GRAPE GRAPE-DR V-GRAPE

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1 GRAPE-DR / 2006/11/20-22

2 GRAPE GRAPE-DR V-GRAPE

7 ( ) SDSS

8 Genzel et al 2003 Adaptive Optics SgrA ( )

9 12 1

10 :

11 GRAPE : (Barnes-Hut tree, FMM, Particle- Mesh Ewald(PPPM)...): ( )

12 1988

13 GRAPE-1(1989) Mflops

14 GRAPE-2(1990) 8 ( ) 40Mflops

15 GRAPE-3(1991) MHz 7.2Gflops

16 GRAPE-3 1µm MHz 600 Mflops

17 GRAPE-4(1995) Tflops

18 GRAPE-4 Xi Xi sqrt Pcut Fcut Xi Xi m/r FiFiPi m j Xi Xi r 2 Xi Xi Func. eval. Xi Xi Xi Xi Xi Xi Xi Xi m/r 3 Xi Xi Xi FiFiFi Xj Xi Xi Vi Xi Xi r. v m/r 5 Xi Xi Vj Xi Xi Xi Xi FiFiJi Xi Xi Xi Xi 1µm 10 (40 ) 640Mflops

19 GRAPE-6(2002) Tflops

20 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

21 2006 GRAPE-6 Core 2 Extreme 250nm 65nm 90MHz 2.93GHz 32.4Gflops 23.44Gflops 10W 75W 1W 3.24Gflops Gflops

22 GRAPE-4

23 GRAPE-6 MDGRAPE-3 : MDGRAPE-4, 20Pflops@2010 MDGRAPE-3 GRAPE-DR

24 GRAPE-DR GRAPE : 2 Petaflops Tflops GRAPE : GRAPE

25 GRAPE ( ( N )) µm µm nm nm 10

26 1.

27 1. 2.

29 GRAPE-DR (3)

30 1

31 : ( ) 1. GRAPE SIMD

32 SIMD SIMD (Single Instruction Multiple Data): GRAPE

33 SIMD SIMD SSE MMX SIMD GRAPE-DR SIMD

34 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

35 SIMD Pentium III, 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

36 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)

37 *,+ (M) PE PEID BBID A x + "! B T 32W 256W ALU 256 # $ % & (' #)$ & (' (K M )

39 32PE( ) 16 18mm

40 GRAPE-DR 500MHz 100 Gflops ( )

41 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 LINPACK が動作したらしい

42 GRAPE

43 : g i = j f(x i, x j ) i j j i j, i j ( )

44 ( 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)

45 / int SING_send_j_particle(struct grape_j_particle_struct *jp, int index_in_em); int SING_send_i_particle(struct grape_i_particle_struct *ip, int n); int SING_get_result(struct grape_result_struct *rp); void SING_grape_init(); int SING_grape_run(int n);

46 2 ( )

47 V-GRAPE GRAPE-DR = V-GRAPE

48 GRAPE-DR 256Gflops MDGRAPE-3 FPGA FFT CG 2

49 FFT CG :

50 FFT FFT FFT : 10 log n 4GB/s 10 Gflops CPU

51 CG : O(10)

52 GRAPE-DR: 1MB Intel Itanium : 24MB? DRAM : 32 MB

53 V-GRAPE PE PE PE PE PE PE PE PE GRAPE-DR V-GRAPE PE

54 V-GRAPE / : ( ) :

55 : PIC

56 PIC Charge assignment Charge assignment: GRAPE- DR :

57 Charge 1 : 50 ( ) 1 : 12 ( ) : 1 4 GRAPE-DR : 2 GB/s 8 Gflops

58 GRAPE-DR GPGPU V-GRAPE

59 GPGPU nvidia 8800: C 768MB 90GB/s(SX-7 3 ) GPU C 400Gflops 1 (8 )

60 V-GRAPE 128MB GB/s 1.5Tflops (50 )

61 : = 3 10 GRAPE-DR 100Gflops

62 GRAPE LSI GRAPE-DR SIMD GRAPE V-GRAPE PIC GRAPE-DR GPGPU V-GRAPE

64 Memory Wall : : : :

65 1990 I/O

67 : 30

68 V-GRAPE BLAS, LAPACK PE PGDL ( FPGA ) SPH ( 150)

69 :

