[Cfp-interest 2227] Re: quantum

[Vincent Lefevre]

On 2021-10-07 20:01:51 +0100, Mike Cowlishaw wrote:
> > 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 *is* defined in Clause 2.1:

  floating-point representation: An unencoded member of a
  floating-point format, representing a finite number, a signed
  infinity, a quiet NaN, or a signaling NaN. A representation of a
  finite number has three components: a sign, an exponent, and a
  significand; its numerical value is the signed product of its
  significand and its radix raised to the power of its exponent.

> 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.).  

Perhaps in some contexts. But unlike the ulp, there is no way to
define the quantum on general real numbers without an additional
parameter (providing information about the quantum). So this is
off-topic here.

-- 
Vincent Lefèvre <vincent at vinc17.net> - Web: <https://www.vinc17.net/>
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