1 2 import unittest, struct 3 import os 4 from test import test_support 5 import math 6 from math import isinf, isnan, copysign, ldexp 7 import operator 8 import random 9 import fractions 10 import sys 11 import time 12 13 INF = float("inf") 14 NAN = float("nan") 15 16 have_getformat = hasattr(float, "__getformat__") 17 requires_getformat = unittest.skipUnless(have_getformat, 18 "requires __getformat__") 19 requires_setformat = unittest.skipUnless(hasattr(float, "__setformat__"), 20 "requires __setformat__") 21 # decorator for skipping tests on non-IEEE 754 platforms 22 requires_IEEE_754 = unittest.skipUnless(have_getformat and 23 float.__getformat__("double").startswith("IEEE"), 24 "test requires IEEE 754 doubles") 25 26 #locate file with float format test values 27 test_dir = os.path.dirname(__file__) or os.curdir 28 format_testfile = os.path.join(test_dir, 'formatfloat_testcases.txt') 29 30 class FloatSubclass(float): 31 pass 32 33 class OtherFloatSubclass(float): 34 pass 35 36 class GeneralFloatCases(unittest.TestCase): 37 38 def test_float(self): 39 self.assertEqual(float(3.14), 3.14) 40 self.assertEqual(float(314), 314.0) 41 self.assertEqual(float(314L), 314.0) 42 self.assertEqual(float(" 3.14 "), 3.14) 43 self.assertRaises(ValueError, float, " 0x3.1 ") 44 self.assertRaises(ValueError, float, " -0x3.p-1 ") 45 self.assertRaises(ValueError, float, " +0x3.p-1 ") 46 self.assertRaises(ValueError, float, "++3.14") 47 self.assertRaises(ValueError, float, "+-3.14") 48 self.assertRaises(ValueError, float, "-+3.14") 49 self.assertRaises(ValueError, float, "--3.14") 50 # check that we don't accept alternate exponent markers 51 self.assertRaises(ValueError, float, "-1.7d29") 52 self.assertRaises(ValueError, float, "3D-14") 53 if test_support.have_unicode: 54 self.assertEqual(float(unicode(" 3.14 ")), 3.14) 55 self.assertEqual(float(unicode(" \u0663.\u0661\u0664 ",'raw-unicode-escape')), 3.14) 56 57 # extra long strings should no longer be a problem 58 # (in 2.6, long unicode inputs to float raised ValueError) 59 float('.' + '1'*1000) 60 float(unicode('.' + '1'*1000)) 61 62 def test_non_numeric_input_types(self): 63 # Test possible non-numeric types for the argument x, including 64 # subclasses of the explicitly documented accepted types. 65 class CustomStr(str): pass 66 class CustomByteArray(bytearray): pass 67 factories = [str, bytearray, CustomStr, CustomByteArray, buffer] 68 69 if test_support.have_unicode: 70 class CustomUnicode(unicode): pass 71 factories += [unicode, CustomUnicode] 72 73 for f in factories: 74 with test_support.check_py3k_warnings(quiet=True): 75 x = f(" 3.14 ") 76 msg = 'x has value %s and type %s' % (x, type(x).__name__) 77 try: 78 self.assertEqual(float(x), 3.14, msg=msg) 79 except TypeError, err: 80 raise AssertionError('For %s got TypeError: %s' % 81 (type(x).__name__, err)) 82 errmsg = "could not convert" 83 with self.assertRaisesRegexp(ValueError, errmsg, msg=msg), \ 84 test_support.check_py3k_warnings(quiet=True): 85 float(f('A' * 0x10)) 86 87 def test_float_buffer(self): 88 with test_support.check_py3k_warnings(): 89 self.assertEqual(float(buffer('12.3', 1, 3)), 2.3) 90 self.assertEqual(float(buffer('12.3\x00', 1, 3)), 2.3) 91 self.assertEqual(float(buffer('12.3 ', 1, 3)), 2.3) 92 self.assertEqual(float(buffer('12.3A', 1, 3)), 2.3) 93 self.assertEqual(float(buffer('12.34', 1, 3)), 2.3) 94 95 def check_conversion_to_int(self, x): 96 """Check that int(x) has the correct value and type, for a float x.""" 97 n = int(x) 98 if x >= 0.0: 99 # x >= 0 and n = int(x) ==> n <= x < n + 1 100 self.assertLessEqual(n, x) 101 self.assertLess(x, n + 1) 102 else: 103 # x < 0 and n = int(x) ==> n >= x > n - 1 104 self.assertGreaterEqual(n, x) 105 self.assertGreater(x, n - 1) 106 107 # Result should be an int if within range, else a long. 108 if -sys.maxint-1 <= n <= sys.maxint: 109 self.assertEqual(type(n), int) 110 else: 111 self.assertEqual(type(n), long) 112 113 # Double check. 114 self.assertEqual(type(int(n)), type(n)) 115 116 def test_conversion_to_int(self): 117 # Check that floats within the range of an int convert to type 118 # int, not long. (issue #11144.) 119 boundary = float(sys.maxint + 1) 120 epsilon = 2**-sys.float_info.mant_dig * boundary 121 122 # These 2 floats are either side of the positive int/long boundary on 123 # both 32-bit and 64-bit systems. 124 self.check_conversion_to_int(boundary - epsilon) 125 self.check_conversion_to_int(boundary) 126 127 # These floats are either side of the negative long/int boundary on 128 # 64-bit systems... 129 self.check_conversion_to_int(-boundary - 2*epsilon) 130 self.check_conversion_to_int(-boundary) 131 132 # ... and these ones are either side of the negative long/int 133 # boundary on 32-bit systems. 134 self.check_conversion_to_int(-boundary - 1.0) 135 self.check_conversion_to_int(-boundary - 1.0 + 2*epsilon) 136 137 @test_support.run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE') 138 def test_float_with_comma(self): 139 # set locale to something that doesn't use '.' for the decimal point 140 # float must not accept the locale specific decimal point but 141 # it still has to accept the normal python syntax 142 import locale 143 if not locale.localeconv()['decimal_point'] == ',': 144 self.skipTest('decimal_point is not ","') 145 146 self.assertEqual(float(" 3.14 "), 3.14) 147 self.assertEqual(float("+3.14 "), 3.14) 148 self.assertEqual(float("-3.14 "), -3.14) 149 self.assertEqual(float(".14 "), .14) 150 self.assertEqual(float("3. "), 3.0) 151 self.assertEqual(float("3.e3 "), 3000.0) 152 self.assertEqual(float("3.2e3 "), 3200.0) 153 self.assertEqual(float("2.5e-1 "), 0.25) 154 self.assertEqual(float("5e-1"), 0.5) 155 self.assertRaises(ValueError, float, " 3,14 ") 156 self.assertRaises(ValueError, float, " +3,14 ") 157 self.assertRaises(ValueError, float, " -3,14 ") 158 self.assertRaises(ValueError, float, " 0x3.1 ") 159 self.assertRaises(ValueError, float, " -0x3.p-1 ") 160 self.assertRaises(ValueError, float, " +0x3.p-1 ") 161 self.assertEqual(float(" 25.e-1 "), 2.5) 162 self.assertEqual(test_support.fcmp(float(" .25e-1 "), .025), 0) 163 164 def test_floatconversion(self): 165 # Make sure that calls to __float__() work properly 166 class Foo0: 167 def __float__(self): 168 return 42. 169 170 class Foo1(object): 171 def __float__(self): 172 return 42. 173 174 class Foo2(float): 175 def __float__(self): 176 return 42. 177 178 class Foo3(float): 179 def __new__(cls, value=0.): 180 return float.__new__(cls, 2*value) 181 182 def __float__(self): 183 return self 184 185 class Foo4(float): 186 def __float__(self): 187 return 42 188 189 # Issue 5759: __float__ not called on str subclasses (though it is on 190 # unicode subclasses). 191 class FooStr(str): 192 def __float__(self): 193 return float(str(self)) + 1 194 195 class FooUnicode(unicode): 196 def __float__(self): 197 return float(unicode(self)) + 1 198 199 self.assertAlmostEqual(float(Foo0()), 42.) 200 self.assertAlmostEqual(float(Foo1()), 42.) 201 self.assertAlmostEqual(float(Foo2()), 42.) 202 self.assertAlmostEqual(float(Foo3(21)), 42.) 203 self.assertRaises(TypeError, float, Foo4(42)) 204 self.assertAlmostEqual(float(FooUnicode('8')), 9.) 205 self.assertAlmostEqual(float(FooStr('8')), 9.) 