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Global Address Space Applications

Global Address Space Applications. Kathy Yelick NERSC/LBNL and U.C. Berkeley. Algorithm Space. Search. Two-sided dense linear algebra. Grobner Basis (“Symbolic LU”). FFTs. Sorting. Reuse. Sparse iterative solvers. Asynchronous discrete even simulation. Sparse direct solvers.

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Global Address Space Applications

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  1. Global Address Space Applications Kathy Yelick NERSC/LBNL and U.C. Berkeley

  2. Algorithm Space Search Two-sided dense linear algebra Grobner Basis (“Symbolic LU”) FFTs Sorting Reuse Sparse iterative solvers Asynchronous discrete even simulation Sparse direct solvers One-sided dense linear algebra Regularity

  3. Scaling Applications • Machine Parameters • Floating point performance • Application dependent, not theoretical peak • Amount of memory per processor • Use 1/10th for algorithm data • Communication Overhead • Time processor is busy sending a message • Cannot be overlapped • Communication Latency • Time across the network (can be overlapped) • Communication Bandwidth • Single node and bisection • Back-of-the envelope calculations !

  4. Running Sparse MVM on a Pflop • 1 GHz * 8 pipes * 8 ALUs/Pipe = 64 GFLOPS/node peak • 8 Address generators limit performance to 16 Gflops • 500ns latency, 1 cycle put/get overhead, 100 cycle MP overhead • Programmability differences too: packing vs. global address space

  5. Effect of Memory Size • Low overhead is important for • Small memory nodes or smaller problem sizes • Programmability

  6. Parallel Applications in Titanium • Genome Application • Heart simulation • AMR elliptic and hyperbolic solvers • Scalable Poisson for infinite domains • Genome application • Several smaller benchmarks: EM3D, MatMul, LU, FFT, Join

  7. MOOSE Application • Problem: Microarray construction • Used for genome experiments • Possible medical applications long-term • Microarray Optimal Oligo Selection Engine (MOOSE) • A parallel engine for selecting the best oligonucleotide sequences for genetic microarray testing • Uses dynamic load balancing within Titanium

  8. Heart Simulation • Problem: compute blood flow in the heart • Model as elastic structure in incompressible fluid. • “Immersed Boundary Method” [Peskin and McQueen] • Particle/Mesh method stress communication performance • 20 years of development in model • Many other applications: blood clotting, inner ear, insect flight, embryo growth,… • Can be used for design of prosthetics • Artificial heart valves • Cochlear implants

  9. -6.47x10-9 0 1.31x10-9 Scalable Poisson Solver • MLC for Finite-Differences by Balls and Colella • Poisson equation with infinite boundaries • arise in astrophysics, some biological systems, etc. • Method is scalable • Low communication • Performance on • SP2 (shown) and t3e • scaled speedups • nearly ideal (flat) • Currently 2D and non-adaptive • Point charge example shown • Rings & star charges • Relative error shown

  10. AMR Gas Dynamics • Developed by McCorquodale and Colella • 2D Example (3D supported) • Mach-10 shock on solid surface at oblique angle • Future: Self-gravitating gas dynamics package

  11. UPC Application Investigations • Pyramid • 3D Mesh generation [Shewchuk] • 2D version (triangle) critical in Quake project • Written in C, challenge to parallelize • SuperLU • Sparse direct solver [Li,Demmel] • Written in C+MPI or threads • UPC may enable new algorithmic techniques • N-Body simulation • “Simulating the Universe”

  12. Summary • UPC Killer App should • Leverage programmability: hard in MPI • Use fine-grained, irregular, asynchronous communication • Libraries • Must allow for interface to libraries • MPI libraries, multithreaded libraries, serial libraries • Compilation needs • High performance on at least one machine • Portability across many machines

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