Lib/test/test_long_future.py

   1 from __future__ import division
   2 # When true division is the default, get rid of this and add it to
   3 # test_long.py instead.  In the meantime, it's too obscure to try to
   4 # trick just part of test_long into using future division.
   5
   6 import sys
   7 import random
   8 import math
   9 import unittest
  10 from test.test_support import run_unittest
  11
  12 # decorator for skipping tests on non-IEEE 754 platforms
  13 requires_IEEE_754 = unittest.skipUnless(
  14     float.__getformat__("double").startswith("IEEE"),
  15     "test requires IEEE 754 doubles")
  16
  17 DBL_MAX = sys.float_info.max
  18 DBL_MAX_EXP = sys.float_info.max_exp
  19 DBL_MIN_EXP = sys.float_info.min_exp
  20 DBL_MANT_DIG = sys.float_info.mant_dig
  21 DBL_MIN_OVERFLOW = 2**DBL_MAX_EXP - 2**(DBL_MAX_EXP - DBL_MANT_DIG - 1)
  22
  23 # pure Python version of correctly-rounded true division
  24 def truediv(a, b):
  25     """Correctly-rounded true division for integers."""
  26     negative = a^b < 0
  27     a, b = abs(a), abs(b)
  28
  29     # exceptions:  division by zero, overflow
  30     if not b:
  31         raise ZeroDivisionError("division by zero")
  32     if a >= DBL_MIN_OVERFLOW * b:
  33         raise OverflowError("int/int too large to represent as a float")
  34
  35    # find integer d satisfying 2**(d - 1) <= a/b < 2**d
  36     d = a.bit_length() - b.bit_length()
  37     if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
  38         d += 1
  39
  40     # compute 2**-exp * a / b for suitable exp
  41     exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
  42     a, b = a << max(-exp, 0), b << max(exp, 0)
  43     q, r = divmod(a, b)
  44
  45     # round-half-to-even: fractional part is r/b, which is > 0.5 iff
  46     # 2*r > b, and == 0.5 iff 2*r == b.
  47     if 2*r > b or 2*r == b and q % 2 == 1:
  48         q += 1
  49
  50     result = math.ldexp(float(q), exp)
  51     return -result if negative else result
  52
  53 class TrueDivisionTests(unittest.TestCase):
  54     def test(self):
  55         huge = 1L << 40000
  56         mhuge = -huge
  57         self.assertEqual(huge / huge, 1.0)
  58         self.assertEqual(mhuge / mhuge, 1.0)
  59         self.assertEqual(huge / mhuge, -1.0)
  60         self.assertEqual(mhuge / huge, -1.0)
  61         self.assertEqual(1 / huge, 0.0)
  62         self.assertEqual(1L / huge, 0.0)
  63         self.assertEqual(1 / mhuge, 0.0)
  64         self.assertEqual(1L / mhuge, 0.0)
  65         self.assertEqual((666 * huge + (huge >> 1)) / huge, 666.5)
  66         self.assertEqual((666 * mhuge + (mhuge >> 1)) / mhuge, 666.5)
  67         self.assertEqual((666 * huge + (huge >> 1)) / mhuge, -666.5)
  68         self.assertEqual((666 * mhuge + (mhuge >> 1)) / huge, -666.5)
  69         self.assertEqual(huge / (huge << 1), 0.5)
  70         self.assertEqual((1000000 * huge) / huge, 1000000)
  71
  72         namespace = {'huge': huge, 'mhuge': mhuge}
  73
  74         for overflow in ["float(huge)", "float(mhuge)",
  75                          "huge / 1", "huge / 2L", "huge / -1", "huge / -2L",
  76                          "mhuge / 100", "mhuge / 100L"]:
  77             # If the "eval" does not happen in this module,
  78             # true division is not enabled
  79             with self.assertRaises(OverflowError):
  80                 eval(overflow, namespace)
  81
  82         for underflow in ["1 / huge", "2L / huge", "-1 / huge", "-2L / huge",
  83                          "100 / mhuge", "100L / mhuge"]:
  84             result = eval(underflow, namespace)
  85             self.assertEqual(result, 0.0, 'expected underflow to 0 '
  86                              'from {!r}'.format(underflow))
  87
  88         for zero in ["huge / 0", "huge / 0L", "mhuge / 0", "mhuge / 0L"]:
  89             with self.assertRaises(ZeroDivisionError):
  90                 eval(zero, namespace)
  91
  92     def check_truediv(self, a, b, skip_small=True):
  93         """Verify that the result of a/b is correctly rounded, by
  94         comparing it with a pure Python implementation of correctly
  95         rounded division.  b should be nonzero."""
  96
  97         a, b = long(a), long(b)
  98
  99         # skip check for small a and b: in this case, the current
 100         # implementation converts the arguments to float directly and
 101         # then applies a float division.  This can give doubly-rounded
 102         # results on x87-using machines (particularly 32-bit Linux).
