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      1 from test.test_support import run_unittest
      2 from test.test_math import parse_testfile, test_file
      3 import unittest
      4 import cmath, math
      5 from cmath import phase, polar, rect, pi
      6 
      7 INF = float('inf')
      8 NAN = float('nan')
      9 
     10 complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]]
     11 complex_infinities = [complex(x, y) for x, y in [
     12         (INF, 0.0),  # 1st quadrant
     13         (INF, 2.3),
     14         (INF, INF),
     15         (2.3, INF),
     16         (0.0, INF),
     17         (-0.0, INF), # 2nd quadrant
     18         (-2.3, INF),
     19         (-INF, INF),
     20         (-INF, 2.3),
     21         (-INF, 0.0),
     22         (-INF, -0.0), # 3rd quadrant
     23         (-INF, -2.3),
     24         (-INF, -INF),
     25         (-2.3, -INF),
     26         (-0.0, -INF),
     27         (0.0, -INF), # 4th quadrant
     28         (2.3, -INF),
     29         (INF, -INF),
     30         (INF, -2.3),
     31         (INF, -0.0)
     32         ]]
     33 complex_nans = [complex(x, y) for x, y in [
     34         (NAN, -INF),
     35         (NAN, -2.3),
     36         (NAN, -0.0),
     37         (NAN, 0.0),
     38         (NAN, 2.3),
     39         (NAN, INF),
     40         (-INF, NAN),
     41         (-2.3, NAN),
     42         (-0.0, NAN),
     43         (0.0, NAN),
     44         (2.3, NAN),
     45         (INF, NAN)
     46         ]]
     47 
     48 class CMathTests(unittest.TestCase):
     49     # list of all functions in cmath
     50     test_functions = [getattr(cmath, fname) for fname in [
     51             'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
     52             'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',
     53             'sqrt', 'tan', 'tanh']]
     54     # test first and second arguments independently for 2-argument log
     55     test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
     56     test_functions.append(lambda x : cmath.log(14.-27j, x))
     57 
     58     def setUp(self):
     59         self.test_values = open(test_file)
     60 
     61     def tearDown(self):
     62         self.test_values.close()
     63 
     64     def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323,
     65                            msg=None):
     66         """Fail if the two floating-point numbers are not almost equal.
     67 
     68         Determine whether floating-point values a and b are equal to within
     69         a (small) rounding error.  The default values for rel_err and
     70         abs_err are chosen to be suitable for platforms where a float is
     71         represented by an IEEE 754 double.  They allow an error of between
     72         9 and 19 ulps.
     73         """
     74 
     75         # special values testing
     76         if math.isnan(a):
     77             if math.isnan(b):
     78                 return
     79             self.fail(msg or '{!r} should be nan'.format(b))
     80 
     81         if math.isinf(a):
     82             if a == b:
     83                 return
     84             self.fail(msg or 'finite result where infinity expected: '
     85                       'expected {!r}, got {!r}'.format(a, b))
     86 
     87         # if both a and b are zero, check whether they have the same sign
     88         # (in theory there are examples where it would be legitimate for a
     89         # and b to have opposite signs; in practice these hardly ever
     90         # occur).
     91         if not a and not b:
     92             if math.copysign(1., a) != math.copysign(1., b):
     93                 self.fail(msg or 'zero has wrong sign: expected {!r}, '
     94                           'got {!r}'.format(a, b))
     95 
     96         # if a-b overflows, or b is infinite, return False.  Again, in
     97         # theory there are examples where a is within a few ulps of the
     98         # max representable float, and then b could legitimately be
     99         # infinite.  In practice these examples are rare.
    100         try:
    101             absolute_error = abs(b-a)
    102         except OverflowError:
    103             pass
    104         else:
    105             # test passes if either the absolute error or the relative
    106             # error is sufficiently small.  The defaults amount to an
    107             # error of between 9 ulps and 19 ulps on an IEEE-754 compliant
    108             # machine.
