import unittest
from test import support
import sys
import random
import math
import array
# 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]
DBL_MAX = sys.float_info.max
DBL_MAX_EXP = sys.float_info.max_exp
DBL_MIN_EXP = sys.float_info.min_exp
DBL_MANT_DIG = sys.float_info.mant_dig
DBL_MIN_OVERFLOW = 2**DBL_MAX_EXP - 2**(DBL_MAX_EXP - DBL_MANT_DIG - 1)
# Pure Python version of correctly-rounded integer-to-float conversion.
def int_to_float(n):
"""
Correctly-rounded integer-to-float conversion.
"""
# Constants, depending only on the floating-point format in use.
# We use an extra 2 bits of precision for rounding purposes.
PRECISION = sys.float_info.mant_dig + 2
SHIFT_MAX = sys.float_info.max_exp - PRECISION
Q_MAX = 1 << PRECISION
ROUND_HALF_TO_EVEN_CORRECTION = [0, -1, -2, 1, 0, -1, 2, 1]
# Reduce to the case where n is positive.
if n == 0:
return 0.0
elif n < 0:
return -int_to_float(-n)
# Convert n to a 'floating-point' number q * 2**shift, where q is an
# integer with 'PRECISION' significant bits. When shifting n to create q,
# the least significant bit of q is treated as 'sticky'. That is, the
# least significant bit of q is set if either the corresponding bit of n
# was already set, or any one of the bits of n lost in the shift was set.
shift = n.bit_length() - PRECISION
q = n << -shift if shift < 0 else (n >> shift) | bool(n & ~(-1 << shift))
# Round half to even (actually rounds to the nearest multiple of 4,
# rounding ties to a multiple of 8).
q += ROUND_HALF_TO_EVEN_CORRECTION[q & 7]
# Detect overflow.
if shift + (q == Q_MAX) > SHIFT_MAX:
raise OverflowError("integer too large to convert to float")
# Checks: q is exactly representable, and q**2**shift doesn't overflow.
assert q % 4 == 0 and q // 4 <= 2**(sys.float_info.mant_dig)
assert q * 2**shift <= sys.float_info.max
# Some circularity here, since float(q) is doing an int-to-float
# conversion. But here q is of bounded size, and is exactly representable
# as a float. In a low-level C-like language, this operation would be a
# simple cast (e.g., from unsigned long long to double).
return math.ldexp(float(q), shift)
# pure Python version of correctly-rounded true division
def truediv(a, b):
"""Correctly-rounded true division for integers."""
negative = a^b < 0
a, b = abs(a), abs(b)
# exceptions: division by zero, overflow
if not b:
raise ZeroDivisionError("division by zero")
if a >= DBL_MIN_OVERFLOW * b:
raise OverflowError("int/int too large to represent as a float")
# find integer d satisfying 2**(d - 1) <= a/b < 2**d
d = a.bit_length() - b.bit_length()
if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
d += 1
# compute 2**-exp * a / b for suitable exp
exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
a, b = a << max(-exp, 0), b << max(exp, 0)
q, r = divmod(a, b)
