Re: Requiring the EDP in 754 (or 1788.1 for that matter)

[Ulrich Kulisch <ulrich.kulisch@xxxxxxx>]

Am 27.01.2016 um 15:27 schrieb Michel Hack:

On Tue, 26 Jan 2016 14:26:48 +0000, Lester Holt wrote:

Anyway, wouldn't an EDP instruction requirement fit more naturally
into IEEE-754 if it's needed at all?

Yes, it would, as was pointed out several times while this issue was
being discussed in the 1788 working group (2008-2015).  Note that it
would be called "operation", not "instruction".

The 754-2008 standard is undergoing revision for 2018 -- but early on
the group decided (to my disappointment, actually) that no new mandated
features should be included in 2018, and should be deferred to the next
major revision for 2028.  The 2018 revision should only be concerned with
corrections and clarifications.

Similarly, 1788.1 is supposed to be a *subset* of 1788-2015, which again
precludes new requirements.

In any case, as I've pointed out repeatedly, the EDP cannot be defined in
isolation -- it has to be accompanied by a reasonably complete definition
of Complete Arithmetic (CA) and its corresponding datum types, such as
Kulisch Accumulators of one or more sizes.  Very early drafts of 1788 did
attempt to do that, but then the effort was dropped.

Without defined CA types, 1788-2015 did the best that could be done: it
does *require* a correctly-rounded overflow-free dot product, thus going
beyond the reduction operations of 754-2008.  This allows the operation
to be fully defined within the existing type system, leaving the choice
of types to be used for intermediate results to the implementation, and
in fact recommending the use of an EDP for that purpose.

What you say here shows again that the matter is not yet really understood.
Just see the mail of your colleague Ian McIntosh of January 21, 2016:
An exact dot product can easily be provided by a function call or by operator
overloading in languages which provide this.
If x and y are vectors why shouldn't it be possible to call the EDP by  x×y.

But the real point is this:  A correctly rounded dot product is slower by at least one magnitude
than a possibly wrong computation of the dot product in conventional floating-pooint arithmetic.
An exact dot product would be 6 times faster than the latter. So
the EDP is at least 60 times faster than a possibly wrong correctly rounded dot product.
Speed and accuracy are essential for acceptance and success of interval arithmetic.

Ignoring these facts is a terrible service to the standard.

Now, the 754-2018 revision is going well, so perhaps we can revisit the
initial restraint.  I urge those who care to join the 754 working group.

In the meantime I take every opportunity to remind my colleagues at IBM
who are involved in processor design of the properties and advantages of
Complete Arithmetic (as we had 30 years ago for HFP, easier due to the
narrower exponent range of the old S/360 format) -- but I have no direct
influence.

I very much appreciate this.

Michel
---Sent: 2016-01-27 14:34:34 UTC

Best regards
Ulrich

-- 
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Prof. Ulrich Kulisch
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