def test_705836(self):
# SF bug 705836. "<f" and ">f" had a severe rounding bug, where a carry
# from the low-order discarded bits could propagate into the exponent
# field, causing the result to be wrong by a factor of 2.
import math
for base in range(1, 33):
# smaller <- largest representable float less than base.
delta = 0.5
while base - delta / 2.0 != base:
delta /= 2.0
smaller = base - delta
# Packing this rounds away a solid string of trailing 1 bits.
packed = struct.pack("<f", smaller)
unpacked = struct.unpack("<f", packed)[0]
# This failed at base = 2, 4, and 32, with unpacked = 1, 2, and
# 16, respectively.
self.assertEqual(base, unpacked)
bigpacked = struct.pack(">f", smaller)
self.assertEqual(bigpacked, string_reverse(packed))
unpacked = struct.unpack(">f", bigpacked)[0]
self.assertEqual(base, unpacked)
# Largest finite IEEE single.
big = (1 << 24) - 1
big = math.ldexp(big, 127 - 23)
packed = struct.pack(">f", big)
unpacked = struct.unpack(">f", packed)[0]
self.assertEqual(big, unpacked)
# The same, but tack on a 1 bit so it rounds up to infinity.
big = (1 << 25) - 1
big = math.ldexp(big, 127 - 24)
self.assertRaises(OverflowError, struct.pack, ">f", big)
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