T app, Pe e ; Facchi, Ch is ian
Wo king Pape
Pe o mance imp o emen using dynamic pe o mance
s ubs
A bei sbe ich e - Wo king Pape s, No. 14
P o ided in Coope a ion wi h:
Technische Hochschule Ingols ad (THI)
Sugges ed Ci a ion: T app, Pe e ; Facchi, Ch is ian (2007) : Pe o mance imp o emen using
dynamic pe o mance s ubs, A bei sbe ich e - Wo king Pape s, No. 14, Fachhochschule Ingols ad -
Uni e si y o Applied Sciences, Ingols ad ,
h ps://nbn- esol ing.de/u n:nbn:de:b b:573-292
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h ps://hdl.handle.ne /10419/202566
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Pe o mance Imp o emen
Using Dynamic
Pe o mance S ubs
Dipl.-Ing. (FH) Pe e T app
P o . D . Ch is ian Facchi
A bei sbe ich e
Wo king Pape s
Kompe enz scha Zukun
C ea ing compe ence o he u u e
F a c h ho c h s c h u l e
I n g o l s a d
U n i e s i y o
Applied Sciences
Pe o mance Imp o emen
Using Dynamic
Pe o mance S ubs
Dipl.-Ing. (FH) Pe e T app
P o . D . Ch is ian Facchi
A bei sbe ich e
Wo king Pape s
He N . 14 aus de Reihe
"A bei sbe ich e - Wo king Pape s"
ISSN 1612-6483
Ingols ad , im Augus 2007
Abs ac
DynamicPe o manceS ubs suppo pe o mance imp o e-
men .Theycan beused o iden i y“hidden”bo lenecks
and also o p o idebe e es ima ions o he gain om pe -
o mance imp o emen . The ideabehind heses ubbing
mechanismwill bedesc ibed, he co e concep willbeex-
plained andaclose look on he possibili yo c ea ings ubs
will begi en. Fu he mo e an in oduc ion on “How o use
dynamicpe o mances ubs”is also included.
Dynamic Pe o mance S ubs
1In oduc ion
Cu en pe o mance imp o emen s ollowa
s ic line:analysis- es -imp o emen - e -
i ica ion.Thisp ocedu e dependss ongly on
he expe ience o he pe son ealizing a pe o -
mance op imiza ion and can only oughly be
used o es ima ions. Oneo he p oblems us-
ing hisme hodology is hecos -bene i anal-
ysis o imp o emen possibili ies. The expe
has o know hecomple e sys em a a e y
de ailedle elwhichis ha dlypossible wi hin
la ge so wa ep ojec s.Ano he p oblem o
his app oachis ha heop imiza ion has o be
donewi hou eally knowing howmucho he
module has o beop imized [1]. Is i enough o
sligh ly modi y pe o mance-c i ical unc ions
o is i necessa y o ind anewalgo i hm o
he comple e p ocedu e?
A e he op imiza ion o some pa s no -
mally o he addi ional pe o mance bo le-
necksdelay he execu ion imeo he compo-
nen unde s udy (CUS) [1].Wi hou knowing
all bo lenecks inad ance heimp o emen e -
o maylead o an unexpec edly smallgain.
Mos o hese p oblemscan bebypassed
wi h he dynamicpe o mance s ub.I com-
bines pe o mance measu emen s wi h he well-
known echniques o s ubbingused in heim-
plemen a ion and es phase o so wa e de-
elopmen . Tode elop dynamicpe o mance
s ubs hepe o mance o he al eadyexis ing
so wa emodules(sys ems unde es , SUT)
ha e o bes udieda a e y de ailedle el and
se e al bo lenecksha e o beiden i ied.This
pe o mance beha io can bemodeled using
hepe o mancesimula ion unc ions(PSF).
The esul ingpe o mance s ub can beused
o modeling di e en pe o mance beha io s
o he eplaced uni , o es ima ing heachie -
ablegain o o iden i y o he bo lenecks.
