Hermes: A Tutorial and Reference Manual - Researcher - IBM
Hermes: A Tutorial and Reference Manual - Researcher - IBM
Hermes: A Tutorial and Reference Manual - Researcher - IBM
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types.Additionally,theoperations\<strong>and</strong>",\or",<strong>and</strong>\not"aresupported. Booleantypessupportthesameoperationsasunorderedenumeration Thereisapredenedbooleantypecalledpredefined!booleanwhose boolean{association ::=false:named{literal,true:named{literal ::=true:named{literal,false:named{literal 11.<strong>Hermes</strong>Operations103<br />
namedliteralsare'true'<strong>and</strong>'false'.Youc<strong>and</strong>eneyourownboolean typeswithdierentliterals.Example: typedenitiondenesanewintegerdomain. bit:boolean(true:'0',false:'1'); Anintegerdomainconsistsofthemathematicalintegers.Eachinteger<br />
orangesdomain.Butyoucanconvertbetweentwointegerdomainsusing Example:::=realofaccuracyinteger{literal/integer{literal apples:integer; oranges:integer; Asusual,5intheapplesintegerdomaincan'tbecomparedto5inthe type{construction<br />
theconvertoperation. ::=integer<br />
numberthatcantinawordofcomputermemory.Incontrast,<strong>Hermes</strong> usestheusualmathematicaldenitionofinteger.Theresultofaninteger operationisalwayseitherthemathematicallycorrectresult,orelseno discretesubsetofrealnumbersspacedsucientlyclosetogethertomeet asafenumbersuchthattherelativeerror(thedistancebetweenthesafe result<strong>and</strong>aDepletionexception. auser-denedaccuracyrequirement.Foreveryrealnumber,thereexists Insomelanguages\integers"aredenedmodulothesizeofthelargest<br />
number<strong>and</strong>therealnumberdividedbytherealnumber)islessthanor equaltotheaccuracyrequirement. Arealdomainconsistsofasetofsafenumbers.Safenumbersarea<br />
isidenticaltothatshownforintegersabove.Approximaterealarithmetic tegerbetweenthemmusthaveasafeintegerbetweenthem. \preferred"assafenumbers,i.e.anypairofsafenon-integerswithaningrammersaresupported:(1)Zeroisasafenumber,<strong>and</strong>(2)integersare<br />
Theusualrealarithmeticoperationsaresupported;theexpressionsyntax Twootherpropertiesofapproximatearithmeticoftenassumedbypro-<br />
velocity:realofaccuracy1/1000000; Theaccuracyisexpressedasafraction,e.g.1/1000000.Example:<br />
isperformedasfollows.Theresultiscomputed<strong>and</strong>asafenumbernearest theexactresultisusedastheresult.Ifthereismorethanonenearestsafe numbertoanumber,anondeterministicselectionismade.
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