Clustering Techniques for Coarse-grained, Antifuse-based FPGAs

Transcription

1 Clustring Thniqus or Cors-grin, Antius-s FPGAs Chng-woo Kng n Mssou Prm Astrt In this ppr, w prsnt r n prormn-rivn lustring thniqus or ors-grin, ntius-s FPGAs. A mro logi ll in this lss o FPGAs hs multipl inputs n multipl outputs. Strting with this mro ll, lirry o smll logi lls n gnrt n trgt ntwork ws mpp with th lirry. For th minimum-r lustring, our lgorithm minimizs th numr o rquir mro logi lls to ovr ntwork. Two linr qutions wr st up n w oun th optiml mpping solution y using th qutions. For th prormn-rivn lustring, th numr o mro logi lls on th ritil pth is minimiz y using th xtnsion o Lwlr s lgorithm. Th rsults show tht th r-rivn lustring lgorithm ru th numr o mro logi lls y 2.29% n th prormnrivn lustring ru th mximum pth y 44.75% ompr to ommril tool.. Introution Fil progrmml gt rrys (FPGAs) n provi mny vntgs ovr stnr lls. Fst tim-to-mrkt stisis inustry signrs to kp up with nwly rt stnrs, n onigurility provis lxil hrwr on mn o oth nw stnrs without riting nw hip. On th othr hn, thr r som spts, whih must signiintly improv in th nr utur. Ar, sp, n powr issiption r still r hin stnr lls. Th rtios o r, sp, n powr issiption o SRAM-s FPGAs ompr to stti CMOS implmnttion r 0x, 3x, n 00x, rsptivly, oring to [7] n [8]. Cors-grin, ntius-s FPGAs hv mrg s promising thnology or smll r, high sp, n low powr. Figur shows ors-grin, ntius-s pasic3 logi ll [9], whih hs 29 inputs inluing th lok n iv outputs. Th untion o th logi ll is trmin y th logi lvls ppli to th inputs o th AND gts n multiplxrs. Th high logi pity n n-in o th logi ll ommot mny usr untions with singl lvl o logi ly. Cors-grin, ntius-s FPGA rhittur mns highly intllignt CAD lgorithms, us th rhittur provis trmnous lxiility with smll hrwr ovrh. For xmpl, th siz o n ntius, to onnt two mtl wirs is smllr thn vi [9]. In this ppr, w prsnt oth r-rivn n prormnrivn lustring thniqus. Evn w trgt spii logi ll rhittur, our mtho n ppli to similr typ o orsgrin, ntius FPGAs with slight moiition. W hv ivi it into svrl s gts n thn mpp ntwork. Atr thnology mpping, w oun th minimum numr o mro logi lls to ovr th ntwork y stting up two linr qutions. From th qutions, w oun ithr th minimum rossing points or th minimum vlu unr rtin rngs. For prormn-rivn lustring, w minimiz th numr o pasic3 logi lls on th ritil pth y optiml lling n lustring. Slk-tim rlxtion ws ppli to minimiz logi uplition without violting th mximum rquir lls t primry outputs. Mrging ws on y rnomly slting lustr n grily mrging losly lot lustrs. This ppr is orgniz s ollows: In stion 2, ri kgroun is provi. Th r-rivn lustring lgorithm is prsnt in stion 3. Th prormn-rivn lustring lgorithm is isuss in stion 4. In stion 5, xprimntl rsults r provi. Finlly, w onlu in stion 6. QS A A2 A3 A4 A5 A6 OS OP 2 C C2 MP MS D D2 E E2 NP NS F F2 F3 F4 F5 F6 Clok QR mux mux2 mux3 2. kgroun Clustring thniqus or two irnt thnologis, SRAM n ntius, r somwht irnt. A lookup tl is univrsl untion tl, whih n rliz ny untion i n only i th numr o inputs o th untion