The 19th Annual International Symposium on Computer Architecture. Alternative Implementations of TwoLevel Adaptive Branch Prediction


 Giles Sparks
 1 years ago
 Views:
Transcription
1 he 19th nnl Intentionl Smposim on Compte hitete pp , M 1921, 1992, Gold Cost, stli ltentive Implementtions of wolevel dptive Bnh Pedition se{y Yeh nd Yle Ptt Deptment of Eletil Engineeing nd Compte Siene he Univesit of Mihign nn bo, Mihign bstt s the isse te nd depth of pipelining of high pefomne Spesl poessos inese, the impotne of n exellent bnh pedito beomes moe vitl to deliveing the potentil pefomne of wideisse, deep pipelined miohitete We popose new dnmi bnh pedito (wolevel dptive Bnh Pedition) tht hieves sbstntill highe thn n othe sheme epoted in the litete he mehnism ses twolevels of bnh histo infomtion to mke peditions, the histo of the lst k bnhes enonteed, nd the bnh behvio fo the lst s oenes of the spei ptten of these k bnhes We hve identied thee vitions of the wolevel dptive Bnh Pedition, depending on how nel we esolve the histo infomtion gtheed We ompte the hdwe osts of implementing eh of the thee vitions, nd se these osts in evlting thei eltive effetiveness We mese the bnh pedition of the thee vitions of wolevel dptive Bnh Pedition, long with sevel othe popl poposed dnmi nd stti pedition shemes, on the SPEC benhmks We showthtthevege pedition fo wolevel dptive Bnh Pedition is 97 peent, while the othe known shemes hieve t most 944 peent vege pedition We mese the eetiveness of dieent pedition lgoithms nd dieent monts of histo nd ptten infomtion We mese the osts of eh vition to obtin the sme pedition 1 Intodtion s the isse te nd depth of pipelining of high pefomne Spesl poessos inese, the mont of speltive wok de to bnh pedition beomes mh lge Sine ll sh wok mst be thown w if the pedition is inoet, n exellent bnh pedito is vitl to deliveing the potentil pefomne of wideisse, deep pipelined miohitete Even 0 pedition miss te of 5 peent eslts in sbstntil loss in pefomne de to the nmbe of insttions fethed eh le nd the nmbe of les these insttions e in the pipeline befoe n inoet bnh pedition beomes known he litete is fll of sggested bnh pedition shemes [6, 13, 14, 17] Some e stti in tht the se opode infomtion nd poling sttistis to mke peditions Othes e dnmi in tht the se ntime exetion histo to mke peditions Stti shemes n be s simple s lws pediting tht the bnh will be tken, o n be bsed on the opode, o on the dietion of the bnh, s in \if the bnh isbkwd, pedit tken, if fowd, pedit not tken" [17] his ltte sheme is eetive fo loop intensive ode, bt does not wok well fo pogms whee the bnh behvio is iegl lso, poling [6, 13] n be sed to pedit bnhes b mesing the tenden of bnh on smple dt sets nd pesetting stti pedition bit in the opode oding to tht tenden Unfotntel, bnh behvio fo the smple dt mbe ve dieent fom the dt tht ppes t ntime Dnmi bnh pedition lso n be s simple s in keeping tk onl of the lst exetion of tht bnh insttion nd pediting the bnh will behve the sme w, o it n be elbote s in mintining ve lge monts of histo infomtion In ll ses, the ft tht the dnmi pedition is being mde on the bsis of ntime histo infomtion implies tht sbstntil dditionl hdwe is eqied J Smith [17] poposed tilizing bnh tget be to stoe, fo eh bnh, twobit stting pdown onte whih ollets nd sbseqentl bses its pedition on bnh histo infomtion bot tht bnh Lee nd Smith poposed [14] Stti ining method whih ses sttistis gtheed pio to exetion time opled with the histo ptten of the lst k ntime exetions of the bnh tomke the next pedition s to whih w tht bnh will go he mjo disdvntge of Stti ining methods hs been mentioned bove with espet to poling the ptten histo sttistis gtheed fo the smple dt set m not be pplible to the dt tht ppes t ntime In this ppe we popose new dnmi bnh pedito tht hieves sbstntill highe thn n othe sheme epoted in the litete he mehnism ses two levels of bnh histo infomtion to mke peditions he st level is the histo of the
2 lst k bnhes enonteed (Vitions of o sheme eet whethe this mens the tl lst k bnhes enonteed, o the lst k oenes of the sme bnh insttion) he seond level is the bnh behvio fo the lst s oenes of the spei ptten of these k bnhes Pedition is bsed on the bnh behvio fo the lst s oenes of the ptten in qestion Fo exmple, sppose, fo k = 8, thelstk bnhes hd the behvio (whee 1 epesents tht the bnh ws tken, 0 tht the bnh ws not tken) Sppose fthe tht s = 6, nd tht in eh of the lst six times the pevios eight bnhes hd the ptten , the bnh ltented between tken nd not tken hen the seond level wold ontin the histo O bnh pedito wold pedit \tken" he histo infomtion fo level 1 nd the ptten infomtion fo level 2 e olleted t n time, eliminting the bove mentioned disdvntges of the Stti ining method We ll o method wolevel dptive Bnh Pedition We hve identied thee vitions of wolevel dptive Bnh Pedition, depending on how nel we esolve the histo infomtion gtheed We ompte the hdwe osts of implementing eh of the thee vitions, nd se these osts in evlting thei eltive eetiveness Using tediven simltion of nine of the ten SPEC benhmks 1,we mese the bnh pedition of the thee vitions of wolevel dptive Bnh Pedition, long with sevel othe popl poposed dnmi nd stti pedition shemes We mese the eetiveness of dieent pedition lgoithms nd dieent monts of histo nd ptten infomtion We mese the osts of eh vition to obtin the sme pedition Finll we ompe the wolevel dptive bnh peditos to the sevel popl shemes vilble in the litete We show tht the vege pedition fo wo Level dptive Bnh Pedition is bot 97 peent, while the othe shemes hieve t most 944 peent vege pedition his ppe is ognized in six setions Setion two intodes o wolevel dptive Bnh Pedition nd its thee vitions Setion thee desibes the oesponding implementtions nd omptes the ssoited hdwe osts Setion fo dissses the Simltion model nd tes sed in this std Setion ve epots the simltion eslts nd o nlsis Setion six ontins some onlding emks 2 Denition of wolevel dptive Bnh Pedition 21 Oveview wolevel dptive Bnh Pedition ses two levels of bnh histo infomtion to mke peditions he st level is the histo of the lst k bnhes enonteed (Vitions of o sheme eet whethe this 1 he s7 benhmk ws not simlted bese this benhmk onsists of seven independent loops It tkes too long to simlte the bnh behvio of these seven kenels, so we omitted these loops mens the tl lst k bnhes enonteed, o the lst k oenes of the sme bnh insttion) he seond level is the bnh behvio fo the lst s oenes of the spei ptten of these k bnhes Pedition is bsed on the bnh behvio fo the lst s oenes of the ptten in qestion o mintin the two levels of infomtion, wolevel dptive Bnh Pedition ses two mjo dt sttes, the bnh histo egiste (HR) nd the ptten histo tble (PH), see Fige 1 Insted of mlting sttistis b poling pogms, the infomtion on whih bnh peditions e bsed is olleted t ntime b pdting the ontents of the histo egistes nd the ptten histo bits in the enties of the ptten histo tble depending on the otomes of the bnhes he histo egiste is kbit shift egiste whih shifts in bits epesenting the bnh eslts of the most eent k bnhes Bnh Histo Registe (BHR) (Shift left when pdte) Rk Rk+1 R2 R Index Ptten Histo ble (PH) Bnh Histo Ptten R : Bnh Reslt of B S Ptten Histo Bit(s) S Stte nsition Logi fo d l(s) Pedition of B S+1=d(S,R) Fige 1: Stte of wolevel dptive Bnh Pedition If the bnh ws tken, then \1" is eoded if not, \0" is eoded Sine thee e k bits in the histo egiste, t most 2 k dieent pttens ppe in the histo egiste Fo eh of these 2 k pttens, thee is oesponding ent in the ptten histo tble whih ontins bnh eslts fo the lst s times the peeding k bnhes wee epesented b tht spei ontent of the histo egiste When onditionl bnh B is being pedited, the ontent of its histo egiste, HR, denoted s R ;kr ;k+1::::::r ;1, is sed to ddess the ptten histo tble he ptten histo bits S in the ddessed ent PH R;kR ;k+1::::::r ;1 in the ptten histo tble e then sed fo pediting the bnh he pedition of the bnh is z = (S ) (1) whee is the pedition deision fntion fte the onditionl bnh is esolved, the otome R is shifted left into the histo egiste HR in the lest signint bit position nd is lso sed to pdte the ptten histo bits in the ptten histo tble ent PH R;kR ;k+1::::::r ;1 fte being
