2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Ding, Y

Fung, YF

Ho, TK

Liu, HD

Mao, BH

PolyU Institutional Repository

????:1001-8360(2003)04-0019-04SSE在电气化铁路列车运行模拟中的应用丁　勇1 , 　何天键2 , 　冯汝辉2 , 　刘海东1 , 　毛保华1(1 ?????? ?????? , ??　100044;2?????? ??? , ??)?　?:???????????????????? , ?????????????????????????????? ,????????????? 、???????????? SSE ????。???? I ntel???(Pentium Ⅲ , Pentium Ⅳ)??? SSE(????????????)?? , ?PC ?????????????? ,??????? , ???????????????????????。???:??????;??????;?????;????;SSE?????:U223.2;U260.13　　?????:AApplications of SSE on electrified railwaytrain operation simulationDING Yong1 , 　HO Tin-kin2 , 　FUNG Yu-fai2 , 　LIU Hai-dong1 , 　MAO Bao-hua1(1School of T raff ic and T ransportation , Northern Jiaotong University , Beijing 100044 , China;　2Department of Elect rical Engineering , Hong Kong Polytechnic University , Hong Kong , China)Abstract:This paper discusses the key issues about t rain operation simulation on electrified railw ays.A simulat ionsy stem has been developed fo r computational simulation and scheme evaluation.As an emphasis , the paper introducesthe system structure , flow chart and traction power supply model.The calculating of traction power supply is a CPU-intensive wo rk.The Intel archi tecture processors(Pentium Ⅲ , Pentium Ⅳ)introduces S treaming SIMD Ex tensions(SSE), that is an ef ficient execution model to accelerate the applications.The paper discusses the methods to acceler-ate the calculation of traction pow er supply .Main procedures have been redesigned by exploiting SIMD parallelism inthe PC plat form.Finally , the experimental results demonst rate that SSE can speed up the calculation of traction pow-er supply .Compared w ith convention algori thm implementation , the parallel alg orithm enhances performance abouttw o times.Keywords:t rain operation simulation;calculation of traction pow er supply ;computer simulation;parallel algorithm;SSE　　????????????? 。?????????????????????????????????? ,??????? 、?? 、?????????????。??[ 1 ～ 3]???????????????????? ,?????????????????????? 。?????????????? ,?????????????????????????????。??????? ,??????? 、????? 、????:2002-09-27;????:2003-03-07????:?????????????????(2001-01);????????????(EE/ P00044)????:?　?(1974—), ? , ??????? , ?????。??????????????????? 。??????????????????????????? ,??????? ,?????????????????????????? ,???? ,???? 。??????????????????? ,??????????????????????????。???????? 、????????? ,???????????(??????)?????? 。?????????????? 。????????????????????????? ,????。???? Intel?????? SSE[ 4]?? ,???? 25?? 4?　　　　　　　　　　　　　　　?　　?　　?　　? Vol.25　No.42 0 0 3 ? 8 ? JOURNAL OF THE CHINA RAILWAY SOCIETY August 2003??????????? ,?? PC?????? ,?????????????????? 。1　?????????????????????????????????????????????[ 5] ???? , ??????????。???????????????????????。???????????????????? ,???????????????????? 、?????? 、???;????????????? ,?????????? ,??????????????????????。1.1　????????????????? ,?????? 1。“??????”????????????????????。??????????? 、?? 、?? 、?? 、??? 、??? 、???????;??????????? 、?? 、???????????????。“??????”?????? ,??????????????????? ,???? 、?? 、???????? ,??????????????。“??????”??????????? 、???? ,?????????????????????????。“????????”??????—???? 、??—???? 、????? 、????????????CAD?????????。??????????????????? ,?? 2。?????????????? ,???????????????????????? 。????? ,????????? 、?? 、??????????? ,?????????[ 6] 。??????????? 、?? 、??????。?????????????? 、?? 、??? ,??????????????? ,???????????????? ,????????????????? 、??????。??????? 、??????????????????? 、?????????????? 、???? 、??? ,?????????????????? ,???????????。1.2　???????????????? , ????????????[ 7] 。?????????????? 、????? 、??????? 。????????????????????????。?? ,????????????????????????? 、AT ????? BT ?????[ 8] 。??????? ,??????????? ,???????????? 。? 3??????????。????????????????YV = I (1)?? , I ???????? ,????;V???????? ,????;Y ??????? 。??????(1),??????????????????????? 。2　?? SSE?????PC???? Intel ???(Pentium Ⅲ 、PentiumⅣ)??? SSE?? ,??????????? SIMD?? 、??????? ,?????? 8? 128???? , ?? PSF (Packed Single-precision Floating-point)??[ 5] 。