white box testing

White‐boxtes,ngCorsodiLaureaMagistraleinIngegneriaInforma,ca

Lecturer:Valen,naPresu>AcademicYear:2008/2009

Summary

•  White‐box(orGlass‐box)tes,ng:generalcharacteris,cs

•  Statementcoverage

•  Decisioncoverage•  Condi,oncoverage•  Decisionandcondi,oncoverage•  Coverageofalinearlyindependentsetofpaths

SoNwareEngineeringa.a.2008/2009White‐boxtes,ng 2

White‐boxtes,ng:generalcharacteris,cs

•  Alsocalled– Glass‐boxtes,ng– Structuraltes,ng(comparedtofunc,onal)

•  Exploitsthecontrolstructure,thatmeansthecontrolorflowgraphofprogramsinordertodesigntestcases

•  Typicallyperformedduringcoding


White‐boxtes,ng:generalcharacteris,cscont.d

•  Allowstotestpartsoftheprogram– Withblack‐boxisnotpossible

•  Allowstocoversystema,callyeverypartoftheprogram– ONenerrorsarefoundinspecialcases


Typesofwhite‐boxtests


Statementcoverage

•  Itistheeasiestcriterionforareasonablewhite‐boxtest

•  Necessarybutnotsufficient

•  Goal– Toiden,fyasetoftestcasessufficienttoexerciseallstatementsatleastonce


Statementcoveragecont.d

•  Thetestcase{x!=0;y=any}

•  Coversthestatements


Javaexample:

/*A*/floatx=InOut.readFloat(),y=InOut.readFloat();/*B*/if(x!=0)/*C*/y+=10;/*D*/y=y/x;/*E*/System.out.println(x+''+y);

A

B

C

D

E

x==0

x!=0

Controlflowgraphfortheexample

Statementcoveragecont.d

•  Possibleproblem– Eveninacaseofaprogramwithoutitera,ons,theexecu,onofeverystatementdoesnotguaranteethatallpossiblepathsareexercised

•  Possiblenega,veconsequence:–  Inpreviousjavaexampleprogramtheerrorofdivisionby0isnotiden,fied(statementD)


Decisioncoverage

•  Properlyincludesstatementcoverage•  Viceversadoesnothold•  Focusonallpossibledecisionsinaprogram•  Decisionsareinstatements

–  if,switch,while,for,do•  Goal

– Toiden,fyasetoftestcasessufficientforguaranteeingthateachdecisionwillhavevalue“true”atleastonceandvalue“false”atleastonce


Decisioncoveragecont.d


Javaexample:

/*A*/floatx=InOut.readFloat(),y=InOut.readFloat();/*B*/if(x!=0)/*C*/y+=10;/*D*/y=y/x;/*E*/System.out.println(x+''+y);

A

B

C

D

E

x==0

x!=0

Testcases1.  {x=20;y=30}2.  {x=0;y=30}

Coverdecisionshencestatements.Thesecondcaseiden,fiestheerrorofdivisionbyzeroinstatementD


•  Possibleproblem•  Ifdecisionsarecomposedofseveralcondi,ons(AND,OR),decisioncoveragecanbenotsufficient


EsempioJava:/*A*/floatz=InOut.readFloat(),w=InOut.readFloat();t=InOut.readFloat();/*B*/if(z==0||w>0)/*C*/w=w/z;/*D*/elsew=w+2/t;/*E*/System.out.println(z+''+w+''+t);

Whatistheproblemhere?


•  Testcases:–  {t=0;z=5;w=5}decisionTRUE–  {t=0;z=5;w=‐5}decisionFALSE

•  Coverdecision•  Thesecondoneiden,fiesthedivisionbyzeroinDbut

•  TheriskofdivisionbyzeroinCisnotiden,fies•  Weneedacriterionthatconsidersbothstructureandcomponentsofdecisions


Condi,oncoverage

•  Doesnotproperlyincludedecisioncoverage•  Itisnotproperlyincludedbydecisioncoverage•  Focusonallpossiblecondi,onsinaprogram•  Condi,onsaretheoperandsofnon‐atomicbooleanexpressions

•  Goal:–  Toiden,fyasetoftestcasessufficientforguaranteeingthateverycondi,on(atomicbooleanexpression)includedintheprogram’sdecisionshavevalue“true”atleastonceandvalue“false”atleastonce


Condi,oncoveragecont.d


Testcases{t=0;z=0;w=‐5}1ac.=T,2ac.=F{t=0;z=5;w=5}1ac.=F,2ac.=TCovercondi,ons

Whatproblemdosuchcasetestsmakeemerge?

