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From: herndon@umn-cs.UUCP
Newsgroups: net.arch
Subject: Re: Representations of Real Numbers
Message-ID: <17200002@umn-cs.UUCP>
Date: Thu, 13-Feb-86 00:13:00 EST
Article-I.D.: umn-cs.17200002
Posted: Thu Feb 13 00:13:00 1986
Date-Received: Sat, 15-Feb-86 03:31:17 EST
References: <931@houxa.UUCP>
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Nf-ID: #R:houxa:-93100:umn-cs:17200002:000:1607
Nf-From: umn-cs!herndon    Feb 12 23:13:00 1986


  There've been some interesting representations suggested
for "real" numbers (I shouldn't say floating point, but they
aren't real either.)  One article which appeared in Journal
of the ACM a while back suggested using a very odd scheme
involving a mantissa and another field which was (if I recall
aright) the number of times e should be raised to itself before
multiplying by the mantissa.  Very useful for LARGE(!) and SMALL(!)
numbers (we're talking numbers you couldn't even write down in
scientific notation, they have so many zeroes).   Mentioned
lots of useful properties of these things, but computational
efficiency wasn't one of them.  This article appeared a year
or two ago.
  There was an article in byte a while back suggesting an alternate
representation for floating point numbers which might be useful
on a micro... unfortunately I've forgotten all the details.  I
think the idea was to keep the logarithm of the number, and then
do multiplies and divisions by adding and subtracting... mildly
interesting, anyway.
  I heard something interesting from one of the hardware designers
where I used to work (Phoenix, AZ) about a FP representation under
consideration for large arrays of processing elements.  I seem to
recall that it involved non-unique representations for numbers,
allowing arithmetic operations to be performed much faster since
the representation put a finite bound on the number of carries which
ever had to be performed (something like gray codes for FP numbers).
  Sorry I don't have more details, but maybe these notes will
prompt somebody to mention more about them.