The e a e wodi e en esea chscopesin
simula ion o hepe o mance beha io . In
[2] i isexplained howpe o mance o inne
loopscan bemodeled a heins uc ion le el
and whiche ec heyha eon hememo y/-
cache pe o mance. Al hough he possibil-
i yo modelingso wa e modules exis s, he
high deg ee o g anula i yo his app oach e-
duces heusabili y o s ubbing whole so -
wa e unc ions/modules. In [3] he usage o
sma s ubs o so wa e analysis o unc ions
and modules whicha epa ly no a ailable
ye is desc ibed.The e o e he s ubs simula e
hebudge ega ding s o age and iming e-
sou ces, whichha ebeen es ima ed, o he o-
be-implemen edso wa e pa s. Also mainly a
managemen poin o iew o he non-exis ing
so wa ewill be aken.Howe e , hedynamic
pe o mances ubs in ou app oachwill beused
o s ubbing al eadyimplemen ed and mea-
su ed so wa epa sin o de o ind he bounds
o he pe o mance imp o emen wi hin ha
pa . This p ocedu ehelps o iden i y he eal
gain o he pe o mance imp o emen wi hou
eally imp o ingi andaddi ionally shows he
nex bo leneck. So hecos -bene i analysis
o imp o emen ac i i iescan beachie ed in
amo e ealis ic way,because ap ope simu-
la ed esul is be e han asimple es ima ion.
All esul s willbe e i iedinp ac ice on
aso wa epla o m o UMTS deli e ed by
Nokia Siemens Ne wo ks.
The es o hepape is s uc u ed in he
ollowing way.Sec ion 2p o ides asmall
o e iew abou cu en pe o mance imp o e-
men sand he me hodo pe o mance engi-
nee ing ega ding o pe o mance s ubs.Sec-
ion 3desc ibes he design o dynamicpe o -
mances ubs.Ame hodo using s ubs o pe -
o mance imp o emen can be oundin Sec ion
4. Sec ions 5and 6handle head an agesas
well as p oblemsand es ic ions o he pe o -
mance s ubs. Conclusions and u u ewo k a e
desc ibed in Sec ion 7.
2Classi ica ion o Dynamic
Pe o mance S ubs
The aim o eachso wa e pe o mance op i-
miza ion p ojec is o ind bo lenecks and o
op imize he co esponding so wa e uni in o -
de o educe he execu ion ime [4, 5]. A
bo leneckis he pa o heso wa ewi h he
highes u iliza ion/delayandcon ibu es mos
-1-

Dynamic Pe o mance S ubs
o he used ime in o al espec i ely o he
h oughpu o asys em. Imp o ing his bo -
leneckhas he s onges e ec on hesys em
pe o mance and iden i yingi is hemos chal-
lengingpa in each pe o mance enginee ing
p ojec [5].
An o e iew o ape o mance e alua ion
s udycan beseen in he Box2.2o [5] o in
[6]. In o ma ion abou ools usedin pe o -
mance imp o emen s udiesa edesc ibed and
classi ied, e.g. in [7] and[8].
Beside o he s aigh o wa d so wa e pe -
o mance op imiza ion p ocedu e he e is also
amo e gene al app oach o ensu e he qual-
i yo he so wa e ela ing o he pe o mance.
I ’s called“pe o mance enginee ing” (seealso
[9]) and combines se e al concep so so wa e
enginee ingand pe o mance imp o emen dis-
ciplines.
Pe o mance imp o emen usingdynamic
pe o mances ubs con ibu es o someo he
pa s o hepe o mance enginee ingme hod.
The desc ip ions a e aken om [6]:
•Pe o mance Measu emen
Measu emen s on exis ing so wa e o e -
i ype o mance c i e ia o oiden i yspe-
ci ic pe o mance p oblems.
•Pe o mance Tuning
Adiscipline o imp o eslowcodein o de
o each hepe o mance a ge s.
•So wa eEnginee ing
Adiscipline o de elop la ge so wa esys-
ems.
•So wa eQuali yAssu ance
Includes equi emen s o audi sand o
so wa ep oduc quali ye alua ions.
The dynamicpe o mance s ubs models he
pe o mance beha io o so wa e moduleso
bo lenecks andcan beused o measu ingand
uning heso wa e. Addi ionally heycan be
aken o es ing whichisapa o he so wa e
de elopmen p ocess. The e o ei con ibu es
o he “so wa e quali yassu ance”.
3DynamicPe o mance
S ubs
As al eadydesc ibed, he concep o dynamic
pe o mances ubs combines he me hods o
so wa e es ing [10, 11, 12] and pe o mance
imp o emen s[5, 7, 8, 13]. The ea e only li le
di e encesbe ween s ubbing o pe o mance
imp o emen sand s ubbing o es ing easons.
