BFCA+: Automatic Synthesis of Parallel Code with TLS Capabilities

Noname manusc ip No. (will be inse ed by he edi o ) BFCA+: Au oma ic syn hesis o pa allel code wi h TLS capabili ies Se gio Aldea, Diego R. Llanos, A u o Gonzalez-Esc ibano he da e o eceip and accep ance should be inse ed la e Abs ac Pa alleliza ion o sequen ial applica ions equi es ex ac ing in o - ma ion abou he loops and how hei a iables a e accessed, and a e wa ds, augmen ing he sou ce code wi h ex a code depending on such in o ma ion. In his pape we p opose a amewo k ha a oids such an e o -p one, ime- consuming ask. Ou solu ion le e ages he compile- ime in o ma ion ex ac ed om he sou ce code o classi y all a iables used inside each loop acco ding o hei accesses. Then, ou sys em, called BFCA+, au oma ically ins umen s he sou ce code wi h he necessa y OpenMP di ec i es and clauses o allow i s pa allel execu ion, using he s anda d sha ed and p i a e clauses o a i- able classi ica ion. The amewo k is also capable o ins umen ing loops o specula i e pa alleliza ion, wi h he help o he ATLaS un ime sys em, ha de ines a new specula i e clause o poin ou hose a iables ha may lead o a dependency iola ion. As a esul , he a ge loop is gua an eed o co ec ly un in pa allel, ensu ing ha i s execu ion ollows sequen ial seman ics e en in he p esence o dependency iola ions. Ou expe imen al e alua ion shows ha he amewo k no only sa es de elopmen ime, bu also leads o a as e code han he one manually pa allelized. Keywo ds: Au oma ic pa alleliza ion, compile amewo k, OpenMP, sou ce syn hesis, sou ce ans o ma ion, specula i e pa alleliza ion, XML. 1 In oduc ion One o he main conce ns o cu en compu e science is he s udy o pa allel capabili ies o bo h p og ams and p ocesso s ha execu e hem. Due o he huge numbe o sequen ial p og ams al eady w i en o many decades un il now, complexi y o pa allel p og amming languages, and knowledge equi ed o pa allelize sou ce code, a echnique ha au oma ically pa allelizes hem is ETS Ingenie a In o m ica, Uni e sidad de Valladolid, Paseo Beln 15, 47011 Valladolid, Spain Tel.: +34-983185642, ax: +34-983423671. E-mail: {se gio,a u o,diego}@in o .u a.es. 2 Se gio Aldea, Diego R. Llanos, A u o Gonzalez-Esc ibano qui e desi able. Howe e , au oma ic pa alleliza ion echniques cu en ly im- plemen ed in many comme cial compile s a e no able o pa allelize mos o he loops because o he possibili y o da a dependencies [3]. Th ead-Le el Specula ion (TLS) [6,8] is a un ime echnique ha can be used o un loops in pa allel ha may p esen dependency iola ions. TLS op imis ically assumes ha he code can be execu ed in pa allel, elying on a un ime moni o o ensu e co ec ness. I a dependency iola ion appea s a un ime, hese lib a y unc ions s op he o ending h eads and es a hem in o de o use he upda ed alues, hus p ese ing sequen ial seman ics. Un il now, specula i e echniques we e expe imen al, equi ing he manual in e en ion o expe p og amme s. These p og amme s i s ly needed o ex- ac ce ain in o ma ion abou he sou ce code ha hey aim o pa allelize, such as a iable usages wi hin each loop, o I/O unc ions ha complica e, o e en p eclude, he pa alleliza ion. The second s ep was o manually add all he unc ions and s uc u es needed o handle he specula i e execu ion. Ou esea ch g oup ha e been wo king se e al yea s in he p oblem o au oma ic syn hesis o pa allel code wi h TLS capabili ies. Ou p io wo k included he de elopmen o bo h an analysis amewo k, called BFCA, and a TLS un ime sys em, called ATLaS. –BFCA [2,4] is an analysis amewo k ha ex ac s p o iling and depen- dency in o ma ion o o loops in C code, in o de o de ec which o loops a e he bes candida es o pa alleliza ion. –ATLaS is a Th