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1 VASP

2 VASP 100 PC 3,4 VASP VASP VASP FFT. (LAPACK,BLAS,FFT), CPU VASP. 1 C LAPACK,BLAS VASP VASP VASP VASP bench.hg VASP CPU CPU CPU northwood LAPACK lmkl lapack64, BLAS lmkl p4 LA- PACK liblapack, BLAS libblas 51% CPU prescott LAPACK lapack double, BLAS libgoto LAPACK lapack double, BLAS lmkl em64t 40% -O0 -O1 60% 2 VASP CPU northwood LAPACK lmkl lapack64, BLAS lmkl CPU2 36% CPU3 95% CPU4 249%

3 CPU BLAS,LAPACK Northwood Prescott CPU VASP Northwood Prescott Northwood Prescott VASP VASP A 18 B 20 C VASP 22 D MPICH 27 1

4 1 VASP 100 PC 3,4 VASP VASP VASP FFT. (LAPACK,BLAS,FFT), CPU VASP. 2

5 C LAPACK,BLAS 2. VASP VASP VASP VASP VASP bench.hg 3. CPU 2.1 CPU 1. CPU: Intel Pentium4 Northwood (3.2GHz FSB=800MHz) OS: SuSE Linux9.3 : ASUS P4C800 : 2 :512KB : 1GB (Trancend PC MB ECC DIMM 2) : Seagate ST380817AS(SerialATA 80GB) 1 2. CPU: Intel Pentium4 Prescott 650(3.4GHz FSB=800MHz) OS: SuSE Linux9.3 : SuperMicro PDSGE : 2 :2MB : 2GB (PC ECC 1GB DIMM 2) : Seagate ST AS(SerialATA 80GB) 1 3

6 3 BLAS,LAPACK C (A ) LAPACK,BLAS. LAPACK(Linear Algebra PACKage) netlib FORTRAN 77 CLAPACK C LAPACK CPU BLAS(Basic Linear Algebraic Subprograms) BLAS LAPACK BLAS CPU BLAS( ) C BLAS BLAS LAPACK LAPACK,BLAS LAPACK [1] n n LAPACK N Northwood CPU Intel Pentium4 northwood 3.2GHz 1 C LAPACK,BLAS. 3.1 LAPACK liblapack,blas libblas Mflops Mflops ( ) flops Floating point number Operations Per Second 1 1 M( ) 100 (10 6 ) Mflops 2 4

7 3.1: N N. LAPACK BLAS N =1000 N =2000 time Mflops time Mflops libblas liblapack lmkl p libgoto libblas lmkl-lapack64 lmkl p libgoto VASP LAPACK liblapack,blas libgoto Mflops Mflops LAPACK libgoto libblas liblapack LAPACK liblapack,blas lmkl p Mflops Mflops LAPACK lmkl p4 libgoto libblas liblapack. LAPACK lmkl lapack64,blas libbas, lmkl p4, libgoto , 0.2, , 3350, 3350Mflops , 1.32, , 2030, 2045Mflops LAPACK lmkl lapack64 liblapack lmkl lapack64 BLAS 3.1 LAPACK,BLAS liblapack SuSE Linux LAPACK lmkl lapack64 lmkl lib Math Kernal LIbrary 5

8 lapack64 LAPACK libblas SuSE Linux BLAS lmkl p4 Intel Math Kernal Library p4 Pentium4 (BLAS,FFT) libgoto Intel Pentium4 northwood BLAS Prescott CPU Intel Pentium4 prescott 3.4GHz 1 C LAPACK,BLAS. 3.2: N N. LAPACK BLAS N =1000 N =2000 time Mflops time Mflops liblapack libblas lmkl lapack64 lmkl em64t lmkl lapack64 libgoto LAPACK liblapack,blas libblas Mflops Mflops VASP 6

9 LAPACK lmkl lapack64,blas lmkl em64t Mflops Mflops LAPACK lmkl lapack64, BLAS libgoto Mflops Mflops CPU Prescott Intel Math Kernal Library BLAS libgoto Intel Math Kernal Library LAPACK 3.2 LAPACK,BLAS liblapack CLAPACK LAPACK CLAPACK Fortran LAPACK C lmkl lapack64 libblas Intel Math Kernal Library EM64T LAPACK CLAPACK BLAS lmkl em64t libgoto Intel Math Kernal Library EM64T libgoto Intel Pentium4 prescott BLAS 7

