| import unittest | |
| from test import test_support | |
| import sys | |
| import random | |
| import math | |
| # Used for lazy formatting of failure messages | |
| class Frm(object): | |
| def __init__(self, format, *args): | |
| self.format = format | |
| self.args = args | |
| def __str__(self): | |
| return self.format % self.args | |
| # SHIFT should match the value in longintrepr.h for best testing. | |
| SHIFT = sys.long_info.bits_per_digit | |
| BASE = 2 ** SHIFT | |
| MASK = BASE - 1 | |
| KARATSUBA_CUTOFF = 70 # from longobject.c | |
| # Max number of base BASE digits to use in test cases. Doubling | |
| # this will more than double the runtime. | |
| MAXDIGITS = 15 | |
| # build some special values | |
| special = map(long, [0, 1, 2, BASE, BASE >> 1]) | |
| special.append(0x5555555555555555L) | |
| special.append(0xaaaaaaaaaaaaaaaaL) | |
| # some solid strings of one bits | |
| p2 = 4L # 0 and 1 already added | |
| for i in range(2*SHIFT): | |
| special.append(p2 - 1) | |
| p2 = p2 << 1 | |
| del p2 | |
| # add complements & negations | |
| special = special + map(lambda x: ~x, special) + \ | |
| map(lambda x: -x, special) | |
| L = [ | |
| ('0', 0), | |
| ('1', 1), | |
| ('9', 9), | |
| ('10', 10), | |
| ('99', 99), | |
| ('100', 100), | |
| ('314', 314), | |
| (' 314', 314), | |
| ('314 ', 314), | |
| (' \t\t 314 \t\t ', 314), | |
| (repr(sys.maxint), sys.maxint), | |
| (' 1x', ValueError), | |
| (' 1 ', 1), | |
| (' 1\02 ', ValueError), | |
| ('', ValueError), | |
| (' ', ValueError), | |
| (' \t\t ', ValueError) | |
| ] | |
| if test_support.have_unicode: | |
| L += [ | |
| (unicode('0'), 0), | |
| (unicode('1'), 1), | |
| (unicode('9'), 9), | |
| (unicode('10'), 10), | |
| (unicode('99'), 99), | |
| (unicode('100'), 100), | |
| (unicode('314'), 314), | |
| (unicode(' 314'), 314), | |
| (unicode('\u0663\u0661\u0664 ','raw-unicode-escape'), 314), | |
| (unicode(' \t\t 314 \t\t '), 314), | |
| (unicode(' 1x'), ValueError), | |
| (unicode(' 1 '), 1), | |
| (unicode(' 1\02 '), ValueError), | |
| (unicode(''), ValueError), | |
| (unicode(' '), ValueError), | |
| (unicode(' \t\t '), ValueError), | |
| (unichr(0x200), ValueError), | |
| ] | |
| class LongTest(unittest.TestCase): | |
| # Get quasi-random long consisting of ndigits digits (in base BASE). | |
| # quasi == the most-significant digit will not be 0, and the number | |
| # is constructed to contain long strings of 0 and 1 bits. These are | |
| # more likely than random bits to provoke digit-boundary errors. | |
| # The sign of the number is also random. | |
| def getran(self, ndigits): | |
| self.assertTrue(ndigits > 0) | |
| nbits_hi = ndigits * SHIFT | |
| nbits_lo = nbits_hi - SHIFT + 1 | |
| answer = 0L | |
| nbits = 0 | |
| r = int(random.random() * (SHIFT * 2)) | 1 # force 1 bits to start | |
| while nbits < nbits_lo: | |
| bits = (r >> 1) + 1 | |
| bits = min(bits, nbits_hi - nbits) | |
| self.assertTrue(1 <= bits <= SHIFT) | |
| nbits = nbits + bits | |
| answer = answer << bits | |
| if r & 1: | |
| answer = answer | ((1 << bits) - 1) | |
| r = int(random.random() * (SHIFT * 2)) | |
| self.assertTrue(nbits_lo <= nbits <= nbits_hi) | |
| if random.random() < 0.5: | |
| answer = -answer | |
| return answer | |
| # Get random long consisting of ndigits random digits (relative to base | |
| # BASE). The sign bit is also random. | |
| def getran2(ndigits): | |
| answer = 0L | |
| for i in xrange(ndigits): | |
| answer = (answer << SHIFT) | random.randint(0, MASK) | |
| if random.random() < 0.5: | |
| answer = -answer | |
| return answer | |
| def check_division(self, x, y): | |
| eq = self.assertEqual | |
| q, r = divmod(x, y) | |
| q2, r2 = x//y, x%y | |
| pab, pba = x*y, y*x | |
| eq(pab, pba, Frm("multiplication does not commute for %r and %r", x, y)) | |
| eq(q, q2, Frm("divmod returns different quotient than / for %r and %r", x, y)) | |
| eq(r, r2, Frm("divmod returns different mod than %% for %r and %r", x, y)) | |
| eq(x, q*y + r, Frm("x != q*y + r after divmod on x=%r, y=%r", x, y)) | |
| if y > 0: | |
