| import unittest |
| from test import 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.int_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 = [0, 1, 2, BASE, BASE >> 1, 0x5555555555555555, 0xaaaaaaaaaaaaaaaa] |
| # some solid strings of one bits |
| p2 = 4 # 0 and 1 already added |
| for i in range(2*SHIFT): |
| special.append(p2 - 1) |
| p2 = p2 << 1 |
| del p2 |
| # add complements & negations |
| special += [~x for x in special] + [-x for x in 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.maxsize), sys.maxsize), |
| (' 1x', ValueError), |
| (' 1 ', 1), |
| (' 1\02 ', ValueError), |
| ('', ValueError), |
| (' ', ValueError), |
| (' \t\t ', 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 = 0 |
| 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 = 0 |
| for i in range(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 = list(range(1, MAXDIGITS+1)) + list(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 1 |
| 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(1231948412290879395966702881, |
| 1147341367131428698) |
| self.check_division(815427756481275430342312021515587883, |
| 707270836069027745) |
| self.check_division(627976073697012820849443363563599041, |
| 643588798496057020) |
| self.check_division(1115141373653752303710932756325578065, |
| 1038556335171453937726882627) |
| # 30-bit cases that require the post-subtraction correction step |
| self.check_division(922498905405436751940989320930368494, |
| 949985870686786135626943396) |
| self.check_division(768235853328091167204009652174031844, |
| 1091555541180371554426545266) |
| |
| # 15-bit cases involving a quotient digit estimate of BASE+1 |
| self.check_division(20172188947443, 615611397) |
| self.check_division(1020908530270155025, 950795710) |
| self.check_division(128589565723112408, 736393718) |
| self.check_division(609919780285761575, 18613274546784) |
| # 15-bit cases that require the post-subtraction correction step |
| self.check_division(710031681576388032, 26769404391308) |
| self.check_division(1933622614268221, 30212853348836) |
| |
| |
| |
| def test_karatsuba(self): |
| digits = list(range(1, 5)) + list(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 = (1 << abits) - 1 |
| for bbits in bits: |
| if bbits < abits: |
| continue |
| b = (1 << bbits) - 1 |
| x = a * b |
| y = ((1 << (abits + bbits)) - |
| (1 << abits) - |
| (1 << 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 range(2*SHIFT): |
| p2 = 2 ** 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 = range(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): |
| 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] + \ |
| {2: '0b', 8: '0o', 10: '', 16: '0x'}[base] + \ |
| "".join(map(lambda i: "0123456789abcdef"[i], digits)) |
| |
| 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(int(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) |
| 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 range(10): |
| for lenx in range(1, MAXDIGITS+1): |
| x = self.getran(lenx) |
| self.check_format_1(x) |
| |
| def test_long(self): |
| self.assertEqual(int(314), 314) |
| self.assertEqual(int(3.14), 3) |
| self.assertEqual(int(314), 314) |
| # Check that conversion from float truncates towards zero |
| self.assertEqual(int(-3.14), -3) |
| self.assertEqual(int(3.9), 3) |
| self.assertEqual(int(-3.9), -3) |
| self.assertEqual(int(3.5), 3) |
| self.assertEqual(int(-3.5), -3) |
| self.assertEqual(int("-3"), -3) |
| # Different base: |
