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Diffstat (limited to 'Lib/test/test_long_future.py')
| -rw-r--r-- | Lib/test/test_long_future.py | 221 |
1 files changed, 0 insertions, 221 deletions
diff --git a/Lib/test/test_long_future.py b/Lib/test/test_long_future.py deleted file mode 100644 index 76c3bfbdbc5..00000000000 --- a/Lib/test/test_long_future.py +++ /dev/null @@ -1,221 +0,0 @@ -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 - -# 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)) - - @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() |