| self.assertTrue(0 <= r < y, Frm("bad mod from divmod on %r and %r", x, y)) | |
| else: | |
| self.assertTrue(y < r <= 0, Frm("bad mod from divmod on %r and %r", x, y)) | |
| def test_division(self): | |
| digits = range(1, MAXDIGITS+1) + range(KARATSUBA_CUTOFF, | |
| KARATSUBA_CUTOFF + 14) | |
| digits.append(KARATSUBA_CUTOFF * 3) | |
| for lenx in digits: | |
| x = self.getran(lenx) | |
| for leny in digits: | |
| y = self.getran(leny) or 1L | |
| self.check_division(x, y) | |
| # specific numbers chosen to exercise corner cases of the | |
| # current long division implementation | |
| # 30-bit cases involving a quotient digit estimate of BASE+1 | |
| self.check_division(1231948412290879395966702881L, | |
| 1147341367131428698L) | |
| self.check_division(815427756481275430342312021515587883L, | |
| 707270836069027745L) | |
| self.check_division(627976073697012820849443363563599041L, | |
| 643588798496057020L) | |
| self.check_division(1115141373653752303710932756325578065L, | |
| 1038556335171453937726882627L) | |
| # 30-bit cases that require the post-subtraction correction step | |
| self.check_division(922498905405436751940989320930368494L, | |
| 949985870686786135626943396L) | |
| self.check_division(768235853328091167204009652174031844L, | |
| 1091555541180371554426545266L) | |
| # 15-bit cases involving a quotient digit estimate of BASE+1 | |
| self.check_division(20172188947443L, 615611397L) | |
| self.check_division(1020908530270155025L, 950795710L) | |
| self.check_division(128589565723112408L, 736393718L) | |
| self.check_division(609919780285761575L, 18613274546784L) | |
| # 15-bit cases that require the post-subtraction correction step | |
| self.check_division(710031681576388032L, 26769404391308L) | |
| self.check_division(1933622614268221L, 30212853348836L) | |
| def test_karatsuba(self): | |
| digits = range(1, 5) + range(KARATSUBA_CUTOFF, KARATSUBA_CUTOFF + 10) | |
| digits.extend([KARATSUBA_CUTOFF * 10, KARATSUBA_CUTOFF * 100]) | |
| bits = [digit * SHIFT for digit in digits] | |
| # Test products of long strings of 1 bits -- (2**x-1)*(2**y-1) == | |
| # 2**(x+y) - 2**x - 2**y + 1, so the proper result is easy to check. | |
| for abits in bits: | |
| a = (1L << abits) - 1 | |
| for bbits in bits: | |
| if bbits < abits: | |
| continue | |
| b = (1L << bbits) - 1 | |
| x = a * b | |
| y = ((1L << (abits + bbits)) - | |
| (1L << abits) - | |
| (1L << bbits) + | |
| 1) | |
| self.assertEqual(x, y, | |
| Frm("bad result for a*b: a=%r, b=%r, x=%r, y=%r", a, b, x, y)) | |
| def check_bitop_identities_1(self, x): | |
| eq = self.assertEqual | |
| eq(x & 0, 0, Frm("x & 0 != 0 for x=%r", x)) | |
| eq(x | 0, x, Frm("x | 0 != x for x=%r", x)) | |
| eq(x ^ 0, x, Frm("x ^ 0 != x for x=%r", x)) | |
| eq(x & -1, x, Frm("x & -1 != x for x=%r", x)) | |
| eq(x | -1, -1, Frm("x | -1 != -1 for x=%r", x)) | |
| eq(x ^ -1, ~x, Frm("x ^ -1 != ~x for x=%r", x)) | |
| eq(x, ~~x, Frm("x != ~~x for x=%r", x)) | |
| eq(x & x, x, Frm("x & x != x for x=%r", x)) | |
| eq(x | x, x, Frm("x | x != x for x=%r", x)) | |
| eq(x ^ x, 0, Frm("x ^ x != 0 for x=%r", x)) | |
| eq(x & ~x, 0, Frm("x & ~x != 0 for x=%r", x)) | |
| eq(x | ~x, -1, Frm("x | ~x != -1 for x=%r", x)) | |
| eq(x ^ ~x, -1, Frm("x ^ ~x != -1 for x=%r", x)) | |
| eq(-x, 1 + ~x, Frm("not -x == 1 + ~x for x=%r", x)) | |
| eq(-x, ~(x-1), Frm("not -x == ~(x-1) forx =%r", x)) | |
| for n in xrange(2*SHIFT): | |
| p2 = 2L ** n | |
| eq(x << n >> n, x, | |
| Frm("x << n >> n != x for x=%r, n=%r", (x, n))) | |
| eq(x // p2, x >> n, | |
| Frm("x // p2 != x >> n for x=%r n=%r p2=%r", (x, n, p2))) | |
| eq(x * p2, x << n, | |
| Frm("x * p2 != x << n for x=%r n=%r p2=%r", (x, n, p2))) | |
| eq(x & -p2, x >> n << n, | |
| Frm("not x & -p2 == x >> n << n for x=%r n=%r p2=%r", (x, n, p2))) | |
| eq(x & -p2, x & ~(p2 - 1), | |
| Frm("not x & -p2 == x & ~(p2 - 1) for x=%r n=%r p2=%r", (x, n, p2))) | |
| def check_bitop_identities_2(self, x, y): | |
| eq = self.assertEqual | |
| eq(x & y, y & x, Frm("x & y != y & x for x=%r, y=%r", (x, y))) | |
| eq(x | y, y | x, Frm("x | y != y | x for x=%r, y=%r", (x, y))) | |