| self.assertEqual(int("10",16), 16) |
| # Check conversions from string (same test set as for int(), and then some) |
| LL = [ |
| ('1' + '0'*20, 10**20), |
| ('1' + '0'*100, 10**100) |
| ] |
| L2 = L[:] |
| 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(int(ss), int(vv)) |
| except ValueError: |
| pass |
| |
| self.assertRaises(ValueError, int, '123\0') |
| self.assertRaises(ValueError, int, '53', 40) |
| # trailing L should no longer be accepted... |
| self.assertRaises(ValueError, int, '123L') |
| self.assertRaises(ValueError, int, '123l') |
| self.assertRaises(ValueError, int, '0L') |
| self.assertRaises(ValueError, int, '-37L') |
| self.assertRaises(ValueError, int, '0x32L', 16) |
| self.assertRaises(ValueError, int, '1L', 21) |
| # ... but it's just a normal digit if base >= 22 |
| self.assertEqual(int('1L', 22), 43) |
| |
| self.assertRaises(TypeError, int, 1, 12) |
| |
| # SF patch #1638879: embedded NULs were not detected with |
| # explicit base |
| self.assertRaises(ValueError, int, '123\0', 10) |
| self.assertRaises(ValueError, int, '123\x00 245', 20) |
| |
| self.assertEqual(int('100000000000000000000000000000000', 2), |
| 4294967296) |
| self.assertEqual(int('102002022201221111211', 3), 4294967296) |
| self.assertEqual(int('10000000000000000', 4), 4294967296) |
| self.assertEqual(int('32244002423141', 5), 4294967296) |
| self.assertEqual(int('1550104015504', 6), 4294967296) |
| self.assertEqual(int('211301422354', 7), 4294967296) |
| self.assertEqual(int('40000000000', 8), 4294967296) |
| self.assertEqual(int('12068657454', 9), 4294967296) |
| self.assertEqual(int('4294967296', 10), 4294967296) |
| self.assertEqual(int('1904440554', 11), 4294967296) |
| self.assertEqual(int('9ba461594', 12), 4294967296) |
| self.assertEqual(int('535a79889', 13), 4294967296) |
| self.assertEqual(int('2ca5b7464', 14), 4294967296) |
| self.assertEqual(int('1a20dcd81', 15), 4294967296) |
| self.assertEqual(int('100000000', 16), 4294967296) |
| self.assertEqual(int('a7ffda91', 17), 4294967296) |
| self.assertEqual(int('704he7g4', 18), 4294967296) |
| self.assertEqual(int('4f5aff66', 19), 4294967296) |
| self.assertEqual(int('3723ai4g', 20), 4294967296) |
| self.assertEqual(int('281d55i4', 21), 4294967296) |
| self.assertEqual(int('1fj8b184', 22), 4294967296) |
| self.assertEqual(int('1606k7ic', 23), 4294967296) |
| self.assertEqual(int('mb994ag', 24), 4294967296) |
| self.assertEqual(int('hek2mgl', 25), 4294967296) |
| self.assertEqual(int('dnchbnm', 26), 4294967296) |
| self.assertEqual(int('b28jpdm', 27), 4294967296) |
| self.assertEqual(int('8pfgih4', 28), 4294967296) |
| self.assertEqual(int('76beigg', 29), 4294967296) |
| self.assertEqual(int('5qmcpqg', 30), 4294967296) |
| self.assertEqual(int('4q0jto4', 31), 4294967296) |
| self.assertEqual(int('4000000', 32), 4294967296) |
| self.assertEqual(int('3aokq94', 33), 4294967296) |
| self.assertEqual(int('2qhxjli', 34), 4294967296) |
| self.assertEqual(int('2br45qb', 35), 4294967296) |
| self.assertEqual(int('1z141z4', 36), 4294967296) |
| |
| self.assertEqual(int('100000000000000000000000000000001', 2), |
| 4294967297) |
| self.assertEqual(int('102002022201221111212', 3), 4294967297) |
| self.assertEqual(int('10000000000000001', 4), 4294967297) |
| self.assertEqual(int('32244002423142', 5), 4294967297) |
| self.assertEqual(int('1550104015505', 6), 4294967297) |
| self.assertEqual(int('211301422355', 7), 4294967297) |
| self.assertEqual(int('40000000001', 8), 4294967297) |
