History
Motions
Miscellaneous
Conclusion
IEEE-1788 working group
Standardization of Interval arithmetic
EVA-Flo
Lyon, 22 et 23 septembre 2009
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
History
Motions
Miscellaneous
Conclusion
Agenda
History
Motions
Miscellaneous
Conclusion
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
History
Motions
Miscellaneous
Conclusion
IEEE-1788 WG: creation
Seed: Dagstuhl seminar, January 2008
Creation/acceptance by IEEE: 12 June 2008
First meeting: SCAN 2008
29 Sept-3 Oct 2008, El Paso, Texas, USA
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
History
Motions
Miscellaneous
Conclusion
IEEE-1788 WG: some facts
Since then: very active mailing list
over 140 participants, over 20 nationalities
over 1500 messages
Work already done:
adoption of officers, of procedures and policy
roster of voting members: 74 members, 14 nationalities
vote on 5 motions: passed
2 motions withdrawn
currently: 1 motion in discussion.
IEEE auspices: 1 report + 1 teleconference quarterly
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
History
Motions
Miscellaneous
Conclusion
Agenda
History
Motions
Miscellaneous
Conclusion
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
History
Motions
Miscellaneous
Conclusion
Motion 1
Motion 1: Standardized notations
Cf. ”Standardized notation in interval analysis” by R.B. Kearfott,
M.T. Nakao, A. Neumaier, S.M. Rump, S.P. Shary, and P. van
Hentenryck,
http://www.mat.univie.ac.at/~neum/papers.html
(open to amendment after sufficient experience of using it)
A box of dimension n is a pair x = [x, x] consisting of two real
column vectors x and x of length n with x ≤ x. The set of all
boxes of dimension n is denoted by IRn .
f ([−1, 1]) denotes the image of [−1, 1] under f ; f([−1, 1]) specifies
it as the result of applying the operations in f to the interval
[−1, 1] in its intrinsic arithmetic.
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
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Motion 2
Motion 2: Process Structure
I
Level 1: mathematical level
I
Level 2: datum level: IF the set of machine intervals
I
Level 3: representation level (∅, NaI,. . . )
I
Level 4: bit strings
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
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Motion 2
Relationships between different specication levels: interval version
Number system R.
Mathematical
Set IR of allowed intervals over R.
Model level. No
Level 1
Principles of how + − ∗ / and standard
NaN or NaI at this
functions are extended to intervals.
level.
many-to-one
↓ interval hull
identity map, except NaI ↑
one-to-one
The set F of “machine intervals”
Level 2
Interval data level.
in IR ∪ {NaI, if used }
one-to-many? ↓ representation specification
↑
many-to-one?
Representation of nonempty [x, x̄] as two
Representations of
Level 3
FP numbers x, x̄ or alternative. Repreinterval data.
sentation of ∅ and NaI.
one-to-many?
↓ encoding specifcation
↑
many-to-one?
Level 4
0111000 . . .
Bit strings.
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
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Motion 3
Motion 3: definition of intervals
intervals are connected closed sets of reals
(and not of extended reals, i.e. infinites are not included)
(no reversed interval either)
Discussion about modal intervals etc.
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
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Motion 4
Motion 4: link with floating-point arithmetic IEEE-754 :
aborted
interval arithmetic IEEE-1788 limited to systems that support
floating-point arithmetic IEEE 754-2008
implementation on non-conforming systems is out of scope
I do not remember why it aborted. . .
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
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Conclusion
Motion 5
Motion 5: definition of operations
mathematical definition
implementation/formulas not concerned
proposed by U. Kulisch.
Division by 0:
[a1 , a2 ]/[b1 , b2 ] = (−∞, +∞)
when a1 < 0 < a2 and b1 < 0 < b2
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
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Motion 6
Motion 6:
multi-format and conversions between floating-point formats
passed
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
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Motion 7
Motion 7: NaI
one unique NaI
lively discussion, that led to the withdrawal of motion 7 and the
proposal of motion 8
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
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Motion 8: discussion period
Motion 8: exception handling
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
History
Motions
Miscellaneous
Conclusion
Agenda
History
Motions
Miscellaneous
Conclusion
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
History
Motions
Miscellaneous
Conclusion
Other topics
Several position papers (Vienna proposal, Kulisch’ proposal, modal
intervals)
Many topics of discussion. . . with or without conclusion:
I
out of range values
I
division by 0
I
interval comparison
I
...
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
History
Motions
Miscellaneous
Conclusion
Agenda
History
Motions
Miscellaneous
Conclusion
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic
History
Motions
Miscellaneous
Conclusion
IEEE 1788 WG: in short
Web site: http://grouper.ieee.org/groups/1788/
(or google ”IEEE 1788”).
To participate:
I
subscribe to the mailing list
I
subscribe to the voting roster
Standard expected in December 2011. . .
I hope we will have produced at least a substantial part of it!-)
EVA-Flo
IEEE-1788 working group Standardization of Interval arithmetic