Lib/test/test_math.py

   1 # Python test set -- math module
   2 # XXXX Should not do tests around zero only
   3
   4 from test.test_support import run_unittest, verbose
   5 import unittest
   6 import math
   7 import os
   8 import sys
   9 import random
  10
  11 eps = 1E-05
  12 NAN = float('nan')
  13 INF = float('inf')
  14 NINF = float('-inf')
  15
  16 # detect evidence of double-rounding: fsum is not always correctly
  17 # rounded on machines that suffer from double rounding.
  18 x, y = 1e16, 2.9999 # use temporary values to defeat peephole optimizer
  19 HAVE_DOUBLE_ROUNDING = (x + y == 1e16 + 4)
  20
  21 # locate file with test values
  22 if __name__ == '__main__':
  23     file = sys.argv[0]
  24 else:
  25     file = __file__
  26 test_dir = os.path.dirname(file) or os.curdir
  27 test_file = os.path.join(test_dir, 'cmath_testcases.txt')
  28
  29 def parse_testfile(fname):
  30     """Parse a file with test values
  31
  32     Empty lines or lines starting with -- are ignored
  33     yields id, fn, arg_real, arg_imag, exp_real, exp_imag
  34     """
  35     with open(fname) as fp:
  36         for line in fp:
  37             # skip comment lines and blank lines
  38             if line.startswith('--') or not line.strip():
  39                 continue
  40
  41             lhs, rhs = line.split('->')
  42             id, fn, arg_real, arg_imag = lhs.split()
  43             rhs_pieces = rhs.split()
  44             exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1]
  45             flags = rhs_pieces[2:]
  46
  47             yield (id, fn,
  48                    float(arg_real), float(arg_imag),
  49                    float(exp_real), float(exp_imag),
  50                    flags
  51                   )
  52
  53 class MathTests(unittest.TestCase):
  54
  55     def ftest(self, name, value, expected):
  56         if abs(value-expected) > eps:
  57             # Use %r instead of %f so the error message
  58             # displays full precision. Otherwise discrepancies
  59             # in the last few bits will lead to very confusing
  60             # error messages
  61             self.fail('%s returned %r, expected %r' %
  62                       (name, value, expected))
  63
  64     def testConstants(self):
  65         self.ftest('pi', math.pi, 3.1415926)
  66         self.ftest('e', math.e, 2.7182818)
  67
  68     def testAcos(self):
  69         self.assertRaises(TypeError, math.acos)
  70         self.ftest('acos(-1)', math.acos(-1), math.pi)
  71         self.ftest('acos(0)', math.acos(0), math.pi/2)
  72         self.ftest('acos(1)', math.acos(1), 0)
  73         self.assertRaises(ValueError, math.acos, INF)
  74         self.assertRaises(ValueError, math.acos, NINF)
  75         self.assert_(math.isnan(math.acos(NAN)))
  76
  77     def testAcosh(self):
  78         self.assertRaises(TypeError, math.acosh)
  79         self.ftest('acosh(1)', math.acosh(1), 0)
  80         self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
  81         self.assertRaises(ValueError, math.acosh, 0)
  82         self.assertRaises(ValueError, math.acosh, -1)
  83         self.assertEquals(math.acosh(INF), INF)
  84         self.assertRaises(ValueError, math.acosh, NINF)
  85         self.assert_(math.isnan(math.acosh(NAN)))
  86
  87     def testAsin(self):
  88         self.assertRaises(TypeError, math.asin)
  89         self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
  90         self.ftest('asin(0)', math.asin(0), 0)
  91         self.ftest('asin(1)', math.asin(1), math.pi/2)
  92         self.assertRaises(ValueError, math.asin, INF)
  93         self.assertRaises(ValueError, math.asin, NINF)
  94         self.assert_(math.isnan(math.asin(NAN)))
  95
  96     def testAsinh(self):
  97         self.assertRaises(TypeError, math.asinh)
  98         self.ftest('asinh(0)', math.asinh(0), 0)
  99         self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)
 100         self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)
 101         self.assertEquals(math.asinh(INF), INF)
 102         self.assertEquals(math.asinh(NINF), NINF)
 103         self.assert_(math.isnan(math.asinh(NAN)))
 104
 105     def testAtan(self):
 106         self.assertRaises(TypeError, math.atan)
 107         self.ftest('atan(-1)', math.atan(-1), -math.pi/4)
 108         self.ftest('atan(0)', math.atan(0), 0)
 109         self.ftest('atan(1)', math.atan(1), math.pi/4)
 110         self.ftest('atan(inf)', math.atan(INF), math.pi/2)
 111         self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2)
 112         self.assert_(math.isnan(math.atan(NAN)))
 113
 114     def testAtanh(self):
 115         self.assertRaises(TypeError, math.atan)
 116         self.ftest('atanh(0)', math.atanh(0), 0)
 117         self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489)
 118         self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489)
 119         self.assertRaises(ValueError, math.atanh, 1)
 120         self.assertRaises(ValueError, math.atanh, -1)
 121         self.assertRaises(ValueError, math.atanh, INF)
 122         self.assertRaises(ValueError, math.atanh, NINF)
 123         self.assert_(math.isnan(math.atanh(NAN)))
 124
 125     def testAtan2(self):
 126         self.assertRaises(TypeError, math.atan2)
 127         self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)
 128         self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)
 129         self.ftest('atan2(0, 1)', math.atan2(0, 1), 0)
 130         self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4)
 131         self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2)
 132
 133         # math.atan2(0, x)
 134         self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi)
 135         self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi)
 136         self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi)
 137         self.assertEqual(math.atan2(0., 0.), 0.)
