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