mirror of
https://github.com/python/cpython.git
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515 lines
21 KiB
Python
515 lines
21 KiB
Python
import unittest, os
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from test import support
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from random import random
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from math import atan2, isnan, copysign
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INF = float("inf")
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NAN = float("nan")
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# These tests ensure that complex math does the right thing
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class ComplexTest(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.assert_(abs((x-y)/y) < eps)
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def assertFloatsAreIdentical(self, x, y):
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"""assert that 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 isnan(x) or isnan(y):
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if isnan(x) and 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 copysign(1.0, x) == 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 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 assertIs(self, a, b):
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self.assert_(a is b)
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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.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j)
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# FIXME: The following currently crashes on Alpha
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# self.assertRaises(OverflowError, pow, 1e200+1j, 1e200+1j)
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def test_truediv(self):
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self.assertAlmostEqual(complex.__truediv__(2+0j, 1+1j), 1-1j)
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self.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j)
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def test_floordiv(self):
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self.assertRaises(TypeError, complex.__floordiv__, 3+0j, 1.5+0j)
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self.assertRaises(TypeError, complex.__floordiv__, 3+0j, 0+0j)
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def test_richcompare(self):
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self.assertRaises(OverflowError, complex.__eq__, 1+1j, 1<<10000)
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self.assertEqual(complex.__lt__(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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self.assertRaises(TypeError, complex.__lt__, 1+1j, 2+2j)
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self.assertRaises(TypeError, complex.__le__, 1+1j, 2+2j)
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self.assertRaises(TypeError, complex.__gt__, 1+1j, 2+2j)
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self.assertRaises(TypeError, complex.__ge__, 1+1j, 2+2j)
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def test_mod(self):
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# % is no longer supported on complex numbers
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self.assertRaises(TypeError, (1+1j).__mod__, 0+0j)
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self.assertRaises(TypeError, lambda: (3.33+4.43j) % 0)
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self.assertRaises(TypeError, (1+1j).__mod__, 4.3j)
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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, 0+0j)
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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.assertRaises(ZeroDivisionError, pow, 0+0j, 1j)
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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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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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def test_boolcontext(self):
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for i in range(100):
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self.assert_(complex(random() + 1e-6, random() + 1e-6))
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self.assert_(not complex(0.0, 0.0))
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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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class OS:
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def __init__(self, value): self.value = value
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def __complex__(self): return self.value
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class NS(object):
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def __init__(self, value): self.value = value
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def __complex__(self): return self.value
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self.assertEqual(complex(OS(1+10j)), 1+10j)
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self.assertEqual(complex(NS(1+10j)), 1+10j)
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self.assertRaises(TypeError, complex, OS(None))
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self.assertRaises(TypeError, complex, NS(None))
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self.assertAlmostEqual(complex("1+10j"), 1+10j)
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self.assertAlmostEqual(complex(10), 10+0j)
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self.assertAlmostEqual(complex(10.0), 10+0j)
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self.assertAlmostEqual(complex(10), 10+0j)
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self.assertAlmostEqual(complex(10+0j), 10+0j)
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self.assertAlmostEqual(complex(1,10), 1+10j)
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self.assertAlmostEqual(complex(1,10), 1+10j)
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self.assertAlmostEqual(complex(1,10.0), 1+10j)
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self.assertAlmostEqual(complex(1,10), 1+10j)
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self.assertAlmostEqual(complex(1,10), 1+10j)
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self.assertAlmostEqual(complex(1,10.0), 1+10j)
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self.assertAlmostEqual(complex(1.0,10), 1+10j)
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self.assertAlmostEqual(complex(1.0,10), 1+10j)
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self.assertAlmostEqual(complex(1.0,10.0), 1+10j)
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self.assertAlmostEqual(complex(3.14+0j), 3.14+0j)
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self.assertAlmostEqual(complex(3.14), 3.14+0j)
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self.assertAlmostEqual(complex(314), 314.0+0j)
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self.assertAlmostEqual(complex(314), 314.0+0j)
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self.assertAlmostEqual(complex(3.14+0j, 0j), 3.14+0j)
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self.assertAlmostEqual(complex(3.14, 0.0), 3.14+0j)
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self.assertAlmostEqual(complex(314, 0), 314.0+0j)
