import unittest from random import random from math import atan2, isnan, copysign import operator 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.assertTrue(abs((x-y)/y) < eps) def assertFloatsAreIdentical(self, x, y): """assert that floats x and y are identical, in the sense that: (1) both x and y are nans, or (2) both x and y are infinities, with the same sign, or (3) both x and y are zeros, with the same sign, or (4) x and y are both finite and nonzero, and x == y """ msg = 'floats {!r} and {!r} are not identical' if isnan(x) or isnan(y): if isnan(x) and isnan(y): return elif x == y: if x != 0.0: return # both zero; check that signs match elif copysign(1.0, x) == copysign(1.0, y): return else: msg += ': zeros have different signs' self.fail(msg.format(x, y)) 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 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.__truediv__(x) self.assertClose(q, y) if y != 0: q = z / y self.assertClose(q, x) q = z.__truediv__(y) self.assertClose(q, x) def test_truediv(self): simple_real = [float(i) for i in range(-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 range(100): self.check_div(complex(random(), random()), complex(random(), random())) self.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j) # FIXME: The following currently crashes on Alpha # self.assertRaises(OverflowError, pow, 1e200+1j, 1e200+1j) self.assertAlmostEqual(complex.__truediv__(2+0j, 1+1j), 1-1j) self.assertRaises(ZeroDivisionError, complex.__truediv__, 1+1j, 0+0j) for denom_real, denom_imag in [(0, NAN), (NAN, 0), (NAN, NAN)]: z = complex(0, 0) / complex(denom_real, denom_imag) self.assertTrue(isnan(z.real)) self.assertTrue(isnan(z.imag)) def test_floordiv(self): self.assertRaises(TypeError, complex.__floordiv__, 3+0j, 1.5+0j) self.assertRaises(TypeError, complex.__floordiv__, 3+0j, 0+0j) def test_richcompare(self): self.assertIs(complex.__eq__(1+1j, 1 << 10000), False) self.assertRaises(TypeError, complex.__lt__, 1+1j, None) 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.assertFalse(complex.__eq__(1j, None), False) self.assertFalse(complex.__eq__(1j, NotImplemented), False) for i in range(1, 100): f = i / 100.0 self.assertIs(complex.__eq__(f+0j, f), True) self.assertIs(complex.__ne__(f+0j, f), False) self.assertIs(complex.__eq__(complex(f, f), f), False) self.assertIs(complex.__ne__(complex(f, f), f), 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) self.assertRaises(TypeError, operator.lt, 1+1j, 2+2j) self.assertRaises(TypeError, operator.le, 1+1j, 2+2j) self.assertRaises(TypeError, operator.gt, 1+1j, 2+2j) self.assertRaises(TypeError, operator.ge, 1+1j, 2+2j) self.assertIs(operator.eq(1+1j, 1+1j), True) self.assertIs(operator.eq(1+1j, 2+2j), False) self.assertIs(operator.ne(1+1j, 1+1j), False) self.assertIs(operator.ne(1+1j, 2+2j), True) #def test_richcompare_boundaries(self): #def check(n, deltas, is_equal, imag=0.0): #for delta in deltas: # i = n + delta #z = complex(i, imag) #self.assertIs(complex.__eq__(z, i), is_equal(delta)) #self.assertIs(complex.__ne__(z, i), not is_equal(delta)) # currently failing, though normal ones are working, maybe due to # currently buggy div operation # For IEEE-754 doubles the following should hold: # x in [2 ** (52 + i), 2 ** (53 + i + 1)] -> x mod 2 ** i == 0 # where the interval is representable, of course. #for i in range(1, 10): # pow = 52 + i # mult = 2 ** i # check(2 ** pow, range(1, 101), lambda delta: delta % mult == 0) # check(2 ** pow, range(1, 101), lambda delta: False, float(i)) #check(2 ** 53, range(-100, 0), lambda delta: True) def test_mod(self): # % is no longer supported on complex numbers self.assertRaises(TypeError, (1+1j).__mod__, 0+0j) self.assertRaises(TypeError, lambda: (3.33+4.43j) % 0) self.assertRaises(TypeError, (1+1j).__mod__, 4.3j) def test_divmod(self): # actually divmod is deprecated, though we have still the impl. #self.assertRaises(TypeError, divmod, 1+1j, 1+0j) #self.assertRaises(TypeError, divmod, 1+1j, 0+0j) # dummy test c = 1+1j self.assertEqual(str(c.