is not lrgr thn tht o th lookup tl. Th numr o lookup tls insi mro progrmml lok limits lustring. Howvr, ors-grin, ntius mro logi ll onsists o gts onnt y multiplxrs n th logi ll is not univrsl, s shown in Figur. Sin it is too iiult to mp ntwork with multipl output logi lls, th mro logi ll must ivi into smll s gts n lirry lls r gnrt rom thos s gts. Atr thnology mpping, th lirry lls must pk to it th mro logi ll. Th onstrint or pking is mor stringnt. Clustring thniqus or SRAM-s FPGAs hv n volving [0]-[3]. Th lgorithms rli on goo s sltion n smrt gin untions to vlut gin o soring nighor no oring to thir ojtivs. A ynmi progrmming mtho ws prsnt to in th minimum numr o paisc3 logi lls to ovr mpp ntwork [4]. Th pasic3 logi ll ws ivi into svrl s gts, n lirry lls wr gnrt rom thos s gts y riging inputs or stiking inputs to V or GND. Eh ll ws gnrt rom irnt s gts n pning on whih s-gts gnrt th ll, th ll typ ws trmin. Sin thr n irnt omintions to ompos pasic3 logi ll, ll omintions oul numrt. An xtnsion o oin-hng prolm, whih is solvl y ynmi progrmming, gv th optiml solution. For this rsrh, w hv gnrt th lirry lls s in [4]. Thror, w opt th trminology o tht rrn. Thr r our irnt progrmml gt groups insi pasic3 logi ll. mux4 Figur : pasic3 logi ll AZ OZ QZ NZ FZ

2 W ll h o ths gt groups s gt s shown in Figur 2. Atr riving s gts, ll gnrtion is prorm or h s gt. Cll prsonliztion is on ithr y ssigning onstnt or 0 to som o th inputs or y onnting som o th inputs togthr. W ll th ormr oprtion stiking n th lttr oprtion riging. y pplying ll possil omintions o ths two oprtions to s gt, mny irnt lirry lls n gnrt. W ll thos prsonliz lls primitiv lls. Howvr, som o th primitiv lls gnrt rom irnt s gts my hv th sm ooln untion. In t, w n rw Vnn s igrm to pit th st rltionship mong th primitiv lls tht r gnrt rom irnt s gts, s pit in Figur 3. Not tht th totl numr o primitiv lls o ny typ is mor thn 5,000. Finlly, w iltr out rrly-us primitiv lls s on xprimnts with MCNC9 nhmrk iruits. Consquntly, w slt 886 primitiv lls shown in Tl. All lirry gnrtion prossing hs n utomt with prl sripts. () s-gt A () s-gt g h i j k Tl : Cll istriution or th slt primitiv lls. Typ st S AD S ACD S CD S C S D S CD S ACD Clls () s-gt C 3. Ar-Drivn Clustring In this stion, w provi n lgorithm to in th minimum numr o pasic3 logi lls to ovr mpp ntwork. 3. Prolm Sttmnt Atr mpp ntlist is gnrt tr thnology mpping, w must solv th prolm o lustring th primitiv lls us in th mpp ntlist to th pasic3 logi lls. Routing ost o th onntions in th mpp ntlist tns to lrg or th FPGAs. Sin th mpping is prorm or plmnt n routing, physil inormtion is not vill. In ition, ntius-s FPGAs hv rltivly rih routing rsours sin routing swiths r unnt n mny lyrs o mtl wirs n ross ovr th pasic3 logi lls [9]. Thus, w opt to minimiz th totl r tkn y th pasic3 logi lls uring th lustring n pasic3 ssignmnt stp. g h i j k l () s-gt D Figur 2: s gts xtrt rom pasic3 logi ll D A S D S AD S ACD S S ACD CD S CD S C Figur 3: Vnn s igrm o or th st o lls tht n prsonliz rom s gts C Prolm : Givn mpp ntlist, w wnt to in th minimum numr o pasic3 logi lls tht n rliz th ntwork. 