    109             if absolute_error <= max(abs_err, rel_err * abs(a)):
    110                 return
    111         self.fail(msg or
    112                   '{!r} and {!r} are not sufficiently close'.format(a, b))
    113 
    114     def test_constants(self):
    115         e_expected = 2.71828182845904523536
    116         pi_expected = 3.14159265358979323846
    117         self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
    118             msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
    119         self.assertAlmostEqual(cmath.e, e_expected, places=9,
    120             msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))
    121 
    122     def test_user_object(self):
    123         # Test automatic calling of __complex__ and __float__ by cmath
    124         # functions
    125 
    126         # some random values to use as test values; we avoid values
    127         # for which any of the functions in cmath is undefined
    128         # (i.e. 0., 1., -1., 1j, -1j) or would cause overflow
    129         cx_arg = 4.419414439 + 1.497100113j
    130         flt_arg = -6.131677725
    131 
    132         # a variety of non-complex numbers, used to check that
    133         # non-complex return values from __complex__ give an error
    134         non_complexes = ["not complex", 1, 5L, 2., None,
    135                          object(), NotImplemented]
    136 
    137         # Now we introduce a variety of classes whose instances might
    138         # end up being passed to the cmath functions
    139 
    140         # usual case: new-style class implementing __complex__
    141         class MyComplex(object):
    142             def __init__(self, value):
    143                 self.value = value
    144             def __complex__(self):
    145                 return self.value
    146 
    147         # old-style class implementing __complex__
    148         class MyComplexOS:
    149             def __init__(self, value):
    150                 self.value = value
    151             def __complex__(self):
    152                 return self.value
    153 
    154         # classes for which __complex__ raises an exception
    155         class SomeException(Exception):
    156             pass
    157         class MyComplexException(object):
    158             def __complex__(self):
    159                 raise SomeException
    160         class MyComplexExceptionOS:
    161             def __complex__(self):
    162                 raise SomeException
    163 
    164         # some classes not providing __float__ or __complex__
    165         class NeitherComplexNorFloat(object):
    166             pass
    167         class NeitherComplexNorFloatOS:
    168             pass
    169         class MyInt(object):
    170             def __int__(self): return 2
    171             def __long__(self): return 2L
    172             def __index__(self): return 2
    173         class MyIntOS:
    174             def __int__(self): return 2
    175             def __long__(self): return 2L
    176             def __index__(self): return 2
    177 
    178         # other possible combinations of __float__ and __complex__
    179         # that should work
    180         class FloatAndComplex(object):
    181             def __float__(self):
    182                 return flt_arg
    183             def __complex__(self):
    184                 return cx_arg
    185         class FloatAndComplexOS:
    186             def __float__(self):
    187                 return flt_arg
    188             def __complex__(self):
    189                 return cx_arg
    190         class JustFloat(object):
    191             def __float__(self):
    192                 return flt_arg
    193         class JustFloatOS:
    194             def __float__(self):
    195                 return flt_arg
    196 
    197         for f in self.test_functions:
    198             # usual usage
    199             self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
    200             self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg))
    201             # other combinations of __float__ and __complex__
    202             self.assertEqual(f(FloatAndComplex()), f(cx_arg))
    203             self.assertEqual(f(FloatAndComplexOS()), f(cx_arg))
    204             self.assertEqual(f(JustFloat()), f(flt_arg))
    205             self.assertEqual(f(JustFloatOS()), f(flt_arg))
    206             # TypeError should be raised for classes not providing
    207             # either __complex__ or __float__, even if they provide
    208             # __int__, __long__ or __index__.  An old-style class
    209             # currently raises AttributeError instead of a TypeError;
    210             # this could be considered a bug.
    211             self.assertRaises(TypeError, f, NeitherComplexNorFloat())
    212             self.assertRaises(TypeError, f, MyInt())
    213             self.assertRaises(Exception, f, NeitherComplexNorFloatOS())
    214             self.assertRaises(Exception, f, MyIntOS())
    215             # non-complex return value from __complex__ -> TypeError
    216             for bad_complex in non_complexes:
    217                 self.assertRaises(TypeError, f, MyComplex(bad_complex))
    218                 self.assertRaises(TypeError, f, MyComplexOS(bad_complex))
    219             # exceptions in __complex__ should be propagated correctly
    220             self.assertRaises(SomeException, f, MyComplexException())
    221             self.assertRaises(SomeException, f, MyComplexExceptionOS())
    222 
    223     def test_input_type(self):
    224         # ints and longs should be acceptable inputs to all cmath
    225         # functions, by virtue of providing a __float__ method
    226         for f in self.test_functions:
    227             for arg in [2, 2L, 2.]:
    228                 self.assertEqual(f(arg), f(arg.__float__()))
    229 
    230         # but strings should give a TypeError
    231         for f in self.test_functions:
    232             for arg in ["a", "long_string", "0", "1j", ""]:
    233                 self.assertRaises(TypeError, f, arg)
    234 
    235     def test_cmath_matches_math(self):
    236         # check that corresponding cmath and math functions are equal
    237         # for floats in the appropriate range
    238 
    239         # test_values in (0, 1)
    240         test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
    241 
    242         # test_values for functions defined on [-1., 1.]
    243         unit_interval = test_values + [-x for x in test_values] + \
    244             [0., 1., -1.]
