ESE535: Electronic Design Automation. Today. Topological Worst-Case Delay. Topological Worst-Case Delay. Topological Worst-Case Delay.

Transcription

1 ESE535: Elctronic Dsin Automation Day 2: April 4, 2 Static Timin Analysis an Multi-Lvl Spup Pnn ESE535 Sprin 2 -- DHon Toay Topoloical Worst Cas not aquat (too consrvativ) Snsitization Conitions Tim Calculus Dlay-justii paths Tim-PODEM Spup Bhavioral (C, MATLAB, ) Arch. Slct Schul RTL FSM assin Gat Ntlist Placmnt Routin Layout Masks Two-lvl Multilvl opt. Covrin Rtimin Pnn ESE535 Sprin 2 -- DHon 2 Topoloical Worst-Cas Dlay Topoloical Worst-Cas Dlay Comput ASAP schul Tak max o arrival tims Apply no Dlay No Dlays 2 Pnn ESE535 Sprin 2 -- DHon 3 Pnn ESE535 Sprin 2 -- DHon 4 Topoloical Worst-Cas Dlay 7 Comput Dlays Pnn ESE535 Sprin 2 -- DHon 5 Fals Paths Onc consir loic or nos Thr ar loical constraints on ata valus Thr ar paths that cannot loically occur Call thm als paths Pnn ESE535 Sprin 2 -- DHon 6

2 What can w o N to assss what paths ar ral Brut orc or vry pair o inputs comput lay in outputs rom in in2 input transition tak worst cas How many such lay tracs 2 2n lay tracs Pnn ESE535 Sprin 2 -- DHon 7 Altrnatly Look at sinl vctor an trmin what controls lay o circuit I.. look at valus on path an trmin path snsitiz to chan with input Pnn ESE535 Sprin 2 -- DHon 8 Controllin Inputs Controllin input to a at: input whos valu will trmin at output.. on a AND at on a OR at Static Snsitization A path is statically snsitiz i all th si (non-path) inputs ar noncontrollin I.. this path valu lips with th input Pnn ESE535 Sprin 2 -- DHon 9 Pnn ESE535 Sprin 2 -- DHon Statically Snsitiz Path Suicincy Static Snsitization is suicint or a path to b a tru path in circuit Pnn ESE535 Sprin 2 -- DHon Pnn ESE535 Sprin 2 -- DHon 2 2

3 Static Snsitization not Ncssary Static Snsitization not Ncssary Possibl path o lnth 3 Pnn ESE535 Sprin 2 -- DHon 3 Pnn ESE535 Sprin 2 -- DHon 4 Non-controllin = Static Snsitization not Ncssary Non-controllin = Static Snsitization not Ncssary Tru Path o Dlay @ 3 Non-controllin = Paths o lnth 3 not statically 2 Pnn ESE535 Sprin 2 -- DHon 5 Pnn ESE535 Sprin 2 -- DHon 6 Static Co-snsitization Each output with a controll valu has a controllin valu as input on path (an vic-vrsa or non-controll) Ncssary Static Co-snsitization is a ncssary conition or a path to b tru Pnn ESE535 Sprin 2 -- DHon 7 May trac multipl s Pnn ESE535 Sprin 2 -- DHon 8 3

4 Cosnsitization not Suicint Combinin Combin ths ias into a timcalculus or computin lays or an input vctor Cosnsitiz path o lnth 6. Ral lay is 5. Static co-snsitization Tru lay Static snsitization Pnn ESE535 Sprin 2 -- DHon 9 Pnn ESE535 Sprin 2 -- DHon 2 AND Timin Calculus Computin Dlays Ruls I at output is at a controllin valu, pick th minimum input an a at lay I at output is at a non-controllin valu, pick th maximum input an a at lay Pnn ESE535 Sprin 2 -- DHon 2 Pnn ESE535 Sprin 2 -- DHon 22 Exampl Pnn ESE535 Sprin 2 -- DHon 23 Pnn ESE535 Sprin 2 -- DHon 24 4

5 Exampl @5 W know how to t th lay o a sinl input conition Coul: in critical path sarch or an input vctor to snsitiz i ail, in nxt path until in lonst tru path May b O(2 n ) Pnn ESE535 Sprin 2 -- DHon 25 Pnn ESE535 Sprin 2 -- DHon 26 Bttr Approach Ask i can justiy a lay ratr than T Sarch or satisyin vctor or monstration that non xists Binary sarch to in tihtst lay Dlay Computation Moiication o a tstin routin us to justiy an output valu or a circuit similar to SAT PODEM (Path Orint DEcision Makin) backtrackin sarch to in a suitabl input vctor associat with som tart output branchin sarch with implication prunin Huristic or smart variabl orrin Pnn ESE535 Sprin 2 -- DHon 27 Pnn ESE535 Sprin 2 -- DHon 28 Sarch Taks two lists outputs to st; inputs alray st Propaat valus an implications I all outputs satisi succ Pick nxt PI to st an st valu Sarch (rcursiv call) with this valu st I inconsistnt I PI not impli Invrt valu o PI Sarch with this valu st I inconsistnt ail Els succ Els ail Els succ Pnn ESE535 Sprin 2 -- DHon 29 Pickin nxt variabl to st Follow back ats w/ unknown valus somtims output ictat input must b (AND nin output; with on input alray assin ) Implication somtims hav to uss what to ollow (OR with output an no inputs st) Uss huristics to ci what to ollow Pnn ESE535 Sprin 2 -- DHon 3 5

