Cache Performance of the Integer SPEC Benchmarks on a RISC t

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1 Cche Perfrmnce f he Ineger SPEC Benchmrks n RISC Dnss N. Pnevmks rk D. Hll Cmpuer Scences Deprmen Unversy f Wscnsn-dsn 121 W. Dyn Sree dsn, WI 5376 ABSTRACT SPEC s new se f benchmrk prgrms desgned mesure cmpuer sysem's perfrmnce. The perfrmnce mesured by benchmrks s srngly ffeced by he exsence nd cnfgurn f cche memry. In hs pper we evlue he cche mss r f he Ineger SPEC benchmrks. We shw h he cche mss r depends srngly n he prgrm, nd h lrge cches re n cmpleely exercsed by hese benchmrks. 1. Inrducn The SPEC benchmrks re new se f benchmrk prgrms desgned evlue he perfrmnce f cmpuer sysems [9]. In he desgn f hs se, cnsderble effr s mde s h he resuls re ndcve frm he expeced perfrmnce n envrnmens lke Cmpuer Aded Sfwre Engneerng nd Cmpuer Aded Engneerng. T cheve hs gl, publc dmn rel pplcns frm he bve res re used. The perfrmnce mesured s scled he perfrmnce f he VAX 11/7/8 fr ech prgrm n he se, nd he rs re verged usng he gemerc men s prpsed n [1]. The frs relese f he SPEC benchmrks cnsss f en prgrms: GNU C cmpler, Eqn, Xlsp, Espress, Spce 2g6, Dduc, Ns7, rx3, Fpppp nd TmcV. The frs fur re neger-nensve prgrms wren n C, nd he res re flng-pn-nensve prgrms wren n Frrn. Snce ms hgh-perfrmnce cmpuer sysems nclude ne r mre cches reduce he verge memry ccess me nd herefre mprve perfrmnce [7], quesn h cn be sked s wh s he effec f cches n he perfrmnce mesured by he benchmrk prgrms. Knwng he cche behvr f he benchmrkng prgrms, ne cn predc he perfrmnce chnge fr gven chnge n he memry herrchy. Hwever, he perfrmnce f sysem wll n be ccurely predcble f he cche behvr shws shrp chnges rund sme prmeer vlues, becuse smll chnges n cche cnfgurn cn yeld lrge chnges n he mesured perfrmnce. Als mprn re cche cnfgurn szes where mss rs becme neglgble, snce mprvng cche prmeers beynd hese szes wll n mprve he perfrmnce mesured by hese benchmrks. The merl presened here s bsed n reserch suppred n pr by he Nnl Scence Fundn's Presdenl Yung Invesgr nd Cmpuer end Cmpun Reserch Prgrms under grns IPS nd CCR , A.T.&T. Bell Lbrres, Cry Reserch, Dgl Equpmen Crprn, Texs Insrumens, nd he grdue schl he Unversy f Wscnsn--dsn. 53

