from test.support import requires_IEEE_754, cpython_only, import_helper
from test.test_math import parse_testfile, test_file
import test.test_math as test_math
import unittest
import cmath, math
from cmath import phase, polar, rect, pi
import platform
import sys
INF = float('inf')
NAN = float('nan')
complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]]
complex_infinities = [complex(x, y) for x, y in [
(INF, 0.0), # 1st quadrant
(INF, 2.3),
(INF, INF),
(2.3, INF),
(0.0, INF),
(-0.0, INF), # 2nd quadrant
(-2.3, INF),
(-INF, INF),
(-INF, 2.3),
(-INF, 0.0),
(-INF, -0.0), # 3rd quadrant
(-INF, -2.3),
(-INF, -INF),
(-2.3, -INF),
(-0.0, -INF),
(0.0, -INF), # 4th quadrant
(2.3, -INF),
(INF, -INF),
(INF, -2.3),
(INF, -0.0)
]]
complex_nans = [complex(x, y) for x, y in [
(NAN, -INF),
(NAN, -2.3),
(NAN, -0.0),
(NAN, 0.0),
(NAN, 2.3),
(NAN, INF),
(-INF, NAN),
(-2.3, NAN),
(-0.0, NAN),
(0.0, NAN),
(2.3, NAN),
(INF, NAN)
]]
class CMathTests(unittest.TestCase):
# list of all functions in cmath
test_functions = [getattr(cmath, fname) for fname in [
'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',
'sqrt', 'tan', 'tanh']]
# test first and second arguments independently for 2-argument log
test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
test_functions.append(lambda x : cmath.log(14.-27j, x))
def setUp(self):
self.test_values = open(test_file, encoding="utf-8")
def tearDown(self):
self.test_values.close()
def assertFloatIdentical(self, x, y):
"""Fail unless 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 math.isnan(x) or math.isnan(y):
if math.isnan(x) and math.isnan(y):
return
elif x == y:
if x != 0.0:
return
# both zero; check that signs match
elif math.copysign(1.0, x) == math.copysign(1.0, y):
return
else:
msg += ': zeros have different signs'
self.fail(msg.format(x, y))
def assertComplexIdentical(self, x, y):
"""Fail unless complex numbers x and y have equal values and signs.
In particular, if x and y both have real (or imaginary) part
zero, but the zeros have different signs, this test will fail.
"""
self.assertFloatIdentical(x.real, y.real)
self.assertFloatIdentical(x.imag, y.imag)
def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323,
msg=None):
"""Fail if the two floating-point numbers are not almost equal.
Determine whether floating-point values a and b are equal to within
a (small) rounding error. The default values for rel_err and
abs_err are chosen to be suitable for platforms where a float is
represented by an IEEE 754 double. They allow an error of between
9 and 19 ulps.
"""
# special values testing
if math.isnan(a):
if math.isnan(b):
return
self.fail(msg or '{!r} should be nan'.format(b))
if math.isinf(a):
if a == b:
return
self.fail(msg or 'finite result where infinity expected: '
'expected {!r}, got {!r}'.format(a, b))
# if both a and b are zero, check whether they have the same sign
# (in theory there are examples where it would be legitimate for a
# and b to have opposite signs; in practice these hardly ever
# occur).
if not a and not b:
if math.copysign(1., a) != math.copysign(1., b):
self.fail(msg or 'zero has wrong sign: expected {!r}, '
'got {!r}'.format(a, b))
# if a-b overflows, or b is infinite, return False. Again, in
# theory there are examples where a is within a few ulps of the
# max representable float, and then b could legitimately be
# infinite. In practice these examples are rare.
try:
absolute_error = abs(b-a)
except OverflowError:
pass
else:
