[Cfp-interest] TS 18661-4/N1785 - Reduction functions, correct rounding

[Jim Thomas]

Thanks for the information. Expanding IEEE 754-2008 is generally out of scope for the TS, but we’ll take another look at this.

Dan, please see comments and questions  below.

- Jim

On Feb 6, 2014, at 4:59 PM, Vincent Lefevre <vincent at vinc17.net> wrote:

> Jim,
> 
> On 2014-02-05 11:35:06 -0800, Jim Thomas wrote:
>> On Jan 8, 2014, at 7:34 AM, Vincent Lefevre <vincent at vinc17.net> wrote:
>>> * TS 18661-4 should reserve names for correctly rounded versions of
>>> the reduction operations. Note that the current P1788 draft standard
>>> for interval arithmetic requires correctly rounded reduction
>>> operations sum, dot, sumSquare and sumAbs.
>> 
>> IEEE 754-2008 specifies the reduction operations to allow high
>> performance implementation for general use, and does not address
>> correctly rounded reductions. I think doing so in TS 18661 would be
>> out of scope.
> 
> That's not what Dan Zuras (in Cc) says:
> 
>  http://grouper.ieee.org/groups/1788/email/msg06382.html
> 
> |Alas, Vincent may point out that we did NOT specify them as being
> |exactly computed.  Indeed, we were not able to at the time, due
> |to there being so many 754s out there that did not support it.
> |So these functions are defined but without specified result
> |precision.  (Although we DID specify exceptions in a standard way.)
> |
> |However, correctly rounded versions WERE our intention.  


> Indeed,
> |it is silly to define them just as they would come out of any
> |C-compiler.

That would have been silly, but not what’s in 754. C compilers are limited to C semantics for evaluation order and types, which 754 reduction functions are not.

> |
> |Then, shortly after the standard was published a number of papers
> |appeared that show you how to correctly round your result in all
> |cases using 754 arithmetic, just a bit of extra precision, &
> |some sorting.  It is quite clever & not at all difficult to do.
> |And, indeed, had we known they were possible (& fast) at the time
> |we WOULD have required them as many (perhaps most) existing 754
> |implementations have done now.

What 754 implementations are you referring to? Are you saying they provide correctly rounded reductions now? 

> 
> So, if the intention was correctly rounded results instead of
> high performance, then TS 18661 should address that.
> 
> -- 
> Vincent Lefèvre <vincent at vinc17.net> - Web: <https://www.vinc17.net/>
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