| self.assertEqual(int('12068657455', 9), 4294967297) |
| self.assertEqual(int('4294967297', 10), 4294967297) |
| self.assertEqual(int('1904440555', 11), 4294967297) |
| self.assertEqual(int('9ba461595', 12), 4294967297) |
| self.assertEqual(int('535a7988a', 13), 4294967297) |
| self.assertEqual(int('2ca5b7465', 14), 4294967297) |
| self.assertEqual(int('1a20dcd82', 15), 4294967297) |
| self.assertEqual(int('100000001', 16), 4294967297) |
| self.assertEqual(int('a7ffda92', 17), 4294967297) |
| self.assertEqual(int('704he7g5', 18), 4294967297) |
| self.assertEqual(int('4f5aff67', 19), 4294967297) |
| self.assertEqual(int('3723ai4h', 20), 4294967297) |
| self.assertEqual(int('281d55i5', 21), 4294967297) |
| self.assertEqual(int('1fj8b185', 22), 4294967297) |
| self.assertEqual(int('1606k7id', 23), 4294967297) |
| self.assertEqual(int('mb994ah', 24), 4294967297) |
| self.assertEqual(int('hek2mgm', 25), 4294967297) |
| self.assertEqual(int('dnchbnn', 26), 4294967297) |
| self.assertEqual(int('b28jpdn', 27), 4294967297) |
| self.assertEqual(int('8pfgih5', 28), 4294967297) |
| self.assertEqual(int('76beigh', 29), 4294967297) |
| self.assertEqual(int('5qmcpqh', 30), 4294967297) |
| self.assertEqual(int('4q0jto5', 31), 4294967297) |
| self.assertEqual(int('4000001', 32), 4294967297) |
| self.assertEqual(int('3aokq95', 33), 4294967297) |
| self.assertEqual(int('2qhxjlj', 34), 4294967297) |
| self.assertEqual(int('2br45qc', 35), 4294967297) |
| self.assertEqual(int('1z141z5', 36), 4294967297) |
| |
| # tests with base 0 |
| self.assertEqual(int('000', 0), 0) |
| self.assertEqual(int('0o123', 0), 83) |
| self.assertEqual(int('0x123', 0), 291) |
| self.assertEqual(int('0b100', 0), 4) |
| self.assertEqual(int(' 0O123 ', 0), 83) |
| self.assertEqual(int(' 0X123 ', 0), 291) |
| self.assertEqual(int(' 0B100 ', 0), 4) |
| self.assertEqual(int('0', 0), 0) |
| self.assertEqual(int('+0', 0), 0) |
| self.assertEqual(int('-0', 0), 0) |
| self.assertEqual(int('00', 0), 0) |
| self.assertRaises(ValueError, int, '08', 0) |
| self.assertRaises(ValueError, int, '-012395', 0) |
| |
| def test_conversion(self): |
| # Test __int__() |
| class ClassicMissingMethods: |
| pass |
| self.assertRaises(TypeError, int, ClassicMissingMethods()) |
| |
| class MissingMethods(object): |
| pass |
| self.assertRaises(TypeError, int, MissingMethods()) |
| |
| class Foo0: |
| def __int__(self): |
| return 42 |
| |
| class Foo1(object): |
| def __int__(self): |
| return 42 |
| |
| class Foo2(int): |
| def __int__(self): |
| return 42 |
| |
| class Foo3(int): |
| def __int__(self): |
| return self |
| |
| class Foo4(int): |
| def __int__(self): |
| return 42 |
| |
| class Foo5(int): |
| def __int__(self): |
| return 42. |
| |
| self.assertEqual(int(Foo0()), 42) |
| self.assertEqual(int(Foo1()), 42) |
| self.assertEqual(int(Foo2()), 42) |
| self.assertEqual(int(Foo3()), 0) |
| self.assertEqual(int(Foo4()), 42) |
| self.assertRaises(TypeError, int, Foo5()) |
| |
| class Classic: |
| pass |
| for base in (object, Classic): |
| class IntOverridesTrunc(base): |
| def __int__(self): |
| return 42 |
| def __trunc__(self): |
| return -12 |
| self.assertEqual(int(IntOverridesTrunc()), 42) |
| |
| class JustTrunc(base): |
| def __trunc__(self): |
| return 42 |
| self.assertEqual(int(JustTrunc()), 42) |
| |
| class JustLong(base): |
| # test that __long__ no longer used in 3.x |
| def __long__(self): |
| return 42 |
| self.assertRaises(TypeError, int, JustLong()) |
