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5d0 ri1i2i3 025d0 ri1 1i2i3 ri11i2i3

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Unformatted text preview: to understand from the code –  terse variable names –  SPMD-style programming details http://www.nas.nasa.gov/Software/NPB/ The NAS MG Benchmark Mathematically: use a 3D multigrid method to find an approximate solution to a discrete Poisson problem (∇2u = v) MG’s arrays V: input array U: hierarchical work arrays R: Overview of MG run timed portion initialize V output norms & timings MG’s Timed Portion repeat nit times resid resid norm2u3 rnm2 rnmu Configurations mg3p S: W: A: B: C: D: 3 23 6 43 2563 2563 5123 10243 (4 iterations) (40 iterations) (4 iterations) (20 iterations) (20 iterations) (50 iterations) Hierarchical Arrays level 0 level 1 level 2 (1:8,1:8) (1:4,1:4) (1:2,1:2) level 3 conceptually: dense indexing: (1:1,1:1) Requires a distinct conceptual distribution per level strided indexing: (1:8:1,1:8:1) (1:8:2,1:8:2) (1:8:4,1:8:4) (1:8:8,1:8:8) Admits a single conceptual distribution across levels Hierarchical Arrays level 0 level 1 level 2 (1:8,1:8) (1:4,1:4) (1:2,1:2) level 3 conceptually: dense indexing: (1:1,1:1) strided indexing: (1:8:1,1:8:1) (2:8:2,2:8:2) (4:8:4,4:8:4) (8:8:8,8:8:8) MG’s Guts (mg3P) resid psinv rprj3 interp resid psinv rprj3 interp resid psinv rprj3 interp psinv 27-point stencils = w1 = w2 = w3 = = w4 = + + Our First Stencil: resid(R, V, U) R V = R , - convolve( =...
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