| eq(x ^ y, y ^ x, Frm("x ^ y != y ^ x for x=%r, y=%r", (x, y))) | |
| eq(x ^ y ^ x, y, Frm("x ^ y ^ x != y for x=%r, y=%r", (x, y))) | |
| eq(x & y, ~(~x | ~y), Frm("x & y != ~(~x | ~y) for x=%r, y=%r", (x, y))) | |
| eq(x | y, ~(~x & ~y), Frm("x | y != ~(~x & ~y) for x=%r, y=%r", (x, y))) | |
| eq(x ^ y, (x | y) & ~(x & y), | |
| Frm("x ^ y != (x | y) & ~(x & y) for x=%r, y=%r", (x, y))) | |
| eq(x ^ y, (x & ~y) | (~x & y), | |
| Frm("x ^ y == (x & ~y) | (~x & y) for x=%r, y=%r", (x, y))) | |
| eq(x ^ y, (x | y) & (~x | ~y), | |
| Frm("x ^ y == (x | y) & (~x | ~y) for x=%r, y=%r", (x, y))) | |
| def check_bitop_identities_3(self, x, y, z): | |
| eq = self.assertEqual | |
| eq((x & y) & z, x & (y & z), | |
| Frm("(x & y) & z != x & (y & z) for x=%r, y=%r, z=%r", (x, y, z))) | |
| eq((x | y) | z, x | (y | z), | |
| Frm("(x | y) | z != x | (y | z) for x=%r, y=%r, z=%r", (x, y, z))) | |
| eq((x ^ y) ^ z, x ^ (y ^ z), | |
| Frm("(x ^ y) ^ z != x ^ (y ^ z) for x=%r, y=%r, z=%r", (x, y, z))) | |
| eq(x & (y | z), (x & y) | (x & z), | |
| Frm("x & (y | z) != (x & y) | (x & z) for x=%r, y=%r, z=%r", (x, y, z))) | |
| eq(x | (y & z), (x | y) & (x | z), | |
| Frm("x | (y & z) != (x | y) & (x | z) for x=%r, y=%r, z=%r", (x, y, z))) | |
| def test_bitop_identities(self): | |
| for x in special: | |
| self.check_bitop_identities_1(x) | |
| digits = xrange(1, MAXDIGITS+1) | |
| for lenx in digits: | |
| x = self.getran(lenx) | |
| self.check_bitop_identities_1(x) | |
| for leny in digits: | |
| y = self.getran(leny) | |
| self.check_bitop_identities_2(x, y) | |
| self.check_bitop_identities_3(x, y, self.getran((lenx + leny)//2)) | |
| def slow_format(self, x, base): | |
| if (x, base) == (0, 8): | |
| # this is an oddball! | |
| return "0L" | |
| digits = [] | |
| sign = 0 | |
| if x < 0: | |
| sign, x = 1, -x | |
| while x: | |
| x, r = divmod(x, base) | |
| digits.append(int(r)) | |
| digits.reverse() | |
| digits = digits or [0] | |
| return '-'[:sign] + \ | |
| {8: '0', 10: '', 16: '0x'}[base] + \ | |
| "".join(map(lambda i: "0123456789abcdef"[i], digits)) + "L" | |
| def check_format_1(self, x): | |
| for base, mapper in (8, oct), (10, repr), (16, hex): | |
| got = mapper(x) | |
| expected = self.slow_format(x, base) | |
| msg = Frm("%s returned %r but expected %r for %r", | |
| mapper.__name__, got, expected, x) | |
| self.assertEqual(got, expected, msg) | |
| self.assertEqual(long(got, 0), x, Frm('long("%s", 0) != %r', got, x)) | |
| # str() has to be checked a little differently since there's no | |
| # trailing "L" | |
| got = str(x) | |
| expected = self.slow_format(x, 10)[:-1] | |
| msg = Frm("%s returned %r but expected %r for %r", | |
| mapper.__name__, got, expected, x) | |
| self.assertEqual(got, expected, msg) | |
| def test_format(self): | |
| for x in special: | |
| self.check_format_1(x) | |
| for i in xrange(10): | |
| for lenx in xrange(1, MAXDIGITS+1): | |
| x = self.getran(lenx) | |
| self.check_format_1(x) | |
| def test_long(self): | |
| self.assertEqual(long(314), 314L) | |
| self.assertEqual(long(3.14), 3L) | |
| self.assertEqual(long(314L), 314L) | |
| # Check that long() of basic types actually returns a long | |
| self.assertEqual(type(long(314)), long) | |
| self.assertEqual(type(long(3.14)), long) | |
| self.assertEqual(type(long(314L)), long) | |
| # Check that conversion from float truncates towards zero | |
| self.assertEqual(long(-3.14), -3L) | |
| self.assertEqual(long(3.9), 3L) | |
| self.assertEqual(long(-3.9), -3L) | |
| self.assertEqual(long(3.5), 3L) | |
| self.assertEqual(long(-3.5), -3L) | |
| self.assertEqual(long("-3"), -3L) | |
| self.assertEqual(long("0b10", 2), 2L) | |
| self.assertEqual(long("0o10", 8), 8L) | |
| self.assertEqual(long("0x10", 16), 16L) | |
| if test_support.have_unicode: | |
| self.assertEqual(long(unicode("-3")), -3L) | |
| # Different base: | |
| self.assertEqual(long("10",16), 16L) | |
| if test_support.have_unicode: | |
| self.assertEqual(long(unicode("10"),16), 16L) | |
| # Check conversions from string (same test set as for int(), and then some) | |
| LL = [ | |
| ('1' + '0'*20, 10L**20), | |
