[Cfp-interest 2934] Re: TS-4r augmented arithmetic terminology

[Jim Thomas]

> On Oct 23, 2023, at 4:03 PM, Damian McGuckin <damianm at esi.com.au> wrote:
> 
> 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'.

I think the example using augadd makes this point. We could add a reference to the example:

     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 . See EXAMPLE in this clause.

- Jim Thomas

> 
> 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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