ead-Le el Specula ion (TLS) compile [19] and un ime sys em [1] ha ex ends OpenMP unc ionali ies wi h a new specula i e clause, o allow he pa alleliza ion o o loops ha a e no gua an eed a compile ime o be dependency- ee1. Du ing pa allel execu ion, a iables ha we e labeled as specula i e a e moni o ed a un ime. I a dependency iola ion occu , he h ead ha has consumed an inco ec alue is s opped and es a ed, ensu ing sequen ial seman ics. The use o bo h amewo ks g ea ly simpli ied he de elopmen o pa al- lel code, bu he in e en ion o an expe p og amme was s ill needed o ans o m he sequen ial code in o a pa allel e sion. The amewo k p esen ed in his pape closes he loop, allowing o he i s ime he au oma ic syn hesis o pa allel code wi h TLS capabili ies. BFCA+ elies on he da a e u ned by BFCA o au oma ically add he OpenMP di ec- i es needed o un a chosen loop in pa allel, ei he using he classic OpenMP di ec i es i he loop does no p esen dependencies among i e a ions, o us- ing he new OpenMP specula i e clause p o ided by ATLaS i he lack o dependencies canno be gua an eed a compile ime. Despi e i s in e nal complexi y, BFCA+usage is simple. A i s un ob ains p o ile in o ma ion o all loops in he applica ion, oge he wi h a classi ica ion o a iables usage in all o hem. A e examining hese esul s, he use should 1Only well- o med o loops whe e he numbe o i e a ions a e known a he beginning o he loop can be pa allelized by he ATLaS amewo k. See [1] o addi ional de ails. BFCA+: Au oma ic syn hesis o pa allel code wi h TLS capabili ies 3 choose a loop o pa allel execu ion. A second un o BFCA+wi h he line numbe o he chosen loop gene a es an OpenMP-based pa allel e sion o he loop, using he sha ed,p i a e, and he non-s anda d specula i e clauses o classi y loop a iables acco ding o hei usage. Thanks o his solu ion, any a ge loop is gua an eed o co ec ly un in pa allel while p ese ing i s sequen ial seman ics. Rega ding pa allel pe o mance, ou expe imen al esul s, ob ained by he execu ion o ou di e en benchma ks ha p esen dependency iola ions a un ime, show bo h a no iceable speedup (up o 13.5×speedup wi h 56 co es in he p esence o dependency iola ions) and good scalabili y. In e es ingly, he au oma ic ans o ma ion o he sequen ial code leads o be e pe o mance han hose ob ained when he use manually ans o ms he code o he same pu pose using ATLaS un ime unc ions di ec ly. 2 Rela ed wo k The gene a ion o sou ce code is a p oblem ha conce ns di e en a eas, such as e ac o ing, op imiza ion, and pa alleliza ion o sou ce codes. In he case o BFCA+, he e a e many di e en p oposals o he au oma ic pa alleliza ion o sou ce codes, and mo e pa icula ly, ocused on he syn hesis o OpenMP cons uc s. One o he i s a emp s o au oma ize he gene a ion o OpenMP con- s uc s is he POST p ojec [15], ha p o ides a simple en i onmen ha also allows he in e en ion o he use . A mo e ad anced sys em is Pa aWise/- CAPO [12,13,20], which uses a dependency analysis o c ea e he app op ia e OpenMP di ec i es o pa allelize simple and nes ed loops in Fo an applica- ions. I also applies a ce ain le el o op imiza ion ans o ma ions o enhance he quali y o he gene a ed code. This is also he case o PLuTo [21], a sou ce- o-sou ce amewo k ha uses he polyhed al model o op imize he code and gene a e OpenMP pa allel code au oma ically. G aphi e [14] is a b anch o GCC ha applies he polyhed al model o di e en pu poses, including he gene a ion o pa allel code, and p oposes an au o-pa alleliza ion op ion o GCC ha uses OpenMP s uc u es o de ine pa allel sec ions. This wo k inspi ed Polly [22], a simila p oposal bu ocused on a di e en compile : LLVM [24]. O he wo ks ha also use he polyhed al model such as Pa 4All [18]and PYPS [23] a e based on PIPS [17], a sou ce- o- sou ce amewo k. Pa 4All uses he analysis pe o med by PIPS o op imize and c ea e OpenMP (among o he s anda ds) sou ce codes. PYPS is a Py hon- based p og ammable pass manage , ha also gene a es OpenMP cons uc s. Unlike mos o he app oaches, which a e sou ce- o-sou ce pa allelize s ha au oma ically gene a e OpenMP di ec i es and clauses (e.g. Liao e al. [11], Ce us [10], o se e al o he p oposals seen abo e), Gaspa d2 [25] ollows a model- o-sou ce app oach. Gaspa d2 is a g aphical amewo k ha needs ha he code and he a ailable pa allelism be exp essed by he use wi h an UML- based model, which is hen ans o med in o an OpenMP model ha gene - 4 Se gio Aldea, Diego R. Llanos, A u o Gonzalez-Esc ibano a es he pa allel e sion o he sou ce code. Finally, YAO [16] is a g aph-based amewo k, ocused on he da a assimila ion mos ly o geophysical applica- ions, able o gene a e no only OpenMP cons uc s o pa allelize code egions, bu also a omic di ec i es o a oid ace condi ions. As we will see, like mos o he app oaches desc ibed abo e, BFCA+ ol- lows a sou ce- o-sou ce app oach, le e aging i s XML-based ep esen a ion o he sou ce code o analyze and augmen he code wi h OpenMP pa al- lel cons uc s, including ou specula i e clause [19]. This di e s om o he app oaches: BFCA+is able o syn hesize he code needed o handle he spec- ula i e execu ion o a ce ain p og am, c ea ing an OpenMP-based pa allel e sion om he sequen ial sou ce code. 3 BFCA+a chi ec u e and usage As we s a ed in Sec . 1, ou p oposal has been buil upon wo di e en solu- ions ha , un il now, wo ked independen ly o each o he . The i s solu ion is BFCA [4], an XML-based amewo k ha combines s a ic analysis o sou ce code wi h p o iling in o ma ion o gene a e comple e epo s ega ding all loops in a C applica ion, including loop co e age, loop sui abili y o pa al- leliza ion, a axonomy o hei a iables based on hei accesses, as well as o he hu dles ha es ic he pa alleliza ion. BFCA a chi ec u e is depic ed inside a dashed-line box in Fig. 1. BFCA+ex ends his amewo k o enable he syn hesis o sou ce code augmen ed wi h OpenMP di ec i es and clauses, in ended no only o au oma ically classi y a iables acco ding o hei usage (sha ed o p i a e), bu also o inse app op ia e OpenMP di ec i es o enable he au oma ic pa alleliza ion o he a ge loop (see he solid box in Fig. 1). In ce ain si ua ions, howe e , he pa allel execu ion o a gi en loop may ail due o he possibili y o un ime dependencies among i e a ions. This is whe e specula i e pa alleliza ion comes in o scene. When BFCA+de ec s such a si ua ion, i is also able o label as specula i e all a iables whose de ini ion o use may po en ially lead o a dependency iola ion. Unlike sha ed and p i a e clauses, he specula i e clause is no pa o he OpenMP s anda d, bu a new clause i s p oposed by ou g oup [2]. This p oposal was la e implemen ed in he ATLaS amewo k, he second solu ion BFCA+is buil upon. Wi h espec o he ATLaS compile and un ime amewo k [1], i is com- posed by wo main elemen s. The i s one is he compile suppo , hanks o a specialized GCC compile plugin ha de ec s he use o he specula i e clause, and augmen s he sou ce code wi h so wa e ha con ols he spec- ula i e execu ion o he loop. The second one is he un ime suppo , wi h unc ions ha moni o s a un ime he exis ence o dependency iola ions, and pe o ms co ec i e ac ions i such a iola ion akes place. These wo building blocks, BFCA and ATLaS, a e used oge he in BFCA+ o gi e a comple e solu ion o he au oma ic syn hesis o pa allel e sions o o loops. The use should i s un he amewo k o see which loops can be pa allelized, choose one, and le he au oma ic ans o ma ion sys