Motion M0045.02: YES -- resend
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