 138         self.assertEqual(math.atan2(0., 2.3), 0.)
 139         self.assertEqual(math.atan2(0., INF), 0.)
 140         self.assert_(math.isnan(math.atan2(0., NAN)))
 141         # math.atan2(-0, x)
 142         self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi)
 143         self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi)
 144         self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi)
 145         self.assertEqual(math.atan2(-0., 0.), -0.)
 146         self.assertEqual(math.atan2(-0., 2.3), -0.)
 147         self.assertEqual(math.atan2(-0., INF), -0.)
 148         self.assert_(math.isnan(math.atan2(-0., NAN)))
 149         # math.atan2(INF, x)
 150         self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4)
 151         self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2)
 152         self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2)
 153         self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2)
 154         self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2)
 155         self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4)
 156         self.assert_(math.isnan(math.atan2(INF, NAN)))
 157         # math.atan2(NINF, x)
 158         self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4)
 159         self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2)
 160         self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2)
 161         self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2)
 162         self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2)
 163         self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4)
 164         self.assert_(math.isnan(math.atan2(NINF, NAN)))
 165         # math.atan2(+finite, x)
 166         self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi)
 167         self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2)
 168         self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2)
 169         self.assertEqual(math.atan2(2.3, INF), 0.)
 170         self.assert_(math.isnan(math.atan2(2.3, NAN)))
 171         # math.atan2(-finite, x)
 172         self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi)
 173         self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2)
 174         self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2)
 175         self.assertEqual(math.atan2(-2.3, INF), -0.)
 176         self.assert_(math.isnan(math.atan2(-2.3, NAN)))
 177         # math.atan2(NAN, x)
 178         self.assert_(math.isnan(math.atan2(NAN, NINF)))
 179         self.assert_(math.isnan(math.atan2(NAN, -2.3)))
 180         self.assert_(math.isnan(math.atan2(NAN, -0.)))
 181         self.assert_(math.isnan(math.atan2(NAN, 0.)))
 182         self.assert_(math.isnan(math.atan2(NAN, 2.3)))
 183         self.assert_(math.isnan(math.atan2(NAN, INF)))
 184         self.assert_(math.isnan(math.atan2(NAN, NAN)))
 185
 186     def testCeil(self):
 187         self.assertRaises(TypeError, math.ceil)
 188         # These types will be int in py3k.
 189         self.assertEquals(float, type(math.ceil(1)))
 190         self.assertEquals(float, type(math.ceil(1L)))
 191         self.assertEquals(float, type(math.ceil(1.0)))
 192         self.ftest('ceil(0.5)', math.ceil(0.5), 1)
 193         self.ftest('ceil(1.0)', math.ceil(1.0), 1)
 194         self.ftest('ceil(1.5)', math.ceil(1.5), 2)
 195         self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)
 196         self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)
 197         self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)
 198         self.assertEquals(math.ceil(INF), INF)
 199         self.assertEquals(math.ceil(NINF), NINF)
 200         self.assert_(math.isnan(math.ceil(NAN)))
 201
 202         class TestCeil(object):
 203             def __float__(self):
 204                 return 41.3
 205         class TestNoCeil(object):
 206             pass
 207         self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42)
 208         self.assertRaises(TypeError, math.ceil, TestNoCeil())
 209
 210         t = TestNoCeil()
 211         t.__ceil__ = lambda *args: args
 212         self.assertRaises(TypeError, math.ceil, t)
 213         self.assertRaises(TypeError, math.ceil, t, 0)
 214
 215     if float.__getformat__("double").startswith("IEEE"):
 216         def testCopysign(self):
 217             self.assertRaises(TypeError, math.copysign)
 218             # copysign should let us distinguish signs of zeros
 219             self.assertEquals(copysign(1., 0.), 1.)
 220             self.assertEquals(copysign(1., -0.), -1.)
 221             self.assertEquals(copysign(INF, 0.), INF)
 222             self.assertEquals(copysign(INF, -0.), NINF)
 223             self.assertEquals(copysign(NINF, 0.), INF)
 224             self.assertEquals(copysign(NINF, -0.), NINF)
 225             # and of infinities
 226             self.assertEquals(copysign(1., INF), 1.)
 227             self.assertEquals(copysign(1., NINF), -1.)
 228             self.assertEquals(copysign(INF, INF), INF)
 229             self.assertEquals(copysign(INF, NINF), NINF)
 230             self.assertEquals(copysign(NINF, INF), INF)
 231             self.assertEquals(copysign(NINF, NINF), NINF)
 232             self.assert_(math.isnan(copysign(NAN, 1.)))
 233             self.assert_(math.isnan(copysign(NAN, INF)))
 234             self.assert_(math.isnan(copysign(NAN, NINF)))
 235             self.assert_(math.isnan(copysign(NAN, NAN)))
 236             # copysign(INF, NAN) may be INF or it may be NINF, since
 237             # we don't know whether the sign bit of NAN is set on any
 238             # given platform.
 239             self.assert_(math.isinf(copysign(INF, NAN)))
 240             # similarly, copysign(2., NAN) could be 2. or -2.
 241             self.assertEquals(abs(copysign(2., NAN)), 2.)