em o BFCA+: Au oma ic syn hesis o pa allel code wi h TLS capabili ies 5 Inpu se P ofiling In o ma ion Sequen ial C sou ce code Loop co e age and a iables cha ac e iza ion XMLCe us In el Compile Bina y code XML sou ce code ep esen a ion P ofilaze XML sou ce code wi h p ofiling da a BonaFide C Analyze and T as o me (BFCA+) (Builds XML ee) (Me ges XML in o ma ion) Si ius (Rebuilds C sou ce) GCC 4.6.2 + plugin Run ime pa ame e s, including: - Th eads - Block size - Max. numbe o i e a ions - Max. numbe o specula i e elemen s TLS un ime lib a y Pa allel bina y execu able The ATLaS amewo k Linke XML sou ce code wi h OpenMP di ec i es (Queues XML ee) Loopes OMPlize (Augmen s XML ee) BFCA line numbe o he loop o be pa allelized (p og amme 's decision) C sou ce code anno a ed wi h OpenMP di ec i es (possibly including new specula i e clause) Fig. 1 O e iew o he BFCA+plus ATLaS a chi ec u e, ha analyzes he code, gene a es an OpenMP-based specula i ely-pa allel e sion o he code, and inally compiles i o c ea e an execu able ha uns in pa allel specula i ely. BFCA+ ./b ca+ -c <file>.c C sou ce code XML file BFCA+ ./b ca+ -x <file>.xml -p <loop_line> Loop epo + a iable classifica ion Specula i ely pa allelized C sou ce code Fig. 2 O e iew o he p ocess ha ans o ms a sequen ial C code in o a pa allel one. BFCA+au oma ically gene a es he OpenMP cons uc s, including he specula i e clause. gene a e an execu able ha is gua an eed o un co ec ly in pa allel. Wi hou BFCA+, p og amme s needed o manually classi y a iables o he loop ha hey aim o pa allelize, and hen, inse all he OpenMP cons uc s equi ed by ATLaS o pa allelize i specula i ely. BFCA+also sol es his p oblem, eeing p og amme s om his e o -p one, edious ask. Figu e 1 shows he a chi ec u e o BFCA+, and how i gene a es an OpenMP- based sou ce code ha is compilable by ATLaS o gene a e a specula i ely pa allel e sion o he code. As can be seen in he igu e, BFCA+ elies hea ily on BFCA, composed in u n by h ee main subsys ems: (1) XMLCe us, a mod- i ied e sion o Ce us [10] ha builds an XML ee ep esen ing he o iginal C sou ce code; (2) P o ilaze , ha execu es he code and augmen s he XML ee wi h p o iling in o ma ion; and (3) Loopes , ha exploi s XML capabili ies o 6 Se gio Aldea, Diego R. Llanos, A u o Gonzalez-Esc ibano 1#de ine NITER 1000000, MAX 100 2in a ay[MAX]; 3... 4 5 o (P=0;P<NITER;P++) 6Q = P % (MAX) + 1; 7aux = a ay[Q −1]; 8Q = (4 ∗aux) % (MAX) + 1; 9a ay[Q −1] = aux; 10 } Fig. 3 File p og am.c: F agmen o C code ha depic s a loop whe e he use o a da a s uc u e (a ay) may lead o a dependency iola ion. cha ac e ize e e y loop in he sou ce code, and pe o ms a axonomy o he a iables based on how hey a e accessed. BFCA+adds o his solu ion a new module, called OMPlize , ha syn hesizes OpenMP-based cons uc s o spec- ula i ely pa allelize he code. Finally, a i h module, called Si ius, ans o ms he XML ep esen a ion back o C. Figu e 2 summa izes he p ocess ha ans o ms a sequen ial sou ce code in o a pa allel one. In a i s execu ion, BFCA+ epo s abou each loop and how i s a iables a e accessed. Then, he p og amme only needs o poin ou he line numbe o he loop o be pa allelized. In a second execu ion, BFCA+ uses he in o ma ion on he a iable accesses o au oma ically augmen he XML ep esen a ion o he code by using OMPlize . OMPlize modi ies he XML node ha ep esen s he FOR loop, and inse s a new XML node wi h he OpenMP pa allel di ec i e and he co esponding clauses, acco ding o he a iable classi ica ion ha Loopes c ea es. This includes he inse ion o he specula i e clause wi h hose a iables ha may lead o a dependency iola- ion. Once OMPlize has augmen ed he XML ep esen a ion o he sou ce code, Si ius ans o ms i back in