Re-synthesis for Delay Variation Tolerance

Transcription

1 49.1 R-sytss or Dly Vrto Tolr S-C C Dprtmt o CS Ntol Ts Hu Uvrsty Hsu, Tw s@s.tu.u.tw C-To Hs Dprtmt o CS Ntol Ts Hu Uvrsty Hsu, Tw s@tu.s.tu.u.tw K-C Wu Dprtmt o CS Ntol Ts Hu Uvrsty Hsu, Tw Alx@tu.s.tu.u.tw ABSTRACT Svrl tors su s pross vrto, oss, ly ts r t rllts o rut. Trtol mtos pssmst tm mr to rsolv ly vrto prolms. I ts ppr, st o sr t prorm, w propos r-sytss tqu w s rut los to prott t prorm. Bus os t rtl pts v zro sls r vulrl to ly vrto, w ormult t prolm o tolrt ly vrto to t prolm o rs t sls o os. Our r-sytss tqu rs t sls o ll os or wrs to lrr t pr-trm vlu. Our xprmtl rsults sow tt tol r plty s rou 21% or 10% o ly vrto tolr. Ctors Sut Dsrptors B.8.1 [Prorm Rllty]: Rllty, Tst, Fult-Tolr Grl Trms Ds, Prorm, Rllty Kywors Dly vrto, tolr 1. INTRODUCTION Du to t s tr o sr v omtrs, lowr powr volts, r rqus, rut prorm s rsly sstv to tors su s pross vrto, oss, ly ts [1][2]. Ts tors tvly t t tm vor o rut tror, us ly vrto p. To llvt ly vrto prolms, srs ot v to opt t worst-s ly mol or mploy tm mr to prott t prorm rom ly lututo. Howvr, su osrvtsm s om ussry Prmsso to m tl or r ops o ll or prt o ts wor or prsol or lssroom us s rt wtout prov tt ops r ot m or strut or prot or ommrl vt tt ops r ts ot t ull tto o t rst p. To opy otrws, or rpuls, to post o srvrs or to rstrut to lsts, rqurs pror sp prmsso /or. DAC 2004, Ju 7 11, 2004, S Do, Clor, USA Copyrt 2004 ACM /04/0006 $5.00. Auxlry lo A 1 T orl rut A 2 Auxlry lo A 3 Fur 1: A ly tolr strutur. Vot m pssmsm [4][6]. It s rport [3] tt rt ASIC my ru up to 40% str t prt y t str (worst-s) tm lyss. O t otr, v w or t ovr-s plty, trm pproprt worst orr s ult u to multpl sours o ly vrto tr omplx lu o rut prorm. Morovr, tm mr my ot possl or tm rtl s. I ts ppr, st o sr t prorm, w propos ovl wy to tr r or ly vrto tolr. I rut, som ts (wrs) su s tos lo t rtl pts r vulrl to ly vrto us y ly vrto tos ts (wrs) my vrsly t t wol rut ly. T vulrlty st rtrz y t s sl, t qutty tt rprsts t orl mr wtout volt t rut s ly. T smllr t sl o t s, t mor vulrl t t wll. W sy rut s t ly tolr t ly o t (or wr) rs t wtout t t rut s ly; otr wors, t sl o t (or wr) s t lst t. Gv ly tolr vlu t rut, our ol s to r-sytsz t rut su tt vry t (or wr) t w rut tolrt t lst ly vrto t. I Fur 1, our tqu uls w strutur osst o vot m, t orl rut A 2, two tol uxlry los A 1 A 3. Svrl proprts o t w strutur r rly summrz s ollows. Frst, t lys o uxlry los, A 1 A 3, r lwys smllr t or qul to t ly o t orl rut A 2. By trou t r plty o A 1 A 3, t wol rut tolrt t lst 814

