Michael Clark Harvard University

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Gflops 140 120 100 80 Wednesday, 18 November 2009 12 reconstruct 8 reconstruct 0 32 64 96 128 Temporal Extent Wilson Matrix-Vector Performance Single Precision (V=24 3 xT)
ions SpMV IV CD software to use the DeGrand-Rossi basis ch appear in the Wilson-Dirac operator offre given by ⎞ ±i • Can impose similarity transforms to improve sparsity 0 ⎟ 0 ⎠ • Can globally change Dirac matrix basis 1 P ±2 We must always load all spinor components regardless of the dimension or direction. An alternative basis is the UKQCD basis, in which the projectors have the form ⎛ ⎞ 1 0 0 ∓1 ⎜ = ⎜ 0 1 ±1 0 ⎟ ⎝ P 0 ±1 1 0 ⎠ ∓1 0 0 1 ±1 ⎛ ⎞ 1 0 0 ±i ⎜ = ⎜ 0 1 ±i 0 ⎟ ⎝ 0 ∓i 1 0 ⎠ ∓i 0 0 1 P ±2 ⎛ ⎞ 1 0 0 ±1 ⎜ = ⎜ 0 1 ∓1 0 ⎟ ⎝ 0 ∓1 1 0 ⎠ ±1 0 0 1 0 i 0 1 ⎞ ⎟ ⎠ P ±4 = ⎛ ⎜ ⎝ P ±3 = 1 0 ±1 ⎞ 0 ±1 0 1 0 ±1 ⎟ 0 1 0 ⎠ 0 ±1 0 1 . P ±3 ⎛ 1 0 ⎜ = ⎜ 0 1 ⎝ ∓i 0 ±i 0 1 0 ∓i 0 0 ±i 0 1 components regardless of the dimension or s the UKQCD basis, in which the projectors • Impose local color transformation (gauge transformation) ⎞ ±i • SU(3) field = unit matrix in temporal direction 0 ⎟ 0 ⎠ • Must calculate this transformation (done once only) 1 • In total 33% reduction in bandwidth P ±2 ⎛ ⎞ 1 0 0 ±1 ⎜ = ⎜ 0 1 ∓1 0 ⎟ ⎝ 0 ∓1 1 0 ⎠ ±1 0 0 1 ⎛ 2 ⎜ +4 = ⎜ 0 ⎝ 0 0 2 0 ⎞ 0 0 0 0 ⎟ 0 0 ⎠ 0 0 0 0 P −4 ⎛ ⎞ 0 0 0 0 ⎜ = ⎜ 0 0 0 0 ⎟ ⎝ 0 0 2 0 ⎠ 0 0 0 2 . The advantage of this approach is that in the temporal dimension we need only load the upper (lower) spin components for the backwards (forwards) gather. This halves the amount of bandwidth required to perform the temporal gather, and so increases the kernel’s performance. References [1] G. I. Egri, Z. Fodor, C. Hoelbling, S. D. Katz, D. Nogradi and K. K. Szabo, “Lattice QCD as a video game,” Comput. Phys. Commun. 177 (2007) 631 [arXiv:hep-lat/0611022]. 18 is that in the temporal dimension we need Wednesday, 18 November 2009 ⎛ ⎜ ⎝ 1 0 ±i 0 0 1 0 ∓i ∓i 0 1 0 0 ±i 0 1 ⎞ ⎞ ⎟ ⎠ P +4 = ⎟ ⎠ P ±4 = ⎛ ⎜ ⎝ ⎛ ⎜ ⎝ 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 ±1 0 0 1 0 ±1 ±1 0 1 0 0 ±1 0 1 ⎞ ⎟ ⎠ P −4 = ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ . 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 ⎞ ⎟ ⎠ .
Page 1 and 2: Wednesday, 18 November 2009 GPU Mix
Page 3 and 4: Quantum ChromoDynamics • QCD is t
Page 5 and 6: Wednesday, 18 November 2009 topolog
Page 7 and 8: Wednesday, 18 November 2009
Page 9 and 10: Wednesday, 18 November 2009 Lattice
Page 11 and 12: GPU Hardware GTX 280 Flops: single
Page 13 and 14: Iterative Linear Solvers • Many p
Page 15 and 16: Wednesday, 18 November 2009 Dirac o
Page 17 and 18: Wednesday, 18 November 2009 Wilson
Page 23 and 24: !"#$%&' $" $! #" #! " ! Wednesday,
Page 25: Wednesday, 18 November 2009 SpMV II
Page 29 and 30: Gflops 140 120 100 Wednesday, 18 No
Page 31 and 32: Wednesday, 18 November 2009 Krylov
Page 33 and 34: Mixed-Precision Solvers • Require
Page 35 and 36: Number of iterations 3000 2500 2000
Page 37 and 38: Wednesday, 18 November 2009 Half Pr
Page 39 and 40: Time to solution / s 300 250 200 15
Page 41 and 42: Wednesday, 18 November 2009 Perform
Page 43 and 44: Wednesday, 18 November 2009 Perform
Page 45 and 46: Wednesday, 18 November 2009 • Nee
Page 47 and 48: Matrix-vector products 20000 15000
Page 49 and 50: Wednesday, 18 November 2009 Conclus

Michael Clark Harvard University

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