6 Exampl Exampl (oal =) Pnn ESE535 Sprin 2 -- DHon 3 Pnn ESE535 Sprin 2 -- DHon 32 Exampl (oal =) Exampl (oal =) Try B= Try B= Pnn ESE535 Sprin 2 -- DHon 33 Duc any inputs Pnn ESE535 Sprin 2 -- DHon 34 Exampl (oal =) Exampl (oal =) Impli A= Impli C= Duc any inputs Pnn ESE535 Sprin 2 -- DHon 35 Pnn ESE535 Sprin 2 -- DHon 36 6

7 For Tim Justiication Also want to comput lay on incompltly spcii valus Comput bouns on timin uppr boun, lowr boun Aain, us our tim calculus xpan to unknowns AND ruls Dlay Calculation Unknowns orc us to rprsnt uppr/lowr boun on lay. Pnn ESE535 Sprin 2 -- DHon 37 Pnn ESE535 Sprin 2 -- DHon 38 Tim PODEM Exampl (oal =@3) Input: valu to justiy an lay T Goal: in input vctor which proucs valu an xcs lay T Alorithm similar implications chck timin as wll @(,) Pnn ESE535 Sprin 2 -- DHon 39 Pnn ESE535 Sprin 2 -- DHon 4 Exampl (oal =@3) Exampl (oal =@3) @(,) @(,) Pnn ESE535 Sprin 2 -- DHon 4 Duc any inputs Pnn ESE535 Sprin 2 -- DHon 42 7

8 Exampl Exampl (oal @(,) @(,) Duc any inputs Pnn ESE535 Sprin 2 -- DHon 43 Fail to Pnn ESE535 Sprin 2 -- DHon 44 Exampl (oal =@3) Sarch @(,) Lss than 2 n prunin u to implications hr saw a must b no n to sarch xx subtr Pnn ESE535 Sprin 2 -- DHon 45 Pnn ESE535 Sprin 2 -- DHon 46 Qustions Any qustions on static timin analysis Sp Up (sktch lavor) Pnn ESE535 Sprin 2 -- DHon 47 Pnn ESE535 Sprin 2 -- DHon 48 8

9 Sp Up Start with ara optimiz ntwork Know tart arrival tims Know lay rom static analysis Want to ruc lay o no Improv sp by: Collapsin no(s) Basic Ia Ractorin collaps subraph to ruc hiht Pnn ESE535 Sprin 2 -- DHon 49 Pnn ESE535 Sprin 2 -- DHon 5 Sp Up Whil (lay crasin, timin not mt) Comput lay (slack) Static timin analysis Gnrat ntwork clos to critical path w/in som lay ε, to som istanc Wiht nos in ntwork Lss wiht = mor potntial to improv, prr to cut Comput mincut o nos on wiht ntwork For ach no in cutst Partial collaps For ach no in cutst Timin rcompos MinCut o Nos Cut nos not s Typically will n to transorm to ual raph All s bcom nos, nos bcom s Thn us maxlow/mincut Pnn ESE535 Sprin 2 -- DHon 5 Pnn ESE535 Sprin 2 -- DHon 52 MinCut o Nos MinCut o Nos What ar possibl cuts Pnn ESE535 Sprin 2 -- DHon 53 Pnn ESE535 Sprin 2 -- DHon 54 9

10 MinCut o Nos Wiht Cut W=W t +αw a α tunin paramtr Want to minimiz ara xpansion (W a ) Thins in collaps ntwork may b uplicat E.. W a =litrals in uplicat loic Want to maximiz likly bnit (W t ) Prr nos with irnt input tims to th nar critical path ntwork Quantiy: lar irnc in arrival tims Prr nos with critical path on lonr paths Pnn ESE535 Sprin 2 -- DHon 55 Pnn ESE535 Sprin 2 -- DHon 56 Wihin Bnit Want to maximiz likly bnit (W t ) Prr nos with irnt input tims to th nar critical path ntwork Wihin Bnit Want to maximiz likly bnit (W t ) Prr nos with critical path on lonr paths Pnn ESE535 Sprin 2 -- DHon Pnn ESE535 Sprin 2 -- DHon 58 Timin Dcomposition Dlay Dcompositions Extract ara savin krnls that o not inclu critical inputs to no =abc+abc+ab Krnls={c+c+,+,c+} (nxt tim) F=ab(c+)+abc, ab(c+c+), abc(+)+ab What composition us (an how inish compos) Critical input is {a,} Whn compos (.. into nan2 s) similarly balanc with critical inputs closst to output Pnn ESE535 Sprin 2 -- DHon 59 last: abc(+)+ab *((ab))+((ab)(c(+))) last: ab(c+)+abc *((*ab)(c+))+((ab)(c)) Pnn ESE535 Sprin 2 -- DHon 6

11 Dlay Dcompositions last: ab(c+)+abc *((ab)c)+((ab)((c+))) {a,} last: ab(c+)+abc a((b)(c+)+(bc)) Sp Up (rviw) Whil (lay crasin, timin not mt) Comput lay (slack) Static timin analysis Gnrat ntwork clos to critical path w/in som lay ε, to som istanc Wiht nos in ntwork Lss wiht = mor potntial to improv, prr to cut Comput mincut o nos on wiht ntwork For ach no in cutst Partial collaps For ach no in cutst timin rcompos Pnn ESE535 Sprin 2 -- DHon 6 Pnn ESE535 Sprin 2 -- DHon 62 Amin Rain Wnsay on blackboar Assinmnt 5 ra Try to look at Assin 6 toniht Normal oic hours this wk (T) Nxt wk oic hours (4/2) push back 5:35pm Pnn ESE535 Sprin 2 -- DHon 63 Bi Ias Topoloical Worst-cas lays ar consrvativ Onc consir loical constraints may hav als paths Ncssary an suicint conitions on tru paths Sarch or paths by lay or monstrat non xistnc Sarch with implications Itrativ improvmnt Pnn ESE535 Sprin 2 -- DHon 64