# round-half-to-even: fractional part is r/b, which is > 0.5 iff
# 2*r > b, and == 0.5 iff 2*r == b.
if 2*r > b or 2*r == b and q % 2 == 1:
q += 1
result = math.ldexp(q, exp)
return -result if negative else result
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.assertGreater(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
with self.subTest(x=x, y=y):
q, r = divmod(x, y)
q2, r2 = x//y, x%y
pab, pba = x*y, y*x
eq(pab, pba, "multiplication does not commute")
eq(q, q2, "divmod returns different quotient than /")
eq(r, r2, "divmod returns different mod than %")
eq(x, q*y + r, "x != q*y + r after divmod")
if y > 0:
self.assertTrue(0 <= r < y, "bad mod from divmod")
else:
self.assertTrue(y < r <= 0, "bad mod from divmod")
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
with self.subTest(abits=abits, bbits=bbits):
b = (1 << bbits) - 1
x = a * b
y = ((1 << (abits + bbits)) -
(1 << abits) -
(1 << bbits) +
1)
self.assertEqual(x, y)
def check_bitop_identities_1(self, x):
eq = self.assertEqual
with self.subTest(x=x):
eq(x & 0, 0)
eq(x | 0, x)
eq(x ^ 0, x)
eq(x & -1, x)
eq(x | -1, -1)
eq(x ^ -1, ~x)
eq(x, ~~x)
eq(x & x, x)
eq(x | x, x)
eq(x ^ x, 0)
eq(x & ~x, 0)
eq(x | ~x, -1)
eq(x ^ ~x, -1)
eq(-x, 1 + ~x)
eq(-x, ~(x-1))
for n in range(2*SHIFT):
p2 = 2 ** n
with self.subTest(x=x, n=n, p2=p2):
eq(x << n >> n, x)
eq(x // p2, x >> n)
eq(x * p2, x << n)
eq(x & -p2, x >> n << n)
eq(x & -p2, x & ~(p2 - 1))
def check_bitop_identities_2(self, x, y):
eq = self.assertEqual
with self.subTest(x=x, y=y):
eq(x & y, y & x)
eq(x | y, y | x)
eq(x ^ y, y ^ x)
eq(x ^ y ^ x, y)
eq(x & y, ~(~x | ~y))
eq(x | y, ~(~x & ~y))
eq(x ^ y, (x | y) & ~(x & y))
eq(x ^ y, (x & ~y) | (~x & y))
eq(x ^ y, (x | y) & (~x | ~y))
def check_bitop_identities_3(self, x, y, z):
eq = self.assertEqual
with self.subTest(x=x, y=y, z=z):
eq((x & y) & z, x & (y & z))
eq((x | y) | z, x | (y | z))
eq((x ^ y) ^ z, x ^ (y ^ z))
eq(x & (y | z), (x & y) | (x & z))
eq(x | (y & z), (x | y) & (x | 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("0123456789abcdef"[i] for i in digits)
def check_format_1(self, x):
for base, mapper in (2, bin), (8, oct), (10, str), (10, repr), (16, hex):
got = mapper(x)
with self.subTest(x=x, mapper=mapper.__name__):
expected = self.slow_format(x, base)
self.assertEqual(got, expected)
with self.subTest(got=got):
self.assertEqual(int(got, 0), x)
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):
# Check conversions from string
LL = [
('1' + '0'*20, 10**20),
('1' + '0'*100, 10**100)
]
for s, v in 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), vv)
except ValueError:
pass
# 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)
# 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)
# invalid bases
invalid_bases = [-909,
2**31-1, 2**31, -2**31, -2**31-1,
2**63-1, 2**63, -2**63, -2**63-1,
2**100, -2**100,
]
for base in invalid_bases:
self.assertRaises(ValueError, int, '42', base)
# Invalid unicode string
# See bpo-34087
self.assertRaises(ValueError, int, '\u3053\u3093\u306b\u3061\u306f')
def test_conversion(self):
class JustLong:
# test that __long__ no longer used in 3.x
def __long__(self):
return 42
self.assertRaises(TypeError, int, JustLong())
class LongTrunc:
# __long__ should be ignored in 3.x
def __long__(self):
return 42
def __trunc__(self):
return 1729
self.assertEqual(int(LongTrunc()), 1729)
def check_float_conversion(self, n):
# Check that int -> float conversion behaviour matches
# that of the pure Python version above.
try:
actual = float(n)
except OverflowError:
actual = 'overflow'
try:
expected = int_to_float(n)
except OverflowError:
expected = 'overflow'
msg = ("Error in conversion of integer {} to float. "
"Got {}, expected {}.".format(n, actual, expected))
self.assertEqual(actual, expected, msg)
@support.requires_IEEE_754
def test_float_conversion(self):
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)