10 3.2 CPU Intel Pentium4 northwood 3.2GHz C (B ) LAPACK,BLAS. LAPACK,BLAS LAPACK [1] n n LAPACK 1.33 N 3 3.3: N N. LAP ACK BLAS N=1000 N=2000 time Mflops time Mflops liblapack libblas liblapack lmkl p lmkl lapack64 lmkl p LAPACK liblapack, BLAS libblas Mflops Mflops BLAS lmkl p Mflops Mflops LAPACK lmkl lapack64, BLAS lmkl p Mflops Mflops 3.3 CPU libgoto BLAS Northwood Intel Math Kernal Library BLAS Prescott libgoto CPU 8

11 4 CPU VASP Northwood CPU Intel Pentium4 northwood 3.2GHz VASP (C ) VASP VASP bench.hg Intel 4.1 VASP 4.1: VASP. BLAS LAP ACK time lmkl p4 lapack double lmkl lapack liblapack libgoto lapack double libblas liblapack

12 4.1.2 Prescott CPU Intel Pentium4 prescott 3.4GHz VASP VASP VASP bench.hg Intel 4.2 VASP 4.2: VASP. BLAS LAP ACK time lmkl em64t lapack double lmkl lapack libgoto lapack double (, ) VASP 4.2 Intel O0,O1,O2,O3. O0 O1 / O2 IA-32 Linux O1 O2 O3 O1 Pentium4 IA-32 O3. x{k W N B P} x Intel 1 10

13 K Pentium III Katmai, W Pentium 4 Willamete, N Northwood, B Pentium M Banias, P Prescott -xp Intel SSE3 SSE2 -xn -xw northwood SSE3 -xp This program was not built to run on the processor in your system. ax{k W N B P} Northwood CPU Intel Pentium4 northwood 3.2GHz VASP VASP VASP bench.hg 4.3: VASP. OPTION BLAS LAP ACK time -O0 lmkl p4 lapack double O O3 -xw -tpp O3 -axn -xn-tpp7 -ip -mp O0 lmkl p4 lmkl lapack O O3 -xw -tpp O3 -axn -xn-tpp7 -ip -mp O0 libgoto lapack double O O3 -xw -tpp O3 -axn -xn-tpp7 -ip -mp

14 4.2.2 Prescott CPU Intel Pentium4 prescott 3.4GHz VASP VASP VASP bench.hg 4.4: VASP. OPTION BLAS LAP ACK time -O0 libgoto lapack double O O3 -xw -tpp O3 -axp -xp-tpp7 -ip -mp O0 lmkl em64t llapack double O O3 -xw -tpp O3 -axp -xp-tpp7 -ip -mp O0 lmkl em64t lmkl lapack O O3 -xw -tpp O3 -axp -xp-tpp7 -ip -mp , 4.4 -O0 -O O0,-O1 VASP 12

15 5 VASP CPU Intel Pentium4 prescott 3.4GHz 2 VASP CPU CPU CPU MPI(Message Passing Interface) MPI C Fortran MPI MPICH MPICH(C ) VASP MPI MPICH mpirun 5.2 CPU 1 BLAS lmkl em64t,lapack lmkl lapack64 VASP CPU CPU 2 VASP 58% CPU 1 BLAS lmkl em64t,lapack lapack double VASP CPU CPU 2 VASP 58% CPU 1 BLAS libgoto,lapack lapack double VASP CPU CPU 2 VASP 47% CPU 2 VASP 13

16 5.1: CPU VASP. NODE BLAS LAP ACK time 1 lmkl em64t lmkl lapack lmkl em64t lmkl lapack lmkl em64t lapack double lmkl em64t lapack double libgoto lapack double libgoto lapack double VASP CPU Intel Pentium4 northwood 3.2GHz VASP 1 CPU VASP 2 VASP CPU 1/CPU VASP MPICH 5.1 CPU 2 CPU BLAS lmkl libgoto LAPACK -lmkl lapack64 lapack double -O0 -O3 -mp1 -tpp7 5.1 CPU CPU 2 4 1/CPU CPU 8 CPU 4 14

17 5.2: CPU VASP. BLAS LAP ACK OPTION NODE time lmkl lmkl lapack64 -O0 -mp lmkl lmkl lapack64 -O1 -mp lmkl lmkl lapack64 -O3 -mp1 -tpp libgoto lapack double -O3 -mp1 -tpp