3 pdted, the ontent of the histo egiste beomes R ;k+1r ;k+2::::::r nd the stte epesented b the ptten histo bits beomes S +1 he tnsition of the ptten histo bits in the ptten histo tble ent is done b the stte tnsition fntion whih tkes in the old ptten histo bits nd the otome of the bnh s inpts to genete the new ptten histo bits heefoe, the new ptten histo bits S +1 beome S +1 = (S R ): (2) stightfowd ombintionl logi iit is sed to implement the fntion to pdte the ptten histo bits in the enties of the ptten histo tble he tnsition fntion, pediting fntion, ptten histo bits S nd the otome R of the bnh ompise nitestte Mooe mhine, hteized b eqtions 1 nd 2 Stte digms of the nitestte Mooe mhines sed in this std fo pdting the ptten histo in the ptten histo tble ent nd fo pediting whih pth the bnh will tke e shown in Fige 2 he tomton Lstime stoes in the ptten histo onl the otome of the lst exetion of the bnh when the histo ptten ppeed he next time the sme histo ptten ppes the pedition will be wht hppened lst time Onl one bit is needed to stoe tht ptten histo infomtion he tomton 1 eods the eslts of the lst two times the sme histo ptten ppeed Onl when thee is no tken bnh eoded, the next exetion of the bnh when the histo egiste hs the sme histo ptten will be pedited s not tken othewise, the bnh will be pedited s tken he tomton 2 is stting pdown onte, simil to the tomton sed in J Smith's bnh tget be design fo keeping bnh histo [17] 1/ 0/ tomton Lstime (L) 3/ 2/ 3/ 2/ 1/ 0/ tomton 3 1/ 0/ tomton 1 3/ 2/ 1/ 0/ tomton 2 (2bit Stting Updown Conte) 3/ 2/ 1/ 0/ tomton 4 Fige 2: Stte digms of the nitestte Mooe mhines sed fo mking pedition nd pdting the ptten histo tble ent In J Smith's design the 2bit stting pdown onte keeps tk of the bnh histo of etin bnh he onte is inemented when the bnh is tken nd is deemented when the bnh isnot tken he bnh pth of the next exetion of the bnh will be pedited s tken when the onte vle is gete thn o eql to two othewise, the bnh will be pedited s not tken In wolevel dptive Bnh Pedition, the 2bit stting pdown onte keeps tk of the histo of etin histo ptten he onte is inemented when the eslt of bnh, whose histo egiste ontent is the sme s the ptten histo tble ent index, is tken othewise, the onte is deemented he next time the bnh hs the sme histo egiste ontent whih esses the sme ptten histo tble ent, the bnhis pedited tken if the onte vle is gete o eql to two othewise, the bnh is pedited not tken tomt 3 nd4 e vitions of 2 Both Stti ining [14] ndwolevel dptive Bnh Pedition e dnmi bnh peditos, bese thei peditions e bsed on ntime infomtion, ie the dnmi bnh histo he mjo diffeene between these two shemes is tht the ptten histo infomtion in the ptten histo tble hnges dnmill in wolevel dptive Bnh Pedition bt is peset in Stti ining fom poling In Stti ining, the inpt to the pedition deision fntion,, fogiven bnh histo ptten is known befoe exetion heefoe, the otpt of is detemined befoe exetion fo given bnh histo ptten ht is, the sme bnh peditions e mde if the sme histo ptten ppes t dieent times ding exetion wolevel dptive Bnh Pedition, on the othe hnd, pdtes the ptten histo infomtion kept in the ptten histo tble with the tl eslts of bnhes s eslt, given the sme bnh histo ptten, dieent ptten histo infomtion n be fond in the ptten histo tble theefoe, thee n be dieent inpts to the pedition deision fntion fo wolevel dptive Bnh Pedition Peditions of wolevel dptive Bnh Pedition hnge dptivel s the pogm exetes Sine the ptten histo bits hnge in wolevel dptivebnh Pedition, the pedito n djst to the ent bnh exetion behvio of the pogm to mke pope peditions With these ntime pdtes, wolevel dptive Bnh Pedition n be highl te ove mn dieent pogms nd dt sets Stti ining, on the ont, m not pedit well if hnging dt sets bings bot dieent exetion behvio 22 ltentive Implementtions of wolevel dptive Bnh Pedition hee e thee ltentive implementtions of the wo Level dptive Bnh Pedition, s shown in Fige 3 he e dieentited s follows: wolevel dptive Bnh Pedition Using Globl Histo Registe nd Globl Ptten Histo ble (Gg) In Gg, thee is onl single globl histo egiste (GHR) nd single globl ptten histo tble (GPH) sed b the wolevel dptive Bnh Pe
4 Gg Pg Pp Globl Bnh Histo Registe (GBHR) Index Globl Ptten Histo ble (GPH) Peddess Bnh Histo ble (PBH) Index Globl Ptten Histo ble (GPH) Peddess Bnh Histo ble (PBH) Index Peddess Ptten Histo bles (PPH) In ode to ompletel emove the intefeene in both levels, eh stti bnh hs its own ptten histo tble set of whih is lled peddess ptten histo tble (PPH) heefoe, peddess histo egiste nd peddess ptten histo tble e ssoited with eh stti onditionl bnh ll histo egistes e goped in peddess bnh histo tble Sine this vition of wolevel dptive Bnh Pedition keeps septe histo nd ptten infomtion fo eh distint stti onditionl bnh, it is lled Peddess wolevel dptive Bnh Pedition sing Peddess ptten histo tbles (Pp) 3 Implementtion Considetions Fige 3: Globl view of thee vitions of wolevel dptive Bnh Pedition dition ll bnh peditions e bsed on the sme globl histo egiste nd globl ptten histo tble whih e pdted fte eh bnh is esolved his vition theefoe is lled Globl wolevel dptive Bnh Pedition sing globl ptten histo tble (Gg) Sine the otomes of dieent bnhes pdte the sme histo egiste nd the sme ptten histo tble, the infomtion of both bnh histo nd ptten histo is inened b eslts of dieent bnhes he pedition fo onditionl bnh in this sheme is tll dependent on the otomes of othe bnhes wolevel dptive Bnh Pedition Using Peddess Bnh Histo ble nd Globl Ptten Histo ble (Pg) In ode the ede the intefeene in the st level bnh histo infomtion, one histo egiste is ssoited with eh distint stti onditionl bnh to ollet bnh histo infomtion individll he histo egistes e ontined in peddess bnh histo tble (PBH) in whih ehent is essible b one spei stti bnh insttion nd is essed b bnh insttion ddesses Sine the bnh histo is kept fo eh distint stti onditionl bnh individll nd ll histo egistes ess the sme globl ptten histo tble, this vition is lled Peddess wolevel dptive Bnh Pedition sing globl ptten histo tble (Pg) he exetion eslts of stti onditionl bnh pdte the bnh's own histo egiste nd the globl ptten histo tble he pedition fo onditionl bnh is bsed on the bnh's own histo nd the ptten histo bits in the globl ptten histo tble ent indexed b the ontent of the bnh's histo egiste Sine ll bnhes pdte the sme ptten histo tble, the ptten histo intefeene still exists wolevel dptive Bnh Pedition Using Peddess Bnh Histo ble nd Peddess Ptten Histo bles (Pp) 31 Pipeline iming of Bnh Pedition nd Infomtion Updte wolevel dptive Bnh Pedition eqies two seqentil tble esses to mke pedition It is dif lt to sqeeze the two esses into one le High pefomne eqies tht pedition be mde within one le fom the time the bnh ddess is known o stisf this eqiement, the two seqentil esses e pefomed in two dieent les s follows: When bnh eslt beomes known, the bnh's histo egiste is pdted In the sme le, the ptten histo tble n be essed fo the next pedition with the pdted histo egiste ontents deived b ppending the eslt to the old histo he pedition fethed fom the ptten histo tble is then stoed long with the bnh's histo in the bnh histo tble he ptten histo n lso be pdted t tht time he next time tht bnh isenonteed, the pedition is vilble s soon s the bnh histo tble is essed heefoe, onl one le lten is ined fom the time the bnh ddess is known to the time the pedition is vilble Sometimes the pevios bnh eslts m notbe ed befoe the pedition of sbseqent bnh tkes ple If the obsolete bnh histo is sed fo mking the pedition, the is degded In sh se, the peditions of the pevios bnhes n be sed to pdte the bnh histo Sine the pedition of wolevel dptive Bnh Pedition is ve high, pedition is enhned b pdting the bnh histo speltivel he pdte timing fo the ptten histo tble, on the othe hnd, is not s itil s tht of the bnh histo theefoe, its pdte n be deled ntil the bnh eslt is known With speltive pdting, when mispedition os, the bnh histo n eithe be einitilized o epied depending on the hdwe bdget vilble to the bnh pedito lso, if two instnes of the sme stti bnh o in onsetive les, the lten of pedition n be eded fo the seond bnh b sing the pedition fethed fom the ptten histo tble dietl 32 get ddess Ching fte the dietion of bnh is pedited, thee is still the possibilit of pipeline bbble de to the time it tkes to genete the tget ddess o eliminte
