Re: [Qemu-devel] [RFC PATCH v0] softfloat: Add round-to-odd rounding mode

[Peter Maydell]

On 19 January 2017 at 14:47, Eric Blake <address@hidden> wrote:
> On 01/18/2017 11:14 PM, Bharata B Rao wrote:
>> round-to-odd mode is explained as under:
>>
>> Let Z be the intermediate arithmetic result or the operand of a convert
>> operation. If Z can be represented exactly in the target format, the
>> result is Z. Otherwise the result is either Z1 or Z2 whichever is odd.
>> Here Z1 and Z2 are the next larger and smaller numbers representable
>> in the target format respectively.
>
> IEEE 854 and thus POSIX <float.h> specifies round-to-zero,
> round-to-pos-inf, round-to-neg-inf, and round-to-even. It sounds like
> round-to-odd is similar to round-to-even, only that the ties are broken
> in the opposite direction.

No, round-to-even does "round ties to even" -- the rounding is
to the closest representable number, and only if the two
surrounding numbers are both equally near do we pick the even
one. round-to-odd is "always round to the odd number, even
if that's much further from the infinitely-precise result
than the even number is". (This is also sometimes called
von Neumann rounding or sticky rounding -- the motivation is
that you can for instance do 64bit -> 32bit -> 16bit
conversions in two steps without double rounding errors if
you do the first conversion with round-to-odd.)

thanks
-- PMM