| ('1' + '0'*100, 10L**100) | |
| ] | |
| L2 = L[:] | |
| if test_support.have_unicode: | |
| L2 += [ | |
| (unicode('1') + unicode('0')*20, 10L**20), | |
| (unicode('1') + unicode('0')*100, 10L**100), | |
| ] | |
| for s, v in L2 + LL: | |
| for sign in "", "+", "-": | |
| for prefix in "", " ", "\t", " \t\t ": | |
| ss = prefix + sign + s | |
| vv = v | |
| if sign == "-" and v is not ValueError: | |
| vv = -v | |
| try: | |
| self.assertEqual(long(ss), long(vv)) | |
| except v: | |
| pass | |
| self.assertRaises(ValueError, long, '123\0') | |
| self.assertRaises(ValueError, long, '53', 40) | |
| self.assertRaises(TypeError, long, 1, 12) | |
| # tests with base 0 | |
| self.assertEqual(long(' 0123 ', 0), 83) | |
| self.assertEqual(long(' 0123 ', 0), 83) | |
| self.assertEqual(long('000', 0), 0) | |
| self.assertEqual(long('0o123', 0), 83) | |
| self.assertEqual(long('0x123', 0), 291) | |
| self.assertEqual(long('0b100', 0), 4) | |
| self.assertEqual(long(' 0O123 ', 0), 83) | |
| self.assertEqual(long(' 0X123 ', 0), 291) | |
| self.assertEqual(long(' 0B100 ', 0), 4) | |
| self.assertEqual(long('0', 0), 0) | |
| self.assertEqual(long('+0', 0), 0) | |
| self.assertEqual(long('-0', 0), 0) | |
| self.assertEqual(long('00', 0), 0) | |
| self.assertRaises(ValueError, long, '08', 0) | |
| self.assertRaises(ValueError, long, '-012395', 0) | |
| # SF patch #1638879: embedded NULs were not detected with | |
| # explicit base | |
| self.assertRaises(ValueError, long, '123\0', 10) | |
| self.assertRaises(ValueError, long, '123\x00 245', 20) | |
| self.assertEqual(long('100000000000000000000000000000000', 2), | |
| 4294967296) | |
| self.assertEqual(long('102002022201221111211', 3), 4294967296) | |
| self.assertEqual(long('10000000000000000', 4), 4294967296) | |
| self.assertEqual(long('32244002423141', 5), 4294967296) | |
| self.assertEqual(long('1550104015504', 6), 4294967296) | |
| self.assertEqual(long('211301422354', 7), 4294967296) | |
| self.assertEqual(long('40000000000', 8), 4294967296) | |
| self.assertEqual(long('12068657454', 9), 4294967296) | |
| self.assertEqual(long('4294967296', 10), 4294967296) | |
| self.assertEqual(long('1904440554', 11), 4294967296) | |
| self.assertEqual(long('9ba461594', 12), 4294967296) | |
| self.assertEqual(long('535a79889', 13), 4294967296) | |
| self.assertEqual(long('2ca5b7464', 14), 4294967296) | |
| self.assertEqual(long('1a20dcd81', 15), 4294967296) | |
| self.assertEqual(long('100000000', 16), 4294967296) | |
| self.assertEqual(long('a7ffda91', 17), 4294967296) | |
| self.assertEqual(long('704he7g4', 18), 4294967296) | |
| self.assertEqual(long('4f5aff66', 19), 4294967296) | |
| self.assertEqual(long('3723ai4g', 20), 4294967296) | |
| self.assertEqual(long('281d55i4', 21), 4294967296) | |
| self.assertEqual(long('1fj8b184', 22), 4294967296) | |
| self.assertEqual(long('1606k7ic', 23), 4294967296) | |
| self.assertEqual(long('mb994ag', 24), 4294967296) | |
| self.assertEqual(long('hek2mgl', 25), 4294967296) | |
| self.assertEqual(long('dnchbnm', 26), 4294967296) | |
| self.assertEqual(long('b28jpdm', 27), 4294967296) | |
| self.assertEqual(long('8pfgih4', 28), 4294967296) | |
| self.assertEqual(long('76beigg', 29), 4294967296) | |
| self.assertEqual(long('5qmcpqg', 30), 4294967296) | |
| self.assertEqual(long('4q0jto4', 31), 4294967296) | |
| self.assertEqual(long('4000000', 32), 4294967296) | |
| self.assertEqual(long('3aokq94', 33), 4294967296) | |
| self.assertEqual(long('2qhxjli', 34), 4294967296) | |
| self.assertEqual(long('2br45qb', 35), 4294967296) | |
| self.assertEqual(long('1z141z4', 36), 4294967296) | |
| self.assertEqual(long('100000000000000000000000000000001', 2), | |
| 4294967297) | |
| self.assertEqual(long('102002022201221111212', 3), 4294967297) | |
| self.assertEqual(long('10000000000000001', 4), 4294967297) | |
| self.assertEqual(long('32244002423142', 5), 4294967297) | |
| self.assertEqual(long('1550104015505', 6), 4294967297) | |
| self.assertEqual(long('211301422355', 7), 4294967297) | |
| self.assertEqual(long('40000000001', 8), 4294967297) | |