 242
 243     def testCos(self):
 244         self.assertRaises(TypeError, math.cos)
 245         self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0)
 246         self.ftest('cos(0)', math.cos(0), 1)
 247         self.ftest('cos(pi/2)', math.cos(math.pi/2), 0)
 248         self.ftest('cos(pi)', math.cos(math.pi), -1)
 249         try:
 250             self.assert_(math.isnan(math.cos(INF)))
 251             self.assert_(math.isnan(math.cos(NINF)))
 252         except ValueError:
 253             self.assertRaises(ValueError, math.cos, INF)
 254             self.assertRaises(ValueError, math.cos, NINF)
 255         self.assert_(math.isnan(math.cos(NAN)))
 256
 257     def testCosh(self):
 258         self.assertRaises(TypeError, math.cosh)
 259         self.ftest('cosh(0)', math.cosh(0), 1)
 260         self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
 261         self.assertEquals(math.cosh(INF), INF)
 262         self.assertEquals(math.cosh(NINF), INF)
 263         self.assert_(math.isnan(math.cosh(NAN)))
 264
 265     def testDegrees(self):
 266         self.assertRaises(TypeError, math.degrees)
 267         self.ftest('degrees(pi)', math.degrees(math.pi), 180.0)
 268         self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0)
 269         self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)
 270
 271     def testExp(self):
 272         self.assertRaises(TypeError, math.exp)
 273         self.ftest('exp(-1)', math.exp(-1), 1/math.e)
 274         self.ftest('exp(0)', math.exp(0), 1)
 275         self.ftest('exp(1)', math.exp(1), math.e)
 276         self.assertEquals(math.exp(INF), INF)
 277         self.assertEquals(math.exp(NINF), 0.)
 278         self.assert_(math.isnan(math.exp(NAN)))
 279
 280     def testFabs(self):
 281         self.assertRaises(TypeError, math.fabs)
 282         self.ftest('fabs(-1)', math.fabs(-1), 1)
 283         self.ftest('fabs(0)', math.fabs(0), 0)
 284         self.ftest('fabs(1)', math.fabs(1), 1)
 285
 286     def testFactorial(self):
 287         def fact(n):
 288             result = 1
 289             for i in range(1, int(n)+1):
 290                 result *= i
 291             return result
 292         values = range(10) + [50, 100, 500]
 293         random.shuffle(values)
 294         for x in range(10):
 295             for cast in (int, long, float):
 296                 self.assertEqual(math.factorial(cast(x)), fact(x), (x, fact(x), math.factorial(x)))
 297         self.assertRaises(ValueError, math.factorial, -1)
 298         self.assertRaises(ValueError, math.factorial, math.pi)
 299
 300     def testFloor(self):
 301         self.assertRaises(TypeError, math.floor)
 302         # These types will be int in py3k.
 303         self.assertEquals(float, type(math.floor(1)))
 304         self.assertEquals(float, type(math.floor(1L)))
 305         self.assertEquals(float, type(math.floor(1.0)))
 306         self.ftest('floor(0.5)', math.floor(0.5), 0)
 307         self.ftest('floor(1.0)', math.floor(1.0), 1)
 308         self.ftest('floor(1.5)', math.floor(1.5), 1)
 309         self.ftest('floor(-0.5)', math.floor(-0.5), -1)
 310         self.ftest('floor(-1.0)', math.floor(-1.0), -1)
 311         self.ftest('floor(-1.5)', math.floor(-1.5), -2)
 312         # pow() relies on floor() to check for integers
 313         # This fails on some platforms - so check it here
 314         self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)
 315         self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)
 316         self.assertEquals(math.ceil(INF), INF)
 317         self.assertEquals(math.ceil(NINF), NINF)
 318         self.assert_(math.isnan(math.floor(NAN)))
 319
 320         class TestFloor(object):
 321             def __float__(self):
 322                 return 42.3
 323         class TestNoFloor(object):
 324             pass
 325         self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42)
 326         self.assertRaises(TypeError, math.floor, TestNoFloor())
 327
 328         t = TestNoFloor()
 329         t.__floor__ = lambda *args: args
 330         self.assertRaises(TypeError, math.floor, t)
 331         self.assertRaises(TypeError, math.floor, t, 0)
 332
 333     def testFmod(self):
 334         self.assertRaises(TypeError, math.fmod)
 335         self.ftest('fmod(10,1)', math.fmod(10,1), 0)
 336         self.ftest('fmod(10,0.5)', math.fmod(10,0.5), 0)
 337         self.ftest('fmod(10,1.5)', math.fmod(10,1.5), 1)
 338         self.ftest('fmod(-10,1)', math.fmod(-10,1), 0)
 339         self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0)
 340         self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1)
 341         self.assert_(math.isnan(math.fmod(NAN, 1.)))
 342         self.assert_(math.isnan(math.fmod(1., NAN)))
 343         self.assert_(math.isnan(math.fmod(NAN, NAN)))
 344         self.assertRaises(ValueError, math.fmod, 1., 0.)
 345         self.assertRaises(ValueError, math.fmod, INF, 1.)
 346         self.assertRaises(ValueError, math.fmod, NINF, 1.)
 347         self.assertRaises(ValueError, math.fmod, INF, 0.)
