Lib.test.test_long_future.py Maven / Gradle / Ivy
Go to download
Show more of this group Show more artifacts with this name
Show all versions of jython Show documentation
Show all versions of jython Show documentation
Jython is an implementation of the high-level, dynamic, object-oriented
language Python written in 100% Pure Java, and seamlessly integrated with
the Java platform. It thus allows you to run Python on any Java platform.
from __future__ import division
# When true division is the default, get rid of this and add it to
# test_long.py instead. In the meantime, it's too obscure to try to
# trick just part of test_long into using future division.
import sys
import random
import math
import unittest
from test.test_support import run_unittest, cpython_only
# decorator for skipping tests on non-IEEE 754 platforms
requires_IEEE_754 = unittest.skipUnless(
float.__getformat__("double").startswith("IEEE"),
"test requires IEEE 754 doubles")
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(float(q), exp)
return -result if negative else result
class TrueDivisionTests(unittest.TestCase):
def test(self):
huge = 1L << 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(1L / huge, 0.0)
self.assertEqual(1 / mhuge, 0.0)
self.assertEqual(1L / 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 / 2L", "huge / -1", "huge / -2L",
"mhuge / 100", "mhuge / 100L"]:
# If the "eval" does not happen in this module,
# true division is not enabled
with self.assertRaises(OverflowError):
eval(overflow, namespace)
for underflow in ["1 / huge", "2L / huge", "-1 / huge", "-2L / huge",
"100 / mhuge", "100L / mhuge"]:
result = eval(underflow, namespace)
self.assertEqual(result, 0.0, 'expected underflow to 0 '
'from {!r}'.format(underflow))
for zero in ["huge / 0", "huge / 0L", "mhuge / 0", "mhuge / 0L"]:
with 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."""
a, b = long(a), long(b)
# 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))
@cpython_only
@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_main():
run_unittest(TrueDivisionTests)
if __name__ == "__main__":
test_main()