5 this bbble, we he the tget ddesses of bnhes One ext eld is eqied in eh ent of the bnh histo tble fo doing this When bnh is pedited tken, the tget ddess is sed to feth the following insttions othewise, the fllthogh ddess is sed Ching the tget ddesses mkes pedition in onsetive les possible withot n del his lso eqies the bnh histo tble to be essed b the fething ddess of the insttion blok the thn b the ddess of the bnh in the insttion blok being fethed bese the bnh ddess is not known ntil the insttion blok is deoded If the ddess hits in the bnh histo tble, the pedition of the bnh in the insttion blok n be mde befoe the insttions e deoded If the ddess misses in the bnh histo tble, eithe thee is no bnh in the insttion blok fethed in tht le o the bnh histo infomtion is not pesent in the bnh histo tble In this se, the next seqentil ddess is sed to feth new insttions fte the insttions e deoded, if thee is bnh in the insttion blok nd if the insttion blok ddess missed in the bnh histo tble, stti bnh pedition is sed to detemine whethe o not the new insttions fethed fom the next seqentil ddess shold be sqshed 33 Peddess Bnh Histo ble Implementtion Pg nd Pp bnh peditos ll se peddess bnh histo tbles in thei stte It is not fesible to hve bnh histo tble lge enogh to hold ll bnhes' exetion histo in el implementtions heefoe, ptil ppoh fo the peddess bnh histo tble is poposed hee he peddess bnh histo tble n be implemented s setssoitive o dietmpped he xed nmbe of enties in the tble e goped togethe s set Within set, LestReentlUsed (LRU) lgoithm is sed fo eplement he lowe pt of bnh ddess is sed to index into the tble nd the highe pt is stoed s tg in the ent ssoited with tht bnh When onditionl bnh istobe pedited, the bnh's ent in the bnh histo tble is loted st If the tg in the ent mthes the essing ddess, the bnh infomtion in the ent is sed to pedit the bnh If the tg does not mth the ddess, new ent is lloted fo the bnh In this std, both the bove ptil ppoh nd n Idel Bnh Histo ble (IBH), in whih thee is histo egiste fo eh stti onditionl bnh, wee simlted fo wolevel dptive Bnh Pedition he bnh histo tble ws simlted with fo ongtions: 4w setssoitive 512ent, 4w setssoitive 256ent, dietmpped 512ent nd dietmpped 256ent hes he IBH simltion dt is povided to show the loss de to the histo intefeene in ptil bnh histo tble implementtions 34 Hdwe Cost Estimtes he hip e eqied fo ntime bnh pedition mehnism is not inonseqentil he following hdwe ost estimtes e poposed to hteize the eltive osts of the thee vitions he bnh histo tble nd the ptten histo tble e the two mjo pts Detiled items inlde stoge spe fo keeping histo infomtion, pedition bits, tgs, nd LRU bits nd the essing nd pdting logi of the tbles he essing nd pdting logi onsists of omptos, MUXes, LRU bits inementos, nd ddess deodes fo the bnh histo tble, nd ddess deodes nd ptten histo bit pdte iits fo the ptten histo tble he stoge spe fo hing tget ddesses is not inlded in the following eqtions bese it is not eqied fo the bnh pedito ssmptions of these estimtes e: hee e ddess bits, sbset of whih issed to index the bnh histo tble nd the est e stoed s tg in the indexed bnh histo tble ent In n ent of the bnh histo tble, thee e elds fo bnh histo, n ddess tg, pedition bit, nd LRU bits he bnh histo tble size is h he bnh histo tble is 2 j w setssoitive Eh histo egiste ontins k bits Eh ptten histo tble ent ontins s bits Ptten histo tble set size is p (In Pp, p is eql to the size of the bnh histo tble, h, while in Gg nd Pg, p is lws eql to one) C s, C d, C, C m, C sh, C i,ndc e the onstnt bse osts fo the stoge, the deode, the ompto, the mltiplexe, the shifte, the inemento, nd the nitestte mhine Fthemoe, i is eql to log 2 h nd is nonnegtive intege When thee e k bits in histo egiste, ptten histo tble lws hs 2 k enties he hdwe ost of wolevel dptive Bnh Pedition is s follows: Cost Sheme(BH(h j k) p PH(2 k s)) = Cost BH (h j k)+p Cost PH(2 k s) = fbh Stoge Spe + BH essing Logi + BH Updting Logig + p fphstoge Spe + PH essing Logi + PH Updting Logig = f[h (g (;i+j) bit + HR k bit + P edition Bit 1 bit +LRU Bits j bit)] + [1 ddess Deode i bit +2 j Comptos (;i+j) bit +1 2 j X1 MUX k bit]+ [h Shifte k bit +2 j LRU Inementos j bit]g + p f[2 k Histo Bits s bit]+ [1 ddess Deode k bit]+[stte Updte s bit]g
6 = fh [( ; i + j)+k +1+j] C s + [h C d +2 j ( ; i + j) C +2 j k C m]+ [h k C sh +2 j j C i]g + p f[2 k s C s]+ [2 k C d]+[s 2 s+1 C ]g + j i: (3) In Gg, onl one histo egiste nd one globl ptten histo tble e sed, so h nd p e both eql to one o tg nd no bnh histo tble essing logi e neess fo the single histo egiste Besides, ptten histo stte pdting logi is smll omped to the othe two tems in the ptten histo tble ost heefoe, ost estimtion fntion fo Gg n be simplied fom Fntion 3 to the following Fntion: Cost Gg(BH(1 k) 1 PH(2 k s)) = Cost BH(1 k)+1 Cost PH(2 k s) ' f[k +1] C s + k C shg + f2 k (s C s + C d)g (4) It is le to see tht the ost of Gg gows exponentill with espet to the histo egiste length In Pg, onl one ptten histo tble is sed, so p is eql to one Sine j nd s e sll smll omped to the othe vibles, b sing Fntion 3, the estimted ost fo Pg sing bnh histo tble is s follows: Cost Pg(BH(h j k) 1 PH(2 k s)) = Cost BH (h j k)+1 Cost PH(2 k s) ' fh [( +2 j + k +1; i) C s + C d + k C sh]g + f2 k (s C s + C d)g + j i: (5) he ost of Pg sheme gows exponentill with espet to the histo egiste length nd linel with espet to the bnh histo tble size InPp sheme sing bnh histo tble s de ned bove, h ptten histo tbles e sed, so p is eql to h B sing Fntion 3, the estimted ost fo Pp is s follows: Cost Pp(BH(h j k) h PH(2 k s)) = Cost BH (h j k)+h Cost PH(2 k s) ' fh [( +2 j + k +1; i) C s + C d + k C sh]g + h f2 k (s C s + C d)g + j i: (6) When the histo egiste is sientl lge, the ost of Pp sheme gows exponentill with espet to the histo egiste length nd linel with espet to the bnh histo tble size Howeve, the bnh histo tble size beomes moe dominnt fto thn it is in Pg sheme 4 Simltion Model ediven simltions wee sed in this std Motool insttion level simlto is sed fo geneting insttion tes he insttion nd ddess tes e fed into the bnh pedition simlto whih deodes insttions, pedits bnhes, nd veies the peditions with the bnh eslts to ollet sttistis fo bnh pedition 41 Desiption of es ine benhmks fom the SPEC benhmk site e sed in this bnh pedition std Five e oting point benhmks nd fo e intege benhmks he oting point benhmks inlde dod,, mtix300, spie2g6 ndtomtv nd the intege ones inlde, espesso, g, ndli s7 is not inlded bese it tkes too long to pte the bnh behvio of ll seven kenels mong the ve oting point benhmks,, mtix300 nd tomtv hve epetitive loop exetion ths, ve high pedition is ttinble, independent of the peditos sed Dod, spie2g6 nd the intege benhmks e moe inteesting he hve mn onditionl bnhes nd iegl bnh behvio heefoe, it is on the intege benhmks whee bnh pedito's mettle is tested Sine this std of bnh pedition foses on the pedition fo onditionl bnhes, ll benhmks wee simlted fo twent million onditionl bnh insttions exept g whih nished befoe twent million onditionl bnh insttions e exeted Fpppp, mtix300, nd tomtv wee simlted fo 100 million insttion bese of thei egl bnh behvio thogh ot the pogms he nmbeofstti onditionl bnhes in the insttion tes of the benhmks e listed in ble 1 Histo egiste hit te sll depends on the nmbe of stti bnhes in the benhmks he testing nd tining dt sets fo eh benhmk sed in this std e listed in ble 2 Benhmk mbe of Benhmk mbe of Stti Stti me Cnd B me Cnd B 277 espesso 556 g 6922 li 489 dod mtix spie2g6 606 tomtv 370 ble 1: mbe of stti onditionl bnhes in eh benhmk Benhmk ining esting me Dt Set Dt Set int pi 3eqn espesso ps b g expi dbxoti towe of hnoi eight qeens dod tin dodin dodin ntoms mtix300 Biltin spie2g6 shot geodein geodein tomtv Biltin ble 2: ining nd testing dt sets of benhmks
7 In the tes geneted with the testing dt sets, bot 24 peent of the dnmi insttions fo the intege benhmks nd bot 5 peent of the dnmi insttions fo the oting point benhmks e bnh insttions Fige 4 shows bot 80 peent of the dnmi bnh insttions e onditionl bnhes theefoe, the pedition mehnism fo onditionl bnhes is the most impotnt mong the pedition mehnisms fo dieent lsses of bnhes P e e n t g e Dnmi Bnh Insttion Distibtion ot Int eqnt esp g l i FP dod mt spie tom Men Men Men 300 2g6 Benhmk Retn Fom Sb Inst Imm Bnh Inst Jmp Registe Inst Conditionl Bnh Inst Fige 4: Distibtion of dnmi bnh insttions 42 Chteiztion of Bnh Peditos he thee vitions of wolevel dptive Bnh Pedition wee simlted with sevel ongtions Othe known dnmi nd stti bnh peditos wee lso simlted he ongtions of the dnmi bnh peditos e shown in ble 3 In ode to distingish the dieent shemes we nlzed, the following nming onvention is sed: Sheme( Histo( Size, ssoitivit, Ent Content), P tten ble Set Size P tten( Size, Ent Content), Context Swith) If pedito does not hve etin fete in the nming onvention, the oesponding eld is left blnk Sheme speies the sheme, fo exmple, Gg, Pg, Pp o Bnh get Be design (BB) [17] In Histo( Size, ssoitivit, Ent Content), Histo is the entit sed to keep histo infomtion of bnhes, fo exmple, HR ( single histo egiste), IBH, o BH Size speies the nmbeofenties in tht entit, ssoitivit is the ssoitivit of the tble, nd Ent Content speies the ontent ineh bnh histo tble ent When ssoitivit is set to 1, the bnh histo tble is dietmpped he ontent