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-rw-r--r--Lib/test/test_long.py765
1 files changed, 420 insertions, 345 deletions
diff --git a/Lib/test/test_long.py b/Lib/test/test_long.py
index 9c2bac7..04066ec 100644
--- a/Lib/test/test_long.py
+++ b/Lib/test/test_long.py
@@ -1,9 +1,11 @@
import unittest
from test import support
+
import sys
import random
import math
+import array
# Used for lazy formatting of failure messages
class Frm(object):
@@ -35,25 +37,41 @@ 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)
-]
+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 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):
@@ -254,7 +272,7 @@ class LongTest(unittest.TestCase):
digits = digits or [0]
return '-'[:sign] + \
{2: '0b', 8: '0o', 10: '', 16: '0x'}[base] + \
- "".join(map(lambda i: "0123456789abcdef"[i], digits))
+ "".join("0123456789abcdef"[i] for i in digits)
def check_format_1(self, x):
for base, mapper in (8, oct), (10, repr), (16, hex):
@@ -263,7 +281,7 @@ class LongTest(unittest.TestCase):
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))
+ self.assertEqual(int(got, 0), x, Frm('int("%s", 0) != %r', got, x))
# str() has to be checked a little differently since there's no
# trailing "L"
got = str(x)
@@ -281,25 +299,12 @@ class LongTest(unittest.TestCase):
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)
+ # Check conversions from string
LL = [
('1' + '0'*20, 10**20),
('1' + '0'*100, 10**100)
]
- L2 = L[:]
- for s, v in L2 + LL:
+ for s, v in LL:
for sign in "", "+", "-":
for prefix in "", " ", "\t", " \t\t ":
ss = prefix + sign + s
@@ -307,12 +312,10 @@ class LongTest(unittest.TestCase):
if sign == "-" and v is not ValueError:
vv = -v
try:
- self.assertEqual(int(ss), int(vv))
+ self.assertEqual(int(ss), 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')
@@ -323,87 +326,6 @@ class LongTest(unittest.TestCase):
# ... 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)
@@ -419,228 +341,34 @@ class LongTest(unittest.TestCase):
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())
+ # 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)
- class Foo0:
- def __int__(self):
- return 42
- class Foo1(object):
- def __int__(self):
- return 42
+ def test_conversion(self):
- class Foo2(int):
- def __int__(self):
+ class JustLong:
+ # test that __long__ no longer used in 3.x
+ def __long__(self):
return 42
+ self.assertRaises(TypeError, int, JustLong())
- class Foo3(int):
- def __int__(self):
- return self
-
- class Foo4(int):
- def __int__(self):
+ class LongTrunc:
+ # __long__ should be ignored in 3.x
+ def __long__(self):
return 42
+ def __trunc__(self):
+ return 1729
+ self.assertEqual(int(LongTrunc()), 1729)
- class Foo5(int):
- def __int__(self):
- return 42.
-
- self.assertEqual(int(Foo0()), 42)
- self.assertEqual(int(Foo1()), 42)
- self.assertEqual(int(Foo2()), 42)
- self.assertEqual(int(Foo3()), 0)
- self.assertEqual(int(Foo4()), 42)
- self.assertRaises(TypeError, int, Foo5())
-
- class Classic:
- pass
- for base in (object, Classic):
- class IntOverridesTrunc(base):
- def __int__(self):
- return 42
- def __trunc__(self):
- return -12
- self.assertEqual(int(IntOverridesTrunc()), 42)
-
- class JustTrunc(base):
- def __trunc__(self):
- return 42
- self.assertEqual(int(JustTrunc()), 42)
-
- class JustLong(base):
- # test that __long__ no longer used in 3.x
- def __long__(self):
- return 42
- self.assertRaises(TypeError, int, JustLong())
-
- class LongTrunc(base):
- # __long__ should be ignored in 3.x
- def __long__(self):
- return 42
- def __trunc__(self):
- return 1729
- self.assertEqual(int(LongTrunc()), 1729)
-
- for trunc_result_base in (object, Classic):
- class Integral(trunc_result_base):
- def __int__(self):
- return 42
-
- class TruncReturnsNonLong(base):
- def __trunc__(self):
- return Integral()
- self.assertEqual(int(TruncReturnsNonLong()), 42)
-
- class NonIntegral(trunc_result_base):
- def __trunc__(self):
- # Check that we avoid infinite recursion.
- return NonIntegral()
-
- class TruncReturnsNonIntegral(base):
- def __trunc__(self):
- return NonIntegral()
- try:
- int(TruncReturnsNonIntegral())
- except TypeError as e:
- self.assertEqual(str(e),
- "__trunc__ returned non-Integral"
- " (type NonIntegral)")
- else:
- self.fail("Failed to raise TypeError with %s" %
- ((base, trunc_result_base),))
-
- def test_misc(self):
-
- # check the extremes in int<->long conversion
- hugepos = sys.maxsize
- hugeneg = -hugepos - 1
- hugepos_aslong = int(hugepos)
- hugeneg_aslong = int(hugeneg)
- self.assertEqual(hugepos, hugepos_aslong, "long(sys.maxsize) != sys.maxsize")
- self.assertEqual(hugeneg, hugeneg_aslong,
- "long(-sys.maxsize-1) != -sys.maxsize-1")
-
- # long -> int should not fail for hugepos_aslong or hugeneg_aslong
- x = int(hugepos_aslong)
- try:
- self.assertEqual(x, hugepos,
- "converting sys.maxsize to long and back to int fails")
- except OverflowError:
- self.fail("int(long(sys.maxsize)) overflowed!")
