Characteristics of Fault Simulation. Fault Simulation Techniques. Parallel Fault Simulation. Parallel Fault Simulation

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1 Chrtristis o Fult Simultion Fult tivity with rspt to ult-r iruit is otn sprs oth in tim n sp. For mpl F is not tivt y th givn pttrn, whil F2 ts only th lowr prt o this iruit. Fult Simultion Thniqus Prlll Fult Simultion utiv Fult Simultion F(s--) F2(s--) Prlll Fult Simultion Simult multipl iruits simultnously Th inhrnt prlll oprtion o omputr wors to simult ulty iruits in prlll with ult-r iruit Th numr o ulty iruits or ults n pross simultnously is limit y th wor lngth,.g., 32 iruits or 32-it omputr Complition An vnt or vlu hng o singl ulty or ultr iruit ls to th omputtion o n ntir wor Th ult-r logi simultion is rpt or h pss Prlll Fult Simultion Empl Consir thr ults: (J s--, B s--, n F s--) Bit-sp: (FF nots ult-r) ult-r J/ B/ F/ FF B/ A J/ C E G B J H F 59 F/ 6

2 utiv Fult Simultion Simult ll ulty iruits in on pss For h pttrn, swp th iruit rom PIs to POs. uring th pross, list o ults is ssoit with h wir Th list ontins ults tht woul prou ult t on this wir Th union ult list t vry PO ontins th tt ults y th simult input vtor Min oprtion is ult list propgtion pning on gt typs n vlus Th siz o th list my grow ynmilly, ling to th potntil mmory plosion prolm Illustrtion o Fult List Propgtion Consir two-input AN-gt: Non-ontrolling s: Controlling ss: LA LB A B C LC Cs : A=, B=, C= t ult-r, LC = LA LB {C/} Cs 2: A=, B=, C= t ult-r, LC = (LA LB) {C/} Cs 3: A=, B=, C= t ult-r, LC = (LA LB) {C/} 6 LA is th st o ll ults not in LA 62 Rul o Fult List Propgtion utiv Fult Simultion Empl (/4) Consir 3 ults: B/, F/, n J/ unr (A,B,F) = (,,) A G B F C E H J 63 Fult list t PIs: LB = {B/}, LF = {F/}, LA =, LC=L = {B/} 64

3 utiv Fult Simultion utiv Fult Simultion Empl (2/4) Consir 3 ults: B/, F/, n J/ unr (A,B,F) = (,,) B F A C E LB = {B/}, LF = {F/}, LA =, LC = L = {B/} Fult lists t G n E: LG = (LA LC) G/ = {B/, G/} G H J Empl (3/4) Consir 3 ults: B/, F/, n J/ unr (A,B,F) = (,,) A G LE = (L) E/ = {B/, E/} B F C E LB = {B/}, LF = {F/}, LA =, LC = L = {B/}, LG = {B/, G/}, LE = {B/, E/} Fult list t H: LH = (LE LF) LH = {B/, E/, F/, H/} H J utiv Fult Simultion utiv Fult Simultion Empl (4/4) Consir 3 ults: B/, F/, n J/ unr (A,B,F) = (,,) A G B F C E LB = {B/}, LF = {F/}, LA =, LC = L = {B/}, LG = {B/, G/}, LE = {B/, E/}, LH = {B/, E/, F/, H/} Finl ult list t PO J: H J Empl (ont ) Consir 3 ults: B/, F/, n J/ unr (A,B,F) = (,,) Evnt rivn upts: LB = {B/}, LF = {F/}, LA =, LC = L = LE = {B/}, LG = {G/}, LH = {B/, F/}, LJ = {B/, F/, J/} LJ = (LH LG) LJ = {E/, F/, J/} B A F C E G H J

