from test.test_support import run_unittest
from test.test_math import parse_testfile, test_file
import unittest
import cmath, math
from cmath import phase, polar, rect, pi
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)
def tearDown(self):
self.test_values.close()
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_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, 5L, 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(object):
def __init__(self, value):
self.value = value
def __complex__(self):
return self.value
# old-style class implementing __complex__
class MyComplexOS:
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(object):
def __complex__(self):
raise SomeException
class MyComplexExceptionOS:
def __complex__(self):
raise SomeException
# some classes not providing __float__ or __complex__
class NeitherComplexNorFloat(object):
pass
class NeitherComplexNorFloatOS:
pass
class MyInt(object):
def __int__(self): return 2
def __long__(self): return 2L
def __index__(self): return 2
class MyIntOS:
def __int__(self): return 2
def __long__(self): return 2L
def __index__(self): return 2
# other possible combinations of __float__ and __complex__
# that should work
class FloatAndComplex(object):
def __float__(self):
return flt_arg
def __complex__(self):
return cx_arg
class FloatAndComplexOS:
def __float__(self):
return flt_arg
def __complex__(self):
return cx_arg
class JustFloat(object):
def __float__(self):
return flt_arg
class JustFloatOS:
def __float__(self):
return flt_arg
for f in self.test_functions:
# usual usage
self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg))
# other combinations of __float__ and __complex__
self.assertEqual(f(FloatAndComplex()), f(cx_arg))
self.assertEqual(f(FloatAndComplexOS()), f(cx_arg))
self.assertEqual(f(JustFloat()), f(flt_arg))
self.assertEqual(f(JustFloatOS()), f(flt_arg))
# TypeError should be raised for classes not providing
# either __complex__ or __float__, even if they provide
# __int__, __long__ or __index__. An old-style class
# currently raises AttributeError instead of a TypeError;
# this could be considered a bug.
self.assertRaises(TypeError, f, NeitherComplexNorFloat())
self.assertRaises(TypeError, f, MyInt())
self.assertRaises(Exception, f, NeitherComplexNorFloatOS())
self.assertRaises(Exception, f, MyIntOS())
# non-complex return value from __complex__ -> TypeError
for bad_complex in non_complexes:
self.assertRaises(TypeError, f, MyComplex(bad_complex))
self.assertRaises(TypeError, f, MyComplexOS(bad_complex))
# exceptions in __complex__ should be propagated correctly
self.assertRaises(SomeException, f, MyComplexException())
self.assertRaises(SomeException, f, MyComplexExceptionOS())
def test_input_type(self):
# ints and longs 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, 2L, 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)
def test_specific_values(self):
if not float.__getformat__("double").startswith("IEEE"):
return
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)
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 assertCISEqual(self, a, b):
eps = 1E-7
if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps:
self.fail((a ,b))
def test_polar(self):
self.assertCISEqual(polar(0), (0., 0.))
self.assertCISEqual(polar(1.), (1., 0.))
self.assertCISEqual(polar(-1.), (1., pi))
self.assertCISEqual(polar(1j), (1., pi/2))
self.assertCISEqual(polar(-1j), (1., -pi/2))
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))))
# result overflows
if float.__getformat__("double").startswith("IEEE"):
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_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)))
def test_main():
run_unittest(CMathTests)
if __name__ == "__main__":
test_main()