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P1788,
Voting is underway on three motions. Baker's calls for each are appended below.
Motion M0033.01 Number Format
Current tally: Yes: 0; No: 0; Required for quorum: 24
Voting by rules for position papers
Voting closes Wednesday, June 6
Motion M0034.01 Notation
Current tally: Yes: 7; No: 0; Required for quorum: 24
Voting by rules for position papers
Voting closes Wednesday, June 6
Motion M0034.01 Overflow before Unbounded
Current tally: Yes: 0; No: 0; Required for quorum: 24
Voting by rules for position papers
Voting closes Tuesday, June 19
Recall that according to our Policies and Procedures, if you do not vote on two consecutive motions, you can be removed from the official roster of Voting Members. Re-instatement is easy, but why not consider each of these motions and VOTE SOON.
George Corliss
George.Corliss@xxxxxxxxxxxxx
Begin forwarded message:
> From: Ralph Baker Kearfott <rbk@xxxxxxxxxxxx>
> Subject: Motion P1788/M0033.01:NumberFormat -- voting period begins
> Date: May 16, 2012 9:22:15 PM CDT
>
> P-1788:
>
> The voting period herewith begins. Voting will continue until after Wednesday, June 6, 2012.
> Voting on this motion will proceed according to the rules for position papers (quorum and simple majority).
> Comment can continue during voting, but the motion cannot be changed during voting.
>
> Juergen: Please update the web page with this action.
>
> Acting secretary: Please record the transaction in the minutes.
>
> The motion appears in the private area of the IEEE P-1788 site:
>
> http://grouper.ieee.org/groups/1788/private/Motions/AllMotions.html
>
> I have also appended the motion, for your convenience.
>
> As usual, please contact me if you need the password to the private area.
>
> Best regards,
>
> Baker (acting as chair, P-1788)
>
> ---------------------------------------------------------------
>
>> On 04/11/2012 07:44 PM, Vincent Lefevre wrote:
>>> Note: Here, IEEE 754 is IEEE 754-2008 (currently the latest version
>>> of the IEEE 754 standard). Since not everyone can read Unicode symbols,
>>> the infinity symbol is denoted oo (not inf, because inf is also an
>>> operation defined by P1788).
>>>
>>> Motion
>>> ======
>>>
>>> An argument or a result of some operations covered by the standard
>>> can be a number. A number is defined at Level 1 as being any member
>>> of the set Rbar = R U { -oo, +oo } of extended reals. This motion
>>> defines the corresponding notion at Level 2, called "number format"
>>> and denoted here F. For an inf-sup interval type, the bounds are
>>> the members of a number format F. An implementation must support
>>> at least one number format F. The requirements and recommendations
>>> are:
>>>
>>> A1. F corresponds to a finite subset of R together with 3 special
>>> datums: -oo, +oo (the infinities of Rbar) and NaN (not-a-number).
>>>
>>> A2. A datum can have different variants or different representations
>>> (e.g. IEEE 754 qNaN / sNaN, cohorts for decimal floating-point
>>> numbers, signed zeros), but they are not distinguished in F, possibly
>>> except for the number 0, which may be regarded as signed by the P1788
>>> implementation; in such a case, it has exactly two possible values,
>>> denoted -0 and +0. When 0 is unsigned, the notation -0 or +0 can be
>>> used and simply denotes 0.
>>>
>>> A3. The number 0 (either a single element 0 or the two elements -0
>>> and +0) must be in F.
>>>
>>> A4. The format must be symmetric, i.e. if a real x is in F, then -x
>>> is also in F.
>>>
>>> A5. An element of Rbar (Level 1) is mapped (rounded) to an element
>>> of F (Level 2) according to the following rules:
>>> * A constraint can be given on the rounding direction. It must
>>> be satisfied.
>>> * Following this constraint, the rounded result should be an
>>> element of F that is the closest to the exact result (with
>>> a special implementation-defined rule for the distance to
>>> an infinity).
>>> * In general, this element is unique, but there may exist two
>>> elements satisfying this property (halfway cases). How these
>>> cases are rounded should be documented by the implementation.