ofnent in the bnh histo tble n be n tomton shown in Fige 2 o simpl histo egiste In P tten ble Set Size P tten( Size, Ent Content), P tten ble Set Size is the nmbe of ptten histo tbles sed in the sheme, P tten is the implementtion fo keeping ptten histo infomtion, Size speies the nmbe of enties in the implementtion, nd Ent Content speies the ontent inehent he ontent ofnent in the ptten histo tble n be n tomton shown in Fige 2 Fo Bnhget Be designs, the P tten pt is not inlded, bese thee is no ptten histo infomtion kept in thei designs Context Swith is g fo ontext swithes When Context Swith is speied s, ontext swithes e simlted If it is not speied, no ontext swithes e simlted Sine thee e moe tken bnhes thn not tken bnhes oding to o simltion eslts, histo egiste in the bnh histo tble is initilized to ll 1's when miss on the bnh histo tble os fte the eslt of the bnh whih ses the bnh histo tble miss is known, the eslt bit is extended thoghot the histo egiste ontext swith eslts in shing nd einitiliztion of the bnh histo tble Model BH Config PH PH Config #of s Ent Set #of Ent me Ent Cont Size Ent Cont Gg(HR(1,,s), 1 bit 1 2 tm 1PH(2,2),[]) s 2 Pg(BH(256,1,s), bit 1 2 tm 1PH(2,2),[]) s 2 Pg(BH(256,4,s), bit 1 2 tm 1PH(2,2),[]) s 2 Pg(BH(512,1,s), bit 1 2 tm 1PH(2,2),[]) s 2 Pg(BH(512,4,s), bit 1 2 tm 1PH(2,1),[]) s 1 Pg(BH(512,4,s), bit 1 2 tm 1PH(2,2),[]) s 2 Pg(BH(512,4,s), bit 1 2 tm 1PH(2,3),[]) s 3 Pg(BH(512,4,s), bit 1 2 tm 1PH(2,4),[]) s 4 Pg(BH(512,4,s), bit 1 2 tm 1PH(2,L),[]) s L Pg(IBH(inf,,s), 1 bit 1 2 tm 1PH(2,2),[]) s 2 Pp(BH(512,4,s), bit tm 512PH(2,2),[]) s 2 GSg(HR(1,,s), 1 bit 1 2 PB 1PH(2,PB),[]) s PSg(BH(512,4,s), bit 1 2 PB 1PH(2,PB),[]) s BB(BH(512,4,2), tm,[]) 2 BB(BH(512,4,L), tm,[]) L s { ble Setssoitivit, tm { tomton, BH { Bnh Histo ble, BB { Bnh get Be Design, Cong { Congtion, Ent { Enties, Gg { Globl wolevel dptive Bnh Pedition Using Globl Ptten Histo ble, GSg { Globl Stti ining Using Peset Globl Ptten Histo ble, IBH { Idel Bnh Histo ble, inf { Innite, L { Lstime, Pg { Peddess wolevel dptive Bnh Pedition Using Globl Ptten Histo ble, Pp { Peddess wolevel dptive Bnh Pedition Using Peddess Ptten Histo bles, PB { Peset Pedition Bit, PSg { Peddess Stti ining Using Peset Globl Ptten Histo ble, PH { Ptten Histo ble, s { Shift Registe ble 3: Congtions of simlted bnh peditos he ptten histo bits in the ptten histo tble enties e lso initilized t the beginning of exetion Sine tken bnhes e moe likel fo those ptten histo tbles sing tomt 1, 2, 3, nd 4, ll enties e initilized to stte 3 Fo Lstime, ll enties e initilized to stte 1 sh tht the bnhes t
8 the beginning of exetion will be moe likel to be pedited tken It is not neess to einitilize ptten histo tbles ding exetion In ddition to the wolevel dptive shemes, Lee nd Smith's Stti ining shemes, Bnh get Be designs, nd some dnmi nd stti bnh pedition shemes wee simlted fo ompison pposes Lee nd Smith's Stti ining sheme is simil in stte to the Peddess wolevel dptive sheme with n IBH bt with the impotnt dieene tht the pedition fo given ptten is pedetemined b poling In this std, Lee nd Smith's Stti ining is identied s PSg, mening peddess Stti ining sing globl peset ptten histo tble Simill, the sheme whih hs simil stte to Gg bt with the dieene tht the seondlevel ptten histo infomtion is olleted fom poling is bbevited PSg, mening Globl Stti ining sing peset globl ptten histo tble Peddess Stti ining sing peddess ptten histo tbles (PSp) is nothe pplition of Stti ining to dieent stte howeve, this sheme eqies lot of stoge to keep tk of ptten behvio of ll bnhes sttill heefoe, no PSp shemes wee simlted in this std Lee nd Smith's Stti ining shemes wee simlted with the sme bnh histo tble ongtions s sed b thewolevel dptive shemes fo fi ompison he ost to implementsttiin ing is not less expensive thn the ost to implementthe wolevel dptive Sheme bese the bnh histo tble nd the ptten histo tble eqied bboth shemes e simil In Stti ining, befoe pogm exetion stts, ext time is needed to lod the peset ptten pedition bits into the ptten histo tble Bnh get Be designs wee simlted with tomt 2 ndlstime he stti bnh pedition shemes simlted inlde the lws ken, Bkwd ken nd Fowd ot ken, nd po ling sheme lws ken sheme pedits tken fo ll bnhes Bkwd ken nd Fowd ot ken (BF) sheme pedits tken if bnh bnhes bkwd nd not tken if the bnh bnhes fowd he BF sheme is eetive fo loopbond pogms, bese it mispedits onl one in the exetion of loop he poling sheme onts the feqen of tken nd nottken fo eh stti bnh in the poling exetion he pedited dietion of bnh is the one the bnh tkes most feqentl he poling infomtion of pogm exeted with tining dt set is sed fo bnh peditions fo the pogm exeted with testing dt sets, ths llting the pedition 5 Bnh Pedition Simltion Reslts Figes 5 thogh 11 show the pedition of the bnh peditos desibed in the pevios session on the nine SPEC benhmks \ot GMen" is the geometi men oss ll the benhmks, \Int GMen" is the geometi men oss ll the intege benhmks, nd \FP GMen" is the geometi men oss ll the oting point benhmks he vetil xis shows the pedition sled fom 76 peent to 100 peent 51 Evltion of the Pmetes of the wo Level dptive Bnh Pedition Bnh Pedition he thee vitions of wolevel dptive Bnh Pedition wee simlted with dieent histo egiste lengths to ssess the eetiveness of inesing the eoded histo length he Pg nd Pp shemes wee eh simlted with n idel bnh histo tble (IBH) nd with ptil bnh histo tbles to show the eet of the bnh histo tble hit tio 511 Eet of Ptten Histo ble tomton Fige 5 shows the eien of sing dieent nitestte tomt Five tomt 1, 2, 3, 4, nd Lstime wee simlted with Pg bnh pedito, hving 12bit histo egistes in fow setssoitive 512ent BH 1, 2, 3, nd 4 ll pefom bette thn Lstime he fostte tomt 1, 2, 3, nd 4 mintin moe histo infomtion thn Lstime whih onl eods wht hppened the lst time the e theefoe moe tolent to the devitions in the exetion histo mong the fostte tomt, 1 pefoms wose thn the othes he pefomne of 2, 3, nd 4eve lose to eh othe howeve, 2 sll pefoms best In ode to show the following ges lel, ehwolevel dptive Sheme is shown with tomton 2 wolevel dptive Sheme Using Diffeent Stte nsition tomt ot GMen Int GMen espesso g FP GMen Benhmk dod mtix 300 spie 2g6 tomtv Pg( BH(512,4,12s), PH(2^12,L),) Pg( BH(512,4,12s), PH(2^12,1),) Pg( BH(512,4,12s), PH(2^12,2),) Pg( BH(512,4,12s), PH(2^12,3),) Pg( BH(512,4,12s), PH(2^12,4),) Fige 5: Compison of wolevel dptive Bnh Peditos sing dieent nitestte tomt 512 Eet of Histo Registe Length hee vitions sing histo egistes of the sme length Fige 6 shows the eets of histo egiste length on the pedition of wolevel dptiveshemes Eve sheme in the gph ws simlted with the sme histo egiste length mong the vitions, Pp pefoms the best, Pg the seond, nd Gg the wost
9 Gg is not eetive with 6bit histo egistes, bese eve bnh pdtes the sme histo egiste, sing exessive intefeene Pg pefoms bette thn Gg, bese it hs bnh histo tble whih edes the intefeene in bnh histo Pp pedits the best, bese the intefeene in the ptten histo is emoved Compison of wolevel dptive Shemes sing histo egistes of the sme length ot GMen Int GMen espesso g FP GMen Benhmk dod mtix 300 spie 2g6 tomtv Pp( BH(512,4,6s), 2^9*PH(64,2),) Pg( BH(512,4,6s), PH(64,2),) Gg( BHR(1,,6s), PH(64,2),) 513 Hdwe Cost Eien of hee Vitions In Fige 6, pedition fo the shemes with the sme histo egiste length wee omped Howeve, the vios wolevel dptive shemes hve diffeent osts Pp is the most expensive, Pg the seond, nd Gg the lest, s o wold expet When evlting the thee vitions of wolevel dptive Bnh Pedition, it is sefl to know whihvition is the lest expensive when the pedit with ppoximtel the sme Fige 8 illsttes thee shemes whihhievebot 97 peent pedition Onesheme is hosen fo eh vition to show thevition's ongtion eqiements to obtin tht pedition o hieve 97 peent pedition, Gg eqies n 18bit histo egiste, Pg eqies 12bit histo egistes, nd Pp eqies 6bit histo egistes oding to o ost estimtes, Pg is the hepest mong these thee Gg's ptten histo tble is expensive when long histo egiste is sed Pp is expensive de to the eqied mltiple ptten histo tbles wolevel dptive Shemes hieving 97% pedition Fige 6: Compison of the wolevel dptive shemes sing histo egistes of the sme length Eets of vios histo egiste lengths o fthe investigte the eet of histo egiste length, Fige 7 shows the of Gg with vios histo egiste lengths hee is n inese of 9 peent in b lengthening the histo egiste fom 6 bits to 18 bits he eet of histo egiste length is obvios on Gg shemes he histo egiste length hs smlle eet on Pg shemes nd even smlle eet on Pp shemes bese of the less intefeene in the bnh histo nd ptten histo nd thei eetiveness with shot histo egistes ot GMen Int GMen espesso g FP GMen dod Benhmk mtix 300 spie 2g6 tomtv Gg( BHR(1,,18s), PH(2^18,2),) Pp( BH(512,4,6s), 2^9*PH(64,2),) Pg( BH(512,4,12s), PH(2^12,2),) Effet of histo egiste length Fige 8: he wolevel dptive shemes hieve bot 97 peent pedition ot GMen Int GMen espesso g FP GMen Benhmk dod mtix 300 spie 2g6 tomtv Gg( BHR(1,,18s), PH(2^18,2),) Gg( BHR(1,,16s), PH(2^16,2),) Gg( BHR(1,,14s), PH(2^14,2),) Gg( BHR(1,,12s), PH(2^12,2),) Gg( BHR(1,,6s), PH(64,2),) Fige 7: Eet of vios histo egiste lengths on Gg shemes 514 Eet of Context Swith Sine wolevel dptive Bnh Pedition ses the bnh histo tble to keep tk of bnh histo, the tble needs to be shed ding ontext swith Fige 9 shows the dieene in the pedition fo thee shemes simlted with nd withot ontext swithes Ding the simltion, wheneve tp os in the insttion te o eve 500,000 insttions if no tp os, ontext swith issimlted fte ontext swith, the ptten histo tble is not einitilized, bese the ptten histo tble of the sved poess is moe likel to be simil to the ent poess's ptten histo tble thn to einitilized ptten histo tble he vle 500,000 is deived b ssming tht 50 MHz lok is sed nd ontext swithes o eve 10 ms in 1 IPC mhine he vege degdtions fo the thee shemes e
