j, 1<<10000), False)
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self.assertIs(complex.__lt__(1+1j, None), NotImplemented)
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self.assertIs(complex.__eq__(1+1j, None), NotImplemented)
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self.assertIs(complex.__eq__(1+1j, 1+1j), True)
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self.assertIs(complex.__eq__(1+1j, 2+2j), False)
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self.assertIs(complex.__ne__(1+1j, 1+1j), False)
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self.assertIs(complex.__ne__(1+1j, 2+2j), True)
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for i in range(1, 100):
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f = i / 100.0
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self.assertIs(complex.__eq__(f+0j, f), True)
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self.assertIs(complex.__ne__(f+0j, f), False)
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self.assertIs(complex.__eq__(complex(f, f), f), False)
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self.assertIs(complex.__ne__(complex(f, f), f), True)
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self.assertIs(complex.__lt__(1+1j, 2+2j), NotImplemented)
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self.assertIs(complex.__le__(1+1j, 2+2j), NotImplemented)
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self.assertIs(complex.__gt__(1+1j, 2+2j), NotImplemented)
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self.assertIs(complex.__ge__(1+1j, 2+2j), NotImplemented)
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self.assertRaises(TypeError, operator.lt, 1+1j, 2+2j)
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self.assertRaises(TypeError, operator.le, 1+1j, 2+2j)
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self.assertRaises(TypeError, operator.gt, 1+1j, 2+2j)
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self.assertRaises(TypeError, operator.ge, 1+1j, 2+2j)
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self.assertIs(operator.eq(1+1j, 1+1j), True)
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self.assertIs(operator.eq(1+1j, 2+2j), False)
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self.assertIs(operator.ne(1+1j, 1+1j), False)
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self.assertIs(operator.ne(1+1j, 2+2j), True)
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self.assertIs(operator.eq(1+1j, 2.0), False)
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def test_richcompare_boundaries(self):
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def check(n, deltas, is_equal, imag = 0.0):
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for delta in deltas:
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i = n + delta
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z = complex(i, imag)
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self.assertIs(complex.__eq__(z, i), is_equal(delta))
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self.assertIs(complex.__ne__(z, i), not is_equal(delta))
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# For IEEE-754 doubles the following should hold:
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# x in [2 ** (52 + i), 2 ** (53 + i + 1)] -> x mod 2 ** i == 0
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# where the interval is representable, of course.
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for i in range(1, 10):
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pow = 52 + i
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mult = 2 ** i
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check(2 ** pow, range(1, 101), lambda delta: delta % mult == 0)
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check(2 ** pow, range(1, 101), lambda delta: False, float(i))
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check(2 ** 53, range(-100, 0), lambda delta: True)
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def test_add(self):
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self.assertEqual(1j + int(+1), complex(+1, 1))
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self.assertEqual(1j + int(-1), complex(-1, 1))
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self.assertRaises(OverflowError, operator.add, 1j, 10**1000)
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self.assertRaises(TypeError, operator.add, 1j, None)
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self.assertRaises(TypeError, operator.add, None, 1j)
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def test_sub(self):
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self.assertEqual(1j - int(+1), complex(-1, 1))
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self.assertEqual(1j - int(-1), complex(1, 1))
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self.assertRaises(OverflowError, operator.sub, 1j, 10**1000)
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self.assertRaises(TypeError, operator.sub, 1j, None)
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self.assertRaises(TypeError, operator.sub, None, 1j)
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def test_mul(self):
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self.assertEqual(1j * int(20), complex(0, 20))
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self.assertEqual(1j * int(-1), complex(0, -1))
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self.assertRaises(OverflowError, operator.mul, 1j, 10**1000)
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self.assertRaises(TypeError, operator.mul, 1j, None)
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self.assertRaises(TypeError, operator.mul, None, 1j)
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def test_mod(self):
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# % is no longer supported on complex numbers
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with self.assertRaises(TypeError):
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(1+1j) % (1+0j)
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with self.assertRaises(TypeError):
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(1+1j) % 1.0
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with self.assertRaises(TypeError):
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(1+1j) % 1
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with self.assertRaises(TypeError):
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1.0 % (1+0j)
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with self.assertRaises(TypeError):
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1 % (1+0j)
