1# Python test set -- math module 2# XXXX Should not do tests around zero only 3 4from test.test_support import run_unittest, verbose 5import unittest 6import math 7import os 8import sys 9import random 10import struct 11 12eps = 1E-05 13NAN = float('nan') 14INF = float('inf') 15NINF = float('-inf') 16 17# decorator for skipping tests on non-IEEE 754 platforms 18requires_IEEE_754 = unittest.skipUnless( 19 float.__getformat__("double").startswith("IEEE"), 20 "test requires IEEE 754 doubles") 21 22# detect evidence of double-rounding: fsum is not always correctly 23# rounded on machines that suffer from double rounding. 24x, y = 1e16, 2.9999 # use temporary values to defeat peephole optimizer 25HAVE_DOUBLE_ROUNDING = (x + y == 1e16 + 4) 26 27# locate file with test values 28if __name__ == '__main__': 29 file = sys.argv[0] 30else: 31 file = __file__ 32test_dir = os.path.dirname(file) or os.curdir 33math_testcases = os.path.join(test_dir, 'math_testcases.txt') 34test_file = os.path.join(test_dir, 'cmath_testcases.txt') 35 36def to_ulps(x): 37 """Convert a non-NaN float x to an integer, in such a way that 38 adjacent floats are converted to adjacent integers. Then 39 abs(ulps(x) - ulps(y)) gives the difference in ulps between two 40 floats. 41 42 The results from this function will only make sense on platforms 43 where C doubles are represented in IEEE 754 binary64 format. 44 45 """ 46 n = struct.unpack('<q', struct.pack('<d', x))[0] 47 if n < 0: 48 n = ~(n+2**63) 49 return n 50 51def ulps_check(expected, got, ulps=20): 52 """Given non-NaN floats `expected` and `got`, 53 check that they're equal to within the given number of ulps. 54 55 Returns None on success and an error message on failure.""" 56 57 ulps_error = to_ulps(got) - to_ulps(expected) 58 if abs(ulps_error) <= ulps: 59 return None 60 return "error = {} ulps; permitted error = {} ulps".format(ulps_error, 61 ulps) 62 63def acc_check(expected, got, rel_err=2e-15, abs_err = 5e-323): 64 """Determine whether non-NaN floats a and b are equal to within a 65 (small) rounding error. The default values for rel_err and 66 abs_err are chosen to be suitable for platforms where a float is 67 represented by an IEEE 754 double. They allow an error of between 68 9 and 19 ulps.""" 69 70 # need to special case infinities, since inf - inf gives nan 71 if math.isinf(expected) and got == expected: 72 return None 73 74 error = got - expected 75 76 permitted_error = max(abs_err, rel_err * abs(expected)) 77 if abs(error) < permitted_error: 78 return None 79 return "error = {}; permitted error = {}".format(error, 80 permitted_error) 81 82def parse_mtestfile(fname): 83 """Parse a file with test values 84 85 -- starts a comment 86 blank lines, or lines containing only a comment, are ignored 87 other lines are expected to have the form 88 id fn arg -> expected [flag]* 89 90 """ 91 with open(fname) as fp: 92 for line in fp: 93 # strip comments, and skip blank lines 94 if '--' in line: 95 line = line[:line.index('--')] 96 if not line.strip(): 97 continue 98 99 lhs, rhs = line.split('->') 100 id, fn, arg = lhs.split() 101 rhs_pieces = rhs.split() 102 exp = rhs_pieces[0] 103 flags = rhs_pieces[1:] 104 105 yield (id, fn, float(arg), float(exp), flags) 106 107def parse_testfile(fname): 108 """Parse a file with test values 109 110 Empty lines or lines starting with -- are ignored 111 yields id, fn, arg_real, arg_imag, exp_real, exp_imag 112 """ 113 with open(fname) as fp: 114 for line in fp: 115 # skip comment lines and blank lines 116 if line.startswith('--') or not line.strip(): 117 continue 118 119 lhs, rhs = line.split('->') 120 id, fn, arg_real, arg_imag = lhs.split() 121 rhs_pieces = rhs.split() 122 exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1] 123 flags = rhs_pieces[2:] 124 125 yield (id, fn, 126 float(arg_real), float(arg_imag), 127 float(exp_real), float(exp_imag), 128 flags 129 ) 130 131class MathTests(unittest.TestCase): 132 133 def ftest(self, name, value, expected): 134 if abs(value-expected) > eps: 135 # Use %r instead of %f so the error message 136 # displays full precision. Otherwise discrepancies 137 # in the last few bits will lead to very confusing 138 # error messages 139 self.fail('%s returned %r, expected %r' % 140 (name, value, expected)) 141 142 def testConstants(self): 143 self.ftest('pi', math.pi, 3.1415926) 144 self.ftest('e', math.e, 2.7182818) 145 146 def testAcos(self): 147 self.assertRaises(TypeError, math.acos) 148 self.ftest('acos(-1)', math.acos(-1), math.pi) 149 self.ftest('acos(0)', math.acos(0), math.pi/2) 150 self.ftest('acos(1)', math.acos(1), 0) 151 self.assertRaises(ValueError, math.acos, INF) 152 self.assertRaises(ValueError, math.acos, NINF) 153 self.assertTrue(math.isnan(math.acos(NAN))) 154 155 def testAcosh(self): 156 self.assertRaises(TypeError, math.acosh) 157 self.ftest('acosh(1)', math.acosh(1), 0) 158 self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168) 159 self.assertRaises(ValueError, math.acosh, 0) 160 self.assertRaises(ValueError, math.acosh, -1) 