2 pr- tolr t. Morovr, t pr- tolr vlu trms t szs o t uxlry los tt r rlly mu smllr t tt o t orl o. W t ly tolr s 10% (15%) o t orl rut s ly, our xprmtl rsults sow tt o t vr, t w strutur s 21% (41%) o r ovr. W lso ru otr st o xprmts y ssum t ly o t s v s prolty sty uto [5]. W stmt t sttstl ly o rut y ru 10,000 tms o Mot-Crlo xprmts. T rsults sow tt o t vr, 68% o smpls o rut v som ly rqurmt. O t otr, 87% o smpls o t r-sytsz rut v t sm ly rqurmt. A, our otv s to r-sytsz rut so tt t sl o o s t lst t. Tou TMR strutur s ot prtl or our otv, t os prov oo strt pot or mprov t sls o os. To ru t rqur r, w rmov rut wrs TMR strutur. Howvr, w rut wr s rmov, som os sls r. T m o ts ppr s to rmov rut wrs wl p t sls o ll os to qul to or rtr t t. Lt us suss som mportt proprts TMR strutur. p 1 w s w 1 Vot m p 2 Duplto lo A 1 w 2 p 3 w 3 Duplto lo A 2 Duplto lo A 3 Vot m Fur 3: Isomorp pts TMR. Fur 2: A TMR strutur. 2. DELAY VARIATION TOLERANCE IN A TMR STRUCTURE My prvous pprs prst rtturs or utol ult tolr. Howvr, to t st o our owl, tr s o rsr m or ly vrto tolr. Amo t utol ult tolr tqus, Trpl Moulr Ruy (TMR) [7], llustrt Fur 2, s wly us sm. I TMR strutur, v rut s rplt to tr uplto los (A 1, A 2, A 3 ) wos outputs r ot to t puts o (morty) vot rut. T us o t vot rut llows TMR to prou orrt rsults s lo s y two uplto los rt orrt rsults. I TMR, wr or t s rut us rmovl o o wr or t wll ot t t rut utolty. Tou TMR strutur s prmrly us or utol tolr, TMR strutur lso tolrt ly vrto us o TMR s t sl. (W wll xpl t proprty o t sl ltr.) O t otr, our otv o ly vrto my us 10% - 20% mor ly t t orl rut s ly. Tror, t t sl or t TMR s ovr-prottv. Bss, TMR rqurs tr tms t r o t orl rut, m t sm mprtl or our otv. I TMR, ompot su s wr, t, pt s tr rpltos. W sy tr rpltos o ompot r somorp ompots. For xmpl Fur 3, pts p 1, p 2, p 3 r somorp pts wrs w 1, w 2, w 3 r somorp wrs. Cosr pt p 1 ts two otr somorp pts p 2 p 3. Lt t ly o pt p (p), w s qul to t summto o ll ly lmts lo t pt. Illy, ll tr somorp pts v t sm ly, (p 1 )=(p 2 )=(p 3 ). Suppos u to ly vrto, (p 1 ), (p 2 ), (p 3 ) r rt. S vot m trms ts output w two o ts puts v rt orrt rsults, t l ly wll omt y t so rrv sl. I otr wors, t l ly o TMR or t sm omputtos s ot trm y t ltst ly. T proprty o oos t so rrv sl or vot m ms ll tr somorp pts ot vulrl vully to ly vrto. W pt to strtly-ls pt t pt rms or oms ls pt or y rmt o t pt ly. I TMR, tr somorp pts v t sm ly (p 1 )=(p 2 )=(p 3 ), ll tr pts r strtly-ls pts us o oos t so rrv sl. I t, ll t pts TMR r ll strtly-ls pts. Morovr, ll pts pss o r ll strtly-ls, t o s t sl. T rsos r xpl t ollow. Frst, w woul l to lry t opt o o s sl. W t sl o o to t lrst orl mr tt to t o s ly wtout rs t wol rut ly. T xt sl s ult to omput. Howvr, w 815

