🚀 go-pugleaf

         I said:
>   I don't believe interval arithmetic is used enough to justify
>   any hardware support.
         Keith Bierman said:
This falls into the "H.R." chicken and egg rathole. If interval
arithmetic (or anything else new and claimed to be good) is 100x
slower than the traditional approach, it will simply never get off the
ground.
         Some comments:
    1. Interval arithmetic is not "new".  People have been writing
books and papers on it for at least 30 years.
    2. Herman Rubin is still trying to get people to implement his
proposed instructions.  The interval arithmetic people got their
instructions into the IEEE standard and they have been implemented
in hardware in many machines.  Interval arithmetic still hasn't
gotten off the ground.  How long are we expected to wait until
concluding it's not going to fly.
    3. The real problem with interval arithmetic is not that it's
slow but that on real applications its error estimates are gener-
ally so pessimistic as to be useless.  Extended precision generally
gives better estimates with less work.
         There are many ideas which have seemed promising but never
quite made it, bubble memory for example.  While judgement can
never be final, automatic error estimation in general and interval
arithmetic in particular seems unlikely to ever fulfill the hopes
many had for it.
                      James B. Shearer