 348         self.assertEquals(math.fmod(3.0, INF), 3.0)
 349         self.assertEquals(math.fmod(-3.0, INF), -3.0)
 350         self.assertEquals(math.fmod(3.0, NINF), 3.0)
 351         self.assertEquals(math.fmod(-3.0, NINF), -3.0)
 352         self.assertEquals(math.fmod(0.0, 3.0), 0.0)
 353         self.assertEquals(math.fmod(0.0, NINF), 0.0)
 354
 355     def testFrexp(self):
 356         self.assertRaises(TypeError, math.frexp)
 357
 358         def testfrexp(name, (mant, exp), (emant, eexp)):
 359             if abs(mant-emant) > eps or exp != eexp:
 360                 self.fail('%s returned %r, expected %r'%\
 361                           (name, (mant, exp), (emant,eexp)))
 362
 363         testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1))
 364         testfrexp('frexp(0)', math.frexp(0), (0, 0))
 365         testfrexp('frexp(1)', math.frexp(1), (0.5, 1))
 366         testfrexp('frexp(2)', math.frexp(2), (0.5, 2))
 367
 368         self.assertEquals(math.frexp(INF)[0], INF)
 369         self.assertEquals(math.frexp(NINF)[0], NINF)
 370         self.assert_(math.isnan(math.frexp(NAN)[0]))
 371
 372     @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
 373                          "test requires IEEE 754 doubles")
 374     @unittest.skipUnless(not HAVE_DOUBLE_ROUNDING,
 375                          "fsum is not exact on machines with double rounding")
 376     def testFsum(self):
 377         # math.fsum relies on exact rounding for correct operation.
 378         # There's a known problem with IA32 floating-point that causes
 379         # inexact rounding in some situations, and will cause the
 380         # math.fsum tests below to fail; see issue #2937.  On non IEEE
 381         # 754 platforms, and on IEEE 754 platforms that exhibit the
 382         # problem described in issue #2937, we simply skip the whole
 383         # test.
 384
 385         # Python version of math.fsum, for comparison.  Uses a
 386         # different algorithm based on frexp, ldexp and integer
 387         # arithmetic.
 388         from sys import float_info
 389         mant_dig = float_info.mant_dig
 390         etiny = float_info.min_exp - mant_dig
 391
 392         def msum(iterable):
 393             """Full precision summation.  Compute sum(iterable) without any
 394             intermediate accumulation of error.  Based on the 'lsum' function
 395             at http://code.activestate.com/recipes/393090/
 396
 397             """
 398             tmant, texp = 0, 0
 399             for x in iterable:
 400                 mant, exp = math.frexp(x)
 401                 mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
 402                 if texp > exp:
 403                     tmant <<= texp-exp
 404                     texp = exp
 405                 else:
 406                     mant <<= exp-texp
 407                 tmant += mant
 408             # Round tmant * 2**texp to a float.  The original recipe
 409             # used float(str(tmant)) * 2.0**texp for this, but that's
 410             # a little unsafe because str -> float conversion can't be
 411             # relied upon to do correct rounding on all platforms.
 412             tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
 413             if tail > 0:
 414                 h = 1 << (tail-1)
 415                 tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)
 416                 texp += tail
 417             return math.ldexp(tmant, texp)
 418
 419         test_values = [
 420             ([], 0.0),
 421             ([0.0], 0.0),
 422             ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),
 423             ([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0),
 424             ([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0),
 425             ([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0),
 426             ([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0),
 427             ([1./n for n in range(1, 1001)],
 428              float.fromhex('0x1.df11f45f4e61ap+2')),
 429             ([(-1.)**n/n for n in range(1, 1001)],
 430              float.fromhex('-0x1.62a2af1bd3624p-1')),
 431             ([1.7**(i+1)-1.7**i for i in range(1000)] + [-1.7**1000], -1.0),
 432             ([1e16, 1., 1e-16], 10000000000000002.0),
 433             ([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0),
 434             # exercise code for resizing partials array
 435             ([2.**n - 2.**(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] +
 436              [-2.**1022],
 437              float.fromhex('0x1.5555555555555p+970')),
 438             ]
 439
 440         for i, (vals, expected) in enumerate(test_values):
 441             try:
 442                 actual = math.fsum(vals)
 443             except OverflowError:
 444                 self.fail("test %d failed: got OverflowError, expected %r "
 445                           "for math.fsum(%.100r)" % (i, expected, vals))
 446             except ValueError:
 447                 self.fail("test %d failed: got ValueError, expected %r "
 448                           "for math.fsum(%.100r)" % (i, expected, vals))
 449             self.assertEqual(actual, expected)
 450
 451         from random import random, gauss, shuffle
 452         for j in xrange(1000):
 453             vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
 454             s = 0
 455             for i in xrange(200):
 456                 v = gauss(0, random()) ** 7 - s
 457                 s += v
 458                 vals.append(v)
 459             shuffle(vals)
 460
 461             s = msum(vals)
 462             self.assertEqual(msum(vals), math.fsum(vals))
 463
 464     def testHypot(self):
 465         self.assertRaises(TypeError, math.hypot)
 466         self.ftest('hypot(0,0)', math.hypot(0,0), 0)
 467         self.ftest('hypot(3,4)', math.hypot(3,4), 5)
 468         self.assertEqual(math.hypot(NAN, INF), INF)
 469         self.assertEqual(math.hypot(INF, NAN), INF)
 470         self.assertEqual(math.hypot(NAN, NINF), INF)
 471         self.assertEqual(math.hypot(NINF, NAN), INF)
 472         self.assert_(math.isnan(math.hypot(1.0, NAN)))
 473         self.assert_(math.isnan(math.hypot(NAN, -2.0)))
 474
 475     def testLdexp(self):
 476         self.assertRaises(TypeError, math.ldexp)
 477         self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
 478         self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
 479         self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
 480         self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
 481         self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
 482         self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
 483         self.assertEquals(math.ldexp(1., -1000000), 0.)