18 5.1: VASP CPU 16

19 6 1. BLAS,LAPACK CPU 2. CPU VASP CPU northwood LAPACK lmkl lapack64, BLAS lmkl p4 LAPACK liblapack, BLAS libblas 51% CPU prescott LAPACK lapack double, BLAS libgoto LAPACK lapack double, BLAS lmkl em64t 40% -O0 -O1 60% 2 3. VASP CPU northwood LAPACK lmkl lapack64, BLAS lmkl CPU2 36% CPU3 95% CPU4 249% 17

20 A #include <stdio.h> #include <stdlib.h> #include <math.h> #include <time.h> //#include <veclib/veclib.h> #include "/usr/local/include/f2c.h" #include "/usr/local/include/clapack.h" void printmatrix(double *a, double *b, int n); int main(void){ long n, nrhs=1, lda, ldb, info; // double A[LDA*LDA], B[LDA*NRHS]; clock_t start, end; int i,j; double *a, *b; long *ipiv; scanf("%ld",&n); printf("%dn",n); lda=ldb=n; a=(double *)malloc(n*n*sizeof(double)); b=(double *)malloc(n*sizeof(double)); ipiv=(long *)malloc(n*sizeof(long)); for(i=0;i<n;i++){ for(j=0;j<n;j++){ a[i*n+j]=2*(double)random() / RAND_MAX -1.0; } } 18

21 for(i=0;i<n;i++){ b[i]=2*(double)random() / RAND_MAX -1.0; } // printmatrix(a,b,n); start=clock(); dgesv_(&n,&nrhs, a, &lda, ipiv, b, &ldb, &info); // MatrixInverse(a,b,n); // printmatrix(a,b,n); end=clock(); printf("%10.4fn",(double)(end-start)/clocks_per_sec); free(a); free(b); } return 0; void printmatrix(double *a, double *b, int n){ int i,j; for(i=0;i<n;i++){ for(j=0;j<n;j++){ printf("%10.5f",a[i*n+j]); } printf("%10.5f",b[i]); printf("n"); } printf("n"); return; } 19

22 B #include <stdio.h> #include <stdlib.h> #include <math.h> #include <time.h> //#include <veclib/veclib.h> #include "/usr/local/include/f2c.h" #include "/usr/local/include/clapack.h" void printmatrix(double *a, double *b, int n); int main(void){ long n, lda, lwork, info; // double A[LDA*LDA], B[LDA*NRHS]; char jobs= V, uplo= U ; clock_t start, end; int i,j; double *a, *w, *work; long *ipiv; scanf("%ld",&n); printf("%dn",n); lda=n; lwork=n*3; a=(double *)malloc(n*n*sizeof(double)); w=(double *)malloc(n*sizeof(double)); work=(double *)malloc(n*sizeof(double)); for(i=0;i<n;i++){ for(j=0;j<n;j++){ a[i*n+j]=2*(double)random() / RAND_MAX -1.0; } } 20

23 // printmatrix(a,w,n); start=clock(); //dgesv_(&n,&nrhs, a, &lda, ipiv, b, &ldb, &info); dsyev_( &jobs, &uplo, &n, a, &lda, w, work, &lwork, &info); // MatrixInverse(a,b,n); // printmatrix(a,b,n); end=clock(); printf("%10.4fn",(double)(end-start)/clocks_per_sec); free(a); free(w); return 0; } void printmatrix(double *a, double *b, int n){ int i,j; for(i=0;i<n;i++){ for(j=0;j<n;j++){ printf("%10.5f",a[i*n+j]); } printf("%10.5f",b[i]); printf("n"); } printf("n"); return; } 21

24 C VASP 1. Intel Fortran Compiler Version 9 (*.lic) /opt/intel/liceses/ mv /Desktop/commercial for l *.lic /opt/intel/licenses/ $ cd /media/l fc p 9 0 Intel Fortran Compiler Version 9 $./install.sh Please type a selection: 1 Please type a selection: 2 /opt/intel/liceses/commercial for l *.lic accept x.exit 2. Intel C++ Compiler Version 9 Fortran /opt/intel/liceses/ $ cd /media/l cc p 9 0 $./install.sh 22