Javaexample:/*A*/floatz=InOut.readFloat(),w=InOut.readFloat();t=InOut.readFloat();/*B*/if(z==0||w>0)/*C*/w=w/z;/*D*/elsew=w+2/t;/*E*/System.out.println(z+''+w+''+t);

Condi,oncoverage

•  Testcases–  {t=0;z=0;w=‐5}1acondi,on=T,2acondi,on=F–  {t=0;z=5;w=5}1acondi,on=F,2acondi,on=T

•  Covercondi,ons•  Thefirstoneiden,fiesthedivisionbyzeroin

C•  TheriskofdivisionbyzeroinDisnot

iden,fiedasDisneverexcercised•  Decisionisalways“true”


Decisionandcondi,oncoverage

•  Properlyincludes– Decisioncoverage– Condi,oncoverage

•  Goal– Toiden,fyasetoftestcasessufficientforguaranteeingthat•  Eachdecisionis“true”atleastonceand“false”atleastonce

•  Allcondi,onscomposingdecisionsis“true”atleastonceand“false”atleastonce


Decisionandcondi,oncoveragecont.d


Testcases{t=0;z=0;w=5}1ac.=T,2ac.=T,dec.=T{t=0;z=5;w=‐5}1ac.=F,2ac.=F,dec.=FCoverdecisionsandcondi,onsandiden,fybothdivisionbyzero

instatementsCandD

/*A*/floatz=InOut.readFloat(),w=InOut.readFloat();t=InOut.readFloat();/*B*/if(z==0||w>0)/*C*/w=w/z;/*D*/elsew=w+2/t;/*E*/System.out.println(z+''+w+''+t);

Summaryoftestcasessofar


Testcase

t z w cond.1 cond.2 decis. FindserrorinC?

FindserrorinD?

C1 0 0 5 T T T yes no

C2 0 5 5 F T T no no

C3 0 0 ‐5 T F T yes no

C4 0 5 ‐5 F F F no yes


Coveragecriterion

Associatedtestcases

FindserrorinC?

FindserrorinD?

Decision C2+C4 no yes

Condi,on C2+C3 yes no

Decisionandcondi,on

C1+C4,or

C2+C3+C4 yes yes

Methodologicalissue

•  Therearedifferentcombina,onoftestcasesthatguaranteedecisionandcondi,oncoveragebutitisnotalwaystrivialtofindone

•  Weneedasimpleandeffec,vemethodforiden,fyingtestcasesthatcoverbothdecisionsandcondi,ons


Controlflowgraph’spathscoverage

•  Basedon– Criteriaofdecisionandcondi,oncoverage– Program’scontrolflowgraph

•  Goal– Toprovideasimplemethodforguaranteeingdecisionandcondi,oncoverage


Controlflowgraph


while(A){if(B){C}else{D}E}F;

node

arc

region Example:V(G)=7‐6+2=3V(G)=3

Predicatenodes

A

B

CD

E

F

Cycloma,cnumber• V(G)=E‐N+2(E=numberofarcs,N=numberofnodes)• V(G)=R(R=numberofregions)

Controlflowgraph


Sequenceofstatements

Simpleif

un,l

whilecase

Controlflowgraphwithoutcondi,ons


A

B

CD

E

False True

Thecontrolflowgraphshouldbemoredetailed


Controlflowgraphwithcomplexdecisions


if(a||b)x;elsey;

b==F

...

a

b

xy

...

a==Ta==F

b==T

if(a&&b)

x;elsey;

...

a

b

yx

...

a==Fa==T

b==Fb==T

Controlflowgraphfortheprogram


A

B

CD

E

False True

A

z

w

CD

E

==0!=0

<=0 >0

ControlflowgraphWithoutcondi:ons

Controlflowgraphwithcondi:ons


Controlflowgraph,condi,onsanddecisions

•  Booleanvalues(“true”and“false”)associatedwithcondi,onsanddecisionshavecorrepondingarcs

•  Todesignasetoftestcasessuchthatallarcsofthecontrolflowgrapharetraversedimpliescondi,onanddecisioncoverage


Pathsofthecontrolflowgraph

•  Thesetoftestcasescorrespondstoasetofpathssuchthatalleveryarcistraversedatleastonce

•  Thenumberofpathssufficientforcoveringallarcsisalwaysequalorlessthanthecycloma,ccomplexity


Forthepreviousexample


ThreetestcasesC2.{t=0;z=5;w=5}C3.{t=0;z=0;w=‐5}C4.{t=0;z=5;w=‐5}Coverallarcs,hencedecisionsandcondi,ons

