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1385fb32855cd658f03e617bf776bb1ceacbec94
cpython/Lib/test/test_long.py
Mark Dickinson 053ce7e51d Merged revisions 68814-68815 via svnmerge from 
svn+ssh://pythondev@svn.python.org/python/branches/py3k

........
  r68814 | mark.dickinson | 2009-01-20 20:43:58 +0000 (Tue, 20 Jan 2009) | 5 lines

  Issue #4842, patch 1/2: fix pickle in Python 3.x so that pickling with the
  'L' opcode always appends an 'L' on output, just as 2.x does.  When
  unpickling, remove the trailing 'L' (if present) before passing the
  result to PyLong_FromString.
........
  r68815 | mark.dickinson | 2009-01-20 20:45:53 +0000 (Tue, 20 Jan 2009) | 2 lines

  Issue 4842, patch 2/2:  int('3L') should be invalid in Python 3.x.
........
2009-01-20 21:20:01 +00:00

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import unittest
from test import support
import sys
import random
# 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 = 15
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.assert_(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.assert_(1 <= bits <= SHIFT)
nbits = nbits + bits
answer = answer << bits
if r & 1:
answer = answer | ((1 << bits) - 1)
r = int(random.random() * (SHIFT * 2))
self.assert_(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.assert_(0 <= r < y, Frm("bad mod from divmod on %r and %r", x, y))
else:
self.assert_(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)
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)
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.assertEquals(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.assert_(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.assert_(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.assert_(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))
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)
return cmp(self.n * other.d, self.d * other.n)
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 = 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__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_main():
support.run_unittest(LongTest)
if __name__ == "__main__":
test_main()
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