2 T evlue he cche perfrmnce f he SPEC benchmrks, he fur neger-nensve prgrms were rced nd smuled fr lrge number f cche cnfgurns. The prgrms were cmpled n DECsn 31 bsed n he IPS R2 rchecure runnng he Ulrx perng sysem. 2. Trcng nd smuln The rces were bned usng he Absrc Execun mehd [6], fr speed nd cmpressn resns. AE pses sme resrcns n he rces h cn be bned, he ms mprn f whch re h hey cn nly be sngle prcess rces, h he perng sysem clls cnn be rced, nd h he GNU C cmpler mus be used. Even hugh AE cn rce hrugh lbrry clls, he sndrd C lbrres were n rced n hs smuln. Hwever, we feel h he prgrms d n use hem very much nd he dfference n he resuls wuld be smll. All prgrms were cmpled wh he pmzng flg enbled. Fr he cche smuln, he All Asscvy smuln lgrhm [5] s mplemened n Tych [4] ws used. The cche prmeers used hrughu he smuln were: cche sze frm 1 Kbye up 1 bye, sscvy frm 1 (drec mpped) up 8 wy se-sscve, nd blck sze frm up 256 byes. All seps hrugh hese prmeers re n fcrs f w. The replcemen lgrhm used ws LRU nd he se-mppng funcn ws b selecn. All he bve cche cnfgurns were smuled fr nsrucn, d nd unfed cches. The repred mss r s he l number f msses fr he enre execun f he prgrm, dvded by he l number f references. Snce he enre execun f he prgrm s rced, he cld msses re ncluded n he mss r. Fr Gcc nd Espress, h re run fr severl npu fles, he msses fr ll npu fles re summed nd dvded by he l number f references mde. Due me lmns, Espress ws smuled fr nly w f he egh npu fles h cnsue he benchmrk. The cmplee resuls re gven n bulr frm n he Appendx. In he resuls, zer mss r mens h he cul mss r s less hn.1. The l number f references fr ech prgrm nd he brekdwn nsrucn nd d ccesses s gven n Tble I. Tble I Prgrm Insrucn Tl Eqn Xlsp GNU C Cmpler Espress 1,129,738,935 1,28,576,271 1,3,734,885 1,415,583, ,685, ,7,976 44,43, ,76,87 1,418,424,159 1,873,277,247 1,435,5,8 1,89,659,66 3. Smuln resuls Ths secn presen he fur neger SPEC benchmrks n sme del nd he crrespndng smuln resuls. Addnl nsgh cn be bned frm Fgures 1, 2 nd 3 h gve sme f he resuls n grphcl frm. Fgure 1 pls he mss r s funcn f cche sze, Fgure 2 pls he chnge n he mss r when he blck sze s dubled nd Fgure 3 pls he chnge n mss r when degree f sscvy s dubled. Fr he res f hs secn, he msses re dvded n hree cegres [2]: cnflc msses due mny cve blcks mppng frcn f he ses, cpcy msses due he fxed cche sze nd cmpulsry msses, he nes h frs reference n em. 54

3 3.1. Eqn Eqn s prgrm h rnsles lgcl represenn f blen equn rh ble. The prmry cmpun perfrms s srng, usng he qucksr lgrhm. Prflng hs prgrm shws h 95% f he me s spen n he qucksr rune. The sze f d fr he benchmrk npu s pprxmely 1.8 byes. The perfrmnce f he nsrucn cche fr Eqn cn be seen clerly n he bles: fr nsrucn cches f sze lrger hn 2Kbyes he mss r s smller hn.1. Snce 95% f he me s spen n he qucksr rune, ny cche f sze lrger hn h wll gve he sme perfrmnce. The behvr f he d cche fr Eqn s resul f he nure f qucksr, whch des n shw prculrly hgh emprl lcly, nd f he lrge d sze. Becuse f he lw emprl lcly f he lgrhm, he cpcy msses dmne nd gve relvely hgh mss r fr cches f sze up 256 Kbyes (.3 fr 128 Kbye egh-wy se-sscve cche wh byes blck sze). In he sme rnge, he mss r s lms nsensve chnges n sscvy s cn be seen n Fgure 3. Fr lrger cches, sscvy mprves sgnfcnly he mss r. Ths behvr dffers cnsderbly frm he ne repred n prevus sudes [3], [5]. Furhermre, he mss r fr medum nd lrge sze cches drps very quckly s he blck sze s ncresed, s he cmpulsry msses re reduced. The unfed cche perfrmnce f Eqn, becuse f s degenere nsrucn behvr, cn be esly clculed by mulplyng he d mss r by he frcn f d references f he prgrm. Ths smple reln hlds nly when he number f ses s enugh s h he cnflcs beween nsrucn nd d ccesses re rre Xlsp Xlsp s smll mplemenn f fsp nerpreer, whch ls prvdes sme bjec-rened prgrmrnng hks. The npu fle s smll bckrckng prgrm h slves he Egh Queens prblem. The smll sze f he prgrm cn be seen n he ble fr sscvy 8: cche sze lrger hn Kbyes fr nsrucn nd 32 Kbyes fr d cche gve mss r less hn.1. Fr Xlsp, smll nsrucn cche gves hgh mss r, becuse he nerpreer shws lw emprl lcly (.1 fr 2Kbye drec mpped cche wh byes blck sze). Hwever he mss r drps fs wh he cche sze nd wh he sscvy, snce he cve pr f he cde s smll. The d ccesses f Xlsp shw greer emprl lcly, s he mss r fr smll d cches s smller hn fr nsrucn. I shws ls sgnfcn spl lcly s cn be seen n Fgure 2. Incresng he blck sze mprves he mss r cnsderbly. Chnges n he sscvy re whn prevusly repred lms, excep fr cches h re lrge enugh hld he enre wrkng se, n whch cse he mprvemen cn be lrger hn fcr f w (chnge frm drec mpped w-wy sesscve cche f sze lrger hn 32Kbyes). The unfed cche behvr fllws he lnes f he nsrucn nd d cche behvr. The mgnude f he mss r s lrger becuse f nerference beween nsrucn nd d ccesses. Th nerference cn be reduced by ncresng he sscfvy GNU C Cmpler The GNU C cmpler r Gcc s he versn 1.35 f he cmpler s dsrbued by he Free Sfwre Fundn. The benchmrk cnsss f cnverng 19 preprcessed surce fles n pmzed 682 ssembly lnguge usng he Sun-3 ssembly frm. Ths prgrm s expeced predc ccurely he cmplng perfrmnce f he sysem n sfwre engneenng envrnmen. 55