No mally s ubs a e used o simula ing emo e
sys ems o o non-exis ingso wa e modules
and unc ions,as in so wa e es ing [14]. In
his app oach he CUS will be eplaced bydy-
namic pe o mances ubs in o de o simula e
hepe o mance beha io o his so wa e uni
as ap ima ygoal. Thisp ocedu e ela es o
s ubbing a single so wa e uni and hence i will
be called“local”. The pe o mancesimula ion
unc ions (PSF) can also beused o change he
beha io o he comple e sys em. The e o e a
so wa emodulehas o be c ea ed whichin-
e ac s “global” in he sense o in luencing he
whole sys em ins ead o only one so wa euni .
sys em
so wa e componen
(SUT)
bo leneck
(CUS)
dynamic pe o mance s ub
(local)
simula ed so wa e
unc ionali y (SSF)
pe o mance simula ion
unc ions (PSF)
pe o mance measu emen
unc ions (PMF)
calib a ion unc ions
(CF)
dynamic pe o mance
s ub (global)
Figu e 1: In e ac ions o “Dynamic Pe o -
mance S ubs”
Figu e 1ske ches hedesign and he in e -
ac ion be weena eal sys em and he dynamic
pe o mances ubs.Thelined a owdesc ibes
a eplacemen . Filleda owheadsdesc ibe he
ex ension o auni by his ea u eand he
dashed blockp o ides an addi ional unc ion-
ali y o hedynamicpe o mances ub and will
no eallys ubaso wa e uni .
The amewo ko hedynamicpe o mance
s ub consis s o he ollowing pa s whicha e
p esen edinFigu e 1:
-2-
Dynamic Pe o mance S ubs
•simula ed so wa e unc ionali y(SSF)
•pe o mance simula ion unc ions (PSF)
•pe o mance measu emen unc ions
(PMF)
•calib a ion unc ions(CF)
The simula edso wa e unc ionali y (SSF)
is addi ionally implemen edcode in o de o
simula e he unc ional beha io o heal eady
exi ingCUS. Mo e in o ma ion abou apossi-
bleme hodology o s ubbing o al eady exis -
ingso wa emodules will bedesc ibed in Sec-
ion 3.2.
A e c ea ing he unc ional s ub(using he
SSF) he pe o mance beha io o he CUS
can bemodeled using hepe o mancesimu-
la ion unc ions (PSF). They will p o ide he
possibili y o simula e di e en isola ed pe o -
mance pa ame e s suchas he ime spen in he
componen . The unc ions can be combinedin
o de o simula e he“ eal” pe o mance be-
ha io . Please e e o Sec ion 3.3 o awide
iew o pe o mance pa ame e s whichcan be
simula ed by he PSF.
Some basic pe o mance e alua ionscan
bedone wi h he pe o mancemeasu emen
unc ions (PMF). Theywillp o ide a ough
o e iew o he sys em beha io , e.g. henum-
be o con ex swi ches while he s ub has been
execu ed. Thepe o mancemeasu emen unc-
ions onlyex end he possibili ies o hes ubs
and does no ha e o beincludedin he s ub.
They can also be eplaced bymo e speci ico
de ailed pe o mance measu emen ools,such
as [15, 16, 17].
Addi ionally he concep o he dynamicpe -
o mance s ubs con ains hecalib a ion unc-
ions (CF). These a e impo an o he ini-
ial se upo he s ubs o he a ge , e.g. he
ime needed o an “emp yloop”will bede-
e mined ino de o se upa ealis icbeha -
io .This measu emen will bedone using he
pe o mancemeasu emen unc ions.The cali-
b a ion unc ions ha e o be execu edonce o
eachha dwa e sys em.
3.1 BasicDesign Decisions
The majo decisions ega ding he design and
implemen a ion o he dynamicpe o mance
s ub a e:
1. The p og amming language usedin he
p ojec byNokiaSiemens Ne wo ks is
C/C++. The e o e he dynamicpe o -
mances ubs ha e o bew i en in C. This
language has se e al ad an ages suchas
hepossibili yo inling assemble code i a
high op imiza ion le el is necessa y.Addi-
ionally C/C++ can be compiled andused
as abina yexecu able code o he na i e
machine language o he CPU used. This
is highly ecommendedin [18] since he
p og amming language in luences hepe -
o mance o hecomple e sys em. Mo e-
o e ,mos o heC/C++ compile s p o-
idedi e en op imiza ion lags, e.g. [19].
