Is the maximum error bound in __mul really 1.001ULP?

[Siddhesh Poyarekar]

On 20 April 2013 01:07, Joseph S. Myers <joseph@codesourcery.com> wrote:
> On Fri, 19 Apr 2013, Siddhesh Poyarekar wrote:
>
>> Hi,
>>
>> I've been trying to reproduce the computation that resulted in the
>> conclusion that the __mul implementation in mpa.c has a maximum error
>> bound of 1.001ULP.  I haven't succeeded in doing that and the best
>> estimate I have for maximum error bound is in the range of R^-1ULP,
>> i.e. 2^-24ULP.  I'm sure I must be doing something wrong, but I can't
>> figure out what it is:
>
> A conclusion that the error bound is less than 0.5ulp (that is, ulps of a
> value with the precision to which the result gets rounded) is implausible.
> If you get such a conclusion I suppose you must be counting ulps in some
> way different from the statement that the bound is 1.001ulp.

Agreed, which is why I posted my derivation too.  Do you think there's
something wrong with it?

Thanks,
Siddhesh
--
http://siddhesh.in