3 w 1 w 2 w p =(,,, vot_m) Fur 4: Rmovl o wr w 1 uss t sls o som ts (wrs) to. quly stmt t vlu us t ormuls o (1) t rqur tm mus t rrvl tm o o or (2) t rut ly mus t ly o t lost pt pss t o. T ov omputto or o s sl s osrvtv or uppr ou us strtly-ls pts soul ot osr. W ot mor urt stmto y t rut ly mus t ly o t lost o-strtly-ls pt pss t o. S ll pts r strtly-ls TMR, t sls o ll os TMR r t. 3. REMOVING WIRES IN A TMR WHILE MAINTAINING t DELAY TOLERANCE W ow suss t t o wr rmovl o sl. Bslly, rmovl o wrs wll us som pts to rom strtly-ls pts to tru pts. Cosr tr somorp wrs (w 1, w 2, w 3 ) Fur 3, wr wr w s lo pt p. I TMR, tr somorp wrs r rut vully ut rmov o my us otr two rrut. Suppos wr w 1 s rmov pt p 1 ss to xst. Bus oly two pts p 2 p 3 r somorp prou orrt rsults, t vot m wll oos t ltst rrv rsult o p 2 p 3, w mpls pts p 2 p 3 om tru pts. Bus pts p 2 p 3 r o lor strtly-ls pts, t sls o os lo p 2 p 3 r o lor t. For xmpl, osr TMR strutur Fur 4. Assum t t vot m v t ly o 1. Wrs (w 1, w 2, w 3 ) pts (p 1, p 2, p 3 ) r somorp. Suppos ol wr w 1 s rmov (or rpl y ostt zro). Atr rmovl, lt us omput t sl or o 2. S pts p 2 p 3 om tru pts, t lost tru pt pss o 2 s p 2. Tror, t sl o o 2 s t rut s ly mus (p 2 )=3. I t rut s ly s 5, t sl o o 2 s 2. 1 p 1 2 p 2 3 p 3 V o t I TMR, rmov wr ltr som pts rom strtly-ls pts to om tru pts lso ltr som wr s t sls to om t. I t ollow, w sow t ssry sut otos or wr rmovl wl mt t sl o o to t lst t. I t orl rut, w sy o s t -rtl o t o s sl s lss t t. A rut ro s ll t -rtl ro, w ossts o oly t -rtl os wrs tw t -rtl os. For xmpl osr t orl rut Fur 5 wr t s ly s 1. Suppos t ly tolr vlu t s 2. No s t -rtl o us t sl o s 0 lss t t =2. I t, os {,,,,,, } (rw y ol ls) r ll t -rtl os. Morovr, t t -rtl ro ossts o tos lt (ol) ts wrs t ur. Lmm 1: For t ly tolr, ll somorp pts t -rtl ros ot tru pts. Proo: Omtt. Torm 1: A wr w t -rtl ros ot rmov to mt t ly tolr rqurmt. Proo: Omtt. T ov torm sys tt or t ly tolr, wrs tr somorp t -rtl ros ot rmov. Wt t -rtl ro, w sy o s t -omtor ll pts rom prmry puts to prmry outputs must pss t o. Also, o (wr) s s-put to t -omtor t o (wr) s mmt put to t t -omtor ut os ot lo to o (wr) t t -rtl ro. For xmpl, osr t sm xmpl Fur 5. Tr r our pts (rom prmry puts to output q) t t -rtl ro. Nos {,,,, } r t -omtors us ll our pts pss tos os. Morovr, o (wr w ) s s-put to t -omtor. Torm 2: A s-put wr w to t -omtor rmov (rpl y o-otroll vlu) wtout volt t rqurmt o t ly tolr. Proo: Omtt. w s w Cosr t sm xmpl Fur 5. A TMR ostrut y uplt tr ops o t orl rut. l m w Fur 5: T orl rut. w q 816