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self.assertAlmostEqual(complex(314, 0), 314.0+0j)
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self.assertAlmostEqual(complex(0j, 3.14j), -3.14+0j)
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self.assertAlmostEqual(complex(0.0, 3.14j), -3.14+0j)
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self.assertAlmostEqual(complex(0j, 3.14), 3.14j)
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self.assertAlmostEqual(complex(0.0, 3.14), 3.14j)
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self.assertAlmostEqual(complex("1"), 1+0j)
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self.assertAlmostEqual(complex("1j"), 1j)
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self.assertAlmostEqual(complex(), 0)
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self.assertAlmostEqual(complex("-1"), -1)
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self.assertAlmostEqual(complex("+1"), +1)
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self.assertAlmostEqual(complex("(1+2j)"), 1+2j)
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self.assertAlmostEqual(complex("(1.3+2.2j)"), 1.3+2.2j)
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self.assertAlmostEqual(complex("3.14+1J"), 3.14+1j)
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self.assertAlmostEqual(complex(" ( +3.14-6J )"), 3.14-6j)
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self.assertAlmostEqual(complex(" ( +3.14-J )"), 3.14-1j)
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self.assertAlmostEqual(complex(" ( +3.14+j )"), 3.14+1j)
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self.assertAlmostEqual(complex("J"), 1j)
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self.assertAlmostEqual(complex("( j )"), 1j)
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self.assertAlmostEqual(complex("+J"), 1j)
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self.assertAlmostEqual(complex("( -j)"), -1j)
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self.assertAlmostEqual(complex('1e-500'), 0.0 + 0.0j)
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self.assertAlmostEqual(complex('-1e-500j'), 0.0 - 0.0j)
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self.assertAlmostEqual(complex('-1e-500+1e-500j'), -0.0 + 0.0j)
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class complex2(complex): pass
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self.assertAlmostEqual(complex(complex2(1+1j)), 1+1j)
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self.assertAlmostEqual(complex(real=17, imag=23), 17+23j)
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self.assertAlmostEqual(complex(real=17+23j), 17+23j)
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self.assertAlmostEqual(complex(real=17+23j, imag=23), 17+46j)
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self.assertAlmostEqual(complex(real=1+2j, imag=3+4j), -3+5j)
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# check that the sign of a zero in the real or imaginary part
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# is preserved when constructing from two floats. (These checks
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# are harmless on systems without support for signed zeros.)
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def split_zeros(x):
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"""Function that produces different results for 0. and -0."""
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return atan2(x, -1.)
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self.assertEqual(split_zeros(complex(1., 0.).imag), split_zeros(0.))
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self.assertEqual(split_zeros(complex(1., -0.).imag), split_zeros(-0.))
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self.assertEqual(split_zeros(complex(0., 1.).real), split_zeros(0.))
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self.assertEqual(split_zeros(complex(-0., 1.).real), split_zeros(-0.))
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c = 3.14 + 1j
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self.assert_(complex(c) is c)
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del c
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self.assertRaises(TypeError, complex, "1", "1")
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self.assertRaises(TypeError, complex, 1, "1")
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# SF bug 543840: complex(string) accepts strings with \0
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# Fixed in 2.3.
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self.assertRaises(ValueError, complex, '1+1j\0j')
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self.assertRaises(TypeError, int, 5+3j)
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self.assertRaises(TypeError, int, 5+3j)
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self.assertRaises(TypeError, float, 5+3j)
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self.assertRaises(ValueError, complex, "")
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self.assertRaises(TypeError, complex, None)
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self.assertRaises(ValueError, complex, "\0")
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self.assertRaises(ValueError, complex, "3\09")
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self.assertRaises(TypeError, complex, "1", "2")
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self.assertRaises(TypeError, complex, "1", 42)
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self.assertRaises(TypeError, complex, 1, "2")
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self.assertRaises(ValueError, complex, "1+")
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self.assertRaises(ValueError, complex, "1+1j+1j")
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self.assertRaises(ValueError, complex, "--")
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self.assertRaises(ValueError, complex, "(1+2j")
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self.assertRaises(ValueError, complex, "1+2j)")
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self.assertRaises(ValueError, complex, "1+(2j)")
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self.assertRaises(ValueError, complex, "(1+2j)123")
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self.assertRaises(ValueError, complex, "1"*500)
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self.assertRaises(ValueError, complex, "x")
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self.assertRaises(ValueError, complex, "1j+2")
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self.assertRaises(ValueError, complex, "1e1ej")
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self.assertRaises(ValueError, complex, "1e++1ej")
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self.assertRaises(ValueError, complex, ")1+2j(")
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# the following three are accepted by Python 2.6
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self.assertRaises(ValueError, complex, "1..1j")
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self.assertRaises(ValueError, complex, "1.11.1j")
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self.assertRaises(ValueError, complex, "1e1.1j")
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class EvilExc(Exception):
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pass