4 Outlin Fult Moling Typil ATPG Flow st phs: rnom tst pttrn gnrtion Fult Simultion Automti Tst Pttrn Gnrtion (ATPG) Funtionl pproh Booln irn Struturl pproh -lgorithm POEM sign or Tstility 69 7 Typil ATPG Flow (ont ) 2n phs: trministi tst pttrn gnrtion Tst Pttrn Gnrtion Th tst st T o ult with rspt to som PO z n omput y T() = z() z () A tst pttrn n ully spii or prtilly spii pning on whthr th vlus o PIs r ll ssign Empl z z Input vtors (,,) n (,,-) r ully n prtilly spii tst pttrns o ult, rsptivly. 7 72

5 Struturl Tst Gnrtion -Algorithm Struturl Tst Gnrtion -Algorithm Tst gnrtion rom iruit strutur Two si gols () Fult tivtion (FA) (2) Fult propgtion (FP) Both o whih rquirs Lin Justiition (LJ), i.., ining input omintions tht or rtin signls to thir sir vlus Nottions: / is not s, mning tht goo-vlu is whil ulty vlu is Similrly, / is not Both n r ll ult ts (FE) / ult tivtion ult propgtion Fult tivtion Stting th ulty signl to ithr or is Lin Justiition prolm Fult propgtion () slt pth to PO isions (2) On th pth is slt st o lin justiition (LJ) prolms r to solv Lin justiition Involvs isions or implitions Inorrt isions: n ktrking To justiy = = n = (implition) To justiy = = or = (ision) Struturl Tst Gnrtion -Algorithm: Fult Propgtion G2 G G3 G5 G4 ision tr Fult tivtion G= { =, =, = } { G3= } Fult propgtion: through G5 or G6 ision through G5: G2= { =, = } inonsistny t ktrk!! ision through G6: G4= = on!! Th rsulting tst is () G6 2 G5 il -rontirs: r th gts whos output vlu is, whil on or mor Inputs r or. For mpl, initilly, th -rontir is { G5, G6 }. { G5, G6 } G6 suss 75 Struturl Tst Gnrtion -Algorithm: Lin Justiition h k l p m n o q r FA st h to FP =, = (o=) ; FP q=, r= To justiy q= l= or k= ision: l = =, = m=, n= r= inonsistny t r ktrk! ision: k= =, = To justiy r= m= or n= (= or =) on! (J-rontir is ) s orrsponing ision tr l= k= il q= r= m= o= n= suss J-rontir: is th st o gts whos output vlu is known (i.., or ), ut is not impli y its input vlus. E: initilly, J-rontir is {q=, r=} 76

6 Tst Gnrtion A rnh-n-oun srh Evry ision point is rnhing point I st o isions l to onlit, ktrk is tkn to plor othr isions A tst is oun whn () ult t is propgt to PO, n (2) ll intrnl lins r justii No tst is oun tr ll possil isions r tri Thn, trgt ult is unttl Sin th srh is hustiv, it will in tst i on ists For omintionl iruit, n unttl ult is lso runnt ult Cn us to simpliy iruit. Implition Implition Comput th vlus tht n uniquly trmin Lol implition: propgtion o vlus rom on lin to its immit sussors or prssors Glol implition: th propgtion involving lrgr r o th iruit n r-onvrgnt nout Mimum implition prinipl Prorm s mny implitions s possil It hlps to ithr ru th numr o prolms tht n isions or to rh n inonsistny soonr Forwr Implition Bkwr Implition Bor Atr Bor Atr ' J-rontir={..., } -rontir={..., } ' J-rontir={... } -rontir={... } J-rontir={... } J-rontir={..., } 79 8