70 (M. Flynn) SISD/SIMD/MISD/MIMD (SI) (MI) (SD) (MD) SIMD SIMD ( ) MIMD

71 SIMD GRAPE ( ) : : ( ) : 1000 ( / )

72 (PE) (j- ) j- j- j- i- PE PE PE PE PE i- PE PE PE PE PE i- PE PE PE PE PE i- PE PE PE PE PE i- PE PE PE PE PE i- PE PE PE PE PE j- j- (GRAPE-6 ) 2 : 2

73 PE PE PE PE PE PE broadcast memory PE PE PE PE broadcast memory PE PE PE PE broadcast memory PE PE PE PE broadcast memory ( ) Memory controller/host

74 SING: Sing Is Not GRAPE DRAM DRAM DRAM DRAM FPGA CP SING FPGA CP SING FPGA CP SING FPGA CP SING FPGA Host interface PCI-X/PCIE PCI

75 GRAPE : SIMD GDR : (FPGA ) =

76 PE PE ( )

77 var vector long xi hlt flt64to72 var vector long yi hlt flt64to72 var vector long zi hlt flt64to72 var vector short idxi hlt fix32to36ru bvar long xj elt flt64to72 bvar long yj elt flt64to72 bvar long zj elt flt64to72 bvar long vxj xj bvar short mj elt flt64to36 bvar short eps2 elt flt64to36 bvar short idxj elt fix32to36ru var short lmj var short leps2 var short lidxj var vector long accx rrn flt72to64 fadd var vector long accy rrn flt72to64 fadd var vector long accz rrn flt72to64 fadd var vector long pot rrn flt72to64 fadd hlt, elt, rrn

78 loop initialization vlen 4 uxor $t $t $t upassa $ti $ti $lr40v upassa $t $t $lr48v upassa $t $t $lr56v upassa $t $t pot loop body vlen 3 bm vxj $lr0v vlen 1 bm mj lmj bm eps2 leps2 bm idxj lidxj ( ) ( ) ( )

79 vlen 4 nop upassa idxi idxi $t uxor $ti lidxj $t moi 2 ( ) ulnot $ti $ti $t # mreg 1 indicates i!= j moi 0 nop fsub $lr0 xi $r6v $t fsub $lr2 yi $r10v ; fmul $ti $ti $t fsub $lr4 zi $r14v fmul $r10v $r10v $r18v ; fadd $t leps2 $t fmul $r14v $r14v ; fadd $fb $ti $t fadd $fb $ti $r18v $t # rsq is now in r18 t, dx, dy,dz are in 2

80 ( ) ulsr $ti il"60" $t $lr22v ulsr $ti il"1" $t uadd $ti $lr22v $t usub hl"9fd" $ti $t # $lr8v 1.5 ulsl $ti il"60" $lr30v moi 1 uand il"1" $lr22v moi 0 uand $r18v h"000ffffff" $t uor $ti h"3ff000000" $t fmul $ti f"0.57" $t fsub f"1.57" $ti $t mi 1 fmul f"1.414" $ti $t mi 0 nop fmul $t $lr30v $t $r22v # Here the result is the initial guess r 3 1

81 ( ) fmul $r18v $r18v $r26v $t fmul $r18v $ti $r26v $t fmul $ti f"0.5" $r26v # r26v is a**3/2 fmul $r22v $r22v $t fmul $ti $r26v $t fsub f"1.5" $ti $t fmul $r22v $ti $t $r22v fmul $ti $ti $t fmul $ti $r26v $t ( ) fsub f"1.5" $ti $t fmul $r22v $ti $t $r22v fmul $ti $ti $t fmul $ti $r26v $t fsub f"0.5" $ti $t fmul $r22v $ti $t fadd $r22v $ti $t fmul lmj $ti $t $r22v

82 ( ) mi 2 fmul $r6v $ti ; upassa pot pot $lr0v fmul $r10v $t ; fadd $fb $lr40v $lr40v accx fmul $r14v $t ; fadd $fb $lr48v $lr48v accy fmul $r18v $t ; fadd $fb $lr56v $lr56v accz fadd $fb $lr0v pot

83 int SING_send_j_particle(struct grape_j_particle_struct *jp, int index_in_em); int SING_send_i_particle(struct grape_i_particle_struct *ip, int n); int SING_get_result(struct grape_result_struct *rp); void SING_grape_init(); int SING_grape_run(int n); GRAPE-3/5

84 struct grape_j_particle_struct{ double xj; double yj; double zj; double mj; double eps2; UINT32 idxj; }; struct grape_i_particle_struct{ double xi; double yi; double zi; UINT32 idxi; }; struct grape_result_struct{ double accx; double accy; double accz; double pot; };

85 17mm

87 PE

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