A Novel Thermal Optimization Flow Using Incremental Floorplanning for 3D ICs *

Transcription

1 A Novel Termal Optmzaton Flow Ung Incremental Floorplannng for 3D IC * 4B- Xn L Yucun Ma Xanlong Hong Department of Computer Scence & Tecnolog, Tngua Unvert, Beng 00084, P.R.Cna Emal: mc@mal.tngua.edu.cn Abtract: Termal ue a crtcal callenge n 3D IC degn. To elmnate otpot, pcal laout are alwa aduted b ftng or duplcatng ot block. However, tee modfcaton ma degrade te packng area a well a nterconnect dtrbuton greatl. In t paper, we propoe ome novel termal-aware ncremental cange to optmze tee multple obectve ncludng termal ue n 3D IC. Furtermore, to avod random ncremental modfcaton, wc ma be neffcent and need long runtme to converge, ere potental gan modeled for eac canddate ncremental cange. Baed on te potental gan, a novel termal optmzaton flow to ntellgentl cooe te bet ncremental operaton preented. We dtngu te termal-aware ncremental cange n tree dfferent categore: mgratng computaton, growng unt and movng otpot. Mxed nteger lnear programmng (MILP model are deved accordng to tee dfferent ncremental cange. Expermental reult ow tat mgratng computaton, growng unt and movng otpot can reduce max on-cp temperature b 7%, 3% and 5% repectvel on MCNC/GSRC bencmark. Stll, expermental reult alo ow tat te termal optmzaton flow can reduce max on-cp temperature b 4% compared to an extng 3D floorplan tool CBA, and aceve better area and total wrelengt mprovement tan ndvdual operaton do. I. INTRODUCTION Wt te fat rnkng of devce ze, nterconnect dela become te crtcal bottleneck of cp performance. Treedmenonal (3D ntegraton, a fgure ow, recentl a drawn muc attenton due to t potental for reducng te nterconnect dela and complext a well a promng g ntegraton dent. Fgure 3D IC tecnolog Toug 3D IC a man advantage, tere are ome gnfcant callenge along wt t adopton and furter development. Wt mult-devce laer degn, te vertcall tacked multple laer of actve devce caue a rapd ncreae of power dent and te termal conductvt of te delectrc laer nerted between devce laer for nulaton qute low. Conequentl, one extremel mportant ue n 3D IC degn te termal problem reultng from bot ger power dent and lower termal conductvt. Recentl, everal work on termal optmzaton durng floorplannng for 3D IC ave been propoed [,, 3, 4]. [] propoed a termal-drven floorplannng algortm for 3D IC. It ue a mulated annealng wt an ntegrated compact termal *T work upported b te NSFC and Tngua Bac Reearc Fund JC00700 model. [] propoed termal-aware floorplannng for 3D mcroproceor. Te power conumpton of nterconnect condered durng floorplannng. Toug te termal-aware SAbaed approace can ndeed dtrbute eat evenl acro te cp to mtgate termal ue, tere no guarantee to elmnate otpot completel, ometme otpot tll ext. To aceve muc lower on-cp temperature, mnor cange ma requre a tart-over of te floorplannng proce, wc uffer from long runtme and poor performance calablt. Incremental floorplannng, owever, could provde a novel approac: once a good reult obtaned, extra termal mprovement can be aceved effectvel b elmnatng te otpot ncrementall rater tan retartng a new general floorplannng. In te meantme, for an extng floorplan, [5] pont out tat allocatng more de area to block epecall to ot functonal unt(growng unt actuall a an mmedate mpact on te temperature. Stll, mgratng computaton(mc[6, 7] provde an attractve wa to mtgate termal ue. It requre a duplcated block of te ot block to are computaton tak, wc can effcentl reduce power dent of te ot block o a to reduce te max on-cp temperature. Evaluaton from [8] ow tat mgratng computaton urel an effcent tecnque to decreae max on-cp temperature. Indeed, all tee metod can be mplemented b effectve ncremental modfcaton to avod random operaton. (a