7 -Algorithm (/4) -Algorithm (2/4) Empl Fiv logi vlus {,,,, } g ' ' ' G h i j k l m G2 Try to propgt ult t thru G St to Try to propgt ult t thru G2 St j,k,l,m to n Conlit t k Bktrk! 8 Empl Fiv logi vlus {,,,, } g ' ' ' G h i j k l m Try to propgt ult t thru G2 St j,l,m to G2 n (nt -rontir hosn) Conlit t m Bktrk! 82 -Algorithm (3/4) -Algorithm (4/4) Empl Fiv logi vlus {,,,, } g ' ' ' G h i j k l m Try to propgt ult t thru G2 St j,l to Fult propgtion n lin justiition r oth omplt A tst is oun! G2 n This is s o multipl pth snsitiztion! (nt -rontir hosn) 83 ision Implition Commnts = Ativ th ult h= = Uniqu -riv = g= = Propgt vi i i= = j= Propgt vi n k= l= m= n= = = k= Contrition = Propgt vi k k= = j= l= Propgt vi n m= n= = = m= Contrition = Propgt vi m m= = l= n= 84

8 ision Tr on -Frontir POEM Algorithm Th ision tr No -rontir Brnh ision tkn A pth-first-srh (FS) strtgy is otn us POEM: Pth-Orint Eision Mking Fult Ativtion (FA) n Propgtion (FP) l to sts o Lin Justiition (LJ) prolms. Th LJ prolms n solv vi vlu ssignmnts. In -lgorithm TG is on through inirt signl ssignmnt or FA, FP, n LJ, tht vntully mps into ssignmnts t PI s Th ision points r t intrnl lins Th worst-s numr o ktrks is ponntil in trms o th numr o ision points (.g., t lst 2 k or k ision nos) In POEM Th tst gnrtion is on through squn o irt ssignmnts t PI s ision points r t PIs, thus th numr o ktrking might wr POEM Algorithm Srh Sp o POEM Complt srh sp A inry tr with 2 n l nos, whr n is th numr o PIs Fst tst gnrtion N to in pth ling to SUCCESS trminl quikly POEM Algorithm Ojtiv n Bktr POEM Also ims t stlishing snsitiztion pth s on ult tivtion n propgtion lik -lgorithm Inst o justiying th signl vlus rquir or snsitizing th slt pth, ojtivs r stup to gui th ision pross t PIs Ojtiv is signl-vlu pir (w, v w ) Bktr Bktr mps sir ojtiv into PI ssignmnt tht is likly to ontriut to th hivmnt o th ojtiv Is pross tht trvrss th iruit k rom th ojtiv signl to PIs Th rsult is PI signl-vlu pir (, v ) No signl vlu is tully ssign uring ktr (towr PI)! F F F F S S F F 87 88

9 POEM Algorithm Ojtiv Ojtiv routin involvs sltion o -rontir, G sltion o n unspii input gt o G Ojtiv() { /* Th trgt ult is w s--v */ /* Lt vril oj signl-vlu pir */ i (th vlu o w is ) oj = ( w, v ); ls { slt gt (G) rom th -rontir; slt n input (j) o G with vlu ; = ontrolling vlu o G; oj = (j, ); } rturn (oj); } ult tivtion ult propgtion 89 POEM Algorithm Bktr Bktr routin involvs ining n ll- pth rom ojtiv sit to PI, i.., vry signl in this pth hs vlu Bktr(w, v w ) { /* Mps ojtiv into PI ssignmnt */ G = w; /* ojtiv no */ v = v w ; /* ojtiv vlu */ whil (G is gt output) { /* not rh PI yt */ inv = invrsion o G; slt n input (j) o G with vlu ; G = j; /* nw ojtiv no */ v = v inv; /* nw ojtiv vlu */ } /* G is PI */ rturn (G, v); } 9 POEM Algorithm PI Assignmnt POEM Algorithm PIs: {,,, } Currnt Assignmnts: { = } ision: = ojtiv ils Rvrs ision: = ision: = ojtiv ils Rvrs ision: = ision: = ilur Filur mns ult t nnot propgt to ny PO unr urrnt PI ssignmnts ilur S POEM () /* using pth-irst-srh */ gin I(rror t PO) rturn(success); I(tst not possil) rturn(failure); (k, v k ) = Ojtiv(); /* hoos lin to justii */ (j, v j ) = Bktr(k, v k ); /* hoos th PI to ssign */ Imply (j, v j ); /* mk ision */ I ( POEM()==SUCCESS ) rturn (SUCCESS); Imply (j, v j ); /* rvrs ision */ I ( POEM()==SUCCESS ) rturn(success); Imply (j, ); Rturn (FAILURE); n 9 92