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def test_mod_zero_division(self):
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for a, b in ZERO_DIVISION:
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with self.assertRaises(TypeError):
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a % b
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def test_divmod(self):
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self.assertRaises(TypeError, divmod, 1+1j, 1+0j)
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self.assertRaises(TypeError, divmod, 1+1j, 1.0)
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self.assertRaises(TypeError, divmod, 1+1j, 1)
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self.assertRaises(TypeError, divmod, 1.0, 1+0j)
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self.assertRaises(TypeError, divmod, 1, 1+0j)
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def test_divmod_zero_division(self):
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for a, b in ZERO_DIVISION:
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self.assertRaises(TypeError, divmod, a, b)
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def test_pow(self):
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self.assertAlmostEqual(pow(1+1j, 0+0j), 1.0)
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self.assertAlmostEqual(pow(0+0j, 2+0j), 0.0)
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self.assertEqual(pow(0+0j, 2000+0j), 0.0)
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self.assertEqual(pow(0, 0+0j), 1.0)
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self.assertEqual(pow(-1, 0+0j), 1.0)
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self.assertRaises(ZeroDivisionError, pow, 0+0j, 1j)
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self.assertRaises(ZeroDivisionError, pow, 0+0j, -1000)
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self.assertAlmostEqual(pow(1j, -1), 1/1j)
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self.assertAlmostEqual(pow(1j, 200), 1)
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self.assertRaises(ValueError, pow, 1+1j, 1+1j, 1+1j)
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self.assertRaises(OverflowError, pow, 1e200+1j, 1e200+1j)
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self.assertRaises(TypeError, pow, 1j, None)
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self.assertRaises(TypeError, pow, None, 1j)
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self.assertAlmostEqual(pow(1j, 0.5), 0.7071067811865476+0.7071067811865475j)
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a = 3.33+4.43j
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self.assertEqual(a ** 0j, 1)
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self.assertEqual(a ** 0.+0.j, 1)
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self.assertEqual(3j ** 0j, 1)
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self.assertEqual(3j ** 0, 1)
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try:
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0j ** a
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except ZeroDivisionError:
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pass
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else:
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self.fail("should fail 0.0 to negative or complex power")
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try:
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0j ** (3-2j)
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except ZeroDivisionError:
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pass
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else:
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self.fail("should fail 0.0 to negative or complex power")
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# The following is used to exercise certain code paths
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self.assertEqual(a ** 105, a ** 105)
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self.assertEqual(a ** -105, a ** -105)
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self.assertEqual(a ** -30, a ** -30)
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self.assertEqual(0.0j ** 0, 1)
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b = 5.1+2.3j
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self.assertRaises(ValueError, pow, a, b, 0)
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# Check some boundary conditions; some of these used to invoke
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# undefined behaviour (https://bugs.python.org/issue44698). We're
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# not actually checking the results of these operations, just making
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# sure they don't crash (for example when using clang's
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# UndefinedBehaviourSanitizer).
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values = (sys.maxsize, sys.maxsize+1, sys.maxsize-1,
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-sys.maxsize, -sys.maxsize+1, -sys.maxsize+1)
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for real in values:
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for imag in values:
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with self.subTest(real=real, imag=imag):
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c = complex(real, imag)
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try:
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c ** real
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except OverflowError:
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pass
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try:
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c ** c
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except OverflowError:
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pass
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def test_pow_with_small_integer_exponents(self):
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# Check that small integer exponents are handled identically
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# regardless of their type.
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values = [
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complex(5.0, 12.0),
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complex(5.0e100, 12.0e100),
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complex(-4.0, INF),
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complex(INF, 0.0),