161 self.assertEqual(math.acosh(INF), INF) 162 self.assertRaises(ValueError, math.acosh, NINF) 163 self.assertTrue(math.isnan(math.acosh(NAN))) 164 165 def testAsin(self): 166 self.assertRaises(TypeError, math.asin) 167 self.ftest('asin(-1)', math.asin(-1), -math.pi/2) 168 self.ftest('asin(0)', math.asin(0), 0) 169 self.ftest('asin(1)', math.asin(1), math.pi/2) 170 self.assertRaises(ValueError, math.asin, INF) 171 self.assertRaises(ValueError, math.asin, NINF) 172 self.assertTrue(math.isnan(math.asin(NAN))) 173 174 def testAsinh(self): 175 self.assertRaises(TypeError, math.asinh) 176 self.ftest('asinh(0)', math.asinh(0), 0) 177 self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305) 178 self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305) 179 self.assertEqual(math.asinh(INF), INF) 180 self.assertEqual(math.asinh(NINF), NINF) 181 self.assertTrue(math.isnan(math.asinh(NAN))) 182 183 def testAtan(self): 184 self.assertRaises(TypeError, math.atan) 185 self.ftest('atan(-1)', math.atan(-1), -math.pi/4) 186 self.ftest('atan(0)', math.atan(0), 0) 187 self.ftest('atan(1)', math.atan(1), math.pi/4) 188 self.ftest('atan(inf)', math.atan(INF), math.pi/2) 189 self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2) 190 self.assertTrue(math.isnan(math.atan(NAN))) 191 192 def testAtanh(self): 193 self.assertRaises(TypeError, math.atan) 194 self.ftest('atanh(0)', math.atanh(0), 0) 195 self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489) 196 self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489) 197 self.assertRaises(ValueError, math.atanh, 1) 198 self.assertRaises(ValueError, math.atanh, -1) 199 self.assertRaises(ValueError, math.atanh, INF) 200 self.assertRaises(ValueError, math.atanh, NINF) 201 self.assertTrue(math.isnan(math.atanh(NAN))) 202 203 def testAtan2(self): 204 self.assertRaises(TypeError, math.atan2) 205 self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2) 206 self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4) 207 self.ftest('atan2(0, 1)', math.atan2(0, 1), 0) 208 self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4) 209 self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2) 210 211 # math.atan2(0, x) 212 self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi) 213 self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi) 214 self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi) 215 self.assertEqual(math.atan2(0., 0.), 0.) 216 self.assertEqual(math.atan2(0., 2.3), 0.) 217 self.assertEqual(math.atan2(0., INF), 0.) 218 self.assertTrue(math.isnan(math.atan2(0., NAN))) 219 # math.atan2(-0, x) 220 self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi) 221 self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi) 222 self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi) 223 self.assertEqual(math.atan2(-0., 0.), -0.) 224 self.assertEqual(math.atan2(-0., 2.3), -0.) 225 self.assertEqual(math.atan2(-0., INF), -0.) 226 self.assertTrue(math.isnan(math.atan2(-0., NAN))) 227 # math.atan2(INF, x) 228 self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4) 229 self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2) 230 self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2) 231 self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2) 232 self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2) 233 self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4) 234 self.assertTrue(math.isnan(math.atan2(INF, NAN))) 235 # math.atan2(NINF, x) 236 self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4) 237 self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2) 238 self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2) 239 self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2) 240 self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2) 241 self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4) 242 self.assertTrue(math.isnan(math.atan2(NINF, NAN))) 243 # math.atan2(+finite, x) 244 self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi) 245 self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2) 246 self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2) 247 self.assertEqual(math.atan2(2.3, INF), 0.) 248 self.assertTrue(math.isnan(math.atan2(2.3, NAN))) 249 # math.atan2(-finite, x) 250 self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi) 251 self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2) 252 self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2) 253 self.assertEqual(math.atan2(-2.3, INF), -0.) 254 self.assertTrue(math.isnan(math.atan2(-2.3, NAN))) 255 # math.atan2(NAN, x) 256 self.assertTrue(math.isnan(math.atan2(NAN, NINF))) 257 self.assertTrue(math.isnan(math.atan2(NAN, -2.3))) 258 self.assertTrue(math.isnan(math.atan2(NAN, -0.))) 259 self.assertTrue(math.isnan(math.atan2(NAN, 0.))) 