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cpython/Lib/test/test_long.py

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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.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.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()
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