Lecture Outline. Memory Hierarchy Management. Register Allocation. Register Allocation. Lecture 38. Cache Management. Managing the Memory Hierarchy
|
|
- Alexina Young
- 5 years ago
- Views:
Transcription
1 Ltur Outlin Mmory Hirrhy Mngmnt Rgistr Allotion Ltu8 (rom nots y G. Nul n R. Boik) Rgistr Allotion Rgistr intrrn grph Grph oloring huristis Spilling Ch Mngmnt 4/27/08 Pro. Hilingr CS164 Ltu8 1 4/27/08 Pro. Hilingr CS164 Ltu8 2 Th Mmory Hirrhy Mnging th Mmory Hirrhy Rgistrs 1 yl yts Progrms r writtn s i thr r only two kins o mmory: min mmory n isk Ch yls 256k-16M Min mmory yls 32M-16G Disk M yls 10G-1T Progrmmr is rsponsil or moving t rom isk to mmory (.g., il I/O) Hrwr is rsponsil or moving t twn mmory n hs Compilr is rsponsil or moving t twn mmory n rgistrs 4/27/08 Pro. Hilingr CS164 Ltu8 3 4/27/08 Pro. Hilingr CS164 Ltu8 4 Currnt Trns Ch n rgistr sizs r growing slowly Prossor sp improvs str thn mmory sp n isk sp Th ost o h miss is growing Th wining gp is rig with mor hs It is vry importnt to: Mng rgistrs proprly Mng hs proprly Compilrs r goo t mnging rgistrs 4/27/08 Pro. Hilingr CS164 Ltu8 5 Th Rgistr Allotion Prolm Intrmit o uss s mny tmporris s nssry This omplits inl trnsltion to ssmly But simpliis o gnrtion n optimiztion Typil intrmit o uss too mny tmporris Th rgistr llotion prolm: Rwrit th intrmit o to us wr tmporris thn thr r mhin rgistrs Mtho: ssign mor tmporris to rgistr But without hnging th progrm hvior 4/27/08 Pro. Hilingr CS164 Ltu8 6 1
2 History Rgistr llotion is s ol s intrmit o Rgistr llotion ws us in th originl FORTRAN ompilr in th 50s Vry ru lgorithms A rkthrough ws not hiv until 1980 whn Chitin invnt rgistr llotion shm s on grph oloring Rltivly simpl, glol n works wll in prti 4/27/08 Pro. Hilingr CS164 Ltu8 7 An Exmpl Consir th progrm := + := + := - 1 with th ssumption tht n i tr us Tmporry n rus tr + Sm with tmporry tr - 1 Cn llot,, n ll to on rgistr (r 1 ): r 1 := + r 1 := r 1 + r 1 := r 1-1 4/27/08 Pro. Hilingr CS164 Ltu8 8 Bsi Rgistr Allotion I Algorithm: Prt I Th vlu in tmporry is not n or th rst o th omputtion A tmporry n rus Bsi rul: Tmporris t 1 n t 2 n shr th sm rgistr i t ny point in th progrm t most on o t 1 or t 2 is liv! 4/27/08 Pro. Hilingr CS164 Ltu8 9 Comput liv vrils or h point: := + {,,} {,,} := - {,,} := + {,,,} {,} := 2 * := + := + := - 1 {,,,} 4/27/08 Pro. Hilingr CS164 Ltu8 10 Th Rgistr Intrrn Grph Two tmporris tht r liv simultnously nnot llot in th sm rgistr W onstrut n unirt grph A no or h tmporry An g twn t 1 n t 2 i thy r liv simultnously t som point in th progrm This is th rgistr intrrn grph (RIG) Two tmporris n llot to th sm rgistr i thr is no g onnting thm 4/27/08 Pro. Hilingr CS164 Ltu8 11 Rgistr Intrrn Grph. Exmpl. For our xmpl: E.g., n nnot in th sm rgistr E.g., n n in th sm rgistr 4/27/08 Pro. Hilingr CS164 Ltu8 12 2
3 Rgistr Intrrn Grph. Proprtis. It xtrts xtly th inormtion n to hrtriz lgl rgistr ssignmnts It givs glol (i.., ovr th ntir low grph) pitur o th rgistr rquirmnts Atr RIG onstrution th rgistr llotion lgorithm is rhittur inpnnt Grph Coloring. Dinitions. A oloring o grph is n ssignmnt o olors to nos, suh tht nos onnt y n g hv irnt olors A grph is k-olorl i it hs oloring with k olors 4/27/08 Pro. Hilingr CS164 Ltu8 13 4/27/08 Pro. Hilingr CS164 Ltu8 14 Rgistr Allotion Through Grph Coloring In our prolm, olors = rgistrs W n to ssign olors (rgistrs) to grph nos (tmporris) Lt k = numr o mhin rgistrs I th RIG is k-olorl thn thr is rgistr ssignmnt tht uss no mor thn k rgistrs 4/27/08 Pro. Hilingr CS164 Ltu8 15 Grph Coloring. Exmpl. Consir th smpl RIG r 1 Thr is no oloring with wr thn 4 olors Thr r 4-olorings o this grph 4/27/08 Pro. Hilingr CS164 Ltu8 16 r 4 Grph Coloring. Exmpl. Computing Grph Colorings Unr this oloring th o oms: := + r 4 := - := + r 1 r 1 := 2 * := + := - 1 := r 1 + r 4 Th rmining prolm is to omput oloring or th intrrn grph But: 1. This prolm is vry hr (NP-hr). No iint lgorithms r known. 2. A oloring might not xist or givn numr or rgistrs Th solution to (1) is to us huristis W ll onsir ltr th othr prolm 4/27/08 Pro. Hilingr CS164 Ltu8 17 4/27/08 Pro. Hilingr CS164 Ltu8 18 3
4 Grph Coloring Huristi Osrvtion: Pik no t with wr thn k nighors in RIG Elimint t n its gs rom RIG I th rsulting grph hs k-oloring thn so os th originl grph Why: Lt 1,, n th olors ssign to th nighors o t in th ru grph Sin n < k w n pik som olor or t tht is irnt rom thos o its nighors 4/27/08 Pro. Hilingr CS164 Ltu8 19 Grph Coloring Huristi Th ollowing works wll in prti: Pik no t with wr thn k nighors Push t on stk n rmov it rom th RIG Rpt until th grph hs on no Thn strt ssigning olors to nos in th stk (strting with th lst no ) At h stp pik olor irnt rom thos ssign to lry olor nighors 4/27/08 Pro. Hilingr CS164 Ltu8 20 Grph Coloring Exmpl (1) Strt with th RIG n with k = 4: Stk: {} Rmov n thn Grph Coloring Exmpl (2) Rsulting grph: Stk: {, } Now ll nos hv wr thn 4 nighors n n rmov:,,, Lving n mpty grph n stk ontining {,,,,, } 4/27/08 Pro. Hilingr CS164 Ltu8 21 4/27/08 Pro. Hilingr CS164 Ltu8 22 Grph Coloring Exmpl (2) Wht i th Huristi Fils? Strt ssigning olors to:,,,,, At h stp, gurnt thr s r olor r 1 4/27/08 Pro. Hilingr CS164 Ltu8 23 r 4 Wht i uring simpliition w gt to stt whr ll nos hv k or mor nighors? Exmpl: try to in 3-oloring o th RIG: 4/27/08 Pro. Hilingr CS164 Ltu8 24 4