260 self.assertTrue(math.isnan(math.atan2(NAN, 2.3))) 261 self.assertTrue(math.isnan(math.atan2(NAN, INF))) 262 self.assertTrue(math.isnan(math.atan2(NAN, NAN))) 263 264 def testCeil(self): 265 self.assertRaises(TypeError, math.ceil) 266 # These types will be int in py3k. 267 self.assertEqual(float, type(math.ceil(1))) 268 self.assertEqual(float, type(math.ceil(1L))) 269 self.assertEqual(float, type(math.ceil(1.0))) 270 self.ftest('ceil(0.5)', math.ceil(0.5), 1) 271 self.ftest('ceil(1.0)', math.ceil(1.0), 1) 272 self.ftest('ceil(1.5)', math.ceil(1.5), 2) 273 self.ftest('ceil(-0.5)', math.ceil(-0.5), 0) 274 self.ftest('ceil(-1.0)', math.ceil(-1.0), -1) 275 self.ftest('ceil(-1.5)', math.ceil(-1.5), -1) 276 self.assertEqual(math.ceil(INF), INF) 277 self.assertEqual(math.ceil(NINF), NINF) 278 self.assertTrue(math.isnan(math.ceil(NAN))) 279 280 class TestCeil(object): 281 def __float__(self): 282 return 41.3 283 class TestNoCeil(object): 284 pass 285 self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42) 286 self.assertRaises(TypeError, math.ceil, TestNoCeil()) 287 288 t = TestNoCeil() 289 t.__ceil__ = lambda *args: args 290 self.assertRaises(TypeError, math.ceil, t) 291 self.assertRaises(TypeError, math.ceil, t, 0) 292 293 @requires_IEEE_754 294 def testCopysign(self): 295 self.assertEqual(math.copysign(1, 42), 1.0) 296 self.assertEqual(math.copysign(0., 42), 0.0) 297 self.assertEqual(math.copysign(1., -42), -1.0) 298 self.assertEqual(math.copysign(3, 0.), 3.0) 299 self.assertEqual(math.copysign(4., -0.), -4.0) 300 301 self.assertRaises(TypeError, math.copysign) 302 # copysign should let us distinguish signs of zeros 303 self.assertEqual(math.copysign(1., 0.), 1.) 304 self.assertEqual(math.copysign(1., -0.), -1.) 305 self.assertEqual(math.copysign(INF, 0.), INF) 306 self.assertEqual(math.copysign(INF, -0.), NINF) 307 self.assertEqual(math.copysign(NINF, 0.), INF) 308 self.assertEqual(math.copysign(NINF, -0.), NINF) 309 # and of infinities 310 self.assertEqual(math.copysign(1., INF), 1.) 311 self.assertEqual(math.copysign(1., NINF), -1.) 312 self.assertEqual(math.copysign(INF, INF), INF) 313 self.assertEqual(math.copysign(INF, NINF), NINF) 314 self.assertEqual(math.copysign(NINF, INF), INF) 315 self.assertEqual(math.copysign(NINF, NINF), NINF) 316 self.assertTrue(math.isnan(math.copysign(NAN, 1.))) 317 self.assertTrue(math.isnan(math.copysign(NAN, INF))) 318 self.assertTrue(math.isnan(math.copysign(NAN, NINF))) 319 self.assertTrue(math.isnan(math.copysign(NAN, NAN))) 320 # copysign(INF, NAN) may be INF or it may be NINF, since 321 # we don't know whether the sign bit of NAN is set on any 322 # given platform. 323 self.assertTrue(math.isinf(math.copysign(INF, NAN))) 324 # similarly, copysign(2., NAN) could be 2. or -2. 325 self.assertEqual(abs(math.copysign(2., NAN)), 2.) 326 327 def testCos(self): 328 self.assertRaises(TypeError, math.cos) 329 self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0) 330 self.ftest('cos(0)', math.cos(0), 1) 331 self.ftest('cos(pi/2)', math.cos(math.pi/2), 0) 332 self.ftest('cos(pi)', math.cos(math.pi), -1) 333 try: 334 self.assertTrue(math.isnan(math.cos(INF))) 335 self.assertTrue(math.isnan(math.cos(NINF))) 336 except ValueError: 337 self.assertRaises(ValueError, math.cos, INF) 338 self.assertRaises(ValueError, math.cos, NINF) 339 self.assertTrue(math.isnan(math.cos(NAN))) 340 341 def testCosh(self): 342 self.assertRaises(TypeError, math.cosh) 343 self.ftest('cosh(0)', math.cosh(0), 1) 344 self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert 345 self.assertEqual(math.cosh(INF), INF) 346 self.assertEqual(math.cosh(NINF), INF) 347 self.assertTrue(math.isnan(math.cosh(NAN))) 348 349 def testDegrees(self): 350 self.assertRaises(TypeError, math.degrees) 351 self.ftest('degrees(pi)', math.degrees(math.pi), 180.0) 352 self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0) 353 self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0) 354 355 def testExp(self): 356 self.assertRaises(TypeError, math.exp) 357 self.ftest('exp(-1)', math.exp(-1), 1/math.e) 358 self.ftest('exp(0)', math.exp(0), 1) 359 self.ftest('exp(1)', math.exp(1), math.e) 360 self.assertEqual(math.exp(INF), INF) 361 self.assertEqual(math.exp(NINF), 0.) 362 self.assertTrue(math.isnan(math.exp(NAN))) 363 364 def testFabs(self): 365 self.assertRaises(TypeError, math.fabs) 366 self.ftest('fabs(-1)', math.fabs(-1), 1) 367 self.ftest('fabs(0)', math.fabs(0), 0) 368 self.ftest('fabs(1)', math.fabs(1), 1) 369 370 def testFactorial(self): 371 def fact(n): 372 result = 1 373 for i in range(1, int(n)+1): 374 result *= i 375 return result 376 values = range(10) + [50, 100, 500] 377 random.shuffle(values) 378 for x in values: 379 for cast in (int, long, float): 380 self.assertEqual(math.factorial(cast(x)), fact(x), (x, fact(x), math.factorial(x))) 381 self.assertRaises(ValueError, math.factorial, -1) 382 self.assertRaises(ValueError, math.factorial, math.pi) 383 384 def testFloor(self): 385 self.assertRaises(TypeError, math.floor) 386 # These types will be int in py3k. 387 self.assertEqual(float, type(math.floor(1))) 388 self.assertEqual(float, type(math.floor(1L))) 389 self.assertEqual(float, type(math.floor(1.0))) 