3.2 St ontinmnt rltions s gts n put into two lsss: simpl n omplx s gts. Th omplx s gt is on tht onsists o multipl s gts n intrnl multiplxrs, whil th simpl s gt nnot ompos y othr s gts. s-gts C n D r omplx, whrs s-gts A n r simpl. Th inlusion rltionship twn ths s-gts is xprss s ollows: sgt sgt C sgt sgt D () sgt A sgt D Noti tht whn oth simpl s gt n omplx s gt n implmnt primitiv ll, th simpl s gt will slt or rlizing th untion o th primitiv ll. Rlizing th untion y th omplx s gt not only wsts r o th pasic3 logi ll ut lso nlssly inrss th iruit ly. Thror, w n sly stt tht s-gts C n D r inrior to s-gts A n whn thy implmnt th sm logi untion. Intrnl multiplxrs in pasic3 logi lls wr us to ivi th logi ll into our s gts. Somtims, y utilizing ths intrnl multiplxrs, olltion o primitiv lls my trnsorm to singl primitiv ll o irnt typ. Th trnsormtion will ru r, ly, n powr issiption y utilizing intrnlly hr-wir onntions insi th pasic3 logi ll. 3.3 Minimum numr o pasic3 logi lls with givn s gts Givn th numr o s gts or h typ, th ky qustion is how mny pasic3 logi lls r rquir to ontin ll o th s gts. Thr r thr typs o pasic3: 2A + 2, 2A+C, n A++D. A typ 2A+2 pasic3 logi ll is in s th pasic3 logi ll tht hs two s-gt A s n two s-gt s in it. Othr typs n in similrly. Not tht only on sgt D n it in on pasic3 logi ll rom its logi rhittur in Figur. Thorm : Lt n A not th numr o s-gts A. n, n C, n n D r similrly in. Th minimum numr o pasic3 logi lls N pasic3 n to implmnt mpp ntlist ontining n A, n, n C, n n D s-gts n nlytilly lult s ollows: NpASIC3 = mx ( Np, Np2) na + nd, i nd < na N p = 2 nd, othrwis (2) n + nd + nc, i nd < n N p2 = 2 nd + nc, othrwis Proo: At most two s-gt A s n pk insi singl pasic3 logi ll. Similrly t most on s-gt D n pk insi singl logi ll ut it uss only on s-gt A. Thror, i on s-gt D is pk, thr xists n mpty sp or n s-gt A. Whn n A is lrgr thn n D. Th lowr oun on th numr o pasic3 logi ll is n A n n D A + D N n p = + nd =. 2 2 Howvr, whn n A is qul to or lss thn n D, sin thr shoul nough sps or s-gt A s, whih r not oupi y sgt D s, th low oun oms Np = n. Similr rgumnt yils D 2

3 nothr lowr oun: n nd n + nd Np2 = + nc + nd = + n or n D < C 2 2 n n Np2 = nd + n or n C D n. Clrly, th ovrll lowr oun is th mximum o ths two ouns, whih is th sir rsult.! 3.4 Typ istriution tl Thorm n us to signiintly simpliy th prolm. Atr thnology mpping, w ount th numr o primitiv lls o spii typs. Lt ns Γ not th numr o th primitiv lls o typ Γ in th mpp ntwork. For xmpl, ns AD is th numr o typ-ad primitiv lls, i.., th numr o thos lls tht long to st S AD. Th prolm n rstt ollows: Prolm 2: Givn primitiv ll lirry gnrt rom th pasic3 logi ll strutur n mpp ntwork omprising o th primitiv lls, w wnt to in th st hois o s gts A,, C n D or rlizing ll o th primitiv lls in th ntwork so s to minimiz th numr o rquir pasic3 logi lls. Not tht tr th s gt ounts r known, th minimum numr o logi lls n omput strightorwrly s on Thorm. Tl 2: Th typ istriution tl or primitiv ll to sgt mpping. # o primitiv # o s-gt typs ll