 484         self.assertEquals(math.ldexp(-1., -1000000), -0.)
 485         self.assertEquals(math.ldexp(INF, 30), INF)
 486         self.assertEquals(math.ldexp(NINF, -213), NINF)
 487         self.assert_(math.isnan(math.ldexp(NAN, 0)))
 488
 489         # large second argument
 490         for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
 491             self.assertEquals(math.ldexp(INF, -n), INF)
 492             self.assertEquals(math.ldexp(NINF, -n), NINF)
 493             self.assertEquals(math.ldexp(1., -n), 0.)
 494             self.assertEquals(math.ldexp(-1., -n), -0.)
 495             self.assertEquals(math.ldexp(0., -n), 0.)
 496             self.assertEquals(math.ldexp(-0., -n), -0.)
 497             self.assert_(math.isnan(math.ldexp(NAN, -n)))
 498
 499             self.assertRaises(OverflowError, math.ldexp, 1., n)
 500             self.assertRaises(OverflowError, math.ldexp, -1., n)
 501             self.assertEquals(math.ldexp(0., n), 0.)
 502             self.assertEquals(math.ldexp(-0., n), -0.)
 503             self.assertEquals(math.ldexp(INF, n), INF)
 504             self.assertEquals(math.ldexp(NINF, n), NINF)
 505             self.assert_(math.isnan(math.ldexp(NAN, n)))
 506
 507     def testLog(self):
 508         self.assertRaises(TypeError, math.log)
 509         self.ftest('log(1/e)', math.log(1/math.e), -1)
 510         self.ftest('log(1)', math.log(1), 0)
 511         self.ftest('log(e)', math.log(math.e), 1)
 512         self.ftest('log(32,2)', math.log(32,2), 5)
 513         self.ftest('log(10**40, 10)', math.log(10**40, 10), 40)
 514         self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)
 515         self.assertEquals(math.log(INF), INF)
 516         self.assertRaises(ValueError, math.log, NINF)
 517         self.assert_(math.isnan(math.log(NAN)))
 518
 519     def testLog1p(self):
 520         self.assertRaises(TypeError, math.log1p)
 521         self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1)
 522         self.ftest('log1p(0)', math.log1p(0), 0)
 523         self.ftest('log1p(e-1)', math.log1p(math.e-1), 1)
 524         self.ftest('log1p(1)', math.log1p(1), math.log(2))
 525         self.assertEquals(math.log1p(INF), INF)
 526         self.assertRaises(ValueError, math.log1p, NINF)
 527         self.assert_(math.isnan(math.log1p(NAN)))
 528         n= 2**90
 529         self.assertAlmostEquals(math.log1p(n), 62.383246250395075)
 530         self.assertAlmostEquals(math.log1p(n), math.log1p(float(n)))
 531
 532     def testLog10(self):
 533         self.assertRaises(TypeError, math.log10)
 534         self.ftest('log10(0.1)', math.log10(0.1), -1)
 535         self.ftest('log10(1)', math.log10(1), 0)
 536         self.ftest('log10(10)', math.log10(10), 1)
 537         self.assertEquals(math.log(INF), INF)
 538         self.assertRaises(ValueError, math.log10, NINF)
 539         self.assert_(math.isnan(math.log10(NAN)))
 540
 541     def testModf(self):
 542         self.assertRaises(TypeError, math.modf)
 543
 544         def testmodf(name, (v1, v2), (e1, e2)):
 545             if abs(v1-e1) > eps or abs(v2-e2):
 546                 self.fail('%s returned %r, expected %r'%\
 547                           (name, (v1,v2), (e1,e2)))
 548
 549         testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))
 550         testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))
 551
 552         self.assertEquals(math.modf(INF), (0.0, INF))
 553         self.assertEquals(math.modf(NINF), (-0.0, NINF))
 554
 555         modf_nan = math.modf(NAN)
 556         self.assert_(math.isnan(modf_nan[0]))
 557         self.assert_(math.isnan(modf_nan[1]))
 558
 559     def testPow(self):
 560         self.assertRaises(TypeError, math.pow)
 561         self.ftest('pow(0,1)', math.pow(0,1), 0)
 562         self.ftest('pow(1,0)', math.pow(1,0), 1)
 563         self.ftest('pow(2,1)', math.pow(2,1), 2)
 564         self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)
 565         self.assertEqual(math.pow(INF, 1), INF)
 566         self.assertEqual(math.pow(NINF, 1), NINF)
 567         self.assertEqual((math.pow(1, INF)), 1.)
 568         self.assertEqual((math.pow(1, NINF)), 1.)
 569         self.assert_(math.isnan(math.pow(NAN, 1)))
 570         self.assert_(math.isnan(math.pow(2, NAN)))
 571         self.assert_(math.isnan(math.pow(0, NAN)))
 572         self.assertEqual(math.pow(1, NAN), 1)
 573
 574         # pow(0., x)
 575         self.assertEqual(math.pow(0., INF), 0.)