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]
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exponents = [-19, -5, -3, -2, -1, 0, 1, 2, 3, 5, 19]
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for value in values:
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for exponent in exponents:
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with self.subTest(value=value, exponent=exponent):
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try:
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int_pow = value**exponent
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except OverflowError:
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int_pow = "overflow"
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try:
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float_pow = value**float(exponent)
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except OverflowError:
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float_pow = "overflow"
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try:
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complex_pow = value**complex(exponent)
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except OverflowError:
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complex_pow = "overflow"
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self.assertEqual(str(float_pow), str(int_pow))
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self.assertEqual(str(complex_pow), str(int_pow))
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def test_boolcontext(self):
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for i in range(100):
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self.assertTrue(complex(random() + 1e-6, random() + 1e-6))
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self.assertTrue(not complex(0.0, 0.0))
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self.assertTrue(1j)
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def test_conjugate(self):
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self.assertClose(complex(5.3, 9.8).conjugate(), 5.3-9.8j)
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def test_constructor(self):
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def check(z, x, y):
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self.assertIs(type(z), complex)
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self.assertFloatsAreIdentical(z.real, x)
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self.assertFloatsAreIdentical(z.imag, y)
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check(complex(), 0.0, 0.0)
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check(complex(10), 10.0, 0.0)
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check(complex(4.25), 4.25, 0.0)
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check(complex(4.25+0j), 4.25, 0.0)
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check(complex(4.25+0.5j), 4.25, 0.5)
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check(complex(ComplexSubclass(4.25+0.5j)), 4.25, 0.5)
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check(complex(WithComplex(4.25+0.5j)), 4.25, 0.5)
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check(complex(1, 10), 1.0, 10.0)
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check(complex(1, 10.0), 1.0, 10.0)
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check(complex(1, 4.25), 1.0, 4.25)
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check(complex(1.0, 10), 1.0, 10.0)
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check(complex(4.25, 10), 4.25, 10.0)
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check(complex(1.0, 10.0), 1.0, 10.0)
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check(complex(4.25, 0.5), 4.25, 0.5)
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with self.assertWarnsRegex(DeprecationWarning,
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"argument 'real' must be a real number, not complex"):
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check(complex(4.25+0j, 0), 4.25, 0.0)
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with self.assertWarnsRegex(DeprecationWarning,
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"argument 'real' must be a real number, not .*ComplexSubclass"):
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check(complex(ComplexSubclass(4.25+0j), 0), 4.25, 0.0)
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with self.assertWarnsRegex(DeprecationWarning,
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"argument 'real' must be a real number, not .*WithComplex"):
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check(complex(WithComplex(4.25+0j), 0), 4.25, 0.0)
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with self.assertWarnsRegex(DeprecationWarning,
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"argument 'real' must be a real number, not complex"):
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check(complex(4.25j, 0), 0.0, 4.25)
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with self.assertWarnsRegex(DeprecationWarning,
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"argument 'real' must be a real number, not complex"):
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check(complex(0j, 4.25), 0.0, 4.25)
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with self.assertWarnsRegex(DeprecationWarning,
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"argument 'imag' must be a real number, not complex"):
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check(complex(0, 4.25+0j), 0.0, 4.25)
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with self.assertWarnsRegex(DeprecationWarning,
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"argument 'imag' must be a real number, not .*ComplexSubclass"):
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check(complex(0, ComplexSubclass(4.25+0j)), 0.0, 4.25)
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with self.assertRaisesRegex(TypeError,
|
|
"argument 'imag' must be a real number, not .*WithComplex"):
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complex(0, WithComplex(4.25+0j))
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|
with self.assertWarnsRegex(DeprecationWarning,
|
|
"argument 'imag' must be a real number, not complex"):
|
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check(complex(0.0, 4.25j), -4.25, 0.0)
|
|
with self.assertWarnsRegex(DeprecationWarning,
|
|
"argument 'real' must be a real number, not complex"):
|
|
check(complex(4.25+0j, 0j), 4.25, 0.0)
|
|
with self.assertWarnsRegex(DeprecationWarning,
|
|
"argument 'real' must be a real number, not complex"):
|
|
check(complex(4.25j, 0j), 0.0, 4.25)
|
|
