/Lib/test/test_complex.py
http://unladen-swallow.googlecode.com/ · Python · 398 lines · 339 code · 45 blank · 14 comment · 27 complexity · 2d3b675df939f2cdd180b82aa5fc4a3f MD5 · raw file
- import unittest, os
- from test import test_support
- import warnings
- warnings.filterwarnings(
- "ignore",
- category=DeprecationWarning,
- message=".*complex divmod.*are deprecated"
- )
- from random import random
- from math import atan2
- INF = float("inf")
- NAN = float("nan")
- # These tests ensure that complex math does the right thing
- class ComplexTest(unittest.TestCase):
- def assertAlmostEqual(self, a, b):
- if isinstance(a, complex):
- if isinstance(b, complex):
- unittest.TestCase.assertAlmostEqual(self, a.real, b.real)
- unittest.TestCase.assertAlmostEqual(self, a.imag, b.imag)
- else:
- unittest.TestCase.assertAlmostEqual(self, a.real, b)
- unittest.TestCase.assertAlmostEqual(self, a.imag, 0.)
- else:
- if isinstance(b, complex):
- unittest.TestCase.assertAlmostEqual(self, a, b.real)
- unittest.TestCase.assertAlmostEqual(self, 0., b.imag)
- else:
- unittest.TestCase.assertAlmostEqual(self, a, b)
- def assertCloseAbs(self, x, y, eps=1e-9):
- """Return true iff floats x and y "are close\""""
- # put the one with larger magnitude second
- if abs(x) > abs(y):
- x, y = y, x
- if y == 0:
- return abs(x) < eps
- if x == 0:
- return abs(y) < eps
- # check that relative difference < eps
- self.assert_(abs((x-y)/y) < eps)
- def assertClose(self, x, y, eps=1e-9):
- """Return true iff complexes x and y "are close\""""
- self.assertCloseAbs(x.real, y.real, eps)
- self.assertCloseAbs(x.imag, y.imag, eps)
- def assertIs(self, a, b):
- self.assert_(a is b)
- def check_div(self, x, y):
- """Compute complex z=x*y, and check that z/x==y and z/y==x."""
- z = x * y
- if x != 0:
- q = z / x
- self.assertClose(q, y)
- q = z.__div__(x)
- self.assertClose(q, y)
- q = z.__truediv__(x)
- self.assertClose(q, y)
- if y != 0:
- q = z / y
- self.assertClose(q, x)
- q = z.__div__(y)
- self.assertClose(q, x)
- q = z.__truediv__(y)
- self.assertClose(q, x)
- def test_div(self):
- simple_real = [float(i) for i in xrange(-5, 6)]
- simple_complex = [complex(x, y) for x in simple_real for y in simple_real]
- for x in simple_complex:
- for y in simple_complex:
- self.check_div(x, y)
- # A naive complex division algorithm (such as in 2.0) is very prone to
- # nonsense errors for these (overflows and underflows).
- self.check_div(complex(1e200, 1e200), 1+0j)
- self.check_div(complex(1e-200, 1e-200), 1+0j)
- # Just for fun.