# Compare builtin float conversion with pure Python int_to_float
# function above.
test_values = [
int_dbl_max-1, int_dbl_max, int_dbl_max+1,
halfway-1, halfway, halfway + 1,
top_power-1, top_power, top_power+1,
2*top_power-1, 2*top_power, top_power*top_power,
]
test_values.extend(exact_values)
for p in range(-4, 8):
for x in range(-128, 128):
test_values.append(2**(p+53) + x)
for value in test_values:
self.check_float_conversion(value)
self.check_float_conversion(-value)
def test_float_overflow(self):
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):
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
# We're mostly concerned with that mixing floats and ints does the
# right stuff, even when ints 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 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" % value)
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 __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)])
# 1 << 20000 should exceed all double formats. int(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)
with self.subTest(x=x, y=y, Rcmp=Rcmp):
xycmp = (x > y) - (x < y)
eq(Rcmp, xycmp)
eq(x == y, Rcmp == 0)
eq(x != y, Rcmp != 0)
eq(x < y, Rcmp < 0)
eq(x <= y, Rcmp <= 0)
eq(x > y, Rcmp > 0)
eq(x >= y, Rcmp >= 0)
def test__format__(self):
self.assertEqual(format(123456789, 'd'), '123456789')
self.assertEqual(format(123456789, 'd'), '123456789')
self.assertEqual(format(123456789, ','), '123,456,789')
self.assertEqual(format(123456789, '_'), '123_456_789')
# 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")
self.assertRaises(ValueError, format, 1234567890, ',x')
self.assertEqual(format(1234567890, '_x'), '4996_02d2')
self.assertEqual(format(1234567890, '_X'), '4996_02D2')
# octal
self.assertEqual(format(3, "o"), "3")
self.assertEqual(format(-3, "o"), "-3")
self.assertEqual(format(1234, "o"), "2322")
self.assertEqual(format(-1234, "o"), "-2322")
self.assertEqual(format(1234, "-o"), "2322")
self.assertEqual(format(-1234, "-o"), "-2322")
self.assertEqual(format(1234, " o"), " 2322")
self.assertEqual(format(-1234, " o"), "-2322")
self.assertEqual(format(1234, "+o"), "+2322")
self.assertEqual(format(-1234, "+o"), "-2322")
self.assertRaises(ValueError, format, 1234567890, ',o')
self.assertEqual(format(1234567890, '_o'), '111_4540_1322')
# binary
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")
self.assertRaises(ValueError, format, 1234567890, ',b')
self.assertEqual(format(12345, '_b'), '11_0000_0011_1001')
# make sure these are errors
self.assertRaises(ValueError, format, 3, "1.3") # precision disallowed
self.assertRaises(ValueError, format, 3, "_c") # underscore,
self.assertRaises(ValueError, format, 3, ",c") # comma, and
self.assertRaises(ValueError, format, 3, "+c") # sign not allowed
# with 'c'
self.assertRaisesRegex(ValueError, 'Cannot specify both', format, 3, '_,')
self.assertRaisesRegex(ValueError, 'Cannot specify both', format, 3, ',_')
self.assertRaisesRegex(ValueError, 'Cannot specify both', format, 3, '_,d')
self.assertRaisesRegex(ValueError, 'Cannot specify both', format, 3, ',_d')
self.assertRaisesRegex(ValueError, "Cannot specify ',' with 's'", format, 3, ',s')
self.assertRaisesRegex(ValueError, "Cannot specify '_' with 's'", format, 3, '_s')
# 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_mod_division(self):
with self.assertRaises(ZeroDivisionError):
_ = 1 % 0
self.assertEqual(13 % 10, 3)
self.assertEqual(-13 % 10, 7)
self.assertEqual(13 % -10, -7)
self.assertEqual(-13 % -10, -3)
self.assertEqual(12 % 4, 0)
self.assertEqual(-12 % 4, 0)
self.assertEqual(12 % -4, 0)
self.assertEqual(-12 % -4, 0)
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_floordiv(self):
with self.assertRaises(ZeroDivisionError):
_ = 1 // 0
self.assertEqual(2 // 3, 0)
self.assertEqual(2 // -3, -1)
self.assertEqual(-2 // 3, -1)
self.assertEqual(-2 // -3, 0)
self.assertEqual(-11 // -3, 3)
self.assertEqual(-11 // 3, -4)
self.assertEqual(11 // -3, -4)
self.assertEqual(11 // 3, 3)
self.assertEqual(-12 // -3, 4)
self.assertEqual(-12 // 3, -4)
self.assertEqual(12 // -3, -4)
self.assertEqual(12 // 3, 4)
def check_truediv(self, a, b, skip_small=True):
"""Verify that the result of a/b is correctly rounded, by
comparing it with a pure Python implementation of correctly
rounded division. b should be nonzero."""
