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Leading Computational Methods on Scalar and Vector HEC Platforms
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  1. Leading Computational Methods on Scalar and Vector HEC Platforms Leonid OlikerJonathan Carter, Michael Wehner, Andrew Canning Lawrence Berkeley National Laboratory Stephane Ethier Princeton Plasma Physics Laboratory Art Mirin, Govindasamy Bala Lawrence Livermore National Laboratory David Parks NEC Solutions America Patrick Worley Oak Ridge National Laboratory Shigemune Kitawaki, Yoshinori Tsuda Earth Simulator Center

  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 • In order to continuously increase computing power and reap its benefits: major strides necessary in architecture development, software infrastructure, and application development

  3. 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 • Effective code vectorization is an integral part of the process • First US team to conduct Earth Simulator performance study

  4. 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.

  5. Architectural Comparison • Custom vector architectures: High mem vs peak, superior interconnects • ES shows best balance between memory and peak performance • Data caches of superscalar systems and X1(E) potential reduce mem costs • X1E: 2 MSP’s per MCM - increases contention for memory and interconnect • A key ‘balance point’ for vector systems is the scalar:vector ratio • Opteron/IB shows best balance for superscalar, Itanium2/Quadrics lowest latency • 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

  6. Application Overview • Examining candidate ultra-scale applications with abundant data parallelism • Codes designed for superscalar architectures, required vectorization effort • ES use requires minimum vectorization and parallelization hurdles

  7. Climate: FVCAM • Atmospheric component of CCSM • AGCM: consists of physics (PS) and dynamical core (DC) • DC approximates Navier-Stokes equations to describe dynamics of atmosphere • PS: calculates source terms to equations of motion: • Turbulence, radiative transfer, clouds, etc • Default uses spectral transform - maps onto sphere • Allows 1D decomposition in latitude • Finite volume (FV) grid is rectangular (long, lat, level) • Allows 2D decomp (lat, level) in dynamics phase • Requires remapping between Lagrangian surfaces and Eulerian reference frame Simulated Class IV hurricane at 0.5. This storm was produced solely through the chaos of the atmospheric model. It is one of the many events produced by FVCAM at resolution of 0.5. • Hybrid (MPI/OpenMP) programming • MPI tasks limited by number of latitude lines • minimum 3 per domain • Increase potential parallelism • Improves surface to volume ratio • Not available on Thunder • Did not increase performance on X1/X1E Experiments/vectorization Art Mirin, Dave Parks, Michael Wehner, Pat Worley

  8. FVCAM Decomposition and Vectorization • Processor communication topology and volume for 1D Spectral and 2D FVCAM • Generated by IPM profiling tool - used to understand interconnect requirements • 1D approach straightforward nearest neighbor communication • 2D communication bulk is nearest neighbor - however: • Complex pattern due to vertical decomp and transposition during remapping • Total volume in 2D remap is reduced due to improved surface/volume ratio • Vectorization • Move latitude calculation to inner loops to maximize parallelism • Reduce number of branches, performing logical tests in advance (indirect indexing) • Vectorize across (not within) FFT’s for Polar filters • Finer domain decomp fixed size problem, limit performance of vectorized FFTs

  9. FVCAM3.1: Performance • FVCAM 2D decomp allows effective use of >2X as many procs • Increasing vertical discretizations (1,4,7) allows higher concurrencies • First results showing high resolution vector performance 361x576x26 (0.5 x 0.625) • X1E achieves speedup of over 4500 on P=672 - highest ever achieved • Power3 limited to speedup of 600 regardless of concurrency • Factor of at least 1000x necessary for simulation to be tractable • Raw speed X1E: 1.14X X1, 1.4X ES, 3.7X Thunder, 13X Seaborg • At high concurrencies (P= 672) all platforms achieve low % peak (< 7%) • ES achieves highest sustained performance (over 10% at P=256) • Vectors suffer from short vector length of fixed problem size, esp FFTs • Superscalars generally achieve lower efficiencies/performance than vectors • Finer resolutions requires increased number of more powerful processors

