1 import unittest 2 import sys 3 4 import random 5 import math 6 7 from test import test_int, test_support 8 9 # Used for lazy formatting of failure messages 10 class Frm(object): 11 def __init__(self, format, *args): 12 self.format = format 13 self.args = args 14 15 def __str__(self): 16 return self.format % self.args 17 18 # SHIFT should match the value in longintrepr.h for best testing. 19 SHIFT = sys.long_info.bits_per_digit 20 BASE = 2 ** SHIFT 21 MASK = BASE - 1 22 KARATSUBA_CUTOFF = 70 # from longobject.c 23 24 # Max number of base BASE digits to use in test cases. Doubling 25 # this will more than double the runtime. 26 MAXDIGITS = 15 27 28 # build some special values 29 special = map(long, [0, 1, 2, BASE, BASE >> 1]) 30 special.append(0x5555555555555555L) 31 special.append(0xaaaaaaaaaaaaaaaaL) 32 # some solid strings of one bits 33 p2 = 4L # 0 and 1 already added 34 for i in range(2*SHIFT): 35 special.append(p2 - 1) 36 p2 = p2 << 1 37 del p2 38 # add complements & negations 39 special = special + map(lambda x: ~x, special) + \ 40 map(lambda x: -x, special) 41 42 L = [ 43 ('0', 0), 44 ('1', 1), 45 ('9', 9), 46 ('10', 10), 47 ('99', 99), 48 ('100', 100), 49 ('314', 314), 50 (' 314', 314), 51 ('314 ', 314), 52 (' \t\t 314 \t\t ', 314), 53 (repr(sys.maxint), sys.maxint), 54 (' 1x', ValueError), 55 (' 1 ', 1), 56 (' 1\02 ', ValueError), 57 ('', ValueError), 58 (' ', ValueError), 59 (' \t\t ', ValueError) 60 ] 61 if test_support.have_unicode: 62 L += [ 63 (unicode('0'), 0), 64 (unicode('1'), 1), 65 (unicode('9'), 9), 66 (unicode('10'), 10), 67 (unicode('99'), 99), 68 (unicode('100'), 100), 69 (unicode('314'), 314), 70 (unicode(' 314'), 314), 71 (unicode('\u0663\u0661\u0664 ','raw-unicode-escape'), 314), 72 (unicode(' \t\t 314 \t\t '), 314), 73 (unicode(' 1x'), ValueError), 74 (unicode(' 1 '), 1), 75 (unicode(' 1\02 '), ValueError), 76 (unicode(''), ValueError), 77 (unicode(' '), ValueError), 78 (unicode(' \t\t '), ValueError), 79 (unichr(0x200), ValueError), 80 ] 81 82 class LongSubclass(long): 83 pass 84 85 class OtherLongSubclass(long): 86 pass 87 88 class LongTest(test_int.IntLongCommonTests, unittest.TestCase): 89 90 ntype = long 91 92 # Get quasi-random long consisting of ndigits digits (in base BASE). 93 # quasi == the most-significant digit will not be 0, and the number 94 # is constructed to contain long strings of 0 and 1 bits. These are 95 # more likely than random bits to provoke digit-boundary errors. 96 # The sign of the number is also random. 97 98 def getran(self, ndigits): 99 self.assertGreater(ndigits, 0) 100 nbits_hi = ndigits * SHIFT 101 nbits_lo = nbits_hi - SHIFT + 1 102 answer = 0L 103 nbits = 0 104 r = int(random.random() * (SHIFT * 2)) | 1 # force 1 bits to start 105 while nbits < nbits_lo: 106 bits = (r >> 1) + 1 107 bits = min(bits, nbits_hi - nbits) 108 self.assertTrue(1 <= bits <= SHIFT) 109 nbits = nbits + bits 110 answer = answer << bits 111 if r & 1: 112 answer = answer | ((1 << bits) - 1) 113 r = int(random.random() * (SHIFT * 2)) 114 self.assertTrue(nbits_lo <= nbits <= nbits_hi) 115 if random.random() < 0.5: 116 answer = -answer 117 return answer 118 119 # Get random long consisting of ndigits random digits (relative to base 120 # BASE). The sign bit is also random. 121 122 def getran2(ndigits): 123 answer = 0L 124 for i in xrange(ndigits): 125 answer = (answer << SHIFT) | random.randint(0, MASK) 126 if random.random() < 0.5: 127 answer = -answer 128 return answer 129 130 def check_division(self, x, y): 131 eq = self.assertEqual 132 q, r = divmod(x, y) 133 q2, r2 = x//y, x%y 134 pab, pba = x*y, y*x 135 eq(pab, pba, Frm("multiplication does not commute for %r and %r", x, y)) 136 eq(q, q2, Frm("divmod returns different quotient than / for %r and %r", x, y)) 137 eq(r, r2, Frm("divmod returns different mod than %% for %r and %r", x, y)) 138 eq(x, q*y + r, Frm("x != q*y + r after divmod on x=%r, y=%r", x, y)) 139 if y > 0: 140 self.assertTrue(0 <= r < y, Frm("bad mod from divmod on %r and %r", x, y)) 141 else: 142 self.assertTrue(y < r <= 0, Frm("bad