# skip check for small a and b: in this case, the current
# implementation converts the arguments to float directly and
# then applies a float division. This can give doubly-rounded
# results on x87-using machines (particularly 32-bit Linux).
if skip_small and max(abs(a), abs(b)) < 2**DBL_MANT_DIG:
return
try:
# use repr so that we can distinguish between -0.0 and 0.0
expected = repr(truediv(a, b))
except OverflowError:
expected = 'overflow'
except ZeroDivisionError:
expected = 'zerodivision'
try:
got = repr(a / b)
except OverflowError:
got = 'overflow'
except ZeroDivisionError:
got = 'zerodivision'
self.assertEqual(expected, got, "Incorrectly rounded division {}/{}: "
"expected {}, got {}".format(a, b, expected, got))
@support.requires_IEEE_754
def test_correctly_rounded_true_division(self):
# more stringent tests than those above, checking that the
# result of true division of ints is always correctly rounded.
# This test should probably be considered CPython-specific.
# Exercise all the code paths not involving Gb-sized ints.
# ... divisions involving zero
self.check_truediv(123, 0)
self.check_truediv(-456, 0)
self.check_truediv(0, 3)
self.check_truediv(0, -3)
self.check_truediv(0, 0)
# ... overflow or underflow by large margin
self.check_truediv(671 * 12345 * 2**DBL_MAX_EXP, 12345)
self.check_truediv(12345, 345678 * 2**(DBL_MANT_DIG - DBL_MIN_EXP))
# ... a much larger or smaller than b
self.check_truediv(12345*2**100, 98765)
self.check_truediv(12345*2**30, 98765*7**81)
# ... a / b near a boundary: one of 1, 2**DBL_MANT_DIG, 2**DBL_MIN_EXP,
# 2**DBL_MAX_EXP, 2**(DBL_MIN_EXP-DBL_MANT_DIG)
bases = (0, DBL_MANT_DIG, DBL_MIN_EXP,
DBL_MAX_EXP, DBL_MIN_EXP - DBL_MANT_DIG)
for base in bases:
for exp in range(base - 15, base + 15):
self.check_truediv(75312*2**max(exp, 0), 69187*2**max(-exp, 0))
self.check_truediv(69187*2**max(exp, 0), 75312*2**max(-exp, 0))
# overflow corner case
for m in [1, 2, 7, 17, 12345, 7**100,
-1, -2, -5, -23, -67891, -41**50]:
for n in range(-10, 10):
self.check_truediv(m*DBL_MIN_OVERFLOW + n, m)
self.check_truediv(m*DBL_MIN_OVERFLOW + n, -m)
# check detection of inexactness in shifting stage
for n in range(250):
# (2**DBL_MANT_DIG+1)/(2**DBL_MANT_DIG) lies halfway
# between two representable floats, and would usually be
# rounded down under round-half-to-even. The tiniest of
# additions to the numerator should cause it to be rounded
# up instead.
self.check_truediv((2**DBL_MANT_DIG + 1)*12345*2**200 + 2**n,
2**DBL_MANT_DIG*12345)
# 1/2731 is one of the smallest division cases that's subject
# to double rounding on IEEE 754 machines working internally with
# 64-bit precision. On such machines, the next check would fail,
# were it not explicitly skipped in check_truediv.
self.check_truediv(1, 2731)