| self.assertEqual(long('12068657455', 9), 4294967297) | |
| self.assertEqual(long('4294967297', 10), 4294967297) | |
| self.assertEqual(long('1904440555', 11), 4294967297) | |
| self.assertEqual(long('9ba461595', 12), 4294967297) | |
| self.assertEqual(long('535a7988a', 13), 4294967297) | |
| self.assertEqual(long('2ca5b7465', 14), 4294967297) | |
| self.assertEqual(long('1a20dcd82', 15), 4294967297) | |
| self.assertEqual(long('100000001', 16), 4294967297) | |
| self.assertEqual(long('a7ffda92', 17), 4294967297) | |
| self.assertEqual(long('704he7g5', 18), 4294967297) | |
| self.assertEqual(long('4f5aff67', 19), 4294967297) | |
| self.assertEqual(long('3723ai4h', 20), 4294967297) | |
| self.assertEqual(long('281d55i5', 21), 4294967297) | |
| self.assertEqual(long('1fj8b185', 22), 4294967297) | |
| self.assertEqual(long('1606k7id', 23), 4294967297) | |
| self.assertEqual(long('mb994ah', 24), 4294967297) | |
| self.assertEqual(long('hek2mgm', 25), 4294967297) | |
| self.assertEqual(long('dnchbnn', 26), 4294967297) | |
| self.assertEqual(long('b28jpdn', 27), 4294967297) | |
| self.assertEqual(long('8pfgih5', 28), 4294967297) | |
| self.assertEqual(long('76beigh', 29), 4294967297) | |
| self.assertEqual(long('5qmcpqh', 30), 4294967297) | |
| self.assertEqual(long('4q0jto5', 31), 4294967297) | |
| self.assertEqual(long('4000001', 32), 4294967297) | |
| self.assertEqual(long('3aokq95', 33), 4294967297) | |
| self.assertEqual(long('2qhxjlj', 34), 4294967297) | |
| self.assertEqual(long('2br45qc', 35), 4294967297) | |
| self.assertEqual(long('1z141z5', 36), 4294967297) | |
| def test_conversion(self): | |
| # Test __long__() | |
| class ClassicMissingMethods: | |
| pass | |
| self.assertRaises(AttributeError, long, ClassicMissingMethods()) | |
| class MissingMethods(object): | |
| pass | |
| self.assertRaises(TypeError, long, MissingMethods()) | |
| class Foo0: | |
| def __long__(self): | |
| return 42L | |
| class Foo1(object): | |
| def __long__(self): | |
| return 42L | |
| class Foo2(long): | |
| def __long__(self): | |
| return 42L | |
| class Foo3(long): | |
| def __long__(self): | |
| return self | |
| class Foo4(long): | |
| def __long__(self): | |
| return 42 | |
| class Foo5(long): | |
| def __long__(self): | |
| return 42. | |
| self.assertEqual(long(Foo0()), 42L) | |
| self.assertEqual(long(Foo1()), 42L) | |
| self.assertEqual(long(Foo2()), 42L) | |
| self.assertEqual(long(Foo3()), 0) | |
| self.assertEqual(long(Foo4()), 42) | |
| self.assertRaises(TypeError, long, Foo5()) | |
| class Classic: | |
| pass | |
| for base in (object, Classic): | |
| class LongOverridesTrunc(base): | |
| def __long__(self): | |
| return 42 | |
| def __trunc__(self): | |
| return -12 | |
| self.assertEqual(long(LongOverridesTrunc()), 42) | |
| class JustTrunc(base): | |
| def __trunc__(self): | |
| return 42 | |
| self.assertEqual(long(JustTrunc()), 42) | |
| for trunc_result_base in (object, Classic): | |
| class Integral(trunc_result_base): | |
| def __int__(self): | |
| return 42 | |
| class TruncReturnsNonLong(base): | |
| def __trunc__(self): | |
| return Integral() | |
| self.assertEqual(long(TruncReturnsNonLong()), 42) | |
| class NonIntegral(trunc_result_base): | |
| def __trunc__(self): | |
| # Check that we avoid infinite recursion. | |
| return NonIntegral() | |
| class TruncReturnsNonIntegral(base): | |
| def __trunc__(self): | |
| return NonIntegral() | |
| try: | |
| long(TruncReturnsNonIntegral()) | |
| except TypeError as e: | |
| self.assertEqual(str(e), | |
| "__trunc__ returned non-Integral" | |
| " (type NonIntegral)") | |
| else: | |
| self.fail("Failed to raise TypeError with %s" % | |
| ((base, trunc_result_base),)) | |
| def test_misc(self): | |
| # check the extremes in int<->long conversion | |
| hugepos = sys.maxint | |
| hugeneg = -hugepos - 1 | |
| hugepos_aslong = long(hugepos) | |
| hugeneg_aslong = long(hugeneg) | |
| self.assertEqual(hugepos, hugepos_aslong, "long(sys.maxint) != sys.maxint") | |
| self.assertEqual(hugeneg, hugeneg_aslong, | |
| "long(-sys.maxint-1) != -sys.maxint-1") | |