206 207 class Foo5: 208 def __float__(self): 209 return "" 210 self.assertRaises(TypeError, time.sleep, Foo5()) 211 212 # Issue #24731 213 class F: 214 def __float__(self): 215 return OtherFloatSubclass(42.) 216 self.assertAlmostEqual(float(F()), 42.) 217 self.assertIs(type(float(F())), OtherFloatSubclass) 218 self.assertAlmostEqual(FloatSubclass(F()), 42.) 219 self.assertIs(type(FloatSubclass(F())), FloatSubclass) 220 221 def test_is_integer(self): 222 self.assertFalse((1.1).is_integer()) 223 self.assertTrue((1.).is_integer()) 224 self.assertFalse(float("nan").is_integer()) 225 self.assertFalse(float("inf").is_integer()) 226 227 def test_floatasratio(self): 228 for f, ratio in [ 229 (0.875, (7, 8)), 230 (-0.875, (-7, 8)), 231 (0.0, (0, 1)), 232 (11.5, (23, 2)), 233 ]: 234 self.assertEqual(f.as_integer_ratio(), ratio) 235 236 for i in range(10000): 237 f = random.random() 238 f *= 10 ** random.randint(-100, 100) 239 n, d = f.as_integer_ratio() 240 self.assertEqual(float(n).__truediv__(d), f) 241 242 R = fractions.Fraction 243 self.assertEqual(R(0, 1), 244 R(*float(0.0).as_integer_ratio())) 245 self.assertEqual(R(5, 2), 246 R(*float(2.5).as_integer_ratio())) 247 self.assertEqual(R(1, 2), 248 R(*float(0.5).as_integer_ratio())) 249 self.assertEqual(R(4728779608739021, 2251799813685248), 250 R(*float(2.1).as_integer_ratio())) 251 self.assertEqual(R(-4728779608739021, 2251799813685248), 252 R(*float(-2.1).as_integer_ratio())) 253 self.assertEqual(R(-2100, 1), 254 R(*float(-2100.0).as_integer_ratio())) 255 256 self.assertRaises(OverflowError, float('inf').as_integer_ratio) 257 self.assertRaises(OverflowError, float('-inf').as_integer_ratio) 258 self.assertRaises(ValueError, float('nan').as_integer_ratio) 259 260 def assertEqualAndEqualSign(self, a, b): 261 # fail unless a == b and a and b have the same sign bit; 262 # the only difference from assertEqual is that this test 263 # distinguishes -0.0 and 0.0. 264 self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b))) 265 266 @requires_IEEE_754 267 def test_float_mod(self): 268 # Check behaviour of % operator for IEEE 754 special cases. 269 # In particular, check signs of zeros. 270 mod = operator.mod 271 272 self.assertEqualAndEqualSign(mod(-1.0, 1.0), 0.0) 273 self.assertEqualAndEqualSign(mod(-1e-100, 1.0), 1.0) 274 self.assertEqualAndEqualSign(mod(-0.0, 1.0), 0.0) 275 self.assertEqualAndEqualSign(mod(0.0, 1.0), 0.0) 276 self.assertEqualAndEqualSign(mod(1e-100, 1.0), 1e-100) 277 self.assertEqualAndEqualSign(mod(1.0, 1.0), 0.0) 278 279 self.assertEqualAndEqualSign(mod(-1.0, -1.0), -0.0) 280 self.assertEqualAndEqualSign(mod(-1e-100, -1.0), -1e-100) 281 self.assertEqualAndEqualSign(mod(-0.0, -1.0), -0.0) 282 self.assertEqualAndEqualSign(mod(0.0, -1.0), -0.0) 283 self.assertEqualAndEqualSign(mod(1e-100, -1.0), -1.0) 284 self.assertEqualAndEqualSign(mod(1.0, -1.0), -0.0) 285 286 @requires_IEEE_754 287 def test_float_pow(self): 288 # test builtin pow and ** operator for IEEE 754 special cases. 289 # Special cases taken from section F.9.4.4 of the C99 specification 290 291 for pow_op in pow, operator.pow: 292 # x**NAN is NAN for any x except 1 293 self.assertTrue(isnan(pow_op(-INF, NAN))) 294 self.assertTrue(isnan(pow_op(-2.0, NAN))) 295 self.assertTrue(isnan(pow_op(-1.0, NAN))) 296 self.assertTrue(isnan(pow_op(-0.5, NAN))) 297 self.assertTrue(isnan(pow_op(-0.0, NAN))) 298 self.assertTrue(isnan(pow_op(0.0, NAN))) 299 self.assertTrue(isnan(pow_op(0.5, NAN))) 300 self.assertTrue(isnan(pow_op(2.0, NAN))) 301 self.assertTrue(isnan(pow_op(INF, NAN))) 302 self.assertTrue(isnan(pow_op(NAN, NAN))) 303 304 # NAN**y is NAN for any y except +-0 305 self.assertTrue(isnan(pow_op(NAN, -INF))) 306 self.assertTrue(isnan(pow_op(NAN, -2.0))) 307 self.assertTrue(isnan(pow_op(NAN, -1.0))) 308 self.assertTrue(isnan(pow_op(NAN, -0.5))) 309 self.assertTrue(isnan(pow_op(NAN, 0.5))) 310 self.assertTrue(isnan(pow_op(NAN, 1.0))) 311 self.assertTrue(isnan(pow_op(NAN, 2.0))) 312 self.assertTrue(isnan(pow_op(NAN, INF))) 313 314 # (+-0)**y raises ZeroDivisionError for y a negative odd integer 315 self.assertRaises(ZeroDivisionError, pow_op, -0.0, -1.0) 316 self.assertRaises(ZeroDivisionError, pow_op, 0.0, -1.0) 317 318 # (+-0)**y raises ZeroDivisionError for y finite and negative 319 # but not an odd integer 320 self.assertRaises(ZeroDivisionError, pow_op, -0.0, -2.0) 321 self.assertRaises(ZeroDivisionError, pow_op, -0.0, -0.5) 322 self.assertRaises(ZeroDivisionError, pow_op, 0.0, -2.0) 323 self.assertRaises(ZeroDivisionError, pow_op, 0.0, -0.5) 324 325 # (+-0)**y is +-0 for y a positive odd integer 326 self.assertEqualAndEqualSign(pow_op(-0.0, 1.0), -0.0) 327 self.assertEqualAndEqualSign(pow_op(0.0, 1.0), 0.0) 328 329 # (+-0)**y is 0 for y finite and positive but not an odd integer 330 self.assertEqualAndEqualSign(pow_op(-0.0, 0.5), 0.0) 331 self.assertEqualAndEqualSign(pow_op(-0.0, 2.0), 0.0) 332 self.assertEqualAndEqualSign(pow_op(0.0, 0.5), 0.0) 333 self.assertEqualAndEqualSign(pow_op(0.0, 2.0), 0.0) 334 335 # (-1)**+-inf is 1 336 self.assertEqualAndEqualSign(pow_op(-1.0, -INF), 1.0) 337 self.assertEqualAndEqualSign(pow_op(-1.0, INF), 1.0) 338 339 # 1**y is 1 for any y, even if y is an infinity or nan 340 self.assertEqualAndEqualSign(pow_op(1.0, -INF), 1.0) 341 self.assertEqualAndEqualSign(pow_op(1.0, -2.0), 1.0) 342 self.assertEqualAndEqualSign(pow_op(1.0, -1.0), 1.0) 343 self.assertEqualAndEqualSign(pow_op(1.0, -0.5), 1.0) 344 self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0) 345 self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0) 346 self.assertEqualAndEqualSign(pow_op(1.0, 0.5), 1.0) 347 self.assertEqualAndEqualSign(pow_op(1.0, 1.0), 1.0) 348 self.assertEqualAndEqualSign(pow_op(1.0, 2.0), 1.0) 349 self.assertEqualAndEqualSign(pow_op(1.0, INF), 1.0) 350 self.assertEqualAndEqualSign(pow_op(1.0, NAN), 1.0) 351 352 # x**+-0 is 1 for any x, even if x is a zero, infinity, or nan 353 self.assertEqualAndEqualSign(pow_op(-INF, 0.0), 1.0) 354 self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0) 355 self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0) 356 self.assertEqualAndEqualSign(pow_op(-0.5, 0.0), 1.0) 357 self.assertEqualAndEqualSign(pow_op(-0.0, 0.0), 1.0) 358 self.assertEqualAndEqualSign(pow_op(0.0, 0.0), 1.0) 359 self.assertEqualAndEqualSign(pow_op(0.5, 0.0), 1.0) 360 self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0) 361 self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0) 362 self.assertEqualAndEqualSign(pow_op(INF, 0.0), 1.0) 363 self.assertEqualAndEqualSign(pow_op(NAN, 0.0), 1.0) 364 self.assertEqualAndEqualSign(pow_op(-INF, -0.0), 1.0) 365 self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0) 366 self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0) 367 self.assertEqualAndEqualSign(pow_op(-0.5, -0.0), 1.0) 368 self.assertEqualAndEqualSign(pow_op(-0.0, -0.0), 1.0) 369 self.assertEqualAndEqualSign(pow_op(0.0, -0.0), 1.0) 370 self.assertEqualAndEqualSign(pow_op(0.5, -0.0), 1.0) 371 self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0) 372 self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0) 373 self.assertEqualAndEqualSign(pow_op(INF, -0.0), 1.0) 374 self.assertEqualAndEqualSign(pow_op(NAN, -0.0), 1.0) 375 376 # x**y