ntal floorplan (b ncremental floorplan Fgure growng unt and addng duplcated block Obvoul, mgratng computaton demand a new duplcated block wle growng unt wll enlarge te otpot block. In fact, bot tee metod, a addng block and expandng block, wll modf te ntal floorplan, wc would degrade total wrelengt or overall packng area. Take Fgure a an llutraton, te lne wt arrow denote nterconnecton between block. In te ntal floorplan a own n fgure (a, block B need a duplcated one to mgrate computaton and block A need to grow. Fgure (b te ncremental floorplan, were block A enlarged and block C a clone of block B wc newl added. After re-placng te block, te total wrelengt mgt be ncreaed. Tu an effcent model requred for ncremental modfcaton to aceve good tradeoff between termal optmzaton and oter obectve. Epecall n 3D IC degn, ncremental optmzaton a promng wa to andle mult-obectve optmzaton wt complcated contrant and facltate te degn reue tecnolog. Several work concerned wt ncremental floorplannng for D IC degn [9, 0,, ] ave been propoed, but none a taken termal-aware 3D IC degn nto conderaton. [3] propoed a LP baed approac to optmze wte pace to facltate termal va nerton, but t ard to be extended to manage uc ncremental cange a movng block between dfferent laer /09/$ IEEE 347

2 4B- Addtonall, te model formulaton alone barel guarantee preemnent reult on bot runtme and fnal obectve. For te purpoe of optmzng termal ue durng floorplannng, te queton raed: tere ndeed ext everal ncremental cange to cooe, but wc operaton te bet one tat brng excellent tradeoff? Select randoml or attempt b brute-force? It eem to be not a good dea, for t ma be neffcent and need long runtme to converge. To free degner from t dffcult decon-makng, n t paper, we propoe a novel termal optmzaton flow, wc can automatcall cooe te bet procedure, baed on potental gan for eac poble ncremental operaton. Te flow would brng great beneft to degner mung about ow to appl ncremental metod. Our contrbuton are ummarzed a follow: MILP baed termal-aware ncremental metod. We categorze tree dfferent ncremental cange n 3D IC and provde correpondng MILP formulaton repectvel. Smultaneou optmzaton for cp area, total wrelengt and termal-drven ncremental cange. Wt effectve MILP baed formulaton, our approac can andle multple obectve and varou contrant for 3D IC at te ame tme. Termal-aware optmzaton flow. Mot mportantl, we propoe a novel termal-aware optmzaton flow, wc cooe te ncremental operaton automatcall rater tan manuall to cut degn cot and attan g-qualt reult. II. OVERVIEW OF THERMAL-AWARE INCREMENTAL FLOORPLANNING PROBLEM Te otpot, wt gnfcantl ger temperature tan urroundng cooler regon, could reduce cp relablt and lead to catatropc falure. To effectvel elmnate te otpot, ome ncremental cange can be ued wle te orgnal packng doe not need to be canged gnfcantl. Our termal-aware ncremental floorplannng an teratve optmzaton flow. Te correpondng problem can be decrbed a: Gven a multlaer packng wt a et of n block M={M, M,, M n } n K laer, were w and pecf te dmenon of block M repectvel, a et of net N={N, N,, N m } were N, =,,, m decrbe te connecton between block, we want to generate a new packng were te orgnal topologcal relaton between mot block reman uncanged o tat: te max on-cp temperature can be reduced a muc a poble; total wrelengt and cp area are degraded lttle compared wt te orgnal degn. To mtgate termal ue, tree dfferent ncremental floorplannng tratege can be appled:. Growng unt to allocate more de area around otpot to reduce max on-cp temperature. In growng unt, te power dent decreaed proportonall to te ncreae of te de area, wc can effectvel reduce temperature ncreae from te otermal pont accordng to [5].. Mgratng computaton among duplcated block. In mgratng computaton, te otpot block requre a duplcated one to are computaton tak, wc mean to alve te power dent to reduce te temperature of otpot block. 