with self.assertWarnsRegex(DeprecationWarning,
|
|
"argument 'real' must be a real number, not complex"):
|
|
check(complex(0j, 4.25+0j), 0.0, 4.25)
|
|
with self.assertWarnsRegex(DeprecationWarning,
|
|
"argument 'real' must be a real number, not complex"):
|
|
check(complex(0j, 4.25j), -4.25, 0.0)
|
|
|
|
check(complex(real=4.25), 4.25, 0.0)
|
|
with self.assertWarnsRegex(DeprecationWarning,
|
|
"argument 'real' must be a real number, not complex"):
|
|
check(complex(real=4.25+0j), 4.25, 0.0)
|
|
with self.assertWarnsRegex(DeprecationWarning,
|
|
"argument 'real' must be a real number, not complex"):
|
|
check(complex(real=4.25+1.5j), 4.25, 1.5)
|
|
check(complex(imag=1.5), 0.0, 1.5)
|
|
check(complex(real=4.25, imag=1.5), 4.25, 1.5)
|
|
check(complex(4.25, imag=1.5), 4.25, 1.5)
|
|
|
|
# check that the sign of a zero in the real or imaginary part
|
|
# is preserved when constructing from two floats.
|
|
for x in 1.0, -1.0:
|
|
for y in 0.0, -0.0:
|
|
check(complex(x, y), x, y)
|
|
check(complex(y, x), y, x)
|
|
|
|
c = complex(4.25, 1.5)
|
|
self.assertIs(complex(c), c)
|
|
c2 = ComplexSubclass(c)
|
|
self.assertEqual(c2, c)
|
|
self.assertIs(type(c2), ComplexSubclass)
|
|
del c, c2
|
|
|
|
self.assertRaisesRegex(TypeError,
|
|
"argument must be a string or a number, not dict",
|
|
complex, {})
|
|
self.assertRaisesRegex(TypeError,
|
|
"argument must be a string or a number, not NoneType",
|
|
complex, None)
|
|
self.assertRaisesRegex(TypeError,
|
|
"argument 'real' must be a real number, not dict",
|
|
complex, {1:2}, 0)
|
|
self.assertRaisesRegex(TypeError,
|
|
"argument 'real' must be a real number, not str",
|
|
complex, '1', 0)
|
|
self.assertRaisesRegex(TypeError,
|
|
"argument 'imag' must be a real number, not dict",
|
|
complex, 0, {1:2})
|
|
self.assertRaisesRegex(TypeError,
|
|
"argument 'imag' must be a real number, not str",
|
|
complex, 0, '1')
|
|
|
|
self.assertRaises(TypeError, complex, WithComplex(1.5))
|
|
self.assertRaises(TypeError, complex, WithComplex(1))
|
|
self.assertRaises(TypeError, complex, WithComplex(None))
|
|
self.assertRaises(TypeError, complex, WithComplex(4.25+0j), object())
|
|
self.assertRaises(TypeError, complex, WithComplex(1.5), object())
|
|
self.assertRaises(TypeError, complex, WithComplex(1), object())
|
|
self.assertRaises(TypeError, complex, WithComplex(None), object())
|
|
|
|
class EvilExc(Exception):
|
|
pass
|
|
|
|
class evilcomplex:
|
|
def __complex__(self):
|
|
raise EvilExc
|
|
|
|
self.assertRaises(EvilExc, complex, evilcomplex())
|
|
|
|
check(complex(WithFloat(4.25)), 4.25, 0.0)
|
|
check(complex(WithFloat(4.25), 1.5), 4.25, 1.5)
|
|
check(complex(1.5, WithFloat(4.25)), 1.5, 4.25)
|
|
self.assertRaises(TypeError, complex, WithFloat(42))
|
|
self.assertRaises(TypeError, complex, WithFloat(42), 1.5)
|
|
self.assertRaises(TypeError, complex, 1.5, WithFloat(42))
|
|
self.assertRaises(TypeError, complex, WithFloat(None))
|
|
self.assertRaises(TypeError, complex, WithFloat(None), 1.5)
|
|
self.assertRaises(TypeError, complex, 1.5, WithFloat(None))
|
|
|
|
check(complex(WithIndex(42)), 42.0, 0.0)
|
|
check(complex(WithIndex(42), 1.5), 42.0, 1.5)
|
|
check(complex(1.5, WithIndex(42)), 1.5, 42.0)
|
|
self.assertRaises(OverflowError, complex, WithIndex(2**2000))
|
|
self.assertRaises(OverflowError, complex, WithIndex(2**2000), 1.5)
|
|
self.assertRaises(OverflowError, complex, 1.5, WithIndex(2**2000))
|
|
self.assertRaises(TypeError, complex, WithIndex(None))
|
|
self.assertRaises(TypeError, complex, WithIndex(None), 1.5)
|
|
self.assertRaises(TypeError, complex, 1.5, WithIndex(None))
|
|
|
|
class MyInt:
|
|
def __int__(self):
|
|
return 42
|
|
|
|
self.assertRaises(TypeError, complex, MyInt())
|
|
self.assertRaises(TypeError, complex, MyInt(), 1.5)
|
|
self.assertRaises(TypeError, complex, 1.5, MyInt())
|
|
|
|
class complex0(complex):
|
|
"""Test usage of __complex__() when inheriting from 'complex'"""
|
|
def __complex__(self):
|
|
return 42j
|
|
|
|
class complex1(complex):
|
|
"""Test usage of __complex__() with a __new__() method"""
|
|
def __new__(self, value=0j):
|
|
return complex.__new__(self, 2*value)
|
|
def __complex__(self):
|
|
return self
|
|
|
|
class complex2(complex):
|
|
"""Make sure that __complex__() calls fail if anything other than a
|
|
complex is returned"""
|
|
def __complex__(self):
|
|
return None
|
|
|
|
check(complex(complex0(1j)), 0.0, 42.0)
|
|
with self.assertWarns(DeprecationWarning):
|
|
check(complex(complex1(1j)), 0.0, 2.0)
|
|
self.assertRaises(TypeError, complex, complex2(1j))
|
|
|
|
def test___complex__(self):
|
|
z = 3 + 4j
|
|
self.assertEqual(z.__complex__(), z)
|
|
self.assertEqual(type(z.__complex__()), complex)
|
|
|
|
z = ComplexSubclass(3 + 4j)
|
|
self.assertEqual(z.__complex__(), 3 + 4j)
|
|
self.assertEqual(type(z.__complex__()), complex)
|
|
|
|
@support.requires_IEEE_754
|
|
def test_constructor_special_numbers(self):
|
|
for x in 0.0, -0.0, INF, -INF, NAN:
|
|
for y in 0.0, -0.0, INF, -INF, NAN:
|
|
with self.subTest(x=x, y=y):
|
|
z = complex(x, y)
|
|
self.assertFloatsAreIdentical(z.real, x)
|
|
self.assertFloatsAreIdentical(z.imag, y)
|
|
z = ComplexSubclass(x, y)
|
|
self.assertIs(type(z), ComplexSubclass)
|
|
self.assertFloatsAreIdentical(z.real, x)
|
|
self.assertFloatsAreIdentical(z.imag, y)
|
|
z = complex(ComplexSubclass(x, y))
|
|
self.assertIs(type(z), complex)
|
|
self.assertFloatsAreIdentical(z.real, x)
|
|
self.assertFloatsAreIdentical(z.imag, y)
|
|
z = ComplexSubclass(complex(x, y))
|
|
self.assertIs(type(z), ComplexSubclass)
|
|
self.assertFloatsAreIdentical(z.real, x)
|
|
self.assertFloatsAreIdentical(z.imag, y)
|
|
|
|
def test_constructor_from_string(self):
|
|
def check(z, x, y):
|
|
self.assertIs(type(z), complex)
|
|
self.assertFloatsAreIdentical(z.real, x)
|
|
self.assertFloatsAreIdentical(z.imag, y)
|
|
|
|
check(complex("1"), 1.0, 0.0)
|
|
check(complex("1j"), 0.0, 1.0)
|
|
check(complex("-1"), -1.0, 0.0)
|
|
check(complex("+1"), 1.0, 0.0)
|
|
check(complex("1+2j"), 1.0, 2.0)
|
|
check(complex("(1+2j)"), 1.0, 2.0)
|
|
check(complex("(1.5+4.25j)"), 1.5, 4.25)
|
|
check(complex("4.25+1J"), 4.25, 1.0)
|
|
check(complex(" ( +4.25-6J )"), 4.25, -6.0)
|
|
check(complex(" ( +4.25-J )"), 4.25, -1.0)
|
|
check(complex(" ( +4.25+j )"), 4.25, 1.0)
|
|
check(complex("J"), 0.0, 1.0)
|
|
check(complex("( j )"), 0.0, 1.0)
|
|
check(complex("+J"), 0.0, 1.0)
|
|
check(complex("( -j)"), 0.0, -1.0)
|
|
check(complex('1-1j'), 1.0, -1.0)
|
|
check(complex('1J'), 0.0, 1.0)
|
|
|
|
check(complex('1e-500'), 0.0, 0.0)
|
|
check(complex('-1e-500j'), 0.0, -0.0)
|
|
check(complex('1e-500+1e-500j'), 0.0, 0.0)
|
|
check(complex('-1e-500+1e-500j'), -0.0, 0.0)
|
|
check(complex('1e-500-1e-500j'), 0.0, -0.0)
|
|
check(complex('-1e-500-1e-500j'), -0.0, -0.0)