raises ValueError for finite negative x and non-integral y 377 self.assertRaises(ValueError, pow_op, -2.0, -0.5) 378 self.assertRaises(ValueError, pow_op, -2.0, 0.5) 379 self.assertRaises(ValueError, pow_op, -1.0, -0.5) 380 self.assertRaises(ValueError, pow_op, -1.0, 0.5) 381 self.assertRaises(ValueError, pow_op, -0.5, -0.5) 382 self.assertRaises(ValueError, pow_op, -0.5, 0.5) 383 384 # x**-INF is INF for abs(x) < 1 385 self.assertEqualAndEqualSign(pow_op(-0.5, -INF), INF) 386 self.assertEqualAndEqualSign(pow_op(-0.0, -INF), INF) 387 self.assertEqualAndEqualSign(pow_op(0.0, -INF), INF) 388 self.assertEqualAndEqualSign(pow_op(0.5, -INF), INF) 389 390 # x**-INF is 0 for abs(x) > 1 391 self.assertEqualAndEqualSign(pow_op(-INF, -INF), 0.0) 392 self.assertEqualAndEqualSign(pow_op(-2.0, -INF), 0.0) 393 self.assertEqualAndEqualSign(pow_op(2.0, -INF), 0.0) 394 self.assertEqualAndEqualSign(pow_op(INF, -INF), 0.0) 395 396 # x**INF is 0 for abs(x) < 1 397 self.assertEqualAndEqualSign(pow_op(-0.5, INF), 0.0) 398 self.assertEqualAndEqualSign(pow_op(-0.0, INF), 0.0) 399 self.assertEqualAndEqualSign(pow_op(0.0, INF), 0.0) 400 self.assertEqualAndEqualSign(pow_op(0.5, INF), 0.0) 401 402 # x**INF is INF for abs(x) > 1 403 self.assertEqualAndEqualSign(pow_op(-INF, INF), INF) 404 self.assertEqualAndEqualSign(pow_op(-2.0, INF), INF) 405 self.assertEqualAndEqualSign(pow_op(2.0, INF), INF) 406 self.assertEqualAndEqualSign(pow_op(INF, INF), INF) 407 408 # (-INF)**y is -0.0 for y a negative odd integer 409 self.assertEqualAndEqualSign(pow_op(-INF, -1.0), -0.0) 410 411 # (-INF)**y is 0.0 for y negative but not an odd integer 412 self.assertEqualAndEqualSign(pow_op(-INF, -0.5), 0.0) 413 self.assertEqualAndEqualSign(pow_op(-INF, -2.0), 0.0) 414 415 # (-INF)**y is -INF for y a positive odd integer 416 self.assertEqualAndEqualSign(pow_op(-INF, 1.0), -INF) 417 418 # (-INF)**y is INF for y positive but not an odd integer 419 self.assertEqualAndEqualSign(pow_op(-INF, 0.5), INF) 420 self.assertEqualAndEqualSign(pow_op(-INF, 2.0), INF) 421 422 # INF**y is INF for y positive 423 self.assertEqualAndEqualSign(pow_op(INF, 0.5), INF) 424 self.assertEqualAndEqualSign(pow_op(INF, 1.0), INF) 425 self.assertEqualAndEqualSign(pow_op(INF, 2.0), INF) 426 427 # INF**y is 0.0 for y negative 428 self.assertEqualAndEqualSign(pow_op(INF, -2.0), 0.0) 429 self.assertEqualAndEqualSign(pow_op(INF, -1.0), 0.0) 430 self.assertEqualAndEqualSign(pow_op(INF, -0.5), 0.0) 431 432 # basic checks not covered by the special cases above 433 self.assertEqualAndEqualSign(pow_op(-2.0, -2.0), 0.25) 434 self.assertEqualAndEqualSign(pow_op(-2.0, -1.0), -0.5) 435 self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0) 436 self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0) 437 self.assertEqualAndEqualSign(pow_op(-2.0, 1.0), -2.0) 438 self.assertEqualAndEqualSign(pow_op(-2.0, 2.0), 4.0) 439 self.assertEqualAndEqualSign(pow_op(-1.0, -2.0), 1.0) 440 self.assertEqualAndEqualSign(pow_op(-1.0, -1.0), -1.0) 441 self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0) 442 self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0) 443 self.assertEqualAndEqualSign(pow_op(-1.0, 1.0), -1.0) 444 self.assertEqualAndEqualSign(pow_op(-1.0, 2.0), 1.0) 445 self.assertEqualAndEqualSign(pow_op(2.0, -2.0), 0.25) 446 self.assertEqualAndEqualSign(pow_op(2.0, -1.0), 0.5) 447 self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0) 448 self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0) 449 self.assertEqualAndEqualSign(pow_op(2.0, 1.0), 2.0) 450 self.assertEqualAndEqualSign(pow_op(2.0, 2.0), 4.0) 451 452 # 1 ** large and -1 ** large; some libms apparently 453 # have problems with these 454 self.assertEqualAndEqualSign(pow_op(1.0, -1e100), 1.0) 455 self.assertEqualAndEqualSign(pow_op(1.0, 1e100), 1.0) 456 self.assertEqualAndEqualSign(pow_op(-1.0, -1e100), 1.0) 457 self.assertEqualAndEqualSign(pow_op(-1.0, 1e100), 1.0) 458 459 # check sign for results that underflow to 0 460 self.assertEqualAndEqualSign(pow_op(-2.0, -2000.0), 0.0) 461 self.assertRaises(ValueError, pow_op, -2.0, -2000.5) 462 self.assertEqualAndEqualSign(pow_op(-2.0, -2001.0), -0.0) 463 self.assertEqualAndEqualSign(pow_op(2.0, -2000.0), 0.0) 464 self.assertEqualAndEqualSign(pow_op(2.0, -2000.5), 0.0) 465 self.assertEqualAndEqualSign(pow_op(2.0, -2001.0), 0.0) 466 self.assertEqualAndEqualSign(pow_op(-0.5, 2000.0), 0.0) 467 self.assertRaises(ValueError, pow_op, -0.5, 2000.5) 468 self.assertEqualAndEqualSign(pow_op(-0.5, 2001.0), -0.0) 469 self.assertEqualAndEqualSign(pow_op(0.5, 2000.0), 0.0) 470 self.assertEqualAndEqualSign(pow_op(0.5, 2000.5), 0.0) 471 self.assertEqualAndEqualSign(pow_op(0.5, 2001.0), 0.0) 472 473 # check we don't raise an exception for subnormal results, 474 # and validate signs. Tests currently disabled, since 475 # they fail on systems where a subnormal result from pow 476 # is flushed to zero (e.g. Debian/ia64.) 477 #self.assertTrue(0.0 < pow_op(0.5, 1048) < 1e-315) 478 #self.assertTrue(0.0 < pow_op(-0.5, 1048) < 1e-315) 479 #self.assertTrue(0.0 < pow_op(0.5, 1047) < 1e-315) 480 #self.assertTrue(0.0 > pow_op(-0.5, 1047) > -1e-315) 481 #self.assertTrue(0.0 < pow_op(2.0, -1048) < 1e-315) 482 #self.assertTrue(0.0 < pow_op(-2.0, -1048) < 1e-315) 483 #self.assertTrue(0.0 < pow_op(2.0, -1047) < 1e-315) 484 #self.assertTrue(0.0 > pow_op(-2.0, -1047) > -1e-315) 485 486 487 @requires_setformat 488 class FormatFunctionsTestCase(unittest.TestCase): 489 490 def setUp(self): 491 self.save_formats = {'double':float.__getformat__('double'), 492 'float':float.__getformat__('float')} 493 494 def tearDown(self): 495 float.__setformat__('double', self.save_formats['double']) 496 float.__setformat__('float', self.save_formats['float']) 497 498 def test_getformat(self): 499 self.assertIn(float.__getformat__('double'), 500 ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) 501 self.assertIn(float.__getformat__('float'), 502 ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) 503 self.assertRaises(ValueError, float.__getformat__, 'chicken') 504 self.assertRaises(TypeError, float.__getformat__, 1) 505 506 def test_setformat(self): 507 for t in 'double', 'float': 508 float.__setformat__(t, 'unknown') 509 if self.save_formats[t] == 'IEEE, big-endian': 510 self.assertRaises(ValueError, float.__setformat__, 511 t, 'IEEE, little-endian') 512 elif self.save_formats[t] == 'IEEE, little-endian': 513 self.assertRaises(ValueError, float.__setformat__, 514 t, 'IEEE, big-endian') 515 else: 516 self.assertRaises(ValueError, float.__setformat__, 517 t, 'IEEE, big-endian') 518 self.assertRaises(ValueError, float.__setformat__, 519 t, 'IEEE, little-endian') 520 self.assertRaises(ValueError, float.__setformat__, 521 t, 'chicken') 522 self.assertRaises(ValueError, float.__setformat__, 523 'chicken', 'unknown') 524 525 BE_DOUBLE_INF = '\x7f\xf0\x00\x00\x00\x00\x00\x00' 526 LE_DOUBLE_INF = ''.join(reversed(BE_DOUBLE_INF)) 527 BE_DOUBLE_NAN = '\x7f\xf8\x00\x00\x00\x00\x00\x00' 528 LE_DOUBLE_NAN = ''.join(reversed(BE_DOUBLE_NAN)) 529 530 BE_FLOAT_INF = '\x7f\x80\x00\x00' 531 LE_FLOAT_INF = ''.join(reversed(BE_FLOAT_INF)) 532 BE_FLOAT_NAN = '\x7f\xc0\x00\x00' 533 LE_FLOAT_NAN = ''.join(reversed(BE_FLOAT_NAN)) 534 535 # on non-IEEE platforms, attempting to unpack a bit pattern 536 # representing an infinity or a NaN should raise an exception. 