3. Movng certan ot block to cooler regon. W te otpot come nto beng tat te regon t locate at uuall a g power dent and poor eat dpaton. Terefore, movng certan ot block from te ottet regon to relatvel cooler area, actuall can reduce termal couplng n te ottet regon and decreae te max on-cp temperature, nce t could reduce power dent and mprove te eat dpaton of te ottet area,. It mut be notced tat tee modfcaton are ut bac ncremental cange n 3D floorplannng wc wat for te degner to cooe. Moreover, ut coong one operaton randoml, rater tan ung an effcent tactc to gude, ardl enure a derable reult of toe multple obectve. To accompl a better tradeoff, we roll out an evaluaton crteron, a potental gan, to elect te mot utable operaton to proce te teratve flow to mtgate te termal ue, and optmze area and total wrelengt. III. THERMAL RESISTANCE MODEL For temperature proflng, we ue te ame termal retve model a []. Te 3D crcut dvded b a two-dmenonal arra of tle tack, a own n Fgure 3(a. A tle tack modeled a a retve network. Eac tle tack compoed of everal vertcalltacked tle, a own n Fgure 3(b. Tee tle tack are connected b lateral termal retance R lateral. Wtn eac tle tack, a termal retor R modeled for te -t devce laer, wle termal retance of te bottom laer and lcon ubtrate modeled a R b a own n Fgure 3(c. Te otermal bae of room temperature are modeled a a voltage ource. A current ource preent at ever node n te network to repreent te eat ource. One can patall dcretze te tem and olve te followng equaton to determne te teadtate termal profle a a functon of power profle. T P A ( were A an K K pare termal conductvt matrx. T and P(t are K temperature and power vector. K te number of termal conducton edge. (a Tle Stack Arra (b Sngle Tle Stack (ctle Stack Anal Fgure 3 Retve termal model for 3D IC IV. MILP FORMULATION FOR GENERAL FLOORPLANS To develop MILP baed metod for termal-aware ncremental cange n 3D IC, multple obectve and varou contrant ould be condered at te ame tme. In t ecton, we wll frtl ow ow to model tee ue n general floorplannng. We ue te tecnque from [7] n te followng ubecton A and B. A. LP model for certan topologcal Relaton Gven a multlaer packng, t ea to repreent te topologcal relaton n lnear contrant to prevent overlappng between an par of rectangular block and on te ame laer, followng te tecnque n [7]. In te ncremental optmzaton, block would devate from te orgnal packng poton. Let (x, and (x, denote te poton of te lower left corner of block and repectvel. From te extng floorplan baed on certan multlaer repreentaton uc a CBA[] and LTCG[5], we can fnd te correpondng relatve poton of block, wc keep uncanged n te optmzaton proce. A a conequence, to prevent overlappng between orgnal block and on te ame laer, one of te followng lnear nequalte mut old: x w x f left to ( x w x f rgt to f below f above B. MILP model for uncertan topologcal relaton If a new block added to te extng packng, te relatve relaton between t new block and te old block are unknown. To enure tat one of te nequalte n ( old uc tat te new block doe not overlap te preent block, two addtonal 0- nteger varable x and, wc take onl eter 0 or value, can be ntroduced a n [7]. Let u defne boundng contant B w and B 348