5 Wht i th Huristi Fils? Rmov n gt stuk (s shown low) Pik no s nit or spilling A spill tmporry livs in mmory Assum tht is pik s nit Wht i th Huristi Fils? Rmov n ontinu th simpliition Simpliition now sus:,,, 4/27/08 Pro. Hilingr CS164 Ltu8 25 4/27/08 Pro. Hilingr CS164 Ltu8 26 Wht i th Huristi Fils? Spilling On th ssignmnt phs w gt to th point whn w hv to ssign olor to W hop tht mong th 4 nighors o w us lss thn 3 olors optimisti oloring? r2 r3 4/27/08 Pro. Hilingr CS164 Ltu8 27 r 1 Sin optimisti oloring il w must spill tmporry W must llot mmory lotion s th hom o Typilly this is in th urrnt stk rm Cll this rss Bor h oprtion tht uss, insrt := lo Atr h oprtion tht ins, insrt stor, 4/27/08 Pro. Hilingr CS164 Ltu8 28 Spilling. Exmpl. Romputing Livnss Inormtion This is th nw o tr spilling := 2 * stor, := + := - := lo := + := lo := + := + := - 1 4/27/08 Pro. Hilingr CS164 Ltu8 29 Th nw livnss inormtion tr spilling: {,,} {,,} {,,} {,} := 2 * stor, := + := - := lo := + := lo := + := + := - 1 {,,,} {,,} {,,,} 4/27/08 Pro. Hilingr CS164 Ltu8 30 5
6 Romputing Livnss Inormtion Th nw livnss inormtion is lmost s or is liv only Btwn := lo n th nxt instrution Btwn stor, n th pring instr. Spilling rus th liv rng o An thus rus its intrrns Whih rsult in wr nighors in RIG or 4/27/08 Pro. Hilingr CS164 Ltu8 31 Romput RIG Atr Spilling Th only hngs r in rmoving som o th gs o th spill no In our s still intrrs only with n An th rsulting RIG is 3-olorl 4/27/08 Pro. Hilingr CS164 Ltu8 32 Spilling (Cont.) Aitionl spills might rquir or oloring is oun Th triky prt is iing wht to spill Possil huristis: Spill tmporris with most onlits Spill tmporris with w initions n uss Avoi spilling in innr loops Any huristi is orrt Chs Compilrs r vry goo t mnging rgistrs Muh ttr thn progrmmr oul Compilrs r not goo t mnging hs This prolm is still lt to progrmmrs It is still n opn qustion whthr ompilr n o nything gnrl to improv prormn Compilrs n, n w o, prorm som simpl h optimiztion 4/27/08 Pro. Hilingr CS164 Ltu8 33 4/27/08 Pro. Hilingr CS164 Ltu8 34 Ch Optimiztion Consir th loop or(j = 1; j < 10; j++) or(i=1; i< ; i++) [i] *= [i] This progrm hs trril h prormn Why? Ch Optimiztion (II) Consir th progrm: or(i=1; i< ; i++) or(j = 1; j < 10; j++) [i] *= [i] Computs th sm thing But with muh ttr h hvior Might tully mor thn 10x str A ompilr n prorm this optimiztion ll loop intrhng 4/27/08 Pro. Hilingr CS164 Ltu8 35 4/27/08 Pro. Hilingr CS164 Ltu8 36 6
7 Ch Optimiztion (III) Othr kins o mmory lyout isions possil, suh s ping rows o mtrix or ttr it in h. Prthing inorms h o ntiipt utur mmory ths so tht thy n pro in prlll. Hrwr otn os this, in whih s ompilr my hv to tll it whn not to prth. Conlusions Rgistr llotion is must hv optimiztion in most ompilrs: Bus intrmit o uss too mny tmporris Bus it mks ig irn in prormn Grph oloring is powrul rgistr llotion shm Goo h mngmnt oul giv muh lrgr pyos, ut it is iiult. 4/27/08 Pro. Hilingr CS164 Ltu8 37 4/27/08 Pro. Hilingr CS164 Ltu8 38 7
Lecture Outline. Memory Hierarchy Management. Register Allocation. Register Allocation. Lecture 19. Cache Management. The Memory Hierarchy
Ltur Outlin Mmory Hirrhy Mngmnt Rgistr Allotion Ltur 19 Rgistr Allotion Rgistr intrrn grph Grph oloring huristis Spilling Ch Mngmnt Pro. Boik CS 164 Ltur 17 1 Pro. Boik CS 164 Ltur 17 2 Th Mmory Hirrhy
More informationGlobal Register Allocation
Ltur Outlin Glol Rgistr Allotion Mmory Hirrhy Mngmnt Rgistr Allotion vi Grph Coloring Rgistr intrrn grph Grph oloring huristis Spilling Ch Mngmnt 2 Th Mmory Hirrhy Rgistrs 1 yl 256-8000 yts Ch 3 yls 256k-16M
More informationHistory Rgistr Allotion Exmpl As ol s intrmit o Consir this progrm with six vrils: := + := + := - 1 Us in th originl FORTRAN ompilr (1950 s) Vry ru lg
Th Mmory Hirrhy Avn Compilrs CMPSCI 710 Spring 2003 Highr = smllr, str, losr to CPU A rl sktop mhin (min) Rgistr Allotion Emry Brgr rgistrs 8 intgr, 8 loting-point; 1-yl ltny L1 h 8K t & instrutions; 2-yl
More informationLecture 39: Register Allocation. The Memory Hierarchy. The Register Allocation Problem. Managing the Memory Hierarchy
Ltur 39: Rgistr Alloation [Aapt rom nots y R. Boik an G. Nula] Topis: Mmory Hirarhy Managmnt Rgistr Alloation: Rgistr intrrn graph Graph oloring huristis Spilling Cah Managmnt Th Mmory Hirarhy Computrs
More informationCSE P 501 Compilers. Register Allocation Hal Perkins Spring UW CSE P 501 Spring 2018 P-1