mod from divmod on %r and %r", x, y)) 143 144 def test_division(self): 145 digits = range(1, MAXDIGITS+1) + range(KARATSUBA_CUTOFF, 146 KARATSUBA_CUTOFF + 14) 147 digits.append(KARATSUBA_CUTOFF * 3) 148 for lenx in digits: 149 x = self.getran(lenx) 150 for leny in digits: 151 y = self.getran(leny) or 1L 152 self.check_division(x, y) 153 154 # specific numbers chosen to exercise corner cases of the 155 # current long division implementation 156 157 # 30-bit cases involving a quotient digit estimate of BASE+1 158 self.check_division(1231948412290879395966702881L, 159 1147341367131428698L) 160 self.check_division(815427756481275430342312021515587883L, 161 707270836069027745L) 162 self.check_division(627976073697012820849443363563599041L, 163 643588798496057020L) 164 self.check_division(1115141373653752303710932756325578065L, 165 1038556335171453937726882627L) 166 # 30-bit cases that require the post-subtraction correction step 167 self.check_division(922498905405436751940989320930368494L, 168 949985870686786135626943396L) 169 self.check_division(768235853328091167204009652174031844L, 170 1091555541180371554426545266L) 171 172 # 15-bit cases involving a quotient digit estimate of BASE+1 173 self.check_division(20172188947443L, 615611397L) 174 self.check_division(1020908530270155025L, 950795710L) 175 self.check_division(128589565723112408L, 736393718L) 176 self.check_division(609919780285761575L, 18613274546784L) 177 # 15-bit cases that require the post-subtraction correction step 178 self.check_division(710031681576388032L, 26769404391308L) 179 self.check_division(1933622614268221L, 30212853348836L) 180 181 182 183 def test_karatsuba(self): 184 digits = range(1, 5) + range(KARATSUBA_CUTOFF, KARATSUBA_CUTOFF + 10) 185 digits.extend([KARATSUBA_CUTOFF * 10, KARATSUBA_CUTOFF * 100]) 186 187 bits = [digit * SHIFT for digit in digits] 188 189 # Test products of long strings of 1 bits -- (2**x-1)*(2**y-1) == 190 # 2**(x+y) - 2**x - 2**y + 1, so the proper result is easy to check. 191 for abits in bits: 192 a = (1L << abits) - 1 193 for bbits in bits: 194 if bbits < abits: 195 continue 196 b = (1L << bbits) - 1 197 x = a * b 198 y = ((1L << (abits + bbits)) - 199 (1L << abits) - 200 (1L << bbits) + 201 1) 202 self.assertEqual(x, y, 203 Frm("bad result for a*b: a=%r, b=%r, x=%r, y=%r", a, b, x, y)) 204 205 def test_lshift_of_zero(self): 206 self.assertEqual(0L << 0, 0) 207 self.assertEqual(0L << 10, 0) 208 with self.assertRaises(ValueError): 209 0L << -1 210 211 @test_support.cpython_only 212 def test_huge_lshift_of_zero(self): 213 # Shouldn't try to allocate memory for a huge shift. See issue #27870. 214 # Other implementations may have a different boundary for overflow, 215 # or not raise at all. 216 self.assertEqual(0L << sys.maxsize, 0) 217 with self.assertRaises(OverflowError): 218 0L << (sys.maxsize + 1) 219 220 def check_bitop_identities_1(self, x): 221 eq = self.assertEqual 222 eq(x & 0, 0, Frm("x & 0 != 0 for x=%r", x)) 223 eq(x | 0, x, Frm("x | 0 != x for x=%r", x)) 224 eq(x ^ 0, x, Frm("x ^ 0 != x for x=%r", x)) 225 eq(x & -1, x, Frm("x & -1 != x for x=%r", x)) 226 eq(x | -1, -1, Frm("x | -1 != -1 for x=%r", x)) 227 eq(x ^ -1, ~x, Frm("x ^ -1 != ~x for x=%r", x)) 228 eq(x, ~~x, Frm("x != ~~x for x=%r", x)) 229 eq(x & x, x, Frm("x & x != x for x=%r", x)) 230 eq(x | x, x, Frm("x | x != x for x=%r", x)) 231 eq(x ^ x, 0, Frm("x ^ x != 0 for x=%r", x)) 232 eq(x & ~x, 0, Frm("x & ~x != 0 for x=%r", x)) 233 eq(x | ~x, -1, Frm("x | ~x != -1 for x=%r", x)) 234 eq(x ^ ~x, -1, Frm("x ^ ~x != -1 for x=%r", x)) 235 eq(-x, 1 + ~x, Frm("not -x == 1 + ~x for x=%r", x)) 236 eq(-x, ~(x-1), Frm("not -x == ~(x-1) forx =%r", x)) 237 for n in xrange(2*SHIFT): 238 p2 = 2L ** n 239 eq(x << n >> n, x, 240 Frm("x << n >> n != x for x=%r, n=%r", x, n)) 241 eq(x // p2, x >> n, 242 Frm("x // p2 != x >> n for x=%r n=%r p2=%r", x, n, p2)) 243 eq(x * p2, x << n, 244 Frm("x * p2 != x << n for x=%r n=%r p2=%r", x, n, p2)) 245 eq(x & -p2, x >> n << n, 246 Frm("not x & -p2 == x >> n << n for x=%r n=%r p2=%r", x, n, p2)) 247 