From: "trans.  (T. Onoma)" <transami@...>
Date: 2004-10-31T17:58:46+09:00
Subject: Re: Rounding error ... [remainder of huge subject line truncated]

| Using floating point numbers, there is no way to guarantee that all
| pairs of calculations that fit the pattern in your example will yield
| the same results.  Sorry, but that's just the nature of the beast.

You are constraining the solution set to a system that can not provide a 
solution --current float-pointing representation. It's tautological. My point 
all along has been an _extension_ to the system to deal with the diffculties 
you speak-of. Which is how floating-slash and SLI arithmetic came up. Also, 
if you'll recall, Markus presented some points along the lines of my own 
train of thought on such an extension.

| Of course the results of the calculations I specified can be easily
| represented in a number of textual formats.  However, none of those
| calculations can be done in floating point without precision being lost
| and approximation being necessary.

Floating-point is a representation, no less, or more, than any other. The 
differences lie in the pragmatics of application of that representation. 
Roman numerals, for instance, generally suck for arithmetic production. 
Floating-points are much better, of course, but they too have limitations --a 
beastly nature, as you put it. Just becasue fp is modern does not mean that 
there may not a another system that will be to fp as fp is to rn (so to 
speak). And in fact, as I pointed out above, there are already some potential 
candidates.

T.