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 the Earth

Simulator

Leonid Oliker

Lawrence Berkeley National Laboratory

Joint work with:

Julian Borrill, Andrew Canning, Stephane Ethier, Art Mirin, David Parks, John Shalf, David Skinner, Michael Wehner, Patrick Worley

Motivation

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 Achieving next order of magnitude in computing will require

O(100K) - O(1M) processors: interconnect that scale nonlinearly in cost (crossbar, fattree) become impractical

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 Allows advanced optimizations for given architectural platforms

In-depth studies reveal limitation of compilers, operating systems, and hardware, since all of these components must work together at scale

Our recent efforts have focused on the potential of modern parallel vector systems

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

Vector Paradigm

High memory bandwidth Allows systems to effectively feed ALUs (high byte to flop ratio)

Flexible memory addressing modes Supports fine grained strided and irregular data access

Vector Registers Hide memory latency via deep pipelining of memory load/stores

Vector ISA Single instruction specifies large number of identical operations

Vector architectures allow for: Reduced control complexity Efficiently utilize large number of computational resources Potential for automatic discovery of parallelism

Can some of these features can be added to modern micros?

However: most effective if sufficient regularity discoverable in program structure• Suffers even if small % of code non-vectorizable (Amdahl’s Law)

ES Processor Overview

Cachless Architecture

8 CPU per SMP

8 way replicatedvector pipes

72 vec registers, 256 64-bit words

Divide Unit

32 GB/s pipe to FPLRAM

4-way superscalar o-o-o @ 1 Gflop

64KB I$ & D$

ES: specially developed FPLRAM (Full Pipelined RAM) SX6: DDR-SDRAM 128/256Mb

ES: uses IN 12.3 GB/s bi-dir btw any 2 nodes, 640 nodes SX6: uses IXS 8GB/s bi-dir btw any 2 nodes, max 128 nodes

In April 2002, the Earth Simulator (ES) became operational: Peak ES performance > all DOE and DOD systems combined

Stayed #1 Top 500 for an unprecedented 2.5 years!

Earth Simulator Overview

Machine Type : 640 nodes, each node is 8-way SMP vector processors (5120 total procs) Machine Peak: 40TF/s (proc peak 8GF/s)OS : Extended version of Super-UX: 64 bit Unix OS based on System V-R3Connection structure : a single stage crossbar network (1400 miles of cable), 83,000 copper cables

7.9 TB/s aggregate switching capacity 12.3 GB/s bi-di between any two nodes

Global Barrier Counter within interconnect allows global barrier synch <3.5usecStorage: 480 TB Disk, 1.5 PB TapeCompilers : Fortran 90, HPF, ANSI C, C++Batch: similar to NQS, PBSParallelization: vectorization processor level OpenMP, Pthreads, MPI, HPFNo Parallel I/O: Each node has separate file systemNo remote access (until recently)

Architectural 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 vectors : High Bandwidth, Flexible addressing, Many Register, vector ISA Less control complexity, use many ALUs, auto parallelism 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 certain class of problems/resolutions regardless of processor count!

Application Overview

NAME Discipline Problem/Method Structure

Cactus Astrophysics Theory of GRADM-BSSN, Method of Lines

Grid

LBMHD Plasma Physics Magneto-Hydrodyamics, Lattice-Boltzmann

Lattice/Grid

MADCAP Cosmology Cosmic Microwave Background,Dense Linear Algebra, high I/O

Dense Matrix

GTC Magnetic Fusion Particle in Cell,Vlasov-Poisson

Particle/Grid

PARATEC Material Science Density Functional Theory, Kohn Shan, 3DFFT

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

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 differencesVisualization of grazing collision of two black holes

Developed at Max Planck Institute, vectorized by John Shalf LBNL

CACTUS: Performance

SX8 attains highest per-processor performance ever attained for Cactus ES achieves highest overall performance and efficiency to date: 39X faster than Power3!

Vector performance related to x-dim (vector length) Excellent scaling on ES using fixed data size per proc (weak scaling) Opens possibility of computations at unprecedented scale

X1 surprisingly poor (4X slower than ES) - low ratio scalar:vector Unvectorized boundary, required 15% of runtime on ES and 30+% on X1 < 5% for the scalar version: unvectorized code can quickly dominate cost

Poor superscalar performance despite high computational intensity Register spilling due to large number of loop variables Prefetch engines inhibited due to multi-layer ghost zones calculations

ProblemSize

P

Power 3

SeaborgItanium2Thunder

X1Phoenix

SX6*ES

SX8

GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %pk GFs/P %peak

250x80x80per

processor

16 0.10 6% 0.58 10% 0.81 6% 2.8 35% 4.3 27%

64 0.08 6% 0.56 10% 0.72 6% 2.7 34%

256 0.07 5% 0.55 10% 0.68 5% 2.7 34%

Plasma Physics: LBMHD

LBMHD uses a Lattice Boltzmann method to model magneto-hydrodynamics (MHD)

Performs 2D/3D simulation of high temperature 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 HPCS Benchmark

Ported by Jonathan Carter, developed by George Vahala’s group College of William & Mary

Evolution of vorticity into turbulent structures

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 Unlike superscalar approach, large vector register sets hide latency Opteron shows impressive superscalar performance, 2X speed vs. Itanium2

Opteron has >2x STREAM BW, and Itanium2 cannot store FP in L1 cache ES sustains 68% of peak up to 4800 processors: 26TFlops -SC2005 GB Finalizst

