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  1. Scientific Application Performance on Candidate PetaScale Applications Leonid OlikerAndrew Canning, Jonathan Carter, Costin Iancu, Michael Lijewski,Shoaib Kamil, John Shalf, Hongzhang Shan, Erich Strohmaier Lawrence Berkeley National LaboratoryStephane EthierPrinceton Plasma Physics Laboratory Tom GoodaleCardiff University and Louisiana State University Winner Best Paper Application Track, IPDPS 07, Long Beach, CA, March 26-30, 2007

  2. Overview • Stagnating application performance is well-know problem in scientific computing • By end of decade numerous mission critical applications expected to have 100X computational demands of current levels • Many HEC platforms are poorly balanced for demands of leading applications • Memory-CPU gap, deep memory hierarchies, poor network-processor integration, low-degree network topology • Traditional superscalar trends slowing down • Mined most benefits of ILP and pipelining,Clock frequency limited by power concerns

  3. Declining Single Processor Performance • Moore’s Law • Silicon lithography will improve by 2x every 18 months • Double the number of transistors per chip every 18mo. • CMOS Power Total Power = V2 * f * C + V * Ileakage active power passive power • As we reduce feature size Capacitance ( C ) decreases proportionally to transistor size • Enables increase of clock frequency ( f) proportionally to Moore’s law lithography improvements, with same power use • This is called “Fixed Voltage Clock Frequency Scaling” (Borkar `99) • Since ~90nm • V2 * f * C ~= V * Ileakage • Can no longer take advantage of frequency scaling because passive power (V * Ileakage ) dominates • Result is recent clock-frequency stall reflected in Patterson Graph at right • Multicore is here SPEC_Int benchmark performance since 1978 from Patterson & Hennessy Vol 4.

  4. Application Evaluation • Microbenchmarks, algorithmic kernels, performance modeling and prediction, are important components of understanding and improving architectural efficiency • However full-scale application performance is the final arbiter of system utility and necessary as baseline to support all complementary approaches • Our evaluation work emphasizes full applications, with real input data, at the appropriate scale • Requires coordination of computer scientists and application experts from highly diverse backgrounds • Our initial efforts have focused on comparing performance between high-end vector and scalar platforms • Currently evaluating ultra-scale systems (soon to be petascale) • NERSC 100TF/s in FY07, 500 TF/s in FY10 (XT4) • ORNL 250TF/s in FY07, 1000TF/s in FY08/09 (XT4) • ANL 100TF/s in FY07, 500TF/s in FY08/09 (BG/P) • SNL ~1000TF/s in FY 08 (XT4) • Hypothetical 1PT/s sustained (2011) will contain 1.5M-6.5M processors! • Important understand algorithmic aspects allow/prevent petascale computation

  5. Benefits of Evaluation • Full scale application evaluation lead to more efficient use of the community resources • For both current installation and future designs • Head-to-head comparisons on full applications: • Help identify the suitability of a particular architecture for a given application class • Give application scientists information about how well various numerical methods perform across systems • Reveal performance-limiting system bottlenecks that can aid designers of the next generation systems. • Science Driven Architecture • In-depth studies reveal limitation of compilers, operating systems, and hardware, since all of these components must work together at scale to achieve high performance.

  6. Application Overview Examining set of applications with a variety of numerical methods and communication patterns with the potential to run at petascale

  7. Architectural Comparison • These architectures represent main stream petaflop candidate systems • Power5 aggregates 4 DDR233 for high 6.8 GB/s Stream bandwidth • Jaguar XT3 dual-core w/ SeaStar routing (Catamount) - future Petascale systems • Jacquard single-core Opteron with non-custom communication integration • BG/L, power eff, 5 networks, dual-core w/o L1 cohere, 512MB/node, 2 SIMD FPU • Brief access to 20K node BG/L during BGW day • Phoenix, X1E custom HPC platform, X1 upgrade (double MSP w/o BW increase) • Yes Cost is a critical metric - however we are unable to provide such data • Proprietary, pricing varies based on customer and time frame • Poorly balanced systems cannot solve important problems/resolutions regardless of cost!

  8. Astrophysics: CACTUS • Numerical solution of Einstein’s equations from theory of general relativity • Among most complex in physics: set of coupled nonlinear hyperbolic & elliptic systems with thousands of terms • CACTUS evolves these equations to simulate high gravitational fluxes, such as collision of two black holes • Evolves PDE’s on regular grid using finite differences Visualization of grazing collision of two black holes Developed at Max Planck Institute, vectorized/ported by John Shalf & Tom Goodale

  9. Cactus Performance: Weak Scaling • Bassi shows highest raw and sustained performance • Remains to be seen if scalability will continue to thousands of processors • Jacquard shows modest scaling due to (relatively) loosely coupled nature of interconnect • Phoenix X1 shows lowest % of peak - Cactus crashed on X1E • Small fraction unvectorizable code (boundary condition) leads to large penalty • Uses only 1 of 4 SSP within an MSP for an unvectorizable code portion • BG/L lowest raw performance - expected simple (power efficient) dual-issue in-order PPC440 • Achieves near perfect scalability to highest concurrency ever attained • Virtual node mode (32K procs) showed no performance degradation (smaller problem) • Topology mapping attempts did not improve performance • Overall shows potential of Cactus to run at Petascale