typs A C D ns AD ns AD ns ACD x 0 ns ACD x 0 ns CD 0 ns CD 0 0 ns D ns D ns C 0 0 ns C 0 ns CD 0 0 ns CD y y ns ACD z ns ACD z 0 0 Tl 2 shows how primitiv ll o typ Γ in th mpp ntwork is rliz with s gt o typ A,, C, or D. Noti tht mny o th primitiv ll typs hv uniqu rliztion in singl s-gt typ. Exmpls inlu typs CD o primitiv lls. Not tht typ CD primitiv ll shoul rliz only using typ s gts us o th inlusion rltionship o qution () n th t tht omplx s-gts r lwys mor ostly thn th orrsponing simpl s gts. Thr o th primitiv ll typs, howvr, n rliz y using ithr o two s gts. For xmpl typ ACD primitiv ll n rliz s ithr typ A or typ C s gt. This tl shows tht, to solv prolm 2, ll w hv to o is to trmin vrils x, y n z whr x nots th numr o primitiv lls o typ ACD tht r rliz s typ A primitiv gt, y nots th numr o primitiv lls o typ CD tht r rliz s typ D primitiv gt, n z nots th numr o primitiv lls o typ ACD tht r rliz s typ A primitiv gt. Prolm 3: Givn th ourrn ount o irnt primitiv ll typs in mpp ntwork, in th vlus o vrils x, y n z so s to minimiz th numr o pasic3 logi lls rquir to ovr th ntwork. 3.5 Prolm ormultion n solution W ormult Prolm 3 s linr progrmming prolm n thn otin th optiml solution y ining ithr th minimum point o n intrst pln o two qutions [0] or th minimum point o n qution tht is lwys ov th othr within rtin rngs o vrils. Eqution (2) n rstt s in (3). { ( )} NpASIC3 = min mx Np ( xyz,, ), Np2( xyz,, ) 0 x nsacd;0 y nscd ;0 z nsacd ( nsad + x + z + nsd + y), i nsd + y < nsad + x + z Np = 2 nsd + y, othrwis ( nscd + nsacd z + nsd y) + ( nsacd x + nsc + nscd ), 2 N = i ns + y< ns + ns z p2 D CD ACD nsd+ nsacd x + nsc+ nscd, othrwis Th rut-or lgorithm is to srh or th optiml solution y trying out vry possil omintions o x, y, n z within thir llow rngs (0 x ns ACD, 0 y ns CD, 0 z ns ACD ). Th omputtionl omplxity, howvr, is O( ns ns ns ), (3) ACD CD ACD whih n quit high. Fortuntly, qution (3) hs n importnt proprty tht llows us to sp up th srh: As x, y, n z inrs, N p inrss ut N p2 rss. Thror, within llow rngs o x, y, n z, qutions or N p n N p2 my intrst in pln or on qution is ov th othr ll th tim. W xplin th solution or th two ss s ollows. Cs : Whn N p n N p2 intrst in pln, t th intrst pln, N p n N p2 om qul: F( xyz,, ) = Np ( xyz,, ) Np2( xyz,, ) = x+ y+ z+ = 0 (4) whr,,, n r oiints o n qution o pln tr th sutrtion. All points in this pln gurnt tht logi lls r ull us N p n N p2 r qul ut hoosing on ritrry point on th pln my not giv th optiml solution. Thror, w n to in th point tht givs th optiml solution in this pln. Noti tht w shoul onsir only points on th pln within th spii rngs or x, y, n z. Furthr mor, w n to hk only ornrs o th pln us o th proprty o N p n N p2 mntion ov. Cs 2: N p n N p2 my not intrst t ll, rsulting in on qution lying ov th othr in th rngs o x, y, n z. In this s, simply, two points r vlut: (x=0, y= 0, z = 0) n (x = ns ACD, y = ns CD, z = ns ACD ). I N p is lrgr thn N p2 t x=0, y= 0, n z = 0, N p (x=0, y= 0, z = 0) is th minimum solution. Othrwis, N p2 (x = ns ACD, y = ns CD, z = ns ACD ) is th minimum