    245 
    246         # test_values for log, log10, sqrt
    247         positive = test_values + [1.] + [1./x for x in test_values]
    248         nonnegative = [0.] + positive
    249 
    250         # test_values for functions defined on the whole real line
    251         real_line = [0.] + positive + [-x for x in positive]
    252 
    253         test_functions = {
    254             'acos' : unit_interval,
    255             'asin' : unit_interval,
    256             'atan' : real_line,
    257             'cos' : real_line,
    258             'cosh' : real_line,
    259             'exp' : real_line,
    260             'log' : positive,
    261             'log10' : positive,
    262             'sin' : real_line,
    263             'sinh' : real_line,
    264             'sqrt' : nonnegative,
    265             'tan' : real_line,
    266             'tanh' : real_line}
    267 
    268         for fn, values in test_functions.items():
    269             float_fn = getattr(math, fn)
    270             complex_fn = getattr(cmath, fn)
    271             for v in values:
    272                 z = complex_fn(v)
    273                 self.rAssertAlmostEqual(float_fn(v), z.real)
    274                 self.assertEqual(0., z.imag)
    275 
    276         # test two-argument version of log with various bases
    277         for base in [0.5, 2., 10.]:
    278             for v in positive:
    279                 z = cmath.log(v, base)
    280                 self.rAssertAlmostEqual(math.log(v, base), z.real)
    281                 self.assertEqual(0., z.imag)
    282 
    283     def test_specific_values(self):
    284         if not float.__getformat__("double").startswith("IEEE"):
    285             return
    286 
    287         def rect_complex(z):
    288             """Wrapped version of rect that accepts a complex number instead of
    289             two float arguments."""
    290             return cmath.rect(z.real, z.imag)
    291 
    292         def polar_complex(z):
    293             """Wrapped version of polar that returns a complex number instead of
    294             two floats."""
    295             return complex(*polar(z))
    296 
    297         for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
    298             arg = complex(ar, ai)
    299             expected = complex(er, ei)
    300             if fn == 'rect':
    301                 function = rect_complex
    302             elif fn == 'polar':
    303                 function = polar_complex
    304             else:
    305                 function = getattr(cmath, fn)
    306             if 'divide-by-zero' in flags or 'invalid' in flags:
    307                 try:
    308                     actual = function(arg)
    309                 except ValueError:
    310                     continue
    311                 else:
    312                     self.fail('ValueError not raised in test '
    313                           '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
    314 
    315             if 'overflow' in flags:
    316                 try:
    317                     actual = function(arg)
    318                 except OverflowError:
    319                     continue
    320                 else:
    321                     self.fail('OverflowError not raised in test '
    322                           '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))
    323 
    324             actual = function(arg)
    325 
    326             if 'ignore-real-sign' in flags:
    327                 actual = complex(abs(actual.real), actual.imag)
    328                 expected = complex(abs(expected.real), expected.imag)
    329             if 'ignore-imag-sign' in flags:
    330                 actual = complex(actual.real, abs(actual.imag))
    331                 expected = complex(expected.real, abs(expected.imag))
    332 
    333             # for the real part of the log function, we allow an
    334             # absolute error of up to 2e-15.
    335             if fn in ('log', 'log10'):
    336                 real_abs_err = 2e-15
    337             else:
    338                 real_abs_err = 5e-323
    339 
    340             error_message = (
    341                 '{}: {}(complex({!r}, {!r}))\n'
    342                 'Expected: complex({!r}, {!r})\n'
    343                 'Received: complex({!r}, {!r})\n'
    344                 'Received value insufficiently close to expected value.'
    345                 ).format(id, fn, ar, ai,
    346                      expected.real, expected.imag,
    347                      actual.real, actual.imag)
    348             self.rAssertAlmostEqual(expected.real, actual.real,
    349                                         abs_err=real_abs_err,
    350                                         msg=error_message)
    351             self.rAssertAlmostEqual(expected.imag, actual.imag,
    352                                         msg=error_message)
    353 
    354     def assertCISEqual(self, a, b):
    355         eps = 1E-7
    356         if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps:
    357             self.fail((a ,b))
    358 
    359     def test_polar(self):
    360         self.assertCISEqual(polar(0), (0., 0.))
    361         self.assertCISEqual(polar(1.), (1., 0.))
    362         self.assertCISEqual(polar(-1.), (1., pi))
    363         self.assertCISEqual(polar(1j), (1., pi/2))
    364         self.assertCISEqual(polar(-1j), (1., -pi/2))
    365 
    366     def test_phase(self):
    367         self.assertAlmostEqual(phase(0), 0.)
    368         self.assertAlmostEqual(phase(1.), 0.)