3 4B- uc tat we alwa ave x -x B w and - B. Poble coce for B w and B are: B w =w and B =. Aume block te newl added block, we can derve te followng contrant: x w x Bw ( x x w x Bw ( x (3 B ( x B ( x Snce tat x and take ut eter 0 or value, t obvou tat onl one of te nequalte n ( take effect for an combnaton of value of x and. For an ntance, f and onl f x =0 and =0, te frt contrant of ( appled, wc allow block to be anwere left to block. Bede, te remanng tree contrant are defntel actve for an admble coce of (x,, (x,. In addton, f te new block allowed to rotate n te ncremental floorplannng, an addtonal bnar varable r can be emploed to meet t requrement. We can defne r a follow: wen r=0 te new block added n t orgnal orentaton wle r= te new block nerted b rotatng 90 o. Terefore, (3 can be rewrtten a follow: x ( r w r* x M ( x x w x M ( x (4 ( r r* w M ( x M ( x Were: M = max(b w, B (5 C. LP formulaton of cp area We propoe a new optmzaton model for cp area. Aume W and H are te wdt and te egt of te orgnal packng repectvel, to preerve te ntal mnmum packng area, addtonal nequalte for eac block are needed a follow: x 0, 0, xw W, H (6 If te extng floorplan a enoug wte pace to enlarge block or add block, fxed-outlne contrant (6 can be atfed naturall. However, f te floorplan are tgtl packed, te entre cp area mgt be expanded f ome block mut be enlarged or ome new block mut be nerted. To mnmze te area ncreae, we can ntroduce two lack varable lack and w lack a follow: mn wlack * lack t.. wlack 0, lack 0 for te extng block : (7 x 0, 0, xw W* wlack, H* lack for newl added block : x 0, x ( r wr* W* wlack, 0, r* w ( r H* lack were r te rotaton 0- varable. Evdentl, cp area mnmzed f and onl f w lack * lack mnmzed. Obectve w lack * lack not lnear, but f we note te nequalt: w lack lack w lack * (8 lack wc ugget tat (w lack + lack / te upremum of w lack * lack, ten we can ue te followng approxmaton for area obectve: mnmze w lack * lack (equvalent to mnmze w lack * lack ere b mnmzng t upremum (w lack + lack /. In realt, te dfference between te wdt and te egt of te ame extng floorplan o mall tat t lnearzaton could ow good approxmaton. Even f te contrant allow lack and w lack to be an large value, te optmal LP oluton wll enure tat lack and w lack are et to be te mallet value from tee contrant. D. LP model for wrelengt(hpwl We model HPWL optmzaton ung model from [5]. Aume te pn are at te center of te correpondng block and eac net a four varable x max, x mn, max, and mn repreentng t four boundar edge of te boundng box, (x pn, pn repreent te pn locaton of block I, N te et of net of te floorplan. Obvoul eac block of net n te net boundng box, wc ultmatel reult n LP contrant a follow: xpn xmn, xpn xmax (9 pn mn, pn max x pn x w /, pn / Total wrelengt etmated b HPWL could be mnmzed a: mn ( (0 x x N max mn max mn V. MILP BASED THERMAL AWARE INCREMENTAL FLOORPLANNING METHODS A. Specal 3D contraned modfcaton Our formulaton could provde a flexble wa to andle contraned modfcaton n 3D IC. Here we demontrate two knd of uc modfcaton: addng block wt algnment contrant and movng block between laer. Addng block wt algnment contrant: Suppoe we ave two block M and M n te extng floorplan wc mut be algned from g-level degn requrement. Wen a new block added, t contrant ould tll be atfed undoubtedl. A fgure 4 ow, new block A doe not dturb te algnment of M and M. M M (a M and M are algned (b nert A wle algnng M and M Fgure 4 addng block wt algnment contrant To meet t requrement, we frt contruct te contrant for uncertan topologcal relaton between te new block and te block on target laer. In addton, we et te algnment contrant between M and M b algnng ter lower left corner a: x = x, = ( In fact, alo we can multaneoul add multple block tat ave algnment contrant wt eac oter. T contrant ueful epecall n uc floorplan tat ave cube block, wc are packed acro everal laer n 3D IC. Movng block between laer: In qute a few cae, block ould be moved to oter laer for better reult uc a maller cp area. To andle t modfcaton, we can delete te block from t orgnal laer ten contruct new contrant for te uncertan topologcal relaton