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

[Vincent Lefevre]

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.
|
|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.

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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