CSE P 501 Compilrs Rgistr Allotion Hl Prkins Spring 2018 UW CSE P 501 Spring 2018 P-1 Agn Rgistr llotion onstrints Lol mthos Fstr ompil, slowr o, ut goo nough or lots o things (JITs, ) Glol llotion rgistr
More informationReachability. Directed DFS. Strong Connectivity Algorithm. Strong Connectivity. DFS tree rooted at v: vertices reachable from v via directed paths
irt Grphs OR SFO FW LX JFK MI OS irph is rph whos s r ll irt Short or irt rph pplitions on-wy strts lihts tsk shulin irphs ( 12.) irt Grphs 1 irt Grphs 2 irph Proprtis rph G=(V,) suh tht h os in on irtion:
More informationOutline. Graphs Describing Precedence. Graphs Describing Precedence. Topological SorFng of DAGs. Graphs Describing Precedence 4/25/12. Part 10.
4// Outlin Prt. Grphs CS Algorithms n Dt Struturs Introution Trminology Implmnting Grphs Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits Grphs Dsriing Prn Grphs Dsriing
More informationReview: Binary Trees. CSCI 262 Data Structures. Search Trees. In Order Traversal. Binary Search Trees 4/10/2018. Review: Binary Tree Implementation
Rviw: Binry Trs CSCI 262 Dt Struturs 21 Binry Srh Trs A inry tr is in rursivly: = or A inry tr is (mpty) root no with lt hil n riht hil, h o whih is inry tr. Rviw: Binry Tr Implmnttion Just ollow th rursiv
More informationInterference graph. Register Allocation. A bigger example. Units of allocation
Rgistr Alloation Intrfrn graph Th prolm: assign mahin rsours (rgistrs, stak loations) to hol run-tim ata Constraint: simultanously liv ata alloat to iffrnt loations Goal: minimiz ovrha of stak loas & stors
More informationFinding a Funicular Curve Through Two Points
This is th glss pyrmi t th Louvr Musum in Pris, sign y rhitt I.M. Pi. It is support from nth y stl ls. In signing strutur suh s this, it is oftn most usful to slt l of rtin siz n tnsil strngth, n thn to
More informationRegister Allocation. Register Allocation
Rgistr Allocation Jingk Li Portlan Stat Univrsity Jingk Li (Portlan Stat Univrsity) CS322 Rgistr Allocation 1 / 28 Rgistr Allocation Assign an unboun numbr of tmporaris to a fix numbr of rgistrs. Exampl:
More informationCompiling: Examples and Sample Problems
REs for Kywors Compiling: Exmpls n mpl Prolms IC312 Mchin-Lvl n ystms Progrmming Hnri Csnov (hnric@hwii.u) It is sy to fin RE tht scris ll kywors Ky = if ls for whil int.. Ths cn split in groups if n Kywor
More informationGraph Theory & Applications. Boundaries Using Graphs. Graph Search. Find the route that minimizes. cost
Graph Thory & Appliations Bounaris Using Graphs 3 4 3 4 5 Fin th rout that minimizs osts Fin th ritial path in a projt Fin th optimal borr aroun a rgion Fin loop an no quations or analog iruit analysis
More informationCSE 401/M501 Compilers
CSE 401/M501 Compilrs Compilr Bckn Survy Hl Prkins Spring 2018 UW CSE 401/M501 Spring 2018 Q-1 Aministrivi Compilr projct: floting-point u tomorrow (plus lt ys if you hv thm); short rport u Stury night
More informationCS 331: Artificial Intelligence Bayesian Networks (Inference) Inference
S 331: rtificil Intllignc ysin Ntworks Infrnc 1 Infrnc Suppos you r givn ysin ntwork with th grph structur n th prmtrs ll figur out Now you woul lik to us it to o infrnc You n infrnc to mk prictions or
More informationPortability, Scalability, and Numerical Stability in Accelerated Kernels
Portility, Slility, nd Numril Stility in Alrtd Krnls John Strtton Dotorl Cndidt: Univrsity of Illinois t Urn-Chmpign Snior Arhitt: MultiorWr In Outlin Prformn Portility Wht CPU progrmmrs nd to lrn from
More informationCS553 Lecture Introduction to Data-flow Analysis 1
! Ide Introdution to Dt-flow nlysis!lst Time! Implementing Mrk nd Sweep GC!Tody! Control flow grphs! Liveness nlysis! Register llotion CS553 Leture Introdution to Dt-flow Anlysis 1 Dt-flow Anlysis! Dt-flow
More informationWORKSHOP 2 Solid Shell Composites Modeling
WORKSHOP 2 Soli Shll Composits Moling WS2-1 WS2-2 Workshop Ojtivs Bom fmilir with stting up soli omposit shll mol Softwr Vrsion Ptrn 2011 MD Nstrn 2011.1 Fils Rquir soli_shll. WS2-3 Prolm Dsription Simult
More informationCharacteristics of Fault Simulation. Fault Simulation Techniques. Parallel Fault Simulation. Parallel Fault Simulation
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
More information12/3/2008. Schedule. Target Code Generation. Target Code Generation. Gap: machine code. Tasks of Code Generator. These tasks interact
Shul Trgt Co Gnrtion Dvi Notkin Autumn 2008 Projt D: intrmit o gnrtion Du: Dmr 3 Du Dmr 10, 5PM (vill Mony 11/17) Projt E: trgt o gnrtion [MiniJv++] Writtn ssignmnt [MiniJv--] Finl on Dmr 11 (on hour,
More informationLesson 4.4. Euler Circuits and Paths. Explore This
Lesson 4.4 Euler Ciruits nd Pths Now tht you re fmilir with some of the onepts of grphs nd the wy grphs onvey onnetions nd reltionships, it s time to egin exploring how they n e used to model mny different
More informationOverview Linear Algebra Review Linear Algebra Review. What is a Matrix? Additional Resources. Basic Operations.