10 POEM Algorithm (/4) POEM Algorithm (2/4) Empl g ' ' ' G h i j k l m Slt -rontir G2 n st ojtiv to (k,) = y ktr rk th snsitiztion ross G2 (j=) Bktrk! G2 n 93 Empl g ' ' ' G G3 G4 h Slt -rontir G3 n st ojtiv to (,) No ktr is n i Suss t G3 j k l m G2 n 94 POEM Algorithm (3/4) POEM Algorithm (4/4) Empl g ' ' ' G G3 G4 h i j Slt -rontir G4 n st ojtiv to (,) No ktr is n Su t G4 n G2 pprs t on PO A tst is oun!! n Ojtiv PI ssignmnt Implitions -rontir Commnts = = h= g = = g = = g= i,k,m = = = i= k,m,n k= = = Assignmnts n to j= rvrs uring ktrking k= G2 n= m no solutions! ktrk k = = lip PI ssignmnt j= ' h l k= m,n i l= = = j ' n l= g k m m= ' l m 95 n= 96

11 POEM Algorithm ision Tr Trmintion Conitions ision no: PI slt through ktr or vlu ssignmnt Brnh: vlu ssignmnt to th slt PI il -lgorithm Suss: () Fult t t n output (-rontir my not mpty) (2) J-rontir is mpty Filur: () -rontir is mpty (ll possil pths r ls) (2) J-rontir is not mpty POEM Suss: Fult t sn t n output Filur: Evry PI ssignmnt ls to ilur, in whih -rontir is mpty whil ult hs n tivt suss POEM Ovrviw POEM mins ll possil input pttrns impliitly ut hustivly (rnh-n-oun) or ining tst omplt lik -lgorithm (i.., will in tst i ists) Othr ky turs No J-rontir, sin thr r no vlus tht rquir justiition No onsistny hk, s onlits n nvr our No kwr implition, us vlus r propgt only orwr Bktrking is impliitly on y simultion rthr thn y n pliit n tim-onsuming sv/rstor pross Eprimnts show tht POEM is gnrlly str thn - lgorithm Outlin Fult Moling Fult Simultion Automti Tst Pttrn Gnrtion sign or Tstility 99

12 Why FT? irt tsting is wy too iiult! Lrg numr o FFs Em mmory loks Em nlog loks sign or Tstility inition sign or tstility (FT) rrs to thos sign thniqus tht mk tst gnrtion n tsting osttiv FT mthos A-ho mthos, ull n prtil sn, uilt-in sl-tst (BIST), ounry sn Cost o FT Pin ount, r, prormn, sign-tim, tst-tim, t. 2 Importnt Ftors Controllility Msur th s o ontrolling lin Osrvility Msur th s o osrving lin t PO FT ls with wys o improving Controllility n osrvility Tst Point Insrtion Employ tst points to nhn ontrollility n osrvility CP: Control Points Primry inputs us to nhn ontrollility OP: Osrvility Points Primry outputs us to nhn osrvility A -CP A -CP A OP PO 3 4

13 Control Point Insrtion Control Point Sltion C CP CP_nl MUX Norml oprtion: Whn CP_nl = Injt : St CP_nl = n CP = Injt : St CP_nl = n CP = w C2 Insrt iruit or ontrolling lin w 5 Gol Controllility o th nout-on o th point is improv Common sltions Control, rss, n t uss Enl/hol inputs Enl n r/writ inputs to mmory Clok n prst/lr signls o lip-lops t slt inputs to multiplrs n multiplrs 6 Osrvtion Point Sltion Gol Osrvility o th trnsitiv nins o th point is improv Prolms with Tst Point Insrtion Lrg numr o I/O pins Cn rsolv y ing MUXs to ru th numr o I/O pins, or y ing shit-rgistrs to impos CP vlus Common hoi Stm lins with mor nouts Glol k pths Runnt signl lins Output o logi vis hving mny inputs MUX, XOR trs Output rom stt vis Arss, ontrol n t uss X Shit-rgistr R ontrol X Z Z Shit-rgistr R2 Osrv 7 8

