Re: Motion M0045.02: YES -- resend
Michael,
Received, with thanks.
George Corliss
On Jul 29, 2013, at 2:17 PM, Michel Hack <mhack@xxxxxxx> wrote:
> Sorry, I messed up the Message-ID field in my earlier submission of a few
> minutes ago (14:54:06 -0400). My P.S. also forgot that we are voting on
> actual text after all...
>
> I vote YES on motion 45, requiring correctly-rounded dot product,
> but only recommending exact dot product (EDP), not requiring it.
>
> I do this with a heavy heart because Complete Arithmetic keeps
> getting short shrift. However, the EDP alone would not help much;
> one would have to specify support of a complete Complete Arithmetic
> package along the lines of VanSnyderP1788.pdf (in our list of position
> papers posted on ieee.grouper.org). Complete Arithmetic deserves its
> own standard, which could be useful in non-interval environments where
> full support of 1788 might be considered too much.
>
> I do have a nit to pick with the text however, concerning the requirement
> for an exact zero to be returned as +0. This might clash with a future
> version of 754 that also requires a correctly-rounded dot product. I
> propose the following revised text:
>
> Correctly rounded means that the returned result is defined as follows.
> - If the exact result is defined as an extended-real number, return this
> after rounding to the relevant format according to the current rounding
> direction. An exact zero shall be returned as +0 in all rounding
> directions, except for roundTowardNegative, where -0 shall be returned.
> - For dot and sum, if a NaN is encountered, or if infinities of both signs
> were encountered in the sum, NaN shall be returned. ("NaN encountered"
> includes the case oo*0 for dot.)
> - For sumAbs and sumSquare, if an Infinity is encountered, +Inf shall be
> returned. Otherwise, if a NaN is encountered, NaN shall be returned.
>
> (Note that these rules allow for short-circuit evaluation in certain cases.)
>
> All other behavior, such as overflow, underflow, setting of IEEE 754 flags,
> raising of exceptions, and behavior on vectors whose length is given as
> non-integral, zero or negative, shall be as specified in IEEE 754-2008
> §9.4. In particular, evaluation is as if in exact arithmetic up to the
> final rounding, with no possibility of intermediate overflow or underflow.
>
> Also, since correct rounding applies, the Inexact flag shall be set unless
> an exact extended-numeric result is returned. (If a final overflow or
> underflow is indicated, the result is inexact.)
>
> This might still not match a future 754 requirement, which might insist
> that a sum where ALL terms are +0 (or all terms -0) shall preserve the
> sign, regardless of rounding direction. I find that extra requirement
> to be excessively burdensome as it only applies in extreme cases, and
> I would (if I were a member of the next P754R group) recommend the
> simpler rule -- unless Prof. Kahan convinces us that the complete sign
> rule for pairs must be extended to sums of arbitrary number of terms.
>
> Michel.
>
> ---Sent: 2013-07-29 19:30:21 UTC