Oriw Ro Jnow Mon, Sptmr 2, 24 si mtri oprtions (, -, *) Cross n ot prouts Dtrminnts n inrss Homonous oorints Ortonorml sis itionl Rsours 8.6 Tt ook 6.837 Tt ook 6.837-stff@rpis.sil.mit.u Ck t ours wsit
More informationCS153: Compilers Lecture 20: Register Allocation I
CS153: Copilrs Ltur 20: Ristr Alloation I Stpn Con ttps://www.sas.arvar.u/ourss/s153 Pr-lass Puzzl Wat s t iniu nur o olors n to olor a ap o t USA? Evry stat is assin on olor Aant stats ust ivn irnt olors
More informationStore Tours Washington DC
Things To Look For: Th Customr Journy == Entrn == Cln n inviting? Opning hours post? Wht o you noti vn for you ntr? == First Imprssion == Lighting? Musi plying? Dos th stor fl wloming? Dos somon grt you
More informationTiling the plane with equilateral convex pentagons
Prol Volum 52, Issu 3 (2016) Tiling th pln with quiltrl onvx pntgons Mri Fishr 1 Mthmtiins n non-mthmtiins hv n onrn with fining pntgonl tilings for lmost 100 yrs, yt tiling th pln with onvx pntgons rmins
More information1⅝" - 3¾" (40-95mm) FIXTURE BASE. 3/4" (19mm) 4" - 6¾" ( mm) ALLEN KEY (INCLUDED)
PG: 1 O 7 IMPORTNT - R RULLY OR INSTLLING IXTUR. RTIN THS INSTRUTIONS OR UTUR RRN. THIS PROUT MUST INSTLL IN ORN WITH TH NTIONL LTRIL O N LL PPLIL LOL OS, Y PRSON MILIR WITH TH ONSTRUTION N OPRTION O TH
More informationWORKSHOP 12 ANCHOR LOADS AND BOUNDARY CONDITIONS USING A FIELD
WORKSHOP 12 ANCHOR LOADS AND BOUNDARY CONDITIONS USING A FIELD WS12-1 WS12-2 Workshop Ojtivs Using fil for prssur loing, n rting onstrints t th lotions for wshrs Prolm Dsription Crt fil with th sin funtion,
More informationReading. K-D Trees and Quad Trees. Geometric Data Structures. k-d Trees. Range Queries. Nearest Neighbor Search. Chapter 12.6
Rn Cptr 12.6 K-D Trs n Qu Trs CSE 326 Dt Struturs Ltur 9 2/2/05 K-D Trs n Qu Trs - Ltur 9 2 Gomtr Dt Struturs Ornzton o ponts, lns, plns, to support str prossn Appltons Astropsl smulton voluton o ls Grps
More informationCS453 INTRODUCTION TO DATAFLOW ANALYSIS
CS453 INTRODUCTION TO DATAFLOW ANALYSIS CS453 Leture Register llotion using liveness nlysis 1 Introdution to Dt-flow nlysis Lst Time Register llotion for expression trees nd lol nd prm vrs Tody Register
More informationQuadrilateral Decomposition by Two-Ear Property Resulting in CAD Segmentation
Quriltrl Domposition y wo-er Proprty Rsulting in CAD Sgmnttion Mhrvo Rnrinrivony Astrt W minly im t splitting simply onnt polygon into st o onvx quriltrls without insrting nw ounry nos. Our pproh is s
More informationGreedy Algorithm. Algorithm Fall Semester
Greey Algorithm Algorithm 0 Fll Semester Optimiztion prolems An optimiztion prolem is one in whih you wnt to fin, not just solution, ut the est solution A greey lgorithm sometimes works well for optimiztion
More informationWORKSHOP 17 BOX BEAM WITH TRANSIENT LOAD
WORKSHOP 17 BOX BEAM WITH TRANSIENT LOAD WS17-1 WS17-2 Workshop Ojtivs Prform mol nlysis for linr ynmi mol. Also, prform linr trnsint nlysis for th mol. Viw th shp of th mol ovr tim. Crt n X vs Y plot
More informationThe Network Layer: Routing Algorithms. The Network Layer: Routing & Addressing Outline
PS 6 Ntwork Programming Th Ntwork Layr: Routing lgorithms Michl Wigl partmnt of omputr Scinc lmson Univrsity mwigl@cs.clmson.du http://www.cs.clmson.du/~mwigl/courss/cpsc6 Th Ntwork Layr: Routing & ddrssing
More information2018 How to Apply. Application Guide. BrandAdvantage
2018 How to Apply Application Guid BrandAdvantag Contnts Accssing th Grant Sit... 3 Wlcom pag... 3 Logging in To Pub Charity... 4 Rgistration for Nw Applicants ( rgistr now )... 5 Organisation Rgistration...
