Lib/test/test_cmath.py

   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()