# test passes if either the absolute error or the relative
# error is sufficiently small. The defaults amount to an
# error of between 9 ulps and 19 ulps on an IEEE-754 compliant
# machine.
if absolute_error <= max(abs_err, rel_err * abs(a)):
return
self.fail(msg or
'{!r} and {!r} are not sufficiently close'.format(a, b))
def test_constants(self):
e_expected = 2.71828182845904523536
pi_expected = 3.14159265358979323846
self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
self.assertAlmostEqual(cmath.e, e_expected, places=9,
msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
def test_infinity_and_nan_constants(self):
self.assertEqual(cmath.inf.real, math.inf)
self.assertEqual(cmath.inf.imag, 0.0)
self.assertEqual(cmath.infj.real, 0.0)
self.assertEqual(cmath.infj.imag, math.inf)
self.assertTrue(math.isnan(cmath.nan.real))
self.assertEqual(cmath.nan.imag, 0.0)
self.assertEqual(cmath.nanj.real, 0.0)
self.assertTrue(math.isnan(cmath.nanj.imag))
# Also check that the sign of all of these is positive:
self.assertEqual(math.copysign(1., cmath.nan.real), 1.)
self.assertEqual(math.copysign(1., cmath.nan.imag), 1.)
self.assertEqual(math.copysign(1., cmath.nanj.real), 1.)
self.assertEqual(math.copysign(1., cmath.nanj.imag), 1.)
# Check consistency with reprs.
self.assertEqual(repr(cmath.inf), "inf")
self.assertEqual(repr(cmath.infj), "infj")
self.assertEqual(repr(cmath.nan), "nan")
self.assertEqual(repr(cmath.nanj), "nanj")
def test_user_object(self):
# Test automatic calling of __complex__ and __float__ by cmath
# functions
# some random values to use as test values; we avoid values
# for which any of the functions in cmath is undefined
# (i.e. 0., 1., -1., 1j, -1j) or would cause overflow
cx_arg = 4.419414439 + 1.497100113j
flt_arg = -6.131677725
# a variety of non-complex numbers, used to check that
# non-complex return values from __complex__ give an error
non_complexes = ["not complex", 1, 5, 2., None,
object(), NotImplemented]
# Now we introduce a variety of classes whose instances might
# end up being passed to the cmath functions
# usual case: new-style class implementing __complex__
class MyComplex:
def __init__(self, value):
self.value = value
def __complex__(self):
return self.value
# classes for which __complex__ raises an exception
class SomeException(Exception):
pass
class MyComplexException:
def __complex__(self):
raise SomeException
# some classes not providing __float__ or __complex__
class NeitherComplexNorFloat(object):
pass
class Index:
def __int__(self): return 2
def __index__(self): return 2
class MyInt:
def __int__(self): return 2
# other possible combinations of __float__ and __complex__
# that should work
class FloatAndComplex:
def __float__(self):
return flt_arg
def __complex__(self):
return cx_arg
class JustFloat:
def __float__(self):
return flt_arg
for f in self.test_functions:
# usual usage
self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
# other combinations of __float__ and __complex__
self.assertEqual(f(FloatAndComplex()), f(cx_arg))
self.assertEqual(f(JustFloat()), f(flt_arg))
self.assertEqual(f(Index()), f(int(Index())))
# TypeError should be raised for classes not providing
# either __complex__ or __float__, even if they provide
# __int__ or __index__:
self.assertRaises(TypeError, f, NeitherComplexNorFloat())
self.assertRaises(TypeError, f, MyInt())
# non-complex return value from __complex__ -> TypeError
for bad_complex in non_complexes:
self.assertRaises(TypeError, f, MyComplex(bad_complex))
# exceptions in __complex__ should be propagated correctly
self.assertRaises(SomeException, f, MyComplexException())
def test_input_type(self):
# ints should be acceptable inputs to all cmath
# functions, by virtue of providing a __float__ method
for f in self.test_functions:
for arg in [2, 2.]:
self.assertEqual(f(arg), f(arg.__float__()))
# but strings should give a TypeError
for f in self.test_functions:
for arg in ["a", "long_string", "0", "1j", ""]:
self.assertRaises(TypeError, f, arg)
def test_cmath_matches_math(self):
# check that corresponding cmath and math functions are equal
# for floats in the appropriate range
# test_values in (0, 1)
test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
# test_values for functions defined on [-1., 1.]
unit_interval = test_values + [-x for x in test_values] + \
[0., 1., -1.]
