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cpython/Lib/test/test_long.py
Robert Smallshire 58a7da9e12
bpo-26680: Incorporate is_integer in all built-in and standard library numeric types (GH-6121) 
* bpo-26680: Adds support for int.is_integer() for compatibility with float.is_integer().

The int.is_integer() method always returns True.

* bpo-26680: Adds a test to ensure that False.is_integer() and True.is_integer() are always True.

* bpo-26680: Adds Real.is_integer() with a trivial implementation using conversion to int.

This default implementation is intended to reduce the workload for subclass
implementers. It is not robust in the presence of infinities or NaNs and
may have suboptimal performance for other types.

* bpo-26680: Adds Rational.is_integer which returns True if the denominator is one.

This implementation assumes the Rational is represented in it's
lowest form, as required by the class docstring.

* bpo-26680: Adds Integral.is_integer which always returns True.

* bpo-26680: Adds tests for Fraction.is_integer called as an instance method.

The tests for the Rational abstract base class use an unbound
method to sidestep the inability to directly instantiate Rational.
These tests check that everything works correct as an instance method.

* bpo-26680: Updates documentation for Real.is_integer and built-ins int and float.

The call x.is_integer() is now listed in the table of operations
which apply to all numeric types except complex, with a reference
to the full documentation for Real.is_integer().  Mention of
is_integer() has been removed from the section 'Additional Methods
on Float'.

The documentation for Real.is_integer() describes its purpose, and
mentions that it should be overridden for performance reasons, or
to handle special values like NaN.

* bpo-26680: Adds Decimal.is_integer to the Python and C implementations.

The C implementation of Decimal already implements and uses
mpd_isinteger internally, we just expose the existing function to
Python.

The Python implementation uses internal conversion to integer
using to_integral_value().

In both cases, the corresponding context methods are also
implemented.

Tests and documentation are included.

* bpo-26680: Updates the ACKS file.

* bpo-26680: NEWS entries for int, the numeric ABCs and Decimal.

Co-authored-by: Robert Smallshire <rob@sixty-north.com>
2020-10-01 17:30:08 +01:00

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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_negative_shift_count(self):
with self.assertRaises(ValueError):
42 << -3
with self.assertRaises(ValueError):
42 << -(1 << 1000)
with self.assertRaises(ValueError):
42 >> -3
with self.assertRaises(ValueError):
42 >> -(1 << 1000)
def test_lshift_of_zero(self):
self.assertEqual(0 << 0, 0)
self.assertEqual(0 << 10, 0)
with self.assertRaises(ValueError):
0 << -1
self.assertEqual(0 << (1 << 1000), 0)
with self.assertRaises(ValueError):
0 << -(1 << 1000)
@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)
self.assertEqual(0 << (sys.maxsize + 1), 0)
@support.cpython_only
@support.bigmemtest(sys.maxsize + 1000, memuse=2/15 * 2, dry_run=False)
def test_huge_lshift(self, size):
self.assertEqual(1 << (sys.maxsize + 1000), 1 << 1000 << sys.maxsize)
def test_huge_rshift(self):
self.assertEqual(42 >> (1 << 1000), 0)
self.assertEqual((-42) >> (1 << 1000), -1)
@support.cpython_only
@support.bigmemtest(sys.maxsize + 500, memuse=2/15, dry_run=False)
def test_huge_rshift_of_huge(self, size):
huge = ((1 << 500) + 11) << sys.maxsize
self.assertEqual(huge >> (sys.maxsize + 1), (1 << 499) + 5)
self.assertEqual(huge >> (sys.maxsize + 1000), 0)
@support.cpython_only
def test_small_ints_in_huge_calculation(self):
a = 2 ** 100
b = -a + 1
c = a + 1
self.assertIs(a + b, 1)
self.assertIs(c - a, 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_bit_count(self):
for a in range(-1000, 1000):
self.assertEqual(a.bit_count(), bin(a).count("1"))
for exp in [10, 17, 63, 64, 65, 1009, 70234, 1234567]:
a = 2**exp
self.assertEqual(a.bit_count(), 1)
self.assertEqual((a - 1).bit_count(), exp)
self.assertEqual((a ^ 63).bit_count(), 7)
self.assertEqual(((a - 1) ^ 510).bit_count(), exp - 8)
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)
def test_as_integer_ratio(self):
class myint(int):
pass
tests = [10, 0, -10, 1, sys.maxsize + 1, True, False, myint(42)]
for value in tests:
numerator, denominator = value.as_integer_ratio()
self.assertEqual((numerator, denominator), (int(value), 1))
self.assertEqual(type(numerator), int)
self.assertEqual(type(denominator), int)
def test_int_always_is_integer(self):
# Issue #26680: Incorporating number.is_integer into int
self.assertTrue(all(x.is_integer() for x in (-1, 0, 1, 42)))
if __name__ == "__main__":
unittest.main()
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