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class evilcomplex:
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def __complex__(self):
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raise EvilExc
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self.assertRaises(EvilExc, complex, evilcomplex())
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class float2:
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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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self.assertAlmostEqual(complex(float2(42.)), 42)
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self.assertAlmostEqual(complex(real=float2(17.), imag=float2(23.)), 17+23j)
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self.assertRaises(TypeError, complex, float2(None))
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class complex0(complex):
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"""Test usage of __complex__() when inheriting from 'complex'"""
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def __complex__(self):
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return 42j
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class complex1(complex):
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"""Test usage of __complex__() with a __new__() method"""
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def __new__(self, value=0j):
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return complex.__new__(self, 2*value)
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def __complex__(self):
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return self
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class complex2(complex):
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"""Make sure that __complex__() calls fail if anything other than a
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complex is returned"""
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def __complex__(self):
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return None
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self.assertAlmostEqual(complex(complex0(1j)), 42j)
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self.assertAlmostEqual(complex(complex1(1j)), 2j)
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self.assertRaises(TypeError, complex, complex2(1j))
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def test_hash(self):
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for x in range(-30, 30):
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self.assertEqual(hash(x), hash(complex(x, 0)))
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x /= 3.0 # now check against floating point
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self.assertEqual(hash(x), hash(complex(x, 0.)))
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def test_abs(self):
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nums = [complex(x/3., y/7.) for x in range(-9,9) for y in range(-9,9)]
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for num in nums:
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self.assertAlmostEqual((num.real**2 + num.imag**2) ** 0.5, abs(num))
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def test_repr(self):
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self.assertEqual(repr(1+6j), '(1+6j)')
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self.assertEqual(repr(1-6j), '(1-6j)')
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self.assertNotEqual(repr(-(1+0j)), '(-1+-0j)')
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self.assertEqual(1-6j,complex(repr(1-6j)))
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self.assertEqual(1+6j,complex(repr(1+6j)))
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self.assertEqual(-6j,complex(repr(-6j)))
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self.assertEqual(6j,complex(repr(6j)))
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self.assertEqual(repr(complex(1., INF)), "(1+infj)")
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self.assertEqual(repr(complex(1., -INF)), "(1-infj)")
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self.assertEqual(repr(complex(INF, 1)), "(inf+1j)")
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self.assertEqual(repr(complex(-INF, INF)), "(-inf+infj)")
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self.assertEqual(repr(complex(NAN, 1)), "(nan+1j)")
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self.assertEqual(repr(complex(1, NAN)), "(1+nanj)")
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self.assertEqual(repr(complex(NAN, NAN)), "(nan+nanj)")
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self.assertEqual(repr(complex(0, INF)), "infj")
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self.assertEqual(repr(complex(0, -INF)), "-infj")
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self.assertEqual(repr(complex(0, NAN)), "nanj")
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def test_neg(self):
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self.assertEqual(-(1+6j), -1-6j)
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def test_file(self):
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a = 3.33+4.43j
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b = 5.1+2.3j
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fo = None
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try:
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fo = open(support.TESTFN, "w")
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print(a, b, file=fo)
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fo.close()
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fo = open(support.TESTFN, "r")
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self.assertEqual(fo.read(), ("%s %s\n" % (a, b)))
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finally:
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if (fo is not None) and (not fo.closed):
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fo.close()
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try:
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os.remove(support.TESTFN)
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except (OSError, IOError):
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pass
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def test_getnewargs(self):
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self.assertEqual((1+2j).__getnewargs__(), (1.0, 2.0))
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self.assertEqual((1-2j).__getnewargs__(), (1.0, -2.0))
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self.assertEqual((2j).__getnewargs__(), (0.0, 2.0))
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self.assertEqual((-0j).__getnewargs__(), (0.0, -0.0))
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self.assertEqual(complex(0, INF).__getnewargs__(), (0.0, INF))
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self.assertEqual(complex(INF, 0).__getnewargs__(), (INF, 0.0))
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if float.__getformat__("double").startswith("IEEE"):
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def test_plus_minus_0j(self):
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# test that -0j and 0j literals are not identified
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z1, z2 = 0j, -0j
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self.assertEquals(atan2(z1.imag, -1.), atan2(0., -1.))