537 538 @requires_setformat 539 class UnknownFormatTestCase(unittest.TestCase): 540 def setUp(self): 541 self.save_formats = {'double':float.__getformat__('double'), 542 'float':float.__getformat__('float')} 543 float.__setformat__('double', 'unknown') 544 float.__setformat__('float', 'unknown') 545 546 def tearDown(self): 547 float.__setformat__('double', self.save_formats['double']) 548 float.__setformat__('float', self.save_formats['float']) 549 550 def test_double_specials_dont_unpack(self): 551 for fmt, data in [('>d', BE_DOUBLE_INF), 552 ('>d', BE_DOUBLE_NAN), 553 ('<d', LE_DOUBLE_INF), 554 ('<d', LE_DOUBLE_NAN)]: 555 self.assertRaises(ValueError, struct.unpack, fmt, data) 556 557 def test_float_specials_dont_unpack(self): 558 for fmt, data in [('>f', BE_FLOAT_INF), 559 ('>f', BE_FLOAT_NAN), 560 ('<f', LE_FLOAT_INF), 561 ('<f', LE_FLOAT_NAN)]: 562 self.assertRaises(ValueError, struct.unpack, fmt, data) 563 564 565 # on an IEEE platform, all we guarantee is that bit patterns 566 # representing infinities or NaNs do not raise an exception; all else 567 # is accident (today). 568 # let's also try to guarantee that -0.0 and 0.0 don't get confused. 569 570 class IEEEFormatTestCase(unittest.TestCase): 571 572 @requires_IEEE_754 573 def test_double_specials_do_unpack(self): 574 for fmt, data in [('>d', BE_DOUBLE_INF), 575 ('>d', BE_DOUBLE_NAN), 576 ('<d', LE_DOUBLE_INF), 577 ('<d', LE_DOUBLE_NAN)]: 578 struct.unpack(fmt, data) 579 580 @requires_IEEE_754 581 def test_float_specials_do_unpack(self): 582 for fmt, data in [('>f', BE_FLOAT_INF), 583 ('>f', BE_FLOAT_NAN), 584 ('<f', LE_FLOAT_INF), 585 ('<f', LE_FLOAT_NAN)]: 586 struct.unpack(fmt, data) 587 588 @requires_IEEE_754 589 def test_negative_zero(self): 590 def pos_pos(): 591 return 0.0, math.atan2(0.0, -1) 592 def pos_neg(): 593 return 0.0, math.atan2(-0.0, -1) 594 def neg_pos(): 595 return -0.0, math.atan2(0.0, -1) 596 def neg_neg(): 597 return -0.0, math.atan2(-0.0, -1) 598 self.assertEqual(pos_pos(), neg_pos()) 599 self.assertEqual(pos_neg(), neg_neg()) 600 601 @requires_IEEE_754 602 def test_underflow_sign(self): 603 # check that -1e-1000 gives -0.0, not 0.0 604 self.assertEqual(math.atan2(-1e-1000, -1), math.atan2(-0.0, -1)) 605 self.assertEqual(math.atan2(float('-1e-1000'), -1), 606 math.atan2(-0.0, -1)) 607 608 def test_format(self): 609 # these should be rewritten to use both format(x, spec) and 610 # x.__format__(spec) 611 612 self.assertEqual(format(0.0, 'f'), '0.000000') 613 614 # the default is 'g', except for empty format spec 615 self.assertEqual(format(0.0, ''), '0.0') 616 self.assertEqual(format(0.01, ''), '0.01') 617 self.assertEqual(format(0.01, 'g'), '0.01') 618 619 # empty presentation type should format in the same way as str 620 # (issue 5920) 621 x = 100/7. 622 self.assertEqual(format(x, ''), str(x)) 623 self.assertEqual(format(x, '-'), str(x)) 624 self.assertEqual(format(x, '>'), str(x)) 625 self.assertEqual(format(x, '2'), str(x)) 626 627 self.assertEqual(format(1.0, 'f'), '1.000000') 628 629 self.assertEqual(format(-1.0, 'f'), '-1.000000') 630 631 self.assertEqual(format( 1.0, ' f'), ' 1.000000') 632 self.assertEqual(format(-1.0, ' f'), '-1.000000') 633 self.assertEqual(format( 1.0, '+f'), '+1.000000') 634 self.assertEqual(format(-1.0, '+f'), '-1.000000') 635 636 # % formatting 637 self.assertEqual(format(-1.0, '%'), '-100.000000%') 638 639 # conversion to string should fail 640 self.assertRaises(ValueError, format, 3.0, "s") 641 642 # other format specifiers shouldn't work on floats, 643 # in particular int specifiers 644 for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] + 645 [chr(x) for x in range(ord('A'), ord('Z')+1)]): 646 if not format_spec in 'eEfFgGn%': 647 self.assertRaises(ValueError, format, 0.0, format_spec) 648 self.assertRaises(ValueError, format, 1.0, format_spec) 649 self.assertRaises(ValueError, format, -1.0, format_spec) 650 self.assertRaises(ValueError, format, 1e100, format_spec) 651 self.assertRaises(ValueError, format, -1e100, format_spec) 652 self.assertRaises(ValueError, format, 1e-100, format_spec) 653 self.assertRaises(ValueError, format, -1e-100, format_spec) 654 655 # issue 3382: 'f' and 'F' with inf's and nan's 656 self.assertEqual('{0:f}'.format(INF), 'inf') 657 self.assertEqual('{0:F}'.format(INF), 'INF') 658 self.assertEqual('{0:f}'.format(-INF), '-inf') 659 self.assertEqual('{0:F}'.format(-INF), '-INF') 660 self.assertEqual('{0:f}'.format(NAN), 'nan') 661 self.assertEqual('{0:F}'.format(NAN), 'NAN') 662 663 @requires_IEEE_754 664 def test_format_testfile(self): 665 with open(format_testfile) as testfile: 666 for line in open(format_testfile): 667 if line.startswith('--'): 668 continue 669 line = line.strip() 670 if not line: 671 continue 672 673 lhs, rhs = map(str.strip, line.split('->')) 674 fmt, arg = lhs.split() 675 arg = float(arg) 676 self.assertEqual(fmt % arg, rhs) 677 if not math.isnan(arg) and copysign(1.0, arg) > 0.0: 678 self.assertEqual(fmt % -arg, '-' + rhs) 679 680 def test_issue5864(self): 681 self.assertEqual(format(123.456, '.4'), '123.5') 682 self.assertEqual(format(1234.56, '.4'), '1.235e+03') 683 self.assertEqual(format(12345.6, '.4'), '1.235e+04') 684 685 class ReprTestCase(unittest.TestCase): 686 def test_repr(self): 687 floats_file = open(os.path.join(os.path.split(__file__)[0], 688 'floating_points.txt')) 689 for line in floats_file: 690 line = line.strip() 691 if not line or line.startswith('#'): 692 continue 693 v = eval(line) 694 self.assertEqual(v, eval(repr(v))) 695 floats_file.close() 696 697 @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', 698 "applies only when using short float repr style") 699 def test_short_repr(self): 700 # test short float repr introduced in Python 3.1. One aspect 701 # of this repr is that we get some degree of str -> float -> 702 # str roundtripping. In particular, for any numeric string 703 # containing 15 or fewer significant digits, those exact same 704 # digits (modulo trailing zeros) should appear in the output. 705 # No more repr(0.03) -> "0.029999999999999999"! 706 707 test_strings = [ 708 # output always includes *either* a decimal point and at 709 # least one digit after that point, or an exponent. 710 '0.0', 711 '1.0', 712 '0.01', 713 '0.02', 714 '0.03', 715 '0.04', 716 '0.05', 717 '1.23456789', 718 '10.0', 719 '100.0', 720 # values >= 1e16 get an exponent... 721 '1000000000000000.0', 722 '9999999999999990.0', 723 '1e+16', 724 '1e+17', 725 # ... and so do values < 1e-4 726 '0.001', 727 '0.001001', 728 '0.00010000000000001', 729 '0.0001', 730 '9.999999999999e-05', 731 '1e-05', 732 # values designed to provoke failure if the FPU rounding 733 # precision isn't set correctly 734 '8.72293771110361e+25', 735 '7.47005307342313e+26', 736 '2.86438000439698e+28', 737 '8.89142905246179e+28', 738 '3.08578087079232e+35', 739 ] 740 741 for s in test_strings: 742 negs = '-'+s 743 self.assertEqual(s, repr(float(s))) 744 self.assertEqual(negs, repr(float(negs))) 745 746 747 @requires_IEEE_754 748 class RoundTestCase(unittest.TestCase): 749 def test_second_argument_type(self): 750 # any type with an __index__ method should be permitted as 751 # a second argument 752 self.assertAlmostEqual(round(12.34, True), 12.3) 753 754 class MyIndex(object): 755 def __index__(self): return 4 756 self.assertAlmostEqual(round(-0.123456, MyIndex()), -0.1235) 757 # but floats should be illegal 758 self.assertRaises(TypeError, round, 3.14159, 2.0) 759 760 def test_inf_nan(self): 761 # rounding an infinity or nan returns the same number; 762 # (in py3k, rounding an infinity or nan raises an error, 763 # since the result can't be represented as a long). 