|
|
|
|
# SF bug 543840: complex(string) accepts strings with \0
|
|
# Fixed in 2.3.
|
|
self.assertRaises(ValueError, complex, '1+1j\0j')
|
|
self.assertRaises(ValueError, complex, "")
|
|
self.assertRaises(ValueError, complex, "\0")
|
|
self.assertRaises(ValueError, complex, "3\09")
|
|
self.assertRaises(ValueError, complex, "1+")
|
|
self.assertRaises(ValueError, complex, "1+1j+1j")
|
|
self.assertRaises(ValueError, complex, "--")
|
|
self.assertRaises(ValueError, complex, "(1+2j")
|
|
self.assertRaises(ValueError, complex, "1+2j)")
|
|
self.assertRaises(ValueError, complex, "1+(2j)")
|
|
self.assertRaises(ValueError, complex, "(1+2j)123")
|
|
self.assertRaises(ValueError, complex, "x")
|
|
self.assertRaises(ValueError, complex, "1j+2")
|
|
self.assertRaises(ValueError, complex, "1e1ej")
|
|
self.assertRaises(ValueError, complex, "1e++1ej")
|
|
self.assertRaises(ValueError, complex, ")1+2j(")
|
|
# the following three are accepted by Python 2.6
|
|
self.assertRaises(ValueError, complex, "1..1j")
|
|
self.assertRaises(ValueError, complex, "1.11.1j")
|
|
self.assertRaises(ValueError, complex, "1e1.1j")
|
|
|
|
# check that complex accepts long unicode strings
|
|
self.assertIs(type(complex("1"*500)), complex)
|
|
# check whitespace processing
|
|
self.assertEqual(complex('\N{EM SPACE}(\N{EN SPACE}1+1j ) '), 1+1j)
|
|
# Invalid unicode string
|
|
# See bpo-34087
|
|
self.assertRaises(ValueError, complex, '\u3053\u3093\u306b\u3061\u306f')
|
|
|
|
def test_constructor_negative_nans_from_string(self):
|
|
self.assertEqual(copysign(1., complex("-nan").real), -1.)
|
|
self.assertEqual(copysign(1., complex("-nanj").imag), -1.)
|
|
self.assertEqual(copysign(1., complex("-nan-nanj").real), -1.)
|
|
self.assertEqual(copysign(1., complex("-nan-nanj").imag), -1.)
|
|
|
|
def test_underscores(self):
|
|
# check underscores
|
|
for lit in VALID_UNDERSCORE_LITERALS:
|
|
if not any(ch in lit for ch in 'xXoObB'):
|
|
self.assertEqual(complex(lit), eval(lit))
|
|
self.assertEqual(complex(lit), complex(lit.replace('_', '')))
|
|
for lit in INVALID_UNDERSCORE_LITERALS:
|
|
if lit in ('0_7', '09_99'): # octals are not recognized here
|
|
continue
|
|
if not any(ch in lit for ch in 'xXoObB'):
|
|
self.assertRaises(ValueError, complex, lit)
|
|
|
|
def test_from_number(self, cls=complex):
|
|
def eq(actual, expected):
|
|
self.assertEqual(actual, expected)
|
|
self.assertIs(type(actual), cls)
|
|
|
|
eq(cls.from_number(3.14), 3.14+0j)
|
|
eq(cls.from_number(3.14j), 3.14j)
|
|
eq(cls.from_number(314), 314.0+0j)
|
|
eq(cls.from_number(OtherComplexSubclass(3.14, 2.72)), 3.14+2.72j)
|
|
eq(cls.from_number(WithComplex(3.14+2.72j)), 3.14+2.72j)
|
|
eq(cls.from_number(WithFloat(3.14)), 3.14+0j)
|
|
eq(cls.from_number(WithIndex(314)), 314.0+0j)
|
|
|
|
cNAN = complex(NAN, NAN)
|
|
x = cls.from_number(cNAN)
|
|
self.assertTrue(x != x)
|
|
self.assertIs(type(x), cls)
|
|
if cls is complex:
|
|
self.assertIs(cls.from_number(cNAN), cNAN)
|
|
|
|
self.assertRaises(TypeError, cls.from_number, '3.14')
|
|
self.assertRaises(TypeError, cls.from_number, b'3.14')
|
|
self.assertRaises(TypeError, cls.from_number, MyInt(314))
|
|
self.assertRaises(TypeError, cls.from_number, {})
|
|
self.assertRaises(TypeError, cls.from_number)
|
|
|
|
def test_from_number_subclass(self):
|
|
self.test_from_number(ComplexSubclass)
|
|
|
|
def test_hash(self):
|
|
for x in range(-30, 30):
|
|
self.assertEqual(hash(x), hash(complex(x, 0)))
|
|
x /= 3.0 # now check against floating-point
|
|
self.assertEqual(hash(x), hash(complex(x, 0.)))
