Re: It All Comes Down to the IBM 704

In article <1120678467.822313.137950@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<jsavard@xxxxxxxxx> wrote:
>Herman Rubin wrote:
>> This is not the "bad" part of the 754 standard; it is
>> the use of forced normalization. I do not know about
>> the PDP, but I believe that none of the earlier
>> computers in the list had this requirement.

>It was indeed, as noted in my post, the PDP-11 that invented the hidden
>bit.

>I'm not saying it's "bad" that IEEE 754 happens to have a heritage that
>is two or three jumps away from the IBM 704, simply that it is somewhat
>surprising.

>Incidentally, using unnormalized numbers to indicate loss of
>significance somewhat limits the range of representable numbers when
>significance is lost. To prevent losing the high end of the range, one
>can pad on the right instead; for example, with 0, 01, 011, 0111, and
>so on, so that the last 0 in the mantissa indicates the end of its
>significance.

This can make arithmetic somewhat difficult. Significance
arithmetic needs its own rules, especially for such
operations as multiplication and division.

>John Savard

Significance was never the important indication for me.
What I find to be important is multiple precision
arithmetic, not necessarily too many, but say 3-10. Now
the easiest way to do this is to have excellent "integer"
arithmetic, but this seems to be almost nonexistent today.
Without forced normalization, it is relatively easy to do
with floating arithmetic. With it, it is much harder.
BTW, even when handling low significance data, I find it
very often pays to use high significance arithmetic to
avoid losing essential accuracy which is there.

BTW, I consider the present "double precision" to be
essentially single precision, and single to be half.

--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.