import unittest import sys from test import support from test.test_grammar import (VALID_UNDERSCORE_LITERALS, INVALID_UNDERSCORE_LITERALS) 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 ZERO_DIVISION = ( (1+1j, 0+0j), (1+1j, 0.0), (1+1j, 0), (1.0, 0+0j), (1, 0+0j), ) 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.assertAlmostEqual(complex.__truediv__(2+0j, 1+1j), 1-1j) self.assertRaises(TypeError, operator.truediv, 1j, None) self.assertRaises(TypeError, operator.truediv, None, 1j) 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_truediv_zero_division(self): for a, b in ZERO_DIVISION: with self.assertRaises(ZeroDivisionError): a / b def test_floordiv(self): with self.assertRaises(TypeError): (1+1j) // (1+0j) with self.assertRaises(TypeError): (1+1j) // 1.0 with self.assertRaises(TypeError): (1+1j) // 1 with self.assertRaises(TypeError): 1.0 // (1+0j) with self.assertRaises(TypeError): 1 // (1+0j) def test_floordiv_zero_division(self): for a, b in ZERO_DIVISION: with self.assertRaises(TypeError): a // b def test_richcompare(self): self.assertIs(complex.__eq__(1+1j, 1<<10000), False) self.assertIs(complex.__lt__(1+1j, None), NotImplemented) self.assertIs(complex.__eq__(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) 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.assertIs(complex.__lt__(1+1j, 2+2j), NotImplemented) self.assertIs(complex.__le__(1+1j, 2+2j), NotImplemented) self.assertIs(complex.__gt__(1+1j, 2+2j), NotImplemented) self.assertIs(complex.__ge__(1+1j, 2+2j), NotImplemented) 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) self.assertIs(operator.eq(1+1j, 2.0), False) 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)) # 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_add(self): self.assertEqual(1j + int(+1), complex(+1, 1)) self.assertEqual(1j + int(-1), complex(-1, 1)) self.assertRaises(OverflowError, operator.add, 1j, 10**1000) self.assertRaises(TypeError, operator.add, 1j, None) self.assertRaises(TypeError, operator.add, None, 1j) def test_sub(self): self.assertEqual(1j - int(+1), complex(-1, 1)) self.assertEqual(1j - int(-1), complex(1, 1)) self.assertRaises(OverflowError, operator.sub, 1j, 10**1000) self.assertRaises(TypeError, operator.sub, 1j, None) self.assertRaises(TypeError, operator.sub, None, 1j) def test_mul(self): self.assertEqual(1j * int(20), complex(0, 20)) self.assertEqual(1j * int(-1), complex(0, -1)) self.assertRaises(OverflowError, operator.mul, 1j, 10**1000) self.assertRaises(TypeError, operator.mul, 1j, None) self.assertRaises(TypeError, operator.mul, None, 1j) def test_mod(self): # % is no longer supported on complex numbers with self.assertRaises(TypeError): (1+1j) % (1+0j) with self.assertRaises(TypeError): (1+1j) % 1.0 with self.assertRaises(TypeError): (1+1j) % 1 with self.assertRaises(TypeError): 1.0 % (1+0j) with self.assertRaises(TypeError): 1 % (1+0j) def test_mod_zero_division(self): for a, b in ZERO_DIVISION: with self.assertRaises(TypeError): a % b def test_divmod(self): self.assertRaises(TypeError, divmod, 1+1j, 1+0j) self.assertRaises(TypeError, divmod, 1+1j, 1.0) self.assertRaises(TypeError, divmod, 1+1j, 1) self.assertRaises(TypeError, divmod, 1.0, 1+0j) self.assertRaises(TypeError, divmod, 1, 1+0j) def test_divmod_zero_division(self): for a, b in ZERO_DIVISION: self.assertRaises(TypeError, divmod, a, b) def test_pow(self): self.assertAlmostEqual(pow(1+1j, 0+0j), 1.0) self.assertAlmostEqual(pow(0+0j, 2+0j), 0.0) self.assertEqual(pow(0+0j, 2000+0j), 0.0) self.assertEqual(pow(0, 0+0j), 1.0) self.assertEqual(pow(-1, 0+0j), 1.0) self.assertRaises(ZeroDivisionError, pow, 0+0j, 1j) self.assertRaises(ZeroDivisionError, pow, 0+0j, -1000) self.assertAlmostEqual(pow(1j, -1), 1/1j) self.assertAlmostEqual(pow(1j, 200), 1) self.assertRaises(ValueError, pow, 1+1j, 1+1j, 1+1j) self.assertRaises(OverflowError, pow, 1e200+1j, 1e200+1j) self.assertRaises(TypeError, pow, 1j, None) self.assertRaises(TypeError, pow, None, 1j) self.assertAlmostEqual(pow(1j, 0.5), 0.7071067811865476+0.7071067811865475j) 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) # Check some boundary conditions; some of these used to invoke # undefined behaviour (https://bugs.python.org/issue44698). We're # not actually checking the results of these operations, just making # sure they don't crash (for example when using clang's # UndefinedBehaviourSanitizer). values = (sys.maxsize, sys.maxsize+1, sys.maxsize-1, -sys.maxsize, -sys.maxsize+1, -sys.maxsize+1) for real in values: for imag in values: with self.subTest(real=real, imag=imag): c = complex(real, imag) try: c ** real except OverflowError: pass try: c ** c except OverflowError: pass def test_pow_with_small_integer_exponents(self): # Check that small integer exponents are handled identically # regardless of their type. values = [ complex(5.0, 12.0), complex(5.0e100, 12.0e100), complex(-4.0, INF), complex(INF, 0.0), ] exponents = [-19, -5, -3, -2, -1, 0, 1, 2, 3, 5, 19] for value in values: for exponent in exponents: with self.subTest(value=value, exponent=exponent): try: int_pow = value**exponent except OverflowError: int_pow = "overflow" try: float_pow = value**float(exponent) except OverflowError: float_pow = "overflow" try: complex_pow = value**complex(exponent) except OverflowError: complex_pow = "overflow" self.assertEqual(str(float_pow), str(int_pow)) self.assertEqual(str(complex_pow), str(int_pow)) 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)) self.assertTrue(1j) def test_conjugate(self): self.assertClose(complex(5.3, 9.8).conjugate(), 5.3-9.8j) def test_constructor(self): class NS: def __init__(self, value): self.value = value def __complex__(self): return self.value self.assertEqual(complex(NS(1+10j)), 1+10j) self.assertRaises(TypeError, complex, NS(None)) self.assertRaises(TypeError, complex, {}) self.assertRaises(TypeError, complex, NS(1.5)) self.assertRaises(TypeError, complex, NS(1)) self.assertRaises(TypeError, complex, object()) self.assertRaises(TypeError, complex, NS(4.25+0.5j), object()) 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) self.assertEqual(complex('1-1j'), 1.0 - 1j) self.assertEqual(complex('1J'), 1j) 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.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(") self.assertRaisesRegex( TypeError, "first argument must be a string or a number, not 'dict'", complex, {1:2}, 1) self.assertRaisesRegex( TypeError, "second argument must be a number, not 'dict'", complex, 1, {1:2}) # 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) # Invalid unicode string # See bpo-34087 self.assertRaises(ValueError, complex, '\u3053\u3093\u306b\u3061\u306f') 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 MyIndex: def __init__(self, value): self.value = value def __index__(self): return self.value self.assertAlmostEqual(complex(MyIndex(42)), 42.0+0.0j) self.assertAlmostEqual(complex(123, MyIndex(42)), 123.0+42.0j) self.assertRaises(OverflowError, complex, MyIndex(2**2000)) self.assertRaises(OverflowError, complex, 123, MyIndex(2**2000)) class MyInt: def __int__(self): return 42 self.assertRaises(TypeError, complex, MyInt()) self.assertRaises(TypeError, complex, 123, 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 self.assertEqual(complex(complex0(1j)), 42j) with self.assertWarns(DeprecationWarning): self.assertEqual(complex(complex1(1j)), 2j) self.assertRaises(TypeError, complex, complex2(1j)) def test___complex__(self): z = 3 + 4j self.assertEqual(z.__complex__(), z) self.assertEqual(type(z.__complex__()), complex) class complex_subclass(complex): pass z = complex_subclass(3 + 4j) self.assertEqual(z.__complex__(), 3 + 4j) self.assertEqual(type(z.__complex__()), complex) @support.requires_IEEE_754 def test_constructor_special_numbers(self): class complex2(complex): pass 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 = complex2(x, y) self.assertIs(type(z), complex2) self.assertFloatsAreIdentical(z.real, x) self.assertFloatsAreIdentical(z.imag, y) z = complex(complex2(x, y)) self.assertIs(type(z), complex) self.assertFloatsAreIdentical(z.real, x) self.assertFloatsAreIdentical(z.imag, y) z = complex2(complex(x, y)) self.assertIs(type(z), complex2) self.assertFloatsAreIdentical(z.real, x) self.assertFloatsAreIdentical(z.imag, y) 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_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)) 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): class ComplexSubclass(complex): pass 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.assertEqual(atan2(z1.imag, -1.), atan2(0., -1.)) self.assertEqual(atan2(z2.imag, -1.), atan2(-0., -1.)) @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.assertFloatsAreIdentical(z.real, roundtrip.real) self.assertFloatsAreIdentical(z.imag, roundtrip.imag) # 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)) self.assertEqual(format(3.2+0j, ''), str(3.2+0j)) # empty presentation type should still be analogous to str, # even when format string is nonempty (issue #5920). self.assertEqual(format(3.2+0j, '-'), str(3.2+0j)) self.assertEqual(format(3.2+0j, '<'), str(3.2+0j)) z = 4/7. - 100j/7. self.assertEqual(format(z, ''), str(z)) self.assertEqual(format(z, '-'), str(z)) self.assertEqual(format(z, '<'), str(z)) self.assertEqual(format(z, '10'), str(z)) z = complex(0.0, 3.0) self.assertEqual(format(z, ''), str(z)) self.assertEqual(format(z, '-'), str(z)) self.assertEqual(format(z, '<'), str(z)) self.assertEqual(format(z, '2'), str(z)) z = complex(-0.0, 2.0) self.assertEqual(format(z, ''), str(z)) self.assertEqual(format(z, '-'), str(z)) self.assertEqual(format(z, '<'), str(z)) self.assertEqual(format(z, '3'), str(z)) self.assertEqual(format(1+3j, 'g'), '1+3j') 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(1.5+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()