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self.assertEquals(atan2(z2.imag, -1.), atan2(-0., -1.))
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@unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
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"test requires IEEE 754 doubles")
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def test_repr_roundtrip(self):
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vals = [0.0, 1e-500, 1e-315, 1e-200, 0.0123, 3.1415, 1e50, INF, NAN]
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vals += [-v for v in vals]
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|
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# complex(repr(z)) should recover z exactly, even for complex
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# numbers involving an infinity, nan, or negative zero
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for x in vals:
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for y in vals:
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z = complex(x, y)
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roundtrip = complex(repr(z))
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self.assertFloatsAreIdentical(z.real, roundtrip.real)
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self.assertFloatsAreIdentical(z.imag, roundtrip.imag)
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|
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# if we predefine some constants, then eval(repr(z)) should
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# also work, except that it might change the sign of zeros
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inf, nan = float('inf'), float('nan')
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infj, nanj = complex(0.0, inf), complex(0.0, nan)
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for x in vals:
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for y in vals:
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z = complex(x, y)
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roundtrip = eval(repr(z))
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# adding 0.0 has no effect beside changing -0.0 to 0.0
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self.assertFloatsAreIdentical(0.0 + z.real,
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0.0 + roundtrip.real)
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self.assertFloatsAreIdentical(0.0 + z.imag,
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0.0 + roundtrip.imag)
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|
|
|
def test_format(self):
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# empty format string is same as str()
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self.assertEqual(format(1+3j, ''), str(1+3j))
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self.assertEqual(format(1.5+3.5j, ''), str(1.5+3.5j))
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self.assertEqual(format(3j, ''), str(3j))
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|
self.assertEqual(format(3.2j, ''), str(3.2j))
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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))
|
|
self.assertEqual(format(z, '-'), str(z))
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|
self.assertEqual(format(z, '<'), str(z))
|
|
self.assertEqual(format(z, '10'), str(z))
|
|
|
|
self.assertEqual(format(1+3j, 'g'), '1+3j')
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|
self.assertEqual(format(3j, 'g'), '0+3j')
|
|
self.assertEqual(format(1.5+3.5j, 'g'), '1.5+3.5j')
|
|
|
|
self.assertEqual(format(1.5+3.5j, '+g'), '+1.5+3.5j')
|
|
self.assertEqual(format(1.5-3.5j, '+g'), '+1.5-3.5j')
|
|
self.assertEqual(format(1.5-3.5j, '-g'), '1.5-3.5j')
|
|
self.assertEqual(format(1.5+3.5j, ' g'), ' 1.5+3.5j')
|
|
self.assertEqual(format(1.5-3.5j, ' g'), ' 1.5-3.5j')
|
|
self.assertEqual(format(-1.5+3.5j, ' g'), '-1.5+3.5j')
|
|
self.assertEqual(format(-1.5-3.5j, ' g'), '-1.5-3.5j')
|
|
|
|
self.assertEqual(format(-1.5-3.5e-20j, 'g'), '-1.5-3.5e-20j')
|
|
self.assertEqual(format(-1.5-3.5j, 'f'), '-1.500000-3.500000j')
|
|
self.assertEqual(format(-1.5-3.5j, 'F'), '-1.500000-3.500000j')
|
|
self.assertEqual(format(-1.5-3.5j, 'e'), '-1.500000e+00-3.500000e+00j')
|
|
self.assertEqual(format(-1.5-3.5j, '.2e'), '-1.50e+00-3.50e+00j')
|
|
self.assertEqual(format(-1.5-3.5j, '.2E'), '-1.50E+00-3.50E+00j')
|
|
self.assertEqual(format(-1.5e10-3.5e5j, '.2G'), '-1.5E+10-3.5E+05j')
|
|
|
|
self.assertEqual(format(1.5+3j, '<20g'), '1.5+3j ')
|
|
self.assertEqual(format(1.5+3j, '*<20g'), '1.5+3j**************')
|
|
self.assertEqual(format(1.5+3j, '>20g'), ' 1.5+3j')
|
|
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(1.5e20+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')
|
|
|
|
# alternate is invalid
|
|
self.assertRaises(ValueError, (1.5+0.5j).__format__, '#f')
|
|
|
|
# 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*')
|
|
|
|
def test_main():
|
|
support.run_unittest(ComplexTest)
|
|
|
|
if __name__ == "__main__":
|
|
test_main()
|