10 ll less thn 1 peent he degdtions fo g when Pg nd Pp e sed e mh gete thn those of the othe pogms bese of the lge nmbe of tps in g Howeve, the exessive nmbe of tps do not degde the pedition of the Gg sheme, bese n initilized globl histo egiste n be elled qikl he pedition of sing Gg tll ineses when ontext swithes e simlted hee e ve few onditionl bnhes in nd ll the onditionl bnhes hve egl behvio theefoe, initilizing the globl histo egiste helps le ot the noise Compison of bnh histo tble onfigtions sed in Pg Pg( IBH(inf,,12s), PH(2^12,2),) Pg( BH(512,4,12s), PH(2^12,2),) Pg( BH(256,4,12s), PH(2^12,2),) Pg( BH(512,1,12s), PH(2^12,2),) Pg( BH(256,1,12s), PH(2^12,2),) Effet of ontext swith ot GMen Int GMen espesso g FP GMen dod mtix 300 spie 2g6 tomtv Benhmk ot GMen Int espess GMen o g FP GMen Benhmk Gg( BHR(1,,18s), PH(2^18,2),) Gg( BHR(1,,18s), PH(2^18,2),) Pg( BH(512,4,12s), PH(2^12,2),) Pg( BH(512,4,12s), PH(2^12,2),) Pp( BH(512,4,6s), 2^9*PH(64,2),) Pp( BH(512,4,6s), 2^9*PH(64,2),) dod mtix 300 spie 2g6 tomtv Fige 9: Eet of ontext swith on pedition 515 Eet of Bnh Histo ble Implementtion Fige 10 illsttes the eets of the size nd ssoitivit of the bnh histo tble in the pesene of ontext swithes Fo ptil bnh histo tble implementtions nd n idel bnh histo tble wee simlted he fow setssoitive 512ent bnh histo tble's pefomne is ve lose to tht of the idel bnh histo tble, bese most bnhes in the pogms n t in the tble Pedition deeses s tble miss te ineses, whih is lso seen in the Pp shemes 52 Compison of wolevel dptive Bnh Pedition nd Othe Pedition shemes Fige 11 ompes the bnh pedition shemes he Pg sheme whih hieves 97 peent pedition is hosen fo ompison with othe wellknown shemes, bese it osts the lest mong the thee vitions of wolevel dptive Bnh Pedition he 4w setssoitive 512ent BH is seleted to be sed b ll shemes whih keep the stlevel bnh histo infomtion, bese it is simple enogh to be implemented he wolevel dptive sheme nd the Stti ining sheme wee hosen on the bsis of simil osts he top ve is hieved b the wolevel dptive sheme whose pedition is bot 97 peent Fige 10: Eet of bnh histo tble implementtion on Pg shemes Sine the dt fo the Stti ining shemes e not omplete de to the nvilbilit of ppopite dt sets, the dt points fo,, mtix300, nd tomtv e not gphed PSg is bot 1 to 4 peent lowe thn the top ve fo the benhmks tht e vilble nd GSg is bot 4 to 19 peent lowe with vege pedition of 944 peent nd 89 peent individll ote tht thei depends getl on the similities between the dt sets sed fo tining nd testing he pedition fo the bnh tget be sing 2bit stting pdown ontes [17] is ond 93 peent he Poling sheme hieves bot 91 peent pedition he bnh tget be sing Lstime hieves bot 89 peent pedition Most of the pedition ves of BF nd lws ken e below the bse line (76 peent) BF's vege pedition is bot 685 peent nd lws ken's is bot 625 peent In this ge, the wolevel dptive sheme is speio to the othe shemes b t lest 26 peent ot GMen Compison of Bnh Pedition Shemes Int GMen espesso g FP GMen Benhmk dod mtix 300 spie 2g6 tomtv Pg( BH(512,4,12s), PH(2^12,2),) GSg( BHR(1,,18s), PH(2^18,PB),) PSg( BH(512,4,12s), PH(2^12,PB),) BB( BH(512,4,L),) BB( BH(512,4,2),) Pofiling BF (685%) lws ken (625%) Fige 11: Compison of bnh pedition shemes
11 6 Conlding Remks In this ppe we hve poposed new dnmi bnh pedito (wolevel dptive Bnh Pedition) tht hieves sbstntill highe thn n othe sheme tht we ewe of We ompted the hdwe osts of implementing thee vitions of this sheme nd detemined tht the most eetive implementtion of wolevel dptive Bnh Pedition tilizes peddess bnh histo tble nd globl ptten histo tble We hve mesed the pedition of the thee vitions of wolevel dptive Bnh Pedition nd sevel othe popl poposed dnmi nd stti pedition shemes sing tediven simltion of nine of the ten SPEC benhmks We hve shown tht the vege pedition fo wo Level dptive Bnh Pedition is bot 97 peent, while the othe known shemes hieve t most 944 peent vege pedition We hve mesed the eets of ving the pmetes of the wolevel dptive peditos We noted the sensitivit tok, the length of the histo egiste, nd s, the size of eh ent in the ptten histo tble We epoted on the eetiveness of the vios pedition lgoithms tht se the ptten histo tble infomtion We showed the eets of ontext swithing Finll, we shold point ot tht we feel o 97 peent pedition ges e not good enogh nd tht fte eseh in bnh pedition is still needed High pefomne ompting engines in the fte will inese the isse te nd the depth of the pipeline, whih will ombine to inese fthe the mont of speltive wok tht will hve tobethown ot de to bnh pedition miss hs, the 3 peent pedition miss te needs impovement We e exmining tht 3 peent to t to hteize it nd hopefll ede it knowledgments he thos wish to knowledge with gtitde the othe membes of the HPS eseh gop t Mihign fo the stimlting envionment the povide, nd in ptil, fo thei omments nd sggestions on this wok We e lso gtefl to Motool Copotion fo tehnil nd nnil sppot, nd to CR Copotion fo the gift of n CR owe, Model o 32, whih ws ve sefl in o wok Refeenes [1] Y Yeh nd Y Ptt, \wolevel dptive Bnh Pedition", ehnil Repot CSER , Compte Siene nd Engineeing Division, Deptment of EECS, he Univesit of Mihign, (ov 1991) [2] Y Yeh nd Y Ptt, \wolevel dptive Bnh Pedition", he 24th CM/IEEE Intentionl Smposim nd Wokshop on Miohitete, (ov 1991), pp [3] M Btle, Y Yeh, Y Ptt, M lsp, H Sles, nd M Shebnow, \Insttion Level Pllelism is Gete hn wo", Poeedings of the 18th Intentionl Smposim on Compte hitete, (M 1991), pp [4] D R Keli nd P G Emm, \Bnh Histo ble Pedition of Moving get Bnhes De to Sbotine Retns", Poeedings of the 18th Intentionl Smposim on Compte hitete,(m 1991), pp [5] Motool In, \M88100 Use's Mnl", Phoenix, izon, (Mh 13, 1989) [6] WW Hw, MConte, nd PPChng, \Comping Softwe nd Hdwe Shemes fo Reding the Cost of Bnhes", Poeedings of the 16th Intentionl Smposim on Compte hitete, (M 1989) [7] P Joppi nd D Wll, \vilble InsttionLevel Pllelism fo Spesl nd Spepipelined Mhines", Poeedings of the hid Intentionl Confeene on hitetl Sppot fo Pogmming Lngges nd Opeting Sstems, (pil 1989), pp [8] D J Lilj, \Reding the Bnh Penlt in Pipelined Poessos ", IEEE Compte, (Jl 1988), pp4755 [9] WW Hw nd Y Ptt, \Chekpoint Repi fo Otofode Exetion Mhines", IEEE nstions on Comptes, (Deembe 1987), pp [10] P G Emm nd E S Dvidson, \Chteiztion of Bnh nd Dt Dependenies in Pogms fo Evlting Pipeline Pefomne", IEEE nstions on Comptes, (Jl 1987), pp [11] J DeRos nd H M Lev, \n Evltion of Bnh hitetes ", Poeedings of the 14th Intentionl Smposim on Compte hitete, (Jne 1987), pp1016 [12] DR Ditzel nd HR MLelln, \Bnh Folding in the CRISP Miopoesso: Reding Bnh Del to Zeo", Poeedings of the 14th Intentionl Smposim on Compte hitete, (Jne 1987), pp29 [13] S MFling nd J Henness, \Reding the Cost of Bnhes", Poeedings of the 13th Intentionl Smposim on Compte hitete, (1986), pp [14] J Lee nd J Smith, \Bnh Pedition Sttegies nd Bnh get Be Design", IEEE Compte, (Jn 1984), pp622 [15] R Goss nd J Henness, \Optimizing Deled Bnhes", Poeedings of the 15th nnl Wokshop on Miopogmming, (Ot 1982), pp [16] D Ptteson nd CH Seqin, \RISCI: Reded Insttion Set VLSI Compte", Poeedings of the 8th Intentionl Smposim on Compte hitete, (M 1981), pp [17] JE Smith, \ Std of Bnh Pedition Sttegies", Poeedings of the 8th Intentionl Smposim on Compte hitete,(m 1981), pp [18] C Chen, \Pllelism, Pipelining nd Compte Ef ien", Compte Design,Vol 10, o 1, (Jn 1971), pp6974