More informationCPSC 826 Internetworking. The Network Layer: Routing & Addressing Outline. The Network Layer: Routing Algorithms. Routing Algorithms Taxonomy
PS Intrntworking Th Ntwork Layr: Routing & ddrssing Outlin Th Ntwork Layr: Routing lgorithms Michl Wigl partmnt of omputr Scinc lmson Univrsity mwigl@cs.clmson.du Novmbr, Ntwork layr functions Routr architctur
More informationCMPUT101 Introduction to Computing - Summer 2002
CMPUT Introdution to Computing - Summer 22 %XLOGLQJ&RPSXWHU&LUFXLWV Chpter 4.4 3XUSRVH We hve looked t so fr how to uild logi gtes from trnsistors. Next we will look t how to uild iruits from logi gtes,
More informationShift. Reduce. Review: Shift-Reduce Parsing. Bottom-up parsing uses two actions: Bottom-Up Parsing II. ABC xyz ABCx yz. Lecture 8.
Rviw: Shift-Rduc Parsing Bottom-up parsing uss two actions: Bottom-Up Parsing II Lctur 8 Shift ABC xyz ABCx yz Rduc Cbxy ijk CbA ijk Prof. Aikn CS 13 Lctur 8 1 Prof. Aikn CS 13 Lctur 8 2 Rcall: h Stack
More information8.3 INTEGRATION BY PARTS
8.3 Intgration By Parts Contmporary Calculus 8.3 INTEGRATION BY PARTS Intgration by parts is an intgration mthod which nabls us to find antidrivativs of som nw functions such as ln(x) and arctan(x) as
More information10.2 Graph Terminology and Special Types of Graphs
10.2 Grph Terminology n Speil Types of Grphs Definition 1. Two verties u n v in n unirete grph G re lle jent (or neighors) in G iff u n v re enpoints of n ege e of G. Suh n ege e is lle inient with the
More informationDefinition of Regular Expression
Definition of Regulr Expression After the definition of the string nd lnguges, we re redy to descrie regulr expressions, the nottion we shll use to define the clss of lnguges known s regulr sets. Recll
More informationSoftware Pipelining Can we decrease the latency? Goal of SP Lecture. Seth Copen Goldstein Software Pipelining
5-4 Ltur 5-745 Sotwr Piplinin Copyrit St Copn Goltin -8 Sotwr Piplinin Sotwr piplinin i n IS tniqu tt rorr t intrution in loop. Poily movin intrution rom on itrtion to t prviou or t nxt itrtion. Vry lr
More informationModel Intelli-INCH. Miniature Stepper Motor Controllers/Drivers. Electrical Specifications. Models. Key Features. i/o connector, Intelli-inch-lr
Model Intelli-INH lectrical Specifications Supply Input 9V to 30V 1 xamples: igikey part 271-2446 or 62-1068 imensions 1 X 1 (254mm X 254mm) square Step Resolution 1/16 microstep Operating Modes Standalone
More informationCS 241 Week 4 Tutorial Solutions
CS 4 Week 4 Tutoril Solutions Writing n Assemler, Prt & Regulr Lnguges Prt Winter 8 Assemling instrutions utomtilly. slt $d, $s, $t. Solution: $d, $s, nd $t ll fit in -it signed integers sine they re 5-it
More informationISO VIEW COVER, EXPRESS EXIT 4X4 FLIP COVER OPEN VIEW EXPRESS EXIT ON TROUGH VIEW
RV MO WN T 00899MO OVL 07-JN-5 0078MO HUH 7-SP-5 5.90 RF.87 RF.000 RF ISO VIW SL OVR, 0.50 OVR XTNSION X FLIP OVR FGS-MX-- (NOT INLU IN KIT).07 RF 7.7 RF FLIP OVR OPN VIW SL X STRIGHT STION RF RKT, XPRSS
More information" dx v(x) $ % You may also have seen this written in shorthand form as. & ' v(x) + u(x) '# % ! d
Calculus II MAT 146 Mthods of Intgration: Intgration by Parts Just as th mthod of substitution is an intgration tchniqu that rvrss th drivativ procss calld th chain rul, Intgration by parts is a mthod
More informationBelow, are instructions about how to set each goal and report achievements in Your Club, Service, and Foundation Giving.
Rotry Clu Cntrl is n onlin tool to hlp lus st nd trk lu gols nd hivmnts. This rfrn guid outlins th stps you nd to tk to st nd dit gols s wll s rport hivmnts in Rotry Clu Cntrl. If ny dt is displyd inorrtly,
More informationChapter 9. Greedy Technique. Copyright 2007 Pearson Addison-Wesley. All rights reserved.
Chpter 9 Greey Tehnique Copyright 2007 Person Aison-Wesley. All rights reserve. Greey Tehnique Construts solution to n optimiztion prolem piee y piee through sequene of hoies tht re: fesile lolly optiml
More informationFelony Sentences in State Courts, 2002
U.S. Dprtmnt o Justi Oi o Justi Progrms Buru o Justi Sttistis Bulltin Dmr 004, NCJ 0696 Flony Sntns in Stt Courts, 00 By Mtthw R. Duros n Ptrik A. Lngn, Ph.D. BJS Sttistiins In 00 Stt ourts onvit n stimt,0,000
More informationInternet Routing. IP Packet Format. IP Fragmentation & Reassembly. Principles of Internet Routing. Computer Networks 9/29/2014.