  10. Fluid Dynamics: ELB3D 4 14 12 2 25 0 9 6 8 18 21 15 22 23 11 10 16 5 13 20 3 1 24 7 19 17 • LBM concept: develop simplified kinetic model with incorporated physics, to reproduce correct macroscopic averaged properties • Unlike explicit LBM methods, entropic approach not prone to nonlinear instabilities • ELBM develop to simulate Navier-Stokes turbulence • Non-linear equation is solved at each grid point and time step to satisfy constraints, followed by streaming of data • The equation is solved via a Newton-Raphson iteration (heavy use of log function) • Spatial grid overlayed with phase-space velocity lattice • Block distributed over processor grid Evolution of vorticity into turbulent structures Developed by George Vahala’s group College of William & Mary, ported Jonathan Carter

  11. ELB3D Performance:Strong Scaling • Specialized log functions (ASSV, ACML) used on all platforms w/ significant improvement • Shows high % of peak and good scaling across all platforms - good load balance • Results show that high comp cost of entropic algorithm can be designed in efficient manner • X1E attains the highest raw performance: • Innermost gridpoint loop taken inside nonlinear equation to allow for vectorization • Bassi shows highest fraction of peak: high memory BW, large caches, advanced prefetch • BG/L shows lowest efficiency, but value is based on peak with double hummer • Except for highly-tuned libraries, peak will almost always be 50% of potential • Overall results show promising performance of ELB methods at PetaScale

  12. LBMHD Cell Performance • Multi-core scientific kernel optimization work by Samuel Williams (UCB/LBNL) • Cell achieves impressive performance for MHD problem (explicit LB method) • Ability to explicitly control local memory (more programming complexity) • Results shown only for collision phase (>>85% of overall time) • Multi-blade (MPI) Cell results to come

  13. Magnetic Fusion: GTC • Gyrokinetic Toroidal Code: transport of thermal energy (plasma microturbulence) • Goal magnetic fusion is burning plasma power plant producing cleaner energy • GTC solves 3D gyroaveraged gyrokinetic system w/ particle-in-cell approach (PIC) • PIC scales N instead of N2 – particles interact w/ electromagnetic field on grid • Allows solving equation of particle motion with ODEs (instead of nonlinear PDEs) • Vectorization inhibited since multiple particles may attempt to concurrently update same grid point Whole volume and cross section of electrostatic potential field, showing elongated turbulence eddies Developed at PPPL, vectorized/optimized by Stephane Ethier

  14. GTC Performance:Weak Scaling • Generally expect low % of peak due to scatter gather • Extensive X1E optimization (such as reversing array dimensions) paid off • Although dropping at higher concurrency • Three commodity superscalers (Power5, Opteron) achieve similar raw performance • However Bassi, only attains 1/2 %peak of Opteron • High Opteron partially due to low main memory latency • Bassi, Jaguar, and BG/L show excellent scalability • BG/L scales to 32K processors: virtual node mode only 5% slower than coprocessor • Optimizations: vector MASSV functions (60%) and mapping onto 3D Torus (30%) • Results show GTC prime candidate for Petascale systems • Perfect load balancing up to 32K processors and low communication

  15. High Energy Physics: BeamBeam3D • BB3D models collisions of counter-rotating charge particle beams • Code used to study beam-beam collisions at world’s highest energy accelerators • Particle-in-cell method, where particles are deposited on 3D grid to calculate charge density distribution • At collision points electric/magnetic fields calculated using Vlasov-Poisson via FFT • Particle are advances using computed fields and accelerator forces • High communication requirements: • Global gather charge density • Broadcast electric/magnetic fields • Global FFT transpose • GTC and BB3D both PIC w/ charged particle interactions, however: • GTC requires relatively small particle movements • Allows local solve of Poisson equation • BB3D has longer range particle forces • Requires high communication, global FFTs • Limited number of subdomains available (2048 for test case) • Pure domain decomposition not possible Developed by Ji Qiang, ported/optimized by Hongzhang Shan

  16. BeamBeam3D Performance:Strong Scaling • Phoenix attains fastest per-processor performance, however scalability is poor at high P • At P=256 > 50% communication, at high P vector length decreases (fixed size problem) • At P=512 Bassi surpasses Phoenix • Outperforms Opterons by 1.8x, BG/L by 4.5X • Jacquard and Jaguar show similar behavior, even though vastly different interconnects • Notice all platforms achieve < 5% of peak for high concurrencies! • Indirect addressing, global all-to-all comm, extensive (non-flop) data movement • BG/L achieves just 1% of peak at high concurrencies • Higher scalability experiments not possible due to limited number of domains • To reach Petascale for BB3D requires extensive code reengineering: • Additional decomposition schemes, reduce communication bottleneck