| |
| class LongTrunc(base): |
| # __long__ should be ignored in 3.x |
| def __long__(self): |
| return 42 |
| def __trunc__(self): |
| return 1729 |
| self.assertEqual(int(LongTrunc()), 1729) |
| |
| 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(int(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: |
| int(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.maxsize |
| hugeneg = -hugepos - 1 |
| hugepos_aslong = int(hugepos) |
| hugeneg_aslong = int(hugeneg) |
| self.assertEqual(hugepos, hugepos_aslong, "long(sys.maxsize) != sys.maxsize") |
| self.assertEqual(hugeneg, hugeneg_aslong, |
| "long(-sys.maxsize-1) != -sys.maxsize-1") |
| |
| # long -> int should not fail for hugepos_aslong or hugeneg_aslong |
| x = int(hugepos_aslong) |
| try: |
| self.assertEqual(x, hugepos, |
| "converting sys.maxsize to long and back to int fails") |
| except OverflowError: |
| self.fail("int(long(sys.maxsize)) overflowed!") |
| if not isinstance(x, int): |
| raise TestFailed("int(long(sys.maxsize)) should have returned int") |
| x = int(hugeneg_aslong) |
| try: |
| self.assertEqual(x, hugeneg, |
| "converting -sys.maxsize-1 to long and back to int fails") |
| except OverflowError: |
| self.fail("int(long(-sys.maxsize-1)) overflowed!") |
| if not isinstance(x, int): |
| raise TestFailed("int(long(-sys.maxsize-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.maxsize) + 1) mustn't overflow") |
| self.assertTrue(isinstance(y, int), |
| "int(long(sys.maxsize) + 1) should have returned long") |
| |
| x = hugeneg_aslong - 1 |
| try: |
| y = int(x) |
| except OverflowError: |
| self.fail("int(long(-sys.maxsize-1) - 1) mustn't overflow") |
| self.assertTrue(isinstance(y, int), |
| "int(long(-sys.maxsize-1) - 1) should have returned long") |
| |
| class long2(int): |
| pass |
| x = long2(1<<100) |
| y = int(x) |
| self.assertTrue(type(y) is int, |
| "overflowing int conversion must return long not long subtype") |
| |
| # ----------------------------------- tests of auto int->long conversion |
| |
| def test_auto_overflow(self): |
| import math, sys |
| |
| special = [0, 1, 2, 3, sys.maxsize-1, sys.maxsize, sys.maxsize+1] |
| sqrt = int(math.sqrt(sys.maxsize)) |
| 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 = int(x) |
| |
| expected = -longx |
| got = -x |
| checkit('-', x) |
| |
| for y in special: |
| longy = int(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: |
| 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, int(z)) |
| got = pow(x, y, z) |
| checkit('pow', x, y, '%', z) |
| else: |
| self.assertRaises(TypeError, pow,longx, longy, int(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 = [0, 1, 2, |
| 2**53-3, |
| 2**53-2, |
| 2**53-1, |
| 2**53, |
| 2**53+2, |
| 2**54-4, |
| 2**54-2, |
| 2**54, |
| 2**54+4] |
| for x in exact_values: |
| self.assertEqual(float(x), x) |
| self.assertEqual(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 range(15): |
| self.assertEqual(int(float(2**p*(2**53+x))), 2**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 range(15): |
| self.assertEqual(int(float(2**p*(2**54+x))), 2**p*(2**54+y)) |
| |
| # behaviour near extremes of floating-point range |
| int_dbl_max = int(DBL_MAX) |
| top_power = 2**DBL_MAX_EXP |
| halfway = (int_dbl_max + top_power)//2 |
| self.assertEqual(float(int_dbl_max), DBL_MAX) |
| self.assertEqual(float(int_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 range(100): |
| x = 2**p * (2**53 + 1) + 1 |