between te movng block and oter block on target laer. We delete block b ut makng t wdt and egt to be zero: w = 0, = 0 ( B. MILP model for growng unt Aume te area of block enlarged to, allocatng more de area to te ot functonal unt(growng unt allow w and to var atfng w =. T equaton n nature nonlnear and cannot be appled drectl n te MILP approac. Smlar to [9], we can lnearze te nonlnear relaton w = / b ung a et of everal lnear contrant a own n Fgure 5. Dfferent from [9], wc olved LP model teratvel to reze floorplan, we create MILP model to grow te block ut once. A M M 349

4 4B- w l 4 w = Fgure 5 lnear approxmaton of w = / Eac lnear contrant fned b applng te frt two member of te Talor ere for eac nterval: l 3 l mn 3 max w ( f (, max 3 max max w ( f (, ] w ( f (, ] w ( f (, ] mn l 3 max ] (3 In order to make ure tat onl one of above equalte old n te growng unt proce, we ntroduce two addtonal ntermedate 0- nteger varable a and b to aceve correpondence between te lnear equalte and te nterval of. Frtl we fnd te one to one correpondence between te nterval and value of a and b : max M( a b, 3 M( a b 3 M( a b, M( a b (4 M( a b, M( a b M( a b, mn M( a b Te defnton of M te ame a (5. It ea to ee tat for eac of te four poble coce of (a,b =(0,0,(0,,(,0,(,, onl one nterval contan, and vce vera. For example, wt a =0 and b =0, onl te frt couple of nequalte n (4 can take off M, and te remanng contrant are automatcall atfed for an poble value of. Tat mean tat can not be located n an oter nterval but n ( 3, max ]. In te followng we could aceve te contrant to atf te correpondng relaton between nterval and lnear functon: w lm( a b, w lm( a b w lm( a b, w lm( a b (5 w l3m( a b, w l3m( a b w l M( a b, w l M( a b 4 4 were: l ( max, l ( 3 max max 3 3 l3 (, l 4 ( (6 Now te one-to-one correpondence between nterval and lnear functon created. To demontrate te relaton more clearl, we ee a more pecfc llutraton: If n nterval (, ], due to contrant (4, ten te (a,b mut be (,0, wc ugget tat onl te trd couple of nequalte n (5 take effect, tat w =l 3. Clearl t content wt (3, were f n nterval (, ], ten w =l 3. In fact, te accurac of lnear approxmaton can be mproved b ung a larger et of lnear contrant, wc et conume longer runtme nce more nteger varable are requred. In our experment, we ave approxmated t quadratc functon b a et of 4 lnear contrant, wc tll ow bot good approxmaton and runtme performance b mulaton reult. C MILP model for movng ot block W te otpot come nto beng tat te regon t locate at uuall a g power dent and poor eat dpaton. Terefore, removng te ot block from te ot regon to relatvel cooler area, wc could reduce power dent and mprove te eat dpaton of te ot area, actuall reduce termal couplng n te ot regon tu reaonabl can decreae te max on-cp temperature. Te target laer, were te ot block wll be moved to, could be an laer ncludng t orgnal laer. T a pecal 3D modfcaton dcued prevoul n ubecton V-A: Movng block between laer. More mportantl, te ot block ould be eparated from te orgnal ot regon a far a poble,.e., to approac te cooler block on target laer a cloe a poble. Here we appl Manattan dtance between te pn to approxmate te dtance between te ot block and te relatvel cooler block. Aume C te et of cooler block on coolet regon, t proce can be formulated a follow: mn E ( x x ot max mn max mn C pn max pn max pn mn, pn mn pn max, pn max pn xmn, pn mn t.. x x, x x x x (7 were (x pn, pn and (x pn, pn repreent te locaton of pn of otpot block and te cooler block, repectvel. B mnmzng te Manattan dtance, we can make ot block to ecape from te ot regon. E ot can be ued a an etmaton for termal optmzaton, for t etmate te dtance between te block moved and te cooler block. D. Termal-aware computaton mgratng Mgratng computaton requre