- for i in xrange(100):
- self.check_div(complex(random(), random()),
- complex(random(), random()))
- self.assertRaises(ZeroDivisionError, complex.__div__, 1+1j, 0+0j)
- # FIXME: The following currently crashes on Alpha
- # self.assertRaises(OverflowError, pow, 1e200+1j, 1e200+1j)
- def test_truediv(self):
- self.assertAlmostEqual(complex.__truediv__(2+0j, 1+1j), 1-1j)
- self.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j)
- def test_floordiv(self):
- self.assertAlmostEqual(complex.__floordiv__(3+0j, 1.5+0j), 2)
- self.assertRaises(ZeroDivisionError, complex.__floordiv__, 3+0j, 0+0j)
- def test_coerce(self):
- self.assertRaises(OverflowError, complex.__coerce__, 1+1j, 1L<<10000)
- def test_richcompare(self):
- self.assertRaises(OverflowError, complex.__eq__, 1+1j, 1L<<10000)
- self.assertEqual(complex.__lt__(1+1j, None), NotImplemented)
- self.assertIs(complex.__eq__(1+1j, 1+1j), True)
- self.assertIs(complex.__eq__(1+1j, 2+2j), False)
- self.assertIs(complex.__ne__(1+1j, 1+1j), False)
- self.assertIs(complex.__ne__(1+1j, 2+2j), True)
- self.assertRaises(TypeError, complex.__lt__, 1+1j, 2+2j)
- self.assertRaises(TypeError, complex.__le__, 1+1j, 2+2j)
- self.assertRaises(TypeError, complex.__gt__, 1+1j, 2+2j)
- self.assertRaises(TypeError, complex.__ge__, 1+1j, 2+2j)
- def test_mod(self):
- self.assertRaises(ZeroDivisionError, (1+1j).__mod__, 0+0j)
- a = 3.33+4.43j
- try:
- a % 0
- except ZeroDivisionError:
- pass
- else:
- self.fail("modulo parama can't be 0")
- def test_divmod(self):
- self.assertRaises(ZeroDivisionError, divmod, 1+1j, 0+0j)
- def test_pow(self):
- self.assertAlmostEqual(pow(1+1j, 0+0j), 1.0)
- self.assertAlmostEqual(pow(0+0j, 2+0j), 0.0)
- self.assertRaises(ZeroDivisionError, pow, 0+0j, 1j)
- self.assertAlmostEqual(pow(1j, -1), 1/1j)
- self.assertAlmostEqual(pow(1j, 200), 1)
- self.assertRaises(ValueError, pow, 1+1j, 1+1j, 1+1j)
- a = 3.33+4.43j
- self.assertEqual(a ** 0j, 1)
- self.assertEqual(a ** 0.+0.j, 1)
- self.assertEqual(3j ** 0j, 1)
- self.assertEqual(3j ** 0, 1)
- try:
- 0j ** a
- except ZeroDivisionError:
- pass
- else:
- self.fail("should fail 0.0 to negative or complex power")
- try:
- 0j ** (3-2j)
- except ZeroDivisionError:
- pass
- else:
- self.fail("should fail 0.0 to negative or complex power")
- # The following is used to exercise certain code paths
- self.assertEqual(a ** 105, a ** 105)
- self.assertEqual(a ** -105, a ** -105)
- self.assertEqual(a ** -30, a ** -30)
- self.assertEqual(0.0j ** 0, 1)
- b = 5.1+2.3j
- self.assertRaises(ValueError, pow, a, b, 0)
- def test_boolcontext(self):
- for i in xrange(100):
- self.assert_(complex(random() + 1e-6, random() + 1e-6))
- self.assert_(not complex(0.0, 0.0))
- def test_conjugate(self):
- self.assertClose(complex(5.3, 9.8).conjugate(), 5.3-9.8j)
- def test_constructor(self):
- class OS:
- def __init__(self, value): self.value = value
- def __complex__(self): return self.value
- class NS(object):
- def __init__(self, value): self.value = value
- def __complex__(self): return self.value
- self.assertEqual(complex(OS(1+10j)), 1+10j)
- self.assertEqual(complex(NS(1+10j)), 1+10j)
- self.assertRaises(TypeError, complex, OS(None))
