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845 lines (737 loc) · 35.4 KB
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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)
# TODO: RUSTPYTHON
@unittest.expectedFailure
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()