eq(x & -p2, x & ~(p2 - 1), 248 Frm("not x & -p2 == x & ~(p2 - 1) for x=%r n=%r p2=%r", x, n, p2)) 249 250 def check_bitop_identities_2(self, x, y): 251 eq = self.assertEqual 252 eq(x & y, y & x, Frm("x & y != y & x for x=%r, y=%r", x, y)) 253 eq(x | y, y | x, Frm("x | y != y | x for x=%r, y=%r", x, y)) 254 eq(x ^ y, y ^ x, Frm("x ^ y != y ^ x for x=%r, y=%r", x, y)) 255 eq(x ^ y ^ x, y, Frm("x ^ y ^ x != y for x=%r, y=%r", x, y)) 256 eq(x & y, ~(~x | ~y), Frm("x & y != ~(~x | ~y) for x=%r, y=%r", x, y)) 257 eq(x | y, ~(~x & ~y), Frm("x | y != ~(~x & ~y) for x=%r, y=%r", x, y)) 258 eq(x ^ y, (x | y) & ~(x & y), 259 Frm("x ^ y != (x | y) & ~(x & y) for x=%r, y=%r", x, y)) 260 eq(x ^ y, (x & ~y) | (~x & y), 261 Frm("x ^ y == (x & ~y) | (~x & y) for x=%r, y=%r", x, y)) 262 eq(x ^ y, (x | y) & (~x | ~y), 263 Frm("x ^ y == (x | y) & (~x | ~y) for x=%r, y=%r", x, y)) 264 265 def check_bitop_identities_3(self, x, y, z): 266 eq = self.assertEqual 267 eq((x & y) & z, x & (y & z), 268 Frm("(x & y) & z != x & (y & z) for x=%r, y=%r, z=%r", x, y, z)) 269 eq((x | y) | z, x | (y | z), 270 Frm("(x | y) | z != x | (y | z) for x=%r, y=%r, z=%r", x, y, z)) 271 eq((x ^ y) ^ z, x ^ (y ^ z), 272 Frm("(x ^ y) ^ z != x ^ (y ^ z) for x=%r, y=%r, z=%r", x, y, z)) 273 eq(x & (y | z), (x & y) | (x & z), 274 Frm("x & (y | z) != (x & y) | (x & z) for x=%r, y=%r, z=%r", x, y, z)) 275 eq(x | (y & z), (x | y) & (x | z), 276 Frm("x | (y & z) != (x | y) & (x | z) for x=%r, y=%r, z=%r", x, y, z)) 277 278 def test_bitop_identities(self): 279 for x in special: 280 self.check_bitop_identities_1(x) 281 digits = xrange(1, MAXDIGITS+1) 282 for lenx in digits: 283 x = self.getran(lenx) 284 self.check_bitop_identities_1(x) 285 for leny in digits: 286 y = self.getran(leny) 287 self.check_bitop_identities_2(x, y) 288 self.check_bitop_identities_3(x, y, self.getran((lenx + leny)//2)) 289 290 def slow_format(self, x, base): 291 if (x, base) == (0, 8): 292 # this is an oddball! 293 return "0L" 294 digits = [] 295 sign = 0 296 if x < 0: 297 sign, x = 1, -x 298 while x: 299 x, r = divmod(x, base) 300 digits.append(int(r)) 301 digits.reverse() 302 digits = digits or [0] 303 return '-'[:sign] + \ 304 {8: '0', 10: '', 16: '0x'}[base] + \ 305 "".join(map(lambda i: "0123456789abcdef"[i], digits)) + "L" 306 307 def check_format_1(self, x): 308 for base, mapper in (8, oct), (10, repr), (16, hex): 309 got = mapper(x) 310 expected = self.slow_format(x, base) 311 msg = Frm("%s returned %r but expected %r for %r", 312 mapper.__name__, got, expected, x) 313 self.assertEqual(got, expected, msg) 314 self.assertEqual(long(got, 0), x, Frm('long("%s", 0) != %r', got, x)) 315 # str() has to be checked a little differently since there's no 316 # trailing "L" 317 got = str(x) 318 expected = self.slow_format(x, 10)[:-1] 319 msg = Frm("%s returned %r but expected %r for %r", 320 mapper.__name__, got, expected, x) 321 self.assertEqual(got, expected, msg) 322 323 def test_format(self): 324 for x in special: 325 self.check_format_1(x) 326 for i in xrange(10): 327 for lenx in xrange(1, MAXDIGITS+1): 328 x = self.getran(lenx) 329 self.check_format_1(x) 330 331 def test_long(self): 332 self.assertEqual(long(314), 314L) 333 self.assertEqual(long(3.14), 3L) 334 self.assertEqual(long(314L), 314L) 335 # Check that long() of basic types actually returns a long 336 self.assertEqual(type(long(314)), long) 337 self.assertEqual(type(long(3.14)), long) 338 self.assertEqual(type(long(314L)), long) 339 # Check that conversion from float truncates towards zero 340 self.assertEqual(long(-3.14), -3L) 341 self.assertEqual(long(3.9), 3L) 342 self.assertEqual(long(-3.9), -3L) 343 self.assertEqual(long(3.5), 3L) 344 self.assertEqual(long(-3.5), -3L) 345 self.assertEqual(long("-3"), -3L) 346 self.assertEqual(long("0b10", 2), 2L) 347 self.assertEqual(long("0o10", 8), 8L) 348 self.assertEqual(long("0x10", 16), 16L) 349 if test_support.have_unicode: 350 self.assertEqual(long(unicode("-3")), -3L) 351 # Different base: 352 self.assertEqual(long("10",16), 16L) 353 if test_support.have_unicode: 