|
|
|
|
self.assertNotEqual(hash(2000005 - 1j), -1)
|
|
|
|
def test_abs(self):
|
|
nums = [complex(x/3., y/7.) for x in range(-9,9) for y in range(-9,9)]
|
|
for num in nums:
|
|
self.assertAlmostEqual((num.real**2 + num.imag**2) ** 0.5, abs(num))
|
|
|
|
self.assertRaises(OverflowError, abs, complex(DBL_MAX, DBL_MAX))
|
|
|
|
def test_repr_str(self):
|
|
def test(v, expected, test_fn=self.assertEqual):
|
|
test_fn(repr(v), expected)
|
|
test_fn(str(v), expected)
|
|
|
|
test(1+6j, '(1+6j)')
|
|
test(1-6j, '(1-6j)')
|
|
|
|
test(-(1+0j), '(-1+-0j)', test_fn=self.assertNotEqual)
|
|
|
|
test(complex(1., INF), "(1+infj)")
|
|
test(complex(1., -INF), "(1-infj)")
|
|
test(complex(INF, 1), "(inf+1j)")
|
|
test(complex(-INF, INF), "(-inf+infj)")
|
|
test(complex(NAN, 1), "(nan+1j)")
|
|
test(complex(1, NAN), "(1+nanj)")
|
|
test(complex(NAN, NAN), "(nan+nanj)")
|
|
test(complex(-NAN, -NAN), "(nan+nanj)")
|
|
|
|
test(complex(0, INF), "infj")
|
|
test(complex(0, -INF), "-infj")
|
|
test(complex(0, NAN), "nanj")
|
|
|
|
self.assertEqual(1-6j,complex(repr(1-6j)))
|
|
self.assertEqual(1+6j,complex(repr(1+6j)))
|
|
self.assertEqual(-6j,complex(repr(-6j)))
|
|
self.assertEqual(6j,complex(repr(6j)))
|
|
|
|
@support.requires_IEEE_754
|
|
def test_negative_zero_repr_str(self):
|
|
def test(v, expected, test_fn=self.assertEqual):
|
|
test_fn(repr(v), expected)
|
|
test_fn(str(v), expected)
|
|
|
|
test(complex(0., 1.), "1j")
|
|
test(complex(-0., 1.), "(-0+1j)")
|
|
test(complex(0., -1.), "-1j")
|
|
test(complex(-0., -1.), "(-0-1j)")
|
|
|
|
test(complex(0., 0.), "0j")
|
|
test(complex(0., -0.), "-0j")
|
|
test(complex(-0., 0.), "(-0+0j)")
|
|
test(complex(-0., -0.), "(-0-0j)")
|
|
|
|
def test_pos(self):
|
|
self.assertEqual(+(1+6j), 1+6j)
|
|
self.assertEqual(+ComplexSubclass(1, 6), 1+6j)
|
|
self.assertIs(type(+ComplexSubclass(1, 6)), complex)
|
|
|
|
def test_neg(self):
|
|
self.assertEqual(-(1+6j), -1-6j)
|
|
|
|
def test_getnewargs(self):
|
|
self.assertEqual((1+2j).__getnewargs__(), (1.0, 2.0))
|
|
self.assertEqual((1-2j).__getnewargs__(), (1.0, -2.0))
|
|
self.assertEqual((2j).__getnewargs__(), (0.0, 2.0))
|
|
self.assertEqual((-0j).__getnewargs__(), (0.0, -0.0))
|
|
self.assertEqual(complex(0, INF).__getnewargs__(), (0.0, INF))
|
|
self.assertEqual(complex(INF, 0).__getnewargs__(), (INF, 0.0))
|
|
|
|
@support.requires_IEEE_754
|
|
def test_plus_minus_0j(self):
|
|
# test that -0j and 0j literals are not identified
|
|
z1, z2 = 0j, -0j
|
|
self.assertFloatsAreIdentical(z1.imag, 0.0)
|
|
self.assertFloatsAreIdentical(z2.imag, -0.0)
|
|
|
|
@support.requires_IEEE_754
|
|
def test_negated_imaginary_literal(self):