- if not isinstance(x, int):
- raise TestFailed("int(long(sys.maxsize)) should have returned int")
- x = int(hugeneg_aslong)
- try:
- self.assertEqual(x, hugeneg,
- "converting -sys.maxsize-1 to long and back to int fails")
- except OverflowError:
- self.fail("int(long(-sys.maxsize-1)) overflowed!")
- if not isinstance(x, int):
- raise TestFailed("int(long(-sys.maxsize-1)) should have "
- "returned int")
- # but long -> int should overflow for hugepos+1 and hugeneg-1
- x = hugepos_aslong + 1
- try:
- y = int(x)
- except OverflowError:
- self.fail("int(long(sys.maxsize) + 1) mustn't overflow")
- self.assertTrue(isinstance(y, int),
- "int(long(sys.maxsize) + 1) should have returned long")
-
- x = hugeneg_aslong - 1
- try:
- y = int(x)
- except OverflowError:
- self.fail("int(long(-sys.maxsize-1) - 1) mustn't overflow")
- self.assertTrue(isinstance(y, int),
- "int(long(-sys.maxsize-1) - 1) should have returned long")
-
- class long2(int):
- pass
- x = long2(1<<100)
- y = int(x)
- self.assertTrue(type(y) is int,
- "overflowing int conversion must return long not long subtype")
-
-# ----------------------------------- tests of auto int->long conversion
-
- def test_auto_overflow(self):
- import math, sys
-
- special = [0, 1, 2, 3, sys.maxsize-1, sys.maxsize, sys.maxsize+1]
- sqrt = int(math.sqrt(sys.maxsize))
- special.extend([sqrt-1, sqrt, sqrt+1])
- special.extend([-i for i in special])
-
- def checkit(*args):
- # Heavy use of nested scopes here!
- self.assertEqual(got, expected,
- Frm("for %r expected %r got %r", args, expected, got))
-
- for x in special:
- longx = int(x)
-
- expected = -longx
- got = -x
- checkit('-', x)
-
- for y in special:
- longy = int(y)
-
- expected = longx + longy
- got = x + y
- checkit(x, '+', y)
-
- expected = longx - longy
- got = x - y
- checkit(x, '-', y)
-
- expected = longx * longy
- got = x * y
- checkit(x, '*', y)
-
- if y:
- expected = longx / longy
- got = x / y
- checkit(x, '/', y)
-
- expected = longx // longy
- got = x // y
- checkit(x, '//', y)
-
- expected = divmod(longx, longy)
- got = divmod(longx, longy)
- checkit(x, 'divmod', y)
-
- if abs(y) < 5 and not (x == 0 and y < 0):
- expected = longx ** longy
- got = x ** y
- checkit(x, '**', y)
-
- for z in special:
- if z != 0 :
- if y >= 0:
- expected = pow(longx, longy, int(z))
- got = pow(x, y, z)
- checkit('pow', x, y, '%', z)
- else:
- self.assertRaises(TypeError, pow,longx, longy, int(z))
-
- @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
- "test requires IEEE 754 doubles")
+ @support.requires_IEEE_754
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,
@@ -694,8 +422,6 @@ class LongTest(unittest.TestCase):
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)
@@ -721,14 +447,12 @@ class LongTest(unittest.TestCase):
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)")
+ # 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]:
@@ -748,7 +472,6 @@ class LongTest(unittest.TestCase):
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.
@@ -794,7 +517,7 @@ class LongTest(unittest.TestCase):
self.d = d
assert float(n) / float(d) == value
else:
- raise TypeError("can't deal with %r" % val)
+ raise TypeError("can't deal with %r" % value)
def _cmp__(self, other):
if not isinstance(other, Rat):
@@ -821,7 +544,7 @@ class LongTest(unittest.TestCase):
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
+ # 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])
@@ -945,6 +668,127 @@ class LongTest(unittest.TestCase):
for zero in ["huge / 0", "mhuge / 0"]:
self.assertRaises(ZeroDivisionError, eval, zero, namespace)
+ 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_small_ints(self):
for i in range(-5, 257):
@@ -1072,6 +916,237 @@ class LongTest(unittest.TestCase):
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.assertTrue(type(myint.from_bytes(b'\x00', 'big')) is myint)
+ self.assertEqual(myint.from_bytes(b'\x01', 'big'), 1)
+ self.assertTrue(
+ type(myint.from_bytes(b'\x00', 'big', signed=False)) is myint)
+ self.assertEqual(myint.from_bytes(b'\x01', 'big', signed=False), 1)
+ self.assertTrue(type(myint.from_bytes(b'\x00', 'little')) is myint)
+ self.assertEqual(myint.from_bytes(b'\x01', 'little'), 1)
+ self.assertTrue(type(myint.from_bytes(
+ b'\x00', 'little', signed=False)) is 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)
def test_main():
generated by cgit v0.12 at 2025-11-16 04:18:27 (GMT)