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