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>
> > 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.
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