354 self.assertEqual(long(unicode("10"),16), 16L) 355 # Check conversions from string (same test set as for int(), and then some) 356 LL = [ 357 ('1' + '0'*20, 10L**20), 358 ('1' + '0'*100, 10L**100) 359 ] 360 L2 = L[:] 361 if test_support.have_unicode: 362 L2 += [ 363 (unicode('1') + unicode('0')*20, 10L**20), 364 (unicode('1') + unicode('0')*100, 10L**100), 365 ] 366 for s, v in L2 + LL: 367 for sign in "", "+", "-": 368 for prefix in "", " ", "\t", " \t\t ": 369 ss = prefix + sign + s 370 vv = v 371 if sign == "-" and v is not ValueError: 372 vv = -v 373 try: 374 self.assertEqual(long(ss), long(vv)) 375 except v: 376 pass 377 378 self.assertRaises(ValueError, long, '123\0') 379 self.assertRaises(ValueError, long, '53', 40) 380 self.assertRaises(TypeError, long, 1, 12) 381 382 # tests with base 0 383 self.assertEqual(long(' 0123 ', 0), 83) 384 self.assertEqual(long(' 0123 ', 0), 83) 385 self.assertEqual(long('000', 0), 0) 386 self.assertEqual(long('0o123', 0), 83) 387 self.assertEqual(long('0x123', 0), 291) 388 self.assertEqual(long('0b100', 0), 4) 389 self.assertEqual(long(' 0O123 ', 0), 83) 390 self.assertEqual(long(' 0X123 ', 0), 291) 391 self.assertEqual(long(' 0B100 ', 0), 4) 392 self.assertEqual(long('0', 0), 0) 393 self.assertEqual(long('+0', 0), 0) 394 self.assertEqual(long('-0', 0), 0) 395 self.assertEqual(long('00', 0), 0) 396 self.assertRaises(ValueError, long, '08', 0) 397 self.assertRaises(ValueError, long, '-012395', 0) 398 399 # SF patch #1638879: embedded NULs were not detected with 400 # explicit base 401 self.assertRaises(ValueError, long, '123\0', 10) 402 self.assertRaises(ValueError, long, '123\x00 245', 20) 403 404 self.assertEqual(long('100000000000000000000000000000000', 2), 405 4294967296) 406 self.assertEqual(long('102002022201221111211', 3), 4294967296) 407 self.assertEqual(long('10000000000000000', 4), 4294967296) 408 self.assertEqual(long('32244002423141', 5), 4294967296) 409 self.assertEqual(long('1550104015504', 6), 4294967296) 410 self.assertEqual(long('211301422354', 7), 4294967296) 411 self.assertEqual(long('40000000000', 8), 4294967296) 412 self.assertEqual(long('12068657454', 9), 4294967296) 413 self.assertEqual(long('4294967296', 10), 4294967296) 414 self.assertEqual(long('1904440554', 11), 4294967296) 415 self.assertEqual(long('9ba461594', 12), 4294967296) 416 self.assertEqual(long('535a79889', 13), 4294967296) 417 self.assertEqual(long('2ca5b7464', 14), 4294967296) 418 self.assertEqual(long('1a20dcd81', 15), 4294967296) 419 self.assertEqual(long('100000000', 16), 4294967296) 420 self.assertEqual(long('a7ffda91', 17), 4294967296) 421 self.assertEqual(long('704he7g4', 18), 4294967296) 422 self.assertEqual(long('4f5aff66', 19), 4294967296) 423 self.assertEqual(long('3723ai4g', 20), 4294967296) 424 self.assertEqual(long('281d55i4', 21), 4294967296) 425 self.assertEqual(long('1fj8b184', 22), 4294967296) 426 self.assertEqual(long('1606k7ic', 23), 4294967296) 427 self.assertEqual(long('mb994ag', 24), 4294967296) 428 self.assertEqual(long('hek2mgl', 25), 4294967296) 429 self.assertEqual(long('dnchbnm', 26), 4294967296) 430 self.assertEqual(long('b28jpdm', 27), 4294967296) 431 self.assertEqual(long('8pfgih4', 28), 4294967296) 432 self.assertEqual(long('76beigg', 29), 4294967296) 433 self.assertEqual(long('5qmcpqg', 30), 4294967296) 434 self.assertEqual(long('4q0jto4', 31), 4294967296) 435 self.assertEqual(long('4000000', 32), 4294967296) 436 self.assertEqual(long('3aokq94', 33), 4294967296) 437 self.assertEqual(long('2qhxjli', 34), 4294967296) 438 self.assertEqual(long('2br45qb', 35), 4294967296) 439 self.assertEqual(long('1z141z4', 36), 4294967296) 440 441 self.assertEqual(long('100000000000000000000000000000001', 2), 442 4294967297) 443 self.assertEqual(long('102002022201221111212', 3), 4294967297) 444 self.assertEqual(long('10000000000000001', 4), 4294967297) 445 self.assertEqual(long('32244002423142', 5), 4294967297) 446 self.assertEqual(long('1550104015505', 6), 4294967297) 447 self.assertEqual(long('211301422355', 7), 4294967297) 448 