4 Becuse Gcc s bg prgrm, he mss rs shws re mng he hghes nes. The behvr f Gcc s cn be seen n Fgures 1, 2 nd 3 s unfrm nd cnssen wh erler sudes [3], [5], [8] ver wde rnge f prmeers. In h sense, Gcc s well-behved prgrm nd s behvr cn be esly nd ccurely predced r nerpled frm ncmplee d whu lrge errrs. Becuse f s sze nd srucure, s demnds frm he memry herrchy re sgnfcn Espress Fnlly, Espress s l fr genern nd pmzn f Prgrmmble Lgc Arrys frm he Berkeley CAD sfwre dsrbun. The mn cmpuns perfrms re se perns lke unn nd nersecn, he ses beng represened s rrys f bs. The se perns re hen mplemened s lgcl perns n hese rrys. The benchmrk cnsss f cnverng se f egh npu mdels n he crrespndng pmzed PLA upu. Fr he w f he npus h were rced, he brekdwn n nsrucn nd d references s shwn n Tble II. Tble II Espress Inpu Fle Insr Tl bc 446,395, ,213, ,69,275 l 969,188,27 276,862,124 1,246,5,331 Snce Espress s relvely smll prgrm h spends l f s me n nner lps perng n rrys, he nsrucn cche mss r s smll The mss r s dmned by cnflc msses, s cn be seen by he effec f ncresng he sscvy. Fr Espress, ny w-wy se-sscve nsrucn cche f sze lrger hn 32Kbyes hs mss r less hn.1. The rry mnpuln ls lms he emprl lcly f he d ccesses nd resuls n hgh mss r fr d cches. Hwever, he cve d sze s bu 64 Khyes, s cches f hs r lrger sze hve essenlly he sme perfrmnce. FnUy, he unfed cche perfrmnce les beween he perfrmnce f spl nsrucn nd d cches. Hwever, we shuld ne h even hugh he resuls fr Espress pper be cnssen nd resnble, ne shuld be creful when generlzng snce nly w f he egh npus were smuled. 4. Cnclusns The cche perfrmnce f Ineger SPEC benchmrks vres grely dependng n he prgrm. Wh he mjr excepn f Eqn, he rends fr smll cches re smlr. Hwever, lrge cches shw lms zer mss r fr Xlsp nd Espress (.2 fr 64 Kbye w-wy se sscve cche wh byes blck sze). The behvr f Eqn, becuse f s specl srucure, deves grely frm he her prgrms. I fvrs cnfgurns wh smll nsrucn cche nd lrge d r unfed cche. Overll, spl nsrucn/d cche f sze 128 Kbyes ech wll gve very lw mss rs fr ll prgrms nd furher mprvemens wll n be clerly refleced n he SPEC resuls. I mgh be rguble h, snce he rces re n mulprgrmmed s n ms prevus sudes, he cche perfrmnce cn be dfferen. Hwever, SPEC mesure he perfrmnce n prcclly sngle prcess envrnmen, whle he cul use f he mchnes s mulprgrmmed. The Ineger SPEC benchmrks, lhugh sgnfcn mprvemen ver ps sndrd benchmrks, wll fl cmpleely exercse hgh perfrmnce memry herrches desgned fr such sysems. 56