25 Fortarn Linux Application Debugger Fortran. 3. Fortran, C++.cshrc $ emacs./cshrc set path= /opt/intel/fc/9.0/bin /opt/intel/cc/9.0/bin setenv LD LIBRARY PATH /opt/intel/mkl72/lib32: /opt/intel/fc/9.0/lib 4. YaST2 gcc glibc fftw3 (fftw fftw3 fftw3-debuginfo fftw3-devel fftw3-threads) lapack,blas 5. vasp.4.6.tar vasp.4.lib.tar $ tar -xvf vasp.4.6.tar $ tar -xvf vasp.4.lib.tar vasp.4.6/ vasp.4.lib/. 6. vasp.lib $ cd vasp.lib/ $ cp makefile.linux ifc P4 makefile vasp.lib/ Linux Intel fortran compiler(ifc),p4 makefile makefile 23

26 $ emacs makefile FC=ifc FC=ifort Intel fortran compiler ifc ifort $ make 7. vasp.4.6 $ cd vasp.4.6 $ cp makefile.linux ifc P4 makefile $ emacs makefile 7.1. FC=ifc FC=ifort 7.2. BLAS makefile BLAS /opt/libs/lbgoto p4 512-r0.6.so northwood BLAS=-L/opt/intel/mkl72/lib/32 -lmkl p4 -lsvml prescott BLAS=-L/opt/intel/mkl72/lib/em64t -lmkl em64t -lpthread -lsvml libgoto BLAS $ cd /opt/libs/ $ mkdir libgoto libgoto libgoto BLAS makefile CPU Intel northwood(presccot) BLAS=-L/opt/libs/libgoto/libgoto northwood(prescott)32p-r1.00.so -lpthread -lsvml 24

27 LINK = -lirc -lguide -lsvml -lcprts -lunwind -lcxa -lifport Wl,-rpath=/opt/libs/libgoto 7.3. LAPACK LAPACK=../vasp4.lib/lapack double.o Intel Math Kernel Library LAPACK northwood LAPACK=-L/opt/intel/mkl72/lib/32 -Imkl lapack64 presccot LAPACK= -L/opt/intel/mkl72/lib/em64t -lmkl lapack64 -lguide 7.4. FFT3D northwood FFT3D = fftw3d.o fft3dlib.o /usr/lib/libfftw3.a presccot FFT3D= fft3dfurth.o fft3dlib.o /usr/lib64/libffw3.a 7.5. MPI D MPICH FC=ifort -I/usr/lib/mpich / FCL=/usr/lib/mpich /bin/mpif $ make cannot open shared object file PATH 25

28 vasp.4.6./vasp 8. VASP Hg.tar $ tar -xvf Hg.tar $ cd Hg $ directory where VASP resides/vasp 26

29 D MPICH 1. /etc/hosts IP bob bob2 /etc/hosts.equiv./hosts bob1 bob2 1. MPICH mpich tar.gz $ tar -xvf mpich tar.gz $ cd mpich $./configure prefix=/usr/lib/mpich prefix= $./configure with-arch=linux with-device=ch p4 -fc=ifort -f90=ifort -prefix=/usr/local/bin mpich

30 $ make $ make install 2. $ cd /usr/lib/mpich /examples $ make cpi $./mpirun -np 1 cpi Process 0 on takeda1 pi is approximately , Error is wall clock time = $ cd /usr/local/mpich /share/ machines.linux takeda1 takeda2 # takeda1 takeda PATH /usr/local/mpich /bin bsh $ export PATH=$PATH:/usr/local/mpich /bin 28

31 csh.cshrc set path=/usr/local/mpich /bin 3.3. $./mpirun -np 2 cpi Process 0 on takeda1 Process 1 on takeda2 pi is approximately , Error is wall clock time = VASP $ directory where VASP resides/vasp $./mpirun -np 2 $./mpirun -np 2 directory where VASP resides/vasp 29

32 30

33 [1] E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorense, LAPACK ( 1995) [2] P. MPI ( 2001) [3] VASP 31

AutoTuned-RB

ABCLib Working Notes No.10 AutoTuned-RB Version 1.00 AutoTuned-RB AutoTuned-RB RB_DGEMM RB_DGEMM ( TransA, TransB, M, N, K, a, A, lda, B, ldb, b, C, ldc ) L3BLAS DGEMM (C a Trans(A) Trans(B) b C) (1) TransA: