| 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() |
