Race Conditions and Cycles. Race Conditions. Outline. Example 3: Asynchronous Analysis. Race-Free State Assignment. Race-Free State Assignment

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1 Olie La ime: Racefee Sae Aigme Exciaio Eqaio eig Example: Implemeaio Smmay of Aychoo eig Poce Race Codiio ad Cycle S Q S Q L L2 R Q' R Q' Thi lece: Aychoo Example Sae Aigme i Aychoo Eo eecio & Coecio Reiew: Badwidh ad Laecy Biay eciio iagam QQ2 QQ2 CS Newo/Pie.. CS Newo/Pie..2 Race Codiio QQ2 Example : Aychoo Aalyi (a) Aalyze he followig aychoo ewok ig a flow able. Saig i he able oal ae ae fo which =Z=, deemie he ae ad he op eqece whe he ip eqece i =,,,,,... (b) Fid ay ciical ace which ae pee i he able. Z CS Newo/Pie.. CS Newo/Pie.. RaceFee Sae Aigme A acefee ae aigme fo ay ow able ca be fod ig hee ae aiable Example: RaceFee Sae Aigme The aigme below i a ieal aeaigme map ha will wok fo ay ow able The example ca he be expaded a how, wih he addiioal ow added CS Newo/Pie.. CS Newo/Pie..6 CS Spig 97 Page..

2 RaceFee Sae Aigme Aohe ieal aigme fo ow able i how below (M. Mao, Logic ad Compe eig, Peice Hall) Uig hi appoach, he expaded example fom befoe become a how below igh Thi appoach fae ha peio geeal appoach aboe. Why? RaceFee Sae Aigme o cae ca be ed o make acefee aigme I example belowlef, we eed: col d a; col a b, c d; col b c; col a c, b d Look like we eed exa ow, b e he do cae: CS Newo/Pie..7 CS Newo/Pie..8 ShaedRow Aigme ShaedRow Aigme How do we ge hee? Tial ad eo... o o o Coide he example aboe. We eed a lea hee ae aiable ad maybe ee fo. e a, c a; e c a; c e a o ay of hee goig hogh a iemediae ae CS Newo/Pie..9 o o o ( ) CS Newo/Pie.. ShaedRow Aigme Rel of ig ecod opio fom peio lide: Eo eecio & Coecio A aio & wie become malle, he mbe of eleco ed o epee a oed o deceae The pobabiliy ha a comic ay, alpha paicle, local elecic field (coalk) o ome ohe dibace will chage a oed ale (o ee he ale o a wie) iceae Two apec: Eo deecio (e.g. paiy) Eo coecio (e.g. Hammig Code) 2bi deec, bi coec CS Newo/Pie.. CS Newo/Pie..2 CS Spig 97 Page..2 2

3 Hammig Code Mo commo ype of eocoecig code ed i RAM Baed o wok of R. W. Hammig k paiy bi ae added o a bi wod, fomig a ew +k bi wod The poiio mbeed wih powe of wo ae eeed fo he paiy bi Ca be ed wih wod of ay legh Example: 8bi daa wod P P 2 P P 8 Hammig Code Calclae paiy bi a follow: P = xo(,,7,9,) = = P 2 = xo(,6,7,,) = P = xo(,6,7,2) = P 8 = xo(9,,,2) = Whe bi ae ead fom memoy, compe check bi: C = xo(,,,7,9,) C 2 = xo(2,,6,7,,) C = xo(,,6,7,2) C 8 = xo(8,9,,,2) CS Newo/Pie.. CS Newo/Pie.. Hammig Code C=C 8 C C 2 C = idicae o eo ha occed Example: o eo eo i bi eo i bi C 8 C C 2 C o eo eo bi eo bi Hammig Code Fo daa bi ad k check bi, +k 2 k Gopig of bi fo paiy geeaio ca be obeed fom liig of biay mbe: B B 2 B B = fo (,,,7) B 2 = fo (2,,6,7) B = fo (,,6,7) CS Newo/Pie.. CS Newo/Pie..6 Hammig Code NMM: Combiaioal Implemeaio ff ff ff ff Add P a a oeall paiy bi: P eec/coec Rle a follow: If C=, P=o eo If C, P= igle eo, coecable If C, P= doble eo, coecable If C=, P=eo occed i P Ca alo hae fa moe ophiicaed cheme Coeed i deail i commicaio & ifomaio heoy coe CS Newo/Pie..7 ff ff ff ff ff ff ff op ip ime ^ ^ ^ ^ clock CS Newo/Pie ick..8 CS Spig 97 Page..

