CUBE：高可扩展宇宙学 N 体问题模拟程序.pdf

1、CUBE高可扩展宇宙学N体问题模拟程序Shenggan ChengHang HuDereck InmanHao-ran Yu James Lin8ESHANGHAI JIAO TONG厦門大学UNIVERSITY#page#IntroductionOverview of CUBEPorting and optimization of CUBE on GPUAdvanced Optiimization#page#Nbody Empower Many Scientific ResearchNeutrino Masss Particle physics determineslower bounds

2、0.05 eVAstrophysics cosmology determinesupperbound Grid Density (Cloud-in-Cell）Process 22. Solve the Poisson Equationon the mesh (FFT）Tile 4Tile 3Physical Region3.Calculate force field from the mesh-defined potentialBuffer Region4.Interpolate force on gridto find forces on particlesGlobal FFT: apply

3、 on coarse-mesh need MPIFFTProcess 3Process 4Local FFT:apply on fine-meshGlobal FFTSHANGHAI JIAO TONGUNIVERSIT#page#Overview of CUBE- PM-PM-PPx一xSolve for ForcesF(t)= FclobalPM + FLocalPM +FppFpp=Gmi（e+1x-x）312Local FETTile 1softeningProcess2OOTile 4Tile 3Physical RegionBuffer Region2Process 3Proces

4、s 40Global FFTSHANGHAI JIAO TONGUNIVERSIT#page#Data Struct in PP1D Format Storage for ParticlesOrdered by Coarse Mesh (Consider Memory Cost）x-xFpp=Gmi（e+1x-x1)3/2PPRangeFine MeshCoarse MeshMemory Disorder forFine MeshNullHead ofthe LinkListIndex ofnext pratiacleSHANGHAI JIAO TONGUNIVERSIT#page#Overv

5、iew of CUBE- Mixed PrecisionSimulating the Nbody problemrequires a lot of memory.For exampleifyou usefloat to store particleinformation, 1012 particles need more than 105TB of memory CUBE uses int16/int8 to store particle information， breaking the memory capacity bottleneck（3,5）1.00.8（8,3）0.602（3+21

6、）mod16,5）（8.5）0.0（a/（）(=Xa=2%x(a-a）-2nx-1，a=(nc-1)+2-8x(xa+2%x-1+1/2)，）202/mSHANGHAI JIAO TONGUNIVERSITY#page#Overview of CUBE- Mixed Precisionfloat-point format:A100:A64FX:。float16，bfloat16FP64/32/16FP64/32/16fix-point format:TF32INT64/32/16/8INT8/4/2integer16，integer8至星在程验理 dynamic fixed-pointMixe