390 self.ftest('floor(0.5)', math.floor(0.5), 0) 391 self.ftest('floor(1.0)', math.floor(1.0), 1) 392 self.ftest('floor(1.5)', math.floor(1.5), 1) 393 self.ftest('floor(-0.5)', math.floor(-0.5), -1) 394 self.ftest('floor(-1.0)', math.floor(-1.0), -1) 395 self.ftest('floor(-1.5)', math.floor(-1.5), -2) 396 # pow() relies on floor() to check for integers 397 # This fails on some platforms - so check it here 398 self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167) 399 self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167) 400 self.assertEqual(math.ceil(INF), INF) 401 self.assertEqual(math.ceil(NINF), NINF) 402 self.assertTrue(math.isnan(math.floor(NAN))) 403 404 class TestFloor(object): 405 def __float__(self): 406 return 42.3 407 class TestNoFloor(object): 408 pass 409 self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42) 410 self.assertRaises(TypeError, math.floor, TestNoFloor()) 411 412 t = TestNoFloor() 413 t.__floor__ = lambda *args: args 414 self.assertRaises(TypeError, math.floor, t) 415 self.assertRaises(TypeError, math.floor, t, 0) 416 417 def testFmod(self): 418 self.assertRaises(TypeError, math.fmod) 419 self.ftest('fmod(10,1)', math.fmod(10,1), 0) 420 self.ftest('fmod(10,0.5)', math.fmod(10,0.5), 0) 421 self.ftest('fmod(10,1.5)', math.fmod(10,1.5), 1) 422 self.ftest('fmod(-10,1)', math.fmod(-10,1), 0) 423 self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0) 424 self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1) 425 self.assertTrue(math.isnan(math.fmod(NAN, 1.))) 426 self.assertTrue(math.isnan(math.fmod(1., NAN))) 427 self.assertTrue(math.isnan(math.fmod(NAN, NAN))) 428 self.assertRaises(ValueError, math.fmod, 1., 0.) 429 self.assertRaises(ValueError, math.fmod, INF, 1.) 430 self.assertRaises(ValueError, math.fmod, NINF, 1.) 431 self.assertRaises(ValueError, math.fmod, INF, 0.) 432 self.assertEqual(math.fmod(3.0, INF), 3.0) 433 self.assertEqual(math.fmod(-3.0, INF), -3.0) 434 self.assertEqual(math.fmod(3.0, NINF), 3.0) 435 self.assertEqual(math.fmod(-3.0, NINF), -3.0) 436 self.assertEqual(math.fmod(0.0, 3.0), 0.0) 437 self.assertEqual(math.fmod(0.0, NINF), 0.0) 438 439 def testFrexp(self): 440 self.assertRaises(TypeError, math.frexp) 441 442 def testfrexp(name, result, expected): 443 (mant, exp), (emant, eexp) = result, expected 444 if abs(mant-emant) > eps or exp != eexp: 445 self.fail('%s returned %r, expected %r'%\ 446 (name, (mant, exp), (emant,eexp))) 447 448 testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1)) 449 testfrexp('frexp(0)', math.frexp(0), (0, 0)) 450 testfrexp('frexp(1)', math.frexp(1), (0.5, 1)) 451 testfrexp('frexp(2)', math.frexp(2), (0.5, 2)) 452 453 self.assertEqual(math.frexp(INF)[0], INF) 454 self.assertEqual(math.frexp(NINF)[0], NINF) 455 self.assertTrue(math.isnan(math.frexp(NAN)[0])) 456 457 @requires_IEEE_754 458 @unittest.skipIf(HAVE_DOUBLE_ROUNDING, 459 "fsum is not exact on machines with double rounding") 460 def testFsum(self): 461 # math.fsum relies on exact rounding for correct operation. 462 # There's a known problem with IA32 floating-point that causes 463 # inexact rounding in some situations, and will cause the 464 # math.fsum tests below to fail; see issue #2937. On non IEEE 465 # 754 platforms, and on IEEE 754 platforms that exhibit the 466 # problem described in issue #2937, we simply skip the whole 467 # test. 468 469 # Python version of math.fsum, for comparison. Uses a 470 # different algorithm based on frexp, ldexp and integer 471 # arithmetic. 472 from sys import float_info 473 mant_dig = float_info.mant_dig 474 etiny = float_info.min_exp - mant_dig 475 476 def msum(iterable): 477 """Full precision summation. Compute sum(iterable) without any 478 intermediate accumulation of error. Based on the 'lsum' function 479 at http://code.activestate.com/recipes/393090/ 480 481 """ 482 tmant, texp = 0, 0 483 for x in iterable: 484 mant, exp = math.frexp(x) 485 mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig 486 if texp > exp: 487 tmant <<= texp-exp 488 texp = exp 489 else: 490 mant <<= exp-texp 491 tmant += mant 492 # Round tmant * 2**texp to a float. The original recipe 493 # used float(str(tmant)) * 2.0**texp for this, but that's 494 # a little unsafe because str -> float conversion can't be 495 # relied upon to do correct rounding on all platforms. 496 tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp) 497 if tail > 0: 498 h = 1 << (tail-1) 499 tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1) 500 texp += tail 501 return math.ldexp(tmant, texp) 502 503 test_values = [ 504 ([], 0.0), 505 ([0.0], 0.0), 506 ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100), 507 ([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0), 508 ([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0), 509 ([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0), 510 ([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0), 511 ([1./n for n in range(1, 1001)], 512 float.fromhex('0x1.df11f45f4e61ap+2')), 513 ([(-1.)