# a particularly bad case for the old algorithm: gives an
# error of close to 3.5 ulps.
self.check_truediv(295147931372582273023, 295147932265116303360)
for i in range(1000):
self.check_truediv(10**(i+1), 10**i)
self.check_truediv(10**i, 10**(i+1))
# test round-half-to-even behaviour, normal result
for m in [1, 2, 4, 7, 8, 16, 17, 32, 12345, 7**100,
-1, -2, -5, -23, -67891, -41**50]:
for n in range(-10, 10):
self.check_truediv(2**DBL_MANT_DIG*m + n, m)
# test round-half-to-even, subnormal result
for n in range(-20, 20):
self.check_truediv(n, 2**1076)
# largeish random divisions: a/b where |a| <= |b| <=
# 2*|a|; |ans| is between 0.5 and 1.0, so error should
# always be bounded by 2**-54 with equality possible only
# if the least significant bit of q=ans*2**53 is zero.
for M in [10**10, 10**100, 10**1000]:
for i in range(1000):
a = random.randrange(1, M)
b = random.randrange(a, 2*a+1)
self.check_truediv(a, b)
self.check_truediv(-a, b)
self.check_truediv(a, -b)
self.check_truediv(-a, -b)
# and some (genuinely) random tests
for _ in range(10000):
a_bits = random.randrange(1000)
b_bits = random.randrange(1, 1000)
x = random.randrange(2**a_bits)
y = random.randrange(1, 2**b_bits)
self.check_truediv(x, y)
self.check_truediv(x, -y)
self.check_truediv(-x, y)
self.check_truediv(-x, -y)
def test_lshift_of_zero(self):
self.assertEqual(0 << 0, 0)
self.assertEqual(0 << 10, 0)
with self.assertRaises(ValueError):
0 << -1
@support.cpython_only
def test_huge_lshift_of_zero(self):
# Shouldn't try to allocate memory for a huge shift. See issue #27870.
# Other implementations may have a different boundary for overflow,
# or not raise at all.
self.assertEqual(0 << sys.maxsize, 0)
with self.assertRaises(OverflowError):
0 << (sys.maxsize + 1)
def test_small_ints(self):
for i in range(-5, 257):
self.assertIs(i, i + 0)
self.assertIs(i, i * 1)
self.assertIs(i, i - 0)
self.assertIs(i, i // 1)
self.assertIs(i, i & -1)
self.assertIs(i, i | 0)
self.assertIs(i, i ^ 0)
self.assertIs(i, ~~i)
self.assertIs(i, i**1)
self.assertIs(i, int(str(i)))
self.assertIs(i, i<<2>>2, str(i))
# corner cases
i = 1 << 70
self.assertIs(i - i, 0)
self.assertIs(0 * i, 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.assertIs(type(got), 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.assertIs(type(got), 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.assertIs(type(got), 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.assertIs(type(got), int)
# bad second argument
bad_exponents = ('brian', 2.0, 0j)
for e in bad_exponents:
self.assertRaises(TypeError, round, 3, e)
def test_to_bytes(self):
def check(tests, byteorder, signed=False):
for test, expected in tests.items():
try:
self.assertEqual(
test.to_bytes(len(expected), byteorder, signed=signed),
expected)
except Exception as err:
raise AssertionError(
"failed to convert {0} with byteorder={1} and signed={2}"
.format(test, byteorder, signed)) from err
# Convert integers to signed big-endian byte arrays.
tests1 = {
0: b'\x00',
1: b'\x01',
-1: b'\xff',
-127: b'\x81',
-128: b'\x80',
-129: b'\xff\x7f',
127: b'\x7f',
129: b'\x00\x81',
-255: b'\xff\x01',
-256: b'\xff\x00',
255: b'\x00\xff',
256: b'\x01\x00',
32767: b'\x7f\xff',
-32768: b'\xff\x80\x00',
65535: b'\x00\xff\xff',
-65536: b'\xff\x00\x00',
-8388608: b'\x80\x00\x00'
}
check(tests1, 'big', signed=True)
# Convert integers to signed little-endian byte arrays.
tests2 = {
0: b'\x00',
1: b'\x01',
-1: b'\xff',
-127: b'\x81',
-128: b'\x80',
-129: b'\x7f\xff',
127: b'\x7f',
129: b'\x81\x00',
-255: b'\x01\xff',
-256: b'\x00\xff',
255: b'\xff\x00',
256: b'\x00\x01',
32767: b'\xff\x7f',
-32768: b'\x00\x80',
65535: b'\xff\xff\x00',
-65536: b'\x00\x00\xff',
-8388608: b'\x00\x00\x80'
}
check(tests2, 'little', signed=True)