- self.assertRaises(TypeError, complex, NS(None))
- self.assertAlmostEqual(complex("1+10j"), 1+10j)
- self.assertAlmostEqual(complex(10), 10+0j)
- self.assertAlmostEqual(complex(10.0), 10+0j)
- self.assertAlmostEqual(complex(10L), 10+0j)
- self.assertAlmostEqual(complex(10+0j), 10+0j)
- self.assertAlmostEqual(complex(1,10), 1+10j)
- self.assertAlmostEqual(complex(1,10L), 1+10j)
- self.assertAlmostEqual(complex(1,10.0), 1+10j)
- self.assertAlmostEqual(complex(1L,10), 1+10j)
- self.assertAlmostEqual(complex(1L,10L), 1+10j)
- self.assertAlmostEqual(complex(1L,10.0), 1+10j)
- self.assertAlmostEqual(complex(1.0,10), 1+10j)
- self.assertAlmostEqual(complex(1.0,10L), 1+10j)
- self.assertAlmostEqual(complex(1.0,10.0), 1+10j)
- self.assertAlmostEqual(complex(3.14+0j), 3.14+0j)
- self.assertAlmostEqual(complex(3.14), 3.14+0j)
- self.assertAlmostEqual(complex(314), 314.0+0j)
- self.assertAlmostEqual(complex(314L), 314.0+0j)
- self.assertAlmostEqual(complex(3.14+0j, 0j), 3.14+0j)
- self.assertAlmostEqual(complex(3.14, 0.0), 3.14+0j)
- self.assertAlmostEqual(complex(314, 0), 314.0+0j)
- self.assertAlmostEqual(complex(314L, 0L), 314.0+0j)
- self.assertAlmostEqual(complex(0j, 3.14j), -3.14+0j)
- self.assertAlmostEqual(complex(0.0, 3.14j), -3.14+0j)
- self.assertAlmostEqual(complex(0j, 3.14), 3.14j)
- self.assertAlmostEqual(complex(0.0, 3.14), 3.14j)
- self.assertAlmostEqual(complex("1"), 1+0j)
- self.assertAlmostEqual(complex("1j"), 1j)
- self.assertAlmostEqual(complex(), 0)
- self.assertAlmostEqual(complex("-1"), -1)
- self.assertAlmostEqual(complex("+1"), +1)
- self.assertAlmostEqual(complex("(1+2j)"), 1+2j)
- self.assertAlmostEqual(complex("(1.3+2.2j)"), 1.3+2.2j)
- self.assertAlmostEqual(complex("1E-500"), 1e-500+0j)
- self.assertAlmostEqual(complex("1e-500J"), 1e-500j)
- self.assertAlmostEqual(complex("+1e-315-1e-400j"), 1e-315-1e-400j)
- class complex2(complex): pass
- self.assertAlmostEqual(complex(complex2(1+1j)), 1+1j)
- self.assertAlmostEqual(complex(real=17, imag=23), 17+23j)
- self.assertAlmostEqual(complex(real=17+23j), 17+23j)
- self.assertAlmostEqual(complex(real=17+23j, imag=23), 17+46j)
- self.assertAlmostEqual(complex(real=1+2j, imag=3+4j), -3+5j)
- # check that the sign of a zero in the real or imaginary part
- # is preserved when constructing from two floats. (These checks
- # are harmless on systems without support for signed zeros.)
- def split_zeros(x):
- """Function that produces different results for 0. and -0."""
- return atan2(x, -1.)
- self.assertEqual(split_zeros(complex(1., 0.).imag), split_zeros(0.))
- self.assertEqual(split_zeros(complex(1., -0.).imag), split_zeros(-0.))
- self.assertEqual(split_zeros(complex(0., 1.).real), split_zeros(0.))
- self.assertEqual(split_zeros(complex(-0., 1.).real), split_zeros(-0.))
- c = 3.14 + 1j
- self.assert_(complex(c) is c)
- del c
- self.assertRaises(TypeError, complex, "1", "1")
- self.assertRaises(TypeError, complex, 1, "1")
- self.assertEqual(complex(" 3.14+J "), 3.14+1j)
- if test_support.have_unicode:
- self.assertEqual(complex(unicode(" 3.14+J ")), 3.14+1j)
- # SF bug 543840: complex(string) accepts strings with \0
- # Fixed in 2.3.