self.assertEqual(long('40000000001', 8), 4294967297) 449 self.assertEqual(long('12068657455', 9), 4294967297) 450 self.assertEqual(long('4294967297', 10), 4294967297) 451 self.assertEqual(long('1904440555', 11), 4294967297) 452 self.assertEqual(long('9ba461595', 12), 4294967297) 453 self.assertEqual(long('535a7988a', 13), 4294967297) 454 self.assertEqual(long('2ca5b7465', 14), 4294967297) 455 self.assertEqual(long('1a20dcd82', 15), 4294967297) 456 self.assertEqual(long('100000001', 16), 4294967297) 457 self.assertEqual(long('a7ffda92', 17), 4294967297) 458 self.assertEqual(long('704he7g5', 18), 4294967297) 459 self.assertEqual(long('4f5aff67', 19), 4294967297) 460 self.assertEqual(long('3723ai4h', 20), 4294967297) 461 self.assertEqual(long('281d55i5', 21), 4294967297) 462 self.assertEqual(long('1fj8b185', 22), 4294967297) 463 self.assertEqual(long('1606k7id', 23), 4294967297) 464 self.assertEqual(long('mb994ah', 24), 4294967297) 465 self.assertEqual(long('hek2mgm', 25), 4294967297) 466 self.assertEqual(long('dnchbnn', 26), 4294967297) 467 self.assertEqual(long('b28jpdn', 27), 4294967297) 468 self.assertEqual(long('8pfgih5', 28), 4294967297) 469 self.assertEqual(long('76beigh', 29), 4294967297) 470 self.assertEqual(long('5qmcpqh', 30), 4294967297) 471 self.assertEqual(long('4q0jto5', 31), 4294967297) 472 self.assertEqual(long('4000001', 32), 4294967297) 473 self.assertEqual(long('3aokq95', 33), 4294967297) 474 self.assertEqual(long('2qhxjlj', 34), 4294967297) 475 self.assertEqual(long('2br45qc', 35), 4294967297) 476 self.assertEqual(long('1z141z5', 36), 4294967297) 477 478 479 def test_conversion(self): 480 # Test __long__() 481 class ClassicMissingMethods: 482 pass 483 self.assertRaises(AttributeError, long, ClassicMissingMethods()) 484 485 class MissingMethods(object): 486 pass 487 self.assertRaises(TypeError, long, MissingMethods()) 488 489 class Foo0: 490 def __long__(self): 491 return 42L 492 493 class Foo1(object): 494 def __long__(self): 495 return 42L 496 497 class Foo2(long): 498 def __long__(self): 499 return 42L 500 501 class Foo3(long): 502 def __long__(self): 503 return self 504 505 class Foo4(long): 506 def __long__(self): 507 return 42 508 509 class Foo5(long): 510 def __long__(self): 511 return 42. 512 513 self.assertEqual(long(Foo0()), 42L) 514 self.assertEqual(long(Foo1()), 42L) 515 self.assertEqual(long(Foo2()), 42L) 516 self.assertEqual(long(Foo3()), 0) 517 self.assertEqual(long(Foo4()), 42) 518 self.assertRaises(TypeError, long, Foo5()) 519 520 class Classic: 521 pass 522 for base in (object, Classic): 523 class LongOverridesTrunc(base): 524 def __long__(self): 525 return 42 526 def __trunc__(self): 527 return -12 528 self.assertEqual(long(LongOverridesTrunc()), 42) 529 530 class JustTrunc(base): 531 def __trunc__(self): 532 return 42 533 self.assertEqual(long(JustTrunc()), 42) 534 535 for trunc_result_base in (object, Classic): 536 class Integral(trunc_result_base): 537 def __int__(self): 538 return 42 539 540 class TruncReturnsNonLong(base): 541 def __trunc__(self): 542 return Integral() 543 self.assertEqual(long(TruncReturnsNonLong()), 42) 544 545 class NonIntegral(trunc_result_base): 546 def __trunc__(self): 547 # Check that we avoid infinite recursion. 548 return NonIntegral() 549 550 class TruncReturnsNonIntegral(base): 551 def __trunc__(self): 552 return NonIntegral() 553 try: 554 long(TruncReturnsNonIntegral()) 555 except TypeError as e: 556 self.assertEqual(str(e), 557 "__trunc__ returned non-Integral" 558 " (type NonIntegral)") 559 else: 560 self.fail("Failed to raise TypeError with %s" % 561 ((base, trunc_result_base),)) 562 563 class TruncReturnsLongSubclass(base): 564 def __long__(self): 565 return OtherLongSubclass(42L) 566 good_int = TruncReturnsLongSubclass() 567 n = long(good_int) 568 self.assertEqual(n, 42L) 569 self.assertIs(type(n), OtherLongSubclass) 570 n = LongSubclass(good_int) 571 self.assertEqual(n, 42L) 572 self.assertIs(type(n), LongSubclass) 573 574 def test_misc(self): 575 576 # check the extremes in int<->long conversion 577 hugepos = sys.maxint 578 hugeneg = -hugepos - 1 579 hugepos_aslong = long(hugepos) 580 hugeneg_aslong = long(hugeneg) 581 self.assertEqual(hugepos, hugepos_aslong, "long(sys.maxint) != sys.maxint") 582 self.assertEqual(hugeneg, hugeneg_aslong, 583 "long(-sys.maxint-1) != -sys.maxint-1") 584 585 # long -> int should not fail for hugepos_aslong or hugeneg_aslong 586 x = int(hugepos_aslong) 587 try: 588 self.assertEqual(x, hugepos, 589 "converting sys.maxint to long and back to int fails") 590 except OverflowError: 591 self.fail("int(long(sys.maxint)) overflowed!") 