# Convert integers to unsigned big-endian byte arrays.
tests3 = {
0: b'\x00',
1: b'\x01',
127: b'\x7f',
128: b'\x80',
255: b'\xff',
256: b'\x01\x00',
32767: b'\x7f\xff',
32768: b'\x80\x00',
65535: b'\xff\xff',
65536: b'\x01\x00\x00'
}
check(tests3, 'big', signed=False)
# Convert integers to unsigned little-endian byte arrays.
tests4 = {
0: b'\x00',
1: b'\x01',
127: b'\x7f',
128: b'\x80',
255: b'\xff',
256: b'\x00\x01',
32767: b'\xff\x7f',
32768: b'\x00\x80',
65535: b'\xff\xff',
65536: b'\x00\x00\x01'
}
check(tests4, 'little', signed=False)
self.assertRaises(OverflowError, (256).to_bytes, 1, 'big', signed=False)
self.assertRaises(OverflowError, (256).to_bytes, 1, 'big', signed=True)
self.assertRaises(OverflowError, (256).to_bytes, 1, 'little', signed=False)
self.assertRaises(OverflowError, (256).to_bytes, 1, 'little', signed=True)
self.assertRaises(OverflowError, (-1).to_bytes, 2, 'big', signed=False)
self.assertRaises(OverflowError, (-1).to_bytes, 2, 'little', signed=False)
self.assertEqual((0).to_bytes(0, 'big'), b'')
self.assertEqual((1).to_bytes(5, 'big'), b'\x00\x00\x00\x00\x01')
self.assertEqual((0).to_bytes(5, 'big'), b'\x00\x00\x00\x00\x00')
self.assertEqual((-1).to_bytes(5, 'big', signed=True),
b'\xff\xff\xff\xff\xff')
self.assertRaises(OverflowError, (1).to_bytes, 0, 'big')
def test_from_bytes(self):
def check(tests, byteorder, signed=False):
for test, expected in tests.items():
try:
self.assertEqual(
int.from_bytes(test, byteorder, signed=signed),
expected)
except Exception as err:
raise AssertionError(
"failed to convert {0} with byteorder={1!r} and signed={2}"
.format(test, byteorder, signed)) from err
# Convert signed big-endian byte arrays to integers.
tests1 = {
b'': 0,
b'\x00': 0,
b'\x00\x00': 0,
b'\x01': 1,
b'\x00\x01': 1,
b'\xff': -1,
b'\xff\xff': -1,
b'\x81': -127,
b'\x80': -128,
b'\xff\x7f': -129,
b'\x7f': 127,
b'\x00\x81': 129,
b'\xff\x01': -255,
b'\xff\x00': -256,
b'\x00\xff': 255,
b'\x01\x00': 256,
b'\x7f\xff': 32767,
b'\x80\x00': -32768,
b'\x00\xff\xff': 65535,
b'\xff\x00\x00': -65536,
b'\x80\x00\x00': -8388608
}
check(tests1, 'big', signed=True)
# Convert signed little-endian byte arrays to integers.
tests2 = {
b'': 0,
b'\x00': 0,
b'\x00\x00': 0,
b'\x01': 1,
b'\x00\x01': 256,
b'\xff': -1,
b'\xff\xff': -1,
b'\x81': -127,
b'\x80': -128,
b'\x7f\xff': -129,
b'\x7f': 127,
b'\x81\x00': 129,
b'\x01\xff': -255,
b'\x00\xff': -256,
b'\xff\x00': 255,
b'\x00\x01': 256,
b'\xff\x7f': 32767,
b'\x00\x80': -32768,
b'\xff\xff\x00': 65535,
b'\x00\x00\xff': -65536,
b'\x00\x00\x80': -8388608
}
check(tests2, 'little', signed=True)
# Convert unsigned big-endian byte arrays to integers.
tests3 = {
b'': 0,
b'\x00': 0,
b'\x01': 1,
b'\x7f': 127,
b'\x80': 128,
b'\xff': 255,
b'\x01\x00': 256,
b'\x7f\xff': 32767,
b'\x80\x00': 32768,
b'\xff\xff': 65535,
b'\x01\x00\x00': 65536,
}
check(tests3, 'big', signed=False)
