[Cfp-interest 2221] Re: quantum

[Mike Cowlishaw]

> > 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.

We're going to have to agree to differ, here :-).  To me, the representation
is defined by the three integers. 
 
> What matters 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).

Which in turn is those three integers; hence "used when the significand is
regarded as an integer" (which refers to p18 of 754-2019).

> 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.

I'll take your word for it -- I've never found a use for 'ulp' although I
probably (and confusingly) used 'ulp' to mean what is now called 'quantum'
about 25 years ago.  It's probably best for it to rest in peace, like
'mantissa' in similar contexts...

Mike