| import unittest |
| 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 |
| |
| 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.assertIs(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) |
| 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) |
| |
| 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_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): |
| self.assertRaises(TypeError, divmod, 1+1j, 1+0j) |
| self.assertRaises(TypeError, 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 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) |
| 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) |
| |
| 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)) |
| |
| @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_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.))) |
| |
| 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(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_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(support.TESTFN, "w") |
| print(a, b, file=fo) |
| fo.close() |
| fo = open(support.TESTFN, "r") |
| self.assertEqual(fo.read(), ("%s %s\n" % (a, b))) |
| finally: |
| if (fo is not None) and (not fo.closed): |
| fo.close() |
| support.unlink(support.TESTFN) |
| |
| 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') |
| |
| def test_main(): |
| support.run_unittest(ComplexTest) |
| |
| if __name__ == "__main__": |
| test_main() |