# in place of a digit.

[Gerald Jay Sussman <gjs@martigny.ai.mit.edu>]

     Date: Mon, 5 Dec 94 12:12:26 -0500
     From: Gerald Jay Sussman <gjs@martigny.ai.mit.edu>
     Return-Path: <gjs@martigny.ai.mit.edu>
     To: blume@cs.Princeton.EDU, carlton@math.mit.edu,
	     rrrs-authors@martigny.ai.mit.edu
     Subject: # in place of a digit. 


     My intention was to allow any implementation that might try to keep
     track of the significance of a number to have a notation that could
     indicate that some of the digits are not known.  Thus, a number, such
     as 180+-5, that is only known to two significant places could be
     described as 18#.  Note that 18# is not quite the same idea as #i180
     because #i180 does not try to communicate a measure of our knowledge
     of the number whereas 18# is trying to communicate that we know 2
     significant places of the number (in decimal).

     I have only used this feature in a few experimental cases, where I was
     dealing with interval arithmetic.  I believe that it is reasonably
     harmless, reserving flexibility for implementors to try to build
     interesting representations of inexact numbers that keep track of
     significance (to the small extent that it is possible to do so).

Sorry, I just realized that I can remember more of the idea, and that
I was a bit quick to answer that, so my answer was inexact (and
somewhat wrong!).

The idea was that one might print a number with an output format that
produces more digits than are available in the internal machine
representation of the number.  The idea is that such a format would
fill out the printed representation of the number with "#"s rather
than filling it out with useless (and misleadingly precise) digits.
This was not originally intended to make the statement that the system
actually kept track of the significance of the number, just that the
system knows that the significance demanded by the output routine was
not available in the representation.

On the other hand, if the system kept track of the significance of a
number, it could very well use this format to indicate known lack of
significance.  As such this is potentially a very nice feature.