solution. Th worst s o th ov lgorithm is whn it rquirs hking ll o th nit points. Thos nit points n numrt y stting minimum or mximum vlus to vrils k xpt on vril. Thror, th omplxity is Ok ( 2 ) whr k is th numr o vrils. In this s, k=3. Noti tht th omputtionl omplxity o this lgorithm is inpnnt o th ntwork siz. In orr or lustring lgorithm to lustr primitiv lls with th minimum numr o pasic3 logi lls, w n to know th istriution o pasic3 logi ll typs s wll. Lt us in n 2A+2 s th numr o typ 2A+2 pasic3 logi lls, n n 2A+2 n n 2A+C n in similrly. Thn th ollowing qutions omput th numr o pasic3 logi lls or h typ: na+ + D= nsd+ y n = ( ns + x+ z) n, n = ( ns + ns z) n n2 A+ C= nsacd x + nsc + nscd y na = na 2n2 A+ C na n n2a+ 2 = mx, 2 2 A AD A+ + D CD ACD A+ + D (5) 3

4 3.6 Clustring A lustr is group o primitiv lls, whih n implmnt in pasic3 logi ll. Our solution so r os not tk into ount th plmnt n routing inormtion. Th intronnt ost must onsir rully so s not to pk nos, whih r pl r wy rom h othr. To rss this issu, irst, w prorm glol plmnt o th mpp ntwork omprising o th primitiv lls y using stt-o-th-rt plmnt pkg (i.., DRAGON2000 [9].) Th plmnt rsult is us to spiy th sptil proximity o primitiv lls. Nxt, w i whih s gt will rliz h primitiv ll in trministi orr oring to solution prsnt. Thn, w rnomly pik no, n th no oms s or lustr. Thn, w try to in th losst no to this lustr. A simpl lgorithm hks i th no n mrg into th lustr oring to th istriution o typs o pasic3 logi lls. Srhing or nw no rpts until th lustr is ull. This whol prour ontinus until ll nos r sor in lustrs. W implmnt this simpl lgorithm to mk sur th orrtnss or rl iruits. W r unr vlopmnt o lgorithms to improv prormn sujt to th minimum r onstrint. 4. Prormn-Drivn Clustring In this stion, w prsnt lling lgorithm to minimiz th numr o pasic3 logi lls on th longst input-output pth n provi lustring lgorithm with slk-tim rlxtion. 4. Prolm sttmnt Dly us y intr-lustr intronnt, whih onnts pasic3 logi lls through intronnt wirs n ntiuss, tns to muh lrgr thn th ly us y intr-lustr intronnt. Thror, w n ssum tht intr-lustr ly hs unit ly whil th intr-lustr ly is ngligil. This ssumption is rsonl us no plmnt n routing inormtion is known n th intr-lustr intronnt ly is muh longr thn th intr-lustr intronnt ly. Th prormn-rivn lustring prolm n stt s ollows. Prolm sttmnt: A omintionl ntwork n rprsnt s irt yli grph G = (V, E), whr V is th st o nos, n E is th st o irt gs. Eh no in V rprsnts primitiv ll in th ntwork n h g (u, v) in E rprsnts n intronntion twn primitiv lls u n v in th ntwork. Prolm 4: Givn ntwork G mpp with th lirry gnrt. W wnt to in lustring solution so tht th numr o pasic3 lls on th ritil pth is th minimum. Noti tht h lustr must sil in th sns tht it must rlizl with singl pasic3 logi ll. ll(u) nots th ll o no u in th ntwork. 