|
|
z0 = -0j
|
|
z1 = -7j
|
|
z2 = -1e1000j
|
|
# Note: In versions of Python < 3.2, a negated imaginary literal
|
|
# accidentally ended up with real part 0.0 instead of -0.0, thanks to a
|
|
# modification during CST -> AST translation (see issue #9011). That's
|
|
# fixed in Python 3.2.
|
|
self.assertFloatsAreIdentical(z0.real, -0.0)
|
|
self.assertFloatsAreIdentical(z0.imag, -0.0)
|
|
self.assertFloatsAreIdentical(z1.real, -0.0)
|
|
self.assertFloatsAreIdentical(z1.imag, -7.0)
|
|
self.assertFloatsAreIdentical(z2.real, -0.0)
|
|
self.assertFloatsAreIdentical(z2.imag, -INF)
|
|
|
|
@support.requires_IEEE_754
|
|
def test_overflow(self):
|
|
self.assertEqual(complex("1e500"), complex(INF, 0.0))
|
|
self.assertEqual(complex("-1e500j"), complex(0.0, -INF))
|
|
self.assertEqual(complex("-1e500+1.8e308j"), complex(-INF, INF))
|
|
|
|
@support.requires_IEEE_754
|
|
def test_repr_roundtrip(self):
|
|
vals = [0.0, 1e-500, 1e-315, 1e-200, 0.0123, 3.1415, 1e50, INF, NAN]
|
|
vals += [-v for v in vals]
|
|
|
|
# complex(repr(z)) should recover z exactly, even for complex
|
|
# numbers involving an infinity, nan, or negative zero
|
|
for x in vals:
|
|
for y in vals:
|
|
z = complex(x, y)
|
|
roundtrip = complex(repr(z))
|
|
self.assertComplexesAreIdentical(z, roundtrip)
|
|
|
|
# if we predefine some constants, then eval(repr(z)) should
|
|
# also work, except that it might change the sign of zeros
|
|
inf, nan = float('inf'), float('nan')
|
|
infj, nanj = complex(0.0, inf), complex(0.0, nan)
|
|
for x in vals:
|
|
for y in vals:
|
|
z = complex(x, y)
|
|
roundtrip = eval(repr(z))
|
|
# adding 0.0 has no effect beside changing -0.0 to 0.0
|
|
self.assertFloatsAreIdentical(0.0 + z.real,
|
|
0.0 + roundtrip.real)
|
|
self.assertFloatsAreIdentical(0.0 + z.imag,
|
|
0.0 + roundtrip.imag)
|
|
|
|
def test_format(self):
|
|
# empty format string is same as str()
|
|
self.assertEqual(format(1+3j, ''), str(1+3j))
|
|
self.assertEqual(format(1.5+3.5j, ''), str(1.5+3.5j))
|
|
self.assertEqual(format(3j, ''), str(3j))
|
|
self.assertEqual(format(3.2j, ''), str(3.2j))
|
|
self.assertEqual(format(3+0j, ''), str(3+0j))
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self.assertEqual(format(3.2+0j, ''), str(3.2+0j))
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# empty presentation type should still be analogous to str,
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# even when format string is nonempty (issue #5920).
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self.assertEqual(format(3.2+0j, '-'), str(3.2+0j))
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self.assertEqual(format(3.2+0j, '<'), str(3.2+0j))
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z = 4/7. - 100j/7.
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self.assertEqual(format(z, ''), str(z))
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self.assertEqual(format(z, '-'), str(z))
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self.assertEqual(format(z, '<'), str(z))
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self.assertEqual(format(z, '10'), str(z))
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z = complex(0.0, 3.0)
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self.assertEqual(format(z, ''), str(z))
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self.assertEqual(format(z, '-'), str(z))
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self.assertEqual(format(z, '<'), str(z))
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self.assertEqual(format(z, '2'), str(z))
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z = complex(-0.0, 2.0)
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self.assertEqual(format(z, ''), str(z))
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self.assertEqual(format(z, '-'), str(z))
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self.assertEqual(format(z, '<'), str(z))
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self.assertEqual(format(z, '3'), str(z))
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self.assertEqual(format(1+3j, 'g'), '1+3j')
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self.assertEqual(format(3j, 'g'), '0+3j')
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self.assertEqual(format(1.5+3.5j, 'g'), '1.5+3.5j')
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self.assertEqual(format(1.5+3.5j, '+g'), '+1.5+3.5j')
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self.assertEqual(format(1.5-3.5j, '+g'), '+1.5-3.5j')
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self.assertEqual(format(1.5-3.5j, '-g'), '1.5-3.5j')
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self.assertEqual(format(1.5+3.5j, ' g'), ' 1.5+3.5j')
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self.assertEqual(format(1.5-3.5j, ' g'), ' 1.5-3.5j')
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self.assertEqual(format(-1.5+3.5j, ' g'), '-1.5+3.5j')
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self.assertEqual(format(-1.5-3.5j, ' g'), '-1.5-3.5j')