 576         self.assertEqual(math.pow(0., 3.), 0.)
 577         self.assertEqual(math.pow(0., 2.3), 0.)
 578         self.assertEqual(math.pow(0., 2.), 0.)
 579         self.assertEqual(math.pow(0., 0.), 1.)
 580         self.assertEqual(math.pow(0., -0.), 1.)
 581         self.assertRaises(ValueError, math.pow, 0., -2.)
 582         self.assertRaises(ValueError, math.pow, 0., -2.3)
 583         self.assertRaises(ValueError, math.pow, 0., -3.)
 584         self.assertRaises(ValueError, math.pow, 0., NINF)
 585         self.assert_(math.isnan(math.pow(0., NAN)))
 586
 587         # pow(INF, x)
 588         self.assertEqual(math.pow(INF, INF), INF)
 589         self.assertEqual(math.pow(INF, 3.), INF)
 590         self.assertEqual(math.pow(INF, 2.3), INF)
 591         self.assertEqual(math.pow(INF, 2.), INF)
 592         self.assertEqual(math.pow(INF, 0.), 1.)
 593         self.assertEqual(math.pow(INF, -0.), 1.)
 594         self.assertEqual(math.pow(INF, -2.), 0.)
 595         self.assertEqual(math.pow(INF, -2.3), 0.)
 596         self.assertEqual(math.pow(INF, -3.), 0.)
 597         self.assertEqual(math.pow(INF, NINF), 0.)
 598         self.assert_(math.isnan(math.pow(INF, NAN)))
 599
 600         # pow(-0., x)
 601         self.assertEqual(math.pow(-0., INF), 0.)
 602         self.assertEqual(math.pow(-0., 3.), -0.)
 603         self.assertEqual(math.pow(-0., 2.3), 0.)
 604         self.assertEqual(math.pow(-0., 2.), 0.)
 605         self.assertEqual(math.pow(-0., 0.), 1.)
 606         self.assertEqual(math.pow(-0., -0.), 1.)
 607         self.assertRaises(ValueError, math.pow, -0., -2.)
 608         self.assertRaises(ValueError, math.pow, -0., -2.3)
 609         self.assertRaises(ValueError, math.pow, -0., -3.)
 610         self.assertRaises(ValueError, math.pow, -0., NINF)
 611         self.assert_(math.isnan(math.pow(-0., NAN)))
 612
 613         # pow(NINF, x)
 614         self.assertEqual(math.pow(NINF, INF), INF)
 615         self.assertEqual(math.pow(NINF, 3.), NINF)
 616         self.assertEqual(math.pow(NINF, 2.3), INF)
 617         self.assertEqual(math.pow(NINF, 2.), INF)
 618         self.assertEqual(math.pow(NINF, 0.), 1.)
 619         self.assertEqual(math.pow(NINF, -0.), 1.)
 620         self.assertEqual(math.pow(NINF, -2.), 0.)
 621         self.assertEqual(math.pow(NINF, -2.3), 0.)
 622         self.assertEqual(math.pow(NINF, -3.), -0.)
 623         self.assertEqual(math.pow(NINF, NINF), 0.)
 624         self.assert_(math.isnan(math.pow(NINF, NAN)))
 625
 626         # pow(-1, x)
 627         self.assertEqual(math.pow(-1., INF), 1.)
 628         self.assertEqual(math.pow(-1., 3.), -1.)
 629         self.assertRaises(ValueError, math.pow, -1., 2.3)
 630         self.assertEqual(math.pow(-1., 2.), 1.)
 631         self.assertEqual(math.pow(-1., 0.), 1.)
 632         self.assertEqual(math.pow(-1., -0.), 1.)
 633         self.assertEqual(math.pow(-1., -2.), 1.)
 634         self.assertRaises(ValueError, math.pow, -1., -2.3)
 635         self.assertEqual(math.pow(-1., -3.), -1.)
 636         self.assertEqual(math.pow(-1., NINF), 1.)
 637         self.assert_(math.isnan(math.pow(-1., NAN)))
 638
 639         # pow(1, x)
 640         self.assertEqual(math.pow(1., INF), 1.)
 641         self.assertEqual(math.pow(1., 3.), 1.)
 642         self.assertEqual(math.pow(1., 2.3), 1.)
 643         self.assertEqual(math.pow(1., 2.), 1.)
 644         self.assertEqual(math.pow(1., 0.), 1.)
 645         self.assertEqual(math.pow(1., -0.), 1.)
 646         self.assertEqual(math.pow(1., -2.), 1.)
 647         self.assertEqual(math.pow(1., -2.3), 1.)
 648         self.assertEqual(math.pow(1., -3.), 1.)
 649         self.assertEqual(math.pow(1., NINF), 1.)
 650         self.assertEqual(math.pow(1., NAN), 1.)
 651
 652         # pow(x, 0) should be 1 for any x
 653         self.assertEqual(math.pow(2.3, 0.), 1.)
 654         self.assertEqual(math.pow(-2.3, 0.), 1.)
 655         self.assertEqual(math.pow(NAN, 0.), 1.)
 656         self.assertEqual(math.pow(2.3, -0.), 1.)
 657         self.assertEqual(math.pow(-2.3, -0.), 1.)
 658         self.assertEqual(math.pow(NAN, -0.), 1.)