592 if not isinstance(x, int): 593 self.fail("int(long(sys.maxint)) should have returned int") 594 x = int(hugeneg_aslong) 595 try: 596 self.assertEqual(x, hugeneg, 597 "converting -sys.maxint-1 to long and back to int fails") 598 except OverflowError: 599 self.fail("int(long(-sys.maxint-1)) overflowed!") 600 if not isinstance(x, int): 601 self.fail("int(long(-sys.maxint-1)) should have returned int") 602 # but long -> int should overflow for hugepos+1 and hugeneg-1 603 x = hugepos_aslong + 1 604 try: 605 y = int(x) 606 except OverflowError: 607 self.fail("int(long(sys.maxint) + 1) mustn't overflow") 608 self.assertIsInstance(y, long, 609 "int(long(sys.maxint) + 1) should have returned long") 610 611 x = hugeneg_aslong - 1 612 try: 613 y = int(x) 614 except OverflowError: 615 self.fail("int(long(-sys.maxint-1) - 1) mustn't overflow") 616 self.assertIsInstance(y, long, 617 "int(long(-sys.maxint-1) - 1) should have returned long") 618 619 class long2(long): 620 pass 621 x = long2(1L<<100) 622 y = int(x) 623 self.assertIs(type(y), long, 624 "overflowing int conversion must return long not long subtype") 625 626 # long -> Py_ssize_t conversion 627 class X(object): 628 def __getslice__(self, i, j): 629 return i, j 630 631 with test_support.check_py3k_warnings(): 632 self.assertEqual(X()[-5L:7L], (-5, 7)) 633 # use the clamping effect to test the smallest and largest longs 634 # that fit a Py_ssize_t 635 slicemin, slicemax = X()[-2L**100:2L**100] 636 self.assertEqual(X()[slicemin:slicemax], (slicemin, slicemax)) 637 638 def test_issue9869(self): 639 # Issue 9869: Interpreter crash when initializing an instance 640 # of a long subclass from an object whose __long__ method returns 641 # a plain int. 642 class BadLong(object): 643 def __long__(self): 644 return 1000000 645 646 class MyLong(long): 647 pass 648 649 x = MyLong(BadLong()) 650 self.assertIsInstance(x, long) 651 self.assertEqual(x, 1000000) 652 653 654 # ----------------------------------- tests of auto int->long conversion 655 656 def test_auto_overflow(self): 657 special = [0, 1, 2, 3, sys.maxint-1, sys.maxint, sys.maxint+1] 658 sqrt = int(math.sqrt(sys.maxint)) 659 special.extend([sqrt-1, sqrt, sqrt+1]) 660 special.extend([-i for i in special]) 661 662 def checkit(*args): 663 # Heavy use of nested scopes here! 664 self.assertEqual(got, expected, 665 Frm("for %r expected %r got %r", args, expected, got)) 666 667 for x in special: 668 longx = long(x) 669 670 expected = -longx 671 got = -x 672 checkit('-', x) 673 674 for y in special: 675 longy = long(y) 676 677 expected = longx + longy 678 got = x + y 679 checkit(x, '+', y) 680 681 expected = longx - longy 682 got = x - y 683 checkit(x, '-', y) 684 685 expected = longx * longy 686 got = x * y 687 checkit(x, '*', y) 688 689 if y: 690 with test_support.check_py3k_warnings(): 691 expected = longx / longy 692 got = x / y 693 checkit(x, '/', y) 694 695 expected = longx // longy 696 got = x // y 697 checkit(x, '//', y) 698 699 expected = divmod(longx, longy) 700 got = divmod(longx, longy) 701 checkit(x, 'divmod', y) 702 703 if abs(y) < 5 and not (x == 0 and y < 0): 704 expected = longx ** longy 705 got = x ** y 706 checkit(x, '**', y) 707 708 for z in special: 709 if z != 0 : 710 if y >= 0: 711 expected = pow(longx, longy, long(z)) 712 got = pow(x, y, z) 713 checkit('pow', x, y, '%', z) 714 else: 715 self.assertRaises(TypeError, pow,longx, longy, long(z)) 716 717 @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"), 718 "test requires IEEE 