# test_values for log, log10, sqrt
positive = test_values + [1.] + [1./x for x in test_values]
nonnegative = [0.] + positive
# test_values for functions defined on the whole real line
real_line = [0.] + positive + [-x for x in positive]
test_functions = {
'acos' : unit_interval,
'asin' : unit_interval,
'atan' : real_line,
'cos' : real_line,
'cosh' : real_line,
'exp' : real_line,
'log' : positive,
'log10' : positive,
'sin' : real_line,
'sinh' : real_line,
'sqrt' : nonnegative,
'tan' : real_line,
'tanh' : real_line}
for fn, values in test_functions.items():
float_fn = getattr(math, fn)
complex_fn = getattr(cmath, fn)
for v in values:
z = complex_fn(v)
self.rAssertAlmostEqual(float_fn(v), z.real)
self.assertEqual(0., z.imag)
# test two-argument version of log with various bases
for base in [0.5, 2., 10.]:
for v in positive:
z = cmath.log(v, base)
self.rAssertAlmostEqual(math.log(v, base), z.real)
self.assertEqual(0., z.imag)
@requires_IEEE_754
def test_specific_values(self):
# Some tests need to be skipped on ancient OS X versions.
# See issue #27953.
SKIP_ON_TIGER = {'tan0064'}
osx_version = None
if sys.platform == 'darwin':
version_txt = platform.mac_ver()[0]
try:
osx_version = tuple(map(int, version_txt.split('.')))
except ValueError:
pass
def rect_complex(z):
"""Wrapped version of rect that accepts a complex number instead of
two float arguments."""
return cmath.rect(z.real, z.imag)
def polar_complex(z):
"""Wrapped version of polar that returns a complex number instead of
two floats."""
return complex(*polar(z))
for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
arg = complex(ar, ai)
expected = complex(er, ei)
# Skip certain tests on OS X 10.4.
if osx_version is not None and osx_version < (10, 5):
if id in SKIP_ON_TIGER:
continue
if fn == 'rect':
function = rect_complex
elif fn == 'polar':
function = polar_complex
else:
function = getattr(cmath, fn)
if 'divide-by-zero' in flags or 'invalid' in flags:
try:
actual = function(arg)
except ValueError:
continue
else:
self.fail('ValueError not raised in test '
'{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
if 'overflow' in flags:
try:
actual = function(arg)
except OverflowError:
continue
else:
self.fail('OverflowError not raised in test '
'{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
actual = function(arg)
if 'ignore-real-sign' in flags:
actual = complex(abs(actual.real), actual.imag)
expected = complex(abs(expected.real), expected.imag)
if 'ignore-imag-sign' in flags:
actual = complex(actual.real, abs(actual.imag))
expected = complex(expected.real, abs(expected.imag))
# for the real part of the log function, we allow an
# absolute error of up to 2e-15.
if fn in ('log', 'log10'):
real_abs_err = 2e-15
else:
real_abs_err = 5e-323
error_message = (
'{}: {}(complex({!r}, {!r}))\n'
'Expected: complex({!r}, {!r})\n'
'Received: complex({!r}, {!r})\n'
'Received value insufficiently close to expected value.'