| # long -> int should not fail for hugepos_aslong or hugeneg_aslong | |
| x = int(hugepos_aslong) | |
| try: | |
| self.assertEqual(x, hugepos, | |
| "converting sys.maxint to long and back to int fails") | |
| except OverflowError: | |
| self.fail("int(long(sys.maxint)) overflowed!") | |
| if not isinstance(x, int): | |
| self.fail("int(long(sys.maxint)) should have returned int") | |
| x = int(hugeneg_aslong) | |
| try: | |
| self.assertEqual(x, hugeneg, | |
| "converting -sys.maxint-1 to long and back to int fails") | |
| except OverflowError: | |
| self.fail("int(long(-sys.maxint-1)) overflowed!") | |
| if not isinstance(x, int): | |
| self.fail("int(long(-sys.maxint-1)) should have returned int") | |
| # but long -> int should overflow for hugepos+1 and hugeneg-1 | |
| x = hugepos_aslong + 1 | |
| try: | |
| y = int(x) | |
| except OverflowError: | |
| self.fail("int(long(sys.maxint) + 1) mustn't overflow") | |
| self.assertIsInstance(y, long, | |
| "int(long(sys.maxint) + 1) should have returned long") | |
| x = hugeneg_aslong - 1 | |
| try: | |
| y = int(x) | |
| except OverflowError: | |
| self.fail("int(long(-sys.maxint-1) - 1) mustn't overflow") | |
| self.assertIsInstance(y, long, | |
| "int(long(-sys.maxint-1) - 1) should have returned long") | |
| class long2(long): | |
| pass | |
| x = long2(1L<<100) | |
| y = int(x) | |
| self.assertTrue(type(y) is long, | |
| "overflowing int conversion must return long not long subtype") | |
| # long -> Py_ssize_t conversion | |
| class X(object): | |
| def __getslice__(self, i, j): | |
| return i, j | |
| with test_support.check_py3k_warnings(): | |
| self.assertEqual(X()[-5L:7L], (-5, 7)) | |
| # use the clamping effect to test the smallest and largest longs | |
| # that fit a Py_ssize_t | |
| slicemin, slicemax = X()[-2L**100:2L**100] | |
| self.assertEqual(X()[slicemin:slicemax], (slicemin, slicemax)) | |
| def test_issue9869(self): | |
| # Issue 9869: Interpreter crash when initializing an instance | |
| # of a long subclass from an object whose __long__ method returns | |
| # a plain int. | |
| class BadLong(object): | |
| def __long__(self): | |
| return 1000000 | |
| class MyLong(long): | |
| pass | |
| x = MyLong(BadLong()) | |
| self.assertIsInstance(x, long) | |
| self.assertEqual(x, 1000000) | |
| # ----------------------------------- tests of auto int->long conversion | |
| def test_auto_overflow(self): | |
| special = [0, 1, 2, 3, sys.maxint-1, sys.maxint, sys.maxint+1] | |
| sqrt = int(math.sqrt(sys.maxint)) | |
| special.extend([sqrt-1, sqrt, sqrt+1]) | |
| special.extend([-i for i in special]) | |
| def checkit(*args): | |
| # Heavy use of nested scopes here! | |
| self.assertEqual(got, expected, | |
| Frm("for %r expected %r got %r", args, expected, got)) | |
| for x in special: | |
| longx = long(x) | |
| expected = -longx | |
| got = -x | |
| checkit('-', x) | |
| for y in special: | |
| longy = long(y) | |
| expected = longx + longy | |
| got = x + y | |
| checkit(x, '+', y) | |
| expected = longx - longy | |
| got = x - y | |
| checkit(x, '-', y) | |
| expected = longx * longy | |
| got = x * y | |
| checkit(x, '*', y) | |
| if y: | |
| with test_support.check_py3k_warnings(): | |
| expected = longx / longy | |
| got = x / y | |
| checkit(x, '/', y) | |
| expected = longx // longy | |
| got = x // y | |
| checkit(x, '//', y) | |
| expected = divmod(longx, longy) | |
| got = divmod(longx, longy) | |
| checkit(x, 'divmod', y) | |
| if abs(y) < 5 and not (x == 0 and y < 0): | |
| expected = longx ** longy | |
| got = x ** y | |
| checkit(x, '**', y) | |
| for z in special: | |
| if z != 0 : | |
| if y >= 0: | |
| expected = pow(longx, longy, long(z)) | |
| got = pow(x, y, z) | |
| checkit('pow', x, y, '%', z) | |
| else: | |
| self.assertRaises(TypeError, pow,longx, longy, long(z)) | |
| @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"), | |
| "test requires IEEE 754 doubles") | |
| def test_float_conversion(self): | |
| import sys | |
| DBL_MAX = sys.float_info.max | |
| DBL_MAX_EXP = sys.float_info.max_exp | |
| DBL_MANT_DIG = sys.float_info.mant_dig | |
| exact_values = [0L, 1L, 2L, | |