754 doubles") 719 def test_float_conversion(self): 720 import sys 721 DBL_MAX = sys.float_info.max 722 DBL_MAX_EXP = sys.float_info.max_exp 723 DBL_MANT_DIG = sys.float_info.mant_dig 724 725 exact_values = [0L, 1L, 2L, 726 long(2**53-3), 727 long(2**53-2), 728 long(2**53-1), 729 long(2**53), 730 long(2**53+2), 731 long(2**54-4), 732 long(2**54-2), 733 long(2**54), 734 long(2**54+4)] 735 for x in exact_values: 736 self.assertEqual(long(float(x)), x) 737 self.assertEqual(long(float(-x)), -x) 738 739 # test round-half-even 740 for x, y in [(1, 0), (2, 2), (3, 4), (4, 4), (5, 4), (6, 6), (7, 8)]: 741 for p in xrange(15): 742 self.assertEqual(long(float(2L**p*(2**53+x))), 2L**p*(2**53+y)) 743 744 for x, y in [(0, 0), (1, 0), (2, 0), (3, 4), (4, 4), (5, 4), (6, 8), 745 (7, 8), (8, 8), (9, 8), (10, 8), (11, 12), (12, 12), 746 (13, 12), (14, 16), (15, 16)]: 747 for p in xrange(15): 748 self.assertEqual(long(float(2L**p*(2**54+x))), 2L**p*(2**54+y)) 749 750 # behaviour near extremes of floating-point range 751 long_dbl_max = long(DBL_MAX) 752 top_power = 2**DBL_MAX_EXP 753 halfway = (long_dbl_max + top_power)//2 754 self.assertEqual(float(long_dbl_max), DBL_MAX) 755 self.assertEqual(float(long_dbl_max+1), DBL_MAX) 756 self.assertEqual(float(halfway-1), DBL_MAX) 757 self.assertRaises(OverflowError, float, halfway) 758 self.assertEqual(float(1-halfway), -DBL_MAX) 759 self.assertRaises(OverflowError, float, -halfway) 760 self.assertRaises(OverflowError, float, top_power-1) 761 self.assertRaises(OverflowError, float, top_power) 762 self.assertRaises(OverflowError, float, top_power+1) 763 self.assertRaises(OverflowError, float, 2*top_power-1) 764 self.assertRaises(OverflowError, float, 2*top_power) 765 self.assertRaises(OverflowError, float, top_power*top_power) 766 767 for p in xrange(100): 768 x = long(2**p * (2**53 + 1) + 1) 769 y = long(2**p * (2**53+ 2)) 770 self.assertEqual(long(float(x)), y) 771 772 x = long(2**p * (2**53 + 1)) 773 y = long(2**p * 2**53) 774 self.assertEqual(long(float(x)), y) 775 776 def test_float_overflow(self): 777 for x in -2.0, -1.0, 0.0, 1.0, 2.0: 778 self.assertEqual(float(long(x)), x) 779 780 shuge = '12345' * 120 781 huge = 1L << 30000 782 mhuge = -huge 783 namespace = {'huge': huge, 'mhuge': mhuge, 'shuge': shuge, 'math': math} 784 for test in ["float(huge)", "float(mhuge)", 785 "complex(huge)", "complex(mhuge)", 786 "complex(huge, 1)", "complex(mhuge, 1)", 787 "complex(1, huge)", "complex(1, mhuge)", 788 "1. + huge", "huge + 1.", "1. + mhuge", "mhuge + 1.", 789 "1. - huge", "huge - 1.", "1. - mhuge", "mhuge - 1.", 790 "1. * huge", "huge * 1.", "1. * mhuge", "mhuge * 1.", 791 "1. // huge", "huge // 1.", "1. // mhuge", "mhuge // 1.", 792 "1. / huge", "huge / 1.", "1. / mhuge", "mhuge / 1.", 793 "1. ** huge", "huge ** 1.", "1. ** mhuge", "mhuge ** 1.", 794 "math.sin(huge)", "math.sin(mhuge)", 795 "math.sqrt(huge)", "math.sqrt(mhuge)", # should do better 796 "math.floor(huge)", "math.floor(mhuge)"]: 797 798 self.assertRaises(OverflowError, eval, test, namespace) 799 800 # XXX Perhaps float(shuge) can raise OverflowError on some box? 801 # The comparison should not. 802 self.assertNotEqual(float(shuge), int(shuge), 803 "float(shuge) should not equal int(shuge)") 804 805 def test_logs(self): 806 LOG10E = math.log10(math.e) 807 808 for exp in range(10) + [100, 1000, 10000]: 809 value = 10 ** exp 810 log10 = math.log10(value) 811 self.assertAlmostEqual(log10, exp) 812 813 # log10(value) == exp, so log(value) == log10(value)/log10(e) == 814 # exp/LOG10E 815 expected = exp / LOG10E 816 log = math.log(value) 817 self.assertAlmostEqual(log, expected) 818 819 for bad in -(1L << 10000), -2L, 0L: 820 self.assertRaises(ValueError, math.log, bad) 821 self.assertRaises(ValueError, math.log10, bad) 822 823 def test_mixed_compares(self): 824 eq = self.assertEqual 825 826 # We're mostly concerned with that mixing floats and longs does the 827 # right stuff, even when longs are too large to fit in a float. 