Howe e , he me hodology o hedynamic
pe o mances ubis independen o he
implemen a ion language andcan alsobe
used wi h in e p e ed, jus -in- ime compi-
la ion o in e media e code.
2. The simula ion unc ionsshould becon ig-
u able and adjus able o he a ge . This
should bedone only once du ing he se up
o hes ubs.
3. Some basicpe o mance measu emen
unc ionsshould bea ailable.Thisisnec-
essa y o calib a ing he pe o mance sim-
ula ion p ope ies and o p o ing ha he
s ubsa e wo king p ope ly.
4. The simula ion unc ions o he pe o -
mance beha io should beused as a
oolse . All unc ions should beaccessible
wi hou u he need o con igu a ion.
3.2 Simula ed So wa e Func ional-
i y(SSF) -S ub Gene a ion
Commonly as ub inso wa e enginee ing is
used as ap oxy and p o ides an adequa e
eplacemen o hebeha io o he o-be-
implemen edso wa emodulesand unc ions.
-3-
Dynamic Pe o mance S ubs
I is mainly usedin so wa e es ing o dis-
ibu edsys ems o in modula izedso wa e
[12].
The e o e he s ubbed unc ion uses he
sameI/O pa ame e s o simula e he missing
p ocedu e and p o ides only abasic unc ional-
i y,e.g. i e u ns he esul s by eading hem
om ahash able,doesno hingo i maysim-
plyw i e ace messages.F om hesys ems
poin o iew hes ubwill beincluded and
wo k jus as he eal p ocedu e [14].
The ideabehind he simula edso wa e unc-
ionali y and he unc ional s ubsisnea ly he
same. Theonly di e ence be weens ubbing
o pe o mance easons and hegene a ion o
“ es -s ubs” as men ioned is he pa o so -
wa e whichwill beused. S ubbing o pe -
o mance easons means o eplacean al eady
exis ing code whe eas s ubbing o es ingc e-
a es basic unc ionali yo non-exis ingso wa e
[12, 14] o hey a e used o emo e sys ems.
Ame hodology o s ubbingal eady exis ing
and de e minis ic so wa e unc ions can bede-
sc ibed as ollows.Fi s o all hein- and ou -
pu alues o heCUS ha e o beiden i ied
while acing hem. The e o e p ope ace-
poin s ha e o beinse edin he sou ce code
and hen he so wa e has o be e- un wi h
ap ope andde e minis ic es casescena io.
Rew i e he CUS using he in-and ou pu al-
ues (e.g. using a hash able)and by eplacing
he ime consuming unc ions whe e he so -
wa e no mally walks h ough. Now he s ub
should bewo king p ope ly.
3.3Pe o mance Simula ionFunc-
ions (PSF)
APSFsimula es he non- unc ional beha io
o a unc ion ega ding o one aspec o pe -
o mance. Theya e di ided in o ou classes
acco ding o he pe o mance bounds o which
aso wa ecan belong. Fo amo ede ailed
desc ip ion he eade is e e ed o [20]. The
classesa e as ollows:
•CPU
•Memo y
•I/O
•Ne wo k
A i h ca ego y can be hough o is heUse
[5], in ou app oachi will beincluded o sim-
pli ica ion in he I/O ca ego yo he PSF.
Almos eacho he ca ego ies can bedi ided
in o a globally isibleand alocally isiblepa .
Thesesubdi ision indica eswhe he he s ub
will only ha elocal in e ac ions o i i will a -
ec he whole so wa e sys em (global). This
is needed o classi ica ion o hePSFand
shouldno bemixedwi h heglobal-and local
dynamicpe o mances ub men ioned in Sec-
ion 3whe e he s ub can be ealized as e-
placemen o aso wa e pa o can beused
globally,e.g. as ake nel module.Aclose look
in he ca ego ies will begi en in he ollowing
subsec ions.
3.3.1CPU-PSF
This PSF ela es o heclockcycles used by
heso wa e. One pa o he CPU-PSFis he
ime spen in hes ub, whilei is scheduled.