| long(2**53-3), | |
| long(2**53-2), | |
| long(2**53-1), | |
| long(2**53), | |
| long(2**53+2), | |
| long(2**54-4), | |
| long(2**54-2), | |
| long(2**54), | |
| long(2**54+4)] | |
| for x in exact_values: | |
| self.assertEqual(long(float(x)), x) | |
| self.assertEqual(long(float(-x)), -x) | |
| # test round-half-even | |
| for x, y in [(1, 0), (2, 2), (3, 4), (4, 4), (5, 4), (6, 6), (7, 8)]: | |
| for p in xrange(15): | |
| self.assertEqual(long(float(2L**p*(2**53+x))), 2L**p*(2**53+y)) | |
| for x, y in [(0, 0), (1, 0), (2, 0), (3, 4), (4, 4), (5, 4), (6, 8), | |
| (7, 8), (8, 8), (9, 8), (10, 8), (11, 12), (12, 12), | |
| (13, 12), (14, 16), (15, 16)]: | |
| for p in xrange(15): | |
| self.assertEqual(long(float(2L**p*(2**54+x))), 2L**p*(2**54+y)) | |
| # behaviour near extremes of floating-point range | |
| long_dbl_max = long(DBL_MAX) | |
| top_power = 2**DBL_MAX_EXP | |
| halfway = (long_dbl_max + top_power)//2 | |
| self.assertEqual(float(long_dbl_max), DBL_MAX) | |
| self.assertEqual(float(long_dbl_max+1), DBL_MAX) | |
| self.assertEqual(float(halfway-1), DBL_MAX) | |
| self.assertRaises(OverflowError, float, halfway) | |
| self.assertEqual(float(1-halfway), -DBL_MAX) | |
| self.assertRaises(OverflowError, float, -halfway) | |
| self.assertRaises(OverflowError, float, top_power-1) | |
| self.assertRaises(OverflowError, float, top_power) | |
| self.assertRaises(OverflowError, float, top_power+1) | |
| self.assertRaises(OverflowError, float, 2*top_power-1) | |
| self.assertRaises(OverflowError, float, 2*top_power) | |
| self.assertRaises(OverflowError, float, top_power*top_power) | |
| for p in xrange(100): | |
| x = long(2**p * (2**53 + 1) + 1) | |
| y = long(2**p * (2**53+ 2)) | |
| self.assertEqual(long(float(x)), y) | |
| x = long(2**p * (2**53 + 1)) | |
| y = long(2**p * 2**53) | |
| self.assertEqual(long(float(x)), y) | |
| def test_float_overflow(self): | |
| for x in -2.0, -1.0, 0.0, 1.0, 2.0: | |
| self.assertEqual(float(long(x)), x) | |
| shuge = '12345' * 120 | |
| huge = 1L << 30000 | |
| mhuge = -huge | |
| namespace = {'huge': huge, 'mhuge': mhuge, 'shuge': shuge, 'math': math} | |
| for test in ["float(huge)", "float(mhuge)", | |
| "complex(huge)", "complex(mhuge)", | |
| "complex(huge, 1)", "complex(mhuge, 1)", | |
| "complex(1, huge)", "complex(1, mhuge)", | |
| "1. + huge", "huge + 1.", "1. + mhuge", "mhuge + 1.", | |
| "1. - huge", "huge - 1.", "1. - mhuge", "mhuge - 1.", | |
| "1. * huge", "huge * 1.", "1. * mhuge", "mhuge * 1.", | |
| "1. // huge", "huge // 1.", "1. // mhuge", "mhuge // 1.", | |
| "1. / huge", "huge / 1.", "1. / mhuge", "mhuge / 1.", | |
| "1. ** huge", "huge ** 1.", "1. ** mhuge", "mhuge ** 1.", | |
| "math.sin(huge)", "math.sin(mhuge)", | |
| "math.sqrt(huge)", "math.sqrt(mhuge)", # should do better | |
| "math.floor(huge)", "math.floor(mhuge)"]: | |
| self.assertRaises(OverflowError, eval, test, namespace) | |
| # XXX Perhaps float(shuge) can raise OverflowError on some box? | |
| # The comparison should not. | |
| self.assertNotEqual(float(shuge), int(shuge), | |
| "float(shuge) should not equal int(shuge)") | |
| def test_logs(self): | |
| LOG10E = math.log10(math.e) | |
| for exp in range(10) + [100, 1000, 10000]: | |
| value = 10 ** exp | |
| log10 = math.log10(value) | |
| self.assertAlmostEqual(log10, exp) | |
| # log10(value) == exp, so log(value) == log10(value)/log10(e) == | |
| # exp/LOG10E | |
| expected = exp / LOG10E | |
| log = math.log(value) | |
| self.assertAlmostEqual(log, expected) | |
| for bad in -(1L << 10000), -2L, 0L: | |
| self.assertRaises(ValueError, math.log, bad) | |
| self.assertRaises(ValueError, math.log10, bad) | |
| def test_mixed_compares(self): | |
| eq = self.assertEqual | |
| # We're mostly concerned with that mixing floats and longs does the | |
| # right stuff, even when longs are too large to fit in a float. | |
| # The safest way to check the results is to use an entirely different | |
| # method, which we do here via a skeletal rational class (which | |
| # represents all Python ints, longs and floats exactly). | |