| y = 2**p * (2**53 + 2) |
| self.assertEqual(int(float(x)), y) |
| |
| x = 2**p * (2**53 + 1) |
| y = 2**p * 2**53 |
| self.assertEqual(int(float(x)), y) |
| |
| def test_float_overflow(self): |
| import math |
| |
| for x in -2.0, -1.0, 0.0, 1.0, 2.0: |
| self.assertEqual(float(int(x)), x) |
| |
| shuge = '12345' * 120 |
| huge = 1 << 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() of an int returns an int now |
| ##"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): |
| import math |
| |
| LOG10E = math.log10(math.e) |
| |
| for exp in list(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 -(1 << 10000), -2, 0: |
| self.assertRaises(ValueError, math.log, bad) |
| self.assertRaises(ValueError, math.log10, bad) |
| |
| def test_mixed_compares(self): |
| eq = self.assertEqual |
| import math |
| |
| # 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): |
| 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" % val) |
| |
| def _cmp__(self, other): |
| if not isinstance(other, Rat): |
| other = Rat(other) |
| x, y = self.n * other.d, self.d * other.n |
| return (x > y) - (x < y) |
| def __eq__(self, other): |
| return self._cmp__(other) == 0 |
| def __ne__(self, other): |
| return self._cmp__(other) != 0 |
| def __ge__(self, other): |
| return self._cmp__(other) >= 0 |
| def __gt__(self, other): |
| return self._cmp__(other) > 0 |
| def __le__(self, other): |
| return self._cmp__(other) <= 0 |
| def __lt__(self, other): |
| return self._cmp__(other) < 0 |
| |
| 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, |
| int(t-1), int(t), int(t+1)]) |
| cases.extend([0, 1, 2, sys.maxsize, float(sys.maxsize)]) |
| # 1L<<20000 should exceed all double formats. long(1e200) is to |
| # check that we get equality with 1e200 above. |
| t = int(1e200) |
| cases.extend([0, 1, 2, 1 << 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 = (Rx > Ry) - (Rx < Ry) |
| xycmp = (x > y) - (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__format__(self): |
| self.assertEqual(format(123456789, 'd'), '123456789') |
| self.assertEqual(format(123456789, 'd'), '123456789') |
| |
| # sign and aligning are interdependent |
| self.assertEqual(format(1, "-"), '1') |
| self.assertEqual(format(-1, "-"), '-1') |
| self.assertEqual(format(1, "-3"), ' 1') |
| self.assertEqual(format(-1, "-3"), ' -1') |
| self.assertEqual(format(1, "+3"), ' +1') |
| self.assertEqual(format(-1, "+3"), ' -1') |
| self.assertEqual(format(1, " 3"), ' 1') |
| self.assertEqual(format(-1, " 3"), ' -1') |
| self.assertEqual(format(1, " "), ' 1') |
| self.assertEqual(format(-1, " "), '-1') |
| |
| # hex |
| self.assertEqual(format(3, "x"), "3") |
| self.assertEqual(format(3, "X"), "3") |
| self.assertEqual(format(1234, "x"), "4d2") |
| self.assertEqual(format(-1234, "x"), "-4d2") |
| self.assertEqual(format(1234, "8x"), " 4d2") |
| self.assertEqual(format(-1234, "8x"), " -4d2") |
| self.assertEqual(format(1234, "x"), "4d2") |
| self.assertEqual(format(-1234, "x"), "-4d2") |
| self.assertEqual(format(-3, "x"), "-3") |
| self.assertEqual(format(-3, "X"), "-3") |
| self.assertEqual(format(int('be', 16), "x"), "be") |
| self.assertEqual(format(int('be', 16), "X"), "BE") |
| self.assertEqual(format(-int('be', 16), "x"), "-be") |
| self.assertEqual(format(-int('be', 16), "X"), "-BE") |
| |
| # octal |
| self.assertEqual(format(3, "b"), "11") |
| self.assertEqual(format(-3, "b"), "-11") |
| self.assertEqual(format(1234, "b"), "10011010010") |