4.2 Multi-imnsionl lling lgorithm Whn h no hs ix n known siz, th lustring onstrint is monoton, n th unit ly mol is us, Lwlr s lgorithm gurnts th minimum numr o lustrs on th ritil pth or omintionl ntwork [5] whil no lustr siz xs th mximum siz onstrint. Rll tht lustring onstrint is monoton i n only i ny onnt sust o nos in sil lustr is lso sil. Th lustring onstrint or our prolm is monoton s wll. Mor prisly, whn olltion o primitiv lls in th mpp ntwork n rliz in pasic3 logi ll, sust o ths primitiv lls n lso rliz in singl pasic3 ll. W ll this onstrint rsour onstrint. W propos lling lgorithm to gurnt th optiml solution, whih is sujt to th rsour onstrint. Th psuo-o or th lgorithm is provi in Figur 4. Noti tht sin multipl s gts n rliz no, thos s gts must hk to rt lustr. In ition, oring to th topologil ontinmnt sri in stion 3.2, som s gts r inrior to othrs. Thror, inrior s gts n ropp s ws on or th r-rivn lustring. This signiintly rus th omplxity o gnrting lustrs uring th lling phs.. Algorithm Multi-imnsionl lling 2. gin 3. orh primry input v o 4. ll(v) = 0; 5. n or; 6. Gnrt list T o non-primry inputs in 7. topologil orr; 8. Whil T is not mpty, thn 9. Rmov no v rom th h o T; 0.! = mx{ll(u) u input(v)};. lustrst(v) = ; 2. Gnrt list M o s gts or no v; 3. orh s gt rom M, 4. R = orm lustrs rom no v n lustrs with 5. ll! in nins o no v 6. orh lustr rom R, 7. i lustr is sil or pasic3 rliztion, 8. lustrst(v) = lustrst(v) lustr; 9. n i; 20. n or; 2. n or; 22. i lustrst(v), thn 23. ll(v) =!; 24. ls 25. ll(v) =! + ; 26. n i; 27. n whil; 28. En Figur 4: Multi-imnsionl lling lgorithm Th lgorithm strts y stting ll lls o primry inputs to zro. In lin 2, nit s gts or th no r oun to rt lustrs or irnt s gts. In lins 3 to 2, w rt ll sil lustrs omprising o no v n its nin nos with ll!. I thr xists ny sil lustr, th ll o no v rmins t!. I no sil lustr xists, th ll is inrmnt y on. Th totl numr o lustrs or siility tst in lin 4 is n importnt tor to trmin or omputtionl omplxity o th lgorithm. W not this numr with k. In ition, up to our s-gts n it in pasic3 logi ll. Thror, i th numr o nin nos with ll! in lin 4 is lrgr thn thr nins, thn w will not hv to gnrt lustrs or siility tst. W not th numr o nin nos with ll!, whih is lss thn our, with. m nots th numr o s gts or no v. Sin thr n nin nos with ll!, h o whih n hv up to k lustrs, no v n hoos s gt out o m s gts, th totl lustrs or siility tst gnrt in lin 4 will t most m k, whih is inpnnt o ntwork siz. Thror, th omplxity o this lgorithm oms O( V m k ), whr V is th numr o nos. An xmpl is provi in Figur 5. For th sk o simpliity, only two lustr (pasic3 logi ll) typs r onsir: 2A+2 4

5 n 2A+C. Eh hrtr nnottion in no rprsnts nit s gt or rliztion. Thr n irnt lustr typs. Slting th lustr typ or r minimiztion uring th mrging phs is n opn qustion. W will sri our strtgy in stion 4.4. AC A(0) A A A(0) C(0) A-A-(0) C-A-A(0) A (0) -A-A(0) -A-(0) A A(0) lustr A() () A -A--A(0) AC A-A() A-C() -A() AC lustr2 A-() -() Figur 5: Clustring xmpl. lustr3 A-A-() -A-() lustr4 4.3 Slk-tim rlxtion Th lling lgorithm gnrts lustr solution whr som lustrs n ovr intil nos. I thr is no slk-tim rlxtion, th nos must uplit in ths lustrs. For xmpl, lustr3 n lustr4 ovr th sm no. I signr spiis rquir mximum ll in th primry outputs, thn w n omput th slk tim or h no y sutrting