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, 9, "cmath.pi is %s; should be %s" % (cmath.pi, pi_expected)) self.assertAlmostEqual(cmath.e, e_expected, 9, "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, 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.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, 2L, 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()