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|
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self.assertEqual(format(-1.5-3.5e-20j, 'g'), '-1.5-3.5e-20j')
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self.assertEqual(format(-1.5-3.5j, 'f'), '-1.500000-3.500000j')
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self.assertEqual(format(-1.5-3.5j, 'F'), '-1.500000-3.500000j')
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self.assertEqual(format(-1.5-3.5j, 'e'), '-1.500000e+00-3.500000e+00j')
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self.assertEqual(format(-1.5-3.5j, '.2e'), '-1.50e+00-3.50e+00j')
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self.assertEqual(format(-1.5-3.5j, '.2E'), '-1.50E+00-3.50E+00j')
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self.assertEqual(format(-1.5e10-3.5e5j, '.2G'), '-1.5E+10-3.5E+05j')
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|
|
|
self.assertEqual(format(1.5+3j, '<20g'), '1.5+3j ')
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self.assertEqual(format(1.5+3j, '*<20g'), '1.5+3j**************')
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self.assertEqual(format(1.5+3j, '>20g'), ' 1.5+3j')
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|
self.assertEqual(format(1.5+3j, '^20g'), ' 1.5+3j ')
|
|
self.assertEqual(format(1.5+3j, '<20'), '(1.5+3j) ')
|
|
self.assertEqual(format(1.5+3j, '>20'), ' (1.5+3j)')
|
|
self.assertEqual(format(1.5+3j, '^20'), ' (1.5+3j) ')
|
|
self.assertEqual(format(1.123-3.123j, '^20.2'), ' (1.1-3.1j) ')
|
|
|
|
self.assertEqual(format(1.5+3j, '20.2f'), ' 1.50+3.00j')
|
|
self.assertEqual(format(1.5+3j, '>20.2f'), ' 1.50+3.00j')
|
|
self.assertEqual(format(1.5+3j, '<20.2f'), '1.50+3.00j ')
|
|
self.assertEqual(format(1.5e20+3j, '<20.2f'), '150000000000000000000.00+3.00j')
|
|
self.assertEqual(format(1.5e20+3j, '>40.2f'), ' 150000000000000000000.00+3.00j')
|
|
self.assertEqual(format(1.5e20+3j, '^40,.2f'), ' 150,000,000,000,000,000,000.00+3.00j ')
|
|
self.assertEqual(format(1.5e21+3j, '^40,.2f'), ' 1,500,000,000,000,000,000,000.00+3.00j ')
|
|
self.assertEqual(format(1.5e21+3000j, ',.2f'), '1,500,000,000,000,000,000,000.00+3,000.00j')
|
|
|
|
# Issue 7094: Alternate formatting (specified by #)
|
|
self.assertEqual(format(1+1j, '.0e'), '1e+00+1e+00j')
|
|
self.assertEqual(format(1+1j, '#.0e'), '1.e+00+1.e+00j')
|
|
self.assertEqual(format(1+1j, '.0f'), '1+1j')
|
|
self.assertEqual(format(1+1j, '#.0f'), '1.+1.j')
|
|
self.assertEqual(format(1.1+1.1j, 'g'), '1.1+1.1j')
|
|
self.assertEqual(format(1.1+1.1j, '#g'), '1.10000+1.10000j')
|
|
|
|
# Alternate doesn't make a difference for these, they format the same with or without it
|
|
self.assertEqual(format(1+1j, '.1e'), '1.0e+00+1.0e+00j')
|
|
self.assertEqual(format(1+1j, '#.1e'), '1.0e+00+1.0e+00j')
|
|
self.assertEqual(format(1+1j, '.1f'), '1.0+1.0j')
|
|
self.assertEqual(format(1+1j, '#.1f'), '1.0+1.0j')
|
|
|
|
# Misc. other alternate tests
|
|
self.assertEqual(format((-1.5+0.5j), '#f'), '-1.500000+0.500000j')
|
|
self.assertEqual(format((-1.5+0.5j), '#.0f'), '-2.+0.j')
|
|
self.assertEqual(format((-1.5+0.5j), '#e'), '-1.500000e+00+5.000000e-01j')
|
|
self.assertEqual(format((-1.5+0.5j), '#.0e'), '-2.e+00+5.e-01j')
|
|
self.assertEqual(format((-1.5+0.5j), '#g'), '-1.50000+0.500000j')
|
|
self.assertEqual(format((-1.5+0.5j), '.0g'), '-2+0.5j')
|
|
self.assertEqual(format((-1.5+0.5j), '#.0g'), '-2.+0.5j')
|
|
|
|
# zero padding is invalid
|
|
self.assertRaises(ValueError, (1.5+0.5j).__format__, '010f')
|
|
|
|
# '=' alignment is invalid
|
|
self.assertRaises(ValueError, (1.5+3j).__format__, '=20')
|
|
|
|
# integer presentation types are an error
|
|
for t in 'bcdoxX':
|
|
self.assertRaises(ValueError, (1.5+0.5j).__format__, t)
|
|
|
|
# make sure everything works in ''.format()
|
|
self.assertEqual('*{0:.3f}*'.format(3.14159+2.71828j), '*3.142+2.718j*')
|
|
|
|
# issue 3382
|
|
self.assertEqual(format(complex(NAN, NAN), 'f'), 'nan+nanj')
|
|
self.assertEqual(format(complex(1, NAN), 'f'), '1.000000+nanj')
|
|
self.assertEqual(format(complex(NAN, 1), 'f'), 'nan+1.000000j')
|
|
self.assertEqual(format(complex(NAN, -1), 'f'), 'nan-1.000000j')
|
|
self.assertEqual(format(complex(NAN, NAN), 'F'), 'NAN+NANj')
|
|
self.assertEqual(format(complex(1, NAN), 'F'), '1.000000+NANj')
|
|
self.assertEqual(format(complex(NAN, 1), 'F'), 'NAN+1.000000j')
|
|
self.assertEqual(format(complex(NAN, -1), 'F'), 'NAN-1.000000j')
|
|
self.assertEqual(format(complex(INF, INF), 'f'), 'inf+infj')
|
|
self.assertEqual(format(complex(1, INF), 'f'), '1.000000+infj')
|
|
self.assertEqual(format(complex(INF, 1), 'f'), 'inf+1.000000j')
|
|
self.assertEqual(format(complex(INF, -1), 'f'), 'inf-1.000000j')
|
|
self.assertEqual(format(complex(INF, INF), 'F'), 'INF+INFj')
|
|
self.assertEqual(format(complex(1, INF), 'F'), '1.000000+INFj')
|
|
self.assertEqual(format(complex(INF, 1), 'F'), 'INF+1.000000j')
|
|
self.assertEqual(format(complex(INF, -1), 'F'), 'INF-1.000000j')
|
|
|
|
|
|
if __name__ == "__main__":
|
|
unittest.main()
|