764 self.assertEqual(round(INF), INF) 765 self.assertEqual(round(-INF), -INF) 766 self.assertTrue(math.isnan(round(NAN))) 767 for n in range(-5, 5): 768 self.assertEqual(round(INF, n), INF) 769 self.assertEqual(round(-INF, n), -INF) 770 self.assertTrue(math.isnan(round(NAN, n))) 771 772 self.assertRaises(TypeError, round, INF, 0.0) 773 self.assertRaises(TypeError, round, -INF, 1.0) 774 self.assertRaises(TypeError, round, NAN, "ceci n'est pas un integer") 775 self.assertRaises(TypeError, round, -0.0, 1j) 776 777 def test_large_n(self): 778 for n in [324, 325, 400, 2**31-1, 2**31, 2**32, 2**100]: 779 self.assertEqual(round(123.456, n), 123.456) 780 self.assertEqual(round(-123.456, n), -123.456) 781 self.assertEqual(round(1e300, n), 1e300) 782 self.assertEqual(round(1e-320, n), 1e-320) 783 self.assertEqual(round(1e150, 300), 1e150) 784 self.assertEqual(round(1e300, 307), 1e300) 785 self.assertEqual(round(-3.1415, 308), -3.1415) 786 self.assertEqual(round(1e150, 309), 1e150) 787 self.assertEqual(round(1.4e-315, 315), 1e-315) 788 789 def test_small_n(self): 790 for n in [-308, -309, -400, 1-2**31, -2**31, -2**31-1, -2**100]: 791 self.assertEqual(round(123.456, n), 0.0) 792 self.assertEqual(round(-123.456, n), -0.0) 793 self.assertEqual(round(1e300, n), 0.0) 794 self.assertEqual(round(1e-320, n), 0.0) 795 796 def test_overflow(self): 797 self.assertRaises(OverflowError, round, 1.6e308, -308) 798 self.assertRaises(OverflowError, round, -1.7e308, -308) 799 800 @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', 801 "test applies only when using short float repr style") 802 def test_previous_round_bugs(self): 803 # particular cases that have occurred in bug reports 804 self.assertEqual(round(562949953421312.5, 1), 805 562949953421312.5) 806 self.assertEqual(round(56294995342131.5, 3), 807 56294995342131.5) 808 809 @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', 810 "test applies only when using short float repr style") 811 def test_halfway_cases(self): 812 # Halfway cases need special attention, since the current 813 # implementation has to deal with them specially. Note that 814 # 2.x rounds halfway values up (i.e., away from zero) while 815 # 3.x does round-half-to-even. 816 self.assertAlmostEqual(round(0.125, 2), 0.13) 817 self.assertAlmostEqual(round(0.375, 2), 0.38) 818 self.assertAlmostEqual(round(0.625, 2), 0.63) 819 self.assertAlmostEqual(round(0.875, 2), 0.88) 820 self.assertAlmostEqual(round(-0.125, 2), -0.13) 821 self.assertAlmostEqual(round(-0.375, 2), -0.38) 822 self.assertAlmostEqual(round(-0.625, 2), -0.63) 823 self.assertAlmostEqual(round(-0.875, 2), -0.88) 824 825 self.assertAlmostEqual(round(0.25, 1), 0.3) 826 self.assertAlmostEqual(round(0.75, 1), 0.8) 827 self.assertAlmostEqual(round(-0.25, 1), -0.3) 828 self.assertAlmostEqual(round(-0.75, 1), -0.8) 829 830 self.assertEqual(round(-6.5, 0), -7.0) 831 self.assertEqual(round(-5.5, 0), -6.0) 832 self.assertEqual(round(-1.5, 0), -2.0) 833 self.assertEqual(round(-0.5, 0), -1.0) 834 self.assertEqual(round(0.5, 0), 1.0) 835 self.assertEqual(round(1.5, 0), 2.0) 836 self.assertEqual(round(2.5, 0), 3.0) 837 self.assertEqual(round(3.5, 0), 4.0) 838 self.assertEqual(round(4.5, 0), 5.0) 839 self.assertEqual(round(5.5, 0), 6.0) 840 self.assertEqual(round(6.5, 0), 7.0) 841 842 # same but without an explicit second argument; in 3.x these 843 # will give integers 844 self.assertEqual(round(-6.5), -7.0) 845 self.assertEqual(round(-5.5), -6.0) 846 self.assertEqual(round(-1.5), -2.0) 847 self.assertEqual(round(-0.5), -1.0) 848 self.assertEqual(round(0.5), 1.0) 849 self.assertEqual(round(1.5), 2.0) 850 self.assertEqual(round(2.5), 3.0) 851 self.assertEqual(round(3.5), 4.0) 852 self.assertEqual(round(4.5), 5.0) 853 self.assertEqual(round(5.5), 6.0) 854 self.assertEqual(round(6.5), 7.0) 855 856 self.assertEqual(round(-25.0, -1), -30.0) 857 self.assertEqual(round(-15.0, -1), -20.0) 858 self.assertEqual(round(-5.0, -1), -10.0) 859 self.assertEqual(round(5.0, -1), 10.0) 860 self.assertEqual(round(15.0, -1), 20.0) 861 self.assertEqual(round(25.0, -1), 30.0) 862 self.assertEqual(round(35.0, -1), 40.0) 863 self.assertEqual(round(45.0, -1), 50.0) 864 self.assertEqual(round(55.0, -1), 60.0) 865 self.assertEqual(round(65.0, -1), 70.0) 866 self.assertEqual(round(75.0, -1), 80.0) 867 self.assertEqual(round(85.0, -1), 90.0) 868 self.assertEqual(round(95.0, -1), 100.0) 869 self.assertEqual(round(12325.0, -1), 12330.0) 870 871 self.assertEqual(round(350.0, -2), 400.0) 872 self.assertEqual(round(450.0, -2), 500.0) 873 874 self.assertAlmostEqual(round(0.5e21, -21), 1e21) 875 self.assertAlmostEqual(round(1.5e21, -21), 2e21) 876 self.assertAlmostEqual(round(2.5e21, -21), 3e21) 877 self.assertAlmostEqual(round(5.5e21, -21), 6e21) 878 self.assertAlmostEqual(round(8.5e21, -21), 9e21) 879 880 self.assertAlmostEqual(round(-1.5e22, -22), -2e22) 881 self.assertAlmostEqual(round(-0.5e22, -22), -1e22) 882 self.assertAlmostEqual(round(0.5e22, -22), 1e22) 883 self.assertAlmostEqual(round(1.5e22, -22), 2e22) 884 885 886 @requires_IEEE_754 887 def test_format_specials(self): 888 # Test formatting of nans and infs. 889 890 def test(fmt, value, expected): 891 # Test with both % and format(). 892 self.assertEqual(fmt % value, expected, fmt) 893 if not '#' in fmt: 894 # Until issue 7094 is implemented, format() for floats doesn't 895 # support '#' formatting 896 fmt = fmt[1:] # strip off the % 897 self.assertEqual(format(value, fmt), expected, fmt) 898 899 for fmt in ['%e', '%f', '%g', '%.0e', '%.6f', '%.20g', 900 '%#e', '%#f', '%#g', '%#.20e', '%#.15f', '%#.3g']: 901 pfmt = '%+' + fmt[1:] 902 sfmt = '% ' + fmt[1:] 903 test(fmt, INF, 'inf') 904 test(fmt, -INF, '-inf') 905 test(fmt, NAN, 'nan') 906 test(fmt, -NAN, 'nan') 907 # When asking for a sign, it's always provided. nans are 908 # always positive. 909 test(pfmt, INF, '+inf') 910 test(pfmt, -INF, '-inf') 911 test(pfmt, NAN, '+nan') 912 test(pfmt, -NAN, '+nan') 913 # When using ' ' for a sign code, only infs can be negative. 914 # Others have a space. 