a duplcated unt to are computaton tak wt otpot block, wc mean alf te wtcng power dent o a to reduce te max on-cp temperature[7]. Te duplcated block te clone of te otpot block. Meanwle, te net(pat tat are attaced to otpot block ould alo be replcated for te new block. Stll, a movng otpot doe, wen nerted nto te cp, te duplcated block alo ould be eparated from te ottet regon a far a poble b contrant mlar to formulaton (7. Bede, te wrelengt contrant (9 and (0 ould be et up between te duplcated block wt toe block wc are among te ame net (pat wt te otpot block. E. Smultaneou optmzaton of multple obectve After all relevant MILP model ave been completed, we can etabl te metrc for tee termal-aware ncremental modfcaton. Multple obectve,.e., cp area(a, termal(e ot, and total wrelengt(wl, can be condered a follow: mn * A * E ot * W L (8 Were, and are normalzed wegt factor. VI. THERMAL-AWARE OPTIMIZATION FLOW In order to reduce maxmal on-cp temperature a muc a poble, we propoe a novel termal-aware ncremental optmzaton flow. An ntellgent gudance appled to pck te bet ncremental modfcaton to be executed n te teratve flow. To better control te optmzaton proce, we mut analze te temperature contrbuton from dfferent block to te otpot. Over tee temperature ncreae and block area, we can calculate potental gan for eac canddate ncremental modfcaton. Fnall, t te operaton tat could brng te larget potental gan to be elected to carr out. A. temperature ncreae from block on te ame laer [0] provde an analtcal model for termal profle n D cp. T approac model te block a a round regon wt te ame area value a te orgnal block telf, and te radu of te equvalent crculart etmated b a= w /. Baed on t aumpton, temperature ncreae from block to te otpot could be calculated b: T (, * * / (9 a r P a k Were, 350

5 4B- t ci 0 ( m r 0 r ( a, r ab c 4 K 0 ( m r r t / ab I ( m c, c c ( ( m 4 I m I 0 ( m K 0 ( m K K ( m (0 r t r, B, m a a k kt Te meanng of te mbol are: r dtance between te otpot and te center of block, te coeffcent of termal tranfer, t block tckne, k te termal conductvt of materal per unt volume, P block power, I 0 and I are modfed Beel functon of te frt knd wle K 0 and K are modfed Beel functon of te econd knd. Upon tee equaton, te termal effect on te otpot from toe block n te ame D plane can be reolved. B.Temperature ncreae from block on lower laer Accordng to te termal retance model, block n lower laer alo affect te termal dtrbuton n otpot regon. To deal wt t cae, te etmaton for temperature ncreae would be determned n two ucceve tage. Frtl, te block on te lower laer wll be proected to te top laer. In te econd tage, temperature ncreae from te proecton block to te otpot determned b (9. A C Were T te temperature ncreae, A te block area(for rezng block, t te rezed area, and are normalzed wegt. T computaton wll be ncorporated nto te optmzaton flow a a gudance to cooe te mot favorable ncremental operaton. D. Optmzaton flow In te flow, we frt ue termal mulator to fnd out te poton of te otpot, ten calculate te potental gan agant toe fve canddate modfcaton. Afterward, we do cooe te one tat can brng maxmal potental gan for executng. Mxed nteger lnear programmng(milp model created accordngl. Te flow wll reterate above procedure unle obectve value cannot be optmzed. Followng our teratve flow cart: movng adacent block movng otpot block movng te block under te otpot Intal floorplan Temperature profle and fnd te otpot block rezng otpot bock compute potental gan for tee canddate operaton repectvel cooe te block k wt maxmal potental gan execute te correpondng operaton mgratng computaton B R4 R3 R R+Rb Fgure 6 Proecton from B to C Take fgure 6 for example, otpot block A on top laer, block B on te ub-top laer wle block C, te