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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