🚀 go-pugleaf

         Hugh LaMaster states:
But, the reason that the standard is so entrenched is that it is so useful!
Manufacturers are forced to use it because users have requirements for it.

         I believe the standard has become entrenched for reasons other
than technical merit.  If the IEEE had chosen some other standard it
would probably be equally entrenched by now.
         Hugh LaMaster also states:
There are always programs which run on the ragged edge of precision,
and which don't work right on a slightly poorer implementation.

         I am skeptical about this statement.  Do you have some non-
contrived examples?  I believe 64 bits with any reasonable format is
enough for most problems.  Certainly I have not noticed any great demand
for more than 64 bits which suggests to me there is still some pre-
cision to spare.  Many users get by with 32 bits.
         Hugh LaMaster also states:
2)  IEEE is very well behaved, compared with other representations.  I won't
bother to substantiate this, other than to state that many experts agreed
at the time it was developed that there was no known way to improve it
numerically.

         I do not consider this a point in favor of the IEEE standard.
It is very rare that the optimum design in cases where there is trade-
off between qualities A and B, consists of maximizing A and ignoring B.
This is because there is usually a diminishing returns effect in which
one must give up greater and greater amounts of B to obtain further im-
provements in A.  The above statement suggests the IEEE standard gave
undue weight to numerical quality to the exclusion of factors such as
performance and ease of implementation.
         Couldn't we do without some or all of the following features of
the IEEE standard?  4 rounding modes (why only 4?  why not 8?).  Inf and
NaN.  Denormalized numbers.  Distinction between +0 and -0.
         Will Nasa ever build a spacecraft of which experts will say
"there is no known way to make this vehicle safer"?
         Hugh LaMaster also states:
The down side of IEEE is a performance hit in heavily pipelined FP units, for
some input values.  On the other hand, it is nice to get the right answer, even
if some cases slow down.

         You are understating the downside.  The standard is complex
which increases design time and cost.  This added design cost applies
to software such as compilers as well hardware.  The performance hits
are not confined to heavily pipelined floating point units on denorm-
alized inputs.
         As to wrong answers, wrong answers are generally caused by
users not knowing what they are doing.  Users who do know what they are
doing don't need IEEE arithmetic to get right answers, users who don't
know what they are doing will have no problems getting wrong answers
using IEEE arithmetic.
                           James B. Shearer