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 def almostEqualF(a, b, rel_err=2e-15, abs_err = 5e-323):
  50     """Determine whether floating-point values a and b are equal to within
  51     a (small) rounding error.  The default values for rel_err and
  52     abs_err are chosen to be suitable for platforms where a float is
  53     represented by an IEEE 754 double.  They allow an error of between
  54     9 and 19 ulps."""
  55
  56     # special values testing
  57     if math.isnan(a):
  58         return math.isnan(b)
  59     if math.isinf(a):
  60         return a == b
  61
  62     # if both a and b are zero, check whether they have the same sign
  63     # (in theory there are examples where it would be legitimate for a
  64     # and b to have opposite signs; in practice these hardly ever
  65     # occur).
  66     if not a and not b:
  67         return math.copysign(1., a) == math.copysign(1., b)
  68
  69     # if a-b overflows, or b is infinite, return False.  Again, in
  70     # theory there are examples where a is within a few ulps of the
  71     # max representable float, and then b could legitimately be
  72     # infinite.  In practice these examples are rare.
  73     try:
  74         absolute_error = abs(b-a)
  75     except OverflowError:
  76         return False
  77     else:
  78         return absolute_error <= max(abs_err, rel_err * abs(a))
  79
  80 class CMathTests(unittest.TestCase):
  81     # list of all functions in cmath
  82     test_functions = [getattr(cmath, fname) for fname in [
  83             'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
  84             'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',
  85             'sqrt', 'tan', 'tanh']]
  86     # test first and second arguments independently for 2-argument log
  87     test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
  88     test_functions.append(lambda x : cmath.log(14.-27j, x))
  89
  90     def setUp(self):
  91         self.test_values = open(test_file)
  92
  93     def tearDown(self):
  94         self.test_values.close()
  95
  96     def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323):
  97         """Check that two floating-point numbers are almost equal."""
  98
  99         # special values testing
 100         if math.isnan(a):
 101             if math.isnan(b):
 102                 return
 103             self.fail("%s should be nan" % repr(b))
 104
 105         if math.isinf(a):
 106             if a == b:
 107                 return
 108             self.fail("finite result where infinity excpected: "
 109                       "expected %s, got %s" % (repr(a), repr(b)))
 110
 111         if not a and not b:
 112             if math.atan2(a, -1.) != math.atan2(b, -1.):
 113                 self.fail("zero has wrong sign: expected %s, got %s" %
 114                           (repr(a), repr(b)))
 115
 116         # test passes if either the absolute error or the relative
 117         # error is sufficiently small.  The defaults amount to an
 118         # error of between 9 ulps and 19 ulps on an IEEE-754 compliant
 119         # machine.
 120
 121         try:
 122             absolute_error = abs(b-a)
 123         except OverflowError:
 124             pass
 125         else:
 126             if absolute_error <= max(abs_err, rel_err * abs(a)):
 127                 return
 128         self.fail("%s and %s are not sufficiently close" % (repr(a), repr(b)))
 129
 130     def test_constants(self):
 131         e_expected = 2.71828182845904523536
 132         pi_expected = 3.14159265358979323846
 133         self.rAssertAlmostEqual(cmath.pi, pi_expected, 9,
 134             "cmath.pi is %s; should be %s" % (cmath.pi, pi_expected))
 135         self.rAssertAlmostEqual(cmath.e,  e_expected, 9,
 136             "cmath.e is %s; should be %s" % (cmath.e, e_expected))
 137
 138     def test_user_object(self):
 139         # Test automatic calling of __complex__ and __float__ by cmath
 140         # functions
 141
 142         # some random values to use as test values; we avoid values
 143         # for which any of the functions in cmath is undefined
 144         # (i.e. 0., 1., -1., 1j, -1j) or would cause overflow
 145         cx_arg = 4.419414439 + 1.497100113j
 146         flt_arg = -6.131677725
 147
 148         # a variety of non-complex numbers, used to check that
 149         # non-complex return values from __complex__ give an error
 150         non_complexes = ["not complex", 1, 5L, 2., None,
 151                          object(), NotImplemented]
 152
 153         # Now we introduce a variety of classes whose instances might
 154         # end up being passed to the cmath functions
 155
 156         # usual case: new-style class implementing __complex__