915 test(sfmt, INF, ' inf') 916 test(sfmt, -INF, '-inf') 917 test(sfmt, NAN, ' nan') 918 test(sfmt, -NAN, ' nan') 919 920 921 # Beginning with Python 2.6 float has cross platform compatible 922 # ways to create and represent inf and nan 923 class InfNanTest(unittest.TestCase): 924 def test_inf_from_str(self): 925 self.assertTrue(isinf(float("inf"))) 926 self.assertTrue(isinf(float("+inf"))) 927 self.assertTrue(isinf(float("-inf"))) 928 self.assertTrue(isinf(float("infinity"))) 929 self.assertTrue(isinf(float("+infinity"))) 930 self.assertTrue(isinf(float("-infinity"))) 931 932 self.assertEqual(repr(float("inf")), "inf") 933 self.assertEqual(repr(float("+inf")), "inf") 934 self.assertEqual(repr(float("-inf")), "-inf") 935 self.assertEqual(repr(float("infinity")), "inf") 936 self.assertEqual(repr(float("+infinity")), "inf") 937 self.assertEqual(repr(float("-infinity")), "-inf") 938 939 self.assertEqual(repr(float("INF")), "inf") 940 self.assertEqual(repr(float("+Inf")), "inf") 941 self.assertEqual(repr(float("-iNF")), "-inf") 942 self.assertEqual(repr(float("Infinity")), "inf") 943 self.assertEqual(repr(float("+iNfInItY")), "inf") 944 self.assertEqual(repr(float("-INFINITY")), "-inf") 945 946 self.assertEqual(str(float("inf")), "inf") 947 self.assertEqual(str(float("+inf")), "inf") 948 self.assertEqual(str(float("-inf")), "-inf") 949 self.assertEqual(str(float("infinity")), "inf") 950 self.assertEqual(str(float("+infinity")), "inf") 951 self.assertEqual(str(float("-infinity")), "-inf") 952 953 self.assertRaises(ValueError, float, "info") 954 self.assertRaises(ValueError, float, "+info") 955 self.assertRaises(ValueError, float, "-info") 956 self.assertRaises(ValueError, float, "in") 957 self.assertRaises(ValueError, float, "+in") 958 self.assertRaises(ValueError, float, "-in") 959 self.assertRaises(ValueError, float, "infinit") 960 self.assertRaises(ValueError, float, "+Infin") 961 self.assertRaises(ValueError, float, "-INFI") 962 self.assertRaises(ValueError, float, "infinitys") 963 964 def test_inf_as_str(self): 965 self.assertEqual(repr(1e300 * 1e300), "inf") 966 self.assertEqual(repr(-1e300 * 1e300), "-inf") 967 968 self.assertEqual(str(1e300 * 1e300), "inf") 969 self.assertEqual(str(-1e300 * 1e300), "-inf") 970 971 def test_nan_from_str(self): 972 self.assertTrue(isnan(float("nan"))) 973 self.assertTrue(isnan(float("+nan"))) 974 self.assertTrue(isnan(float("-nan"))) 975 976 self.assertEqual(repr(float("nan")), "nan") 977 self.assertEqual(repr(float("+nan")), "nan") 978 self.assertEqual(repr(float("-nan")), "nan") 979 980 self.assertEqual(repr(float("NAN")), "nan") 981 self.assertEqual(repr(float("+NAn")), "nan") 982 self.assertEqual(repr(float("-NaN")), "nan") 983 984 self.assertEqual(str(float("nan")), "nan") 985 self.assertEqual(str(float("+nan")), "nan") 986 self.assertEqual(str(float("-nan")), "nan") 987 988 self.assertRaises(ValueError, float, "nana") 989 self.assertRaises(ValueError, float, "+nana") 990 self.assertRaises(ValueError, float, "-nana") 991 self.assertRaises(ValueError, float, "na") 992 self.assertRaises(ValueError, float, "+na") 993 self.assertRaises(ValueError, float, "-na") 994 995 def test_nan_as_str(self): 996 self.assertEqual(repr(1e300 * 1e300 * 0), "nan") 997 self.assertEqual(repr(-1e300 * 1e300 * 0), "nan") 998 999 self.assertEqual(str(1e300 * 1e300 * 0), "nan") 1000 self.assertEqual(str(-1e300 * 1e300 * 0), "nan") 1001 1002 def notest_float_nan(self): 1003 self.assertTrue(NAN.is_nan()) 1004 self.assertFalse(INF.is_nan()) 1005 self.assertFalse((0.).is_nan()) 1006 1007 def notest_float_inf(self): 1008 self.assertTrue(INF.is_inf()) 1009 self.assertFalse(NAN.is_inf()) 1010 self.assertFalse((0.).is_inf()) 1011 1012 def test_hash_inf(self): 1013 # the actual values here should be regarded as an 1014 # implementation detail, but they need to be 1015 # identical to those used in the Decimal module. 1016 self.assertEqual(hash(float('inf')), 314159) 1017 self.assertEqual(hash(float('-inf')), -271828) 1018 self.assertEqual(hash(float('nan')), 0) 1019 1020 1021 fromHex = float.fromhex 1022 toHex = float.hex 1023 class HexFloatTestCase(unittest.TestCase): 1024 MAX = fromHex('0x.fffffffffffff8p+1024') # max normal 1025 MIN = fromHex('0x1p-1022') # min normal 1026 TINY = fromHex('0x0.0000000000001p-1022') # min subnormal 1027 EPS = fromHex('0x0.0000000000001p0') # diff between 1.0 and next float up 1028 1029 def identical(self, x, y): 1030 # check that floats x and y are identical, or that both 1031 # are NaNs 1032 if isnan(x) or isnan(y): 1033 if isnan(x) == isnan(y): 1034 return 1035 elif x == y and (x != 0.0 or copysign(1.0, x) == copysign(1.0, y)): 1036 return 1037 self.fail('%r not identical to %r' % (x, y)) 1038 1039 def test_ends(self): 1040 self.identical(self.MIN, ldexp(1.0, -1022)) 1041 self.identical(self.TINY, ldexp(1.0, -1074)) 1042 self.identical(self.EPS, ldexp(1.0, -52)) 1043 self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970))) 1044 1045 def test_invalid_inputs(self): 1046 invalid_inputs = [ 1047 'infi', # misspelt infinities and nans 1048 '-Infinit', 1049 '++inf', 1050 '-+Inf', 1051 '--nan', 1052 '+-NaN', 1053 'snan', 1054 'NaNs', 1055 'nna', 1056 'an', 1057 'nf', 1058 'nfinity', 1059 'inity', 1060 'iinity', 1061 '0xnan', 1062 '', 1063 ' ', 1064 'x1.0p0', 1065 '0xX1.0p0', 1066 '+ 0x1.0p0', # internal whitespace 1067 '- 0x1.0p0', 1068 '0 x1.0p0', 1069 '0x 1.0p0', 1070 '0x1 2.0p0', 1071 '+0x1 .0p0', 1072 '0x1. 0p0', 1073 '-0x1.0 1p0', 1074 '-0x1.0 p0', 1075 '+0x1.0p +0', 1076 '0x1.0p -0', 1077 '0x1.0p 0', 1078 '+0x1.0p+ 0', 1079 '-0x1.0p- 0', 1080 '++0x1.0p-0', # double signs 1081 '--0x1.0p0', 1082 '+-0x1.0p+0', 1083 '-+0x1.0p0', 1084 '0x1.0p++0', 1085 '+0x1.0p+-0', 1086 '-0x1.0p-+0', 1087 '0x1.0p--0', 1088 '0x1.0.p0', 1089 '0x.p0', # no hex digits before or after point 1090 '0x1,p0', # wrong decimal point character 1091 '0x1pa', 1092 u'0x1p\uff10', # fullwidth Unicode digits 1093 u'\uff10x1p0', 1094 u'0x\uff11p0', 1095 u'0x1.\uff10p0', 1096 '0x1p0 \n 0x2p0', 1097 '0x1p0\0 0x1p0', # embedded null byte is not end of string 1098 ] 1099 for x in invalid_inputs: 1100 try: 1101 result = fromHex(x) 1102 except ValueError: 1103 pass 1104 else: 1105 self.fail('Expected float.fromhex(%r) to raise ValueError; ' 1106 'got %r instead' % (x, result)) 1107 1108 1109 def test_whitespace(self): 1110 value_pairs = [ 1111 ('inf', INF), 1112 ('-Infinity', -INF), 1113 ('nan', NAN), 1114 ('1.0', 1.0), 1115 ('-0x.2', -0.125), 1116 ('-0.0', -0.0) 1117 ] 1118 whitespace = [ 1119 '', 1120 ' ', 1121 '\t', 1122 '\n', 1123 '\n \t', 1124 '\f', 1125 '\v', 1126 '\r' 1127 ] 1128 for inp, expected in value_pairs: 1129 for lead in whitespace: 1130 for trail in whitespace: 1131 got = fromHex(lead + inp + trail) 1132 self.identical(got, expected) 1133 1134 1135 def test_from_hex(self): 1136 MIN = self.MIN; 1137 MAX = self.MAX; 1138 TINY = self.TINY; 1139 EPS = self.EPS; 1140 1141 # two spellings of infinity, with optional signs; case-insensitive 1142 self.identical(fromHex('inf'), INF) 1143 self.identical(fromHex('+Inf'), INF) 1144 self.identical(fromHex('-INF'), -INF) 1145 self.identical(fromHex('iNf'), INF) 1146 self.identical(fromHex('Infinity'), INF) 1147 self.identical(fromHex('+INFINITY'), INF) 1148 self.identical(fromHex('-infinity'), -INF) 1149 self.identical(fromHex('-iNFiNitY'), -INF) 1150 1151 # nans with optional sign; case insensitive 1152 self.identical(fromHex('nan'), NAN) 1153 self.identical(fromHex('+NaN'), NAN) 1154 self.identical(fromHex('-NaN'), NAN) 1155 self.identical(fromHex('-nAN'), NAN) 1156 1157 # variations in input format 1158 self.identical(fromHex('1'), 1.0) 1159 self.identical(fromHex('+1'), 1.0) 1160 self.identical(fromHex('1.'), 1.0) 1161 self.identical(fromHex('1.0'), 1.0) 1162 self.identical(fromHex('1.0p0'), 1.0) 1163 self.identical(fromHex('01'), 1.0) 1164 self.identical(fromHex('01.'), 1.0) 1165 self.identical(fromHex('0x1'), 1.0) 1166 self.identical(fromHex('0x1.'), 