**n/n for n in range(1, 1001)], 514 float.fromhex('-0x1.62a2af1bd3624p-1')), 515 ([1.7**(i+1)-1.7**i for i in range(1000)] + [-1.7**1000], -1.0), 516 ([1e16, 1., 1e-16], 10000000000000002.0), 517 ([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0), 518 # exercise code for resizing partials array 519 ([2.**n - 2.**(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] + 520 [-2.**1022], 521 float.fromhex('0x1.5555555555555p+970')), 522 ] 523 524 for i, (vals, expected) in enumerate(test_values): 525 try: 526 actual = math.fsum(vals) 527 except OverflowError: 528 self.fail("test %d failed: got OverflowError, expected %r " 529 "for math.fsum(%.100r)" % (i, expected, vals)) 530 except ValueError: 531 self.fail("test %d failed: got ValueError, expected %r " 532 "for math.fsum(%.100r)" % (i, expected, vals)) 533 self.assertEqual(actual, expected) 534 535 from random import random, gauss, shuffle 536 for j in xrange(1000): 537 vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10 538 s = 0 539 for i in xrange(200): 540 v = gauss(0, random()) ** 7 - s 541 s += v 542 vals.append(v) 543 shuffle(vals) 544 545 s = msum(vals) 546 self.assertEqual(msum(vals), math.fsum(vals)) 547 548 def testHypot(self): 549 self.assertRaises(TypeError, math.hypot) 550 self.ftest('hypot(0,0)', math.hypot(0,0), 0) 551 self.ftest('hypot(3,4)', math.hypot(3,4), 5) 552 self.assertEqual(math.hypot(NAN, INF), INF) 553 self.assertEqual(math.hypot(INF, NAN), INF) 554 self.assertEqual(math.hypot(NAN, NINF), INF) 555 self.assertEqual(math.hypot(NINF, NAN), INF) 556 self.assertTrue(math.isnan(math.hypot(1.0, NAN))) 557 self.assertTrue(math.isnan(math.hypot(NAN, -2.0))) 558 559 def testLdexp(self): 560 self.assertRaises(TypeError, math.ldexp) 561 self.ftest('ldexp(0,1)', math.ldexp(0,1), 0) 562 self.ftest('ldexp(1,1)', math.ldexp(1,1), 2) 563 self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5) 564 self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2) 565 self.assertRaises(OverflowError, math.ldexp, 1., 1000000) 566 self.assertRaises(OverflowError, math.ldexp, -1., 1000000) 567 self.assertEqual(math.ldexp(1., -1000000), 0.) 568 self.assertEqual(math.ldexp(-1., -1000000), -0.) 569 self.assertEqual(math.ldexp(INF, 30), INF) 570 self.assertEqual(math.ldexp(NINF, -213), NINF) 571 self.assertTrue(math.isnan(math.ldexp(NAN, 0))) 572 573 # large second argument 574 for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]: 575 self.assertEqual(math.ldexp(INF, -n), INF) 576 self.assertEqual(math.ldexp(NINF, -n), NINF) 577 self.assertEqual(math.ldexp(1., -n), 0.) 578 self.assertEqual(math.ldexp(-1., -n), -0.) 579 self.assertEqual(math.ldexp(0., -n), 0.) 580 self.assertEqual(math.ldexp(-0., -n), -0.) 581 self.assertTrue(math.isnan(math.ldexp(NAN, -n))) 582 583 self.assertRaises(OverflowError, math.ldexp, 1., n) 584 self.assertRaises(OverflowError, math.ldexp, -1., n) 585 self.assertEqual(math.ldexp(0., n), 0.) 586 self.assertEqual(math.ldexp(-0., n), -0.) 587 self.assertEqual(math.ldexp(INF, n), INF) 588 self.assertEqual(math.ldexp(NINF, n), NINF) 589 self.assertTrue(math.isnan(math.ldexp(NAN, n))) 590 591 def testLog(self): 592 self.assertRaises(TypeError, math.log) 593 self.ftest('log(1/e)', math.log(1/math.e), -1) 594 self.ftest('log(1)', math.log(1), 0) 595 self.ftest('log(e)', math.log(math.e), 1) 596 self.ftest('log(32,2)', math.log(32,2), 5) 597 self.ftest('log(10**40, 10)', math.log(10**40, 10), 40) 598 self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2) 599 self.assertEqual(math.log(INF), INF) 600 self.assertRaises(ValueError, math.log, NINF) 601 self.assertTrue(math.isnan(math.log(NAN))) 602 # Log values should match for int and long (issue #18739). 603 for n in range(1, 1000): 604 self.assertEqual(math.log(n), math.log(long(n))) 605 606 def testLog1p(self): 607 self.assertRaises(TypeError, math.log1p) 608 self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1) 609 self.ftest('log1p(0)', math.log1p(0), 0) 610 self.ftest('log1p(e-1)', math.log1p(math.e-1), 1) 611 self.ftest('log1p(1)', math.log1p(1), math.log(2)) 612 self.assertEqual(math.log1p(INF), INF) 613 self.assertRaises(ValueError, math.log1p, NINF) 614 self.assertTrue(math.isnan(math.log1p(NAN))) 615 n= 2**90 616 self.assertAlmostEqual(math.log1p(n), 62.383246250395075) 617 self.assertAlmostEqual(math.log1p(n), math.log1p(float(n))) 618 619 def testLog10(self): 620 self.assertRaises(TypeError, math.log10) 621 self.ftest('log10(0.1)', math.log10(0.1), -1) 622 self.ftest('log10(1)', math.log10(1), 0) 623 self.ftest('log10(10)', math.log10(10), 1) 624 self.assertEqual(math.log(INF), INF) 625 self.assertRaises(ValueError, math.log10, NINF) 626 self.assertTrue(math.isnan(math.log10(NAN))) 627 # Log values should match for int and long (issue #18739). 