1、 IEEE Standard for Interval Arithmetic (Simplified) Sponsored by the Microprocessor Standards Committee IEEE 3 Park Avenue New York, NY 10016-5997 USA IEEE Computer Society IEEE Std 1788.1-2017 IEEE Std 1788.1TM-2017IEEE Standard for Interval Arithmetic(Simpli ed)SponsorMicroprocessor Standards Comm
2、itteeof theIEEE Computer SocietyApproved 6 December 2017IEEE-SA Standards BoardAbstract: This standard is a simplified version and a subset of the IEEE Std 1788TM-2015 for Interval Arithmetic and includes those operations and features of the latter that in the the editors view are most commonly used
3、 in practice. IEEE Std 1788.1-2017 specifies interval arithmetic operations based on intervals whose endpoints are IEEE Std 754TM-2008 binary64 floating-point numbers and a decoration system for exception-free computations and propagation of properties of the computed results.A program built on top
4、of an implementation of IEEE Std 1788.1-2017 should compile and run, and give identical output within round o, using an implementation of IEEE Std 1788-2015, or any superset of the former.Compared to IEEE Std 1788-2015, this standard aims to be minimalistic, yet to cover much of the functionality ne
5、eded for interval computations. As such, it is more accessible and will be much easier to implement, and thus will speed up production of implementations.Keywords: arithmetic, computing, decoration, enclosure, interval, IEEE 754TM, IEEE 1788TM, operation, verified.The Institute of Electrical and Ele
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35、ssociation.vCopyright c 2018 IEEE. All rights reserved.ParticipantsAt the time this IEEE standard was completed, the Interval Standard Working Group had the followingmembership:Nathalie Revol, ChairR. Baker Kearfott, Vice ChairGuillaume Melquiond, SecretaryJ. Wol Von Gudenberg, Web MasterGeorge Corl
36、iss, Vote TabulatorNed Nedialkov, Technical EditorJohn Pryce, Technical EditorChristian Keil, Deputy Technical EditorMichel Hack, Vincent Lefevre, Ian McIntosh, Dmitry Nadezhin,and J. Wol Von Gudenberg, Assistant Technical EditorsAlexandru AmaricaiAyman BakrAhmed BelhaniGerd BohlenderGilles ChabertG
37、eorge CorlissRudnei Dias da CunhaHend DawoodWilliam EdmonsonBo EinarssonAlan EliasenHossam FahmyRichard FatemanScott FersonHaitham GadKathy GerberAlexandre GoldsztejnFrederic GoualardMichael GroszkiewiczMohamed GuerfelMichel HackRobert HanekBehnam HashemiOliver HeimlichTimothy HickeyWerner Hofschust
38、erChenyi HuTrevor Jackson-IIIMalgorzata JankowskaRalph KearfottChristian KeilMichel Kie erVladik KreinovichUlrich KulischDorina LanzaVincent LefevreDavid LesterDominique LohezWolfram LutherAmin MaherSvetoslav MarkovGuenter MayerR. Ian McintoshGuillaume MelquiondJean-Pierre MerletJean-Michel MullerHu
39、mberto MunozJose Antonio MunozDmitry NadezhinKaori NagatouMitsuhiro NakaoNed NedialkovMarkus NeherDiep NguyenMichael NoonerShinichi OishiSylvain PionEvgenija PopovaJohn PryceTarek RaissiNacim RamdaniAndreas RauhNathalie RevolMichael SchulteKyarash ShahriariStefan SiegelIwona SkalnaMark StadtherrJame
40、s StinePipop ThienprapasithWarwick TuckerAlfredo VaccaroMaarten van EmdenErik-Jan van KampenVan SnyderJosep VehiJulio Villalba-MorenoJ. Wol Von GudenbergG. William WalsterYan WangLee WinterPierre-Alain YvarsSergei ZhilinMohamed ZidanDan ZurasviCopyright c 2018 IEEE. All rights reserved.The following
41、 members of the individual balloting committee voted on this standard. Balloters may havevoted for approval, disapproval, or abstention.Demetrio Bucaneg Jr.Juan CarreonKeith ChowGeorge CorlissHossam FahmyAndrew FieldsendEric W GrayRandall GrovesMichel HackWerner HoelzlChenyi HuNoriyuki IkeuchiMalgor
42、zata JankowskaPiotr KarockiRalph KearfottVladik KreinovichVincent LefevreJean-Michel MullerDmitry NadezhinNed NedialkovJohn PryceNathalie RevolIwona SkalnaJames StineEugene StoudenmireWalter StrupplerGerald StueveJian YuOren YuenWhen the IEEE-SA Standards Board approved this standard on 6 December 2
43、017, it had the following mem-bership:Jean-Philippe Faure, ChairGary Ho man, Vice ChairJohn D. Kulick, Past ChairKonstantinos Karachalios, SecretaryChuck AdamsMasayuki AriyoshiTed BurseStephen DukesDoug EdwardsJ. Travis Gri thMichael JanezicThomas KoshyJoseph L. Koep nger Kevin LuDaleep MohlaDamir N
44、ovoselRonald C. PetersenAnnette D. ReillyRobby RobsonDorothy StanleyAdrian StephensMehmet UlemaPhil WennblomHoward WolfmanYu YuanMember EmeritusviiCopyright c 2018 IEEE. All rights reserved.IntroductionThis introduction is not part of IEEE Std 1788.1TM-2017, IEEE Standard for Interval Arithmetic(Sim
45、pli ed).This standard is a simpli ed version of the (full) IEEE Std 1788-2015 for Interval Arithmetic. As such, IEEEStd 1788.1-2017 featuresa) set-based intervals,b) the inf-sup interval type based on the IEEE Std 754-2008 binary64 oating-point format,c) the decoration system, andd) simpli ed I/O.Th
46、e full standard extends this standard with extra features, aimed at current applications of interval com-putation and at anticipated future developments, such as the following. Finite-precision intervals of di erent kinds are supported, e.g. one can build a system where intervalendpoints are numbers
47、 from an arbitrary-precision oating-point system such as MPFR. Besides the model in IEEE Std 1788.1-2017, where a mathematical interval is any closed connected subsetof the real numbers, other foundational models are supported in a controlled way by the concept of avors.For instance a avor may suppo
48、rt half-open and open real intervals; or Kaucher/modal intervals like 4,3as well as 3,4.IEEE Std 1788.1-2017 satis es all General Requirements of IEEE Std 1788-2015 and can be considered aavor of that standard. The set of required operations is extended by operations useful in specialized applicatio
49、ns, such as reverse-mode functions for constraint programming, and two-output division used in the interval Newton root-nding method.This document consists of two parts. Part 1 contains general requirements: overview, scope and purpose ofthis standard and various de nitions and abbreviations. Part 2 is the actual standard, presented in four levels.Level 1 summarizes the theory of set-based intervals including decorations; Level 2 is about representing Level1 entities in nite precision and the corresponding operations; Level 3 represents Level 2 entities, and Level4 speci es