    369         self.assertAlmostEqual(phase(-1.), pi)
    370         self.assertAlmostEqual(phase(-1.+1E-300j), pi)
    371         self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
    372         self.assertAlmostEqual(phase(1j), pi/2)
    373         self.assertAlmostEqual(phase(-1j), -pi/2)
    374 
    375         # zeros
    376         self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
    377         self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
    378         self.assertEqual(phase(complex(-0.0, 0.0)), pi)
    379         self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
    380 
    381         # infinities
    382         self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
    383         self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
    384         self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
    385         self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
    386         self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
    387         self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
    388         self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
    389         self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
    390         self.assertEqual(phase(complex(INF, -2.3)), -0.0)
    391         self.assertEqual(phase(complex(INF, -0.0)), -0.0)
    392         self.assertEqual(phase(complex(INF, 0.0)), 0.0)
    393         self.assertEqual(phase(complex(INF, 2.3)), 0.0)
    394         self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
    395         self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
    396         self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
    397         self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
    398         self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
    399         self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
    400         self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
    401         self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
    402 
    403         # real or imaginary part NaN
    404         for z in complex_nans:
    405             self.assertTrue(math.isnan(phase(z)))
    406 
    407     def test_abs(self):
    408         # zeros
    409         for z in complex_zeros:
    410             self.assertEqual(abs(z), 0.0)
    411 
    412         # infinities
    413         for z in complex_infinities:
    414             self.assertEqual(abs(z), INF)
    415 
    416         # real or imaginary part NaN
    417         self.assertEqual(abs(complex(NAN, -INF)), INF)
    418         self.assertTrue(math.isnan(abs(complex(NAN, -2.3))))
    419         self.assertTrue(math.isnan(abs(complex(NAN, -0.0))))
    420         self.assertTrue(math.isnan(abs(complex(NAN, 0.0))))
    421         self.assertTrue(math.isnan(abs(complex(NAN, 2.3))))
    422         self.assertEqual(abs(complex(NAN, INF)), INF)
    423         self.assertEqual(abs(complex(-INF, NAN)), INF)
    424         self.assertTrue(math.isnan(abs(complex(-2.3, NAN))))
    425         self.assertTrue(math.isnan(abs(complex(-0.0, NAN))))
    426         self.assertTrue(math.isnan(abs(complex(0.0, NAN))))
    427         self.assertTrue(math.isnan(abs(complex(2.3, NAN))))
    428         self.assertEqual(abs(complex(INF, NAN)), INF)
    429         self.assertTrue(math.isnan(abs(complex(NAN, NAN))))
    430 
    431         # result overflows
    432         if float.__getformat__("double").startswith("IEEE"):
    433             self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308))
    434 
    435     def assertCEqual(self, a, b):
    436         eps = 1E-7
    437         if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:
    438             self.fail((a ,b))
    439 
    440     def test_rect(self):
    441         self.assertCEqual(rect(0, 0), (0, 0))
    442         self.assertCEqual(rect(1, 0), (1., 0))
    443         self.assertCEqual(rect(1, -pi), (-1., 0))
    444         self.assertCEqual(rect(1, pi/2), (0, 1.))
    445         self.assertCEqual(rect(1, -pi/2), (0, -1.))
    446 
    447     def test_isnan(self):
    448         self.assertFalse(cmath.isnan(1))
    449         self.assertFalse(cmath.isnan(1j))
    450         self.assertFalse(cmath.isnan(INF))
    451         self.assertTrue(cmath.isnan(NAN))
    452         self.assertTrue(cmath.isnan(complex(NAN, 0)))
    453         self.assertTrue(cmath.isnan(complex(0, NAN)))
    454         self.assertTrue(cmath.isnan(complex(NAN, NAN)))
    455         self.assertTrue(cmath.isnan(complex(NAN, INF)))
    456         self.assertTrue(cmath.isnan(complex(INF, NAN)))
    457 
    458     def test_isinf(self):
    459         self.assertFalse(cmath.isinf(1))
    460         self.assertFalse(cmath.isinf(1j))
    461         self.assertFalse(cmath.isinf(NAN))
    462         self.assertTrue(cmath.isinf(INF))
    463         self.assertTrue(cmath.isinf(complex(INF, 0)))
    464         self.assertTrue(cmath.isinf(complex(0, INF)))
    465         self.assertTrue(cmath.isinf(complex(INF, INF)))
    466         self.assertTrue(cmath.isinf(complex(NAN, INF)))
    467         self.assertTrue(cmath.isinf(complex(INF, NAN)))
    468 
    469 
    470 def test_main():
    471     run_unittest(CMathTests)
    472 
    473 if __name__ == "__main__":
    474     test_main()
    475