Path: utzoo!mnetor!uunet!husc6!hao!ames!sri-spam!rutgers!mcnc!ecsvax!hes
From: hes@ecsvax.UUCP (Henry Schaffer)
Newsgroups: comp.arch
Subject: Re: Round-off
Message-ID: <4412@ecsvax.UUCP>
Date: 11 Jan 88 21:21:13 GMT
References: <189@mithras> <614@PT.CS.CMU.EDU> <4404@ecsvax.UUCP> <589@mcrware.UUCP>
Organization: NC State Univ.
Lines: 26
Keywords: IBM HEX ???
Summary: is binary the only acceptable base for numeric analysis?

In article <589@mcrware.UUCP>, jejones@mcrware.UUCP (James Jones) writes:
> In article <4404@ecsvax.UUCP>, hes@ecsvax.UUCP (Henry Schaffer) writes:
> > Why not?  Why can't [numerical analysts] just treat it as hex roundoff -
> > without worrying that the first bit in hex 1-7 is a 0?
> 
> It turns out that there are some proofs of convergence that count on the
> property
> 
> 			(x * 2) / 2 = x
> 
> (aside from over/underflow), and using base 16 violates that property.
  Clearly this is always true for binary floating point, because the mult
and div only affect the exponent.  In hex it is not always true - but this
also is (it seems to me) to be the case for *any* other base than binary.
Does this mean that only computers with binary floating point (including
binary normalization) are acceptable for numerical analysis?

  If so, then I object.  The only reason we build computers with binary
circuitry is the conjunction of economics with engineering/physics.  If we
had good deci-stable devices (cf. bi-stable) then we could have computers
which were internally decimal - and that would be preferable.  I would hope
that numerical analysts could deal with such computers.   Humph!  :-)

>... 
> 		James Jones
--henry schaffer  n c state univ