th ll o th no rom th rquir ll t th no. A positiv slk o no nots th mount y whih th no n slow own without inrsing th mximum ll. Thror, w n sort nos y thir sning slk vlus. Nxt, w pross h no rom th sort orr. I othr lustrs ovr nin no o th urrnt no n th slk o th no is positiv, this will tll us tht th nin no n rmov rom th lustr, whih ontins th no n its nin no. y oing this, th urrnt no will rs its slk y on. I this oprtion hngs th slk tim o th nin no, thn th slk tim o trnsitiv nin on o th no is omput gin. This prour prvnts unnssry no uplition whil th rquir mximum ll is still mt. 4.4 Mrging lgorithm Atr ining ll lustrs in ntwork, w my l to mrg som o ths lustrs i th mrging still rsults in sil lustr (on tht n mpp to singl pasic3 logi ll.) In orr to gt insight out how to mrg lustrs, w prorm glol plmnt o th lustr ntwork y using DRAGON2000 [9]. W thn rnomly hoos s lustr n in th losst lustr to it (on with th shortst Eulin istn rom th s lustr.) W thn ttmpt to mrg th two lustrs into on. O ours, th mrg lustr must sil. I th mrg lustr still hs room in it, thn w ontinu to look or nothr nry lustr. This pross is ontinu until th mrg lustr is ull. Nxt, w o th sm xpnsion/mrging pross strting with nothr s lustr. This prour is rpt until no lustr with low r utiliztion is lt or until no mor mrging is possil. 5. Exprimnt Rsults W hv slt 8 lrg omintionl iruits rom th MCNC9 nhmrk. SIS [7] rs th iruits in li ormt. To vlut our lirry gnrtion n r-rivn lustring, w ompr our rsults to thos rom ommril tool, ll QuikWorks 4. rom QuikLogi. For QuikWorks 4., th ollowing options wr slt to minimiz r: Logi optimiztion: lvl thnology mp, mo-ovrnight, typr, n no ur insrtion Tl 3: Rsults o r-rivn lustring QuikWorks Pkr-r Improvmnt (%) Numr Numr PASIC3 PASIC3 Ciruits Cll Mxpth lls pth pth primitiv pasic3 Primitiv Mx- Mx- o o logi logi rgmnts lls lls lls logi lls i rot i pir v x C C lu px C C lu C C C C Avrg improvmnt Plmnt n Rout: ovrnight QuikWorks uss th trm ll rgmnt to init lirry ll gnrt rom pasic3 logi ll. Th rsults wr tkn tr plmnt [6]. For our simultion st-up, th lirry ws r n sript.rugg ws us to optimiz iruit. SIS ws us or thnology mpping with th lirry. W stimt th minimum numr o logi lls y using our lgorithms, PkGnr. Tl 3 rports th rsults o th r-rivn lustring. In most o th ss, PkGn-r us wr primitiv lls thn QuikWorks. PkGn-r ru th numr o pasic3 logi lls y 2.29% on vrg ompr to QuikWorks. On th othr hn, PkGn-r givs mor pth o pasic3 logi lls thn QuikWorks or mny ss. For this ppr, w i not pply lgorithms to minimiz th pth. Vrious huristi lgorithms r unr vlopmnt. For xmpl, piking up s no with high proility o ruing pth will ru th pth thn rnomly slting s, n so orth. Rsults o th prormn-rivn lustring lgorithm, ll PkGn-ly, r provi in Tl 4. QuikWorks is st to minimiz ly uring logi optimiztion. Plmnt n routing is lso st to th ovrnight mo or th st rsult. Th mximum pth o iruit in th tl is th numr o pasic3 logi lls on th longst input-output pth. Th omprison o th numrs o primitiv lls or n tr slk-tim (ST) rlxtion shows tht our propos mtho tivly vois logi uplition. Th numr o lustrs or h iruit ws ru tr th mrging phs. For this ppr, w o not giv th thrshol o istn twn pl lustrs, n som r-wy lustrs might hv n mrg togthr. Howvr, w n ontrol th rsults y hnging th thrshol. As rsult, QuikWorks us muh mor pasic3 logi lls thn th rsults rom th r-rivn lustring. us o th logi uplition, our lgorithm on vrg uss mor pasic3 logi lls tr mrging. Compr to QuikWorks, 5