  10. 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

  11. GTC Particle Decomposition • GTC originally optimized for superscalar SMPs using MPI/OpenMP • OpenMP achieved limited perform & severely increase memory for vectors • Vectorization and thread-level parallelism compete w/ each other • Previous vector experiments limited to only 64-way MPI parallelism • 64 is optimal domains for 1D toroidal (independent of # particles) • New GTC version introduces a third level of parallelism: • Algorithm splits particles between several processors (within 1D domain) • Allows increase concurrency and number of studied particles • Larger particle simulations allow increase resolution studies • Particles not subject to Courant condition (same timestep) • Allows multiple species calculations

  12. GTC: Performance • New decomposition algorithm efficiently utilizes high P (as opposed to 64 on ES) • Breakthrough of Tflop barrier on ES for important SciDAC code • 7.2 Tflop/s on 4096 processors • SX8 highest raw performance (ever) but lower efficiency than ES • Opens possibility of new set of high-phase space-resolution simulations • Scalar architectures suffer from low computational intensity, irregular data access, and register spilling • Opteron/IB is 50% faster than Itanium2/Quadrics and only 1/2 speed of X1 • Opteron: on-chip memory controller and caching of FP L1 data • X1 suffers from overhead of scalar code portions • Original (unmodified) X1 version performed 12% *slower* on X1E • Recent additional optimizations increased performance by 50%! • Chosen as HPCS benchmark

  13. Plasma Physics: LBMHD • LBMHD uses a Lattice Boltzmann method to model magneto-hydrodynamics (MHD) • Performs 2D/3D simulation of high temp plasma • Evolves from initial conditions and decaying to form current sheets • Spatial grid coupled to octagonal streaming lattice • Block distributed over processor grid • Main computational components: • Collision, Stream, Interpolation • Vectorization: loop interchange, unrolling Evolution of vorticity into turbulent structures Ported by Jonathan Carter, developed by George Vahala’s group College of William & Mary

  14. LBMHD-3D: Performance • Not unusual to see vector achieve > 40% peak while superscalar architectures achieve < 10% • There exists plenty of computation, however large working set causes register spilling scalars • Opteron shows impressive superscalar performance, 2X speed vs. Itanium2 • Opteron has >2x STREAM BW, and Itanium2 cannot store FP in L1 cache • Large vector register sets hide latency • ES sustains 68% of peak up to 4800 processors: 26TFlops - the highest performance ever attained for this code by far! • SX8 shows highest raw performance, but lags behind ES in terms of efficiency • SX8: Commodity DDR2-SDRAM vs. ES: high performance custom FPLRAM • X1E achieved same performance as X1 using original code version • By turning off caching resulted in about 10% improvement over X1

  15. Material 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 • 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 Conduction band minimum electron state forCdSe quantum dot Developed by Andrew Canning with Louie and Cohen’s groups (UCB, LBNL)

  16. PARATEC: Performance • All architectures generally perform well due to computational intensity of code (BLAS3, FFT) • ES achieves highest overall performance to date: 5.5Tflop/s on 2048 procs • Main ES advantage for this code is fast interconnect • Allows never before possible, high resolution simulations • Qdot: Largest cell-size atomistic experiment ever run using PARATEC • SX8 achieves highest per-processor performance • X1/X1E shows lowest % of peak • Non-vectorizable code much more expensive on X1/X1E (32:1) • Lower bisection bandwidth to computational ratio (4D-hypercube) • X1 Performance is comparable to Itanium2 • Itanium2 outperforms Opteron (unlike LBMHD/GTC) because • Paratec less sensitive to memory access issues (BLAS3) • Opteron lacks FMA unit • Quadrics shows better scaling of all-to-all at large concurrencies

  17. Performance Overview • Tremendous potential of vector systems - unprecedented aggregate performance: • >4500x simulation speedup of FVCAM on 672 processors of X1E • New GTC decomposition algorithm achieves 7.2 TF/s on 4096 ES processors • LBMHD-3D achieves 26 TF/s using 4800 ES procs (68% of peak) - GB finalist • PARATEC achieves 5.5 TF/s on 2048 processors of ES • ES highest efficiency, SX8 achieves highest raw performance (X1E for FVCAM) • X1E faster absolute performance X1, but lower sustained performance • SSP vs MSP experiments: tradeoffs between comp granularity and scalar work • Opteron vs Itanium2 • Opteron faster GTC, LBMHD: low CI, register spilling, irregular memory access • Itanium2 faster PARATEC: High CI, FMA support, all-to-all on Quadrics • Future: Sparse, Unstructured, AMR codes on latest Power5, BG/*, XT3.