4 Pipelied Implemeaio ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff age age 2 age age Badwidh ad Laecy Laecy: The miimm ime o ge he fi el (ec.) he oeime co. Badwidh: The maximm ae a which el ca be podced i he eadyae (ale/ec.) he icemeal co Fo example, dic die, RAM (omal, ideo), ewok, igalpoceo (e.g. HTV, ada) op ime ip ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ CS Newo/Pie..9 CS Newo/Pie..2 Simple aaflow ecipio: B^2 AC B A C Schedlig of Fcioal Ui Gie a ceai mbe of fcioal i (e.g. ALU', RAM'), chedle a paicla compaio (fom he HL o ofwae) oo a paicla fcioal i a a paicla ime elaie o ohe opeaio. Aalogo poblem chedlig "wie" Wha abo he ale o he wie? CS Newo/Pie..2 CS Newo/Pie..22 Allocaio of Fcioal Ui: aa epedecie Allocaio of Fcioal Ui: TimeSpace Tadeoff B A C "pace" 2 6 "ime" "pace" 2 "pace" 2 "ime" CS Newo/Pie..2 CS Newo/Pie..2 CS Spig 97 Page..

5 Allocaio of Fcioal Ui: Shaig of Sigal Lik B A C d g b a e h z k l m "pace" 2 6 CS Newo/Pie..2 d e h b z g a l k m "ime" Allocaio of Fcioal Ui: Moe Efficie Ue of Lik "pace" d e h b g a z 2 6 CS Newo/Pie..26 l k m "ime" eig Uig Mliplexe Biay eciio iagam I geeal: f = ' flow + fhigh AB A C B 8 9 C Z low child high child f = Z = AB + C + B S2 S S CS Newo/Pie..27 CS Newo/Pie..28 Implemeaio of Logic Uig Swiche Shao Expaio: (T) F(,Y,Z) = F(,Y,Z) + ' F(,Y,Z) (T') F(,Y,Z) = (+F(,Y,Z)) ('+F(,Y,Z)) low child high child Biay eciio iagam f =.2 + V f = 2' + 2 V2 f2 = V f = CS Newo/Pie..29 CS Newo/Pie.. CS Spig 97 Page..

6 Ue of B fo Veificaio Codiio o edge foce ode o aiable. Ode m be coie wih all edge. Fo each edge, pae befoe child i he ode. 2 Ue of B fo Veificaio V i a edda eex V2, V epee he ame fcio A B i a edced biay deciio gaph Redcio i O(Nlog(N)) fo N eicie V V2 V CS Newo/Pie.. CS Newo/Pie..2 Ue of B fo Veificaio Each eex coepod o a paial aigme of ip. V:, Rel of edcio i a caoical fom. V CS Newo/Pie.. Combiaioal Veificaio Uig Caoical Fom Behaio Fcio he he yem yem m m impleme Implemeaioidepede decipio Regie Compoe ad ad hei hei iecoecio Sd. Sd. compoe & ROM, ROM, ASIC, ASIC, PL PL Gae Gae Lowleel compoe & e e I I em em of of ASIC ASIC libay libay Swich Swich Taioleel decipio Logic Logic Vale Vale ad ad Segh Elecical Volage, ce ce ad ad deailed deailed model model Coe o B Coe o B Iomophim Check CS Newo/Pie.. Coeciiy Veificaio Coeciiy Veificaio Newok compe igae Hah Hah Table Table compe igae Newok 2 () Read Newok ad Newok2 io epaae gaph daa ce (ally, ode = aio o gae, edge = coecio). (2) Compe igae fo ode o edge o boh. Typepecific: Gae ype, #ip, #op Newokpecific (local): Fai ype, #fao, fao ype Newokpecific (global): iace fom pimay ip, pimay op, ode ha ae kow o be he ame i each ewok (e.g. amed, pimay ip o op ("eed")). () Hah igae fom boh ewok io igle hah able. () If a hah able cell ha: > 2 ode: igoe fo ow = 2 ode: a mach ha bee fod = ode: a (eay!) eo ha bee fod () Add lik bewee ewok fo ode ha hae bee mached. (6) Recompe hah fcio fo bod ode ad epea il doe o o chage. CS Newo/Pie.. CS Newo/Pie..6 CS Spig 97 Page..6 6