32. The Tangency Problem of Apollonius.
. The Tngeny olem of Apollonius. Constut ll iles tngent to thee given iles. This eleted polem ws posed y Apollinius of eg (. 6070 BC), the getest mthemtiin of ntiquity fte Eulid nd Ahimedes. His mjo wok
More informationOrbits and Kepler s Laws
Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how
More information(1) continuity equation: 0. momentum equation: u v g (2) u x. 1 a
Comment on The effect of vible viscosity on mied convection het tnsfe long veticl moving sufce by M. Ali [Intentionl Jounl of Theml Sciences, 006, Vol. 45, pp. 6069] Asteios Pntoktos Associte Pofesso
More informationXML Data Integration using Fragment Join
XML Dt Integtion using Fgment Join Jin Gong, Dvi W. Cheung, Nikos Mmoulis, n Ben Ko Deptment of Compute Siene, The Univesity of Hong Kong Pokfulm, Hong Kong, Chin {jgong,heung,nikos,ko}@s.hku.hk Astt.
More informationMath 1105: Calculus II (Math/Sci majors) MWF 11am / 12pm, Campion 235 Written homework 5
Mth 5: Clculus II Mth/Sci mjos) MWF m / pm, Cmpion 35 Witten homewok 5 6.6, p. 458 3,33), 6.7, p. 467 8,3), 6.875), 7.58,6,6), 7.44,48) Fo pctice not to tun in): 6.6, p. 458,8,,3,4), 6.7, p. 467 4,6,8),
More informationCombinatorial Testing for TreeStructured Test Models with Constraints
Comintoil Testing fo TeeStutued Test Models with Constints Tkshi Kitmu, Akihis Ymd, Goo Htym, Cyille Atho, EunHye Choi, Ngo Thi Bih Do, Yutk Oiw, Shiny Skugi Ntionl Institute of Advned Industil Siene
More informationSummary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:
Summ: Vectos ) Rtio Theoem (RT) This theoem is used to find n points (o position vectos) on given line (diection vecto). Two ws RT cn e pplied: Cse : If the point lies BETWEEN two known position vectos
More informationQuick Guide to Lisp Implementation
isp Implementtion Hndout Pge 1 o 10 Quik Guide to isp Implementtion Representtion o si dt strutures isp dt strutures re lled Sepressions. The representtion o n Sepression n e roken into two piees, the
More informationN V V L. R a L I. Transformer Equation Notes
Tnsfome Eqution otes This file conts moe etile eivtion of the tnsfome equtions thn the notes o the expeiment 3 witeup. t will help you to unestn wht ssumptions wee neee while eivg the iel tnsfome equtions
More informationBasic Principles of Homing Guidance
si Piniples of Homing Guidne Neil F Plumbo, Ross A luwkmp, nd Justin M Lloyd his tile povides oneptul foundtion with espet to homing guidne upon whih the next sevel tiles e nhoed To this end, bsi geometi
More informationThe Casino Experience. Let us entertain you
The Csio Expeiee Let us eteti you The Csio Expeiee If you e lookig fo get ight out, Csio Expeiee is just fo you. 10 The Stight Flush Expeiee 25 pe peso This is get itodutio to gmig tht sves you moey Kik
More informationIntro to Circle Geometry By Raymond Cheong
Into to Cicle Geomety By Rymond Cheong Mny poblems involving cicles cn be solved by constucting ight tingles then using the Pythgoen Theoem. The min chllenge is identifying whee to constuct the ight tingle.
More informationImplementation and Evaluation of Transparent FaultTolerant Web Service with KernelLevel Support
Poceedings of the IEEE Intentionl Confeence on Compute Communictions nd Netwoks Mimi, Floid, pp. 6368, Octobe 2002. Implementtion nd Evlution of Tnspent FultTolent Web Sevice with KenelLevel Suppot
More informationLAPLACE S EQUATION IN SPHERICAL COORDINATES. With Applications to Electrodynamics
LALACE S EQUATION IN SHERICAL COORDINATES With Appitions to Eetodynmis We hve seen tht Lpe s eqution is one of the most signifint equtions in physis. It is the soution to pobems in wide viety of fieds
More informationAdaptive Control of a Production and Maintenance System with Unknown Deterioration and Obsolescence Rates
Int J of Mthemtic Sciences nd Appictions, Vo, No 3, Septembe Copyight Mind Rede Pubictions wwwjounshubcom Adptive Conto of Poduction nd Mintennce System with Unknown Deteiotion nd Obsoescence Rtes Fwzy
More informationGFI MilEssentils & GFI MilSecuity vs Tend Mico ScnMil Suite fo Micosoft Exchnge GFI Softwe www.gfi.com GFI MilEssentils & GFI MilSecuity vs Tend Mico ScnMil Suite fo Micosoft Exchnge Exchnge Seve 2000/2003
More informationHighest Pefomnce Lowest Pice PRODUCT COMPARISON GFI MilAchive vs Symntec Entepise Vult GFI Softwe www.gfi.com GFI MilAchive vs Symntec Entepise Vult GFI MilAchive 6 Symntec Entepise Vult Who we e Genel
More informationCellular network with continuum priority set
Cellla netwok with ontinm pioity set JeanMa Kelif Fane Teleom eseah Development 9794 ssy Molinea, Fane jeanma.kelif@oangeftgop.om Eitan Alman A P 9 69 Sophia Antipolis, Fane Eitan.Altman@sophia.inia.f
More informationv o a y = = * Since H < 1m, the electron does not reach to the top plate.
. The uniom electic ield between two conducting chged pltes shown in the igue hs mgnitude o.40 N/C. The plte seption is m, nd we lunch n electon om the bottom plte diectl upwd with v o 6 m/s. Will the
More informationGFI MilAchive 6 vs H&S Exchnge@PAM GFI Softwe www.gfi.com GFI MilAchive 6 vs H&S Exchnge@PAM GFI MilAchive 6 H&S Exchnge@PAM Who we e Genel fetues Suppots Micosoft Exchnge 2000, 2003 & 2007 Suppots distibuted
More informationTHE PRICING OF IMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS A GENERAL APPROACH USING MULTIVARIATE TREE STRUCTURES
BTCT TH PICING OF IMPLICIT OPTION IN LIF INUNC CONTCT GNL PPOCH UING MULTIVIT T TUCTU By Tois Dillnn n Johen ss * In the esent e we intoe new oel fo the iing of iliit otions in life insne ontts Mny oels
More informationScreentrade Car Insurance Policy Summary
Sceentde C Insunce Policy Summy This is summy of the policy nd does not contin the full tems nd conditions of the cove, which cn be found in the policy booklet nd schedule. It is impotnt tht you ed the
More informationr (1+cos(θ)) sin(θ) C θ 2 r cos θ 2
icles xmple 66: Rounding one ssume we hve cone of ngle θ, nd we ound it off with cuve of dius, how f wy fom the cone does the ound stt? nd wht is the chod length? (1+cos(θ)) sin(θ) θ 2 cos θ 2 xmple 67:
More informationRandom Variables and Distribution Functions
Topic 7 Rndom Vibles nd Distibution Functions 7.1 Intoduction Fom the univese of possible infomtion, we sk question. To ddess this question, we might collect quntittive dt nd ognize it, fo emple, using
More informationGFI MilEssentils & GFI MilSecuity vs Bcud Spm Fiewll GFI Softwe www.gfi.com GFIMilEssentils & GFI MilSecuity vs Bcud Spm Fiewll GFI MilEssentils 12 & GFI MilSecuity 10 Bcud Spm Fiewll Who we e Integtes
More informationGFI EventsMnge vs Netikus.net EventSenty GFI Softwe www.gfi.com GFI EventsMnge vs Netikus.net EventSenty GFI EventsMnge EventSenty Who we e Suppot fo MS SQL Seve Suppot fo MSDE / MS SQL Expess Suppot fo
More informationM 2 STABILITY ANALYSIS AND OPTIMAL CONTROL ON THE MODEL HARVESTING OF PREY PREDATOR WITH FUNGSIONAL RESPONSE TYPE III
Poeeding of Intentionl Confeene On Reseh, Implementtion nd dution Of Mthemtis nd Sienes 5, Yogt Stte Univesit, 79 M 5 M STBILITY NLYSIS ND OPTIML CONTROL ON TH MODL HRVSTING OF PRY PRDTOR WITH FUNGSIONL
More informationGFI MilEssentils & GFI MilSecuity vs Symntec Bightmil 6 & Anti Vius GFI Softwe www.gfi.com GFI MilEssentils & GFI MilSecuity vs Symntec Bightmil 6 & Anti Vius GFI MilEssentils & GFI MilSecuity Bightmil
More informationEquivalence Checking. Sean Weaver
Equivlene Cheking Sen Wever Equivlene Cheking Given two Boolen funtions, prove whether or not two they re funtionlly equivlent This tlk fouses speifilly on the mehnis of heking the equivlene of pirs of
More information(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?