V=7‐6+2=3Thethreepaths1.  A‐z‐w‐C‐E (C2)2.  A‐z‐C‐E (C3)3.  A‐z‐w‐D‐E (C4)


A

z

w

CD

E

==0!=0

<=0 >0

Howtochoosepaths

•  Pragma,crule–  Experimentsshowthatthethenumberoferrors

increasewithincreasingofthecycloma,ccomplexity

–  Chooseanumberofpathsequaltothecycloma,ccomplexity

–  Youhaveapropor,onbetweennumberoftestcasesandcomplexityofthecode


Linearlyindependentpaths

•  Agoodcriterionforchoosingpathsisbasedontheconceptoflinearindependency

•  Amaximalsetoflinearlyindependentpathsiscalledabase–  ItisNOTunique

•  Abasecontainsanumberofpathsequaltothecycloma,ccomplexity

•  Intui,vely,everypathinput‐outputcanbeobtainedasalinearcombina,onofpathsofabase

•  Bychoosingabase,acertainextendofreliabilityidguaranteedwithrespectofcombina,onsoferrorsthathideeachother


Exampleofpaths


while(A){if(B){C}else{D}E}F;

Pathsα. A‐Fβ. A‐B‐D‐E‐A‐Fγ. A‐B‐C‐E‐A‐F

A

B

CD

E

F

1

2 3

4 5

67

Arcs/paths

1 2 3 4 5 6 7

α 0 0 0 0 0 0 1 β 1 1 0 1 0 1 1 γ 1 0 1 0 1 1 1

Thematrixrankis3(themaximum){αβγ}isabase

Remarks•  Everypathcorrespondstoabinaryrowvector(0/1)•  Viceversadoesnothold•  Amatrixrepresen,ngpathshasmaximum2Edis,nct

rows(E=n°archi)•  McCabeprovedthatforeachgraphG:

1.  ThematrixrankcannotbegreaterthanV(G)(cycloma,ccomplexity)

2.  ThereexistsalwaysamatrixmadeofpathswithrankequaltoV(G)

•  Abaseisanysetofpaths(rows)withmaximumrank•  Note:MacCabe’sresultispurelytopological

/*B*/if(5>7)/*C*/i=9•  ArcB‐Cisnevercovered•  Inothercasesisnecessarytore‐iteratethecyclesin

ordertotraverseallarcs


A

B

CD

E

F

1

2 3

4 5

67

Arcstraversableonlybyitera,ons


/*A*/intz=InOut.readInt();intt=0;/*B*/while(t<100)/*C*/ if(t>20)/*D*/t=t+90;/*E*/elset=t+z*z;/*F*/System.out.println(t);

A

B

C

ED

K

t>=100t<100

t<=20t>20

F

B‐FC‐DRequireatleastoneitera,oninordertobetraversed{10}A‐B‐C‐E‐K‐B‐F{5}A‐B‐C‐E‐K‐B‐C‐D‐K‐B‐F

Fakenode

Addi,onalconsidera,ons

•  Pathscoveragemethoddoesnotconsiderexplicitlyloopsitera,ons

•  Insomecasesitisnecessarytoperformitera,onsinordertotraverseallarcs

•  Itmightbeinteres,ngtoconsidersomeitera,oninanycasebutthenumberoftestcasesincreasesexponen,ally

•  Itisimportanttodecidethetypeofitera,ons


Pragma,cchoicesforloops

•  Tolimitthenumberofitera,onston–  Itiscalled“loopcoverage”

•  Toexecuteonlycertainloops•  Tolimitthenumberofpathstobetraversedbasedonweightedarcsandfunc,ontobemaximized–  Probabilityofexecu,on–  Resourcesoccupancy

•  Tolimitthenumberofpathsbyiden,fyingthepathsthatdefineanduseprogramvariables(DataFlowtes,ng)–  Defini,onofavariablevalue–  Useofsuchvalueinatest


DataFlowTes,ng


...Aintx,y,a,b;Bscanf(“%d%d”,&x,&y);Ca=x;Db=yEwhile(a!=b)Fif(a>b)Ga=a‐b;Helseb=b‐a;Iprin~(“%d”,a);....

D

E

I

F

a!=b

C

B

HG

a==b

a<=ba>b

Forxandyitisnotneededtoexecutetheloop(loopcoverage=0)Forthedefini,onofaandbtheloophastobeiteratedonce(loopcoverage=1)Forthedefini,onandusageofaandbtheloophastobeiteratedtwice(loopcoverage=2)

white box testing

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