# Convert integers to unsigned little-endian byte arrays.
tests4 = {
b'': 0,
b'\x00': 0,
b'\x01': 1,
b'\x7f': 127,
b'\x80': 128,
b'\xff': 255,
b'\x00\x01': 256,
b'\xff\x7f': 32767,
b'\x00\x80': 32768,
b'\xff\xff': 65535,
b'\x00\x00\x01': 65536,
}
check(tests4, 'little', signed=False)
class myint(int):
pass
self.assertIs(type(myint.from_bytes(b'\x00', 'big')), myint)
self.assertEqual(myint.from_bytes(b'\x01', 'big'), 1)
self.assertIs(
type(myint.from_bytes(b'\x00', 'big', signed=False)), myint)
self.assertEqual(myint.from_bytes(b'\x01', 'big', signed=False), 1)
self.assertIs(type(myint.from_bytes(b'\x00', 'little')), myint)
self.assertEqual(myint.from_bytes(b'\x01', 'little'), 1)
self.assertIs(type(myint.from_bytes(
b'\x00', 'little', signed=False)), myint)
self.assertEqual(myint.from_bytes(b'\x01', 'little', signed=False), 1)
self.assertEqual(
int.from_bytes([255, 0, 0], 'big', signed=True), -65536)
self.assertEqual(
int.from_bytes((255, 0, 0), 'big', signed=True), -65536)
self.assertEqual(int.from_bytes(
bytearray(b'\xff\x00\x00'), 'big', signed=True), -65536)
self.assertEqual(int.from_bytes(
bytearray(b'\xff\x00\x00'), 'big', signed=True), -65536)
self.assertEqual(int.from_bytes(
array.array('B', b'\xff\x00\x00'), 'big', signed=True), -65536)
self.assertEqual(int.from_bytes(
memoryview(b'\xff\x00\x00'), 'big', signed=True), -65536)
self.assertRaises(ValueError, int.from_bytes, [256], 'big')
self.assertRaises(ValueError, int.from_bytes, [0], 'big\x00')
self.assertRaises(ValueError, int.from_bytes, [0], 'little\x00')
self.assertRaises(TypeError, int.from_bytes, "", 'big')
self.assertRaises(TypeError, int.from_bytes, "\x00", 'big')
self.assertRaises(TypeError, int.from_bytes, 0, 'big')
self.assertRaises(TypeError, int.from_bytes, 0, 'big', True)
self.assertRaises(TypeError, myint.from_bytes, "", 'big')
self.assertRaises(TypeError, myint.from_bytes, "\x00", 'big')
self.assertRaises(TypeError, myint.from_bytes, 0, 'big')
self.assertRaises(TypeError, int.from_bytes, 0, 'big', True)
class myint2(int):
def __new__(cls, value):
return int.__new__(cls, value + 1)
i = myint2.from_bytes(b'\x01', 'big')
self.assertIs(type(i), myint2)
self.assertEqual(i, 2)
class myint3(int):
def __init__(self, value):
self.foo = 'bar'
i = myint3.from_bytes(b'\x01', 'big')
self.assertIs(type(i), myint3)
self.assertEqual(i, 1)
self.assertEqual(getattr(i, 'foo', 'none'), 'bar')
def test_access_to_nonexistent_digit_0(self):
# http://bugs.python.org/issue14630: A bug in _PyLong_Copy meant that
# ob_digit[0] was being incorrectly accessed for instances of a
# subclass of int, with value 0.
class Integer(int):
def __new__(cls, value=0):
self = int.__new__(cls, value)
self.foo = 'foo'
return self
integers = [Integer(0) for i in range(1000)]
for n in map(int, integers):
self.assertEqual(n, 0)
def test_shift_bool(self):
# Issue #21422: ensure that bool << int and bool >> int return int
for value in (True, False):
for shift in (0, 2):
self.assertEqual(type(value << shift), int)
self.assertEqual(type(value >> shift), int)
if __name__ == "__main__":
unittest.main()