o a C ep esen a ion. Du ing his p ocess, he o iginal sequen ial code has been anno a ed wi h OpenMP cons uc s ha pa allelize i . Finally, ATLaS p ocesses hese OpenMP anno a ions, and pe - o ms all he changes needed in he loop o be un in pa allel using ou TLS un ime lib a y, including he eplacemen o he accesses o e specula i e a iables wi h he co esponding specula i e e sions o hese accesses. I is impo an o ema k ha , i he FOR loop being pa allelized does no con ain specula i e a iables, BFCA+gene a es he OpenMP cons uc s in o de o be pa allelized acco ding o he OpenMP s anda d. Despi e he complexi y o he ans o ma ion p ocess, he usage o he BFCA+ amewo k is simple. As an example, conside he sequen ial code de- pic ed in Fig. 3. A i s in oca ion o BFCA+(shown in Fig. 4) analyzes he sequen ial code s a ically and dynamically, p oducing bo h a epo wi h he cha ac e iza ion o he loop, and an XML ile ha me ges his s a ic cha ac- e iza ion wi h he p o iling in o ma ion o he loop co e age (Fig. 5). A second un o BFCA+, also shown in Fig. 4, allows he p og amme o indica e he s a ing line o he loop ha should be pa allelized. This second in oca ion gene a es an augmen ed e sion o he XML ile, called BFCA+: Au oma ic syn hesis o pa allel code wi h TLS capabili ies 7 $ b ca+ −c p og am.c ... p og am.c:5: Line numbe : 5 p og am.c:5: Numbe o lines: 5 p og am.c:5: Inclusi e Time Pe cen : 34.2 p og am.c:5: Exclusi e Time Pe cen : 34.2 p og am.c:5: I doesn’ con ain poin e a i hme ic. p og am.c:5: Numbe o Loop Con ol Va iables: 1 p og am.c:5: Loop Con ol Va iable: (in ) P. p og am.c:5: Va iables ead and w i en: (in ) Q, (in ) aux, (in ) a ay[100]. p og am.c:5: Va iables only ead: (in ) P. p og am.c:5: P i a e Va iables: (in ) Q, (in ) aux, (in ) P. p og am.c:5: Specula i e Va iables: (in ) a ay[100]. p og am.c:5: I is a well- o med FOR Loop. ... $ ls p og am.c p og am.xml $ b ca+ −x p og am.xml −p 5 $ ls p og am.c p og am.spec.c p og am.xml p og am.spec.xml $ ./a las − h eads 4 −block 100 −c p og am.spec.c −e p og am $ ls p og am.c p og am.spec.c p og am p og am.xml p og am.spec.xml Fig. 4 Usage o BFCA+in he pa alleliza ion o he loop in line 5 o he p og am.c ile depic ed in Fig. 3. The in oca ion o he ATLaS compile amewo k is also shown. p og am.spec.xml, ha includes he di ec i es needed o pa allelize he loop (Fig. 6). In addi ion, his second in oca ion ans o m he augmen ed XML ep esen a ion back o C. The esul , shown in Fig. 7, is a C ile con ain- ing a pa allel, specula i e e sion o a loop ha can no be pa allelized by pa allelizing compile s due o he possibili y o dependency iola ions. Finally, ATLaS is esponsible o ans o m he pa allel e sion o he code ha con ains he non-s anda d specula i e clause in o s anda d OpenMP di- ec i es plus addi ional code. The in e media e esul (be o e being e ec i ely compiled) is shown in Fig. 8. 4 E alua ion In o de o e alua e he capabili ies o BFCA+, we ha e used i o gene a e he OpenMP cons uc s (including ou p oposed specula i e clause) o some syn he ic and eal-wo ld benchma ks. The expe imen s ha e been designed o e i y ha he use o BFCA+leads o execu able iles ha a e unc ionally equi alen o hose manually pa allelized by an expe ienced p og amme . All he benchma ks used in he expe imen s a e no pa allelizable a com- pile ime due o se e al da a dependencies, equi ing un ime specula i e pa - alleliza ion. We ha e used se e al eal-wo ld applica ions whose main loops a e no pa allelizable a compile ime because o he possibili y o depen- dence iola ions, and he e o e equi e TLS o un in pa allel. They a e he 8 Se gio Aldea, Diego R. Llanos, A u o Gonzalez-Esc ibano 1<Fo Loop condi ion="P<1000000" ini ial="P=0;" leng h="7" lineNumbe ="6" 2s ep="P ++" en yCoun ="1" absTime="3161466" absTimePe cen ="41.6" 3sel Time="3161466" sel TimePe cen ="41.6"> 4<S a emen lineNumbe ="−1"> 5<Exp essionS a emen lineNumbe ="−1"> 6<Exp ession> 7<Bina yExp ession lhs="P" ope a o ="=" hs="0"> 8<Assignmen Exp ession> 9<Exp ession> 10 <IDExp ession> 11 <Iden i ie a ay="" name="P" opUna y="" ype="in "/> 12 </IDExp ession> 13 </Exp ession> 14 <Exp ession> 15 <Li e al> 16 <In ege Li e al alue="0"/> 17 </Li e al> 18 </Exp ession> 19 </Assignmen Exp ession> 20 </Bina yExp ession> 21 </Exp ession> 22 </Exp essionS a emen > 23 </S a emen > 24 <Exp ession> 25 <Bina yExp ession lhs="P" ope a o ="<" hs="1000000"> 26 <Exp ession> 27 ... Fig. 5 File p og am.xml: F agmen o he XML ep esen a ion c ea ed by BFCA o he loop in line 5 o Fig. 4 be o e being pa allelized. 1<Fo Loop anno a ion="OpenMP" condi ion="P<1000000" ini ial="P=0;" leng h ="5" 2lineNumbe ="6" s ep="P ++" en yCoun ="1" 3absTime="3161466" absTimePe cen ="41.6" sel Time="3161466" sel TimePe cen ="41.6"> 4 5<Anno a ion anno a ion="#p agma omp pa allel o de aul (none) 6schedule(s a ic) specula i e(a ay) 7p i a e(Q, aux, P)"/> 8 9<S a emen lineNumbe ="−1"> 10 <Exp essionS a emen lineNumbe ="−1"> 11 <Exp ession> 12 ... Fig. 6 File p og am.spec.xml: XML ep esen a ion o Fig. 5 augmen ed by OMPlize (high- ligh ed code). 2-dimensional Con ex Hull p oblem (2D-Hull) [7], he Delaunay T iangula ion using he Jump-and-Walk s a egy [9], he 2-dimensional Minimun Enclosing Ci cle (2D-MEC) p oblem [26], and a C implemen a ion o TREE [5]. The loops conside ed in he i s h ee applica ions a e he main loop o he codes, ha consumes almos 100% o he execu ion ime. Fo TREE, we ha e pa - allelized he ACCEL loop, ha consumes 95.17% o he o al execu ion ime. 2D-Hull and 2D-MEC a e execu ed wi h a en-million-poin da ase , Delaunay wi h a one-million-poin da ase , and TREE wi h a da ase o 4096 nodes. BFCA+: Au oma ic syn hesis o pa allel code wi h TLS capabili ies 9 1#de ine NITER 1000000, MAX 100 2in a ay[MAX]; 3... 4#p agma omp pa allel de aul (none) 5p i a e(P, Q, aux) specula i e(a ay) 6 o (P=0;P<NITER;P++) 7Q = P % (MAX) + 1; 8aux = a ay[Q −1]; 9Q = (4 ∗aux) % (MAX) + 1; 10 a ay[Q −1] = aux; 11 } Fig. 7 File p og am.spec.c: C ep esen a ion o p og am.spec.xml as e u ned by he Si ius module o BFCA+. 1#de ine NITER 1000000, MAX 100 2in a ay[MAX]; 3... 4specbegin(NITER) 5#p agma omp pa allel de aul (none) 6p i a e(P, Q, aux, ini, cu en , id, e lag, alue) 7sha ed(a ay, wheel_ns, wheel_ms, wheel, uppe _limi , a block) 8{ 9#p agma omp o schedule(s a ic) nowai 10 o ( id = 0; id <= 3; id = id + 1) { 11 ini = 0; 12 cu en = id; 13 P = a block[0][cu en ]+ini; 14 i (i > uppe _limi - 1) 15 go o labelSquash_1; 16 a block[2][cu en ] = a block[2][cu en ]+1; 17 labelS a I e a ion_1: 18 Q = P % (MAX) + 1; 19 //aux = a ay[Q −1]; 20 i (specload_poin e ((unsigned cha *) &(a ay[Q-1]), 21 sizeo (a ay[Q-1]), cu en , (unsigned cha *) & alue) == -1) 22 ea lySquash(1); 23 aux= alue; 24 Q = (4 ∗aux) % (MAX) + 1; 25 //a ay[Q −1] = aux; 26 specs o e_poin e ((unsigned cha *) &(a ay[Q-1]), 27 sizeo (a ay[Q-1]),cu en ,(unsigned cha *) & alue); 28 labelEndI e a ion_1: 29 i ((P != a block[1][cu en ] + ini) && (i < NITER - 1)) { 30 P=P+1; 31 go o labelS a I e a ion_1; 32 } 33 labelSquash_1: 34 e lag = h eadend_poin e (¤ ); 35 i ( e lag == JOBDONE) go o labelEndLoop_1; 36 i ( e lag == JOBTODO) { 37 i = a block[0][cu en ] + ini; 38 a block[2][cu en ] = a block[2][cu en ] + 1; 39 go o labelS a I e a ion_1; 40 } 41 labelEndLoop_1: 42 ; 43 }// o loop 44 }// p agma omp pa allel Fig. 8 Code gene a ed by ATLaS a e p ocessing he sou ce code o he syn he ic bench- ma k augmen ed by BFCA+(shown in Fig. 7).