__divmod__), " of (1.0000000000000000+1.0000000000000000j)>") 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 range(100): self.assertTrue(complex(random() + 1e-6, random() + 1e-6)) self.assertTrue(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.assertRaises(TypeError, complex, {}) self.assertRaises(TypeError, complex, NS(1.5)) self.assertRaises(TypeError, complex, NS(1)) self.assertAlmostEqual(complex("1+10j"), 1+10j) self.assertAlmostEqual(complex(10), 10+0j) self.assertAlmostEqual(complex(10.0), 10+0j) self.assertAlmostEqual(complex(10), 10+0j) self.assertAlmostEqual(complex(10+0j), 10+0j) self.assertAlmostEqual(complex(1, 10), 1+10j) self.assertAlmostEqual(complex(1, 10), 1+10j) self.assertAlmostEqual(complex(1, 10.0), 1+10j) self.assertAlmostEqual(complex(1, 10), 1+10j) self.assertAlmostEqual(complex(1, 10), 1+10j) self.assertAlmostEqual(complex(1, 10.0), 1+10j) self.assertAlmostEqual(complex(1.0, 10), 1+10j) self.assertAlmostEqual(complex(1.0, 10), 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(314), 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(314, 0), 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("3.14+1J"), 3.14+1j) self.assertAlmostEqual(complex(" ( +3.14-6J )"), 3.14-6j) self.assertAlmostEqual(complex(" ( +3.14-J )"), 3.14-1j) self.assertAlmostEqual(complex(" ( +3.14+j )"), 3.14+1j) self.assertAlmostEqual(complex("J"), 1j) self.assertAlmostEqual(complex("( j )"), 1j) self.assertAlmostEqual(complex("+J"), 1j) self.assertAlmostEqual(complex("( -j)"), -1j) self.assertAlmostEqual(complex('1e-500'), 0.0 + 0.0j) self.assertAlmostEqual(complex('-1e-500j'), 0.0 - 0.0j) self.assertAlmostEqual(complex('-1e-500+1e-500j'), -0.0 + 0.0j) # class complex2(complex): pass # self.assertAlmostEqual(complex(complex2(1+1j)), 1+1j) # currently no support for keyword arguments #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.assertTrue(complex(c) is c) del c self.assertRaises(TypeError, complex, "1", "1") self.assertRaises(TypeError, complex, 1, "1") # 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, int, 5+3j) self.assertRaises(TypeError, float, 5+3j) self.assertRaises(ValueError, complex, "") self.assertRaises(TypeError, complex, None) #self.assertRaisesRegex(TypeError, "not 'NoneType'", 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") 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.assertEqual(type(complex("1"*500)), complex) # check whitespace processing # self.assertEqual(complex('\N{EM SPACE}(\N{EN SPACE}1+1j ) '), 1+1j) # FIXME: subclassing exceptions is not really working! #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 # FIXME: currently complex does not call internal __float__ method # FIXME: complex does not support keyword args 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 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.))) 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)) def test_repr_str(self): # this test case is actually working but failing nevertheless o.O? #self.assertNotEqual(len(str(-(1+0j))), len('(-1+-0j)')) self.assertEqual(str(complex(1., INF)), "(1+infj)") self.assertEqual(str(complex(1., -INF)), "(1-infj)") self.assertEqual(str(complex(INF, 1)), "(inf+1j)") self.assertEqual(str(complex(-INF, INF)), "(-inf+infj)") self.assertEqual(str(complex(NAN, 1)), "(nan+1j)") self.assertEqual(str(complex(1, NAN)), "(1+nanj)") self.assertEqual(str(complex(NAN, NAN)), "(nan+nanj)") self.assertEqual(str(complex(0, INF)), "infj") self.assertEqual(str(complex(0, -INF)), "-infj") self.assertEqual(str(complex(0, NAN)), "nanj") 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)) def test_plus_minus_0j(self): # test that -0j and 0j literals are not identified z1, z2 = 0j, -0j self.assertEqual(atan2(z1.imag, -1.), atan2(0., -1.)) self.assertEqual(atan2(z2.imag, -1.), atan2(-0., -1.)) 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) 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)) 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.assertFloatsAreIdentical(z.real, roundtrip.real) self.assertFloatsAreIdentical(z.imag, roundtrip.imag) # Removed some tests that require eval() def test_main(): unittest.main() if __name__ == "__main__": test_main()