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from test.test_support import run_unittest
import unittest
import cmath, math
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 cAssertAlmostEqual(self, a, b, rel_eps = 1e-10, abs_eps = 1e-100):
"""Check that two complex numbers are almost equal."""
# the two complex numbers are considered almost equal if
# either the relative error is <= rel_eps or the absolute error
# is tiny, <= abs_eps.
if a == b == 0:
return
absolute_error = abs(a-b)
relative_error = absolute_error/max(abs(a), abs(b))
if relative_error > rel_eps and absolute_error > abs_eps:
self.fail("%s and %s are not almost equal" % (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 %s; should be %s" % (cmath.pi, pi_expected))
self.assertAlmostEqual(cmath.e, e_expected, places=9,
msg="cmath.e is %s; should be %s" % (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, 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(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 2
def __index__(self): return 2
class MyIntOS:
def __int__(self): return 2
def __long__(self): return 2
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.cAssertAlmostEqual(f(MyComplex(cx_arg)), f(cx_arg))
self.cAssertAlmostEqual(f(MyComplexOS(cx_arg)), f(cx_arg))
# other combinations of __float__ and __complex__
self.cAssertAlmostEqual(f(FloatAndComplex()), f(cx_arg))
self.cAssertAlmostEqual(f(FloatAndComplexOS()), f(cx_arg))
self.cAssertAlmostEqual(f(JustFloat()), f(flt_arg))
self.cAssertAlmostEqual(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, 2.]:
self.cAssertAlmostEqual(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:
self.cAssertAlmostEqual(float_fn(v), complex_fn(v))
# test two-argument version of log with various bases
for base in [0.5, 2., 10.]:
for v in positive:
self.cAssertAlmostEqual(cmath.log(v, base), math.log(v, base))
def test_main():
run_unittest(CMathTests)
if __name__ == "__main__":
test_main()
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