roundTiesToEven in precision 1

[Michel Hack <hack@xxxxxxxxxxxxxx>]

Yes, this is an interesting case.  I would however not involve the
exponent, and instead state that the rounding rule does not take
rounding overflow into account, and that if rounding overflow occurs,
the significand is shifted right, without further rounding, as the
digit dropped on the right is guaranteed to be zero.

One could then point out that the LSD could be odd in the case of
precision one.  (Note that in a binary format with precision one,
the trailing significand field is empty, and the LSD of a non-zero
number is always 1; it is also the MSD of course.  Such a format
has no subnormals, btw.)

Note that precision 1 can only occur for character output (base 10
or base 16) and for extendable formats (whose representation is not
defined by 754-2008 -- but that does not affect the rounding rule,
only my comment about a trailing significand field).

(I also verified that precision zero is explicitly excluded in 5.12;
one could have interpreted it as only returning the exponent, for an
implied significand of 1.)

Michel.
Sent: 2009-03-25 05:11:15 UTC