[Cfp-interest 2220] Re: quantum

[Vincent Lefevre]

On 2021-10-07 13:17:01 +0100, Mike Cowlishaw wrote:
> Maybe we're talking at cross-purposes, here. 
> 
> > > > but ditto with the quantum (which also depends on the 
> > > > representation).
> > > 
> > > I'm not quite sure what you mean by 'representation' here.
> > 
> > The meaning from the IEEE 754 standard:
> > 
> >   Level 3  (sign, exponent, significand) ? ...  Representations of
> >                                                 floating-point data.
> > 
> > > The quantum of a floating-point number only depends on its 
> > > radix and exponent, not on how it is depicted.
> > 
> > But the exponent depends on the representation (see above).
> 
> I would interpret that line as a definition of 'Level 3' in column 2,
> followed by a 'plain English' description of what the level is.  So, to me,
> a representation of a (finite) number is its sign, exponent, and
> significant.  That is, the representation depends on the exponent (and hence
> the quantum), not the other way around.

This depends on the point of view. In the IEEE 754 standard, the
quantum is defined as follows:

  quantum: The quantum of a finite floating-point representation is
  the value of a unit in the last position of its significand. This
  is equal to the radix raised to the exponent q, which is used when
  the significand is regarded as an integer.

i.e. one has a floating-point representation, and from that, one
defines what the quantum is, as a function of the representation.

What maters is that the data that are manipulated are FP numbers
(Level 2), FP representations (Level 3) or FP encodings (Level 4).
So it makes sense to say which level some property depends on.
For the quantum, it would depend on FP representations (Level 3).
For the ulp, it would depend on FP numbers only (Level 2), but the
ulp function can be extended to Level 1 for practical reasons.

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