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

[Jim Thomas]

Vincent,

Thank you for the comments. Please see (my) responses below. They will be reviewed at the February CFP teleconference.

-Jim

On Jan 8, 2014, at 7:34 AM, Vincent Lefevre <vincent at vinc17.net> wrote:

> Hi,
> 
> * TS 18661-4/N1785 §8 (reduction functions) doesn't say anything about
> the sign of 0, except for n = 0. It is ambiguous because one doesn't
> know whether the sign follows the usual IEEE 754 rules (which make
> sense even here, as the order of the operations doesn't matter) or it
> is unspecified.

Right, the sign of zero is not specified, except for n = 0. These functions are not specified to be correctly rounded, so further requirements on the sign of zero does not seem helpful.
> 
> * For the sums of length n = 0, is the value +0 even in
> roundTowardNegative?

Yes. (I believe 0 - 0 is the only case of the rounding direction affecting an operation that doesn’t entail rounding.)
> 
> * 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.

> * TS 18661-4 should reserve names for correctly rounded versions of
> all math functions, such as asinpi, even though IEEE 754-2008 doesn't
> recommend all functions: future revisions may add them. See also §9.1
> of IEEE 754-2008: the functions in §9.2 are recommended, but otherwise
> this is not an exhaustive list of what a language can specify.

Agreed. Looks like tanpi, asinpi, and acospi are missing.
> 
> Regards,
> 
> -- 
> Vincent Lefèvre <vincent at vinc17.net> - Web: <http://www.vinc17.net/>
> 100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
> Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)
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