- self.assertRaises(ValueError, complex, '1+1j\0j')
- self.assertRaises(TypeError, int, 5+3j)
- self.assertRaises(TypeError, long, 5+3j)
- self.assertRaises(TypeError, float, 5+3j)
- self.assertRaises(ValueError, complex, "")
- self.assertRaises(TypeError, complex, None)
- self.assertRaises(ValueError, complex, "\0")
- self.assertRaises(ValueError, complex, "3\09")
- self.assertRaises(TypeError, complex, "1", "2")
- self.assertRaises(TypeError, complex, "1", 42)
- self.assertRaises(TypeError, complex, 1, "2")
- 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")
- if test_support.have_unicode:
- self.assertRaises(ValueError, complex, unicode("1"*500))
- self.assertRaises(ValueError, complex, unicode("x"))
- class EvilExc(Exception):
- pass
- class evilcomplex:
- def __complex__(self):
- raise EvilExc
- self.assertRaises(EvilExc, complex, evilcomplex())
- class float2:
- def __init__(self, value):
- self.value = value
- def __float__(self):
- return self.value
- self.assertAlmostEqual(complex(float2(42.)), 42)
- self.assertAlmostEqual(complex(real=float2(17.), imag=float2(23.)), 17+23j)
- self.assertRaises(TypeError, complex, float2(None))
- 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
- self.assertAlmostEqual(complex(complex0(1j)), 42j)
- self.assertAlmostEqual(complex(complex1(1j)), 2j)
- self.assertRaises(TypeError, complex, complex2(1j))
- def test_hash(self):
- for x in xrange(-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.)))
- def test_abs(self):
- nums = [complex(x/3., y/7.) for x in xrange(-9,9) for y in xrange(-9,9)]
- for num in nums:
- self.assertAlmostEqual((num.real**2 + num.imag**2) ** 0.5, abs(num))
- def test_repr(self):
- self.assertEqual(repr(1+6j), '(1+6j)')
- self.assertEqual(repr(1-6j), '(1-6j)')
- self.assertNotEqual(repr(-(1+0j)), '(-1+-0j)')
- 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)))
- self.assertEqual(repr(complex(1., INF)), "(1+inf*j)")
- self.assertEqual(repr(complex(1., -INF)), "(1-inf*j)")
- self.assertEqual(repr(complex(INF, 1)), "(inf+1j)")
- self.assertEqual(repr(complex(-INF, INF)), "(-inf+inf*j)")
- self.assertEqual(repr(complex(NAN, 1)), "(nan+1j)")
- self.assertEqual(repr(complex(1, NAN)), "(1+nan*j)")
- self.assertEqual(repr(complex(NAN, NAN)), "(nan+nan*j)")
- self.assertEqual(repr(complex(0, INF)), "inf*j")
- self.assertEqual(repr(complex(0, -INF)), "-inf*j")
- self.assertEqual(repr(complex(0, NAN)), "nan*j")
- def test_neg(self):
- self.assertEqual(-(1+6j), -1-6j)
- def test_file(self):
- a = 3.33+4.43j
- b = 5.1+2.3j
- fo = None
- try:
- fo = open(test_support.TESTFN, "wb")
- print >>fo, a, b
- fo.close()
- fo = open(test_support.TESTFN, "rb")
- self.assertEqual(fo.read(), "%s %s\n" % (a, b))
- finally:
- if (fo is not None) and (not fo.closed):
- fo.close()
- try:
- os.remove(test_support.TESTFN)
- except (OSError, IOError):
- pass
- 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))
- if float.__getformat__("double").startswith("IEEE"):
- def test_plus_minus_0j(self):
- # test that -0j and 0j literals are not identified
- z1, z2 = 0j, -0j
- self.assertEquals(atan2(z1.imag, -1.), atan2(0., -1.))
- self.assertEquals(atan2(z2.imag, -1.), atan2(-0., -1.))
- def test_main():
- test_support.run_unittest(ComplexTest)
- if __name__ == "__main__":
- test_main()