proecton of B on top laer, a te ame ape and orzontal poton wt B. To make tee two block ave te ame termal effect, te power of block C mut be determned accordng to te termal retance model a follow: 3 R b R (0 PC PB * 4 R R b Now, proecton block C on te ame laer wt otpot block A, wc ndcate tat we can ue (9 to compute te termal contrbuton of block C: T PC * ( a, r* a / k ( T temperature ncreae could be condered a contrbuton from block B. C. Potental gan for te ncremental cange In te optmzaton flow, we wll conder te followng poble ncremental modfcaton a canddate operaton: movng adacent block of te otpot block, movng te otpot block, movng te block under te otpot, rezng te otpot block, and mgratng computaton. To cooe te bet canddate tat would brng good tradeoff between termal and cp-area, we mut conder te potental gan f certan operaton on te block executed to make t n te deal locaton. Snce tat t dffcult to etmate te nfluence on wreleng n t tage, we make total wrelengt a one obectve to optmze rater tan a a crteron for electng a canddate. Terefore, te potental gan for takng operaton on block could be aceved a follow: g * T + * ( A no obectve mproved? fn e Update te optmal value Fgure 7 termal-aware ncremental modfcaton flow VII. EXPERIMENTAL RESULTS We ave mplemented te termal-aware ncremental floorplannng n C++ language, and all experment are performed on a.6ghz Intel PC. We olve te MILP problem ung a leadng LP olver glpk[8]. Te tle arra n eac laer et a 3030 for eac bencmark and te temperature profle are generated b a fat retance mulator from[]. Te power dpaton of eac block are agned to te ame value wt [](rangng from 0 5 W/m to 0 7 W/m. Te ambent temperature et to be 7 o C. We tet te propoed algortm on MCNC and GSRC bencmark. All ntal floorplan are 4 laer tacked and generated from SA-baed 3D floorplannng algortm CBA[]. Table ow te parameter of te ntal floorplan, ncludng block number, net number, cp area, max temperature and total wreleng. Man tecnque uc a plp( n Parquet[8] could be ued to recontruct te SP/contrant grap from te extng placement. Table : Intal Floorplan Block# Net# Area(um T max ( o C WL(um Am Am N N N Avg. Jut a [7] propoed, b mgratng computaton between two te, te actvt for eac block alved, wc mean alf te wtcng power dent and alf te temperature ncreae from te otermal pont. Hence, to facltate mulaton, we can add a duplcated unt for otpot block ten alf te power dent of bot otpot block and duplcated block to mplement mgratng computaton. A. Termal-aware ncremental floorplannng metod We mplement toe tree bac termal-drven ncremental operaton: movng ot block, growng unt and mgratng computaton. In te movng operaton, we onl elect otpot block to move nce ere we ut compare tee tree bac operaton and 35

6 4B- movng ot block of oter tpe wll be ntroduced n ubecton B. Eac acton executed onl once ere. Becaue te ntal floorplan are packed tgtl, te fnal packng are all enlarged to facltate addton and growt of block. Table ow te expermental reult of our approace. Growng unt enlarge te otpot block b 3 tme on average. A can be een, growng unt, mgratng computaton and movng otpot block reduce max oncp temperature b 7%, 3% and 5% repectvel. Movng otpot te bet n mtgatng termal ue. Growng unt decreae temperature te leat, but t brng te lgtet area ncreae and can reduce total wrelengt a well. Mgratng computaton can notabl reduce max temperature but enlarge total wrelengt nce te duplcated block ntroduce extra connecton wt oter block. B. Optmzaton flow for te 3D cp We run our flow tat nclude fve poble ncremental cange on toe floorplan generated from CBA[]. Te flow wll not ext untl no obectve mprovement can be aceved, or te cp area enlarged b more tan 0% toug t ma brng great termal abatement. Table 3 ow te reult