628 for n in range(1, 1000): 629 self.assertEqual(math.log10(n), math.log10(long(n))) 630 631 def testModf(self): 632 self.assertRaises(TypeError, math.modf) 633 634 def testmodf(name, result, expected): 635 (v1, v2), (e1, e2) = result, expected 636 if abs(v1-e1) > eps or abs(v2-e2): 637 self.fail('%s returned %r, expected %r'%\ 638 (name, (v1,v2), (e1,e2))) 639 640 testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0)) 641 testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0)) 642 643 self.assertEqual(math.modf(INF), (0.0, INF)) 644 self.assertEqual(math.modf(NINF), (-0.0, NINF)) 645 646 modf_nan = math.modf(NAN) 647 self.assertTrue(math.isnan(modf_nan[0])) 648 self.assertTrue(math.isnan(modf_nan[1])) 649 650 def testPow(self): 651 self.assertRaises(TypeError, math.pow) 652 self.ftest('pow(0,1)', math.pow(0,1), 0) 653 self.ftest('pow(1,0)', math.pow(1,0), 1) 654 self.ftest('pow(2,1)', math.pow(2,1), 2) 655 self.ftest('pow(2,-1)', math.pow(2,-1), 0.5) 656 self.assertEqual(math.pow(INF, 1), INF) 657 self.assertEqual(math.pow(NINF, 1), NINF) 658 self.assertEqual((math.pow(1, INF)), 1.) 659 self.assertEqual((math.pow(1, NINF)), 1.) 660 self.assertTrue(math.isnan(math.pow(NAN, 1))) 661 self.assertTrue(math.isnan(math.pow(2, NAN))) 662 self.assertTrue(math.isnan(math.pow(0, NAN))) 663 self.assertEqual(math.pow(1, NAN), 1) 664 665 # pow(0., x) 666 self.assertEqual(math.pow(0., INF), 0.) 667 self.assertEqual(math.pow(0., 3.), 0.) 668 self.assertEqual(math.pow(0., 2.3), 0.) 669 self.assertEqual(math.pow(0., 2.), 0.) 670 self.assertEqual(math.pow(0., 0.), 1.) 671 self.assertEqual(math.pow(0., -0.), 1.) 672 self.assertRaises(ValueError, math.pow, 0., -2.) 673 self.assertRaises(ValueError, math.pow, 0., -2.3) 674 self.assertRaises(ValueError, math.pow, 0., -3.) 675 self.assertRaises(ValueError, math.pow, 0., NINF) 676 self.assertTrue(math.isnan(math.pow(0., NAN))) 677 678 # pow(INF, x) 679 self.assertEqual(math.pow(INF, INF), INF) 680 self.assertEqual(math.pow(INF, 3.), INF) 681 self.assertEqual(math.pow(INF, 2.3), INF) 682 self.assertEqual(math.pow(INF, 2.), INF) 683 self.assertEqual(math.pow(INF, 0.), 1.) 684 self.assertEqual(math.pow(INF, -0.), 1.) 685 self.assertEqual(math.pow(INF, -2.), 0.) 686 self.assertEqual(math.pow(INF, -2.3), 0.) 687 self.assertEqual(math.pow(INF, -3.), 0.) 688 self.assertEqual(math.pow(INF, NINF), 0.) 689 self.assertTrue(math.isnan(math.pow(INF, NAN))) 690 691 # pow(-0., x) 692 self.assertEqual(math.pow(-0., INF), 0.) 693 self.assertEqual(math.pow(-0., 3.), -0.) 694 self.assertEqual(math.pow(-0., 2.3), 0.) 695 self.assertEqual(math.pow(-0., 2.), 0.) 696 self.assertEqual(math.pow(-0., 0.), 1.) 697 self.assertEqual(math.pow(-0., -0.), 1.) 698 self.assertRaises(ValueError, math.pow, -0., -2.) 699 self.assertRaises(ValueError, math.pow, -0., -2.3) 700 self.assertRaises(ValueError, math.pow, -0., -3.) 701 self.assertRaises(ValueError, math.pow, -0., NINF) 702 self.assertTrue(math.isnan(math.pow(-0., NAN))) 703 704 # pow(NINF, x) 705 self.assertEqual(math.pow(NINF, INF), INF) 706 self.assertEqual(math.pow(NINF, 3.), NINF) 707 self.assertEqual(math.pow(NINF, 2.3), INF) 708 self.assertEqual(math.pow(NINF, 2.), INF) 709 self.assertEqual(math.pow(NINF, 0.), 1.) 710 self.assertEqual(math.pow(NINF, -0.), 1.) 711 self.assertEqual(math.pow(NINF, -2.), 0.) 712 self.assertEqual(math.pow(NINF, -2.3), 0.) 713 self.assertEqual(math.pow(NINF, -3.), -0.) 714 self.assertEqual(math.pow(NINF, NINF), 0.) 715 self.assertTrue(math.isnan(math.pow(NINF, NAN))) 716 717 # pow(-1, x) 718 self.assertEqual(math.pow(-1., INF), 1.) 719 self.assertEqual(math.pow(-1., 3.), -1.) 720 self.assertRaises(ValueError, math.pow, -1., 2.3) 721 self.assertEqual(math.pow(-1., 2.), 1.) 722 self.assertEqual(math.pow(-1., 0.), 1.) 723 self.assertEqual(math.pow(-1., -0.), 1.) 724 self.assertEqual(math.pow(-1., -2.), 1.) 725 self.assertRaises(ValueError, math.pow, -1., -2.3) 726 self.assertEqual(math.pow(-1., -3.), -1.) 727 self.assertEqual(math.pow(-1., NINF), 1.) 728 self.assertTrue(math.isnan(math.pow(-1., NAN))) 729 730 # pow(1, x) 731 self.assertEqual(math.pow(1., INF), 1.) 732 self.assertEqual(math.pow(1., 3.), 1.) 733 self.assertEqual(math.pow(1., 2.3), 1.) 734 self.assertEqual(math.pow(1., 2.), 1.) 735 self.assertEqual(math.pow(1., 0.), 1.) 736 self.assertEqual(math.pow(1., -0.), 1.) 737 self.assertEqual(math.pow(1., -2.), 1.) 738 self.assertEqual(math.pow(1., -2.3), 1.) 739 self.assertEqual(math.pow(1., -3.), 1.) 740 self.assertEqual(math.pow(1., NINF), 1.) 741 self.assertEqual(math.pow(1., NAN), 1.) 742 743 # pow(x, 0) should be 1 for any x 744 self.assertEqual(math.pow(2.3, 0.), 1.) 745 self.assertEqual(math.pow(-2.3, 0.), 1.) 746 self.assertEqual(math.pow(NAN, 0.), 1.) 747 self.assertEqual(math.pow(2.3, -0.), 1.) 748 self.assertEqual(math.pow(-2.3, -0.), 1.) 749 self.assertEqual(math.pow(NAN, -0.), 1.) 750 751 # pow(x, y) is invalid if x is negative and y is not integral 752 self.assertRaises(ValueError, math.pow, -1., 2.3) 753 self.assertRaises(ValueError, math.pow, -15., -3.1) 754 755 # pow(x, NINF) 756 self.assertEqual(math.pow(1.9, NINF), 0.) 757 self.assertEqual(math.pow(1.1, NINF), 0.) 