[Cfp-interest 2933] Re: TS-4r augmented arithmetic terminology

[Damian McGuckin]

On Mon, 23 Oct 2023, Jim Thomas wrote:

> a new paragraph which says:
>
>       The functions in this clause use these structures to return a ?head?
>       value h and ?tail? value t to represent an extra-precise result
>       value given by h + t .
> 
> What do you think?

I think head/tail is too widespread to change. I think that your words are 
are a very useful additin. Can the sentence say something like

 	|h| >> |t|

to highlight that 't' is a very close approximation to the exact result 
and 't' is a approximate measure of the relative error between the exact 
result and 'h'.

At the risk of pointing out the obvious, some extra words to fuel the 
conversation (or augment the explanation) follows (which may be totally
irrelevent and for that I apologize in advance):

Programmatically, I tend to write

 	hi/lo

but that assumes the reader understands bit structure and the numberng 
scheme for the bits and I think is out of place here.

Mathematically, I prefer to use

 	v + dv
where
 	|v| >> |dv|

I have reasons why I disagree with the use of this terminology in TS-4r
which focuses around the fact that the signss of 'v' and 'dv' in this 
content do not agree. So again, probably out of place in this discussion.

Note that 'dv' would have the same sign as 'v' with truncation. But IEEE 
754 mandates 'round to nearest' which miniizes the error and means that 
the 'dv' (or the tail) can have either sign.

Thanks - Damian

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