Just out of curiosity how many bits does the IEEE standard require for
floating point?

On Oct 17, 2016 3:51 PM, "Leo Broukhis" <l...@mailcom.com> wrote:

> Dijkstra is above reproach; I try to compare the averages.
>
> Having eps^2 = eps is cute, but, given that the idea didn't spread to
> other pre-IEEE f.p. implementations nor to IEEE (it is possible to
> iteratively square a number x with 0 < abs(x) < 1 down to 0, given enough
> iterations, denormals or not), it appears that the Electrologica floating
> point turned out to be impractical.
>
>
>
> On Mon, Oct 17, 2016 at 11:35 AM, Paul Koning <paulkon...@comcast.net>
> wrote:
>
>>
>> > On Oct 17, 2016, at 2:26 PM, Leo Broukhis <l...@mailcom.com> wrote:
>> >
>> > > I think that the same answer applies to your narrower question,
>> though I didn't see it mentioned specifically in the documents I've read.
>> >
>> > That's somewhat comforting; I'd hate to think that the BESM-6
>> programmers were substantially sloppier than their Western colleagues. :)
>>
>> As you probably know, Dijkstra was a whole lot more disciplined than the
>> vast majority of his colleagues.
>>
>> > > For example, the treatment of underflow and very small numbers in
>> Electrologica was novel at the time; Knuth specifically refers to it in a
>> > > footnote of Volume 2.  The EL-X8 would never turn a non-zero result
>> into zero, for example.
>> >
>> > For most but not all values of "never", I presume. What was the result
>> of squaring the number with the least representable absolute value?
>>
>> The least representable positive value.  See the paper by F. E. J.
>> Kruseman Aretz that I mentioned.
>>
>> >
>> > > I think IEEE ended up doing the same thing, but  that was almost 20
>> years later.
>> >
>> > Are you're thinking about denormals?
>>
>> I think so, but I'll be the first to admit that I don't really know
>> floating point.
>>
>>         paul
>>
>>
>
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