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1、AComprehensiveStudyofReal-WorldNumericalBugCharacteristicsAnthonyDiFranco*,HuiGuo*,andCindyRubio-GonzálezDepartmentofComputerScienceUniversityofCalifornia,Davis,USA{acdifranco,higuo,crubio}@ucdavis.eduAbstract—Numericalsoftwareisusedinawidevarietyofap-accuracy[9,12,45]andinstabilityproblems[10,26].
2、However,plicationsincludingsafety-criticalsystems,whichhavestringentthereisagapofknowledgeinunderstandingthecharacteristicscorrectnessrequirements,andwhosefailureshavecatastrophicofnumericalbugsinreal-worldnumericalsoftware.Whatareconsequencesthatendangerhumanlife.Numericalbugsarethemostcommonnumer
3、icalbugs?Howprevalentaretheseknowntobeparticularlydifficulttodiagnoseandfix,largelyduetotheuseofapproximaterepresentationsofnumberssuchbugs?Areexistingtoolscapableofdetectingthem?Howareasfloatingpoint.Understandingthecharacteristicsofnumericalsuchbugsfixed?Areexistingprogramrepairtoolssuitablebugsisthe
4、firststeptocombatthemmoreeffectively.Inthistofixthem?Thispapertakesafirststeptowardsansweringpaper,wepresentthefirstcomprehensivestudyofreal-worldthesequestionsbyconductingthefirstcomprehensivestudyofnumericalbugs.Specifically,weidentifyandcarefullyexaminereal-worldnumericalbugcharacteristics.Thegoalofth
5、ispaper269numericalbugsfromfivewidely-usednumericalsoftwarelibraries:NumPy,SciPy,LAPACK,GNUScientificLibrary,andistostudythecauses,symptoms,andfixesofnumericalbugsElemental.Weproposeacategorizationofnumericalbugs,andinnumericallibraries,andprovideahigh-levelcategorizationdiscusstheirfrequency,symptoms
6、andfixes.Ourstudyopensthatcanserveasaguideforresearcherstodeveloptoolsfornewdirectionsintheareasofprogramanalysis,testing,andfindingandfixingnumericalbugs.automatedprogramrepairofnumericalsoftware,andprovidesEmpiricalstudiesofbugcharacteristicshavebeenconductedacollectionofreal-worldnumericalbugs.inth
7、epasttolearnaboutconcurrencybugs[27,33],perfor-I.INTRODUCTIONmancebugs[23,40],anderrorhandlingbugs[13,16],amongNumericalsoftwareprovidesthefoundationforawidemanyothers.Thesestudieshaverevealedpatternsforbot