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1 GRAPE-DR /
2 GRAPE GRAPE-DR
3 GRAPE ( ): (Barnes-Hut tree, FMM, Particle- Mesh Ewald(PPPM)...): ( )
4 1988
5 32 IC m 3 400
6 GRAPE-1(1989) Mflops
7 GRAPE-2(1990) 8 ( ) 40Mflops
8 GRAPE-3(1991) MHz 7.2Gflops
9 GRAPE-3 1µm MHz 600 Mflops
10 GRAPE-4(1995) Tflops
11 GRAPE-4 sqrt Pcut Fcut m/r FiFiPi m j r 2 Func. eval. m/r 3 Xi FiFiFi Xj Vi r. v m/r 5 Vj Xi Xi FiFiJi Xi Xi 1µm 10 (40 ) 640Mflops
12 GRAPE-4 Control Logic HARP LSI #0 Particle Data Memory PROMETHEUS LSI HARP LSI #15 HARP LSI #16 LSI HARP LSI #31 HARP LSI #32 HARP LSI #47
13 GRAPE-6(2002) Tflops
14 パイプライン LSI 0.25 µm ルール (東芝 TC-240, 1.8M ゲート) 90 MHz 動作 6 パイプラインを集積 チップあたり 31 Gflops
15 2006 GRAPE-6 Athlon FX nm 90nm 90MHz 2.8Gflops 32.4Gflops 11.2Gflops 10W 95W 1W 3.24Gflops 0.12 Gflops
16 GRAPE 1991 GRAPE-1A : GRAPE-1 : 1992 GRAPE-2A : MD GRAPE : 1992 HARP-1: Hermite 1993 GRAPE-3A: 1996 MD-GRAPE: MD GRAPE : 2001 MDM (MDG2): 75T 2006 PE (MDG3): 1P MD-Engine: ( NEC)
17 GRAPE 1991 DREAM: ZEBRA : Radiocity 1995 General: LU 2002? MACE: LU
18 GRAPE-4
19 GRAPE-3 GRAPE GRAPE-6 American Museum of Natural History Drexel University Indiana University Rochester Institute of Technology Rutgers University Rochester Institute of Technology University of Michigan University of California McMaster University The University of Cambridge University of Edinburgh Observatoire Astronomique Marseille-Provence(OAMP) Astronomisches Rechen-Institute (ARI) Ludwing-Maximillans University Max-Planck-Institute fur Astronomic
20 GRAPE-6 ( ) University of Bonn University of Mannheim Holland University of Amsterdam Nanjing Univesity Citec Co., Ltd Gunma Astronomical Observatory Hokkai-Gakuen University Kansai University Kyoto University National Institute for Fusion Science (NIFS) National Astronomical Observatory of Japan Osaka University The University of Tokyo Tokyo Institute of Technology University of Tsukuba 30 60Tflops MDGRAPE-2
21 GRAPE-6 MDGRAPE-3 : MDGRAPE-4, 20Pflops@2010 MDGRAPE-3 GRAPE-DR
22 GRAPE-DR GRAPE : 2 Petaflops Tflops GRAPE : GRAPE
23 GRAPE 12-bit fixed m j 64 bit fixed X i 36-bit float r 2 sqrt Func. eval. Pcut Fcut m/r m/r 3 64 bit fixed φ i FiFi ai Xj 36-bit float V i r. v 32-bit float m/r 5 Vj Xi Xi 32 bit fixed Fi. a i Xi Xi
24 GRAPE ( ( N )) µm µm nm nm 10
25 1.
26 1. 2.