 103         if skip_small and max(abs(a), abs(b)) < 2**DBL_MANT_DIG:
 104             return
 105
 106         try:
 107             # use repr so that we can distinguish between -0.0 and 0.0
 108             expected = repr(truediv(a, b))
 109         except OverflowError:
 110             expected = 'overflow'
 111         except ZeroDivisionError:
 112             expected = 'zerodivision'
 113
 114         try:
 115             got = repr(a / b)
 116         except OverflowError:
 117             got = 'overflow'
 118         except ZeroDivisionError:
 119             got = 'zerodivision'
 120
 121         self.assertEqual(expected, got, "Incorrectly rounded division {}/{}: "
 122                          "expected {}, got {}".format(a, b, expected, got))
 123
 124     @requires_IEEE_754
 125     def test_correctly_rounded_true_division(self):
 126         # more stringent tests than those above, checking that the
 127         # result of true division of ints is always correctly rounded.
 128         # This test should probably be considered CPython-specific.
 129
 130         # Exercise all the code paths not involving Gb-sized ints.
 131         # ... divisions involving zero
 132         self.check_truediv(123, 0)
 133         self.check_truediv(-456, 0)
 134         self.check_truediv(0, 3)
 135         self.check_truediv(0, -3)
 136         self.check_truediv(0, 0)
 137         # ... overflow or underflow by large margin
 138         self.check_truediv(671 * 12345 * 2**DBL_MAX_EXP, 12345)
 139         self.check_truediv(12345, 345678 * 2**(DBL_MANT_DIG - DBL_MIN_EXP))
 140         # ... a much larger or smaller than b
 141         self.check_truediv(12345*2**100, 98765)
 142         self.check_truediv(12345*2**30, 98765*7**81)
 143         # ... a / b near a boundary: one of 1, 2**DBL_MANT_DIG, 2**DBL_MIN_EXP,
 144         #                 2**DBL_MAX_EXP, 2**(DBL_MIN_EXP-DBL_MANT_DIG)
 145         bases = (0, DBL_MANT_DIG, DBL_MIN_EXP,
 146                  DBL_MAX_EXP, DBL_MIN_EXP - DBL_MANT_DIG)
 147         for base in bases:
 148             for exp in range(base - 15, base + 15):
 149                 self.check_truediv(75312*2**max(exp, 0), 69187*2**max(-exp, 0))
 150                 self.check_truediv(69187*2**max(exp, 0), 75312*2**max(-exp, 0))
 151
 152         # overflow corner case
 153         for m in [1, 2, 7, 17, 12345, 7**100,
 154                   -1, -2, -5, -23, -67891, -41**50]:
 155             for n in range(-10, 10):
 156                 self.check_truediv(m*DBL_MIN_OVERFLOW + n, m)
 157                 self.check_truediv(m*DBL_MIN_OVERFLOW + n, -m)
 158
 159         # check detection of inexactness in shifting stage
 160         for n in range(250):
 161             # (2**DBL_MANT_DIG+1)/(2**DBL_MANT_DIG) lies halfway
 162             # between two representable floats, and would usually be
 163             # rounded down under round-half-to-even.  The tiniest of
 164             # additions to the numerator should cause it to be rounded
 165             # up instead.
 166             self.check_truediv((2**DBL_MANT_DIG + 1)*12345*2**200 + 2**n,
 167                            2**DBL_MANT_DIG*12345)
 168
 169         # 1/2731 is one of the smallest division cases that's subject
 170         # to double rounding on IEEE 754 machines working internally with
 171         # 64-bit precision.  On such machines, the next check would fail,
 172         # were it not explicitly skipped in check_truediv.
 173         self.check_truediv(1, 2731)
 174
 175         # a particularly bad case for the old algorithm:  gives an
 176         # error of close to 3.5 ulps.
 177         self.check_truediv(295147931372582273023, 295147932265116303360)
 178         for i in range(1000):
 179             self.check_truediv(10**(i+1), 10**i)
 180             self.check_truediv(10**i, 10**(i+1))
 181
 182         # test round-half-to-even behaviour, normal result
 183         for m in [1, 2, 4, 7, 8, 16, 17, 32, 12345, 7**100,
 184                   -1, -2, -5, -23, -67891, -41**50]:
 185             for n in range(-10, 10):
 186                 self.check_truediv(2**DBL_MANT_DIG*m + n, m)
 187
 188         # test round-half-to-even, subnormal result
 189         for n in range(-20, 20):
 190             self.check_truediv(n, 2**1076)
 191
 192         # largeish random divisions: a/b where |a| <= |b| <=
 193         # 2*|a|; |ans| is between 0.5 and 1.0, so error should
 194         # always be bounded by 2**-54 with equality possible only
 195         # if the least significant bit of q=ans*2**53 is zero.
 196         for M in [10**10, 10**100, 10**1000]:
 197             for i in range(1000):
 198                 a = random.randrange(1, M)
 199                 b = random.randrange(a, 2*a+1)
 200                 self.check_truediv(a, b)
 201                 self.check_truediv(-a, b)
 202                 self.check_truediv(a, -b)
 203                 self.check_truediv(-a, -b)
 204
 205         # and some (genuinely) random tests
 206         for _ in range(10000):
 207             a_bits = random.randrange(1000)
 208             b_bits = random.randrange(1, 1000)
 209             x = random.randrange(2**a_bits)
 210             y = random.randrange(1, 2**b_bits)
 211             self.check_truediv(x, y)
 212             self.check_truediv(x, -y)
 213             self.check_truediv(-x, y)
 214             self.check_truediv(-x, -y)
 215
 216
 217 def test_main():
 218     run_unittest(TrueDivisionTests)
 219
 220 if __name__ == "__main__":
 221     test_main()