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1
2 ( ) ( ) HPC SPH FPGA Web
3 : 1 4 : 2 6 : 3 6 GPU : ~ : ~ Google : ~ : ~
4 GPU, Cell, FPGA GRAPE-DR/GRAPE-MP ( )
5 GPU
6 GPU : Matsumoto, NN, Sakai, Sedukhin (2010)
7 s0 : swap_128 port map ( f => dx(11), x => x, y => y, xs => xx, ys => yy); with dx(11) select diff <= dy when '1', dx when others; e0 : extract_128_116_11 port map ( x => xx, s => sx, m => mx0, e => ex); e1 : extract_128_116_11 port map ( x => yy, s => sy, m => my0, e => ey); with ex select mx <= (others => '0') when " ", mx0 when others; with ey select my <= (others => '0') when " ", my0 when others; qx <= mx; ff <= diff(10) or diff(9) or diff(8) or diff(7); with ff select shft <= " " when '1', diff(6 downto 0) when others; rs : int_rshift_v port map ( c => shft, i => my, o => qy0, s => rf1); qy(0) <= qy0(0) or rf1; -- force1 rounding qy(116 downto 1) <= qy0(116 downto 1);,,
8 GRAPE-MP/Network board GRAPE-MP 四倍精度演算用計算機 メッシュ型クラスター 高エネルギー加速器研究機構, 東京工業大学 一橋大との共同研究
9 SIMD (LLVM )
10
11 LSUMP VARI xx, yy, cnt4; VARJ x30_1, gw30; VARF res; CONST tt, ramda, fme, fmf, s, one; ~ 10 zz = x30_1*cnt4; d = -xx*yy*s-tt*zz*(one-xx-yy-zz)+(xx+yy)*ramda**2 + (one-xx-yy-zz)*(one-xx-yy)*fme**2+zz*(one-xx-yy) *fmf**2; res += gw30/d**2;
12 LLVM LLVM define %xx, double %yy, double %cnt4, double %x30_1, double %gw30) { %multmp = mul double %x30_1, %cnt4 ; <double> [#uses=3] %negtmp = sub double e+00, %xx %multmp1 = mul double %negtmp, %yy %gtmp = load %multmp2 = mul double %multmp1, %gtmp %gtmp3 = load %multmp4 = mul double %gtmp3, %multmp %gtmp5 = load %subtmp = sub double %gtmp5, %xx %subtmp6 = sub double %subtmp, %yy ; <double> [#uses=3] %subtmp7 = sub double %subtmp6, %multmp ; <double> [#uses=2] %multmp8 = mul double %multmp4, %subtmp7 %subtmp9 = sub double %multmp2, %multmp8 %addtmp = add double %xx, %yy %gtmp10 = load ; <double> [#uses=2] %exptmp = mul double %gtmp10, %gtmp10 %multmp11 = mul double %addtmp, %exptmp %addtmp12 = add double %subtmp9, %multmp11 %multmp20 = mul double %subtmp7, %subtmp6 %gtmp21 = load ; <double> [#uses=2] %exptmp22 = mul double %gtmp21, %gtmp21 %multmp23 = mul double %multmp20, %exptmp22 %addtmp24 = add double %addtmp12, %multmp23 %multmp28 = mul double %multmp, %subtmp6 %gtmp29 = load ; <double> [#uses=2] %exptmp30 = mul double %gtmp29, %gtmp29 %multmp31 = mul double %multmp28, %exptmp30 %addtmp32 = add double %addtmp24, %multmp31 ; <double> [#uses=2] %exptmp33 = mul double %addtmp32, %addtmp32 %divtmp = fdiv double %gw30, %exptmp33 %accumtmp = tail call %divtmp) store double %accumtmp, ret double e+00 } ~ 50
13 LLVM GPU sample_resource(0)_sampler(0) r100, v0.xy sample_resource(1)_sampler(1) r101, v0.xy sample_resource(2)_sampler(2) r102, v0.xy ;load constants mov r500, cb0[0] mov r501, cb0[1] mov r502, cb0[2] mov r503, cb0[3] mov r504, cb0[4] mov r505, cb0[5] ~ 600 ; zero accum mov r300, l10.xxxx mov r200.xy, l11.xy mov r201.w, cb10[0].w mov r201.z, cb10[0].z ixor r201.x, r201.x, r201.x itof r203.x, r201.z whileloop sample_resource(3)_sampler(3) r120, r200.xy sample_resource(4)_sampler(4) r121, r200.xy mov r30, r120 mov r31, r102 call 2 mov r310, r32 mov r320, r100_neg(yw) mov r30, r320 mov r31, r101 call 2 mov r311, r32 mov r30, r311 mov r31, r504 call 2 mov r313, r32 mov r30, r500 mov r31, r310 call 2 mov r318, r32 mov r30, r505 mov r31, r100 call 1
14 242-B 242-E
15 1 (90 ) (3 4 ) 2008 Structure and Interpretation of Computer Program 2009,2010,2011 Algorithm Design Manual (4 ) 4
アクセラレータのデモと プログラミング手法
アクセラレータのデモと プログラミング手法 会津大学中里直人 アクセラレータボードを使った高速化スクール 2009/12/07 アクセラレータとは (1) ホスト計算機を補佐して特定の計算を高速化する計算機デバイス ホスト (CPU) で動作するプログラムを補佐 アクセラレータの例 Cell/PowerXCell8iブレード ボード : 計算 GPU ボード (NVIDIA, AMD, S3) :
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
スライド 1
ATI Stream SDK による 天文 物理計算の高速化 会津大学中里直人 計算事例 : 重力 N 体計算 No.2 プログラム :N 体の重力計算 (1) No.3 既存のアルゴリズムやアプリケーションを CAL で実装するには 前提として 並列計算可能な問題でなくては 利用する意味がない GPU のアーキテクチャにあわせて アルゴリズムを変更する必要あり GPU のメモリに合わせた 効率のよいデータ構造を考える必要あり
QD library! Feature! Easy to use high precision! Easy to understand the structure of arithmetic! 2 type high precision arithmetic! Double-Double precision (pseudo quadruple precision)! Quad-Double precision
Agenda Motivation How it works Performance Limitation Conclusion
py2llvm: Python to LLVM translator Syoyo Fujita Agenda Motivation How it works Performance Limitation Conclusion Agenda Motivation How it works Performance Limitation Conclusion py2llvm Python LLVM Python,
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スライド 1
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II 231017 1 1.1. R n k +1 v 0,, v k k v 1 v 0,, v k v 0 1.2. v 0,, v k R n 1 a 0,, a k a 0 v 0 + a k v k v 0 v k k k v 0,, v k σ kσ dimσ = k 1.3. k σ {v 0,...,v k } {v i0,...,v il } l σ τ < τ τ σ 1.4.
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変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +
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1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2
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