| self.assertEqual(format(-1234, "b"), "-10011010010") |
| self.assertEqual(format(1234, "-b"), "10011010010") |
| self.assertEqual(format(-1234, "-b"), "-10011010010") |
| self.assertEqual(format(1234, " b"), " 10011010010") |
| self.assertEqual(format(-1234, " b"), "-10011010010") |
| self.assertEqual(format(1234, "+b"), "+10011010010") |
| self.assertEqual(format(-1234, "+b"), "-10011010010") |
| |
| # make sure these are errors |
| self.assertRaises(ValueError, format, 3, "1.3") # precision disallowed |
| self.assertRaises(ValueError, format, 3, "+c") # sign not allowed |
| # with 'c' |
| |
| # ensure that only int and float type specifiers work |
| for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] + |
| [chr(x) for x in range(ord('A'), ord('Z')+1)]): |
| if not format_spec in 'bcdoxXeEfFgGn%': |
| self.assertRaises(ValueError, format, 0, format_spec) |
| self.assertRaises(ValueError, format, 1, format_spec) |
| self.assertRaises(ValueError, format, -1, format_spec) |
| self.assertRaises(ValueError, format, 2**100, format_spec) |
| self.assertRaises(ValueError, format, -(2**100), format_spec) |
| |
| # ensure that float type specifiers work; format converts |
| # the int to a float |
| for format_spec in 'eEfFgG%': |
| for value in [0, 1, -1, 100, -100, 1234567890, -1234567890]: |
| self.assertEqual(format(value, format_spec), |
| format(float(value), format_spec)) |
| |
| def test_nan_inf(self): |
| self.assertRaises(OverflowError, int, float('inf')) |
| self.assertRaises(OverflowError, int, float('-inf')) |
| self.assertRaises(ValueError, int, float('nan')) |
| |
| def test_true_division(self): |
| huge = 1 << 40000 |
| mhuge = -huge |
| self.assertEqual(huge / huge, 1.0) |
| self.assertEqual(mhuge / mhuge, 1.0) |
| self.assertEqual(huge / mhuge, -1.0) |
| self.assertEqual(mhuge / huge, -1.0) |
| self.assertEqual(1 / huge, 0.0) |
| self.assertEqual(1 / huge, 0.0) |
| self.assertEqual(1 / mhuge, 0.0) |
| self.assertEqual(1 / mhuge, 0.0) |
| self.assertEqual((666 * huge + (huge >> 1)) / huge, 666.5) |
| self.assertEqual((666 * mhuge + (mhuge >> 1)) / mhuge, 666.5) |
| self.assertEqual((666 * huge + (huge >> 1)) / mhuge, -666.5) |
| self.assertEqual((666 * mhuge + (mhuge >> 1)) / huge, -666.5) |
| self.assertEqual(huge / (huge << 1), 0.5) |
| self.assertEqual((1000000 * huge) / huge, 1000000) |
| |
| namespace = {'huge': huge, 'mhuge': mhuge} |
| |
| for overflow in ["float(huge)", "float(mhuge)", |
| "huge / 1", "huge / 2", "huge / -1", "huge / -2", |
| "mhuge / 100", "mhuge / 200"]: |
| self.assertRaises(OverflowError, eval, overflow, namespace) |
| |
| for underflow in ["1 / huge", "2 / huge", "-1 / huge", "-2 / huge", |
| "100 / mhuge", "200 / mhuge"]: |
| result = eval(underflow, namespace) |
| self.assertEqual(result, 0.0, |
| "expected underflow to 0 from %r" % underflow) |
| |
| for zero in ["huge / 0", "mhuge / 0"]: |
| self.assertRaises(ZeroDivisionError, eval, zero, namespace) |
| |
| |
| def test_small_ints(self): |
| for i in range(-5, 257): |
| self.assertTrue(i is i + 0) |
| self.assertTrue(i is i * 1) |
| self.assertTrue(i is i - 0) |
| self.assertTrue(i is i // 1) |
| self.assertTrue(i is i & -1) |
| self.assertTrue(i is i | 0) |
| self.assertTrue(i is i ^ 0) |
| self.assertTrue(i is ~~i) |
| self.assertTrue(i is i**1) |
| self.assertTrue(i is int(str(i))) |
| self.assertTrue(i is i<<2>>2, str(i)) |
| # corner cases |
| i = 1 << 70 |
| self.assertTrue(i - i is 0) |
| self.assertTrue(0 * i is 0) |