828 # The safest way to check the results is to use an entirely different 829 # method, which we do here via a skeletal rational class (which 830 # represents all Python ints, longs and floats exactly). 831 class Rat: 832 def __init__(self, value): 833 if isinstance(value, (int, long)): 834 self.n = value 835 self.d = 1 836 elif isinstance(value, float): 837 # Convert to exact rational equivalent. 838 f, e = math.frexp(abs(value)) 839 assert f == 0 or 0.5 <= f < 1.0 840 # |value| = f * 2**e exactly 841 842 # Suck up CHUNK bits at a time; 28 is enough so that we suck 843 # up all bits in 2 iterations for all known binary double- 844 # precision formats, and small enough to fit in an int. 845 CHUNK = 28 846 top = 0 847 # invariant: |value| = (top + f) * 2**e exactly 848 while f: 849 f = math.ldexp(f, CHUNK) 850 digit = int(f) 851 assert digit >> CHUNK == 0 852 top = (top << CHUNK) | digit 853 f -= digit 854 assert 0.0 <= f < 1.0 855 e -= CHUNK 856 857 # Now |value| = top * 2**e exactly. 858 if e >= 0: 859 n = top << e 860 d = 1 861 else: 862 n = top 863 d = 1 << -e 864 if value < 0: 865 n = -n 866 self.n = n 867 self.d = d 868 assert float(n) / float(d) == value 869 else: 870 raise TypeError("can't deal with %r" % value) 871 872 def __cmp__(self, other): 873 if not isinstance(other, Rat): 874 other = Rat(other) 875 return cmp(self.n * other.d, self.d * other.n) 876 877 cases = [0, 0.001, 0.99, 1.0, 1.5, 1e20, 1e200] 878 # 2**48 is an important boundary in the internals. 2**53 is an 879 # important boundary for IEEE double precision. 880 for t in 2.0**48, 2.0**50, 2.0**53: 881 cases.extend([t - 1.0, t - 0.3, t, t + 0.3, t + 1.0, 882 long(t-1), long(t), long(t+1)]) 883 cases.extend([0, 1, 2, sys.maxint, float(sys.maxint)]) 884 # 1L<<20000 should exceed all double formats. long(1e200) is to 885 # check that we get equality with 1e200 above. 886 t = long(1e200) 887 cases.extend([0L, 1L, 2L, 1L << 20000, t-1, t, t+1]) 888 cases.extend([-x for x in cases]) 889 for x in cases: 890 Rx = Rat(x) 891 for y in cases: 892 Ry = Rat(y) 893 Rcmp = cmp(Rx, Ry) 894 xycmp = cmp(x, y) 895 eq(Rcmp, xycmp, Frm("%r %r %d %d", x, y, Rcmp, xycmp)) 896 eq(x == y, Rcmp == 0, Frm("%r == %r %d", x, y, Rcmp)) 897 eq(x != y, Rcmp != 0, Frm("%r != %r %d", x, y, Rcmp)) 898 eq(x < y, Rcmp < 0, Frm("%r < %r %d", x, y, Rcmp)) 899 eq(x <= y, Rcmp <= 0, Frm("%r <= %r %d", x, y, Rcmp)) 900 eq(x > y, Rcmp > 0, Frm("%r > %r %d", x, y, Rcmp)) 901 eq(x >= y, Rcmp >= 0, Frm("%r >= %r %d", x, y, Rcmp)) 902 903 def test_nan_inf(self): 904 self.assertRaises(OverflowError, long, float('inf')) 905 self.assertRaises(OverflowError, long, float('-inf')) 906 self.assertRaises(ValueError, long, float('nan')) 907 908 def test_bit_length(self): 909 tiny = 1e-10 910 for x in xrange(-65000, 65000): 911 x = long(x) 912 k = x.bit_length() 913 # Check equivalence with Python version 914 self.assertEqual(k, len(bin(x).lstrip('-0b'))) 915 # Behaviour as specified in the docs 916 if x != 0: 917 self.assertTrue(2**(k-1) <= abs(x) < 2**k) 918 else: 919 self.assertEqual(k, 0) 920 # Alternative definition: x.bit_length() == 1 + floor(log_2(x)) 921 if x != 0: 922 # When x is an exact power of 2, numeric errors can 923 # cause floor(log(x)/log(2)) to be one too small; for 924 # small x this can be fixed by adding a small quantity 925 # to the quotient before taking the floor. 926 self.assertEqual(k, 1 + math.floor( 927 math.log(abs(x))/math.log(2) + tiny)) 928 929 self.assertEqual((0L).bit_length(), 0) 930 self.assertEqual((1L).bit_length(), 1) 931 self.assertEqual((-1L).bit_length(), 1) 932 self.assertEqual((2L).bit_length(), 2) 933 self.assertEqual((-2L).bit_length(), 2) 934 for i in [2, 3, 15, 16, 17, 31, 32, 33, 63, 64, 234]: 935 a = 2L**i 936 self.assertEqual((a-1).bit_length(), i) 937 self.assertEqual((1-a).bit_length(), i) 938 self.assertEqual((a).bit_length(), i+1) 939 self.assertEqual((-a).bit_length(), i+1) 940 self.assertEqual((a+1).bit_length(), i+1) 941 self.assertEqual((-a-1).bit_length(), i+1) 942 943 944 def test_main(): 945 test_support.run_unittest(LongTest) 946 947 if __name__ == "__main__": 948 test_main() 949