5 Acknwledgmens We wuld wuld lke hnk Jmes Lrus fr hs hgh quly suppr f AE, nd Rchrd Kessler fr redng nd mprvng drfs f hs pper. References [1] Phlp Hemmng nd Jhn WUce, "Hw n le wh sscs: The crrec wy summrze benchmrk resuls," Cmmuncns fac, Vl 29, 3, rch 1986, [2] rk D. Hll, "Aspecs f Cche emry nd Insrucn Buffer Perfrmnce," Ph.D. Thess, Unv. f Clfrn Berkeley, Techncl Repr UCB/CSD 87/381, Nvember [3] rk D. Hll, "A Cse Fr Drec-pped Cches," IEEE Cmpuer, Vl 21, pp , December [4] rk D. Hll, "Tych," Unpublshed UNIX syle mnul pge. [5] rk D. Hll nd Aln J. Smh, "Evlung Asscvy n CPU Cches," n IEEE Trnscns On Cmpuer, Vl 38, 12, December [6] Jmes Lrus, "Absrc Execun: A Technque fr Effcenly Trcng Prgrms," Unv. Of Wscnsn, dsn, Techncl Repr #912, Februry 199. [7] Aln J. Smh, "Cche emres," Cmpung Surveys, Vl 14, 3, Sepember [8] Aln J. Smh, "Lne (Blck) Chce fr CPU Cche emres," IEEE Trnscns n Cmpuers, Vl C-36, 9, Sepember 1987, [9] SPEC newsleer, Vl 1, 1, Fll

6 Fgure 1. ss r s funcn f cche sze fr w-wy se sscve cches nd fr blck sze nd 32 byes. Ne h he y-xs scle vry..2. GNU C Cmpler.6 Eqn lr~rucn Insxucdn x Unfed Unfed Blck sze Blck sze 32.4 s s Blck sze Blck sze 32 R.1 R `3 1`4 1"5 Cche (byes) 1"6 1"7. 1"3 v v vl v v v v v v,v 1`4 1^5 1"6 1"7 Cche (byes).2 Xlsp.1 Espress Insrucn.9 O Insrucn X.8 X.15 + Unfed.7. + Unfed 8 R.1 Blck sze Blck sze 32.6, s R.5.4 \ \ Blck sze Blck sze I, 1"3 1"4 1"5 Cche (byes) 1"6 1"3 1"4 1`5 1`6 Cche (byes) 58

7 Fgure 2. Chnge n mss r s funcn f blck sze. Ech pn s he r f he mss r fr cche wh blck sze 2*B dvded by he mss r fr cche f blck sze B. Ths vlue gves he benefs f dublng he blck sze fr w-wy se-sscve cches f sze nd 64 Kbyes. Smller vlues men h dublng blck sze s mre wrhwhle. The nsrucn cche s med where he mss r s zer (Eqn bh szes, Espress 32Kbyes) GNU C Cmpler 1.4. Eqn O Insrucn Insrucn R 1.2, X + Unfed K R 1.2. X + Unfed K f K f K s.8. R s.6. 8 s.8 R 8 s.6.4, Blck (byes) Blck (byes) 1.4. Xlsp 1.4. Espress Insrucn In.erecn R 1.2. X + Unfed K R 1.2. X + Unfed K f K 1.. f 32 K s s.8 s s.8, / R s.6 R Blck (byes) Blck (byes) 59

8 Fgure 3. Chnge n mss r s funcn f sscvy. Ech pn s he r f mss r fr cche f sscvy 2*A dvded by he mss r fr cche f sscvy A. Ths vlue gves he benefs f dublng he sscvy fr blck sze 32 byes. Smller vlues men h dublng he sscvy s mre wrhwhle. The nsrucn cche s med where he mss r s zer (Eqn bh szes, Espress 32Kbyes). 1.2 GNU C Cmpler 1.2, Eqn O Insrucn ] O Insrucn R 1.1.8, f.6 s s./ R X 1. + Unfed K.8 32 K //.6 // "/ s f R.4 s.2 + Unfed K 32 K. m 2 4 Asscdvy. I 4 Assevy R ]\.8. Xlsp \ f \ ~-.6. R.4 s.2 O Insrucn X + Unfed K 32 K f 8 8 R //// //! / / E~p/:essx // / ~ O Insrucn X 4- Unfed K 32 K. 2 4 Assdvy.,2 4 Asscdvy 6