1.0) 1167 self.identical(fromHex('0x1.0'), 1.0) 1168 self.identical(fromHex('+0x1.0'), 1.0) 1169 self.identical(fromHex('0x1p0'), 1.0) 1170 self.identical(fromHex('0X1p0'), 1.0) 1171 self.identical(fromHex('0X1P0'), 1.0) 1172 self.identical(fromHex('0x1P0'), 1.0) 1173 self.identical(fromHex('0x1.p0'), 1.0) 1174 self.identical(fromHex('0x1.0p0'), 1.0) 1175 self.identical(fromHex('0x.1p4'), 1.0) 1176 self.identical(fromHex('0x.1p04'), 1.0) 1177 self.identical(fromHex('0x.1p004'), 1.0) 1178 self.identical(fromHex('0x1p+0'), 1.0) 1179 self.identical(fromHex('0x1P-0'), 1.0) 1180 self.identical(fromHex('+0x1p0'), 1.0) 1181 self.identical(fromHex('0x01p0'), 1.0) 1182 self.identical(fromHex('0x1p00'), 1.0) 1183 self.identical(fromHex(u'0x1p0'), 1.0) 1184 self.identical(fromHex(' 0x1p0 '), 1.0) 1185 self.identical(fromHex('\n 0x1p0'), 1.0) 1186 self.identical(fromHex('0x1p0 \t'), 1.0) 1187 self.identical(fromHex('0xap0'), 10.0) 1188 self.identical(fromHex('0xAp0'), 10.0) 1189 self.identical(fromHex('0xaP0'), 10.0) 1190 self.identical(fromHex('0xAP0'), 10.0) 1191 self.identical(fromHex('0xbep0'), 190.0) 1192 self.identical(fromHex('0xBep0'), 190.0) 1193 self.identical(fromHex('0xbEp0'), 190.0) 1194 self.identical(fromHex('0XBE0P-4'), 190.0) 1195 self.identical(fromHex('0xBEp0'), 190.0) 1196 self.identical(fromHex('0xB.Ep4'), 190.0) 1197 self.identical(fromHex('0x.BEp8'), 190.0) 1198 self.identical(fromHex('0x.0BEp12'), 190.0) 1199 1200 # moving the point around 1201 pi = fromHex('0x1.921fb54442d18p1') 1202 self.identical(fromHex('0x.006487ed5110b46p11'), pi) 1203 self.identical(fromHex('0x.00c90fdaa22168cp10'), pi) 1204 self.identical(fromHex('0x.01921fb54442d18p9'), pi) 1205 self.identical(fromHex('0x.03243f6a8885a3p8'), pi) 1206 self.identical(fromHex('0x.06487ed5110b46p7'), pi) 1207 self.identical(fromHex('0x.0c90fdaa22168cp6'), pi) 1208 self.identical(fromHex('0x.1921fb54442d18p5'), pi) 1209 self.identical(fromHex('0x.3243f6a8885a3p4'), pi) 1210 self.identical(fromHex('0x.6487ed5110b46p3'), pi) 1211 self.identical(fromHex('0x.c90fdaa22168cp2'), pi) 1212 self.identical(fromHex('0x1.921fb54442d18p1'), pi) 1213 self.identical(fromHex('0x3.243f6a8885a3p0'), pi) 1214 self.identical(fromHex('0x6.487ed5110b46p-1'), pi) 1215 self.identical(fromHex('0xc.90fdaa22168cp-2'), pi) 1216 self.identical(fromHex('0x19.21fb54442d18p-3'), pi) 1217 self.identical(fromHex('0x32.43f6a8885a3p-4'), pi) 1218 self.identical(fromHex('0x64.87ed5110b46p-5'), pi) 1219 self.identical(fromHex('0xc9.0fdaa22168cp-6'), pi) 1220 self.identical(fromHex('0x192.1fb54442d18p-7'), pi) 1221 self.identical(fromHex('0x324.3f6a8885a3p-8'), pi) 1222 self.identical(fromHex('0x648.7ed5110b46p-9'), pi) 1223 self.identical(fromHex('0xc90.fdaa22168cp-10'), pi) 1224 self.identical(fromHex('0x1921.fb54442d18p-11'), pi) 1225 # ... 1226 self.identical(fromHex('0x1921fb54442d1.8p-47'), pi) 1227 self.identical(fromHex('0x3243f6a8885a3p-48'), pi) 1228 self.identical(fromHex('0x6487ed5110b46p-49'), pi) 1229 self.identical(fromHex('0xc90fdaa22168cp-50'), pi) 1230 self.identical(fromHex('0x1921fb54442d18p-51'), pi) 1231 self.identical(fromHex('0x3243f6a8885a30p-52'), pi) 1232 self.identical(fromHex('0x6487ed5110b460p-53'), pi) 1233 self.identical(fromHex('0xc90fdaa22168c0p-54'), pi) 1234 self.identical(fromHex('0x1921fb54442d180p-55'), pi) 1235 1236 1237 # results that should overflow... 1238 self.assertRaises(OverflowError, fromHex, '-0x1p1024') 1239 self.assertRaises(OverflowError, fromHex, '0x1p+1025') 1240 self.assertRaises(OverflowError, fromHex, '+0X1p1030') 1241 self.assertRaises(OverflowError, fromHex, '-0x1p+1100') 1242 self.assertRaises(OverflowError, fromHex, '0X1p123456789123456789') 1243 self.assertRaises(OverflowError, fromHex, '+0X.8p+1025') 1244 self.assertRaises(OverflowError, fromHex, '+0x0.8p1025') 1245 self.assertRaises(OverflowError, fromHex, '-0x0.4p1026') 1246 self.assertRaises(OverflowError, fromHex, '0X2p+1023') 1247 self.assertRaises(OverflowError, fromHex, '0x2.p1023') 1248 self.assertRaises(OverflowError, fromHex, '-0x2.0p+1023') 1249 self.assertRaises(OverflowError, fromHex, '+0X4p+1022') 1250 self.assertRaises(OverflowError, fromHex, '0x1.ffffffffffffffp+1023') 1251 self.assertRaises(OverflowError, fromHex, '-0X1.fffffffffffff9p1023') 1252 self.assertRaises(OverflowError, fromHex, '0X1.fffffffffffff8p1023') 1253 self.assertRaises(OverflowError, fromHex, '+0x3.fffffffffffffp1022') 1254 self.assertRaises(OverflowError, fromHex, '0x3fffffffffffffp+970') 1255 self.assertRaises(OverflowError, fromHex, '0x10000000000000000p960') 1256 self.assertRaises(OverflowError, fromHex, '-0Xffffffffffffffffp960') 1257 1258 # ...and those that round to +-max float 1259 self.identical(fromHex('+0x1.fffffffffffffp+1023'), MAX) 1260 self.identical(fromHex('-0X1.fffffffffffff7p1023'), -MAX) 1261 self.identical(fromHex('0X1.fffffffffffff7fffffffffffffp1023'), MAX) 1262 1263 # zeros 1264 self.identical(fromHex('0x0p0'), 0.0) 1265 self.identical(fromHex('0x0p1000'), 0.0) 1266 self.identical(fromHex('-0x0p1023'), -0.0) 1267 self.identical(fromHex('0X0p1024'), 0.0) 1268 self.identical(fromHex('-0x0p1025'), -0.0) 1269 self.identical(fromHex('0X0p2000'), 0.0) 1270 self.identical(fromHex('0x0p123456789123456789'), 0.0) 1271 self.identical(fromHex('-0X0p-0'), -0.0) 1272 self.identical(fromHex('-0X0p-1000'), -0.0) 1273 self.identical(fromHex('0x0p-1023'), 0.0) 1274 self.identical(fromHex('-0X0p-1024'), -0.0) 1275 self.identical(fromHex('-0x0p-1025'), -0.0) 1276 self.identical(fromHex('-0x0p-1072'), -0.0) 1277 self.identical(fromHex('0X0p-1073'), 0.0) 1278 self.identical(fromHex('-0x0p-1074'), -0.0) 1279 self.identical(fromHex('0x0p-1075'), 0.0) 1280 self.identical(fromHex('0X0p-1076'), 0.0) 1281 self.identical(fromHex('-0X0p-2000'), -0.0) 1282 self.identical(fromHex('-0x0p-123456789123456789'), -0.0) 1283 1284 # values that should underflow to 0 1285 self.identical(fromHex('0X1p-1075'), 0.0) 1286 self.identical(fromHex('-0X1p-1075'), -0.0) 1287 self.identical(fromHex('-0x1p-123456789123456789'), -0.0) 1288 self.identical(fromHex('0x1.00000000000000001p-1075'), TINY) 1289 self.identical(fromHex('-0x1.1p-1075'), -TINY) 1290 self.identical(fromHex('0x1.fffffffffffffffffp-1075'), TINY) 1291 1292 # check round-half-even is working correctly near 0 ... 1293 self.identical(fromHex('0x1p-1076'), 0.0) 1294 self.identical(fromHex('0X2p-1076'), 0.0) 1295 self.identical(fromHex('0X3p-1076'), TINY) 1296 self.identical(fromHex('0x4p-1076'), TINY) 1297 self.identical(fromHex('0X5p-1076'), TINY) 1298 self.identical(fromHex('0X6p-1076'), 2*TINY) 1299 self.identical(fromHex('0x7p-1076'), 2*TINY) 1300 self.identical(fromHex('0X8p-1076'), 2*TINY) 1301 self.identical(fromHex('0X9p-1076'), 2*TINY) 1302 self.identical(fromHex('0xap-1076'), 2*TINY) 1303 self.identical(fromHex('0Xbp-1076'), 3*TINY) 1304 self.identical(fromHex('0xcp-1076'), 3*TINY) 1305 self.identical(fromHex('0Xdp-1076'), 3*TINY) 1306 self.identical(fromHex('0Xep-1076'), 4*TINY) 1307 self.identical(fromHex('0xfp-1076'), 4*TINY) 1308 self.identical(fromHex('0x10p-1076'), 4*TINY) 1309 self.identical(fromHex('-0x1p-1076'), -0.0) 1310 self.identical(fromHex('-0X2p-1076'), -0.0) 1311 self.identical(fromHex('-0x3p-1076'), -TINY) 1312 self.identical(fromHex('-0X4p-1076'), -TINY) 1313 self.identical(fromHex('-0x5p-1076'), -TINY) 1314 self.identical(fromHex('-0x6p-1076'), -2*TINY) 1315 self.identical(fromHex('-0X7p-1076'), -2*TINY) 1316 self.identical(fromHex('-0X8p-1076'), -2*TINY) 1317 self.identical(fromHex('-0X9p-1076'), -2*TINY) 1318 self.identical(fromHex('-0Xap-1076'), -2*TINY) 1319 self.identical(fromHex('-0xbp-1076'), -3*TINY) 1320 self.identical(fromHex('-0xcp-1076'), -3*TINY) 1321 self.identical(fromHex('-0Xdp-1076'), -3*TINY) 1322 self.identical(fromHex('-0xep-1076'), -4*TINY) 1323 self.identical(fromHex('-0Xfp-1076'), -4*TINY) 1324 self.identical(fromHex('-0X10p-1076'), -4*TINY) 1325 1326 # ... and near MIN ... 