6 PkGn-ly ru th mximum pth o th iruit y 44.75% on vrg with 2.05% r ovrh. 6. Conlusion In this ppr, w prsnt r-rivn n prormn-rivn lustring lgorithms or ors-grin, nti-us s FPGAs. For r-rivn lustring, w st up pir o linr qutions n oun th optiml solution to in th minimum numr o rquir pasic3 logi lls. For prormn-rivn lustring, w propos lling lgorithm so tht it n gnrt th minimum numr o lustrs on th ritil pth. A slk-tim rlxtion ws us to voi runnt logi uplition without violting prormn onstrint. In ition, rnom mrging ws us to lustr losly pl prtilly ill lustrs. Exprimntl rsults show tht th r-rivn lustring lgorithm us wr numrs o pasic3 logi lls y 2.29 % on vrg n th prormn-rivn lustring lgorithm ru th mximum pth y 44.75%, on vrg. Rrns [7] Eri Kuss, n Rn Ry, Low-nrgy m FPGA rhittur, in Pro. Intrntionl Symposium on Low Powr Eltronis n Dsigns, pp , 998. [8] Alxnr Mrqurt, Vughn tz, n Jonthn Ros, Sp n r tros in lustr-s FPGA rhittur, IEEE Trnstions on Vry Lrg Sl Intgrtion (VLSI) Systms, vol. 8, no., Frury 2000, pp [9] pasic3 FPGA Fmily Dtsht, QuikLogi Corportion ( [0] J. Cong, J. Pk, n Y. Ding, RASP: gnrl logi synthsis systm or SRAM-s FPGAs, in Pro. FPGA, pp , 996. [] V. tz n J. Ros, Clustr-s logi loks or FPGAs: r-iiny vs. input shring n siz, in Pro Custom Intgrt Ciruits Conrn, 997, pp [2] Alxnr Mrqurt, Vughn tz, n Jonthn Ros, Using lustr-s logi loks n timing-rivn pking to improv FPGA sp n nsity, in Pro. FPGA, pp , 999. [3] E.ozogzh, S. Ogrni-Mmik, M. Srrzh, Rpk: routilityrivn pking or lustr-s FPGA, in Pro. Asi-South Pii Dsign Automtion Conrn, pp , 200. [4] Chng Woo Kng, Ali Irnli, n Mssou Prm, Thnology mpping n pking or ors-grin, nti-us s FPGAs, in Pro. Asi n South Pii Dsign Automtion Conrn, Jnury [5] E. L. Lwlr, K. N. Lvitt, J. Turnr, Moul lustring to minimiz ly in igitl ntworks, IEEE Trnstions on Computrs, vol. C-8, no., Jnury 969, pp [6] QuikLogi.om, QuikWorks Usr Mnul [7] Sntovih, E.M., t l., SIS: A systm or squntil iruit synthsis, 992, Eltronis Rsrh Lortory, Collg o Enginring, Univrsity o Cliorni, rkly. [8] Thoms H. Cormn, Chrls E. Lisrson, n Ronl, L. Rivst, Introution to Algorithms, MCrw-Hill ook Compny, [9] M. Wng, X. Yng, n M. Srrzh, Drgon2000: stnr-ll plmnt tool or lrg inustry iruits, in Pro. Intrntionl Conrn on Computr Ai Dsign, 2000, pp [20] Tl 4: Rsults o prormn-rivn lustring QuikWorks 4. PkGn-prormn Improvmnt (%) Numr Numr Mximu Numr Numr o primitiv Numr o lustrs Mximu Numr Mximu o o m pth o lls tr uplition (pasic3 logi m pth o m pth rgmn pasic3 primitiv lls) pasic t lls logi lls lls tr thnolog or STrlxtion Atr STrlxtion or mrging Atr mrging logi lls Ciruits y mpping i rot i pir v x C C lu px C C lu C C C C Avrg Improvmnt 6