Post on 02-Jan-2016
description
C O M P U T A T I O N A L R E S E A R C H D I V I S I O N
BIPSBIPS
Leading Computational Methods on Scalar and Vector
HEC Platforms
Leonid OlikerJonathan Carter, Michael Wehner, Andrew Canning
Lawrence Berkeley National Laboratory
Stephane EthierPrinceton Plasma Physics Laboratory
Art Mirin, Govindasamy BalaLawrence Livermore National Laboratory
David ParksNEC Solutions America
Patrick WorleyOak Ridge National Laboratory
Shigemune Kitawaki, Yoshinori TsudaEarth Simulator Center
BIPSBIPS 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
BIPSBIPS 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
BIPSBIPS 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.
BIPSBIPSArchitectural Comparison
Node Type Where NetworkCPU/Node
ClockMHz
PeakGFlop
Stream BW
GB/s/P
Peak byte/flop
MPIBW
GB/s/P
MPI Latency
sec
NetworkTopology
Power3 NERSC Colony 16 375 1.5 0.4 0.26 0.13 16.3 Fat-tree
Itanium2 LLNL Quadrics 4 1400 5.6 1.1 0.19 0.25 3.0 Fat-tree
Opteron NERSCInfiniBan
d2 2200 4.4 2.3 0.51 0.59 6.0 Fat-tree
X1 ORNL Custom 4 800 12.8 14.9 1.16 6.3 7.1 4D-Hypercube
X1E ORNL Custom 4 1130 18.0 9.7 0.54 2.9 5.0 4D-Hypercube
ES ESC IN 8 1000 8.0 26.3 3.29 1.5 5.6 Crossbar
SX-8 HLRS INX 8 2000 16.0 41.0 2.56 2.0 5.0 Crossbar
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
BIPSBIPS Application Overview
NAME Discipline Problem/Method Structure
LBMHD Plasma Physics Magneto-Hydrodyamics, Lattice-Boltzmann
Lattice/Grid
GTC Magnetic Fusion Particle in Cell,Vlasov-Poisson
Particle/Grid
PARATEC Material Science Density Functional Theory, Kohn Shan, FFT
Fourier/Grid
FVCAM Climate Modeling AGCM,Finite Volume, Navier-Stokes, FFT
Grid
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
BIPSBIPSClimate: 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
Experiments/vectorization Art Mirin, Dave Parks, Michael Wehner, Pat Worley
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
BIPSBIPSFVCAM 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
BIPSBIPS 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
Simulated Speedup
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 200 400 600 800
Processors
Simulated Years / Wallclock Years
Power3Itanium2ESX1X1E
Percent of Theoretical Peak
3%
5%
7%
9%
11%
13%
15%
17%
P=32 (1D) P=256 (2D:4) P=336 (2D:7) P=672 (2D:7)
Configuration
% of Theoretical Peak
Power3
Itanium2
ES
X1
X1E
BIPSBIPSMagnetic 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
BIPSBIPS 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
BIPSBIPS 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
PPart/Cell
Power3 Seaborg
Itanium2 Thunder
OpteronJacquard
X1Phoenix
X1EPhoenix
SX6 ES
SX8HLRS
GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk
128 200 0.14 9% 0.39 7% 0.59 13% 1.2 9% 1.7 10% 1.9 23% 2.3 14%
256 400 0.14 9% 0.39 7% 0.57 13% 1.2 9% 1.7 10% 1.8 22% 2.3 15%
512 800 0.14 9% 0.38 7% 0.51 12% 1.7 9% 1.8 22%
1024 1600 0.14 9% 0.37 7% 1.8 22%
BIPSBIPSPlasma 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
Ported by Jonathan Carter, developed by George Vahala’s group College of William & Mary
Evolution of vorticity into turbulent structures
BIPSBIPS LBMHD-3D: Performance
Grid Size
P
Power3 Seaborg
Itanium2 Thunder
OpteronJacquard
X1Phoenix
X1EPhoenix
SX6 ES
SX8HLRS
GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk
2563 16 0.14 9% 0.26 5% 0.70 16% 5.2 41% 6.6 37% 5.5 69% 7.9 49%
5123 64 0.15 9% 0.35 6% 0.68 15% 5.2 41% 5.8 32% 5.3 66% 8.1 51%
10243 256 0.14 9% 0.32 6% 0.60 14% 5.2 41% 6.0 33% 5.5 68% 9.6 60%
20483 512 0.14 9% 0.35 6% 0.59 13% 5.8 32% 5.2 65%
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
BIPSBIPSMaterial 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 wavefunctionConduction band minimum electron state forCdSe quantum dot
Developed by Andrew Canning with Louie and Cohen’s groups (UCB, LBNL)
BIPSBIPS 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
Problem P
Power3 Seaborg
Itanium2 Thunder
OpteronJacquard
X1Phoenix
X1EPhoenix
SX6 ES
SX8HLRS
GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk GF/s/P %pk GFs/P %pk GFs/P %pk
488 AtomCdSe
QuantumDot
128 0.93 62% 2.8 51% 3.2 25% 3.8 21% 5.1 64% 7.5 49%
256 0.85 67% 2.6 47% 2.0 45% 3.0 24% 3.3 18% 5.0 62% 6.8 43%
512 0.73 49% 2.4 44% 1.0 22% 2.2 12% 4.4 55%
1024 0.60 40% 1.8 32% 3.6 46%
BIPSBIPS 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.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
FVCAM GTC LBMHD3D PARATEC
Application
Speedup vs. ES
Power3
Itanium2
Opteron
ES
SX-8
X1
X1E
0%
10%
20%
30%
40%
50%
60%
70%
FVCAM GTC LBMHD3D PARATEC
Application
% of Theoretical Peak
Power3
Itanium2
Opteron
ES
SX-8
X1
X1E