| |
| def test_bit_length(self): |
| tiny = 1e-10 |
| for x in range(-65000, 65000): |
| 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((0).bit_length(), 0) |
| self.assertEqual((1).bit_length(), 1) |
| self.assertEqual((-1).bit_length(), 1) |
| self.assertEqual((2).bit_length(), 2) |
| self.assertEqual((-2).bit_length(), 2) |
| for i in [2, 3, 15, 16, 17, 31, 32, 33, 63, 64, 234]: |
| a = 2**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_round(self): |
| # check round-half-even algorithm. For round to nearest ten; |
| # rounding map is invariant under adding multiples of 20 |
| test_dict = {0:0, 1:0, 2:0, 3:0, 4:0, 5:0, |
| 6:10, 7:10, 8:10, 9:10, 10:10, 11:10, 12:10, 13:10, 14:10, |
| 15:20, 16:20, 17:20, 18:20, 19:20} |
| for offset in range(-520, 520, 20): |
| for k, v in test_dict.items(): |
| got = round(k+offset, -1) |
| expected = v+offset |
| self.assertEqual(got, expected) |
| self.assertTrue(type(got) is int) |
| |
| # larger second argument |
| self.assertEqual(round(-150, -2), -200) |
| self.assertEqual(round(-149, -2), -100) |
| self.assertEqual(round(-51, -2), -100) |
| self.assertEqual(round(-50, -2), 0) |
| self.assertEqual(round(-49, -2), 0) |
| self.assertEqual(round(-1, -2), 0) |
| self.assertEqual(round(0, -2), 0) |
| self.assertEqual(round(1, -2), 0) |
| self.assertEqual(round(49, -2), 0) |
| self.assertEqual(round(50, -2), 0) |
| self.assertEqual(round(51, -2), 100) |
| self.assertEqual(round(149, -2), 100) |
| self.assertEqual(round(150, -2), 200) |
| self.assertEqual(round(250, -2), 200) |
| self.assertEqual(round(251, -2), 300) |
| self.assertEqual(round(172500, -3), 172000) |
| self.assertEqual(round(173500, -3), 174000) |
| self.assertEqual(round(31415926535, -1), 31415926540) |
| self.assertEqual(round(31415926535, -2), 31415926500) |
| self.assertEqual(round(31415926535, -3), 31415927000) |
| self.assertEqual(round(31415926535, -4), 31415930000) |
| self.assertEqual(round(31415926535, -5), 31415900000) |
| self.assertEqual(round(31415926535, -6), 31416000000) |
| self.assertEqual(round(31415926535, -7), 31420000000) |
| self.assertEqual(round(31415926535, -8), 31400000000) |
| self.assertEqual(round(31415926535, -9), 31000000000) |
| self.assertEqual(round(31415926535, -10), 30000000000) |
| self.assertEqual(round(31415926535, -11), 0) |
| self.assertEqual(round(31415926535, -12), 0) |
| self.assertEqual(round(31415926535, -999), 0) |
| |
| # should get correct results even for huge inputs |
| for k in range(10, 100): |
| got = round(10**k + 324678, -3) |
| expect = 10**k + 325000 |
| self.assertEqual(got, expect) |
| self.assertTrue(type(got) is int) |
| |
| # nonnegative second argument: round(x, n) should just return x |
| for n in range(5): |
| for i in range(100): |
| x = random.randrange(-10000, 10000) |
| got = round(x, n) |
| self.assertEqual(got, x) |
| self.assertTrue(type(got) is int) |
| for huge_n in 2**31-1, 2**31, 2**63-1, 2**63, 2**100, 10**100: |
| self.assertEqual(round(8979323, huge_n), 8979323) |
| |
| # omitted second argument |
| for i in range(100): |
| x = random.randrange(-10000, 10000) |
| got = round(x) |
| self.assertEqual(got, x) |
| self.assertTrue(type(got) is int) |
| |
| # bad second argument |
| bad_exponents = ('brian', 2.0, 0j, None) |
| for e in bad_exponents: |
| self.assertRaises(TypeError, round, 3, e) |
| |
| |
| |
| def test_main(): |
| support.run_unittest(LongTest) |
| |
| if __name__ == "__main__": |
| test_main() |