758 self.assertEqual(math.pow(0.9, NINF), INF) 759 self.assertEqual(math.pow(0.1, NINF), INF) 760 self.assertEqual(math.pow(-0.1, NINF), INF) 761 self.assertEqual(math.pow(-0.9, NINF), INF) 762 self.assertEqual(math.pow(-1.1, NINF), 0.) 763 self.assertEqual(math.pow(-1.9, NINF), 0.) 764 765 # pow(x, INF) 766 self.assertEqual(math.pow(1.9, INF), INF) 767 self.assertEqual(math.pow(1.1, INF), INF) 768 self.assertEqual(math.pow(0.9, INF), 0.) 769 self.assertEqual(math.pow(0.1, INF), 0.) 770 self.assertEqual(math.pow(-0.1, INF), 0.) 771 self.assertEqual(math.pow(-0.9, INF), 0.) 772 self.assertEqual(math.pow(-1.1, INF), INF) 773 self.assertEqual(math.pow(-1.9, INF), INF) 774 775 # pow(x, y) should work for x negative, y an integer 776 self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0) 777 self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0) 778 self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0) 779 self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0) 780 self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0) 781 self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5) 782 self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25) 783 self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125) 784 self.assertRaises(ValueError, math.pow, -2.0, -0.5) 785 self.assertRaises(ValueError, math.pow, -2.0, 0.5) 786 787 # the following tests have been commented out since they don't 788 # really belong here: the implementation of ** for floats is 789 # independent of the implementation of math.pow 790 #self.assertEqual(1**NAN, 1) 791 #self.assertEqual(1**INF, 1) 792 #self.assertEqual(1**NINF, 1) 793 #self.assertEqual(1**0, 1) 794 #self.assertEqual(1.**NAN, 1) 795 #self.assertEqual(1.**INF, 1) 796 #self.assertEqual(1.**NINF, 1) 797 #self.assertEqual(1.**0, 1) 798 799 def testRadians(self): 800 self.assertRaises(TypeError, math.radians) 801 self.ftest('radians(180)', math.radians(180), math.pi) 802 self.ftest('radians(90)', math.radians(90), math.pi/2) 803 self.ftest('radians(-45)', math.radians(-45), -math.pi/4) 804 805 def testSin(self): 806 self.assertRaises(TypeError, math.sin) 807 self.ftest('sin(0)', math.sin(0), 0) 808 self.ftest('sin(pi/2)', math.sin(math.pi/2), 1) 809 self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1) 810 try: 811 self.assertTrue(math.isnan(math.sin(INF))) 812 self.assertTrue(math.isnan(math.sin(NINF))) 813 except ValueError: 814 self.assertRaises(ValueError, math.sin, INF) 815 self.assertRaises(ValueError, math.sin, NINF) 816 self.assertTrue(math.isnan(math.sin(NAN))) 817 818 def testSinh(self): 819 self.assertRaises(TypeError, math.sinh) 820 self.ftest('sinh(0)', math.sinh(0), 0) 821 self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1) 822 self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0) 823 self.assertEqual(math.sinh(INF), INF) 824 self.assertEqual(math.sinh(NINF), NINF) 825 self.assertTrue(math.isnan(math.sinh(NAN))) 826 827 def testSqrt(self): 828 self.assertRaises(TypeError, math.sqrt) 829 self.ftest('sqrt(0)', math.sqrt(0), 0) 830 self.ftest('sqrt(1)', math.sqrt(1), 1) 831 self.ftest('sqrt(4)', math.sqrt(4), 2) 832 self.assertEqual(math.sqrt(INF), INF) 833 self.assertRaises(ValueError, math.sqrt, NINF) 834 self.assertTrue(math.isnan(math.sqrt(NAN))) 835 836 def testTan(self): 837 self.assertRaises(TypeError, math.tan) 838 self.ftest('tan(0)', math.tan(0), 0) 839 self.ftest('tan(pi/4)', math.tan(math.pi/4), 1) 840 self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1) 841 try: 842 self.assertTrue(math.isnan(math.tan(INF))) 843 self.assertTrue(math.isnan(math.tan(NINF))) 844 except: 845 self.assertRaises(ValueError, math.tan, INF) 846 self.assertRaises(ValueError, math.tan, NINF) 847 self.assertTrue(math.isnan(math.tan(NAN))) 848 849 def testTanh(self): 850 self.assertRaises(TypeError, math.tanh) 851 self.ftest('tanh(0)', math.tanh(0), 0) 852 self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0) 853 self.ftest('tanh(inf)', math.tanh(INF), 1) 854 self.ftest('tanh(-inf)', math.tanh(NINF), -1) 855 self.assertTrue(math.isnan(math.tanh(NAN))) 856 # check that tanh(-0.) == -0. on IEEE 754 systems 857 if float.__getformat__("double").startswith("IEEE"): 858 self.assertEqual(math.tanh(-0.), -0.) 859 self.assertEqual(math.copysign(1., math.tanh(-0.)), 860 math.copysign(1., -0.)) 861 862 def test_trunc(self): 863 self.assertEqual(math.trunc(1), 1) 864 self.assertEqual(math.trunc(-1), -1) 865 self.assertEqual(type(math.trunc(1)), int) 866 self.assertEqual(type(math.trunc(1.5)), int) 867 self.assertEqual(math.trunc(1.5), 1) 868 self.assertEqual(math.trunc(-1.5), -1) 869 self.assertEqual(math.trunc(1.999999), 1) 870 self.assertEqual(math.trunc(-1.999999), -1) 871 self.assertEqual(math.trunc(-0.999999), -0) 872 self.assertEqual(math.trunc(-100.999), -100) 873 874 class TestTrunc(object): 875 def __trunc__(self): 876 return 23 877 878 class TestNoTrunc(object): 879 pass 880 881 self.assertEqual(math.trunc(TestTrunc()), 23) 882 883 self.assertRaises(TypeError, math.trunc) 884 self.assertRaises(TypeError, math.trunc, 1, 2) 885 self.assertRaises((AttributeError, TypeError), math.trunc, 886 TestNoTrunc()) 887 888 def testIsnan(self): 889 self.assertTrue(math.isnan(float("nan"))) 890 self.assertTrue(math.isnan(float("inf")* 0.)) 