 157         class MyComplex(object):
 158             def __init__(self, value):
 159                 self.value = value
 160             def __complex__(self):
 161                 return self.value
 162
 163         # old-style class implementing __complex__
 164         class MyComplexOS:
 165             def __init__(self, value):
 166                 self.value = value
 167             def __complex__(self):
 168                 return self.value
 169
 170         # classes for which __complex__ raises an exception
 171         class SomeException(Exception):
 172             pass
 173         class MyComplexException(object):
 174             def __complex__(self):
 175                 raise SomeException
 176         class MyComplexExceptionOS:
 177             def __complex__(self):
 178                 raise SomeException
 179
 180         # some classes not providing __float__ or __complex__
 181         class NeitherComplexNorFloat(object):
 182             pass
 183         class NeitherComplexNorFloatOS:
 184             pass
 185         class MyInt(object):
 186             def __int__(self): return 2
 187             def __long__(self): return 2L
 188             def __index__(self): return 2
 189         class MyIntOS:
 190             def __int__(self): return 2
 191             def __long__(self): return 2L
 192             def __index__(self): return 2
 193
 194         # other possible combinations of __float__ and __complex__
 195         # that should work
 196         class FloatAndComplex(object):
 197             def __float__(self):
 198                 return flt_arg
 199             def __complex__(self):
 200                 return cx_arg
 201         class FloatAndComplexOS:
 202             def __float__(self):
 203                 return flt_arg
 204             def __complex__(self):
 205                 return cx_arg
 206         class JustFloat(object):
 207             def __float__(self):
 208                 return flt_arg
 209         class JustFloatOS:
 210             def __float__(self):
 211                 return flt_arg
 212
 213         for f in self.test_functions:
 214             # usual usage
 215             self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
 216             self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg))
 217             # other combinations of __float__ and __complex__
 218             self.assertEqual(f(FloatAndComplex()), f(cx_arg))
 219             self.assertEqual(f(FloatAndComplexOS()), f(cx_arg))
 220             self.assertEqual(f(JustFloat()), f(flt_arg))
 221             self.assertEqual(f(JustFloatOS()), f(flt_arg))
 222             # TypeError should be raised for classes not providing
 223             # either __complex__ or __float__, even if they provide
 224             # __int__, __long__ or __index__.  An old-style class
 225             # currently raises AttributeError instead of a TypeError;
 226             # this could be considered a bug.
 227             self.assertRaises(TypeError, f, NeitherComplexNorFloat())
 228             self.assertRaises(TypeError, f, MyInt())
 229             self.assertRaises(Exception, f, NeitherComplexNorFloatOS())
 230             self.assertRaises(Exception, f, MyIntOS())
 231             # non-complex return value from __complex__ -> TypeError
 232             for bad_complex in non_complexes:
 233                 self.assertRaises(TypeError, f, MyComplex(bad_complex))
 234                 self.assertRaises(TypeError, f, MyComplexOS(bad_complex))
 235             # exceptions in __complex__ should be propagated correctly
 236             self.assertRaises(SomeException, f, MyComplexException())
 237             self.assertRaises(SomeException, f, MyComplexExceptionOS())
 238
 239     def test_input_type(self):
 240         # ints and longs should be acceptable inputs to all cmath
 241         # functions, by virtue of providing a __float__ method
 242         for f in self.test_functions:
 243             for arg in [2, 2L, 2.]:
 244                 self.assertEqual(f(arg), f(arg.__float__()))
 245
 246         # but strings should give a TypeError
 247         for f in self.test_functions:
 248             for arg in ["a", "long_string", "0", "1j", ""]:
 249                 self.assertRaises(TypeError, f, arg)
 250
 251     def test_cmath_matches_math(self):
 252         # check that corresponding cmath and math functions are equal
 253         # for floats in the appropriate range
 254
 255         # test_values in (0, 1)
 256         test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
 257
 258         # test_values for functions defined on [-1., 1.]
 259         unit_interval = test_values + [-x for x in test_values] + \
 260             [0., 1., -1.]