 659
 660         # pow(x, y) is invalid if x is negative and y is not integral
 661         self.assertRaises(ValueError, math.pow, -1., 2.3)
 662         self.assertRaises(ValueError, math.pow, -15., -3.1)
 663
 664         # pow(x, NINF)
 665         self.assertEqual(math.pow(1.9, NINF), 0.)
 666         self.assertEqual(math.pow(1.1, NINF), 0.)
 667         self.assertEqual(math.pow(0.9, NINF), INF)
 668         self.assertEqual(math.pow(0.1, NINF), INF)
 669         self.assertEqual(math.pow(-0.1, NINF), INF)
 670         self.assertEqual(math.pow(-0.9, NINF), INF)
 671         self.assertEqual(math.pow(-1.1, NINF), 0.)
 672         self.assertEqual(math.pow(-1.9, NINF), 0.)
 673
 674         # pow(x, INF)
 675         self.assertEqual(math.pow(1.9, INF), INF)
 676         self.assertEqual(math.pow(1.1, INF), INF)
 677         self.assertEqual(math.pow(0.9, INF), 0.)
 678         self.assertEqual(math.pow(0.1, INF), 0.)
 679         self.assertEqual(math.pow(-0.1, INF), 0.)
 680         self.assertEqual(math.pow(-0.9, INF), 0.)
 681         self.assertEqual(math.pow(-1.1, INF), INF)
 682         self.assertEqual(math.pow(-1.9, INF), INF)
 683
 684         # pow(x, y) should work for x negative, y an integer
 685         self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0)
 686         self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0)
 687         self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0)
 688         self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0)
 689         self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0)
 690         self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5)
 691         self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25)
 692         self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125)
 693         self.assertRaises(ValueError, math.pow, -2.0, -0.5)
 694         self.assertRaises(ValueError, math.pow, -2.0, 0.5)
 695
 696         # the following tests have been commented out since they don't
 697         # really belong here:  the implementation of ** for floats is
 698         # independent of the implemention of math.pow
 699         #self.assertEqual(1**NAN, 1)
 700         #self.assertEqual(1**INF, 1)
 701         #self.assertEqual(1**NINF, 1)
 702         #self.assertEqual(1**0, 1)
 703         #self.assertEqual(1.**NAN, 1)
 704         #self.assertEqual(1.**INF, 1)
 705         #self.assertEqual(1.**NINF, 1)
 706         #self.assertEqual(1.**0, 1)
 707
 708     def testRadians(self):
 709         self.assertRaises(TypeError, math.radians)
 710         self.ftest('radians(180)', math.radians(180), math.pi)
 711         self.ftest('radians(90)', math.radians(90), math.pi/2)
 712         self.ftest('radians(-45)', math.radians(-45), -math.pi/4)
 713
 714     def testSin(self):
 715         self.assertRaises(TypeError, math.sin)
 716         self.ftest('sin(0)', math.sin(0), 0)
 717         self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)
 718         self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)
 719         try:
 720             self.assert_(math.isnan(math.sin(INF)))
 721             self.assert_(math.isnan(math.sin(NINF)))
 722         except ValueError:
 723             self.assertRaises(ValueError, math.sin, INF)
 724             self.assertRaises(ValueError, math.sin, NINF)
 725         self.assert_(math.isnan(math.sin(NAN)))
 726
 727     def testSinh(self):
 728         self.assertRaises(TypeError, math.sinh)
 729         self.ftest('sinh(0)', math.sinh(0), 0)
 730         self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
 731         self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
 732         self.assertEquals(math.sinh(INF), INF)
 733         self.assertEquals(math.sinh(NINF), NINF)
 734         self.assert_(math.isnan(math.sinh(NAN)))
 735
 736     def testSqrt(self):
 737         self.assertRaises(TypeError, math.sqrt)
 738         self.ftest('sqrt(0)', math.sqrt(0), 0)
 739         self.ftest('sqrt(1)', math.sqrt(1), 1)
 740         self.ftest('sqrt(4)', math.sqrt(4), 2)
 741         self.assertEquals(math.sqrt(INF), INF)
 742         self.assertRaises(ValueError, math.sqrt, NINF)
 743         self.assert_(math.isnan(math.sqrt(NAN)))
 744
 745     def testTan(self):
 746         self.assertRaises(TypeError, math.tan)
 747         self.ftest('tan(0)', math.tan(0), 0)
 748         self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)
 749         self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)
 750         try:
 751             self.assert_(math.isnan(math.tan(INF)))
 752             self.assert_(math.isnan(math.tan(NINF)))
 753         except:
 754             self.assertRaises(ValueError, math.tan, INF)
 755             self.assertRaises(ValueError, math.tan, NINF)
 756         self.assert_(math.isnan(math.tan(NAN)))
 757
 758     def testTanh(self):
 759         self.assertRaises(TypeError, math.tanh)
 760         self.ftest('tanh(0)', math.tanh(0), 0)
 761         self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)
 762         self.ftest('tanh(inf)', math.tanh(INF), 1)
 763         self.ftest('tanh(-inf)', math.tanh(NINF), -1)
 764         self.assert_(math.isnan(math.tanh(NAN)))
 765         # check that tanh(-0.) == -0. on IEEE 754 systems
 766         if float.__getformat__("double").startswith("IEEE"):
 767             self.assertEqual(math.tanh(-0.), -0.)
 768             self.assertEqual(math.copysign(1., math.tanh(-0.)),
 769                              math.copysign(1., -0.))