PSF ????? SSE???????????????? ,?????????????20 　　　　　　　　　　　　　　　　?　　?　　?　　?　　　　　　　　　　　　　　　? 25??。SSE??? SIMD????????? 4 ,?? ? op?? ? 、? 、? 、? 、?? 、???。　　?? SSE ?????????????? ,?? ,?? SSE ????????????????。???? SSE ?? ,??????????? SIMD??? ,???????????? ,?????????????????(1 )????????????Ax =b (2)?? , A ????????;b?????;x ?????????? 。?????(2)?????? LU ??[ 9] ,? n???A ???? LU ?????????? L ???????? U ??? ,?LUx =b (3)　　????????????? xLx′=b (4)Ux =x′ (5)　　??? L ? U????? ,??????(4)???????? x′,??????????(5)????? x 。LU??? , n ??? A ???? a ij??????a ij -aik ×akjakk =a ij (6)　　????For(k=0;k<n-1;k++)/ ＊???＊/For(i=k+1;i<n;i++)/ ＊???＊/aik=aik/akk　　/ ＊???＊/For(j=k+1;j<n;j++)/ ＊???＊/aij=aij-aik×akj/ ＊????＊/SSE?????? PSF ???? ,?? ,??????????? PSF ???? 。????????????????? ,???? SSE ??????????? 。????? ,?????? PSF ???? ,??? 16 ???????[ 4] 。? LU ????? ,?? A ???? ,???? aij?????????? ,? akj??????????。???????? ,?????????????? PSF ???? ,???????????????? ,????????? 。a ik??????? ,????? ,????PSF ????。?? SSE? LU????????ai , jai , j+1ai , j+2ai , j+3-a ik/akka ik/akka ik/akka ik/akk×ak , jak , j+1ak , j+2ak , j+3=a i , ja i , j+1a i , j+2a i , j+3(7)　　????F32vec4 C ,A1 ,A2;/ ＊PSF ????＊/　For (k=0;k<n-1;k++){/ ＊???＊/For(i=k+1;i<n;i++){/ ＊???＊/aik=aik/akk　　/ ＊???＊/_mm_load_ps1(C , aik);/ ＊? aik????????C ?＊/For(j=k+1;j<n;j+=4){/＊???＊/_mm_load_ps(A1 , akj);/ ＊? akj? ak , j+3???????? A1?＊/_mm_load_ps(A2 , aij);/ ＊? aij? ai , j+3???????? A2?＊/A2=A2-(A1×C);/ ＊????＊/_mm_store_ps(aij ,A2);}}}/ ＊? A2??? aij?21? 4 ?　　　　　　　　　　　　　　SSE ????????????????　　　　　　　　　　　　　　ai , j+3??????＊/?????? ,?(4)????x′i =bi -∑i-1j=1x′j ×L ij (8)　　SSE ????????? x′j ×L ij? 。????? , x′j ? Lij??????????? 2????PSF??????????? 。??????? ,?(5)????xj = 1U ij [ x′j -∑mn=j+1x n ×U jn] (9)　　???????? ,? x n×Ujn????? ,????? , xn ?U jn???????????? 2???? PSF ???????????。3　????????? ,???? Intel9 SSE C/ C++???? ,???????? 、????[ 10]???????????。?????????? SSE ?????? ,? C/C++??????? SSE ?? 。??SSE???????????????? SIMD ?? ,?????? ,????????? 4.0。?????????? ,???????????? SIMD????? ,?????? ,????? 、????????? 。?? ,???????? ,?? Intel9???????? ,???????? 、????[ 10] 、????????? 。????????? ,?????????? LU ?????????? ,? 1???SSE? LU????????(???????????? 733 MHz? Pentium Ⅲ?????)。? 1　LU ?????????????50 100 150 200 250 300? SSE??/m s 0.66 5.15 17.50 52.94 175.90 292.48SSE??/m s 0.22 1.59 5.23 20.16 83.90 143.74??? 3.00 3.24 3.35 2.63 2.10 2.04?? 1?????:????? 200??? ,???????? ,????????? 3.35 ,????? 4.0???。??????? 200? ,??????? ,?????? 2.0?? ,???? SSE ????? LU ??????? 。? 2 ????? SSE ?? ,??????????????? 。?????????????? ,??????????????????????。??????5??? ,?????? 10??? ,?????? 15??? ,?????? 20???。?? 2 ????? ,??SSE? ,???????????????。???????????? ,????????? ,SSE?????????。? 2　?????????????????? SSE??/minSSE??/min ??? ????????? 3.45 2.25 1.53 102????? 7.15 2.78 2.57 132????? 13.07 6.70 1.95 162????? 27.28 10.75 2.54 1924　?????? Intel9?????? SSE?? ,? PC?????????????? ,??????? ,???????????????????????。?????????? ,? 2002? 4???????? ,???????????? 、???? 、? 、? 、??????????????? ,?????????? 。????:[ 1] ??.??????????????[ J] .???? ,1995 , 17(??):20—26.[ 2] ?? ,???.?????????????????[ J] .???? , 1997 , 9(3):61—68.[ 3] ??? ,??? , ?.???????????[ J] .?????? , 1995 , 16(1):14—26.[ 4] Intel Corpo ration.Intel C/C++Compiler Class Libraries fo rSIMD Operation User' s Guide [ EB/OL] .http:// developer.intel.com/ design/ pentium4/ manuals.[ 5] ??? ,??? , ?.??????????????[ J] .???? , 2000 , 22(1):1—6.[ 6] ??.??????[ M] .???.??:??????? , 2002.4—56.[ 7] Mellit B , Goddman C J.Simulator for studying operationaland pow r-supply conditions in rapid-transit railways[ J] .IEEProc., 1978 , 125(4):298—303.[ 8] ?????????????????.??????[ M] .??:??????? , 1988.9—10 .[ 9] ????.????[ M] .???.??:??????? ,2001.10—25 .[ 10] Intel Co rporation.Intel9 Pentium 4 Processor OptimizationReference Manual[ EB/ OL] .http://developer.intel.com/design/pentium4/manuals.(????　?　?)22 　　　　　　　　　　　　　　　　?　　?　　?　　?　　　　　　　　　　　　　　　? 25?

Applications of SSE on electrified railway train operation simulation

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