891 self.assertFalse(math.isnan(float("inf"))) 892 self.assertFalse(math.isnan(0.)) 893 self.assertFalse(math.isnan(1.)) 894 895 def testIsinf(self): 896 self.assertTrue(math.isinf(float("inf"))) 897 self.assertTrue(math.isinf(float("-inf"))) 898 self.assertTrue(math.isinf(1E400)) 899 self.assertTrue(math.isinf(-1E400)) 900 self.assertFalse(math.isinf(float("nan"))) 901 self.assertFalse(math.isinf(0.)) 902 self.assertFalse(math.isinf(1.)) 903 904 # RED_FLAG 16-Oct-2000 Tim 905 # While 2.0 is more consistent about exceptions than previous releases, it 906 # still fails this part of the test on some platforms. For now, we only 907 # *run* test_exceptions() in verbose mode, so that this isn't normally 908 # tested. 909 @unittest.skipUnless(verbose, 'requires verbose mode') 910 def test_exceptions(self): 911 try: 912 x = math.exp(-1000000000) 913 except: 914 # mathmodule.c is failing to weed out underflows from libm, or 915 # we've got an fp format with huge dynamic range 916 self.fail("underflowing exp() should not have raised " 917 "an exception") 918 if x != 0: 919 self.fail("underflowing exp() should have returned 0") 920 921 # If this fails, probably using a strict IEEE-754 conforming libm, and x 922 # is +Inf afterwards. But Python wants overflows detected by default. 923 try: 924 x = math.exp(1000000000) 925 except OverflowError: 926 pass 927 else: 928 self.fail("overflowing exp() didn't trigger OverflowError") 929 930 # If this fails, it could be a puzzle. One odd possibility is that 931 # mathmodule.c's macros are getting confused while comparing 932 # Inf (HUGE_VAL) to a NaN, and artificially setting errno to ERANGE 933 # as a result (and so raising OverflowError instead). 934 try: 935 x = math.sqrt(-1.0) 936 except ValueError: 937 pass 938 else: 939 self.fail("sqrt(-1) didn't raise ValueError") 940 941 @requires_IEEE_754 942 def test_testfile(self): 943 for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file): 944 # Skip if either the input or result is complex, or if 945 # flags is nonempty 946 if ai != 0. or ei != 0. or flags: 947 continue 948 if fn in ['rect', 'polar']: 949 # no real versions of rect, polar 950 continue 951 func = getattr(math, fn) 952 try: 953 result = func(ar) 954 except ValueError: 955 message = ("Unexpected ValueError in " + 956 "test %s:%s(%r)\n" % (id, fn, ar)) 957 self.fail(message) 958 except OverflowError: 959 message = ("Unexpected OverflowError in " + 960 "test %s:%s(%r)\n" % (id, fn, ar)) 961 self.fail(message) 962 self.ftest("%s:%s(%r)" % (id, fn, ar), result, er) 963 964 @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"), 965 "test requires IEEE 754 doubles") 966 def test_mtestfile(self): 967 ALLOWED_ERROR = 20 # permitted error, in ulps 968 fail_fmt = "{}:{}({!r}): expected {!r}, got {!r}" 969 970 failures = [] 971 for id, fn, arg, expected, flags in parse_mtestfile(math_testcases): 972 func = getattr(math, fn) 973 974 if 'invalid' in flags or 'divide-by-zero' in flags: 975 expected = 'ValueError' 976 elif 'overflow' in flags: 977 expected = 'OverflowError' 978 979 try: 980 got = func(arg) 981 except ValueError: 982 got = 'ValueError' 983 except OverflowError: 984 got = 'OverflowError' 985 986 accuracy_failure = None 987 if isinstance(got, float) and isinstance(expected, float): 988 if math.isnan(expected) and math.isnan(got): 989 continue 990 if not math.isnan(expected) and not math.isnan(got): 991 if fn == 'lgamma': 992 # we use a weaker accuracy test for lgamma; 993 # lgamma only achieves an absolute error of 994 # a few multiples of the machine accuracy, in 995 # general. 996 accuracy_failure = acc_check(expected, got, 997 rel_err = 5e-15, 998 abs_err = 5e-15) 999 elif fn == 'erfc': 1000 # erfc has less-than-ideal accuracy for large 1001 # arguments (x ~ 25 or so), mainly due to the 1002 # error involved in computing exp(-x*x). 1003 # 1004 # XXX Would be better to weaken this test only 1005 # for large x, instead of for all x. 1006 accuracy_failure = ulps_check(expected, got, 2000) 1007 1008 else: 1009 accuracy_failure = ulps_check(expected, got, 20) 1010 if accuracy_failure is None: 1011 continue 1012 1013 if isinstance(got, str) and isinstance(expected, str): 1014 if got == expected: 1015 continue 1016 1017 fail_msg = fail_fmt.format(id, fn, arg, expected, got) 1018 if accuracy_failure is not None: 1019 fail_msg += ' ({})'.format(accuracy_failure) 1020 failures.append(fail_msg) 1021 1022 if failures: 1023 self.fail('Failures in test_mtestfile:\n ' + 1024 '\n '.join(failures)) 1025 1026 1027def test_main(): 1028 from doctest import DocFileSuite 1029 suite = unittest.TestSuite() 1030 suite.addTest(unittest.makeSuite(MathTests)) 1031 suite.addTest(DocFileSuite("ieee754.txt")) 1032 run_unittest(suite) 1033 1034if __name__ == '__main__': 1035 test_main() 1036