 261
 262         # test_values for log, log10, sqrt
 263         positive = test_values + [1.] + [1./x for x in test_values]
 264         nonnegative = [0.] + positive
 265
 266         # test_values for functions defined on the whole real line
 267         real_line = [0.] + positive + [-x for x in positive]
 268
 269         test_functions = {
 270             'acos' : unit_interval,
 271             'asin' : unit_interval,
 272             'atan' : real_line,
 273             'cos' : real_line,
 274             'cosh' : real_line,
 275             'exp' : real_line,
 276             'log' : positive,
 277             'log10' : positive,
 278             'sin' : real_line,
 279             'sinh' : real_line,
 280             'sqrt' : nonnegative,
 281             'tan' : real_line,
 282             'tanh' : real_line}
 283
 284         for fn, values in test_functions.items():
 285             float_fn = getattr(math, fn)
 286             complex_fn = getattr(cmath, fn)
 287             for v in values:
 288                 z = complex_fn(v)
 289                 self.rAssertAlmostEqual(float_fn(v), z.real)
 290                 self.assertEqual(0., z.imag)
 291
 292         # test two-argument version of log with various bases
 293         for base in [0.5, 2., 10.]:
 294             for v in positive:
 295                 z = cmath.log(v, base)
 296                 self.rAssertAlmostEqual(math.log(v, base), z.real)
 297                 self.assertEqual(0., z.imag)
 298
 299     def test_specific_values(self):
 300         if not float.__getformat__("double").startswith("IEEE"):
 301             return
 302
 303         def rect_complex(z):
 304             """Wrapped version of rect that accepts a complex number instead of
 305             two float arguments."""
 306             return cmath.rect(z.real, z.imag)
 307
 308         def polar_complex(z):
 309             """Wrapped version of polar that returns a complex number instead of
 310             two floats."""
 311             return complex(*polar(z))
 312
 313         for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
 314             arg = complex(ar, ai)
 315             expected = complex(er, ei)
 316             if fn == 'rect':
 317                 function = rect_complex
 318             elif fn == 'polar':
 319                 function = polar_complex
 320             else:
 321                 function = getattr(cmath, fn)
 322             if 'divide-by-zero' in flags or 'invalid' in flags:
 323                 try:
 324                     actual = function(arg)
 325                 except ValueError:
 326                     continue
 327                 else:
 328                     test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai)
 329                     self.fail('ValueError not raised in test %s' % test_str)
 330
 331             if 'overflow' in flags:
 332                 try:
 333                     actual = function(arg)
 334                 except OverflowError:
 335                     continue
 336                 else:
 337                     test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai)
 338                     self.fail('OverflowError not raised in test %s' % test_str)
 339
 340             actual = function(arg)
 341
 342             if 'ignore-real-sign' in flags:
 343                 actual = complex(abs(actual.real), actual.imag)
 344                 expected = complex(abs(expected.real), expected.imag)
 345             if 'ignore-imag-sign' in flags:
 346                 actual = complex(actual.real, abs(actual.imag))
 347                 expected = complex(expected.real, abs(expected.imag))
 348
 349             # for the real part of the log function, we allow an
 350             # absolute error of up to 2e-15.
 351             if fn in ('log', 'log10'):
 352                 real_abs_err = 2e-15
 353             else:
 354                 real_abs_err = 5e-323
 355
 356             if not (almostEqualF(expected.real, actual.real,
 357                                  abs_err = real_abs_err) and
 358                     almostEqualF(expected.imag, actual.imag)):
 359                 error_message = (
 360                     "%s: %s(complex(%r, %r))\n" % (id, fn, ar, ai) +
 361                     "Expected: complex(%r, %r)\n" %
 362                                     (expected.real, expected.imag) +
 363                     "Received: complex(%r, %r)\n" %
 364                                     (actual.real, actual.imag) +
 365                     "Received value insufficiently close to expected value.")
 366                 self.fail(error_message)
 367
 368     def assertCISEqual(self, a, b):
 369         eps = 1E-7
 370         if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps:
 371             self.fail((a ,b))
 372
 373     def test_polar(self):
 374         self.assertCISEqual(polar(0), (0., 0.))
 375         self.assertCISEqual(polar(1.), (1., 0.))
 376         self.assertCISEqual(polar(-1.), (1., pi))
 377         self.assertCISEqual(polar(1j), (1., pi/2))
 378         self.assertCISEqual(polar(-1j), (1., -pi/2))
 379
 380     def test_phase(self):
 381         self.assertAlmostEqual(phase(0), 0.)
 382         self.assertAlmostEqual(phase(1.), 0.)