4 S wr w s s-put to t -omtor, or to Torm 2, w rmov wr w. Atr rmovl, t rsult rut s sow Fur 6. Tr my s-put wrs to t -omtors. T ollow torm wll sow tt rmovl o svrl s-put wrs stll stss t t ly tolr rqurmt. Lt wrs (w 11, w 12, w 13 ) r tr somorp wrs r s-put wrs. I to, wrs (w 21, w 22, w 23 ) r somorp wrs r s-put wrs. Torm 3: O wr mo tr somorp wrs (w 11, w 12, w 13 ) o wr mo tr somorp wrs (w 21, w 22, w 23 ) rmov smultously wtout volt t rqurmt o t ly tolr. Proo: Omtt Fur 6: Rmovl o s-put w. 1 l m 1 A 1 A 2 q V o t Aor to t ov torm, o rmov svrl s-put wrs t t sm tm. I tr r s-put wrs to t -omtors, o w s two somorp s-put wrs, w rmov s-put wrs. Tou tr r my wys to rmov s-put wrs, our lortm vly struts t rmovl to two uplto los su s A 1 A 3 Fur 1. T rsos r s ollows. Not tt rmov wr wll sort t ly o pt. I to, vot m ooss t so rrv put. To ru ovrll rut s ly, t s srl to ru two uplto los lys. A, Fur 5 o t orl rut totlly s our s-put wrs {w, w, w, w s }. W rmov two somorp wrs to {w, w } uplto lo A 1 two somorp wrs to {w, w s } A 3 t rsult rut s sow Fur SIGNAL SHARING OUTSIDE THE t -CRITICAL REGIONS Not tt ts ot t t -rtl ros v sls t lst t. For tos ts ot t t -rtl ros, w my urtr ru t r y sr (lolly) quvlt sls w mplmt t sm uto. For xmpl Fur 7, t output uto o o 1 A 1 t output uto o o A 2 v t sm utolty. W sr t output uto o o o 1 Fur 8. Atr sr, t rqur tm or o os ot ut t rrvl tm my rs u to t tol out rom o to o 1. W to r-omput t sl o o. I t sl o o s qul to or rtr t t, w prorm t sr; otrws, t sr s ot llow. Suppos ll quvlt sls r llow to sr, t l rut s sow Fur 8. Blo A l m 1 A 1 A 2 V o t A 3 3 l 3 m 3 3 A Fur 7: Rmov s-put wrs t two uplto los. Fur 8: T tr los t rsult rut. 817

5 Crut Ar Tl 1: Comprso tw t orl rut t orrspo ly tolr strutur Orl rut Dly tolr strutur ( t = 10%) Dly tolr strutur ( t = 15%) Crut ly Av. sl Ar Ar ovr (%) Crut ly #os wt t sl Av. sl Ar Ar ovr (%) Crut ly #os wt t sl Av. sl Sttstl lyss Orl rut Dly tolr t =10% Alu Alu Apx Apx B Fr Fr Pr Rot S S S S S S S S S Av A 3 Fur 8 om t two uxlry los our ly tolr strutur Fur 1. Not tt t ly o r-sytsz rut lrr or smllr t tt o t orl o. T ly o r-sytsz rut my lrr us o t xtr ly o vot m. O t otr, us som rtl pts my om ls, t ly o r-sytsz rut my smllr. For xmpl Fur 8, ll t ol pts A 2 om ls so ty soul ot osr t l tm. 5. EXPERIMENTAL RESULTS W v mplmt our lortm xprmt o lr st o MCNC ISCAS mr ruts. For rut, w rst us srpt.ly to mmz t ly o t rut. T, w us t ly tolr vlu o 10% 15% o t orl rut s ly to r-sytsz rut to two ly tolr ruts. T xprmtl rsults r mostrt Tl 1. Not rut C t two orrspo ly tolr ruts my v rt lys. To ompr sls rly mo tr ruts, t rqur tm or ll tr ruts s st to t ly o t orl rut C. I Tl 1, olum o vs t m o orl rut. Colum two sows t r, olum tr sows t ly, olum our sows t vr sl o ts t orl rut. Colum v