omputer Networks 9/29/2014 IP Pket Formt Internet Routing Ki Shen IP protool version numer heder length (words) for qulity of servie mx numer remining hops (deremented t eh router) upper lyer protool to
More informationDistance vector protocol
istne vetor protool Irene Finohi finohi@i.unirom.it Routing Routing protool Gol: etermine goo pth (sequene of routers) thru network from soure to Grph strtion for routing lgorithms: grph noes re routers
More informationFLASHING CHRISTMAS TREE KIT
R4 FLASHING CHRISTMAS TREE KIT 9 10 8 7 11 6 R3 12 T4 C4 5 T3 R5 R7 13 C3 C2 4 14 R1 T2 R6 3 OWNER S MANUAL T1 R8 15 2 C1 R2 1 16 Cat. No. 277-8001 CUSTOM MANUFACTURED FOR TANDY CORPORATION LTD ASSEMBLY
More informationPerformance, Scalability, and Numerical Stability of Manycore. Wen-mei Hwu University of Illinois at Urbana-Champaign
Prformn, Slility, nd Numril Stility of Mnyor Algorithms Wn-mi Hwu Univrsity of Illinois t Urn-Chmpign Cry XE6 Nods Blu Wtrs ontins,64 Cry XE6 omput nods. Dul-sokt Nod Two AMD Intrlgos hips 6 or moduls,
More informationCMST 220 PUBLIC SPEAKING
MST 220 PUBLI SPKING R G. MTZGR, INSTRUTOR OI: RINIR 213 PHON: 253-964-6659 fmetzger@pierce.ctc.edu O V R V I W PUBLI SPKING IS N OPPORTUNITY TO LOOK GOO IN RONT O POPL. LL YOUR LI YOUR SPH WILL HLP YOU
More informationHow to fix your 260Z or 280Z clock.
Sujt Fixing th Kanto Siki lok Author E. Bttio How to fix your 260Z or 280Z lok. I first wrot this up aout two yars ago. This is th sond vrsion of this produr. It is not vry muh diffrnt to my first ffort
More informationTHE OTTAWA CHINESE ALLIANCE CHURCH
T OTTW INS LLIN UR LS, OTTW, ONTRIO Sheet List 0.00 TITL ST 0..6 ISSU OR SIT PLN ONTROL.00 SIT PLN 0..6 ISSU OR SIT PLN ONTROL.0 ONSTRUTION SSMLIS.0 SIT TILS.50 UILIN PRKIN & LVL MO.00 LVL 0 - PRKIN LVL
More informationOn Some Maximum Area Problems I
On Som Maximum Ara Problms I 1. Introdution Whn th lngths of th thr sids of a triangl ar givn as I 1, I and I 3, thn its ara A is uniquly dtrmind, and A=s(s-I 1 )(s-i )(s-i 3 ), whr sis th smi-primtr t{i
More informationType Checking. Roadmap (Where are we?) Last lecture Context-sensitive analysis. This lecture Type checking. Symbol tables
Type Cheking Rodmp (Where re we?) Lst leture Contet-sensitie nlysis Motition Attriute grmmrs Ad ho Synt-direted trnsltion This leture Type heking Type systems Using synt direted trnsltion Symol tles Leil
More informationMERGE-BASED SpMV PERFECT WORKLOAD BALANCE. GUARANTEED. Duane Merrill, NVIDIA Research
MERGE-BASED SpMV PERFECT WORKLOAD BALANCE. GUARANTEED. Dun Mrrill, NVIDIA Rsr SPARSE MATRIX-VECTOR MULTIPLICATION SpMV (Ax = y) -- -- -- -- -- -- -- -- * = 2.0 0.0 2.0 4.0 sprs mtrix A ns vtor x ns vtor
More informationCS 340, Fall 2016 Sep 29th Exam 1 Note: in all questions, the special symbol ɛ (epsilon) is used to indicate the empty string.
CS 340, Fll 2016 Sep 29th Exm 1 Nme: Note: in ll questions, the speil symol ɛ (epsilon) is used to indite the empty string. Question 1. [10 points] Speify regulr expression tht genertes the lnguge over
More informationCompression Outline :Algorithms in the Real World. Lempel-Ziv Algorithms. LZ77: Sliding Window Lempel-Ziv
Compression Outline 15-853:Algorithms in the Rel World Dt Compression III Introduction: Lossy vs. Lossless, Benchmrks, Informtion Theory: Entropy, etc. Proility Coding: Huffmn + Arithmetic Coding Applictions
More informationECO GUIDE TO Unstratified Samples
ECO GUIDE TO Unstrtifid Smpls Wht Is n Unstrtifid Smpld? If you hv didd to ondut smpl invntory, you will b ollting dt for plots lotd throughout your study r. In this typ of projt, you n hoos to strtify
More informationEE 231 Fall EE 231 Homework 10 Due November 5, 2010
EE 23 Fall 2 EE 23 Homwork Du Novmbr 5, 2. Dsign a synhronous squntial iruit whih gnrats th following squn. (Th squn should rpat itslf.) (a) Draw a stat transition diagram for th iruit. This is a systm
More informationS675, S750 Stretchair Parts List A D
Page of 7 F G PRTS LIST Number Part Number escription M675-038 STR, 6" NTRL LOKING, TOTL LK TWIN WHL M675-04 STR, 6" NTRL LOKING, IR LK, TWIN WHL S-HX-ZP-M6-0 SRW, HX H, M6 X 0 MM LG 4 W-LI-ZP-5-47-03
More informationLecture 8: Graph-theoretic problems (again)
COMP36111: Advned Algorithms I Leture 8: Grph-theoreti prolems (gin) In Prtt-Hrtmnn Room KB2.38: emil: iprtt@s.mn..uk 2017 18 Reding for this leture: Sipser: Chpter 7. A grph is pir G = (V, E), where V
More informationCONVEX POLYGONS FOR APERIODIC TILING
Rsrh n ommunitions in Mthmtis n Mthmtil Sins Vol. 8, Issu 1, 2017, Pgs 69-79 ISSN 2319-6939 Pulish Onlin on Sptmr 7, 2017 2017 Jyoti Ami Prss http://jyotimiprss.org ONVX POLYGONS FOR APRIOI TILING TRUHISA
More informationGreedy Algorithms. Interval Scheduling. Greedy Algorithm. Optimality. Greedy Algorithm (cntd) Greed is good. Greed is right. Greed works.