of te optmzaton flow. A can be een from te table, compared wt CBA, our approac can reduce te maxmal temperature b about 4%, ntroducng lttle tme overead, wc ow rapd degn convergence. Meanwle, total wrelengt alo decreaed b %. Becaue te orgnal floorplan are packed tgtl, te cp area enlarged b 3% and te optmzaton terate onl a few tme accordng te area contrant. Te runtme manl pent on olvng te MILP formulaton rater tan nvokng te olver. Note tat t flow eem to ave almot te ame termal optmzaton effect a movng otpot block doe, owever, te flow can attan maller cp area and total wrelengt, wc ow te effectvene of te flow to brng better tradeoff. VIII. CONCLUSION In t paper, we propoe ome novel termal-aware ncremental cange to optmze tee multple obectve ncludng termal ue n 3D IC. Furtermore, to mprove tme-to-market va degn ccle reducton, ncremental degn mut move from an expert metodolog to a mantream degn metodolog: one tat automated, ntegrated, relable, and repeatable. To avod random ncremental modfcaton, wc ma be neffcent and need long runtme to converge, ere potental gan modeled for eac canddate ncremental cange. Baed on te potental gan, a novel termal optmzaton flow to ntellgentl cooe te bet ncremental operaton preented. We dtngu te termal-aware ncremental cange n tree dfferent categore: mgratng computaton, growng unt and movng otpot. Mxed nteger lnear programmng (MILP model are deved accordng to tee dfferent ncremental cange. Expermental reult ow tat mgratng computaton, growng unt and movng otpot block can reduce max on-cp temperature b 7%, 3% and 5% repectvel on MCNC/GSRC bencmark. Stll, expermental reult alo ow tat te termal optmzaton flow can reduce max on-cp temperature b 4% compared to an extng 3D floorplan tool CBA, and aceve better area and total wrelengt mprovement tan ndvdual operaton do. REFERENCES [] J.Cong, J. We and Y. Zang, A Termal-Drven Floorplannng Algortm for 3D IC, n Procceedng of ICCAD, 004 [] W. L. Huang, G.M. Lnk, Y. Xe, N. Vakrnan and M.J Irwn, Interconnect and Termal-Drven floorplannng for 3D mcroproceor, n Procceedng of ISQED, Mar. 006 [3] Z.P. Gu, Y. Yang, J. Wang, R.P. Dck and L. Sang, TAPHS: Termal aware unfed pcal-level and g-level nte, n Procceedng of ASP-DAC, 006 [4] P. Zou, Y. Ma, Z. L, R.P. Dck, L. Sang, H. zou, X.L. Hong and Q. Zou, 3D-STAF: Scalable Temperature and Leakage Aware Floorplannng for Tree Dmenonal Integrated Crcut, In procceedng of ICCAD, 007 [5] C.H. Ta and S.M.S Kang, Standard cell placement for even on-cp termal dtrbuton, n Procceedng of ISPD, 999 [6] K. Skadron, M.R Stan, W. Huang, S. Veluam, K. Sankaranaraanan D. Taran, Temperature-aware Mcroarctecture, n Procceedng of ISCA, 003. [7] S. Heo, K. Barr and K. Aanovc, Reducng power dent troug actvt mgraton, n Procceedng of ISLPED, Aug., 003. [8] T.D. Rcardon and Y. Xe, Evaluaton of Termal-aware degn Tecnque for Mcroproceor, n Proceedng of ASICON, 005. [9] J. Cong and M. 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Markov, Fxed-outlne Floorplannng: Enablng Herarccal Degn, IEEE Tran. On VLSI tem, Vol.,No., pp.0-35, Dec.003. [9] P. Cen and E.S. Ku, Floorplan Szng B lnear Programmng Approxmaton, n Proceedng of DAC, 000 [0] B. Lall, A. Ortega and H. Kabr, Termal Degn Rule for Electronc Component on Conductng Board n Pavel Cooled Encloure, n Proceedng of nter-ocet Conference on Termal Penomerna, 994 Table : Reult of dfferent termal-aware Incremental Floorplannng Growng unt Mgratng computaton Movng otpot block Area(um T max ( o C WL(um Cpu( Area(um T max ( o C WL(um Cpu( Area(um T max ( o C WL(um Cpu( Am Am N N N Avg Bencmark Table 3: Reult of te teratve optmzaton flow CBA CBA + optmzaton flow Block# Net# Area(um T max ( o C WL(um Cpu( Area(um T max ( o C WL(um Cpu( Iteraton# Am Am N N N Avg