to rport t xprmtl rsults w t s 10% o t orl rut s ly. Colum v sows t r. Colum sx vs t r plty t r-sytsz rut. Colum sv prsts t ly o t rut. Colum t rports t umr o ts wt t sl. Colum sows t vr sl or tos ts wt t sls. Cosr rut Alu2 s xmpl. T rut s t r o 487,664 t ly o T vr sl s Assum t ly tolr s 1.87 (=0.1*18.71). T r-sytsz rut s t r o 531,744 t ly o T w rut s o ts wt t sl. T vr sl s 3.62 ssum t rqur tm s Colum t to ourt sow t xprmtl rsults w t s 15% o t orl rut s ly. Assum t ly tolr s 2.81 (=0.15*18.71). T r-sytsz rut s t r o 617,584 t ly o T w rut s 10 ts wt t sl. A, w ssum t rqur tm to t vr sl s O t vr, w tt to v 10% o ly tolr, t r ovr s out 21% wl to v 15% o ly tolr, t r ovr s out 41%. T ly o t r-sytsz rut s out t sm s tt o t orl rut. I to, or r-sytss, ll mr ruts s wt muts o CPU tm o Su Bl 2000 worstto. W v prorm otr st o xprmts ssum t ly o t s v s prolty sty uto smlr to t wy [5]. W t ru 10,000 tms o t Mot-Crlo xprmt. Dur t xprmt, w lult t rut s ly o smpl rut ompr to pr- ly rqurmt w s st to {1.1*t rut s ly olum 3} or mr rut. W t out t umr o smpls wos lult lys r lss t t pr- ly 818

6 rqurmt. T rsults r sow olum t Tl 1. W t s 10% o t orl rut ly, olum sxt sows t umr o smpls wos lys r lss t t ly rqurmt or r-sytsz rut. T rut S1488 s xmpl. Amo 10,000 smpls, 6,933 smpls v ly lss t 14.49(=1.1*13.17) wl tr r-sytss, 9,990 smpls v ly lss t O t vr 68% o smpls o orl ruts v t ly rqurmt. O t otr, 87% o smpls o r-sytsz ruts v t sm ly rqurmt. T xprmtl rsults sow tt o t vr o 19% mor rut smpls v som ly rqurmts tr our r-sytss or ly tolr. 6. CONCLUSION W v prst rmwor to r-sytsz v rut or t ly tolr. Our mto opts wr rmovl sl sr to ru t r ovr our ly tolr strutur. Our xprmtl rsults sow tt t r plty s out 21% or 10% ly vrto tolr. REFERENCES [1] K. Br, G. Grotou, M. Lousr, I. Sstr, C. Hws, Dt-s ly tst o rsstv vs-otts, rtl vluto, Pro. o IEEE Itrtol Tst Cor, pp , Sp [2] M. A. Brur, C. Glso, S. Gupt, Nw vlto tst prolms or prorm p su-mro VLSI ruts, Tutorl Nots, IEEE VLSI Tst Symposum, Aprl [3] D. G. Cry K. Kutzr, Clos t p tw ASIC ustom: ASIC prsptv, Pro. o Ds Automto Co., pp , Ju 5-9, [4] Kurt Kutzr Ml Orssy, From l rtty to orm urtty, Pro. o t 8t ACM/IEEE It. Worsop o Tm Issus t Spto Sytss o Dtl Systms, pp , [5] J-J Lou, Al Krst, L-C. W, Kw-T C, Fls-pt-wr sttstl tm lyss t pt slto or ly tst tm vlto, Pro. o Ds Automto Co., pp , Ju 10-14, [6] Ero Mlvs, Sto Zll, Jul Usrso, M Mslo, Crlo Gur, Impt lyss o pross vrlty o tl ruts wt prorm lmt yl, IEEE It. Worsop o Sttstl Mtooloy, pp , Ju [7] Vo Num, J., Prolst los t sytss o rll orsms rom urll ompots, Automt Stus, A. o Mt. Stus, o. 34, C. E. So J. MCrty, Es., Prto Uvrsty Prss, pp ,