>>>
>>> The notion of a 754-conforming implementation has been introduced
>>> in Motion 6.04. A 754 format must have the following additional
>>> requirements:
>>>
>>> B1. The infinities correspond to the IEEE 754 infinities.
>>>
>>> B2. NaN corresponds to the IEEE 754 Level 2 NaN. At IEEE 754 Level 3,
>>> it can be either qNaN or sNaN, but if a NaN is produced as a result,
>>> it must be a qNaN (except documented otherwise by P1788).
>>>
>>> B3. The number 0 is signed.
>>>
>>> B4. Concerning A5, for each operation where an interval of type T is
>>> involved, there must be at least one number format F (the one of the
>>> interval bounds for inf-sup, or documented by the implementation for
>>> implicit interval types) such that the rounding must be done according
>>> to the rules given by the IEEE 754 standard (correct rounding).
>>> In the case of rounding-to-nearest (no constraints on the direction),
>>> which rounding function (among the two possible rounding-direction
>>> attributes) is used must be defined by the implementation.
>>>
>>> The notion of number format F compatible with an interval type T can
>>> be defined, if need be. The idea is to require F to be dense enough
>>> in order to satisfy some properties when returning a numeric value.
>>> Later motions can require that for some specific operations, F must
>>> be compatible with T (but shouldn't if this isn't really necessary).
>>> A number format F is said to be compatible with an interval type T
>>> if:
>>>
>>> C1. For each non-empty interval I of type T (Level 2), there exists
>>> a finite number x of F such that x \in I.
>>>
>>> Later motions may define other constraints (when need be).
>>>
>>> Rationale
>>> =========
>>>
>>> The above constraints have been chosen not to be too strict in order
>>> to allow conventional formats, such as floating-point numbers (with
>>> or without subnormals), fixed-point numbers (including integers),
>>> rational numbers (with bounded numerator and denominator),
>>> double-double numbers (provided by the "long double" C type in the
>>> current PowerPC ABI).
>>>
>>> A1. We require the subset to be finite is order to be able to specify
>>> the rounding without ambiguity. A discrete subset would be sufficient
>>> for this purpose, but P1788 will probably also need the notion of
>>> smallest and largest finite element (see the discussions about the
>>> midpoint). Arbitrary precision formats need to be parameterized (for
>>> instance, by the precision and possibly the exponent size), so that
>>> each format instance is finite.
>>>
>>> A2. Ideally, one should not need to distinguish -0 and +0 as far
>>> as P1788 is concerned, but this is done mainly for 754-conforming
>>> implementations.
>>>
>>> A3. The number 0 will probably be needed for some functions. And it
>>> would be awkward not to require it anyway.
>>>
>>> A4. Symmetry may not really be necessary, but it may expected by the
>>> user, and all known formats are symmetric (well, in general, not the
>>> native C integer types, but this is the cause of various bugs and
>>> they don't have infinities and NaN anyway).
>>>
>>> A5. Correct rounding is recommended, but not required because it may
>>> be difficult or may not really be useful in exotic number formats.
>>> For 754-conforming implementations, it is however required for some
>>> number format associated with the interval type T, but not necessarily
>>> for all supported number formats, so that we do not disallow things
>>> like mixed radix.
>>>
>>> C1. A consequence: one can define a Level 2 midpoint that belongs to
>>> any non-empty interval of type T.
>>>
>>> Note: The standard doesn't define operations on the number format
>>> itself (e.g. the additions of two numbers). That's why the motion
>>> doesn't contain any requirement concerning such operations.
>>>
>
Subject: Motion P1788/M0034.01:Notation-- voting period begins
Date: May 16, 2012 9:24:01 PM CDT
P1788:
The voting period herewith begins. Voting will continue until after Wednesday, June 6, 2012.
Voting on this motion will proceed according to the rules for position papers (quorum and simple majority).
Comment can continue during voting, but the motion cannot be changed during voting.
Juergen: Please update the web page with this action.
Acting secretary: Please record the transaction in the minutes.