This is called globally isiblebecause no o he
module can use he CPU while he s ub is un-
ning a he same ime.In hecaseo alocally
isible CPU-PSF hemodule will beblocked
due o a iminge en . He e heCPU is ee
o o he p ocesses.An exampleimplemen a-
ion o aglobal-and local isible ealiza ion o
hePSFsimula ing heCPU is alsogi en.
Example o alocally isible CPU-PSF
Tosimula e he locally isibleCPU-PSF,which
means ha he eal p ocess is blocked/wai ing
o an e en , can behandled easily byle ing
i sleep o he desi ed ime.
Implemen a ion Fo ins ance in he
UNIX en i onmen he “usleep()” unc ion can
beused.Fo de ails see“unis d.h”.
Example o aglobally isible CPU-PSF
The globally isible s ubbingo CPUcycles can
be ealized using“noope a ion”(NOP) so ha
-4-
Dynamic Pe o mance S ubs
he esou ce CPU will beused by his PSF.
They ha e o beexecu ed in aloop in o de o
each he desi ed ime consump ion. The main
p oblem is ha he “used cycle”should no a -
ec anyo he pa o he sys em,e.g. he da a
L1-Cache o hep ocesso . Addi ionally he
NOPsand also he loop ha e o bep o ec ed
agains compile op imiza ions.
Implemen a ion An exampleimplemen-
a ion can beseen in Lis ing 1. The unc-
ion “useCycles” akesa alue s anding o he
p ocesso cycleswo king o “usec” as inpu .
The “TIME” cons an is de inedwi hin he dy-
namic pe o mances ub and has been e alu-
a ed using he calib a ion unc ions.He eeach
i e a ion will exac ly consume 1µswhile loop-
inga ound he emp ys a emen “;”.
oiduseCycles(longusec )
{
longi=0;
o (i=0; i <usec ∗TIME; i++)
{
;
}
}
Lis ing1: example implemen a ion o aglobally
isible CPU-PSF
This is onlyasimpli iedexample andcould
lead o non- ep oduceable esul s i he h o -
ling unc ionali yo he CPUis swi ched on.
3.3.2Memo y-PSF
Memo y wi h espec o PSF e e s o he
ola ile s o age. Mo e in de ail hedi e en
ypeso memo y desc ibed in his sec ions a e:
•main memo y
•caches
• egis e s
Main Memo y The delay ime o he main
memo y s ongly depends on hea chi ec u e
[21]. These dependencies can behandledin he
se upo hedynamicpe o mances ubs using
hecalib a ion unc ions.Al hough hepag-
ing/swapping mechanisms a e o en handled as
I/O, i will bein eg a ed o his PSFca e-
go y.The eason o his is he cohe ence be-
ween he lacko memo y and paging/swap-
ping. Mo eo e , ou de ini ion abou I/O-PSF
doesno ma ch due o he ac ha he eis no
sys emcall caused by he applica ion o dopag-
ing/swapping. Addi ionally i is ecommended
o deac i a e paging/swapping in high pe o -
mance applica ions o inc ease hep edic abil-
i yo hesys emsbeha io .
The classi ica ion in o locally-and globally
isible can also bedone.An only locally isible
in e ac ion o he PSF o he main memo y
can be ealized bylocking anysize o memo y
whichisonly locally a ailable o he s ub.As
longas enough memo y emains o hesys em,
no swapping o paginghas been caused by he
lockedpa s.Thesys emwill “s ays able” and
hes ubcan use i is own memo y.
Fo aglobally isible in luence he same
me hodology can beused.Ins ead o p o ec -
ing hesys em om paging/swapping hisbe-
ha io willbe o ced bylocking a la ge amoun
o memo y.This will lead o memo y misses
and esul s in ha d discaccesses.
Caches Cu en p ocesso s ha e cache hie -
a chies,e.g. he L1-, L2- and L3-Caches. De-
pendingon he model he e can alsobedi e -
en L1-Caches o da a and ins uc ions [22].
The a chi ec u e whichis cu en ly used wi hin
ou esea ch p ojec does no p o ideaL1 In-
s uc ion Cache. The e o e in his i s ap-
p oachonly L1 Da a Cacheswill be akenin o
conside a ion.The sys emp o ides hepossi-
bili yo con olling he caching o ins uc ions
and da a h ough di e en dedica ed egis e s
and se e al bi s.Also hepossibili y o lush
o o disable hecaches is gi en.These p op-
e ies can beused o he globally-and locally
isible manipula ion o he caches.Fo he
globally isible manipula ion heal eady men-
ioned ea u e o disabling he caching mech-
anismcan beused. This will lead o an in-
-5-
Dynamic Pe o mance S ubs
dence. Also mul ip ocesso a chi ec u es
ha e obe aken in o accoun .