14 Wht Is Sn? Ojtiv To provi ontrollility n osrvility t intrnl stt vrils or tsting Mtho A tst mo ontrol signl(s) to iruit Connt lip-lops to orm shit rgistrs in tst mo Mk inputs/outputs o th lip-lops in th shit rgistr ontrolll n osrvl Sn Conpt Mo Swith (norml or tst) Sn In Comintionl Logi FF Typs Intrnl sn Full sn, prtil sn, rnom ss Bounry sn 9 FF FF Sn Out Logi sign or Sn Insrtion Logi sign tr Sn Insrtion input pins Comintionl Logi output pins input pins Comintionl Logi q q 2 g stuk-t- q 3 output pins q q 2 q 3 lok Q Q Q Squntil ATPG is trmly iiult: u to th lk o ontrollility n osrvility t lip-lops. sn-input sn-nl lok MUX Q MUX Q Q Sn Chin provis n sy ss to lip-lops Pttrn gnrtion is muh sir!! MUX sn-output 2

15 Sn Insrtion Empl 3-stg ountr input pins lok Q Comintionl Logi q q 2 q 3 q q2 q 3 g stuk-t- Q Q output pins Ovrh o Sn sign Cs stuy #CMOS gts = 2 Frtion o lip-lops =.478 Frtion o norml routing =.47 Sn implmnttion Non Hirrhil Optimiz Prit ovrh 4.5% 4.5% Atul r ovrh 6.93%.9% Normliz oprting rquny It tks 8 lok yls to st th lip-lops to (,, ), or tting th trgt ult g stuk-t- ult (22 yls or 2-stg ountr!) 3 4 Full Sn Prolms Prolms Ar ovrh Possil prormn grtion High tst pplition tim Powr issiption Fturs o ommril tools Sn-rul violtion hk (.g., FT rul hk) Sn insrtion (onvrt FF to its sn vrsion) ATPG (oth omintionl n squntil) Sn hin rorring tr lyout Sn-Chin Rorring Sn-hin orr is otn i t gt-lvl without knowing th ll plmnt Sn-hin onsums lot o routing rsours, n oul minimiz y r-orring th lip-lops in th hin tr lyout is on Sn-In Sn-Out Sn-In Sn ll Sn-Out 5 Lyout o ll-s sign A ttr sn-hin orr 6

16 Prtil Sn Bsi i Slt sust o lip-lops or sn Lowr ovrh (r n sp) Rl sign ruls Cyl-rking thniqu Chng & Agrwl, IEEE Trns. On Computrs, April 99 Slt sn lip-lops to simpliy squntil ATPG Ovrh is out 25% o thn ull sn Timing-rivn prtil sn Jou & Chng, ICCA, Nov. 99 Allow optimiztion o r, timing, n tstility simultnously 7 Full Sn vs. Prtil Sn sn sign ull sn prtil sn vry lip-lop is sn-ff NOT vry lip-lop is sn-ff sn tim hrwr ovrh ult ovrg s-o-us longr mor ~% sir shortr lss unpritl hrr 8 Ar Ovrh vs. Tst Eort Conlusions tst ort tst gnrtion omplity r ovrh Tsting Conut tr mnuturing Must onsir uring th sign pross Mjor ult mols Stuk-t, riging, stuk-opn, ly ult, Mjor tools n sign-or-tstility By sn hin insrtion or uilt-in sl-tst Fult simultion ATPG no sn prtil sn ull sn r ovrh Othr Applitions in CA ATPG is wy o Booln rsoning n is pplil to my logi-omin CA prolms 9 2