9 Appendx. Cmplee bles f mss rs. Ne h vlue mens h he mss r s less hn.1. Eqn : Asscllvly 1 Insrucn 1K K K 8K K 32K 64K 128K 256K 512K 1 (byes) IK 2K 4K 8K K 32K 64K 128K 256K 512K I UnJfed 1K K K K K K K K K K Eqn : Asscllvy 2 Insrucn 2K 4K 8K K 32K 64K 128K 256K 512K 1 2K K K K K K K K K ~ Uned (byes) K K K K K K K K K ~ ~7.~2..~8.OOO2 61

10 Eqn : Asscllvly 4 Insrucn 4K 8K K 32K 64K 128K 256K 512K 1 (byes) K K K K K K K K, Unfed 4K K K K K K , K , K.6.5.5, (byes) 8K K 32K 64K 128K 256K 512K 1 (byes) Eqn : Assclvy 8 Insrucn j I K K K K K K K (byes) 8K K 32K 64K 128K 256K 512K 1 Un~ ed

11 Xlsp : Asscvy 1 Insrucn 1K K K K K K K K 256K 512K 1 1K K K K K K K K 256K 512K 1 Unfed 1K K K K K K K K K K (byes) XUsp : Asscvy 2 Insrucn 2K K K K K K K 256K 512K 1 (byes) 32 64! K K K K K K K 256K 512K 1 Unfed (byes) 2K K K K K K K K 512K 1 63

12 Xlsp : Assc lvly 4 Insrucn 4K K K K K 128K 256K 512K 1 4K K K K K.2 128K 256K 512K 1 Unfed 4K K K K K K 256K 512K 1 (byes) 8K.11 K 32K 64K 128K 256K 512K 1 (byes) 8K.159 K K.69 64K 128K 256K 512K 1 (byes) 8K.153 K.59 32K.34 64K.4 128K 256K 512K 1 Xlsp : Asscllvly 8 Insrucn 32 [ Unfed

13 GNU C Cmpler : Asscvly 1 Insrucn (byes) I K K K K K K K K K K K K K K K K K K K K Unfed 1K K K K K K K K K K GNU C Cmpler : Asscllvly 2 Insrucn 2K K K K K K K K K K K K K K K K K K Unfed 2K K K ,384 K K K ,55 128K K K

14 GNU C Cmpler : Assclvy 4 Insrucn 4K K K K K K K K K K K K K K K K Unfed 4K K K K K K K K GNU C Cmpler : Asscvy 8 Insrucn 8K K K K K K K K K K K K K K Unfed (byes) K ~ K K K K K K

15 Espress : Assclvy 1 Insrucn 1K K K K K,53,33,21,,14 32K , K , K K K 1 1K ,3287 2K K ,1 8K K K K K K.1 512K 1 UnWed 1K K K K K, K, K, K K K (byes) Espress : Asscllvy 2 Insrucn 32 ] K ! K K K K O3.3 64K I 128K 256K 512K 1 (byes) 2K K K K, K K K K 512K 1 Unfed (byes) 2K K K K K K K.3,2.2,1,1 256K.2 512K 1 67

16 I (byes) 4K 8K K 32K 64K 128K 256K 512K I Espress : Assdlvy 4 Insrucn ,.1 4K K K K K K 256K 512K 1 Umfed 4K K K K K K 256K 512K! 1 (byes) Espress : Asscfvly 8 Insrucn 8K K.1 32K 64K 128K 256K 512K 1 (byes) 8K K 32K 64K 128K 256K 512K 1 (byes) Blck sze(byes) I Unfed 8K K K K K 256K 512K 1 68

ENGI 4421 Probability and Statistics Faculty of Engineering and Applied Science Problem Set 10 Solutions Chi-Square Tests; Simple Linear Regression

ENGI 4421 Probability and Statistics Faculty of Engineering and Applied Science Problem Set 10 Solutions Chi-Square Tests; Simple Linear Regression ENGI 441 Prbbly nd Sscs Fculy f Engneerng nd Appled Scence Prblem Se 10 Sluns Ch-Squre Tess; Smple Lner Regressn 1. Is he fllwng se f bservns f bjecs n egh dfferen drecns cnssen wh unfrm dsrbun? Drecn