•The combina ion o di e en PSFshas o
beexamined o simula e ealis ic sys em
beha io .
•The me hodologyo heusage o pe o -
mance s ubshas o be elabo a ed mo e in
de ail and o be e i ied bydi e en case
s udies. Especially ame hodhow o eal-
ize decomposi ion o pe o mance a ge s
o smalle componen s has o be c ea ed.
•Ame hodology o s ubbing non-
de e minis ic unc ions has o be
elabo a edas well as he e alua ion
echniques, e.g. s a is ical e alua ionso
hepe o mance measu emen esul s.
•Awide ange o e alua ion echniques
and he esul ingconclusions, e.g. iden-
i yingchangeo e s om sys em bounds
should bes udied.
•The loss o p ecision o pe o mance mea-
su emen s using PSFcompa ed wi h eal-
is ic op imiza ions has o be examined.
•The possibili y o suppo heso wa e de-
elopmen p ocessbyusing dynamicpe -
o mance s ubs has o bes udied.
•All unc ions ha e o besuppo ed bya
oolse , whichhas o beimplemen ed.
All desc ibedopen poin s will beexamined
in heongoing esea chp ojec .
8Acknowledgmen
This esea chisg an ed byNokia Siemens Ne -
wo ks. The au ho swould like o hank he
UMTS g oup, especially D .Rudol Baue ,
Helmu Voggenaue and S e en Wagne as ep-
esen a i es o he excellen suppo andcon-
ibu ions o his esea chp ojec .
Fo ca e ul eading and p o iding aluable
commen s on d a e sions o his pape we
would like o hank P o .D . S e an Hah-
ndel, Ma inusLuegmai ,D . Alexande Os
and Fabian Wohlschl¨age .
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-13 -
Biog aghy
Dipl.-Ing. (FH) Pe e T appis a esea chassis an a heIns i u
¨u Angewand e Fo schung o he Fachhochschule Ingols ad . His
esea chin e es s a ein he a eao pe o mance measu emen s
and analysis andin compu e secu i y.
Pe e T appwas bo nin 1978 a Neuende elsau, Ge many.A e
hisg adua e in Ele ical Enginee ingand In o ma ion Technology
a he Fachhochschule Ingols ad he was employed a BMWin he
blue oo h hands ee se de elopmen depa men .
D . Ch is ian Facchi is P o esso o SWEnginee ing, Dis ibu ed
Sys ems and Ma hema icsa he Fachhochschule Ingols ad , Ge -
manysince 2004. Hismajo esea chin e es s a e in hea ea o
pe o mance analysis and modeling, embedded sys ems, es ingo
So wa eand o mal desc ip ion echniques.
D . Facchi was bo n in 1964 a Munich, Ge many.Heholdsa
doc o al deg ee andadiplomadeg ee om he Technische Uni-
e si ¨a M¨unchen,Ge manybo h o Compu e Science. Be o e
he changed o heFachhochschuleIngols ad he has beenemployed
a Siemens in heMobile Phones de elopmen depa men o 9
yea s.Du ing his employmen a SiemensMobilePhones he was
hehead o wo ldwides a egy o SW de elopmen en i onmen s.
Imp essum
He ausgebe
De P äsiden de
Fachhochschule Ingols ad
Esplanade 10
85049 Ingols ad
Tele on: 08 41 / 93 48 - 0
Fax: 08 41 / 93 48 - 200
E-Mail: [email p o ec ed]
D uck
Hausd uck
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"A bei sbe ich e/ Wo king Pape s"
e scheinen in un egelmäßigen Abs änden.
Alle Rech e, insbesonde e das Rech de
Ve iel äl igung und Ve b ei ung sowie de
Übe se zung o behal en. Nachd uck, auch
auszugsweise, is gegen Quellenangabe
ges a e , Belegexempla e be en.
In e ne
Dieses Thema können Sie, ebenso wie die
ühe en Ve ö en lichungen aus de FH-Reihe
"A bei sbe ich e - Wo king Pape s", un e de
Ad esse www. h-ingols ad .de nachlesen.
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