27
28 GRAPE-DR (3)
29 1
30 : ( ) 1. GRAPE SIMD
31 GRAPE 12-bit fixed m j 64 bit fixed X i 36-bit float r 2 sqrt Func. eval. Pcut Fcut m/r m/r 3 64 bit fixed FiFi φ i ai Xj 36-bit float V i r. v 32-bit float m/r 5 Vj Xi Xi 32 bit fixed. a i Fi Xi Xi
32 FPGA IPFlex DAP/DNA 8-32 ALU
33 SIMD SIMD (Single Instruction Multiple Data): GRAPE
34 SIMD SIMD SSE MMX SIMD GRAPE-DR SIMD
35 SIMD Illiac IV, Goodyear MPP, ICL DAP, TMC CM-2, MASPAR MP-1 ALU REG MEM ALU REG MEM ALU REG MEM ALU REG MEM ALU REG MEM : : SIMD
36 SIMD Pentium III, IV R0 R1 R2 R3 R4 R5 R6 R7 W0 W1 W0 W1 W0 W1 W0 W1 W0 W1 W0 W1 W0 W1 W0 W1 W2 W3 W2 W3 W2 W3 W2 W3 W2 W3 W2 W3 W2 W3 W2 W3 ALU0 ALU1 ALU2 ALU3 1 : 4
37 nyo d4prqts B8C*DFEHGFI 7KJ GRAPE-DR SIMD!"$# %'& (*)+,-. /0!"$#%ˆ $Š 'ŒŽ (* & ) \Y]_^[`baTced 1$243$5687*9 (FPGA :';$< ) RTSVUTWYX[Z yz{z z} ~ $ƒ Q 0 w4xzyz{ L$M4N'OQP SING u Xtv (PE) 1 PE = + ( ) (PE ) PE (BB)
38 !"#%$ &(' )*+,-. /0 1!" #%$ &2 34 '5%6 7(8!"#%$ &(' )* 9:;. /0 9:<+;=,> A,CBED%F GHIJ K $ B L,M N 9:?@ A,CBED%F PE OQP!R
39 *,+ (M) PE PEID BBID A x + "! B T 32W 256W ALU # $ % & (' #)$ & (' (256 ),K M
40 PE : 36 ( ) : 72 ( ) 36/72 ( ) ( / / ) : (GRAPE-6 ) ( )
41 PE ( ) T T ( ) SIMD CM-2, MasPar MP-1 PE
42 Memory Wall 3
43 PE 3 : Embarassingly Parallel SIMD : Goodyear MPP, ICL DAP, TMC CM-1/2, Maspar MP- 1/2 PE :
44 f i = j f(x i, x j ) PE :
45 c ij = k a ik b kj PE A PE B 1 PE B A
46 : : : :
47 GRAPE-DR ( ) 500MHz 25-50W
48 GRAPE-DR 別ボード こっちが プロジェ クト公式 中身は殆ど同じ 何故か大きい 500MHz 動作まで 確認済
49 ( 2006) /VARI xi, yi, zi, e2; /VARJ xj, yj, zj, mj; /VARF fx, fy, fz; dx = xi - xj; dy = yi - yj; dz = zi - zj; r2 = dx*dx + dy*dy + dz*dz + e2; r3i= powm32(r2); ff = mj*r3i; fx += ff*dx; fy += ff*dy; fz += ff*dz; GRAPE PGR (FPGA PROGRAPE D 2006)
50 GRAPE LSI LSI GRAPE-DR SIMD GRAPE Pflops
GRAPE GRAPE-DR V-GRAPE
GRAPE-DR / 2006/11/20-22 GRAPE GRAPE-DR V-GRAPE http://antwrp.gsfc.nasa.gov/apod/ap950917.html ( ) SDSS Genzel et al 2003 Adaptive Optics SgrA ( ) 12 1 : GRAPE : (Barnes-Hut tree, FMM, Particle- Mesh
GRAPE GRAPE-DR V-GRAPE
V-GRAPE / CCSR 2007/1/24 GRAPE GRAPE-DR V-GRAPE http://antwrp.gsfc.nasa.gov/apod/ap950917.html ( ) SDSS GRAPE : (Barnes-Hut tree, FMM, Particle- Mesh Ewald(PPPM)...): ( ) 1988 GRAPE-1(1989) 16 8 32
HPC / (CfCA) HPC 2007/11/23-25
HPC / (CfCA) HPC 2007/11/23-25 CfCA GRAPE GRAPE GRAPE-DR HPC : : 1 1 (II ) Ia 100 1 ( ) 0.1 pc 1 AU 3 : 1 100 Top-down Katz and Gunn 1992 Dark Matter + + DM, : :SPH 10 4 Cray YMP 500-1000 : 10 7 Saitoh
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Agenda GRAPE-MPの紹介と性能評価 GRAPE-MPの概要 OpenCLによる四倍精度演算 (preliminary) 4倍精度演算用SIM 加速ボード 6 processor elem with 128 bit logic Peak: 1.2Gflops
Agenda GRAPE-MPの紹介と性能評価 GRAPE-MPの概要 OpenCLによる四倍精度演算 (preliminary) 4倍精度演算用SIM 加速ボード 6 processor elem with 128 bit logic Peak: 1.2Gflops ボードの概要 Control processor (FPGA by Altera) GRAPE-MP chip[nextreme
A 99% MS-Free Presentation
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並列計算の数理とアルゴリズム サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
並列計算の数理とアルゴリズム サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/080711 このサンプルページの内容は, 初版 1 刷発行時のものです. Calcul scientifique parallèle by Frédéric Magoulès and François-Xavier
スパコンに通じる並列プログラミングの基礎
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スパコンに通じる並列プログラミングの基礎
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