Em I Solutions PHY049 Summe 0 (Ch..5). Two smll, positively chged sphees hve combined chge of 50 μc. If ech sphee is epelled fom the othe by n electosttic foce of N when the sphees e.0 m pt, wht is the
More informationMulticriteria Decision Model for Information Systems Priorities Based on Business Process Management
Multiiteia Deision Model fo Infomation Systems Pioities Based on Business Poess Management Adiel Teixei de Almeida* and Mila Neves Souza** The pape pesents a multiiteia deision model fo infomation system
More informationWords Symbols Diagram. abcde. a + b + c + d + e
Logi Gtes nd Properties We will e using logil opertions to uild mhines tht n do rithmeti lultions. It s useful to think of these opertions s si omponents tht n e hooked together into omplex networks. To
More informationpayments Excess demand (Expenditure>output) r > r Excess demand (Expenditure>output) r > r Excess supply (Expenditure
Chpte Review Questions. The IS model defines six egions, eh oesponding to disequiliium in the money mket, goods mket nd/o the lne of pyments. Identify nd desie eh of these when pitl is pefetly moile,
More informationChapter. Contents: A Constructing decimal numbers
Chpter 9 Deimls Contents: A Construting deiml numers B Representing deiml numers C Deiml urreny D Using numer line E Ordering deimls F Rounding deiml numers G Converting deimls to frtions H Converting
More informationON THE CHINESE CHECKER SPHERE. Mine TURAN, Nihal DONDURMACI ÇİN DAMA KÜRESİ ÜZERİNE
DÜ Fen Bilimlei Enstitüsü Degisi Sı 9 Ağustos 9 On The Chinese Cheke Sphee M. Tun N. Donumı ON THE CHINESE CHECKER SHERE Mine TURAN Nihl DONDURMACI Deptment of Mthemtis Fult of Ats n Sienes Dumlupin Univesit
More informationGFI MilAchive 6 vs Wtefod Technologies MilMete Achive GFI Softwe www.gfi.com GFI MilAchive 6 vs Wtefod Technologies MilMete Achive Genel fetues Suppots Micosoft Exchnge 2000, 2003 & 2007 Suppots distibuted
More informationc b 5.00 10 5 N/m 2 (0.120 m 3 0.200 m 3 ), = 4.00 10 4 J. W total = W a b + W b c 2.00
Chter 19, exmle rolems: (19.06) A gs undergoes two roesses. First: onstnt volume @ 0.200 m 3, isohori. Pressure inreses from 2.00 10 5 P to 5.00 10 5 P. Seond: Constnt ressure @ 5.00 10 5 P, isori. olume
More informationModule 5. Threephase AC Circuits. Version 2 EE IIT, Kharagpur
Module 5 Threehse A iruits Version EE IIT, Khrgur esson 8 Threehse Blned Suly Version EE IIT, Khrgur In the module, ontining six lessons (7), the study of iruits, onsisting of the liner elements resistne,
More informationDerivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity)
Aity Deivatios 4/4/ Deivatio of Aity ad Pepetity Fomlae A. Peset Vale of a Aity (Defeed Paymet o Odiay Aity 3 4 We have i the show i the lecte otes ad i ompodi ad Discoti that the peset vale of a set of
More informationby K.H. Rutsch*, P.J. Viljoen*, and H. Steyn* The need for systematic project portfolio selection
An investigtion into the cuent pctice of poject potfolio selection in esech nd development division of the South Aficn minels nd enegy industy by K.H. Rutsch*, P.J. Viljoen*, nd H. Steyn* J o u n l Synopsis
More informationtools for Web data extraction
HTMLwe tools fo Web dt extction Thesis pesenttion 1 Student: Xvie Azg Supeviso: Andes Tho Tble of contents Intoduction Dt Extction Pocess Dt Extction Tools Relized tests Futue Wok 2 Intoduction We e going
More informationr Curl is associated w/rotation X F
13.5 ul nd ivegence ul is ssocited w/ottion X F ivegence is F Tody we define two opetions tht cn e pefomed on vecto fields tht ply sic ole in the pplictions of vecto clculus to fluid flow, electicity,
More informationABSORPTIONFREE SUPERLUMINAL LIGHT PROPAGATION IN A VTYPE SYSTEM
Amenin Jounl of Physis 0 vol. 4 issue. 3848 ABSORPTIONFREE SUPERLUMINAL LIGHT PROPAGATION IN A VTYPE SYSTEM S. W. Rbiei* Kh. Sidi B. Ruzbhni M. Mhmoudi 3 Islmi Azd Univesity  Snndj Bnh Snndj In Physis
More informationCircles and Tangents with Geometry Expressions
icles nd Tngents with eomety xpessions IRLS N TNNTS WITH OMTRY XPRSSIONS... INTROUTION... 2 icle common tngents... 3 xmple : Loction of intesection of common tngents... 4 xmple 2: yclic Tpezium defined
More informationCurvature. (Com S 477/577 Notes) YanBin Jia. Oct 8, 2015
Cuvtue Com S 477/577 Notes YnBin Ji Oct 8, 205 We wnt to find mesue of how cuved cuve is. Since this cuvtue should depend only on the shpe of the cuve, it should not be chnged when the cuve is epmetized.
More informationLaplace s Equation on a Disc
LECTURE 15 Lplce s Eqution on Disc Lst time we solved the Diichlet poblem fo Lplce s eqution on ectngul egion. Tody we ll look t the coesponding Diichlet poblem fo disc. Thus, we conside disc of dius 1
More informationGFI MilAchive 6 vs EMC EmilXtende Achive Edition GFI Softwe www.gfi.com GFI MilAchive 6 vs EMC EmilXtende Achive Edition GFI MilAchive 6 EMC EmilXtende Achive Edition Who we e Genel fetues Suppots Micosoft
More informationexcenters and excircles
21 onurrene IIi 2 lesson 21 exenters nd exirles In the first lesson on onurrene, we sw tht the isetors of the interior ngles of tringle onur t the inenter. If you did the exerise in the lst lesson deling
More informationPractice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn
Prtie Test 2 1. A highwy urve hs rdius of 0.14 km nd is unnked. A r weighing 12 kn goes round the urve t speed of 24 m/s without slipping. Wht is the mgnitude of the horizontl fore of the rod on the r?
More informationA Note on Risky Bond Valuation
A Note on Risky Bond Valuation C. H. Hui Banking Poliy Depatment Hong Kong Monetay Authoity 0th Floo,, Gaden Road, Hong Kong Email: ChoHoi_Hui@hkma.gov.hk C. F. Lo Physis Depatment The Chinese Univesity
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
More informationThe area of the larger square is: IF it s a right triangle, THEN + =
8.1 Pythgoren Theorem nd 2D Applitions The Pythgoren Theorem sttes tht IF tringle is right tringle, THEN the sum of the squres of the lengths of the legs equls the squre of the hypotenuse lengths. Tht
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More information2.016 Hydrodynamics Prof. A.H. Techet
.016 Hydodynmics Reding #5.016 Hydodynmics Po. A.H. Techet Fluid Foces on Bodies 1. Stedy Flow In ode to design oshoe stuctues, suce vessels nd undewte vehicles, n undestnding o the bsic luid oces cting
More informationUNIVERSITY AND WORKSTUDY EMPLOYERS WEBSITE USER S GUIDE
UNIVERSITY AND WORKSTUDY EMPLOYERS WEBSITE USER S GUIDE Tble of Contents 1 Home Pge 1 2 Pge 2 3 Your Control Pnel 3 4 Add New Job (ThreeStep Form) 46 5 Mnging Job Postings (Mnge Job Pge) 78 6 Additionl
More informationLightweight Java Profiling with Partial Safepoints and Incremental Stack Tracing
Lightweight J Profiling with Prtil Sfepoints nd Inrementl Stk Tring Peter Hofer Did Gnedt peter.hofer@jk.t did.gnedt@jk.t Christin Doppler Lortory on Monitoring nd Eoltion of VeryLrgeSle Softwre Systems
More informationgrow scouting s impact.
