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1

2

3

4 CP-PACS CP-PACS

5 CP-PACS : 2048PU+128IOU 614GFLOPS peak 128GByte memory 1058GByte disk SR2201 :

6 CP-PACS Top 500 List ranking No. 1 November 1996 Linpack 368.2Gflops No. 24 Novermber 1999 (still No. 4 within Japan)

7 CP-PACS

8

9 CP-PACS QCD 32^3 x PU 40^3 x PU 48^3 x PU 64^ PU

10 April 96 CP-PACS (1024PU) starts operation October 96 CP-PACS (2048PU) starts operation 31 days (100% busy) Average CPU usage over 3 years = 82%

11 u d e ν e s t c b µ ν τ µ ν τ W, Z g γ Weinberg Salam QCD

12 Quantum Chromodynamics Gross-Wilczek, Politzer (1973)

13 K. G. Wilson 1974 φ n Z ( φ ) S = n d φn e n O 1 Z S ( φ ) ( φ ) = dφ ( ) n n O φ e n

14

15 October October 1997 September present QCD CP-PACS Performance (ratio to peak): 50% for quenched run 64^3 x PU 34% for full QCD 24^3 x PU

16 QCD 1981

17 QCD Meson hyperfine splitting Strange quark mass Eta meson mass B meson decay constant

18

19

20 1 I ν + n Iν = ν ( ν ν ) χ S c t I 3D ( space) + 2D( directions) + 1D( frequency) N 3 = # flop = f N N θ = N φ = 128 N ν = 6 3 iter N Nθ Nφ = 1.14Tflops hour( f 200, N iter 100) Sequential high Wave Front Method parallelization efficiency ( 98 % for N, = 128 on 2048PU ) θ φ

21 Big Bang 10 5 Z 15 5

22 CP-PACS

23 2 h n H = i 2m i= 1 Z = Tr + V DFT Marx-Parrinello (1994) ({} r ) i βh βh / P P 1 P β V { } ( ) ( ) eff r e = Tr e = dr dr e i s ( ) N = 64 hydrogen / supercell P = MD steps 10 CG steps 1MD step / for 1MD step ( 1Tflops min) ( t = fs)

24

25 QCD

26 QCD : RG -gauge + clover quark for 2 dynamical flavors HMC algorithm BiCGStab solver FLOP V FLOP = inv sec/ τ ( A + B N ) TFLOPS trajectory CP-PACS experience A = 45600, B=8800 Ninv= /mq Dt = (0.223mq mq^2)x 24/L ( mq in GeV )

27 QCD : 3 fm 2.5fm 15 MeV (pi/rho=0.4) 44 MeV (0.6) GeV 2 GeV 48^3 x 96 32^3 x 64 x 10 CPU 409 days 343 days 25% 20% : 32Gflops/PU, 16^3 = 4096PU 131 Tflops total

28 TCA /

29 FFT N 2 log N pseudo potential calculation N 2 Gram Schmidt diagonalization N 3 N=5000 CPU 1000 sec/1 MD step 1 ps/100days 16Gflops*5000PU=80Tflops 32GB/PU 4-8GB/sec network throughput (

30 field problem algorithm effective speed (TFLOPS) 1 particle physics size CPU hours main memory lattice QCD HMC method ^3x days 176GB 2 nuclear physics nuclear properties from realistic nuclear potential 3 astrophysics radiation hydrodynamics quantum MC method 100 Carbon with A=12 14 days 150GB SWT method ^5x6 9.2 hours 114GB 4 material science determination of material properties 5 biophysics electronic calculation of biochemical reactions density functional method ab initio MD path integral atoms atoms 6 biophysics protein folding MD amino acids 127 days 115GB 100 days 32GB/PU 1300 days 50GB O(100Tflops) needed

31 SIA roadmap on semiconductor technology Year rule (um) clock(mhz) tr. in MPU 21M 40M 76M 200M 520M 1.4B power(w) GHz clock / 4 pipelines of add&mult = 16Gflops around CPU s = 131 Tflops

32 Earth Simulator Project (2002) 8Gflops vector CPU x 8 = 64 Gflops / node 64 Gflops x 640 nodes = 40Tflops ASCI Project 10 Tflops (2000) by IBM 30 Tflops (2002) 100 Tflops (2004)

33 9 13 CPU SCIMA CPU

34 SCIMA concept FPU s will be running much faster than data can be fed from off-chip memory use SRAM memory on-chip to secure the bandwidth (data repeatedly used are kept on-chip in a controlled way)

35 20 21

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untitled taisuke@cs.tsukuba.ac.jp http://www.hpcs.is.tsukuba.ac.jp/~taisuke/ CP-PACS HPC PC post CP-PACS CP-PACS II 1990 HPC RWCP, HPC かつての世界最高速計算機も 1996年11月のTOP500 第一位 ピーク性能 614 GFLOPS Linpack性能 368 GFLOPS (地球シミュレータの前

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