).format(id, fn, ar, ai,
expected.real, expected.imag,
actual.real, actual.imag)
self.rAssertAlmostEqual(expected.real, actual.real,
abs_err=real_abs_err,
msg=error_message)
self.rAssertAlmostEqual(expected.imag, actual.imag,
msg=error_message)
def check_polar(self, func):
def check(arg, expected):
got = func(arg)
for e, g in zip(expected, got):
self.rAssertAlmostEqual(e, g)
check(0, (0., 0.))
check(1, (1., 0.))
check(-1, (1., pi))
check(1j, (1., pi / 2))
check(-3j, (3., -pi / 2))
inf = float('inf')
check(complex(inf, 0), (inf, 0.))
check(complex(-inf, 0), (inf, pi))
check(complex(3, inf), (inf, pi / 2))
check(complex(5, -inf), (inf, -pi / 2))
check(complex(inf, inf), (inf, pi / 4))
check(complex(inf, -inf), (inf, -pi / 4))
check(complex(-inf, inf), (inf, 3 * pi / 4))
check(complex(-inf, -inf), (inf, -3 * pi / 4))
nan = float('nan')
check(complex(nan, 0), (nan, nan))
check(complex(0, nan), (nan, nan))
check(complex(nan, nan), (nan, nan))
check(complex(inf, nan), (inf, nan))
check(complex(-inf, nan), (inf, nan))
check(complex(nan, inf), (inf, nan))
check(complex(nan, -inf), (inf, nan))
def test_polar(self):
self.check_polar(polar)
@cpython_only
def test_polar_errno(self):
# Issue #24489: check a previously set C errno doesn't disturb polar()
_testcapi = import_helper.import_module('_testcapi')
def polar_with_errno_set(z):
_testcapi.set_errno(11)
try:
return polar(z)
finally:
_testcapi.set_errno(0)
self.check_polar(polar_with_errno_set)
def test_phase(self):
self.assertAlmostEqual(phase(0), 0.)
self.assertAlmostEqual(phase(1.), 0.)
self.assertAlmostEqual(phase(-1.), pi)
self.assertAlmostEqual(phase(-1.+1E-300j), pi)
self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
self.assertAlmostEqual(phase(1j), pi/2)
self.assertAlmostEqual(phase(-1j), -pi/2)
# zeros
self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
self.assertEqual(phase(complex(-0.0, 0.0)), pi)
self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
# infinities
self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
self.assertEqual(phase(complex(INF, -2.3)), -0.0)
self.assertEqual(phase(complex(INF, -0.0)), -0.0)
self.assertEqual(phase(complex(INF, 0.0)), 0.0)
self.assertEqual(phase(complex(INF, 2.3)), 0.0)
self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
# real or imaginary part NaN
for z in complex_nans:
self.assertTrue(math.isnan(phase(z)))
def test_abs(self):
# zeros
for z in complex_zeros:
self.assertEqual(abs(z), 0.0)
# infinities
for z in complex_infinities:
self.assertEqual(abs(z), INF)
# real or imaginary part NaN
self.assertEqual(abs(complex(NAN, -INF)), INF)
self.assertTrue(math.isnan(abs(complex(NAN, -2.3))))
self.assertTrue(math.isnan(abs(complex(NAN, -0.0))))
self.assertTrue(math.isnan(abs(complex(NAN, 0.0))))
self.assertTrue(math.isnan(abs(complex(NAN, 2.3))))
self.assertEqual(abs(complex(NAN, INF)), INF)
self.assertEqual(abs(complex(-INF, NAN)), INF)
self.assertTrue(math.isnan(abs(complex(-2.3, NAN))))
self.assertTrue(math.isnan(abs(complex(-0.0, NAN))))
self.assertTrue(math.isnan(abs(complex(0.0, NAN))))
self.assertTrue(math.isnan(abs(complex(2.3, NAN))))
self.assertEqual(abs(complex(INF, NAN)), INF)
self.assertTrue(math.isnan(abs(complex(NAN, NAN))))
@requires_IEEE_754
def test_abs_overflows(self):
# result overflows
self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308))
def assertCEqual(self, a, b):
eps = 1E-7
if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:
self.fail((a ,b))
def test_rect(self):
self.assertCEqual(rect(0, 0), (0, 0))
self.assertCEqual(rect(1, 0), (1., 0))
self.assertCEqual(rect(1, -pi), (-1., 0))
self.assertCEqual(rect(1, pi/2), (0, 1.))
self.assertCEqual(rect(1, -pi/2), (0, -1.))
def test_isfinite(self):
real_vals = [float('-inf'), -2.3, -0.0,
0.0, 2.3, float('inf'), float('nan')]
for x in real_vals:
for y in real_vals:
z = complex(x, y)
self.assertEqual(cmath.isfinite(z),
math.isfinite(x) and math.isfinite(y))
def test_isnan(self):
self.assertFalse(cmath.isnan(1))
self.assertFalse(cmath.isnan(1j))
self.assertFalse(cmath.isnan(INF))
self.assertTrue(cmath.isnan(NAN))
self.assertTrue(cmath.isnan(complex(NAN, 0)))
self.assertTrue(cmath.isnan(complex(0, NAN)))
self.assertTrue(cmath.isnan(complex(NAN, NAN)))
self.assertTrue(cmath.isnan(complex(NAN, INF)))
self.assertTrue(cmath.isnan(complex(INF, NAN)))
def test_isinf(self):
self.assertFalse(cmath.isinf(1))
self.assertFalse(cmath.isinf(1j))
self.assertFalse(cmath.isinf(NAN))
self.assertTrue(cmath.isinf(INF))
self.assertTrue(cmath.isinf(complex(INF, 0)))
self.assertTrue(cmath.isinf(complex(0, INF)))
self.assertTrue(cmath.isinf(complex(INF, INF)))
self.assertTrue(cmath.isinf(complex(NAN, INF)))
self.assertTrue(cmath.isinf(complex(INF, NAN)))
@requires_IEEE_754
def testTanhSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.tanh(z), z)
# The algorithm used for atan and atanh makes use of the system
# log1p function; If that system function doesn't respect the sign
# of zero, then atan and atanh will also have difficulties with
# the sign of complex zeros.
@requires_IEEE_754
def testAtanSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.atan(z), z)
@requires_IEEE_754
def testAtanhSign(self):
for z in complex_zeros:
self.assertComplexIdentical(cmath.atanh(z), z)
class IsCloseTests(test_math.IsCloseTests):
isclose = cmath.isclose
def test_reject_complex_tolerances(self):
with self.assertRaises(TypeError):
self.isclose(1j, 1j, rel_tol=1j)
with self.assertRaises(TypeError):
self.isclose(1j, 1j, abs_tol=1j)
with self.assertRaises(TypeError):
self.isclose(1j, 1j, rel_tol=1j, abs_tol=1j)
def test_complex_values(self):
# test complex values that are close to within 12 decimal places
complex_examples = [(1.0+1.0j, 1.000000000001+1.0j),
(1.0+1.0j, 1.0+1.000000000001j),
(-1.0+1.0j, -1.000000000001+1.0j),
(1.0-1.0j, 1.0-0.999999999999j),
]
self.assertAllClose(complex_examples, rel_tol=1e-12)
self.assertAllNotClose(complex_examples, rel_tol=1e-13)
def test_complex_near_zero(self):
# test values near zero that are near to within three decimal places
near_zero_examples = [(0.001j, 0),
(0.001, 0),
(0.001+0.001j, 0),
(-0.001+0.001j, 0),
(0.001-0.001j, 0),
(-0.001-0.001j, 0),
]
self.assertAllClose(near_zero_examples, abs_tol=1.5e-03)
self.assertAllNotClose(near_zero_examples, abs_tol=0.5e-03)
self.assertIsClose(0.001-0.001j, 0.001+0.001j, abs_tol=2e-03)
self.assertIsNotClose(0.001-0.001j, 0.001+0.001j, abs_tol=1e-03)
def test_complex_special(self):
self.assertIsNotClose(INF, INF*1j)
self.assertIsNotClose(INF*1j, INF)
self.assertIsNotClose(INF, -INF)
self.assertIsNotClose(-INF, INF)
self.assertIsNotClose(0, INF)
self.assertIsNotClose(0, INF*1j)
if __name__ == "__main__":
unittest.main()
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