[Cfp-interest 2226] Re: quantum

[Mike Cowlishaw]

> Unlike quantum, the ulp is useful in many places, such as 
> error analysis. You often cannot use the quantum, as this 
> would mean that you should also specify the representation, 
> which is not practical and is useless in this context. For 
> instance, ulp(1) = ß^(1-p), whatever the representation of 1, 
> while quantum(1) will depend on the representation of 1.

I think we are going around in circles.  754 does not define
'representation' -- that word is used in its ordinary English sense.  It is
not defined in Clause 2.1 for that very reason.  It's a handy label for the
collection of specifications for floating-point data that describe
floating-point data in Table 3.1 level 3 (and probably should be in column 3
for level 2, also). 

Although you imply otherwise, the quantum of a number is both important and
useful (especially in radix 10, but also in radix 2 if you live in the USA
-- where, for example, woodworking measurements are often given in 1/32
inch, etc.).  

Vast numbers of people rely on the concept of quantum explicitly or tacitly
every day, if not by that name.  It's a part of the way humans communicate;
it is an essential part of the context of the way we work with numbers.

For more information on why this is so, please see:
http://speleotrove.com/decimal/decifaq1.html, and in particular
http://speleotrove.com/decimal/decifaq1.html#tzeros

In contrast, I posit that there are very few people who use 'ulp' as a
concept, other than in these (754, CFP) rarefied circles.

Mike