  17. Materials Science: PARATEC • PARATEC performs first-principles quantum mechanical total energy calculation using pseudopotentials & plane wave basis set • Density Functional Theory to calc structure & electronic properties of new materials using QM principles • DFT calc are one of the largest consumers of supercomputer cycles in the world • 33% 3D FFT, 33% BLAS3, 33% Hand coded F90 • Part of calculation in real space other in Fourier space • Uses specialized 3D FFT to transform wavefunction • QDOTs have important photo-luminscent properties Conduction band minimum electron state forCdSe quantum dot Developed by Andrew Canning with Louie and Cohen’s groups (UCB, LBNL)

  18. PARATEC Performance:Strong Scaling • PARATEC attains high % peak due to 1D FFTs and BLAS3 • Bassi achieves highest performance and good scaling up to 512 processors • 1024 Power5 performance from LLNL Purple system • Jaguar outperforms Jacquard due partially to high interconnect bandwidth • BG/L lowest overall raw performance - but uses smaller system due to mem constraints • Performance drops between 512 and 1024, due to moving off topology half-plane • Phoenix shows lowest % peak • Low scalar/vector ratio, vector length drops for custom F90 routines and BLAS3/FFT • PARATEC scaling decreases and limited to ~2K processors - due to 1 level decomposition • For Petascale must introduce second level of decomposition, over electronic band indices • Will increase scaling and reduce memory requirements for systems like BG/L

  19. Gas Dynamics: HyperCLaw • Adaptive Mesh Refinement (AMR): powerful technique to solve otherwise intractable problems - typically applied to physical systems solving PDEs • AMR dynamically refines underlying grid in regions of scientific interest • Naively increasing grid resolution prohibitive in computation and memory • Price paid for additional power is complexity: significant software infrastructure • Regridding, interpolation between coarse/fine grids, dynamic load balancing • Generally written in flexible/modular fashion • Causing performance reduction even for unrefined grid calculations • Complex communication looks more like many-to-many than stencil exchange • Berger-Colella Hyperbolic Conservation laws C++/Fortran hybrid programming model • Godunov - Advances the solution at a given refinement level • TimeStep - Prepares grids at next level of Godunov solver • Regrid - Replace existing grid hierarchy to maintain numerical accuracy • Knapsack - Load balancing algorithm Developed by CCSE LBNL, ported/optimized by Michael Lijewski and Michael Welcome

  20. X1E Optimization • Two X1E optimizations undertaken since our original study in CF06 • Knapsack and Regridding originally prevents X1E scalability • Knapsack optimized by swapping pointers instead of lists • Results in almost cost free X1E Knapsack algorithm • Regridding originally required O(N^2) box list intersection calculation • Updated hashing scheme reduced overhead to O(NlogN) • Significantly reduced X1E regridding overhead

  21. HyperCLaw Performance:Weak Scaling • Due to code complexity, all platforms achieve < 5% of peak • Increasing adaptivity level introduces grid management overheads, reducing performance • Bassi shows highest raw performance, BG/L the lowest • Jacquard and Jaguar shoe similar raw performance • X1E shows lowest fraction of peak ~1%, before optimization this was much lower • Hierarchical data structures management is scalar work • Higher concurrency reduces vector length • AMR designed for small grid patches, causes short vector length • Adding more complexity (elliptic, chemistry) would certainly reduce vector performance • May be possible to design AMR parallel vector code, but only from the ground up • Despite low efficiency, systems show good scalability - potential for petascale systems

  22. Performance Summary • Evaluating HPC on realistic problems is complex task, requires diverse group domain scientists • Work presents one of most extensive performance analyses to date • Overall Power5 Bassi achieves highest raw and sustained performance • High mem BW, tight interconnect integration, latency hiding via advanced prefetching • Phoenix X1E achieved high perf for GTC and ELB3D, but showed poor results for several codes • Opteron systems show similar performance • However, Jaguar’s XT3 interconnect outperformed Jacquard for GTC & PARATEC • BG/L lowest raw/sustained perf, but achieved unprecedented concurrency on several codes • Potential to run at petascale: • GTC, Cactus - very encouraging, linear scaling to 32K processors • ELB3D, Hyperclaw - promising scaling at lower concurrencies • BB3D and Paratec - require reengineering to incorporate additional levels of parallelism

  23. Comparing Jaguar single vs dual core • Preliminary performance comparison shows that, for the most part, having a dual-core architecture does not significantly inhibit performance compared to a single core. • This is not the case with BB3D where extensive communication and memory transfer but high strain on a sockets resources. • Understanding and optimizing multi-core systems is one of greatest challenges in HPC and industrial computing today

  24. Future and Related Work • Future Evaluation Work: • Explore more complex methods and irregular data structures • Continue evaluating leading HPC systems as they come online • Perform in-depth application characterizations • Related research activities: • Developing an application-derived I/O benchmark based on CMB • Investigating automatic tuning for stencil computations • Investigating scientific kernel performance on multi-core systems • Investigating potential of dynamically reconfigurable interconnects to achieve fat-tree performance at fraction of switch components Papers at http://crd.lbl.gov/~oliker