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1、RestructuringtheBLASLevel1RoutineforComputingtheModi edGivensTransformationTimHopkins(trh@ukc.ac.uk)ComputingLaboratoryUniversityofKentCanterbury,CT27NFKent,UK.November19,1997AbstractWelookathowbothlogicalrestructuringandimprovementsavailablefromsuccessiveversionsofF
2、ortranallowustoreducethecomplexity(measuredbyanumberofthecom-monlyusedsoftwaremetrics)oftheLevel1BLAScodeusedtocomputethemodi edGivenstransformation.Withthesereductionsincomplexityweclaimthatwehaveimprovedboththemaintainabilityandclarityofthecode;inaddition,wereporta
3、 xtoaminorproblemwiththeoriginalcode.TheperformanceoftwocommercialFortranrestructuringtoolsisalsoreported.1IntroductionTheLevel1BLAS[LHKK79],originallypublishedinFortran66[ANS66],implementedanumberofcommonvectoroperationsandweredesignedtobeusedasbuildingblocksforline
4、aralgebrasoftware.Hopkins[Hop96]usedknotcounts[WHH79]andpathcounts[Nej88]toidentifyroutinesfromtheLevel1BLASwhichmightbene tfromcoderestructuringTwosetsofroutines,*NRM2,usedtocomputetheEuclideannormofavectorand*ROTMG,forcomputingthemodi edGivenstransformation,wereide
5、nti edashavingextremelyhighmetricvaluesgiventheirrelativelylownumberofexecutablestatements.Therestructuringofthe*NRM2routines,alongwithadramaticdecreaseinthemetricvalues,wasreportedbyHopkins[Hop96];the*ROTMGroutinesareconsideredhere.Followingabriefdescriptionofthesof
6、twaremetricsusedtocompareversionsofthe*ROTMGroutines,wepresenta
owgraphofthepublishedcodeandlookathowtwoFortrancoderestruc-turingtoolsfaredonthisoriginalsource.Wethencomparethemetricvaluesobtainedfortheoriginalandautomaticallyrestructuredcodewithhand-codedFortran66an
7、dFortran77versions.Section5looksathowthemetricvaluesmaybereducedfurtherbyusingFortran90andweshowhowtheuseofsomeofthenewfacilitiesavailableinFortran90maybeusedtoimprovetheseroutinesfurther.Finallywelookbrie
yatthetestingofthenewroutineandreporta xtoaminorproblemintheo
8、riginalcode.2Modi edGivensRotationMatrixTTheinputvaluesto*ROTMG,d,d,xandy,de neatwo-vector[a;a]inthepartitionedform121112as"#12
