| 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() |