Algorithm Grdy Algorithm 5- Grdy Algorithm Grd i good. Grd i right. Grd work. Wall Strt Data Structur and Algorithm Andri Bulatov Algorithm Grdy Algorithm 5- Algorithm Grdy Algorithm 5- Intrval Schduling
More informationVAT GX - IP VIDEO FIELD ADD-ON/RETROFIT SPECIFICATIONS PERSPECTIVE SIDE VIEW MOUNTING CONNECTIONS CALL SINGLE CHANNEL ENCODER
VT GX - IP VIDO ILD DD-ON/RTROIT L00 LL -800-999-600 SINGL HNNL NODR SPIITIONS NTWORK ONNTORS SING: MTRIL: P + BS X7240 OLOR: DRK BLU DIMNSIONS IN MILLIMTRS (DIMNSIONS IN INHS) SUSTINBILITY: MMORY: PV
More informationVAT GX - IP VIDEO FIELD ADD-ON/RETROFIT SINGLE CHANNEL ENCODER
L00 LL -800-999-600 VT GX - IP VIDO ILD DD-ON/RTROIT SINGL HNNL NODR NTWORK ONNTORS SING: MTRIL: P + BS X7240 OLOR: DRK BLU SUSTINBILITY: MMORY: PV R 256 MB RM, 256 MB LSH BTTRY BKD- RL TIM LOK POWR: POWR
More informationMTH 146 Conics Supplement
105- Review of Conics MTH 146 Conics Supplement In this section we review conics If ou ne more detils thn re present in the notes, r through section 105 of the ook Definition: A prol is the set of points
More informationCS412/413. Introduction to Compilers Tim Teitelbaum. Lecture 4: Lexical Analyzers 28 Jan 08
CS412/413 Introduction to Compilers Tim Teitelum Lecture 4: Lexicl Anlyzers 28 Jn 08 Outline DFA stte minimiztion Lexicl nlyzers Automting lexicl nlysis Jlex lexicl nlyzer genertor CS 412/413 Spring 2008
More informationFig.25: the Role of LEX
The Lnguge for Specifying Lexicl Anlyzer We shll now study how to uild lexicl nlyzer from specifiction of tokens in the form of list of regulr expressions The discussion centers round the design of n existing
More informationTorrance Transit Park and Ride. Regional Terminal. PHASE II CLIENT PROJECT #: B Drawing Title
I M QUIMNT LGN VI SITION T I M ONTOL NL MIN I M TMINL INT I M NNUNITO NL WTH-OO MULTI N HON/STO, WLL MOUNT MULTI N HON/STO, WLL MOUNT HON, WLL MOUNT HON, ILING MOUNT MULTI N HON/STO, ILING MOUNT WTH-OO
More informationCS321 Languages and Compiler Design I. Winter 2012 Lecture 5
CS321 Lnguges nd Compiler Design I Winter 2012 Lecture 5 1 FINITE AUTOMATA A non-deterministic finite utomton (NFA) consists of: An input lphet Σ, e.g. Σ =,. A set of sttes S, e.g. S = {1, 3, 5, 7, 11,
More informationMinimal Memory Abstractions
Miniml Memory Astrtions (As implemented for BioWre Corp ) Nthn Sturtevnt University of Alert GAMES Group Ferury, 7 Tlk Overview Prt I: Building Astrtions Minimizing memory requirements Performnes mesures
More informationCustomer documentation
SAP Printing: Customr oumnttion: Volum 1 pg 1 / 14 SAP Printing Customr oumnttion Volum 1 RM: Support y Rioh Vrsion: 1.49 Astrt: This oumnt ontins irst-stp inormtion out support y Rioh or printing rom
More informationDuality in linear interval equations
Aville online t http://ijim.sriu..ir Int. J. Industril Mthemtis Vol. 1, No. 1 (2009) 41-45 Dulity in liner intervl equtions M. Movhedin, S. Slhshour, S. Hji Ghsemi, S. Khezerloo, M. Khezerloo, S. M. Khorsny
More informationPartitioning a Polygon into Two Mirror Congruent Pieces
rtitioning olygon into Two Mirror Congrunt is Dni El-Khhn Thoms Fvns John Iono 1 Introution olygon omposition prolms r wll stui in th litrtur [6], yt mny vrints o ths prolms rmin opn. In this ppr, w r
More informationDOCUMENT STATUS: - NOTICE OF PROPRIETARY INFORMATION
RVSON STORY RV T SRPTON O Y 50 /0/00 PROUTON RLS 4 MM //0 RPL P/N 40- WT 40-; RPL P/N 40-00 & 40-0 WT 40-45 N RMOV P/N 40-54 & 40-000 ROM T SSMLY 55 S //0 UPT NLR N ST SSY 5 MM 0//0 RPL 40- WT 40- TO SR
More informationUndecidability of bounded security protocols
Unciabilit of boun scurit protocols urgin Licoln itchll Scrov FSP Trnto Ital Jul 999 /5/0 Outlin Goals an motivations Snta an smantics oun protocols Eampl LLF Conclusions Qustions /5/0 otivation Scurit
More informationObjectives. Two Ways to Implement Lists. Lists. Chapter 24 Implementing Lists, Stacks, Queues, and Priority Queues
Chaptr 24 Implmnting Lists, Stacks, Quus, and Priority Quus CS2: Data Structurs and Algorithms Colorado Stat Univrsity Original slids by Danil Liang Modifid slids by Chris Wilcox Objctivs q To dsign common
More informationIn the last lecture, we discussed how valid tokens may be specified by regular expressions.
LECTURE 5 Scnning SYNTAX ANALYSIS We know from our previous lectures tht the process of verifying the syntx of the progrm is performed in two stges: Scnning: Identifying nd verifying tokens in progrm.