The motion appears in the private area of the IEEE P-1788 site:
http://grouper.ieee.org/groups/1788/private/Motions/AllMotions.html
I have also attached the motion, for your convenience.
As usual, please contact me if you need the password to the private area.
Best regards,
Baker (acting as chair, P-1788)
On 04/16/2012 10:13 AM, Ulrich Kulisch wrote:
The text of a new Motion is attached. The following mail exchange gives the rationale.
Best regards
Ulrich
On March 26, 2012 Ulrich Kulisch wrote:
Dear all,
There are some discrepancies in the notations of Drafts 4.02 and 4.04 and I think
we should straighten these out before less suited denotations spread. Let me briefly
comment on the history of these notations.
The real numbers R are defined as conditionally complete, linearly ordered field.
Conditionally complete means: Every bounded subset has an infimum and a supremum.
Every conditionally completely ordered set can be completed by joining a least and a
greatest element. In case of the real numbers R these are −∞ and +∞. However, these
new elements are not real numbers. For instance ∞−∞ not= 0, or ∞/∞ not= 1. I think
there was general agreement that the completion should be expressed by overlining the
R. So \overline{R} := R ∪ {−∞,+∞}.
Since the early days of interval arithmetic the set of nonempty, closed and bounded
real intervals has been denoted by IR. The ordering of the set {IR, ⊆} also is only
conditionally complete. For every bounded subset the infimum is the intersection and
the supremum is the interval hull. Completion of {IR, ⊆} brings the empty set and
unbounded intervals into the game. In my book (2008) and in the paper I prepared
for the proceedings of the Dagstuhl meeting (January 2008) I denoted the completed
set by (IR). This was critisized within P1788. Then I suggested writing JR for the
completed set. After some discussion I think we all agreed indicating the completion
again by overlining the set IR. In \overline{IR} the empty set is the least element.
However, the empty set is not an interval arithmetically. As −∞ and +∞ are not real
numbers the empty set does not follow conventional rules of interval
arithmetic, for instance, ∅ · 0 not= 0.
For consistency the same scheme of denotations should be kept for the subsets
representable on computers. This leads to the following denotations:
R the set of real numbers.
\overline{R} \overline{R} := R ∪ {−∞,+∞}.
IR the set of nonempty, closed and bounded real intervals.
\overline{IR} the set of closed real intervals, including unbounded intervals and the empty set.
F the set of (finite) floating-point numbers representable in some floating-point format.
\overline{F} \overline{F} := F ∪ {−∞,+∞}.
IF the intervals of IR whose bounds are in F.
\overline{IF} the intervals of \overline{IR} whose bounds are in \overline{F} and the empty set.
Best regards
Ulrich
--
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik (IANM2)
D-76128 Karlsruhe, Germany
Prof. Ulrich Kulisch
Telefon: +49 721 608-42680
Fax: +49 721 608-46679
E-Mail:ulrich.kulisch@xxxxxxx
www.kit.edu
www.math.kit.edu/ianm2/~kulisch/
KIT - Universität des Landes Baden-Württemberg und nationales Großforschungszentrum in der Helmholtz-Gemeinschaft
Begin forwarded message:
> From: Ralph Baker Kearfott <rbk@xxxxxxxxxxxx>
> Subject: Motion P1788/M0035.01:OverflowBeforeUnbounded -- voting period begins
> Date: May 28, 2012 8:36:56 PM CDT
>
> P1788:
>
> The voting period herewith begins. Voting will continue until after Tuesday, June 19, 2012.
> Voting on this motion will proceed according to the rules for position papers (quorum and simple majority). Comment can continue during voting, but the motion cannot be changed during voting.
>
> Juergen: Please update the web page with this action.
>
> Acting secretary: Please record the transaction in the minutes.
>
> The motion appears in the private area of the IEEE P-1788 site:
>
> http://grouper.ieee.org/groups/1788/private/Motions/AllMotions.html
>
> I have also attached the motion and accompanying paper, for your convenience.
>
> As usual, please contact me if you need the password to the private area.
>
> Best regards,
>
> Baker (acting as chair, P-1788)
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