 770
 771     def test_trunc(self):
 772         self.assertEqual(math.trunc(1), 1)
 773         self.assertEqual(math.trunc(-1), -1)
 774         self.assertEqual(type(math.trunc(1)), int)
 775         self.assertEqual(type(math.trunc(1.5)), int)
 776         self.assertEqual(math.trunc(1.5), 1)
 777         self.assertEqual(math.trunc(-1.5), -1)
 778         self.assertEqual(math.trunc(1.999999), 1)
 779         self.assertEqual(math.trunc(-1.999999), -1)
 780         self.assertEqual(math.trunc(-0.999999), -0)
 781         self.assertEqual(math.trunc(-100.999), -100)
 782
 783         class TestTrunc(object):
 784             def __trunc__(self):
 785                 return 23
 786
 787         class TestNoTrunc(object):
 788             pass
 789
 790         self.assertEqual(math.trunc(TestTrunc()), 23)
 791
 792         self.assertRaises(TypeError, math.trunc)
 793         self.assertRaises(TypeError, math.trunc, 1, 2)
 794         # XXX: This is not ideal, but see the comment in math_trunc().
 795         self.assertRaises(AttributeError, math.trunc, TestNoTrunc())
 796
 797         t = TestNoTrunc()
 798         t.__trunc__ = lambda *args: args
 799         self.assertEquals((), math.trunc(t))
 800         self.assertRaises(TypeError, math.trunc, t, 0)
 801
 802     def testCopysign(self):
 803         self.assertEqual(math.copysign(1, 42), 1.0)
 804         self.assertEqual(math.copysign(0., 42), 0.0)
 805         self.assertEqual(math.copysign(1., -42), -1.0)
 806         self.assertEqual(math.copysign(3, 0.), 3.0)
 807         self.assertEqual(math.copysign(4., -0.), -4.0)
 808
 809     def testIsnan(self):
 810         self.assert_(math.isnan(float("nan")))
 811         self.assert_(math.isnan(float("inf")* 0.))
 812         self.failIf(math.isnan(float("inf")))
 813         self.failIf(math.isnan(0.))
 814         self.failIf(math.isnan(1.))
 815
 816     def testIsinf(self):
 817         self.assert_(math.isinf(float("inf")))
 818         self.assert_(math.isinf(float("-inf")))
 819         self.assert_(math.isinf(1E400))
 820         self.assert_(math.isinf(-1E400))
 821         self.failIf(math.isinf(float("nan")))
 822         self.failIf(math.isinf(0.))
 823         self.failIf(math.isinf(1.))
 824
 825     # RED_FLAG 16-Oct-2000 Tim
 826     # While 2.0 is more consistent about exceptions than previous releases, it
 827     # still fails this part of the test on some platforms.  For now, we only
 828     # *run* test_exceptions() in verbose mode, so that this isn't normally
 829     # tested.
 830
 831     if verbose:
 832         def test_exceptions(self):
 833             try:
 834                 x = math.exp(-1000000000)
 835             except:
 836                 # mathmodule.c is failing to weed out underflows from libm, or
 837                 # we've got an fp format with huge dynamic range
 838                 self.fail("underflowing exp() should not have raised "
 839                           "an exception")
 840             if x != 0:
 841                 self.fail("underflowing exp() should have returned 0")
 842
 843             # If this fails, probably using a strict IEEE-754 conforming libm, and x
 844             # is +Inf afterwards.  But Python wants overflows detected by default.
 845             try:
 846                 x = math.exp(1000000000)
 847             except OverflowError:
 848                 pass
 849             else:
 850                 self.fail("overflowing exp() didn't trigger OverflowError")
 851
 852             # If this fails, it could be a puzzle.  One odd possibility is that
 853             # mathmodule.c's macros are getting confused while comparing
 854             # Inf (HUGE_VAL) to a NaN, and artificially setting errno to ERANGE
 855             # as a result (and so raising OverflowError instead).
 856             try:
 857                 x = math.sqrt(-1.0)
 858             except ValueError:
 859                 pass
 860             else:
 861                 self.fail("sqrt(-1) didn't raise ValueError")
 862
 863     def test_testfile(self):
 864         if not float.__getformat__("double").startswith("IEEE"):
 865             return
 866         for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
 867             # Skip if either the input or result is complex, or if
 868             # flags is nonempty
 869             if ai != 0. or ei != 0. or flags:
 870                 continue
 871             if fn in ['rect', 'polar']:
 872                 # no real versions of rect, polar
 873                 continue
 874             func = getattr(math, fn)
 875             try:
 876                 result = func(ar)
 877             except ValueError:
 878                 message = ("Unexpected ValueError in " +
 879                            "test %s:%s(%r)\n" % (id, fn, ar))
 880                 self.fail(message)
 881             except OverflowError:
 882                 message = ("Unexpected OverflowError in " +
 883                            "test %s:%s(%r)\n" % (id, fn, ar))
 884                 self.fail(message)
 885             self.ftest("%s:%s(%r)" % (id, fn, ar), result, er)
 886
 887 def test_main():
 888     from doctest import DocFileSuite
 889     suite = unittest.TestSuite()
 890     suite.addTest(unittest.makeSuite(MathTests))
 891     suite.addTest(DocFileSuite("ieee754.txt"))
 892     run_unittest(suite)
 893
 894 if __name__ == '__main__':
 895     test_main()