grow scouting s impct. 20 16 Fmi ly F r ien d s of S c o u t i ng U ni t C h i r m n G u i debook Cr o s s r o d s o f Americ Council, Boy Scouts of Americ this isn t your fr s scout progrm. sure we like
More informationDRIVER BEHAVIOR MODELING USING HYBRID DYNAMIC SYSTEMS FOR DRIVERAWARE ACTIVE VEHICLE SAFETY
DRIVER BEHAVIOR MODELING USING HYBRID DYNAMIC SYSTEMS FOR DRIVERAWARE ACTIVE VEHICLE SAFETY Pin Boyz, Amdeep Sthynyn, John H.L. Hnsen Eik Jonsson School o Engineeing nd Compute Science Univesity o Texs
More informationMore than 2 full working days before the seminar:
The Pesentes Rebecca Mogan Rebecca is a Taxation Consltant with the NTAA and has ove 12 yeas tax expeience. Rebecca holds a Bachelo of Ats and Law and a Mastes of Taxation. Rebecca has pesented a nmbe
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationSE3BB4: Software Design III Concurrent System Design. Sample Solutions to Assignment 1
SE3BB4: Softwre Design III Conurrent System Design Winter 2011 Smple Solutions to Assignment 1 Eh question is worth 10pts. Totl of this ssignment is 70pts. Eh ssignment is worth 9%. If you think your solution
More informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
More informationG.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS
G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS Regul polygon e of inteet to u becue we begin looking t the volume of hexgonl pim o Tethedl nd to do thee type of clcultion we need to be ble to olve fit
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More informationUPS Virginia District Package Car Fleet Optimization
UPS Viginia Distit Pakage Ca Fleet Otimization Tavis Manning, Divaka Mehta, Stehen Sheae, Malloy Soldne, and Bian Togesen Abstat United Pael Sevie (UPS) is onstantly haged with ealigning its akage a fleet
More informationfor Student Service Members and Veterans in Indiana
Apil 2009 The Highe Eduction Lndscpe fo Student Sevice Membes nd Vetens in Indin Mtin Stenbeg, Shelley McDemid Wdswoth, Jo Vughn, nd Ryn Clson Mility Fmily Resech Institute t Pudue Univesity Suppot Len
More informationKEY SKILLS INFORMATION TECHNOLOGY Level 3. Question Paper. 29 January 9 February 2001
KEY SKILLS INFORMATION TECHNOLOGY Level 3 Question Pper 29 Jnury 9 Ferury 2001 WHAT YOU NEED This Question Pper An Answer Booklet Aess to omputer, softwre nd printer You my use ilingul ditionry Do NOT
More informationPROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * challenge questions
PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * hllenge questions e The ll will strike the ground 1.0 s fter it is struk. Then v x = 20 m s 1 nd v y = 0 + (9.8 m s 2 )(1.0 s) = 9.8 m s 1 The speed
More informationOxCORT v4 Quick Guide Revision Class Reports
OxCORT v4 Quik Guie Revision Clss Reports This quik guie is suitble for the following roles: Tutor This quik guie reltes to the following menu options: Crete Revision Clss Reports pg 1 Crete Revision Clss
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More information16. Mean Square Estimation
6 Me Sque stmto Gve some fomto tht s elted to uow qutty of teest the poblem s to obt good estmte fo the uow tems of the obseved dt Suppose epeset sequece of dom vbles bout whom oe set of obsevtos e vlble
More informationEnterprise Digital Signage Create a New Sign
Enterprise Digitl Signge Crete New Sign Intended Audiene: Content dministrtors of Enterprise Digitl Signge inluding stff with remote ess to sign.pitt.edu nd the Content Mnger softwre pplition for their
More informationVictims Compensation Claim Status of All Pending Claims and Claims Decided Within the Last Three Years
Claim#:021914174 Initials: J.T. Last4SSN: 6996 DOB: 5/3/1970 Crime Date: 4/30/2013 Status: Claim is currently under review. Decision expected within 7 days Claim#:041715334 Initials: M.S. Last4SSN: 2957
More informationDefinitions and terminology
I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More information1. Definition, Basic concepts, Types 2. Addition and Subtraction of Matrices 3. Scalar Multiplication 4. Assignment and answer key 5.
. Definition, Bsi onepts, Types. Addition nd Sutrtion of Mtries. Slr Multiplition. Assignment nd nswer key. Mtrix Multiplition. Assignment nd nswer key. Determinnt x x (digonl, minors, properties) summry
More informationRatio and Proportion
Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationMathematics Higher Level
Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:
More informationDensity Curve. Continuous Distributions. Continuous Distribution. Density Curve. Meaning of Area Under Curve. Meaning of Area Under Curve
Continuous Distributions Rndom Vribles of the Continuous Tye Density Curve Perent Density funtion f () f() A smooth urve tht fit the distribution 6 7 9 Test sores Density Curve Perent Probbility Density
More informationGuidelines on the calibration of nonautomatic weighing instruments
9 This pblition is identil to the originl EURAMET "Gidelines on the librtion of nontomti weighing instrments" (EURAMET/g18/v.). The opyright of the originl doment is held by EURAMET e.v. 7. The Clibrtion
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More information8. Hyperbolic triangles
8. Hyperoli tringles Note: This yer, I m not doing this mteril, prt from Pythgors theorem, in the letures (nd, s suh, the reminder isn t exminle). I ve left the mteril s Leture 8 so tht (i) nyody interested
More informationTHE LONGITUDINAL FIELD IN THE GTEM 1750 AND THE NATURE OF THE TERMINATION.
THE LONGITUDINAL FIELD IN THE GTEM 175 AND THE NATURE OF THE TERMINATION. Benjmin Guy Loder Ntionl Physil Lbortory, Queens Rod, Teddington, Middlesex, Englnd. TW11 LW Mrtin Alexnder Ntionl Physil Lbortory,
More informationEffects of Sleep Hygiene Education on Subjective Sleep Quality and Academic Performance l
e A þ t ý m Effects of Sleep Hygiene Eduction on Subjective Sleep Qulity nd Acdemic Pefomnce l n i j i O O i g in Uyku Hijyen Eğitiminin Subjektif Uyku Klitesi ve Akdemik Pefomnsı Üzeine Etkilei h c s
More informationEE247 Lecture 4. For simplicity, will start with all pole ladder type filters. Convert to integrator based form example shown
EE247 Lecture 4 Ldder type filters For simplicity, will strt with ll pole ldder type filters Convert to integrtor bsed form exmple shown Then will ttend to high order ldder type filters incorporting zeros
More informationThe strategic and tactical value of a 3D geotechnical model for mining optimization, Anglo Platinum, Sandsloot open pit
The sttegic nd tcticl vlue of 3D geotechnicl model fo mining optimiztion, Anglo Pltinum, Sndsloot open pit by A. Bye* J o u n l Synopsis Sndsloot open pit is situted on the nothen limb of the Bushveld
More informationExponents base exponent power exponentiation
Exonents We hve seen counting s reeted successors ddition s reeted counting multiliction s reeted ddition so it is nturl to sk wht we would get by reeting multiliction. For exmle, suose we reetedly multily
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More informationReal Analysis HW 10 Solutions
Rel Anlysis HW 10 Solutions Problem 47: Show tht funtion f is bsolutely ontinuous on [, b if nd only if for eh ɛ > 0, there is δ > 0 suh tht for every finite disjoint olletion {( k, b k )} n of open intervls
More informationNetwork Configuration Independence Mechanism
3GPP TSG SA WG3 Security S3#19 S3010323 36 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting
More information1 GSW IPv4 Addressing
1 For s long s I ve een working with the Internet protools, people hve een sying tht IPv6 will e repling IPv4 in ouple of yers time. While this remins true, it s worth knowing out IPv4 ddresses. Even when
More informationExam in physics, Elgrunder (Electromagnetism), 20140326, kl 9.0015.00
Umeå Univesitet, Fysik 1 Vitly Bychkov Em in physics, Elgunde (Electomgnetism, 146, kl 9.15. Hjälpmedel: Students my use ny book(s. Mino notes in the books e lso llowed. Students my not use thei lectue
More informationInterdomain Routing
COMP 631: COMPUTER NETWORKS Interdomin Routing Jsleen Kur Fll 2014 1 Internetsle Routing: Approhes DV nd linkstte protools do not sle to glol Internet How to mke routing slle? Exploit the notion of
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationHow to Graphically Interpret the Complex Roots of a Quadratic Equation
Universit of Nersk  Linoln DigitlCommons@Universit of Nersk  Linoln MAT Em Epositor Ppers Mth in the Middle Institute Prtnership 7007 How to Grphill Interpret the Comple Roots of Qudrti Eqution Crmen
More informationOPABSYV45GUQN OS PROCESSOS CRIATIVOS DO LIBER NOVUS E OS FUTUROS. OPABSYV45GUQN PDF 106 Pages 1021.16KB 25 Oct, 2014
OS PROCESSOS CRIATIVOS DO LIBER NOVUS E OS FUTUROS OPABSYV45GUQN OPABSYV45GUQN PDF 106 Pges 1021.16KB 25 Ot, 2014 PDF file: os roessos ritivos do liber novus e os futuros Pge: 1 OS PROCESSOS CRIATIVOS
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments  they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More informationc. Values in statements are broken down by fiscal years; many projects are
Lecture 18: Finncil Mngement (Continued)/Csh Flow CEE 498 Construction Project Mngement L Schedules A. Schedule.of Contrcts Completed See Attchment # 1 ll. 1. Revenues Erned 2. Cost of Revenues 3. Gross
More informationOUTLINE SYSTEMONCHIP DESIGN. GETTING STARTED WITH VHDL August 31, 2015 GAJSKI S YCHART (1983) TOPDOWN DESIGN (1)
August 31, 2015 GETTING STARTED WITH VHDL 2 Topdown design VHDL history Min elements of VHDL Entities nd rhitetures Signls nd proesses Dt types Configurtions Simultor sis The testenh onept OUTLINE 3 GAJSKI
More information