 383         self.assertAlmostEqual(phase(-1.), pi)
 384         self.assertAlmostEqual(phase(-1.+1E-300j), pi)
 385         self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
 386         self.assertAlmostEqual(phase(1j), pi/2)
 387         self.assertAlmostEqual(phase(-1j), -pi/2)
 388
 389         # zeros
 390         self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
 391         self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
 392         self.assertEqual(phase(complex(-0.0, 0.0)), pi)
 393         self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
 394
 395         # infinities
 396         self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
 397         self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
 398         self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
 399         self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
 400         self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
 401         self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
 402         self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
 403         self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
 404         self.assertEqual(phase(complex(INF, -2.3)), -0.0)
 405         self.assertEqual(phase(complex(INF, -0.0)), -0.0)
 406         self.assertEqual(phase(complex(INF, 0.0)), 0.0)
 407         self.assertEqual(phase(complex(INF, 2.3)), 0.0)
 408         self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
 409         self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
 410         self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
 411         self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
 412         self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
 413         self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
 414         self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
 415         self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
 416
 417         # real or imaginary part NaN
 418         for z in complex_nans:
 419             self.assertTrue(math.isnan(phase(z)))
 420
 421     def test_abs(self):
 422         # zeros
 423         for z in complex_zeros:
 424             self.assertEqual(abs(z), 0.0)
 425
 426         # infinities
 427         for z in complex_infinities:
 428             self.assertEqual(abs(z), INF)
 429
 430         # real or imaginary part NaN
 431         self.assertEqual(abs(complex(NAN, -INF)), INF)
 432         self.assertTrue(math.isnan(abs(complex(NAN, -2.3))))
 433         self.assertTrue(math.isnan(abs(complex(NAN, -0.0))))
 434         self.assertTrue(math.isnan(abs(complex(NAN, 0.0))))
 435         self.assertTrue(math.isnan(abs(complex(NAN, 2.3))))
 436         self.assertEqual(abs(complex(NAN, INF)), INF)
 437         self.assertEqual(abs(complex(-INF, NAN)), INF)
 438         self.assertTrue(math.isnan(abs(complex(-2.3, NAN))))
 439         self.assertTrue(math.isnan(abs(complex(-0.0, NAN))))
 440         self.assertTrue(math.isnan(abs(complex(0.0, NAN))))
 441         self.assertTrue(math.isnan(abs(complex(2.3, NAN))))
 442         self.assertEqual(abs(complex(INF, NAN)), INF)
 443         self.assertTrue(math.isnan(abs(complex(NAN, NAN))))
 444
 445         # result overflows
 446         if float.__getformat__("double").startswith("IEEE"):
 447             self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308))
 448
 449     def assertCEqual(self, a, b):
 450         eps = 1E-7
 451         if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:
 452             self.fail((a ,b))
 453
 454     def test_rect(self):
 455         self.assertCEqual(rect(0, 0), (0, 0))
 456         self.assertCEqual(rect(1, 0), (1., 0))
 457         self.assertCEqual(rect(1, -pi), (-1., 0))
 458         self.assertCEqual(rect(1, pi/2), (0, 1.))
 459         self.assertCEqual(rect(1, -pi/2), (0, -1.))
 460
 461     def test_isnan(self):
 462         self.assertFalse(cmath.isnan(1))
 463         self.assertFalse(cmath.isnan(1j))
 464         self.assertFalse(cmath.isnan(INF))
 465         self.assertTrue(cmath.isnan(NAN))
 466         self.assertTrue(cmath.isnan(complex(NAN, 0)))
 467         self.assertTrue(cmath.isnan(complex(0, NAN)))
 468         self.assertTrue(cmath.isnan(complex(NAN, NAN)))
 469         self.assertTrue(cmath.isnan(complex(NAN, INF)))
 470         self.assertTrue(cmath.isnan(complex(INF, NAN)))
 471
 472     def test_isinf(self):
 473         self.assertFalse(cmath.isinf(1))
 474         self.assertFalse(cmath.isinf(1j))
 475         self.assertFalse(cmath.isinf(NAN))
 476         self.assertTrue(cmath.isinf(INF))
 477         self.assertTrue(cmath.isinf(complex(INF, 0)))
 478         self.assertTrue(cmath.isinf(complex(0, INF)))
 479         self.assertTrue(cmath.isinf(complex(INF, INF)))
 480         self.assertTrue(cmath.isinf(complex(NAN, INF)))
 481         self.assertTrue(cmath.isinf(complex(INF, NAN)))
 482
 483
 484 def test_main():
 485     run_unittest(CMathTests)
 486
 487 if __name__ == "__main__":
 488     test_main()