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:: Floating Point Computation By Pat Sterbenz Pdf Download ::

 
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MessagePosté le: Lun 31 Oct - 19:25 (2016)    Sujet du message: Floating Point Computation By Pat Sterbenz Pdf Download Répondre en citant




Floating Point Computation By Pat Sterbenz Pdf Download > bit.ly/2eN0mcq

























































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With,a,single,guard,digit,,the,relative,error,of,the,result,may,be,greater,than,,,as,in,110,-,8.59.,The,,error,,is,,0.5,,ulps,,,the,,relative,,error,,is,,0.8.,,This,operation,,called,a,fused,multiply-add,,can,cause,the,same,program,to,produce,different,results,across,different,single/double,systems,,and,,like,extended,precision,,it,can,even,cause,the,same,program,to,produce,different,results,on,the,same,system,depending,on,whether,and,when,it,is,used.,Thus,,neither,the,double,nor,the,doublet,type,can,be,compiled,to,produce,the,fastest,code,on,current,extended-based,hardware.,Of,,,course,,,,most,,,programmers,,,know,,,that,,,these,,,features,,,lie,,,beyond,,,the,,,scope,,,of,,,the,,,IEEE,,,standard.,,,It,turns,out,that,9,decimal,digits,are,enough,to,recover,a,single,precision,binary,number,(see,the,section,Binary,to,Decimal,Conversion).,Sign/magnitude,,,is,,,the,,,system,,,used,,,for,,,the,,,sign,,,of,,,the,,,significand,,,in,,,the,,,IEEE,,,formats:,,,one,,,bit,,,is,,,used,,,to,,,hold,,,the,,,sign,,,,the,,,rest,,,of,,,the,,,bits,,,represent,,,the,,,magnitude,,,of,,,the,,,number.,,,

There,,is,,a,,problem,,closely,,related,,to,,preserving,,parentheses,,that,,is,,illustrated,,by,,the,,following,,code,,eps,,=,,1;,,do,,eps,,=,,0.5*eps;,,while,,(eps,,+,,1,,>,,1);,,:,,.,,When,using,interval,arithmetic,,the,sum,of,two,numbers,x,and,y,is,an,interval,,,where,is,x,y,rounded,toward,-,,and,is,x,y,rounded,toward,+.,Or,,,to,,,put,,,it,,,another,,,way,,,,when,,,=2,,,,equation,,,(3),,,shows,,,that,,,the,,,number,,,of,,,contaminated,,,digits,,,is,,,log2(1/),,,=,,,log2(2p),,,=,,,p.,,,A,,summary,,of,,the,,behavior,,of,,all,,five,,exceptions,,is,,given,,in,,TABLED-4.,,When,,data,,in,,memory,,are,,stored,,in,,double,,precision,,,the,,machine,,epsilon,,is,,usually,,taken,,to,,be,,the,,largest,,relative,,roundoff,,error,,in,,that,,precision,,,since,,the,,input,,data,,are,,(rightly,,or,,wrongly),,assumed,,to,,have,,been,,rounded,,when,,they,,were,,entered,,and,,the,,results,,will,,likewise,,be,,rounded,,when,,they,,are,,stored.,,The,,,top,,,number,,,line,,,in,,,the,,,figure,,,shows,,,normalized,,,floating-point,,,numbers.,,,In,,the,,example,,above,,,the,,relative,,error,,was,,.00159/3.14159,,.0005.,,But,,the,,other,,addition,,(subtraction),,in,,one,,of,,the,,formulas,,will,,have,,a,,catastrophic,,cancellation.,,The,,picture,,below,,shows,,the,,computation,,of,,m,,x,,-,,x,,rounded,,,that,,is,,,(m,,x),,x.,,

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