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

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 kinetic 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: multiple particles may attempt to concurrently update same point in charge deposition

Whole volume and cross section of electrostatic potential field, showing elongated turbulence eddies

Developed at PPPL, vectorized/optimized by Stephane Ethier and ORNL/Cray/NEC

GTC Particle Decomposition

Vectorization: Particle charge deposited amongst nearest grid points Several particles can contribute to same grid point preventing vectorization Solution: VLEN copies of charge deposition array with reduction after main loop

Greatly increases memory footprint (8x) GTC originally optimized for superscalar SMPs using MPI/OpenMP However: OpenMP severely increase memory for vector implementation

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) Updated GTC algorithm 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

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 (of any arch) but lower efficiency than ES

Opens possibility of new set of high-phase space-resolution simulations Scalar architectures suffer from low CI, 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

Additional optimizations increased performance by 50%! Recent ORNL work increases performance additional 75%

SciDAC code, 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%

Material Science: PARATEC

First-principles quantum mechanical total energy calc 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 forCadmium Selenide (CdSe) quantum dot

Developed by Andrew Canning with Louie and Cohen’s groups (LBNL, UCB)

Global transpose Fourier to real space Multiple

FFTs: reduce communication latency

Vectorize across (not within) FFTs

Custom FFT: only nonzeros sent

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 CdSE Q-dot: Largest cell-size atomistic experiment ever run using PARATEC

• Important uses: can be attached to organic molecules as electronic dye tags 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 (high computational intensity) 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%

Atmospheric Modeling: FVCAM

CAM3.1: Atmospheric component of CCSM3.0 Our focus is the Finite Volume (FV) approach

AGCM: consists of physics (PS) and dynamical core (DC)

DC approximates dynamics of atmosphere

PS: calculates source terms to equations of motion:

Turbulence, radiative transfer, clouds, boundary, etc

DC default: Eulerian spectral transform - maps onto sphere

Allows only 1D decomposition in latitude

FVCAM grid is rectangular (longitude, latitude, level)

Allows 2D decomp (latitude, level) in dynamics phase

Singularity at pole prevents longitude decomposition

Dynamical eqns bounded by Lagrangian surfaces Requires remapping to Eulerian reference frame

Hybrid (MPI/OpenMP) programming MPI tasks limited by # of latitude lines Increase potential parallelism and improves S2V ratio Is not always effective on some platforms

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.

FVCAM Decomposition and Vectorization

Processor communication topology and volume for 1D 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 - 5 routines, about 1000 lines 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 However, higher concurrency for fixed size problem limit performance of vectorized FFTs

FVCAM3.1: Performance

FVCAM 2D decomposition allows effective use of >2X as many processors Increasing vertical discretizations (1,4,7) allows higher concurrencies 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

Cosmology: MADCAP

Anisotropy Dataset Computational Analysis Package

Optimal general algorithm for extracting key cosmological data from Cosmic Microwave Background Radiation (CMB)

Anisotropies in the CMB contains early history of the Universe

Recasts problem in dense linear algebra: ScaLAPACK

Out of core calculation: holds ~3 of the 50 matrices in memory

Temperature anisotropies in CMB (Boomerang)

Developed by Julian Borrill, LBNL

MADCAP: Performance

Overall performance can be surprising low, for dense linear algebra code

I/O takes a heavy toll on Phoenix and Columbia: I/O optimization currently in progress

NERSC Power3 shows best system balance with respect to I/O ES lacks high-performance parallel I/O - code rewritten to utilize

local disks HPCS I/O candidate benchmark

NumberPixels

PNERSC (Power3) Columbia (Itan2) Phoenix (X1) ES (SX6*)

Gflops/P %peak Gflops/P %peak Gflops/P %peak Gflops/P %peak

10K 64 0.73 49% 1.2 20% 2.2 17% 2.9 37%

20K 256 0.76 51% 1.1 19% 0.6 5% 4.0 50%

40K 1024 0.75 50% 4.6 58%

0%

20%

40%

60%

80%

100%

P=16 P=16 P=16 P=16 P=64 P=64 P=64 P=64P=256P=256P=256P=256

P=1024P=1024

Sbg ES Phx Cmb Sbg ES Phx Cmb Sbg ES Phx Cmb Sbg ES

LBST

Calc

MPI

I/O

Performance Overview

Tremendous potential of vector systems: ES achieves unprecedented aggregate performance on almost all test applications

LBMHD-3D achieves 26 TF/s using 4800 ES procs (68% of peak) - GB finalist GTC achieves 7.2 TF/s on 4096 ES processors PARATEC achieves 5.5 TF/s on 2048 processors of ES

ES consistently achieves highest efficiency Investigating how to incorporate vector-like facilities into modern micros To date we have mostly looked at mostly regularly structured algorithms Many methods unexamined (more difficult to vectorize): Implicit, Multigrid, AMR,

Unstructured (Adaptive), Iterative and Direct Sparse Solvers, N-body, Fast Multiple One size does not fit all: need a range of architectural designs to best fit

algorithms

0%

10%

20%

30%

40%

50%

60%

70%

CACTUS FVCAM GTC LBMHD3D PARATEC

Application

% of Theoretical Peak

SX-8

ES

X1

X1E

Power3

Itanium2

Opteron

% of Theoretical Peak

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

CACTUS FVCAM GTC LBMHD3D PARATEC

Application

Speedup vs. ES

SX-8

ES

X1

X1E

Power3

Itanium2

Opteron

Speedup vs. ES