More informationMath 227 Problem Set V Solutions. f ds =
Mth 7 Problem Set V Solutions If is urve with prmetriztion r(t), t b, then we define the line integrl f ds b f ( r(t) ) dr dt (t) dt. Evlute the line integrl f(x,y,z)ds for () f(x,y,z) xosz, the urve with
More informationAbout Notes And Symbols
About Nots And Symbols by Batric Wildr Contnts Sht 1 Sht 2 Sht 3 Sht 4 Sht 5 Sht 6 Sht 7 Sht 8 Sht 9 Sht 10 Sht 11 Sht 12 Sht 13 Sht 14 Sht 15 Sht 16 Sht 17 Sht 18 Sht 19 Sht 20 Sht 21 Sht 22 Sht 23 Sht
More informationShould be done. Do Soon. Structure of a Typical Compiler. Plan for Today. Lab hours and Office hours. Quiz 1 is due tonight, was posted Tuesday night
Should e done L hours nd Office hours Sign up for the miling list t, strting to send importnt info to list http://groups.google.com/group/cs453-spring-2011 Red Ch 1 nd skim Ch 2 through 2.6, red 3.3 nd
More informationParadigm 5. Data Structure. Suffix trees. What is a suffix tree? Suffix tree. Simple applications. Simple applications. Algorithms
Prdigm. Dt Struture Known exmples: link tble, hep, Our leture: suffix tree Will involve mortize method tht will be stressed shortly in this ourse Suffix trees Wht is suffix tree? Simple pplitions History
More informationASSIGNMENT 9: CACHE MEMORY NAME. Assume we are building a cache for a memory system that s just 16 bytes big 4 address bits.
. SSIGNMNT : H MMORY NM PROLM : -YT H OR -YT MMORY. ssume we are building a cache for a memory system that s just bytes big address bits. We will make a direct mapped cache that has four set, so there
More informationAdvertising Rates for the L.A. Roadster s 46th Annual Show Program. Deadline May 1, 2010 Contact Don Wilson (818)
dvrtising Rts for th.. Rodstr s 46th nnul how rogrm dlin y 1, 2010 Contct on Wilson (818) 348-1929 Fu Color g ll W tnd Bhind vry Brookvill Body. dy. W lso tnd In It, y Undr It, nd wt Ov It,Til It s Just
More informationIn order to learn which questions have been answered correctly: 1. Print these pages. 2. Answer the questions.
XML: Mnging with th Jv Pltform In ordr to lrn whih qustions hv n nswrd orrtly: 1. Print ths pgs. 2. Answr th qustions. 3. Snd this ssssmnt with th nswrs vi:. FAX to (212) 967-3498. Or. Mil th nswrs to
More informationFinal Exam Review F 06 M 236 Be sure to look over all of your tests, as well as over the activities you did in the activity book
inl xm Review 06 M 236 e sure to loo over ll of your tests, s well s over the tivities you did in the tivity oo 1 1. ind the mesures of the numered ngles nd justify your wor. Line j is prllel to line.
More informationDynamic Programming. Andreas Klappenecker. [partially based on slides by Prof. Welch] Monday, September 24, 2012
Dynmic Progrmming Andres Klppenecker [prtilly bsed on slides by Prof. Welch] 1 Dynmic Progrmming Optiml substructure An optiml solution to the problem contins within it optiml solutions to subproblems.
More informationCSc 453 Compilers and Systems Software. 6 : Top-Down Parsing I
C 45 Compilers n ystems oftwre 6 : op-down Prsing I Christin Collberg Deprtment of Computer iene University of rizon ollberg@gmil.om Copyright 2009 Christin Collberg eptember 14, 2009 1 Overview 2 Compiler
More informationLanguages. L((a (b)(c))*) = { ε,a,bc,aa,abc,bca,... } εw = wε = w. εabba = abbaε = abba. (a (b)(c)) *
Pln for Tody nd Beginning Next week Interpreter nd Compiler Structure, or Softwre Architecture Overview of Progrmming Assignments The MeggyJv compiler we will e uilding. Regulr Expressions Finite Stte
More informationWhat are suffix trees?
Suffix Trees 1 Wht re suffix trees? Allow lgorithm designers to store very lrge mount of informtion out strings while still keeping within liner spce Allow users to serch for new strings in the originl
More informationChapter 4 Fuzzy Graph and Relation
Chpter 4 Fuzzy Grph nd Reltion Grph nd Fuzzy Grph! Grph n G = (V, E) n V : Set of verties(node or element) n E : Set of edges An edge is pir (x, y) of verties in V.! Fuzzy Grph ~ n ( ~ G = V, E) n V :
More informationA Brief Summary of Draw Tools in MS Word with Examples! ( Page 1 )
A Brif Summary of Draw Tools in MS Word with Exampls! ( Pag 1 ) Click Viw command at top of pag thn Click Toolbars thn Click Drawing! A chckmark appars in front of Drawing! A toolbar appars at bottom of
More informationIntroduction to Algebra
INTRODUCTORY ALGEBRA Mini-Leture 1.1 Introdution to Alger Evlute lgeri expressions y sustitution. Trnslte phrses to lgeri expressions. 1. Evlute the expressions when =, =, nd = 6. ) d) 5 10. Trnslte eh
More informationGENG2140 Modelling and Computer Analysis for Engineers
GENG4 Moelling n Computer Anlysis or Engineers Letures 9 & : Gussin qurture Crete y Grn Romn Joles, PhD Shool o Mehnil Engineering, UWA GENG4 Content Deinition o Gussin qurture Computtion o weights n points
More information12/9/14. CS151 Fall 20124Lecture (almost there) 12/6. Graphs. Seven Bridges of Königsberg. Leonard Euler
CS5 Fll 04Leture (lmost there) /6 Seven Bridges of Königserg Grphs Prof. Tny Berger-Wolf Leonrd Euler 707-783 Is it possile to wlk with route tht rosses eh ridge e Seven Bridges of Königserg Forget unimportnt
More informationHSHM-H110AX-5CPX HSHM-H105BX-5CPX TYPE B21, 105 SIGNAL CONTACTS HSHM-HXXXXXX-5CPX-XXXXX
M TM HSHM PRSS-FIT HR, -ROW, HSHM SRIS FOR HIGH SP HR MTRI PPLITIONS * UP TO Gb/s T RTS * LOW ROSSTLK T HIGH FRQUNIS * / (SINGL-N/IFFRNTIL) IMPN * MOULR/SLL FORMT I -- * MT LINS PR INH * SHIPS WITH PROTTIV
More informationLexical Analysis: Constructing a Scanner from Regular Expressions
Lexicl Anlysis: Constructing Scnner from Regulr Expressions Gol Show how to construct FA to recognize ny RE This Lecture Convert RE to n nondeterministic finite utomton (NFA) Use Thompson s construction
More information