| class Rat: | |
| def __init__(self, value): | |
| if isinstance(value, (int, long)): | |
| self.n = value | |
| self.d = 1 | |
| elif isinstance(value, float): | |
| # Convert to exact rational equivalent. | |
| f, e = math.frexp(abs(value)) | |
| assert f == 0 or 0.5 <= f < 1.0 | |
| # |value| = f * 2**e exactly | |
| # Suck up CHUNK bits at a time; 28 is enough so that we suck | |
| # up all bits in 2 iterations for all known binary double- | |
| # precision formats, and small enough to fit in an int. | |
| CHUNK = 28 | |
| top = 0 | |
| # invariant: |value| = (top + f) * 2**e exactly | |
| while f: | |
| f = math.ldexp(f, CHUNK) | |
| digit = int(f) | |
| assert digit >> CHUNK == 0 | |
| top = (top << CHUNK) | digit | |
| f -= digit | |
| assert 0.0 <= f < 1.0 | |
| e -= CHUNK | |
| # Now |value| = top * 2**e exactly. | |
| if e >= 0: | |
| n = top << e | |
| d = 1 | |
| else: | |
| n = top | |
| d = 1 << -e | |
| if value < 0: | |
| n = -n | |
| self.n = n | |
| self.d = d | |
| assert float(n) / float(d) == value | |
| else: | |
| raise TypeError("can't deal with %r" % value) | |
| def __cmp__(self, other): | |
| if not isinstance(other, Rat): | |
| other = Rat(other) | |
| return cmp(self.n * other.d, self.d * other.n) | |
| cases = [0, 0.001, 0.99, 1.0, 1.5, 1e20, 1e200] | |
| # 2**48 is an important boundary in the internals. 2**53 is an | |
| # important boundary for IEEE double precision. | |
| for t in 2.0**48, 2.0**50, 2.0**53: | |
| cases.extend([t - 1.0, t - 0.3, t, t + 0.3, t + 1.0, | |
| long(t-1), long(t), long(t+1)]) | |
| cases.extend([0, 1, 2, sys.maxint, float(sys.maxint)]) | |
| # 1L<<20000 should exceed all double formats. long(1e200) is to | |
| # check that we get equality with 1e200 above. | |
| t = long(1e200) | |
| cases.extend([0L, 1L, 2L, 1L << 20000, t-1, t, t+1]) | |
| cases.extend([-x for x in cases]) | |
| for x in cases: | |
| Rx = Rat(x) | |
| for y in cases: | |
| Ry = Rat(y) | |
| Rcmp = cmp(Rx, Ry) | |
| xycmp = cmp(x, y) | |
| eq(Rcmp, xycmp, Frm("%r %r %d %d", x, y, Rcmp, xycmp)) | |
| eq(x == y, Rcmp == 0, Frm("%r == %r %d", x, y, Rcmp)) | |
| eq(x != y, Rcmp != 0, Frm("%r != %r %d", x, y, Rcmp)) | |
| eq(x < y, Rcmp < 0, Frm("%r < %r %d", x, y, Rcmp)) | |
| eq(x <= y, Rcmp <= 0, Frm("%r <= %r %d", x, y, Rcmp)) | |
| eq(x > y, Rcmp > 0, Frm("%r > %r %d", x, y, Rcmp)) | |
| eq(x >= y, Rcmp >= 0, Frm("%r >= %r %d", x, y, Rcmp)) | |
| def test_nan_inf(self): | |
| self.assertRaises(OverflowError, long, float('inf')) | |
| self.assertRaises(OverflowError, long, float('-inf')) | |
| self.assertRaises(ValueError, long, float('nan')) | |
| def test_bit_length(self): | |
| tiny = 1e-10 | |
| for x in xrange(-65000, 65000): | |
| x = long(x) | |
| k = x.bit_length() | |
| # Check equivalence with Python version | |
| self.assertEqual(k, len(bin(x).lstrip('-0b'))) | |
| # Behaviour as specified in the docs | |
| if x != 0: | |
| self.assertTrue(2**(k-1) <= abs(x) < 2**k) | |
| else: | |
| self.assertEqual(k, 0) | |
| # Alternative definition: x.bit_length() == 1 + floor(log_2(x)) | |
| if x != 0: | |
| # When x is an exact power of 2, numeric errors can | |
| # cause floor(log(x)/log(2)) to be one too small; for | |
| # small x this can be fixed by adding a small quantity | |
| # to the quotient before taking the floor. | |
| self.assertEqual(k, 1 + math.floor( | |
| math.log(abs(x))/math.log(2) + tiny)) | |
| self.assertEqual((0L).bit_length(), 0) | |
| self.assertEqual((1L).bit_length(), 1) | |
| self.assertEqual((-1L).bit_length(), 1) | |
| self.assertEqual((2L).bit_length(), 2) | |
| self.assertEqual((-2L).bit_length(), 2) | |
| for i in [2, 3, 15, 16, 17, 31, 32, 33, 63, 64, 234]: | |
| a = 2L**i | |
| self.assertEqual((a-1).bit_length(), i) | |
| self.assertEqual((1-a).bit_length(), i) | |
| self.assertEqual((a).bit_length(), i+1) | |
| self.assertEqual((-a).bit_length(), i+1) | |
| self.assertEqual((a+1).bit_length(), i+1) | |
| self.assertEqual((-a-1).bit_length(), i+1) | |
| def test_main(): | |
| test_support.run_unittest(LongTest) | |
| if __name__ == "__main__": | |
| test_main() |