from test.support import run_unittest, requires_IEEE_754 from test.test_math import parse_testfile, test_file import unittest import cmath, math from cmath import phase, polar, rect, pi import sysconfig 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 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_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 __index__(self): return 2 class MyIntOS: def __int__(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.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__ 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.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): 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)))) @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 @unittest.skipIf(sysconfig.get_config_var('TANH_PRESERVES_ZERO_SIGN') == 0, "system tanh() function doesn't copy the sign") 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) def test_main(): run_unittest(CMathTests) if __name__ == "__main__": test_main()