1327 self.identical(fromHex('0x0.ffffffffffffd6p-1022'), MIN-3*TINY) 1328 self.identical(fromHex('0x0.ffffffffffffd8p-1022'), MIN-2*TINY) 1329 self.identical(fromHex('0x0.ffffffffffffdap-1022'), MIN-2*TINY) 1330 self.identical(fromHex('0x0.ffffffffffffdcp-1022'), MIN-2*TINY) 1331 self.identical(fromHex('0x0.ffffffffffffdep-1022'), MIN-2*TINY) 1332 self.identical(fromHex('0x0.ffffffffffffe0p-1022'), MIN-2*TINY) 1333 self.identical(fromHex('0x0.ffffffffffffe2p-1022'), MIN-2*TINY) 1334 self.identical(fromHex('0x0.ffffffffffffe4p-1022'), MIN-2*TINY) 1335 self.identical(fromHex('0x0.ffffffffffffe6p-1022'), MIN-2*TINY) 1336 self.identical(fromHex('0x0.ffffffffffffe8p-1022'), MIN-2*TINY) 1337 self.identical(fromHex('0x0.ffffffffffffeap-1022'), MIN-TINY) 1338 self.identical(fromHex('0x0.ffffffffffffecp-1022'), MIN-TINY) 1339 self.identical(fromHex('0x0.ffffffffffffeep-1022'), MIN-TINY) 1340 self.identical(fromHex('0x0.fffffffffffff0p-1022'), MIN-TINY) 1341 self.identical(fromHex('0x0.fffffffffffff2p-1022'), MIN-TINY) 1342 self.identical(fromHex('0x0.fffffffffffff4p-1022'), MIN-TINY) 1343 self.identical(fromHex('0x0.fffffffffffff6p-1022'), MIN-TINY) 1344 self.identical(fromHex('0x0.fffffffffffff8p-1022'), MIN) 1345 self.identical(fromHex('0x0.fffffffffffffap-1022'), MIN) 1346 self.identical(fromHex('0x0.fffffffffffffcp-1022'), MIN) 1347 self.identical(fromHex('0x0.fffffffffffffep-1022'), MIN) 1348 self.identical(fromHex('0x1.00000000000000p-1022'), MIN) 1349 self.identical(fromHex('0x1.00000000000002p-1022'), MIN) 1350 self.identical(fromHex('0x1.00000000000004p-1022'), MIN) 1351 self.identical(fromHex('0x1.00000000000006p-1022'), MIN) 1352 self.identical(fromHex('0x1.00000000000008p-1022'), MIN) 1353 self.identical(fromHex('0x1.0000000000000ap-1022'), MIN+TINY) 1354 self.identical(fromHex('0x1.0000000000000cp-1022'), MIN+TINY) 1355 self.identical(fromHex('0x1.0000000000000ep-1022'), MIN+TINY) 1356 self.identical(fromHex('0x1.00000000000010p-1022'), MIN+TINY) 1357 self.identical(fromHex('0x1.00000000000012p-1022'), MIN+TINY) 1358 self.identical(fromHex('0x1.00000000000014p-1022'), MIN+TINY) 1359 self.identical(fromHex('0x1.00000000000016p-1022'), MIN+TINY) 1360 self.identical(fromHex('0x1.00000000000018p-1022'), MIN+2*TINY) 1361 1362 # ... and near 1.0. 1363 self.identical(fromHex('0x0.fffffffffffff0p0'), 1.0-EPS) 1364 self.identical(fromHex('0x0.fffffffffffff1p0'), 1.0-EPS) 1365 self.identical(fromHex('0X0.fffffffffffff2p0'), 1.0-EPS) 1366 self.identical(fromHex('0x0.fffffffffffff3p0'), 1.0-EPS) 1367 self.identical(fromHex('0X0.fffffffffffff4p0'), 1.0-EPS) 1368 self.identical(fromHex('0X0.fffffffffffff5p0'), 1.0-EPS/2) 1369 self.identical(fromHex('0X0.fffffffffffff6p0'), 1.0-EPS/2) 1370 self.identical(fromHex('0x0.fffffffffffff7p0'), 1.0-EPS/2) 1371 self.identical(fromHex('0x0.fffffffffffff8p0'), 1.0-EPS/2) 1372 self.identical(fromHex('0X0.fffffffffffff9p0'), 1.0-EPS/2) 1373 self.identical(fromHex('0X0.fffffffffffffap0'), 1.0-EPS/2) 1374 self.identical(fromHex('0x0.fffffffffffffbp0'), 1.0-EPS/2) 1375 self.identical(fromHex('0X0.fffffffffffffcp0'), 1.0) 1376 self.identical(fromHex('0x0.fffffffffffffdp0'), 1.0) 1377 self.identical(fromHex('0X0.fffffffffffffep0'), 1.0) 1378 self.identical(fromHex('0x0.ffffffffffffffp0'), 1.0) 1379 self.identical(fromHex('0X1.00000000000000p0'), 1.0) 1380 self.identical(fromHex('0X1.00000000000001p0'), 1.0) 1381 self.identical(fromHex('0x1.00000000000002p0'), 1.0) 1382 self.identical(fromHex('0X1.00000000000003p0'), 1.0) 1383 self.identical(fromHex('0x1.00000000000004p0'), 1.0) 1384 self.identical(fromHex('0X1.00000000000005p0'), 1.0) 1385 self.identical(fromHex('0X1.00000000000006p0'), 1.0) 1386 self.identical(fromHex('0X1.00000000000007p0'), 1.0) 1387 self.identical(fromHex('0x1.00000000000007ffffffffffffffffffffp0'), 1388 1.0) 1389 self.identical(fromHex('0x1.00000000000008p0'), 1.0) 1390 self.identical(fromHex('0x1.00000000000008000000000000000001p0'), 1391 1+EPS) 1392 self.identical(fromHex('0X1.00000000000009p0'), 1.0+EPS) 1393 self.identical(fromHex('0x1.0000000000000ap0'), 1.0+EPS) 1394 self.identical(fromHex('0x1.0000000000000bp0'), 1.0+EPS) 1395 self.identical(fromHex('0X1.0000000000000cp0'), 1.0+EPS) 1396 self.identical(fromHex('0x1.0000000000000dp0'), 1.0+EPS) 1397 self.identical(fromHex('0x1.0000000000000ep0'), 1.0+EPS) 1398 self.identical(fromHex('0X1.0000000000000fp0'), 1.0+EPS) 1399 self.identical(fromHex('0x1.00000000000010p0'), 1.0+EPS) 1400 self.identical(fromHex('0X1.00000000000011p0'), 1.0+EPS) 1401 self.identical(fromHex('0x1.00000000000012p0'), 1.0+EPS) 1402 self.identical(fromHex('0X1.00000000000013p0'), 1.0+EPS) 1403 self.identical(fromHex('0X1.00000000000014p0'), 1.0+EPS) 1404 self.identical(fromHex('0x1.00000000000015p0'), 1.0+EPS) 1405 self.identical(fromHex('0x1.00000000000016p0'), 1.0+EPS) 1406 self.identical(fromHex('0X1.00000000000017p0'), 1.0+EPS) 1407 self.identical(fromHex('0x1.00000000000017ffffffffffffffffffffp0'), 1408 1.0+EPS) 1409 self.identical(fromHex('0x1.00000000000018p0'), 1.0+2*EPS) 1410 self.identical(fromHex('0X1.00000000000018000000000000000001p0'), 1411 1.0+2*EPS) 1412 self.identical(fromHex('0x1.00000000000019p0'), 1.0+2*EPS) 1413 self.identical(fromHex('0X1.0000000000001ap0'), 1.0+2*EPS) 1414 self.identical(fromHex('0X1.0000000000001bp0'), 1.0+2*EPS) 1415 self.identical(fromHex('0x1.0000000000001cp0'), 1.0+2*EPS) 1416 self.identical(fromHex('0x1.0000000000001dp0'), 1.0+2*EPS) 1417 self.identical(fromHex('0x1.0000000000001ep0'), 1.0+2*EPS) 1418 self.identical(fromHex('0X1.0000000000001fp0'), 1.0+2*EPS) 1419 self.identical(fromHex('0x1.00000000000020p0'), 1.0+2*EPS) 1420 1421 def test_roundtrip(self): 1422 def roundtrip(x): 1423 return fromHex(toHex(x)) 1424 1425 for x in [NAN, INF, self.MAX, self.MIN, self.MIN-self.TINY, self.TINY, 0.0]: 1426 self.identical(x, roundtrip(x)) 1427 self.identical(-x, roundtrip(-x)) 1428 1429 # fromHex(toHex(x)) should exactly recover x, for any non-NaN float x. 1430 import random 1431 for i in xrange(10000): 1432 e = random.randrange(-1200, 1200) 1433 m = random.random() 1434 s = random.choice([1.0, -1.0]) 1435 try: 1436 x = s*ldexp(m, e) 1437 except OverflowError: 1438 pass 1439 else: 1440 self.identical(x, fromHex(toHex(x))) 1441 1442 1443 def test_main(): 1444 test_support.run_unittest( 1445 GeneralFloatCases, 1446 FormatFunctionsTestCase, 1447 UnknownFormatTestCase, 1448 IEEEFormatTestCase, 1449 ReprTestCase, 1450 RoundTestCase, 1451 InfNanTest, 1452 HexFloatTestCase, 1453 ) 1454 1455 if __name__ == '__main__': 1456 test_main() 1457
